Finite Group Databasebeta

← #17193887

Subgroups — #17193887

Order 4352.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763317C211yesmaximal, characteristic
2C2×C4×#63254C211yesmaximal, characteristic, complemented
3C2×#117×D17C211yesmaximal, characteristic, complemented
4#14531823C211yesmaximal, characteristic, complemented
5#14531817C211yesmaximal, characteristic, complemented
6#14531812C211yesmaximal, characteristic, complemented
7#14531806C211yesmaximal, characteristic, complemented
8#14531803C211yesmaximal, characteristic, complemented
9#14531797C211yesmaximal, characteristic, complemented
10#14531792C211yesmaximal, characteristic, complemented
11#14531786C211yesmaximal, characteristic, complemented
12#14531780C211yesmaximal, characteristic, complemented
13#14531776C211yesmaximal, characteristic, complemented
14#14531772C211yesmaximal, characteristic, complemented
15#14531766C211yesmaximal, characteristic, complemented
16#14531764C211yesmaximal, characteristic, complemented
17#14531761C211yesmaximal, characteristic, complemented
18#14531760C211yesmaximal, characteristic, complemented
19#14531269C211yesmaximal, characteristic, complemented
20#14531263C211yesmaximal, characteristic, complemented
21#14531244C211yesmaximal, characteristic, complemented
22#14531242C211yesmaximal, characteristic, complemented
23#14531226C211yesmaximal, characteristic, complemented
24#14531222C211yesmaximal, characteristic, complemented
25#14531222C211yesmaximal, characteristic, complemented
26#14531220C211yesmaximal, characteristic, complemented
27C4×#10587579C211yesmaximal, characteristic, complemented
28C4×#10587567C211yesmaximal, characteristic, complemented
29C4×#10587563C211yesmaximal, characteristic, complemented
30C2×#11762656C211yesmaximal, characteristic, complemented
31C17×#2359C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763317C4116yescomplemented
35C2×#10587615C2211yescharacteristic
36C2×#10587582C2211yescharacteristic
37C2×#10587582C2211yescharacteristic
38C2×#10587570C2211yescharacteristic
39C2×#10587570C2211yescharacteristic
40C2×#10587568C2211yescharacteristic
41C2×#10587623C2211yescharacteristic
42C4×#63254—28no—
43C2×C4×Dic34C2211yescharacteristic, complemented
44C2×#10587573C2211yescharacteristic, complemented
45C2×C4×D68C2211yescharacteristic
46C2×D4×Dic17C2211yescharacteristic
47C2×#10587579C2211yescharacteristic
48C2×#10587579C2211yescharacteristic
49C2×#10587579C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic
52C2×C4×C22⋊D17C2211yescharacteristic, complemented
53C2×#10587567C2211yescharacteristic
54C2×#10587567C2211yescharacteristic
55C2×#10587567C2211yescharacteristic
56C2×#10587567C2211yescharacteristic
57C2×#10587567C2211yescharacteristic, complemented
58C2×#10587612C2211yescharacteristic
59C2×#10587578C2211yescharacteristic
60C2×#10587578C2211yescharacteristic
61C2×#10587578C2211yescharacteristic, complemented
62C2×#10587558C2211yescharacteristic
63C2×#10587558C2211yescharacteristic
64C2×#10587563C2211yescharacteristic
65C2×#10587563C2211yescharacteristic
66C2×#10587563C2211yescharacteristic
67C2×#10587563C2211yescharacteristic, complemented
68#117×D17—28no—
69C2×C4⋊C4×D17C2211yescharacteristic
70C2×C4⋊C4×D17C2211yescharacteristic
71C22×#63227C2211yescharacteristic
72C22×#63227C2211yescharacteristic
73C2×C22⋊C4×D17C2211yescharacteristic
74C2×C22⋊C4×D17C2211yescharacteristic
75C22×C4×Dic17C2211yescharacteristic
76C22×C4×Dic17C2211yescharacteristic
77C22×C4×Dic17C2211yescharacteristic, complemented
78C2×C42×D17C2211yescharacteristic
79C2×C42×D17C2211yescharacteristic
80C2×C42×D17C2211yescharacteristic, complemented
81#11762713C2211yescharacteristic, complemented
82#11762713C2211yescharacteristic, complemented
83#11762711C2211yescharacteristic
84#11762710C2211yescharacteristic
85#11762709C2211yescharacteristic
86#11762709C2211yescharacteristic
87#11762709C2211yescharacteristic, complemented
88#11762709C2211yescharacteristic, complemented
89#11762708C2211yescharacteristic, complemented
90#11762706C2211yescharacteristic, complemented
91#11762706C2211yescharacteristic, complemented
92#11762706C2211yescharacteristic, complemented
93#11762704C2211yescharacteristic, complemented
94#11762704C2211yescharacteristic, complemented
95#11762704C2211yescharacteristic, complemented
96#11762702C2211yescharacteristic, complemented
97#11762702C2211yescharacteristic, complemented
98#11762701C2211yescharacteristic
99#11762701C2211yescharacteristic
100#11762701C2211yescharacteristic, complemented
101#11762700C2211yescharacteristic
102#11762700C2211yescharacteristic
103#11762700C2211yescharacteristic, complemented
104#11762699C2211yescharacteristic
105#11762699C2211yescharacteristic
106#11762699C2211yescharacteristic, complemented
107#11762698C2211yescharacteristic
108#11762698C2211yescharacteristic
109#11762698C2211yescharacteristic, complemented
110#11762696C2211yescharacteristic, complemented
111#11762695C2211yescharacteristic, complemented
112#11762695C2211yescharacteristic, complemented
113#11762693C2211yescharacteristic, complemented
114#11762691C2211yescharacteristic, complemented
115#11762690C2211yescharacteristic, complemented
116#11762689C2211yescharacteristic
117#11762688C2211yescharacteristic
118#11762688C2211yescharacteristic
119#11762687C2211yescharacteristic
120#11762687C2211yescharacteristic
121#11762687C2211yescharacteristic
122#11762687C2211yescharacteristic
123#11762686C2211yescharacteristic
124#11762686C2211yescharacteristic
125#11762685C2211yescharacteristic
126#11762685C2211yescharacteristic
127#11762684C2211yescharacteristic
128#11762684C2211yescharacteristic, complemented
129#11762683C2211yescharacteristic
130#11762683C2211yescharacteristic
131#11762683C2211yescharacteristic, complemented
132#11762682C2211yescharacteristic
133#11762681C2211yescharacteristic
134#11762680C2211yescharacteristic
135#11762680C2211yescharacteristic
136#11762680C2211yescharacteristic, complemented
137C4⋊C4×Dic17C2211yescharacteristic, complemented
138C4⋊C4×Dic17C2211yescharacteristic, complemented
139C4⋊C4×Dic17C2211yescharacteristic, complemented
140C4×#63225C2211yescharacteristic, complemented
141C4×#63225C2211yescharacteristic, complemented
142C4×#63225C2211yescharacteristic, complemented
143#11762660C2211yescharacteristic, complemented
144#11762660C2211yescharacteristic, complemented
145#11762660C2211yescharacteristic, complemented
146#11762660C2211yescharacteristic, complemented
147#11762660C2211yescharacteristic, complemented
148C22⋊C4×Dic17C2211yescharacteristic
149C22⋊C4×Dic17C2211yescharacteristic
150C22⋊C4×Dic17C2211yescharacteristic, complemented
151C22⋊C4×Dic17C2211yescharacteristic, complemented
152C22⋊C4×Dic17C2211yescharacteristic, complemented
153C4×#63227C2211yescharacteristic
154C4×#63227C2211yescharacteristic
155C4×#63227C2211yescharacteristic, complemented
156C4×C22⋊Dic17C2211yescharacteristic
157#11762656C2211yescharacteristic
158#11762656C2211yescharacteristic
159#11762656C2211yescharacteristic
160#11762656C2211yescharacteristic
161#11762656C2211yescharacteristic
162#11762656C2211yescharacteristic
163#11762656C2211yescharacteristic
164#11762656C2211yescharacteristic
165#11762656C2211yescharacteristic
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762656C2211yescharacteristic, complemented
170#11762654C2211yescharacteristic, complemented
171#11762654C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic
173C42×Dic17C2211yescharacteristic, complemented
174C42×Dic17C2211yescharacteristic, complemented
175C2×C17×#123C2211yescharacteristic
176C2×C4×D4×C17C2211yescharacteristic
177C2×C17×#117C2211yescharacteristic
178C17×#389C2211yescharacteristic, complemented
179C17×#388C2211yescharacteristic, complemented
180C17×#388C2211yescharacteristic, complemented
181C17×#387C2211yescharacteristic, complemented
182C17×#387C2211yescharacteristic, complemented
183C17×#386C2211yescharacteristic
184C17×#385C2211yescharacteristic
185C17×#385C2211yescharacteristic, complemented
186C4×C4⋊C4×C17C2211yescharacteristic, complemented
187C4×C22⋊C4×C17C2211yescharacteristic
188C4×C22⋊C4×C17C2211yescharacteristic, complemented
189C2×C17×#95C2211yescharacteristic
190C24×D17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C2×#63254—24no—
206C2×#63254—24no—
207C2×#63254C2×C418yescomplemented
208C22×D68C2311yescharacteristic
209C22×D68C2311yescharacteristic
210C22×C4×D17—24no—
211C22×C4×D17—24no—
212C22×C4×D17C2×C418yescomplemented
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×Dic34C2311yescharacteristic
225C17×#123C2×C418yescomplemented
226C4×D4×C17—24no—
227C17×#117—24no—
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C42×C17C2311yescharacteristic
244C2×C42×C17C2311yescharacteristic
245C2×C42×C17C2311yescharacteristic
246C2×C42×C17C2311yescharacteristic
247C2×C42×C17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254#10587623C2×C418yescomplemented
255D4×Dic17—24no—
256#10587615C2×C418yescomplemented
257C4×C22⋊D17—24no—
258C4×C22⋊D17—24no—
259C4×C22⋊D17—24no—
260C2×#63227—24no—
261C2×#63227—24no—
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286#10587612—24no—
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×C4×Dic17—24no—
307C2×C4×Dic17—24no—
308C2×C4×Dic17—24no—
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333C2×C4×Dic17C2311yescharacteristic
334#10587582C2×C418yescomplemented
335#10587582C2×C418yescomplemented
336#10587579—24no—
337#10587579C2×C418yescomplemented
338#10587579C2×C418yescomplemented
339#10587578—24no—
340#10587578—24no—
341#10587578—24no—
342C4⋊C4×D17—24no—
343C4⋊C4×D17—24no—
344#10587573—24no—
345#10587570C2×C418yescomplemented
346#10587570C2×C418yescomplemented
347#10587568C2×C418yescomplemented
348#10587567—24no—
349#10587567—24no—
350#10587567—24no—
351#10587567C2×C418yescomplemented
352#10587567C2×C418yescomplemented
353C22⋊C4×D17—24no—
354C22⋊C4×D17—24no—
355#10587563—24no—
356#10587563—24no—
357#10587563C2×C418yescomplemented
358#10587563D418yescomplemented
359C4×D68—24no—
360#10587558—24no—
361#10587558—24no—
362C42×D17—24no—
363C42×D17—24no—
364C42×D17—24no—
365C4×Dic34—24no—
366C17×#95C2311yescharacteristic
367C17×#95C2311yescharacteristic
368C17×#95C2311yescharacteristic
369C17×#95C2311yescharacteristic
370C17×#95C2311yescharacteristic
371C17×#95C2311yescharacteristic
372C17×#95C2311yescharacteristic
373C17×#95C2311yescharacteristic
374C17×#95C2311yescharacteristic
375C17×#95C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391#10587502C2311yescharacteristic
392#10587502C2311yescharacteristic
393#10587502C2311yescharacteristic
394#10587502C2311yescharacteristic
395#10587502C2311yescharacteristic
396#10587502C2311yescharacteristic
397#10587502C2311yescharacteristic
398C24×C17C2411yescharacteristic
399C24×C17C2411yescharacteristic
400C23×D17—22no—
401C23×D17—22no—
402C23×D17—22no—
403C23×D17—22no—
404C23×D17—41no—
405C23×D17—41no—
406C23×D17C22×C414yes—
407C23×D17C2411yescharacteristic
408C23×D17C2411yescharacteristic
409C23×D17C2411yescharacteristic
410C2×D4×C17—22no—
411C2×D4×C17—22no—
412C2×D4×C17C22×C414yes—
413C22×C4×C17—22no—
414C22×C4×C17—22no—
415C22×C4×C17—22no—
416C22×C4×C17—22no—
417C22×C4×C17—22no—
418C22×C4×C17—22no—
419C22×C4×C17—22no—
420C22×C4×C17—22no—
421C22×C4×C17—41no—
422C22×C4×C17—41no—
423C22×C4×C17—41no—
424C22×C4×C17C22×C414yes—
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C22×C4×C17C2411yescharacteristic
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
440C2×C22⋊D17—22no—
441C2×C22⋊D17—22no—
442C2×C22⋊D17—22no—
443C2×C22⋊D17—22no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17—41no—
446C2×C22⋊D17C22×C414yes—
447C2×C22⋊D17C22×C414yes—
448C2×C22⋊D17C22×C414yes—
449C2×C22⋊D17C22×C414yes—
450C22×Dic17—22no—
451C22×Dic17—22no—
452C22×Dic17—22no—
453C22×Dic17—22no—
454C22×Dic17—22no—
455C22×Dic17—22no—
456C22×Dic17—22no—
457C22×Dic17—22no—
458C22×Dic17—41no—
459C22×Dic17—41no—
460C22×Dic17—41no—
461C22×Dic17C22×C414yes—
462C22×Dic17C22×C414yes—
463C22×Dic17C2×D414yes—
464C22×Dic17#4114yes—
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478#63254—232no—
479C2×D68—22no—
480C2×D68—22no—
481C2×D68—41no—
482C2×D68—41no—
483C2×D68C22×C414yes—
484C2×D68C22×C414yes—
485C2×C4×D17—232no—
486C2×C4×D17—22no—
487C2×C4×D17—22no—
488C2×C4×D17—22no—
489C2×C4×D17—22no—
490C2×C4×D17—22no—
491C2×C4×D17—22no—
492C2×C4×D17—22no—
493C2×C4×D17—22no—
494C2×C4×D17—22no—
495C2×C4×D17—22no—
496C2×C4×D17—22no—
497C2×C4×D17—22no—
498C2×C4×D17—22no—
499C2×C4×D17—22no—
500C2×C4×D17—22no—
501C2×C4×D17—22no—
502C2×C4×D17—22no—
503C2×C4×D17—22no—
504C2×C4×D17—22no—
505C2×C4×D17—22no—
506C2×C4×D17—22no—
507C2×C4×D17—22no—
508C2×C4×D17—41no—
509C2×C4×D17—41no—
510C2×C4×D17—41no—
511C2×C4×D17—41no—
512C2×C4×D17—41no—
513C2×C4×D17—41no—
514C2×C4×D17C22×C414yes—
515C2×C4×D17C22×C414yes—
516C2×C4×D17C22×C414yes—
517C2×C4×D17C22×C414yes—
518C2×C4×D17C22×C414yes—
519C2×Dic34—22no—
520C2×Dic34—22no—
521C2×Dic34C22×C414yes—
522C4⋊C4×C17—22no—
523C4⋊C4×C17—22no—
524C4⋊C4×C17—22no—
525C4⋊C4×C17—22no—
526C4⋊C4×C17—41no—
527C4⋊C4×C17C22×C414yes—
528C4⋊C4×C17C22×C414yes—
529C22⋊C4×C17—22no—
530C22⋊C4×C17—22no—
531C22⋊C4×C17—22no—
532C22⋊C4×C17—41no—
533C22⋊C4×C17C22×C414yes—
534C22⋊C4×C17C22×C414yes—
535C22⋊C4×C17C22×C414yes—
536C22⋊C4×C17C2×D414yes—
537C42×C17—22no—
538C42×C17—22no—
539C42×C17—22no—
540C42×C17—22no—
541C42×C17—41no—
542C22⋊Dic17—22no—
543C22⋊Dic17—22no—
544C22⋊Dic17—22no—
545C22⋊Dic17—41no—
546C22⋊Dic17C22×C414yes—
547C22⋊Dic17C2×D414yes—
548#63227—22no—
549#63227—22no—
550#63227—22no—
551#63227—22no—
552#63227—22no—
553#63227—22no—
554#63227—22no—
555#63227—22no—
556#63227—22no—
557#63227—22no—
558#63227—22no—
559#63227—22no—
560#63227—22no—
561#63227—22no—
562#63227—41no—
563#63227—41no—
564#63227C22×C414yes—
565#63227C22×C414yes—
566#63227C22×C414yes—
567#63227C22×C414yes—
568#63227C22×C414yes—
569#63227C22×C414yes—
570#63227#4114yescomplemented
571#63227#4114yescomplemented
572C4⋊Dic17—22no—
573C4⋊Dic17—22no—
574C4⋊Dic17—22no—
575C4⋊Dic17—22no—
576C4⋊Dic17—41no—
577#63225—22no—
578#63225—22no—
579#63225—22no—
580#63225—22no—
581#63225—22no—
582#63225—22no—
583#63225—41no—
584#63225—41no—
585#63225C22×C414yes—
586#63225C22×C414yes—
587#63225C22×C414yes—
588#63225C22×C414yes—
589#63225C2×D414yes—
590#63225C2×D414yes—
591C4×Dic17—22no—
592C4×Dic17—22no—
593C4×Dic17—22no—
594C4×Dic17—22no—
595C4×Dic17—22no—
596C4×Dic17—22no—
597C4×Dic17—22no—
598C4×Dic17—22no—
599C4×Dic17—22no—
600C4×Dic17—22no—
601C4×Dic17—22no—
602C4×Dic17—22no—
603C4×Dic17—22no—
604C4×Dic17—22no—
605C4×Dic17—22no—
606C4×Dic17—22no—
607C4×Dic17—22no—
608C4×Dic17—22no—
609C4×Dic17—41no—
610C4×Dic17—41no—
611C4×Dic17—41no—
612C4×Dic17C22×C414yes—
613C4×Dic17C22×C414yes—
614C4×Dic17C2×D414yes—
615C4×Dic17C2×D414yes—
616#34136—171nomaximal, Sylow
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—21no—
622C23×C17—21no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17—21no—
626C23×C17—21no—
627C23×C17C23×C412yes—
628C23×C17C23×C412yes—
629C23×C17C22×D412yes—
630C23×C17C2×#4112yes—
631C23×C17C2511yescharacteristic
632C22×D17—21no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—21no—
636C22×D17—28no—
637C22×D17—21no—
638C22×D17—21no—
639C22×D17—21no—
640C22×D17—21no—
641C22×D17—21no—
642C22×D17—21no—
643C22×D17—21no—
644C22×D17—21no—
645C22×D17—21no—
646C22×D17—21no—
647C22×D17—21no—
648C22×D17—21no—
649C22×D17—28no—
650C22×D17—44no—
651C22×D17—44no—
652C22×D17—44no—
653C22×D17—44no—
654C22×D17—44no—
655C22×D17C23×C412yes—
656C22×D17C23×C412yes—
657C22×D17C23×C412yes—
658C22×D17C2×#4112yes—
659C22×D17C2×#4112yes—
660D4×C17—28no—
661C2×C4×C17—28no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—44no—
693C2×C4×C17—44no—
694C2×C4×C17—44no—
695C2×C4×C17C23×C412yes—
696C2×C4×C17C23×C412yes—
697C2×C4×C17C23×C412yes—
698C2×C4×C17C23×C412yes—
699C2×C4×C17C23×C412yes—
700C2×C4×C17C22×D412yes—
701C2×C4×C17C22×D412yes—
702C2×C4×C17C2×#4112yes—
703C2×C4×C17C2×#4112yes—
704C22⋊D17—28no—
705C22⋊D17—28no—
706C22⋊D17—28no—
707C22⋊D17—44no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—28no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—44no—
736C2×Dic17—44no—
737C2×Dic17—44no—
738C2×Dic17C4×D4116yescomplemented
739C2×Dic17C23×C412yes—
740C2×Dic17C23×C412yes—
741C2×Dic17C23×C412yes—
742C2×Dic17C23×C412yes—
743C2×Dic17C23×C412yes—
744C2×Dic17C22×D412yes—
745C2×Dic17C22×D412yes—
746C2×Dic17C22×D412yes—
747C2×Dic17C22×D412yes—
748C2×Dic17C2×#4112yes—
749C2×Dic17C2×#4112yes—
750C2×Dic17C2×#4112yes—
751C2×Dic17C2×#4112yes—
752D68—28no—
753D68—44no—
754C4×D17—28no—
755C4×D17—28no—
756C4×D17—28no—
757C4×D17—28no—
758C4×D17—28no—
759C4×D17—44no—
760C4×D17—44no—
761C4×D17—44no—
762C4×D17—44no—
763C4×D17—44no—
764C4×D17—44no—
765Dic34—28no—
766C2×#525—171no—
767C2×C4×#41—171no—
768C22×#117—171no—
769#2363—171no—
770#2363—171no—
771#2362—171no—
772#2362—171no—
773#2361—171no—
774#2361—171no—
775#2360—171no—
776#2360—171no—
777#2359—171no—
778#2359—171no—
779#2359—171no—
780#2359D1711yescharacteristic, complemented
781#2358—171no—
782#2358—171no—
783#2358—171no—
784#2358—171no—
785#2297—171no—
786#2296—171no—
787#2293—171no—
788#2293—171no—
789#2290—171no—
790#2290—171no—
791#2290—171no—
792#2290—171no—
793C42×D4—171no—
794C42×D4—171no—
795C4×#117—171no—
796C2×C4×C22⋊C4—171no—
797C22×C17—22no—
798C22×C17—22no—
799C22×C17—22no—
800C22×C17—22no—
801C22×C17—22no—
802C22×C17—22no—
803C22×C17—22no—
804C22×C17—22no—
805C22×C17—22no—
806C22×C17—41no—
807C22×C17—41no—
808C22×C17—41no—
809C22×C17—41no—
810C22×C17C2×C4×D414yes—
811C22×C17C24×C411yescharacteristic
812C22×C17C23×D411yescharacteristic
813C22×C17C22×#4111yescharacteristic
814C22×C17C22×#4111yescharacteristic
815C22×C17C22×#4111yescharacteristic
816C22×C17#58511yescharacteristic
817C22×C17#58511yescharacteristic
818C2×D17—22no—
819C2×D17—22no—
820C2×D17—22no—
821C2×D17—22no—
822C2×D17—22no—
823C2×D17—22no—
824C2×D17—22no—
825C2×D17—22no—
826C2×D17—22no—
827C2×D17—22no—
828C2×D17—22no—
829C2×D17—22no—
830C2×D17—416no—
831C2×D17—41no—
832C2×D17—41no—
833C2×D17—41no—
834C2×D17—41no—
835C2×D17—41no—
836C2×D17—41no—
837C2×D17—41no—
838C2×D17—41no—
839C2×D17C4×#4114yescomplemented
840C4×C17—22no—
841C4×C17—22no—
842C4×C17—22no—
843C4×C17—22no—
844C4×C17—22no—
845C4×C17—22no—
846C4×C17—22no—
847C4×C17—22no—
848C4×C17—22no—
849C4×C17—41no—
850C4×C17—41no—
851C4×C17—41no—
852C4×C17—41no—
853Dic17—22no—
854Dic17—22no—
855Dic17—22no—
856Dic17—22no—
857Dic17—22no—
858Dic17—22no—
859Dic17—22no—
860Dic17—41no—
861Dic17—41no—
862Dic17—41no—
863Dic17—41no—
864Dic17C2×C4×D414yes—
865Dic17C2×C4×D414yes—
866C22×#41—171no—
867C24×C4—171no—
868#525—1716no—
869C2×#123—171no—
870C2×#123C2×D1711yescharacteristic
871C2×C22⋊Q8—171no—
872C2×C22⋊Q8—171no—
873C2×#121—171no—
874C2×#121—171no—
875C2×#120—171no—
876C2×#120—171no—
877C4×#41—348no—
878C2×C4×Q8—171no—
879C2×C4×Q8—171no—
880C2×C4×D4—171no—
881C2×C4×D4—171no—
882C2×C4×D4—171no—
883C2×C4×D4—171no—
884C2×C4×D4—171no—
885C2×C4×D4—171no—
886C2×C4×D4—171no—
887C2×C4×D4—171no—
888C2×C4×D4—171no—
889C2×C4×D4—171no—
890C2×C4×D4—171no—
891C2×C4×D4—171no—
892C2×C4×D4—171no—
893C2×C4×D4C2×D1711yescharacteristic
894C2×#117—171no—
895C2×#117—171no—
896C2×#117—171no—
897C2×#117—171no—
898C2×#117—171no—
899C2×#117—171no—
900C2×#117—171no—
901C2×#117—171no—
902C2×#117—171no—
903C2×#117—171no—
904C2×#117—348no—
905C2×#117C2×D1711yescharacteristic
906C22×C4⋊C4—171no—
907C22×C4⋊C4—171no—
908C22×C22⋊C4—171no—
909C22×C22⋊C4—171no—
910C22×C22⋊C4—171no—
911C22×C22⋊C4—171no—
912C22×C42—171no—
913C22×C42—171no—
914C22×C42—171no—
915C22×C42—171no—
916C22×C42—171no—
917C22×C42—171no—
918#391—171no—
919#391—171no—
920#390—171no—
921#390—171no—
922#390—171no—
923#390—171no—
924#390—171no—
925#390—171no—
926#389—171no—
927#389—171no—
928#389—171no—
929#389—171no—
930#389—171no—
931#389—171no—
932#389—171no—
933#389C2×D1711yescharacteristic, complemented
934#388—171no—
935#388—171no—
936#388—171no—
937#388—171no—
938#388—171no—
939#388—171no—
940#388—171no—
941#388—171no—
942#388—171no—
943#388—171no—
944#388—171no—
945#388—171no—
946#388—171no—
947#388—171no—
948#388C2×D1711yescharacteristic, complemented
949#388C2×D1711yescharacteristic, complemented
950#387—171no—
951#387—171no—
952#387—171no—
953#387—171no—
954#387—171no—
955#387—171no—
956#387C2×D1711yescharacteristic, complemented
957#387C2×D1711yescharacteristic, complemented
958#386—171no—
959#386—171no—
960#386—171no—
961#386—171no—
962#386—171no—
963#386—171no—
964#386—171no—
965#386—171no—
966#386—171no—
967#386—171no—
968#386—171no—
969#386C2×D1711yescharacteristic
970#385—171no—
971#385—171no—
972#385—171no—
973#385—171no—
974#385—171no—
975#385—171no—
976#385—171no—
977#385—171no—
978#385—171no—
979#385—171no—
980#385C2×D1711yescharacteristic
981#385C2×D1711yescharacteristic, complemented
982C4×C4⋊C4—171no—
983C4×C4⋊C4—171no—
984C4×C4⋊C4—171no—
985C4×C4⋊C4—171no—
986C4×C4⋊C4—171no—
987C4×C4⋊C4—171no—
988C4×C4⋊C4—171no—
989C4×C4⋊C4—171no—
990C4×C4⋊C4—171no—
991C4×C4⋊C4—171no—
992C4×C4⋊C4—171no—
993C4×C4⋊C4C2×D1711yescharacteristic, complemented
994C4×C22⋊C4—171no—
995C4×C22⋊C4—171no—
996C4×C22⋊C4—171no—
997C4×C22⋊C4—171no—
998C4×C22⋊C4—171no—
999C4×C22⋊C4—171no—
1000C4×C22⋊C4—171no—
1001C4×C22⋊C4—171no—
1002C4×C22⋊C4—171no—
1003C4×C22⋊C4—171no—
1004C4×C22⋊C4—171no—
1005C4×C22⋊C4—171no—
1006C4×C22⋊C4—171no—
1007C4×C22⋊C4—171no—
1008C4×C22⋊C4—171no—
1009C4×C22⋊C4—171no—
1010C4×C22⋊C4—171no—
1011C4×C22⋊C4—171no—
1012C4×C22⋊C4—171no—
1013C4×C22⋊C4—171no—
1014C4×C22⋊C4—171no—
1015C4×C22⋊C4—171no—
1016C4×C22⋊C4C2×D1711yescharacteristic
1017C4×C22⋊C4C2×D1711yescharacteristic, complemented
1018#376—171no—
1019#376—171no—
1020C2×#95—171no—
1021C2×#95C2×D1711yescharacteristic
1022C43—171no—
1023C43—171no—
1024C2×C17—24no—
1025C2×C17—42no—
1026C2×C17C22×C4×D411yescharacteristic
1027C2×C17C2×C4×#4111yescharacteristic
1028C2×C17#342811yescharacteristic
1029C2×C17D4×#4111yescharacteristic
1030C2×C17D4×#4111yescharacteristic
1031C2×C17#347511yescharacteristic
1032C2×C17#347511yescharacteristic
1033D17—24no—
1034D17—42no—
1035D17—42no—
1036C25—171no—
1037C2×#41—178no—
1038C2×#41—344no—
1039C2×#41—344no—
1040C22×Q8—171no—
1041C22×D4—171no—
1042C22×D4—171no—
1043C22×D4—171no—
1044C22×D4—171no—
1045C22×D4—171no—
1046C22×D4—171no—
1047C22×D4C22×D1711yescharacteristic
1048C23×C4—171no—
1049C23×C4—171no—
1050C23×C4—178no—
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—171no—
1055C23×C4—171no—
1056C23×C4—171no—
1057C23×C4—171no—
1058C23×C4—171no—
1059C23×C4—171no—
1060C23×C4—171no—
1061C23×C4—171no—
1062C23×C4—171no—
1063C23×C4—171no—
1064C23×C4—171no—
1065C23×C4—344no—
1066C23×C4—344no—
1067C23×C4C22×D1711yescharacteristic
1068C23×C4C22×D1711yescharacteristic
1069C23×C4C22×D1711yescharacteristic
1070C23×C4C22×D1711yescharacteristic
1071#123—178no—
1072#123C4×D1718yescomplemented
1073C22⋊Q8—178no—
1074C22⋊Q8—178no—
1075#121—178no—
1076#121—178no—
1077#120—178no—
1078#120—178no—
1079C4×Q8—344no—
1080C4×Q8—344no—
1081C4×D4—24no—
1082C4×D4—178no—
1083C4×D4—178no—
1084C4×D4—178no—
1085C4×D4—178no—
1086C4×D4—344no—
1087C4×D4—344no—
1088C4×D4—344no—
1089C4×D4—344no—
1090C4×D4—344no—
1091C4×D4—344no—
1092C4×D4—344no—
1093C4×D4—344no—
1094C4×D4—344no—
1095#117—24no—
1096#117—178no—
1097#117—178no—
1098#117—344no—
1099#117—344no—
1100#117—344no—
1101#117—344no—
1102#117—344no—
1103#117—344no—
1104#117—344no—
1105#117—344no—
1106C2×C4⋊C4—171no—
1107C2×C4⋊C4—171no—
1108C2×C4⋊C4—171no—
1109C2×C4⋊C4—171no—
1110C2×C4⋊C4—171no—
1111C2×C4⋊C4—171no—
1112C2×C4⋊C4—171no—
1113C2×C4⋊C4—171no—
1114C2×C4⋊C4—171no—
1115C2×C4⋊C4—171no—
1116C2×C4⋊C4—171no—
1117C2×C4⋊C4—171no—
1118C2×C4⋊C4—171no—
1119C2×C4⋊C4—171no—
1120C2×C4⋊C4—171no—
1121C2×C4⋊C4—171no—
1122C2×C4⋊C4—171no—
1123C2×C4⋊C4—171no—
1124C2×C4⋊C4—171no—
1125C2×C4⋊C4—344no—
1126C2×C4⋊C4—344no—
1127C2×C4⋊C4C22×D1711yescharacteristic
1128C2×C4⋊C4C22×D1711yescharacteristic
1129C2×C4⋊C4C22×D1711yescharacteristic
1130C2×C4⋊C4C22×D1711yescharacteristic
1131C2×C4⋊C4C22×D1711yescharacteristic
1132C2×C4⋊C4C22×D1711yescharacteristic
1133C2×C4⋊C4C22×D1711yescharacteristic
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—344no—
1165C2×C22⋊C4—344no—
1166C2×C22⋊C4—344no—
1167C2×C22⋊C4—344no—
1168C2×C22⋊C4C22×D1711yescharacteristic
1169C2×C22⋊C4C22×D1711yescharacteristic
1170C2×C22⋊C4C22×D1711yescharacteristic
1171C2×C22⋊C4C22×D1711yescharacteristic
1172C2×C22⋊C4C22×D1711yescharacteristic
1173C2×C22⋊C4C22×D1711yescharacteristic
1174C2×C22⋊C4C22×D1711yescharacteristic
1175C2×C22⋊C4C22×D1711yescharacteristic
1176C2×C42—171no—
1177C2×C42—171no—
1178C2×C42—171no—
1179C2×C42—171no—
1180C2×C42—171no—
1181C2×C42—171no—
1182C2×C42—171no—
1183C2×C42—171no—
1184C2×C42—171no—
1185C2×C42—171no—
1186C2×C42—171no—
1187C2×C42—171no—
1188C2×C42—171no—
1189C2×C42—171no—
1190C2×C42—171no—
1191C2×C42—171no—
1192C2×C42—171no—
1193C2×C42—171no—
1194C2×C42—171no—
1195C2×C42—171no—
1196C2×C42—171no—
1197C2×C42—171no—
1198C2×C42—171no—
1199C2×C42—171no—
1200C2×C42—171no—
1201C2×C42—344no—
1202C2×C42—344no—
1203C2×C42—344no—
1204C2×C42—344no—
1205C2×C42—344no—
1206C2×C42—344no—
1207C2×C42C22×D1711yescharacteristic
1208C2×C42C22×D1711yescharacteristic
1209C2×C42C22×D1711yescharacteristic
1210C2×C42C22×D1711yescharacteristic
1211C2×C42C22×D1711yescharacteristic
1212#95—171no—
1213#95—171no—
1214#95—171no—
1215#95—171no—
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95—171no—
1220#95—171no—
1221#95—171no—
1222#95—171no—
1223#95—171no—
1224#95—171no—
1225#95—171no—
1226#95—171no—
1227#95—171no—
1228#95—171no—
1229#95—171no—
1230#95—171no—
1231#95—171no—
1232#95—171no—
1233#95—171no—
1234#95C22×D1711yescharacteristic
1235#95C22×D1711yescharacteristic
1236#95C22×D1711yescharacteristic
1237#95C22×D1711yescharacteristic
1238#95C22×D1711yescharacteristic
1239#95C22×D1711yescharacteristic
1240#95C22×D1711yescharacteristic
1241#95C22×D1711yescharacteristic
1242#95C22×D1711yescharacteristic
1243#95C22×D1711yescharacteristic
1244C17#3413611yescharacteristic, complemented, Sylow
1245C24—171no—
1246C24—171no—
1247C24—171no—
1248C24—174no—
1249C24—342no—
1250C24—342no—
1251C24—342no—
1252C24—342no—
1253C24—681no—
1254C24—681no—
1255C24C23×D1711yescharacteristic
1256C24C23×D1711yescharacteristic
1257#41—3432no—
1258C2×Q8—174no—
1259C2×Q8—342no—
1260C2×Q8—342no—
1261C2×D4—22no—
1262C2×D4—22no—
1263C2×D4—174no—
1264C2×D4—174no—
1265C2×D4—174no—
1266C2×D4—174no—
1267C2×D4—174no—
1268C2×D4—174no—
1269C2×D4—342no—
1270C2×D4—342no—
1271C2×D4—342no—
1272C2×D4—342no—
1273C2×D4—342no—
1274C2×D4—342no—
1275C2×D4—342no—
1276C2×D4—342no—
1277C2×D4—681no—
1278C2×D4—681no—
1279C2×D4—681no—
1280C2×D4—681no—
1281C2×D4C2×C4×D1714yes—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—22no—
1290C22×C4—41no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—174no—
1294C22×C4—174no—
1295C22×C4—174no—
1296C22×C4—171no—
1297C22×C4—171no—
1298C22×C4—174no—
1299C22×C4—171no—
1300C22×C4—171no—
1301C22×C4—171no—
1302C22×C4—171no—
1303C22×C4—171no—
1304C22×C4—171no—
1305C22×C4—171no—
1306C22×C4—174no—
1307C22×C4—174no—
1308C22×C4—174no—
1309C22×C4—174no—
1310C22×C4—174no—
1311C22×C4—171no—
1312C22×C4—171no—
1313C22×C4—171no—
1314C22×C4—171no—
1315C22×C4—342no—
1316C22×C4—342no—
1317C22×C4—342no—
1318C22×C4—342no—
1319C22×C4—342no—
1320C22×C4—3432no—
1321C22×C4—342no—
1322C22×C4—342no—
1323C22×C4—342no—
1324C22×C4—342no—
1325C22×C4—342no—
1326C22×C4—342no—
1327C22×C4—342no—
1328C22×C4—342no—
1329C22×C4—342no—
1330C22×C4—342no—
1331C22×C4—342no—
1332C22×C4—342no—
1333C22×C4—342no—
1334C22×C4—342no—
1335C22×C4—342no—
1336C22×C4—342no—
1337C22×C4—342no—
1338C22×C4—342no—
1339C22×C4—342no—
1340C22×C4—342no—
1341C22×C4—342no—
1342C22×C4—342no—
1343C22×C4—342no—
1344C22×C4—342no—
1345C22×C4—342no—
1346C22×C4—681no—
1347C22×C4—681no—
1348C22×C4—681no—
1349C22×C4—681no—
1350C22×C4—681no—
1351C22×C4—681no—
1352C22×C4—681no—
1353C22×C4—681no—
1354C22×C4—681no—
1355C22×C4C2×C4×D1714yes—
1356C22×C4C23×D1711yescharacteristic
1357C22×C4C23×D1711yescharacteristic
1358C22×C4C23×D1711yescharacteristic
1359C22×C4C23×D1711yescharacteristic
1360C22×C4C23×D1711yescharacteristic
1361C22×C4C23×D1711yescharacteristic
1362C22×C4C23×D1711yescharacteristic
1363C22×C4C23×D1711yescharacteristic
1364C22×C4C23×D1711yescharacteristic
1365C22×C4C23×D1711yescharacteristic
1366C22×C4C23×D1711yescharacteristic
1367C22×C4C23×D1711yescharacteristic
1368C22×C4C23×D1711yescharacteristic
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—22no—
1372C4⋊C4—22no—
1373C4⋊C4—41no—
1374C4⋊C4—174no—
1375C4⋊C4—174no—
1376C4⋊C4—174no—
1377C4⋊C4—174no—
1378C4⋊C4—174no—
1379C4⋊C4—174no—
1380C4⋊C4—342no—
1381C4⋊C4—342no—
1382C4⋊C4—342no—
1383C4⋊C4—342no—
1384C4⋊C4—342no—
1385C4⋊C4—342no—
1386C4⋊C4—342no—
1387C4⋊C4—342no—
1388C4⋊C4—342no—
1389C4⋊C4—342no—
1390C4⋊C4—681no—
1391C4⋊C4—681no—
1392C4⋊C4—681no—
1393C4⋊C4C2×C4×D1714yes—
1394C4⋊C4C2×C4×D1714yes—
1395C22⋊C4—22no—
1396C22⋊C4—22no—
1397C22⋊C4—22no—
1398C22⋊C4—41no—
1399C22⋊C4—174no—
1400C22⋊C4—174no—
1401C22⋊C4—174no—
1402C22⋊C4—174no—
1403C22⋊C4—174no—
1404C22⋊C4—174no—
1405C22⋊C4—174no—
1406C22⋊C4—174no—
1407C22⋊C4—174no—
1408C22⋊C4—174no—
1409C22⋊C4—342no—
1410C22⋊C4—342no—
1411C22⋊C4—342no—
1412C22⋊C4—342no—
1413C22⋊C4—342no—
1414C22⋊C4—342no—
1415C22⋊C4—342no—
1416C22⋊C4—342no—
1417C22⋊C4—342no—
1418C22⋊C4—342no—
1419C22⋊C4—342no—
1420C22⋊C4—342no—
1421C22⋊C4—342no—
1422C22⋊C4—342no—
1423C22⋊C4—342no—
1424C22⋊C4—342no—
1425C22⋊C4—342no—
1426C22⋊C4—681no—
1427C22⋊C4—681no—
1428C22⋊C4—681no—
1429C22⋊C4C2×C4×D1714yes—
1430C22⋊C4C2×C4×D1714yes—
1431C22⋊C4C2×C4×D1714yes—
1432C22⋊C4D4×D1714yes—
1433C42—22no—
1434C42—22no—
1435C42—22no—
1436C42—22no—
1437C42—41no—
1438C42—174no—
1439C42—174no—
1440C42—174no—
1441C42—174no—
1442C42—342no—
1443C42—342no—
1444C42—342no—
1445C42—342no—
1446C42—342no—
1447C42—342no—
1448C42—342no—
1449C42—342no—
1450C42—342no—
1451C42—342no—
1452C42—342no—
1453C42—342no—
1454C42—342no—
1455C42—342no—
1456C42—342no—
1457C42—342no—
1458C42—342no—
1459C42—342no—
1460C42—681no—
1461C42—681no—
1462C42—681no—
1463C23—21no—
1464C23—21no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—172no—
1474C23—172no—
1475C23—172no—
1476C23—172no—
1477C23—172no—
1478C23—348no—
1479C23—341no—
1480C23—341no—
1481C23—341no—
1482C23—341no—
1483C23—348no—
1484C23—341no—
1485C23—341no—
1486C23—341no—
1487C23—341no—
1488C23—341no—
1489C23—341no—
1490C23—341no—
1491C23—341no—
1492C23—341no—
1493C23—341no—
1494C23—341no—
1495C23—341no—
1496C23—684no—
1497C23—684no—
1498C23—684no—
1499C23—684no—
1500C23—684no—
1501C23C22×C4×D1712yes—
1502C23C22×C4×D1712yes—
1503C23C2×D4×D1712yes—
1504C23#41×D1712yes—
1505C23C24×D1711yescharacteristic
1506Q8—348no—
1507D4—28no—
1508D4—348no—
1509D4—348no—
1510D4—348no—
1511D4—348no—
1512D4—684no—
1513D4—684no—
1514C2×C4—28no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—44no—
1546C2×C4—44no—
1547C2×C4—44no—
1548C2×C4—1716no—
1549C2×C4—172no—
1550C2×C4—172no—
1551C2×C4—172no—
1552C2×C4—172no—
1553C2×C4—172no—
1554C2×C4—172no—
1555C2×C4—172no—
1556C2×C4—172no—
1557C2×C4—172no—
1558C2×C4—172no—
1559C2×C4—172no—
1560C2×C4—172no—
1561C2×C4—172no—
1562C2×C4—348no—
1563C2×C4—348no—
1564C2×C4—348no—
1565C2×C4—348no—
1566C2×C4—348no—
1567C2×C4—348no—
1568C2×C4—341no—
1569C2×C4—341no—
1570C2×C4—341no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—341no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—341no—
1579C2×C4—341no—
1580C2×C4—341no—
1581C2×C4—341no—
1582C2×C4—341no—
1583C2×C4—341no—
1584C2×C4—341no—
1585C2×C4—341no—
1586C2×C4—341no—
1587C2×C4—341no—
1588C2×C4—341no—
1589C2×C4—341no—
1590C2×C4—341no—
1591C2×C4—341no—
1592C2×C4—341no—
1593C2×C4—341no—
1594C2×C4—684no—
1595C2×C4—684no—
1596C2×C4—684no—
1597C2×C4—684no—
1598C2×C4—684no—
1599C2×C4—684no—
1600C2×C4—684no—
1601C2×C4—684no—
1602C2×C4—684no—
1603C2×C4C22×C4×D1712yes—
1604C2×C4C22×C4×D1712yes—
1605C2×C4C22×C4×D1712yes—
1606C2×C4C22×C4×D1712yes—
1607C2×C4C22×C4×D1712yes—
1608C2×C4C2×D4×D1712yes—
1609C2×C4C2×D4×D1712yes—
1610C2×C4#41×D1712yes—
1611C2×C4#41×D1712yes—
1612C22—22no—
1613C22—22no—
1614C22—22no—
1615C22—22no—
1616C22—22no—
1617C22—22no—
1618C22—22no—
1619C22—22no—
1620C22—22no—
1621C22—41no—
1622C22—41no—
1623C22—41no—
1624C22—41no—
1625C22—174no—
1626C22—342no—
1627C22—342no—
1628C22—342no—
1629C22—342no—
1630C22—342no—
1631C22—342no—
1632C22—342no—
1633C22—342no—
1634C22—342no—
1635C22—342no—
1636C22—342no—
1637C22—342no—
1638C22—6816no—
1639C22—681no—
1640C22—681no—
1641C22—681no—
1642C22—681no—
1643C22—681no—
1644C22—681no—
1645C22—681no—
1646C22—681no—
1647C22C4×D4×D1714yes—
1648C22C23×C4×D1711yescharacteristic
1649C22C22×D4×D1711yescharacteristic
1650C22C2×#41×D1711yescharacteristic
1651C22C2×#41×D1711yescharacteristic
1652C22C2×#41×D1711yescharacteristic
1653C22#1176364411yescharacteristic
1654C22#1176364611yescharacteristic
1655C4—22no—
1656C4—22no—
1657C4—22no—
1658C4—22no—
1659C4—22no—
1660C4—22no—
1661C4—22no—
1662C4—22no—
1663C4—22no—
1664C4—41no—
1665C4—41no—
1666C4—41no—
1667C4—41no—
1668C4—174no—
1669C4—174no—
1670C4—342no—
1671C4—342no—
1672C4—342no—
1673C4—342no—
1674C4—342no—
1675C4—342no—
1676C4—342no—
1677C4—681no—
1678C4—681no—
1679C4—681no—
1680C4—681no—
1681C2—24no—
1682C2—42no—
1683C2—344no—
1684C2—682no—
1685C2—682no—
1686C2C2×C4×D4×D1711yescharacteristic
1687C2C4×#41×D1711yescharacteristic
1688C2#1454198411yescharacteristic
1689C2#1454226811yescharacteristic
1690C2#1454227111yescharacteristic
1691C2#1454233911yescharacteristic
1692C2#1454234911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2359C2
socle, cosocleC23×C17C25
prime radicalC2×#11763317C2
hypercenter#2359D17
hypocenterC17#34136
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2359

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×#63254C2semidirect
3. C2×#117×D17C2semidirect
4. #14531823C2semidirect
5. #14531817C2semidirect
6. #14531812C2semidirect
7. #14531806C2semidirect
8. #14531803C2semidirect
9. #14531797C2semidirect
10. #14531792C2semidirect
11. #14531786C2semidirect
12. #14531780C2semidirect
13. #14531776C2semidirect
14. #14531772C2semidirect
15. #14531766C2semidirect
16. #14531764C2semidirect
17. #14531761C2semidirect
18. #14531760C2semidirect
19. #14531269C2semidirect
20. #14531263C2semidirect
21. #14531244C2semidirect
22. #14531242C2semidirect
23. #14531226C2semidirect
24. #14531222C2semidirect
25. #14531222C2semidirect
26. #14531220C2semidirect
27. C4×#10587579C2semidirect
28. C4×#10587567C2semidirect
29. C4×#10587563C2semidirect
30. C2×#11762656C2semidirect
31. C17×#2359C2semidirect
34. #11763317C4semidirect
43. C2×C4×Dic34C22semidirect
44. C2×#10587573C22semidirect
52. C2×C4×C22⋊D17C22semidirect
57. C2×#10587567C22semidirect
61. C2×#10587578C22semidirect
67. C2×#10587563C22semidirect
77. C22×C4×Dic17C22semidirect
80. C2×C42×D17C22semidirect
81. #11762713C22semidirect
82. #11762713C22semidirect
87. #11762709C22semidirect
88. #11762709C22semidirect
89. #11762708C22semidirect
90. #11762706C22semidirect
91. #11762706C22semidirect
92. #11762706C22semidirect
93. #11762704C22semidirect
94. #11762704C22semidirect
95. #11762704C22semidirect
96. #11762702C22semidirect
97. #11762702C22semidirect
100. #11762701C22semidirect
103. #11762700C22semidirect
106. #11762699C22semidirect
109. #11762698C22semidirect
110. #11762696C22semidirect
111. #11762695C22semidirect
112. #11762695C22semidirect
113. #11762693C22semidirect
114. #11762691C22semidirect
115. #11762690C22semidirect
128. #11762684C22semidirect
131. #11762683C22semidirect
136. #11762680C22semidirect
137. C4⋊C4×Dic17C22semidirect
138. C4⋊C4×Dic17C22semidirect
139. C4⋊C4×Dic17C22semidirect
140. C4×#63225C22semidirect
141. C4×#63225C22semidirect
142. C4×#63225C22semidirect
143. #11762660C22semidirect
144. #11762660C22semidirect
145. #11762660C22semidirect
146. #11762660C22semidirect
147. #11762660C22semidirect
150. C22⋊C4×Dic17C22semidirect
151. C22⋊C4×Dic17C22semidirect
152. C22⋊C4×Dic17C22semidirect
155. C4×#63227C22semidirect
167. #11762656C22semidirect
168. #11762656C22semidirect
169. #11762656C22semidirect
170. #11762654C22semidirect
171. #11762654C22semidirect
173. C42×Dic17C22semidirect
174. C42×Dic17C22semidirect
178. C17×#389C22semidirect
179. C17×#388C22semidirect
180. C17×#388C22semidirect
181. C17×#387C22semidirect
182. C17×#387C22semidirect
185. C17×#385C22semidirect
186. C4×C4⋊C4×C17C22semidirect
188. C4×C22⋊C4×C17C22semidirect
207. C2×#63254C2×C4semidirect
212. C22×C4×D17C2×C4semidirect
225. C17×#123C2×C4semidirect
254. #10587623C2×C4semidirect
256. #10587615C2×C4semidirect
334. #10587582C2×C4semidirect
335. #10587582C2×C4semidirect
337. #10587579C2×C4semidirect
338. #10587579C2×C4semidirect
345. #10587570C2×C4semidirect
346. #10587570C2×C4semidirect
347. #10587568C2×C4semidirect
351. #10587567C2×C4semidirect
352. #10587567C2×C4semidirect
357. #10587563C2×C4semidirect
358. #10587563D4semidirect
570. #63227#41semidirect
571. #63227#41semidirect
738. C2×Dic17C4×D4semidirect
780. #2359D17semidirect
839. C2×D17C4×#41semidirect
933. #389C2×D17semidirect
948. #388C2×D17semidirect
949. #388C2×D17semidirect
956. #387C2×D17semidirect
957. #387C2×D17semidirect
981. #385C2×D17semidirect
993. C4×C4⋊C4C2×D17semidirect
1017. C4×C22⋊C4C2×D17semidirect
1072. #123C4×D17semidirect
1244. C17#34136semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633172
C2×C4×#632542
C2×#117×D172
#145318232
#145318172
#145318122
#145318062
#145318032
#145317972
#145317922
#145317862
#145317802
#145317762
#145317722
#145317662
#145317642
#145317612
#145317602
#145312692
#145312632
#145312442
#145312422
#145312262
#145312222
#145312202
C4×#105875792
C4×#105875672
C4×#105875632
C2×#117626562
C17×#23592
#3413617