Finite Group Databasebeta

← #17193883

Subgroups — #17193883

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×#11763315C211yesmaximal, characteristic
2C2×C4×#63254C211yesmaximal, characteristic, complemented
3C22×#10587563C211yesmaximal, characteristic, complemented
4#14531825C211yesmaximal, characteristic, complemented
5#14531819C211yesmaximal, characteristic, complemented
6#14531814C211yesmaximal, characteristic, complemented
7#14531808C211yesmaximal, characteristic, complemented
8#14531801C211yesmaximal, characteristic, complemented
9#14531795C211yesmaximal, characteristic, complemented
10#14531790C211yesmaximal, characteristic, complemented
11#14531784C211yesmaximal, characteristic, complemented
12#14531782C211yesmaximal, characteristic, complemented
13#14531778C211yesmaximal, characteristic, complemented
14#14531774C211yesmaximal, characteristic, complemented
15#14531770C211yesmaximal, characteristic, complemented
16#14531768C211yesmaximal, characteristic, complemented
17#14531763C211yesmaximal, characteristic, complemented
18#14531763C211yesmaximal, characteristic, complemented
19#14531269C211yesmaximal, characteristic, complemented
20#14531263C211yesmaximal, characteristic, complemented
21#14531246C211yesmaximal, characteristic, complemented
22#14531244C211yesmaximal, characteristic, complemented
23#14531226C211yesmaximal, characteristic, complemented
24#14531224C211yesmaximal, characteristic, complemented
25#14531224C211yesmaximal, characteristic, complemented
26#14531220C211yesmaximal, characteristic, complemented
27C4×D4×Dic17C211yesmaximal, characteristic, complemented
28C4×#10587567C211yesmaximal, characteristic, complemented
29C4×#10587563C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
31C17×#2358C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C24×Dic17C2211yescharacteristic
34#11763315C4116yescomplemented
35C2×#10587572C2211yescharacteristic
36C2×#10587621C2211yescharacteristic
37C2×#10587564C2211yescharacteristic
38C2×#10587564C2211yescharacteristic
39C2×#10587625C2211yescharacteristic
40C2×#10587625C2211yescharacteristic
41C2×#10587639C2211yescharacteristic
42C4×#63254—28no—
43C2×C4×Dic34C2211yescharacteristic, complemented
44C2×#10587573C2211yescharacteristic, complemented
45C2×D4×Dic17C2211yescharacteristic
46C2×D4×Dic17C2211yescharacteristic
47C2×D4×Dic17C2211yescharacteristic
48C2×D4×Dic17C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic, complemented
52C2×#10587567C2211yescharacteristic
53C2×#10587567C2211yescharacteristic
54C2×#10587567C2211yescharacteristic
55C2×#10587567C2211yescharacteristic
56C2×#10587567C2211yescharacteristic, complemented
57C2×#10587578C2211yescharacteristic, complemented
58C2×#10587563—28no—
59C2×#10587563C2211yescharacteristic
60C2×#10587563C2211yescharacteristic
61C2×#10587563C2211yescharacteristic
62C2×#10587563C2211yescharacteristic
63C2×#10587563C2211yescharacteristic
64C2×#10587563C2211yescharacteristic
65C2×#10587563C2211yescharacteristic
66C2×#10587563C2211yescharacteristic
67C2×#10587563C2211yescharacteristic
68C2×#10587563C2211yescharacteristic, complemented
69C22×#63225C2211yescharacteristic
70C22×#63225C2211yescharacteristic
71C22×C22⋊Dic17C2211yescharacteristic
72C22×C22⋊Dic17C2211yescharacteristic
73C22×C4×Dic17C2211yescharacteristic
74C22×C4×Dic17C2211yescharacteristic
75C22×C4×Dic17C2211yescharacteristic
76C22×C4×Dic17C2211yescharacteristic
77C22×C4×Dic17C2211yescharacteristic, complemented
78C2×C42×D17C2211yescharacteristic, complemented
79#11762713C2211yescharacteristic, complemented
80#11762713C2211yescharacteristic, complemented
81#11762712C2211yescharacteristic
82#11762709C2211yescharacteristic
83#11762709C2211yescharacteristic
84#11762709C2211yescharacteristic, complemented
85#11762709C2211yescharacteristic, complemented
86#11762707C2211yescharacteristic, complemented
87#11762706C2211yescharacteristic, complemented
88#11762706C2211yescharacteristic, complemented
89#11762706C2211yescharacteristic, complemented
90#11762705C2211yescharacteristic, complemented
91#11762704C2211yescharacteristic, complemented
92#11762704C2211yescharacteristic, complemented
93#11762704C2211yescharacteristic, complemented
94#11762703C2211yescharacteristic
95#11762703C2211yescharacteristic
96#11762703C2211yescharacteristic, complemented
97#11762703C2211yescharacteristic, complemented
98#11762702C2211yescharacteristic
99#11762702C2211yescharacteristic
100#11762701C2211yescharacteristic, complemented
101#11762700C2211yescharacteristic, complemented
102#11762699C2211yescharacteristic, complemented
103#11762698C2211yescharacteristic, complemented
104#11762697C2211yescharacteristic
105#11762697C2211yescharacteristic
106#11762697C2211yescharacteristic, complemented
107#11762697C2211yescharacteristic, complemented
108#11762696C2211yescharacteristic, complemented
109#11762694C2211yescharacteristic, complemented
110#11762694C2211yescharacteristic, complemented
111#11762693C2211yescharacteristic, complemented
112#11762692C2211yescharacteristic, complemented
113#11762692C2211yescharacteristic, complemented
114#11762691C2211yescharacteristic, complemented
115#11762690C2211yescharacteristic, complemented
116#11762689C2211yescharacteristic
117#11762689C2211yescharacteristic
118#11762689C2211yescharacteristic
119#11762688C2211yescharacteristic
120#11762688C2211yescharacteristic
121#11762686C2211yescharacteristic
122#11762686C2211yescharacteristic
123#11762685C2211yescharacteristic
124#11762685C2211yescharacteristic
125#11762684C2211yescharacteristic
126#11762684C2211yescharacteristic
127#11762683C2211yescharacteristic, complemented
128#11762682C2211yescharacteristic
129#11762682C2211yescharacteristic
130#11762682C2211yescharacteristic, complemented
131#11762681C2211yescharacteristic
132#11762681C2211yescharacteristic
133#11762681C2211yescharacteristic, complemented
134#11762680C2211yescharacteristic, complemented
135C4⋊C4×Dic17C2211yescharacteristic, complemented
136C4⋊C4×Dic17C2211yescharacteristic, complemented
137C4⋊C4×Dic17C2211yescharacteristic, complemented
138C4×#63225C2211yescharacteristic, complemented
139C4×#63225C2211yescharacteristic, complemented
140C4×#63225C2211yescharacteristic, complemented
141C4×C4⋊Dic17C2211yescharacteristic, complemented
142#11762660C2211yescharacteristic, complemented
143#11762660C2211yescharacteristic, complemented
144#11762660C2211yescharacteristic, complemented
145#11762660C2211yescharacteristic, complemented
146#11762660C2211yescharacteristic, complemented
147C22⋊C4×Dic17C2211yescharacteristic
148C22⋊C4×Dic17C2211yescharacteristic
149C22⋊C4×Dic17C2211yescharacteristic
150C22⋊C4×Dic17C2211yescharacteristic
151C22⋊C4×Dic17C2211yescharacteristic
152C22⋊C4×Dic17C2211yescharacteristic
153C22⋊C4×Dic17C2211yescharacteristic
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic, complemented
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C22⋊C4×Dic17C2211yescharacteristic, complemented
162C4×#63227C2211yescharacteristic, complemented
163C4×C22⋊Dic17C2211yescharacteristic
164C4×C22⋊Dic17C2211yescharacteristic
165C4×C22⋊Dic17C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762654C2211yescharacteristic, complemented
170#11762654C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic
172C2×#10587502C2211yescharacteristic
173C42×Dic17C2211yescharacteristic, complemented
174C42×Dic17C2211yescharacteristic, complemented
175C2×C17×#120C2211yescharacteristic
176C2×C4×D4×C17C2211yescharacteristic
177C2×C4×D4×C17C2211yescharacteristic
178C22×C22⋊C4×C17C2211yescharacteristic
179C22×C22⋊C4×C17C2211yescharacteristic
180C17×#390C2211yescharacteristic
181C17×#388C2211yescharacteristic
182C17×#388C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#385C2211yescharacteristic
187C17×#385C2211yescharacteristic
188C4×C22⋊C4×C17C2211yescharacteristic
189C4×C22⋊C4×C17C2211yescharacteristic
190C25×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C23×Dic17—24no—
204C23×Dic17—24no—
205C23×Dic17C2×C418yescomplemented
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C23×Dic17C2311yescharacteristic
216C23×Dic17C2311yescharacteristic
217C23×Dic17C2311yescharacteristic
218C2×#63254—24no—
219C2×#63254—24no—
220C2×#63254C2×C418yescomplemented
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×Dic34C2311yescharacteristic
225C17×#120C2×C418yescomplemented
226C4×D4×C17—24no—
227C4×D4×C17—24no—
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17—24no—
232C2×C22⋊C4×C17—24no—
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊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×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C42×C17C2311yescharacteristic
248C2×C42×C17C2311yescharacteristic
249C2×C42×C17C2311yescharacteristic
250#10587639C2×C418yescomplemented
251C2×C22⋊Dic17—24no—
252C2×C22⋊Dic17—24no—
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269#10587625C2×C418yescomplemented
270#10587625C2×C418yescomplemented
271#10587621C2×C418yescomplemented
272D4×Dic17—24no—
273D4×Dic17—24no—
274D4×Dic17C2×C418yescomplemented
275D4×Dic17C2×C418yescomplemented
276C4×C22⋊D17—24no—
277C4×C22⋊D17—24no—
278C4×C22⋊D17—24no—
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×#63225—24no—
293C2×#63225—24no—
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×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×C4×Dic17—24no—
313C2×C4×Dic17—24no—
314C2×C4×Dic17—24no—
315C2×C4×Dic17—24no—
316C2×C4×Dic17—24no—
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
334C2×C4×Dic17C2311yescharacteristic
335C2×C4×Dic17C2311yescharacteristic
336C2×C4×Dic17C2311yescharacteristic
337C2×C4×Dic17C2311yescharacteristic
338C2×C4×Dic17C2311yescharacteristic
339C2×C4×Dic17C2311yescharacteristic
340C2×C4×Dic17C2311yescharacteristic
341C2×C4×Dic17C2311yescharacteristic
342C2×C4×Dic17C2311yescharacteristic
343C2×C4×Dic17C2311yescharacteristic
344#10587578—24no—
345#10587573—24no—
346#10587572C2×C418yescomplemented
347#10587567—24no—
348#10587567—24no—
349#10587567—24no—
350#10587567C2×C418yescomplemented
351#10587567C2×C418yescomplemented
352#10587564C2×C418yescomplemented
353#10587564C2×C418yescomplemented
354#10587563—24no—
355#10587563—24no—
356#10587563—24no—
357#10587563—24no—
358#10587563—24no—
359#10587563—24no—
360#10587563—24no—
361#10587563—24no—
362#10587563C2×C418yescomplemented
363#10587563D418yescomplemented
364C42×D17—24no—
365C4×Dic34—24no—
366C17×#95C2311yescharacteristic
367C17×#95C2311yescharacteristic
368C17×#95C2311yescharacteristic
369C17×#95C2311yescharacteristic
370C17×#95C2311yescharacteristic
371C17×#95C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
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×C17—22no—
399C24×C17—22no—
400C24×C17—22no—
401C24×C17—22no—
402C24×C17—41no—
403C24×C17—41no—
404C24×C17C22×C414yes—
405C24×C17C2411yescharacteristic
406C24×C17C2411yescharacteristic
407C24×C17C2411yescharacteristic
408C24×C17C2411yescharacteristic
409C23×D17C2411yescharacteristic
410C2×D4×C17—22no—
411C2×D4×C17—22no—
412C2×D4×C17—22no—
413C2×D4×C17—22no—
414C2×D4×C17—41no—
415C2×D4×C17—41no—
416C2×D4×C17C22×C414yes—
417C2×D4×C17C22×C414yes—
418C2×D4×C17C22×C414yes—
419C22×C4×C17—22no—
420C22×C4×C17—22no—
421C22×C4×C17—22no—
422C22×C4×C17—22no—
423C22×C4×C17—22no—
424C22×C4×C17—22no—
425C22×C4×C17—22no—
426C22×C4×C17—22no—
427C22×C4×C17—22no—
428C22×C4×C17—22no—
429C22×C4×C17—41no—
430C22×C4×C17—41no—
431C22×C4×C17—41no—
432C22×C4×C17—41no—
433C22×C4×C17—41no—
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C22×C4×C17C2411yescharacteristic
438C22×C4×C17C2411yescharacteristic
439C22×C4×C17C2411yescharacteristic
440C22×C4×C17C2411yescharacteristic
441C22×C4×C17C2411yescharacteristic
442C22×C4×C17C2411yescharacteristic
443C22×C4×C17C2411yescharacteristic
444C22×C4×C17C2411yescharacteristic
445C2×C22⋊D17—22no—
446C2×C22⋊D17—22no—
447C2×C22⋊D17—22no—
448C2×C22⋊D17—22no—
449C2×C22⋊D17—22no—
450C2×C22⋊D17—22no—
451C2×C22⋊D17—41no—
452C2×C22⋊D17—41no—
453C2×C22⋊D17C22×C414yes—
454C2×C22⋊D17C22×C414yes—
455C2×C22⋊D17C22×C414yes—
456C2×C22⋊D17C22×C414yes—
457C22×Dic17—22no—
458C22×Dic17—22no—
459C22×Dic17—232no—
460C22×Dic17—22no—
461C22×Dic17—22no—
462C22×Dic17—22no—
463C22×Dic17—22no—
464C22×Dic17—22no—
465C22×Dic17—22no—
466C22×Dic17—22no—
467C22×Dic17—22no—
468C22×Dic17—22no—
469C22×Dic17—22no—
470C22×Dic17—22no—
471C22×Dic17—22no—
472C22×Dic17—22no—
473C22×Dic17—22no—
474C22×Dic17—22no—
475C22×Dic17—22no—
476C22×Dic17—22no—
477C22×Dic17—22no—
478C22×Dic17—22no—
479C22×Dic17—22no—
480C22×Dic17—41no—
481C22×Dic17—41no—
482C22×Dic17—41no—
483C22×Dic17—41no—
484C22×Dic17—41no—
485C22×Dic17C22×C414yes—
486C22×Dic17C22×C414yes—
487C22×Dic17C22×C414yes—
488C22×Dic17C22×C414yes—
489C22×Dic17C22×C414yes—
490C22×Dic17C22×C414yes—
491C22×Dic17C22×C414yes—
492C22×Dic17C2×D414yes—
493C22×Dic17#4114yes—
494C22×Dic17C2411yescharacteristic
495C22×Dic17C2411yescharacteristic
496C22×Dic17C2411yescharacteristic
497C22×Dic17C2411yescharacteristic
498C22×Dic17C2411yescharacteristic
499C22×Dic17C2411yescharacteristic
500C22×Dic17C2411yescharacteristic
501C22×Dic17C2411yescharacteristic
502C22×Dic17C2411yescharacteristic
503C22×Dic17C2411yescharacteristic
504C22×Dic17C2411yescharacteristic
505C22×Dic17C2411yescharacteristic
506C22×Dic17C2411yescharacteristic
507C22×Dic17C2411yescharacteristic
508C22×Dic17C2411yescharacteristic
509#63254—232no—
510C2×C4×D17—22no—
511C2×C4×D17—22no—
512C2×C4×D17—22no—
513C2×C4×D17—22no—
514C2×C4×D17—22no—
515C2×C4×D17—22no—
516C2×C4×D17—41no—
517C2×C4×D17—41no—
518C2×C4×D17C22×C414yes—
519C2×Dic34—22no—
520C2×Dic34—22no—
521C2×Dic34C22×C414yes—
522C4⋊C4×C17—22no—
523C4⋊C4×C17—22no—
524C4⋊C4×C17—41no—
525C22⋊C4×C17—22no—
526C22⋊C4×C17—22no—
527C22⋊C4×C17—22no—
528C22⋊C4×C17—22no—
529C22⋊C4×C17—22no—
530C22⋊C4×C17—22no—
531C22⋊C4×C17—22no—
532C22⋊C4×C17—22no—
533C22⋊C4×C17—41no—
534C22⋊C4×C17C22×C414yes—
535C22⋊C4×C17C22×C414yes—
536C22⋊C4×C17C22×C414yes—
537C22⋊C4×C17C2×D414yes—
538C22⋊C4×C17#4114yescomplemented
539C42×C17—22no—
540C42×C17—22no—
541C42×C17—41no—
542C22⋊Dic17—22no—
543C22⋊Dic17—22no—
544C22⋊Dic17—22no—
545C22⋊Dic17—22no—
546C22⋊Dic17—22no—
547C22⋊Dic17—22no—
548C22⋊Dic17—22no—
549C22⋊Dic17—22no—
550C22⋊Dic17—41no—
551C22⋊Dic17C22×C414yes—
552C22⋊Dic17C22×C414yes—
553C22⋊Dic17C22×C414yes—
554C22⋊Dic17C22×C414yes—
555C22⋊Dic17C22×C414yes—
556C22⋊Dic17C2×D414yes—
557C22⋊Dic17#4114yescomplemented
558#63227—22no—
559#63227—22no—
560#63227—22no—
561#63227—22no—
562#63227—41no—
563#63227—41no—
564#63227C22×C414yes—
565#63227C22×C414yes—
566C4⋊Dic17—22no—
567C4⋊Dic17—22no—
568C4⋊Dic17—41no—
569C4⋊Dic17C22×C414yes—
570C4⋊Dic17C22×C414yes—
571#63225—22no—
572#63225—22no—
573#63225—22no—
574#63225—22no—
575#63225—22no—
576#63225—22no—
577#63225—22no—
578#63225—22no—
579#63225—22no—
580#63225—22no—
581#63225—41no—
582#63225—41no—
583#63225C22×C414yes—
584#63225C22×C414yes—
585#63225C22×C414yes—
586#63225C22×C414yes—
587#63225C2×D414yes—
588#63225C2×D414yes—
589C4×Dic17—22no—
590C4×Dic17—22no—
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—28no—
626C23×C17—28no—
627C23×C17—21no—
628C23×C17—21no—
629C23×C17—21no—
630C23×C17—21no—
631C23×C17—21no—
632C23×C17—21no—
633C23×C17—21no—
634C23×C17—21no—
635C23×C17—21no—
636C23×C17—21no—
637C23×C17—21no—
638C23×C17—21no—
639C23×C17—44no—
640C23×C17—44no—
641C23×C17—44no—
642C23×C17—44no—
643C23×C17—44no—
644C23×C17C23×C412yes—
645C23×C17C23×C412yes—
646C23×C17C23×C412yes—
647C23×C17C23×C412yes—
648C23×C17C22×D412yes—
649C23×C17C2×#4112yes—
650C23×C17C2×#4112yes—
651C23×C17C2×#4112yes—
652C23×C17C2511yescharacteristic
653C22×D17—21no—
654C22×D17—21no—
655C22×D17—21no—
656C22×D17—21no—
657C22×D17—21no—
658C22×D17—21no—
659C22×D17C23×C412yes—
660D4×C17—28no—
661D4×C17—28no—
662D4×C17—44no—
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—44no—
690C2×C4×C17—44no—
691C2×C4×C17—44no—
692C2×C4×C17—44no—
693C2×C4×C17—44no—
694C2×C4×C17C23×C412yes—
695C2×C4×C17C23×C412yes—
696C2×C4×C17C23×C412yes—
697C2×C4×C17C22×D412yes—
698C2×C4×C17C22×D412yes—
699C2×C4×C17C2×#4112yes—
700C2×C4×C17C2×#4112yes—
701C22⋊D17—28no—
702C22⋊D17—28no—
703C22⋊D17—28no—
704C22⋊D17—44no—
705C2×Dic17—28no—
706C2×Dic17—21no—
707C2×Dic17—21no—
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—21no—
723C2×Dic17—21no—
724C2×Dic17—28no—
725C2×Dic17—28no—
726C2×Dic17—28no—
727C2×Dic17—28no—
728C2×Dic17—28no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—21no—
739C2×Dic17—21no—
740C2×Dic17—21no—
741C2×Dic17—44no—
742C2×Dic17—44no—
743C2×Dic17—44no—
744C2×Dic17—44no—
745C2×Dic17—44no—
746C2×Dic17C4×D4116yescomplemented
747C2×Dic17C23×C412yes—
748C2×Dic17C23×C412yes—
749C2×Dic17C23×C412yes—
750C2×Dic17C23×C412yes—
751C2×Dic17C23×C412yes—
752C2×Dic17C23×C412yes—
753C2×Dic17C23×C412yes—
754C2×Dic17C22×D412yes—
755C2×Dic17C22×D412yes—
756C2×Dic17C22×D412yes—
757C2×Dic17C22×D412yes—
758C2×Dic17C2×#4112yes—
759C2×Dic17C2×#4112yes—
760C2×Dic17C2×#4112yes—
761C2×Dic17C2×#4112yes—
762C4×D17—28no—
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#2359—171no—
781#2358—171no—
782#2358—171no—
783#2358—171no—
784#2358D1711yescharacteristic, complemented
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—22no—
807C22×C17—22no—
808C22×C17—22no—
809C22×C17—22no—
810C22×C17—22no—
811C22×C17—22no—
812C22×C17—22no—
813C22×C17—22no—
814C22×C17—22no—
815C22×C17—416no—
816C22×C17—41no—
817C22×C17—41no—
818C22×C17—41no—
819C22×C17—41no—
820C22×C17—41no—
821C22×C17—41no—
822C22×C17—41no—
823C22×C17—41no—
824C22×C17C2×C4×D414yes—
825C22×C17C4×#4114yescomplemented
826C22×C17C24×C411yescharacteristic
827C22×C17C23×D411yescharacteristic
828C22×C17C22×#4111yescharacteristic
829C22×C17C22×#4111yescharacteristic
830C22×C17C22×#4111yescharacteristic
831C22×C17#58511yescharacteristic
832C22×C17#58511yescharacteristic
833C2×D17—22no—
834C2×D17—22no—
835C2×D17—22no—
836C2×D17—41no—
837C2×D17—41no—
838C2×D17—41no—
839C2×D17—41no—
840C4×C17—22no—
841C4×C17—22no—
842C4×C17—22no—
843C4×C17—22no—
844C4×C17—22no—
845C4×C17—22no—
846C4×C17—22no—
847C4×C17—41no—
848C4×C17—41no—
849C4×C17—41no—
850C4×C17—41no—
851Dic17—22no—
852Dic17—22no—
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×#123—171no—
871C2×C22⋊Q8—171no—
872C2×C22⋊Q8—171no—
873C2×#121—171no—
874C2×#121—171no—
875C2×#120—171no—
876C2×#120C2×D1711yescharacteristic
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×D4C2×D1711yescharacteristic
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—171no—
905C2×#117—348no—
906C22×C4⋊C4—171no—
907C22×C4⋊C4—171no—
908C22×C22⋊C4—171no—
909C22×C22⋊C4—171no—
910C22×C22⋊C4C2×D1711yescharacteristic
911C22×C22⋊C4C2×D1711yescharacteristic
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#390C2×D1711yescharacteristic
926#389—171no—
927#389—171no—
928#389—171no—
929#389—171no—
930#389—171no—
931#389—171no—
932#389—171no—
933#389—171no—
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
949#388C2×D1711yescharacteristic
950#387—171no—
951#387—171no—
952#387—171no—
953#387—171no—
954#387—171no—
955#387—171no—
956#387—171no—
957#387—171no—
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#386C2×D1711yescharacteristic
968#386C2×D1711yescharacteristic
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
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⋊C4—171no—
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
1018#376—171no—
1019#376—171no—
1020C2×#95—171no—
1021C2×#95—171no—
1022C43—171no—
1023C43—171no—
1024C2×C17—24no—
1025C2×C17—24no—
1026C2×C17—42no—
1027C2×C17—42no—
1028C2×C17C22×C4×D411yescharacteristic
1029C2×C17C2×C4×#4111yescharacteristic
1030C2×C17#342811yescharacteristic
1031C2×C17D4×#4111yescharacteristic
1032C2×C17D4×#4111yescharacteristic
1033C2×C17#347511yescharacteristic
1034C2×C17#347511yescharacteristic
1035D17—42no—
1036C25C22×D1711yescharacteristic
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×D4C22×D1711yescharacteristic
1046C22×D4C22×D1711yescharacteristic
1047C22×D4C22×D1711yescharacteristic
1048C23×C4—171no—
1049C23×C4—178no—
1050C23×C4—171no—
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—344no—
1065C23×C4—344no—
1066C23×C4C22×D1711yescharacteristic
1067C23×C4C22×D1711yescharacteristic
1068C23×C4C22×D1711yescharacteristic
1069C23×C4C22×D1711yescharacteristic
1070C23×C4C22×D1711yescharacteristic
1071#123—178no—
1072#123—178no—
1073C22⋊Q8—178no—
1074C22⋊Q8—178no—
1075#121—178no—
1076#121—178no—
1077#120—178no—
1078#120C4×D1718yescomplemented
1079C4×Q8—344no—
1080C4×Q8—344no—
1081C4×D4—24no—
1082C4×D4—24no—
1083C4×D4—178no—
1084C4×D4—178no—
1085C4×D4—178no—
1086C4×D4—178no—
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—178no—
1096#117—178no—
1097#117—344no—
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—171no—
1126C2×C4⋊C4—171no—
1127C2×C4⋊C4—171no—
1128C2×C4⋊C4—171no—
1129C2×C4⋊C4—344no—
1130C2×C4⋊C4—344no—
1131C2×C4⋊C4C22×D1711yescharacteristic
1132C2×C4⋊C4C22×D1711yescharacteristic
1133C2×C4⋊C4C22×D1711yescharacteristic
1134C2×C22⋊C4—24no—
1135C2×C22⋊C4—24no—
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—344no—
1161C2×C22⋊C4—344no—
1162C2×C22⋊C4C22×D1711yescharacteristic
1163C2×C22⋊C4C22×D1711yescharacteristic
1164C2×C22⋊C4C22×D1711yescharacteristic
1165C2×C22⋊C4C22×D1711yescharacteristic
1166C2×C22⋊C4C22×D1711yescharacteristic
1167C2×C22⋊C4C22×D1711yescharacteristic
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—171no—
1202C2×C42—171no—
1203C2×C42—344no—
1204C2×C42—344no—
1205C2×C42—344no—
1206C2×C42—344no—
1207C2×C42—344no—
1208C2×C42—344no—
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#95—171no—
1235#95—171no—
1236#95—171no—
1237#95—171no—
1238#95C22×D1711yescharacteristic
1239#95C22×D1711yescharacteristic
1240#95C22×D1711yescharacteristic
1241#95C22×D1711yescharacteristic
1242#95C22×D1711yescharacteristic
1243#95C22×D1711yescharacteristic
1244C17#3413611yescharacteristic, complemented, Sylow
1245C24—22no—
1246C24—22no—
1247C24—22no—
1248C24—22no—
1249C24—41no—
1250C24—41no—
1251C24—171no—
1252C24C2×C4×D1714yes—
1253C24C23×D1711yescharacteristic
1254C24C23×D1711yescharacteristic
1255C24C23×D1711yescharacteristic
1256C24C23×D1711yescharacteristic
1257#41—3432no—
1258C2×Q8—174no—
1259C2×Q8—342no—
1260C2×Q8—342no—
1261C2×D4—22no—
1262C2×D4—22no—
1263C2×D4—22no—
1264C2×D4—22no—
1265C2×D4—41no—
1266C2×D4—41no—
1267C2×D4—174no—
1268C2×D4—174no—
1269C2×D4—174no—
1270C2×D4—174no—
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×D4C2×C4×D1714yes—
1280C2×D4C2×C4×D1714yes—
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—22no—
1291C22×C4—22no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—41no—
1296C22×C4—41no—
1297C22×C4—174no—
1298C22×C4—174no—
1299C22×C4—174no—
1300C22×C4—171no—
1301C22×C4—171no—
1302C22×C4—174no—
1303C22×C4—174no—
1304C22×C4—174no—
1305C22×C4—174no—
1306C22×C4—174no—
1307C22×C4—174no—
1308C22×C4—171no—
1309C22×C4—171no—
1310C22×C4—171no—
1311C22×C4—171no—
1312C22×C4—171no—
1313C22×C4—171no—
1314C22×C4—171no—
1315C22×C4—171no—
1316C22×C4—171no—
1317C22×C4—174no—
1318C22×C4—171no—
1319C22×C4—171no—
1320C22×C4—171no—
1321C22×C4—171no—
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—3432no—
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—342no—
1347C22×C4—342no—
1348C22×C4—342no—
1349C22×C4—342no—
1350C22×C4—342no—
1351C22×C4—681no—
1352C22×C4—681no—
1353C22×C4—681no—
1354C22×C4—681no—
1355C22×C4—681no—
1356C22×C4—681no—
1357C22×C4—681no—
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—41no—
1372C4⋊C4—174no—
1373C4⋊C4—174no—
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—342no—
1391C4⋊C4—342no—
1392C4⋊C4—681no—
1393C4⋊C4—681no—
1394C4⋊C4—681no—
1395C22⋊C4—22no—
1396C22⋊C4—22no—
1397C22⋊C4—22no—
1398C22⋊C4—22no—
1399C22⋊C4—22no—
1400C22⋊C4—22no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—41no—
1404C22⋊C4—174no—
1405C22⋊C4—174no—
1406C22⋊C4—174no—
1407C22⋊C4—174no—
1408C22⋊C4—174no—
1409C22⋊C4—174no—
1410C22⋊C4—174no—
1411C22⋊C4—174no—
1412C22⋊C4—174no—
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—681no—
1426C22⋊C4—681no—
1427C22⋊C4—681no—
1428C22⋊C4C2×C4×D1714yes—
1429C22⋊C4C2×C4×D1714yes—
1430C22⋊C4C2×C4×D1714yes—
1431C22⋊C4D4×D1714yes—
1432C22⋊C4#6325414yescomplemented
1433C42—22no—
1434C42—22no—
1435C42—41no—
1436C42—174no—
1437C42—174no—
1438C42—174no—
1439C42—174no—
1440C42—342no—
1441C42—342no—
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—28no—
1472C23—28no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—44no—
1486C23—44no—
1487C23—44no—
1488C23—44no—
1489C23—44no—
1490C23—172no—
1491C23—341no—
1492C23—341no—
1493C23—341no—
1494C23—341no—
1495C23—341no—
1496C23—341no—
1497C23C22×C4×D1712yes—
1498C23C22×C4×D1712yes—
1499C23C22×C4×D1712yes—
1500C23C22×C4×D1712yes—
1501C23C2×D4×D1712yes—
1502C23C2×#6325412yes—
1503C23#41×D1712yes—
1504C23#41×D1712yes—
1505C23C24×D1711yescharacteristic
1506Q8—348no—
1507D4—28no—
1508D4—28no—
1509D4—44no—
1510D4—348no—
1511D4—348no—
1512D4—348no—
1513D4—684no—
1514C2×C4—21no—
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—44no—
1541C2×C4—44no—
1542C2×C4—44no—
1543C2×C4—44no—
1544C2×C4—44no—
1545C2×C4—1716no—
1546C2×C4—172no—
1547C2×C4—172no—
1548C2×C4—172no—
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—348no—
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—341no—
1595C2×C4—341no—
1596C2×C4—341no—
1597C2×C4—341no—
1598C2×C4—684no—
1599C2×C4—684no—
1600C2×C4—684no—
1601C2×C4—684no—
1602C2×C4—684no—
1603C2×C4—684no—
1604C2×C4—684no—
1605C2×C4C22×C4×D1712yes—
1606C2×C4C22×C4×D1712yes—
1607C2×C4C22×C4×D1712yes—
1608C2×C4C2×D4×D1712yes—
1609C2×C4C2×D4×D1712yes—
1610C2×C4C2×#6325412yes—
1611C2×C4C2×#6325412yes—
1612C22—22no—
1613C22—22no—
1614C22—22no—
1615C22—22no—
1616C22—22no—
1617C22—22no—
1618C22—22no—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—416no—
1631C22—41no—
1632C22—41no—
1633C22—41no—
1634C22—41no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—342no—
1640C22—342no—
1641C22—342no—
1642C22—681no—
1643C22—681no—
1644C22—681no—
1645C22—681no—
1646C22C4×D4×D1714yes—
1647C22C4×#6325414yescomplemented
1648C22C23×C4×D1711yescharacteristic
1649C22C22×D4×D1711yescharacteristic
1650C22C2×#41×D1711yescharacteristic
1651C22C2×#41×D1711yescharacteristic
1652C22C22×#6325411yescharacteristic
1653C22#1176364411yescharacteristic
1654C22#1176364411yescharacteristic
1655C4—22no—
1656C4—22no—
1657C4—22no—
1658C4—22no—
1659C4—22no—
1660C4—22no—
1661C4—22no—
1662C4—41no—
1663C4—41no—
1664C4—41no—
1665C4—41no—
1666C4—174no—
1667C4—174no—
1668C4—342no—
1669C4—342no—
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—24no—
1683C2—42no—
1684C2—42no—
1685C2—682no—
1686C2C2×C4×D4×D1711yescharacteristic
1687C2C2×C4×#6325411yescharacteristic
1688C2#1454198211yescharacteristic
1689C2D4×#6325411yescharacteristic
1690C2#1454226811yescharacteristic
1691C2#1454233511yescharacteristic
1692C2#1454233911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2358C2
socle, cosocleC23×C17C25
prime radicalC2×#11763315C2
hypercenter#2358D17
hypocenterC17#34136
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2358

Complements

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

NH ≅ G/Ntype
2. C2×C4×#63254C2semidirect
3. C22×#10587563C2semidirect
4. #14531825C2semidirect
5. #14531819C2semidirect
6. #14531814C2semidirect
7. #14531808C2semidirect
8. #14531801C2semidirect
9. #14531795C2semidirect
10. #14531790C2semidirect
11. #14531784C2semidirect
12. #14531782C2semidirect
13. #14531778C2semidirect
14. #14531774C2semidirect
15. #14531770C2semidirect
16. #14531768C2semidirect
17. #14531763C2semidirect
18. #14531763C2semidirect
19. #14531269C2semidirect
20. #14531263C2semidirect
21. #14531246C2semidirect
22. #14531244C2semidirect
23. #14531226C2semidirect
24. #14531224C2semidirect
25. #14531224C2semidirect
26. #14531220C2semidirect
27. C4×D4×Dic17C2semidirect
28. C4×#10587567C2semidirect
29. C4×#10587563C2semidirect
30. C2×C22⋊C4×Dic17C2semidirect
31. C17×#2358C2semidirect
34. #11763315C4semidirect
43. C2×C4×Dic34C22semidirect
44. C2×#10587573C22semidirect
51. C2×C4×C22⋊D17C22semidirect
56. C2×#10587567C22semidirect
57. C2×#10587578C22semidirect
68. C2×#10587563C22semidirect
77. C22×C4×Dic17C22semidirect
78. C2×C42×D17C22semidirect
79. #11762713C22semidirect
80. #11762713C22semidirect
84. #11762709C22semidirect
85. #11762709C22semidirect
86. #11762707C22semidirect
87. #11762706C22semidirect
88. #11762706C22semidirect
89. #11762706C22semidirect
90. #11762705C22semidirect
91. #11762704C22semidirect
92. #11762704C22semidirect
93. #11762704C22semidirect
96. #11762703C22semidirect
97. #11762703C22semidirect
100. #11762701C22semidirect
101. #11762700C22semidirect
102. #11762699C22semidirect
103. #11762698C22semidirect
106. #11762697C22semidirect
107. #11762697C22semidirect
108. #11762696C22semidirect
109. #11762694C22semidirect
110. #11762694C22semidirect
111. #11762693C22semidirect
112. #11762692C22semidirect
113. #11762692C22semidirect
114. #11762691C22semidirect
115. #11762690C22semidirect
127. #11762683C22semidirect
130. #11762682C22semidirect
133. #11762681C22semidirect
134. #11762680C22semidirect
135. C4⋊C4×Dic17C22semidirect
136. C4⋊C4×Dic17C22semidirect
137. C4⋊C4×Dic17C22semidirect
138. C4×#63225C22semidirect
139. C4×#63225C22semidirect
140. C4×#63225C22semidirect
141. C4×C4⋊Dic17C22semidirect
142. #11762660C22semidirect
143. #11762660C22semidirect
144. #11762660C22semidirect
145. #11762660C22semidirect
146. #11762660C22semidirect
159. C22⋊C4×Dic17C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C22⋊C4×Dic17C22semidirect
162. C4×#63227C22semidirect
165. C4×C22⋊Dic17C22semidirect
166. #11762656C22semidirect
167. #11762656C22semidirect
168. #11762656C22semidirect
169. #11762654C22semidirect
170. #11762654C22semidirect
173. C42×Dic17C22semidirect
174. C42×Dic17C22semidirect
205. C23×Dic17C2×C4semidirect
220. C2×#63254C2×C4semidirect
225. C17×#120C2×C4semidirect
250. #10587639C2×C4semidirect
269. #10587625C2×C4semidirect
270. #10587625C2×C4semidirect
271. #10587621C2×C4semidirect
274. D4×Dic17C2×C4semidirect
275. D4×Dic17C2×C4semidirect
346. #10587572C2×C4semidirect
350. #10587567C2×C4semidirect
351. #10587567C2×C4semidirect
352. #10587564C2×C4semidirect
353. #10587564C2×C4semidirect
362. #10587563C2×C4semidirect
363. #10587563D4semidirect
538. C22⋊C4×C17#41semidirect
557. C22⋊Dic17#41semidirect
746. C2×Dic17C4×D4semidirect
784. #2358D17semidirect
825. C22×C17C4×#41semidirect
1078. #120C4×D17semidirect
1244. C17#34136semidirect
1432. C22⋊C4#63254semidirect
1647. C22C4×#63254semidirect

Maximal subgroups

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

subgroupindex
C2×#117633152
C2×C4×#632542
C22×#105875632
#145318252
#145318192
#145318142
#145318082
#145318012
#145317952
#145317902
#145317842
#145317822
#145317782
#145317742
#145317702
#145317682
#145317632
#145312692
#145312632
#145312462
#145312442
#145312262
#145312242
#145312202
C4×D4×Dic172
C4×#105875672
C4×#105875632
C2×C22⋊C4×Dic172
C17×#23582
#3413617