Finite Group Databasebeta

← #17194806

Subgroups — #17194806

Order 4352.

3014 conjugacy classes of subgroups.

The subgroup lattice has 1658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763317C211yesmaximal, characteristic
2#14531868C211yesmaximal, characteristic, complemented
3#14531861C211yesmaximal, characteristic, complemented
4#14531835C211yesmaximal, characteristic, complemented
5#14531828C211yesmaximal, characteristic, complemented
6#14531780C211yesmaximal, characteristic, complemented
7#14531776C211yesmaximal, characteristic, complemented
8#14531772C211yesmaximal, characteristic, complemented
9#14531723C211yesmaximal, characteristic, complemented
10#14531719C211yesmaximal, characteristic, complemented
11#14531693C211yesmaximal, characteristic, complemented
12#14531690C211yesmaximal, characteristic, complemented
13#14531642C211yesmaximal, characteristic, complemented
14#14531638C211yesmaximal, characteristic, complemented
15#14531610C211yesmaximal, characteristic, complemented
16#14531609C211yesmaximal, characteristic, complemented
17#14531518C211yesmaximal, characteristic, complemented
18#14531511C211yesmaximal, characteristic, complemented
19#14531488C211yesmaximal, characteristic, complemented
20#14531481C211yesmaximal, characteristic, complemented
21#14531416C211yesmaximal, characteristic, complemented
22#14531414C211yesmaximal, characteristic, complemented
23#14531289C211yesmaximal, characteristic, complemented
24C4×#10587568C211yesmaximal, characteristic, complemented
25#14531285C211yesmaximal, characteristic, complemented
26C4×#10587623C211yesmaximal, characteristic, complemented
27#14531163C211yesmaximal, characteristic, complemented
28#14531144C211yesmaximal, characteristic, complemented
29#14531143C211yesmaximal, characteristic, complemented
30C2×#95×D17C211yesmaximal, characteristic, complemented
31C17×#2359C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C23×C4×D17C2211yescharacteristic
35C23×C4×D17C2211yescharacteristic
36#11763317C4116yescomplemented
37C2×#10587615C2211yescharacteristic
38C2×#10587582C2211yescharacteristic
39C2×#10587582C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587568C2211yescharacteristic
43C2×#10587623C2211yescharacteristic
44C2×C4×D68C2211yescharacteristic
45C2×C4×D68C2211yescharacteristic
46C2×D4×Dic17C2211yescharacteristic
47C2×#10587579C2211yescharacteristic
48C2×#10587579C2211yescharacteristic
49C2×#10587579C2211yescharacteristic
50C2×#10587579C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic
52C2×C4×C22⋊D17C2211yescharacteristic
53C2×C4×C22⋊D17C2211yescharacteristic
54C2×#10587567C2211yescharacteristic
55C2×#10587567C2211yescharacteristic
56C2×#10587567C2211yescharacteristic
57C2×#10587567C2211yescharacteristic
58C2×#10587567C2211yescharacteristic
59C2×#10587612C2211yescharacteristic
60C2×#10587563C2211yescharacteristic
61#11762715C2211yescharacteristic, complemented
62#11762714C2211yescharacteristic, complemented
63#11762713C2211yescharacteristic, complemented
64#11762713C2211yescharacteristic, complemented
65#11762708C2211yescharacteristic, complemented
66#11762706C2211yescharacteristic, complemented
67#11762704C2211yescharacteristic, complemented
68#11762702C2211yescharacteristic, complemented
69#11762702C2211yescharacteristic, complemented
70#11762701C2211yescharacteristic, complemented
71#11762700C2211yescharacteristic, complemented
72#11762699C2211yescharacteristic, complemented
73#11762698C2211yescharacteristic, complemented
74#11762696C2211yescharacteristic, complemented
75#11762696C2211yescharacteristic, complemented
76#11762696C2211yescharacteristic, complemented
77#11762695C2211yescharacteristic, complemented
78#11762695C2211yescharacteristic, complemented
79#11762693C2211yescharacteristic, complemented
80#11762693C2211yescharacteristic, complemented
81#11762693C2211yescharacteristic, complemented
82#11762691C2211yescharacteristic, complemented
83#11762691C2211yescharacteristic, complemented
84#11762691C2211yescharacteristic, complemented
85#11762690C2211yescharacteristic, complemented
86#11762690C2211yescharacteristic, complemented
87#11762690C2211yescharacteristic, complemented
88#11762689C2211yescharacteristic
89#11762688C2211yescharacteristic
90#11762688C2211yescharacteristic, complemented
91#11762687C2211yescharacteristic
92#11762687C2211yescharacteristic
93#11762687C2211yescharacteristic
94#11762687C2211yescharacteristic
95#11762686C2211yescharacteristic
96#11762686C2211yescharacteristic, complemented
97#11762685C2211yescharacteristic
98#11762685C2211yescharacteristic
99#11762685C2211yescharacteristic
100#11762685C2211yescharacteristic
101#11762685C2211yescharacteristic, complemented
102#11762685C2211yescharacteristic, complemented
103#11762684C2211yescharacteristic
104#11762684C2211yescharacteristic, complemented
105#11762683C2211yescharacteristic
106#11762683C2211yescharacteristic
107#11762683C2211yescharacteristic
108#11762683C2211yescharacteristic
109#11762683C2211yescharacteristic, complemented
110#11762682C2211yescharacteristic
111#11762681C2211yescharacteristic
112#11762680C2211yescharacteristic
113#11762680C2211yescharacteristic
114#11762680C2211yescharacteristic
115#11762680C2211yescharacteristic
116#11762680C2211yescharacteristic, complemented
117#11762676C2211yescharacteristic, complemented
118#11762676C2211yescharacteristic, complemented
119#11762674C2211yescharacteristic, complemented
120#11762673C2211yescharacteristic, complemented
121#11762671C2211yescharacteristic, complemented
122#11762670C2211yescharacteristic
123#11762670C2211yescharacteristic
124#11762670C2211yescharacteristic, complemented
125#11762667C2211yescharacteristic, complemented
126#11762666C2211yescharacteristic
127#11762666C2211yescharacteristic
128#11762666C2211yescharacteristic
129#11762666C2211yescharacteristic
130#11762666C2211yescharacteristic, complemented
131#11762664C2211yescharacteristic
132#11762664C2211yescharacteristic
133C4⋊C4×Dic17C2211yescharacteristic, complemented
134C4⋊C4×Dic17C2211yescharacteristic, complemented
135C4×#63225C2211yescharacteristic, complemented
136C4×#63225C2211yescharacteristic, complemented
137#11762660C2211yescharacteristic, complemented
138C22⋊C4×Dic17C2211yescharacteristic
139C22⋊C4×Dic17C2211yescharacteristic
140C22⋊C4×Dic17C2211yescharacteristic, complemented
141C22⋊C4×Dic17C2211yescharacteristic, complemented
142C4×#63227C2211yescharacteristic
143C4×#63227C2211yescharacteristic
144C4×#63227C2211yescharacteristic
145C4×#63227C2211yescharacteristic
146C4×#63227C2211yescharacteristic
147C4×#63227C2211yescharacteristic
148C4×#63227C2211yescharacteristic
149C4×#63227C2211yescharacteristic
150C4×#63227C2211yescharacteristic, complemented
151C4×#63227C2211yescharacteristic, complemented
152C4×C22⋊Dic17C2211yescharacteristic
153#11762656C2211yescharacteristic
154#11762656C2211yescharacteristic
155#11762656C2211yescharacteristic
156#11762656C2211yescharacteristic
157#11762656C2211yescharacteristic, complemented
158#11762655C2211yescharacteristic, complemented
159#11762654C2211yescharacteristic, complemented
160C2×#10587502C2211yescharacteristic
161C2×#10587502C2211yescharacteristic
162C2×#10587502C2211yescharacteristic
163C2×#10587502C2211yescharacteristic, complemented
164#95×D17C2211yescharacteristic
165#95×D17C2211yescharacteristic
166#95×D17C2211yescharacteristic
167#95×D17C2211yescharacteristic
168#95×D17C2211yescharacteristic
169#95×D17C2211yescharacteristic
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#123C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C2×C17×#117C2211yescharacteristic
176C17×#389C2211yescharacteristic, complemented
177C17×#388C2211yescharacteristic, complemented
178C17×#388C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#387C2211yescharacteristic, complemented
181C17×#386C2211yescharacteristic
182C17×#385C2211yescharacteristic
183C17×#385C2211yescharacteristic, complemented
184C4×C4⋊C4×C17C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C2×C17×#95C2211yescharacteristic
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C2×#63254—42no—
204C2×#63254—42no—
205C2×#63254C2×C418yescomplemented
206C22×D68C2311yescharacteristic
207C22×D68C2311yescharacteristic
208C22×C4×D17—24no—
209C22×C4×D17—24no—
210C22×C4×D17—42no—
211C22×C4×D17—42no—
212C22×C4×D17—42no—
213C22×C4×D17—42no—
214C22×C4×D17—42no—
215C22×C4×D17—42no—
216C22×C4×D17C2×C418yescomplemented
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C22×C4×D17C2311yescharacteristic
229C22×C4×D17C2311yescharacteristic
230C22×C4×D17C2311yescharacteristic
231C22×C4×D17C2311yescharacteristic
232C22×Dic34C2311yescharacteristic
233C17×#123C2×C418yescomplemented
234C4×D4×C17—42no—
235C17×#117—42no—
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C4⋊C4×C17C2311yescharacteristic
238C2×C4⋊C4×C17C2311yescharacteristic
239C2×C4⋊C4×C17C2311yescharacteristic
240C2×C4⋊C4×C17C2311yescharacteristic
241C2×C4⋊C4×C17C2311yescharacteristic
242C2×C4⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C42×C17C2311yescharacteristic
252C2×C42×C17C2311yescharacteristic
253C2×C42×C17C2311yescharacteristic
254C2×C42×C17C2311yescharacteristic
255C2×C42×C17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262#10587623C2×C418yescomplemented
263D4×Dic17—42no—
264#10587615C2×C418yescomplemented
265C4×C22⋊D17—24no—
266C4×C22⋊D17—42no—
267C4×C22⋊D17—42no—
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
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288#10587612—42no—
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317#10587582C2×C418yescomplemented
318#10587582C2×C418yescomplemented
319#10587579—24no—
320#10587579—42no—
321#10587579C2×C418yescomplemented
322#10587579C2×C418yescomplemented
323#10587570C2×C418yescomplemented
324#10587570C2×C418yescomplemented
325#10587568C2×C418yescomplemented
326#10587567—24no—
327#10587567—42no—
328#10587567—42no—
329#10587567C2×C418yescomplemented
330#10587567C2×C418yescomplemented
331#10587563C2×C418yescomplemented
332C4×D68—24no—
333C4×D68—42no—
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382C24×C17C2411yescharacteristic
383C24×C17C2411yescharacteristic
384C23×D17—22no—
385C23×D17—22no—
386C23×D17—22no—
387C23×D17—22no—
388C23×D17—22no—
389C23×D17—22no—
390C23×D17C22×C414yes—
391C23×D17C2411yescharacteristic
392C23×D17C2411yescharacteristic
393C23×D17C2411yescharacteristic
394C2×D4×C17—22no—
395C2×D4×C17—22no—
396C2×D4×C17C22×C414yes—
397C22×C4×C17—22no—
398C22×C4×C17—22no—
399C22×C4×C17—22no—
400C22×C4×C17—22no—
401C22×C4×C17—22no—
402C22×C4×C17—22no—
403C22×C4×C17—22no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17C22×C414yes—
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C2×C22⋊D17—22no—
423C2×C22⋊D17—22no—
424C2×C22⋊D17—22no—
425C2×C22⋊D17—22no—
426C2×C22⋊D17—22no—
427C2×C22⋊D17—22no—
428C2×C22⋊D17—41no—
429C2×C22⋊D17—41no—
430C2×C22⋊D17C22×C414yes—
431C2×C22⋊D17C22×C414yes—
432C2×C22⋊D17C22×C414yes—
433C2×C22⋊D17C22×C414yescomplemented
434C22×Dic17—22no—
435C22×Dic17—22no—
436C22×Dic17—22no—
437C22×Dic17—22no—
438C22×Dic17—22no—
439C22×Dic17—22no—
440C22×Dic17—22no—
441C22×Dic17—41no—
442C22×Dic17—41no—
443C22×Dic17—41no—
444C22×Dic17—41no—
445C22×Dic17—41no—
446C22×Dic17—41no—
447C22×Dic17C22×C414yes—
448C22×Dic17C22×C414yescomplemented
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462#63254—416no—
463C2×D68—22no—
464C2×D68—22no—
465C2×D68—22no—
466C2×D68—22no—
467C2×D68C22×C414yes—
468C2×D68C22×C414yes—
469C2×C4×D17—22no—
470C2×C4×D17—22no—
471C2×C4×D17—22no—
472C2×C4×D17—22no—
473C2×C4×D17—22no—
474C2×C4×D17—22no—
475C2×C4×D17—22no—
476C2×C4×D17—22no—
477C2×C4×D17—22no—
478C2×C4×D17—22no—
479C2×C4×D17—22no—
480C2×C4×D17—22no—
481C2×C4×D17—416no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×C4×D17—41no—
485C2×C4×D17—41no—
486C2×C4×D17—41no—
487C2×C4×D17—41no—
488C2×C4×D17—41no—
489C2×C4×D17—41no—
490C2×C4×D17—41no—
491C2×C4×D17—41no—
492C2×C4×D17—41no—
493C2×C4×D17—41no—
494C2×C4×D17—41no—
495C2×C4×D17—41no—
496C2×C4×D17—41no—
497C2×C4×D17—41no—
498C2×C4×D17—41no—
499C2×C4×D17—41no—
500C2×C4×D17—41no—
501C2×C4×D17—41no—
502C2×C4×D17—41no—
503C2×C4×D17—41no—
504C2×C4×D17—416no—
505C2×C4×D17—416no—
506C2×C4×D17—41no—
507C2×C4×D17—41no—
508C2×C4×D17—41no—
509C2×C4×D17—41no—
510C2×C4×D17C22×C414yes—
511C2×C4×D17C22×C414yes—
512C2×C4×D17C22×C414yes—
513C2×C4×D17C22×C414yes—
514C2×C4×D17C22×C414yescomplemented
515C2×C4×D17#4114yescomplemented
516C2×C4×D17#4114yescomplemented
517C2×Dic34—41no—
518C2×Dic34—41no—
519C2×Dic34C22×C414yescomplemented
520C4⋊C4×C17—22no—
521C4⋊C4×C17—41no—
522C4⋊C4×C17—41no—
523C4⋊C4×C17—41no—
524C4⋊C4×C17—41no—
525C4⋊C4×C17C22×C414yescomplemented
526C4⋊C4×C17C22×C414yescomplemented
527C22⋊C4×C17—22no—
528C22⋊C4×C17—22no—
529C22⋊C4×C17—22no—
530C22⋊C4×C17—41no—
531C22⋊C4×C17—41no—
532C22⋊C4×C17C22×C414yes—
533C22⋊C4×C17C22×C414yescomplemented
534C22⋊C4×C17C22×C414yescomplemented
535C42×C17—22no—
536C42×C17—41no—
537C42×C17—41no—
538C42×C17—41no—
539C42×C17—41no—
540C22⋊Dic17—22no—
541C22⋊Dic17—22no—
542C22⋊Dic17—22no—
543C22⋊Dic17—41no—
544C22⋊Dic17—41no—
545C22⋊Dic17C22×C414yes—
546#63227—22no—
547#63227—22no—
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—41no—
557#63227—41no—
558#63227—41no—
559#63227—41no—
560#63227C22×C414yes—
561#63227C22×C414yes—
562#63227C22×C414yes—
563#63227C22×C414yes—
564#63227C22×C414yescomplemented
565#63227C22×C414yescomplemented
566C4⋊Dic17—22no—
567C4⋊Dic17—41no—
568C4⋊Dic17—41no—
569C4⋊Dic17—41no—
570C4⋊Dic17—41no—
571#63225—22no—
572#63225—22no—
573#63225—41no—
574#63225—41no—
575#63225—41no—
576#63225—41no—
577#63225C22×C414yescomplemented
578#63225C22×C414yescomplemented
579#63225C22×C414yescomplemented
580#63225C22×C414yescomplemented
581C4×Dic17—22no—
582C4×Dic17—22no—
583C4×Dic17—22no—
584C4×Dic17—41no—
585C4×Dic17—41no—
586C4×Dic17—41no—
587C4×Dic17—41no—
588C4×Dic17—41no—
589C4×Dic17—41no—
590C4×Dic17—41no—
591C4×Dic17—41no—
592C4×Dic17C22×C414yescomplemented
593C4×Dic17C22×C414yescomplemented
594#34218—171nomaximal, Sylow
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17C23×C412yes—
606C23×C17C23×C412yes—
607C23×C17H(5,𝔽2)12yes—
608C23×C17H(5,𝔽2)12yes—
609C23×C17C2511yescharacteristic
610C22×D17—28no—
611C22×D17—28no—
612C22×D17—28no—
613C22×D17—28no—
614C22×D17—28no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—28no—
624C22×D17—28no—
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—21no—
628C22×D17—21no—
629C22×D17—21no—
630C22×D17—21no—
631C22×D17C23×C412yes—
632C22×D17C23×C412yes—
633C22×D17C23×C412yes—
634C22×D17C2×#4112yes—
635C22×D17C2×#4112yes—
636C22×D17H(5,𝔽2)12yes—
637C22×D172−1+412yes—
638D4×C17—28no—
639C2×C4×C17—28no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
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—44no—
673C2×C4×C17—44no—
674C2×C4×C17—82no—
675C2×C4×C17C23×C412yes—
676C2×C4×C17C23×C412yes—
677C2×C4×C17C23×C412yes—
678C2×C4×C17C23×C412yes—
679C2×C4×C17C23×C412yes—
680C2×C4×C17C2×#4112yes—
681C2×C4×C17C2×#4112yes—
682C22⋊D17—28no—
683C22⋊D17—28no—
684C22⋊D17—28no—
685C22⋊D17—44no—
686C2×Dic17—28no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
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—44no—
720C2×Dic17—44no—
721C2×Dic17—44no—
722C2×Dic17—82no—
723C2×Dic17C23×C412yes—
724C2×Dic17C23×C412yes—
725C2×Dic17C23×C412yes—
726C2×Dic17C23×C412yes—
727C2×Dic17C23×C412yes—
728C2×Dic17C2×#4112yes—
729C2×Dic17C2×#4112yes—
730D68—28no—
731D68—28no—
732C4×D17—44no—
733C4×D17—44no—
734C4×D17—44no—
735C4×D17—44no—
736C4×D17—44no—
737C4×D17—44no—
738C4×D17—44no—
739C4×D17—44no—
740C4×D17—44no—
741C4×D17—44no—
742C4×D17—44no—
743C4×D17—44no—
744C4×D17—44no—
745C4×D17—82no—
746C4×D17—82no—
747Dic34—44no—
748C2×#525—171no—
749#2368—171no—
750#2368—171no—
751#2364—171no—
752#2364—171no—
753#2359—171no—
754#2359—171no—
755#2359—171no—
756#2359D1711yescharacteristic, complemented
757#2353—171no—
758#2353—171no—
759#2349—171no—
760#2349—171no—
761#2343—171no—
762#2343—171no—
763#2339—171no—
764#2339—171no—
765#2329—171no—
766#2329—171no—
767#2325—171no—
768#2325—171no—
769#2318—171no—
770#2318—171no—
771C4×#120—171no—
772C4×#120—171no—
773C4×#120—171no—
774C4×#120—171no—
775#2280—171no—
776#2275—171no—
777#2275—171no—
778C22×#95—171no—
779C22×C17—22no—
780C22×C17—22no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17—22no—
785C22×C17—22no—
786C22×C17—22no—
787C22×C17—22no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17—41no—
792C22×C17#51814yes—
793C22×C17C24×C411yescharacteristic
794C22×C17C22×#4111yescharacteristic
795C22×C17C22×#4111yescharacteristic
796C22×C17C2×H(5,𝔽2)11yescharacteristic
797C22×C17C2×H(5,𝔽2)11yescharacteristic
798C22×C17C2×H(5,𝔽2)11yescharacteristic
799C22×C17C2×2−1+411yescharacteristic
800C2×D17—232no—
801C2×D17—22no—
802C2×D17—22no—
803C2×D17—22no—
804C2×D17—22no—
805C2×D17—22no—
806C2×D17—22no—
807C2×D17—22no—
808C2×D17—22no—
809C2×D17—22no—
810C2×D17—22no—
811C2×D17—22no—
812C2×D17—22no—
813C2×D17—22no—
814C2×D17—22no—
815C2×D17—22no—
816C2×D17—41no—
817C2×D17—41no—
818C2×D17—41no—
819C2×D17—41no—
820C2×D17C4×#4114yes—
821C2×D17#52014yes—
822C4×C17—22no—
823C4×C17—22no—
824C4×C17—22no—
825C4×C17—22no—
826C4×C17—22no—
827C4×C17—22no—
828C4×C17—22no—
829C4×C17—41no—
830C4×C17—41no—
831C4×C17—41no—
832C4×C17—41no—
833C4×C17—41no—
834C4×C17—41no—
835Dic17—22no—
836Dic17—22no—
837Dic17—22no—
838Dic17—22no—
839Dic17—22no—
840Dic17—22no—
841Dic17—22no—
842Dic17—41no—
843Dic17—41no—
844Dic17—41no—
845Dic17—41no—
846Dic17—41no—
847Dic17—41no—
848C22×#41—171no—
849C24×C4—171no—
850C24×C4—171no—
851C24×C4—171no—
852#525—1716no—
853C2×#123—171no—
854C2×#123C2×D1711yescharacteristic
855C2×C22⋊Q8—171no—
856C2×C22⋊Q8—171no—
857C2×#121—171no—
858C2×#121—171no—
859C2×#120—171no—
860C2×#120—171no—
861C2×C4×D4—171no—
862C2×C4×D4—171no—
863C2×C4×D4—171no—
864C2×C4×D4—171no—
865C2×C4×D4—171no—
866C2×C4×D4—171no—
867C2×C4×D4—171no—
868C2×C4×D4—171no—
869C2×C4×D4—171no—
870C2×C4×D4—171no—
871C2×C4×D4—171no—
872C2×C4×D4—171no—
873C2×C4×D4—171no—
874C2×C4×D4—171no—
875C2×C4×D4—171no—
876C2×C4×D4C2×D1711yescharacteristic
877C2×#117—171no—
878C2×#117—171no—
879C2×#117C2×D1711yescharacteristic
880#391—171no—
881#391—171no—
882#391—171no—
883#391—171no—
884#389—171no—
885#389—171no—
886#389—171no—
887#389C2×D1711yescharacteristic, complemented
888#388—171no—
889#388—171no—
890#388—171no—
891#388—171no—
892#388—171no—
893#388—171no—
894#388C2×D1711yescharacteristic, complemented
895#388C2×D1711yescharacteristic, complemented
896#387—171no—
897#387—171no—
898#387—171no—
899#387—171no—
900#387—171no—
901#387—171no—
902#387—171no—
903#387—171no—
904#387—171no—
905#387—171no—
906#387—171no—
907#387—171no—
908#387—171no—
909#387—171no—
910#387C2×D1711yescharacteristic, complemented
911#387C2×D1711yescharacteristic, complemented
912#386—171no—
913#386—171no—
914#386—171no—
915#386—171no—
916#386—171no—
917#386—171no—
918#386—171no—
919#386—171no—
920#386—171no—
921#386—171no—
922#386—171no—
923#386—171no—
924#386—171no—
925#386—171no—
926#386—171no—
927#386C2×D1711yescharacteristic
928#385—171no—
929#385—171no—
930#385—171no—
931#385—171no—
932#385—171no—
933#385—171no—
934#385—171no—
935#385—171no—
936#385—171no—
937#385—171no—
938#385—171no—
939#385—171no—
940#385—171no—
941#385—171no—
942#385C2×D1711yescharacteristic
943#385C2×D1711yescharacteristic, complemented
944#383—171no—
945#383—171no—
946#382—171no—
947#382—171no—
948#381—171no—
949#381—171no—
950#381—171no—
951#381—171no—
952#380—171no—
953#380—171no—
954#380—171no—
955#380—171no—
956#380—171no—
957#380—171no—
958#379—171no—
959#379—171no—
960C4×C4⋊C4—171no—
961C4×C4⋊C4—171no—
962C4×C4⋊C4—171no—
963C4×C4⋊C4—171no—
964C4×C4⋊C4—171no—
965C4×C4⋊C4C2×D1711yescharacteristic, complemented
966C4×C22⋊C4—171no—
967C4×C22⋊C4—171no—
968C4×C22⋊C4—171no—
969C4×C22⋊C4—171no—
970C4×C22⋊C4—171no—
971C4×C22⋊C4—171no—
972C4×C22⋊C4—171no—
973C4×C22⋊C4—171no—
974C4×C22⋊C4—171no—
975C4×C22⋊C4—171no—
976C4×C22⋊C4—171no—
977C4×C22⋊C4—171no—
978C4×C22⋊C4—171no—
979C4×C22⋊C4—171no—
980C4×C22⋊C4—171no—
981C4×C22⋊C4—171no—
982C4×C22⋊C4—171no—
983C4×C22⋊C4—171no—
984C4×C22⋊C4—171no—
985C4×C22⋊C4—171no—
986C4×C22⋊C4C2×D1711yescharacteristic
987C4×C22⋊C4C2×D1711yescharacteristic, complemented
988#376—171no—
989#376—171no—
990C2×#95—171no—
991C2×#95—171no—
992C2×#95—171no—
993C2×#95—171no—
994C2×#95—171no—
995C2×#95—171no—
996C2×#95—171no—
997C2×#95—171no—
998C2×#95—171no—
999C2×#95—171no—
1000C2×#95—171no—
1001C2×#95—171no—
1002C2×#95—171no—
1003C2×#95C2×D1711yescharacteristic
1004C2×C17—24no—
1005C2×C17—42no—
1006C2×C17C2×C4×#4111yescharacteristic
1007C2×C17C2×#51811yescharacteristic
1008C2×C17C2×#52011yescharacteristic
1009C2×C17#349011yescharacteristic
1010C2×C17#349011yescharacteristic
1011C2×C17#349211yescharacteristic
1012C2×C17#349211yescharacteristic
1013D17—24no—
1014D17—24no—
1015D17—42no—
1016C25—171no—
1017C2×#41—178no—
1018C2×#41—682no—
1019C2×#41—682no—
1020C22×Q8—171no—
1021C22×D4—171no—
1022C22×D4—171no—
1023C22×D4—171no—
1024C22×D4—171no—
1025C22×D4—171no—
1026C22×D4—171no—
1027C22×D4C22×D1711yescharacteristic
1028C23×C4—171no—
1029C23×C4—171no—
1030C23×C4—178no—
1031C23×C4—171no—
1032C23×C4—171no—
1033C23×C4—171no—
1034C23×C4—171no—
1035C23×C4—171no—
1036C23×C4—171no—
1037C23×C4—171no—
1038C23×C4—171no—
1039C23×C4—171no—
1040C23×C4—171no—
1041C23×C4—171no—
1042C23×C4—171no—
1043C23×C4—171no—
1044C23×C4—171no—
1045C23×C4—171no—
1046C23×C4—171no—
1047C23×C4—171no—
1048C23×C4—171no—
1049C23×C4—344no—
1050C23×C4—344no—
1051C23×C4—682no—
1052C23×C4—682no—
1053C23×C4—682no—
1054C23×C4—682no—
1055C23×C4—682no—
1056C23×C4—682no—
1057C23×C4C22×D1711yescharacteristic
1058C23×C4C22×D1711yescharacteristic
1059C23×C4C22×D1711yescharacteristic
1060C23×C4C22×D1711yescharacteristic
1061#123—178no—
1062#123C4×D1718yescomplemented
1063C22⋊Q8—178no—
1064C22⋊Q8—178no—
1065#121—178no—
1066#121—178no—
1067#120—178no—
1068#120—178no—
1069C4×D4—42no—
1070C4×D4—178no—
1071C4×D4—178no—
1072C4×D4—178no—
1073C4×D4—178no—
1074C4×D4—344no—
1075C4×D4—344no—
1076C4×D4—344no—
1077C4×D4—344no—
1078C4×D4—682no—
1079C4×D4—682no—
1080C4×D4—682no—
1081C4×D4—682no—
1082C4×D4—682no—
1083C4×D4—682no—
1084C4×D4—682no—
1085#117—42no—
1086#117—178no—
1087#117—682no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4—171no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4—171no—
1093C2×C4⋊C4—171no—
1094C2×C4⋊C4—171no—
1095C2×C4⋊C4—171no—
1096C2×C4⋊C4—171no—
1097C2×C4⋊C4—171no—
1098C2×C4⋊C4—171no—
1099C2×C4⋊C4—171no—
1100C2×C4⋊C4—171no—
1101C2×C4⋊C4—171no—
1102C2×C4⋊C4—171no—
1103C2×C4⋊C4C22×D1711yescharacteristic
1104C2×C4⋊C4C22×D1711yescharacteristic
1105C2×C4⋊C4C22×D1711yescharacteristic
1106C2×C4⋊C4C22×D1711yescharacteristic
1107C2×C4⋊C4C22×D1711yescharacteristic
1108C2×C4⋊C4C22×D1711yescharacteristic
1109C2×C4⋊C4C22×D1711yescharacteristic
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4C22×D1711yescharacteristic
1137C2×C22⋊C4C22×D1711yescharacteristic
1138C2×C22⋊C4C22×D1711yescharacteristic
1139C2×C22⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4C22×D1711yescharacteristic
1141C2×C22⋊C4C22×D1711yescharacteristic
1142C2×C22⋊C4C22×D1711yescharacteristic
1143C2×C22⋊C4C22×D1711yescharacteristic
1144C2×C42—171no—
1145C2×C42—171no—
1146C2×C42—171no—
1147C2×C42—171no—
1148C2×C42—171no—
1149C2×C42—171no—
1150C2×C42—171no—
1151C2×C42—171no—
1152C2×C42—171no—
1153C2×C42—171no—
1154C2×C42—171no—
1155C2×C42—171no—
1156C2×C42—171no—
1157C2×C42C22×D1711yescharacteristic
1158C2×C42C22×D1711yescharacteristic
1159C2×C42C22×D1711yescharacteristic
1160C2×C42C22×D1711yescharacteristic
1161C2×C42C22×D1711yescharacteristic
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95C22×D1711yescharacteristic
1201#95C22×D1711yescharacteristic
1202#95C22×D1711yescharacteristic
1203#95C22×D1711yescharacteristic
1204#95C22×D1711yescharacteristic
1205#95C22×D1711yescharacteristic
1206#95C22×D1711yescharacteristic
1207#95C22×D1711yescharacteristic
1208#95C22×D1711yescharacteristic
1209#95C22×D1711yescharacteristic
1210C17#3421811yescharacteristic, complemented, Sylow
1211C24—171no—
1212C24—171no—
1213C24—174no—
1214C24—171no—
1215C24—342no—
1216C24—342no—
1217C24—342no—
1218C24—342no—
1219C24—342no—
1220C24—342no—
1221C24C23×D1711yescharacteristic
1222C24C23×D1711yescharacteristic
1223#41—6816no—
1224C2×Q8—174no—
1225C2×Q8—681no—
1226C2×Q8—681no—
1227C2×D4—22no—
1228C2×D4—22no—
1229C2×D4—174no—
1230C2×D4—174no—
1231C2×D4—174no—
1232C2×D4—174no—
1233C2×D4—174no—
1234C2×D4—174no—
1235C2×D4—342no—
1236C2×D4—342no—
1237C2×D4—342no—
1238C2×D4—342no—
1239C2×D4—342no—
1240C2×D4—342no—
1241C2×D4—342no—
1242C2×D4—342no—
1243C2×D4—342no—
1244C2×D4—342no—
1245C2×D4—681no—
1246C2×D4—681no—
1247C2×D4C2×C4×D1714yes—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—41no—
1259C22×C4—174no—
1260C22×C4—171no—
1261C22×C4—171no—
1262C22×C4—171no—
1263C22×C4—171no—
1264C22×C4—171no—
1265C22×C4—171no—
1266C22×C4—171no—
1267C22×C4—174no—
1268C22×C4—174no—
1269C22×C4—174no—
1270C22×C4—174no—
1271C22×C4—174no—
1272C22×C4—174no—
1273C22×C4—174no—
1274C22×C4—174no—
1275C22×C4—171no—
1276C22×C4—171no—
1277C22×C4—171no—
1278C22×C4—171no—
1279C22×C4—171no—
1280C22×C4—171no—
1281C22×C4—342no—
1282C22×C4—342no—
1283C22×C4—342no—
1284C22×C4—342no—
1285C22×C4—342no—
1286C22×C4—342no—
1287C22×C4—342no—
1288C22×C4—342no—
1289C22×C4—342no—
1290C22×C4—342no—
1291C22×C4—342no—
1292C22×C4—342no—
1293C22×C4—342no—
1294C22×C4—342no—
1295C22×C4—342no—
1296C22×C4—342no—
1297C22×C4—342no—
1298C22×C4—342no—
1299C22×C4—342no—
1300C22×C4—6816no—
1301C22×C4—681no—
1302C22×C4—681no—
1303C22×C4—681no—
1304C22×C4—681no—
1305C22×C4—681no—
1306C22×C4—681no—
1307C22×C4—681no—
1308C22×C4—681no—
1309C22×C4—681no—
1310C22×C4—681no—
1311C22×C4—681no—
1312C22×C4—681no—
1313C22×C4—681no—
1314C22×C4—681no—
1315C22×C4—681no—
1316C22×C4—681no—
1317C22×C4—681no—
1318C22×C4—681no—
1319C22×C4—681no—
1320C22×C4—681no—
1321C22×C4—681no—
1322C22×C4—681no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4—681no—
1327C22×C4—6816no—
1328C22×C4—6816no—
1329C22×C4—681no—
1330C22×C4—681no—
1331C22×C4—681no—
1332C22×C4—681no—
1333C22×C4—681no—
1334C22×C4—681no—
1335C22×C4C2×C4×D1714yes—
1336C22×C4C23×D1711yescharacteristic
1337C22×C4C23×D1711yescharacteristic
1338C22×C4C23×D1711yescharacteristic
1339C22×C4C23×D1711yescharacteristic
1340C22×C4C23×D1711yescharacteristic
1341C22×C4C23×D1711yescharacteristic
1342C22×C4C23×D1711yescharacteristic
1343C22×C4C23×D1711yescharacteristic
1344C22×C4C23×D1711yescharacteristic
1345C22×C4C23×D1711yescharacteristic
1346C22×C4C23×D1711yescharacteristic
1347C22×C4C23×D1711yescharacteristic
1348C22×C4C23×D1711yescharacteristic
1349C4⋊C4—22no—
1350C4⋊C4—41no—
1351C4⋊C4—41no—
1352C4⋊C4—41no—
1353C4⋊C4—41no—
1354C4⋊C4—174no—
1355C4⋊C4—174no—
1356C4⋊C4—174no—
1357C4⋊C4—174no—
1358C4⋊C4—342no—
1359C4⋊C4—342no—
1360C4⋊C4—342no—
1361C4⋊C4—681no—
1362C4⋊C4—681no—
1363C4⋊C4—681no—
1364C4⋊C4—681no—
1365C4⋊C4—681no—
1366C4⋊C4—681no—
1367C4⋊C4—681no—
1368C4⋊C4—681no—
1369C4⋊C4C2×C4×D1714yescomplemented
1370C4⋊C4C2×C4×D1714yescomplemented
1371C22⋊C4—22no—
1372C22⋊C4—22no—
1373C22⋊C4—22no—
1374C22⋊C4—41no—
1375C22⋊C4—41no—
1376C22⋊C4—174no—
1377C22⋊C4—174no—
1378C22⋊C4—174no—
1379C22⋊C4—174no—
1380C22⋊C4—174no—
1381C22⋊C4—174no—
1382C22⋊C4—174no—
1383C22⋊C4—342no—
1384C22⋊C4—342no—
1385C22⋊C4—342no—
1386C22⋊C4—342no—
1387C22⋊C4—342no—
1388C22⋊C4—342no—
1389C22⋊C4—342no—
1390C22⋊C4—342no—
1391C22⋊C4—342no—
1392C22⋊C4—342no—
1393C22⋊C4—342no—
1394C22⋊C4—342no—
1395C22⋊C4—342no—
1396C22⋊C4—681no—
1397C22⋊C4—681no—
1398C22⋊C4—681no—
1399C22⋊C4—681no—
1400C22⋊C4—681no—
1401C22⋊C4—681no—
1402C22⋊C4C2×C4×D1714yes—
1403C22⋊C4C2×C4×D1714yescomplemented
1404C22⋊C4C2×C4×D1714yescomplemented
1405C42—22no—
1406C42—41no—
1407C42—41no—
1408C42—41no—
1409C42—41no—
1410C42—174no—
1411C42—174no—
1412C42—342no—
1413C42—342no—
1414C42—342no—
1415C42—681no—
1416C42—681no—
1417C42—681no—
1418C42—681no—
1419C42—681no—
1420C42—681no—
1421C42—681no—
1422C42—681no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—172no—
1434C23—172no—
1435C23—172no—
1436C23—172no—
1437C23—172no—
1438C23—172no—
1439C23—172no—
1440C23—348no—
1441C23—348no—
1442C23—348no—
1443C23—348no—
1444C23—348no—
1445C23—348no—
1446C23—348no—
1447C23—341no—
1448C23—341no—
1449C23—341no—
1450C23—341no—
1451C23—341no—
1452C23—341no—
1453C23—341no—
1454C23—341no—
1455C23—341no—
1456C23—341no—
1457C23—341no—
1458C23—341no—
1459C23—341no—
1460C23—341no—
1461C23C22×C4×D1712yes—
1462C23C22×C4×D1712yes—
1463C23#1058769112yes—
1464C23#1058769612yes—
1465C23C24×D1711yescharacteristic
1466Q8—684no—
1467D4—28no—
1468D4—348no—
1469D4—348no—
1470D4—348no—
1471D4—348no—
1472D4—348no—
1473D4—684no—
1474C2×C4—28no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—44no—
1508C2×C4—44no—
1509C2×C4—82no—
1510C2×C4—172no—
1511C2×C4—172no—
1512C2×C4—172no—
1513C2×C4—172no—
1514C2×C4—172no—
1515C2×C4—172no—
1516C2×C4—172no—
1517C2×C4—348no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—341no—
1550C2×C4—684no—
1551C2×C4—684no—
1552C2×C4—684no—
1553C2×C4—684no—
1554C2×C4—684no—
1555C2×C4—684no—
1556C2×C4—684no—
1557C2×C4—684no—
1558C2×C4—684no—
1559C2×C4—684no—
1560C2×C4—684no—
1561C2×C4—684no—
1562C2×C4—684no—
1563C2×C4—684no—
1564C2×C4—684no—
1565C2×C4—684no—
1566C2×C4—1362no—
1567C2×C4—1362no—
1568C2×C4—1362no—
1569C2×C4C22×C4×D1712yes—
1570C2×C4C22×C4×D1712yes—
1571C2×C4C22×C4×D1712yes—
1572C2×C4C22×C4×D1712yes—
1573C2×C4C22×C4×D1712yes—
1574C2×C4#41×D1712yes—
1575C2×C4#41×D1712yes—
1576C22—22no—
1577C22—22no—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—174no—
1590C22—174no—
1591C22—3432no—
1592C22—342no—
1593C22—342no—
1594C22—342no—
1595C22—342no—
1596C22—342no—
1597C22—342no—
1598C22—342no—
1599C22—342no—
1600C22—342no—
1601C22—342no—
1602C22—342no—
1603C22—342no—
1604C22—342no—
1605C22—342no—
1606C22—342no—
1607C22—681no—
1608C22—681no—
1609C22—681no—
1610C22—681no—
1611C22#1176328114yes—
1612C22C23×C4×D1711yescharacteristic
1613C22C2×#41×D1711yescharacteristic
1614C22C2×#41×D1711yescharacteristic
1615C22H(5,𝔽2)×D1711yescharacteristic
1616C22C2×#1058769111yescharacteristic
1617C22C2×#1058769611yescharacteristic
1618C222−1+4×D1711yescharacteristic
1619C4—22no—
1620C4—22no—
1621C4—22no—
1622C4—22no—
1623C4—22no—
1624C4—22no—
1625C4—22no—
1626C4—41no—
1627C4—41no—
1628C4—41no—
1629C4—41no—
1630C4—41no—
1631C4—41no—
1632C4—342no—
1633C4—342no—
1634C4—342no—
1635C4—342no—
1636C4—342no—
1637C4—342no—
1638C4—342no—
1639C4—681no—
1640C4—681no—
1641C4—681no—
1642C4—681no—
1643C4—681no—
1644C4—681no—
1645C2—24no—
1646C2—42no—
1647C2—344no—
1648C2—344no—
1649C2—682no—
1650C2C4×#41×D1711yescharacteristic
1651C2C2×#1176328111yescharacteristic
1652C2D17×#52011yescharacteristic
1653C2#1454246611yescharacteristic
1654C2#1454246811yescharacteristic
1655C2#1454248411yescharacteristic
1656C2#1454248611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2359C2
socle, cosocleC23×C17C25
prime radicalC2×#11763317C2
hypercenter#2359D17
hypocenterC17#34218
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2359

Complements

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

NH ≅ G/Ntype
2. #14531868C2semidirect
3. #14531861C2semidirect
4. #14531835C2semidirect
5. #14531828C2semidirect
6. #14531780C2semidirect
7. #14531776C2semidirect
8. #14531772C2semidirect
9. #14531723C2semidirect
10. #14531719C2semidirect
11. #14531693C2semidirect
12. #14531690C2semidirect
13. #14531642C2semidirect
14. #14531638C2semidirect
15. #14531610C2semidirect
16. #14531609C2semidirect
17. #14531518C2semidirect
18. #14531511C2semidirect
19. #14531488C2semidirect
20. #14531481C2semidirect
21. #14531416C2semidirect
22. #14531414C2semidirect
23. #14531289C2semidirect
24. C4×#10587568C2semidirect
25. #14531285C2semidirect
26. C4×#10587623C2semidirect
27. #14531163C2semidirect
28. #14531144C2semidirect
29. #14531143C2semidirect
30. C2×#95×D17C2semidirect
31. C17×#2359C2semidirect
36. #11763317C4semidirect
61. #11762715C22semidirect
62. #11762714C22semidirect
63. #11762713C22semidirect
64. #11762713C22semidirect
65. #11762708C22semidirect
66. #11762706C22semidirect
67. #11762704C22semidirect
68. #11762702C22semidirect
69. #11762702C22semidirect
70. #11762701C22semidirect
71. #11762700C22semidirect
72. #11762699C22semidirect
73. #11762698C22semidirect
74. #11762696C22semidirect
75. #11762696C22semidirect
76. #11762696C22semidirect
77. #11762695C22semidirect
78. #11762695C22semidirect
79. #11762693C22semidirect
80. #11762693C22semidirect
81. #11762693C22semidirect
82. #11762691C22semidirect
83. #11762691C22semidirect
84. #11762691C22semidirect
85. #11762690C22semidirect
86. #11762690C22semidirect
87. #11762690C22semidirect
90. #11762688C22semidirect
96. #11762686C22semidirect
101. #11762685C22semidirect
102. #11762685C22semidirect
104. #11762684C22semidirect
109. #11762683C22semidirect
116. #11762680C22semidirect
117. #11762676C22semidirect
118. #11762676C22semidirect
119. #11762674C22semidirect
120. #11762673C22semidirect
121. #11762671C22semidirect
124. #11762670C22semidirect
125. #11762667C22semidirect
130. #11762666C22semidirect
133. C4⋊C4×Dic17C22semidirect
134. C4⋊C4×Dic17C22semidirect
135. C4×#63225C22semidirect
136. C4×#63225C22semidirect
137. #11762660C22semidirect
140. C22⋊C4×Dic17C22semidirect
141. C22⋊C4×Dic17C22semidirect
150. C4×#63227C22semidirect
151. C4×#63227C22semidirect
157. #11762656C22semidirect
158. #11762655C22semidirect
159. #11762654C22semidirect
163. C2×#10587502C22semidirect
172. #95×D17C22semidirect
176. C17×#389C22semidirect
177. C17×#388C22semidirect
178. C17×#388C22semidirect
179. C17×#387C22semidirect
180. C17×#387C22semidirect
183. C17×#385C22semidirect
184. C4×C4⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
205. C2×#63254C2×C4semidirect
216. C22×C4×D17C2×C4semidirect
233. C17×#123C2×C4semidirect
262. #10587623C2×C4semidirect
264. #10587615C2×C4semidirect
317. #10587582C2×C4semidirect
318. #10587582C2×C4semidirect
321. #10587579C2×C4semidirect
322. #10587579C2×C4semidirect
323. #10587570C2×C4semidirect
324. #10587570C2×C4semidirect
325. #10587568C2×C4semidirect
329. #10587567C2×C4semidirect
330. #10587567C2×C4semidirect
331. #10587563C2×C4semidirect
433. C2×C22⋊D17C22×C4semidirect
448. C22×Dic17C22×C4semidirect
514. C2×C4×D17C22×C4semidirect
515. C2×C4×D17#41semidirect
516. C2×C4×D17#41semidirect
519. C2×Dic34C22×C4semidirect
525. C4⋊C4×C17C22×C4semidirect
526. C4⋊C4×C17C22×C4semidirect
533. C22⋊C4×C17C22×C4semidirect
534. C22⋊C4×C17C22×C4semidirect
564. #63227C22×C4semidirect
565. #63227C22×C4semidirect
577. #63225C22×C4semidirect
578. #63225C22×C4semidirect
579. #63225C22×C4semidirect
580. #63225C22×C4semidirect
592. C4×Dic17C22×C4semidirect
593. C4×Dic17C22×C4semidirect
756. #2359D17semidirect
887. #389C2×D17semidirect
894. #388C2×D17semidirect
895. #388C2×D17semidirect
910. #387C2×D17semidirect
911. #387C2×D17semidirect
943. #385C2×D17semidirect
965. C4×C4⋊C4C2×D17semidirect
987. C4×C22⋊C4C2×D17semidirect
1062. #123C4×D17semidirect
1210. C17#34218semidirect
1369. C4⋊C4C2×C4×D17semidirect
1370. C4⋊C4C2×C4×D17semidirect
1403. C22⋊C4C2×C4×D17semidirect
1404. C22⋊C4C2×C4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#117633172
#145318682
#145318612
#145318352
#145318282
#145317802
#145317762
#145317722
#145317232
#145317192
#145316932
#145316902
#145316422
#145316382
#145316102
#145316092
#145315182
#145315112
#145314882
#145314812
#145314162
#145314142
#145312892
C4×#105875682
#145312852
C4×#105876232
#145311632
#145311442
#145311432
C2×#95×D172
C17×#23592
#3421817