Finite Group Databasebeta

← #14914368

Subgroups — #14914368

Order 2816.

2194 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13071717C212yesmaximal, complemented
3#13071708C212yesmaximal, complemented
4#13071648C212yesmaximal
5#13071639C212yesmaximal
6#13071580C212yesmaximal, complemented
7#13071534C212yesmaximal, complemented
8#13071505C212yesmaximal
9#13071500C212yesmaximal
10#13071299C212yesmaximal
11#13071296C212yesmaximal
12#13071263C212yesmaximal, complemented
13C4⋊Q8×Dic11C211yesmaximal, characteristic, complemented
14C4×#66922C211yesmaximal, characteristic, complemented
15#13071183C211yesmaximal, characteristic, complemented
16#13071021C211yesmaximal, characteristic
17#13070980C212yesmaximal, complemented
18C4×#66925C211yesmaximal, characteristic
19C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C4×Q8×C11C2212yes—
22C2×#66999C2212yes—
23C2×Q8×Dic11C2212yes—
24C2×Q8×Dic11C2212yes—
25#10623259C4116yescomplemented
26C2×#66950C2212yes—
27C2×#66945C2212yes—
28C2×#66945C2212yes—
29C2×#66943C2212yes—
30C2×#66940C2212yes—
31C2×#66940C2212yes—
32C2×#66925C2211yescharacteristic
33C2×#66925C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C2×C4×Dic22C2212yes—
37C11×#391C2212yes—
38C11×#389C2212yes—
39C11×#389C2212yes—
40C11×#384C2211yescharacteristic
41C4×C11×C4⋊C4C2212yes—
42C4×C11×C4⋊C4C2212yes—
43C43×C11C2211yescharacteristic
44#10622843C2212yes—
45#10622603C2214yes—
46#10622600C2212yes—
47#10622600C2212yes—
48#10622598C2212yes—
49#10622598C2212yes—
50#10622591C2214yes—
51#10622590C2214yes—
52#10622590C2212yes—
53C4⋊C4×Dic11C2212yes—
54C4⋊C4×Dic11C2212yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2212yes—
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2212yes—
59#10622587C2212yes—
60#10622586C2212yes—
61#10622586C2212yes—
62#10622586C2214yes—
63#10622553C2214yes—
64C4×(C2×D11)⋊C4C2211yescharacteristic
65C4×(C2×D11)⋊C4C2211yescharacteristic
66C4×(C2×D11)⋊C4C2211yescharacteristic
67C4×(C2×D11)⋊C4C2211yescharacteristic
68#10622548C2211yescharacteristic
69C4×C4⋊Dic11C2212yes—
70C4×C4⋊Dic11C2212yes—
71#10622545C2211yescharacteristic
72#10622545C2211yescharacteristic
73C4×Dic11⋊C4C2214yes—
74C4×Dic11⋊C4C2211yescharacteristic
75C4×Dic11⋊C4C2211yescharacteristic
76C4×Dic11⋊C4C2211yescharacteristic
77C4×Dic11⋊C4C2211yescharacteristic
78C4×Dic11⋊C4C2214yes—
79C42×Dic11C2211yescharacteristic
80#10622542C2212yes—
81#10622541C2212yes—
82#10622541C2212yes—
83#10622541C2214yes—
84#10622283C2214yes—
85#10622282C2214yes—
86#10622268C2214yes—
87#10622267C2214yes—
88#10622266C2214yes—
89#10622264C2214yes—
90#10622262C2214yes—
91#10622261C2214yes—
92C22×Q8×C11C2312yes—
93C22×C4×D11C2311yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C22×C4×D11C2311yescharacteristic
96C22×Dic22C2312yes—
97C11×C4⋊Q8C2×C418yes—
98C4×Q8×C11—44no—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2312yes—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2314yes—
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113#66999C2×C4116yes—
114Q8×Dic11—44no—
115Q8×Dic11C2×C4116yes—
116C2×(C2×D11)⋊C4C2311yescharacteristic
117C2×(C2×D11)⋊C4C2311yescharacteristic
118C2×(C2×D11)⋊C4C2311yescharacteristic
119C2×(C2×D11)⋊C4C2311yescharacteristic
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×C4⋊Dic11C2312yes—
123C2×C4⋊Dic11C2312yes—
124C2×C4⋊Dic11C2312yes—
125C2×C4⋊Dic11C2314yes—
126C2×C4⋊Dic11C2312yes—
127C2×C4⋊Dic11C2312yes—
128C2×C4⋊Dic11C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2311yescharacteristic
131C2×Dic11⋊C4C2311yescharacteristic
132C2×Dic11⋊C4C2311yescharacteristic
133C2×Dic11⋊C4C2311yescharacteristic
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2311yescharacteristic
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2311yescharacteristic
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2311yescharacteristic
146C2×C4×Dic11C2311yescharacteristic
147C2×C4×Dic11C2311yescharacteristic
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2311yescharacteristic
150#66950C2×C4116yes—
151#66945—44no—
152#66945C2×C4116yes—
153#66943C2×C4116yes—
154#66940—28no—
155#66940C2×C4116yes—
156#66925—24no—
157#66925—24no—
158C42×D11C2×C418yes—
159#66922C2×C418yes—
160C4×Dic22—28no—
161C11×#95C2314yes—
162C11×#95C2314yes—
163C11⋊#95C2311yescharacteristic
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2311yescharacteristic
167C11⋊#95C2311yescharacteristic
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2311yescharacteristic
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2311yescharacteristic
176C11⋊#95C2311yescharacteristic
177C11⋊#95C2311yescharacteristic
178C11⋊#95C2311yescharacteristic
179#34225—111nomaximal, Sylow
180C23×D11C2411yescharacteristic
181C2×Q8×C11—24no—
182C2×Q8×C11—24no—
183C2×Q8×C11C22×C418yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2414yes—
187C22×C4×C11C2414yes—
188C22×C4×C11C2411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×C4×C11C2411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C22×Dic11C2411yescharacteristic
194C22×Dic11C2414yes—
195C22×Dic11C2411yescharacteristic
196C22×Dic11C2411yescharacteristic
197C22×Dic11C2411yescharacteristic
198C22×Dic11C2414yes—
199C22×Dic11C2411yescharacteristic
200C22×Dic11C2411yescharacteristic
201C22×Dic11C2411yescharacteristic
202C2×C4×D11—22no—
203C2×C4×D11—22no—
204C2×C4×D11—22no—
205C2×C4×D11—22no—
206C2×C4×D11—22no—
207C2×C4×D11—22no—
208C2×C4×D11C22×C414yes—
209C2×C4×D11C22×C414yes—
210C2×C4×D11C22×C414yes—
211C2×Dic22—24no—
212C2×Dic22—24no—
213C2×Dic22C22×C418yes—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—24no—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—44no—
218C11×C4⋊C4C22×C418yes—
219C11×C4⋊C4C22×C418yes—
220C42×C11—22no—
221C42×C11—22no—
222C42×C11—22no—
223C42×C11—22no—
224C42×C11—22no—
225C42×C11—44no—
226C42×C11C22×C414yes—
227C42×C11#4114yes—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—22no—
231(C2×D11)⋊C4—22no—
232(C2×D11)⋊C4—44no—
233(C2×D11)⋊C4C22×C4116yes—
234C4⋊Dic11—24no—
235C4⋊Dic11—24no—
236C4⋊Dic11—24no—
237C4⋊Dic11—44no—
238C4⋊Dic11C22×C418yes—
239C4⋊Dic11C22×C418yes—
240C4⋊Dic11C22×C4116yes—
241Dic11⋊C4—22no—
242Dic11⋊C4—22no—
243Dic11⋊C4—28no—
244Dic11⋊C4—28no—
245Dic11⋊C4—22no—
246Dic11⋊C4—22no—
247Dic11⋊C4C22×C4116yes—
248C4×Dic11—28no—
249C4×Dic11—28no—
250C4×Dic11—22no—
251C4×Dic11—22no—
252C4×Dic11—22no—
253C4×Dic11—22no—
254C4×Dic11—22no—
255C4×Dic11—44no—
256C4×Dic11—44no—
257C4×Dic11C22×C414yes—
258C4×Dic11C22×C414yes—
259C4×Dic11C22×C414yes—
260C4×Dic11C22×C4116yes—
261C4×Dic11#4114yes—
262C2×#533—111no—
263#2370—112no—
264#2370—112no—
265#2362—112no—
266#2362—112no—
267#2356—112no—
268#2351—112no—
269#2347—112no—
270#2346—112no—
271#2323—112no—
272#2323—112no—
273#2320—112no—
274C4×C4⋊Q8—111no—
275C4×C4⋊Q8—111no—
276C4×C4⋊Q8—111no—
277C4×C4⋊Q8D1111yescharacteristic, complemented
278#2285—111no—
279#2276—112no—
280C4×#117—111no—
281C23×C11C2511yescharacteristic
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11C23×C412yes—
289Q8×C11—216no—
290C2×C4×C11—24no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—24no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—24no—
305C2×C4×C11C23×C418yes—
306C2×C4×C11C23×C412yes—
307C2×C4×C11C23×C412yes—
308C2×C4×C11C23×C412yes—
309C2×C4×C11C2×#4112yes—
310C2×C4×C11C2×#4112yes—
311C2×C4×C11C2×#4112yes—
312C2×C4×C11C2×#4112yes—
313C2×C4×C11H(5,𝔽2)12yes—
314C2×C4×C112−1+412yes—
315C2×C4×C112−1+412yes—
316C2×C4×C112−1+412yes—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—24no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—24no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—24no—
338C2×Dic11C23×C412yes—
339C2×Dic11C23×C412yes—
340C2×Dic11C23×C412yes—
341C2×Dic11C23×C418yes—
342C2×Dic11C2×#4112yes—
343C2×Dic11C2×#4112yes—
344C4×D11—28no—
345C4×D11—28no—
346C4×D11—28no—
347Dic22—216no—
348#533—1116no—
349C2×C4⋊Q8—111no—
350C2×C4⋊Q8C2×D1111yescharacteristic
351C2×#125—112no—
352C2×C22⋊Q8—112no—
353C2×C22⋊Q8—112no—
354C2×C4×Q8—112no—
355C2×C4×Q8—112no—
356C2×C4×Q8—112no—
357C2×C4×Q8—112no—
358C2×C4×Q8—112no—
359C2×C4×Q8C2×D1112yes—
360C2×#117—112no—
361C2×#117—112no—
362C2×#117—111no—
363C2×#117—111no—
364C22×C42—111no—
365#391—112no—
366#391—112no—
367#391—112no—
368#391C2×D1112yes—
369#389—112no—
370#389—112no—
371#389—112no—
372#389—112no—
373#389—114no—
374#389—112no—
375#389—112no—
376#389—114no—
377#389C2×D1112yes—
378#389C2×D1112yes—
379#388—114no—
380#388—114no—
381#388—114no—
382#388—114no—
383#387—114no—
384#387—114no—
385#387—114no—
386#387—114no—
387#384—111no—
388#384C2×D1111yescharacteristic
389#383—114no—
390#382—114no—
391#382—112no—
392#380—112no—
393#380—112no—
394C4×C4⋊C4—112no—
395C4×C4⋊C4—112no—
396C4×C4⋊C4—112no—
397C4×C4⋊C4—112no—
398C4×C4⋊C4—112no—
399C4×C4⋊C4—112no—
400C4×C4⋊C4—112no—
401C4×C4⋊C4—112no—
402C4×C4⋊C4—114no—
403C4×C4⋊C4—111no—
404C4×C4⋊C4—111no—
405C4×C4⋊C4—114no—
406C4×C4⋊C4—111no—
407C4×C4⋊C4—111no—
408C4×C4⋊C4—114no—
409C4×C4⋊C4C2×D1112yes—
410C4×C4⋊C4C2×D1112yes—
411C4×C22⋊C4—111no—
412C4×C22⋊C4—111no—
413C4×C22⋊C4—111no—
414C4×C22⋊C4—111no—
415#376—111no—
416#376—111no—
417#376—114no—
418C43—111no—
419C43C2×D1111yescharacteristic
420C22×C11C24×C411yescharacteristic
421C22×C11C22×#4111yescharacteristic
422C22×C11C22×#4111yescharacteristic
423C22×C11C2×H(5,𝔽2)11yescharacteristic
424C22×C11C2×2−1+411yescharacteristic
425C22×C11C2×2−1+411yescharacteristic
426C22×C11C2×2−1+411yescharacteristic
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—41no—
431C2×D11—41no—
432C2×D11—41no—
433C2×D11—41no—
434C4×C11—28no—
435C4×C11—22no—
436C4×C11—22no—
437C4×C11—41no—
438C4×C11—44no—
439C4×C11—41no—
440C4×C11C4×#4114yes—
441C4×C11#51914yes—
442C4×C11#52014yes—
443Dic11—28no—
444Dic11—22no—
445Dic11—22no—
446Dic11—22no—
447Dic11—22no—
448Dic11—22no—
449Dic11—41no—
450Dic11—44no—
451Dic11—41no—
452C22×Q8—112no—
453C22×Q8C22×D1112yes—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C4⋊Q8—118no—
458C4⋊Q8C4×D1118yes—
459#125—1116no—
460C22⋊Q8—1116no—
461C22⋊Q8—1116no—
462C4×Q8—44no—
463C4×Q8—1116no—
464C4×Q8—1116no—
465C4×Q8—228no—
466C4×Q8—228no—
467C4×Q8—444no—
468#117—1116no—
469#117—224no—
470#117—224no—
471#117—444no—
472C2×C4⋊C4—112no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—114no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—112no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—112no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4C22×D1112yes—
487C2×C4⋊C4C22×D1112yes—
488C2×C4⋊C4C22×D1112yes—
489C2×C4⋊C4C22×D1114yes—
490C2×C4⋊C4C22×D1112yes—
491C2×C4⋊C4C22×D1112yes—
492C2×C22⋊C4—114no—
493C2×C22⋊C4—111no—
494C2×C22⋊C4—111no—
495C2×C22⋊C4—111no—
496C2×C22⋊C4—111no—
497C2×C22⋊C4—114no—
498C2×C42—111no—
499C2×C42—114no—
500C2×C42—111no—
501C2×C42—111no—
502C2×C42—111no—
503C2×C42—118no—
504C2×C42—111no—
505C2×C42—111no—
506C2×C42—114no—
507C2×C42—114no—
508C2×C42—111no—
509C2×C42—111no—
510C2×C42—111no—
511C2×C42—114no—
512C2×C42—114no—
513C2×C42C22×D1111yescharacteristic
514C2×C42C22×D1111yescharacteristic
515C2×C42C22×D1111yescharacteristic
516C2×C42C22×D1111yescharacteristic
517C2×C42C22×D1111yescharacteristic
518C2×C42C22×D1114yes—
519C2×C42C22×D1111yescharacteristic
520C2×C42C22×D1111yescharacteristic
521#95—111no—
522#95—111no—
523#95—111no—
524#95—111no—
525#95—111no—
526#95—111no—
527#95—111no—
528#95—111no—
529#95—114no—
530#95—114no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536#95—114no—
537#95C22×D1114yes—
538#95C22×D1114yes—
539C2×C11C2×C4×#4111yescharacteristic
540C2×C11C2×#51911yescharacteristic
541C2×C11C2×#52011yescharacteristic
542C2×C11#350911yescharacteristic
543C2×C11#350911yescharacteristic
544C2×C11#351111yescharacteristic
545C2×C11#351111yescharacteristic
546D11—42no—
547C24—111no—
548C2×Q8—24no—
549C2×Q8—24no—
550C2×Q8—118no—
551C2×Q8—224no—
552C2×Q8—224no—
553C2×Q8C2×C4×D1118yes—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—114no—
558C22×C4—111no—
559C22×C4—111no—
560C22×C4—114no—
561C22×C4—114no—
562C22×C4—114no—
563C22×C4—111no—
564C22×C4—111no—
565C22×C4—114no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4C23×D1111yescharacteristic
573C22×C4C23×D1111yescharacteristic
574C22×C4C23×D1114yes—
575C22×C4C23×D1114yes—
576C22×C4C23×D1111yescharacteristic
577C22×C4C23×D1111yescharacteristic
578C22×C4C23×D1111yescharacteristic
579C22×C4C23×D1111yescharacteristic
580C22×C4C23×D1111yescharacteristic
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—44no—
585C4⋊C4—118no—
586C4⋊C4—1116no—
587C4⋊C4—1116no—
588C4⋊C4—118no—
589C4⋊C4—222no—
590C4⋊C4—222no—
591C4⋊C4—228no—
592C4⋊C4—224no—
593C4⋊C4—222no—
594C4⋊C4—222no—
595C4⋊C4—228no—
596C4⋊C4—224no—
597C4⋊C4—224no—
598C4⋊C4—444no—
599C4⋊C4C2×C4×D1118yes—
600C4⋊C4C2×C4×D1118yes—
601C22⋊C4—1116no—
602C22⋊C4—222no—
603C22⋊C4—222no—
604C22⋊C4—222no—
605C22⋊C4—222no—
606C22⋊C4—444no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—44no—
613C42—114no—
614C42—114no—
615C42—114no—
616C42—1116no—
617C42—114no—
618C42—228no—
619C42—222no—
620C42—222no—
621C42—228no—
622C42—222no—
623C42—222no—
624C42—222no—
625C42—444no—
626C42—444no—
627C42C2×C4×D1114yes—
628C42#434314yes—
629C11#3422511yescharacteristic, complemented, Sylow
630C23—112no—
631C23—221no—
632C23—221no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23C24×D1111yescharacteristic
638Q8—216no—
639Q8—2216no—
640C2×C4—21no—
641C2×C4—24no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—24no—
646C2×C4—21no—
647C2×C4—24no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—24no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—24no—
655C2×C4—112no—
656C2×C4—112no—
657C2×C4—112no—
658C2×C4—118no—
659C2×C4—112no—
660C2×C4—112no—
661C2×C4—221no—
662C2×C4—221no—
663C2×C4—224no—
664C2×C4—221no—
665C2×C4—221no—
666C2×C4—221no—
667C2×C4—224no—
668C2×C4—221no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—228no—
674C2×C4—228no—
675C2×C4—228no—
676C2×C4—221no—
677C2×C4—224no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—224no—
681C2×C4—221no—
682C2×C4—224no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4C22×C4×D1118yes—
686C2×C4C22×C4×D1112yes—
687C2×C4C22×C4×D1112yes—
688C2×C4C22×C4×D1112yes—
689C2×C4#6703712yes—
690C2×C4C2×#434312yes—
691C2×C4C2×#434312yes—
692C2×C4C2×#434312yes—
693C2×C4#6704012yes—
694C2×C4#41×D1112yes—
695C2×C4#6704312yes—
696C2×C4#6704312yes—
697C22—222no—
698C22—222no—
699C22—222no—
700C22—441no—
701C22—441no—
702C22—441no—
703C22—441no—
704C22C23×C4×D1111yescharacteristic
705C22C2×#6703711yescharacteristic
706C22C22×#434311yescharacteristic
707C22C2×#6704011yescharacteristic
708C22C2×#41×D1111yescharacteristic
709C22C2×#6704311yescharacteristic
710C22C2×#6704311yescharacteristic
711C4—22no—
712C4—22no—
713C4—28no—
714C4—41no—
715C4—41no—
716C4—44no—
717C4—222no—
718C4—222no—
719C4—222no—
720C4—228no—
721C4—222no—
722C4—222no—
723C4—441no—
724C4—441no—
725C4—444no—
726C4#1062307714yes—
727C4#1062310314yes—
728C4C4×#434314yes—
729C2—442no—
730C2C2×C4×#434311yescharacteristic
731C2C2×#1062310311yescharacteristic
732C2C2×#1062307711yescharacteristic
733C2#1308249511yescharacteristic
734C2#1308250311yescharacteristic
735C2#1308251711yescharacteristic
736C2#1308252911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×C4⋊Q8C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterC4×C4⋊Q8D11
hypocenterC11#34225
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13071717C2semidirect
3. #13071708C2semidirect
6. #13071580C2semidirect
7. #13071534C2semidirect
12. #13071263C2semidirect
13. C4⋊Q8×Dic11C2semidirect
14. C4×#66922C2semidirect
15. #13071183C2semidirect
17. #13070980C2semidirect
19. C4×C11×C4⋊Q8C2semidirect
25. #10623259C4semidirect
277. C4×C4⋊Q8D11semidirect
629. C11#34225semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130717172
#130717082
#130716482
#130716392
#130715802
#130715342
#130715052
#130715002
#130712992
#130712962
#130712632
C4⋊Q8×Dic112
C4×#669222
#130711832
#130710212
#130709802
C4×#669252
C4×C11×C4⋊Q82
#3422511