Finite Group Databasebeta

← #15626798

Subgroups — #15626798

Order 2816.

1888 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2#13080007C212yesmaximal, complemented
3#13080003C212yesmaximal, complemented
4#13079989C214yesmaximal, complemented
5#13079958C212yesmaximal, complemented
6#13079953C214yesmaximal, complemented
7#13079932C212yesmaximal, complemented
8#13078431C212yesmaximal, complemented
9#13078417C212yesmaximal, complemented
10#13078248C214yesmaximal, complemented
11#13078103C212yesmaximal, complemented
12#13078084C212yesmaximal, complemented
13C2×#10622537C211yesmaximal, characteristic, complemented
14C11×#3444C211yesmaximal, characteristic
15C11×#533C2211yescharacteristic
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C11×#529—21no—
22C11×#529—21no—
23C11×#529—21no—
24C11×#529—21no—
25C11×#529C2212yes—
26C11×#529C2212yes—
27C11×#525—21no—
28C11×#525—21no—
29C11×#525C2212yes—
30C4×C11×#41—21no—
31C4×C11×#41—21no—
32C4×C11×#41C2212yes—
33C22×C42×C11C2211yescharacteristic
34C2×#67004C2214yes—
35C2×#66979—21no—
36C2×#66977—21no—
37C2×#66977C2212yes—
38C22×#4318C2212yes—
39#10623001—21no—
40#10623001—21no—
41#10623001—21no—
42#10623001—21no—
43#10623001C2212yes—
44#10623001C2212yes—
45#10623001C2212yes—
46#10623001C2212yes—
47C2×#66923—21no—
48C2×#66922C2211yescharacteristic
49C2×#66922C2211yescharacteristic
50C2×C4×Dic22—21no—
51C2×C4×Dic22C2212yes—
52#10622845C2214yes—
53#10622707C2214yescomplemented
54#10622704C2214yescomplemented
55#10622703C2214yescomplemented
56#10622688C2214yescomplemented
57#10622676C2218yescomplemented
58#10622667C2218yescomplemented
59#10622665C2218yes—
60#10622664C2218yes—
61#10622655C2218yes—
62#10622654C2218yes—
63#10622644C2214yescomplemented
64#10622644C2214yescomplemented
65#10622634C2214yescomplemented
66#10622633C2214yescomplemented
67#10622632C2214yescomplemented
68#10622632C2214yescomplemented
69#10622621C2214yescomplemented
70#10622620C2214yescomplemented
71#10622617C2214yes—
72#10622608C2214yes—
73#10622537C2212yes—
74#10622537C2212yes—
75#10622537C2212yes—
76#10622537C2212yes—
77C2×C4⋊(C11⋊C8)C2212yes—
78C2×C4⋊(C11⋊C8)C2212yes—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41C2312yes—
82C23×C4×C11D411yescharacteristic
83C23×C4×C11D411yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×Dic22—21no—
86C22×Dic22C2312yes—
87C11×C4⋊Q8C2311yescharacteristic
88C11×C4⋊Q8C2311yescharacteristic
89C11×C4⋊Q8C2311yescharacteristic
90C11×#127C2311yescharacteristic
91C11×#126—22no—
92C11×#126—22no—
93C11×#125—21no—
94C11×#125—21no—
95C11×#125C2312yes—
96C11×#124—21no—
97C11×#124—21no—
98C11×#124C2312yes—
99C11×#123—22no—
100C11×#123—22no—
101C11×#123—22no—
102C11×C22⋊Q8—21no—
103C11×C22⋊Q8—21no—
104C11×C22⋊Q8—21no—
105C11×C22⋊Q8—21no—
106C11×C22⋊Q8C2312yes—
107C11×C22⋊Q8C2312yes—
108C11×#121—21no—
109C11×#121—21no—
110C11×#121—21no—
111C11×#121—21no—
112C11×#121C2312yes—
113C11×#121C2312yes—
114C11×#120—22no—
115C4×Q8×C11—21no—
116C4×Q8×C11—21no—
117C4×Q8×C11—21no—
118C4×Q8×C11—21no—
119C4×Q8×C11C2312yes—
120C4×Q8×C11C2312yes—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—21no—
128C4×D4×C11—21no—
129C4×D4×C11—21no—
130C4×D4×C11—21no—
131C4×D4×C11C2312yes—
132C4×D4×C11C2312yes—
133C11×#117—21no—
134C11×#117—21no—
135C11×#117—22no—
136C11×#117—22no—
137C11×#117—22no—
138C11×#117C2312yes—
139C2×C42×C11—22no—
140C2×C42×C11D411yescharacteristic
141C2×C42×C11D411yescharacteristic
142C2×C42×C11D411yescharacteristic
143C2×C42×C11D411yescharacteristic
144C2×C42×C11D411yescharacteristic
145C2×C42×C11D411yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C22⋊Dic11—22no—
153#67004—48no—
154C2×#4326C2318yes—
155C2×#4324C2318yes—
156#66979—22no—
157#66979—22no—
158#66979—22no—
159#66979—22no—
160C2×C4⋊Dic11—21no—
161C2×C4⋊Dic11—21no—
162C2×C4⋊Dic11—21no—
163C2×C4⋊Dic11C2312yes—
164#66977—22no—
165#66977—22no—
166#66977—22no—
167#66977—22no—
168#66977—22no—
169#66977—22no—
170#66977C2314yes—
171#66977C2314yes—
172C2×Dic11⋊C4—22no—
173C2×Dic11⋊C4—22no—
174C2×C4×Dic11—22no—
175C2×#4318—44no—
176C2×#4318C2314yes—
177C2×#4318C2314yes—
178C22×C11⋊C8C2314yes—
179#66923—22no—
180#66923—22no—
181#66923—22no—
182#66923—22no—
183#66922—21no—
184#66922—21no—
185#66922—21no—
186#66922—21no—
187#66922C2312yes—
188#66922C2312yes—
189#66922C2312yes—
190#66922C2312yes—
191C4×Dic22—22no—
192C4×Dic22—22no—
193C4×Dic22—22no—
194C4×Dic22—22no—
195C4×Dic22—22no—
196C4×Dic22—22no—
197C4×Dic22C2314yes—
198C4×Dic22C2314yes—
199#66899C2318yes—
200#66896C2318yes—
201#66874C2318yes—
202#66874C2318yes—
203#66872C2318yes—
204#66871C2318yes—
205C4⋊(C11⋊C8)C2314yes—
206C4⋊(C11⋊C8)C2314yes—
207C4⋊(C11⋊C8)C2314yes—
208C4⋊(C11⋊C8)C2314yes—
209#60918—111nomaximal, Sylow
210C24×C11C2×D411yescharacteristic
211C11×#41—24no—
212C11×#41—24no—
213C11×#41—44no—
214C11×#41—44no—
215C2×Q8×C11—21no—
216C2×Q8×C11—21no—
217C2×Q8×C11C2412yes—
218C2×D4×C11—22no—
219C2×D4×C11—22no—
220C2×D4×C11—22no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11C2412yes—
224C22×C4×C11—24no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—42no—
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×Dic11—22no—
250C22×Dic11—22no—
251C2×Dic22—22no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22—24no—
255C2×Dic22—24no—
256C2×Dic22—44no—
257C2×Dic22C2414yes—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—22no—
263C11×C4⋊C4—22no—
264C11×C4⋊C4—22no—
265C11×C4⋊C4—22no—
266C11×C4⋊C4—22no—
267C11×C4⋊C4—22no—
268C11×C4⋊C4C2412yes—
269C11×C4⋊C4C2412yes—
270C11×C22⋊C4—22no—
271C11×C22⋊C4—22no—
272C11×C22⋊C4—22no—
273C11×C22⋊C4—22no—
274C11×C22⋊C4—22no—
275C11×C22⋊C4—22no—
276C11×C22⋊C4—22no—
277C11×C22⋊C4—22no—
278C11×C22⋊C4—22no—
279C42×C11—22no—
280C42×C11—22no—
281C42×C11—22no—
282C42×C11C2×D411yescharacteristic
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D411yescharacteristic
292C42×C11C2×D411yescharacteristic
293C42×C11C2×D411yescharacteristic
294C42×C11C2411yescharacteristic
295C42×C11C2411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2411yescharacteristic
298C22⋊Dic11—24no—
299C22⋊Dic11—24no—
300#4326—48no—
301#4324—48no—
302C4⋊Dic11—22no—
303C4⋊Dic11—22no—
304C4⋊Dic11—22no—
305C4⋊Dic11—22no—
306C4⋊Dic11—22no—
307C4⋊Dic11—22no—
308C4⋊Dic11—22no—
309C4⋊Dic11C2414yes—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312Dic11⋊C4—24no—
313Dic11⋊C4—24no—
314C4×Dic11—24no—
315C4×Dic11—24no—
316#4318—28no—
317#4318—44no—
318C2×C11⋊C8—44no—
319C2×C11⋊C8C2418yes—
320#3444D1111yescharacteristic
321C2×#533—111no—
322#3255—112no—
323#3254—112no—
324#3252—114no—
325#3249—112no—
326#3248—114no—
327#3246—112no—
328#3079—112no—
329#3078—112no—
330#3056—114no—
331#3039—112no—
332#3037—112no—
333C2×#423—111no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—41no—
338C23×C11C22×D411yescharacteristic
339C23×C11C22×D411yescharacteristic
340C23×C11C22×D411yescharacteristic
341Q8×C11—22no—
342Q8×C11—22no—
343Q8×C11—42no—
344Q8×C11—42no—
345D4×C11—22no—
346D4×C11—22no—
347D4×C11—42no—
348D4×C11—44no—
349D4×C11—44no—
350D4×C11—44no—
351D4×C11—42no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11#13714yescomplemented
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11H(5,𝔽2)12yes—
389C2×C4×C112−1+412yes—
390C2×C4×C11C2511yescharacteristic
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—44no—
394C2×Dic11—44no—
395Dic22—24no—
396Dic22—24no—
397Dic22—44no—
398Dic22—44no—
399Dic22—44no—
400C11⋊C8—28no—
401C2×#137—114no—
402C22×M16—112no—
403#533—112no—
404#533—112no—
405#533—112no—
406#533—112no—
407#533—221no—
408#533—221no—
409#533—221no—
410#533—221no—
411#533C2×D1111yescharacteristic
412#533C2×D1111yescharacteristic
413#533C2×D1111yescharacteristic
414#532C2×D1111yescharacteristic
415#532C2×D1111yescharacteristic
416#532C2×D1111yescharacteristic
417C2×C4⋊Q8—111no—
418C2×C4⋊Q8—111no—
419#529—21no—
420#529—21no—
421#529—21no—
422#529—21no—
423#529C2×D1112yes—
424#529C2×D1112yes—
425C2×#125—221no—
426#525—21no—
427#525—21no—
428#525C2×D1112yes—
429C2×C22⋊Q8—112no—
430C2×C22⋊Q8—221no—
431C4×#41—21no—
432C4×#41—21no—
433C4×#41C2×D1112yes—
434C2×C4×Q8—112no—
435C2×C4×Q8—221no—
436C2×#117—221no—
437C22×C42C2×D1111yescharacteristic
438#479—118no—
439#477—114no—
440#477—114no—
441#476—114no—
442#475—114no—
443#475—114no—
444#474—114no—
445#470—118no—
446#468—118no—
447#467—118no—
448#465—118no—
449#464—118no—
450#462—114no—
451#462—114no—
452#462—114no—
453#461—114no—
454#461—114no—
455#460—114no—
456#428—114no—
457#423—112no—
458#423—112no—
459#423—112no—
460#423—112no—
461C2×C4⋊C8—112no—
462C2×C4⋊C8—112no—
463#419—114no—
464#417—114no—
465C22×C11—21no—
466C22×C11—21no—
467C22×C11—21no—
468C22×C11—21no—
469C22×C11—21no—
470C22×C11—21no—
471C22×C11—21no—
472C22×C11—44no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11#53712yes—
477C22×C11C2×#13712yes—
478C22×C11C23×D411yescharacteristic
479C4×C11—21no—
480C4×C11—21no—
481C4×C11—21no—
482C4×C11—21no—
483C4×C11—21no—
484C4×C11—21no—
485C4×C11—21no—
486C4×C11—42no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11#53712yes—
490C4×C11C2×#13712yes—
491C4×C11C2×#13712yes—
492C4×C11#57512yes—
493C4×C11C2×H(5,𝔽2)11yescharacteristic
494C4×C11C2×2−1+411yescharacteristic
495Dic11—44no—
496Dic11—44no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41C22×D1112yes—
500C22×Q8—112no—
501C22×Q8—221no—
502C23×C4C22⋊D1111yescharacteristic
503C23×C4C22⋊D1111yescharacteristic
504C23×C4C22×D1111yescharacteristic
505#137—448no—
506C2×Q16—118no—
507C2×SD16—118no—
508C2×M16—114no—
509C2×M16—114no—
510C2×M16—444no—
511C22×C8—114no—
512C4⋊Q8—112no—
513C4⋊Q8—112no—
514C4⋊Q8—112no—
515C4⋊Q8—112no—
516C4⋊Q8—221no—
517C4⋊Q8—221no—
518C4⋊Q8—221no—
519C4⋊Q8—221no—
520C4⋊Q8C22×D1111yescharacteristic
521C4⋊Q8C22×D1111yescharacteristic
522C4⋊Q8C22×D1111yescharacteristic
523#127C22×D1111yescharacteristic
524#126—22no—
525#126—22no—
526#125—21no—
527#125—21no—
528#125—222no—
529#125—222no—
530#125—222no—
531#125—222no—
532#125C22×D1112yes—
533#124—21no—
534#124—21no—
535#124C22×D1112yes—
536#123—22no—
537#123—22no—
538#123—22no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—114no—
544C22⋊Q8—114no—
545C22⋊Q8—222no—
546C22⋊Q8—222no—
547C22⋊Q8—222no—
548C22⋊Q8—222no—
549C22⋊Q8—222no—
550C22⋊Q8—222no—
551C22⋊Q8C22×D1112yes—
552C22⋊Q8C22×D1112yes—
553#121—21no—
554#121—21no—
555#121—21no—
556#121—21no—
557#121C22×D1112yes—
558#121C22×D1112yes—
559#120—22no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—21no—
563C4×Q8—21no—
564C4×Q8—114no—
565C4×Q8—114no—
566C4×Q8—222no—
567C4×Q8—222no—
568C4×Q8—222no—
569C4×Q8—222no—
570C4×Q8—222no—
571C4×Q8—222no—
572C4×Q8C22×D1112yes—
573C4×Q8C22×D1112yes—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4C22×D1112yes—
585C4×D4C22×D1112yes—
586#117—21no—
587#117—21no—
588#117—22no—
589#117—22no—
590#117—22no—
591#117—222no—
592#117—222no—
593#117—222no—
594#117—222no—
595#117C22×D1112yes—
596C2×C4⋊C4—112no—
597C2×C4⋊C4—221no—
598C2×C4⋊C4—221no—
599C2×C4⋊C4—222no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—221no—
602C2×C22⋊C4—222no—
603C2×C42—22no—
604C2×C42—222no—
605C2×C42C22⋊D1111yescharacteristic
606C2×C42C22⋊D1111yescharacteristic
607C2×C42C22⋊D1111yescharacteristic
608C2×C42C22⋊D1111yescharacteristic
609C2×C42C22⋊D1111yescharacteristic
610C2×C42C22⋊D1111yescharacteristic
611C2×C42C22×D1111yescharacteristic
612C2×C42C22×D1111yescharacteristic
613C2×C42C22×D1111yescharacteristic
614C2×C42C22×D1111yescharacteristic
615C2×C42C22×D1111yescharacteristic
616C2×C42C22×D1111yescharacteristic
617#107—118no—
618#106—118no—
619C4⋊C8—114no—
620C4⋊C8—114no—
621C4⋊C8—114no—
622C4⋊C8—114no—
623#103—118no—
624#103—118no—
625#103—118no—
626#102—118no—
627C2×C11—22no—
628C2×C11—22no—
629C2×C11—41no—
630C2×C11—82no—
631C2×C11C2×#53711yescharacteristic
632C2×C11C22×#13711yescharacteristic
633C2×C11C2×#57511yescharacteristic
634C24C2×C22⋊D1111yescharacteristic
635#41—24no—
636#41—24no—
637#41—44no—
638#41—44no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—114no—
642C2×Q8—222no—
643C2×Q8—222no—
644C2×Q8—222no—
645C2×Q8—224no—
646C2×Q8—224no—
647C2×Q8—444no—
648C2×Q8C23×D1112yes—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4C23×D1112yes—
655C22×C4—24no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—42no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4C2×C22⋊D1111yescharacteristic
665C22×C4C2×C22⋊D1111yescharacteristic
666C22×C4C2×C22⋊D1111yescharacteristic
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1111yescharacteristic
669C22×C4C2×C22⋊D1111yescharacteristic
670C22×C4C2×C22⋊D1111yescharacteristic
671C22×C4C2×C22⋊D1111yescharacteristic
672C22×C4C2×C22⋊D1111yescharacteristic
673C22×C4C2×C22⋊D1111yescharacteristic
674C22×C4C2×C22⋊D1111yescharacteristic
675C22×C4C2×C22⋊D1111yescharacteristic
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C23×D1111yescharacteristic
680C22×C4C23×D1111yescharacteristic
681C22×C4C23×D1111yescharacteristic
682Q16—448no—
683SD16—448no—
684M16—228no—
685M16—444no—
686C2×C8—118no—
687C2×C8—444no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—114no—
699C4⋊C4—222no—
700C4⋊C4—222no—
701C4⋊C4—222no—
702C4⋊C4—222no—
703C4⋊C4—222no—
704C4⋊C4—224no—
705C4⋊C4—224no—
706C4⋊C4—224no—
707C4⋊C4—224no—
708C4⋊C4—222no—
709C4⋊C4—222no—
710C4⋊C4C23×D1112yes—
711C4⋊C4C23×D1112yes—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—224no—
722C22⋊C4—224no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—224no—
727C42—224no—
728C42C2×C22⋊D1111yescharacteristic
729C42C2×C22⋊D1111yescharacteristic
730C42C2×C22⋊D1111yescharacteristic
731C42C2×C22⋊D1111yescharacteristic
732C42C2×C22⋊D1111yescharacteristic
733C42C2×C22⋊D1111yescharacteristic
734C42C2×C22⋊D1111yescharacteristic
735C42C2×C22⋊D1111yescharacteristic
736C42C2×C22⋊D1111yescharacteristic
737C42C2×C22⋊D1111yescharacteristic
738C42C2×C22⋊D1111yescharacteristic
739C42C2×C22⋊D1111yescharacteristic
740C42C23×D1111yescharacteristic
741C42C23×D1111yescharacteristic
742C42C23×D1111yescharacteristic
743C42C23×D1111yescharacteristic
744C11#6091811yescharacteristic, complemented, Sylow
745C23—22no—
746C23—22no—
747C23—22no—
748C23—41no—
749C23C22×C22⋊D1111yescharacteristic
750C23C22×C22⋊D1111yescharacteristic
751C23C22×C22⋊D1111yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—42no—
755Q8—42no—
756Q8—224no—
757Q8—224no—
758Q8—444no—
759Q8—444no—
760Q8—444no—
761D4—22no—
762D4—22no—
763D4—42no—
764D4—44no—
765D4—44no—
766D4—44no—
767D4—42no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—224no—
793C2×C4—224no—
794C2×C4—444no—
795C2×C4—444no—
796C2×C4#6700414yescomplemented
797C2×C4#6704212yes—
798C2×C4#6704312yes—
799C2×C4C22×C22⋊D1111yescharacteristic
800C2×C4C22×C22⋊D1111yescharacteristic
801C2×C4C22×C22⋊D1111yescharacteristic
802C2×C4C22×C22⋊D1111yescharacteristic
803C2×C4C22×C22⋊D1111yescharacteristic
804C2×C4C22×C22⋊D1111yescharacteristic
805C2×C4C22×C22⋊D1111yescharacteristic
806C2×C4C22×C22⋊D1111yescharacteristic
807C2×C4C22×C22⋊D1111yescharacteristic
808C2×C4C22×C22⋊D1111yescharacteristic
809C2×C4C22×C22⋊D1111yescharacteristic
810C2×C4C24×D1111yescharacteristic
811C8—228no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—44no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22C2×#6700412yes—
824C22#1062336412yes—
825C22C23×C22⋊D1111yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—444no—
837C4—444no—
838C4#1062335312yes—
839C4C2×#6700412yes—
840C4C2×#6700412yes—
841C4#1062336412yes—
842C4C2×#6704211yescharacteristic
843C4C2×#6704311yescharacteristic
844C2—22no—
845C2—22no—
846C2—41no—
847C2—82no—
848C2C2×#1062336411yescharacteristic
849C2C22×#6700411yescharacteristic
850C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3444C2
socleC22×C11C23×D4
hypercenter#3444D11
hypocenterC11#60918
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. #13080007C2semidirect
3. #13080003C2semidirect
4. #13079989C2semidirect
5. #13079958C2semidirect
6. #13079953C2semidirect
7. #13079932C2semidirect
8. #13078431C2semidirect
9. #13078417C2semidirect
10. #13078248C2semidirect
11. #13078103C2semidirect
12. #13078084C2semidirect
13. C2×#10622537C2semidirect
53. #10622707C22semidirect
54. #10622704C22semidirect
55. #10622703C22semidirect
56. #10622688C22semidirect
57. #10622676C22semidirect
58. #10622667C22semidirect
63. #10622644C22semidirect
64. #10622644C22semidirect
65. #10622634C22semidirect
66. #10622633C22semidirect
67. #10622632C22semidirect
68. #10622632C22semidirect
69. #10622621C22semidirect
70. #10622620C22semidirect
376. C2×C4×C11#137semidirect
744. C11#60918semidirect
796. C2×C4#67004semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130800072
#130800032
#130799892
#130799582
#130799532
#130799322
#130784312
#130784172
#130782482
#130781032
#130780842
C2×#106225372
C11×#34442
#6091811