Finite Group Databasebeta

← #15634385

Subgroups — #15634385

Order 2816.

1750 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2#13081579C214yesmaximal, complemented
3#13081561C214yesmaximal, complemented
4#13081544C212yesmaximal, complemented
5#13081537C212yesmaximal, complemented
6#13081503C212yesmaximal, complemented
7#13081491C212yesmaximal, complemented
8#13079169C212yesmaximal, complemented
9#13079163C211yesmaximal, characteristic, complemented
10#13078438C212yesmaximal
11#13078431C211yesmaximal, characteristic
12#13078417C211yesmaximal, characteristic, complemented
13#13078417C212yesmaximal, complemented
14Q8×#4318C211yesmaximal, characteristic, complemented
15C4×#67004C211yesmaximal, characteristic
16C4×#67004C212yesmaximal
17Q8×C11×#41C211yesmaximal, characteristic
18Q82×C11C2211yescharacteristic
19C11×#557C2211yescharacteristic
20C11×#557C2212yes—
21C11×#554—21no—
22C11×#554—22no—
23C11×#554C2211yescharacteristic
24C11×#554C2212yes—
25D4×Q8×C11—21no—
26D4×Q8×C11C2211yescharacteristic
27C11×#533—21no—
28C11×#533—22no—
29C11×#533C2211yescharacteristic
30C11×#533C2212yes—
31C4×C11×#41C2211yescharacteristic
32C4×C11×#41C2212yes—
33C2×C4×Q8×C11—21no—
34C2×C4×Q8×C11C2211yescharacteristic
35C2×#67004C2211yescharacteristic
36C2×#66997—21no—
37#10623098—21no—
38#10623098—22no—
39#10623098—21no—
40#10623098C2212yes—
41#10623098C2212yes—
42#10623098C2214yes—
43C2×#66942—22no—
44C2×#66940—21no—
45C2×#66923C2212yes—
46C2×#66922C2211yescharacteristic
47C2×C4×Dic22C2212yes—
48C2×C4×Dic22C2211yescharacteristic
49#10622845C2212yes—
50#10622845C2211yescharacteristic
51#10622707C2212yes—
52#10622707C2214yes—
53#10622704C2212yes—
54#10622704C2214yes—
55#10622693C2214yes—
56#10622693C2214yes—
57#10622692C2212yes—
58#10622691C2212yes—
59#10622678C2214yes—
60#10622677C2214yes—
61#10622677C2214yes—
62#10622676C2214yes—
63#10622676C2214yes—
64#10622676C2214yes—
65#10622643C2214yes—
66#10622643C2212yes—
67C4×#4326C2212yes—
68C4×#4326C2214yes—
69#10622637C2212yes—
70#10622637C2214yes—
71Q8×C11⋊C8C2212yes—
72#10622635C2214yes—
73#10622635C2214yes—
74#10622634C2212yes—
75#10622633C2212yes—
76#10622631C2214yes—
77#10622631C2212yes—
78C4×#4324C2212yes—
79C4×#4324C2214yes—
80#10622622C2214yes—
81#10622622C2214yes—
82#10622621C2212yes—
83#10622620C2212yes—
84#10622617C2211yescharacteristic
85#10622617C2212yes—
86#10622608C2212yes—
87#10622608C2212yes—
88#10622608C2211yescharacteristic
89#10622608C2212yes—
90#10622608C2212yes—
91#10622537C2211yescharacteristic
92#10622537C2212yes—
93C4×#4318C2211yescharacteristic
94C4×#4318C2212yes—
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11—21no—
97C22×Q8×C11D411yescharacteristic
98C22×Dic22—21no—
99C22×Dic22C2311yescharacteristic
100C11×C4⋊Q8—21no—
101C11×C4⋊Q8—22no—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8—22no—
104C11×C4⋊Q8C2311yescharacteristic
105C11×C4⋊Q8C2312yes—
106C11×C4⋊Q8C2311yescharacteristic
107C11×C4⋊Q8C2312yes—
108C11×#125—22no—
109C11×#125—22no—
110C11×#125—22no—
111C11×#125C2312yes—
112C11×#125C2312yes—
113C11×#125C2312yes—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8—22no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8—22no—
125C4×Q8×C11—21no—
126C4×Q8×C11—21no—
127C4×Q8×C11—22no—
128C4×Q8×C11—21no—
129C4×Q8×C11—22no—
130C4×Q8×C11—21no—
131C4×Q8×C11—22no—
132C4×Q8×C11D411yescharacteristic
133C4×Q8×C11D411yescharacteristic
134C4×Q8×C11D412yes—
135C4×Q8×C11C2311yescharacteristic
136C4×Q8×C11C2311yescharacteristic
137C4×Q8×C11C2312yes—
138C4×Q8×C11C2312yes—
139C4×Q8×C11C2311yescharacteristic
140C4×Q8×C11C2311yescharacteristic
141C4×Q8×C11C2312yes—
142C4×D4×C11—21no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11—21no—
146C4×D4×C11C2311yescharacteristic
147C4×D4×C11C2311yescharacteristic
148C4×D4×C11C2312yes—
149C4×D4×C11C2312yes—
150C11×#117—21no—
151C11×#117—22no—
152C11×#117C2312yes—
153C11×#117C2311yescharacteristic
154C2×C11×C4⋊C4—21no—
155C2×C11×C4⋊C4—22no—
156C2×C11×C4⋊C4D411yescharacteristic
157C2×C11×C4⋊C4D412yes—
158C2×C42×C11—21no—
159C2×C42×C11—22no—
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2312yes—
162#67004Q818yescomplemented
163#66997—22no—
164#66997—22no—
165#66997—24no—
166C2×#4326C2312yes—
167C2×#4324C2312yes—
168C2×C4⋊Dic11—21no—
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2311yescharacteristic
171C2×Dic11⋊C4—21no—
172C2×Dic11⋊C4—22no—
173C2×Dic11⋊C4—22no—
174C2×Dic11⋊C4—22no—
175C2×C4×Dic11—22no—
176C2×C4×Dic11—21no—
177C2×#4318C2311yescharacteristic
178C2×#4318C2312yes—
179C2×#4318C2311yescharacteristic
180#66942—24no—
181#66942—24no—
182#66942—24no—
183#66942—24no—
184#66940—22no—
185#66940—24no—
186#66940—22no—
187#66923—22no—
188#66923—22no—
189#66923C2314yes—
190#66923C2314yes—
191#66922—21no—
192#66922—21no—
193#66922C2312yes—
194#66922C2312yes—
195C4×Dic22—22no—
196C4×Dic22—22no—
197C4×Dic22—21no—
198C4×Dic22—21no—
199C4×Dic22C2314yes—
200C4×Dic22C2312yes—
201C4×Dic22C2312yes—
202C4×Dic22C2314yes—
203#66899C2314yes—
204#66899C2312yes—
205#66896C2314yes—
206#66896C2312yes—
207#66874C2312yes—
208#66874C2314yes—
209#66874C2314yes—
210#66874C2312yes—
211#66872C2314yes—
212#66872C2314yes—
213#66872C2314yes—
214#66872C2312yes—
215#66872C2314yes—
216#66871C2314yes—
217#66871C2314yes—
218#66871C2314yes—
219#66871C2312yes—
220#66871C2314yes—
221C4⋊(C11⋊C8)C2312yes—
222C4⋊(C11⋊C8)C2312yes—
223C4⋊(C11⋊C8)C2314yes—
224C4⋊(C11⋊C8)C2314yes—
225#66867C2312yes—
226#66867C2314yes—
227C4×C11⋊C8C2314yes—
228C4×C11⋊C8C2312yes—
229#61369—111nomaximal, Sylow
230C11×#41—22no—
231C11×#41C2×Q814yes—
232C2×Q8×C11—22no—
233C2×Q8×C11—21no—
234C2×Q8×C11—22no—
235C2×Q8×C11—21no—
236C2×Q8×C11—42no—
237C2×Q8×C11—44no—
238C2×Q8×C11C2×D411yescharacteristic
239C2×Q8×C11C2×D411yescharacteristic
240C2×Q8×C11C2×D412yes—
241C2×Q8×C11C2411yescharacteristic
242C2×D4×C11—21no—
243C2×D4×C11C2411yescharacteristic
244C22×C4×C11—21no—
245C22×C4×C11—22no—
246C22×C4×C11—21no—
247C22×C4×C11—22no—
248C22×C4×C11—21no—
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D412yes—
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—22no—
257C2×Dic22—21no—
258C2×Dic22—22no—
259C2×Dic22—22no—
260C2×Dic22—22no—
261C2×Dic22—44no—
262C2×Dic22C2×Q814yescomplemented
263C2×Dic22C2412yes—
264C11×C4⋊C4—22no—
265C11×C4⋊C4—22no—
266C11×C4⋊C4—22no—
267C11×C4⋊C4—22no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—22no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4C2×D411yescharacteristic
279C11×C4⋊C4C2×D412yes—
280C11×C4⋊C4C2×D411yescharacteristic
281C11×C4⋊C4C2×D412yes—
282C11×C4⋊C4C2×D412yes—
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2×D412yes—
285C11×C4⋊C4C2411yescharacteristic
286C11×C4⋊C4C2412yes—
287C11×C4⋊C4C2412yes—
288C11×C4⋊C4C2411yescharacteristic
289C11×C22⋊C4—22no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—21no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—21no—
295C42×C11—21no—
296C42×C11—22no—
297C42×C11—22no—
298C42×C11—21no—
299C42×C11—22no—
300C42×C11—21no—
301C42×C11C2×D411yescharacteristic
302C42×C11C2×D411yescharacteristic
303C42×C11C2×D412yes—
304C42×C11C2×D412yes—
305C42×C11C2411yescharacteristic
306C42×C11C2412yes—
307C42×C11C2411yescharacteristic
308C42×C11C2412yes—
309#4326C2×Q818yescomplemented
310#4324C2×Q818yescomplemented
311C4⋊Dic11—22no—
312C4⋊Dic11—21no—
313C4⋊Dic11—22no—
314C4⋊Dic11—22no—
315C4⋊Dic11C2414yes—
316C4⋊Dic11C2412yes—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—24no—
320Dic11⋊C4—24no—
321Dic11⋊C4—24no—
322Dic11⋊C4—24no—
323Dic11⋊C4—24no—
324Dic11⋊C4—24no—
325C4×Dic11—24no—
326C4×Dic11—24no—
327C4×Dic11—22no—
328C4×Dic11—22no—
329#4318—22no—
330#4318—24no—
331#4318C2×Q814yescomplemented
332C2×C11⋊C8C2414yes—
333C2×C11⋊C8C2412yes—
334C2×C11⋊C8C2412yes—
335Q8×#41D1111yescharacteristic
336C2×#557—111no—
337#3390—114no—
338#3388—114no—
339#3387—112no—
340#3386—112no—
341#3383—112no—
342#3381—112no—
343#3166—112no—
344#3165—111no—
345#3080—112no—
346#3079—111no—
347#3078—111no—
348#3078—112no—
349Q8×M16—111no—
350C4×#137—111no—
351C4×#137—112no—
352C23×C11—21no—
353C23×C11C22×D411yescharacteristic
354Q8×C11—22no—
355Q8×C11—22no—
356Q8×C11—21no—
357Q8×C11—42no—
358Q8×C11—44no—
359Q8×C11—42no—
360Q8×C11—82no—
361Q8×C11—81no—
362Q8×C11C22×Q812yes—
363D4×C11—24no—
364D4×C11—21no—
365D4×C11C22×Q812yes—
366C2×C4×C11—21no—
367C2×C4×C11—24no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—21no—
371C2×C4×C11—22no—
372C2×C4×C11—21no—
373C2×C4×C11—42no—
374C2×C4×C11—41no—
375C2×C4×C11—42no—
376C2×C4×C11—44no—
377C2×C4×C11—42no—
378C2×C4×C11—82no—
379C2×C4×C11—81no—
380C2×C4×C11C22×D412yes—
381C2×C4×C11C22×D412yes—
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D412yes—
384C2×C4×C11C22×D412yes—
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×Q812yes—
390C2×C4×C112−1+412yes—
391C2×C4×C11C2511yescharacteristic
392C2×Dic11—24no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—24no—
396C2×Dic11—44no—
397C2×Dic11—42no—
398Dic22—24no—
399Dic22—22no—
400Dic22—44no—
401Dic22—44no—
402Dic22C22×Q814yes—
403C11⋊C8—24no—
404C11⋊C8—22no—
405C11⋊C8C22×Q814yes—
406C2×#137—111no—
407Q82C2×D1111yescharacteristic
408#557—112no—
409#557—112no—
410#557—114no—
411#557—221no—
412#557—222no—
413#557—221no—
414#557C2×D1111yescharacteristic
415#557C2×D1112yes—
416#554—21no—
417#554—22no—
418#554C2×D1111yescharacteristic
419#554C2×D1112yes—
420D4×Q8—21no—
421D4×Q8C2×D1111yescharacteristic
422#533—22no—
423#533—21no—
424#533C2×D1111yescharacteristic
425#533C2×D1112yes—
426C2×C4⋊Q8—111no—
427C2×C4⋊Q8—221no—
428C2×#125—112no—
429C2×#125—222no—
430C4×#41C2×D1111yescharacteristic
431C4×#41C2×D1112yes—
432C2×C4×Q8—21no—
433C2×C4×Q8—112no—
434C2×C4×Q8—111no—
435C2×C4×Q8—221no—
436C2×C4×Q8C2×D1111yescharacteristic
437#501—114no—
438#501—114no—
439#501—114no—
440#500—112no—
441#499—114no—
442#499—114no—
443#498—112no—
444#479—114no—
445#479—114no—
446#479—114no—
447#479—114no—
448#479—114no—
449#478—114no—
450#478—114no—
451#477—112no—
452#477—114no—
453#477—112no—
454#476—112no—
455#475—112no—
456#475—114no—
457#475—112no—
458#474—112no—
459#446—112no—
460#446—114no—
461C8×Q8—112no—
462#441—114no—
463#441—112no—
464#440—114no—
465#440—112no—
466C4×Q16—112no—
467C4×Q16—114no—
468C4×SD16—112no—
469C4×SD16—114no—
470#428—112no—
471#428—112no—
472#428—112no—
473#428—112no—
474#428—111no—
475#423—111no—
476#423—112no—
477#419—112no—
478#419—111no—
479#417—112no—
480#417—111no—
481C4×M16—111no—
482C4×M16—112no—
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—22no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11D4×Q812yes—
489C22×C11C23×D411yescharacteristic
490C4×C11—22no—
491C4×C11—21no—
492C4×C11—22no—
493C4×C11—21no—
494C4×C11—22no—
495C4×C11—21no—
496C4×C11—22no—
497C4×C11—22no—
498C4×C11—42no—
499C4×C11—41no—
500C4×C11—42no—
501C4×C11—41no—
502C4×C11D4×Q812yes—
503C4×C11#57512yes—
504C4×C11C23×Q811yescharacteristic
505C4×C11C2×2−1+411yescharacteristic
506Dic11—24no—
507Dic11—42no—
508Dic11—44no—
509C2×#41C22×D1111yescharacteristic
510C22×Q8—21no—
511C22×Q8—111no—
512C22×Q8—221no—
513C22×Q8C22⋊D1111yescharacteristic
514#137—118no—
515C2×Q16—112no—
516C2×SD16—112no—
517C2×M16—111no—
518C2×M16—111no—
519C2×M16—112no—
520C4⋊Q8—21no—
521C4⋊Q8—22no—
522C4⋊Q8—21no—
523C4⋊Q8—22no—
524C4⋊Q8—112no—
525C4⋊Q8—112no—
526C4⋊Q8—222no—
527C4⋊Q8—222no—
528C4⋊Q8—224no—
529C4⋊Q8—221no—
530C4⋊Q8—221no—
531C4⋊Q8C22×D1111yescharacteristic
532C4⋊Q8C22×D1112yes—
533C4⋊Q8C22×D1112yes—
534C4⋊Q8C22×D1111yescharacteristic
535#125—22no—
536#125—22no—
537#125—22no—
538#125—114no—
539#125—114no—
540#125—224no—
541#125—224no—
542#125—224no—
543#125—224no—
544#125—222no—
545#125—222no—
546#125C22×D1112yes—
547#125C22×D1112yes—
548#125C22×D1112yes—
549C22⋊Q8—21no—
550C22⋊Q8—22no—
551C22⋊Q8—21no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—21no—
565C4×Q8—22no—
566C4×Q8—21no—
567C4×Q8—112no—
568C4×Q8—114no—
569C4×Q8—114no—
570C4×Q8—112no—
571C4×Q8—222no—
572C4×Q8—224no—
573C4×Q8—222no—
574C4×Q8—222no—
575C4×Q8—222no—
576C4×Q8—221no—
577C4×Q8—221no—
578C4×Q8C22⋊D1111yescharacteristic
579C4×Q8C22⋊D1112yes—
580C4×Q8C22⋊D1111yescharacteristic
581C4×Q8C22×D1112yes—
582C4×Q8C22×D1111yescharacteristic
583C4×Q8C22×D1111yescharacteristic
584C4×Q8C22×D1112yes—
585C4×Q8C22×D1111yescharacteristic
586C4×Q8C22×D1111yescharacteristic
587C4×Q8C22×D1112yes—
588C4×D4—21no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—21no—
592C4×D4C22×D1111yescharacteristic
593C4×D4C22×D1112yes—
594C4×D4C22×D1112yes—
595C4×D4C22×D1111yescharacteristic
596#117—22no—
597#117—21no—
598#117C22×D1111yescharacteristic
599#117C22×D1112yes—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—111no—
603C2×C4⋊C4—112no—
604C2×C4⋊C4—221no—
605C2×C4⋊C4—222no—
606C2×C4⋊C4—222no—
607C2×C4⋊C4—222no—
608C2×C4⋊C4—221no—
609C2×C4⋊C4C22⋊D1111yescharacteristic
610C2×C4⋊C4C22⋊D1112yes—
611C2×C42—22no—
612C2×C42—21no—
613C2×C42—222no—
614C2×C42—221no—
615C2×C42C22×D1112yes—
616C2×C42C22×D1111yescharacteristic
617#107—112no—
618#107—114no—
619#107—114no—
620#107—114no—
621#107—114no—
622#106—114no—
623#106—112no—
624#106—114no—
625#106—114no—
626#106—114no—
627C4⋊C8—112no—
628C4⋊C8—114no—
629C4⋊C8—114no—
630C4⋊C8—112no—
631#103—114no—
632#103—112no—
633#103—114no—
634#103—112no—
635#103—112no—
636#103—114no—
637#102—114no—
638#102—112no—
639#97—114no—
640#97—112no—
641C4×C8—112no—
642C4×C8—114no—
643C2×C11—22no—
644C2×C11—42no—
645C2×C11C2×D4×Q811yescharacteristic
646C2×C11C2×#57511yescharacteristic
647C2×C11#358611yescharacteristic
648#41—22no—
649#41Q8×D1114yes—
650C2×Q8—22no—
651C2×Q8—21no—
652C2×Q8—22no—
653C2×Q8—21no—
654C2×Q8—42no—
655C2×Q8—44no—
656C2×Q8—114no—
657C2×Q8—112no—
658C2×Q8—222no—
659C2×Q8—221no—
660C2×Q8—222no—
661C2×Q8—222no—
662C2×Q8—444no—
663C2×Q8C2×C22⋊D1111yescharacteristic
664C2×Q8C2×C22⋊D1111yescharacteristic
665C2×Q8C2×C22⋊D1112yes—
666C2×Q8C23×D1111yescharacteristic
667C2×D4—21no—
668C2×D4C23×D1111yescharacteristic
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—21no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—222no—
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1112yes—
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1112yes—
681C22×C4C23×D1111yescharacteristic
682Q16—118no—
683SD16—118no—
684M16—114no—
685M16—222no—
686M16—224no—
687C2×C8—112no—
688C2×C8—112no—
689C2×C8—114no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—21no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—112no—
705C4⋊C4—114no—
706C4⋊C4—221no—
707C4⋊C4—222no—
708C4⋊C4—222no—
709C4⋊C4—222no—
710C4⋊C4—224no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—224no—
714C4⋊C4—224no—
715C4⋊C4—224no—
716C4⋊C4—222no—
717C4⋊C4—222no—
718C4⋊C4C2×C22⋊D1111yescharacteristic
719C4⋊C4C2×C22⋊D1112yes—
720C4⋊C4C2×C22⋊D1112yes—
721C4⋊C4C2×C22⋊D1111yescharacteristic
722C4⋊C4C2×C22⋊D1112yes—
723C4⋊C4C2×C22⋊D1112yes—
724C4⋊C4C2×C22⋊D1112yes—
725C4⋊C4C23×D1112yes—
726C4⋊C4C23×D1111yescharacteristic
727C4⋊C4C23×D1111yescharacteristic
728C4⋊C4C23×D1112yes—
729C22⋊C4—21no—
730C22⋊C4—22no—
731C22⋊C4—21no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—21no—
735C42—22no—
736C42—21no—
737C42—22no—
738C42—21no—
739C42—22no—
740C42—21no—
741C42—224no—
742C42—224no—
743C42—222no—
744C42—222no—
745C42C2×C22⋊D1112yes—
746C42C2×C22⋊D1111yescharacteristic
747C42C2×C22⋊D1112yes—
748C42C2×C22⋊D1111yescharacteristic
749C42C23×D1112yes—
750C42C23×D1111yescharacteristic
751C42C23×D1112yes—
752C42C23×D1111yescharacteristic
753C11#6136911yescharacteristic, complemented, Sylow
754C23—21no—
755C23C22×C22⋊D1111yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—21no—
759Q8—42no—
760Q8—44no—
761Q8—42no—
762Q8—82no—
763Q8—81no—
764Q8—114no—
765Q8—224no—
766Q8—222no—
767Q8—444no—
768Q8—444no—
769Q8C2×Q8×D1112yes—
770D4—24no—
771D4—21no—
772D4C2×Q8×D1112yes—
773C2×C4—21no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—82no—
786C2×C4—81no—
787C2×C4—224no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—224no—
791C2×C4—444no—
792C2×C4—442no—
793C2×C4C2×Q8×D1112yes—
794C2×C4#6704012yes—
795C2×C4C22×C22⋊D1112yes—
796C2×C4C22×C22⋊D1111yescharacteristic
797C2×C4C22×C22⋊D1112yes—
798C2×C4C22×C22⋊D1111yescharacteristic
799C2×C4C22×C22⋊D1112yes—
800C2×C4C22×C22⋊D1112yes—
801C2×C4C22×C22⋊D1111yescharacteristic
802C2×C4C22×C22⋊D1111yescharacteristic
803C2×C4C22×C22⋊D1111yescharacteristic
804C2×C4C24×D1111yescharacteristic
805C8—114no—
806C8—222no—
807C8—224no—
808C22—21no—
809C22—21no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22Q8×C22⋊D1112yes—
814C22C23×C22⋊D1111yescharacteristic
815C4—22no—
816C4—21no—
817C4—22no—
818C4—21no—
819C4—21no—
820C4—22no—
821C4—22no—
822C4—22no—
823C4—42no—
824C4—41no—
825C4—42no—
826C4—41no—
827C4—224no—
828C4—442no—
829C4—444no—
830C4Q8×C22⋊D1112yes—
831C4#1062335312yes—
832C4C22×Q8×D1111yescharacteristic
833C4C2×#6704011yescharacteristic
834C2—22no—
835C2—42no—
836C2C2×Q8×C22⋊D1111yescharacteristic
837C2C2×#1062335311yescharacteristic
838C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingQ8×C11×#41C2
socleC22×C11C23×D4
prime radicalC2×C11×#41C23
hypercenterQ8×#41D11
hypocenterC11#61369
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
2. #13081579C2semidirect
3. #13081561C2semidirect
4. #13081544C2semidirect
5. #13081537C2semidirect
6. #13081503C2semidirect
7. #13081491C2semidirect
8. #13079169C2semidirect
9. #13079163C2semidirect
12. #13078417C2semidirect
13. #13078417C2semidirect
14. Q8×#4318C2semidirect
162. #67004Q8semidirect
262. C2×Dic22C2×Q8semidirect
309. #4326C2×Q8semidirect
310. #4324C2×Q8semidirect
331. #4318C2×Q8semidirect
753. C11#61369semidirect

Maximal subgroups

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

subgroupindex
C2×#106230982
#130815792
#130815612
#130815442
#130815372
#130815032
#130814912
#130791692
#130791632
#130784382
#130784312
#130784172
Q8×#43182
C4×#670042
Q8×C11×#412
#6136911