Finite Group Databasebeta

← #15634357

Subgroups — #15634357

Order 2816.

1826 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic, complemented
2#13081570C214yesmaximal, complemented
3#13081555C214yesmaximal, complemented
4#13081522C212yesmaximal, complemented
5#13081511C212yesmaximal, complemented
6#13081487C212yesmaximal, complemented
7#13081479C212yesmaximal, complemented
8#13079169C212yesmaximal, complemented
9#13079163C211yesmaximal, characteristic, complemented
10#13078438C212yesmaximal, complemented
11#13078431C211yesmaximal, characteristic, complemented
12#13078409C211yesmaximal, characteristic, complemented
13#13078409C212yesmaximal, complemented
14Q8×#4318C211yesmaximal, characteristic, complemented
15C4×#67002C211yesmaximal, characteristic
16C4×#67002C212yesmaximal
17Q8×C11×#41C211yesmaximal, characteristic, complemented
18Q82×C11C2211yescharacteristic, complemented
19C11×#557C2211yescharacteristic, complemented
20C11×#557C2212yescomplemented
21C11×#554—21no—
22C11×#554—22no—
23C11×#554C2211yescharacteristic, complemented
24C11×#554C2212yescomplemented
25D4×Q8×C11—21no—
26D4×Q8×C11C2211yescharacteristic, complemented
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×#67002C2211yescharacteristic
36C2×#66999—21no—
37#10623110—21no—
38#10623110—21no—
39#10623110—22no—
40#10623110C2212yes—
41#10623110C2212yes—
42#10623110C2214yes—
43C2×#66949—22no—
44C2×C4⋊C4×D11—21no—
45C2×C4×D44C2212yes—
46C2×C4×D44C2211yescharacteristic
47C2×#66923C2212yes—
48C2×#66922C2211yescharacteristic
49#10622845C2212yes—
50#10622845C2211yescharacteristic
51#10622700C2212yes—
52#10622700C2214yes—
53#10622697C2212yes—
54#10622697C2214yes—
55#10622693C2214yescomplemented
56#10622693C2214yescomplemented
57#10622692C2212yescomplemented
58#10622691C2212yescomplemented
59#10622679C2214yes—
60#10622679C2214yes—
61#10622679C2214yes—
62#10622678C2214yescomplemented
63#10622677C2214yescomplemented
64#10622677C2214yescomplemented
65#10622639C2214yes—
66#10622639C2212yes—
67C4×#4325C2212yes—
68C4×#4325C2214yes—
69#10622637C2212yescomplemented
70#10622637C2214yescomplemented
71Q8×C11⋊C8C2212yescomplemented
72#10622635C2214yescomplemented
73#10622635C2214yescomplemented
74#10622634C2212yescomplemented
75#10622633C2212yescomplemented
76#10622627C2214yes—
77#10622627C2212yes—
78C4×#4323C2212yes—
79C4×#4323C2214yes—
80#10622622C2214yescomplemented
81#10622622C2214yescomplemented
82#10622621C2212yescomplemented
83#10622620C2212yescomplemented
84#10622614C2211yescharacteristic
85#10622614C2212yes—
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×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11—22no—
101C22×Dic22—21no—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8—22no—
104C11×C4⋊Q8—21no—
105C11×C4⋊Q8—22no—
106C11×C4⋊Q8C2311yescharacteristic
107C11×C4⋊Q8C2312yes—
108C11×C4⋊Q8C2311yescharacteristic
109C11×C4⋊Q8C2312yes—
110C11×#125—22no—
111C11×#125—22no—
112C11×#125—22no—
113C11×#125C2312yes—
114C11×#125C2312yes—
115C11×#125C2312yes—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8—22no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8—22no—
126C11×C22⋊Q8—22no—
127C4×Q8×C11—21no—
128C4×Q8×C11—21no—
129C4×Q8×C11—22no—
130C4×Q8×C11—21no—
131C4×Q8×C11—22no—
132C4×Q8×C11—21no—
133C4×Q8×C11—22no—
134C4×Q8×C11D411yescharacteristic
135C4×Q8×C11D411yescharacteristic
136C4×Q8×C11D412yes—
137C4×Q8×C11C2311yescharacteristic
138C4×Q8×C11C2311yescharacteristic
139C4×Q8×C11C2312yes—
140C4×Q8×C11C2312yes—
141C4×Q8×C11C2311yescharacteristic
142C4×Q8×C11C2311yescharacteristic
143C4×Q8×C11C2312yes—
144C4×D4×C11—21no—
145C4×D4×C11—22no—
146C4×D4×C11—22no—
147C4×D4×C11—21no—
148C4×D4×C11C2311yescharacteristic
149C4×D4×C11C2311yescharacteristic
150C4×D4×C11C2312yes—
151C4×D4×C11C2312yes—
152C11×#117—21no—
153C11×#117—22no—
154C11×#117C2312yes—
155C11×#117C2311yescharacteristic
156C2×C11×C4⋊C4—21no—
157C2×C11×C4⋊C4—22no—
158C2×C11×C4⋊C4D411yescharacteristic
159C2×C11×C4⋊C4D412yes—
160C2×C42×C11—21no—
161C2×C42×C11—22no—
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2312yes—
164#67002Q818yescomplemented
165#66999—22no—
166#66999—22no—
167#66999—24no—
168C2×#4325C2312yes—
169C2×#4323C2312yes—
170C2×(C2×D11)⋊C4—21no—
171C2×(C2×D11)⋊C4—22no—
172C2×C4⋊Dic11—21no—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×Dic11⋊C4—22no—
176C2×Dic11⋊C4—22no—
177C2×#4318C2311yescharacteristic
178C2×#4318C2312yes—
179C2×#4318C2311yescharacteristic
180#66949—24no—
181#66949—24no—
182#66949—24no—
183#66949—24no—
184C4⋊C4×D11—22no—
185C4⋊C4×D11—24no—
186C4⋊C4×D11—22no—
187C4×D44—22no—
188C4×D44—22no—
189C4×D44—21no—
190C4×D44—21no—
191C4×D44C2314yes—
192C4×D44C2312yes—
193C4×D44C2312yes—
194C4×D44C2314yes—
195#66923—22no—
196#66923—22no—
197#66923C2314yes—
198#66923C2314yes—
199#66922—21no—
200#66922—21no—
201#66922C2312yes—
202#66922C2312yes—
203#66899C2314yes—
204#66899C2312yes—
205#66896C2314yes—
206#66896C2312yes—
207#66873C2312yes—
208#66873C2314yes—
209#66873C2314yes—
210#66873C2312yes—
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#61367—111nomaximal, Sylow
230C23×D11—21no—
231C11×#41—22no—
232C11×#41C2×Q814yes—
233C2×Q8×C11—22no—
234C2×Q8×C11—21no—
235C2×Q8×C11—22no—
236C2×Q8×C11—21no—
237C2×Q8×C11—42no—
238C2×Q8×C11—44no—
239C2×Q8×C11C2×D411yescharacteristic
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2×D412yes—
242C2×Q8×C11C2411yescharacteristic
243C2×D4×C11—21no—
244C2×D4×C11C2411yescharacteristic
245C22×C4×C11—21no—
246C22×C4×C11—22no—
247C22×C4×C11—21no—
248C22×C4×C11—22no—
249C22×C4×C11—21no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C22×Dic11—21no—
256C22×Dic11—22no—
257C2×D44—21no—
258C2×D44—22no—
259C2×D44C2×Q814yescomplemented
260C2×D44C2412yes—
261C2×C4×D11—22no—
262C2×C4×D11—22no—
263C2×C4×D11—24no—
264C2×C4×D11—24no—
265C2×C4×D11—44no—
266C2×C4×D11—84no—
267C2×Dic22—22no—
268C2×Dic22—22no—
269C2×Dic22—82no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4C2×D411yescharacteristic
285C11×C4⋊C4C2×D412yes—
286C11×C4⋊C4C2×D411yescharacteristic
287C11×C4⋊C4C2×D412yes—
288C11×C4⋊C4C2×D412yes—
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2×D412yes—
291C11×C4⋊C4C2411yescharacteristic
292C11×C4⋊C4C2412yes—
293C11×C4⋊C4C2412yes—
294C11×C4⋊C4C2411yescharacteristic
295C11×C22⋊C4—22no—
296C11×C22⋊C4—21no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—21no—
300C11×C22⋊C4—21no—
301C42×C11—21no—
302C42×C11—22no—
303C42×C11—22no—
304C42×C11—21no—
305C42×C11—22no—
306C42×C11—21no—
307C42×C11C2×D411yescharacteristic
308C42×C11C2×D411yescharacteristic
309C42×C11C2×D412yes—
310C42×C11C2×D412yes—
311C42×C11C2411yescharacteristic
312C42×C11C2412yes—
313C42×C11C2411yescharacteristic
314C42×C11C2412yes—
315#4325C2×Q818yescomplemented
316#4323C2×Q818yescomplemented
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321C4⋊Dic11—22no—
322C4⋊Dic11—22no—
323C4⋊Dic11—22no—
324C4⋊Dic11—21no—
325C4⋊Dic11C2414yes—
326C4⋊Dic11C2412yes—
327Dic11⋊C4—24no—
328Dic11⋊C4—24no—
329Dic11⋊C4—24no—
330Dic11⋊C4—24no—
331#4318—22no—
332#4318—24no—
333#4318C2×Q814yescomplemented
334C2×C11⋊C8C2414yes—
335C2×C11⋊C8C2412yes—
336C2×C11⋊C8C2412yes—
337Q8×#41D1111yescharacteristic, complemented
338C2×#554—111no—
339#3389—114no—
340#3388—114no—
341#3385—112no—
342#3384—112no—
343#3381—112no—
344#3380—112no—
345#3166—112no—
346#3165—111no—
347#3080—112no—
348#3079—111no—
349#3077—111no—
350#3077—112no—
351Q8×M16—111no—
352C4×AGL(1,ℤ/8)—111no—
353C4×AGL(1,ℤ/8)—112no—
354C23×C11—21no—
355C23×C11C22×D411yescharacteristic
356C22×D11—24no—
357C22×D11—22no—
358C22×D11—42no—
359C22×D11—42no—
360Q8×C11—22no—
361Q8×C11—22no—
362Q8×C11—21no—
363Q8×C11—42no—
364Q8×C11—44no—
365Q8×C11—42no—
366Q8×C11—81no—
367Q8×C11—82no—
368Q8×C11C22×Q812yes—
369D4×C11—24no—
370D4×C11—21no—
371D4×C11C22×Q812yes—
372C2×C4×C11—21no—
373C2×C4×C11—24no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—21no—
377C2×C4×C11—22no—
378C2×C4×C11—21no—
379C2×C4×C11—41no—
380C2×C4×C11—42no—
381C2×C4×C11—42no—
382C2×C4×C11—44no—
383C2×C4×C11—42no—
384C2×C4×C11—81no—
385C2×C4×C11—82no—
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D412yes—
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×Q812yes—
396C2×C4×C112−1+412yes—
397C2×C4×C11C2511yescharacteristic
398C2×Dic11—22no—
399C2×Dic11—24no—
400C2×Dic11—44no—
401C2×Dic11—42no—
402D44—24no—
403D44—22no—
404D44C22×Q814yes—
405C4×D11—44no—
406C4×D11—44no—
407C4×D11—84no—
408C4×D11—84no—
409Dic22—82no—
410Dic22—82no—
411C11⋊C8—24no—
412C11⋊C8—22no—
413C11⋊C8C22×Q814yes—
414C2×AGL(1,ℤ/8)—111no—
415Q82C2×D1111yescharacteristic, complemented
416#557C2×D1111yescharacteristic, complemented
417#557C2×D1112yescomplemented
418#554—21no—
419#554—22no—
420#554—112no—
421#554—112no—
422#554—114no—
423#554—221no—
424#554—222no—
425#554—221no—
426#554C2×D1111yescharacteristic, complemented
427#554C2×D1112yescomplemented
428D4×Q8—21no—
429D4×Q8C2×D1111yescharacteristic, complemented
430#533—22no—
431#533—21no—
432#533C2×D1111yescharacteristic
433#533C2×D1112yes—
434C2×C4⋊Q8—111no—
435C2×#125—112no—
436C2×C22⋊Q8—221no—
437C2×C22⋊Q8—222no—
438C4×#41C2×D1111yescharacteristic
439C4×#41C2×D1112yes—
440C2×C4×Q8—21no—
441C2×C4×Q8C2×D1111yescharacteristic
442C2×C4×D4—112no—
443C2×C4×D4—111no—
444C22×C4⋊C4—221no—
445#501—114no—
446#501—114no—
447#501—114no—
448#500—112no—
449#499—114no—
450#499—114no—
451#498—112no—
452#479—114no—
453#479—114no—
454#478—114no—
455#478—114no—
456#478—114no—
457#478—114no—
458#478—114no—
459#477—112no—
460#476—112no—
461#476—114no—
462#476—112no—
463#475—112no—
464#474—112no—
465#474—114no—
466#474—112no—
467#446—112no—
468#446—114no—
469C8×Q8—112no—
470#442—114no—
471#442—112no—
472#440—114no—
473#440—112no—
474C4×SD16—112no—
475C4×SD16—114no—
476C4×D8—112no—
477C4×D8—114no—
478#428—112no—
479#428—112no—
480#428—112no—
481#428—112no—
482#428—111no—
483#423—111no—
484#423—112no—
485#418—112no—
486#418—111no—
487#417—112no—
488#417—111no—
489C4×M16—111no—
490C4×M16—112no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—22no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11D4×Q812yes—
497C22×C11C23×D411yescharacteristic
498C2×D11—24no—
499C2×D11—48no—
500C2×D11—42no—
501C2×D11—42no—
502C4×C11—21no—
503C4×C11—22no—
504C4×C11—21no—
505C4×C11—22no—
506C4×C11—22no—
507C4×C11—21no—
508C4×C11—22no—
509C4×C11—22no—
510C4×C11—41no—
511C4×C11—42no—
512C4×C11—42no—
513C4×C11—41no—
514C4×C11D4×Q812yes—
515C4×C11#57512yes—
516C4×C11C23×Q811yescharacteristic
517C4×C11C2×2−1+411yescharacteristic
518Dic11—44no—
519Dic11—42no—
520C2×#41C22×D1111yescharacteristic
521C22×Q8—21no—
522C22×Q8—221no—
523C22×Q8C22⋊D1111yescharacteristic
524C22×D4—111no—
525C23×C4—221no—
526C23×C4—222no—
527AGL(1,ℤ/8)—118no—
528C2×SD16—112no—
529C2×D8—112no—
530C2×M16—111no—
531C2×M16—111no—
532C2×M16—112no—
533C4⋊Q8—21no—
534C4⋊Q8—22no—
535C4⋊Q8—21no—
536C4⋊Q8—22no—
537C4⋊Q8—112no—
538C4⋊Q8—112no—
539C4⋊Q8—221no—
540C4⋊Q8—221no—
541C4⋊Q8C22×D1111yescharacteristic
542C4⋊Q8C22×D1112yes—
543C4⋊Q8C22×D1112yes—
544C4⋊Q8C22×D1111yescharacteristic
545#125—22no—
546#125—22no—
547#125—22no—
548#125—114no—
549#125—114no—
550#125—222no—
551#125—222no—
552#125C22×D1112yes—
553#125C22×D1112yes—
554#125C22×D1112yes—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—22no—
559C22⋊Q8—21no—
560C22⋊Q8—22no—
561C22⋊Q8—21no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—222no—
567C22⋊Q8—222no—
568C22⋊Q8—224no—
569C22⋊Q8—224no—
570C22⋊Q8—224no—
571C22⋊Q8—224no—
572C22⋊Q8—224no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—22no—
576C4×Q8—22no—
577C4×Q8—21no—
578C4×Q8—22no—
579C4×Q8—21no—
580C4×Q8C22⋊D1111yescharacteristic
581C4×Q8C22⋊D1112yes—
582C4×Q8C22⋊D1111yescharacteristic
583C4×Q8C22×D1112yes—
584C4×Q8C22×D1111yescharacteristic
585C4×Q8C22×D1111yescharacteristic
586C4×Q8C22×D1112yes—
587C4×Q8C22×D1111yescharacteristic
588C4×Q8C22×D1111yescharacteristic
589C4×Q8C22×D1112yes—
590C4×D4—21no—
591C4×D4—22no—
592C4×D4—21no—
593C4×D4—22no—
594C4×D4—112no—
595C4×D4—114no—
596C4×D4—114no—
597C4×D4—112no—
598C4×D4—222no—
599C4×D4—221no—
600C4×D4—222no—
601C4×D4—221no—
602C4×D4C22×D1111yescharacteristic
603C4×D4C22×D1112yes—
604C4×D4C22×D1112yes—
605C4×D4C22×D1111yescharacteristic
606#117—22no—
607#117—21no—
608#117C22×D1111yescharacteristic
609#117C22×D1112yes—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—111no—
613C2×C4⋊C4—112no—
614C2×C4⋊C4—222no—
615C2×C4⋊C4—221no—
616C2×C4⋊C4—222no—
617C2×C4⋊C4—222no—
618C2×C4⋊C4—224no—
619C2×C4⋊C4—222no—
620C2×C4⋊C4C22⋊D1111yescharacteristic
621C2×C4⋊C4C22⋊D1112yes—
622C2×C22⋊C4—221no—
623C2×C22⋊C4—222no—
624C2×C42—22no—
625C2×C42—21no—
626C2×C42C22×D1112yes—
627C2×C42C22×D1111yescharacteristic
628#107—112no—
629#107—114no—
630#107—114no—
631#107—114no—
632#107—114no—
633#106—114no—
634#106—112no—
635#106—114no—
636#106—114no—
637#106—114no—
638C4⋊C8—112no—
639C4⋊C8—114no—
640C4⋊C8—112no—
641C4⋊C8—114no—
642#103—114no—
643#103—112no—
644#102—114no—
645#102—112no—
646#102—114no—
647#102—112no—
648#102—112no—
649#102—114no—
650#97—114no—
651#97—112no—
652C4×C8—112no—
653C4×C8—114no—
654C2×C11—22no—
655C2×C11—42no—
656C2×C11C2×D4×Q811yescharacteristic
657C2×C11C2×#57511yescharacteristic
658C2×C11#358511yescharacteristic
659D11—44no—
660C24—221no—
661#41—22no—
662#41Q8×D1114yes—
663C2×Q8—22no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—22no—
667C2×Q8—42no—
668C2×Q8—44no—
669C2×Q8—222no—
670C2×Q8—222no—
671C2×Q8—882no—
672C2×Q8C2×C22⋊D1111yescharacteristic
673C2×Q8C2×C22⋊D1111yescharacteristic
674C2×Q8C2×C22⋊D1112yes—
675C2×Q8C23×D1111yescharacteristic
676C2×D4—21no—
677C2×D4—114no—
678C2×D4—112no—
679C2×D4—222no—
680C2×D4—221no—
681C2×D4C23×D1111yescharacteristic
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—221no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—224no—
692C22×C4—224no—
693C22×C4—444no—
694C22×C4—884no—
695C22×C4C2×C22⋊D1111yescharacteristic
696C22×C4C2×C22⋊D1112yes—
697C22×C4C2×C22⋊D1111yescharacteristic
698C22×C4C2×C22⋊D1112yes—
699C22×C4C23×D1111yescharacteristic
700SD16—118no—
701D8—118no—
702M16—114no—
703M16—222no—
704M16—224no—
705C2×C8—112no—
706C2×C8—112no—
707C2×C8—114no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—21no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—22no—
717C4⋊C4—21no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—22no—
722C4⋊C4—112no—
723C4⋊C4—114no—
724C4⋊C4—221no—
725C4⋊C4—222no—
726C4⋊C4—224no—
727C4⋊C4—224no—
728C4⋊C4—222no—
729C4⋊C4—222no—
730C4⋊C4—224no—
731C4⋊C4—224no—
732C4⋊C4C2×C22⋊D1111yescharacteristic
733C4⋊C4C2×C22⋊D1112yes—
734C4⋊C4C2×C22⋊D1112yes—
735C4⋊C4C2×C22⋊D1111yescharacteristic
736C4⋊C4C2×C22⋊D1112yes—
737C4⋊C4C2×C22⋊D1112yes—
738C4⋊C4C2×C22⋊D1112yes—
739C4⋊C4C23×D1111yescharacteristic
740C4⋊C4C23×D1112yes—
741C4⋊C4C23×D1112yes—
742C4⋊C4C23×D1111yescharacteristic
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—22no—
749C22⋊C4—222no—
750C22⋊C4—222no—
751C22⋊C4—224no—
752C22⋊C4—224no—
753C42—22no—
754C42—21no—
755C42—21no—
756C42—22no—
757C42—22no—
758C42—21no—
759C42C2×C22⋊D1112yes—
760C42C2×C22⋊D1111yescharacteristic
761C42C2×C22⋊D1112yes—
762C42C2×C22⋊D1111yescharacteristic
763C42C23×D1112yes—
764C42C23×D1111yescharacteristic
765C42C23×D1112yes—
766C42C23×D1111yescharacteristic
767C11#6136711yescharacteristic, complemented, Sylow
768C23—21no—
769C23—224no—
770C23—222no—
771C23—442no—
772C23—442no—
773C23C22×C22⋊D1111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—21no—
777Q8—42no—
778Q8—44no—
779Q8—42no—
780Q8—82no—
781Q8—81no—
782Q8—882no—
783Q8—882no—
784Q8C2×Q8×D1112yes—
785D4—24no—
786D4—21no—
787D4—114no—
788D4—224no—
789D4—222no—
790D4C2×Q8×D1112yes—
791C2×C4—21no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—21no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—82no—
804C2×C4—81no—
805C2×C4—222no—
806C2×C4—224no—
807C2×C4—444no—
808C2×C4—442no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4—884no—
812C2×C4—884no—
813C2×C4C2×Q8×D1112yes—
814C2×C4#6704012yes—
815C2×C4C22×C22⋊D1111yescharacteristic
816C2×C4C22×C22⋊D1112yes—
817C2×C4C22×C22⋊D1112yes—
818C2×C4C22×C22⋊D1112yes—
819C2×C4C22×C22⋊D1111yescharacteristic
820C2×C4C22×C22⋊D1111yescharacteristic
821C2×C4C22×C22⋊D1112yes—
822C2×C4C22×C22⋊D1111yescharacteristic
823C2×C4C22×C22⋊D1111yescharacteristic
824C2×C4C24×D1111yescharacteristic
825C8—114no—
826C8—222no—
827C8—224no—
828C22—21no—
829C22—21no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—224no—
834C22—448no—
835C22—442no—
836C22—442no—
837C22Q8×C22⋊D1112yes—
838C22C23×C22⋊D1111yescharacteristic
839C4—22no—
840C4—21no—
841C4—22no—
842C4—21no—
843C4—21no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—42no—
848C4—41no—
849C4—42no—
850C4—41no—
851C4—444no—
852C4—442no—
853C4Q8×C22⋊D1112yes—
854C4#1062335312yes—
855C4C22×Q8×D1111yescharacteristic
856C4C2×#6704011yescharacteristic
857C2—22no—
858C2—42no—
859C2—444no—
860C2C2×Q8×C22⋊D1111yescharacteristic
861C2C2×#1062335311yescharacteristic
862C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingQ8×C11×#41C2
socleC22×C11C23×D4
prime radicalC2×#67002C22
hypercenterQ8×#41D11
hypocenterC11#61367
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×#10623110C2semidirect
2. #13081570C2semidirect
3. #13081555C2semidirect
4. #13081522C2semidirect
5. #13081511C2semidirect
6. #13081487C2semidirect
7. #13081479C2semidirect
8. #13079169C2semidirect
9. #13079163C2semidirect
10. #13078438C2semidirect
11. #13078431C2semidirect
12. #13078409C2semidirect
13. #13078409C2semidirect
14. Q8×#4318C2semidirect
17. Q8×C11×#41C2semidirect
18. Q82×C11C22semidirect
19. C11×#557C22semidirect
20. C11×#557C22semidirect
23. C11×#554C22semidirect
24. C11×#554C22semidirect
26. D4×Q8×C11C22semidirect
55. #10622693C22semidirect
56. #10622693C22semidirect
57. #10622692C22semidirect
58. #10622691C22semidirect
62. #10622678C22semidirect
63. #10622677C22semidirect
64. #10622677C22semidirect
69. #10622637C22semidirect
70. #10622637C22semidirect
71. Q8×C11⋊C8C22semidirect
72. #10622635C22semidirect
73. #10622635C22semidirect
74. #10622634C22semidirect
75. #10622633C22semidirect
80. #10622622C22semidirect
81. #10622622C22semidirect
82. #10622621C22semidirect
83. #10622620C22semidirect
164. #67002Q8semidirect
259. C2×D44C2×Q8semidirect
315. #4325C2×Q8semidirect
316. #4323C2×Q8semidirect
333. #4318C2×Q8semidirect
337. Q8×#41D11semidirect
415. Q82C2×D11semidirect
416. #557C2×D11semidirect
417. #557C2×D11semidirect
426. #554C2×D11semidirect
427. #554C2×D11semidirect
429. D4×Q8C2×D11semidirect
767. C11#61367semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
#130815702
#130815552
#130815222
#130815112
#130814872
#130814792
#130791692
#130791632
#130784382
#130784312
#130784092
Q8×#43182
C4×#670022
Q8×C11×#412
#6136711