Finite Group Databasebeta

← #15630836

Subgroups — #15630836

Order 2816.

2120 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082174C211yesmaximal, characteristic, complemented
2#13080932C212yesmaximal, complemented
3#13080921C212yesmaximal, complemented
4#13080712C214yesmaximal, complemented
5#13080592C214yesmaximal, complemented
6#13080544C212yesmaximal, complemented
7#13080533C212yesmaximal, complemented
8#13078996C211yesmaximal, characteristic, complemented
9#13078560C212yesmaximal, complemented
10#13078413C211yesmaximal, characteristic, complemented
11#13078242C212yesmaximal, complemented
12#13078099C211yesmaximal, characteristic, complemented
13#13077858C212yesmaximal, complemented
14C4×#66985C211yesmaximal, characteristic, complemented
15D4×#4318C211yesmaximal, characteristic, complemented
16#13077135C212yesmaximal, complemented
17C2×C11×#547C211yesmaximal, characteristic, complemented
18C22×C11×#41C2212yes—
19C11×#547—21no—
20C11×#547—22no—
21C11×#547—21no—
22C11×#547C2214yes—
23C11×#547C2212yes—
24C11×#547C2212yes—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#123—22no—
27C2×C11×C22⋊Q8C2212yes—
28C2×C11×#121—21no—
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C22×C11×C4⋊C4—21no—
32C2×#66995C2212yes—
33#10623337—21no—
34C2×#66985C2211yescharacteristic
35#10623322C2212yes—
36C2×#66979C2212yes—
37C22×#4318C2212yes—
38#10623096C2212yescomplemented
39#10623094C2211yescharacteristic, complemented
40#10623088—21no—
41#10623086C2211yescharacteristic, complemented
42#10623074C2211yescharacteristic, complemented
43#10623073C2211yescharacteristic, complemented
44#10623072C2212yescomplemented
45#10623069—22no—
46C4×#4341—21no—
47#10623044—21no—
48#10623026—22no—
49C4×#4339C2211yescharacteristic
50#10623001C2211yescharacteristic
51#10622852C2214yescomplemented
52#10622852C2214yescomplemented
53#10622851C2214yescomplemented
54#10622851C2214yescomplemented
55#10622846C2214yescomplemented
56#10622846C2214yescomplemented
57#10622845C2214yescomplemented
58#10622845C2214yescomplemented
59#10622838C2212yes—
60#10622838C2212yes—
61#10622838C2212yes—
62#10622828C2212yes—
63#10622828C2211yescharacteristic
64#10622820C2212yes—
65#10622703C2212yescomplemented
66#10622703C2212yescomplemented
67#10622696C2212yescomplemented
68#10622696C2212yescomplemented
69#10622695C2214yescomplemented
70#10622694C2212yescomplemented
71#10622694C2212yescomplemented
72#10622665C2214yescomplemented
73#10622664C2214yescomplemented
74#10622662C2214yescomplemented
75#10622661C2214yescomplemented
76#10622658C2214yescomplemented
77#10622658C2214yescomplemented
78#10622657C2214yescomplemented
79#10622656C2214yescomplemented
80#10622631C2212yescomplemented
81C4×#4324C2212yescomplemented
82#10622627C2212yescomplemented
83C4×#4323C2212yescomplemented
84#10622625C2212yescomplemented
85#10622624C2214yescomplemented
86D4×C11⋊C8C2212yescomplemented
87#10622622C2214yescomplemented
88#10622621C2212yescomplemented
89#10622620C2212yescomplemented
90#10622579C2211yescharacteristic
91#10622577C2211yescharacteristic
92#10622577C2212yes—
93#10622537C2211yescharacteristic
94C4×#4318C2211yescharacteristic
95C2×C11×#41—22no—
96C2×C11×#41—22no—
97C2×C11×#41—28no—
98C2×C11×#41—44no—
99C2×C11×#41C2314yes—
100C2×C11×#41C2314yes—
101C22×Q8×C11C2312yes—
102C22×D4×C11—22no—
103C22×D4×C11D411yescharacteristic
104C22×D4×C11C2311yescharacteristic
105C23×C4×C11—21no—
106C23×C4×C11—22no—
107C23×C4×C11C2312yes—
108C2×#4341—21no—
109C2×#4339C2311yescharacteristic
110C11×C4⋊Q8—21no—
111C11×C4⋊Q8—21no—
112C11×C4⋊Q8C2312yes—
113C11×C4⋊Q8C2312yes—
114C11×#123—24no—
115C11×#123—24no—
116C11×#123—24no—
117C11×#123—24no—
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8C2314yes—
121C11×C22⋊Q8C2314yes—
122C11×#121—22no—
123C11×#121—22no—
124C11×#121—24no—
125C4×D4×C11—21no—
126C4×D4×C11—21no—
127C4×D4×C11D411yescharacteristic
128C4×D4×C11D412yes—
129C4×D4×C11D411yescharacteristic
130C4×D4×C11C2312yes—
131C4×D4×C11C2312yes—
132C4×D4×C11C2312yes—
133C4×D4×C11C2311yescharacteristic
134C4×D4×C11C2311yescharacteristic
135C2×C11×C4⋊C4—21no—
136C2×C11×C4⋊C4—22no—
137C2×C11×C4⋊C4—21no—
138C2×C11×C4⋊C4—22no—
139C2×C11×C4⋊C4—24no—
140C2×C11×C4⋊C4—22no—
141C2×C11×C4⋊C4D411yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4—22no—
144C2×C11×C22⋊C4—21no—
145C2×C11×C22⋊C4D412yes—
146C2×C42×C11C2311yescharacteristic
147#67006—22no—
148C2×C22⋊Dic11—22no—
149C2×#4326C2314yes—
150#66995—44no—
151C2×#4325C2314yes—
152#66992—22no—
153#66991—21no—
154#66989—21no—
155#66988—22no—
156D4×Dic11—21no—
157C2×#4324C2312yes—
158#66985—24no—
159C2×#4323C2312yes—
160#66983C2312yes—
161#66983C2312yes—
162#66982—22no—
163C4×C22⋊D11—21no—
164C4×C22⋊D11—21no—
165C4×C22⋊D11—22no—
166C4×C22⋊D11—22no—
167#66979—22no—
168#66979—22no—
169#66979C2312yes—
170#66979C2311yescharacteristic
171#66979C2312yes—
172#66979C2312yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2312yes—
175#66977—21no—
176#66977—21no—
177#66977C2312yes—
178#66977C2312yes—
179C2×C4×Dic11—22no—
180C2×#4318—44no—
181C2×#4318C2311yescharacteristic
182C2×#4318C2311yescharacteristic
183C2×#4318C2312yes—
184C2×#4318C2314yes—
185C22×C11⋊C8C2314yes—
186#66951—22no—
187#66950—21no—
188#66945—21no—
189#66943—21no—
190#66942—22no—
191#66940—21no—
192#66939—22no—
193#66938—22no—
194#66936—22no—
195(C22⋊D11)⋊C4—22no—
196#66932—22no—
197#66932—22no—
198#66931—22no—
199#66930—22no—
200C4×D44C2311yescharacteristic
201C4×D44C2311yescharacteristic
202#66925—21no—
203C42×D11—21no—
204#66923C2312yes—
205#66922C2311yescharacteristic
206#66922C2311yescharacteristic
207C4×Dic22—21no—
208C4×Dic22—21no—
209C4×Dic22C2311yescharacteristic
210C4×Dic22C2311yescharacteristic
211#66899C2314yes—
212#66899C2314yes—
213#66899C2314yes—
214#66899C2314yes—
215#66899C2314yes—
216#66899C2314yes—
217#66896C2312yes—
218#66896C2312yes—
219#66896C2314yes—
220#66896C2314yes—
221C22⋊(C11⋊C8)C2314yes—
222C22⋊(C11⋊C8)C2314yes—
223#66874C2312yes—
224#66873C2312yes—
225#66872C2314yes—
226#66872C2312yes—
227#66871C2314yes—
228#66871C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231#66867C2312yes—
232C4×C11⋊C8C2312yes—
233#61159—111nomaximal, Sylow
234C24×C11—21no—
235C24×C11C2×D412yes—
236C11×#41—28no—
237C11×#41—28no—
238C11×#41—44no—
239C11×#41—44no—
240C11×#41—48no—
241C11×#41—48no—
242C2×Q8×C11—22no—
243C2×Q8×C11—24no—
244C2×Q8×C11—24no—
245C2×Q8×C11C2414yes—
246C2×D4×C11—24no—
247C2×D4×C11—24no—
248C2×D4×C11—21no—
249C2×D4×C11—22no—
250C2×D4×C11—42no—
251C2×D4×C11—48no—
252C2×D4×C11C2×D411yescharacteristic
253C2×D4×C11C2×D411yescharacteristic
254C2×D4×C11C2×D412yes—
255C2×D4×C11#4114yescomplemented
256C2×D4×C11C2412yes—
257C22×C4×C11—24no—
258C22×C4×C11—24no—
259C22×C4×C11—21no—
260C22×C4×C11—22no—
261C22×C4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—24no—
264C22×C4×C11—24no—
265C22×C4×C11—48no—
266C22×C4×C11—44no—
267C22×C4×C11C2×D412yes—
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D412yes—
270C22×C4×C11C2×D412yes—
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2412yes—
273C22×C4×C11C2412yes—
274C22×C4×C11C2411yescharacteristic
275C2×C22⋊D11—22no—
276C2×C22⋊D11—21no—
277C2×C22⋊D11—22no—
278C22×Dic11—22no—
279C22×Dic11—22no—
280#4341—44no—
281#4339—22no—
282#4339—22no—
283C2×D44C2411yescharacteristic
284C2×C4×D11—21no—
285C2×C4×D11—21no—
286C2×C4×D11—21no—
287C2×Dic22—21no—
288C2×Dic22—21no—
289C2×Dic22C2411yescharacteristic
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—24no—
293C11×C4⋊C4—24no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4C2×D411yescharacteristic
298C11×C4⋊C4C2×D412yes—
299C11×C4⋊C4C2×D411yescharacteristic
300C11×C4⋊C4C2412yes—
301C11×C22⋊C4—24no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4C2×D412yes—
306C11×C22⋊C4C2×D412yes—
307C11×C22⋊C4C2×D412yes—
308C11×C22⋊C4C2×D412yes—
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2411yescharacteristic
312C42×C11C2411yescharacteristic
313C22⋊Dic11—22no—
314C22⋊Dic11—22no—
315C22⋊Dic11—22no—
316C22⋊Dic11—22no—
317C22⋊Dic11—22no—
318C22⋊Dic11—21no—
319#4326—44no—
320#4325—44no—
321#4324—24no—
322#4323—24no—
323(C2×D11)⋊C4—21no—
324(C2×D11)⋊C4—21no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327C4⋊Dic11—21no—
328C4⋊Dic11—21no—
329C4⋊Dic11—22no—
330C4⋊Dic11—22no—
331C4⋊Dic11C2411yescharacteristic
332C4⋊Dic11C2412yes—
333C4⋊Dic11C2411yescharacteristic
334C4⋊Dic11C2412yes—
335Dic11⋊C4—22no—
336Dic11⋊C4—22no—
337Dic11⋊C4—21no—
338Dic11⋊C4—21no—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341C4×Dic11—22no—
342C4×Dic11—21no—
343C4×Dic11—21no—
344C4×Dic11—21no—
345C4×Dic11—22no—
346C4×Dic11—22no—
347#4318—22no—
348#4318—22no—
349#4318—24no—
350#4318—44no—
351C2×C11⋊C8—44no—
352C2×C11⋊C8C2412yes—
353C2×C11⋊C8C2412yes—
354C2×C11⋊C8C2414yes—
355#3475—111no—
356C2×#547D1111yescharacteristic, complemented
357#3331—112no—
358#3330—112no—
359#3315—114no—
360#3307—114no—
361#3303—112no—
362#3302—112no—
363#3139—111no—
364#3095—112no—
365#3077—111no—
366#3056—112no—
367#3039—111no—
368#3005—112no—
369C4×AGL(1,ℤ/8)—111no—
370D4×M16—111no—
371#2896—112no—
372C23×C11—24no—
373C23×C11—22no—
374C23×C11—24no—
375C23×C11—42no—
376C23×C11—42no—
377C23×C11—42no—
378C23×C11—42no—
379C23×C11C22×D412yes—
380C23×C11C22×D412yes—
381C23×C11C22×D411yescharacteristic
382C22×D11—21no—
383Q8×C11—24no—
384Q8×C11—24no—
385Q8×C11—44no—
386D4×C11—24no—
387D4×C11—22no—
388D4×C11—22no—
389D4×C11—22no—
390D4×C11—42no—
391D4×C11—48no—
392D4×C11—48no—
393D4×C11C2×#4114yes—
394C2×C4×C11—24no—
395C2×C4×C11—24no—
396C2×C4×C11—24no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—24no—
404C2×C4×C11—41no—
405C2×C4×C11—48no—
406C2×C4×C11—48no—
407C2×C4×C11—44no—
408C2×C4×C11—42no—
409C2×C4×C11—44no—
410C2×C4×C11—44no—
411C2×C4×C11C22×D412yes—
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D412yes—
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C2×#4112yes—
419C2×C4×C11H(5,𝔽2)12yes—
420C2×C4×C11C2511yescharacteristic
421C22⋊D11—44no—
422C22⋊D11—42no—
423C22⋊D11—82no—
424C2×Dic11—21no—
425C2×Dic11—21no—
426C2×Dic11—21no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—44no—
430C2×Dic11—82no—
431D44—21no—
432D44—21no—
433C4×D11—42no—
434C4×D11—42no—
435C4×D11—81no—
436Dic22—21no—
437Dic22—21no—
438Dic22—42no—
439Dic22—81no—
440C11⋊C8—22no—
441C11⋊C8—22no—
442C11⋊C8—24no—
443C22×#41C2×D1112yes—
444C2×#137—112no—
445C2×AGL(1,ℤ/8)—111no—
446C22×M16—112no—
447#556—111no—
448#555—111no—
449#554—111no—
450#553—112no—
451#552—112no—
452#552—221no—
453#551—222no—
454#547—21no—
455#547—21no—
456#547—22no—
457#547—111no—
458#547C2×D1112yes—
459#547C2×D1112yes—
460#547C2×D1114yes—
461#546—221no—
462#533—111no—
463C2×C4⋊Q8C2×D1111yescharacteristic
464#529—222no—
465#529—221no—
466#525—112no—
467C2×#123—22no—
468C2×C22⋊Q8C2×D1112yes—
469C2×#121—21no—
470C4×#41—111no—
471C4×#41—221no—
472C2×C4×D4C2×D1111yescharacteristic
473C2×C4×D4C2×D1111yescharacteristic
474C2×#117—112no—
475C22×C4⋊C4—21no—
476#491—114no—
477#487—112no—
478#487—112no—
479#485—114no—
480#485—114no—
481#484—114no—
482#483—114no—
483#478—114no—
484#476—112no—
485#474—112no—
486#470—114no—
487#468—114no—
488#467—114no—
489#465—114no—
490#462—112no—
491#462—112no—
492#461—112no—
493#461—112no—
494#452—114no—
495#452—114no—
496#449—114no—
497#449—114no—
498#442—112no—
499#440—112no—
500C4×SD16—112no—
501C4×D8—112no—
502#436—112no—
503#435—114no—
504C8×D4—112no—
505#428—112no—
506#428—111no—
507#423—111no—
508#419—112no—
509#419—112no—
510#419—112no—
511#418—112no—
512#418—111no—
513#417—114no—
514#417—114no—
515#417—111no—
516#416—114no—
517#416—114no—
518#407—112no—
519C4×M16—111no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—22no—
523C22×C11—22no—
524C22×C11—22no—
525C22×C11—22no—
526C22×C11—24no—
527C22×C11—22no—
528C22×C11—22no—
529C22×C11—48no—
530C22×C11—42no—
531C22×C11—42no—
532C22×C11—84no—
533C22×C11#54612yes—
534C22×C11C23×D411yescharacteristic
535C2×D11—41no—
536C2×D11—41no—
537C2×D11—41no—
538C4×C11—21no—
539C4×C11—21no—
540C4×C11—22no—
541C4×C11—22no—
542C4×C11—21no—
543C4×C11—44no—
544C4×C11—42no—
545C4×C11#54612yes—
546C4×C11#57512yes—
547C4×C11C22×#4111yescharacteristic
548C4×C11C2×H(5,𝔽2)11yescharacteristic
549Dic11—42no—
550Dic11—41no—
551Dic11—41no—
552Dic11—42no—
553Dic11—41no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—28no—
557C2×#41—44no—
558C2×#41—111no—
559C2×#41—221no—
560C2×#41C22×D1114yes—
561C2×#41C22×D1114yes—
562C22×Q8C22×D1112yes—
563C22×D4—22no—
564C22×D4C22⋊D1111yescharacteristic
565C22×D4C22×D1111yescharacteristic
566C23×C4—21no—
567C23×C4—22no—
568C23×C4C22×D1112yes—
569#137—444no—
570AGL(1,ℤ/8)—224no—
571C2×Q16—114no—
572C2×SD16—112no—
573C2×SD16—114no—
574C2×D8—112no—
575C2×M16—111no—
576C2×M16—112no—
577C2×M16—111no—
578C2×M16—114no—
579C2×M16—444no—
580C22×C8—114no—
581C4⋊Q8—21no—
582C4⋊Q8—21no—
583C4⋊Q8—111no—
584C4⋊Q8—111no—
585C4⋊Q8C22×D1112yes—
586C4⋊Q8C22×D1112yes—
587#126—222no—
588#126—222no—
589#126—222no—
590#125—112no—
591#125—222no—
592#125—221no—
593#124—221no—
594#124—222no—
595#123—24no—
596#123—24no—
597#123—24no—
598#123—24no—
599#123—222no—
600#123—222no—
601#123—222no—
602#123—222no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—112no—
606C22⋊Q8—112no—
607C22⋊Q8—221no—
608C22⋊Q8—221no—
609C22⋊Q8—221no—
610C22⋊Q8—222no—
611C22⋊Q8C22×D1114yes—
612C22⋊Q8C22×D1114yes—
613#121—22no—
614#121—22no—
615#121—24no—
616#121—112no—
617#121—112no—
618#121—222no—
619#121—221no—
620#120—222no—
621C4×Q8—111no—
622C4×Q8—111no—
623C4×Q8—221no—
624C4×Q8—221no—
625C4×Q8—221no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—111no—
629C4×D4—111no—
630C4×D4—221no—
631C4×D4—221no—
632C4×D4—221no—
633C4×D4—222no—
634C4×D4—222no—
635C4×D4—222no—
636C4×D4C22⋊D1111yescharacteristic
637C4×D4C22⋊D1111yescharacteristic
638C4×D4C22⋊D1112yes—
639C4×D4C22×D1112yes—
640C4×D4C22×D1112yes—
641C4×D4C22×D1111yescharacteristic
642C4×D4C22×D1112yes—
643C4×D4C22×D1111yescharacteristic
644#117—111no—
645#117—112no—
646#117—112no—
647#117—112no—
648#117—222no—
649#117—222no—
650#117—221no—
651#117—222no—
652#117—221no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—24no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4C22⋊D1111yescharacteristic
662C2×C4⋊C4C22×D1111yescharacteristic
663C2×C22⋊C4—22no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—222no—
666C2×C22⋊C4C22⋊D1112yes—
667C2×C42—222no—
668C2×C42—221no—
669C2×C42C22×D1111yescharacteristic
670#107—112no—
671#107—114no—
672#106—112no—
673#106—114no—
674C4⋊C8—112no—
675C4⋊C8—112no—
676#103—114no—
677#103—114no—
678#103—114no—
679#103—114no—
680#103—114no—
681#103—114no—
682#103—112no—
683#102—112no—
684#102—112no—
685#102—114no—
686#102—114no—
687#102—112no—
688C22⋊C8—114no—
689C22⋊C8—114no—
690#97—112no—
691C4×C8—112no—
692C2×C11—22no—
693C2×C11—42no—
694C2×C11—42no—
695C2×C11—44no—
696C2×C11C2×#54611yescharacteristic
697C2×C11C2×#57511yescharacteristic
698C2×C11#358611yescharacteristic
699D11—81no—
700C24—21no—
701C24C2×C22⋊D1112yes—
702#41—28no—
703#41—28no—
704#41—44no—
705#41—44no—
706#41—48no—
707#41—48no—
708#41—222no—
709#41—222no—
710#41—444no—
711C2×Q8—22no—
712C2×Q8—24no—
713C2×Q8—24no—
714C2×Q8—111no—
715C2×Q8—221no—
716C2×Q8—221no—
717C2×Q8C23×D1114yes—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—42no—
723C2×D4—48no—
724C2×D4—111no—
725C2×D4—221no—
726C2×D4—222no—
727C2×D4—222no—
728C2×D4#434114yescomplemented
729C2×D4C2×C22⋊D1111yescharacteristic
730C2×D4C2×C22⋊D1111yescharacteristic
731C2×D4C2×C22⋊D1112yes—
732C2×D4C23×D1112yes—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—48no—
742C22×C4—44no—
743C22×C4—222no—
744C22×C4—222no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4C2×C22⋊D1112yes—
749C22×C4C2×C22⋊D1111yescharacteristic
750C22×C4C2×C22⋊D1112yes—
751C22×C4C2×C22⋊D1112yes—
752C22×C4C2×C22⋊D1111yescharacteristic
753C22×C4C23×D1112yes—
754C22×C4C23×D1112yes—
755C22×C4C23×D1111yescharacteristic
756Q16—444no—
757SD16—224no—
758SD16—444no—
759D8—224no—
760M16—222no—
761M16—222no—
762M16—224no—
763M16—444no—
764C2×C8—112no—
765C2×C8—112no—
766C2×C8—114no—
767C2×C8—444no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—22no—
773C4⋊C4—22no—
774C4⋊C4—21no—
775C4⋊C4—111no—
776C4⋊C4—112no—
777C4⋊C4—111no—
778C4⋊C4—112no—
779C4⋊C4—222no—
780C4⋊C4—222no—
781C4⋊C4—221no—
782C4⋊C4—221no—
783C4⋊C4—221no—
784C4⋊C4—222no—
785C4⋊C4—222no—
786C4⋊C4—222no—
787C4⋊C4—222no—
788C4⋊C4—221no—
789C4⋊C4C2×C22⋊D1111yescharacteristic
790C4⋊C4C2×C22⋊D1111yescharacteristic
791C4⋊C4C2×C22⋊D1112yes—
792C4⋊C4C23×D1112yes—
793C22⋊C4—24no—
794C22⋊C4—24no—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—221no—
798C22⋊C4—222no—
799C22⋊C4—222no—
800C22⋊C4—222no—
801C22⋊C4—222no—
802C22⋊C4—222no—
803C22⋊C4—221no—
804C22⋊C4—221no—
805C22⋊C4—222no—
806C22⋊C4—222no—
807C22⋊C4C2×C22⋊D1112yes—
808C22⋊C4C2×C22⋊D1112yes—
809C22⋊C4C2×C22⋊D1112yes—
810C22⋊C4C2×C22⋊D1112yes—
811C42—221no—
812C42—222no—
813C42—222no—
814C42—222no—
815C42—221no—
816C42—221no—
817C42C2×C22⋊D1111yescharacteristic
818C42C2×C22⋊D1111yescharacteristic
819C42C23×D1111yescharacteristic
820C42C23×D1111yescharacteristic
821C11#6115911yescharacteristic, complemented, Sylow
822C23—24no—
823C23—22no—
824C23—24no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—221no—
830C23C22×C22⋊D1112yes—
831C23C22×C22⋊D1112yes—
832C23C22×C22⋊D1111yescharacteristic
833Q8—24no—
834Q8—24no—
835Q8—44no—
836Q8—221no—
837Q8—221no—
838Q8—442no—
839Q8—881no—
840D4—24no—
841D4—22no—
842D4—22no—
843D4—22no—
844D4—42no—
845D4—48no—
846D4—48no—
847D4—221no—
848D4—221no—
849D4—444no—
850D4—442no—
851D4—882no—
852D4C2×#434114yes—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—41no—
864C2×C4—48no—
865C2×C4—48no—
866C2×C4—44no—
867C2×C4—42no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—221no—
871C2×C4—221no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—221no—
875C2×C4—444no—
876C2×C4—442no—
877C2×C4—442no—
878C2×C4—881no—
879C2×C4—882no—
880C2×C4C2×#434112yes—
881C2×C4#6703712yes—
882C2×C4C22×C22⋊D1112yes—
883C2×C4C22×C22⋊D1111yescharacteristic
884C2×C4C22×C22⋊D1111yescharacteristic
885C2×C4C22×C22⋊D1111yescharacteristic
886C2×C4C22×C22⋊D1112yes—
887C2×C4C22×C22⋊D1111yescharacteristic
888C2×C4C22×C22⋊D1111yescharacteristic
889C2×C4C24×D1111yescharacteristic
890C8—222no—
891C8—222no—
892C8—224no—
893C22—21no—
894C22—21no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—24no—
900C22—22no—
901C22—22no—
902C22—48no—
903C22—42no—
904C22—42no—
905C22—84no—
906C22—441no—
907C22—441no—
908C22—441no—
909C22#1062333712yes—
910C22C23×C22⋊D1111yescharacteristic
911C4—21no—
912C4—21no—
913C4—22no—
914C4—22no—
915C4—21no—
916C4—44no—
917C4—42no—
918C4—441no—
919C4—442no—
920C4—441no—
921C4—441no—
922C4—442no—
923C4#1062333712yes—
924C4#1062335312yes—
925C4C22×#434111yescharacteristic
926C4C2×#6703711yescharacteristic
927C2—22no—
928C2—42no—
929C2—42no—
930C2—44no—
931C2—881no—
932C2C2×#1062333711yescharacteristic
933C2C2×#1062335311yescharacteristic
934C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#547C2
socleC22×C11C23×D4
hypercenterC2×#547D11
hypocenterC11#61159
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13082174C2semidirect
2. #13080932C2semidirect
3. #13080921C2semidirect
4. #13080712C2semidirect
5. #13080592C2semidirect
6. #13080544C2semidirect
7. #13080533C2semidirect
8. #13078996C2semidirect
9. #13078560C2semidirect
10. #13078413C2semidirect
11. #13078242C2semidirect
12. #13078099C2semidirect
13. #13077858C2semidirect
14. C4×#66985C2semidirect
15. D4×#4318C2semidirect
16. #13077135C2semidirect
17. C2×C11×#547C2semidirect
38. #10623096C22semidirect
39. #10623094C22semidirect
41. #10623086C22semidirect
42. #10623074C22semidirect
43. #10623073C22semidirect
44. #10623072C22semidirect
51. #10622852C22semidirect
52. #10622852C22semidirect
53. #10622851C22semidirect
54. #10622851C22semidirect
55. #10622846C22semidirect
56. #10622846C22semidirect
57. #10622845C22semidirect
58. #10622845C22semidirect
65. #10622703C22semidirect
66. #10622703C22semidirect
67. #10622696C22semidirect
68. #10622696C22semidirect
69. #10622695C22semidirect
70. #10622694C22semidirect
71. #10622694C22semidirect
72. #10622665C22semidirect
73. #10622664C22semidirect
74. #10622662C22semidirect
75. #10622661C22semidirect
76. #10622658C22semidirect
77. #10622658C22semidirect
78. #10622657C22semidirect
79. #10622656C22semidirect
80. #10622631C22semidirect
81. C4×#4324C22semidirect
82. #10622627C22semidirect
83. C4×#4323C22semidirect
84. #10622625C22semidirect
85. #10622624C22semidirect
86. D4×C11⋊C8C22semidirect
87. #10622622C22semidirect
88. #10622621C22semidirect
89. #10622620C22semidirect
255. C2×D4×C11#41semidirect
356. C2×#547D11semidirect
728. C2×D4#4341semidirect
821. C11#61159semidirect

Maximal subgroups

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

subgroupindex
#130821742
#130809322
#130809212
#130807122
#130805922
#130805442
#130805332
#130789962
#130785602
#130784132
#130782422
#130780992
#130778582
C4×#669852
D4×#43182
#130771352
C2×C11×#5472
#6115911