Finite Group Databasebeta

← #15625750

Subgroups — #15625750

Order 2816.

2072 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082401C211yesmaximal, characteristic, complemented
2#13079719C214yesmaximal, complemented
3#13079671C214yesmaximal, complemented
4#13079640C212yesmaximal, complemented
5#13079607C212yesmaximal, complemented
6#13079588C212yesmaximal, complemented
7#13079538C212yesmaximal, complemented
8#13079088C212yesmaximal, complemented
9#13078986C212yesmaximal, complemented
10#13078103C211yesmaximal, characteristic, complemented
11#13078080C211yesmaximal, characteristic, complemented
12#13078071C211yesmaximal, characteristic, complemented
13C2×#10622632C211yesmaximal, characteristic, complemented
14#13077928C212yesmaximal, complemented
15#13077900C212yesmaximal, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C11×#3460C211yesmaximal, characteristic, complemented
18C2×#67043C2212yes—
19C11×#544C2211yescharacteristic
20C11×#542—21no—
21C11×#542C2212yes—
22C11×#540—21no—
23C11×#540C2212yes—
24C11×#538—22no—
25C11×#537C2211yescharacteristic
26C11×#535C2211yescharacteristic
27C11×#535C2211yescharacteristic
28C11×#532—21no—
29C11×#532C2212yes—
30C11×#529—21no—
31C11×#529C2212yes—
32C11×#525—22no—
33C4×C11×#41C2211yescharacteristic
34C4×C11×#41C2211yescharacteristic
35C2×C4×D4×C11C2211yescharacteristic
36C2×#67004C2212yes—
37C2×#67003C2212yes—
38C22×#4324C2212yes—
39C2×#66985C2212yes—
40Q8×D44—21no—
41Q8×D44—21no—
42#10623086—21no—
43#10623086—21no—
44#10623086—22no—
45#10623086—22no—
46#10623057C2212yes—
47#10623057C2214yescomplemented
48#10623008C2211yescharacteristic
49#10623008C2212yescomplemented
50C2×#66922C2211yescharacteristic
51C2×#66922C2212yescomplemented
52#10622847C2212yes—
53#10622706C2214yescomplemented
54#10622702C2214yescomplemented
55#10622689C2214yes—
56#10622687C2214yes—
57#10622682C2214yescomplemented
58#10622681C2214yescomplemented
59#10622673C2214yes—
60#10622672C2214yes—
61#10622663C2214yescomplemented
62#10622660C2214yescomplemented
63#10622653C2214yes—
64#10622653C2214yes—
65#10622653C2214yescomplemented
66#10622650C2214yes—
67#10622650C2214yes—
68#10622650C2214yescomplemented
69#10622644C2212yescomplemented
70#10622644C2211yescharacteristic, complemented
71#10622644C2212yescomplemented
72#10622641C2212yescomplemented
73#10622640C2211yescharacteristic, complemented
74#10622632C2212yes—
75#10622632C2212yes—
76#10622632C2214yes—
77#10622632C2212yes—
78#10622632C2211yescharacteristic, complemented
79#10622632C2212yescomplemented
80#10622632C2212yescomplemented
81#10622629C2214yes—
82#10622629C2212yescomplemented
83#10622628C2212yes—
84#10622628C2211yescharacteristic, complemented
85#10622617C2212yes—
86#10622615C2212yes—
87#10622613C2214yescomplemented
88#10622610C2212yes—
89C2×#66874C2212yes—
90#10622579C2212yes—
91#10622539C2212yescomplemented
92#10622538C2212yescomplemented
93#10622537C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C2×C11×#41—22no—
96C2×C11×#41C2311yescharacteristic
97C2×C11×#41C2311yescharacteristic
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11—21no—
100#67043—44no—
101#67043—44no—
102C2×Q8×D11—22no—
103C2×#4341—24no—
104C2×#4341—22no—
105C2×#4339C2312yes—
106C2×#4339C2314yes—
107C22×Dic22C2312yes—
108C22×Dic22C2314yes—
109C11×C4⋊Q8—21no—
110C11×C4⋊Q8C2312yes—
111C11×#127—21no—
112C11×#127C2312yes—
113C11×#126—22no—
114C11×#126—22no—
115C11×#125—21no—
116C11×#125C2312yes—
117C11×#124—21no—
118C11×#124—22no—
119C11×#124—22no—
120C11×#124C2312yes—
121C11×#123—22no—
122C11×#123—22no—
123C11×#123—22no—
124C11×#123—22no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—22no—
127C11×C22⋊Q8—22no—
128C11×C22⋊Q8C2312yes—
129C11×#121—22no—
130C11×#121—21no—
131C11×#121—22no—
132C11×#121—21no—
133C11×#121—21no—
134C11×#121—22no—
135C11×#121—22no—
136C11×#121C2312yes—
137C11×#121C2312yes—
138C11×#121C2312yes—
139C11×#120—22no—
140C11×#120—22no—
141C4×Q8×C11D411yescharacteristic
142C4×Q8×C11D411yescharacteristic
143C4×Q8×C11C2311yescharacteristic
144C4×Q8×C11C2311yescharacteristic
145C4×D4×C11—21no—
146C4×D4×C11—21no—
147C4×D4×C11—22no—
148C4×D4×C11—21no—
149C4×D4×C11—21no—
150C4×D4×C11—22no—
151C4×D4×C11D412yes—
152C4×D4×C11D411yescharacteristic
153C4×D4×C11D412yes—
154C4×D4×C11D411yescharacteristic
155C4×D4×C11C2312yes—
156C4×D4×C11C2312yes—
157C4×D4×C11C2311yescharacteristic
158C4×D4×C11C2311yescharacteristic
159C11×#117—21no—
160C11×#117—22no—
161C11×#117C2311yescharacteristic
162C11×#117C2311yescharacteristic
163C11×#117C2312yes—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4—21no—
166C2×C42×C11—21no—
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169#67004—44no—
170#67003—44no—
171C2×#4326C2312yes—
172C2×#4326C2314yes—
173C2×#4325C2312yes—
174C2×#4324—44no—
175C2×#4324C2314yes—
176C2×#4324C2314yes—
177C2×#4324C2314yes—
178C2×#4324C2312yes—
179C2×#4324C2314yes—
180#66985—44no—
181C2×#4323C2314yes—
182C2×#4323C2312yes—
183#66983—21no—
184#66983—21no—
185#66983—22no—
186#66983—22no—
187C2×C4⋊Dic11—21no—
188C2×C4⋊Dic11—21no—
189C2×C4⋊Dic11—22no—
190C2×C4⋊Dic11—22no—
191C2×#4318C2312yes—
192C22×C11⋊C8C2312yes—
193#66950—22no—
194#66950—22no—
195#66950—24no—
196#66950—24no—
197#66939—24no—
198#66939—24no—
199#66939—24no—
200#66928C2312yes—
201#66928C2314yes—
202#66927C2311yescharacteristic
203C4×D44—21no—
204C4×D44—21no—
205C4×D44—22no—
206C4×D44—22no—
207#66922—21no—
208#66922—21no—
209#66922—22no—
210#66922—22no—
211#66922C2312yes—
212#66922C2312yes—
213#66922C2311yescharacteristic
214#66922C2314yes—
215C22⋊(C11⋊C8)C2314yes—
216C22⋊(C11⋊C8)C2314yes—
217#66874C2314yes—
218#66874C2314yes—
219#66874C2314yes—
220#66874C2312yes—
221#66874C2312yes—
222#66874C2314yes—
223#66874C2314yes—
224#66873C2314yes—
225#66873C2312yes—
226#66873C2312yes—
227C4⋊(C11⋊C8)C2311yescharacteristic
228C4⋊(C11⋊C8)C2311yescharacteristic
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231C4⋊(C11⋊C8)C2312yes—
232#66867C2314yes—
233C4×C11⋊C8C2314yes—
234#60836—111nomaximal, Sylow
235C24×C11—21no—
236C11×#41—22no—
237C11×#41—22no—
238C11×#41—22no—
239C11×#41—22no—
240C11×#41—84no—
241C2×Q8×C11—22no—
242C2×Q8×C11C2×D411yescharacteristic
243C2×Q8×C11C2411yescharacteristic
244C2×D4×C11—21no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—22no—
248C2×D4×C11—21no—
249C2×D4×C11—22no—
250C2×D4×C11—22no—
251C2×D4×C11—22no—
252C2×D4×C11—22no—
253C2×D4×C11C2×D412yes—
254C2×D4×C11C2×D411yescharacteristic
255C2×D4×C11C2412yes—
256C2×D4×C11C2411yescharacteristic
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—22no—
261C22×C4×C11—21no—
262C22×C4×C11—22no—
263C22×C4×C11—82no—
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D412yes—
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D412yes—
268C22×C4×C11C2412yes—
269C22×C4×C11C2411yescharacteristic
270C2×C22⋊D11—24no—
271C2×C22⋊D11—22no—
272C22×Dic11—24no—
273C22×Dic11—22no—
274Q8×D11—48no—
275#4341—416no—
276#4341—48no—
277#4339—24no—
278#4339—24no—
279#4339—44no—
280#4339—44no—
281C2×D44—21no—
282C2×D44—21no—
283C2×D44C2412yes—
284C2×C4×D11—24no—
285C2×C4×D11—22no—
286C2×Dic22—24no—
287C2×Dic22—22no—
288C2×Dic22—24no—
289C2×Dic22—24no—
290C2×Dic22—44no—
291C2×Dic22—44no—
292C2×Dic22C2414yes—
293C2×Dic22C2412yes—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—22no—
300C11×C4⋊C4—22no—
301C11×C4⋊C4C2×D411yescharacteristic
302C11×C4⋊C4C2×D411yescharacteristic
303C11×C4⋊C4C2×D412yes—
304C11×C4⋊C4C2×D412yes—
305C11×C4⋊C4C2412yes—
306C11×C4⋊C4C2411yescharacteristic
307C11×C4⋊C4C2411yescharacteristic
308C11×C22⋊C4—21no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—22no—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—21no—
313C11×C22⋊C4—21no—
314C11×C22⋊C4—22no—
315C11×C22⋊C4—22no—
316C11×C22⋊C4—22no—
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4C2×D412yes—
320C11×C22⋊C4C2×D412yes—
321C11×C22⋊C4C2×D412yes—
322C42×C11—21no—
323C42×C11—21no—
324C42×C11—21no—
325C42×C11C2×D411yescharacteristic
326C42×C11C2×D411yescharacteristic
327C42×C11C2×D412yes—
328C42×C11C2×D412yes—
329C42×C11C2412yes—
330C42×C11C2411yescharacteristic
331C42×C11C2411yescharacteristic
332#4326—42no—
333#4326—44no—
334#4325—42no—
335#4324—44no—
336#4324—44no—
337#4324—44no—
338#4324—42no—
339#4324—44no—
340#4323—44no—
341#4323—42no—
342(C2×D11)⋊C4—22no—
343(C2×D11)⋊C4—24no—
344(C2×D11)⋊C4—22no—
345(C2×D11)⋊C4—24no—
346C4⋊Dic11—22no—
347C4⋊Dic11—21no—
348C4⋊Dic11—22no—
349C4⋊Dic11—21no—
350C4⋊Dic11—22no—
351C4⋊Dic11—24no—
352C4⋊Dic11—22no—
353C4⋊Dic11—24no—
354#4318—24no—
355C2×C11⋊C8—24no—
356C2×C11⋊C8C2412yes—
357C2×C11⋊C8C2414yes—
358C2×C11⋊C8C2412yes—
359#3499—111no—
360#3460D1111yescharacteristic, complemented
361#3225—114no—
362#3221—114no—
363#3218—112no—
364#3214—112no—
365#3212—112no—
366#3206—112no—
367#3154—112no—
368#3137—112no—
369#3039—111no—
370#3036—111no—
371#3035—111no—
372C2×#461—111no—
373#3013—112no—
374#3010—112no—
375#2925—111no—
376C23×C11—22no—
377C23×C11—21no—
378C23×C11—42no—
379C23×C11—81no—
380C23×C11—81no—
381C23×C11C22×D412yes—
382C23×C11C22×D411yescharacteristic
383C22×D11—22no—
384Q8×C11—22no—
385Q8×C11—21no—
386Q8×C11—21no—
387Q8×C11—82no—
388D4×C11—24no—
389D4×C11—22no—
390D4×C11—22no—
391D4×C11—21no—
392D4×C11—22no—
393D4×C11—21no—
394D4×C11—42no—
395D4×C11—42no—
396D4×C11—82no—
397D4×C11—82no—
398D4×C11—82no—
399D4×C11—82no—
400D4×C11—82no—
401C2×C4×C11—22no—
402C2×C4×C11—24no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—22no—
409C2×C4×C11—41no—
410C2×C4×C11—42no—
411C2×C4×C11—42no—
412C2×C4×C11—44no—
413C2×C4×C11—42no—
414C2×C4×C11—81no—
415C2×C4×C11—82no—
416C2×C4×C11—81no—
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D412yes—
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D412yes—
422C2×C4×C11C22×D412yes—
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11H(5,𝔽2)12yes—
426C2×C4×C11H(5,𝔽2)12yes—
427C2×C4×C11C2511yescharacteristic
428C22⋊D11—48no—
429C22⋊D11—44no—
430C2×Dic11—24no—
431C2×Dic11—22no—
432C2×Dic11—48no—
433C2×Dic11—44no—
434D44—22no—
435D44—22no—
436D44—42no—
437D44—42no—
438C4×D11—48no—
439C4×D11—44no—
440Dic22—24no—
441Dic22—22no—
442Dic22—24no—
443Dic22—22no—
444Dic22—48no—
445Dic22—44no—
446C11⋊C8—22no—
447C11⋊C8—22no—
448C11⋊C8—24no—
449C2×2−1+4—112no—
450C2×#137—112no—
451C2×AGL(1,ℤ/8)—112no—
452C2×#135—112no—
453C22×SD16—112no—
454D4×Q8—221no—
455D4×Q8—221no—
456#547—222no—
457#547—221no—
458#547—222no—
459#547—221no—
460#544C2×D1111yescharacteristic
461#542—21no—
462#542C2×D1112yes—
463#540—21no—
464#540C2×D1112yes—
465#538—22no—
466#537C2×D1111yescharacteristic
467#536—112no—
468#536—114no—
469#535C2×D1111yescharacteristic
470#535C2×D1111yescharacteristic
471#532—21no—
472#532—111no—
473#532—112no—
474#532C2×D1112yes—
475C2×C4⋊Q8—111no—
476C2×C4⋊Q8—112no—
477#529—21no—
478#529C2×D1112yes—
479#525—22no—
480C4×#41C2×D1111yescharacteristic
481C4×#41C2×D1111yescharacteristic
482C2×C4×D4C2×D1111yescharacteristic
483#497—114no—
484#496—114no—
485#495—114no—
486#492—114no—
487#491—114no—
488#489—114no—
489#488—114no—
490#487—114no—
491#464—112no—
492#463—112no—
493#463—114no—
494#462—112no—
495#462—111no—
496#462—112no—
497#461—111no—
498#461—112no—
499#461—112no—
500#461—112no—
501#461—112no—
502#461—112no—
503#461—114no—
504#460—111no—
505#459—112no—
506#459—111no—
507#452—114no—
508#451—114no—
509#449—114no—
510#449—114no—
511#449—114no—
512#448—114no—
513#448—114no—
514#448—114no—
515#433—114no—
516#432—112no—
517#431—112no—
518#423—111no—
519C2×C4⋊C8—111no—
520#419—112no—
521#417—112no—
522#416—112no—
523C2×#103—112no—
524#408—112no—
525#405—112no—
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—22no—
529C22×C11—22no—
530C22×C11—22no—
531C22×C11—41no—
532C22×C11—42no—
533C22×C11—41no—
534C22×C11—42no—
535C22×C11—42no—
536C22×C11—41no—
537C22×C11—84no—
538C22×C11#53512yes—
539C22×C11C23×D411yescharacteristic
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C4×C11—21no—
544C4×C11—21no—
545C4×C11—22no—
546C4×C11—22no—
547C4×C11—21no—
548C4×C11—22no—
549C4×C11—41no—
550C4×C11—41no—
551C4×C11—42no—
552C4×C11—41no—
553C4×C11#53512yes—
554C4×C11#57712yes—
555C4×C11C2×H(5,𝔽2)11yescharacteristic
556C4×C11C2×H(5,𝔽2)11yescharacteristic
557Dic11—44no—
558Dic11—42no—
5592−1+4—444no—
5602−1+4—444no—
561C2×#41—22no—
562C2×#41—112no—
563C2×#41—114no—
564C2×#41—224no—
565C2×#41—222no—
566C2×#41C22×D1111yescharacteristic
567C2×#41C22×D1111yescharacteristic
568C22×Q8—112no—
569C22×Q8—114no—
570C22×Q8—222no—
571C22×D4C22×D1111yescharacteristic
572C23×C4—21no—
573#137—444no—
574AGL(1,ℤ/8)—444no—
575#135—444no—
576C2×Q16—112no—
577C2×Q16—114no—
578C2×SD16—112no—
579C2×SD16—114no—
580C2×SD16—114no—
581C2×SD16—112no—
582C2×SD16—114no—
583C2×SD16—114no—
584C2×SD16—444no—
585C2×D8—112no—
586C2×D8—114no—
587C2×M16—112no—
588C22×C8—112no—
589C4⋊Q8—21no—
590C4⋊Q8—112no—
591C4⋊Q8—111no—
592C4⋊Q8—112no—
593C4⋊Q8—114no—
594C4⋊Q8—221no—
595C4⋊Q8—221no—
596C4⋊Q8—222no—
597C4⋊Q8—222no—
598C4⋊Q8C22×D1112yes—
599#127—21no—
600#127—111no—
601#127C22×D1112yes—
602#126—22no—
603#126—22no—
604#125—21no—
605#125C22×D1112yes—
606#124—21no—
607#124—22no—
608#124—22no—
609#124—112no—
610#124—114no—
611#124C22×D1112yes—
612#123—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616#123—224no—
617#123—224no—
618#123—224no—
619C22⋊Q8—21no—
620C22⋊Q8—22no—
621C22⋊Q8—22no—
622C22⋊Q8—222no—
623C22⋊Q8—222no—
624C22⋊Q8—224no—
625C22⋊Q8—224no—
626C22⋊Q8C22×D1112yes—
627#121—22no—
628#121—21no—
629#121—22no—
630#121—21no—
631#121—21no—
632#121—22no—
633#121—22no—
634#121—221no—
635#121—222no—
636#121—221no—
637#121—222no—
638#121C22×D1112yes—
639#121C22×D1112yes—
640#121C22×D1112yes—
641#120—22no—
642#120—22no—
643C4×Q8C22⋊D1111yescharacteristic
644C4×Q8C22⋊D1111yescharacteristic
645C4×Q8C22×D1111yescharacteristic
646C4×Q8C22×D1111yescharacteristic
647C4×D4—21no—
648C4×D4—21no—
649C4×D4—22no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—22no—
653C4×D4—221no—
654C4×D4—221no—
655C4×D4—222no—
656C4×D4—222no—
657C4×D4C22⋊D1112yes—
658C4×D4C22⋊D1111yescharacteristic
659C4×D4C22⋊D1112yes—
660C4×D4C22⋊D1111yescharacteristic
661C4×D4C22×D1112yes—
662C4×D4C22×D1112yes—
663C4×D4C22×D1111yescharacteristic
664C4×D4C22×D1111yescharacteristic
665#117—21no—
666#117—22no—
667#117C22×D1111yescharacteristic
668#117C22×D1111yescharacteristic
669#117C22×D1112yes—
670C2×C4⋊C4—221no—
671C2×C4⋊C4—222no—
672C2×C4⋊C4—221no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4C22×D1111yescharacteristic
675C2×C22⋊C4—21no—
676C2×C42—21no—
677C2×C42C22×D1111yescharacteristic
678C2×C42C22×D1112yes—
679C4⋊C8—111no—
680C4⋊C8—111no—
681C4⋊C8—112no—
682C4⋊C8—112no—
683C4⋊C8—112no—
684#103—114no—
685#103—114no—
686#103—112no—
687#103—112no—
688#103—114no—
689#103—114no—
690#103—114no—
691#102—112no—
692#102—112no—
693#102—114no—
694C22⋊C8—114no—
695C22⋊C8—114no—
696#97—114no—
697C4×C8—114no—
698C2×C11—22no—
699C2×C11—42no—
700C2×C11—81no—
701C2×C11—82no—
702C2×C11C2×#53511yescharacteristic
703C2×C11C2×#57711yescharacteristic
704C2×C11#358611yescharacteristic
705D11—82no—
706C24—21no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—84no—
712#41—224no—
713#41—224no—
714#41—444no—
715#41—444no—
716#41—4416no—
717#41—448no—
718C2×Q8—22no—
719C2×Q8—114no—
720C2×Q8—112no—
721C2×Q8—224no—
722C2×Q8—222no—
723C2×Q8—224no—
724C2×Q8—224no—
725C2×Q8—444no—
726C2×Q8—444no—
727C2×Q8—448no—
728C2×Q8C2×C22⋊D1111yescharacteristic
729C2×Q8C23×D1111yescharacteristic
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—21no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—112no—
740C2×D4—224no—
741C2×D4—222no—
742C2×D4—221no—
743C2×D4—221no—
744C2×D4C2×C22⋊D1112yes—
745C2×D4C2×C22⋊D1111yescharacteristic
746C2×D4C23×D1112yes—
747C2×D4C23×D1111yescharacteristic
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—82no—
755C22×C4—224no—
756C22×C4—222no—
757C22×C4—224no—
758C22×C4—222no—
759C22×C4C2×C22⋊D1111yescharacteristic
760C22×C4C2×C22⋊D1112yes—
761C22×C4C2×C22⋊D1111yescharacteristic
762C22×C4C2×C22⋊D1112yes—
763C22×C4C23×D1112yes—
764C22×C4C23×D1111yescharacteristic
765Q16—442no—
766Q16—444no—
767SD16—444no—
768SD16—444no—
769SD16—442no—
770SD16—444no—
771SD16—444no—
772SD16—442no—
773D8—442no—
774D8—444no—
775M16—224no—
776C2×C8—112no—
777C2×C8—114no—
778C2×C8—112no—
779C2×C8—224no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—222no—
788C4⋊C4—221no—
789C4⋊C4—222no—
790C4⋊C4—221no—
791C4⋊C4—222no—
792C4⋊C4—224no—
793C4⋊C4—222no—
794C4⋊C4—224no—
795C4⋊C4C2×C22⋊D1111yescharacteristic
796C4⋊C4C2×C22⋊D1111yescharacteristic
797C4⋊C4C2×C22⋊D1112yes—
798C4⋊C4C2×C22⋊D1112yes—
799C4⋊C4C23×D1112yes—
800C4⋊C4C23×D1111yescharacteristic
801C4⋊C4C23×D1111yescharacteristic
802C22⋊C4—21no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—222no—
814C22⋊C4—224no—
815C22⋊C4—222no—
816C22⋊C4—224no—
817C22⋊C4C2×C22⋊D1112yes—
818C22⋊C4C2×C22⋊D1112yes—
819C22⋊C4C2×C22⋊D1112yes—
820C42—21no—
821C42—21no—
822C42—21no—
823C42C2×C22⋊D1111yescharacteristic
824C42C2×C22⋊D1111yescharacteristic
825C42C2×C22⋊D1112yes—
826C42C2×C22⋊D1112yes—
827C42C23×D1112yes—
828C42C23×D1111yescharacteristic
829C42C23×D1111yescharacteristic
830C11#6083611yescharacteristic, complemented, Sylow
831C23—22no—
832C23—21no—
833C23—42no—
834C23—81no—
835C23—81no—
836C23—222no—
837C23C22×C22⋊D1112yes—
838C23C22×C22⋊D1111yescharacteristic
839Q8—22no—
840Q8—21no—
841Q8—21no—
842Q8—82no—
843Q8—224no—
844Q8—222no—
845Q8—224no—
846Q8—222no—
847Q8—448no—
848Q8—444no—
849D4—24no—
850D4—22no—
851D4—22no—
852D4—21no—
853D4—22no—
854D4—21no—
855D4—42no—
856D4—42no—
857D4—82no—
858D4—82no—
859D4—82no—
860D4—82no—
861D4—82no—
862D4—222no—
863D4—222no—
864D4—442no—
865D4—448no—
866D4—444no—
867D4—442no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—44no—
880C2×C4—42no—
881C2×C4—81no—
882C2×C4—82no—
883C2×C4—81no—
884C2×C4—224no—
885C2×C4—222no—
886C2×C4—448no—
887C2×C4—448no—
888C2×C4—444no—
889C2×C4—444no—
890C2×C4#6704212yes—
891C2×C4#6704212yes—
892C2×C4C22×C22⋊D1111yescharacteristic
893C2×C4C22×C22⋊D1111yescharacteristic
894C2×C4C22×C22⋊D1112yes—
895C2×C4C22×C22⋊D1112yes—
896C2×C4C22×C22⋊D1111yescharacteristic
897C2×C4C22×C22⋊D1112yes—
898C2×C4C22×C22⋊D1111yescharacteristic
899C2×C4C22×C22⋊D1111yescharacteristic
900C2×C4C24×D1111yescharacteristic
901C8—222no—
902C8—222no—
903C8—224no—
904C22—21no—
905C22—21no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—84no—
916C22—442no—
917C22—442no—
918C22—442no—
919C22#1062336112yes—
920C22C23×C22⋊D1111yescharacteristic
921C4—21no—
922C4—21no—
923C4—22no—
924C4—22no—
925C4—21no—
926C4—22no—
927C4—41no—
928C4—41no—
929C4—42no—
930C4—41no—
931C4—444no—
932C4—442no—
933C4#1062336112yes—
934C4#1062336712yes—
935C4C2×#6704211yescharacteristic
936C4C2×#6704211yescharacteristic
937C2—22no—
938C2—42no—
939C2—82no—
940C2—81no—
941C2—882no—
942C2C2×#1062336111yescharacteristic
943C2C2×#1062336711yescharacteristic
944C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3460C2
socleC22×C11C23×D4
hypercenter#3460D11
hypocenterC11#60836
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3460

Complements

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

NH ≅ G/Ntype
1. #13082401C2semidirect
2. #13079719C2semidirect
3. #13079671C2semidirect
4. #13079640C2semidirect
5. #13079607C2semidirect
6. #13079588C2semidirect
7. #13079538C2semidirect
8. #13079088C2semidirect
9. #13078986C2semidirect
10. #13078103C2semidirect
11. #13078080C2semidirect
12. #13078071C2semidirect
13. C2×#10622632C2semidirect
14. #13077928C2semidirect
15. #13077900C2semidirect
16. #13077282C2semidirect
17. C11×#3460C2semidirect
47. #10623057C22semidirect
49. #10623008C22semidirect
51. C2×#66922C22semidirect
53. #10622706C22semidirect
54. #10622702C22semidirect
57. #10622682C22semidirect
58. #10622681C22semidirect
61. #10622663C22semidirect
62. #10622660C22semidirect
65. #10622653C22semidirect
68. #10622650C22semidirect
69. #10622644C22semidirect
70. #10622644C22semidirect
71. #10622644C22semidirect
72. #10622641C22semidirect
73. #10622640C22semidirect
78. #10622632C22semidirect
79. #10622632C22semidirect
80. #10622632C22semidirect
82. #10622629C22semidirect
84. #10622628C22semidirect
87. #10622613C22semidirect
91. #10622539C22semidirect
92. #10622538C22semidirect
360. #3460D11semidirect
830. C11#60836semidirect

Maximal subgroups

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

subgroupindex
#130824012
#130797192
#130796712
#130796402
#130796072
#130795882
#130795382
#130790882
#130789862
#130781032
#130780802
#130780712
C2×#106226322
#130779282
#130779002
#130772822
C11×#34602
#6083611