Finite Group Databasebeta

← #15625767

Subgroups — #15625767

Order 2816.

2008 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082401C211yesmaximal, characteristic, complemented
2#13079719C214yesmaximal, complemented
3#13079693C214yesmaximal, complemented
4#13079640C212yesmaximal, complemented
5#13079623C212yesmaximal, complemented
6#13079588C212yesmaximal, complemented
7#13079561C212yesmaximal, complemented
8#13079107C212yesmaximal, complemented
9#13078986C212yesmaximal, complemented
10#13078103C211yesmaximal, characteristic, complemented
11#13078088C211yesmaximal, characteristic, complemented
12#13078071C211yesmaximal, characteristic, complemented
13C2×#10622644C211yesmaximal, characteristic, complemented
14#13077928C212yesmaximal, complemented
15#13077909C212yesmaximal, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C11×#3461C211yesmaximal, characteristic, complemented
18C2×#67043C2212yes—
19C11×#544C2211yescharacteristic
20C11×#542—21no—
21C11×#542C2212yes—
22C11×#541—21no—
23C11×#541C2212yes—
24C11×#539—22no—
25C11×#537C2211yescharacteristic
26C11×#536C2211yescharacteristic
27C11×#536C2211yescharacteristic
28C11×#533—21no—
29C11×#533C2212yes—
30C11×#529—22no—
31C11×#529—21no—
32C11×#529C2212yes—
33C4×C11×#41C2211yescharacteristic
34C4×C11×#41C2211yescharacteristic
35C2×C4×Q8×C11C2211yescharacteristic
36C2×#67004C2212yes—
37C2×#67003C2212yes—
38C22×#4326C2212yes—
39C2×#66995C2212yes—
40Q8×D44—21no—
41Q8×D44—21no—
42#10623086—21no—
43#10623086—22no—
44#10623086—22no—
45#10623086—21no—
46#10623057C2212yes—
47#10623057C2214yes—
48#10623008C2212yes—
49#10623008C2211yescharacteristic
50C2×#66922C2212yes—
51C2×#66922C2211yescharacteristic
52#10622847C2212yes—
53#10622706C2214yes—
54#10622705C2214yes—
55#10622702C2214yes—
56#10622699C2214yes—
57#10622682C2214yes—
58#10622681C2214yes—
59#10622673C2214yes—
60#10622672C2214yes—
61#10622663C2214yes—
62#10622663C2214yes—
63#10622663C2214yes—
64#10622660C2214yes—
65#10622660C2214yes—
66#10622660C2214yes—
67#10622653C2214yes—
68#10622650C2214yes—
69#10622644C2211yescharacteristic
70#10622644C2212yes—
71#10622644C2212yes—
72#10622644C2212yes—
73#10622644C2212yes—
74#10622644C2214yes—
75#10622644C2212yes—
76#10622641C2212yes—
77#10622641C2214yes—
78#10622640C2212yes—
79#10622640C2211yescharacteristic
80#10622632C2212yes—
81#10622632C2211yescharacteristic
82#10622632C2212yes—
83#10622629C2212yes—
84#10622628C2211yescharacteristic
85#10622617C2212yes—
86#10622615C2212yes—
87#10622613C2214yes—
88#10622610C2212yes—
89C2×#66874C2212yes—
90#10622579C2212yes—
91#10622539C2212yes—
92#10622538C2212yes—
93#10622537C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C2×C11×#41C2311yescharacteristic
96C2×C11×#41C2311yescharacteristic
97C22×Q8×C11C2311yescharacteristic
98#67043—44no—
99#67043—44no—
100C2×Q8×D11—22no—
101C2×#4341—24no—
102C2×#4341—22no—
103C2×#4339C2312yes—
104C2×#4339C2314yes—
105C22×Dic22C2312yes—
106C22×Dic22C2314yes—
107C11×C4⋊Q8—21no—
108C11×C4⋊Q8—21no—
109C11×C4⋊Q8C2312yes—
110C11×C4⋊Q8C2312yes—
111C11×#126—22no—
112C11×#126—22no—
113C11×#126—22no—
114C11×#126—22no—
115C11×#125—22no—
116C11×#125—21no—
117C11×#125—22no—
118C11×#125—22no—
119C11×#125C2312yes—
120C11×#124—21no—
121C11×#124—22no—
122C11×#124C2312yes—
123C11×#123—22no—
124C11×#123—22no—
125C11×#123—22no—
126C11×#123—22no—
127C11×C22⋊Q8—21no—
128C11×C22⋊Q8—22no—
129C11×C22⋊Q8—21no—
130C11×C22⋊Q8—21no—
131C11×C22⋊Q8—22no—
132C11×C22⋊Q8—22no—
133C11×C22⋊Q8C2312yes—
134C11×C22⋊Q8C2312yes—
135C11×C22⋊Q8C2312yes—
136C11×#121—22no—
137C11×#121—21no—
138C11×#121C2312yes—
139C4×Q8×C11—21no—
140C4×Q8×C11—21no—
141C4×Q8×C11—22no—
142C4×Q8×C11D411yescharacteristic
143C4×Q8×C11D411yescharacteristic
144C4×Q8×C11C2312yes—
145C4×Q8×C11C2312yes—
146C4×Q8×C11C2311yescharacteristic
147C4×Q8×C11C2311yescharacteristic
148C4×D4×C11—21no—
149C4×D4×C11—21no—
150C4×D4×C11—22no—
151C4×D4×C11D411yescharacteristic
152C4×D4×C11D412yes—
153C4×D4×C11D412yes—
154C4×D4×C11D411yescharacteristic
155C4×D4×C11C2311yescharacteristic
156C4×D4×C11C2311yescharacteristic
157C11×#117—22no—
158C11×#117—21no—
159C11×#117—22no—
160C11×#117C2311yescharacteristic
161C11×#117C2311yescharacteristic
162C11×#117C2312yes—
163C2×C11×C4⋊C4—21no—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C42×C11—21no—
166C2×C42×C11—21no—
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169#67004—44no—
170#67003—44no—
171C2×#4326—44no—
172C2×#4326C2314yes—
173C2×#4326C2314yes—
174C2×#4326C2314yes—
175C2×#4326C2312yes—
176C2×#4326C2314yes—
177#66995—44no—
178C2×#4325C2314yes—
179C2×#4325C2312yes—
180C2×#4324C2312yes—
181C2×#4324C2314yes—
182C2×#4323C2312yes—
183#66983—21no—
184#66983—22no—
185#66983—21no—
186#66983—22no—
187C2×C4⋊Dic11—21no—
188C2×C4⋊Dic11—22no—
189C2×C4⋊Dic11—21no—
190C2×C4⋊Dic11—22no—
191C2×#4318C2312yes—
192C22×C11⋊C8C2312yes—
193#66950—22no—
194#66950—24no—
195#66950—22no—
196#66950—24no—
197#66939—24no—
198#66939—24no—
199#66939—24no—
200#66928C2312yes—
201#66928C2314yes—
202#66927C2311yescharacteristic
203C4×D44—21no—
204C4×D44—22no—
205C4×D44—21no—
206C4×D44—22no—
207#66922—21no—
208#66922—22no—
209#66922—21no—
210#66922—22no—
211#66922C2311yescharacteristic
212#66922C2312yes—
213#66922C2312yes—
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#60837—111nomaximal, Sylow
235C11×#41—22no—
236C11×#41—22no—
237C11×#41—22no—
238C11×#41—22no—
239C2×Q8×C11—21no—
240C2×Q8×C11—22no—
241C2×Q8×C11—22no—
242C2×Q8×C11—22no—
243C2×Q8×C11C2×D411yescharacteristic
244C2×Q8×C11C2412yes—
245C2×Q8×C11C2411yescharacteristic
246C2×D4×C11—21no—
247C2×D4×C11—22no—
248C2×D4×C11C2×D412yes—
249C2×D4×C11C2×D411yescharacteristic
250C2×D4×C11C2411yescharacteristic
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2412yes—
261C22×C4×C11C2411yescharacteristic
262C2×C22⋊D11—24no—
263C2×C22⋊D11—22no—
264C22×Dic11—24no—
265C22×Dic11—22no—
266Q8×D11—48no—
267#4341—416no—
268#4341—48no—
269#4339—24no—
270#4339—24no—
271#4339—44no—
272#4339—44no—
273C2×D44—21no—
274C2×D44—21no—
275C2×D44C2412yes—
276C2×C4×D11—24no—
277C2×C4×D11—22no—
278C2×Dic22—24no—
279C2×Dic22—22no—
280C2×Dic22—24no—
281C2×Dic22—24no—
282C2×Dic22—44no—
283C2×Dic22—44no—
284C2×Dic22C2414yes—
285C2×Dic22C2412yes—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4C2×D412yes—
300C11×C4⋊C4C2×D411yescharacteristic
301C11×C4⋊C4C2×D411yescharacteristic
302C11×C4⋊C4C2×D412yes—
303C11×C4⋊C4C2412yes—
304C11×C4⋊C4C2411yescharacteristic
305C11×C4⋊C4C2411yescharacteristic
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—21no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—21no—
312C11×C22⋊C4—22no—
313C11×C22⋊C4—22no—
314C11×C22⋊C4—22no—
315C11×C22⋊C4C2×D412yes—
316C11×C22⋊C4C2×D412yes—
317C11×C22⋊C4C2×D412yes—
318C42×C11—22no—
319C42×C11—21no—
320C42×C11—21no—
321C42×C11—21no—
322C42×C11—22no—
323C42×C11C2×D411yescharacteristic
324C42×C11C2×D411yescharacteristic
325C42×C11C2×D412yes—
326C42×C11C2×D412yes—
327C42×C11C2412yes—
328C42×C11C2411yescharacteristic
329C42×C11C2411yescharacteristic
330#4326—44no—
331#4326—44no—
332#4326—44no—
333#4326—42no—
334#4326—44no—
335#4325—44no—
336#4325—42no—
337#4324—42no—
338#4324—44no—
339#4323—42no—
340(C2×D11)⋊C4—22no—
341(C2×D11)⋊C4—22no—
342(C2×D11)⋊C4—24no—
343(C2×D11)⋊C4—24no—
344C4⋊Dic11—22no—
345C4⋊Dic11—21no—
346C4⋊Dic11—22no—
347C4⋊Dic11—21no—
348C4⋊Dic11—22no—
349C4⋊Dic11—22no—
350C4⋊Dic11—24no—
351C4⋊Dic11—24no—
352#4318—24no—
353C2×C11⋊C8—24no—
354C2×C11⋊C8C2412yes—
355C2×C11⋊C8C2414yes—
356C2×C11⋊C8C2412yes—
357#3499—111no—
358#3461D1111yescharacteristic, complemented
359#3225—114no—
360#3223—114no—
361#3218—112no—
362#3216—112no—
363#3212—112no—
364#3209—112no—
365#3156—112no—
366#3137—112no—
367#3039—111no—
368#3037—111no—
369#3035—111no—
370C2×#462—111no—
371#3013—112no—
372#3011—112no—
373#2925—111no—
374C23×C11—21no—
375C23×C11C22×D412yes—
376C23×C11C22×D411yescharacteristic
377C22×D11—22no—
378Q8×C11—22no—
379Q8×C11—22no—
380Q8×C11—21no—
381Q8×C11—22no—
382Q8×C11—21no—
383Q8×C11—42no—
384Q8×C11—82no—
385D4×C11—24no—
386D4×C11—22no—
387D4×C11—21no—
388D4×C11—21no—
389D4×C11—42no—
390D4×C11—82no—
391C2×C4×C11—22no—
392C2×C4×C11—24no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—21no—
396C2×C4×C11—22no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—22no—
400C2×C4×C11—41no—
401C2×C4×C11—42no—
402C2×C4×C11—42no—
403C2×C4×C11—42no—
404C2×C4×C11—42no—
405C2×C4×C11—81no—
406C2×C4×C11—81no—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D412yes—
411C2×C4×C11C22×D412yes—
412C2×C4×C11C22×D412yes—
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11H(5,𝔽2)12yes—
416C2×C4×C11H(5,𝔽2)12yes—
417C2×C4×C11C2511yescharacteristic
418C22⋊D11—48no—
419C22⋊D11—44no—
420C2×Dic11—24no—
421C2×Dic11—22no—
422C2×Dic11—48no—
423C2×Dic11—44no—
424D44—22no—
425D44—22no—
426D44—42no—
427D44—42no—
428C4×D11—48no—
429C4×D11—44no—
430Dic22—24no—
431Dic22—22no—
432Dic22—24no—
433Dic22—22no—
434Dic22—48no—
435Dic22—44no—
436C11⋊C8—22no—
437C11⋊C8—22no—
438C11⋊C8—24no—
439C2×2−1+4—112no—
440C2×#137—112no—
441C2×#137—112no—
442C2×#135—112no—
443C22×Q16—112no—
444D4×Q8—221no—
445D4×Q8—221no—
446#547—222no—
447#547—221no—
448#547—222no—
449#547—221no—
450#544C2×D1111yescharacteristic
451#542—21no—
452#542C2×D1112yes—
453#541—21no—
454#541C2×D1112yes—
455#539—22no—
456#537C2×D1111yescharacteristic
457#536—112no—
458#536—114no—
459#536C2×D1111yescharacteristic
460#536C2×D1111yescharacteristic
461#533—21no—
462#533C2×D1112yes—
463#532—112no—
464#532—111no—
465C2×C4⋊Q8—112no—
466C2×C4⋊Q8—111no—
467#529—22no—
468#529—21no—
469#529C2×D1112yes—
470C4×#41C2×D1111yescharacteristic
471C4×#41C2×D1111yescharacteristic
472C2×C4×Q8C2×D1111yescharacteristic
473#497—114no—
474#497—114no—
475#495—114no—
476#494—114no—
477#491—114no—
478#489—114no—
479#488—114no—
480#487—114no—
481#464—112no—
482#464—114no—
483#463—112no—
484#462—111no—
485#462—112no—
486#462—112no—
487#462—112no—
488#462—112no—
489#462—112no—
490#462—114no—
491#461—112no—
492#461—111no—
493#461—112no—
494#460—112no—
495#460—111no—
496#459—111no—
497#452—114no—
498#452—114no—
499#452—114no—
500#451—114no—
501#451—114no—
502#451—114no—
503#449—114no—
504#448—114no—
505#433—114no—
506#432—112no—
507#431—112no—
508#423—111no—
509C2×C4⋊C8—111no—
510#419—112no—
511#417—112no—
512#416—112no—
513C2×#103—112no—
514#408—112no—
515#405—112no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—22no—
519C22×C11—22no—
520C22×C11—22no—
521C22×C11—41no—
522C22×C11—41no—
523C22×C11—41no—
524C22×C11#53512yes—
525C22×C11C23×D411yescharacteristic
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—22no—
533C4×C11—21no—
534C4×C11—22no—
535C4×C11—42no—
536C4×C11—41no—
537C4×C11—41no—
538C4×C11—42no—
539C4×C11—41no—
540C4×C11#53512yes—
541C4×C11#57812yes—
542C4×C11C2×H(5,𝔽2)11yescharacteristic
543C4×C11C2×H(5,𝔽2)11yescharacteristic
544Dic11—44no—
545Dic11—42no—
5462−1+4—444no—
5472−1+4—444no—
548C2×#41—112no—
549C2×#41—114no—
550C2×#41—224no—
551C2×#41—222no—
552C2×#41C22×D1111yescharacteristic
553C2×#41C22×D1111yescharacteristic
554C22×Q8—112no—
555C22×Q8—114no—
556C22×Q8—222no—
557C22×Q8C22×D1111yescharacteristic
558#137—444no—
559#137—444no—
560#135—444no—
561C2×Q16—114no—
562C2×Q16—114no—
563C2×Q16—112no—
564C2×Q16—114no—
565C2×Q16—114no—
566C2×Q16—444no—
567C2×SD16—112no—
568C2×SD16—114no—
569C2×SD16—112no—
570C2×SD16—114no—
571C2×D8—112no—
572C2×M16—112no—
573C22×C8—112no—
574C4⋊Q8—21no—
575C4⋊Q8—21no—
576C4⋊Q8—111no—
577C4⋊Q8—112no—
578C4⋊Q8—112no—
579C4⋊Q8—114no—
580C4⋊Q8—221no—
581C4⋊Q8—222no—
582C4⋊Q8—221no—
583C4⋊Q8—222no—
584C4⋊Q8C22×D1112yes—
585C4⋊Q8C22×D1112yes—
586#127—111no—
587#126—22no—
588#126—22no—
589#126—22no—
590#126—22no—
591#125—22no—
592#125—21no—
593#125—22no—
594#125—22no—
595#125C22×D1112yes—
596#124—21no—
597#124—22no—
598#124—112no—
599#124—114no—
600#124C22×D1112yes—
601#123—22no—
602#123—22no—
603#123—22no—
604#123—22no—
605#123—224no—
606#123—224no—
607#123—224no—
608C22⋊Q8—21no—
609C22⋊Q8—22no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—22no—
613C22⋊Q8—22no—
614C22⋊Q8—222no—
615C22⋊Q8—224no—
616C22⋊Q8—222no—
617C22⋊Q8—224no—
618C22⋊Q8C22×D1112yes—
619C22⋊Q8C22×D1112yes—
620C22⋊Q8C22×D1112yes—
621#121—22no—
622#121—21no—
623#121—221no—
624#121—222no—
625#121—221no—
626#121—222no—
627#121C22×D1112yes—
628C4×Q8—21no—
629C4×Q8—21no—
630C4×Q8—22no—
631C4×Q8C22⋊D1111yescharacteristic
632C4×Q8C22⋊D1111yescharacteristic
633C4×Q8C22×D1112yes—
634C4×Q8C22×D1112yes—
635C4×Q8C22×D1111yescharacteristic
636C4×Q8C22×D1111yescharacteristic
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—22no—
640C4×D4—221no—
641C4×D4—222no—
642C4×D4—221no—
643C4×D4—222no—
644C4×D4C22⋊D1111yescharacteristic
645C4×D4C22⋊D1112yes—
646C4×D4C22⋊D1112yes—
647C4×D4C22⋊D1111yescharacteristic
648C4×D4C22×D1111yescharacteristic
649C4×D4C22×D1111yescharacteristic
650#117—22no—
651#117—21no—
652#117—22no—
653#117C22×D1111yescharacteristic
654#117C22×D1111yescharacteristic
655#117C22×D1112yes—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—221no—
658C2×C4⋊C4—222no—
659C2×C4⋊C4—221no—
660C2×C4⋊C4—222no—
661C2×C4⋊C4C22×D1111yescharacteristic
662C2×C42—21no—
663C2×C42—21no—
664C2×C42C22×D1111yescharacteristic
665C2×C42C22×D1112yes—
666C4⋊C8—111no—
667C4⋊C8—111no—
668C4⋊C8—112no—
669C4⋊C8—112no—
670C4⋊C8—112no—
671#103—114no—
672#103—114no—
673#103—112no—
674#103—112no—
675#103—114no—
676#103—114no—
677#103—114no—
678#102—112no—
679#102—112no—
680#102—114no—
681C22⋊C8—114no—
682C22⋊C8—114no—
683#97—114no—
684C4×C8—114no—
685C2×C11—22no—
686C2×C11—42no—
687C2×C11—81no—
688C2×C11C2×#53511yescharacteristic
689C2×C11C2×#57811yescharacteristic
690C2×C11#358611yescharacteristic
691D11—82no—
692#41—22no—
693#41—22no—
694#41—22no—
695#41—22no—
696#41—224no—
697#41—224no—
698#41—444no—
699#41—444no—
700#41—4416no—
701#41—448no—
702C2×Q8—21no—
703C2×Q8—22no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—114no—
707C2×Q8—112no—
708C2×Q8—224no—
709C2×Q8—222no—
710C2×Q8—224no—
711C2×Q8—224no—
712C2×Q8—444no—
713C2×Q8—444no—
714C2×Q8—448no—
715C2×Q8C2×C22⋊D1111yescharacteristic
716C2×Q8C23×D1112yes—
717C2×Q8C23×D1111yescharacteristic
718C2×D4—21no—
719C2×D4—22no—
720C2×D4—112no—
721C2×D4—224no—
722C2×D4—222no—
723C2×D4—221no—
724C2×D4—221no—
725C2×D4C2×C22⋊D1112yes—
726C2×D4C2×C22⋊D1111yescharacteristic
727C2×D4C23×D1111yescharacteristic
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—224no—
734C22×C4—222no—
735C22×C4—224no—
736C22×C4—222no—
737C22×C4C2×C22⋊D1111yescharacteristic
738C22×C4C2×C22⋊D1112yes—
739C22×C4C2×C22⋊D1111yescharacteristic
740C22×C4C2×C22⋊D1112yes—
741C22×C4C23×D1112yes—
742C22×C4C23×D1111yescharacteristic
743Q16—444no—
744Q16—444no—
745Q16—442no—
746Q16—444no—
747Q16—444no—
748SD16—442no—
749SD16—444no—
750SD16—442no—
751SD16—444no—
752D8—442no—
753M16—224no—
754C2×C8—112no—
755C2×C8—114no—
756C2×C8—112no—
757C2×C8—224no—
758C4⋊C4—22no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—22no—
764C4⋊C4—22no—
765C4⋊C4—22no—
766C4⋊C4—22no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—22no—
771C4⋊C4—222no—
772C4⋊C4—221no—
773C4⋊C4—222no—
774C4⋊C4—221no—
775C4⋊C4—222no—
776C4⋊C4—222no—
777C4⋊C4—224no—
778C4⋊C4—224no—
779C4⋊C4C2×C22⋊D1112yes—
780C4⋊C4C2×C22⋊D1111yescharacteristic
781C4⋊C4C2×C22⋊D1111yescharacteristic
782C4⋊C4C2×C22⋊D1112yes—
783C4⋊C4C23×D1112yes—
784C4⋊C4C23×D1111yescharacteristic
785C4⋊C4C23×D1111yescharacteristic
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—21no—
789C22⋊C4—22no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—222no—
796C22⋊C4—222no—
797C22⋊C4—224no—
798C22⋊C4—224no—
799C22⋊C4C2×C22⋊D1112yes—
800C22⋊C4C2×C22⋊D1112yes—
801C22⋊C4C2×C22⋊D1112yes—
802C42—22no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—22no—
807C42C2×C22⋊D1111yescharacteristic
808C42C2×C22⋊D1111yescharacteristic
809C42C2×C22⋊D1112yes—
810C42C2×C22⋊D1112yes—
811C42C23×D1112yes—
812C42C23×D1111yescharacteristic
813C42C23×D1111yescharacteristic
814C11#6083711yescharacteristic, complemented, Sylow
815C23—21no—
816C23—222no—
817C23C22×C22⋊D1112yes—
818C23C22×C22⋊D1111yescharacteristic
819Q8—22no—
820Q8—22no—
821Q8—21no—
822Q8—22no—
823Q8—21no—
824Q8—42no—
825Q8—82no—
826Q8—224no—
827Q8—222no—
828Q8—224no—
829Q8—222no—
830Q8—448no—
831Q8—444no—
832D4—24no—
833D4—22no—
834D4—21no—
835D4—21no—
836D4—42no—
837D4—82no—
838D4—222no—
839D4—222no—
840D4—442no—
841D4—448no—
842D4—444no—
843D4—442no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—224no—
861C2×C4—222no—
862C2×C4—448no—
863C2×C4—448no—
864C2×C4—444no—
865C2×C4—444no—
866C2×C4#6704212yes—
867C2×C4#6704212yes—
868C2×C4C22×C22⋊D1111yescharacteristic
869C2×C4C22×C22⋊D1111yescharacteristic
870C2×C4C22×C22⋊D1111yescharacteristic
871C2×C4C22×C22⋊D1112yes—
872C2×C4C22×C22⋊D1112yes—
873C2×C4C22×C22⋊D1112yes—
874C2×C4C22×C22⋊D1111yescharacteristic
875C2×C4C22×C22⋊D1111yescharacteristic
876C2×C4C24×D1111yescharacteristic
877C8—222no—
878C8—222no—
879C8—224no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—442no—
889C22—442no—
890C22—442no—
891C22#1062336112yes—
892C22C23×C22⋊D1111yescharacteristic
893C4—21no—
894C4—21no—
895C4—22no—
896C4—22no—
897C4—21no—
898C4—22no—
899C4—42no—
900C4—41no—
901C4—41no—
902C4—42no—
903C4—41no—
904C4—444no—
905C4—442no—
906C4#1062336112yes—
907C4#1062336912yes—
908C4C2×#6704211yescharacteristic
909C4C2×#6704211yescharacteristic
910C2—22no—
911C2—42no—
912C2—81no—
913C2—882no—
914C2C2×#1062336111yescharacteristic
915C2C2×#1062336911yescharacteristic
916C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3461C2
socleC22×C11C23×D4
hypercenter#3461D11
hypocenterC11#60837
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #13082401C2semidirect
2. #13079719C2semidirect
3. #13079693C2semidirect
4. #13079640C2semidirect
5. #13079623C2semidirect
6. #13079588C2semidirect
7. #13079561C2semidirect
8. #13079107C2semidirect
9. #13078986C2semidirect
10. #13078103C2semidirect
11. #13078088C2semidirect
12. #13078071C2semidirect
13. C2×#10622644C2semidirect
14. #13077928C2semidirect
15. #13077909C2semidirect
16. #13077282C2semidirect
17. C11×#3461C2semidirect
358. #3461D11semidirect
814. C11#60837semidirect

Maximal subgroups

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

subgroupindex
#130824012
#130797192
#130796932
#130796402
#130796232
#130795882
#130795612
#130791072
#130789862
#130781032
#130780882
#130780712
C2×#106226442
#130779282
#130779092
#130772822
C11×#34612
#6083711