Finite Group Databasebeta

← #15625002

Subgroups — #15625002

Order 2816.

2208 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2#13079588C214yesmaximal, complemented
3#13079577C214yesmaximal, complemented
4#13079568C212yesmaximal, complemented
5#13079561C211yesmaximal, characteristic, complemented
6#13079554C211yesmaximal, characteristic, complemented
7#13079545C212yesmaximal, complemented
8#13079538C211yesmaximal, characteristic, complemented
9#13079531C211yesmaximal, characteristic, complemented
10#13079042C212yesmaximal, complemented
11#13078941C212yesmaximal, complemented
12#13078071C214yesmaximal, complemented
13#13077832C214yesmaximal, complemented
14C2×#10622538C211yesmaximal, characteristic, complemented
15C11×#3444C211yesmaximal, characteristic, complemented
16C22×#4339C2212yes—
17C11×#533C2211yescharacteristic
18C11×#533C2211yescharacteristic, complemented
19C11×#533C2211yescharacteristic, complemented
20C11×#532C2211yescharacteristic
21C11×#532C2211yescharacteristic, complemented
22C11×#532C2211yescharacteristic, complemented
23C11×#529—21no—
24C11×#529—21no—
25C11×#529—21no—
26C11×#529—21no—
27C11×#529C2212yes—
28C11×#529C2212yescomplemented
29C11×#525—21no—
30C11×#525—21no—
31C11×#525C2212yes—
32C4×C11×#41—21no—
33C4×C11×#41—21no—
34C4×C11×#41C2212yescomplemented
35C22×C42×C11C2211yescharacteristic
36C2×#67003C2218yescomplemented
37C2×#66983—21no—
38C2×#66983—21no—
39#10623008—21no—
40#10623008—21no—
41#10623008—21no—
42#10623008—21no—
43#10623008C2212yes—
44#10623008C2212yes—
45#10623008C2212yes—
46#10623008C2212yes—
47C2×#66928C2212yes—
48C2×#66927C2211yescharacteristic
49C2×C4×D44—21no—
50C2×C4×D44—21no—
51C2×#66922C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2212yes—
53#10622706C2212yescomplemented
54#10622706C2212yescomplemented
55#10622705C2212yescomplemented
56#10622701C2212yescomplemented
57#10622701C2212yescomplemented
58#10622698C2212yescomplemented
59#10622689C2212yescomplemented
60#10622686C2212yescomplemented
61#10622681C2218yescomplemented
62#10622672C2218yescomplemented
63#10622663C2214yes—
64#10622660C2218yescomplemented
65#10622659C2214yes—
66#10622653C2214yes—
67#10622650C2218yescomplemented
68#10622649C2214yes—
69#10622644C2214yescomplemented
70#10622641C2218yescomplemented
71#10622640C2214yescomplemented
72#10622632C2214yescomplemented
73#10622629C2218yescomplemented
74#10622628C2214yescomplemented
75#10622615C2218yescomplemented
76#10622538C2211yescharacteristic
77#10622538C2211yescharacteristic
78#10622538C2212yes—
79#10622538C2212yescomplemented
80#10622538C2212yescomplemented
81C2×C4⋊(C11⋊C8)C2212yescomplemented
82C2×C4×C11⋊C8C2212yescomplemented
83C2×C11×#41—21no—
84C2×C11×#41—21no—
85C2×C11×#41C2312yes—
86C23×C4×C11D411yescharacteristic
87C23×C4×C11D411yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—22no—
90C2×#4339—22no—
91C2×#4339—22no—
92C2×#4339—48no—
93C2×#4339C2314yes—
94C2×#4339C2314yes—
95C22×D44—21no—
96C22×D44—21no—
97C22×D44C2312yes—
98C22×C4×D11—22no—
99C22×Dic22C2312yes—
100C11×C4⋊Q8C2311yescharacteristic
101C11×C4⋊Q8C2311yescharacteristic
102C11×C4⋊Q8C2311yescharacteristic
103C11×#127C2311yescharacteristic
104C11×#126—22no—
105C11×#126—22no—
106C11×#125—21no—
107C11×#125—21no—
108C11×#125C2312yes—
109C11×#124—21no—
110C11×#124—21no—
111C11×#124C2312yes—
112C11×#123—22no—
113C11×#123—22no—
114C11×#123—22no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8C2312yes—
120C11×C22⋊Q8C2312yes—
121C11×#121—21no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121C2312yes—
126C11×#121C2312yes—
127C11×#120—22no—
128C4×Q8×C11—21no—
129C4×Q8×C11—21no—
130C4×Q8×C11—21no—
131C4×Q8×C11—21no—
132C4×Q8×C11C2312yes—
133C4×Q8×C11C2312yes—
134C4×D4×C11—22no—
135C4×D4×C11—22no—
136C4×D4×C11—22no—
137C4×D4×C11—22no—
138C4×D4×C11—22no—
139C4×D4×C11—22no—
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—21no—
144C4×D4×C11C2312yes—
145C4×D4×C11C2312yes—
146C11×#117—21no—
147C11×#117—21no—
148C11×#117—22no—
149C11×#117—22no—
150C11×#117—22no—
151C11×#117C2312yes—
152C2×C42×C11—22no—
153C2×C42×C11D411yescharacteristic
154C2×C42×C11D411yescharacteristic
155C2×C42×C11D411yescharacteristic
156C2×C42×C11D411yescharacteristic
157C2×C42×C11D411yescharacteristic
158C2×C42×C11D411yescharacteristic
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165#67003—416no—
166C2×#4326C2318yes—
167C2×#4325C2318yes—
168C2×#4324C2318yes—
169C2×#4323C2318yes—
170#66983—22no—
171#66983—22no—
172#66983—22no—
173#66983—22no—
174#66983—22no—
175#66983—22no—
176#66983—22no—
177#66983—22no—
178C2×(C2×D11)⋊C4—22no—
179C2×(C2×D11)⋊C4—22no—
180C2×C4⋊Dic11—21no—
181C2×C4⋊Dic11—21no—
182C22×C11⋊C8C2314yes—
183#66928—22no—
184#66928—22no—
185#66928C2314yes—
186#66928C2314yes—
187#66927—21no—
188#66927—21no—
189#66927C2312yes—
190#66927C2312yes—
191C4×D44—22no—
192C4×D44—22no—
193C4×D44—22no—
194C4×D44—22no—
195C4×D44—22no—
196C4×D44—22no—
197C4×D44—22no—
198C4×D44—22no—
199#66922—21no—
200#66922—21no—
201#66922C2312yes—
202#66922C2312yes—
203C22⋊(C11⋊C8)C2312yes—
204C22⋊(C11⋊C8)C2312yes—
205C22⋊(C11⋊C8)C2314yes—
206#66874C2318yes—
207#66874C2318yes—
208#66873C2318yes—
209#66873C2318yes—
210C4⋊(C11⋊C8)C2312yes—
211C4⋊(C11⋊C8)C2314yes—
212C4⋊(C11⋊C8)C2312yes—
213C4×C11⋊C8C2314yes—
214C4×C11⋊C8C2312yes—
215C4×C11⋊C8C2312yes—
216#60782—111nomaximal, Sylow
217C24×C11C2×D411yescharacteristic
218C23×D11—22no—
219C11×#41—28no—
220C11×#41—44no—
221C11×#41—44no—
222C2×Q8×C11—21no—
223C2×Q8×C11—21no—
224C2×Q8×C11C2412yes—
225C2×D4×C11—22no—
226C2×D4×C11—22no—
227C2×D4×C11—22no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11C2412yes—
231C22×C4×C11—24no—
232C22×C4×C11—24no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—42no—
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C2×C22⋊D11—24no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—48no—
258C22×Dic11—22no—
259#4339—216no—
260#4339—48no—
261#4339—48no—
262#4339—48no—
263C2×D44—22no—
264C2×D44—22no—
265C2×D44—22no—
266C2×D44—22no—
267C2×D44—22no—
268C2×D44—44no—
269C2×D44—44no—
270C2×D44—44no—
271C2×D44C2414yes—
272C2×C4×D11—24no—
273C2×C4×D11—24no—
274C2×C4×D11—48no—
275C2×Dic22—22no—
276C2×Dic22—44no—
277C2×Dic22C2414yes—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4C2412yes—
289C11×C4⋊C4C2412yes—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C42×C11—22no—
300C42×C11—22no—
301C42×C11—22no—
302C42×C11C2×D411yescharacteristic
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D411yescharacteristic
306C42×C11C2×D411yescharacteristic
307C42×C11C2×D411yescharacteristic
308C42×C11C2×D411yescharacteristic
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2×D411yescharacteristic
312C42×C11C2×D411yescharacteristic
313C42×C11C2×D411yescharacteristic
314C42×C11C2411yescharacteristic
315C42×C11C2411yescharacteristic
316C42×C11C2411yescharacteristic
317C42×C11C2411yescharacteristic
318#4326—48no—
319#4325—48no—
320#4324—48no—
321#4323—48no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—24no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—24no—
326C4⋊Dic11—22no—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—22no—
330C2×C11⋊C8—28no—
331C2×C11⋊C8C2414yes—
332C2×C11⋊C8C2414yes—
333#3444D1111yescharacteristic, complemented
334C2×#532—111no—
335#3212—114no—
336#3211—114no—
337#3210—112no—
338#3209—111no—
339#3208—111no—
340#3207—112no—
341#3206—111no—
342#3205—111no—
343#3147—112no—
344#3131—112no—
345#3035—114no—
346#3002—114no—
347C2×#431—111no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—41no—
352C23×C11C22×D411yescharacteristic
353C23×C11C22×D411yescharacteristic
354C23×C11C22×D411yescharacteristic
355C22×D11—24no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
359Q8×C11—24no—
360Q8×C11—42no—
361Q8×C11—42no—
362D4×C11—24no—
363D4×C11—44no—
364D4×C11—44no—
365D4×C11—44no—
366D4×C11—42no—
367D4×C11—42no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—44no—
388C2×C4×C11—44no—
389C2×C4×C11—44no—
390C2×C4×C11#13514yescomplemented
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11H(5,𝔽2)14yes—
403C2×C4×C11C2511yescharacteristic
404C22⋊D11—48no—
405C22⋊D11—48no—
406C2×Dic11—24no—
407C2×Dic11—44no—
408D44—28no—
409D44—44no—
410D44—44no—
411D44—44no—
412D44—44no—
413D44—44no—
414C4×D11—48no—
415C4×D11—48no—
416Dic22—28no—
417Dic22—44no—
418C11⋊C8—24no—
419C11⋊C8—24no—
420C22×#41—112no—
421C2×#135—118no—
422#533C2×D1111yescharacteristic
423#533C2×D1111yescharacteristic, complemented
424#533C2×D1111yescharacteristic, complemented
425#532—112no—
426#532—112no—
427#532—112no—
428#532—112no—
429#532—221no—
430#532—221no—
431#532—221no—
432#532—221no—
433#532C2×D1111yescharacteristic
434#532C2×D1111yescharacteristic, complemented
435#532C2×D1111yescharacteristic, complemented
436C2×C4⋊Q8—111no—
437C2×#127—111no—
438#529—21no—
439#529—21no—
440#529—21no—
441#529—21no—
442#529C2×D1112yes—
443#529C2×D1112yescomplemented
444C2×#124—112no—
445#525—21no—
446#525—21no—
447#525C2×D1112yes—
448C2×#121—221no—
449C2×#121—221no—
450C4×#41—21no—
451C4×#41—21no—
452C4×#41C2×D1112yescomplemented
453C2×C4×D4—221no—
454C2×C4×D4—221no—
455C22×C42C2×D1111yescharacteristic
456#495—118no—
457#494—112no—
458#493—112no—
459#492—112no—
460#492—112no—
461#488—118no—
462#487—112no—
463#487—112no—
464#486—112no—
465#486—112no—
466#464—118no—
467#463—118no—
468#462—114no—
469#461—114no—
470#460—114no—
471#459—114no—
472#452—118no—
473#451—114no—
474#450—114no—
475#449—118no—
476#448—114no—
477#447—114no—
478#431—111no—
479#431—111no—
480#431—112no—
481#431—112no—
482#431—112no—
483C2×C4⋊C8—112no—
484#416—118no—
485C2×C22⋊C8—112no—
486C2×C4×C8—112no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—21no—
494C22×C11—44no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11#53512yes—
499C22×C11C2×#13512yes—
500C22×C11C23×D411yescharacteristic
501C2×D11—44no—
502C2×D11—44no—
503C2×D11—44no—
504C2×D11—88no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11—42no—
513C4×C11—42no—
514C4×C11—42no—
515C4×C11#53512yes—
516C4×C11C2×#13512yes—
517C4×C11C2×#13512yes—
518C4×C11#57512yes—
519C4×C11C2×H(5,𝔽2)12yes—
520Dic11—44no—
521C2×#41—21no—
522C2×#41—21no—
523C2×#41—114no—
524C2×#41—114no—
525C2×#41—222no—
526C2×#41—222no—
527C2×#41—448no—
528C2×#41C22×D1112yes—
529C22×Q8—112no—
530C22×D4—112no—
531C22×D4—222no—
532C22×D4—221no—
533C22×D4—221no—
534C23×C4—222no—
535C23×C4C22⋊D1111yescharacteristic
536C23×C4C22⋊D1111yescharacteristic
537C23×C4C22×D1111yescharacteristic
538#135—4416no—
539C2×Q16—118no—
540C2×SD16—118no—
541C2×SD16—118no—
542C2×D8—118no—
543C22×C8—114no—
544C4⋊Q8—112no—
545C4⋊Q8—112no—
546C4⋊Q8—221no—
547C4⋊Q8—221no—
548C4⋊Q8C22×D1111yescharacteristic
549C4⋊Q8C22×D1111yescharacteristic
550C4⋊Q8C22×D1111yescharacteristic
551#127—112no—
552#127—112no—
553#127—221no—
554#127—221no—
555#127C22×D1111yescharacteristic
556#126—22no—
557#126—22no—
558#125—21no—
559#125—21no—
560#125C22×D1112yes—
561#124—21no—
562#124—21no—
563#124—114no—
564#124—114no—
565#124—222no—
566#124—222no—
567#124C22×D1112yes—
568#123—22no—
569#123—22no—
570#123—22no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8C22×D1112yes—
576C22⋊Q8C22×D1112yes—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—222no—
582#121—222no—
583#121—222no—
584#121—222no—
585#121—222no—
586#121—222no—
587#121—222no—
588#121—222no—
589#121C22×D1112yes—
590#121C22×D1112yes—
591#120—22no—
592C4×Q8—21no—
593C4×Q8—21no—
594C4×Q8—21no—
595C4×Q8—21no—
596C4×Q8C22×D1112yes—
597C4×Q8C22×D1112yes—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—222no—
609C4×D4—222no—
610C4×D4—222no—
611C4×D4—222no—
612C4×D4—222no—
613C4×D4—222no—
614C4×D4—222no—
615C4×D4—222no—
616C4×D4C22×D1112yes—
617C4×D4C22×D1112yes—
618#117—21no—
619#117—21no—
620#117—22no—
621#117—22no—
622#117—22no—
623#117C22×D1112yes—
624C2×C4⋊C4—221no—
625C2×C4⋊C4—221no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C42—22no—
629C2×C42C22⋊D1111yescharacteristic
630C2×C42C22⋊D1111yescharacteristic
631C2×C42C22⋊D1111yescharacteristic
632C2×C42C22⋊D1111yescharacteristic
633C2×C42C22⋊D1111yescharacteristic
634C2×C42C22⋊D1111yescharacteristic
635C2×C42C22×D1111yescharacteristic
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1111yescharacteristic
640C2×C42C22×D1111yescharacteristic
641C4⋊C8—112no—
642C4⋊C8—112no—
643C4⋊C8—114no—
644#103—118no—
645#103—118no—
646#102—118no—
647#102—118no—
648C22⋊C8—112no—
649C22⋊C8—112no—
650C22⋊C8—114no—
651C4×C8—112no—
652C4×C8—112no—
653C4×C8—114no—
654C2×C11—22no—
655C2×C11—22no—
656C2×C11—41no—
657C2×C11—82no—
658C2×C11C2×#53511yescharacteristic
659C2×C11C22×#13511yescharacteristic
660C2×C11C2×#57511yescharacteristic
661D11—84no—
662C24—222no—
663C24C2×C22⋊D1111yescharacteristic
664#41—28no—
665#41—44no—
666#41—44no—
667#41—2216no—
668#41—448no—
669#41—448no—
670#41—448no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—114no—
674C2×Q8—222no—
675C2×Q8—444no—
676C2×Q8C23×D1112yes—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—114no—
683C2×D4—224no—
684C2×D4—224no—
685C2×D4—222no—
686C2×D4—222no—
687C2×D4—222no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—448no—
693C2×D4—444no—
694C2×D4C23×D1112yes—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—42no—
701C22×C4—222no—
702C22×C4—224no—
703C22×C4—224no—
704C22×C4—448no—
705C22×C4C2×C22⋊D1111yescharacteristic
706C22×C4C2×C22⋊D1111yescharacteristic
707C22×C4C2×C22⋊D1111yescharacteristic
708C22×C4C2×C22⋊D1111yescharacteristic
709C22×C4C2×C22⋊D1111yescharacteristic
710C22×C4C2×C22⋊D1111yescharacteristic
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1111yescharacteristic
714C22×C4C2×C22⋊D1111yescharacteristic
715C22×C4C2×C22⋊D1111yescharacteristic
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1111yescharacteristic
718C22×C4C2×C22⋊D1111yescharacteristic
719C22×C4C2×C22⋊D1111yescharacteristic
720C22×C4C23×D1111yescharacteristic
721C22×C4C23×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723Q16—448no—
724SD16—448no—
725SD16—448no—
726D8—448no—
727C2×C8—114no—
728C2×C8—114no—
729C2×C8—228no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—222no—
741C4⋊C4—222no—
742C4⋊C4—222no—
743C4⋊C4—222no—
744C4⋊C4C23×D1112yes—
745C4⋊C4C23×D1112yes—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C22⋊C4—224no—
759C42—22no—
760C42—22no—
761C42—22no—
762C42C2×C22⋊D1111yescharacteristic
763C42C2×C22⋊D1111yescharacteristic
764C42C2×C22⋊D1111yescharacteristic
765C42C2×C22⋊D1111yescharacteristic
766C42C2×C22⋊D1111yescharacteristic
767C42C2×C22⋊D1111yescharacteristic
768C42C2×C22⋊D1111yescharacteristic
769C42C2×C22⋊D1111yescharacteristic
770C42C2×C22⋊D1111yescharacteristic
771C42C2×C22⋊D1111yescharacteristic
772C42C2×C22⋊D1111yescharacteristic
773C42C2×C22⋊D1111yescharacteristic
774C42C23×D1111yescharacteristic
775C42C23×D1111yescharacteristic
776C42C23×D1111yescharacteristic
777C42C23×D1111yescharacteristic
778C11#6078211yescharacteristic, complemented, Sylow
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—224no—
784C23—444no—
785C23—444no—
786C23—444no—
787C23C22×C22⋊D1111yescharacteristic
788C23C22×C22⋊D1111yescharacteristic
789C23C22×C22⋊D1111yescharacteristic
790Q8—24no—
791Q8—42no—
792Q8—42no—
793Q8—228no—
794Q8—444no—
795D4—24no—
796D4—44no—
797D4—44no—
798D4—44no—
799D4—42no—
800D4—42no—
801D4—228no—
802D4—444no—
803D4—444no—
804D4—448no—
805D4—448no—
806D4—444no—
807D4—444no—
808D4—444no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—224no—
832C2×C4—448no—
833C2×C4—444no—
834C2×C4—448no—
835C2×C4#6700314yescomplemented
836C2×C4#6704214yes—
837C2×C4C22×C22⋊D1111yescharacteristic
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C22×C22⋊D1111yescharacteristic
841C2×C4C22×C22⋊D1111yescharacteristic
842C2×C4C22×C22⋊D1111yescharacteristic
843C2×C4C22×C22⋊D1111yescharacteristic
844C2×C4C22×C22⋊D1111yescharacteristic
845C2×C4C22×C22⋊D1111yescharacteristic
846C2×C4C22×C22⋊D1111yescharacteristic
847C2×C4C22×C22⋊D1111yescharacteristic
848C2×C4C24×D1111yescharacteristic
849C8—224no—
850C8—224no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—44no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—444no—
863C22—444no—
864C22—444no—
865C22—888no—
866C22C2×#6700312yes—
867C22#1062336112yes—
868C22C23×C22⋊D1111yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—444no—
880C4C2×#6700312yes—
881C4C2×#6700312yes—
882C4#1062335312yes—
883C4#1062336112yes—
884C4C2×#6704212yes—
885C2—22no—
886C2—22no—
887C2—41no—
888C2—82no—
889C2—884no—
890C2C2×#1062336111yescharacteristic
891C2C22×#6700311yescharacteristic
892C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3444C2
socleC22×C11C23×D4
hypercenter#3444D11
hypocenterC11#60782
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. #13079588C2semidirect
3. #13079577C2semidirect
4. #13079568C2semidirect
5. #13079561C2semidirect
6. #13079554C2semidirect
7. #13079545C2semidirect
8. #13079538C2semidirect
9. #13079531C2semidirect
10. #13079042C2semidirect
11. #13078941C2semidirect
12. #13078071C2semidirect
13. #13077832C2semidirect
14. C2×#10622538C2semidirect
15. C11×#3444C2semidirect
18. C11×#533C22semidirect
19. C11×#533C22semidirect
21. C11×#532C22semidirect
22. C11×#532C22semidirect
28. C11×#529C22semidirect
34. C4×C11×#41C22semidirect
36. C2×#67003C22semidirect
53. #10622706C22semidirect
54. #10622706C22semidirect
55. #10622705C22semidirect
56. #10622701C22semidirect
57. #10622701C22semidirect
58. #10622698C22semidirect
59. #10622689C22semidirect
60. #10622686C22semidirect
61. #10622681C22semidirect
62. #10622672C22semidirect
64. #10622660C22semidirect
67. #10622650C22semidirect
69. #10622644C22semidirect
70. #10622641C22semidirect
71. #10622640C22semidirect
72. #10622632C22semidirect
73. #10622629C22semidirect
74. #10622628C22semidirect
75. #10622615C22semidirect
79. #10622538C22semidirect
80. #10622538C22semidirect
81. C2×C4⋊(C11⋊C8)C22semidirect
82. C2×C4×C11⋊C8C22semidirect
333. #3444D11semidirect
390. C2×C4×C11#135semidirect
423. #533C2×D11semidirect
424. #533C2×D11semidirect
434. #532C2×D11semidirect
435. #532C2×D11semidirect
443. #529C2×D11semidirect
452. C4×#41C2×D11semidirect
778. C11#60782semidirect
835. C2×C4#67003semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
#130795882
#130795772
#130795682
#130795612
#130795542
#130795452
#130795382
#130795312
#130790422
#130789412
#130780712
#130778322
C2×#106225382
C11×#34442
#6078211