Finite Group Databasebeta

← #15622800

Subgroups — #15622800

Order 2816.

2110 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082493C211yesmaximal, characteristic, complemented
2C4×#67043C211yesmaximal, characteristic, complemented
3#13078909C214yesmaximal, complemented
4#13078820C214yesmaximal, complemented
5#13078769C212yesmaximal, complemented
6#13078740C212yesmaximal, complemented
7#13078678C212yesmaximal, complemented
8#13078649C212yesmaximal, complemented
9#13078577C212yesmaximal, complemented
10#13078417C211yesmaximal, characteristic, complemented
11#13078096C211yesmaximal, characteristic, complemented
12C2×#10622461C211yesmaximal, characteristic, complemented
13#13077905C212yesmaximal, complemented
14#13077474C212yesmaximal, complemented
15#13077451C212yesmaximal, complemented
16#13077281C211yesmaximal, characteristic, complemented
17C11×#3076C211yesmaximal, characteristic, complemented
18C2×#67043C2211yescharacteristic
19C11×#533C2211yescharacteristic
20C4×C11×#41C2211yescharacteristic
21#10623358C2211yescharacteristic
22C2×#67002C2212yes—
23C22×#4314C2212yes—
24#10623256C2212yes—
25#10623256C2212yes—
26#10623229C2214yes—
27#10623161—22no—
28#10623161—22no—
29#10623116—21no—
30#10623116—21no—
31#10623108—21no—
32#10623108—21no—
33#10623103C2212yescomplemented
34C4×Q8×D11C2212yescomplemented
35#10623077—22no—
36#10623077C2212yescomplemented
37C4×#4341—22no—
38C4×#4341C2212yescomplemented
39#10623056C2212yes—
40#10623054—21no—
41#10623054C2211yescharacteristic
42#10623052C2212yes—
43#10623047—21no—
44#10623047C2211yescharacteristic
45C2×#66927C2211yescharacteristic
46C4×#4339—21no—
47C4×#4339C2211yescharacteristic
48C2×C4×Dic22—21no—
49C2×C4×Dic22C2211yescharacteristic
50C11×#479C2212yescomplemented
51C11×#478C2212yescomplemented
52C11×#477C2211yescharacteristic, complemented
53C11×#476C2211yescharacteristic, complemented
54C11×#475C2211yescharacteristic, complemented
55C11×#474C2211yescharacteristic, complemented
56C11×#427C2212yes—
57C2×C11×C4⋊C8C2211yescharacteristic
58C11×#416C2212yes—
59C2×#66885C2212yes—
60#10622723C2212yes—
61#10622714C2212yes—
62#10622707C2212yescomplemented
63#10622704C2212yescomplemented
64#10622676C2214yescomplemented
65#10622640C2212yes—
66#10622640C2212yes—
67#10622628C2212yes—
68#10622628C2212yes—
69#10622617C2212yes—
70#10622614C2212yes—
71#10622608C2212yes—
72#10622537C2211yescharacteristic
73#10622502C2214yescomplemented
74#10622502C2214yescomplemented
75#10622498C2214yescomplemented
76#10622495C2214yescomplemented
77#10622479C2214yescomplemented
78#10622476C2214yescomplemented
79#10622465C2214yescomplemented
80#10622465C2214yescomplemented
81#10622461C2214yes—
82#10622461C2212yes—
83#10622461C2212yes—
84#10622453C2214yescomplemented
85#10622448C2212yescomplemented
86#10622446C2212yescomplemented
87#10622430C2214yescomplemented
88#10622419C2214yescomplemented
89#10622419C2214yescomplemented
90#10622401C2214yescomplemented
91#10622398C2214yescomplemented
92#10622394C2214yescomplemented
93#10622394C2214yescomplemented
94#10622369C2214yescomplemented
95C2×C11×#41C2311yescharacteristic
96#67043—24no—
97#67043—24no—
98C2×#4343—22no—
99C2×#4343—22no—
100C2×Q8×D11C2312yes—
101C2×#4341—22no—
102C2×#4341C2312yes—
103C2×#4339—21no—
104C2×#4339C2311yescharacteristic
105C22×D44—21no—
106C22×D44—21no—
107C22×D44C2312yes—
108C22×Dic22—21no—
109C22×Dic22C2311yescharacteristic
110C22×C8×C11C2312yes—
111C11×C4⋊Q8C2311yescharacteristic
112C11×C4⋊Q8C2311yescharacteristic
113C11×#125C2312yes—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C4×Q8×C11—21no—
117C4×Q8×C11—21no—
118C4×Q8×C11C2311yescharacteristic
119C4×Q8×C11C2311yescharacteristic
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11C2311yescharacteristic
123C4×D4×C11C2311yescharacteristic
124C11×#117—21no—
125C11×#117C2311yescharacteristic
126C11×#117C2312yes—
127C2×C42×C11—21no—
128C2×C42×C11C2311yescharacteristic
129#67002—28no—
130#67000—22no—
131#67000—22no—
132Q8×Dic11C2312yes—
133C2×#4325C2314yes—
134D4×Dic11—22no—
135D4×Dic11C2312yes—
136C2×#4323C2314yes—
137C4×C22⋊D11—22no—
138C4×C22⋊D11—22no—
139C4×C22⋊D11D412yes—
140C4×C22⋊D11D412yes—
141#66979—21no—
142#66979C2311yescharacteristic
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—22no—
147C2×C4×Dic11—21no—
148C2×C4×Dic11—22no—
149C2×#4318C2312yes—
150C2×#4314—28no—
151C2×#4314C2314yes—
152C2×#4314C2314yes—
153#66948—22no—
154#66948—22no—
155#66948—24no—
156#66948—24no—
157#66948C2314yes—
158#66948C2314yes—
159#66947—24no—
160#66947—24no—
161#66946—22no—
162#66946—22no—
163#66946C2314yes—
164#66946C2314yes—
165#66945—22no—
166#66945C2312yes—
167C4⋊C4×D11—22no—
168C4⋊C4×D11C2312yes—
169#66940—22no—
170#66940—22no—
171#66940C2312yes—
172#66940C2312yes—
173#66935—24no—
174(C22⋊D11)⋊C4—22no—
175(C22⋊D11)⋊C4—22no—
176(C22⋊D11)⋊C4—22no—
177C22⋊C4×D11—24no—
178#66930—22no—
179#66930—22no—
180#66930—22no—
181#66928—22no—
182#66927—22no—
183#66927—21no—
184#66927—21no—
185#66927C2312yes—
186#66927C2312yes—
187C4×D44—21no—
188C4×D44—22no—
189C4×D44—22no—
190C4×D44D411yescharacteristic
191C4×D44D411yescharacteristic
192#66925—22no—
193#66925C2312yes—
194C42×D11—22no—
195C42×D11C2312yes—
196C4×Dic22—21no—
197C4×Dic22—21no—
198C4×Dic22—21no—
199C4×Dic22—21no—
200C4×Dic22—21no—
201C4×Dic22—22no—
202C4×Dic22—22no—
203C4×Dic22D411yescharacteristic
204C4×Dic22D411yescharacteristic
205C4×Dic22C2312yes—
206C4×Dic22C2312yes—
207C11×#107C2312yes—
208C11×#107C2312yes—
209C11×#106C2312yes—
210C11×#106C2312yes—
211C11×C4⋊C8C2311yescharacteristic
212C11×C4⋊C8C2311yescharacteristic
213C11×C4⋊C8C2312yes—
214C11×#103C2312yes—
215C11×#103C2312yes—
216C11×#102C2312yes—
217C11×#102C2312yes—
218#66885C2314yes—
219#66885C2314yes—
220(C2×D11)⋊C8C2314yes—
221(C2×D11)⋊C8C2314yes—
222#66879C2314yes—
223C8×Dic11C2314yes—
224#66874C2314yes—
225#66874C2314yes—
226#66873C2314yes—
227#66873C2314yes—
228#66872C2314yes—
229#66871C2314yes—
230C4⋊(C11⋊C8)C2312yes—
231C4⋊(C11⋊C8)C2312yes—
232#60593—111nomaximal, Sylow
233C23×D11—22no—
234C11×#41—22no—
235C11×#41#4114yescomplemented
236C2×Q8×C11—21no—
237C2×Q8×C11—21no—
238C2×Q8×C11C2411yescharacteristic
239C2×D4×C11—21no—
240C2×D4×C11C2411yescharacteristic
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C2×C22⋊D11—22no—
248C2×C22⋊D11C2×D412yes—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253#4343—84no—
254#4343—84no—
255Q8×D11—24no—
256Q8×D11—24no—
257#4341—216no—
258#4341—24no—
259#4341—24no—
260#4339—28no—
261#4339—22no—
262#4339—22no—
263C2×D44—24no—
264C2×D44—24no—
265C2×D44—22no—
266C2×D44—22no—
267C2×D44—22no—
268C2×D44—22no—
269C2×D44—22no—
270C2×D44—24no—
271C2×D44—24no—
272C2×D44—82no—
273C2×D44—82no—
274C2×D44C2×D411yescharacteristic
275C2×D44C2414yes—
276C2×C4×D11—24no—
277C2×C4×D11—24no—
278C2×C4×D11—22no—
279C2×C4×D11—22no—
280C2×C4×D11C2×D412yes—
281C2×C4×D11C2×D412yes—
282C2×C4×D11C2412yes—
283C2×Dic22—28no—
284C2×Dic22—22no—
285C2×Dic22—21no—
286C2×Dic22—22no—
287C2×Dic22C2×D411yescharacteristic
288C2×Dic22#4114yescomplemented
289C2×Dic22C2412yes—
290C2×C8×C11—24no—
291C2×C8×C11C2412yes—
292C2×C8×C11C2412yes—
293C11×C4⋊C4—21no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4C2412yes—
300C11×C4⋊C4C2412yes—
301C11×C4⋊C4C2411yescharacteristic
302C11×C4⋊C4C2411yescharacteristic
303C11×C22⋊C4—21no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—21no—
307C42×C11—21no—
308C42×C11—21no—
309C42×C11—21no—
310C42×C11—22no—
311C42×C11C2×D411yescharacteristic
312C42×C11C2×D411yescharacteristic
313C42×C11C2411yescharacteristic
314C42×C11C2411yescharacteristic
315C22⋊Dic11—22no—
316C22⋊Dic11C2×D412yes—
317#4325—28no—
318#4323—28no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4C2×D412yes—
325(C2×D11)⋊C4C2×D412yes—
326C4⋊Dic11—22no—
327C4⋊Dic11—21no—
328C4⋊Dic11C2×D411yescharacteristic
329C4⋊Dic11C2×D411yescharacteristic
330C4⋊Dic11C2412yes—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336Dic11⋊C4C2×D412yes—
337Dic11⋊C4C2×D412yes—
338C4×Dic11—22no—
339C4×Dic11—22no—
340C4×Dic11—22no—
341C4×Dic11—22no—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11C2×D412yes—
345C4×Dic11C2×D412yes—
346C4×Dic11C2412yes—
347#4318—24no—
348C2×C11⋊C8C2414yes—
349#4314—28no—
350#4314—28no—
351#3508—111no—
352C4×2−1+4—111no—
353#3126—114no—
354#3119—114no—
355#3115—112no—
356#3112—112no—
357#3106—112no—
358#3103—112no—
359#3096—112no—
360#3078—111no—
361#3076D1111yescharacteristic, complemented
362#3038—111no—
363C2×#460—111no—
364#3010—112no—
365#2949—112no—
366#2946—112no—
367#2925—111no—
368C23×C11—21no—
369C23×C11C22×D411yescharacteristic
370C22×D11—24no—
371C22×D11—44no—
372C22×D11—82no—
373C22×D11—82no—
374C22×D11C22×D412yes—
375Q8×C11—21no—
376Q8×C11—42no—
377Q8×C11—42no—
378Q8×C11C2×#4112yes—
379D4×C11—24no—
380D4×C11—21no—
381D4×C11C2×#4112yes—
382C2×C4×C11—21no—
383C2×C4×C11—24no—
384C2×C4×C11—22no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—41no—
390C2×C4×C11—42no—
391C2×C4×C11—81no—
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C2×#4112yes—
398C2×C4×C11C2×#4112yes—
399C2×C4×C11C2511yescharacteristic
400C22⋊D11—28no—
401C22⋊D11—24no—
402C2×Dic11—28no—
403C2×Dic11—24no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—82no—
407C2×Dic11—81no—
408C2×Dic11C22×D412yes—
409C2×Dic11C22×D412yes—
410C2×Dic11C22×D412yes—
411D44—22no—
412D44—24no—
413D44—24no—
414D44—44no—
415D44—44no—
416D44—44no—
417D44—82no—
418D44—82no—
419D44—84no—
420D44—84no—
421C4×D11—28no—
422C4×D11—24no—
423C4×D11—22no—
424C4×D11—22no—
425C4×D11—42no—
426C4×D11—84no—
427C4×D11—84no—
428C4×D11—82no—
429Dic22—28no—
430Dic22—22no—
431Dic22—24no—
432Dic22—22no—
433Dic22C2×#4114yes—
434C8×C11—22no—
435C8×C11—22no—
436C11⋊C8—24no—
437C2×2−1+4—111no—
438C2×AGL(1,ℤ/8)—112no—
439C22×SD16—112no—
440#559—221no—
441#559—221no—
442#550—221no—
443#550—221no—
444#546—222no—
445#546—222no—
446#540—114no—
447#535—112no—
448#533C2×D1111yescharacteristic
449#532—112no—
450#532—112no—
451C2×#127—111no—
452#520—111no—
453#520—111no—
454#520—112no—
455#520—221no—
456#520—222no—
457#519—112no—
458#519—111no—
459#519—221no—
460#518—112no—
461C4×#41—111no—
462C4×#41—112no—
463C4×#41—221no—
464C4×#41—222no—
465C4×#41C2×D1111yescharacteristic
466C2×C4×Q8—112no—
467C2×C4×Q8—111no—
468C2×C4×Q8—221no—
469#482—114no—
470#482—114no—
471#481—114no—
472#480—114no—
473#479—114no—
474#479C2×D1112yescomplemented
475#478C2×D1112yescomplemented
476#477—112no—
477#477C2×D1111yescharacteristic, complemented
478#476C2×D1111yescharacteristic, complemented
479#475—112no—
480#475C2×D1111yescharacteristic, complemented
481#474C2×D1111yescharacteristic, complemented
482#460—112no—
483#460—112no—
484#460—112no—
485#460—112no—
486#460—114no—
487#459—112no—
488#459—112no—
489#449—114no—
490#449—114no—
491#448—114no—
492#448—114no—
493#442—114no—
494#440—114no—
495#440—114no—
496#440—114no—
497C4×SD16—114no—
498C4×SD16—114no—
499C4×SD16—114no—
500C4×D8—114no—
501#433—114no—
502#432—112no—
503#431—112no—
504#428—112no—
505#427C2×D1112yes—
506#423—111no—
507C2×C4⋊C8C2×D1111yescharacteristic
508#419—112no—
509#418—112no—
510#416C2×D1112yes—
511C2×#102—112no—
512#408—112no—
513#405—112no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—22no—
517C22×C11—41no—
518C22×C11—41no—
519C22×C11#52512yes—
520C22×C11C23×D411yescharacteristic
521C2×D11—22no—
522C2×D11—22no—
523C2×D11—22no—
524C2×D11—44no—
525C2×D11—44no—
526C2×D11—44no—
527C2×D11—164no—
528C4×C11—21no—
529C4×C11—21no—
530C4×C11—22no—
531C4×C11—21no—
532C4×C11—41no—
533C4×C11—42no—
534C4×C11—41no—
535C4×C11—42no—
536C4×C11#52512yes—
537C4×C11#57712yes—
538C4×C11C22×#4111yescharacteristic
539C4×C11C22×#4111yescharacteristic
540Dic11—22no—
541Dic11—22no—
542Dic11—24no—
543Dic11—22no—
544Dic11—42no—
5452−1+4—224no—
5462−1+4—224no—
547C2×#41—111no—
548C2×#41—112no—
549C2×#41—221no—
550C2×#41—222no—
551C2×#41—222no—
552C2×#41—222no—
553C2×#41C22×D1111yescharacteristic
554C22×Q8—112no—
555C22×Q8—111no—
556C22×Q8—221no—
557C22×D4—112no—
558C22×D4—221no—
559C22×D4—221no—
560AGL(1,ℤ/8)—228no—
561C2×SD16—114no—
562C2×SD16—114no—
563C2×SD16—114no—
564C2×SD16—228no—
565C2×D8—114no—
566C2×M16—112no—
567C22×C8C22×D1112yes—
568C4⋊Q8C22×D1111yescharacteristic
569C4⋊Q8C22×D1111yescharacteristic
570#127—112no—
571#127—112no—
572#127—222no—
573#127—221no—
574#127—221no—
575#125C22×D1112yes—
576#124—222no—
577#124—222no—
578#124—222no—
579#123—224no—
580#123—224no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583#121—114no—
584#121—114no—
585#121—224no—
586#121—224no—
587#121—222no—
588#121—222no—
589#120—224no—
590C4×Q8—21no—
591C4×Q8—21no—
592C4×Q8—111no—
593C4×Q8—111no—
594C4×Q8—112no—
595C4×Q8—112no—
596C4×Q8—112no—
597C4×Q8—112no—
598C4×Q8—112no—
599C4×Q8—222no—
600C4×Q8—221no—
601C4×Q8—222no—
602C4×Q8—221no—
603C4×Q8—221no—
604C4×Q8—222no—
605C4×Q8—222no—
606C4×Q8—221no—
607C4×Q8—221no—
608C4×Q8C22×D1111yescharacteristic
609C4×Q8C22×D1111yescharacteristic
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—112no—
613C4×D4—112no—
614C4×D4—112no—
615C4×D4—114no—
616C4×D4—114no—
617C4×D4—111no—
618C4×D4—111no—
619C4×D4—222no—
620C4×D4—222no—
621C4×D4—221no—
622C4×D4—222no—
623C4×D4—222no—
624C4×D4—222no—
625C4×D4—222no—
626C4×D4—222no—
627C4×D4—222no—
628C4×D4—222no—
629C4×D4—222no—
630C4×D4C22×D1111yescharacteristic
631C4×D4C22×D1111yescharacteristic
632#117—21no—
633#117—111no—
634#117—112no—
635#117—112no—
636#117—222no—
637#117—222no—
638#117—222no—
639#117—222no—
640#117—222no—
641#117—221no—
642#117C22×D1111yescharacteristic
643#117C22×D1112yes—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—222no—
647C2×C4⋊C4—222no—
648C2×C4⋊C4—221no—
649C2×C4⋊C4—221no—
650C2×C22⋊C4—224no—
651C2×C42—21no—
652C2×C42—112no—
653C2×C42—222no—
654C2×C42—222no—
655C2×C42—221no—
656C2×C42C22×D1111yescharacteristic
657#107—114no—
658#107C22×D1112yes—
659#107C22×D1112yes—
660#106—114no—
661#106C22×D1112yes—
662#106C22×D1112yes—
663C4⋊C8—112no—
664C4⋊C8—112no—
665C4⋊C8C22×D1111yescharacteristic
666C4⋊C8C22×D1111yescharacteristic
667C4⋊C8C22×D1112yes—
668#103—114no—
669#103—114no—
670#103C22×D1112yes—
671#103C22×D1112yes—
672#102—114no—
673#102—114no—
674#102—114no—
675#102—114no—
676#102C22×D1112yes—
677#102C22×D1112yes—
678C22⋊C8—114no—
679C22⋊C8—114no—
680#97—114no—
681C4×C8—114no—
682C2×C11—22no—
683C2×C11—42no—
684C2×C11C2×#52511yescharacteristic
685C2×C11C2×#57711yescharacteristic
686C2×C11#358511yescharacteristic
687D11—42no—
688D11—84no—
689C24—222no—
690#41—22no—
691#41—228no—
692#41—224no—
693#41—2216no—
694#41—224no—
695#41—222no—
696#41—222no—
697#41—884no—
698#41—884no—
699#41#434314yescomplemented
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—111no—
703C2×Q8—114no—
704C2×Q8—112no—
705C2×Q8—222no—
706C2×Q8—228no—
707C2×Q8—224no—
708C2×Q8—224no—
709C2×Q8—221no—
710C2×Q8—222no—
711C2×Q8C23×D1111yescharacteristic
712C2×D4—21no—
713C2×D4—112no—
714C2×D4—111no—
715C2×D4—114no—
716C2×D4—224no—
717C2×D4—224no—
718C2×D4—222no—
719C2×D4—222no—
720C2×D4—222no—
721C2×D4—222no—
722C2×D4—222no—
723C2×D4—222no—
724C2×D4—224no—
725C2×D4—224no—
726C2×D4—882no—
727C2×D4—882no—
728C2×D4C23×D1111yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—224no—
736C22×C4—224no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4D4×D1111yescharacteristic
744C22×C4D4×D1111yescharacteristic
745C22×C4C23×D1111yescharacteristic
746SD16—228no—
747SD16—228no—
748SD16—228no—
749D8—228no—
750M16—224no—
751C2×C8—24no—
752C2×C8—114no—
753C2×C8C23×D1112yes—
754C2×C8C23×D1112yes—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—22no—
760C4⋊C4—22no—
761C4⋊C4—111no—
762C4⋊C4—112no—
763C4⋊C4—111no—
764C4⋊C4—112no—
765C4⋊C4—112no—
766C4⋊C4—222no—
767C4⋊C4—222no—
768C4⋊C4—222no—
769C4⋊C4—222no—
770C4⋊C4—221no—
771C4⋊C4—222no—
772C4⋊C4—222no—
773C4⋊C4C23×D1111yescharacteristic
774C4⋊C4C23×D1111yescharacteristic
775C4⋊C4C23×D1112yes—
776C4⋊C4C23×D1112yes—
777C22⋊C4—22no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—112no—
782C22⋊C4—112no—
783C22⋊C4—112no—
784C22⋊C4—224no—
785C22⋊C4—224no—
786C22⋊C4—224no—
787C22⋊C4—224no—
788C22⋊C4—222no—
789C22⋊C4—222no—
790C42—21no—
791C42—21no—
792C42—21no—
793C42—22no—
794C42—112no—
795C42—112no—
796C42—112no—
797C42—222no—
798C42—222no—
799C42—222no—
800C42—222no—
801C42—222no—
802C42—222no—
803C42D4×D1111yescharacteristic
804C42D4×D1111yescharacteristic
805C42C23×D1111yescharacteristic
806C42C23×D1111yescharacteristic
807C11#6059311yescharacteristic, complemented, Sylow
808C23—21no—
809C23—112no—
810C23—224no—
811C23—444no—
812C23—882no—
813C23—882no—
814C23C2×D4×D1111yescharacteristic
815Q8—21no—
816Q8—42no—
817Q8—42no—
818Q8—114no—
819Q8—228no—
820Q8—222no—
821Q8—224no—
822Q8—222no—
823Q8C2×#434312yes—
824D4—24no—
825D4—21no—
826D4—228no—
827D4—224no—
828D4—222no—
829D4—224no—
830D4—224no—
831D4—444no—
832D4—444no—
833D4—444no—
834D4—882no—
835D4—882no—
836D4—884no—
837D4—884no—
838D4C2×#434312yes—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—81no—
849C2×C4—112no—
850C2×C4—112no—
851C2×C4—112no—
852C2×C4—228no—
853C2×C4—228no—
854C2×C4—224no—
855C2×C4—222no—
856C2×C4—224no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—442no—
861C2×C4—884no—
862C2×C4—884no—
863C2×C4—882no—
864C2×C4—882no—
865C2×C4—881no—
866C2×C4C2×D4×D1111yescharacteristic
867C2×C4C2×D4×D1111yescharacteristic
868C2×C4C2×D4×D1111yescharacteristic
869C2×C4C2×D4×D1111yescharacteristic
870C2×C4C2×D4×D1111yescharacteristic
871C2×C4C2×#434312yes—
872C2×C4#41×D1112yes—
873C2×C4C24×D1111yescharacteristic
874C8—22no—
875C8—22no—
876C8—224no—
877C22—21no—
878C22—21no—
879C22—22no—
880C22—41no—
881C22—41no—
882C22—222no—
883C22—222no—
884C22—222no—
885C22—444no—
886C22—444no—
887C22—444no—
888C22—1764no—
889C22#1062315812yes—
890C22C22×D4×D1111yescharacteristic
891C4—21no—
892C4—21no—
893C4—22no—
894C4—21no—
895C4—41no—
896C4—42no—
897C4—41no—
898C4—42no—
899C4—222no—
900C4—222no—
901C4—224no—
902C4—222no—
903C4—442no—
904C4#1062315812yes—
905C4#1062330112yes—
906C4C22×#434311yescharacteristic
907C4C2×#41×D1111yescharacteristic
908C2—22no—
909C2—42no—
910C2—442no—
911C2—884no—
912C2C2×#1062315811yescharacteristic
913C2C2×#1062330111yescharacteristic
914C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3076C2
socleC22×C11C23×D4
hypercenter#3076D11
hypocenterC11#60593
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #13082493C2semidirect
2. C4×#67043C2semidirect
3. #13078909C2semidirect
4. #13078820C2semidirect
5. #13078769C2semidirect
6. #13078740C2semidirect
7. #13078678C2semidirect
8. #13078649C2semidirect
9. #13078577C2semidirect
10. #13078417C2semidirect
11. #13078096C2semidirect
12. C2×#10622461C2semidirect
13. #13077905C2semidirect
14. #13077474C2semidirect
15. #13077451C2semidirect
16. #13077281C2semidirect
17. C11×#3076C2semidirect
33. #10623103C22semidirect
34. C4×Q8×D11C22semidirect
36. #10623077C22semidirect
38. C4×#4341C22semidirect
50. C11×#479C22semidirect
51. C11×#478C22semidirect
52. C11×#477C22semidirect
53. C11×#476C22semidirect
54. C11×#475C22semidirect
55. C11×#474C22semidirect
62. #10622707C22semidirect
63. #10622704C22semidirect
64. #10622676C22semidirect
73. #10622502C22semidirect
74. #10622502C22semidirect
75. #10622498C22semidirect
76. #10622495C22semidirect
77. #10622479C22semidirect
78. #10622476C22semidirect
79. #10622465C22semidirect
80. #10622465C22semidirect
84. #10622453C22semidirect
85. #10622448C22semidirect
86. #10622446C22semidirect
87. #10622430C22semidirect
88. #10622419C22semidirect
89. #10622419C22semidirect
90. #10622401C22semidirect
91. #10622398C22semidirect
92. #10622394C22semidirect
93. #10622394C22semidirect
94. #10622369C22semidirect
235. C11×#41#41semidirect
288. C2×Dic22#41semidirect
361. #3076D11semidirect
474. #479C2×D11semidirect
475. #478C2×D11semidirect
477. #477C2×D11semidirect
478. #476C2×D11semidirect
480. #475C2×D11semidirect
481. #474C2×D11semidirect
699. #41#4343semidirect
807. C11#60593semidirect

Maximal subgroups

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

subgroupindex
#130824932
C4×#670432
#130789092
#130788202
#130787692
#130787402
#130786782
#130786492
#130785772
#130784172
#130780962
C2×#106224612
#130779052
#130774742
#130774512
#130772812
C11×#30762
#6059311