Finite Group Databasebeta

← #15638499

Subgroups — #15638499

Order 2816.

2090 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082412C211yesmaximal, characteristic
2C2×#10623163C211yesmaximal, characteristic
3#13080490C214yesmaximal, complemented
4#13080487C214yesmaximal, complemented
5#13080365C214yesmaximal, complemented
6#13080361C214yesmaximal, complemented
7#13079562C212yesmaximal, complemented
8#13079390C212yesmaximal, complemented
9#13079388C211yesmaximal, characteristic, complemented
10#13078652C212yesmaximal, complemented
11C2×#10622352C211yesmaximal, characteristic, complemented
12C2×#10622663C211yesmaximal, characteristic, complemented
13D11×#451C212yesmaximal, complemented
14#13077638C211yesmaximal, characteristic
15C11×#3189C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20Q8×C22⋊D11C2212yes—
21C2×#66997C2211yescharacteristic
22C22×#4326C2212yescomplemented
23C2×C4×C22⋊D11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×Q16×D11C2214yescomplemented
26C22×Dic44C2212yescomplemented
27#10623167—22no—
28#10623166C2212yes—
29#10623165—21no—
30#10623163—22no—
31#10623163—22no—
32#10623163C2214yes—
33#10623163C2212yes—
34#10623163C2214yes—
35D11×C22⋊Q8C2212yes—
36#10623154—21no—
37#10623153C2212yes—
38#10623042—22no—
39#10623042C2212yes—
40C2×#66950C2211yescharacteristic
41C2×#66949—21no—
42C2×#66941—21no—
43C2×#66940C2211yescharacteristic
44#10623017—21no—
45C2×(C22⋊D11)⋊C4—21no—
46#10623014—21no—
47C2×#66931—21no—
48C11×#484C2212yes—
49C11×#484C2212yescomplemented
50C11×#467C2214yescomplemented
51C11×#451C2212yes—
52C11×#451C2212yescomplemented
53C2×C11×C22⋊C8C2211yescharacteristic
54#10622841C2212yes—
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622799C2214yescomplemented
57#10622795C2214yescomplemented
58#10622794C2214yescomplemented
59C8×C22⋊D11C2214yes—
60C2×#66880C2212yescomplemented
61#10622664C2214yescomplemented
62#10622663C2212yes—
63#10622663C2212yes—
64#10622663C2212yescomplemented
65#10622663C2214yescomplemented
66#10622657C2212yescomplemented
67#10622583C2212yes—
68C2×#66874C2212yescomplemented
69#10622500C2214yescomplemented
70#10622497C2214yescomplemented
71#10622488C2214yescomplemented
72#10622486C2214yescomplemented
73#10622426C2214yescomplemented
74#10622421C2214yescomplemented
75#10622421C2214yescomplemented
76D11×#103C2214yescomplemented
77#10622406C2214yescomplemented
78#10622406C2214yescomplemented
79#10622405C2214yescomplemented
80#10622403C2214yescomplemented
81#10622352C2212yes—
82#10622352C2212yes—
83#10622352C2214yescomplemented
84(C22⋊D11)⋊C8C2214yes—
85D11×C22⋊C8C2212yes—
86#10622331C2212yes—
87C22×Q8×C11C2311yescharacteristic
88C22×Q8×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11D411yescharacteristic
91C23×Dic11—21no—
92C2×Q8×D11—22no—
93C2×Q8×D11—44no—
94C2×Q8×D11C2314yes—
95C2×Q8×D11C2312yes—
96C22×C4×D11—21no—
97C22×C4×D11C2311yescharacteristic
98C22×Dic22—21no—
99C22×Dic22—21no—
100C22×Dic22—21no—
101C22×Dic22—21no—
102C22×Dic22—44no—
103C22×Dic22C2311yescharacteristic
104C22×Dic22C2312yes—
105C22×Dic22C2312yes—
106C22×Dic22C2311yescharacteristic
107C22×Dic22C2311yescharacteristic
108C2×C11×Q16C2314yes—
109C22×C8×C11C2312yes—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8C2312yes—
115C11×C22⋊Q8C2312yes—
116C11×C22⋊Q8C2312yes—
117C11×C22⋊Q8C2312yes—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11D411yescharacteristic
126#66999—22no—
127#66999C2312yes—
128Q8×Dic11C2312yes—
129#66997—22no—
130#66997—22no—
131#66997C2312yes—
132#66997C2314yes—
133C2×#4326—44no—
134C2×#4326C2314yes—
135C2×#4326C2314yes—
136C2×#4326C2314yes—
137C4×C22⋊D11—22no—
138C4×C22⋊D11—22no—
139C4×C22⋊D11D412yes—
140C4×C22⋊D11D412yes—
141C4×C22⋊D11C2312yes—
142C4×C22⋊D11C2312yes—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4D411yescharacteristic
145C2×C4⋊Dic11—21no—
146C2×C4⋊Dic11C2311yescharacteristic
147#66977—21no—
148#66977—21no—
149#66977—22no—
150#66977—22no—
151#66977C2312yes—
152#66977C2312yes—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4—21no—
157C2×Dic11⋊C4D411yescharacteristic
158C2×C4×Dic11—21no—
159C2×C4×Dic11C2311yescharacteristic
160C22×C11⋊C8C2312yes—
161Q16×D11—48no—
162C2×Dic44—44no—
163C2×Dic44C2314yes—
164C2×Dic44C2314yes—
165C2×C8×D11C2314yes—
166#66950—22no—
167#66950—22no—
168#66950C2314yes—
169#66950C2312yes—
170#66949—22no—
171#66949—24no—
172#66949—24no—
173#66949—22no—
174#66949—22no—
175C4⋊C4×D11—22no—
176C4⋊C4×D11C2312yes—
177#66942—22no—
178#66942—22no—
179#66942—22no—
180#66941—24no—
181#66941—24no—
182#66941—22no—
183#66941C2312yes—
184#66940—22no—
185#66940—22no—
186#66940C2312yes—
187#66940C2314yes—
188(C22⋊D11)⋊C4—24no—
189(C22⋊D11)⋊C4—24no—
190(C22⋊D11)⋊C4—22no—
191(C22⋊D11)⋊C4—22no—
192C22⋊C4×D11—22no—
193#66931—22no—
194#66931—22no—
195#66931—24no—
196#66931—24no—
197#66931—22no—
198#66931—22no—
199#66930—22no—
200C11×#107C2314yes—
201C11×#103C2314yes—
202C11×#103C2314yes—
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yes—
205#66899C2314yes—
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2312yes—
208(C2×D11)⋊C8C2314yes—
209#66880C2314yes—
210#66880C2314yes—
211Dic11⋊C8C2314yes—
212C8×Dic11C2314yes—
213#66874C2314yes—
214#66874C2314yes—
215#66874C2314yes—
216#66871C2314yes—
217#61563—111nomaximal, Sylow
218C24×C11C2×D411yescharacteristic
219C23×D11C2×D411yescharacteristic
220C2×Q8×C11—21no—
221C2×Q8×C11—21no—
222C2×Q8×C11—42no—
223C2×Q8×C11—42no—
224C2×Q8×C11C2412yes—
225C2×Q8×C11C2412yes—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—42no—
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2411yescharacteristic
235C22×C4×C11C2411yescharacteristic
236C22×C4×C11C2411yescharacteristic
237C2×C22⋊D11Q1618yescomplemented
238C2×C22⋊D11C2×D412yes—
239C2×C22⋊D11C2×D412yes—
240C22×Dic11—21no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—44no—
247C22×Dic11C2×D411yescharacteristic
248C22×Dic11C2×D411yescharacteristic
249C22×Dic11C2×D411yescharacteristic
250Q8×D11—28no—
251Q8×D11—44no—
252Q8×D11—44no—
253Q8×D11—48no—
254C2×C4×D11—24no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×C4×D11—42no—
258C2×C4×D11—44no—
259C2×C4×D11C2×D412yes—
260C2×C4×D11C2412yes—
261C2×Dic22—24no—
262C2×Dic22—24no—
263C2×Dic22—24no—
264C2×Dic22—24no—
265C2×Dic22—22no—
266C2×Dic22—22no—
267C2×Dic22—21no—
268C2×Dic22—22no—
269C2×Dic22—22no—
270C2×Dic22—21no—
271C2×Dic22—21no—
272C2×Dic22—42no—
273C2×Dic22—42no—
274C2×Dic22—42no—
275C2×Dic22—42no—
276C2×Dic22—44no—
277C2×Dic22—44no—
278C2×Dic22—44no—
279C2×Dic22—44no—
280C2×Dic22C2412yes—
281C2×Dic22C2412yes—
282C2×Dic22C2412yes—
283C11×Q16—44no—
284C2×C8×C11—42no—
285C2×C8×C11C2414yes—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4C2412yes—
293C11×C4⋊C4C2412yes—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C22⋊Dic11—22no—
299C22⋊Dic11—22no—
300C22⋊Dic11C2×D412yes—
301C22⋊Dic11C2×D412yes—
302#4326—28no—
303#4326—44no—
304#4326—44no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4C2×D412yes—
309(C2×D11)⋊C4C2×D412yes—
310C4⋊Dic11—24no—
311C4⋊Dic11—22no—
312C4⋊Dic11—22no—
313C4⋊Dic11—21no—
314C4⋊Dic11C2412yes—
315Dic11⋊C4—22no—
316Dic11⋊C4—22no—
317Dic11⋊C4—24no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322Dic11⋊C4—24no—
323Dic11⋊C4—24no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326Dic11⋊C4C2×D412yes—
327Dic11⋊C4C2×D412yes—
328C4×Dic11—22no—
329C4×Dic11—22no—
330C4×Dic11—24no—
331C4×Dic11C2×D412yes—
332C4×Dic11C2412yes—
333C2×C11⋊C8—42no—
334C2×C11⋊C8C2414yes—
335Dic44—28no—
336Dic44—44no—
337C8×D11—44no—
338#3501—111no—
339C2×D4×Q8—111no—
340#3299—114no—
341#3299—114no—
342D4×Q16—114no—
343D4×Q16—114no—
344#3209—112no—
345#3189—112no—
346#3189—111no—
347#3189D1111yescharacteristic, complemented
348#3104—112no—
349C2×#451—112no—
350C2×#451—111no—
351C2×#451—111no—
352#2972—111no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11C2×Q1614yescomplemented
356C23×C11C22×D411yescharacteristic
357C23×C11C22×D411yescharacteristic
358C23×C11C22×D411yescharacteristic
359C22×D11—41no—
360C22×D11—41no—
361C22×D11C2×Q1614yescomplemented
362C22×D11C22×D412yes—
363Q8×C11—24no—
364Q8×C11—24no—
365Q8×C11—42no—
366Q8×C11—81no—
367C2×C4×C11—22no—
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—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11—81no—
380C2×C4×C11—81no—
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C2511yescharacteristic
385C22⋊D11C2×Q1618yescomplemented
386C22⋊D11C2×Q1618yescomplemented
387C2×Dic11—24no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—44no—
395C2×Dic11—44no—
396C2×Dic11—42no—
397C2×Dic11—81no—
398C2×Dic11—81no—
399C2×Dic11C2×Q1614yescomplemented
400C2×Dic11C22×D412yes—
401C2×Dic11C22×D412yes—
402C2×Dic11C22×D412yes—
403C4×D11—24no—
404C4×D11—42no—
405C4×D11—48no—
406C4×D11—82no—
407C4×D11—82no—
408Dic22—24no—
409Dic22—22no—
410Dic22—24no—
411Dic22—22no—
412Dic22—22no—
413Dic22—48no—
414Dic22—44no—
415Dic22—44no—
416Dic22—42no—
417Dic22—82no—
418Dic22—82no—
419Dic22—81no—
420Dic22H(5,𝔽2)14yes—
421C8×C11—24no—
422C11⋊C8—24no—
423C23×Q8—111no—
424C23×Q8—111no—
425C22×Q16—112no—
426C22×Q16—114no—
427C22×Q16—112no—
428#554—112no—
429#554—112no—
430#554—222no—
431#554—222no—
432D4×Q8—112no—
433D4×Q8—114no—
434D4×Q8—114no—
435D4×Q8—112no—
436D4×Q8—222no—
437D4×Q8—222no—
438#544—221no—
439#543—221no—
440#543—221no—
441#533—112no—
442C2×C4⋊Q8—111no—
443C2×C4⋊Q8—221no—
444C2×C22⋊Q8—111no—
445C2×C22⋊Q8—112no—
446C2×C22⋊Q8—111no—
447C2×C22⋊Q8—221no—
448C2×C22⋊Q8—221no—
449C2×C22⋊Q8C2×D1111yescharacteristic
450C2×C22⋊Q8C2×D1111yescharacteristic
451#518—221no—
452C2×C4×Q8—111no—
453C2×C4×D4—111no—
454C2×C4×D4—221no—
455#494—114no—
456#487—114no—
457#484—112no—
458#484—112no—
459#484—114no—
460#484C2×D1112yes—
461#484C2×D1112yescomplemented
462#477—114no—
463#467—114no—
464#467—114no—
465#467—114no—
466#467C2×D1114yescomplemented
467#462—114no—
468#462—114no—
469#462—114no—
470#451—112no—
471#451—114no—
472#451—112no—
473#451—112no—
474#451—112no—
475#451—114no—
476#451—114no—
477#451—114no—
478#451—112no—
479#451—112no—
480#451—114no—
481#451C2×D1112yes—
482#451C2×D1112yescomplemented
483C4×Q16—114no—
484C4×Q16—114no—
485C8×D4—114no—
486C8×D4—114no—
487#431—112no—
488C2×#103—112no—
489C2×#103—112no—
490C2×#103—114no—
491C2×C22⋊C8—111no—
492C2×C22⋊C8—112no—
493C2×C22⋊C8C2×D1111yescharacteristic
494C22×C11—21no—
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—21no—
499C22×C11—21no—
500C22×C11—44no—
501C22×C11C22×Q1612yes—
502C22×C11C22×Q1612yes—
503C22×C11C22×Q1612yes—
504C22×C11C23×D411yescharacteristic
505C2×D11—22no—
506C2×D11—22no—
507C2×D11—44no—
508C2×D11C22×Q1614yes—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11—42no—
513C4×C11—42no—
514C4×C11—42no—
515C4×C11—42no—
516C4×C11C2×H(5,𝔽2)12yes—
517Dic11—22no—
518Dic11—24no—
519Dic11—22no—
520Dic11—42no—
521Dic11—42no—
522Dic11—42no—
523Dic11C22×Q1614yes—
524C22×Q8—114no—
525C22×Q8—112no—
526C22×Q8—111no—
527C22×Q8—112no—
528C22×Q8—112no—
529C22×Q8—111no—
530C22×Q8—111no—
531C22×Q8—221no—
532C22×Q8—222no—
533C22×Q8—221no—
534C22×Q8—221no—
535C22×Q8—221no—
536C22×Q8—444no—
537C22×Q8—444no—
538C22×Q8C22×D1111yescharacteristic
539C22×Q8C22×D1111yescharacteristic
540C22×D4—111no—
541C23×C4—111no—
542C23×C4—221no—
543C23×C4—221no—
544C23×C4C22×D1111yescharacteristic
545C2×Q16—114no—
546C2×Q16—114no—
547C2×Q16—114no—
548C2×Q16—114no—
549C2×Q16—114no—
550C2×Q16—444no—
551C2×Q16—448no—
552C2×Q16—444no—
553C2×Q16C22×D1114yes—
554C22×C8—112no—
555C22×C8—114no—
556C22×C8C22×D1112yes—
557C4⋊Q8—112no—
558C4⋊Q8—114no—
559C4⋊Q8—112no—
560C4⋊Q8—222no—
561C4⋊Q8—224no—
562C4⋊Q8—224no—
563C4⋊Q8—222no—
564C4⋊Q8—222no—
565#125—222no—
566#125—222no—
567#125—222no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—112no—
573C22⋊Q8—112no—
574C22⋊Q8—112no—
575C22⋊Q8—114no—
576C22⋊Q8—112no—
577C22⋊Q8—224no—
578C22⋊Q8—224no—
579C22⋊Q8—222no—
580C22⋊Q8—222no—
581C22⋊Q8—222no—
582C22⋊Q8—222no—
583C22⋊Q8—224no—
584C22⋊Q8—224no—
585C22⋊Q8—222no—
586C22⋊Q8—222no—
587C22⋊Q8—222no—
588C22⋊Q8—222no—
589C22⋊Q8—222no—
590C22⋊Q8—222no—
591C22⋊Q8—222no—
592C22⋊Q8—222no—
593C22⋊Q8—221no—
594C22⋊Q8—221no—
595C22⋊Q8C22×D1112yes—
596C22⋊Q8C22×D1112yes—
597C22⋊Q8C22×D1112yes—
598C22⋊Q8C22×D1112yes—
599C4×Q8—112no—
600C4×Q8—114no—
601C4×Q8—112no—
602C4×Q8—222no—
603C4×Q8—222no—
604C4×D4—112no—
605C4×D4—112no—
606C4×D4—112no—
607C4×D4—112no—
608C4×D4—224no—
609C4×D4—224no—
610C4×D4—222no—
611C4×D4—222no—
612C4×D4—222no—
613C4×D4—222no—
614#117—222no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—222no—
621C2×C4⋊C4—221no—
622C2×C4⋊C4—221no—
623C2×C4⋊C4—221no—
624C2×C4⋊C4—221no—
625C2×C4⋊C4—221no—
626C2×C4⋊C4C22×D1111yescharacteristic
627C2×C4⋊C4C22×D1111yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—111no—
631C2×C22⋊C4—111no—
632C2×C22⋊C4—222no—
633C2×C22⋊C4—221no—
634C2×C22⋊C4—221no—
635C2×C42—111no—
636C2×C42—221no—
637#107—114no—
638#107C22×D1114yes—
639C4⋊C8—114no—
640#103—114no—
641#103—114no—
642#103—114no—
643#103—114no—
644#103—114no—
645#103—114no—
646#103C22×D1114yes—
647#103C22×D1114yes—
648C22⋊C8—112no—
649C22⋊C8—112no—
650C22⋊C8—114no—
651C22⋊C8C22×D1112yes—
652C22⋊C8C22×D1112yes—
653C4×C8—114no—
654C2×C11—22no—
655C2×C11—22no—
656C2×C11—22no—
657C2×C11#348411yescharacteristic
658C2×C11C23×Q1611yescharacteristic
659C2×C11#358611yescharacteristic
660D11—24no—
661C24—111no—
662C24D4×D1111yescharacteristic
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—42no—
666C2×Q8—42no—
667C2×Q8—112no—
668C2×Q8—112no—
669C2×Q8—112no—
670C2×Q8—224no—
671C2×Q8—222no—
672C2×Q8—222no—
673C2×Q8—224no—
674C2×Q8—224no—
675C2×Q8—224no—
676C2×Q8—221no—
677C2×Q8—222no—
678C2×Q8—222no—
679C2×Q8—221no—
680C2×Q8—221no—
681C2×Q8—228no—
682C2×Q8—442no—
683C2×Q8—442no—
684C2×Q8—442no—
685C2×Q8—442no—
686C2×Q8—444no—
687C2×Q8—444no—
688C2×Q8—444no—
689C2×Q8—444no—
690C2×Q8—444no—
691C2×Q8—444no—
692C2×Q8—448no—
693C2×Q8C23×D1112yes—
694C2×Q8C23×D1112yes—
695C2×D4—118no—
696C2×D4—112no—
697C2×D4—112no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—42no—
703C22×C4—111no—
704C22×C4—111no—
705C22×C4—111no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—224no—
709C22×C4—222no—
710C22×C4—222no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—222no—
714C22×C4—222no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—442no—
718C22×C4—444no—
719C22×C4—444no—
720C22×C4D4×D1111yescharacteristic
721C22×C4D4×D1111yescharacteristic
722C22×C4D4×D1111yescharacteristic
723C22×C4C23×D1111yescharacteristic
724C22×C4C23×D1111yescharacteristic
725C22×C4C23×D1111yescharacteristic
726Q16—44no—
727Q16—228no—
728Q16—228no—
729Q16—444no—
730Q16—444no—
731Q16—444no—
732C2×C8—42no—
733C2×C8—114no—
734C2×C8—444no—
735C2×C8—442no—
736C2×C8C23×D1114yes—
737C4⋊C4—22no—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—112no—
744C4⋊C4—112no—
745C4⋊C4—112no—
746C4⋊C4—222no—
747C4⋊C4—224no—
748C4⋊C4—224no—
749C4⋊C4—222no—
750C4⋊C4—222no—
751C4⋊C4—224no—
752C4⋊C4—224no—
753C4⋊C4—222no—
754C4⋊C4—222no—
755C4⋊C4—222no—
756C4⋊C4—222no—
757C4⋊C4—222no—
758C4⋊C4—221no—
759C4⋊C4—222no—
760C4⋊C4—222no—
761C4⋊C4C23×D1112yes—
762C4⋊C4C23×D1112yes—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—112no—
768C22⋊C4—112no—
769C22⋊C4—112no—
770C22⋊C4—112no—
771C22⋊C4—224no—
772C22⋊C4—222no—
773C22⋊C4—222no—
774C22⋊C4—222no—
775C22⋊C4—222no—
776C42—112no—
777C42—112no—
778C42—224no—
779C42—222no—
780C42—222no—
781C11#6156311yescharacteristic, complemented, Sylow
782C23—41no—
783C23—41no—
784C23—112no—
785C23—114no—
786C23—441no—
787C23—441no—
788C23Q16×D1114yescomplemented
789C23C2×D4×D1111yescharacteristic
790C23C2×D4×D1111yescharacteristic
791C23C2×D4×D1111yescharacteristic
792Q8—24no—
793Q8—24no—
794Q8—42no—
795Q8—81no—
796Q8—114no—
797Q8—224no—
798Q8—222no—
799Q8—224no—
800Q8—222no—
801Q8—222no—
802Q8—444no—
803Q8—444no—
804Q8—442no—
805Q8—448no—
806Q8—881no—
807Q8—882no—
808Q8—882no—
809D4—118no—
810D4—118no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—114no—
826C2×C4—112no—
827C2×C4—112no—
828C2×C4—112no—
829C2×C4—224no—
830C2×C4—222no—
831C2×C4—224no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—442no—
836C2×C4—448no—
837C2×C4—441no—
838C2×C4—441no—
839C2×C4—444no—
840C2×C4—444no—
841C2×C4—442no—
842C2×C4—882no—
843C2×C4—882no—
844C2×C4—881no—
845C2×C4—881no—
846C2×C4C2×D4×D1111yescharacteristic
847C2×C4C2×D4×D1111yescharacteristic
848C2×C4C2×D4×D1111yescharacteristic
849C2×C4C24×D1111yescharacteristic
850C8—24no—
851C8—224no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—44no—
859C22—114no—
860C22—222no—
861C22—222no—
862C22—444no—
863C22C2×Q16×D1112yes—
864C22C2×Q16×D1112yes—
865C22C2×Q16×D1112yes—
866C22C22×D4×D1111yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—114no—
875C4—222no—
876C4—222no—
877C4—224no—
878C4—442no—
879C4—442no—
880C4—442no—
881C4D11×H(5,𝔽2)12yes—
882C2—22no—
883C2—22no—
884C2—22no—
885C2—224no—
886C2#1308224811yescharacteristic
887C2C22×Q16×D1111yescharacteristic
888C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3189C2
socleC22×C11C23×D4
prime radicalC22×C22⋊D11D4
hypercenter#3189D11
hypocenterC11#61563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
3. #13080490C2semidirect
4. #13080487C2semidirect
5. #13080365C2semidirect
6. #13080361C2semidirect
7. #13079562C2semidirect
8. #13079390C2semidirect
9. #13079388C2semidirect
10. #13078652C2semidirect
11. C2×#10622352C2semidirect
12. C2×#10622663C2semidirect
13. D11×#451C2semidirect
15. C11×#3189C2semidirect
22. C22×#4326C22semidirect
25. C2×Q16×D11C22semidirect
26. C22×Dic44C22semidirect
49. C11×#484C22semidirect
50. C11×#467C22semidirect
52. C11×#451C22semidirect
56. #10622799C22semidirect
57. #10622795C22semidirect
58. #10622794C22semidirect
60. C2×#66880C22semidirect
61. #10622664C22semidirect
64. #10622663C22semidirect
65. #10622663C22semidirect
66. #10622657C22semidirect
68. C2×#66874C22semidirect
69. #10622500C22semidirect
70. #10622497C22semidirect
71. #10622488C22semidirect
72. #10622486C22semidirect
73. #10622426C22semidirect
74. #10622421C22semidirect
75. #10622421C22semidirect
76. D11×#103C22semidirect
77. #10622406C22semidirect
78. #10622406C22semidirect
79. #10622405C22semidirect
80. #10622403C22semidirect
83. #10622352C22semidirect
237. C2×C22⋊D11Q16semidirect
347. #3189D11semidirect
355. C23×C11C2×Q16semidirect
361. C22×D11C2×Q16semidirect
385. C22⋊D11C2×Q16semidirect
386. C22⋊D11C2×Q16semidirect
399. C2×Dic11C2×Q16semidirect
461. #484C2×D11semidirect
466. #467C2×D11semidirect
482. #451C2×D11semidirect
781. C11#61563semidirect
788. C23Q16×D11semidirect

Maximal subgroups

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

subgroupindex
#130824122
C2×#106231632
#130804902
#130804872
#130803652
#130803612
#130795622
#130793902
#130793882
#130786522
C2×#106223522
C2×#106226632
D11×#4512
#130776382
C11×#31892
#6156311