Finite Group Databasebeta

← #15617140

Subgroups — #15617140

Order 2816.

2326 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076609C211yesmaximal, characteristic, complemented
2#13075644C212yesmaximal, complemented
3#13075640C211yesmaximal, characteristic, complemented
4#13074300C212yesmaximal, complemented
5#13074299C212yesmaximal, complemented
6#13074296C212yesmaximal, complemented
7#13073689C212yesmaximal, complemented
8#13073688C212yesmaximal, complemented
9#13073686C212yesmaximal, complemented
10#13072232C212yesmaximal, complemented
11#13072231C211yesmaximal, characteristic, complemented
12#13072230C212yesmaximal, complemented
13#13071728C211yesmaximal, characteristic, complemented
14#13071727C211yesmaximal, characteristic, complemented
15#13071725C212yesmaximal, complemented
16#13071724C212yesmaximal, complemented
17#13071107C211yesmaximal, characteristic, complemented
18#13071101C212yesmaximal, complemented
19C11×#2431C211yesmaximal, characteristic, complemented
20C22×C11×#41C2211yescharacteristic
21C22×#4341C2212yes—
22C2×C11×#127C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×#67000C2211yescharacteristic
26C2×#66993C2211yescharacteristic
27C2×#66992C2212yes—
28C2×#66991C2212yes—
29C2×#66989C2212yes—
30C2×#66989C2212yes—
31C2×#66983C2211yescharacteristic
32C2×#66979C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×#66938C2212yes—
35C2×#66938C2212yes—
36C2×#66938C2212yes—
37C2×#66930C2212yes—
38C11×#392C2212yes—
39C11×#392C2212yes—
40C11×#391C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#386C2212yes—
43C11×#386C2212yes—
44C4×C11×C22⋊C4C2211yescharacteristic
45#10622843C2211yescharacteristic
46#10622843C2211yescharacteristic
47#10622843C2211yescharacteristic
48#10622836C2212yes—
49#10622836C2212yes—
50#10622836C2212yes—
51#10622836C2212yes—
52#10622836C2212yes—
53#10622836C2212yes—
54#10622835C2212yes—
55#10622834C2211yescharacteristic
56#10622834C2211yescharacteristic
57#10622834C2211yescharacteristic
58#10622834C2212yes—
59#10622833C2212yes—
60#10622833C2212yes—
61#10622833C2212yes—
62#10622833C2212yes—
63#10622833C2212yes—
64#10622826C2212yes—
65#10622826C2212yes—
66C4×C22⋊Dic11C2212yes—
67C4×C22⋊Dic11C2212yes—
68C4×C22⋊Dic11C2211yescharacteristic
69#10622603C2212yes—
70#10622592C2212yes—
71#10622574C2212yes—
72#10622573C2212yes—
73#10622572C2212yes—
74#10622571C2212yes—
75#10622570C2212yes—
76#10622570C2212yes—
77#10622570C2212yes—
78#10622569C2212yes—
79#10622564C2212yes—
80#10622564C2212yes—
81#10622564C2212yes—
82#10622560C2212yes—
83#10622558C2212yes—
84#10622558C2212yes—
85#10622557C2212yes—
86#10622557C2212yes—
87#10622557C2212yes—
88C22⋊C4×Dic11C2212yes—
89C22⋊C4×Dic11C2212yes—
90C22⋊C4×Dic11C2212yes—
91#10622553C2212yes—
92C4×(C2×D11)⋊C4C2212yes—
93#10622545C2212yes—
94#10622542C2212yes—
95#10622283C2212yes—
96#10622283C2212yes—
97#10622279C2212yes—
98#10622279C2212yes—
99#10622278C2212yes—
100#10622269C2212yes—
101#10622269C2212yes—
102#10622261C2212yes—
103#10622261C2212yes—
104#10622259C2212yes—
105#10622259C2212yes—
106#10622259C2212yes—
107C2×C11×#41—24no—
108C2×C11×#41—42no—
109C2×C11×#41—42no—
110C22×Q8×C11C2311yescharacteristic
111C22×D4×C11C2311yescharacteristic
112C22×D4×C11C2311yescharacteristic
113C22×D4×C11C2312yes—
114C22×D4×C11C2312yes—
115C22×D4×C11C2311yescharacteristic
116C22×D4×C11C2311yescharacteristic
117C22×D4×C11C2312yes—
118C23×C4×C11C2311yescharacteristic
119C23×C4×C11C2311yescharacteristic
120C23×C4×C11C2311yescharacteristic
121C22×C22⋊D11C2312yes—
122C22×C22⋊D11C2312yes—
123C22×C22⋊D11C2312yes—
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2312yes—
126C23×Dic11C2312yes—
127C23×Dic11C2312yes—
128C2×#4341—28no—
129C2×#4341—44no—
130C2×#4341—44no—
131C22×D44C2311yescharacteristic
132C22×C4×D11C2312yes—
133C22×Dic22C2312yes—
134C22×Dic22C2312yes—
135C11×#127—42no—
136C11×#124—24no—
137C11×#121—42no—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C22⋊Dic11C2312yes—
148C2×C22⋊Dic11C2312yes—
149C2×C22⋊Dic11C2312yes—
150C2×C22⋊Dic11C2312yes—
151C2×C22⋊Dic11C2312yes—
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160#67000—24no—
161#66993—42no—
162#66992—44no—
163#66991—44no—
164#66989—28no—
165#66989—44no—
166#66983—42no—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175#66979—42no—
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2311yescharacteristic
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×C4×Dic11—42no—
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2311yescharacteristic
194#66938—28no—
195#66938—44no—
196#66938—44no—
197#66930—44no—
198C11×#95C2312yes—
199C11×#95C2312yes—
200C11×#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206C11⋊#95C2312yes—
207C11⋊#95C2312yes—
208C11⋊#95C2312yes—
209C11⋊#95C2312yes—
210C11⋊#95C2312yes—
211C11⋊#95C2312yes—
212C11⋊#95C2312yes—
213C11⋊#95C2312yes—
214C11⋊#95C2312yes—
215C11⋊#95C2312yes—
216#60048—111nomaximal, Sylow
217C24×C11C2411yescharacteristic
218C24×C11C2411yescharacteristic
219C24×C11C2412yes—
220C24×C11C2411yescharacteristic
221C23×D11C2412yes—
222C11×#41—416no—
223C2×Q8×C11—41no—
224C2×Q8×C11—41no—
225C2×Q8×C11#4114yescomplemented
226C2×D4×C11—22no—
227C2×D4×C11—24no—
228C2×D4×C11—22no—
229C2×D4×C11—24no—
230C2×D4×C11—22no—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—24no—
234C2×D4×C11—22no—
235C2×D4×C11—42no—
236C2×D4×C11—41no—
237C2×D4×C11—41no—
238C2×D4×C11—41no—
239C2×D4×C11—41no—
240C2×D4×C11—42no—
241C2×D4×C11—42no—
242C2×D4×C11—42no—
243C2×D4×C11—41no—
244C2×D4×C11—42no—
245C2×D4×C11—42no—
246C2×D4×C11—41no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—41no—
255C22×C4×C11—41no—
256C22×C4×C11C2412yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2412yes—
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C2×C22⋊D11—24no—
264C2×C22⋊D11—24no—
265C2×C22⋊D11—24no—
266C2×C22⋊D11—24no—
267C2×C22⋊D11—42no—
268C2×C22⋊D11—42no—
269C2×C22⋊D11—42no—
270C2×C22⋊D11—42no—
271C2×C22⋊D11—42no—
272C2×C22⋊D11—42no—
273C2×C22⋊D11—42no—
274C2×C22⋊D11—42no—
275C2×C22⋊D11—42no—
276C2×C22⋊D11—42no—
277C2×C22⋊D11—42no—
278C22×Dic11—24no—
279C22×Dic11—24no—
280C22×Dic11—24no—
281C22×Dic11—24no—
282C22×Dic11—24no—
283C22×Dic11—42no—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2412yes—
287C22×Dic11C2412yes—
288C22×Dic11C2412yes—
289C22×Dic11C2412yes—
290C22×Dic11C2412yes—
291#4341—432no—
292C2×D44—22no—
293C2×D44—41no—
294C2×D44—41no—
295C2×C4×D11—24no—
296C2×C4×D11—24no—
297C2×C4×D11—42no—
298C2×Dic22—42no—
299C2×Dic22—42no—
300C2×Dic22—42no—
301C2×Dic22—42no—
302C2×Dic22—42no—
303C2×Dic22#4118yescomplemented
304C11×C4⋊C4—41no—
305C11×C22⋊C4—24no—
306C11×C22⋊C4—24no—
307C11×C22⋊C4—24no—
308C11×C22⋊C4—24no—
309C11×C22⋊C4—42no—
310C11×C22⋊C4—42no—
311C42×C11—22no—
312C42×C11—41no—
313C22⋊Dic11—24no—
314C22⋊Dic11—24no—
315C22⋊Dic11—24no—
316C22⋊Dic11—24no—
317C22⋊Dic11—24no—
318C22⋊Dic11—24no—
319C22⋊Dic11—24no—
320C22⋊Dic11—24no—
321C22⋊Dic11—42no—
322C22⋊Dic11—42no—
323C22⋊Dic11—42no—
324C22⋊Dic11—42no—
325C22⋊Dic11—42no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—24no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—42no—
333(C2×D11)⋊C4—42no—
334C4⋊Dic11—41no—
335C4⋊Dic11—41no—
336C4⋊Dic11—41no—
337C4⋊Dic11—42no—
338Dic11⋊C4—42no—
339Dic11⋊C4—42no—
340Dic11⋊C4—42no—
341C4×Dic11—24no—
342C4×Dic11—24no—
343C4×Dic11—24no—
344C4×Dic11—24no—
345C4×Dic11—22no—
346C4×Dic11—24no—
347C4×Dic11—42no—
348C4×Dic11—41no—
349C4×Dic11—41no—
350C4×Dic11—41no—
351#2811—111no—
352#2733—112no—
353#2733—111no—
354#2610—112no—
355#2610—112no—
356#2610—112no—
357#2555—112no—
358#2555—112no—
359#2555—112no—
360#2431—112no—
361#2431—111no—
362#2431—112no—
363#2431D1111yescharacteristic, complemented
364#2372—111no—
365#2372—112no—
366#2372—112no—
367#2372—111no—
368#2297—112no—
369#2297—111no—
370C23×C11—22no—
371C23×C11—21no—
372C23×C11—21no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—21no—
380C23×C11—21no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—21no—
391C23×C11H(5,𝔽2)12yes—
392C23×C11C2511yescharacteristic
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400Q8×C11—44no—
401D4×C11—48no—
402D4×C11—44no—
403D4×C11—44no—
404D4×C11—44no—
405D4×C11—82no—
406D4×C11—84no—
407D4×C11—84no—
408C2×C4×C11—28no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—22no—
415C2×C4×C11—21no—
416C2×C4×C11—22no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—44no—
426C2×C4×C11—44no—
427C2×C4×C11C2×#4112yes—
428C2×C4×C11C2×#4112yes—
429C2×C4×C11C2×#4112yes—
430C2×C4×C11C2×#4114yes—
431C2×C4×C11H(5,𝔽2)12yes—
432C22⋊D11—48no—
433C22⋊D11—48no—
434C22⋊D11—84no—
435C22⋊D11—84no—
436C22⋊D11—84no—
437C2×Dic11—216no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—48no—
457C2×Dic11C2×#4114yes—
458C2×Dic11C2×#4114yes—
459C2×Dic11H(5,𝔽2)14yes—
460D44—82no—
461C4×D11—48no—
462Dic22—48no—
463Dic22—84no—
464C22×#41—112no—
465C22×#41C2×D1111yescharacteristic
466C2×#127—111no—
467C2×#127C2×D1111yescharacteristic
468C2×#124—111no—
469C2×#124—112no—
470C2×#124—112no—
471C2×#124—112no—
472C2×#124—112no—
473C2×#124—112no—
474C2×#124C2×D1111yescharacteristic
475C2×#121—112no—
476C2×#121—112no—
477C2×#121—111no—
478C2×#121C2×D1111yescharacteristic
479C2×#117—111no—
480C2×#117—112no—
481C22×C42—111no—
482#395—112no—
483#395—112no—
484#395—112no—
485#394—112no—
486#394—112no—
487#394—112no—
488#393—112no—
489#392—112no—
490#392—112no—
491#392—112no—
492#392—112no—
493#392—112no—
494#392—112no—
495#392—112no—
496#392C2×D1112yes—
497#392C2×D1112yes—
498#391—111no—
499#391—111no—
500#391—111no—
501#391—112no—
502#391—112no—
503#391—112no—
504#391—112no—
505#391C2×D1111yescharacteristic
506#390—111no—
507#390—112no—
508#390—111no—
509#390—111no—
510#390—112no—
511#390—112no—
512#390—112no—
513#390C2×D1111yescharacteristic
514#388—112no—
515#388—112no—
516#388—112no—
517#388—112no—
518#388—112no—
519#388—112no—
520#388—112no—
521#388—112no—
522#388—112no—
523#388—112no—
524#388—112no—
525#388—112no—
526#386—112no—
527#386—112no—
528#386—112no—
529#386—112no—
530#386—112no—
531#386—112no—
532#386—112no—
533#386—112no—
534#386—112no—
535#386—112no—
536#386C2×D1112yes—
537#386C2×D1112yes—
538C4×C22⋊C4—111no—
539C4×C22⋊C4—112no—
540C4×C22⋊C4—112no—
541C4×C22⋊C4—112no—
542C4×C22⋊C4—112no—
543C4×C22⋊C4—112no—
544C4×C22⋊C4—112no—
545C4×C22⋊C4—112no—
546C4×C22⋊C4—112no—
547C4×C22⋊C4C2×D1111yescharacteristic
548#376—112no—
549#376—112no—
550#376—112no—
551C22×C11—22no—
552C22×C11—24no—
553C22×C11—42no—
554C22×C11—41no—
555C22×C11—41no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—41no—
561C22×C11—42no—
562C22×C11—41no—
563C22×C11—41no—
564C22×C11—41no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—41no—
571C22×C11—42no—
572C22×C11—41no—
573C22×C11C22×#4111yescharacteristic
574C22×C11C22×#4112yes—
575C22×C11C2×H(5,𝔽2)11yescharacteristic
576C22×C11C2×H(5,𝔽2)11yescharacteristic
577C22×C11C2×H(5,𝔽2)12yes—
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C2×D11—42no—
585C4×C11—22no—
586C4×C11—22no—
587C4×C11—22no—
588C4×C11—22no—
589C4×C11—24no—
590C4×C11—42no—
591C4×C11—42no—
592Dic11—24no—
593Dic11—24no—
594Dic11—24no—
595Dic11—42no—
596Dic11—42no—
597Dic11—42no—
598Dic11—42no—
599C2×#41—24no—
600C2×#41—42no—
601C2×#41—42no—
602C2×#41—228no—
603C2×#41—444no—
604C2×#41—444no—
605C22×Q8—112no—
606C22×Q8—112no—
607C22×Q8C22×D1111yescharacteristic
608C22×D4—112no—
609C22×D4—112no—
610C22×D4—112no—
611C22×D4—112no—
612C22×D4—112no—
613C22×D4—111no—
614C22×D4C22×D1111yescharacteristic
615C22×D4C22×D1112yes—
616C22×D4C22×D1111yescharacteristic
617C22×D4C22×D1112yes—
618C22×D4C22×D1111yescharacteristic
619C22×D4C22×D1111yescharacteristic
620C22×D4C22×D1112yes—
621C23×C4—112no—
622C23×C4—112no—
623C23×C4—112no—
624C23×C4C22×D1111yescharacteristic
625C23×C4C22×D1111yescharacteristic
626C23×C4C22×D1111yescharacteristic
627#127—42no—
628#127—442no—
629#124—24no—
630#124—228no—
631#124—228no—
632#124—224no—
633#124—444no—
634#124—444no—
635#124—444no—
636#121—42no—
637#121—442no—
638#121—444no—
639#121—444no—
640#117—444no—
641#117—442no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—111no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—111no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4C22×D1111yescharacteristic
650C2×C22⋊C4—112no—
651C2×C22⋊C4—112no—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—112no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—112no—
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—112no—
671C2×C22⋊C4C22×D1112yes—
672C2×C22⋊C4C22×D1112yes—
673C2×C22⋊C4C22×D1112yes—
674C2×C22⋊C4C22×D1112yes—
675C2×C22⋊C4C22×D1112yes—
676C2×C22⋊C4C22×D1112yes—
677C2×C42—112no—
678C2×C42—112no—
679C2×C42—112no—
680C2×C42—112no—
681C2×C42—111no—
682C2×C42—112no—
683C2×C42—111no—
684C2×C42—111no—
685C2×C42—112no—
686C2×C42—111no—
687C2×C42—442no—
688C2×C42C22×D1111yescharacteristic
689C2×C42C22×D1111yescharacteristic
690#95—112no—
691#95—112no—
692#95—112no—
693#95—112no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—112no—
698#95—112no—
699#95—112no—
700#95—112no—
701#95—112no—
702#95—112no—
703#95—112no—
704#95—112no—
705#95C22×D1112yes—
706#95C22×D1112yes—
707#95C22×D1112yes—
708C2×C11—42no—
709C2×C11—81no—
710C2×C11—81no—
711C2×C11—82no—
712C2×C11#348312yes—
713C2×C11#348311yescharacteristic
714C2×C11#349012yes—
715C2×C11#349011yescharacteristic
716C2×C11#354911yescharacteristic
717D11—82no—
718C24—112no—
719C24C23×D1111yescharacteristic
720C24C23×D1111yescharacteristic
721C24C23×D1112yes—
722C24C23×D1111yescharacteristic
723#41—416no—
724#41—4432no—
725C2×Q8—41no—
726C2×Q8—41no—
727C2×Q8—118no—
728C2×Q8—442no—
729C2×Q8—442no—
730C2×Q8—442no—
731C2×Q8—442no—
732C2×Q8—442no—
733C2×Q8#434114yescomplemented
734C2×D4—22no—
735C2×D4—24no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—41no—
744C2×D4—41no—
745C2×D4—41no—
746C2×D4—41no—
747C2×D4—42no—
748C2×D4—41no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—41no—
754C2×D4—42no—
755C2×D4—224no—
756C2×D4—224no—
757C2×D4—224no—
758C2×D4—224no—
759C2×D4—222no—
760C2×D4—441no—
761C2×D4—441no—
762C2×D4—442no—
763C2×D4—442no—
764C2×D4—442no—
765C2×D4—442no—
766C2×D4—442no—
767C2×D4—442no—
768C2×D4—442no—
769C2×D4—442no—
770C2×D4—442no—
771C2×D4—442no—
772C2×D4—442no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—112no—
783C22×C4—112no—
784C22×C4—112no—
785C22×C4—112no—
786C22×C4—112no—
787C22×C4—112no—
788C22×C4—112no—
789C22×C4—224no—
790C22×C4—224no—
791C22×C4—224no—
792C22×C4—224no—
793C22×C4—224no—
794C22×C4—224no—
795C22×C4—224no—
796C22×C4—442no—
797C22×C4—442no—
798C22×C4C23×D1112yes—
799C22×C4C23×D1112yes—
800C22×C4C23×D1111yescharacteristic
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1111yescharacteristic
803C22×C4C23×D1111yescharacteristic
804C22×C4C23×D1112yes—
805C4⋊C4—41no—
806C4⋊C4—442no—
807C4⋊C4—442no—
808C4⋊C4—441no—
809C4⋊C4—441no—
810C4⋊C4—442no—
811C4⋊C4—441no—
812C4⋊C4—442no—
813C22⋊C4—24no—
814C22⋊C4—24no—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—224no—
820C22⋊C4—224no—
821C22⋊C4—224no—
822C22⋊C4—224no—
823C22⋊C4—224no—
824C22⋊C4—224no—
825C22⋊C4—224no—
826C22⋊C4—224no—
827C22⋊C4—224no—
828C22⋊C4—224no—
829C22⋊C4—224no—
830C22⋊C4—224no—
831C22⋊C4—224no—
832C22⋊C4—224no—
833C22⋊C4—442no—
834C22⋊C4—442no—
835C22⋊C4—442no—
836C22⋊C4—442no—
837C22⋊C4—442no—
838C22⋊C4—442no—
839C22⋊C4—442no—
840C42—22no—
841C42—41no—
842C42—224no—
843C42—224no—
844C42—224no—
845C42—222no—
846C42—224no—
847C42—224no—
848C42—442no—
849C42—441no—
850C42—441no—
851C42—441no—
852C11#6004811yescharacteristic, complemented, Sylow
853C23—21no—
854C23—21no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—22no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23#6703712yes—
882C23C24×D1111yescharacteristic
883Q8—44no—
884Q8—448no—
885Q8—884no—
886D4—44no—
887D4—44no—
888D4—48no—
889D4—44no—
890D4—84no—
891D4—82no—
892D4—84no—
893D4—448no—
894D4—448no—
895D4—882no—
896D4—884no—
897D4—884no—
898D4—884no—
899C2×C4—28no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—22no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—44no—
917C2×C4—44no—
918C2×C4—114no—
919C2×C4—114no—
920C2×C4—114no—
921C2×C4—2216no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—448no—
941C2×C4—448no—
942C2×C4C2×#434112yes—
943C2×C4C2×#434112yes—
944C2×C4C2×#434112yes—
945C2×C4#6703712yes—
946C2×C4#41×D1114yes—
947C22—24no—
948C22—22no—
949C22—42no—
950C22—41no—
951C22—41no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—41no—
967C22—41no—
968C22—42no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22—442no—
973C22—442no—
974C22—442no—
975C22—442no—
976C22C22×#434111yescharacteristic
977C22C2×#6703711yescharacteristic
978C22C2×#6703711yescharacteristic
979C22C2×#41×D1112yes—
980C22D11×H(5,𝔽2)12yes—
981C4—24no—
982C4—22no—
983C4—22no—
984C4—22no—
985C4—22no—
986C4—42no—
987C4—42no—
988C4—224no—
989C4—224no—
990C4—224no—
991C4—442no—
992C4—442no—
993C4—442no—
994C4—442no—
995C2—42no—
996C2—81no—
997C2—82no—
998C2—81no—
999C2—882no—
1000C2#1308223912yes—
1001C2#1308224011yescharacteristic
1002C2#1308229812yes—
1003C2#1308230311yescharacteristic
1004C2#1308301911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2431C2
hypercenter#2431D11
hypocenterC11#60048
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2431

Complements

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

NH ≅ G/Ntype
1. #13076609C2semidirect
2. #13075644C2semidirect
3. #13075640C2semidirect
4. #13074300C2semidirect
5. #13074299C2semidirect
6. #13074296C2semidirect
7. #13073689C2semidirect
8. #13073688C2semidirect
9. #13073686C2semidirect
10. #13072232C2semidirect
11. #13072231C2semidirect
12. #13072230C2semidirect
13. #13071728C2semidirect
14. #13071727C2semidirect
15. #13071725C2semidirect
16. #13071724C2semidirect
17. #13071107C2semidirect
18. #13071101C2semidirect
19. C11×#2431C2semidirect
225. C2×Q8×C11#41semidirect
303. C2×Dic22#41semidirect
363. #2431D11semidirect
733. C2×Q8#4341semidirect
852. C11#60048semidirect

Maximal subgroups

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

subgroupindex
#130766092
#130756442
#130756402
#130743002
#130742992
#130742962
#130736892
#130736882
#130736862
#130722322
#130722312
#130722302
#130717282
#130717272
#130717252
#130717242
#130711072
#130711012
C11×#24312
#6004811