Finite Group Databasebeta

← #15662236

Subgroups — #15662236

Order 2816.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082713C212yesmaximal, complemented
2#13082666C216yesmaximal, complemented
3#13082634C212yesmaximal, complemented
4#13082595C216yesmaximal, complemented
5#13082529C213yesmaximal, complemented
6#13082503C213yesmaximal, complemented
7#13082401C211yesmaximal, characteristic, complemented
8#13082371C216yesmaximal, complemented
9#13082297C212yesmaximal, complemented
10#13082237C216yesmaximal, complemented
11#13082236C212yesmaximal, complemented
12Q8×#4343C212yesmaximal, complemented
13#13082182C216yesmaximal, complemented
14#13082050C216yesmaximal, complemented
15#13081913C213yesmaximal, complemented
16C2×#10623259C213yesmaximal, complemented
17#13081827C212yesmaximal, complemented
18C4×#41×D11C211yesmaximal, characteristic, complemented
19C11×#3503C211yesmaximal, characteristic, complemented
20C2×#67043C2212yes—
21C2×#41×D11C2211yescharacteristic
22Q82×C11C2212yescomplemented
23C11×#557C2212yescomplemented
24C11×#554C2216yescomplemented
25D4×Q8×C11C2216yescomplemented
26C11×#544C2216yescomplemented
27C11×#533C2213yescomplemented
28C2×C11×C4⋊Q8C2213yescomplemented
29C11×#520C2212yes—
30C4×C11×#41C2211yescharacteristic
31#41×Dic11C2211yescharacteristic
32#10623348C22112yescomplemented
33C2×#66999C2216yes—
34C2×Q8×Dic11C2216yescomplemented
35#10623265C2216yescomplemented
36#10623264C22112yescomplemented
37#10623264C22112yescomplemented
38#10623263C22112yescomplemented
39#10623263C2216yescomplemented
40#10623261C22112yes—
41#10623261C2216yescomplemented
42#10623259C2216yes—
43#10623259C2216yes—
44#10623259C2213yes—
45#10623259C2216yes—
46#10623259C2216yescomplemented
47#10623259C2216yescomplemented
48#10623259C2216yescomplemented
49#10623259C2216yescomplemented
50#10623259C2213yescomplemented
51#10623259C22112yescomplemented
52#10623257C2216yescomplemented
53#10623256C2211yescharacteristic
54#10623256C2213yescomplemented
55#10623228C22112yescomplemented
56#10623228C22112yescomplemented
57#10623225C22112yes—
58#10623225C22112yescomplemented
59#10623222C2216yes—
60#10623222C2216yescomplemented
61#10623222C22112yescomplemented
62#10623176C22124yescomplemented
63#10623173C22124yescomplemented
64#10623173C22112yescomplemented
65#10623173C22112yescomplemented
66#10623168C22124yes—
67#10623158C2216yes—
68#10623158C2216yes—
69#10623155C2216yescomplemented
70#10623155C2216yescomplemented
71#10623155C22124yescomplemented
72#10623115C2216yescomplemented
73#10623115C2216yescomplemented
74#10623111C2216yes—
75#10623111C2216yescomplemented
76#10623107C2214yes—
77Q8×D44C2214yes—
78Q8×D44C2212yescomplemented
79Q8×D44C2212yescomplemented
80C4×#4343C2211yescharacteristic
81C4×#4343C2216yes—
82C4×#4343C2211yescharacteristic
83C4×#4343C2216yescomplemented
84#10623103C2214yescomplemented
85C4×Q8×D11C2211yescharacteristic
86C4×Q8×D11C2211yescharacteristic
87C4×Q8×D11C2214yescomplemented
88#10623101C2216yescomplemented
89#10623101C2216yescomplemented
90#10623086C22112yes—
91#10623086C2216yescomplemented
92#10623086C2216yescomplemented
93#10623085C22112yes—
94#10623077C22112yescomplemented
95C4×D4×D11C2213yes—
96C4×D4×D11C2213yes—
97C4×#4341C2213yes—
98C4×#4341C2213yes—
99C4×#4341C22112yescomplemented
100#10623057C2216yes—
101#10623057C2216yescomplemented
102#10623055C2216yes—
103#10623053C2213yes—
104#10623053C2216yescomplemented
105D11×#117C2213yes—
106#10623047C2216yescomplemented
107#10623045C22112yescomplemented
108#10623041C2216yes—
109C2×#66950C2216yes—
110#10623035C2216yescomplemented
111C2×#66945C2216yes—
112C2×#66943C2216yescomplemented
113C2×#66940C2216yescomplemented
114#10623008C2213yescomplemented
115C4×#4339C2213yes—
116C2×C42×D11C2213yes—
117C2×#66922C2213yescomplemented
118C2×C11×#41C2311yescharacteristic
119C22×Q8×C11C2316yes—
120#67043—216no—
121#41×D11—28no—
122C2×#4343C2312yes—
123C2×#4343C2311yescharacteristic
124C2×#4343C2316yes—
125C2×Q8×D11C2311yescharacteristic
126C2×Q8×D11C2314yes—
127C2×#4341C2313yes—
128C2×#4341C23112yes—
129C2×D4×D11C2313yes—
130C2×#4339C2313yes—
131C2×#4339C2316yes—
132C22×C4×D11C2313yes—
133C22×C4×D11C2313yes—
134C22×C4×D11C2313yes—
135C22×Dic22C2316yes—
136C11×C4⋊Q8C2311yescharacteristic
137C11×C4⋊Q8C2313yes—
138C11×C4⋊Q8C2316yes—
139C11×C4⋊Q8C2316yes—
140C11×C4⋊Q8C2316yes—
141C11×C4⋊Q8C23112yes—
142C11×#125C2316yes—
143C11×#125C23112yes—
144C11×C22⋊Q8C2316yes—
145C11×C22⋊Q8C2316yes—
146C11×C22⋊Q8C23124yes—
147C4×Q8×C11C2316yes—
148C4×Q8×C11C2316yes—
149C4×Q8×C11C2311yescharacteristic
150C4×Q8×C11C2311yescharacteristic
151C4×Q8×C11C2314yes—
152C4×D4×C11C2313yes—
153C4×D4×C11C2313yes—
154C4×D4×C11C23112yes—
155C11×#117C2316yes—
156C11×#117C2313yes—
157C2×C11×C4⋊C4C2316yes—
158C2×C11×C4⋊C4C2316yes—
159C2×C42×C11C2313yes—
160#67000C2312yes—
161#67000C2316yes—
162#67000C23124yes—
163#66999C23112yes—
164#66999C2316yes—
165#66999C23112yes—
166#66999C23112yes—
167#66999C23124yes—
168#66999C2316yes—
169Q8×Dic11C23112yes—
170Q8×Dic11C2316yes—
171Q8×Dic11C23112yes—
172Q8×Dic11C23112yes—
173Q8×Dic11C2316yes—
174Q8×Dic11C2311yescharacteristic
175Q8×Dic11C2311yescharacteristic
176D4×Dic11C2313yes—
177D4×Dic11C2313yes—
178#66983C2316yes—
179#66983C2316yes—
180#66983C23124yes—
181C4×C22⋊D11C2316yes—
182C4×C22⋊D11C2316yes—
183C4×C22⋊D11C23124yes—
184C2×(C2×D11)⋊C4C23112yes—
185#66979C2313yes—
186C2×C4⋊Dic11C2316yes—
187C2×C4⋊Dic11C2316yes—
188C2×C4⋊Dic11C23112yes—
189C2×Dic11⋊C4C23112yes—
190C2×C4×Dic11C2313yes—
191C2×C4×Dic11C2313yes—
192C2×C4×Dic11C2313yes—
193C2×C4×Dic11C23112yes—
194#66951C23112yes—
195#66951C23124yes—
196#66951C23124yes—
197#66951C23112yes—
198#66951C23124yes—
199#66950C2316yes—
200#66950C23112yes—
201#66950C23112yes—
202#66950C23112yes—
203#66950C23112yes—
204#66950C23112yes—
205#66950C2316yes—
206#66950C23112yes—
207#66948C2312yes—
208#66948C2312yes—
209#66948C2316yes—
210#66948C2316yes—
211#66948C23112yes—
212#66947C23124yes—
213#66947C23112yes—
214#66947C23112yes—
215#66946C2312yes—
216#66946C2312yes—
217#66946C2316yes—
218#66946C2316yes—
219#66946C23112yes—
220#66946C2313yes—
221#66946C2313yes—
222#66946C23112yes—
223#66945C2316yes—
224#66945C23112yes—
225#66945C23112yes—
226#66945C23112yes—
227#66945C23112yes—
228#66945C2316yes—
229#66945C2313yes—
230#66945C23112yes—
231#66945C2313yes—
232#66945C23112yes—
233C4⋊C4×D11C23112yes—
234C4⋊C4×D11C2313yes—
235C4⋊C4×D11C2313yes—
236#66943C2316yes—
237#66943C23112yes—
238#66943C23112yes—
239#66943C23112yes—
240#66943C23124yes—
241#66943C2316yes—
242#66943C23124yes—
243#66940C2316yes—
244#66940C23112yes—
245#66940C23112yes—
246#66940C23112yes—
247#66940C2313yes—
248#66940C2316yes—
249#66940C2313yes—
250#66939C23112yes—
251#66939C23124yes—
252#66939C23124yes—
253#66935C23112yes—
254(C22⋊D11)⋊C4C2316yes—
255(C22⋊D11)⋊C4C2316yes—
256(C22⋊D11)⋊C4C23112yes—
257(C22⋊D11)⋊C4C23112yes—
258C22⋊C4×D11C2316yes—
259#66930C23124yes—
260#66930C2316yes—
261#66928C2316yes—
262#66928C23112yes—
263#66927C2311yescharacteristic
264C4×D44C2313yes—
265C4×D44C2316yes—
266C4×D44C2313yes—
267C4×D44C23112yes—
268C4×D44C2316yes—
269C4×D44C23112yes—
270#66925C2316yes—
271#66925C23112yes—
272C42×D11C2311yescharacteristic
273C42×D11C2313yes—
274C42×D11C2313yes—
275C42×D11C2313yes—
276C42×D11C2313yes—
277C42×D11C2313yes—
278C42×D11C2313yes—
279C42×D11C2313yes—
280C42×D11C23112yes—
281#66922C2313yes—
282#66922C2316yes—
283#66922C2316yes—
284#66922C2316yes—
285#66922C23112yes—
286C4×Dic22C2313yes—
287C4×Dic22C2313yes—
288C4×Dic22C23112yes—
289C4×Dic22C23112yes—
290#62805—111nomaximal, Sylow
291C23×D11C2413yes—
292C11×#41#4118yescomplemented
293C2×Q8×C11—412no—
294C2×Q8×C11C2412yes—
295C2×Q8×C11C2416yes—
296C2×Q8×C11C24112yes—
297C2×Q8×C11C2411yescharacteristic
298C2×D4×C11C2413yes—
299C22×C4×C11C2413yes—
300C22×C4×C11C2413yes—
301C22×C4×C11C24112yes—
302C22×C4×C11C2413yes—
303C2×C22⋊D11C24112yes—
304C2×C22⋊D11C2416yes—
305C22×Dic11C2413yes—
306C22×Dic11C24112yes—
307C22×Dic11C2413yes—
308C22×Dic11C2413yes—
309#4343—28no—
310#4343—24no—
311#4343—412no—
312Q8×D11—24no—
313Q8×D11—216no—
314#4341—212no—
315#4341—248no—
316D4×D11—212no—
317#4339—212no—
318#4339—224no—
319C2×D44C2412yes—
320C2×D44C2412yes—
321C2×D44C2414yes—
322C2×D44C2413yes—
323C2×D44C2412yes—
324C2×D44C24112yes—
325C2×C4×D11—212no—
326C2×C4×D11—212no—
327C2×C4×D11—46no—
328C2×C4×D11C2411yescharacteristic
329C2×C4×D11C2411yescharacteristic
330C2×C4×D11C2414yes—
331C2×C4×D11C2413yes—
332C2×C4×D11C2413yes—
333C2×C4×D11C2413yes—
334C2×C4×D11C2413yes—
335C2×C4×D11C2413yes—
336C2×C4×D11C2413yes—
337C2×C4×D11C2413yes—
338C2×C4×D11C24112yes—
339C2×C4×D11C2413yes—
340C2×C4×D11C2413yes—
341C2×C4×D11C24112yes—
342C2×C4×D11C2411yescharacteristic
343C2×Dic22—224no—
344C2×Dic22C2413yes—
345C2×Dic22C24112yes—
346C2×Dic22C2416yes—
347C11×C4⋊C4C2416yes—
348C11×C4⋊C4C2412yes—
349C11×C4⋊C4C24112yes—
350C11×C4⋊C4C2413yes—
351C11×C4⋊C4C2413yes—
352C11×C4⋊C4C2416yes—
353C11×C4⋊C4C2412yes—
354C11×C4⋊C4C24112yes—
355C11×C4⋊C4C24112yes—
356C11×C4⋊C4C24112yes—
357C11×C22⋊C4C24112yes—
358C11×C22⋊C4C2416yes—
359C42×C11C24112yes—
360C42×C11C2413yes—
361C42×C11C2413yes—
362C42×C11C2411yescharacteristic
363C42×C11C2413yes—
364C22⋊Dic11C2416yes—
365(C2×D11)⋊C4C2414yes—
366(C2×D11)⋊C4C2416yes—
367(C2×D11)⋊C4C2416yes—
368(C2×D11)⋊C4C24112yes—
369(C2×D11)⋊C4C2414yes—
370(C2×D11)⋊C4C24112yes—
371(C2×D11)⋊C4C24112yes—
372(C2×D11)⋊C4C24112yes—
373(C2×D11)⋊C4C24112yes—
374(C2×D11)⋊C4C24112yes—
375(C2×D11)⋊C4C24124yes—
376C4⋊Dic11C2413yes—
377C4⋊Dic11C2413yes—
378C4⋊Dic11C2416yes—
379C4⋊Dic11C2416yes—
380C4⋊Dic11C24112yes—
381C4⋊Dic11C24112yes—
382C4⋊Dic11C24112yes—
383C4⋊Dic11C24124yes—
384C4⋊Dic11C24112yes—
385Dic11⋊C4C24112yes—
386Dic11⋊C4C2416yes—
387Dic11⋊C4C2416yes—
388Dic11⋊C4C24124yes—
389Dic11⋊C4C24112yes—
390C4×Dic11C2413yes—
391C4×Dic11C2413yes—
392C4×Dic11C24112yes—
393C4×Dic11C24124yes—
394C4×Dic11C2413yes—
395C4×Dic11C2411yescharacteristic
396C4×Dic11C2411yescharacteristic
397C4×Dic11C2411yescharacteristic
398C4×Dic11C2413yes—
399C4×Dic11C2413yes—
400C4×Dic11C2413yes—
401C4×Dic11C2413yes—
402C4×Dic11C2413yes—
403C4×Dic11C2413yes—
404C4×Dic11C24112yes—
405#3523—112no—
406#3520—116no—
407#3518—112no—
408#3515—116no—
409#3511—113no—
410#3509—113no—
411#3503D1111yescharacteristic, complemented
412#3499—111no—
413#3495—116no—
414#3489—112no—
415#3482—112no—
416#3482—116no—
417Q8×#41—112no—
418#3475—116no—
419#3461—116no—
420#3444—113no—
421C2×#533—113no—
422C4×2−1+4—112no—
423C2×C4×#41—111no—
424C23×C11C2513yes—
425C22×D11—26no—
426C22×D11—26no—
427C22×D11—43no—
428C22×D11C2513yes—
429C22×D11C2514yes—
430C22×D11C2511yescharacteristic
431Q8×C11—24no—
432Q8×C11—212no—
433Q8×C11—412no—
434Q8×C11C2×#4114yes—
435D4×C11C2×#41112yes—
436C2×C4×C11—26no—
437C2×C4×C11—26no—
438C2×C4×C11—412no—
439C2×C4×C11C2×#41112yes—
440C2×C4×C11C2514yes—
441C2×C4×C11C25112yes—
442C2×C4×C11C2513yes—
443C2×C4×C11C2513yes—
444C2×C4×C11C2511yescharacteristic
445C2×C4×C11C2513yes—
446C2×C4×C11C2511yescharacteristic
447C2×C4×C11C2511yescharacteristic
448C22⋊D11—212no—
449C22⋊D11—224no—
450C2×Dic11—224no—
451C2×Dic11—26no—
452C2×Dic11—26no—
453C2×Dic11—43no—
454C2×Dic11C2513yes—
455C2×Dic11C2511yescharacteristic
456C2×Dic11C2513yes—
457C2×Dic11C2511yescharacteristic
458C2×Dic11C2513yes—
459C2×Dic11C25112yes—
460C2×Dic11C2511yescharacteristic
461D44—28no—
462D44—24no—
463D44—26no—
464D44—24no—
465D44—24no—
466D44—412no—
467C4×D11—26no—
468C4×D11—22no—
469C4×D11—26no—
470C4×D11—26no—
471C4×D11—26no—
472C4×D11—224no—
473C4×D11—26no—
474C4×D11—22no—
475C4×D11—26no—
476C4×D11—26no—
477C4×D11—28no—
478C4×D11—43no—
479C4×D11—43no—
480C4×D11—412no—
481C4×D112−1+414yescomplemented
482Dic22—212no—
483Dic22—224no—
484Dic22—26no—
485C2×2−1+4—112no—
486C22×#41—111no—
487Q82C2×D1112yescomplemented
488#557—116no—
489#557—116no—
490#557C2×D1112yescomplemented
491#556—1112no—
492#556—116no—
493#556—116no—
494#556—116no—
495#555—116no—
496#554—1112no—
497#554—116no—
498#554C2×D1116yescomplemented
499#553—1112no—
500#552—1112no—
501#552—1112no—
502#552—1112no—
503#552—1124no—
504#552—1112no—
505#551—1124no—
506D4×Q8—114no—
507D4×Q8—112no—
508D4×Q8—112no—
509D4×Q8C2×D1116yescomplemented
510#548—1112no—
511#548—114no—
512#547—116no—
513#547—1112no—
514#547—116no—
515#547—116no—
516#546—1112no—
517#544C2×D1116yescomplemented
518#542—1112no—
519#542—1112no—
520#541—1112no—
521#541—1112no—
522#539—1124no—
523#537—116no—
524#536—116no—
525#536—116no—
526#533—113no—
527#533—116no—
528#533—116no—
529#533—116no—
530#533—116no—
531#533—116no—
532#533—116no—
533#533—116no—
534#533—113no—
535#533—1112no—
536#533C2×D1113yescomplemented
537#532—111no—
538#532—113no—
539#532—113no—
540C2×C4⋊Q8—113no—
541C2×C4⋊Q8C2×D1113yescomplemented
542#529—116no—
543#529—116no—
544#529—1112no—
545#529—116no—
546#529—116no—
547#529—1124no—
548#529—116no—
549#529—116no—
550C2×#125—116no—
551#525—116no—
552#525—116no—
553#525—116no—
554C2×C22⋊Q8—116no—
555C2×C22⋊Q8—116no—
556#520—1112no—
557#520—116no—
558#520C2×D1112yes—
559#519—114no—
560#519—116no—
561C4×#41—111no—
562C4×#41—111no—
563C4×#41—111no—
564C4×#41—116no—
565C4×#41—116no—
566C4×#41—113no—
567C4×#41—113no—
568C4×#41—1112no—
569C4×#41—113no—
570C4×#41—116no—
571C4×#41—113no—
572C4×#41C2×D1111yescharacteristic
573C2×C4×Q8—116no—
574C2×C4×Q8—111no—
575C2×C4×Q8—111no—
576C2×C4×Q8—114no—
577C2×C4×Q8—116no—
578C2×C4×D4—113no—
579C2×C4×D4—113no—
580C2×#117—113no—
581C2×#117—116no—
582C22×C42—113no—
583C22×C11—23no—
584C22×C11—23no—
585C22×C11C22×#4116yes—
586C22×C11C2611yescharacteristic
587C2×D11—21no—
588C2×D11—21no—
589C2×D11—23no—
590C2×D11—24no—
591C2×D11—23no—
592C2×D11—24no—
593C2×D11—23no—
594C2×D11—24no—
595C2×D11—412no—
596C2×D11C2×2−1+412yes—
597C4×C11—23no—
598C4×C11—24no—
599C4×C11—23no—
600C4×C11—212no—
601C4×C11C22×#4112yes—
602C4×C11C22×#4116yes—
603C4×C11C2×2−1+412yes—
604C4×C11#58512yes—
605Dic11—212no—
606Dic11—23no—
607Dic11—21no—
608Dic11—23no—
609Dic11—23no—
610Dic11—21no—
611Dic11C2×2−1+412yes—
6122−1+4—2216no—
613C2×#41—112no—
614C2×#41—111no—
615C2×#41—116no—
616C2×#41—113no—
617C2×#41—1112no—
618C2×#41—113no—
619C2×#41—116no—
620C2×#41—228no—
621C2×#41C22×D1111yescharacteristic
622C22×Q8—111no—
623C22×Q8—114no—
624C22×Q8—116no—
625C22×Q8C22×D1116yes—
626C22×D4—113no—
627C23×C4—113no—
628C23×C4—113no—
629C23×C4—113no—
630C4⋊Q8—113no—
631C4⋊Q8—116no—
632C4⋊Q8—116no—
633C4⋊Q8—116no—
634C4⋊Q8—1112no—
635C4⋊Q8C22×D1113yes—
636C4⋊Q8C22×D1116yes—
637C4⋊Q8C22×D1116yes—
638C4⋊Q8C22×D1116yes—
639C4⋊Q8C22×D1111yescharacteristic
640C4⋊Q8C22×D11112yes—
641#127—111no—
642#126—1112no—
643#126—1112no—
644#126—1124no—
645#126—1124no—
646#126—1124no—
647#125—116no—
648#125—1112no—
649#125—1112no—
650#125—1112no—
651#125—116no—
652#125—1124no—
653#125—1124no—
654#125C22×D1116yes—
655#125C22×D11112yes—
656#124—112no—
657#124—116no—
658#124—1124no—
659#124—116no—
660#124—1112no—
661#123—1112no—
662#123—1112no—
663#123—1124no—
664#123—1112no—
665#123—1124no—
666#123—1124no—
667C22⋊Q8—116no—
668C22⋊Q8—1112no—
669C22⋊Q8—1112no—
670C22⋊Q8—1112no—
671C22⋊Q8—116no—
672C22⋊Q8—1124no—
673C22⋊Q8—116no—
674C22⋊Q8—1112no—
675C22⋊Q8—1112no—
676C22⋊Q8—1112no—
677C22⋊Q8—116no—
678C22⋊Q8—1112no—
679C22⋊Q8—1112no—
680C22⋊Q8—1112no—
681C22⋊Q8C22×D1116yes—
682C22⋊Q8C22×D1116yes—
683C22⋊Q8C22×D11124yes—
684#121—116no—
685#121—116no—
686#121—1124no—
687#121—112no—
688#121—112no—
689#121—116no—
690#121—116no—
691#121—1112no—
692#120—1112no—
693C4×Q8—111no—
694C4×Q8—116no—
695C4×Q8—111no—
696C4×Q8—1112no—
697C4×Q8—1112no—
698C4×Q8—1112no—
699C4×Q8—116no—
700C4×Q8—1112no—
701C4×Q8—116no—
702C4×Q8—113no—
703C4×Q8—113no—
704C4×Q8—1112no—
705C4×Q8—1112no—
706C4×Q8—116no—
707C4×Q8—113no—
708C4×Q8—113no—
709C4×Q8—1112no—
710C4×Q8—1112no—
711C4×Q8C22×D1111yescharacteristic
712C4×Q8C22×D1111yescharacteristic
713C4×Q8C22×D1114yes—
714C4×Q8C22×D1116yes—
715C4×Q8C22×D1116yes—
716C4×D4—113no—
717C4×D4—113no—
718C4×D4—116no—
719C4×D4—116no—
720C4×D4—1124no—
721C4×D4—113no—
722C4×D4—113no—
723C4×D4—112no—
724C4×D4—112no—
725C4×D4—116no—
726C4×D4—1112no—
727C4×D4—1112no—
728C4×D4—116no—
729C4×D4—116no—
730C4×D4—116no—
731C4×D4—1112no—
732C4×D4—1112no—
733C4×D4—113no—
734C4×D4—113no—
735C4×D4—1112no—
736C4×D4—1112no—
737C4×D4—116no—
738C4×D4—116no—
739C4×D4C22×D1113yes—
740C4×D4C22×D1113yes—
741C4×D4C22×D11112yes—
742#117—113no—
743#117—116no—
744#117—113no—
745#117—113no—
746#117—1112no—
747#117—1112no—
748#117—1112no—
749#117—1112no—
750#117—116no—
751#117—1112no—
752#117—1112no—
753#117—116no—
754#117—1124no—
755#117—116no—
756#117—1112no—
757#117C22×D1113yes—
758#117C22×D1116yes—
759C2×C4⋊C4—116no—
760C2×C4⋊C4—1112no—
761C2×C4⋊C4—1112no—
762C2×C4⋊C4—116no—
763C2×C4⋊C4—113no—
764C2×C4⋊C4—113no—
765C2×C4⋊C4—1112no—
766C2×C4⋊C4C22×D1116yes—
767C2×C4⋊C4C22×D1116yes—
768C2×C22⋊C4—1112no—
769C2×C22⋊C4—116no—
770C2×C42—1112no—
771C2×C42—113no—
772C2×C42—113no—
773C2×C42—113no—
774C2×C42—113no—
775C2×C42—113no—
776C2×C42—113no—
777C2×C42—1112no—
778C2×C42—113no—
779C2×C42—113no—
780C2×C42—113no—
781C2×C42—113no—
782C2×C42—111no—
783C2×C42C22×D1113yes—
784C2×C11—26no—
785C2×C11C23×#4111yescharacteristic
786C2×C11C22×2−1+411yescharacteristic
787C2×C11C2×#58511yescharacteristic
788D11—22no—
789D11—44no—
790D11—43no—
791C24—113no—
792#41—228no—
793#41—224no—
794#41—2212no—
795#41—2248no—
796#41—2212no—
797#41—2224no—
798#41—4412no—
799#41#434318yescomplemented
800C2×Q8—412no—
801C2×Q8—116no—
802C2×Q8—1112no—
803C2×Q8—113no—
804C2×Q8—224no—
805C2×Q8—2216no—
806C2×Q8—2224no—
807C2×Q8C23×D1112yes—
808C2×Q8C23×D1116yes—
809C2×Q8C23×D11112yes—
810C2×Q8C23×D1111yescharacteristic
811C2×D4—1112no—
812C2×D4—116no—
813C2×D4—114no—
814C2×D4—112no—
815C2×D4—113no—
816C2×D4—112no—
817C2×D4—112no—
818C2×D4—1112no—
819C2×D4—2212no—
820C2×D4C23×D1113yes—
821C22×C4—111no—
822C22×C4—113no—
823C22×C4—113no—
824C22×C4—1112no—
825C22×C4—113no—
826C22×C4—111no—
827C22×C4—111no—
828C22×C4—114no—
829C22×C4—113no—
830C22×C4—113no—
831C22×C4—113no—
832C22×C4—113no—
833C22×C4—113no—
834C22×C4—113no—
835C22×C4—113no—
836C22×C4—1112no—
837C22×C4—113no—
838C22×C4—113no—
839C22×C4—1112no—
840C22×C4—2212no—
841C22×C4—2212no—
842C22×C4—446no—
843C22×C4C23×D1113yes—
844C22×C4C23×D1113yes—
845C22×C4C23×D11112yes—
846C22×C4C23×D1113yes—
847C4⋊C4—113no—
848C4⋊C4—116no—
849C4⋊C4—116no—
850C4⋊C4—1112no—
851C4⋊C4—1124no—
852C4⋊C4—1112no—
853C4⋊C4—113no—
854C4⋊C4—116no—
855C4⋊C4—116no—
856C4⋊C4—1112no—
857C4⋊C4—1124no—
858C4⋊C4—1112no—
859C4⋊C4—1112no—
860C4⋊C4—1112no—
861C4⋊C4C23×D11112yes—
862C4⋊C4C23×D1113yes—
863C4⋊C4C23×D1113yes—
864C4⋊C4C23×D1116yes—
865C4⋊C4C23×D1116yes—
866C4⋊C4C23×D11112yes—
867C4⋊C4C23×D1112yes—
868C4⋊C4C23×D11112yes—
869C4⋊C4C23×D11112yes—
870C4⋊C4C23×D1112yes—
871C22⋊C4—116no—
872C22⋊C4—1112no—
873C22⋊C4—116no—
874C22⋊C4—116no—
875C22⋊C4—1124no—
876C22⋊C4—114no—
877C22⋊C4—114no—
878C22⋊C4—1112no—
879C22⋊C4—1112no—
880C22⋊C4—1112no—
881C22⋊C4—1112no—
882C22⋊C4—1112no—
883C22⋊C4C23×D1116yes—
884C22⋊C4C23×D11112yes—
885C42—111no—
886C42—113no—
887C42—111no—
888C42—111no—
889C42—113no—
890C42—1112no—
891C42—113no—
892C42—113no—
893C42—113no—
894C42—113no—
895C42—113no—
896C42—113no—
897C42—113no—
898C42—1112no—
899C42—1124no—
900C42C23×D1111yescharacteristic
901C42C23×D1113yes—
902C42C23×D1113yes—
903C42C23×D1113yes—
904C42C23×D11112yes—
905C11#6280511yescharacteristic, complemented, Sylow
906C23—111no—
907C23—113no—
908C23—114no—
909C23—226no—
910C23—226no—
911C23—443no—
912C23C24×D1113yes—
913Q8—212no—
914Q8—24no—
915Q8—412no—
916Q8—2224no—
917Q8—2212no—
918Q8—226no—
919Q8C2×#434314yes—
920D4—228no—
921D4—2212no—
922D4—2224no—
923D4—226no—
924D4—224no—
925D4—224no—
926D4—224no—
927D4—4412no—
928D4C2×#4343112yes—
929C2×C4—26no—
930C2×C4—26no—
931C2×C4—412no—
932C2×C4—111no—
933C2×C4—114no—
934C2×C4—113no—
935C2×C4—111no—
936C2×C4—111no—
937C2×C4—113no—
938C2×C4—1112no—
939C2×C4—113no—
940C2×C4—226no—
941C2×C4—228no—
942C2×C4—226no—
943C2×C4—226no—
944C2×C4—226no—
945C2×C4—2224no—
946C2×C4—222no—
947C2×C4—226no—
948C2×C4—226no—
949C2×C4—226no—
950C2×C4—2224no—
951C2×C4—222no—
952C2×C4—226no—
953C2×C4—226no—
954C2×C4—443no—
955C2×C4—443no—
956C2×C4—4412no—
957C2×C4—443no—
958C2×C4C2×#4343112yes—
959C2×C4C24×D1114yes—
960C2×C4C24×D11112yes—
961C2×C4C24×D1113yes—
962C2×C4C24×D1113yes—
963C2×C4C24×D1111yescharacteristic
964C2×C4C24×D1113yes—
965C2×C4C24×D1111yescharacteristic
966C2×C4C24×D1111yescharacteristic
967C22—23no—
968C22—23no—
969C22—112no—
970C22—221no—
971C22—221no—
972C22—224no—
973C22—223no—
974C22—223no—
975C22—224no—
976C22—223no—
977C22—224no—
978C22—4412no—
979C22C22×#434316yes—
980C22C25×D1111yescharacteristic
981C4—23no—
982C4—24no—
983C4—23no—
984C4—212no—
985C4—112no—
986C4—221no—
987C4—223no—
988C4—2212no—
989C4—223no—
990C4—221no—
991C4—223no—
992C4C22×#434316yes—
993C4C22×#434312yes—
994C4#1062345512yes—
995C4D11×2−1+412yes—
996C2—26no—
997C2—222no—
998C2—443no—
999C2—444no—
1000C2C23×#434311yescharacteristic
1001C2C2×D11×2−1+411yescharacteristic
1002C2C2×#1062345511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D11
commutator, socle, cosocleC22×C11C26
FittingC11×#3503C2
hypercenter#3503D11
hypocenterC11#62805
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13082713C2semidirect
2. #13082666C2semidirect
3. #13082634C2semidirect
4. #13082595C2semidirect
5. #13082529C2semidirect
6. #13082503C2semidirect
7. #13082401C2semidirect
8. #13082371C2semidirect
9. #13082297C2semidirect
10. #13082237C2semidirect
11. #13082236C2semidirect
12. Q8×#4343C2semidirect
13. #13082182C2semidirect
14. #13082050C2semidirect
15. #13081913C2semidirect
16. C2×#10623259C2semidirect
17. #13081827C2semidirect
18. C4×#41×D11C2semidirect
19. C11×#3503C2semidirect
22. Q82×C11C22semidirect
23. C11×#557C22semidirect
24. C11×#554C22semidirect
25. D4×Q8×C11C22semidirect
26. C11×#544C22semidirect
27. C11×#533C22semidirect
28. C2×C11×C4⋊Q8C22semidirect
32. #10623348C22semidirect
34. C2×Q8×Dic11C22semidirect
35. #10623265C22semidirect
36. #10623264C22semidirect
37. #10623264C22semidirect
38. #10623263C22semidirect
39. #10623263C22semidirect
41. #10623261C22semidirect
46. #10623259C22semidirect
47. #10623259C22semidirect
48. #10623259C22semidirect
49. #10623259C22semidirect
50. #10623259C22semidirect
51. #10623259C22semidirect
52. #10623257C22semidirect
54. #10623256C22semidirect
55. #10623228C22semidirect
56. #10623228C22semidirect
58. #10623225C22semidirect
60. #10623222C22semidirect
61. #10623222C22semidirect
62. #10623176C22semidirect
63. #10623173C22semidirect
64. #10623173C22semidirect
65. #10623173C22semidirect
69. #10623155C22semidirect
70. #10623155C22semidirect
71. #10623155C22semidirect
72. #10623115C22semidirect
73. #10623115C22semidirect
75. #10623111C22semidirect
78. Q8×D44C22semidirect
79. Q8×D44C22semidirect
83. C4×#4343C22semidirect
84. #10623103C22semidirect
87. C4×Q8×D11C22semidirect
88. #10623101C22semidirect
89. #10623101C22semidirect
91. #10623086C22semidirect
92. #10623086C22semidirect
94. #10623077C22semidirect
99. C4×#4341C22semidirect
101. #10623057C22semidirect
104. #10623053C22semidirect
106. #10623047C22semidirect
107. #10623045C22semidirect
110. #10623035C22semidirect
112. C2×#66943C22semidirect
113. C2×#66940C22semidirect
114. #10623008C22semidirect
117. C2×#66922C22semidirect
292. C11×#41#41semidirect
411. #3503D11semidirect
481. C4×D112−1+4semidirect
487. Q82C2×D11semidirect
490. #557C2×D11semidirect
498. #554C2×D11semidirect
509. D4×Q8C2×D11semidirect
517. #544C2×D11semidirect
536. #533C2×D11semidirect
541. C2×C4⋊Q8C2×D11semidirect
799. #41#4343semidirect
905. C11#62805semidirect

Maximal subgroups

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

subgroupindex
#130827132
#130826662
#130826342
#130825952
#130825292
#130825032
#130824012
#130823712
#130822972
#130822372
#130822362
Q8×#43432
#130821822
#130820502
#130819132
C2×#106232592
#130818272
C4×#41×D112
C11×#35032
#6280511