Finite Group Databasebeta

← #15662235

Subgroups — #15662235

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#13082712C212yesmaximal, complemented
2#13082665C216yesmaximal, complemented
3#13082633C212yesmaximal, complemented
4#13082594C216yesmaximal, complemented
5#13082527C213yesmaximal, complemented
6#13082502C213yesmaximal, complemented
7#13082435C211yesmaximal, characteristic, complemented
8#13082401C211yesmaximal, characteristic, complemented
9#13082368C216yesmaximal, complemented
10#13082296C212yesmaximal, complemented
11#13082238C212yesmaximal, complemented
12#13082231C216yesmaximal, complemented
13Q8×#4339C212yesmaximal, complemented
14#13082174C216yesmaximal, complemented
15#13082043C216yesmaximal, complemented
16#13081912C213yesmaximal, complemented
17C2×#10623001C213yesmaximal, complemented
18C4×#67043C212yesmaximal, complemented
19C2×C4×C11×#41C211yesmaximal, characteristic, complemented
20C22×C11×#41C2211yescharacteristic
21C2×#67043C2212yes—
22C4×C11×#41C2211yescharacteristic
23C4×C11×#41C2211yescharacteristic
24C4×C11×#41C2213yes—
25C4×C11×#41C2211yescharacteristic
26C4×C11×#41C2213yes—
27C4×C11×#41C2213yes—
28C4×C11×#41C2211yescharacteristic
29C4×C11×#41C2213yes—
30C2×C4×Q8×C11C2211yescharacteristic
31C2×C4×Q8×C11C2211yescharacteristic
32C2×C4×D4×C11C2213yes—
33C2×C4×D4×C11C2213yes—
34C2×C11×#117C2213yes—
35C22×C42×C11C2213yes—
36#10623364C2216yes—
37#10623362C2214yes—
38#10623358C2212yes—
39#10623356C2216yes—
40#10623355C22112yes—
41Q8×C22⋊D11C2214yes—
42#10623337C22112yes—
43#10623322C2216yes—
44#10623322C2216yes—
45#10623322C2216yes—
46C2×#66979C2216yes—
47C2×#66977C2216yes—
48C2×#66977C2216yes—
49#10623115C2216yescomplemented
50#10623114C22112yescomplemented
51#10623110C2216yescomplemented
52#10623109C22112yescomplemented
53Q8×D44C2212yescomplemented
54Q8×D44C2212yescomplemented
55#10623103C2214yescomplemented
56C4×Q8×D11C2214yescomplemented
57#10623101C2212yescomplemented
58#10623098C2216yescomplemented
59#10623098C2216yescomplemented
60Q8×Dic22C2212yescomplemented
61#10623096C22112yescomplemented
62#10623095C22124yescomplemented
63#10623094C2216yescomplemented
64#10623092C22112yescomplemented
65#10623088C22112yescomplemented
66#10623086C2216yescomplemented
67#10623086C2216yescomplemented
68#10623083C22112yescomplemented
69#10623082C2216yescomplemented
70#10623077C22112yescomplemented
71#10623074C2216yescomplemented
72#10623073C2216yescomplemented
73#10623073C2216yescomplemented
74#10623072C22112yescomplemented
75#10623072C22112yescomplemented
76#10623069C22124yescomplemented
77D4×Dic22C2216yescomplemented
78C4×#4341C22112yescomplemented
79#10623065C22112yescomplemented
80#10623064C22112yescomplemented
81#10623062C22124yescomplemented
82#10623060C22112yescomplemented
83#10623057C2216yescomplemented
84#10623054C2216yescomplemented
85#10623050C2216yescomplemented
86#10623049C22112yescomplemented
87#10623047C2216yescomplemented
88#10623044C22112yes—
89#10623042C22112yes—
90#10623026C22124yes—
91#10623010C2216yes—
92#10623010C2216yes—
93#10623010C2216yescomplemented
94#10623010C2216yescomplemented
95#10623010C2216yescomplemented
96#10623010C2216yescomplemented
97#10623008C2211yescharacteristic
98#10623008C2213yescomplemented
99#10623008C2213yescomplemented
100C4×#4339C2216yes—
101C4×#4339C2216yescomplemented
102C4×#4339C2216yescomplemented
103#10623001C2216yes—
104#10623001C2216yes—
105#10623001C2213yes—
106#10623001C2216yes—
107#10623001C2216yescomplemented
108#10623001C2216yescomplemented
109#10623001C2216yescomplemented
110#10623001C2216yescomplemented
111#10623001C2213yescomplemented
112#10623001C2213yescomplemented
113C2×#66923C2216yescomplemented
114C2×#66922C2213yescomplemented
115C2×#66922C2213yescomplemented
116C2×C4×Dic22C2216yescomplemented
117C2×C4×Dic22C2216yescomplemented
118C2×C11×#41—28no—
119C2×C11×#41C2313yes—
120C2×C11×#41C2313yes—
121C2×C11×#41C2311yescharacteristic
122C2×C11×#41C2311yescharacteristic
123C22×Q8×C11C2311yescharacteristic
124C22×D4×C11C2313yes—
125C23×C4×C11C2313yes—
126C23×C4×C11C2313yes—
127C23×C4×C11C2313yes—
128#67043—216no—
129C2×Q8×D11C2314yes—
130C2×#4341C23112yes—
131C2×#4339C2312yes—
132C2×#4339C2316yes—
133C2×#4339C2316yes—
134C22×Dic22C2316yes—
135C22×Dic22C2316yes—
136C4×Q8×C11C2311yescharacteristic
137C4×Q8×C11C2313yes—
138C4×Q8×C11C2313yes—
139C4×Q8×C11C2311yescharacteristic
140C4×Q8×C11C2311yescharacteristic
141C4×Q8×C11C2311yescharacteristic
142C4×Q8×C11C2313yes—
143C4×Q8×C11C2313yes—
144C4×D4×C11C2313yes—
145C4×D4×C11C2313yes—
146C4×D4×C11C2316yes—
147C4×D4×C11C2316yes—
148C4×D4×C11C2316yes—
149C4×D4×C11C2313yes—
150C4×D4×C11C2313yes—
151C4×D4×C11C2313yes—
152C4×D4×C11C2313yes—
153C4×D4×C11C2313yes—
154C4×D4×C11C2313yes—
155C4×D4×C11C2316yes—
156C11×#117C2313yes—
157C11×#117C2316yes—
158C11×#117C2313yes—
159C11×#117C2313yes—
160C11×#117C2316yes—
161C11×#117C2313yes—
162C2×C11×C4⋊C4C2313yes—
163C2×C11×C4⋊C4C2313yes—
164C2×C11×C22⋊C4C2316yes—
165C2×C42×C11C2313yes—
166C2×C42×C11C2313yes—
167C2×C42×C11C2313yes—
168C2×C42×C11C2313yes—
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2313yes—
171C2×C42×C11C2313yes—
172C2×C42×C11C2313yes—
173C2×C42×C11C2313yes—
174C2×C42×C11C2313yes—
175C2×C42×C11C2313yes—
176C2×C42×C11C2313yes—
177#67006C23112yes—
178C2×C22⋊Dic11C23112yes—
179#66999C23112yes—
180Q8×Dic11C2314yes—
181#66997C23112yes—
182#66992C23124yes—
183#66991C23112yes—
184#66989C23112yes—
185#66988C23124yes—
186D4×Dic11C23112yes—
187#66983C2312yes—
188#66983C2312yes—
189#66983C2316yes—
190#66983C2316yes—
191#66983C2316yes—
192#66983C2316yes—
193#66982C23112yes—
194#66982C23112yes—
195#66982C23112yes—
196C4×C22⋊D11C23112yes—
197C4×C22⋊D11C23112yes—
198C4×C22⋊D11C23112yes—
199C4×C22⋊D11C23112yes—
200C4×C22⋊D11C23112yes—
201C4×C22⋊D11C23112yes—
202#66979C2316yes—
203#66979C23112yes—
204#66979C23112yes—
205#66979C23112yes—
206#66979C2316yes—
207#66979C2316yes—
208C2×C4⋊Dic11C2316yes—
209C2×C4⋊Dic11C2316yes—
210C2×C4⋊Dic11C2316yes—
211C2×C4⋊Dic11C2316yes—
212#66977C2316yes—
213#66977C2316yes—
214#66977C23112yes—
215#66977C23112yes—
216#66977C23112yes—
217#66977C23112yes—
218#66977C23112yes—
219#66977C23112yes—
220#66977C2316yes—
221#66977C2316yes—
222#66977C2316yes—
223#66977C2316yes—
224C2×Dic11⋊C4C23112yes—
225C2×Dic11⋊C4C23112yes—
226C2×C4×Dic11C23112yes—
227#66951C23124yes—
228#66950C23112yes—
229#66950C23112yes—
230#66949C23124yes—
231#66945C23112yes—
232C4⋊C4×D11C23112yes—
233#66943C23112yes—
234#66942C23124yes—
235#66942C23124yes—
236#66941C23112yes—
237#66940C23112yes—
238#66940C23112yes—
239#66939C23124yes—
240#66938C23124yes—
241#66936C23124yes—
242(C22⋊D11)⋊C4C23124yes—
243#66932C23124yes—
244#66932C23124yes—
245#66931C23124yes—
246#66930C23124yes—
247#66929C23112yes—
248#66929C23112yes—
249#66928C2312yes—
250#66928C2316yes—
251#66928C2316yes—
252#66927C2311yescharacteristic
253C4×D44C2316yes—
254C4×D44C2316yes—
255C4×D44C2312yes—
256C4×D44C2312yes—
257C4×D44C2316yes—
258C4×D44C2316yes—
259#66925C23112yes—
260#66925C23112yes—
261#66925C23112yes—
262C42×D11C23112yes—
263#66923C2316yes—
264#66923C23112yes—
265#66923C23112yes—
266#66923C23112yes—
267#66923C2316yes—
268#66923C2316yes—
269#66922C2313yes—
270#66922C2313yes—
271#66922C2316yes—
272#66922C2316yes—
273#66922C2316yes—
274#66922C2316yes—
275#66922C2316yes—
276#66922C2316yes—
277#66922C2311yescharacteristic
278C4×Dic22C2316yes—
279C4×Dic22C2316yes—
280C4×Dic22C23112yes—
281C4×Dic22C23112yes—
282C4×Dic22C23112yes—
283C4×Dic22C23112yes—
284C4×Dic22C23112yes—
285C4×Dic22C23112yes—
286C4×Dic22C2316yes—
287C4×Dic22C2316yes—
288C4×Dic22C2316yes—
289C4×Dic22C2316yes—
290#62805—111nomaximal, Sylow
291C24×C11C2413yes—
292C11×#41—24no—
293C11×#41—212no—
294C11×#41—212no—
295C11×#41#4118yescomplemented
296C2×Q8×C11—24no—
297C2×Q8×C11C2413yes—
298C2×Q8×C11C2411yescharacteristic
299C2×D4×C11—212no—
300C2×D4×C11C2416yes—
301C2×D4×C11C2413yes—
302C2×D4×C11C2413yes—
303C22×C4×C11—212no—
304C22×C4×C11—212no—
305C22×C4×C11—46no—
306C22×C4×C11C2413yes—
307C22×C4×C11C2413yes—
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2413yes—
311C22×C4×C11C2413yes—
312C22×C4×C11C2413yes—
313C22×C4×C11C2413yes—
314C22×C4×C11C2413yes—
315C22×C4×C11C2413yes—
316C22×C4×C11C2413yes—
317C22×C4×C11C2413yes—
318C22×C4×C11C2413yes—
319C22×C4×C11C2413yes—
320C22×C4×C11C2413yes—
321C22×C4×C11C2413yes—
322C22×C4×C11C2413yes—
323C22×C4×C11C2411yescharacteristic
324C2×C22⋊D11C24112yes—
325C2×C22⋊D11C2414yes—
326C2×C22⋊D11C24112yes—
327C22×Dic11C24112yes—
328C22×Dic11C24112yes—
329Q8×D11—216no—
330#4341—248no—
331#4339—224no—
332#4339—28no—
333#4339—412no—
334C2×D44C2412yes—
335C2×D44C2412yes—
336C2×D44C2412yes—
337C2×C4×D11C2414yes—
338C2×C4×D11C24112yes—
339C2×C4×D11C24112yes—
340C2×Dic22—224no—
341C2×Dic22—412no—
342C2×Dic22C2412yes—
343C2×Dic22C2416yes—
344C2×Dic22C2416yes—
345C2×Dic22C24112yes—
346C2×Dic22C24112yes—
347C11×C4⋊C4C2413yes—
348C11×C4⋊C4C2413yes—
349C11×C4⋊C4C2413yes—
350C11×C4⋊C4C2416yes—
351C11×C4⋊C4C2416yes—
352C11×C4⋊C4C2413yes—
353C11×C22⋊C4C2416yes—
354C11×C22⋊C4C2416yes—
355C11×C22⋊C4C2416yes—
356C11×C22⋊C4C2416yes—
357C42×C11C2411yescharacteristic
358C42×C11C2411yescharacteristic
359C42×C11C2413yes—
360C42×C11C2413yes—
361C42×C11C2413yes—
362C42×C11C2413yes—
363C42×C11C2413yes—
364C42×C11C2413yes—
365C42×C11C2413yes—
366C42×C11C2413yes—
367C42×C11C2413yes—
368C42×C11C2411yescharacteristic
369C42×C11C2413yes—
370C42×C11C2411yescharacteristic
371C42×C11C2413yes—
372C42×C11C2413yes—
373C22⋊Dic11C24112yes—
374C22⋊Dic11C24112yes—
375C22⋊Dic11C24124yes—
376C22⋊Dic11C24112yes—
377(C2×D11)⋊C4C2414yes—
378(C2×D11)⋊C4C2414yes—
379(C2×D11)⋊C4C24112yes—
380(C2×D11)⋊C4C24112yes—
381(C2×D11)⋊C4C24112yes—
382(C2×D11)⋊C4C24112yes—
383C4⋊Dic11C2416yes—
384C4⋊Dic11C2416yes—
385C4⋊Dic11C2412yes—
386C4⋊Dic11C2412yes—
387C4⋊Dic11C24112yes—
388C4⋊Dic11C24112yes—
389C4⋊Dic11C2416yes—
390C4⋊Dic11C2416yes—
391C4⋊Dic11C24112yes—
392C4⋊Dic11C24112yes—
393Dic11⋊C4C24112yes—
394Dic11⋊C4C24112yes—
395Dic11⋊C4C24124yes—
396Dic11⋊C4C24124yes—
397Dic11⋊C4C24112yes—
398Dic11⋊C4C24112yes—
399Dic11⋊C4C24112yes—
400Dic11⋊C4C24112yes—
401C4×Dic11C24112yes—
402C4×Dic11C24124yes—
403C4×Dic11C24112yes—
404C4×Dic11C24112yes—
405#3523—112no—
406#3520—116no—
407#3518—112no—
408#3515—116no—
409#3511—113no—
410#3509—113no—
411#3503—111no—
412#3499—111no—
413#3495—116no—
414#3489—112no—
415#3482—116no—
416#3482—112no—
417Q8×#41—112no—
418#3475—116no—
419#3461—116no—
420#3444—113no—
421C2×#533—113no—
422C4×2−1+4—112no—
423C2×C4×#41D1111yescharacteristic, complemented
424C23×C11—26no—
425C23×C11—26no—
426C23×C11—43no—
427C23×C11C2513yes—
428C23×C11C2513yes—
429C23×C11C2511yescharacteristic
430C22×D11C2514yes—
431Q8×C11—26no—
432Q8×C11C2×#4114yes—
433D4×C11—212no—
434D4×C11—26no—
435D4×C11C2×#41112yes—
436C2×C4×C11—26no—
437C2×C4×C11—26no—
438C2×C4×C11—22no—
439C2×C4×C11—26no—
440C2×C4×C11—26no—
441C2×C4×C11—26no—
442C2×C4×C11—26no—
443C2×C4×C11—26no—
444C2×C4×C11—26no—
445C2×C4×C11—26no—
446C2×C4×C11—26no—
447C2×C4×C11—26no—
448C2×C4×C11—22no—
449C2×C4×C11—43no—
450C2×C4×C11—43no—
451C2×C4×C11—43no—
452C2×C4×C11C2×#41112yes—
453C2×C4×C112−1+414yescomplemented
454C2×C4×C11C2513yes—
455C2×C4×C11C2513yes—
456C2×C4×C11C2511yescharacteristic
457C2×C4×C11C2511yescharacteristic
458C2×C4×C11C2513yes—
459C2×C4×C11C2513yes—
460C2×C4×C11C2513yes—
461C2×C4×C11C2513yes—
462C2×C4×C11C2511yescharacteristic
463C2×C4×C11C2511yescharacteristic
464C2×C4×C11C2511yescharacteristic
465C2×C4×C11C2511yescharacteristic
466C22⋊D11—224no—
467C22⋊D11—28no—
468C22⋊D11—412no—
469C2×Dic11—224no—
470C2×Dic11—412no—
471C2×Dic11C2514yes—
472C2×Dic11C25112yes—
473C2×Dic11C25112yes—
474D44—24no—
475D44—24no—
476D44—24no—
477C4×D11—224no—
478C4×D11—28no—
479C4×D11—412no—
480Dic22—212no—
481Dic22—224no—
482Dic22—24no—
483Dic22—212no—
484Dic22—412no—
485C2×2−1+4—112no—
486C22×#41C2×D1111yescharacteristic
487Q82—112no—
488#557—116no—
489#557—116no—
490#557—112no—
491#556—116no—
492#556—116no—
493#556—116no—
494#556—1112no—
495#555—116no—
496#554—116no—
497#554—116no—
498#554—1112no—
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×Q8—116no—
510#548—114no—
511#548—1112no—
512#547—1112no—
513#547—116no—
514#547—116no—
515#547—116no—
516#546—1112no—
517#544—116no—
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—1112no—
527#533—113no—
528#533—116no—
529#533—116no—
530#533—116no—
531#533—116no—
532#533—116no—
533#533—116no—
534#533—116no—
535#533—113no—
536#533—113no—
537#532—111no—
538#532—113no—
539#532—113no—
540C2×C4⋊Q8—113no—
541C2×C4⋊Q8—113no—
542#529—1124no—
543#529—1112no—
544#529—116no—
545#529—116no—
546#529—116no—
547#529—116no—
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—112no—
557#520—1112no—
558#520—116no—
559#519—114no—
560#519—116no—
561C4×#41—1112no—
562C4×#41—116no—
563C4×#41—116no—
564C4×#41—116no—
565C4×#41C2×D1111yescharacteristic
566C4×#41C2×D1113yes—
567C4×#41C2×D1113yes—
568C4×#41C2×D1111yescharacteristic
569C4×#41C2×D1111yescharacteristic
570C4×#41C2×D1113yes—
571C4×#41C2×D1113yes—
572C4×#41C2×D1111yescharacteristic
573C2×C4×Q8—114no—
574C2×C4×Q8—116no—
575C2×C4×Q8—116no—
576C2×C4×Q8C2×D1111yescharacteristic
577C2×C4×Q8C2×D1111yescharacteristic
578C2×C4×D4C2×D1113yes—
579C2×C4×D4C2×D1113yes—
580C2×#117—116no—
581C2×#117C2×D1113yes—
582C22×C42C2×D1113yes—
583C22×C11—21no—
584C22×C11—23no—
585C22×C11—21no—
586C22×C11—23no—
587C22×C11—23no—
588C22×C11—23no—
589C22×C11—23no—
590C22×C11—412no—
591C22×C11C22×#4116yes—
592C22×C11C2×2−1+412yes—
593C22×C11C2611yescharacteristic
594C2×D11—24no—
595C2×D11—24no—
596C2×D11—24no—
597C4×C11—21no—
598C4×C11—23no—
599C4×C11—23no—
600C4×C11—23no—
601C4×C11—21no—
602C4×C11—23no—
603C4×C11—23no—
604C4×C11C22×#4112yes—
605C4×C11C22×#4116yes—
606C4×C11C2×2−1+412yes—
607C4×C11C2×2−1+412yes—
608C4×C11#58512yes—
609Dic11—212no—
610Dic11—24no—
611Dic11—212no—
6122−1+4—2216no—
613C2×#41—28no—
614C2×#41—1112no—
615C2×#41—112no—
616C2×#41—116no—
617C2×#41—116no—
618C2×#41C22×D1113yes—
619C2×#41C22×D1113yes—
620C2×#41C22×D1111yescharacteristic
621C2×#41C22×D1111yescharacteristic
622C22×Q8—114no—
623C22×Q8—116no—
624C22×Q8—116no—
625C22×Q8C22×D1111yescharacteristic
626C22×D4C22×D1113yes—
627C23×C4C22×D1113yes—
628C23×C4C22×D1113yes—
629C23×C4C22×D1113yes—
630C4⋊Q8—1112no—
631C4⋊Q8—1112no—
632C4⋊Q8—113no—
633C4⋊Q8—113no—
634C4⋊Q8—116no—
635C4⋊Q8—116no—
636C4⋊Q8—116no—
637C4⋊Q8—116no—
638C4⋊Q8—116no—
639C4⋊Q8—116no—
640C4⋊Q8—111no—
641#127—111no—
642#126—1124no—
643#126—1124no—
644#126—1124no—
645#126—1112no—
646#126—1112no—
647#125—1124no—
648#125—1112no—
649#125—1124no—
650#125—116no—
651#125—1112no—
652#125—1112no—
653#125—1112no—
654#125—116no—
655#125—116no—
656#124—1112no—
657#124—1124no—
658#124—112no—
659#124—116no—
660#124—116no—
661#123—1124no—
662#123—1112no—
663#123—1112no—
664#123—1112no—
665#123—1124no—
666#123—1124no—
667C22⋊Q8—1112no—
668C22⋊Q8—116no—
669C22⋊Q8—116no—
670C22⋊Q8—1112no—
671C22⋊Q8—1112no—
672C22⋊Q8—1112no—
673C22⋊Q8—1112no—
674C22⋊Q8—1112no—
675C22⋊Q8—1112no—
676C22⋊Q8—116no—
677C22⋊Q8—116no—
678C22⋊Q8—116no—
679C22⋊Q8—116no—
680C22⋊Q8—1112no—
681C22⋊Q8—1112no—
682C22⋊Q8—1124no—
683C22⋊Q8—1124no—
684#121—1124no—
685#121—1112no—
686#121—112no—
687#121—112no—
688#121—116no—
689#121—116no—
690#121—116no—
691#121—116no—
692#120—1112no—
693C4×Q8—114no—
694C4×Q8—1112no—
695C4×Q8—1112no—
696C4×Q8—1112no—
697C4×Q8—116no—
698C4×Q8—116no—
699C4×Q8—1112no—
700C4×Q8—1112no—
701C4×Q8—1112no—
702C4×Q8—1112no—
703C4×Q8—1112no—
704C4×Q8—116no—
705C4×Q8—116no—
706C4×Q8—116no—
707C4×Q8—116no—
708C4×Q8C22×D1111yescharacteristic
709C4×Q8C22×D1111yescharacteristic
710C4×Q8C22×D1113yes—
711C4×Q8C22×D1113yes—
712C4×Q8C22×D1111yescharacteristic
713C4×Q8C22×D1111yescharacteristic
714C4×Q8C22×D1113yes—
715C4×Q8C22×D1113yes—
716C4×D4—1112no—
717C4×D4—1112no—
718C4×D4—1112no—
719C4×D4—1112no—
720C4×D4—1112no—
721C4×D4—1112no—
722C4×D4—1112no—
723C4×D4—1124no—
724C4×D4—112no—
725C4×D4—112no—
726C4×D4—116no—
727C4×D4—116no—
728C4×D4—116no—
729C4×D4—116no—
730C4×D4C22×D1113yes—
731C4×D4C22×D1113yes—
732C4×D4C22×D1113yes—
733C4×D4C22×D1116yes—
734C4×D4C22×D1116yes—
735C4×D4C22×D1113yes—
736C4×D4C22×D1113yes—
737C4×D4C22×D1113yes—
738C4×D4C22×D1113yes—
739C4×D4C22×D1116yes—
740C4×D4C22×D1116yes—
741C4×D4C22×D1113yes—
742#117—116no—
743#117—1112no—
744#117—1112no—
745#117—1112no—
746#117—116no—
747#117—116no—
748#117—1112no—
749#117—1124no—
750#117—1112no—
751#117—1112no—
752#117—1112no—
753#117C22×D1113yes—
754#117C22×D1113yes—
755#117C22×D1116yes—
756#117C22×D1113yes—
757#117C22×D1116yes—
758#117C22×D1113yes—
759C2×C4⋊C4—116no—
760C2×C4⋊C4—116no—
761C2×C4⋊C4—1112no—
762C2×C4⋊C4—116no—
763C2×C4⋊C4—1112no—
764C2×C4⋊C4—116no—
765C2×C4⋊C4—1112no—
766C2×C4⋊C4C22×D1113yes—
767C2×C4⋊C4C22×D1113yes—
768C2×C22⋊C4—1112no—
769C2×C22⋊C4C22×D1116yes—
770C2×C42—1112no—
771C2×C42—1112no—
772C2×C42C22×D1113yes—
773C2×C42C22×D1113yes—
774C2×C42C22×D1113yes—
775C2×C42C22×D1113yes—
776C2×C42C22×D1113yes—
777C2×C42C22×D1113yes—
778C2×C42C22×D1113yes—
779C2×C42C22×D1113yes—
780C2×C42C22×D1113yes—
781C2×C42C22×D1113yes—
782C2×C42C22×D1113yes—
783C2×C42C22×D1111yescharacteristic
784C2×C11—22no—
785C2×C11—26no—
786C2×C11—43no—
787C2×C11C23×#4111yescharacteristic
788C2×C11C22×2−1+411yescharacteristic
789C2×C11C2×#58511yescharacteristic
790D11—44no—
791C24C23×D1113yes—
792#41—24no—
793#41—212no—
794#41—212no—
795#41—2248no—
796#41—2224no—
797#41—228no—
798#41—4412no—
799#41#433918yescomplemented
800C2×Q8—24no—
801C2×Q8—112no—
802C2×Q8—1112no—
803C2×Q8—116no—
804C2×Q8—116no—
805C2×Q8—1112no—
806C2×Q8—2216no—
807C2×Q8—2224no—
808C2×Q8—4412no—
809C2×Q8C23×D1113yes—
810C2×Q8C23×D1111yescharacteristic
811C2×D4—212no—
812C2×D4—114no—
813C2×D4—1112no—
814C2×D4—1112no—
815C2×D4—112no—
816C2×D4—112no—
817C2×D4—112no—
818C2×D4C23×D1116yes—
819C2×D4C23×D1113yes—
820C2×D4C23×D1113yes—
821C22×C4—212no—
822C22×C4—212no—
823C22×C4—46no—
824C22×C4—1112no—
825C22×C4—1112no—
826C22×C4—1112no—
827C22×C4—114no—
828C22×C4—1112no—
829C22×C4C23×D1111yescharacteristic
830C22×C4C23×D1111yescharacteristic
831C22×C4C23×D1113yes—
832C22×C4C23×D1113yes—
833C22×C4C23×D1113yes—
834C22×C4C23×D1113yes—
835C22×C4C23×D1113yes—
836C22×C4C23×D1113yes—
837C22×C4C23×D1113yes—
838C22×C4C23×D1113yes—
839C22×C4C23×D1113yes—
840C22×C4C23×D1113yes—
841C22×C4C23×D1113yes—
842C22×C4C23×D1113yes—
843C22×C4C23×D1113yes—
844C22×C4C23×D1113yes—
845C22×C4C23×D1113yes—
846C22×C4C23×D1111yescharacteristic
847C4⋊C4—116no—
848C4⋊C4—116no—
849C4⋊C4—1112no—
850C4⋊C4—116no—
851C4⋊C4—116no—
852C4⋊C4—1124no—
853C4⋊C4—1112no—
854C4⋊C4—1112no—
855C4⋊C4—1112no—
856C4⋊C4—1112no—
857C4⋊C4—1124no—
858C4⋊C4—1112no—
859C4⋊C4—112no—
860C4⋊C4—112no—
861C4⋊C4—1112no—
862C4⋊C4—1112no—
863C4⋊C4—1112no—
864C4⋊C4—1112no—
865C4⋊C4C23×D1113yes—
866C4⋊C4C23×D1113yes—
867C4⋊C4C23×D1116yes—
868C4⋊C4C23×D1113yes—
869C4⋊C4C23×D1113yes—
870C4⋊C4C23×D1116yes—
871C22⋊C4—1112no—
872C22⋊C4—1124no—
873C22⋊C4—1112no—
874C22⋊C4—1112no—
875C22⋊C4—114no—
876C22⋊C4—114no—
877C22⋊C4—1112no—
878C22⋊C4—1112no—
879C22⋊C4—1112no—
880C22⋊C4—1112no—
881C22⋊C4C23×D1116yes—
882C22⋊C4C23×D1116yes—
883C22⋊C4C23×D1116yes—
884C22⋊C4C23×D1116yes—
885C42—1112no—
886C42—1124no—
887C42—1112no—
888C42—1112no—
889C42C23×D1111yescharacteristic
890C42C23×D1111yescharacteristic
891C42C23×D1113yes—
892C42C23×D1113yes—
893C42C23×D1113yes—
894C42C23×D1113yes—
895C42C23×D1113yes—
896C42C23×D1113yes—
897C42C23×D1113yes—
898C42C23×D1113yes—
899C42C23×D1113yes—
900C42C23×D1113yes—
901C42C23×D1113yes—
902C42C23×D1111yescharacteristic
903C42C23×D1111yescharacteristic
904C42C23×D1113yes—
905C11#6280511yescharacteristic, complemented, Sylow
906C23—26no—
907C23—26no—
908C23—43no—
909C23—114no—
910C23C24×D1113yes—
911C23C24×D1113yes—
912C23C24×D1111yescharacteristic
913Q8—26no—
914Q8—2212no—
915Q8—2224no—
916Q8—224no—
917Q8—2212no—
918Q8—4412no—
919Q8C2×#433914yes—
920D4—212no—
921D4—26no—
922D4—2224no—
923D4—228no—
924D4—224no—
925D4—224no—
926D4—224no—
927D4—4412no—
928D4C2×#4339112yes—
929C2×C4—26no—
930C2×C4—26no—
931C2×C4—22no—
932C2×C4—26no—
933C2×C4—26no—
934C2×C4—26no—
935C2×C4—26no—
936C2×C4—26no—
937C2×C4—26no—
938C2×C4—26no—
939C2×C4—22no—
940C2×C4—26no—
941C2×C4—26no—
942C2×C4—43no—
943C2×C4—43no—
944C2×C4—43no—
945C2×C4—114no—
946C2×C4—1112no—
947C2×C4—1112no—
948C2×C4—2224no—
949C2×C4—2224no—
950C2×C4—228no—
951C2×C4—4412no—
952C2×C4—4412no—
953C2×C4C2×#4339112yes—
954C2×C4#6704314yescomplemented
955C2×C4C24×D1113yes—
956C2×C4C24×D1113yes—
957C2×C4C24×D1111yescharacteristic
958C2×C4C24×D1111yescharacteristic
959C2×C4C24×D1113yes—
960C2×C4C24×D1113yes—
961C2×C4C24×D1113yes—
962C2×C4C24×D1113yes—
963C2×C4C24×D1111yescharacteristic
964C2×C4C24×D1111yescharacteristic
965C2×C4C24×D1111yescharacteristic
966C2×C4C24×D1111yescharacteristic
967C22—21no—
968C22—23no—
969C22—21no—
970C22—23no—
971C22—23no—
972C22—23no—
973C22—23no—
974C22—412no—
975C22—224no—
976C22—224no—
977C22—224no—
978C22C22×#433916yes—
979C22C2×#6704312yes—
980C22C25×D1111yescharacteristic
981C4—21no—
982C4—23no—
983C4—23no—
984C4—23no—
985C4—21no—
986C4—23no—
987C4—23no—
988C4—2212no—
989C4—224no—
990C4—2212no—
991C4C22×#433912yes—
992C4C22×#433916yes—
993C4C2×#6704312yes—
994C4C2×#6704312yes—
995C4#1062345312yes—
996C2—22no—
997C2—26no—
998C2—43no—
999C2—444no—
1000C2C23×#433911yescharacteristic
1001C2C22×#6704311yescharacteristic
1002C2C2×#1062345311yescharacteristic
subgroupG/H
centerC2×C4C24×D11
commutator, socle, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C4×C11×#41C2
hypercenterC2×C4×#41D11
hypocenterC11#62805
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13082712C2semidirect
2. #13082665C2semidirect
3. #13082633C2semidirect
4. #13082594C2semidirect
5. #13082527C2semidirect
6. #13082502C2semidirect
7. #13082435C2semidirect
8. #13082401C2semidirect
9. #13082368C2semidirect
10. #13082296C2semidirect
11. #13082238C2semidirect
12. #13082231C2semidirect
13. Q8×#4339C2semidirect
14. #13082174C2semidirect
15. #13082043C2semidirect
16. #13081912C2semidirect
17. C2×#10623001C2semidirect
18. C4×#67043C2semidirect
19. C2×C4×C11×#41C2semidirect
49. #10623115C22semidirect
50. #10623114C22semidirect
51. #10623110C22semidirect
52. #10623109C22semidirect
53. Q8×D44C22semidirect
54. Q8×D44C22semidirect
55. #10623103C22semidirect
56. C4×Q8×D11C22semidirect
57. #10623101C22semidirect
58. #10623098C22semidirect
59. #10623098C22semidirect
60. Q8×Dic22C22semidirect
61. #10623096C22semidirect
62. #10623095C22semidirect
63. #10623094C22semidirect
64. #10623092C22semidirect
65. #10623088C22semidirect
66. #10623086C22semidirect
67. #10623086C22semidirect
68. #10623083C22semidirect
69. #10623082C22semidirect
70. #10623077C22semidirect
71. #10623074C22semidirect
72. #10623073C22semidirect
73. #10623073C22semidirect
74. #10623072C22semidirect
75. #10623072C22semidirect
76. #10623069C22semidirect
77. D4×Dic22C22semidirect
78. C4×#4341C22semidirect
79. #10623065C22semidirect
80. #10623064C22semidirect
81. #10623062C22semidirect
82. #10623060C22semidirect
83. #10623057C22semidirect
84. #10623054C22semidirect
85. #10623050C22semidirect
86. #10623049C22semidirect
87. #10623047C22semidirect
93. #10623010C22semidirect
94. #10623010C22semidirect
95. #10623010C22semidirect
96. #10623010C22semidirect
98. #10623008C22semidirect
99. #10623008C22semidirect
101. C4×#4339C22semidirect
102. C4×#4339C22semidirect
107. #10623001C22semidirect
108. #10623001C22semidirect
109. #10623001C22semidirect
110. #10623001C22semidirect
111. #10623001C22semidirect
112. #10623001C22semidirect
113. C2×#66923C22semidirect
114. C2×#66922C22semidirect
115. C2×#66922C22semidirect
116. C2×C4×Dic22C22semidirect
117. C2×C4×Dic22C22semidirect
295. C11×#41#41semidirect
423. C2×C4×#41D11semidirect
453. C2×C4×C112−1+4semidirect
799. #41#4339semidirect
905. C11#62805semidirect
954. C2×C4#67043semidirect

Maximal subgroups

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

subgroupindex
#130827122
#130826652
#130826332
#130825942
#130825272
#130825022
#130824352
#130824012
#130823682
#130822962
#130822382
#130822312
Q8×#43392
#130821742
#130820432
#130819122
C2×#106230012
C4×#670432
C2×C4×C11×#412
#6280511