Finite Group Databasebeta

← #15662227

Subgroups — #15662227

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#13082707C212yesmaximal, complemented
2#13082656C216yesmaximal, complemented
3#13082628C212yesmaximal, complemented
4#13082585C216yesmaximal, complemented
5#13082523C213yesmaximal, complemented
6#13082500C213yesmaximal, complemented
7#13082435C211yesmaximal, characteristic, complemented
8#13082365C216yesmaximal, complemented
9#13082289C212yesmaximal, complemented
10#13082237C212yesmaximal, complemented
11#13082228C216yesmaximal, complemented
12Q8×#4341C212yesmaximal, complemented
13#13082179C216yesmaximal, complemented
14#13082040C216yesmaximal, complemented
15#13081911C213yesmaximal, complemented
16C2×#10623259C213yesmaximal, complemented
172−1+4×Dic11C212yesmaximal, complemented
18C4×#41×D11C211yesmaximal, characteristic, complemented
19C11×#3499C211yesmaximal, characteristic, complemented
20C2×C11×2−1+4C2212yes—
21C2×#41×D11C2211yescharacteristic
22D4×Q8×C11C2212yescomplemented
23D4×Q8×C11C2212yescomplemented
24C11×#547C2216yescomplemented
25C11×#547C2216yescomplemented
26C11×#536C2216yescomplemented
27C11×#532C2213yescomplemented
28C2×C11×C4⋊Q8C2213yescomplemented
29C4×C11×#41C2211yescharacteristic
30#10623364C2216yes—
31#10623360C22112yes—
32#10623359C2216yes—
33#10623358C2212yes—
34#10623358C22112yescomplemented
35#10623358C2216yescomplemented
36#41×Dic11C2211yescharacteristic
37#41×Dic11C2216yescomplemented
38#41×Dic11C22112yescomplemented
39#10623355C22112yes—
40#10623348C2214yes—
41#10623347C2216yes—
42Q8×C22⋊D11C2214yes—
43C2×#66999C2216yes—
44#10623343C2214yescomplemented
45#10623343C2216yescomplemented
46C2×Q8×Dic11C2216yescomplemented
47C2×Q8×Dic11C2214yescomplemented
48#10623263C2216yescomplemented
49#10623263C2216yescomplemented
50#10623262C22112yescomplemented
51#10623259C2216yes—
52#10623259C2213yes—
53#10623259C2216yes—
54#10623259C2216yes—
55#10623259C2216yescomplemented
56#10623259C2216yescomplemented
57#10623259C2216yescomplemented
58#10623259C2216yescomplemented
59#10623259C2213yescomplemented
60#10623252C2216yescomplemented
61#10623252C2216yescomplemented
62#10623247C2211yescharacteristic
63#10623247C2213yescomplemented
64#10623213C22112yescomplemented
65#10623211C2216yes—
66#10623211C2216yescomplemented
67#10623196C22124yescomplemented
68#10623189C22124yes—
69#10623181C22124yescomplemented
70#10623180C22124yescomplemented
71#10623174C22112yescomplemented
72#10623173C22112yescomplemented
73#10623172C22112yescomplemented
74#10623170C22112yes—
75#10623166C22112yes—
76#10623156C22112yescomplemented
77#10623155C22112yescomplemented
78#10623153C22112yescomplemented
79#10623149C22112yescomplemented
80#10623137C2216yes—
81#10623137C2216yes—
82#10623131C2216yescomplemented
83#10623131C2216yescomplemented
84#10623129C22112yescomplemented
85C4×#4343C2211yescharacteristic
86C4×#4343C2211yescharacteristic
87C4×Q8×D11C2211yescharacteristic
88C4×Q8×D11C2211yescharacteristic
89#10623101C2212yescomplemented
90Q8×Dic22C2212yescomplemented
91#10623094C2216yescomplemented
92#10623088C2216yes—
93#10623088C2216yescomplemented
94#10623086C2216yescomplemented
95C4×D4×D11C2213yes—
96C4×D4×D11C2213yes—
97#10623074C2216yescomplemented
98#10623074C2216yescomplemented
99#10623073C2216yescomplemented
100D4×Dic22C2216yescomplemented
101C4×#4341C2216yes—
102C4×#4341C2213yes—
103C4×#4341C2213yes—
104C4×#4341C2216yescomplemented
105#10623053C2213yes—
106D11×#117C2213yes—
107#10623050C2216yescomplemented
108#10623044C22112yescomplemented
109#10623044C22112yescomplemented
110C2×#66950C2216yes—
111C2×#66945C2216yes—
112C2×#66943C2216yescomplemented
113C2×#66940C2216yescomplemented
114C4×#4339C2213yes—
115C2×C42×D11C2213yes—
116#10623001C2213yescomplemented
117C2×#66922C2213yescomplemented
118C11×2−1+4—216no—
119C2×C11×#41C23112yes—
120C2×C11×#41C2316yes—
121C2×C11×#41C2311yescharacteristic
122C22×Q8×C11C2316yes—
123C22×Q8×C11C2314yes—
124#41×D11—28no—
125C2×#4343C2311yescharacteristic
126C2×Q8×D11C2311yescharacteristic
127C2×#4341C2312yes—
128C2×#4341C2313yes—
129C2×#4341C2316yes—
130C2×D4×D11C2313yes—
131C2×#4339C2313yes—
132C22×C4×D11C2313yes—
133C22×C4×D11C2313yes—
134C22×C4×D11C2313yes—
135C22×Dic22C2316yes—
136C11×C4⋊Q8C2316yes—
137C11×C4⋊Q8C2316yes—
138C11×C4⋊Q8C2313yes—
139C11×C4⋊Q8C2316yes—
140C11×#127C2311yescharacteristic
141C11×#124C2316yes—
142C11×#123C23124yes—
143C11×C22⋊Q8C23112yes—
144C11×C22⋊Q8C23112yes—
145C11×#121C2316yes—
146C11×#121C2316yes—
147C4×Q8×C11C2311yescharacteristic
148C4×Q8×C11C2311yescharacteristic
149C4×D4×C11C2313yes—
150C4×D4×C11C2313yes—
151C4×D4×C11C2316yes—
152C4×D4×C11C2316yes—
153C11×#117C2313yes—
154C2×C11×C4⋊C4C2316yes—
155C2×C11×C4⋊C4C2316yes—
156C2×C42×C11C2313yes—
157#67000C23112yes—
158#66999C2316yes—
159#66999C23112yes—
160#66999C23112yes—
161#66999C23112yes—
162#66999C2316yes—
163Q8×Dic11C23112yes—
164Q8×Dic11C23112yes—
165Q8×Dic11C2316yes—
166Q8×Dic11C23112yes—
167Q8×Dic11C23112yes—
168Q8×Dic11C23112yes—
169Q8×Dic11C2316yes—
170Q8×Dic11C2311yescharacteristic
171Q8×Dic11C2314yes—
172Q8×Dic11C2311yescharacteristic
173#66997C23112yes—
174#66992C23124yes—
175#66991C2312yes—
176#66991C2312yes—
177#66991C2316yes—
178#66991C2316yes—
179#66990C23112yes—
180#66989C2312yes—
181#66989C2316yes—
182#66988C23112yes—
183D4×Dic11C2312yes—
184D4×Dic11C2312yes—
185D4×Dic11C2316yes—
186D4×Dic11C2316yes—
187D4×Dic11C2313yes—
188D4×Dic11C2313yes—
189D4×Dic11C23112yes—
190D4×Dic11C23112yes—
191D4×Dic11C23124yes—
192D4×Dic11C23112yes—
193#66983C23112yes—
194#66982C23124yes—
195C4×C22⋊D11C2316yes—
196C4×C22⋊D11C2316yes—
197C4×C22⋊D11C23112yes—
198C4×C22⋊D11C23112yes—
199C2×(C2×D11)⋊C4C23112yes—
200#66979C2316yes—
201#66979C2313yes—
202#66979C23124yes—
203#66979C23112yes—
204#66979C23112yes—
205C2×C4⋊Dic11C2316yes—
206C2×C4⋊Dic11C2316yes—
207C2×C4⋊Dic11C23112yes—
208C2×C4⋊Dic11C23112yes—
209#66977C2316yes—
210#66977C2316yes—
211#66977C23112yes—
212C2×Dic11⋊C4C23112yes—
213C2×C4×Dic11C2313yes—
214C2×C4×Dic11C2313yes—
215C2×C4×Dic11C2313yes—
216C2×C4×Dic11C23112yes—
217C2×C4×Dic11C23112yes—
218#66951C23124yes—
219#66951C23124yes—
220#66950C2316yes—
221#66950C23112yes—
222#66950C23112yes—
223#66950C23112yes—
224#66950C2316yes—
225#66946C2313yes—
226#66946C2313yes—
227#66945C2316yes—
228#66945C23112yes—
229#66945C23112yes—
230#66945C23112yes—
231#66945C2316yes—
232#66945C2313yes—
233#66945C2313yes—
234C4⋊C4×D11C2313yes—
235C4⋊C4×D11C2313yes—
236#66943C2316yes—
237#66943C23112yes—
238#66943C2316yes—
239#66943C23112yes—
240#66943C23112yes—
241#66943C23112yes—
242#66942C23124yes—
243#66942C23124yes—
244#66941C23112yes—
245#66940C2316yes—
246#66940C23112yes—
247#66940C2316yes—
248#66940C23112yes—
249#66940C23112yes—
250#66940C2313yes—
251#66940C2313yes—
252#66939C23124yes—
253#66938C23124yes—
254#66936C23112yes—
255#66936C23112yes—
256(C22⋊D11)⋊C4C2316yes—
257(C22⋊D11)⋊C4C2316yes—
258(C22⋊D11)⋊C4C23112yes—
259(C22⋊D11)⋊C4C23112yes—
260C22⋊C4×D11C2316yes—
261#66932C23124yes—
262#66932C23112yes—
263#66932C23112yes—
264#66931C23124yes—
265#66931C23124yes—
266#66930C2316yes—
267#66930C23112yes—
268#66930C23112yes—
269C4×D44C2313yes—
270C4×D44C2313yes—
271#66925C2316yes—
272C42×D11C2311yescharacteristic
273C42×D11C2313yes—
274C42×D11C2313yes—
275C42×D11C2313yes—
276C42×D11C2313yes—
277C42×D11C2313yes—
278C42×D11C2313yes—
279C42×D11C2313yes—
280#66923C2316yes—
281#66922C2311yescharacteristic
282#66922C2313yes—
283#66922C2316yes—
284#66922C2316yes—
285#66922C2316yes—
286C4×Dic22C2313yes—
287C4×Dic22C2313yes—
288C4×Dic22C2316yes—
289C4×Dic22C2316yes—
290#62805—111nomaximal, Sylow
291C23×D11C2413yes—
292C11×#41—248no—
293C11×#41—224no—
294C11×#41#4118yescomplemented
295C2×Q8×C11—216no—
296C2×Q8×C11—224no—
297C2×Q8×C11C24112yes—
298C2×Q8×C11C2416yes—
299C2×Q8×C11C2411yescharacteristic
300C2×D4×C11C24112yes—
301C2×D4×C11C2412yes—
302C2×D4×C11C2412yes—
303C2×D4×C11C2412yes—
304C2×D4×C11C2413yes—
305C22×C4×C11C24112yes—
306C22×C4×C11C2413yes—
307C22×C4×C11C2413yes—
308C22×C4×C11C24112yes—
309C22×C4×C11C2413yes—
310C2×C22⋊D11C2414yes—
311C2×C22⋊D11C2416yes—
312C2×C22⋊D11C24112yes—
313C22×Dic11C2414yes—
314C22×Dic11C2413yes—
315C22×Dic11C2413yes—
316C22×Dic11C24112yes—
317C22×Dic11C24112yes—
318C22×Dic11C2413yes—
319#4343—24no—
320Q8×D11—24no—
321#4341—28no—
322#4341—212no—
323#4341—412no—
324D4×D11—212no—
325#4339—212no—
326C2×D44C2413yes—
327C2×C4×D11—212no—
328C2×C4×D11—212no—
329C2×C4×D11—46no—
330C2×C4×D11C2411yescharacteristic
331C2×C4×D11C2411yescharacteristic
332C2×C4×D11C2413yes—
333C2×C4×D11C2413yes—
334C2×C4×D11C2413yes—
335C2×C4×D11C2413yes—
336C2×C4×D11C2413yes—
337C2×C4×D11C2413yes—
338C2×C4×D11C2413yes—
339C2×C4×D11C2413yes—
340C2×C4×D11C2413yes—
341C2×C4×D11C2411yescharacteristic
342C2×Dic22—412no—
343C2×Dic22C2412yes—
344C2×Dic22C2413yes—
345C2×Dic22C2416yes—
346C2×Dic22C24112yes—
347C11×C4⋊C4C2416yes—
348C11×C4⋊C4C24112yes—
349C11×C4⋊C4C2413yes—
350C11×C4⋊C4C2413yes—
351C11×C4⋊C4C2416yes—
352C11×C4⋊C4C24112yes—
353C11×C22⋊C4C2416yes—
354C11×C22⋊C4C24112yes—
355C11×C22⋊C4C24112yes—
356C42×C11C2413yes—
357C42×C11C2413yes—
358C42×C11C2411yescharacteristic
359C42×C11C2413yes—
360C22⋊Dic11C2414yes—
361C22⋊Dic11C24112yes—
362C22⋊Dic11C2416yes—
363C22⋊Dic11C24112yes—
364C22⋊Dic11C2414yes—
365C22⋊Dic11C24112yes—
366(C2×D11)⋊C4C2416yes—
367(C2×D11)⋊C4C2416yes—
368(C2×D11)⋊C4C24112yes—
369(C2×D11)⋊C4C24112yes—
370(C2×D11)⋊C4C24124yes—
371C4⋊Dic11C2412yes—
372C4⋊Dic11C2416yes—
373C4⋊Dic11C2413yes—
374C4⋊Dic11C2413yes—
375C4⋊Dic11C2416yes—
376C4⋊Dic11C24112yes—
377C4⋊Dic11C24112yes—
378C4⋊Dic11C2412yes—
379C4⋊Dic11C24124yes—
380C4⋊Dic11C24112yes—
381C4⋊Dic11C24112yes—
382Dic11⋊C4C24112yes—
383Dic11⋊C4C24112yes—
384Dic11⋊C4C2416yes—
385Dic11⋊C4C2416yes—
386Dic11⋊C4C24112yes—
387Dic11⋊C4C24112yes—
388Dic11⋊C4C24124yes—
389C4×Dic11C2413yes—
390C4×Dic11C2413yes—
391C4×Dic11C24112yes—
392C4×Dic11C2411yescharacteristic
393C4×Dic11C2411yescharacteristic
394C4×Dic11C2411yescharacteristic
395C4×Dic11C2413yes—
396C4×Dic11C2413yes—
397C4×Dic11C2413yes—
398C4×Dic11C2413yes—
399C4×Dic11C2413yes—
400C4×Dic11C2413yes—
401C4×Dic11C2413yes—
402C4×Dic11C24112yes—
403C4×Dic11C24112yes—
404C4×Dic11C24124yes—
405#3523—112no—
406#3520—116no—
407#3518—112no—
408#3515—116no—
409#3511—113no—
410#3509—113no—
411#3503—111no—
412#3499D1111yescharacteristic, complemented
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×C11C2514yes—
425C23×C11C2513yes—
426C22×D11—26no—
427C22×D11—26no—
428C22×D11—43no—
429C22×D11C2513yes—
430C22×D11C2511yescharacteristic
431Q8×C11—224no—
432Q8×C11—212no—
433Q8×C11C2×#4114yes—
434D4×C11—224no—
435D4×C11—24no—
436D4×C11—24no—
437D4×C11—24no—
438D4×C11C2×#41112yes—
439C2×C4×C11—224no—
440C2×C4×C11—224no—
441C2×C4×C11—26no—
442C2×C4×C11—26no—
443C2×C4×C11C2×#41112yes—
444C2×C4×C11C25112yes—
445C2×C4×C11C2513yes—
446C2×C4×C11C2513yes—
447C2×C4×C11C2513yes—
448C2×C4×C11C2511yescharacteristic
449C2×C4×C11C2511yescharacteristic
450C2×C4×C11C2511yescharacteristic
451C22⋊D11—212no—
452C22⋊D11—28no—
453C22⋊D11—412no—
454C2×Dic11—26no—
455C2×Dic11—26no—
456C2×Dic11—28no—
457C2×Dic11—412no—
458C2×Dic11—43no—
459C2×Dic11—412no—
460C2×Dic11C2513yes—
461C2×Dic11C2511yescharacteristic
462C2×Dic11C2513yes—
463C2×Dic11C2511yescharacteristic
464C2×Dic11C2514yes—
465C2×Dic11C2513yes—
466C2×Dic11C25112yes—
467C2×Dic11C2511yescharacteristic
468D44—26no—
469C4×D11—26no—
470C4×D11—22no—
471C4×D11—26no—
472C4×D11—26no—
473C4×D11—26no—
474C4×D11—26no—
475C4×D11—22no—
476C4×D11—26no—
477C4×D11—26no—
478C4×D11—43no—
479C4×D11—43no—
480C4×D112−1+414yescomplemented
481Dic22—26no—
482Dic22—24no—
483Dic22—212no—
484Dic22—412no—
485C2×2−1+4C2×D1112yes—
486C22×#41—111no—
487Q82—112no—
488#557—116no—
489#557—116no—
490#557—112no—
491#556—116no—
492#556—116no—
493#556—1112no—
494#556—116no—
495#555—116no—
496#554—1112no—
497#554—116no—
498#554—116no—
499#553—1112no—
500#552—1124no—
501#552—1112no—
502#552—1112no—
503#552—1112no—
504#552—1112no—
505#551—1124no—
506D4×Q8—114no—
507D4×Q8—116no—
508D4×Q8C2×D1112yescomplemented
509D4×Q8C2×D1112yescomplemented
510#548—114no—
511#548—1112no—
512#547—1112no—
513#547—116no—
514#547C2×D1116yescomplemented
515#547C2×D1116yescomplemented
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#536C2×D1116yescomplemented
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#533—113no—
537#532—111no—
538#532—113no—
539#532C2×D1113yescomplemented
540C2×C4⋊Q8—113no—
541C2×C4⋊Q8C2×D1113yescomplemented
542#529—116no—
543#529—116no—
544#529—1124no—
545#529—1112no—
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—116no—
558#520—1112no—
559#519—116no—
560#519—114no—
561C4×#41—111no—
562C4×#41—116no—
563C4×#41—1112no—
564C4×#41—111no—
565C4×#41—111no—
566C4×#41—113no—
567C4×#41—113no—
568C4×#41—116no—
569C4×#41—116no—
570C4×#41—113no—
571C4×#41—113no—
572C4×#41C2×D1111yescharacteristic
573C2×C4×Q8—116no—
574C2×C4×Q8—114no—
575C2×C4×Q8—111no—
576C2×C4×Q8—111no—
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×C11—24no—
586C22×C11—24no—
587C22×C11—24no—
588C22×C11C22×#4116yes—
589C22×C11C2611yescharacteristic
590C2×D11—21no—
591C2×D11—21no—
592C2×D11—23no—
593C2×D11—23no—
594C2×D11—23no—
595C2×D11—412no—
596C2×D11C2×2−1+412yes—
597C4×C11—212no—
598C4×C11—23no—
599C4×C11—23no—
600C4×C11C22×#4116yes—
601C4×C11C22×#4112yes—
602C4×C11C2×2−1+412yes—
603C4×C11#58512yes—
604Dic11—23no—
605Dic11—21no—
606Dic11—24no—
607Dic11—23no—
608Dic11—212no—
609Dic11—21no—
610Dic11—23no—
611Dic11C2×2−1+412yes—
6122−1+4—216no—
613C2×#41—111no—
614C2×#41—112no—
615C2×#41—113no—
616C2×#41—116no—
617C2×#41—113no—
618C2×#41—228no—
619C2×#41C22×D1116yes—
620C2×#41C22×D11112yes—
621C2×#41C22×D1111yescharacteristic
622C22×Q8—111no—
623C22×Q8—116no—
624C22×Q8C22×D1116yes—
625C22×Q8C22×D1114yes—
626C22×D4—113no—
627C23×C4—113no—
628C23×C4—113no—
629C23×C4—113no—
630C4⋊Q8—1112no—
631C4⋊Q8—1112no—
632C4⋊Q8—113no—
633C4⋊Q8—116no—
634C4⋊Q8—116no—
635C4⋊Q8—116no—
636C4⋊Q8—111no—
637C4⋊Q8C22×D1113yes—
638C4⋊Q8C22×D1116yes—
639C4⋊Q8C22×D1116yes—
640C4⋊Q8C22×D1116yes—
641#127C22×D1111yescharacteristic
642#126—1124no—
643#126—1124no—
644#126—1112no—
645#126—1112no—
646#126—1124no—
647#125—116no—
648#125—1112no—
649#125—1112no—
650#125—1112no—
651#125—116no—
652#125—1124no—
653#125—1112no—
654#125—1124no—
655#125—116no—
656#124—1112no—
657#124—112no—
658#124—116no—
659#124—1124no—
660#124C22×D1116yes—
661#123—1112no—
662#123—1124no—
663#123—1112no—
664#123—1112no—
665#123—1124no—
666#123C22×D11124yes—
667C22⋊Q8—116no—
668C22⋊Q8—1112no—
669C22⋊Q8—1112no—
670C22⋊Q8—1112no—
671C22⋊Q8—116no—
672C22⋊Q8—116no—
673C22⋊Q8—116no—
674C22⋊Q8—1112no—
675C22⋊Q8—116no—
676C22⋊Q8—1112no—
677C22⋊Q8—1112no—
678C22⋊Q8—1112no—
679C22⋊Q8—116no—
680C22⋊Q8—1124no—
681C22⋊Q8—1124no—
682C22⋊Q8C22×D11112yes—
683C22⋊Q8C22×D11112yes—
684#121—112no—
685#121—112no—
686#121—116no—
687#121—116no—
688#121—1124no—
689#121—1112no—
690#121C22×D1116yes—
691#121C22×D1116yes—
692#120—1112no—
693C4×Q8—111no—
694C4×Q8—116no—
695C4×Q8—1112no—
696C4×Q8—111no—
697C4×Q8—1112no—
698C4×Q8—1112no—
699C4×Q8—114no—
700C4×Q8—1112no—
701C4×Q8—116no—
702C4×Q8—1112no—
703C4×Q8—116no—
704C4×Q8—113no—
705C4×Q8—113no—
706C4×Q8—1112no—
707C4×Q8—1112no—
708C4×Q8—1112no—
709C4×Q8—116no—
710C4×Q8—113no—
711C4×Q8—113no—
712C4×Q8—116no—
713C4×Q8—116no—
714C4×Q8C22×D1111yescharacteristic
715C4×Q8C22×D1111yescharacteristic
716C4×D4—113no—
717C4×D4—113no—
718C4×D4—1112no—
719C4×D4—112no—
720C4×D4—112no—
721C4×D4—1112no—
722C4×D4—116no—
723C4×D4—1112no—
724C4×D4—1124no—
725C4×D4—116no—
726C4×D4—116no—
727C4×D4—116no—
728C4×D4—1112no—
729C4×D4—1112no—
730C4×D4—113no—
731C4×D4—113no—
732C4×D4—116no—
733C4×D4—116no—
734C4×D4—1112no—
735C4×D4—1112no—
736C4×D4—113no—
737C4×D4—113no—
738C4×D4C22×D1113yes—
739C4×D4C22×D1113yes—
740C4×D4C22×D1116yes—
741C4×D4C22×D1116yes—
742#117—113no—
743#117—116no—
744#117—1112no—
745#117—1124no—
746#117—1112no—
747#117—116no—
748#117—113no—
749#117—113no—
750#117—1112no—
751#117—1112no—
752#117—1112no—
753#117—116no—
754#117—116no—
755#117—1112no—
756#117—1112no—
757#117—116no—
758#117C22×D1113yes—
759C2×C4⋊C4—116no—
760C2×C4⋊C4—1112no—
761C2×C4⋊C4—116no—
762C2×C4⋊C4—1112no—
763C2×C4⋊C4—1112no—
764C2×C4⋊C4—113no—
765C2×C4⋊C4—113no—
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—1112no—
774C2×C42—113no—
775C2×C42—113no—
776C2×C42—113no—
777C2×C42—113no—
778C2×C42—113no—
779C2×C42—113no—
780C2×C42—113no—
781C2×C42—113no—
782C2×C42—111no—
783C2×C42C22×D1113yes—
784C2×C11—26no—
785C2×C11—44no—
786C2×C11C23×#4111yescharacteristic
787C2×C11C22×2−1+411yescharacteristic
788C2×C11C2×#58511yescharacteristic
789D11—22no—
790D11—43no—
791C24—113no—
792#41—248no—
793#41—224no—
794#41—228no—
795#41—224no—
796#41—2212no—
797#41—2212no—
798#41—4412no—
799#41#434118yescomplemented
800C2×Q8—216no—
801C2×Q8—224no—
802C2×Q8—112no—
803C2×Q8—116no—
804C2×Q8—113no—
805C2×Q8—1112no—
806C2×Q8—224no—
807C2×Q8—4412no—
808C2×Q8C23×D1116yes—
809C2×Q8C23×D11112yes—
810C2×Q8C23×D1111yescharacteristic
811C2×D4—114no—
812C2×D4—116no—
813C2×D4—1112no—
814C2×D4—113no—
815C2×D4—2212no—
816C2×D4C23×D11112yes—
817C2×D4C23×D1112yes—
818C2×D4C23×D1112yes—
819C2×D4C23×D1112yes—
820C2×D4C23×D1113yes—
821C22×C4—111no—
822C22×C4—113no—
823C22×C4—114no—
824C22×C4—113no—
825C22×C4—113no—
826C22×C4—1112no—
827C22×C4—1112no—
828C22×C4—111no—
829C22×C4—111no—
830C22×C4—113no—
831C22×C4—113no—
832C22×C4—113no—
833C22×C4—113no—
834C22×C4—113no—
835C22×C4—113no—
836C22×C4—113no—
837C22×C4—113no—
838C22×C4—113no—
839C22×C4—2212no—
840C22×C4—2212no—
841C22×C4—446no—
842C22×C4C23×D1113yes—
843C22×C4C23×D1113yes—
844C22×C4C23×D11112yes—
845C22×C4C23×D11112yes—
846C22×C4C23×D1113yes—
847C4⋊C4—113no—
848C4⋊C4—116no—
849C4⋊C4—1112no—
850C4⋊C4—116no—
851C4⋊C4—1112no—
852C4⋊C4—1112no—
853C4⋊C4—1124no—
854C4⋊C4—113no—
855C4⋊C4—116no—
856C4⋊C4—116no—
857C4⋊C4—1112no—
858C4⋊C4—1124no—
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×D1116yes—
869C4⋊C4C23×D11112yes—
870C4⋊C4C23×D11112yes—
871C22⋊C4—116no—
872C22⋊C4—1112no—
873C22⋊C4—114no—
874C22⋊C4—114no—
875C22⋊C4—1112no—
876C22⋊C4—1112no—
877C22⋊C4—1112no—
878C22⋊C4—116no—
879C22⋊C4—116no—
880C22⋊C4—1124no—
881C22⋊C4—1112no—
882C22⋊C4C23×D1116yes—
883C22⋊C4C23×D11112yes—
884C22⋊C4C23×D11112yes—
885C42—113no—
886C42—111no—
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—
900C42—1112no—
901C42C23×D1111yescharacteristic
902C42C23×D1113yes—
903C42C23×D1113yes—
904C42C23×D1113yes—
905C11#6280511yescharacteristic, complemented, Sylow
906C23—111no—
907C23—113no—
908C23—226no—
909C23—226no—
910C23—443no—
911C23C24×D1114yes—
912C23C24×D1113yes—
913Q8—224no—
914Q8—212no—
915Q8—226no—
916Q8—224no—
917Q8—2212no—
918Q8—4412no—
919Q8C2×#434114yes—
920D4—224no—
921D4—24no—
922D4—24no—
923D4—24no—
924D4—228no—
925D4—2212no—
926D4—226no—
927D4—4412no—
928D4C2×#4341112yes—
929C2×C4—224no—
930C2×C4—224no—
931C2×C4—26no—
932C2×C4—26no—
933C2×C4—111no—
934C2×C4—114no—
935C2×C4—113no—
936C2×C4—111no—
937C2×C4—111no—
938C2×C4—113no—
939C2×C4—114no—
940C2×C4—1112no—
941C2×C4—113no—
942C2×C4—226no—
943C2×C4—226no—
944C2×C4—226no—
945C2×C4—228no—
946C2×C4—226no—
947C2×C4—222no—
948C2×C4—226no—
949C2×C4—226no—
950C2×C4—226no—
951C2×C4—226no—
952C2×C4—222no—
953C2×C4—226no—
954C2×C4—443no—
955C2×C4—443no—
956C2×C4—443no—
957C2×C4—4412no—
958C2×C4—4412no—
959C2×C4C2×#4341112yes—
960C2×C4C24×D11112yes—
961C2×C4C24×D1113yes—
962C2×C4C24×D1113yes—
963C2×C4C24×D1113yes—
964C2×C4C24×D1111yescharacteristic
965C2×C4C24×D1111yescharacteristic
966C2×C4C24×D1111yescharacteristic
967C22—23no—
968C22—23no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—112no—
973C22—221no—
974C22—221no—
975C22—223no—
976C22—223no—
977C22—223no—
978C22—4412no—
979C22C22×#434116yes—
980C22C25×D1111yescharacteristic
981C4—212no—
982C4—23no—
983C4—23no—
984C4—112no—
985C4—221no—
986C4—223no—
987C4—223no—
988C4—224no—
989C4—221no—
990C4—223no—
991C4—2212no—
992C4C22×#434116yes—
993C4C22×#434112yes—
994C4D11×2−1+412yes—
995C4#1062345712yes—
996C2—26no—
997C2—44no—
998C2—222no—
999C2—443no—
1000C2C23×#434111yescharacteristic
1001C2C2×D11×2−1+411yescharacteristic
1002C2C2×#1062345711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D11
commutator, socle, cosocleC22×C11C26
FittingC11×#3499C2
hypercenter#3499D11
hypocenterC11#62805
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #13082707C2semidirect
2. #13082656C2semidirect
3. #13082628C2semidirect
4. #13082585C2semidirect
5. #13082523C2semidirect
6. #13082500C2semidirect
7. #13082435C2semidirect
8. #13082365C2semidirect
9. #13082289C2semidirect
10. #13082237C2semidirect
11. #13082228C2semidirect
12. Q8×#4341C2semidirect
13. #13082179C2semidirect
14. #13082040C2semidirect
15. #13081911C2semidirect
16. C2×#10623259C2semidirect
17. 2−1+4×Dic11C2semidirect
18. C4×#41×D11C2semidirect
19. C11×#3499C2semidirect
22. D4×Q8×C11C22semidirect
23. D4×Q8×C11C22semidirect
24. C11×#547C22semidirect
25. C11×#547C22semidirect
26. C11×#536C22semidirect
27. C11×#532C22semidirect
28. C2×C11×C4⋊Q8C22semidirect
34. #10623358C22semidirect
35. #10623358C22semidirect
37. #41×Dic11C22semidirect
38. #41×Dic11C22semidirect
44. #10623343C22semidirect
45. #10623343C22semidirect
46. C2×Q8×Dic11C22semidirect
47. C2×Q8×Dic11C22semidirect
48. #10623263C22semidirect
49. #10623263C22semidirect
50. #10623262C22semidirect
55. #10623259C22semidirect
56. #10623259C22semidirect
57. #10623259C22semidirect
58. #10623259C22semidirect
59. #10623259C22semidirect
60. #10623252C22semidirect
61. #10623252C22semidirect
63. #10623247C22semidirect
64. #10623213C22semidirect
66. #10623211C22semidirect
67. #10623196C22semidirect
69. #10623181C22semidirect
70. #10623180C22semidirect
71. #10623174C22semidirect
72. #10623173C22semidirect
73. #10623172C22semidirect
76. #10623156C22semidirect
77. #10623155C22semidirect
78. #10623153C22semidirect
79. #10623149C22semidirect
82. #10623131C22semidirect
83. #10623131C22semidirect
84. #10623129C22semidirect
89. #10623101C22semidirect
90. Q8×Dic22C22semidirect
91. #10623094C22semidirect
93. #10623088C22semidirect
94. #10623086C22semidirect
97. #10623074C22semidirect
98. #10623074C22semidirect
99. #10623073C22semidirect
100. D4×Dic22C22semidirect
104. C4×#4341C22semidirect
107. #10623050C22semidirect
108. #10623044C22semidirect
109. #10623044C22semidirect
112. C2×#66943C22semidirect
113. C2×#66940C22semidirect
116. #10623001C22semidirect
117. C2×#66922C22semidirect
294. C11×#41#41semidirect
412. #3499D11semidirect
480. C4×D112−1+4semidirect
508. D4×Q8C2×D11semidirect
509. D4×Q8C2×D11semidirect
514. #547C2×D11semidirect
515. #547C2×D11semidirect
525. #536C2×D11semidirect
539. #532C2×D11semidirect
541. C2×C4⋊Q8C2×D11semidirect
799. #41#4341semidirect
905. C11#62805semidirect

Maximal subgroups

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

subgroupindex
#130827072
#130826562
#130826282
#130825852
#130825232
#130825002
#130824352
#130823652
#130822892
#130822372
#130822282
Q8×#43412
#130821792
#130820402
#130819112
C2×#106232592
2−1+4×Dic112
C4×#41×D112
C11×#34992
#6280511