Finite Group Databasebeta

← #14914838

Subgroups — #14914838

Order 2816.

2462 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623105C211yesmaximal, characteristic
2#13071580C211yesmaximal, characteristic, complemented
3#13071572C211yesmaximal, characteristic, complemented
4#13071557C212yesmaximal, complemented
5#13071548C212yesmaximal, complemented
6#13071525C211yesmaximal, characteristic, complemented
7#13071517C211yesmaximal, characteristic, complemented
8#13071492C211yesmaximal, characteristic, complemented
9#13071484C211yesmaximal, characteristic, complemented
10#13071479C212yesmaximal, complemented
11#13071477C212yesmaximal, complemented
12#13071445C211yesmaximal, characteristic
13#13071445C211yesmaximal, characteristic
14#13071267C211yesmaximal, characteristic, complemented
15#13071248C212yesmaximal, complemented
16#13071221C211yesmaximal, characteristic, complemented
17#13071215C212yesmaximal, complemented
18#13071113C211yesmaximal, characteristic, complemented
19#13071054C212yesmaximal, complemented
20D11×#387C212yesmaximal, complemented
21#13070976C211yesmaximal, characteristic, complemented
22C42×D44C211yesmaximal, characteristic, complemented
23C11×#2295C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27#10623105C4116yescomplemented
28C2×#66946C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×#66946C2211yescharacteristic
31C2×#66946C2212yes—
32C2×#66945C2212yes—
33C2×C4⋊C4×D11C2212yes—
34C2×C4⋊C4×D11C2212yes—
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4×D44C2211yescharacteristic
37C2×C4×D44C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C2×C4×D44C2212yes—
40C2×#66925C2211yescharacteristic
41C2×#66925C2212yes—
42C2×C42×D11C2212yes—
43C11×#391C2211yescharacteristic
44C11×#391C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#387C2212yes—
48C11×#387C2212yes—
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2212yes—
51C11×#376C2212yes—
52C43×C11C2211yescharacteristic
53#10622843C2211yescharacteristic
54#10622843C2211yescharacteristic
55#10622602C2212yes—
56#10622602C2212yes—
57#10622600C2211yescharacteristic
58#10622600C2211yescharacteristic
59#10622600C2212yes—
60#10622600C2212yes—
61#10622598C2211yescharacteristic
62#10622598C2211yescharacteristic
63#10622594C2212yes—
64#10622594C2212yes—
65#10622591C2212yes—
66#10622591C2212yes—
67#10622590C2211yescharacteristic
68#10622589C2211yescharacteristic
69C4⋊C4×Dic11C2211yescharacteristic
70C4⋊C4×Dic11C2211yescharacteristic
71#10622553C2211yescharacteristic
72#10622553C2211yescharacteristic
73#10622553C2211yescharacteristic
74#10622553C2211yescharacteristic
75#10622553C2212yes—
76C4×(C2×D11)⋊C4C2211yescharacteristic
77C4×(C2×D11)⋊C4C2211yescharacteristic
78C4×(C2×D11)⋊C4C2212yes—
79C4×(C2×D11)⋊C4C2212yes—
80C4×(C2×D11)⋊C4C2212yes—
81C4×(C2×D11)⋊C4C2212yes—
82C4×(C2×D11)⋊C4C2212yes—
83#10622550C2212yes—
84#10622549C2212yes—
85C4×C4⋊Dic11C2211yescharacteristic
86C4×C4⋊Dic11C2211yescharacteristic
87C4×C4⋊Dic11C2211yescharacteristic
88#10622546C2211yescharacteristic
89#10622546C2211yescharacteristic
90#10622546C2211yescharacteristic
91#10622546C2211yescharacteristic
92#10622546C2212yes—
93#10622545C2211yescharacteristic
94C4×Dic11⋊C4C2211yescharacteristic
95C4×Dic11⋊C4C2211yescharacteristic
96#10622282C2212yes—
97#10622281C2212yes—
98#10622281C2212yes—
99#10622280C2212yes—
100#10622279C2212yes—
101#10622279C2212yes—
102#10622278C2212yes—
103#10622278C2212yes—
104#10622278C2212yes—
105#10622278C2212yes—
106#10622277C2212yes—
107#10622277C2212yes—
108#10622277C2212yes—
109D11×#95C2212yes—
110D11×#95C2212yes—
111D11×#95C2212yes—
112D11×#95C2212yes—
113#10622268C2212yes—
114#10622268C2212yes—
115#10622267C2212yes—
116#10622267C2212yes—
117#10622266C2212yes—
118#10622266C2212yes—
119#10622265C2212yes—
120#10622264C2212yes—
121#10622263C2212yes—
122#10622262C2212yes—
123#10622261C2212yes—
124C22×Q8×C11C2311yescharacteristic
125C2×#4343—24no—
126C2×#4343—24no—
127C2×#4343C2×C418yes—
128C22×D44C2312yes—
129C22×D44C2311yescharacteristic
130C22×C4×D11C2312yes—
131C22×C4×D11C2312yes—
132C22×C4×D11C2312yes—
133C22×C4×D11C2311yescharacteristic
134C22×C4×D11C2312yes—
135C22×C4×D11C2312yes—
136C22×C4×D11C2312yes—
137C22×C4×D11C2312yes—
138C22×C4×D11C2312yes—
139C4×Q8×C11C2×C418yescomplemented
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2312yes—
153C2×C42×C11C2311yescharacteristic
154C2×C42×C11C2312yes—
155Q8×Dic11C2×C418yescomplemented
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2311yescharacteristic
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2311yescharacteristic
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2311yescharacteristic
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2311yescharacteristic
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2312yes—
175C2×C4⋊Dic11C2311yescharacteristic
176C2×Dic11⋊C4C2311yescharacteristic
177C2×Dic11⋊C4C2311yescharacteristic
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2311yescharacteristic
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×Dic11⋊C4C2311yescharacteristic
184C2×Dic11⋊C4C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2311yescharacteristic
194#66946—24no—
195#66946—24no—
196#66946C2×C418yes—
197#66946C2×C4116yescomplemented
198#66945—44no—
199C4⋊C4×D11—44no—
200C4⋊C4×D11C2×C418yescomplemented
201C4⋊C4×D11C2×C4116yescomplemented
202C4×D44—24no—
203C4×D44—24no—
204C4×D44C2×C418yes—
205C4×D44C2×C4116yescomplemented
206#66925C2×C418yescomplemented
207#66925C2×C4116yescomplemented
208C42×D11—44no—
209C11×#95C2312yes—
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11×#95C2312yes—
216C11⋊#95C2311yescharacteristic
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2311yescharacteristic
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2311yescharacteristic
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2312yes—
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2312yes—
243#34260—111nomaximal, Sylow
244C23×D11C2411yescharacteristic
245C23×D11C2412yes—
246C2×Q8×C11—22no—
247C2×Q8×C11—22no—
248C2×Q8×C11C22×C414yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2412yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2411yescharacteristic
262C22×Dic11C2412yes—
263C22×Dic11C2411yescharacteristic
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2412yes—
266C22×Dic11C2411yescharacteristic
267C22×Dic11C2412yes—
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2411yescharacteristic
270#4343—232no—
271C2×D44—24no—
272C2×D44—24no—
273C2×D44C22×C418yes—
274C2×D44C22×C414yes—
275C2×D44#4114yes—
276C2×D44#4114yes—
277C2×C4×D11—24no—
278C2×C4×D11—24no—
279C2×C4×D11—24no—
280C2×C4×D11—24no—
281C2×C4×D11—24no—
282C2×C4×D11—24no—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—24no—
286C2×C4×D11—24no—
287C2×C4×D11—42no—
288C2×C4×D11—42no—
289C2×C4×D11—42no—
290C2×C4×D11—42no—
291C2×C4×D11—42no—
292C2×C4×D11—42no—
293C2×C4×D11—42no—
294C2×C4×D11—42no—
295C2×C4×D11—42no—
296C2×C4×D11—42no—
297C2×C4×D11—42no—
298C2×C4×D11—42no—
299C2×C4×D11C22×C418yes—
300C2×C4×D11C22×C414yes—
301C2×C4×D11C22×C418yes—
302C2×C4×D11C22×C418yes—
303C2×C4×D11C22×C418yes—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—24no—
307C11×C4⋊C4—42no—
308C11×C4⋊C4C22×C414yes—
309C11×C4⋊C4C22×C418yes—
310C42×C11—22no—
311C42×C11—22no—
312C42×C11—22no—
313C42×C11—22no—
314C42×C11—41no—
315C42×C11—42no—
316C42×C11—41no—
317C42×C11C22×C414yes—
318C42×C11C22×C418yes—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—42no—
326(C2×D11)⋊C4—41no—
327(C2×D11)⋊C4—41no—
328(C2×D11)⋊C4—42no—
329(C2×D11)⋊C4C22×C418yes—
330(C2×D11)⋊C4C22×C414yes—
331(C2×D11)⋊C4C22×C418yes—
332(C2×D11)⋊C4C22×C414yes—
333C4⋊Dic11—22no—
334C4⋊Dic11—22no—
335C4⋊Dic11—42no—
336C4⋊Dic11—42no—
337C4⋊Dic11C22×C414yes—
338C4⋊Dic11C22×C418yes—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341Dic11⋊C4—42no—
342Dic11⋊C4—41no—
343Dic11⋊C4—41no—
344Dic11⋊C4—42no—
345Dic11⋊C4C22×C414yes—
346Dic11⋊C4C22×C414yes—
347Dic11⋊C4C22×C418yes—
348C4×Dic11—22no—
349C4×Dic11—22no—
350C4×Dic11—24no—
351C4×Dic11—42no—
352C4×Dic11—42no—
353C4×Dic11—42no—
354C4×Dic11—42no—
355C4×Dic11C22×C414yes—
356C4×Dic11C22×C418yes—
357C2×#520—111no—
358#2356—111no—
359#2355—111no—
360#2353—112no—
361#2352—112no—
362#2349—111no—
363D4×C4⋊C4—111no—
364#2345—111no—
365#2344—111no—
366#2343—112no—
367#2343—112no—
368#2339—111no—
369#2339—111no—
370#2320—111no—
371#2318—112no—
372#2314—111no—
373#2313—112no—
374#2298—111no—
375#2295D1111yescharacteristic, complemented
376#2290—112no—
377C2×#387—112no—
378#2275—111no—
379C42×D4—111no—
380C23×C11C2511yescharacteristic
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—21no—
386C22×D11—21no—
387C22×D11—21no—
388C22×D11—21no—
389C22×D11—21no—
390C22×D11—21no—
391C22×D11C23×C412yes—
392C22×D11C23×C414yes—
393C22×D11C2×#4114yes—
394C22×D11C2×#4114yes—
395Q8×C11—28no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—22no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—22no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—21no—
414C2×C4×C11—22no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—21no—
420C2×C4×C11C23×C414yes—
421C2×C4×C11C23×C412yes—
422C2×C4×C11C23×C414yes—
423C2×C4×C11C23×C412yes—
424C2×C4×C11C23×C412yes—
425C2×C4×C11C2×#4112yes—
426C2×C4×C11C2×#4112yes—
427C2×C4×C11H(5,𝔽2)12yes—
428C2×C4×C112−1+412yes—
429C2×Dic11—21no—
430C2×Dic11—21no—
431C2×Dic11—22no—
432C2×Dic11—21no—
433C2×Dic11—21no—
434C2×Dic11—22no—
435C2×Dic11—21no—
436C2×Dic11—21no—
437C2×Dic11—21no—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—21no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—21no—
446C2×Dic11—21no—
447C2×Dic11—21no—
448C2×Dic11—21no—
449C2×Dic11—22no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—21no—
453C2×Dic11—21no—
454C2×Dic11—21no—
455C2×Dic11C23×C412yes—
456C2×Dic11C23×C412yes—
457C2×Dic11C23×C414yes—
458C2×Dic11C23×C412yes—
459D44—216no—
460D44#117116yescomplemented
461C4×D11—216no—
462C4×D11—28no—
463C4×D11—48no—
464C4×D11—48no—
465C4×D11—48no—
466C4×D11—48no—
467C4×D11—48no—
468C4×D11—84no—
469C4×D11—84no—
470C22×#41—111no—
471#520—1116no—
472C2×C4×Q8—111no—
473C2×C4×Q8C2×D1111yescharacteristic
474C2×C4×D4—112no—
475C2×C4×D4—111no—
476C2×C4×D4—111no—
477C2×C4×D4—111no—
478C2×C4×D4—112no—
479C2×C4×D4—111no—
480C2×C4×D4—111no—
481C2×C4×D4—111no—
482C2×#117—112no—
483C2×#117—111no—
484C2×#117—112no—
485C22×C4⋊C4—112no—
486C22×C4⋊C4—111no—
487C22×C4⋊C4—112no—
488C22×C42—112no—
489#391—111no—
490#391—111no—
491#391C2×D1111yescharacteristic
492#391C2×D1111yescharacteristic
493#389—111no—
494#389—111no—
495#389C2×D1111yescharacteristic
496#389C2×D1111yescharacteristic
497#388—112no—
498#388—111no—
499#388—111no—
500#388—111no—
501#388—111no—
502#388—112no—
503#387—112no—
504#387—112no—
505#387—112no—
506#387—112no—
507#387—111no—
508#387—112no—
509#387—111no—
510#387—111no—
511#387—111no—
512#387—112no—
513#387—112no—
514#387—112no—
515#387—112no—
516#387—112no—
517#387—112no—
518#387—112no—
519#387C2×D1112yes—
520#387C2×D1112yes—
521#386—112no—
522#386—112no—
523#386—112no—
524#386—112no—
525#385—112no—
526#385—112no—
527#385—112no—
528#385—112no—
529#384—111no—
530#383—112no—
531#383—112no—
532#382—111no—
533#382—112no—
534#382—112no—
535#381—112no—
536#381—112no—
537#381—112no—
538#380—112no—
539#380—111no—
540#380—111no—
541#380—112no—
542#380—112no—
543C4×C4⋊C4—111no—
544C4×C4⋊C4—111no—
545C4×C4⋊C4—111no—
546C4×C4⋊C4—111no—
547C4×C4⋊C4—111no—
548C4×C4⋊C4—111no—
549C4×C4⋊C4—111no—
550C4×C4⋊C4—112no—
551C4×C4⋊C4C2×D1111yescharacteristic
552C4×C4⋊C4C2×D1112yes—
553C4×C22⋊C4—112no—
554C4×C22⋊C4—111no—
555C4×C22⋊C4—111no—
556C4×C22⋊C4—112no—
557C4×C22⋊C4—112no—
558C4×C22⋊C4—112no—
559C4×C22⋊C4—112no—
560C4×C22⋊C4—112no—
561C4×C22⋊C4—112no—
562#376—111no—
563#376—112no—
564#376C2×D1112yes—
565C2×#95—112no—
566C2×#95—112no—
567C2×#95—112no—
568C2×#95—112no—
569C43C2×D1111yescharacteristic
570C22×C11C24×C411yescharacteristic
571C22×C11C22×#4111yescharacteristic
572C22×C11C22×#4111yescharacteristic
573C22×C11C2×H(5,𝔽2)11yescharacteristic
574C22×C11C2×2−1+411yescharacteristic
575C22×C11#58511yescharacteristic
576C22×C11#58511yescharacteristic
577C2×D11—24no—
578C2×D11—24no—
579C2×D11—24no—
580C2×D11—24no—
581C2×D11—24no—
582C2×D11—24no—
583C2×D11—22no—
584C2×D11—22no—
585C2×D11—22no—
586C2×D11—41no—
587C2×D11—41no—
588C2×D11—41no—
589C2×D11—41no—
590C2×D11C2×#11718yes—
591C4×C11—24no—
592C4×C11—22no—
593C4×C11—24no—
594C4×C11—22no—
595C4×C11—22no—
596C4×C11—22no—
597C4×C11—42no—
598C4×C11—41no—
599C4×C11—41no—
600C4×C11—42no—
601C4×C11C2×#11714yes—
602Dic11—22no—
603Dic11—24no—
604Dic11—22no—
605Dic11—22no—
606Dic11—42no—
607Dic11—41no—
608Dic11—41no—
609Dic11—42no—
610Dic11—41no—
611Dic11—41no—
612C2×#41—118no—
613C2×#41—224no—
614C2×#41—224no—
615C22×Q8C22×D1111yescharacteristic
616C22×D4—111no—
617C22×D4—112no—
618C23×C4—112no—
619C23×C4—111no—
620C23×C4—112no—
621C23×C4—112no—
622C23×C4—112no—
623C23×C4—112no—
624C23×C4—112no—
625C23×C4—112no—
626C23×C4—112no—
627C4×Q8—118no—
628C4×Q8C4×D1118yescomplemented
629C4×D4—118no—
630C4×D4—1116no—
631C4×D4—118no—
632C4×D4—1116no—
633C4×D4—224no—
634C4×D4—224no—
635C4×D4—224no—
636C4×D4—224no—
637#117—118no—
638#117—1116no—
639#117—444no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—111no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—1116no—
646C2×C4⋊C4—118no—
647C2×C4⋊C4—111no—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—112no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—111no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—444no—
658C2×C4⋊C4C22×D1112yes—
659C2×C4⋊C4C22×D1111yescharacteristic
660C2×C4⋊C4C22×D1111yescharacteristic
661C2×C4⋊C4C22×D1112yes—
662C2×C4⋊C4C22×D1112yes—
663C2×C4⋊C4C22×D1111yescharacteristic
664C2×C22⋊C4—112no—
665C2×C22⋊C4—112no—
666C2×C22⋊C4—111no—
667C2×C22⋊C4—111no—
668C2×C22⋊C4—111no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—112no—
671C2×C22⋊C4—112no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4—111no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—111no—
676C2×C22⋊C4—112no—
677C2×C22⋊C4—111no—
678C2×C42—112no—
679C2×C42—111no—
680C2×C42—112no—
681C2×C42—111no—
682C2×C42—111no—
683C2×C42—112no—
684C2×C42—112no—
685C2×C42—112no—
686C2×C42—112no—
687C2×C42—444no—
688C2×C42C22×D1111yescharacteristic
689C2×C42C22×D1111yescharacteristic
690C2×C42C22×D1111yescharacteristic
691C2×C42C22×D1111yescharacteristic
692C2×C42C22×D1111yescharacteristic
693C2×C42C22×D1111yescharacteristic
694C2×C42C22×D1112yes—
695C2×C42C22×D1111yescharacteristic
696C2×C42C22×D1112yes—
697#95—111no—
698#95—111no—
699#95—111no—
700#95—111no—
701#95—112no—
702#95—112no—
703#95—112no—
704#95—112no—
705#95—112no—
706#95—112no—
707#95—112no—
708#95—112no—
709#95—111no—
710#95—111no—
711#95—111no—
712#95—111no—
713#95—112no—
714#95—112no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—111no—
720#95—111no—
721#95—111no—
722#95—112no—
723#95—111no—
724#95C22×D1112yes—
725#95C22×D1112yes—
726#95C22×D1112yes—
727#95C22×D1112yes—
728#95C22×D1112yes—
729#95C22×D1112yes—
730#95C22×D1112yes—
731C2×C11C22×#11711yescharacteristic
732C2×C11C4×H(5,𝔽2)11yescharacteristic
733C2×C11C4×2−1+411yescharacteristic
734C2×C11#351311yescharacteristic
735C2×C11#351511yescharacteristic
736C2×C11#352011yescharacteristic
737C2×C11#352111yescharacteristic
738D11—28no—
739D11—42no—
740C24—112no—
741C24—111no—
742#41—2232no—
743C2×Q8—22no—
744C2×Q8—22no—
745C2×Q8C2×C4×D1114yes—
746C2×D4—114no—
747C2×D4—118no—
748C2×D4—114no—
749C2×D4—114no—
750C2×D4—224no—
751C2×D4—224no—
752C22×C4—111no—
753C22×C4—112no—
754C22×C4—111no—
755C22×C4—111no—
756C22×C4—118no—
757C22×C4—114no—
758C22×C4—118no—
759C22×C4—118no—
760C22×C4—118no—
761C22×C4—111no—
762C22×C4—111no—
763C22×C4—112no—
764C22×C4—111no—
765C22×C4—111no—
766C22×C4—112no—
767C22×C4—224no—
768C22×C4—224no—
769C22×C4—224no—
770C22×C4—224no—
771C22×C4—224no—
772C22×C4—224no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—224no—
776C22×C4—224no—
777C22×C4—442no—
778C22×C4—442no—
779C22×C4—442no—
780C22×C4—442no—
781C22×C4—442no—
782C22×C4—442no—
783C22×C4—442no—
784C22×C4—442no—
785C22×C4—442no—
786C22×C4—442no—
787C22×C4—442no—
788C22×C4—442no—
789C22×C4C23×D1112yes—
790C22×C4C23×D1111yescharacteristic
791C22×C4C23×D1111yescharacteristic
792C22×C4C23×D1112yes—
793C22×C4C23×D1112yes—
794C22×C4C23×D1111yescharacteristic
795C22×C4C23×D1111yescharacteristic
796C22×C4C23×D1112yes—
797C22×C4C23×D1111yescharacteristic
798C22×C4C23×D1111yescharacteristic
799C22×C4C23×D1111yescharacteristic
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—24no—
803C4⋊C4—42no—
804C4⋊C4—118no—
805C4⋊C4—114no—
806C4⋊C4—118no—
807C4⋊C4—114no—
808C4⋊C4—114no—
809C4⋊C4—222no—
810C4⋊C4—222no—
811C4⋊C4—222no—
812C4⋊C4—222no—
813C4⋊C4—442no—
814C4⋊C4—442no—
815C4⋊C4—442no—
816C4⋊C4—441no—
817C4⋊C4—441no—
818C4⋊C4—442no—
819C4⋊C4C2×C4×D1118yes—
820C4⋊C4C2×C4×D1114yes—
821C22⋊C4—118no—
822C22⋊C4—114no—
823C22⋊C4—118no—
824C22⋊C4—114no—
825C22⋊C4—224no—
826C22⋊C4—224no—
827C22⋊C4—224no—
828C22⋊C4—224no—
829C22⋊C4—222no—
830C22⋊C4—222no—
831C22⋊C4—442no—
832C22⋊C4—441no—
833C22⋊C4—441no—
834C22⋊C4—442no—
835C42—22no—
836C42—22no—
837C42—22no—
838C42—22no—
839C42—41no—
840C42—42no—
841C42—41no—
842C42—118no—
843C42—114no—
844C42—222no—
845C42—222no—
846C42—224no—
847C42—442no—
848C42—442no—
849C42—442no—
850C42—442no—
851C42C2×C4×D1118yes—
852C42C2×C4×D1114yes—
853C11#3426011yescharacteristic, complemented, Sylow
854C23—114no—
855C23—114no—
856C23—114no—
857C23—112no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—221no—
863C23—221no—
864C23—221no—
865C23—221no—
866C23—221no—
867C23—221no—
868C23C24×D1111yescharacteristic
869Q8—28no—
870D4—1116no—
871D4—2216no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—21no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—112no—
897C2×C4—114no—
898C2×C4—112no—
899C2×C4—112no—
900C2×C4—2216no—
901C2×C4—221no—
902C2×C4—221no—
903C2×C4—221no—
904C2×C4—222no—
905C2×C4—221no—
906C2×C4—222no—
907C2×C4—221no—
908C2×C4—221no—
909C2×C4—228no—
910C2×C4—221no—
911C2×C4—221no—
912C2×C4—222no—
913C2×C4—221no—
914C2×C4—221no—
915C2×C4—221no—
916C2×C4—221no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—221no—
921C2×C4—222no—
922C2×C4—221no—
923C2×C4—221no—
924C2×C4—222no—
925C2×C4—221no—
926C2×C4—221no—
927C2×C4—221no—
928C2×C4—448no—
929C2×C4—448no—
930C2×C4—448no—
931C2×C4—448no—
932C2×C4—448no—
933C2×C4—884no—
934C2×C4—884no—
935C2×C4C22×C4×D1114yes—
936C2×C4C22×C4×D1112yes—
937C2×C4C22×C4×D1112yes—
938C2×C4C22×C4×D1114yes—
939C2×C4C22×C4×D1112yes—
940C2×C4#6704012yes—
941C2×C4#41×D1112yes—
942C2×C4#41×D1112yes—
943C2×C4#6704212yes—
944C22—118no—
945C22—224no—
946C22—224no—
947C22—224no—
948C22—224no—
949C22—224no—
950C22—224no—
951C22—222no—
952C22—222no—
953C22—222no—
954C22—441no—
955C22—441no—
956C22—441no—
957C22—441no—
958C22C23×C4×D1111yescharacteristic
959C22C2×#6704011yescharacteristic
960C22C2×#41×D1111yescharacteristic
961C22C2×#41×D1111yescharacteristic
962C22C2×#6704211yescharacteristic
963C22#1062345311yescharacteristic
964C22#1062345311yescharacteristic
965C4—22no—
966C4—24no—
967C4—22no—
968C4—22no—
969C4—24no—
970C4—22no—
971C4—42no—
972C4—41no—
973C4—42no—
974C4—41no—
975C4—222no—
976C4—224no—
977C4—222no—
978C4—222no—
979C4—442no—
980C4—441no—
981C4—441no—
982C4—442no—
983C4—441no—
984C4—441no—
985C4D11×#11714yes—
986C2—228no—
987C2—442no—
988C2C2×D11×#11711yescharacteristic
989C2C4×#6704211yescharacteristic
990C2C4×#6704011yescharacteristic
991C2#1308255011yescharacteristic
992C2#1308258911yescharacteristic
993C2#1308266011yescharacteristic
994C2#1308267811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2295C2
socle, cosocleC23×C11C25
prime radicalC22×#4343C22
hypercenter#2295D11
hypocenterC11#34260
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2295

Complements

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

NH ≅ G/Ntype
2. #13071580C2semidirect
3. #13071572C2semidirect
4. #13071557C2semidirect
5. #13071548C2semidirect
6. #13071525C2semidirect
7. #13071517C2semidirect
8. #13071492C2semidirect
9. #13071484C2semidirect
10. #13071479C2semidirect
11. #13071477C2semidirect
14. #13071267C2semidirect
15. #13071248C2semidirect
16. #13071221C2semidirect
17. #13071215C2semidirect
18. #13071113C2semidirect
19. #13071054C2semidirect
20. D11×#387C2semidirect
21. #13070976C2semidirect
22. C42×D44C2semidirect
23. C11×#2295C2semidirect
27. #10623105C4semidirect
139. C4×Q8×C11C2×C4semidirect
155. Q8×Dic11C2×C4semidirect
197. #66946C2×C4semidirect
200. C4⋊C4×D11C2×C4semidirect
201. C4⋊C4×D11C2×C4semidirect
205. C4×D44C2×C4semidirect
206. #66925C2×C4semidirect
207. #66925C2×C4semidirect
375. #2295D11semidirect
460. D44#117semidirect
628. C4×Q8C4×D11semidirect
853. C11#34260semidirect

Maximal subgroups

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

subgroupindex
C2×#106231052
#130715802
#130715722
#130715572
#130715482
#130715252
#130715172
#130714922
#130714842
#130714792
#130714772
#130714452
#130712672
#130712482
#130712212
#130712152
#130711132
#130710542
D11×#3872
#130709762
C42×D442
C11×#22952
#3426011