Finite Group Databasebeta

← #14916964

Subgroups — #14916964

Order 2816.

1990 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic
2#13071780C212yesmaximal, complemented
3#13071768C212yesmaximal
4#13071725C212yesmaximal, complemented
5#13071720C212yesmaximal, complemented
6#13071590C211yesmaximal, characteristic, complemented
7#13071584C211yesmaximal, characteristic, complemented
8#13071558C211yesmaximal, characteristic, complemented
9#13071552C211yesmaximal, characteristic, complemented
10#13071511C211yesmaximal, characteristic, complemented
11#13071507C211yesmaximal, characteristic, complemented
12#13071478C211yesmaximal, characteristic, complemented
13#13071472C211yesmaximal, characteristic, complemented
14#13071413C212yesmaximal, complemented
15#13071401C212yesmaximal, complemented
16#13071392C212yesmaximal, complemented
17#13071388C212yesmaximal, complemented
18#13071266C211yesmaximal, characteristic, complemented
19#13071264C211yesmaximal, characteristic, complemented
20#13071249C211yesmaximal, characteristic, complemented
21#13071013C211yesmaximal, characteristic, complemented
22#13071009C211yesmaximal, characteristic, complemented
23C11×#2318C211yesmaximal, characteristic, complemented
24C2×C4×D4×C11C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C2×#66989C2211yescharacteristic
27C2×C4×C22⋊D11C2211yescharacteristic
28C2×C4×C22⋊D11C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31#10623088C4116yescomplemented
32C2×#66950C2211yescharacteristic
33C2×#66943C2211yescharacteristic
34C2×#66936C2211yescharacteristic
35C2×#66936C2211yescharacteristic
36C2×#66932C2211yescharacteristic
37C2×#66932C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40C11×#388C2212yes—
41C11×#387C2212yes—
42C11×#386C2212yes—
43C11×#385C2212yes—
44C11×#383C2211yescharacteristic
45C11×#382C2211yescharacteristic
46C11×#381C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C4×C11×C22⋊C4C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50#10622833C2212yes—
51#10622826C2212yes—
52#10622825C2211yescharacteristic
53#10622824C2211yescharacteristic
54#10622823C2212yes—
55C4×C22⋊Dic11C2212yes—
56C4×C22⋊Dic11C2212yes—
57C4×C22⋊Dic11C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622603C2212yes—
60#10622600C2212yes—
61#10622594C2212yes—
62#10622591C2212yes—
63#10622591C2212yes—
64C4⋊C4×Dic11C2212yes—
65C4⋊C4×Dic11C2212yes—
66#10622586C2212yes—
67#10622585C2212yes—
68#10622571C2212yes—
69#10622570C2212yes—
70#10622570C2212yes—
71#10622564C2212yes—
72#10622563C2212yes—
73#10622559C2212yes—
74#10622558C2212yes—
75#10622558C2212yes—
76#10622558C2212yes—
77#10622557C2212yes—
78#10622557C2212yes—
79#10622557C2212yes—
80C22⋊C4×Dic11C2212yes—
81C22⋊C4×Dic11C2212yes—
82#10622553C2212yes—
83#10622550C2211yescharacteristic
84#10622549C2211yescharacteristic
85C4×C4⋊Dic11C2212yes—
86C4×Dic11⋊C4C2212yes—
87#10622541C2212yes—
88#10622283C2212yes—
89#10622282C2212yes—
90#10622280C2212yes—
91#10622279C2212yes—
92#10622279C2211yescharacteristic
93#10622279C2211yescharacteristic
94#10622277C2212yes—
95#10622277C2211yescharacteristic
96#10622277C2211yescharacteristic
97#10622268C2212yes—
98#10622268C2212yes—
99#10622267C2212yes—
100#10622267C2212yes—
101#10622267C2212yes—
102#10622266C2212yes—
103#10622266C2212yes—
104#10622266C2212yes—
105#10622264C2211yescharacteristic
106#10622264C2211yescharacteristic
107#10622264C2211yescharacteristic
108#10622264C2211yescharacteristic
109#10622263C2212yes—
110#10622263C2211yescharacteristic
111#10622263C2211yescharacteristic
112#10622262C2212yes—
113#10622262C2211yescharacteristic
114#10622262C2211yescharacteristic
115#10622262C2211yescharacteristic
116#10622262C2211yescharacteristic
117#10622261C2212yes—
118#10622261C2212yes—
119#10622261C2211yescharacteristic
120#10622261C2211yescharacteristic
121#10622260C2212yes—
122#10622259C2212yes—
123#10622259C2212yes—
124C22×D4×C11C2311yescharacteristic
125C23×C4×C11C2312yes—
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C22×C22⋊D11C2311yescharacteristic
129C22×C22⋊D11C2311yescharacteristic
130C23×Dic11C2312yes—
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2311yescharacteristic
134C22×Dic22C2311yescharacteristic
135C4×D4×C11C2×C418yes—
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4C2311yescharacteristic
144C2×C42×C11C2312yes—
145C2×C42×C11C2311yescharacteristic
146C2×C22⋊Dic11C2312yes—
147C2×C22⋊Dic11C2312yes—
148C2×C22⋊Dic11C2312yes—
149C2×C22⋊Dic11C2311yescharacteristic
150C2×C22⋊Dic11C2311yescharacteristic
151C2×C22⋊Dic11C2311yescharacteristic
152C2×C22⋊Dic11C2311yescharacteristic
153C2×C22⋊Dic11C2311yescharacteristic
154C2×C22⋊Dic11C2311yescharacteristic
155#66991C2×C418yes—
156#66989C2×C418yes—
157C4×C22⋊D11C2×C418yescomplemented
158C4×C22⋊D11C2×C418yescomplemented
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2311yescharacteristic
164C2×(C2×D11)⋊C4C2311yescharacteristic
165#66979C2×C418yescomplemented
166#66979C2×C418yescomplemented
167C2×C4⋊Dic11C2312yes—
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173C2×C4⋊Dic11C2311yescharacteristic
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2311yescharacteristic
181C2×Dic11⋊C4C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×Dic11⋊C4C2311yescharacteristic
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198#66950C2×C418yescomplemented
199#66943C2×C418yescomplemented
200#66936C2×C418yescomplemented
201#66936C2×C418yescomplemented
202#66932C2×C418yescomplemented
203#66932C2×C418yescomplemented
204C42×D11C2×C418yescomplemented
205C4×Dic22C2×C418yescomplemented
206C11×#95C2312yes—
207C11×#95C2312yes—
208C11×#95C2312yes—
209C11×#95C2311yescharacteristic
210C11×#95C2311yescharacteristic
211C11×#95C2311yescharacteristic
212C11×#95C2311yescharacteristic
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11⋊#95C2312yes—
216C11⋊#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2311yescharacteristic
224C11⋊#95C2311yescharacteristic
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2311yescharacteristic
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238#34395—111nomaximal, Sylow
239C24×C11C2411yescharacteristic
240C24×C11C2411yescharacteristic
241C23×D11C2411yescharacteristic
242C2×D4×C11—42no—
243C2×D4×C11C22×C414yes—
244C22×C4×C11—42no—
245C22×C4×C11—42no—
246C22×C4×C11—42no—
247C22×C4×C11—42no—
248C22×C4×C11—42no—
249C22×C4×C11C22×C414yes—
250C22×C4×C11C22×C414yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—41no—
261C2×C22⋊D11—41no—
262C2×C22⋊D11—41no—
263C2×C22⋊D11—41no—
264C2×C22⋊D11C22×C414yes—
265C2×C22⋊D11C22×C414yes—
266C22×Dic11—42no—
267C22×Dic11—42no—
268C22×Dic11—42no—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2411yescharacteristic
274C22×Dic11C2411yescharacteristic
275C22×Dic11C2411yescharacteristic
276C22×Dic11C2411yescharacteristic
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2411yescharacteristic
279C22×Dic11C2411yescharacteristic
280C2×C4×D11—41no—
281C2×C4×D11—41no—
282C2×C4×D11—42no—
283C2×C4×D11—42no—
284C2×C4×D11C22×C414yes—
285C2×C4×D11C22×C414yes—
286C2×C4×D11C22×C414yes—
287C2×Dic22—42no—
288C2×Dic22C22×C414yes—
289C11×C4⋊C4—42no—
290C11×C4⋊C4—42no—
291C11×C4⋊C4C22×C414yes—
292C11×C22⋊C4—42no—
293C11×C22⋊C4—42no—
294C11×C22⋊C4—42no—
295C11×C22⋊C4C22×C414yes—
296C11×C22⋊C4C22×C414yes—
297C42×C11—42no—
298C42×C11C22×C414yes—
299C22⋊Dic11—42no—
300C22⋊Dic11—42no—
301C22⋊Dic11—42no—
302C22⋊Dic11C22×C414yes—
303C22⋊Dic11C22×C414yes—
304C22⋊Dic11C22×C414yes—
305C22⋊Dic11C22×C414yes—
306C22⋊Dic11C22×C414yes—
307C22⋊Dic11C22×C414yes—
308(C2×D11)⋊C4—42no—
309(C2×D11)⋊C4—42no—
310(C2×D11)⋊C4—42no—
311(C2×D11)⋊C4—42no—
312(C2×D11)⋊C4C22×C414yes—
313(C2×D11)⋊C4C22×C414yes—
314C4⋊Dic11—42no—
315C4⋊Dic11—42no—
316C4⋊Dic11C22×C414yes—
317C4⋊Dic11C22×C414yes—
318C4⋊Dic11C22×C414yes—
319C4⋊Dic11C22×C414yes—
320C4⋊Dic11C22×C414yes—
321Dic11⋊C4—42no—
322Dic11⋊C4—42no—
323Dic11⋊C4—42no—
324Dic11⋊C4—42no—
325Dic11⋊C4—42no—
326Dic11⋊C4—42no—
327Dic11⋊C4C22×C414yes—
328Dic11⋊C4C22×C414yes—
329Dic11⋊C4C22×C414yes—
330Dic11⋊C4C22×C414yes—
331C4×Dic11—42no—
332C4×Dic11—42no—
333C4×Dic11—42no—
334C4×Dic11—42no—
335C4×Dic11—42no—
336C4×Dic11—42no—
337C4×Dic11—42no—
338C4×Dic11—42no—
339C4×Dic11—42no—
340C4×Dic11C22×C414yes—
341C4×Dic11C22×C414yes—
342C4×Dic11C22×C414yes—
343C4×Dic11C22×C414yes—
344C4×Dic11C22×C414yes—
345C2×#529—111no—
346#2378—112no—
347#2377—112no—
348#2372—112no—
349#2371—112no—
350#2357—111no—
351#2357—111no—
352#2353—111no—
353#2353—111no—
354#2347—111no—
355#2347—111no—
356#2343—111no—
357#2343—111no—
358#2335—112no—
359#2335—112no—
360#2334—112no—
361#2334—112no—
362#2320—111no—
363#2320—111no—
364#2318—111no—
365#2318D1111yescharacteristic, complemented
366#2283—111no—
367#2283—111no—
368C23×C11—21no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—21no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—21no—
375C23×C11—21no—
376C23×C11C23×C412yes—
377C23×C11C23×C412yes—
378C23×C11C2511yescharacteristic
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—21no—
382C22×D11—21no—
383C22×D11C23×C412yes—
384D4×C11—44no—
385C2×C4×C11—22no—
386C2×C4×C11—21no—
387C2×C4×C11—22no—
388C2×C4×C11—21no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11—84no—
406C2×C4×C11C23×C412yes—
407C2×C4×C11C23×C412yes—
408C2×C4×C11C23×C412yes—
409C2×C4×C11C23×C412yes—
410C2×C4×C11C23×C412yes—
411C22⋊D11—44no—
412C22⋊D11—44no—
413C2×Dic11—22no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—21no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—21no—
422C2×Dic11—21no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—84no—
436C2×Dic11C23×C412yes—
437C2×Dic11C23×C412yes—
438C2×Dic11C23×C412yes—
439C2×Dic11C23×C412yes—
440C2×Dic11C23×C412yes—
441C2×Dic11C23×C412yes—
442C2×Dic11C23×C412yes—
443C4×D11—44no—
444C4×D11—44no—
445C4×D11—44no—
446Dic22—44no—
447#529—1116no—
448C2×#126—111no—
449C2×#126—111no—
450C2×#125—111no—
451C2×#124—111no—
452C2×#123—111no—
453C2×#123—111no—
454C2×C22⋊Q8—111no—
455C2×#121—111no—
456C2×C4×Q8—111no—
457C2×C4×D4—111no—
458C2×C4×D4—111no—
459C2×C4×D4C2×D1111yescharacteristic
460C2×#117—111no—
461C2×#117—111no—
462C22×C42—111no—
463#391—112no—
464#391—112no—
465#390—112no—
466#390—112no—
467#389—112no—
468#389—112no—
469#389—112no—
470#389—112no—
471#388—112no—
472#388—112no—
473#388—112no—
474#388—112no—
475#388—112no—
476#388—112no—
477#388—112no—
478#388—112no—
479#388—112no—
480#388—112no—
481#388—112no—
482#388C2×D1112yes—
483#387—112no—
484#387—112no—
485#387—112no—
486#387—112no—
487#387—112no—
488#387—112no—
489#387—112no—
490#387—112no—
491#387—112no—
492#387—112no—
493#387—112no—
494#387C2×D1112yes—
495#386—112no—
496#386—112no—
497#386—112no—
498#386C2×D1112yes—
499#385—112no—
500#385—112no—
501#385—112no—
502#385C2×D1112yes—
503#383—111no—
504#383—111no—
505#383—111no—
506#383—111no—
507#383—111no—
508#383C2×D1111yescharacteristic
509#382—111no—
510#382—111no—
511#382—111no—
512#382—112no—
513#382C2×D1111yescharacteristic
514#381—111no—
515#381—111no—
516#381—111no—
517#381—112no—
518#381C2×D1111yescharacteristic
519#380—111no—
520#380—112no—
521#380—112no—
522#380C2×D1111yescharacteristic
523C4×C4⋊C4—112no—
524C4×C4⋊C4—112no—
525C4×C4⋊C4—112no—
526C4×C4⋊C4—112no—
527C4×C4⋊C4—111no—
528C4×C4⋊C4—111no—
529C4×C4⋊C4—112no—
530C4×C4⋊C4—111no—
531C4×C4⋊C4—111no—
532C4×C22⋊C4—111no—
533C4×C22⋊C4—112no—
534C4×C22⋊C4—112no—
535C4×C22⋊C4—112no—
536C4×C22⋊C4—112no—
537C4×C22⋊C4—112no—
538C4×C22⋊C4—111no—
539C4×C22⋊C4—111no—
540C4×C22⋊C4C2×D1111yescharacteristic
541#376—111no—
542#376—111no—
543#376—112no—
544#376—112no—
545C2×#95—111no—
546C2×#95C2×D1111yescharacteristic
547C22×C11—22no—
548C22×C11—22no—
549C22×C11—22no—
550C22×C11—22no—
551C22×C11—22no—
552C22×C11—22no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11C24×C411yescharacteristic
558C22×C11#58512yes—
559C22×C11#58512yes—
560C22×C11#58511yescharacteristic
561C22×C11#58511yescharacteristic
562C2×D11—22no—
563C2×D11—22no—
564C2×D11—22no—
565C2×D11—42no—
566C2×D11—42no—
567C4×C11—22no—
568C4×C11—22no—
569C4×C11—22no—
570C4×C11—22no—
571C4×C11—22no—
572C4×C11—42no—
573C4×C11—42no—
574C4×C11—42no—
575C4×C11—42no—
576Dic11—22no—
577Dic11—22no—
578Dic11—22no—
579Dic11—22no—
580Dic11—22no—
581Dic11—22no—
582Dic11—22no—
583Dic11—42no—
584Dic11—42no—
585Dic11—42no—
586Dic11—42no—
587C22×Q8—111no—
588C22×D4—111no—
589C22×D4—111no—
590C22×D4C22×D1111yescharacteristic
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4—112no—
595C23×C4C22×D1112yes—
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598#126—118no—
599#126—118no—
600#125—118no—
601#124—118no—
602#123—118no—
603#123—118no—
604C22⋊Q8—118no—
605#121—118no—
606C4×Q8—118no—
607C4×D4—118no—
608C4×D4—118no—
609C4×D4C4×D1118yes—
610#117—118no—
611#117—118no—
612C2×C4⋊C4—111no—
613C2×C4⋊C4—111no—
614C2×C4⋊C4—111no—
615C2×C4⋊C4—111no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—111no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4C22×D1112yes—
630C2×C4⋊C4C22×D1112yes—
631C2×C4⋊C4C22×D1111yescharacteristic
632C2×C22⋊C4—111no—
633C2×C22⋊C4—111no—
634C2×C22⋊C4—111no—
635C2×C22⋊C4—111no—
636C2×C22⋊C4—111no—
637C2×C22⋊C4—111no—
638C2×C22⋊C4—111no—
639C2×C22⋊C4—111no—
640C2×C22⋊C4—112no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—112no—
643C2×C22⋊C4—112no—
644C2×C22⋊C4—112no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4C22×D1112yes—
648C2×C22⋊C4C22×D1112yes—
649C2×C22⋊C4C22×D1112yes—
650C2×C22⋊C4C22×D1111yescharacteristic
651C2×C22⋊C4C22×D1111yescharacteristic
652C2×C42—111no—
653C2×C42—111no—
654C2×C42—111no—
655C2×C42—111no—
656C2×C42—111no—
657C2×C42—118no—
658C2×C42—112no—
659C2×C42—112no—
660C2×C42—112no—
661C2×C42—112no—
662C2×C42—112no—
663C2×C42—112no—
664C2×C42—112no—
665C2×C42—112no—
666C2×C42—112no—
667C2×C42C22×D1112yes—
668C2×C42C22×D1111yescharacteristic
669#95—111no—
670#95—111no—
671#95—112no—
672#95—112no—
673#95—112no—
674#95—112no—
675#95—112no—
676#95—112no—
677#95—112no—
678#95—112no—
679#95—112no—
680#95—111no—
681#95—111no—
682#95—112no—
683#95—112no—
684#95—112no—
685#95—112no—
686#95—112no—
687#95—112no—
688#95—112no—
689#95—112no—
690#95—112no—
691#95—112no—
692#95C22×D1111yescharacteristic
693#95C22×D1111yescharacteristic
694#95C22×D1112yes—
695#95C22×D1112yes—
696#95C22×D1112yes—
697#95C22×D1111yescharacteristic
698#95C22×D1112yes—
699#95C22×D1111yescharacteristic
700#95C22×D1112yes—
701C2×C11—42no—
702C2×C11—42no—
703C2×C11#342811yescharacteristic
704C2×C11#342811yescharacteristic
705C2×C11#342811yescharacteristic
706C2×C11#356612yes—
707C2×C11#356612yes—
708D11—42no—
709C24—111no—
710C24C23×D1111yescharacteristic
711C24C23×D1111yescharacteristic
712C2×Q8—114no—
713C2×Q8—442no—
714C2×D4—42no—
715C2×D4—114no—
716C2×D4—114no—
717C2×D4—441no—
718C2×D4—441no—
719C2×D4—441no—
720C2×D4—441no—
721C2×D4C2×C4×D1114yes—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—111no—
728C22×C4—111no—
729C22×C4—111no—
730C22×C4—111no—
731C22×C4—111no—
732C22×C4—111no—
733C22×C4—111no—
734C22×C4—114no—
735C22×C4—114no—
736C22×C4—114no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—442no—
742C22×C4—441no—
743C22×C4—442no—
744C22×C4—441no—
745C22×C4—442no—
746C22×C4—442no—
747C22×C4—442no—
748C22×C4C2×C4×D1114yes—
749C22×C4C2×C4×D1114yes—
750C22×C4C23×D1112yes—
751C22×C4C23×D1112yes—
752C22×C4C23×D1112yes—
753C22×C4C23×D1112yes—
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757C22×C4C23×D1111yescharacteristic
758C22×C4C23×D1111yescharacteristic
759C4⋊C4—42no—
760C4⋊C4—42no—
761C4⋊C4—114no—
762C4⋊C4—114no—
763C4⋊C4—114no—
764C4⋊C4—114no—
765C4⋊C4—114no—
766C4⋊C4—114no—
767C4⋊C4—114no—
768C4⋊C4—114no—
769C4⋊C4—114no—
770C4⋊C4—442no—
771C4⋊C4—442no—
772C4⋊C4—442no—
773C4⋊C4—442no—
774C4⋊C4—442no—
775C4⋊C4—442no—
776C4⋊C4—442no—
777C4⋊C4—442no—
778C4⋊C4C2×C4×D1114yes—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—114no—
783C22⋊C4—114no—
784C22⋊C4—114no—
785C22⋊C4—114no—
786C22⋊C4—114no—
787C22⋊C4—114no—
788C22⋊C4—114no—
789C22⋊C4—114no—
790C22⋊C4—442no—
791C22⋊C4—442no—
792C22⋊C4—442no—
793C22⋊C4—442no—
794C22⋊C4—442no—
795C22⋊C4—442no—
796C22⋊C4—442no—
797C22⋊C4C2×C4×D1114yes—
798C22⋊C4C2×C4×D1114yes—
799C42—42no—
800C42—114no—
801C42—114no—
802C42—114no—
803C42—114no—
804C42—114no—
805C42—442no—
806C42—442no—
807C42—442no—
808C42—442no—
809C42—442no—
810C42—442no—
811C42—442no—
812C42—442no—
813C42—442no—
814C42C2×C4×D1114yes—
815C11#3439511yescharacteristic, complemented, Sylow
816C23—22no—
817C23—22no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—112no—
825C23—222no—
826C23—222no—
827C23—221no—
828C23—221no—
829C23C22×C4×D1112yes—
830C23C22×C4×D1112yes—
831C23C24×D1111yescharacteristic
832Q8—444no—
833D4—44no—
834D4—444no—
835D4—444no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—84no—
857C2×C4—112no—
858C2×C4—112no—
859C2×C4—112no—
860C2×C4—112no—
861C2×C4—112no—
862C2×C4—112no—
863C2×C4—112no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—221no—
869C2×C4—221no—
870C2×C4—221no—
871C2×C4—221no—
872C2×C4—221no—
873C2×C4—221no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—444no—
887C2×C4—444no—
888C2×C4—444no—
889C2×C4—884no—
890C2×C4C22×C4×D1112yes—
891C2×C4C22×C4×D1112yes—
892C2×C4C22×C4×D1112yes—
893C2×C4C22×C4×D1112yes—
894C2×C4C22×C4×D1112yes—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—222no—
906C22—222no—
907C22—222no—
908C22—442no—
909C22—442no—
910C22C23×C4×D1111yescharacteristic
911C22#1062345312yes—
912C22#1062345512yes—
913C22#1062345511yescharacteristic
914C22#1062345711yescharacteristic
915C4—22no—
916C4—22no—
917C4—22no—
918C4—22no—
919C4—22no—
920C4—42no—
921C4—42no—
922C4—42no—
923C4—42no—
924C4—222no—
925C4—222no—
926C4—222no—
927C4—222no—
928C4—222no—
929C4—222no—
930C4—222no—
931C4—442no—
932C4—442no—
933C4—442no—
934C4—442no—
935C2—42no—
936C2—42no—
937C2—442no—
938C2#1308181411yescharacteristic
939C2#1308181611yescharacteristic
940C2#1308181711yescharacteristic
941C2#1308327512yes—
942C2#1308328312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2318C2
socle, cosocleC23×C11C25
prime radicalC2×#66991C22
hypercenter#2318D11
hypocenterC11#34395
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #13071780C2semidirect
4. #13071725C2semidirect
5. #13071720C2semidirect
6. #13071590C2semidirect
7. #13071584C2semidirect
8. #13071558C2semidirect
9. #13071552C2semidirect
10. #13071511C2semidirect
11. #13071507C2semidirect
12. #13071478C2semidirect
13. #13071472C2semidirect
14. #13071413C2semidirect
15. #13071401C2semidirect
16. #13071392C2semidirect
17. #13071388C2semidirect
18. #13071266C2semidirect
19. #13071264C2semidirect
20. #13071249C2semidirect
21. #13071013C2semidirect
22. #13071009C2semidirect
23. C11×#2318C2semidirect
31. #10623088C4semidirect
157. C4×C22⋊D11C2×C4semidirect
158. C4×C22⋊D11C2×C4semidirect
165. #66979C2×C4semidirect
166. #66979C2×C4semidirect
198. #66950C2×C4semidirect
199. #66943C2×C4semidirect
200. #66936C2×C4semidirect
201. #66936C2×C4semidirect
202. #66932C2×C4semidirect
203. #66932C2×C4semidirect
204. C42×D11C2×C4semidirect
205. C4×Dic22C2×C4semidirect
365. #2318D11semidirect
815. C11#34395semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
#130717802
#130717682
#130717252
#130717202
#130715902
#130715842
#130715582
#130715522
#130715112
#130715072
#130714782
#130714722
#130714132
#130714012
#130713922
#130713882
#130712662
#130712642
#130712492
#130710132
#130710092
C11×#23182
#3439511