Finite Group Databasebeta

← #14927201

Subgroups — #14927201

Order 2816.

1964 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076995C211yesmaximal, characteristic, complemented
2#13076990C211yesmaximal, characteristic, complemented
3#13076957C211yesmaximal, characteristic, complemented
4#13076920C211yesmaximal, characteristic, complemented
5#13074685C212yesmaximal, complemented
6#13074640C212yesmaximal, complemented
7#13073892C212yesmaximal, complemented
8#13073865C212yesmaximal, complemented
9#13073225C211yesmaximal, characteristic, complemented
10#13073176C212yesmaximal, complemented
11#13072958C211yesmaximal, characteristic, complemented
12#13072404C211yesmaximal, characteristic, complemented
13#13072366C212yesmaximal, complemented
14#13072334C211yesmaximal, characteristic, complemented
15#13072270C211yesmaximal, characteristic, complemented
16#13072194C211yesmaximal, characteristic, complemented
17#13072050C211yesmaximal, characteristic
18#13071975C211yesmaximal, characteristic, complemented
19#13071319C212yesmaximal, complemented
20#13071250C212yesmaximal, complemented
21C4×#66983C211yesmaximal, characteristic, complemented
22C42×C22⋊D11C211yesmaximal, characteristic, complemented
23C2×C11×#391C211yesmaximal, characteristic, complemented
24C23×Q8×C11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C2×#67000C2211yescharacteristic
28C2×#67000C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×#66999C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×#66983C2212yes—
33C2×C4×C22⋊D11C2212yes—
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×C4×C22⋊D11C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66943C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×C42×D11C2211yescharacteristic
41C11×#391C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#391C2211yescharacteristic
44C11×#391C2212yes—
45C11×#391C2212yes—
46C11×#391C2211yescharacteristic
47C2×C11×#95C2212yes—
48C2×C11×#95C2212yes—
49#10622844C2212yes—
50#10622844C2212yes—
51#10622844C2212yes—
52#10622843C2211yescharacteristic
53#10622843C2211yescharacteristic
54#10622843C2211yescharacteristic
55#10622843C2211yescharacteristic
56#10622842C2212yes—
57#10622826C2212yes—
58#10622826C2212yes—
59#10622826C2212yes—
60#10622826C2212yes—
61#10622826C2212yes—
62#10622825C2212yes—
63#10622825C2211yescharacteristic
64#10622823C2212yes—
65#10622823C2212yes—
66C4×C22⋊Dic11C2211yescharacteristic
67C4×C22⋊Dic11C2211yescharacteristic
68C4×C22⋊Dic11C2211yescharacteristic
69#10622607C2212yes—
70#10622604C2212yes—
71#10622601C2211yescharacteristic
72#10622600C2211yescharacteristic
73#10622599C2212yes—
74#10622598C2211yescharacteristic
75#10622598C2211yescharacteristic
76#10622597C2212yes—
77#10622590C2211yescharacteristic
78#10622586C2211yescharacteristic
79#10622553C2212yes—
80#10622552C2211yescharacteristic
81C4×(C2×D11)⋊C4C2212yes—
82C4×(C2×D11)⋊C4C2211yescharacteristic
83C4×(C2×D11)⋊C4C2211yescharacteristic
84C4×(C2×D11)⋊C4C2211yescharacteristic
85C4×C4⋊Dic11C2211yescharacteristic
86C4×Dic11⋊C4C2211yescharacteristic
87C4×Dic11⋊C4C2211yescharacteristic
88C4×Dic11⋊C4C2211yescharacteristic
89C42×Dic11C2211yescharacteristic
90#10622541C2211yescharacteristic
91#10622288C2212yes—
92#10622288C2212yes—
93#10622288C2212yes—
94#10622287C2212yes—
95#10622285C2212yes—
96#10622283C2212yes—
97#10622283C2212yes—
98#10622283C2212yes—
99#10622282C2212yes—
100#10622282C2212yes—
101#10622282C2212yes—
102#10622282C2212yes—
103#10622281C2212yes—
104#10622281C2212yes—
105#10622280C2212yes—
106#10622278C2212yes—
107#10622278C2212yes—
108#10622278C2212yes—
109#10622277C2212yes—
110#10622277C2212yes—
111C11⋊#401C2212yes—
112#10622273C2212yes—
113#10622273C2212yes—
114#10622268C2212yes—
115#10622267C2212yes—
116#10622266C2212yes—
117#10622266C2212yes—
118#10622265C2212yes—
119#10622265C2212yes—
120#10622264C2212yes—
121#10622264C2212yes—
122#10622263C2212yes—
123C22×Q8×C11—24no—
124C22×Q8×C11—42no—
125C22×Q8×C11—42no—
126C22×Q8×C11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C22×Q8×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2312yes—
132C23×C4×C11C2312yes—
133C23×C4×C11C2311yescharacteristic
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C22×D44C2311yescharacteristic
137C22×D44C2312yes—
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2312yes—
142C2×C11×C4⋊C4—42no—
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2312yes—
146C2×C42×C11—42no—
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C22⋊Dic11C2311yescharacteristic
152C2×C22⋊Dic11C2311yescharacteristic
153C2×C22⋊Dic11C2311yescharacteristic
154C2×C22⋊Dic11C2312yes—
155#67000—42no—
156#67000—42no—
157#66999—42no—
158#66999—42no—
159#66983—24no—
160#66983—28no—
161C4×C22⋊D11—24no—
162C4×C22⋊D11—24no—
163C4×C22⋊D11—28no—
164C4×C22⋊D11—24no—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2311yescharacteristic
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2311yescharacteristic
171C2×(C2×D11)⋊C4C2311yescharacteristic
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×C4⋊Dic11C2311yescharacteristic
183C2×C4⋊Dic11C2311yescharacteristic
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2311yescharacteristic
186C2×C4⋊Dic11C2312yes—
187C2×C4⋊Dic11C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2311yescharacteristic
190C2×Dic11⋊C4C2311yescharacteristic
191C2×Dic11⋊C4C2311yescharacteristic
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206#66948—42no—
207#66943—42no—
208C4×D44—42no—
209C42×D11—42no—
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11×#95C2312yes—
216C11×#95C2312yes—
217C11×#95C2312yes—
218C11⋊#95C2311yescharacteristic
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2311yescharacteristic
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241#35030—111nomaximal, Sylow
242C24×C11C2411yescharacteristic
243C23×D11C2412yes—
244C23×D11C2411yescharacteristic
245C2×Q8×C11—24no—
246C2×Q8×C11—22no—
247C2×Q8×C11—22no—
248C2×Q8×C11—22no—
249C2×Q8×C11—22no—
250C2×Q8×C11—22no—
251C2×Q8×C11—22no—
252C2×Q8×C11—42no—
253C2×Q8×C11—42no—
254C2×Q8×C11—416no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—24no—
259C22×C4×C11—24no—
260C22×C4×C11—22no—
261C22×C4×C11—41no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11—42no—
265C22×C4×C11—42no—
266C22×C4×C11—42no—
267C22×C4×C11—42no—
268C22×C4×C11#4114yes—
269C22×C4×C11#4114yes—
270C22×C4×C11C2412yes—
271C22×C4×C11C2411yescharacteristic
272C22×C4×C11C2412yes—
273C22×C4×C11C2412yes—
274C22×C4×C11C2412yes—
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C2×C22⋊D11—22no—
281C2×C22⋊D11—22no—
282C2×C22⋊D11—24no—
283C2×C22⋊D11—24no—
284C2×C22⋊D11—24no—
285C2×C22⋊D11#4114yes—
286C22×Dic11C2411yescharacteristic
287C22×Dic11C2411yescharacteristic
288C22×Dic11C2412yes—
289C22×Dic11C2411yescharacteristic
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2412yes—
292C22×Dic11C2412yes—
293C22×Dic11C2411yescharacteristic
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2411yescharacteristic
296C2×D44—24no—
297C2×D44—22no—
298C2×D44—22no—
299C2×D44—22no—
300C2×D44—42no—
301C2×D44—42no—
302C2×C4×D11—22no—
303C2×C4×D11—22no—
304C2×C4×D11—22no—
305C2×C4×D11—24no—
306C2×C4×D11—22no—
307C2×C4×D11—22no—
308C2×C4×D11—22no—
309C2×C4×D11—41no—
310C2×C4×D11—41no—
311C2×C4×D11—41no—
312C2×C4×D11—42no—
313C2×C4×D11—42no—
314C11×C4⋊C4—22no—
315C11×C4⋊C4—22no—
316C11×C4⋊C4—42no—
317C42×C11—22no—
318C42×C11—22no—
319C42×C11—41no—
320C42×C11—41no—
321C22⋊Dic11—22no—
322C22⋊Dic11—22no—
323C22⋊Dic11—24no—
324C22⋊Dic11—22no—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—42no—
334(C2×D11)⋊C4—42no—
335(C2×D11)⋊C4—42no—
336(C2×D11)⋊C4—42no—
337(C2×D11)⋊C4—42no—
338(C2×D11)⋊C4—42no—
339(C2×D11)⋊C4—42no—
340(C2×D11)⋊C4—42no—
341(C2×D11)⋊C4—42no—
342C4⋊Dic11—24no—
343C4⋊Dic11—22no—
344C4⋊Dic11—22no—
345C4⋊Dic11—22no—
346C4⋊Dic11—42no—
347C4⋊Dic11—42no—
348Dic11⋊C4—22no—
349Dic11⋊C4—22no—
350Dic11⋊C4—22no—
351Dic11⋊C4—24no—
352Dic11⋊C4—42no—
353Dic11⋊C4—42no—
354Dic11⋊C4—42no—
355Dic11⋊C4—42no—
356C4×Dic11—22no—
357C4×Dic11—22no—
358C4×Dic11—24no—
359C4×Dic11—22no—
360C4×Dic11—22no—
361C4×Dic11—22no—
362C4×Dic11—22no—
363C4×Dic11—41no—
364C4×Dic11—41no—
365C4×Dic11—41no—
366#2863—111no—
367#2861—111no—
368#2855—111no—
369#2850—111no—
370#2653—112no—
371#2650—112no—
372#2574—112no—
373#2572—112no—
374#2514—111no—
375#2510—112no—
376#2489—111no—
377#2447—111no—
378#2444—112no—
379#2442—111no—
380#2436—111no—
381#2427—111no—
382#2416—111no—
383#2409—111no—
384#2325—112no—
385#2318—112no—
386C4×#121—111no—
387C2×#391D1111yescharacteristic, complemented
388C42×D4—111no—
389C23×C11—21no—
390C23×C11—21no—
391C23×C11—21no—
392C23×C11—21no—
393C23×C11C2×#4112yes—
394C23×C11C2×#4112yes—
395C23×C11C2×#4112yes—
396C23×C11C2511yescharacteristic
397C22×D11—21no—
398C22×D11—21no—
399C22×D11—21no—
400C22×D11—21no—
401C22×D11—21no—
402C22×D11—21no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11C2×#4112yes—
411Q8×C11—48no—
412Q8×C11—44no—
413Q8×C11—44no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—28no—
423C2×C4×C11—21no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—21no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—21no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—44no—
439C2×C4×C11—44no—
440C2×C4×C11—48no—
441C2×C4×C11—84no—
442C2×C4×C11C2×#4112yes—
443C2×C4×C11C2×#4112yes—
444C2×C4×C11C2×#4112yes—
445C2×C4×C11C2×#4112yes—
446C2×C4×C11H(5,𝔽2)12yes—
447C2×C4×C11H(5,𝔽2)12yes—
448C2×C4×C112−1+412yes—
449C22⋊D11—28no—
450C22⋊D11—48no—
451C2×Dic11—21no—
452C2×Dic11—21no—
453C2×Dic11—22no—
454C2×Dic11—21no—
455C2×Dic11—21no—
456C2×Dic11—22no—
457C2×Dic11—21no—
458C2×Dic11—21no—
459C2×Dic11—21no—
460C2×Dic11—22no—
461C2×Dic11—21no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—21no—
465C2×Dic11—21no—
466C2×Dic11—21no—
467C2×Dic11—21no—
468C2×Dic11—21no—
469C2×Dic11—22no—
470C2×Dic11—21no—
471C2×Dic11—22no—
472C2×Dic11—21no—
473C2×Dic11—21no—
474C2×Dic11—22no—
475C2×Dic11—21no—
476C2×Dic11—21no—
477C2×Dic11—21no—
478C2×Dic11—22no—
479C2×Dic11—21no—
480C2×Dic11C2×#4112yes—
481D44—44no—
482D44—84no—
483C4×D11—44no—
484C4×D11—44no—
485C4×D11—44no—
486C4×D11—84no—
487C23×Q8C2×D1111yescharacteristic
488C2×#125—111no—
489C2×#124—111no—
490C2×#124—111no—
491C2×C22⋊Q8—111no—
492C2×C22⋊Q8—111no—
493C2×#121—112no—
494C2×#121—111no—
495C2×#121—111no—
496C2×C4×D4—112no—
497C2×C4×D4—111no—
498C2×C4×D4—111no—
499C2×C4×D4—111no—
500C2×C4×D4—111no—
501C22×C4⋊C4C2×D1111yescharacteristic
502C22×C42—111no—
503C22×C42C2×D1111yescharacteristic
504#401—112no—
505#400—112no—
506#400—112no—
507#400—112no—
508#398—112no—
509#397—112no—
510#397—112no—
511#397—112no—
512#397—112no—
513#396—112no—
514#395—112no—
515#394—112no—
516#394—112no—
517#393—112no—
518#393—112no—
519#393—112no—
520#391—111no—
521#391—111no—
522#391—111no—
523#391—111no—
524#391C2×D1112yes—
525#391C2×D1111yescharacteristic
526#391C2×D1111yescharacteristic
527#391C2×D1112yes—
528#391C2×D1111yescharacteristic
529#391C2×D1111yescharacteristic
530#390—111no—
531#390—111no—
532#389—111no—
533#389—111no—
534#389—111no—
535#389—111no—
536#388—112no—
537#388—112no—
538#388—112no—
539#388—112no—
540#388—112no—
541#388—112no—
542#388—112no—
543#388—112no—
544#387—112no—
545#387—112no—
546#387—112no—
547#387—112no—
548#387—112no—
549#387—112no—
550#386—112no—
551#386—112no—
552#386—112no—
553#386—112no—
554#386—112no—
555#386—112no—
556#386—112no—
557#386—112no—
558#385—112no—
559#385—112no—
560#385—112no—
561#385—112no—
562#383—112no—
563#383—112no—
564#382—111no—
565#382—112no—
566#381—112no—
567#381—112no—
568#380—112no—
569#380—111no—
570#380—111no—
571#380—112no—
572C4×C4⋊C4—111no—
573C4×C4⋊C4—111no—
574C4×C4⋊C4—111no—
575C4×C4⋊C4—111no—
576C4×C22⋊C4—111no—
577C4×C22⋊C4—111no—
578C4×C22⋊C4—111no—
579C4×C22⋊C4—111no—
580C4×C22⋊C4—112no—
581C4×C22⋊C4—111no—
582C4×C22⋊C4—111no—
583C2×#95C2×D1112yes—
584C2×#95C2×D1112yes—
585C43—111no—
586C22×C11—22no—
587C22×C11—22no—
588C22×C11—22no—
589C22×C11—22no—
590C22×C11—22no—
591C22×C11—22no—
592C22×C11#52914yes—
593C22×C11C22×#4111yescharacteristic
594C22×C11C22×#4111yescharacteristic
595C22×C11C22×#4111yescharacteristic
596C22×C11C2×H(5,𝔽2)11yescharacteristic
597C22×C11C2×H(5,𝔽2)11yescharacteristic
598C22×C11C2×2−1+411yescharacteristic
599C22×C11#58511yescharacteristic
600C2×D11—22no—
601C2×D11—22no—
602C2×D11—22no—
603C2×D11—41no—
604C2×D11—41no—
605C2×D11—41no—
606C2×D11—41no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C4×C11—22no—
615C4×C11—22no—
616C4×C11—22no—
617C4×C11—22no—
618C4×C11—42no—
619C4×C11—42no—
620C4×C11—42no—
621C4×C11—42no—
622C4×C11—41no—
623C4×C11#53814yes—
624Dic11—22no—
625Dic11—42no—
626Dic11—41no—
627Dic11—41no—
628Dic11—41no—
629Dic11—42no—
630Dic11—41no—
631Dic11—42no—
632Dic11—41no—
633Dic11—41no—
634C22×Q8—24no—
635C22×Q8—42no—
636C22×Q8—42no—
637C22×Q8C22×D1111yescharacteristic
638C22×Q8C22×D1111yescharacteristic
639C22×Q8C22×D1112yes—
640C22×D4—111no—
641C22×D4—112no—
642C22×D4—111no—
643C22×D4—112no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—112no—
647C23×C4—111no—
648C23×C4C22×D1111yescharacteristic
649C23×C4C22×D1111yescharacteristic
650C23×C4C22×D1112yes—
651C23×C4C22×D1112yes—
652C23×C4C22×D1111yescharacteristic
653#125—442no—
654#124—442no—
655#124—442no—
656C22⋊Q8—442no—
657C22⋊Q8—442no—
658#121—228no—
659#121—224no—
660#121—442no—
661C4×D4—224no—
662C4×D4—224no—
663C4×D4—224no—
664C4×D4—228no—
665C4×D4—442no—
666C2×C4⋊C4—42no—
667C2×C4⋊C4—111no—
668C2×C4⋊C4—111no—
669C2×C4⋊C4—111no—
670C2×C4⋊C4—111no—
671C2×C4⋊C4—112no—
672C2×C4⋊C4—111no—
673C2×C4⋊C4—112no—
674C2×C4⋊C4—111no—
675C2×C4⋊C4—112no—
676C2×C4⋊C4—112no—
677C2×C4⋊C4—112no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4—112no—
681C2×C4⋊C4C22×D1111yescharacteristic
682C2×C4⋊C4C22×D1111yescharacteristic
683C2×C4⋊C4C22×D1112yes—
684C2×C22⋊C4—111no—
685C2×C22⋊C4—111no—
686C2×C22⋊C4—111no—
687C2×C22⋊C4—112no—
688C2×C22⋊C4—111no—
689C2×C22⋊C4—111no—
690C2×C22⋊C4—111no—
691C2×C22⋊C4—112no—
692C2×C22⋊C4—112no—
693C2×C22⋊C4—112no—
694C2×C22⋊C4—112no—
695C2×C22⋊C4—112no—
696C2×C22⋊C4—112no—
697C2×C22⋊C4—112no—
698C2×C22⋊C4—112no—
699C2×C22⋊C4—112no—
700C2×C22⋊C4—112no—
701C2×C22⋊C4—112no—
702C2×C22⋊C4—112no—
703C2×C22⋊C4—112no—
704C2×C22⋊C4—112no—
705C2×C42—42no—
706C2×C42—111no—
707C2×C42—111no—
708C2×C42—111no—
709C2×C42—112no—
710C2×C42—111no—
711C2×C42—111no—
712C2×C42—111no—
713C2×C42—111no—
714C2×C42—111no—
715C2×C42—111no—
716C2×C42—442no—
717C2×C42C22×D1111yescharacteristic
718C2×C42C22×D1111yescharacteristic
719C2×C42C22×D1111yescharacteristic
720C2×C42C22×D1111yescharacteristic
721#95—111no—
722#95—111no—
723#95—111no—
724#95—111no—
725#95—111no—
726#95—111no—
727#95—112no—
728#95—112no—
729#95—112no—
730#95—112no—
731#95—112no—
732#95—112no—
733#95—112no—
734#95—112no—
735#95—112no—
736#95—112no—
737#95—112no—
738#95—112no—
739#95—112no—
740#95—112no—
741#95—112no—
742#95—112no—
743#95—112no—
744#95C22×D1112yes—
745#95C22×D1112yes—
746#95C22×D1112yes—
747#95C22×D1112yes—
748#95C22×D1112yes—
749#95C22×D1112yes—
750#95C22×D1112yes—
751#95C22×D1112yes—
752C2×C11—24no—
753C2×C11C2×#52911yescharacteristic
754C2×C11C2×#53811yescharacteristic
755C2×C11#346111yescharacteristic
756C2×C11#350511yescharacteristic
757C2×C11#351111yescharacteristic
758C2×C11#351411yescharacteristic
759C2×C11#352011yescharacteristic
760D11—42no—
761D11—82no—
762C24—111no—
763C24—112no—
764C24C23×D1111yescharacteristic
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—416no—
775C2×D4—114no—
776C2×D4—224no—
777C2×D4—222no—
778C2×D4—222no—
779C2×D4—224no—
780C2×D4—224no—
781C2×D4—224no—
782C2×D4—222no—
783C2×D4—222no—
784C2×D4—222no—
785C2×D4—442no—
786C2×D4—442no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—24no—
790C22×C4—22no—
791C22×C4—24no—
792C22×C4—22no—
793C22×C4—41no—
794C22×C4—41no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—41no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—111no—
801C22×C4—111no—
802C22×C4—111no—
803C22×C4—112no—
804C22×C4—111no—
805C22×C4—111no—
806C22×C4—112no—
807C22×C4—112no—
808C22×C4—111no—
809C22×C4—111no—
810C22×C4—222no—
811C22×C4—222no—
812C22×C4—222no—
813C22×C4—222no—
814C22×C4—222no—
815C22×C4—222no—
816C22×C4—224no—
817C22×C4—441no—
818C22×C4—441no—
819C22×C4—441no—
820C22×C4—442no—
821C22×C4—442no—
822C22×C4#433914yes—
823C22×C4#434314yes—
824C22×C4C23×D1111yescharacteristic
825C22×C4C23×D1112yes—
826C22×C4C23×D1112yes—
827C22×C4C23×D1112yes—
828C22×C4C23×D1112yes—
829C22×C4C23×D1111yescharacteristic
830C22×C4C23×D1111yescharacteristic
831C22×C4C23×D1111yescharacteristic
832C22×C4C23×D1111yescharacteristic
833C22×C4C23×D1111yescharacteristic
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—42no—
837C4⋊C4—222no—
838C4⋊C4—224no—
839C4⋊C4—222no—
840C4⋊C4—222no—
841C4⋊C4—222no—
842C4⋊C4—222no—
843C4⋊C4—222no—
844C4⋊C4—224no—
845C4⋊C4—442no—
846C4⋊C4—442no—
847C4⋊C4—442no—
848C4⋊C4—442no—
849C4⋊C4—442no—
850C4⋊C4—442no—
851C22⋊C4—224no—
852C22⋊C4—222no—
853C22⋊C4—224no—
854C22⋊C4—222no—
855C22⋊C4—222no—
856C22⋊C4—224no—
857C22⋊C4—222no—
858C22⋊C4—222no—
859C22⋊C4—224no—
860C22⋊C4—222no—
861C22⋊C4—224no—
862C22⋊C4—224no—
863C22⋊C4—442no—
864C22⋊C4—442no—
865C22⋊C4—442no—
866C22⋊C4—442no—
867C22⋊C4—442no—
868C22⋊C4—442no—
869C22⋊C4—442no—
870C22⋊C4—442no—
871C22⋊C4—442no—
872C42—22no—
873C42—22no—
874C42—41no—
875C42—41no—
876C42—222no—
877C42—222no—
878C42—222no—
879C42—222no—
880C42—222no—
881C42—224no—
882C42—222no—
883C42—441no—
884C42—441no—
885C42—441no—
886C11#3503011yescharacteristic, complemented, Sylow
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—112no—
892C23—221no—
893C23—221no—
894C23—221no—
895C23—221no—
896C23—221no—
897C23—221no—
898C23—222no—
899C23—222no—
900C23—222no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23C2×#433912yes—
906C23C2×#434312yes—
907C23#41×D1112yes—
908C23C24×D1111yescharacteristic
909Q8—48no—
910Q8—44no—
911Q8—44no—
912D4—228no—
913D4—448no—
914D4—444no—
915D4—884no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—28no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—44no—
941C2×C4—44no—
942C2×C4—48no—
943C2×C4—84no—
944C2×C4—112no—
945C2×C4—221no—
946C2×C4—221no—
947C2×C4—221no—
948C2×C4—221no—
949C2×C4—222no—
950C2×C4—221no—
951C2×C4—221no—
952C2×C4—221no—
953C2×C4—221no—
954C2×C4—221no—
955C2×C4—222no—
956C2×C4—221no—
957C2×C4—222no—
958C2×C4—221no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—221no—
962C2×C4—222no—
963C2×C4—221no—
964C2×C4—221no—
965C2×C4—222no—
966C2×C4—221no—
967C2×C4—221no—
968C2×C4—221no—
969C2×C4—222no—
970C2×C4—221no—
971C2×C4—221no—
972C2×C4—221no—
973C2×C4—222no—
974C2×C4—444no—
975C2×C4—444no—
976C2×C4—444no—
977C2×C4—884no—
978C2×C4C2×#433912yes—
979C2×C4C2×#433912yes—
980C2×C4#6703712yes—
981C2×C4#6703712yes—
982C2×C4C2×#434312yes—
983C2×C4C2×#434312yes—
984C2×C4#6704012yes—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—22no—
991C22—222no—
992C22—222no—
993C22—222no—
994C22—441no—
995C22—441no—
996C22—441no—
997C22—441no—
998C22—442no—
999C22—442no—
1000C22—442no—
1001C22—442no—
1002C22—442no—
1003C22—442no—
1004C22—442no—
1005C22#1062311114yes—
1006C22C22×#433911yescharacteristic
1007C22C2×#6703711yescharacteristic
1008C22C2×#6703711yescharacteristic
1009C22C22×#434311yescharacteristic
1010C22C2×#6704011yescharacteristic
1011C22C2×#41×D1111yescharacteristic
1012C22#1062345311yescharacteristic
1013C4—22no—
1014C4—22no—
1015C4—22no—
1016C4—22no—
1017C4—41no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—222no—
1023C4—442no—
1024C4—441no—
1025C4—441no—
1026C4—442no—
1027C4—441no—
1028C4—441no—
1029C4—442no—
1030C4—441no—
1031C4—441no—
1032C4#1062302514yes—
1033C2—24no—
1034C2—442no—
1035C2—882no—
1036C2C2×#1062311111yescharacteristic
1037C2C2×#1062302511yescharacteristic
1038C2#1308204911yescharacteristic
1039C2#1308245711yescharacteristic
1040C2#1308252911yescharacteristic
1041C2#1308257111yescharacteristic
1042C2#1308265911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#391C2
prime radical#13072050C2
hypercenterC2×#391D11
hypocenterC11#35030
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. #13076995C2semidirect
2. #13076990C2semidirect
3. #13076957C2semidirect
4. #13076920C2semidirect
5. #13074685C2semidirect
6. #13074640C2semidirect
7. #13073892C2semidirect
8. #13073865C2semidirect
9. #13073225C2semidirect
10. #13073176C2semidirect
11. #13072958C2semidirect
12. #13072404C2semidirect
13. #13072366C2semidirect
14. #13072334C2semidirect
15. #13072270C2semidirect
16. #13072194C2semidirect
18. #13071975C2semidirect
19. #13071319C2semidirect
20. #13071250C2semidirect
21. C4×#66983C2semidirect
22. C42×C22⋊D11C2semidirect
23. C2×C11×#391C2semidirect
387. C2×#391D11semidirect
886. C11#35030semidirect

Maximal subgroups

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

subgroupindex
#130769952
#130769902
#130769572
#130769202
#130746852
#130746402
#130738922
#130738652
#130732252
#130731762
#130729582
#130724042
#130723662
#130723342
#130722702
#130721942
#130720502
#130719752
#130713192
#130712502
C4×#669832
C42×C22⋊D112
C2×C11×#3912
#3503011