Finite Group Databasebeta

← #14960476

Subgroups — #14960476

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C2×#10623069C211yesmaximal, characteristic
3#13076686C211yesmaximal, characteristic, complemented
4#13076685C211yesmaximal, characteristic, complemented
5#13076681C211yesmaximal, characteristic, complemented
6#13076679C211yesmaximal, characteristic, complemented
7#13076676C211yesmaximal, characteristic, complemented
8#13076673C211yesmaximal, characteristic, complemented
9#13076672C211yesmaximal, characteristic, complemented
10#13076670C211yesmaximal, characteristic, complemented
11#13076654C212yesmaximal, complemented
12#13076648C212yesmaximal
13#13076635C212yesmaximal, complemented
14#13076633C212yesmaximal, complemented
15#13071910C212yesmaximal, complemented
16#13071903C212yesmaximal, complemented
17#13071892C212yesmaximal, complemented
18#13071890C212yesmaximal, complemented
19#13071876C211yesmaximal, characteristic, complemented
20#13071875C211yesmaximal, characteristic, complemented
21#13071873C211yesmaximal, characteristic, complemented
22#13071010C211yesmaximal, characteristic, complemented
23C11×#2395C211yesmaximal, characteristic, complemented
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C2×#66992C2211yescharacteristic
27C2×#66988C2211yescharacteristic
28C2×C4×C22⋊D11C2211yescharacteristic
29C2×C4×C22⋊D11C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33#10623069—28no—
34#10623048—28no—
35C2×#66951C2211yescharacteristic
36C2×#66943C2211yescharacteristic
37C2×#66943C2211yescharacteristic
38C2×#66942C2211yescharacteristic
39C2×#66941C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66939C2211yescharacteristic
42C2×#66938C2211yescharacteristic
43C2×#66932C2211yescharacteristic
44C2×#66931C2211yescharacteristic
45C2×#66931C2212yes—
46C2×#66931C2212yes—
47C2×#66925C2211yescharacteristic
48C2×C4×Dic22C2212yes—
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2212yes—
51C11×#400C2211yescharacteristic
52C11×#399C2211yescharacteristic
53C11×#398C2211yescharacteristic
54C11×#397C2212yes—
55C11×#397C2211yescharacteristic
56C11×#394C2212yes—
57C4×C11×C4⋊C4C2212yes—
58C4×C11×C22⋊C4C2211yescharacteristic
59C4×C11×C22⋊C4C2212yes—
60#10622835C2212yes—
61C4×C22⋊Dic11C2211yescharacteristic
62C4×C22⋊Dic11C2212yes—
63#10622607C2212yes—
64#10622606C2211yescharacteristic
65#10622605C2211yescharacteristic
66#10622605C2212yes—
67#10622599C2211yescharacteristic
68#10622597C2212yes—
69#10622597C2212yes—
70#10622596C2211yescharacteristic
71#10622595C2211yescharacteristic
72#10622593C2211yescharacteristic
73#10622593C2212yes—
74#10622592C2212yes—
75#10622592C2212yes—
76#10622592C2212yes—
77#10622574C2212yes—
78#10622574C2212yes—
79#10622572C2212yes—
80#10622572C2212yes—
81#10622566C2211yescharacteristic
82#10622566C2212yes—
83#10622565C2212yes—
84#10622565C2212yes—
85#10622565C2212yes—
86#10622562C2211yescharacteristic
87#10622562C2212yes—
88#10622561C2212yes—
89#10622561C2212yes—
90#10622560C2212yes—
91#10622560C2212yes—
92#10622556C2212yes—
93#10622555C2212yes—
94C4×(C2×D11)⋊C4C2212yes—
95C4×(C2×D11)⋊C4C2212yes—
96C4×C4⋊Dic11C2212yes—
97#10622545C2212yes—
98C4×Dic11⋊C4C2212yes—
99C4×Dic11⋊C4C2212yes—
100C4×Dic11⋊C4C2212yes—
101#10622290C2211yescharacteristic
102#10622289C2212yes—
103#10622288C2212yes—
104#10622287C2211yescharacteristic
105#10622286C2212yes—
106#10622286C2212yes—
107#10622274C2211yescharacteristic
108#10622274C2212yes—
109#10622273C2212yes—
110#10622273C2212yes—
111#10622272C2211yescharacteristic
112#10622271C2212yes—
113#10622271C2212yes—
114#10622270C2212yes—
115#10622270C2212yes—
116#10622270C2212yes—
117#10622270C2212yes—
118#10622269C2212yes—
119#10622269C2212yes—
120#10622269C2212yes—
121#10622264C2211yescharacteristic
122#10622264C2211yescharacteristic
123#10622263C2211yescharacteristic
124#10622263C2211yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C22×C22⋊D11C2311yescharacteristic
129C22×C22⋊D11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×Dic22C2311yescharacteristic
134C22×Dic22C2312yes—
135C22×Dic22C2312yes—
136C4×D4×C11—24no—
137C11×#117—24no—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2311yescharacteristic
145C2×C11×C22⋊C4C2311yescharacteristic
146C2×C11×C22⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C42×C11C2312yes—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2312yes—
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2311yescharacteristic
154C2×C22⋊Dic11C2311yescharacteristic
155C2×C22⋊Dic11C2311yescharacteristic
156C2×C22⋊Dic11C2311yescharacteristic
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160#66992—24no—
161#66988—24no—
162C4×C22⋊D11—24no—
163C4×C22⋊D11—24no—
164C2×(C2×D11)⋊C4C2311yescharacteristic
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2311yescharacteristic
167C2×(C2×D11)⋊C4C2311yescharacteristic
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172#66979—24no—
173#66979—24no—
174C2×C4⋊Dic11C2312yes—
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2312yes—
182C2×C4⋊Dic11C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2311yescharacteristic
188C2×Dic11⋊C4C2311yescharacteristic
189C2×Dic11⋊C4C2311yescharacteristic
190C2×Dic11⋊C4C2311yescharacteristic
191C2×Dic11⋊C4C2311yescharacteristic
192C2×Dic11⋊C4C2311yescharacteristic
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×C4×Dic11D418yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207#66951—24no—
208#66943—24no—
209#66943—24no—
210#66942—24no—
211#66941—24no—
212#66941—24no—
213#66939—24no—
214#66938—24no—
215#66932—24no—
216#66931—28no—
217#66931—28no—
218#66931—24no—
219#66925—24no—
220C4×Dic22—28no—
221C4×Dic22—28no—
222C4×Dic22—24no—
223C11×#95C2311yescharacteristic
224C11×#95C2311yescharacteristic
225C11×#95C2312yes—
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11⋊#95C2311yescharacteristic
230C11⋊#95C2311yescharacteristic
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249#36699—111nomaximal, Sylow
250C24×C11C2411yescharacteristic
251C24×C11C2411yescharacteristic
252C23×D11C2411yescharacteristic
253C2×D4×C11—22no—
254C2×D4×C11—41no—
255C2×D4×C11—41no—
256C22×C4×C11—24no—
257C22×C4×C11—22no—
258C22×C4×C11—24no—
259C22×C4×C11C2×D414yes—
260C22×C4×C11C2412yes—
261C22×C4×C11C2412yes—
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2412yes—
265C22×C4×C11C2412yes—
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2411yescharacteristic
269C2×C22⋊D11—22no—
270C2×C22⋊D11—22no—
271C2×C22⋊D11—41no—
272C2×C22⋊D11—41no—
273C2×C22⋊D11—42no—
274C22×Dic11—42no—
275C22×Dic11—41no—
276C22×Dic11—41no—
277C22×Dic11C2×D414yes—
278C22×Dic11C2×D414yes—
279C22×Dic11C2412yes—
280C22×Dic11C2412yes—
281C22×Dic11C2411yescharacteristic
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2412yes—
284C22×Dic11C2412yes—
285C22×Dic11C2411yescharacteristic
286C22×Dic11C2411yescharacteristic
287C22×Dic11C2411yescharacteristic
288C22×Dic11C2411yescharacteristic
289C22×Dic11C2411yescharacteristic
290C2×C4×D11—22no—
291C2×C4×D11—24no—
292C2×Dic22—22no—
293C2×Dic22—24no—
294C2×Dic22—24no—
295C2×Dic22—42no—
296C2×Dic22—42no—
297C2×Dic22—42no—
298C2×Dic22—42no—
299C2×Dic22—42no—
300C11×C4⋊C4—22no—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—22no—
303C11×C4⋊C4—42no—
304C11×C4⋊C4—42no—
305C11×C22⋊C4—24no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—42no—
309C11×C22⋊C4—42no—
310C11×C22⋊C4—42no—
311C42×C11—24no—
312C42×C11—22no—
313C42×C11—24no—
314C22⋊Dic11—22no—
315C22⋊Dic11—22no—
316C22⋊Dic11—22no—
317C22⋊Dic11—24no—
318C22⋊Dic11—22no—
319C22⋊Dic11—42no—
320C22⋊Dic11—42no—
321C22⋊Dic11—42no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—42no—
327(C2×D11)⋊C4—42no—
328(C2×D11)⋊C4—42no—
329(C2×D11)⋊C4—42no—
330C4⋊Dic11—24no—
331C4⋊Dic11—24no—
332C4⋊Dic11—22no—
333C4⋊Dic11—22no—
334C4⋊Dic11—22no—
335C4⋊Dic11—22no—
336C4⋊Dic11—22no—
337C4⋊Dic11—42no—
338C4⋊Dic11—42no—
339Dic11⋊C4—24no—
340Dic11⋊C4—24no—
341Dic11⋊C4—24no—
342Dic11⋊C4—24no—
343Dic11⋊C4—22no—
344Dic11⋊C4—22no—
345Dic11⋊C4—22no—
346Dic11⋊C4—22no—
347Dic11⋊C4—22no—
348Dic11⋊C4—22no—
349Dic11⋊C4—42no—
350Dic11⋊C4—42no—
351Dic11⋊C4—42no—
352Dic11⋊C4—42no—
353Dic11⋊C4—42no—
354Dic11⋊C4—42no—
355C4×Dic11—24no—
356C4×Dic11—22no—
357C4×Dic11—24no—
358C4×Dic11C2×D414yes—
359C4×Dic11C2×D414yes—
360C4×Dic11C2×D414yes—
361C4×Dic11C2×D414yes—
362C2×#533—111no—
363C2×#529—111no—
364#2822—111no—
365#2822—111no—
366#2821—111no—
367#2821—111no—
368#2821—111no—
369#2821—111no—
370#2820—111no—
371#2820—111no—
372#2817—112no—
373#2816—112no—
374#2814—112no—
375#2814—112no—
376#2399—112no—
377#2398—112no—
378#2396—112no—
379#2396—112no—
380#2395—111no—
381#2395—111no—
382#2395—111no—
383#2395D1111yescharacteristic, complemented
384#2283—111no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—22no—
391C23×C11—21no—
392C23×C11—22no—
393C23×C11—21no—
394C23×C11C22×D412yes—
395C23×C11C2511yescharacteristic
396C22×D11—21no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—21no—
400C22×D11—21no—
401D4×C11—44no—
402C2×C4×C11—22no—
403C2×C4×C11—28no—
404C2×C4×C11—21no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—21no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—21no—
423C2×C4×C11—44no—
424C2×C4×C11C22×D412yes—
425C2×C4×C11C22×D412yes—
426C2×C4×C112−1+414yes—
427C22⋊D11—44no—
428C22⋊D11—44no—
429C2×Dic11—21no—
430C2×Dic11—21no—
431C2×Dic11—22no—
432C2×Dic11—21no—
433C2×Dic11—21no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—21no—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—21no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—21no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—44no—
455C2×Dic11—44no—
456C2×Dic11C22×D412yes—
457C2×Dic11C22×D412yes—
458C2×Dic11C22×D412yes—
459C2×Dic11C22×D412yes—
460C4×D11—44no—
461Dic22—48no—
462Dic22—48no—
463Dic22—44no—
464#533—228no—
465C2×C4⋊Q8—111no—
466C2×C4⋊Q8—111no—
467#529—228no—
468C2×#126—111no—
469C2×#126—111no—
470C2×#125—111no—
471C2×#125—111no—
472C2×#125—111no—
473C2×#124—111no—
474C2×#123—111no—
475C2×#123—111no—
476C2×C22⋊Q8—112no—
477C2×C22⋊Q8—111no—
478C2×C22⋊Q8—112no—
479C2×#121—111no—
480C2×C4×Q8—112no—
481C2×C4×Q8—112no—
482C2×C4×Q8—111no—
483C2×C4×D4—111no—
484C2×C4×D4—111no—
485C2×C4×D4C2×D1111yescharacteristic
486C2×#117—111no—
487C2×#117—111no—
488C2×#117—111no—
489C2×#117C2×D1111yescharacteristic
490C22×C42—111no—
491#400—111no—
492#400—111no—
493#400—112no—
494#400—112no—
495#400—112no—
496#400—112no—
497#400—111no—
498#400C2×D1111yescharacteristic
499#399—112no—
500#399—111no—
501#399—112no—
502#399—111no—
503#399—111no—
504#399C2×D1111yescharacteristic
505#398—112no—
506#398—111no—
507#398—111no—
508#398—112no—
509#398—112no—
510#398—112no—
511#398—111no—
512#398—112no—
513#398—112no—
514#398—112no—
515#398—112no—
516#398C2×D1111yescharacteristic
517#397—111no—
518#397—112no—
519#397—112no—
520#397—112no—
521#397—111no—
522#397—112no—
523#397—111no—
524#397—112no—
525#397C2×D1112yes—
526#397C2×D1111yescharacteristic
527#396—112no—
528#396—112no—
529#396—112no—
530#396—112no—
531#395—112no—
532#395—112no—
533#395—112no—
534#395—112no—
535#395—112no—
536#395—112no—
537#394—112no—
538#394—112no—
539#394—112no—
540#394—112no—
541#394—112no—
542#394C2×D1112yes—
543#393—112no—
544#393—112no—
545#393—112no—
546#393—112no—
547#383—111no—
548#383—111no—
549#382—111no—
550#382—111no—
551#381—112no—
552#380—112no—
553C4×C4⋊C4—112no—
554C4×C4⋊C4—112no—
555C4×C4⋊C4—112no—
556C4×C4⋊C4—112no—
557C4×C4⋊C4C2×D1112yes—
558C4×C22⋊C4—111no—
559C4×C22⋊C4—112no—
560C4×C22⋊C4—112no—
561C4×C22⋊C4—112no—
562C4×C22⋊C4C2×D1111yescharacteristic
563C4×C22⋊C4C2×D1112yes—
564#376—112no—
565C22×C11—22no—
566C22×C11—22no—
567C22×C11—22no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—41no—
571C22×C11—41no—
572C22×C11—41no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11C23×D411yescharacteristic
576C22×C11C2×2−1+412yes—
577C22×C11#58512yes—
578C22×C11#58511yescharacteristic
579C22×C11#58511yescharacteristic
580C2×D11—41no—
581C2×D11—41no—
582C2×D11—41no—
583C2×D11—42no—
584C2×D11—42no—
585C4×C11—22no—
586C4×C11—41no—
587C4×C11—41no—
588C4×C11—42no—
589C4×C11—41no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11#53614yes—
594Dic11—22no—
595Dic11—22no—
596Dic11—22no—
597Dic11—22no—
598Dic11—41no—
599Dic11—42no—
600Dic11—41no—
601Dic11—42no—
602Dic11—41no—
603Dic11—42no—
604Dic11—42no—
605C22×Q8—111no—
606C22×Q8—112no—
607C22×Q8—112no—
608C22×D4—111no—
609C22×D4—111no—
610C22×D4C22×D1111yescharacteristic
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—111no—
614C23×C4C22×D1111yescharacteristic
615C23×C4C22×D1111yescharacteristic
616C4⋊Q8—224no—
617C4⋊Q8—224no—
618#126—224no—
619#126—224no—
620#125—224no—
621#125—224no—
622#125—224no—
623#124—224no—
624#123—224no—
625#123—224no—
626C22⋊Q8—224no—
627C22⋊Q8—228no—
628C22⋊Q8—228no—
629#121—224no—
630C4×Q8—224no—
631C4×Q8—228no—
632C4×Q8—228no—
633C4×D4—24no—
634C4×D4—224no—
635C4×D4—224no—
636#117—24no—
637#117—224no—
638#117—224no—
639#117—224no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—111no—
643C2×C4⋊C4—111no—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—111no—
647C2×C4⋊C4—111no—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—112no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—111no—
656C2×C4⋊C4—111no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—112no—
662C2×C4⋊C4—112no—
663C2×C4⋊C4—112no—
664C2×C4⋊C4—112no—
665C2×C4⋊C4C22×D1111yescharacteristic
666C2×C4⋊C4C22×D1111yescharacteristic
667C2×C4⋊C4C22×D1111yescharacteristic
668C2×C4⋊C4C22×D1112yes—
669C2×C4⋊C4C22×D1112yes—
670C2×C22⋊C4—111no—
671C2×C22⋊C4—112no—
672C2×C22⋊C4—111no—
673C2×C22⋊C4—111no—
674C2×C22⋊C4—111no—
675C2×C22⋊C4—111no—
676C2×C22⋊C4—111no—
677C2×C22⋊C4—111no—
678C2×C22⋊C4—111no—
679C2×C22⋊C4—112no—
680C2×C22⋊C4—112no—
681C2×C22⋊C4—112no—
682C2×C22⋊C4—112no—
683C2×C22⋊C4—112no—
684C2×C22⋊C4—112no—
685C2×C22⋊C4—112no—
686C2×C22⋊C4C22×D1112yes—
687C2×C22⋊C4C22×D1111yescharacteristic
688C2×C22⋊C4C22×D1111yescharacteristic
689C2×C22⋊C4C22×D1112yes—
690C2×C22⋊C4C22×D1112yes—
691C2×C22⋊C4C22×D1112yes—
692C2×C42—118no—
693C2×C42—111no—
694C2×C42—111no—
695C2×C42—111no—
696C2×C42—111no—
697C2×C42—111no—
698C2×C42—112no—
699C2×C42—112no—
700C2×C42C22×D1111yescharacteristic
701C2×C42C22×D1112yes—
702C2×C42C22×D1112yes—
703#95—112no—
704#95—112no—
705#95—112no—
706#95—112no—
707#95—111no—
708#95—111no—
709#95—112no—
710#95—112no—
711#95—112no—
712#95—112no—
713#95—112no—
714#95—112no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95C22×D1111yescharacteristic
724#95C22×D1111yescharacteristic
725#95C22×D1112yes—
726#95C22×D1112yes—
727#95C22×D1112yes—
728#95C22×D1112yes—
729C2×C11—42no—
730C2×C11—81no—
731C2×C11C2×#53611yescharacteristic
732C2×C11#344911yescharacteristic
733C2×C11#344911yescharacteristic
734C2×C11#353112yes—
735C2×C11#353112yes—
736D11—81no—
737C24—111no—
738C24C23×D1111yescharacteristic
739C24C23×D1111yescharacteristic
740C2×Q8—222no—
741C2×Q8—224no—
742C2×Q8—224no—
743C2×Q8—442no—
744C2×Q8—442no—
745C2×Q8—442no—
746C2×Q8—442no—
747C2×Q8—442no—
748C2×D4—22no—
749C2×D4—41no—
750C2×D4—41no—
751C2×D4—222no—
752C2×D4—222no—
753C2×D4—442no—
754C2×D4—441no—
755C2×D4—441no—
756C22×C4—24no—
757C22×C4—22no—
758C22×C4—24no—
759C22×C4—111no—
760C22×C4—111no—
761C22×C4—111no—
762C22×C4—111no—
763C22×C4—114no—
764C22×C4—114no—
765C22×C4—112no—
766C22×C4—112no—
767C22×C4—111no—
768C22×C4—111no—
769C22×C4—112no—
770C22×C4—112no—
771C22×C4—111no—
772C22×C4—222no—
773C22×C4—224no—
774C22×C4—441no—
775C22×C4—441no—
776C22×C4—442no—
777C22×C4D4×D1114yes—
778C22×C4C23×D1112yes—
779C22×C4C23×D1112yes—
780C22×C4C23×D1111yescharacteristic
781C22×C4C23×D1111yescharacteristic
782C22×C4C23×D1112yes—
783C22×C4C23×D1112yes—
784C22×C4C23×D1111yescharacteristic
785C22×C4C23×D1111yescharacteristic
786C22×C4C23×D1111yescharacteristic
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—222no—
793C4⋊C4—222no—
794C4⋊C4—222no—
795C4⋊C4—222no—
796C4⋊C4—222no—
797C4⋊C4—222no—
798C4⋊C4—224no—
799C4⋊C4—224no—
800C4⋊C4—224no—
801C4⋊C4—224no—
802C4⋊C4—224no—
803C4⋊C4—224no—
804C4⋊C4—222no—
805C4⋊C4—222no—
806C4⋊C4—222no—
807C4⋊C4—222no—
808C4⋊C4—222no—
809C4⋊C4—442no—
810C4⋊C4—442no—
811C4⋊C4—442no—
812C4⋊C4—442no—
813C4⋊C4—442no—
814C4⋊C4—442no—
815C4⋊C4—442no—
816C4⋊C4—442no—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—22no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—222no—
824C22⋊C4—222no—
825C22⋊C4—222no—
826C22⋊C4—222no—
827C22⋊C4—222no—
828C22⋊C4—222no—
829C22⋊C4—224no—
830C22⋊C4—222no—
831C22⋊C4—222no—
832C22⋊C4—442no—
833C22⋊C4—442no—
834C22⋊C4—442no—
835C22⋊C4—442no—
836C22⋊C4—442no—
837C22⋊C4—442no—
838C22⋊C4—442no—
839C42—24no—
840C42—22no—
841C42—24no—
842C42—114no—
843C42—114no—
844C42—114no—
845C42—114no—
846C42—222no—
847C42—224no—
848C42—224no—
849C11#3669911yescharacteristic, complemented, Sylow
850C23—22no—
851C23—22no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23—22no—
856C23—21no—
857C23—22no—
858C23—21no—
859C23—221no—
860C23—222no—
861C23—222no—
862C23—221no—
863C23—221no—
864C23C2×D4×D1112yes—
865C23C24×D1111yescharacteristic
866Q8—444no—
867Q8—448no—
868Q8—448no—
869D4—44no—
870D4—444no—
871D4—444no—
872C2×C4—22no—
873C2×C4—28no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—21no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—44no—
894C2×C4—112no—
895C2×C4—112no—
896C2×C4—112no—
897C2×C4—112no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—221no—
903C2×C4—221no—
904C2×C4—221no—
905C2×C4—221no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—221no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—221no—
920C2×C4—221no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—444no—
924C2×C4—444no—
925C2×C4—444no—
926C2×C4C2×D4×D1112yes—
927C2×C4C2×D4×D1112yes—
928C2×C4#6704314yes—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—42no—
933C22—42no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—42no—
938C22—42no—
939C22—441no—
940C22—441no—
941C22—441no—
942C22—442no—
943C22—442no—
944C22C22×D4×D1111yescharacteristic
945C22C2×#6704312yes—
946C22#1062345312yes—
947C22#1062345311yescharacteristic
948C22#1062345311yescharacteristic
949C4—22no—
950C4—41no—
951C4—41no—
952C4—42no—
953C4—41no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—222no—
958C4—222no—
959C4—222no—
960C4—222no—
961C4—441no—
962C4—441no—
963C4—442no—
964C4—441no—
965C4—442no—
966C4—442no—
967C4—442no—
968C4#1062317914yes—
969C2—42no—
970C2—81no—
971C2—881no—
972C2C2×#1062317911yescharacteristic
973C2#1308194311yescharacteristic
974C2#1308194611yescharacteristic
975C2#1308276112yes—
976C2#1308276112yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2395C2
prime radicalC2×#66992C22
hypercenter#2395D11
hypocenterC11#36699
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
3. #13076686C2semidirect
4. #13076685C2semidirect
5. #13076681C2semidirect
6. #13076679C2semidirect
7. #13076676C2semidirect
8. #13076673C2semidirect
9. #13076672C2semidirect
10. #13076670C2semidirect
11. #13076654C2semidirect
13. #13076635C2semidirect
14. #13076633C2semidirect
15. #13071910C2semidirect
16. #13071903C2semidirect
17. #13071892C2semidirect
18. #13071890C2semidirect
19. #13071876C2semidirect
20. #13071875C2semidirect
21. #13071873C2semidirect
22. #13071010C2semidirect
23. C11×#2395C2semidirect
383. #2395D11semidirect
849. C11#36699semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106230692
#130766862
#130766852
#130766812
#130766792
#130766762
#130766732
#130766722
#130766702
#130766542
#130766482
#130766352
#130766332
#130719102
#130719032
#130718922
#130718902
#130718762
#130718752
#130718732
#130710102
C11×#23952
#3669911