Finite Group Databasebeta

← #14920993

Subgroups — #14920993

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic, complemented
2C2×C4×#4341C211yesmaximal, characteristic
3#13074536C211yesmaximal, characteristic, complemented
4#13074534C211yesmaximal, characteristic, complemented
5#13074533C211yesmaximal, characteristic, complemented
6#13074496C212yesmaximal, complemented
7#13074488C212yesmaximal, complemented
8#13074439C211yesmaximal, characteristic, complemented
9#13074436C211yesmaximal, characteristic, complemented
10#13074412C212yesmaximal, complemented
11#13074384C211yesmaximal, characteristic, complemented
12#13074381C211yesmaximal, characteristic, complemented
13#13074344C212yesmaximal
14#13071908C211yesmaximal, characteristic, complemented
15#13071906C211yesmaximal, characteristic, complemented
16#13071901C211yesmaximal, characteristic, complemented
17#13071898C211yesmaximal, characteristic, complemented
18#13071874C212yesmaximal, complemented
19#13071872C212yesmaximal, complemented
20#13071150C212yesmaximal, complemented
21#13071148C212yesmaximal, complemented
22#13071007C211yesmaximal, characteristic, complemented
23C11×#2638C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×Q8×Dic11C2211yescharacteristic
28C2×#66997C2211yescharacteristic
29C2×D4×Dic11C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×#66977C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35#10623153—28no—
36C4×#4341—28no—
37C2×#66949C2212yes—
38C2×#66945C2211yescharacteristic
39C2×#66942C2212yes—
40C2×#66941C2211yescharacteristic
41C2×#66940C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66940C2212yes—
44C2×(C22⋊D11)⋊C4C2211yescharacteristic
45C2×(C22⋊D11)⋊C4C2211yescharacteristic
46C2×#66931C2212yes—
47C2×#66931C2212yes—
48C2×#66930C2212yes—
49C2×#66930C2211yescharacteristic
50C2×#66930C2211yescharacteristic
51C2×C42×D11C2211yescharacteristic
52C2×C4×Dic22C2211yescharacteristic
53C11×#398C2211yescharacteristic
54C11×#397C2212yes—
55C11×#397C2211yescharacteristic
56C11×#395C2211yescharacteristic
57C11×#394C2212yes—
58C11×#393C2211yescharacteristic
59C11×#387C2212yes—
60C11×#385C2212yes—
61C11×#381C2211yescharacteristic
62#10622844C2211yescharacteristic
63#10622842C2211yescharacteristic
64#10622835C2212yes—
65#10622824C2211yescharacteristic
66#10622823C2212yes—
67#10622606C2211yescharacteristic
68#10622605C2212yes—
69#10622602C2212yes—
70#10622597C2212yes—
71#10622597C2212yes—
72#10622596C2211yescharacteristic
73#10622593C2211yescharacteristic
74#10622592C2211yescharacteristic
75#10622592C2212yes—
76#10622591C2212yes—
77C4⋊C4×Dic11C2212yes—
78C4⋊C4×Dic11C2212yes—
79#10622585C2212yes—
80#10622574C2212yes—
81#10622574C2212yes—
82#10622572C2212yes—
83#10622572C2212yes—
84#10622566C2212yes—
85#10622566C2211yescharacteristic
86#10622565C2212yes—
87#10622565C2212yes—
88#10622565C2212yes—
89#10622562C2212yes—
90#10622560C2211yescharacteristic
91#10622555C2212yes—
92#10622555C2212yes—
93C22⋊C4×Dic11C2212yes—
94C22⋊C4×Dic11C2212yes—
95C22⋊C4×Dic11C2212yes—
96#10622546C2212yes—
97#10622288C2212yes—
98#10622287C2211yescharacteristic
99#10622286C2211yescharacteristic
100#10622281C2212yes—
101#10622280C2212yes—
102#10622279C2212yes—
103#10622279C2212yes—
104#10622274C2211yescharacteristic
105#10622273C2212yes—
106#10622273C2212yes—
107#10622271C2212yes—
108#10622271C2212yes—
109#10622270C2212yes—
110#10622270C2212yes—
111#10622269C2211yescharacteristic
112#10622269C2212yes—
113#10622266C2212yes—
114#10622264C2212yes—
115#10622263C2211yescharacteristic
116#10622263C2211yescharacteristic
117#10622262C2212yes—
118#10622262C2212yes—
119#10622262C2212yes—
120#10622261C2211yescharacteristic
121#10622261C2211yescharacteristic
122#10622260C2212yes—
123#10622259C2212yes—
124#10622259C2212yes—
125C22×Q8×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C22×C22⋊D11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C2×#4341—24no—
136C2×#4341—24no—
137C2×#4341—24no—
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×Dic22C2311yescharacteristic
142C22×Dic22C2312yes—
143C22×Dic22C2311yescharacteristic
144C11×C22⋊Q8—24no—
145C4×D4×C11—24no—
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C4⋊C4C2312yes—
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C4⋊C4C2312yes—
150C2×C11×C4⋊C4C2312yes—
151C2×C11×C22⋊C4C2312yes—
152C2×C11×C22⋊C4C2311yescharacteristic
153C2×C11×C22⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C42×C11C2311yescharacteristic
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2311yescharacteristic
160C2×C22⋊Dic11C2311yescharacteristic
161C2×C22⋊Dic11C2312yes—
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164Q8×Dic11—24no—
165#66997—24no—
166D4×Dic11—24no—
167C4×C22⋊D11—24no—
168C4×C22⋊D11—24no—
169C2×(C2×D11)⋊C4C2311yescharacteristic
170C2×(C2×D11)⋊C4C2311yescharacteristic
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2312yes—
180#66977—24no—
181C2×Dic11⋊C4C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×Dic11⋊C4C2311yescharacteristic
184C2×Dic11⋊C4C2311yescharacteristic
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×C4×Dic11—24no—
197C2×C4×Dic11D418yes—
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211#66949—28no—
212#66945—24no—
213#66942—28no—
214#66941—24no—
215#66940—24no—
216#66940—24no—
217#66940—28no—
218(C22⋊D11)⋊C4—24no—
219(C22⋊D11)⋊C4—24no—
220#66931—28no—
221#66931—28no—
222#66930—24no—
223#66930—28no—
224#66930—24no—
225C42×D11—24no—
226C4×Dic22—24no—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11×#95C2311yescharacteristic
231C11×#95C2311yescharacteristic
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253#34627—111nomaximal, Sylow
254C24×C11C2411yescharacteristic
255C24×C11C2411yescharacteristic
256C23×D11C2411yescharacteristic
257C2×Q8×C11—22no—
258C2×Q8×C11—42no—
259C2×D4×C11—22no—
260C2×D4×C11—22no—
261C2×D4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—42no—
264C22×C4×C11—42no—
265C22×C4×C11C2×D414yes—
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2412yes—
268C22×C4×C11C2412yes—
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2412yes—
271C22×C4×C11C2412yes—
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C2×C22⋊D11—22no—
276C2×C22⋊D11—22no—
277C2×C22⋊D11—22no—
278C2×C22⋊D11—22no—
279C2×C22⋊D11—22no—
280C2×C22⋊D11—22no—
281C22×Dic11—22no—
282C22×Dic11—22no—
283C22×Dic11—22no—
284C22×Dic11—22no—
285C22×Dic11—24no—
286C22×Dic11—22no—
287C22×Dic11—24no—
288C22×Dic11C2×D414yes—
289C22×Dic11C2×D414yes—
290C22×Dic11#4114yes—
291C22×Dic11C2411yescharacteristic
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2412yes—
296C22×Dic11C2412yes—
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302#4341—232no—
303C2×C4×D11—22no—
304C2×C4×D11—22no—
305C2×C4×D11—22no—
306C2×C4×D11—24no—
307C2×C4×D11—22no—
308C2×C4×D11—42no—
309C2×C4×D11#4114yes—
310C2×Dic22—22no—
311C2×Dic22—22no—
312C2×Dic22—24no—
313C2×Dic22—24no—
314C2×Dic22—24no—
315C2×Dic22—22no—
316C2×Dic22—22no—
317C2×Dic22—42no—
318C11×C4⋊C4—22no—
319C11×C4⋊C4—24no—
320C11×C4⋊C4—22no—
321C11×C4⋊C4—24no—
322C11×C4⋊C4—42no—
323C11×C22⋊C4—24no—
324C11×C22⋊C4—22no—
325C11×C22⋊C4—24no—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—42no—
328C11×C22⋊C4—42no—
329C42×C11—22no—
330C22⋊Dic11—22no—
331C22⋊Dic11—24no—
332C22⋊Dic11—22no—
333C22⋊Dic11—24no—
334C22⋊Dic11—42no—
335C22⋊Dic11—42no—
336(C2×D11)⋊C4—22no—
337(C2×D11)⋊C4—24no—
338(C2×D11)⋊C4—24no—
339(C2×D11)⋊C4—22no—
340(C2×D11)⋊C4—42no—
341(C2×D11)⋊C4—42no—
342C4⋊Dic11—22no—
343C4⋊Dic11—24no—
344C4⋊Dic11—24no—
345C4⋊Dic11—22no—
346C4⋊Dic11—42no—
347Dic11⋊C4—22no—
348Dic11⋊C4—22no—
349Dic11⋊C4—22no—
350Dic11⋊C4—24no—
351Dic11⋊C4—24no—
352Dic11⋊C4—24no—
353Dic11⋊C4—24no—
354Dic11⋊C4—24no—
355Dic11⋊C4—24no—
356Dic11⋊C4—24no—
357Dic11⋊C4—22no—
358Dic11⋊C4—24no—
359Dic11⋊C4—24no—
360Dic11⋊C4—42no—
361Dic11⋊C4—42no—
362C4×Dic11—22no—
363C4×Dic11—22no—
364C4×Dic11—24no—
365C4×Dic11—24no—
366C4×Dic11—22no—
367C4×Dic11—22no—
368C4×Dic11—24no—
369C4×Dic11—24no—
370C4×Dic11—22no—
371C4×Dic11C2×D414yes—
372C4×Dic11C2×D414yes—
373C4×Dic11C2×D414yes—
374C4×Dic11C2×D414yes—
375C2×#533—111no—
376C2×C4×#41—111no—
377#2638—111no—
378#2638—111no—
379#2638—111no—
380#2638D1111yescharacteristic, complemented
381#2634—112no—
382#2633—112no—
383#2628—111no—
384#2628—111no—
385#2625—112no—
386#2621—111no—
387#2621—111no—
388#2616—112no—
389#2399—111no—
390#2399—111no—
391#2398—111no—
392#2398—111no—
393#2395—112no—
394#2395—112no—
395C4×C22⋊Q8—112no—
396C4×C22⋊Q8—112no—
397#2283—111no—
398C23×C11—21no—
399C23×C11—21no—
400C23×C11—21no—
401C23×C11—21no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11C22×D412yes—
407C23×C11C2×#4112yes—
408C23×C11C2511yescharacteristic
409C22×D11—21no—
410C22×D11—21no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11C2×#4112yes—
414Q8×C11—44no—
415D4×C11—28no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—21no—
421C2×C4×C11—22no—
422C2×C4×C11—21no—
423C2×C4×C11—22no—
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—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—44no—
437C2×C4×C11—44no—
438C2×C4×C11C22×D412yes—
439C2×C4×C11C22×D412yes—
440C2×C4×C11C2×#4112yes—
441C22⋊D11—28no—
442C22⋊D11—28no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11—21no—
447C2×Dic11—22no—
448C2×Dic11—28no—
449C2×Dic11—28no—
450C2×Dic11—28no—
451C2×Dic11—21no—
452C2×Dic11—21no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—44no—
468C2×Dic11C22×D412yes—
469C2×Dic11C22×D412yes—
470C2×Dic11C22×D412yes—
471C2×Dic11C22×D412yes—
472C2×Dic11C2×#4112yes—
473C2×Dic11C2×#4112yes—
474C2×Dic11C2×#4112yes—
475C2×Dic112−1+414yes—
476C4×D11—28no—
477C4×D11—44no—
478C4×D11—44no—
479Dic22—28no—
480Dic22—44no—
481Dic22—48no—
482C22×#41—111no—
483#533—228no—
484C2×C4⋊Q8—111no—
485C2×C4⋊Q8—111no—
486C2×#125—112no—
487C2×C22⋊Q8—111no—
488C2×C22⋊Q8—112no—
489C2×C22⋊Q8—112no—
490C2×C22⋊Q8—112no—
491C2×C22⋊Q8C2×D1111yescharacteristic
492C4×#41—228no—
493C2×C4×Q8—111no—
494C2×C4×Q8—111no—
495C2×C4×Q8—111no—
496C2×C4×Q8—112no—
497C2×C4×Q8—111no—
498C2×C4×D4—111no—
499C2×C4×D4—111no—
500C2×C4×D4—111no—
501C2×C4×D4—111no—
502C2×C4×D4—111no—
503C2×C4×D4C2×D1111yescharacteristic
504C2×#117—111no—
505C2×#117—111no—
506C2×#117—111no—
507C2×#117—112no—
508C22×C42—111no—
509C22×C42—111no—
510C22×C42—111no—
511#400—112no—
512#400—112no—
513#400—112no—
514#400—112no—
515#399—112no—
516#399—112no—
517#398—112no—
518#398—111no—
519#398—111no—
520#398—112no—
521#398—112no—
522#398—111no—
523#398—112no—
524#398C2×D1111yescharacteristic
525#397—111no—
526#397—112no—
527#397—111no—
528#397—112no—
529#397—112no—
530#397—112no—
531#397—112no—
532#397—111no—
533#397C2×D1111yescharacteristic
534#397C2×D1112yes—
535#395—111no—
536#395—112no—
537#395—111no—
538#395—112no—
539#395—111no—
540#395C2×D1111yescharacteristic
541#394—112no—
542#394—112no—
543#394—112no—
544#394—112no—
545#394—112no—
546#394C2×D1112yes—
547#393—111no—
548#393—111no—
549#393—111no—
550#393C2×D1111yescharacteristic
551#391—112no—
552#391—112no—
553#389—112no—
554#389—112no—
555#387—112no—
556#387—112no—
557#387—112no—
558#387C2×D1112yes—
559#385—112no—
560#385—112no—
561#385—112no—
562#385C2×D1112yes—
563#383—112no—
564#382—111no—
565#382—111no—
566#381—111no—
567#381C2×D1111yescharacteristic
568#380—112no—
569#380—112no—
570#380—112no—
571C4×C4⋊C4—112no—
572C4×C4⋊C4—112no—
573C4×C4⋊C4—112no—
574C4×C4⋊C4—112no—
575C4×C4⋊C4—112no—
576C4×C22⋊C4—112no—
577C4×C22⋊C4—112no—
578C4×C22⋊C4—112no—
579C4×C22⋊C4—112no—
580C4×C22⋊C4—112no—
581#376—111no—
582#376—111no—
583C22×C11—22no—
584C22×C11—22no—
585C22×C11—22no—
586C22×C11—22no—
587C22×C11—24no—
588C22×C11—41no—
589C22×C11—41no—
590C22×C11—42no—
591C22×C11—42no—
592C22×C11—42no—
593C22×C11C23×D411yescharacteristic
594C22×C11C22×#4111yescharacteristic
595C22×C11C22×#4111yescharacteristic
596C22×C11C2×2−1+412yes—
597C22×C11#58512yes—
598C2×D11—22no—
599C2×D11—24no—
600C2×D11—41no—
601C2×D11—41no—
602C2×D11—42no—
603C4×C11—22no—
604C4×C11—22no—
605C4×C11—22no—
606C4×C11—42no—
607C4×C11—41no—
608C4×C11—41no—
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—42no—
612Dic11—22no—
613Dic11—22no—
614Dic11—22no—
615Dic11—42no—
616Dic11—41no—
617Dic11—42no—
618Dic11—41no—
619Dic11—42no—
620Dic11—42no—
621Dic11#52514yes—
622Dic11#53614yes—
623C2×#41—224no—
624C2×#41—224no—
625C2×#41—224no—
626C22×Q8—111no—
627C22×Q8—112no—
628C22×Q8—111no—
629C22×Q8C22×D1111yescharacteristic
630C22×D4—111no—
631C22×D4—111no—
632C22×D4C22×D1111yescharacteristic
633C23×C4—111no—
634C23×C4—111no—
635C23×C4—111no—
636C23×C4—111no—
637C23×C4—111no—
638C23×C4—111no—
639C23×C4—111no—
640C23×C4C22×D1111yescharacteristic
641C23×C4C22×D1111yescharacteristic
642C4⋊Q8—224no—
643C4⋊Q8—224no—
644#125—228no—
645C22⋊Q8—24no—
646C22⋊Q8—228no—
647C22⋊Q8—228no—
648C22⋊Q8—228no—
649C22⋊Q8—224no—
650C4×Q8—224no—
651C4×Q8—224no—
652C4×Q8—228no—
653C4×Q8—224no—
654C4×Q8—224no—
655C4×D4—24no—
656C4×D4—224no—
657C4×D4—224no—
658C4×D4—224no—
659C4×D4—224no—
660C4×D4—224no—
661#117—224no—
662#117—224no—
663#117—224no—
664#117—228no—
665C2×C4⋊C4—111no—
666C2×C4⋊C4—111no—
667C2×C4⋊C4—111no—
668C2×C4⋊C4—111no—
669C2×C4⋊C4—111no—
670C2×C4⋊C4—112no—
671C2×C4⋊C4—112no—
672C2×C4⋊C4—112no—
673C2×C4⋊C4—112no—
674C2×C4⋊C4—112no—
675C2×C4⋊C4—112no—
676C2×C4⋊C4—111no—
677C2×C4⋊C4—112no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4—112no—
681C2×C4⋊C4—112no—
682C2×C4⋊C4—112no—
683C2×C4⋊C4—112no—
684C2×C4⋊C4—112no—
685C2×C4⋊C4C22×D1111yescharacteristic
686C2×C4⋊C4C22×D1112yes—
687C2×C4⋊C4C22×D1111yescharacteristic
688C2×C4⋊C4C22×D1112yes—
689C2×C4⋊C4C22×D1112yes—
690C2×C22⋊C4—111no—
691C2×C22⋊C4—111no—
692C2×C22⋊C4—112no—
693C2×C22⋊C4—112no—
694C2×C22⋊C4—111no—
695C2×C22⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
703C2×C22⋊C4C22×D1111yescharacteristic
704C2×C22⋊C4C22×D1112yes—
705C2×C22⋊C4C22×D1112yes—
706C2×C22⋊C4C22×D1112yes—
707C2×C22⋊C4C22×D1112yes—
708C2×C42—118no—
709C2×C42—111no—
710C2×C42—111no—
711C2×C42—111no—
712C2×C42—111no—
713C2×C42—111no—
714C2×C42—111no—
715C2×C42—112no—
716C2×C42—112no—
717C2×C42—111no—
718C2×C42—111no—
719C2×C42—111no—
720C2×C42—112no—
721C2×C42—112no—
722C2×C42—224no—
723C2×C42—224no—
724C2×C42C22×D1111yescharacteristic
725#95—112no—
726#95—112no—
727#95—111no—
728#95—111no—
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×D1111yescharacteristic
745#95C22×D1111yescharacteristic
746#95C22×D1112yes—
747#95C22×D1112yes—
748#95C22×D1112yes—
749#95C22×D1112yes—
750#95C22×D1112yes—
751C2×C11—42no—
752C2×C11—42no—
753C2×C11C2×#52511yescharacteristic
754C2×C11C2×#53611yescharacteristic
755C2×C11#344911yescharacteristic
756C2×C11#346112yes—
757C2×C11#346112yes—
758D11—42no—
759C24—111no—
760C24C23×D1111yescharacteristic
761C24C23×D1111yescharacteristic
762#41—2232no—
763C2×Q8—22no—
764C2×Q8—42no—
765C2×Q8—222no—
766C2×Q8—222no—
767C2×Q8—224no—
768C2×Q8—224no—
769C2×Q8—224no—
770C2×Q8—222no—
771C2×Q8—222no—
772C2×Q8—442no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—222no—
777C2×D4—222no—
778C2×D4—222no—
779C2×D4—222no—
780C2×D4—222no—
781C2×D4—222no—
782C22×C4—22no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—111no—
786C22×C4—111no—
787C22×C4—114no—
788C22×C4—114no—
789C22×C4—114no—
790C22×C4—111no—
791C22×C4—111no—
792C22×C4—111no—
793C22×C4—114no—
794C22×C4—111no—
795C22×C4—112no—
796C22×C4—112no—
797C22×C4—111no—
798C22×C4—112no—
799C22×C4—112no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—224no—
804C22×C4—222no—
805C22×C4—222no—
806C22×C4—222no—
807C22×C4—222no—
808C22×C4—224no—
809C22×C4—222no—
810C22×C4—224no—
811C22×C4—222no—
812C22×C4—442no—
813C22×C4D4×D1114yes—
814C22×C4C23×D1111yescharacteristic
815C22×C4C23×D1112yes—
816C22×C4C23×D1112yes—
817C22×C4C23×D1111yescharacteristic
818C22×C4C23×D1112yes—
819C22×C4C23×D1112yes—
820C22×C4C23×D1111yescharacteristic
821C22×C4C23×D1111yescharacteristic
822C22×C4C23×D1111yescharacteristic
823C4⋊C4—22no—
824C4⋊C4—24no—
825C4⋊C4—22no—
826C4⋊C4—24no—
827C4⋊C4—42no—
828C4⋊C4—222no—
829C4⋊C4—222no—
830C4⋊C4—222no—
831C4⋊C4—222no—
832C4⋊C4—224no—
833C4⋊C4—224no—
834C4⋊C4—224no—
835C4⋊C4—224no—
836C4⋊C4—224no—
837C4⋊C4—224no—
838C4⋊C4—224no—
839C4⋊C4—224no—
840C4⋊C4—224no—
841C4⋊C4—222no—
842C4⋊C4—224no—
843C4⋊C4—222no—
844C4⋊C4—224no—
845C4⋊C4—442no—
846C4⋊C4—442no—
847C4⋊C4—442no—
848C22⋊C4—22no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—22no—
852C22⋊C4—42no—
853C22⋊C4—42no—
854C22⋊C4—222no—
855C22⋊C4—224no—
856C22⋊C4—224no—
857C22⋊C4—222no—
858C22⋊C4—222no—
859C22⋊C4—224no—
860C22⋊C4—224no—
861C22⋊C4—222no—
862C22⋊C4—442no—
863C22⋊C4—442no—
864C22⋊C4—442no—
865C22⋊C4—442no—
866C42—22no—
867C42—114no—
868C42—114no—
869C42—114no—
870C42—114no—
871C42—222no—
872C42—222no—
873C42—222no—
874C42—222no—
875C42—224no—
876C42—224no—
877C42—224no—
878C42—224no—
879C42—222no—
880C11#3462711yescharacteristic, complemented, Sylow
881C23—21no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—112no—
890C23—221no—
891C23—221no—
892C23—222no—
893C23—222no—
894C23C2×D4×D1112yes—
895C23#41×D1112yes—
896C23C24×D1111yescharacteristic
897Q8—44no—
898Q8—228no—
899Q8—444no—
900Q8—448no—
901D4—28no—
902D4—228no—
903D4—228no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—112no—
927C2×C4—112no—
928C2×C4—112no—
929C2×C4—112no—
930C2×C4—114no—
931C2×C4—112no—
932C2×C4—112no—
933C2×C4—112no—
934C2×C4—228no—
935C2×C4—228no—
936C2×C4—228no—
937C2×C4—228no—
938C2×C4—221no—
939C2×C4—221no—
940C2×C4—221no—
941C2×C4—221no—
942C2×C4—222no—
943C2×C4—221no—
944C2×C4—221no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—444no—
960C2×C4—444no—
961C2×C4—444no—
962C2×C4C2×D4×D1112yes—
963C2×C4C2×D4×D1112yes—
964C2×C4#41×D1112yes—
965C22—22no—
966C22—22no—
967C22—24no—
968C22—22no—
969C22—22no—
970C22—41no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—224no—
976C22—222no—
977C22—441no—
978C22—441no—
979C22—442no—
980C22C22×D4×D1111yescharacteristic
981C22C2×#41×D1111yescharacteristic
982C22C2×#41×D1111yescharacteristic
983C22#1062345512yes—
984C22D11×2−1+412yes—
985C4—22no—
986C4—22no—
987C4—22no—
988C4—41no—
989C4—41no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—114no—
995C4—114no—
996C4—222no—
997C4—222no—
998C4—222no—
999C4—441no—
1000C4—441no—
1001C4—442no—
1002C4—442no—
1003C4—442no—
1004C4—442no—
1005C2—42no—
1006C2—42no—
1007C2—442no—
1008C2D11×#52511yescharacteristic
1009C2D11×#53611yescharacteristic
1010C2#1308194211yescharacteristic
1011C2#1308204212yes—
1012C2#1308204612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2638C2
prime radicalC22×#4341C22
hypercenter#2638D11
hypocenterC11#34627
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2638

Complements

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

NH ≅ G/Ntype
1. C2×#10623153C2semidirect
3. #13074536C2semidirect
4. #13074534C2semidirect
5. #13074533C2semidirect
6. #13074496C2semidirect
7. #13074488C2semidirect
8. #13074439C2semidirect
9. #13074436C2semidirect
10. #13074412C2semidirect
11. #13074384C2semidirect
12. #13074381C2semidirect
14. #13071908C2semidirect
15. #13071906C2semidirect
16. #13071901C2semidirect
17. #13071898C2semidirect
18. #13071874C2semidirect
19. #13071872C2semidirect
20. #13071150C2semidirect
21. #13071148C2semidirect
22. #13071007C2semidirect
23. C11×#2638C2semidirect
380. #2638D11semidirect
880. C11#34627semidirect

Maximal subgroups

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

subgroupindex
C2×#106231532
C2×C4×#43412
#130745362
#130745342
#130745332
#130744962
#130744882
#130744392
#130744362
#130744122
#130743842
#130743812
#130743442
#130719082
#130719062
#130719012
#130718982
#130718742
#130718722
#130711502
#130711482
#130710072
C11×#26382
#3462711