Finite Group Databasebeta

← #14927046

Subgroups — #14927046

Order 2816.

1766 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076954C211yesmaximal, characteristic, complemented
2#13076949C211yesmaximal, characteristic
3#13076925C211yesmaximal, characteristic, complemented
4#13076918C211yesmaximal, characteristic
5#13074570C212yesmaximal, complemented
6#13074403C212yesmaximal, complemented
7#13074156C212yesmaximal, complemented
8#13074118C212yesmaximal, complemented
9#13073930C212yesmaximal, complemented
10#13073908C212yesmaximal, complemented
11#13073227C211yesmaximal, characteristic, complemented
12#13073207C211yesmaximal, characteristic, complemented
13#13073150C211yesmaximal, characteristic, complemented
14#13072486C211yesmaximal, characteristic, complemented
15#13072478C211yesmaximal, characteristic, complemented
16#13072414C211yesmaximal, characteristic, complemented
17#13072405C211yesmaximal, characteristic, complemented
18#13071280C212yesmaximal, complemented
19#13071248C212yesmaximal, complemented
20C4×#66950C211yesmaximal, characteristic, complemented
21#13071124C211yesmaximal, characteristic
22C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2509C211yesmaximal, characteristic, complemented
24C2×#66950C2211yescharacteristic
25C2×#66948C2211yescharacteristic
26C2×#66947C2212yes—
27C2×#66946C2212yes—
28C2×#66946C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×#66943C2211yescharacteristic
32C2×#66928C2211yescharacteristic
33C2×C42×D11C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#400C2212yes—
38C11×#400C2212yes—
39C11×#389C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#389C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#389C2212yes—
44C11×#387C2212yes—
45C11×#382C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48#10622607C2212yes—
49#10622606C2212yes—
50#10622605C2212yes—
51#10622603C2212yes—
52#10622603C2212yes—
53#10622603C2212yes—
54#10622602C2212yes—
55#10622602C2212yes—
56#10622602C2212yes—
57#10622601C2211yescharacteristic
58#10622601C2211yescharacteristic
59#10622600C2212yes—
60#10622600C2211yescharacteristic
61#10622600C2211yescharacteristic
62#10622599C2212yes—
63#10622598C2211yescharacteristic
64#10622594C2212yes—
65#10622594C2212yes—
66#10622594C2212yes—
67#10622594C2212yes—
68#10622590C2211yescharacteristic
69C4⋊C4×Dic11C2211yescharacteristic
70C4⋊C4×Dic11C2211yescharacteristic
71C4⋊C4×Dic11C2211yescharacteristic
72#10622587C2211yescharacteristic
73#10622587C2211yescharacteristic
74#10622587C2211yescharacteristic
75#10622586C2211yescharacteristic
76#10622586C2211yescharacteristic
77#10622585C2212yes—
78#10622553C2212yes—
79#10622553C2212yes—
80#10622552C2211yescharacteristic
81#10622552C2211yescharacteristic
82C4×(C2×D11)⋊C4C2212yes—
83C4×C4⋊Dic11C2212yes—
84C4×C4⋊Dic11C2211yescharacteristic
85C4×Dic11⋊C4C2211yescharacteristic
86C4×Dic11⋊C4C2211yescharacteristic
87#10622542C2211yescharacteristic
88#10622541C2211yescharacteristic
89#10622290C2212yes—
90#10622288C2212yes—
91#10622288C2212yes—
92#10622288C2212yes—
93#10622288C2212yes—
94#10622283C2212yes—
95#10622283C2212yes—
96#10622282C2212yes—
97#10622282C2212yes—
98#10622281C2212yes—
99#10622281C2212yes—
100#10622281C2212yes—
101#10622279C2212yes—
102#10622278C2212yes—
103#10622278C2212yes—
104#10622278C2212yes—
105#10622278C2212yes—
106#10622277C2212yes—
107#10622277C2212yes—
108D11×#95C2211yescharacteristic
109D11×#95C2211yescharacteristic
110C11⋊#401C2212yes—
111#10622272C2212yes—
112#10622271C2212yes—
113#10622270C2212yes—
114#10622270C2212yes—
115#10622268C2212yes—
116#10622266C2212yes—
117#10622265C2212yes—
118#10622265C2212yes—
119#10622264C2212yes—
120#10622263C2212yes—
121#10622262C2211yescharacteristic
122#10622262C2211yescharacteristic
123C22×D44C2311yescharacteristic
124C22×D44C2312yes—
125C22×C4×D11C2311yescharacteristic
126C22×C4×D11C2311yescharacteristic
127C22×C4×D11C2311yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2312yes—
132C22×C4×D11C2311yescharacteristic
133C22×Dic22C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2312yes—
148C2×(C2×D11)⋊C4C2312yes—
149C2×(C2×D11)⋊C4C2312yes—
150C2×(C2×D11)⋊C4C2312yes—
151C2×(C2×D11)⋊C4C2312yes—
152C2×(C2×D11)⋊C4C2312yes—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2312yes—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×C4⋊Dic11C2311yescharacteristic
164C2×C4⋊Dic11C2311yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2312yes—
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2312yes—
170C2×Dic11⋊C4C2311yescharacteristic
171C2×Dic11⋊C4C2311yescharacteristic
172C2×Dic11⋊C4C2311yescharacteristic
173C2×Dic11⋊C4C2311yescharacteristic
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×C4×Dic11C2311yescharacteristic
180C2×C4×Dic11C2311yescharacteristic
181C2×C4×Dic11C2311yescharacteristic
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2311yescharacteristic
190#66950—24no—
191#66948—24no—
192#66947—28no—
193#66946—28no—
194#66946—42no—
195C4⋊C4×D11—24no—
196C4⋊C4×D11—24no—
197#66943—42no—
198#66928—42no—
199C42×D11—24no—
200C42×D11—42no—
201C42×D11—42no—
202C4×Dic22—42no—
203C11×#95C2311yescharacteristic
204C11×#95C2311yescharacteristic
205C11×#95C2312yes—
206C11×#95C2312yes—
207C11×#95C2312yes—
208C11×#95C2312yes—
209C11×#95C2312yes—
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11⋊#95C2311yescharacteristic
213C11⋊#95C2311yescharacteristic
214C11⋊#95C2311yescharacteristic
215C11⋊#95C2312yes—
216C11⋊#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2311yescharacteristic
231C11⋊#95C2312yes—
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235#35024—111nomaximal, Sylow
236C23×D11C2412yes—
237C23×D11C2411yescharacteristic
238C22×C4×C11C2412yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2411yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2411yescharacteristic
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×Dic11C2411yescharacteristic
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2411yescharacteristic
253C22×Dic11C2411yescharacteristic
254C22×Dic11C2411yescharacteristic
255C22×Dic11C2412yes—
256C22×Dic11C2411yescharacteristic
257C22×Dic11C2411yescharacteristic
258C22×Dic11C2411yescharacteristic
259C2×D44—24no—
260C2×D44—24no—
261C2×D44—24no—
262C2×D44—22no—
263C2×D44—22no—
264C2×D44—22no—
265C2×C4×D11—24no—
266C2×C4×D11—22no—
267C2×C4×D11—22no—
268C2×C4×D11—22no—
269C2×C4×D11—22no—
270C2×C4×D11—22no—
271C2×C4×D11—22no—
272C2×C4×D11—22no—
273C2×C4×D11—22no—
274C2×C4×D11—41no—
275C2×C4×D11—41no—
276C2×C4×D11—41no—
277C2×C4×D11—41no—
278C2×C4×D11—41no—
279C2×C4×D11—41no—
280C2×C4×D11—41no—
281C2×C4×D11—41no—
282C2×C4×D11—41no—
283C2×C4×D11—41no—
284C2×C4×D11—42no—
285C2×C4×D11—42no—
286C2×C4×D11#4114yes—
287C2×C4×D11#4114yes—
288C2×C4×D11#4114yes—
289C2×Dic22—22no—
290C2×Dic22—22no—
291C2×Dic22—22no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—24no—
295C11×C4⋊C4—24no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—22no—
300C11×C4⋊C4—42no—
301C11×C4⋊C4—42no—
302C42×C11—22no—
303C42×C11—22no—
304C42×C11—22no—
305C42×C11—42no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—42no—
314(C2×D11)⋊C4—42no—
315(C2×D11)⋊C4—42no—
316(C2×D11)⋊C4—42no—
317(C2×D11)⋊C4—42no—
318(C2×D11)⋊C4—42no—
319(C2×D11)⋊C4—42no—
320(C2×D11)⋊C4—42no—
321C4⋊Dic11—22no—
322C4⋊Dic11—24no—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11—42no—
327C4⋊Dic11—42no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—24no—
332Dic11⋊C4—22no—
333Dic11⋊C4—42no—
334Dic11⋊C4—42no—
335Dic11⋊C4—42no—
336Dic11⋊C4—42no—
337C4×Dic11—22no—
338C4×Dic11—22no—
339C4×Dic11—24no—
340C4×Dic11—22no—
341C4×Dic11—22no—
342C4×Dic11—22no—
343C4×Dic11—42no—
344C4×Dic11—41no—
345C4×Dic11—41no—
346C4×Dic11—41no—
347C4×Dic11—41no—
348#2855—111no—
349#2854—111no—
350#2851—111no—
351#2850—111no—
352#2643—112no—
353#2623—112no—
354#2596—112no—
355#2594—112no—
356#2577—112no—
357#2575—112no—
358#2514—111no—
359#2513—111no—
360#2509D1111yescharacteristic, complemented
361#2508—111no—
362#2454—111no—
363#2453—111no—
364#2448—111no—
365#2447—111no—
366#2322—112no—
367#2318—112no—
368C4×C22⋊Q8—111no—
369C4×#121—111no—
370C2×C4×C4⋊C4—111no—
371C23×C11C2511yescharacteristic
372C22×D11—21no—
373C22×D11—21no—
374C22×D11—21no—
375C22×D11—21no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11C2×#4112yes—
384C22×D11C2×#4112yes—
385C22×D11C2×#4112yes—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—22no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—21no—
406C2×C4×C11—22no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—22no—
414C2×C4×C11C2×#4112yes—
415C2×C4×C11C2×#4112yes—
416C2×C4×C11C2×#4112yes—
417C2×C4×C11H(5,𝔽2)12yes—
418C2×C4×C112−1+412yes—
419C2×Dic11—21no—
420C2×Dic11—21no—
421C2×Dic11—21no—
422C2×Dic11—21no—
423C2×Dic11—21no—
424C2×Dic11—21no—
425C2×Dic11—21no—
426C2×Dic11—22no—
427C2×Dic11—21no—
428C2×Dic11—21no—
429C2×Dic11—21no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—21no—
433C2×Dic11—21no—
434C2×Dic11—21no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—21no—
441C2×Dic11—22no—
442C2×Dic11—21no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11C2×#4112yes—
447C2×Dic11C2×#4112yes—
448C2×Dic11C2×#4112yes—
449D44—48no—
450D44—44no—
451C4×D11—28no—
452C4×D11—28no—
453C4×D11—44no—
454C4×D11—44no—
455C4×D11—44no—
456C4×D11—44no—
457C4×D11—44no—
458C4×D11—84no—
459Dic22—44no—
460C2×#125—111no—
461C2×#124—111no—
462C2×#123—112no—
463C2×C22⋊Q8—111no—
464C2×#121—111no—
465C2×C4×Q8—111no—
466C2×C4×D4—112no—
467C2×C4×D4—111no—
468C22×C4⋊C4—111no—
469C22×C4⋊C4—111no—
470C22×C42—111no—
471C22×C42—111no—
472C22×C42—111no—
473#401—112no—
474#400—112no—
475#400—112no—
476#400—112no—
477#400C2×D1112yes—
478#400C2×D1112yes—
479#399—112no—
480#399—112no—
481#398—112no—
482#398—112no—
483#397—112no—
484#397—112no—
485#397—112no—
486#397—112no—
487#397—112no—
488#396—112no—
489#391—111no—
490#391—111no—
491#391—111no—
492#391—111no—
493#390—111no—
494#390—111no—
495#390—111no—
496#390—111no—
497#389—112no—
498#389—111no—
499#389—111no—
500#389—111no—
501#389—111no—
502#389C2×D1112yes—
503#389C2×D1111yescharacteristic
504#389C2×D1111yescharacteristic
505#389C2×D1111yescharacteristic
506#389C2×D1111yescharacteristic
507#388—112no—
508#388—112no—
509#388—112no—
510#388—112no—
511#388—112no—
512#388—112no—
513#388—112no—
514#388—112no—
515#388—112no—
516#387—112no—
517#387—112no—
518#387—112no—
519#387—112no—
520#387—112no—
521#387—112no—
522#387—112no—
523#387—112no—
524#387C2×D1112yes—
525#386—112no—
526#386—112no—
527#386—112no—
528#386—112no—
529#385—112no—
530#385—112no—
531#385—112no—
532#385—112no—
533#385—112no—
534#385—112no—
535#383—112no—
536#382—111no—
537#382—112no—
538#382C2×D1111yescharacteristic
539#381—112no—
540#381—112no—
541#380—112no—
542#380—111no—
543#380—111no—
544C4×C4⋊C4—111no—
545C4×C4⋊C4—111no—
546C4×C4⋊C4—111no—
547C4×C4⋊C4—112no—
548C4×C4⋊C4—111no—
549C4×C4⋊C4—111no—
550C4×C4⋊C4—111no—
551C4×C4⋊C4—111no—
552C4×C4⋊C4—111no—
553C4×C4⋊C4C2×D1111yescharacteristic
554C4×C4⋊C4C2×D1111yescharacteristic
555C4×C22⋊C4—112no—
556C4×C22⋊C4—112no—
557C2×#95—111no—
558C2×#95—111no—
559C22×C11C22×#4111yescharacteristic
560C22×C11C22×#4111yescharacteristic
561C22×C11C22×#4111yescharacteristic
562C22×C11C2×H(5,𝔽2)11yescharacteristic
563C22×C11C2×2−1+411yescharacteristic
564C22×C11#58511yescharacteristic
565C22×C11#58511yescharacteristic
566C2×D11—22no—
567C2×D11—22no—
568C2×D11—22no—
569C2×D11—22no—
570C2×D11—22no—
571C2×D11—22no—
572C2×D11—42no—
573C2×D11—42no—
574C2×D11—42no—
575C2×D11—42no—
576C2×D11—42no—
577C2×D11—42no—
578C2×D11—42no—
579C2×D11#52914yes—
580C4×C11—22no—
581C4×C11—22no—
582C4×C11—42no—
583C4×C11—42no—
584C4×C11—41no—
585C4×C11—41no—
586C4×C11—42no—
587C4×C11—41no—
588C4×C11—41no—
589C4×C11—42no—
590C4×C11#53914yes—
591Dic11—22no—
592Dic11—22no—
593Dic11—22no—
594Dic11—42no—
595Dic11—41no—
596Dic11—41no—
597Dic11—41no—
598Dic11—41no—
599Dic11—42no—
600Dic11—42no—
601C22×Q8—111no—
602C22×D4—112no—
603C22×D4—111no—
604C23×C4—111no—
605C23×C4—111no—
606C23×C4—111no—
607C23×C4—111no—
608C23×C4—111no—
609C23×C4—111no—
610C23×C4—112no—
611C23×C4—111no—
612#125—442no—
613#124—442no—
614#123—228no—
615C22⋊Q8—224no—
616#121—224no—
617C4×Q8—442no—
618C4×D4—228no—
619C4×D4—442no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—111no—
622C2×C4⋊C4—111no—
623C2×C4⋊C4—111no—
624C2×C4⋊C4—111no—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—111no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—112no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—112no—
636C2×C4⋊C4—224no—
637C2×C4⋊C4—224no—
638C2×C4⋊C4C22×D1111yescharacteristic
639C2×C4⋊C4C22×D1111yescharacteristic
640C2×C4⋊C4C22×D1111yescharacteristic
641C2×C4⋊C4C22×D1112yes—
642C2×C4⋊C4C22×D1111yescharacteristic
643C2×C4⋊C4C22×D1111yescharacteristic
644C2×C4⋊C4C22×D1112yes—
645C2×C4⋊C4C22×D1111yescharacteristic
646C2×C4⋊C4C22×D1112yes—
647C2×C4⋊C4C22×D1112yes—
648C2×C22⋊C4—112no—
649C2×C22⋊C4—112no—
650C2×C22⋊C4—112no—
651C2×C22⋊C4—112no—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—112no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—112no—
663C2×C42—112no—
664C2×C42—111no—
665C2×C42—111no—
666C2×C42—111no—
667C2×C42—111no—
668C2×C42—111no—
669C2×C42—112no—
670C2×C42—111no—
671C2×C42—111no—
672C2×C42—111no—
673C2×C42—111no—
674C2×C42—224no—
675C2×C42—442no—
676C2×C42—442no—
677C2×C42C22×D1111yescharacteristic
678C2×C42C22×D1111yescharacteristic
679C2×C42C22×D1111yescharacteristic
680C2×C42C22×D1112yes—
681#95—111no—
682#95—111no—
683#95—111no—
684#95—111no—
685#95—111no—
686#95—111no—
687#95—112no—
688#95—112no—
689#95—112no—
690#95—112no—
691#95—112no—
692#95—112no—
693#95—112no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—112no—
698#95—112no—
699#95—112no—
700#95—112no—
701#95—112no—
702#95—112no—
703#95—112no—
704#95C22×D1111yescharacteristic
705#95C22×D1111yescharacteristic
706#95C22×D1112yes—
707#95C22×D1112yes—
708#95C22×D1112yes—
709#95C22×D1112yes—
710#95C22×D1112yes—
711#95C22×D1112yes—
712#95C22×D1112yes—
713C2×C11C2×#52911yescharacteristic
714C2×C11C2×#53911yescharacteristic
715C2×C11#345511yescharacteristic
716C2×C11#350511yescharacteristic
717C2×C11#350611yescharacteristic
718C2×C11#350711yescharacteristic
719C2×C11#350711yescharacteristic
720D11—24no—
721D11—82no—
722C24—111no—
723C24—112no—
724C2×Q8—222no—
725C2×Q8—222no—
726C2×Q8—222no—
727C2×D4—224no—
728C2×D4—224no—
729C2×D4—224no—
730C2×D4—222no—
731C2×D4—222no—
732C2×D4—222no—
733C22×C4—111no—
734C22×C4—111no—
735C22×C4—111no—
736C22×C4—114no—
737C22×C4—114no—
738C22×C4—114no—
739C22×C4—111no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—111no—
743C22×C4—111no—
744C22×C4—111no—
745C22×C4—112no—
746C22×C4—224no—
747C22×C4—222no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—222no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—441no—
756C22×C4—441no—
757C22×C4—441no—
758C22×C4—441no—
759C22×C4—441no—
760C22×C4—441no—
761C22×C4—441no—
762C22×C4—441no—
763C22×C4—441no—
764C22×C4—441no—
765C22×C4—442no—
766C22×C4—442no—
767C22×C4C23×D1112yes—
768C22×C4C23×D1111yescharacteristic
769C22×C4C23×D1112yes—
770C22×C4C23×D1111yescharacteristic
771C22×C4C23×D1112yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1111yescharacteristic
774C22×C4C23×D1111yescharacteristic
775C22×C4C23×D1111yescharacteristic
776C22×C4C23×D1111yescharacteristic
777C22×C4C23×D1111yescharacteristic
778C4⋊C4—22no—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—24no—
782C4⋊C4—22no—
783C4⋊C4—22no—
784C4⋊C4—24no—
785C4⋊C4—22no—
786C4⋊C4—42no—
787C4⋊C4—42no—
788C4⋊C4—222no—
789C4⋊C4—222no—
790C4⋊C4—222no—
791C4⋊C4—222no—
792C4⋊C4—224no—
793C4⋊C4—224no—
794C4⋊C4—222no—
795C4⋊C4—222no—
796C4⋊C4—222no—
797C4⋊C4—222no—
798C4⋊C4—442no—
799C4⋊C4—442no—
800C4⋊C4—442no—
801C4⋊C4—442no—
802C4⋊C4—442no—
803C4⋊C4—442no—
804C22⋊C4—224no—
805C22⋊C4—224no—
806C22⋊C4—224no—
807C22⋊C4—224no—
808C22⋊C4—224no—
809C22⋊C4—224no—
810C22⋊C4—224no—
811C22⋊C4—442no—
812C22⋊C4—442no—
813C22⋊C4—442no—
814C22⋊C4—442no—
815C22⋊C4—442no—
816C22⋊C4—442no—
817C22⋊C4—442no—
818C22⋊C4—442no—
819C42—22no—
820C42—22no—
821C42—22no—
822C42—42no—
823C42—222no—
824C42—222no—
825C42—224no—
826C42—222no—
827C42—222no—
828C42—222no—
829C42—441no—
830C42—441no—
831C42—441no—
832C42—441no—
833C42—442no—
834C11#3502411yescharacteristic, complemented, Sylow
835C23—112no—
836C23—112no—
837C23—112no—
838C23—221no—
839C23—221no—
840C23—221no—
841C23—221no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23C24×D1111yescharacteristic
850Q8—444no—
851D4—448no—
852D4—444no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—112no—
882C2×C4—112no—
883C2×C4—112no—
884C2×C4—228no—
885C2×C4—221no—
886C2×C4—221no—
887C2×C4—221no—
888C2×C4—221no—
889C2×C4—221no—
890C2×C4—221no—
891C2×C4—228no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—221no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—221no—
901C2×C4—221no—
902C2×C4—221no—
903C2×C4—221no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—221no—
907C2×C4—221no—
908C2×C4—221no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—221no—
912C2×C4—221no—
913C2×C4—444no—
914C2×C4—444no—
915C2×C4—444no—
916C2×C4—444no—
917C2×C4—444no—
918C2×C4—884no—
919C2×C4#6704012yes—
920C2×C4#41×D1112yes—
921C2×C4#41×D1112yes—
922C2×C4#41×D1112yes—
923C2×C4#6704212yes—
924C22—114no—
925C22—222no—
926C22—222no—
927C22—222no—
928C22—222no—
929C22—222no—
930C22—222no—
931C22—442no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22C2×#6704011yescharacteristic
939C22C2×#41×D1111yescharacteristic
940C22C2×#41×D1111yescharacteristic
941C22C2×#41×D1111yescharacteristic
942C22C2×#6704211yescharacteristic
943C22#1062345511yescharacteristic
944C22#1062345711yescharacteristic
945C4—22no—
946C4—22no—
947C4—42no—
948C4—41no—
949C4—42no—
950C4—41no—
951C4—41no—
952C4—42no—
953C4—41no—
954C4—42no—
955C4—222no—
956C4—222no—
957C4—222no—
958C4—441no—
959C4—441no—
960C4—441no—
961C4—442no—
962C4—442no—
963C4—442no—
964C4—441no—
965C4#1062322314yes—
966C2—224no—
967C2—882no—
968C2D11×#52911yescharacteristic
969C2C2×#1062322311yescharacteristic
970C2#1308200311yescharacteristic
971C2#1308244511yescharacteristic
972C2#1308246911yescharacteristic
973C2#1308247911yescharacteristic
974C2#1308248211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2509C2
prime radicalC2×#66948C22
hypercenter#2509D11
hypocenterC11#35024
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2509

Complements

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

NH ≅ G/Ntype
1. #13076954C2semidirect
3. #13076925C2semidirect
5. #13074570C2semidirect
6. #13074403C2semidirect
7. #13074156C2semidirect
8. #13074118C2semidirect
9. #13073930C2semidirect
10. #13073908C2semidirect
11. #13073227C2semidirect
12. #13073207C2semidirect
13. #13073150C2semidirect
14. #13072486C2semidirect
15. #13072478C2semidirect
16. #13072414C2semidirect
17. #13072405C2semidirect
18. #13071280C2semidirect
19. #13071248C2semidirect
20. C4×#66950C2semidirect
22. C4×C4⋊C4×D11C2semidirect
23. C11×#2509C2semidirect
360. #2509D11semidirect
834. C11#35024semidirect

Maximal subgroups

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

subgroupindex
#130769542
#130769492
#130769252
#130769182
#130745702
#130744032
#130741562
#130741182
#130739302
#130739082
#130732272
#130732072
#130731502
#130724862
#130724782
#130724142
#130724052
#130712802
#130712482
C4×#669502
#130711242
C4×C4⋊C4×D112
C11×#25092
#3502411