Finite Group Databasebeta

← #14926908

Subgroups — #14926908

Order 2816.

1816 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076999C211yesmaximal, characteristic, complemented
2#13076975C211yesmaximal, characteristic, complemented
3#13076969C211yesmaximal, characteristic, complemented
4#13076954C211yesmaximal, characteristic, complemented
5#13074817C212yesmaximal, complemented
6#13074796C212yesmaximal, complemented
7#13074009C212yesmaximal, complemented
8#13073697C212yesmaximal, complemented
9#13073091C211yesmaximal, characteristic, complemented
10#13073043C211yesmaximal, characteristic, complemented
11#13072931C211yesmaximal, characteristic
12#13072758C212yesmaximal, complemented
13#13072455C211yesmaximal, characteristic, complemented
14#13072420C212yesmaximal
15#13072320C211yesmaximal, characteristic, complemented
16#13072142C211yesmaximal, characteristic, complemented
17#13072065C211yesmaximal, characteristic
18#13071350C212yesmaximal, complemented
19#13071248C212yesmaximal
20C4×#66950C211yesmaximal, characteristic, complemented
21D11×#389C211yesmaximal, characteristic, complemented
22C4×#66946C211yesmaximal, characteristic
23C11×#2507C211yesmaximal, characteristic, complemented
24C2×#66950C2211yescharacteristic
25C2×#66950C2211yescharacteristic
26C2×#66950C2212yes—
27C2×#66949C2212yes—
28C2×#66946C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×C4⋊C4×D11C2212yes—
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×#66942C2212yes—
34C2×C4×D44C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C42×D11C2211yescharacteristic
37C2×#66922C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C11×#398C2212yes—
40C11×#398C2212yes—
41C11×#389C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#389C2212yes—
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#387C2212yes—
47C11×#384C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50#10622607C2212yes—
51#10622605C2212yes—
52#10622605C2212yes—
53#10622602C2212yes—
54#10622602C2212yes—
55#10622602C2212yes—
56#10622602C2212yes—
57#10622600C2211yescharacteristic
58#10622600C2211yescharacteristic
59#10622600C2211yescharacteristic
60#10622600C2212yes—
61#10622600C2212yes—
62#10622600C2211yescharacteristic
63#10622598C2211yescharacteristic
64#10622598C2211yescharacteristic
65#10622598C2212yes—
66#10622597C2212yes—
67#10622597C2212yes—
68#10622597C2212yes—
69#10622594C2212yes—
70#10622594C2212yes—
71#10622594C2212yes—
72#10622592C2212yes—
73#10622592C2212yes—
74#10622591C2212yes—
75#10622589C2211yescharacteristic
76#10622589C2211yescharacteristic
77C4⋊C4×Dic11C2211yescharacteristic
78C4⋊C4×Dic11C2211yescharacteristic
79#10622587C2211yescharacteristic
80#10622587C2211yescharacteristic
81#10622587C2212yes—
82#10622586C2211yescharacteristic
83#10622586C2211yescharacteristic
84#10622585C2212yes—
85#10622585C2212yes—
86#10622553C2212yes—
87C4×(C2×D11)⋊C4C2211yescharacteristic
88C4×(C2×D11)⋊C4C2212yes—
89C4×(C2×D11)⋊C4C2211yescharacteristic
90C4×C4⋊Dic11C2212yes—
91#10622546C2212yes—
92C42×Dic11C2211yescharacteristic
93#10622542C2211yescharacteristic
94#10622542C2211yescharacteristic
95#10622541C2211yescharacteristic
96#10622541C2211yescharacteristic
97#10622289C2212yes—
98#10622282C2212yes—
99#10622281C2212yes—
100#10622281C2212yes—
101#10622279C2211yescharacteristic
102#10622279C2211yescharacteristic
103#10622279C2211yescharacteristic
104#10622279C2211yescharacteristic
105#10622278C2212yes—
106#10622278C2212yes—
107#10622277C2212yes—
108D11×#95C2212yes—
109#10622274C2212yes—
110#10622273C2212yes—
111#10622271C2212yes—
112#10622270C2212yes—
113#10622270C2212yes—
114#10622268C2212yes—
115#10622268C2212yes—
116#10622267C2212yes—
117#10622266C2212yes—
118#10622264C2212yes—
119#10622263C2212yes—
120#10622260C2212yes—
121#10622260C2212yes—
122#10622259C2212yes—
123C22×D44C2311yescharacteristic
124C22×C4×D11C2311yescharacteristic
125C22×C4×D11C2311yescharacteristic
126C22×C4×D11C2311yescharacteristic
127C22×C4×D11C2311yescharacteristic
128C22×C4×D11C2312yes—
129C22×C4×D11C2312yes—
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×Dic22C2311yescharacteristic
133C22×Dic22C2312yes—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2312yes—
150C2×(C2×D11)⋊C4C2311yescharacteristic
151C2×(C2×D11)⋊C4C2311yescharacteristic
152C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
160C2×(C2×D11)⋊C4C2311yescharacteristic
161C2×(C2×D11)⋊C4C2311yescharacteristic
162C2×C4⋊Dic11C2311yescharacteristic
163C2×C4⋊Dic11C2311yescharacteristic
164C2×C4⋊Dic11C2311yescharacteristic
165C2×C4⋊Dic11C2312yes—
166C2×C4⋊Dic11C2312yes—
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193#66950—24no—
194#66950—44no—
195#66950—42no—
196#66949—28no—
197#66946—24no—
198#66946Q818yescomplemented
199C4⋊C4×D11—24no—
200C4⋊C4×D11—44no—
201C4⋊C4×D11—42no—
202#66942—44no—
203C4×D44—24no—
204C42×D11—42no—
205C42×D11—42no—
206#66922—42no—
207C4×Dic22—42no—
208C11×#95C2311yescharacteristic
209C11×#95C2312yes—
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11×#95C2312yes—
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⋊#95C2311yescharacteristic
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2312yes—
236C11⋊#95C2311yescharacteristic
237#35017—111nomaximal, Sylow
238C23×D11C2411yescharacteristic
239C23×D11C2411yescharacteristic
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2411yescharacteristic
243C22×C4×C11C2412yes—
244C22×C4×C11C2411yescharacteristic
245C22×C4×C11C2412yes—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×Dic11C2411yescharacteristic
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2411yescharacteristic
257C22×Dic11C2411yescharacteristic
258C22×Dic11C2411yescharacteristic
259C22×Dic11C2411yescharacteristic
260C22×Dic11C2411yescharacteristic
261C2×D44—22no—
262C2×D44—22no—
263C2×D44C2×Q814yes—
264C2×C4×D11—22no—
265C2×C4×D11—22no—
266C2×C4×D11—24no—
267C2×C4×D11—22no—
268C2×C4×D11—24no—
269C2×C4×D11—22no—
270C2×C4×D11—22no—
271C2×C4×D11—22no—
272C2×C4×D11—22no—
273C2×C4×D11—22no—
274C2×C4×D11—22no—
275C2×C4×D11—41no—
276C2×C4×D11—41no—
277C2×C4×D11—41no—
278C2×C4×D11—41no—
279C2×C4×D11—42no—
280C2×C4×D11—41no—
281C2×C4×D11—41no—
282C2×C4×D11—42no—
283C2×C4×D11—42no—
284C2×C4×D11—42no—
285C2×C4×D11C2×Q814yes—
286C2×C4×D11C2×Q814yes—
287C2×C4×D11#4114yes—
288C2×Dic22—22no—
289C2×Dic22—24no—
290C2×Dic22—22no—
291C2×Dic22—22no—
292C2×Dic22—42no—
293C2×Dic22—42no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—24no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—22no—
300C11×C4⋊C4—42no—
301C11×C4⋊C4—42no—
302C11×C4⋊C4—42no—
303C11×C4⋊C4—42no—
304C11×C4⋊C4—42no—
305C11×C4⋊C4C2×Q814yes—
306C42×C11—22no—
307C42×C11—22no—
308C42×C11—22no—
309C42×C11—42no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—42no—
316(C2×D11)⋊C4—42no—
317(C2×D11)⋊C4—42no—
318(C2×D11)⋊C4—42no—
319(C2×D11)⋊C4C2×Q814yes—
320(C2×D11)⋊C4C2×Q814yes—
321(C2×D11)⋊C4#4114yes—
322C4⋊Dic11—22no—
323C4⋊Dic11—24no—
324C4⋊Dic11—24no—
325C4⋊Dic11—24no—
326C4⋊Dic11—22no—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—42no—
330C4⋊Dic11—42no—
331Dic11⋊C4—24no—
332Dic11⋊C4—24no—
333Dic11⋊C4—24no—
334Dic11⋊C4—24no—
335Dic11⋊C4—42no—
336Dic11⋊C4—42no—
337Dic11⋊C4—42no—
338Dic11⋊C4—42no—
339Dic11⋊C4—42no—
340Dic11⋊C4—42no—
341Dic11⋊C4—42no—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11—22no—
345C4×Dic11—22no—
346C4×Dic11—42no—
347C4×Dic11—41no—
348C4×Dic11—41no—
349C4×Dic11—41no—
350C4×Dic11—41no—
351C4×Dic11—41no—
352C4×Dic11C2×Q814yes—
353#2863—111no—
354#2859—111no—
355#2857—111no—
356#2855—111no—
357#2667—112no—
358#2666—112no—
359#2585—112no—
360#2556—112no—
361#2507D1111yescharacteristic, complemented
362#2502—111no—
363#2497—111no—
364#2487—111no—
365#2473—112no—
366#2451—111no—
367#2449—112no—
368#2440—111no—
369#2423—111no—
370#2417—111no—
371#2329—112no—
372#2318—112no—
373C4×C22⋊Q8—111no—
374C2×#389—111no—
375C42×D4—111no—
376C23×C11C2511yescharacteristic
377C22×D11—21no—
378C22×D11—21no—
379C22×D11—21no—
380C22×D11—21no—
381C22×D11—21no—
382C22×D11—21no—
383C22×D11—21no—
384C22×D11—21no—
385C22×D11—21no—
386C22×D11—21no—
387C22×D11C22×Q812yes—
388C22×D11C22×Q812yes—
389C22×D11C2×#4112yes—
390C22×D11C2×#4112yes—
391C2×C4×C11—21no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—22no—
408C2×C4×C11—21no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—21no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11C22×Q812yes—
418C2×C4×C11C22×Q812yes—
419C2×C4×C11C22×Q812yes—
420C2×C4×C11C2×#4112yes—
421C2×C4×C11C2×#4112yes—
422C2×C4×C11H(5,𝔽2)12yes—
423C2×C4×C112−1+412yes—
424C2×Dic11—21no—
425C2×Dic11—21no—
426C2×Dic11—21no—
427C2×Dic11—21no—
428C2×Dic11—21no—
429C2×Dic11—21no—
430C2×Dic11—21no—
431C2×Dic11—21no—
432C2×Dic11—21no—
433C2×Dic11—21no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—21no—
448C2×Dic11—22no—
449C2×Dic11C22×Q812yes—
450C2×Dic11C22×Q812yes—
451C2×Dic11C2×#4112yes—
452C2×Dic11C2×#4112yes—
453C2×Dic11H(5,𝔽2)12yes—
454D44—28no—
455C4×D11—28no—
456C4×D11—44no—
457C4×D11—44no—
458C4×D11—44no—
459C4×D11—44no—
460C4×D11—48no—
461C4×D11—44no—
462C4×D11—84no—
463Dic22—44no—
464Dic22—84no—
465C2×C4⋊Q8—111no—
466C2×#125—112no—
467C2×C22⋊Q8—112no—
468C2×C22⋊Q8—111no—
469C2×C22⋊Q8—111no—
470C2×C22⋊Q8—112no—
471C2×C4×Q8—111no—
472C2×C4×D4—111no—
473C2×C4×D4—111no—
474C2×C4×D4—111no—
475C22×C4⋊C4—111no—
476C22×C4⋊C4—111no—
477C22×C4⋊C4—112no—
478C22×C42—111no—
479C22×C42—111no—
480#400—112no—
481#400—112no—
482#399—112no—
483#399—112no—
484#398—112no—
485#398—112no—
486#398—112no—
487#398—112no—
488#398—112no—
489#398—112no—
490#398C2×D1112yes—
491#398C2×D1112yes—
492#396—112no—
493#396—112no—
494#395—112no—
495#395—112no—
496#391—112no—
497#391—111no—
498#391—111no—
499#391—111no—
500#391—111no—
501#391—112no—
502#389—112no—
503#389—112no—
504#389—111no—
505#389—111no—
506#389—111no—
507#389—111no—
508#389—112no—
509#389—111no—
510#389—111no—
511#389—112no—
512#389—112no—
513#389C2×D1112yes—
514#389C2×D1111yescharacteristic
515#389C2×D1111yescharacteristic
516#389C2×D1111yescharacteristic
517#389C2×D1111yescharacteristic
518#388—112no—
519#388—112no—
520#387—112no—
521#387—112no—
522#387—112no—
523#387—112no—
524#387—112no—
525#387—112no—
526#387—112no—
527#387—112no—
528#387—112no—
529#387C2×D1112yes—
530#386—112no—
531#386—112no—
532#385—112no—
533#385—112no—
534#385—112no—
535#385—112no—
536#385—112no—
537#385—112no—
538#384—111no—
539#384—111no—
540#384C2×D1111yescharacteristic
541#383—112no—
542#382—112no—
543#381—112no—
544#380—112no—
545#380—112no—
546#380—111no—
547#380—111no—
548#380—111no—
549#380—111no—
550C4×C4⋊C4—111no—
551C4×C4⋊C4—111no—
552C4×C4⋊C4—112no—
553C4×C4⋊C4C2×D1111yescharacteristic
554C4×C4⋊C4C2×D1111yescharacteristic
555C4×C22⋊C4—112no—
556C4×C22⋊C4—111no—
557C4×C22⋊C4—111no—
558C4×C22⋊C4—111no—
559C4×C22⋊C4—111no—
560C4×C22⋊C4—111no—
561C4×C22⋊C4—111no—
562C2×#95—112no—
563C43—111no—
564C22×C11C23×Q811yescharacteristic
565C22×C11C22×#4111yescharacteristic
566C22×C11C22×#4111yescharacteristic
567C22×C11C2×H(5,𝔽2)11yescharacteristic
568C22×C11C2×H(5,𝔽2)11yescharacteristic
569C22×C11C2×2−1+411yescharacteristic
570C22×C11#58511yescharacteristic
571C2×D11—22no—
572C2×D11—22no—
573C2×D11—22no—
574C2×D11—22no—
575C2×D11—22no—
576C2×D11—22no—
577C2×D11—22no—
578C2×D11—22no—
579C2×D11—22no—
580C2×D11—41no—
581C2×D11—41no—
582C2×D11—41no—
583C2×D11—41no—
584C2×D11#53314yes—
585C4×C11—22no—
586C4×C11—22no—
587C4×C11—22no—
588C4×C11—22no—
589C4×C11—42no—
590C4×C11—41no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11—41no—
594C4×C11—42no—
595C4×C11#53914yes—
596Dic11—22no—
597Dic11—22no—
598Dic11—22no—
599Dic11—22no—
600Dic11—22no—
601Dic11—42no—
602Dic11—41no—
603Dic11—42no—
604Dic11—42no—
605Dic11—42no—
606C22×Q8—111no—
607C22×Q8—112no—
608C22×D4—111no—
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—112no—
616C23×C4—112no—
617C4⋊Q8—442no—
618#125—444no—
619C22⋊Q8—228no—
620C22⋊Q8—224no—
621C22⋊Q8—442no—
622C22⋊Q8—444no—
623C4×Q8—442no—
624C4×D4—118no—
625C4×D4—224no—
626C4×D4—224no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—111no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—112no—
636C2×C4⋊C4—112no—
637C2×C4⋊C4—112no—
638C2×C4⋊C4—112no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—224no—
648C2×C4⋊C4—442no—
649C2×C4⋊C4—444no—
650C2×C4⋊C4C22×D1111yescharacteristic
651C2×C4⋊C4C22×D1111yescharacteristic
652C2×C4⋊C4C22×D1111yescharacteristic
653C2×C4⋊C4C22×D1111yescharacteristic
654C2×C4⋊C4C22×D1112yes—
655C2×C4⋊C4C22×D1111yescharacteristic
656C2×C4⋊C4C22×D1112yes—
657C2×C4⋊C4C22×D1112yes—
658C2×C4⋊C4C22×D1112yes—
659C2×C4⋊C4C22×D1112yes—
660C2×C4⋊C4C22×D1112yes—
661C2×C4⋊C4C22×D1111yescharacteristic
662C2×C22⋊C4—111no—
663C2×C22⋊C4—111no—
664C2×C22⋊C4—111no—
665C2×C22⋊C4—111no—
666C2×C22⋊C4—111no—
667C2×C22⋊C4—111no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—112no—
671C2×C22⋊C4—112no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4—112no—
674C2×C42—111no—
675C2×C42—111no—
676C2×C42—111no—
677C2×C42—111no—
678C2×C42—111no—
679C2×C42—112no—
680C2×C42—111no—
681C2×C42—111no—
682C2×C42—111no—
683C2×C42—111no—
684C2×C42—111no—
685C2×C42—442no—
686C2×C42—442no—
687C2×C42C22×D1111yescharacteristic
688C2×C42C22×D1111yescharacteristic
689C2×C42C22×D1111yescharacteristic
690C2×C42C22×D1112yes—
691#95—112no—
692#95—112no—
693#95—112no—
694#95—111no—
695#95—111no—
696#95—111no—
697#95—111no—
698#95—112no—
699#95—112no—
700#95—112no—
701#95—112no—
702#95—112no—
703#95—112no—
704#95—112no—
705#95—112no—
706#95—112no—
707#95—112no—
708#95—112no—
709#95—112no—
710#95—112no—
711#95—112no—
712#95—112no—
713#95C22×D1112yes—
714#95C22×D1111yescharacteristic
715#95C22×D1111yescharacteristic
716#95C22×D1112yes—
717#95C22×D1112yes—
718#95C22×D1112yes—
719#95C22×D1112yes—
720C2×C11C2×#53311yescharacteristic
721C2×C11C2×#53911yescharacteristic
722C2×C11#346011yescharacteristic
723C2×C11#350111yescharacteristic
724C2×C11#350311yescharacteristic
725C2×C11#351511yescharacteristic
726C2×C11#351911yescharacteristic
727D11—24no—
728D11—42no—
729C24—111no—
730C24—111no—
731C2×Q8—222no—
732C2×Q8—222no—
733C2×Q8—224no—
734C2×Q8—222no—
735C2×Q8—442no—
736C2×Q8—442no—
737C2×D4—114no—
738C2×D4—222no—
739C2×D4—222no—
740C22×C4—111no—
741C22×C4—111no—
742C22×C4—111no—
743C22×C4—111no—
744C22×C4—111no—
745C22×C4—114no—
746C22×C4—114no—
747C22×C4—114no—
748C22×C4—111no—
749C22×C4—112no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—224no—
756C22×C4—222no—
757C22×C4—224no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—441no—
765C22×C4—441no—
766C22×C4—441no—
767C22×C4—441no—
768C22×C4—442no—
769C22×C4—441no—
770C22×C4—441no—
771C22×C4—442no—
772C22×C4—442no—
773C22×C4—442no—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C22×C4C23×D1111yescharacteristic
777C22×C4C23×D1112yes—
778C22×C4C23×D1111yescharacteristic
779C22×C4C23×D1112yes—
780C22×C4C23×D1111yescharacteristic
781C22×C4C23×D1111yescharacteristic
782C22×C4C23×D1111yescharacteristic
783C22×C4C23×D1111yescharacteristic
784C22×C4C23×D1111yescharacteristic
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—24no—
790C4⋊C4—22no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—42no—
794C4⋊C4—42no—
795C4⋊C4—42no—
796C4⋊C4—224no—
797C4⋊C4—224no—
798C4⋊C4—224no—
799C4⋊C4—222no—
800C4⋊C4—224no—
801C4⋊C4—224no—
802C4⋊C4—224no—
803C4⋊C4—224no—
804C4⋊C4—222no—
805C4⋊C4—222no—
806C4⋊C4—222no—
807C4⋊C4—442no—
808C4⋊C4—442no—
809C4⋊C4—442no—
810C4⋊C4—442no—
811C4⋊C4—442no—
812C4⋊C4—442no—
813C4⋊C4—442no—
814C4⋊C4—442no—
815C4⋊C4—442no—
816C4⋊C4Q8×D1114yes—
817C22⋊C4—114no—
818C22⋊C4—114no—
819C22⋊C4—114no—
820C22⋊C4—222no—
821C22⋊C4—222no—
822C22⋊C4—222no—
823C22⋊C4—224no—
824C22⋊C4—224no—
825C22⋊C4—442no—
826C22⋊C4—442no—
827C22⋊C4—442no—
828C22⋊C4—442no—
829C42—22no—
830C42—22no—
831C42—22no—
832C42—42no—
833C42—114no—
834C42—222no—
835C42—222no—
836C42—222no—
837C42—222no—
838C42—441no—
839C42—441no—
840C42—441no—
841C42—441no—
842C42—442no—
843C42—441no—
844C11#3501711yescharacteristic, complemented, Sylow
845C23—112no—
846C23—112no—
847C23—112no—
848C23—112no—
849C23—221no—
850C23—221no—
851C23—221no—
852C23—221no—
853C23—221no—
854C23—221no—
855C23—221no—
856C23—221no—
857C23—221no—
858C23—221no—
859C23C24×D1111yescharacteristic
860Q8—444no—
861Q8—884no—
862D4—228no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—112no—
890C2×C4—112no—
891C2×C4—112no—
892C2×C4—112no—
893C2×C4—112no—
894C2×C4—221no—
895C2×C4—221no—
896C2×C4—221no—
897C2×C4—221no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—221no—
901C2×C4—221no—
902C2×C4—221no—
903C2×C4—221no—
904C2×C4—228no—
905C2×C4—221no—
906C2×C4—222no—
907C2×C4—221no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—221no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—444no—
921C2×C4—444no—
922C2×C4—444no—
923C2×C4—444no—
924C2×C4—448no—
925C2×C4—444no—
926C2×C4—884no—
927C2×C4C2×Q8×D1112yes—
928C2×C4C2×Q8×D1112yes—
929C2×C4C2×Q8×D1112yes—
930C2×C4#6704012yes—
931C2×C4#41×D1112yes—
932C2×C4#41×D1112yes—
933C2×C4#6704212yes—
934C22—114no—
935C22—222no—
936C22—222no—
937C22—222no—
938C22—222no—
939C22—222no—
940C22—222no—
941C22—222no—
942C22—222no—
943C22—222no—
944C22—441no—
945C22—441no—
946C22—441no—
947C22—441no—
948C22C22×Q8×D1111yescharacteristic
949C22C2×#6704011yescharacteristic
950C22C2×#41×D1111yescharacteristic
951C22C2×#41×D1111yescharacteristic
952C22C2×#6704211yescharacteristic
953C22D11×H(5,𝔽2)11yescharacteristic
954C22#1062345511yescharacteristic
955C4—22no—
956C4—22no—
957C4—22no—
958C4—22no—
959C4—41no—
960C4—42no—
961C4—42no—
962C4—41no—
963C4—42no—
964C4—42no—
965C4—222no—
966C4—222no—
967C4—222no—
968C4—222no—
969C4—222no—
970C4—442no—
971C4—442no—
972C4—441no—
973C4—442no—
974C4—442no—
975C4#1062322314yes—
976C2—224no—
977C2—442no—
978C2D11×#53311yescharacteristic
979C2C2×#1062322311yescharacteristic
980C2#1308203111yescharacteristic
981C2#1308241311yescharacteristic
982C2#1308243411yescharacteristic
983C2#1308259711yescharacteristic
984C2#1308264111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2507C2
prime radicalC22×D44C23
hypercenter#2507D11
hypocenterC11#35017
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2507

Complements

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

NH ≅ G/Ntype
1. #13076999C2semidirect
2. #13076975C2semidirect
3. #13076969C2semidirect
4. #13076954C2semidirect
5. #13074817C2semidirect
6. #13074796C2semidirect
7. #13074009C2semidirect
8. #13073697C2semidirect
9. #13073091C2semidirect
10. #13073043C2semidirect
12. #13072758C2semidirect
13. #13072455C2semidirect
15. #13072320C2semidirect
16. #13072142C2semidirect
18. #13071350C2semidirect
20. C4×#66950C2semidirect
21. D11×#389C2semidirect
23. C11×#2507C2semidirect
198. #66946Q8semidirect
361. #2507D11semidirect
844. C11#35017semidirect

Maximal subgroups

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

subgroupindex
#130769992
#130769752
#130769692
#130769542
#130748172
#130747962
#130740092
#130736972
#130730912
#130730432
#130729312
#130727582
#130724552
#130724202
#130723202
#130721422
#130720652
#130713502
#130712482
C4×#669502
D11×#3892
C4×#669462
C11×#25072
#3501711