Finite Group Databasebeta

← #14926722

Subgroups — #14926722

Order 2816.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623144C212yesmaximal, complemented
2#13076984C211yesmaximal, characteristic, complemented
3#13076972C211yesmaximal, characteristic, complemented
4#13076959C211yesmaximal, characteristic, complemented
5#13076942C211yesmaximal, characteristic, complemented
6#13074761C212yesmaximal, complemented
7#13074741C212yesmaximal, complemented
8#13073689C212yesmaximal, complemented
9#13073680C212yesmaximal, complemented
10#13073203C211yesmaximal, characteristic, complemented
11#13072979C211yesmaximal, characteristic, complemented
12#13072737C212yesmaximal, complemented
13#13072375C211yesmaximal, characteristic, complemented
14#13072320C211yesmaximal, characteristic, complemented
15#13072250C211yesmaximal, characteristic, complemented
16#13072155C212yesmaximal, complemented
17#13072052C211yesmaximal, characteristic, complemented
18#13071968C211yesmaximal, characteristic, complemented
19#13071272C212yesmaximal, complemented
20C4×#66991C211yesmaximal, characteristic, complemented
21D11×#390C211yesmaximal, characteristic, complemented
22C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
23C11×#2428C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2212yescomplemented
28C2×C11×#121C2211yescharacteristic, complemented
29C2×C4×D4×C11C2211yescharacteristic, complemented
30C2×#66993C2211yescharacteristic
31C2×#66992C2212yescomplemented
32C2×#66992C2212yescomplemented
33C2×#66991C2211yescharacteristic
34C2×#66991C2212yes—
35C2×#66990C2212yes—
36C2×#66990C2212yes—
37C2×#66990C2212yes—
38C2×#66989C2212yescomplemented
39C2×#66989C2212yescomplemented
40C2×#66988C2212yescomplemented
41C2×#66983C2211yescharacteristic
42C2×#66982C2212yescomplemented
43C2×C4×C22⋊D11C2212yes—
44C2×C4×C22⋊D11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic, complemented
46#10623144—216no—
47C2×#66951C2212yescomplemented
48C2×#66949C2212yes—
49C2×C4⋊C4×D11C2211yescharacteristic
50C2×#66938C2212yescomplemented
51C2×(C22⋊D11)⋊C4C2211yescharacteristic
52C2×(C22⋊D11)⋊C4C2211yescharacteristic
53C2×C22⋊C4×D11C2212yes—
54C2×C22⋊C4×D11C2212yes—
55C2×#66932C2212yescomplemented
56C2×C42×D11C2211yescharacteristic
57C2×#66922C2211yescharacteristic, complemented
58C11×#394C2212yescomplemented
59C11×#392C2212yescomplemented
60C11×#390C2211yescharacteristic
61C11×#389C2211yescharacteristic, complemented
62C11×#386C2212yescomplemented
63C4×C11×C22⋊C4C2211yescharacteristic, complemented
64#10622836C2212yes—
65#10622836C2212yes—
66#10622836C2212yes—
67#10622835C2212yescomplemented
68#10622834C2211yescharacteristic
69#10622834C2211yescharacteristic
70#10622834C2211yescharacteristic
71#10622834C2212yescomplemented
72#10622834C2211yescharacteristic, complemented
73#10622834C2212yescomplemented
74#10622834C2211yescharacteristic, complemented
75#10622833C2212yescomplemented
76#10622826C2212yescomplemented
77#10622825C2211yescharacteristic, complemented
78C4×C22⋊Dic11C2212yescomplemented
79#10622603C2212yescomplemented
80#10622601C2211yescharacteristic
81#10622601C2211yescharacteristic
82#10622600C2211yescharacteristic
83#10622598C2211yescharacteristic, complemented
84#10622592C2212yescomplemented
85#10622589C2211yescharacteristic, complemented
86#10622586C2211yescharacteristic, complemented
87#10622586C2211yescharacteristic, complemented
88#10622574C2212yescomplemented
89#10622572C2212yes—
90#10622572C2212yescomplemented
91#10622572C2212yescomplemented
92#10622570C2212yes—
93#10622570C2212yes—
94#10622570C2212yescomplemented
95#10622570C2212yescomplemented
96#10622569C2212yes—
97#10622569C2212yes—
98#10622568C2212yes—
99#10622565C2212yescomplemented
100#10622561C2212yescomplemented
101#10622561C2212yescomplemented
102#10622557C2212yescomplemented
103#10622557C2212yescomplemented
104#10622557C2212yescomplemented
105#10622557C2212yescomplemented
106C22⋊C4×Dic11C2211yescharacteristic, complemented
107C22⋊C4×Dic11C2211yescharacteristic, complemented
108#10622552C2211yescharacteristic
109#10622552C2211yescharacteristic
110C4×(C2×D11)⋊C4C2211yescharacteristic
111C4×C4⋊Dic11C2211yescharacteristic, complemented
112C4×Dic11⋊C4C2211yescharacteristic, complemented
113C42×Dic11C2211yescharacteristic, complemented
114#10622286C2212yescomplemented
115#10622283C2212yescomplemented
116#10622283C2212yescomplemented
117#10622282C2212yescomplemented
118#10622281C2212yes—
119#10622279C2211yescharacteristic
120#10622279C2211yescharacteristic
121#10622270C2212yescomplemented
122#10622262C2211yescharacteristic, complemented
123#10622262C2211yescharacteristic, complemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2312yes—
129C22×D4×C11C2312yes—
130C22×D4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2311yescharacteristic
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C23×Dic11C2311yescharacteristic
140C23×Dic11C2311yescharacteristic
141C2×D4×D11—24no—
142C2×D4×D11—42no—
143C2×D4×D11—42no—
144C22×D44C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2312yes—
150C11×#127—42no—
151C11×#121—28no—
152C11×#121—42no—
153C11×#121—42no—
154C4×D4×C11—42no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180#66993—42no—
181#66992—28no—
182#66992—44no—
183#66991—28no—
184#66991—24no—
185#66990—28no—
186#66990—28no—
187#66990—28no—
188#66989—28no—
189#66989—44no—
190#66988—28no—
191#66983—42no—
192#66982—28no—
193C4×C22⋊D11—28no—
194C4×C22⋊D11—24no—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2311yescharacteristic
207C2×(C2×D11)⋊C4C2311yescharacteristic
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2311yescharacteristic
221C2×C4×Dic11—42no—
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2311yescharacteristic
232C2×C4×Dic11C2311yescharacteristic
233C2×C4×Dic11C2311yescharacteristic
234#66951—28no—
235#66949—28no—
236C4⋊C4×D11—42no—
237#66938—28no—
238(C22⋊D11)⋊C4—24no—
239(C22⋊D11)⋊C4D418yescomplemented
240C22⋊C4×D11—28no—
241C22⋊C4×D11—44no—
242#66932—28no—
243C42×D11—42no—
244#66922—42no—
245C11×#95C2311yescharacteristic
246C11×#95C2311yescharacteristic
247C11×#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2312yes—
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#35007—111nomaximal, Sylow
259C24×C11C2412yes—
260C24×C11C2412yes—
261C24×C11C2411yescharacteristic
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—24no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11—42no—
269C23×D11C2412yes—
270C23×D11C2411yescharacteristic
271C2×D4×C11—24no—
272C2×D4×C11—24no—
273C2×D4×C11—24no—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11—24no—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—42no—
282C2×D4×C11—42no—
283C2×D4×C11—42no—
284C2×D4×C11—42no—
285C2×D4×C11—42no—
286C2×D4×C11—42no—
287C2×D4×C11—42no—
288C2×D4×C11—42no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—22no—
292C22×C4×C11—24no—
293C22×C4×C11—42no—
294C22×C4×C11—42no—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2412yes—
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11C2×D414yes—
321C22×Dic11—22no—
322C22×Dic11—22no—
323C22×Dic11—41no—
324C22×Dic11—41no—
325C22×Dic11—41no—
326C22×Dic11C2×D414yescomplemented
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2412yes—
329C22×Dic11C2412yes—
330C22×Dic11C2412yes—
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2411yescharacteristic
337D4×D11—416no—
338C2×D44—22no—
339C2×D44—22no—
340C2×D44—22no—
341C2×C4×D11—22no—
342C2×C4×D11—24no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—41no—
347C2×C4×D11—41no—
348C2×C4×D11—41no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11C2×D414yes—
352C2×C4×D11#4114yes—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—24no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—42no—
362C11×C22⋊C4—42no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4C2×D414yescomplemented
366C42×C11—22no—
367C42×C11—22no—
368C22⋊Dic11—24no—
369C22⋊Dic11—24no—
370C22⋊Dic11—24no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—22no—
374C22⋊Dic11—24no—
375C22⋊Dic11—24no—
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11—24no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4C2×D414yes—
393(C2×D11)⋊C4#4114yes—
394C4⋊Dic11—24no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—22no—
398C4⋊Dic11—42no—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—24no—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406Dic11⋊C4C2×D414yescomplemented
407C4×Dic11—22no—
408C4×Dic11—24no—
409C4×Dic11—22no—
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—41no—
414C4×Dic11—41no—
415C4×Dic11—41no—
416C4×Dic11—41no—
417C4×Dic11—41no—
418C4×Dic11C2×D414yescomplemented
419C2×#538—112no—
420#2860—111no—
421#2858—111no—
422#2856—111no—
423#2854—111no—
424#2662—112no—
425#2661—112no—
426#2555—112no—
427#2554—112no—
428#2512—111no—
429#2491—111no—
430#2472—112no—
431#2445—111no—
432#2440—111no—
433#2433—111no—
434#2428D1111yescharacteristic, complemented
435#2424—112no—
436#2416—111no—
437#2408—111no—
438#2321—112no—
439C4×#121—111no—
440C2×#390—111no—
441C42×D4—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—22no—
459C23×C11—22no—
460C23×C11—22no—
461C23×C11—22no—
462C23×C11C22×D412yes—
463C23×C11C2511yescharacteristic
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11—84no—
479C22×D11—84no—
480C22×D11—84no—
481C22×D11—84no—
482C22×D11C22×D412yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4112yes—
485D4×C11—44no—
486D4×C11—44no—
487D4×C11—84no—
488D4×C11—84no—
489D4×C11—84no—
490D4×C11—84no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—44no—
510C2×C4×C11—84no—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C22×D412yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11C2×#4112yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C2×C4×C11H(5,𝔽2)12yes—
517C22⋊D11—28no—
518C22⋊D11—48no—
519C22⋊D11—48no—
520C22⋊D11—84no—
521C22⋊D11—84no—
522C22⋊D11—84no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—21no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—21no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—21no—
547C2×Dic11—44no—
548C2×Dic11—44no—
549C2×Dic11C22×D412yes—
550C2×Dic11C22×D412yes—
551C2×Dic11C22×D412yes—
552C2×Dic11C2×#4112yes—
553C2×Dic11C2×#4112yes—
554C2×Dic11H(5,𝔽2)12yes—
555D44—44no—
556C4×D11—28no—
557C4×D11—44no—
558C4×D11—44no—
559C4×D11—84no—
560Dic22—84no—
561C23×D4—111no—
562#538—2216no—
563C2×C4⋊Q8—111no—
564C2×#127—111no—
565C2×#127C2×D1111yescharacteristic
566C2×#126—112no—
567C2×#126—112no—
568C2×#124—112no—
569C2×#124—112no—
570C2×#124—112no—
571C2×#123—112no—
572C2×#123—112no—
573C2×C22⋊Q8—112no—
574C2×#121—112no—
575C2×#121—112no—
576C2×#121—111no—
577C2×#121—112no—
578C2×#121—111no—
579C2×#121C2×D1111yescharacteristic
580C2×#121C2×D1112yescomplemented
581C2×#121C2×D1111yescharacteristic, complemented
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—112no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—111no—
589C2×C4×D4C2×D1111yescharacteristic, complemented
590C22×C4⋊C4—111no—
591C22×C22⋊C4—112no—
592C22×C22⋊C4—112no—
593C22×C42—111no—
594C22×C42—111no—
595#398—112no—
596#397—112no—
597#396—112no—
598#396—112no—
599#395—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394C2×D1112yescomplemented
606#393—112no—
607#392—112no—
608#392—112no—
609#392—112no—
610#392C2×D1112yescomplemented
611#390—112no—
612#390—111no—
613#390—111no—
614#390—111no—
615#390—111no—
616#390—111no—
617#390—112no—
618#390—111no—
619#390—111no—
620#390—112no—
621#390—112no—
622#390—112no—
623#390—112no—
624#390—111no—
625#390—111no—
626#390C2×D1111yescharacteristic
627#389—111no—
628#389—111no—
629#389—111no—
630#389C2×D1111yescharacteristic, complemented
631#388—112no—
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#388—112no—
637#388—112no—
638#388—112no—
639#386—112no—
640#386—112no—
641#386—112no—
642#386—112no—
643#386C2×D1112yescomplemented
644#385—112no—
645#384—111no—
646#380—111no—
647#380—111no—
648#379—112no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4—111no—
653C4×C22⋊C4—112no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4C2×D1111yescharacteristic, complemented
660C43—111no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11—41no—
667C22×C11—41no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11—42no—
681C22×C11—42no—
682C22×C11C23×D411yescharacteristic
683C22×C11C22×#4111yescharacteristic
684C22×C11C22×#4111yescharacteristic
685C22×C11C2×H(5,𝔽2)11yescharacteristic
686C22×C11C2×H(5,𝔽2)11yescharacteristic
687C22×C11C2×H(5,𝔽2)11yescharacteristic
688C22×C11#58511yescharacteristic
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—816no—
703C2×D11#53214yes—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—41no—
708C4×C11—42no—
709C4×C11—42no—
710C4×C11—41no—
711C4×C11#53814yescomplemented
712Dic11—22no—
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—42no—
719Dic11—41no—
720Dic11—42no—
721Dic11—42no—
722C25—112no—
723C22×Q8—112no—
724C22×D4—111no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—111no—
731C22×D4—224no—
732C22×D4—442no—
733C22×D4—442no—
734C22×D4C22×D1111yescharacteristic
735C22×D4C22×D1111yescharacteristic
736C22×D4C22×D1112yes—
737C22×D4C22×D1112yes—
738C22×D4C22×D1112yes—
739C22×D4C22×D1112yes—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—112no—
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1112yes—
748C4⋊Q8—442no—
749#127—42no—
750#127—442no—
751#126—228no—
752#126—228no—
753#124—228no—
754#124—228no—
755#124—444no—
756#123—228no—
757#123—228no—
758C22⋊Q8—228no—
759#121—28no—
760#121—42no—
761#121—42no—
762#121—228no—
763#121—224no—
764#121—228no—
765#121—444no—
766#121—442no—
767#120—228no—
768#120—228no—
769#120—228no—
770C4×D4—42no—
771C4×D4—118no—
772C4×D4—224no—
773C4×D4—228no—
774C4×D4—224no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—111no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—442no—
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1111yescharacteristic
791C2×C4⋊C4C22×D1112yes—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—111no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—228no—
819C2×C22⋊C4—444no—
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1111yescharacteristic
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1111yescharacteristic
827C2×C42—111no—
828C2×C42—112no—
829C2×C42—111no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—111no—
835C2×C42—111no—
836C2×C42—111no—
837C2×C42—111no—
838C2×C42—111no—
839C2×C42—442no—
840C2×C42—442no—
841C2×C42C22×D1111yescharacteristic
842C2×C42C22×D1111yescharacteristic
843#95—111no—
844#95—111no—
845#95—111no—
846#95—111no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95C22×D1111yescharacteristic
854#95C22×D1111yescharacteristic
855#95C22×D1112yes—
856C2×C11—42no—
857C2×C11—82no—
858C2×C11—82no—
859C2×C11C2×#53211yescharacteristic
860C2×C11C2×#53811yescharacteristic
861C2×C11#346011yescharacteristic
862C2×C11#349611yescharacteristic
863C2×C11#349811yescharacteristic
864C2×C11#351411yescharacteristic
865C2×C11#351911yescharacteristic
866D11—24no—
867D11—82no—
868C24—111no—
869C24—112no—
870C24—224no—
871C24—224no—
872C24—224no—
873C24—442no—
874C24—442no—
875C24—442no—
876C24—442no—
877C24C23×D1112yes—
878C24C23×D1112yes—
879C24C23×D1111yescharacteristic
880C2×Q8—224no—
881C2×Q8—442no—
882C2×Q8—442no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—24no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—114no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—224no—
905C2×D4—222no—
906C2×D4—222no—
907C2×D4—224no—
908C2×D4—224no—
909C2×D4—224no—
910C2×D4—224no—
911C2×D4—222no—
912C2×D4—222no—
913C2×D4—222no—
914C2×D4—4416no—
915C2×D4—442no—
916C2×D4—442no—
917C2×D4—442no—
918C2×D4—442no—
919C2×D4—442no—
920C2×D4—442no—
921C2×D4—442no—
922C2×D4—442no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—24no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—111no—
933C22×C4—111no—
934C22×C4—111no—
935C22×C4—114no—
936C22×C4—114no—
937C22×C4—114no—
938C22×C4—111no—
939C22×C4—112no—
940C22×C4—112no—
941C22×C4—112no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—224no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—441no—
955C22×C4—441no—
956C22×C4—441no—
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1112yes—
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—114no—
969C4⋊C4—224no—
970C4⋊C4—222no—
971C4⋊C4—222no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—224no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—22no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—114no—
988C22⋊C4—114no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—222no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—222no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—224no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4—442no—
1012C22⋊C4—442no—
1013C22⋊C4D4×D1114yescomplemented
1014C42—22no—
1015C42—22no—
1016C42—114no—
1017C42—222no—
1018C42—224no—
1019C42—222no—
1020C42—222no—
1021C42—222no—
1022C42—222no—
1023C42—441no—
1024C42—441no—
1025C42—441no—
1026C42—441no—
1027C42—441no—
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—112no—
1050C23—112no—
1051C23—112no—
1052C23—221no—
1053C23—221no—
1054C23—221no—
1055C23—221no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—448no—
1064C23—448no—
1065C23—448no—
1066C23—884no—
1067C23—884no—
1068C23—884no—
1069C23—884no—
1070C23C2×D4×D1112yes—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—44no—
1074D4—44no—
1075D4—84no—
1076D4—84no—
1077D4—84no—
1078D4—84no—
1079D4—228no—
1080D4—448no—
1081D4—448no—
1082D4—444no—
1083D4—884no—
1084D4—884no—
1085D4—884no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—44no—
1105C2×C4—84no—
1106C2×C4—112no—
1107C2×C4—112no—
1108C2×C4—112no—
1109C2×C4—112no—
1110C2×C4—112no—
1111C2×C4—112no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—221no—
1123C2×C4—221no—
1124C2×C4—228no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—222no—
1130C2×C4—221no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—444no—
1140C2×C4—444no—
1141C2×C4—884no—
1142C2×C4C2×D4×D1112yes—
1143C2×C4C2×D4×D1112yes—
1144C2×C4#6703712yes—
1145C2×C4#6703712yes—
1146C2×C4#41×D1112yes—
1147C2×C4#41×D1112yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—114no—
1170C22—222no—
1171C22—222no—
1172C22—222no—
1173C22—222no—
1174C22—222no—
1175C22—222no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—8816no—
1184C22C22×D4×D1111yescharacteristic
1185C22C2×#6703711yescharacteristic
1186C22C2×#6703711yescharacteristic
1187C22C2×#41×D1111yescharacteristic
1188C22C2×#41×D1111yescharacteristic
1189C22D11×H(5,𝔽2)11yescharacteristic
1190C22#1062345511yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—42no—
1195C4—42no—
1196C4—41no—
1197C4—41no—
1198C4—222no—
1199C4—222no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—442no—
1205C4—442no—
1206C4—442no—
1207C4—441no—
1208C4#1062314414yescomplemented
1209C2—42no—
1210C2—82no—
1211C2—82no—
1212C2—224no—
1213C2—882no—
1214C2D11×#53211yescharacteristic
1215C2C2×#1062314411yescharacteristic
1216C2#1308203111yescharacteristic
1217C2#1308237211yescharacteristic
1218C2#1308238811yescharacteristic
1219C2#1308257411yescharacteristic
1220C2#1308264711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2428C2
hypercenter#2428D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2428

Complements

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

NH ≅ G/Ntype
1. C2×#10623144C2semidirect
2. #13076984C2semidirect
3. #13076972C2semidirect
4. #13076959C2semidirect
5. #13076942C2semidirect
6. #13074761C2semidirect
7. #13074741C2semidirect
8. #13073689C2semidirect
9. #13073680C2semidirect
10. #13073203C2semidirect
11. #13072979C2semidirect
12. #13072737C2semidirect
13. #13072375C2semidirect
14. #13072320C2semidirect
15. #13072250C2semidirect
16. #13072155C2semidirect
17. #13072052C2semidirect
18. #13071968C2semidirect
19. #13071272C2semidirect
20. C4×#66991C2semidirect
21. D11×#390C2semidirect
22. C4×(C22⋊D11)⋊C4C2semidirect
23. C11×#2428C2semidirect
27. C2×C11×#121C22semidirect
28. C2×C11×#121C22semidirect
29. C2×C4×D4×C11C22semidirect
31. C2×#66992C22semidirect
32. C2×#66992C22semidirect
38. C2×#66989C22semidirect
39. C2×#66989C22semidirect
40. C2×#66988C22semidirect
42. C2×#66982C22semidirect
45. C22×C4×Dic11C22semidirect
47. C2×#66951C22semidirect
50. C2×#66938C22semidirect
55. C2×#66932C22semidirect
57. C2×#66922C22semidirect
58. C11×#394C22semidirect
59. C11×#392C22semidirect
61. C11×#389C22semidirect
62. C11×#386C22semidirect
63. C4×C11×C22⋊C4C22semidirect
67. #10622835C22semidirect
71. #10622834C22semidirect
72. #10622834C22semidirect
73. #10622834C22semidirect
74. #10622834C22semidirect
75. #10622833C22semidirect
76. #10622826C22semidirect
77. #10622825C22semidirect
78. C4×C22⋊Dic11C22semidirect
79. #10622603C22semidirect
83. #10622598C22semidirect
84. #10622592C22semidirect
85. #10622589C22semidirect
86. #10622586C22semidirect
87. #10622586C22semidirect
88. #10622574C22semidirect
90. #10622572C22semidirect
91. #10622572C22semidirect
94. #10622570C22semidirect
95. #10622570C22semidirect
99. #10622565C22semidirect
100. #10622561C22semidirect
101. #10622561C22semidirect
102. #10622557C22semidirect
103. #10622557C22semidirect
104. #10622557C22semidirect
105. #10622557C22semidirect
106. C22⋊C4×Dic11C22semidirect
107. C22⋊C4×Dic11C22semidirect
111. C4×C4⋊Dic11C22semidirect
112. C4×Dic11⋊C4C22semidirect
113. C42×Dic11C22semidirect
114. #10622286C22semidirect
115. #10622283C22semidirect
116. #10622283C22semidirect
117. #10622282C22semidirect
121. #10622270C22semidirect
122. #10622262C22semidirect
123. #10622262C22semidirect
239. (C22⋊D11)⋊C4D4semidirect
326. C22×Dic11C2×D4semidirect
365. C11×C22⋊C4C2×D4semidirect
406. Dic11⋊C4C2×D4semidirect
418. C4×Dic11C2×D4semidirect
434. #2428D11semidirect
580. C2×#121C2×D11semidirect
581. C2×#121C2×D11semidirect
589. C2×C4×D4C2×D11semidirect
605. #394C2×D11semidirect
610. #392C2×D11semidirect
630. #389C2×D11semidirect
643. #386C2×D11semidirect
659. C4×C22⋊C4C2×D11semidirect
711. C4×C11#538semidirect
1013. C22⋊C4D4×D11semidirect
1028. C11#35007semidirect
1208. C4#10623144semidirect

Maximal subgroups

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

subgroupindex
C2×#106231442
#130769842
#130769722
#130769592
#130769422
#130747612
#130747412
#130736892
#130736802
#130732032
#130729792
#130727372
#130723752
#130723202
#130722502
#130721552
#130720522
#130719682
#130712722
C4×#669912
D11×#3902
C4×(C22⋊D11)⋊C42
C11×#24282
#3500711