Finite Group Databasebeta

← #14968572

Subgroups — #14968572

Order 2816.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077004C211yesmaximal, characteristic, complemented
2#13076986C211yesmaximal, characteristic, complemented
3#13076502C211yesmaximal, characteristic, complemented
4#13076475C211yesmaximal, characteristic
5#13076424C211yesmaximal, characteristic, complemented
6#13076314C211yesmaximal, characteristic, complemented
7#13076242C211yesmaximal, characteristic, complemented
8#13076194C211yesmaximal, characteristic, complemented
9#13076055C211yesmaximal, characteristic, complemented
10#13075986C211yesmaximal, characteristic, complemented
11#13075856C211yesmaximal, characteristic, complemented
12#13075720C211yesmaximal, characteristic, complemented
13#13075500C211yesmaximal, characteristic, complemented
14#13075435C211yesmaximal, characteristic, complemented
15#13075421C211yesmaximal, characteristic, complemented
16#13075397C211yesmaximal, characteristic, complemented
17#13075208C211yesmaximal, characteristic, complemented
18#13074646C211yesmaximal, characteristic, complemented
19#13074639C211yesmaximal, characteristic, complemented
20#13074296C211yesmaximal, characteristic
21#13074262C211yesmaximal, characteristic, complemented
22#13074186C211yesmaximal, characteristic, complemented
23#13073939C211yesmaximal, characteristic, complemented
24#13073753C211yesmaximal, characteristic, complemented
25#13073595C211yesmaximal, characteristic, complemented
26#13073396C211yesmaximal, characteristic, complemented
27#13073392C211yesmaximal, characteristic, complemented
28#13071425C211yesmaximal, characteristic, complemented
29#13071220C211yesmaximal, characteristic, complemented
30#13071091C211yesmaximal, characteristic, complemented
31C11×#2712C211yesmaximal, characteristic
32C2×C11×#124C2211yescharacteristic
33C2×C11×#124C2211yescharacteristic
34C2×Q8×Dic11C2211yescharacteristic
35C2×#66997C2211yescharacteristic
36C2×#66989C2211yescharacteristic
37C2×#66932C2211yescharacteristic
38C2×#66931C2211yescharacteristic
39C2×#66930C2211yescharacteristic
40C2×#66923C2211yescharacteristic
41C11×#397C2211yescharacteristic
42C11×#394C2211yescharacteristic
43C11×#394C2211yescharacteristic
44C11×#393C2211yescharacteristic
45C11×#393C2211yescharacteristic
46C11×#392C2211yescharacteristic
47C11×#391C2211yescharacteristic
48C11×#391C2211yescharacteristic
49C11×#388C2211yescharacteristic
50C11×#388C2211yescharacteristic
51C11×#386C2211yescharacteristic
52C11×#386C2211yescharacteristic
53C11×#385C2211yescharacteristic
54#10622843C2211yescharacteristic
55#10622843C2211yescharacteristic
56#10622843C2211yescharacteristic
57#10622843C2211yescharacteristic
58#10622842C2211yescharacteristic
59#10622842C2211yescharacteristic
60#10622835C2211yescharacteristic
61#10622835C2211yescharacteristic
62#10622835C2211yescharacteristic
63#10622834C2211yescharacteristic
64#10622834C2211yescharacteristic
65#10622834C2211yescharacteristic
66#10622834C2211yescharacteristic
67#10622833C2211yescharacteristic
68#10622833C2211yescharacteristic
69#10622833C2211yescharacteristic
70#10622833C2211yescharacteristic
71#10622825C2211yescharacteristic
72#10622824C2211yescharacteristic
73#10622823C2211yescharacteristic
74C4×C22⋊Dic11C2211yescharacteristic
75#10622599C2211yescharacteristic
76#10622597C2211yescharacteristic
77#10622596C2211yescharacteristic
78#10622595C2211yescharacteristic
79#10622594C2211yescharacteristic
80#10622594C2211yescharacteristic
81#10622592C2211yescharacteristic
82#10622591C2211yescharacteristic
83#10622591C2211yescharacteristic
84#10622589C2211yescharacteristic
85C4⋊C4×Dic11C2211yescharacteristic
86#10622586C2211yescharacteristic
87#10622566C2211yescharacteristic
88#10622566C2211yescharacteristic
89#10622566C2211yescharacteristic
90#10622566C2211yescharacteristic
91#10622565C2211yescharacteristic
92#10622565C2211yescharacteristic
93#10622565C2211yescharacteristic
94#10622565C2211yescharacteristic
95#10622565C2211yescharacteristic
96#10622564C2211yescharacteristic
97#10622564C2211yescharacteristic
98#10622564C2211yescharacteristic
99#10622564C2211yescharacteristic
100#10622564C2211yescharacteristic
101#10622564C2211yescharacteristic
102#10622563C2211yescharacteristic
103#10622563C2211yescharacteristic
104#10622563C2211yescharacteristic
105#10622562C2211yescharacteristic
106#10622561C2211yescharacteristic
107#10622561C2211yescharacteristic
108#10622561C2211yescharacteristic
109#10622561C2211yescharacteristic
110#10622561C2211yescharacteristic
111#10622561C2211yescharacteristic
112#10622561C2211yescharacteristic
113#10622560C2211yescharacteristic
114#10622560C2211yescharacteristic
115#10622560C2211yescharacteristic
116#10622559C2211yescharacteristic
117#10622558C2211yescharacteristic
118#10622558C2211yescharacteristic
119#10622558C2211yescharacteristic
120#10622558C2211yescharacteristic
121#10622558C2211yescharacteristic
122#10622558C2211yescharacteristic
123#10622558C2211yescharacteristic
124#10622558C2211yescharacteristic
125#10622558C2211yescharacteristic
126#10622558C2211yescharacteristic
127#10622558C2211yescharacteristic
128#10622558C2211yescharacteristic
129#10622558C2211yescharacteristic
130#10622558C2211yescharacteristic
131#10622557C2211yescharacteristic
132#10622557C2211yescharacteristic
133#10622557C2211yescharacteristic
134#10622557C2211yescharacteristic
135#10622557C2211yescharacteristic
136#10622556C2211yescharacteristic
137#10622555C2211yescharacteristic
138#10622555C2211yescharacteristic
139C22⋊C4×Dic11C2211yescharacteristic
140#10622546C2211yescharacteristic
141#10622546C2211yescharacteristic
142C4×Dic11⋊C4C2211yescharacteristic
143C42×Dic11C2211yescharacteristic
144#10622542C2211yescharacteristic
145#10622542C2211yescharacteristic
146#10622541C2211yescharacteristic
147C11⋊#401C2211yescharacteristic
148#10622274C2211yescharacteristic
149#10622274C2211yescharacteristic
150#10622273C2211yescharacteristic
151#10622273C2211yescharacteristic
152#10622273C2211yescharacteristic
153#10622272C2211yescharacteristic
154#10622271C2211yescharacteristic
155#10622271C2211yescharacteristic
156#10622270C2211yescharacteristic
157#10622269C2211yescharacteristic
158#10622269C2211yescharacteristic
159#10622268C2211yescharacteristic
160#10622268C2211yescharacteristic
161#10622268C2211yescharacteristic
162#10622268C2211yescharacteristic
163#10622268C2211yescharacteristic
164#10622267C2211yescharacteristic
165#10622267C2211yescharacteristic
166#10622267C2211yescharacteristic
167#10622267C2211yescharacteristic
168#10622267C2211yescharacteristic
169#10622267C2211yescharacteristic
170#10622267C2211yescharacteristic
171#10622266C2211yescharacteristic
172#10622266C2211yescharacteristic
173#10622266C2211yescharacteristic
174#10622265C2211yescharacteristic
175#10622265C2211yescharacteristic
176#10622264C2211yescharacteristic
177#10622264C2211yescharacteristic
178#10622263C2211yescharacteristic
179#10622262C2211yescharacteristic
180#10622262C2211yescharacteristic
181#10622261C2211yescharacteristic
182#10622261C2211yescharacteristic
183#10622260C2211yescharacteristic
184#10622259C2211yescharacteristic
185#10622259C2211yescharacteristic
186#10622259C2211yescharacteristic
187C22×Q8×C11C2311yescharacteristic
188C22×Q8×C11C2311yescharacteristic
189C22×D4×C11C2311yescharacteristic
190C22×D4×C11C2311yescharacteristic
191C22×D4×C11C2311yescharacteristic
192C23×C4×C11C2311yescharacteristic
193C23×Dic11C2311yescharacteristic
194C23×Dic11C2311yescharacteristic
195C22×Dic22C2311yescharacteristic
196C22×Dic22C2311yescharacteristic
197C11×#124—42no—
198C11×#124—42no—
199C2×C11×C4⋊C4C2311yescharacteristic
200C2×C11×C4⋊C4C2311yescharacteristic
201C2×C11×C4⋊C4C2311yescharacteristic
202C2×C11×C22⋊C4C2311yescharacteristic
203C2×C11×C22⋊C4C2311yescharacteristic
204C2×C11×C22⋊C4C2311yescharacteristic
205C2×C11×C22⋊C4C2311yescharacteristic
206C2×C11×C22⋊C4C2311yescharacteristic
207C2×C11×C22⋊C4C2311yescharacteristic
208C2×C11×C22⋊C4C2311yescharacteristic
209C2×C11×C22⋊C4C2311yescharacteristic
210C2×C11×C22⋊C4C2311yescharacteristic
211C2×C11×C22⋊C4C2311yescharacteristic
212C2×C11×C22⋊C4C2311yescharacteristic
213C2×C11×C22⋊C4C2311yescharacteristic
214C2×C11×C22⋊C4C2311yescharacteristic
215C2×C11×C22⋊C4C2311yescharacteristic
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2311yescharacteristic
218C2×C22⋊Dic11C2311yescharacteristic
219C2×C22⋊Dic11C2311yescharacteristic
220C2×C22⋊Dic11C2311yescharacteristic
221C2×C22⋊Dic11C2311yescharacteristic
222C2×C22⋊Dic11C2311yescharacteristic
223C2×C22⋊Dic11C2311yescharacteristic
224C2×C22⋊Dic11C2311yescharacteristic
225C2×C22⋊Dic11C2311yescharacteristic
226C2×C22⋊Dic11C2311yescharacteristic
227C2×C22⋊Dic11C2311yescharacteristic
228C2×C22⋊Dic11C2311yescharacteristic
229C2×C22⋊Dic11C2311yescharacteristic
230C2×C22⋊Dic11C2311yescharacteristic
231C2×C22⋊Dic11C2311yescharacteristic
232C2×C22⋊Dic11C2311yescharacteristic
233C2×C22⋊Dic11C2311yescharacteristic
234C2×C22⋊Dic11C2311yescharacteristic
235C2×C22⋊Dic11C2311yescharacteristic
236C2×C22⋊Dic11C2311yescharacteristic
237C2×C22⋊Dic11C2311yescharacteristic
238C2×C22⋊Dic11C2311yescharacteristic
239C2×C22⋊Dic11C2311yescharacteristic
240Q8×Dic11—24no—
241#66997—42no—
242#66989—24no—
243C2×C4⋊Dic11C2311yescharacteristic
244C2×C4⋊Dic11C2311yescharacteristic
245C2×C4⋊Dic11C2311yescharacteristic
246C2×C4⋊Dic11C2311yescharacteristic
247C2×C4⋊Dic11C2311yescharacteristic
248C2×C4⋊Dic11C2311yescharacteristic
249C2×C4⋊Dic11C2311yescharacteristic
250C2×C4⋊Dic11C2311yescharacteristic
251C2×C4⋊Dic11C2311yescharacteristic
252C2×C4⋊Dic11C2311yescharacteristic
253C2×C4⋊Dic11C2311yescharacteristic
254C2×C4⋊Dic11C2311yescharacteristic
255C2×Dic11⋊C4C2311yescharacteristic
256C2×Dic11⋊C4C2311yescharacteristic
257C2×Dic11⋊C4C2311yescharacteristic
258C2×Dic11⋊C4C2311yescharacteristic
259C2×Dic11⋊C4C2311yescharacteristic
260C2×Dic11⋊C4C2311yescharacteristic
261C2×Dic11⋊C4C2311yescharacteristic
262C2×Dic11⋊C4C2311yescharacteristic
263C2×Dic11⋊C4C2311yescharacteristic
264C2×Dic11⋊C4C2311yescharacteristic
265C2×Dic11⋊C4C2311yescharacteristic
266C2×Dic11⋊C4C2311yescharacteristic
267C2×Dic11⋊C4C2311yescharacteristic
268C2×Dic11⋊C4C2311yescharacteristic
269C2×Dic11⋊C4C2311yescharacteristic
270C2×Dic11⋊C4C2311yescharacteristic
271C2×Dic11⋊C4C2311yescharacteristic
272C2×Dic11⋊C4C2311yescharacteristic
273C2×Dic11⋊C4C2311yescharacteristic
274C2×Dic11⋊C4C2311yescharacteristic
275C2×C4×Dic11C2311yescharacteristic
276C2×C4×Dic11C2311yescharacteristic
277C2×C4×Dic11C2311yescharacteristic
278C2×C4×Dic11C2311yescharacteristic
279C2×C4×Dic11C2311yescharacteristic
280C2×C4×Dic11C2311yescharacteristic
281C2×C4×Dic11C2311yescharacteristic
282C2×C4×Dic11C2311yescharacteristic
283C2×C4×Dic11C2311yescharacteristic
284C2×C4×Dic11C2311yescharacteristic
285C2×C4×Dic11C2311yescharacteristic
286C2×C4×Dic11C2311yescharacteristic
287C2×C4×Dic11C2311yescharacteristic
288C2×C4×Dic11C2311yescharacteristic
289#66932—42no—
290#66931—42no—
291#66930—24no—
292#66923—42no—
293C11×#95C2311yescharacteristic
294C11×#95C2311yescharacteristic
295C11×#95C2311yescharacteristic
296C11×#95C2311yescharacteristic
297C11×#95C2311yescharacteristic
298C11×#95C2311yescharacteristic
299C11×#95C2311yescharacteristic
300C11×#95C2311yescharacteristic
301C11×#95C2311yescharacteristic
302C11×#95C2311yescharacteristic
303C11⋊#95C2311yescharacteristic
304C11⋊#95C2311yescharacteristic
305C11⋊#95C2311yescharacteristic
306C11⋊#95C2311yescharacteristic
307C11⋊#95C2311yescharacteristic
308C11⋊#95C2311yescharacteristic
309C11⋊#95C2311yescharacteristic
310C11⋊#95C2311yescharacteristic
311C11⋊#95C2311yescharacteristic
312C11⋊#95C2311yescharacteristic
313C11⋊#95C2311yescharacteristic
314C11⋊#95C2311yescharacteristic
315C11⋊#95C2311yescharacteristic
316C11⋊#95C2311yescharacteristic
317C11⋊#95C2311yescharacteristic
318C11⋊#95C2311yescharacteristic
319C11⋊#95C2311yescharacteristic
320C11⋊#95C2311yescharacteristic
321C11⋊#95C2311yescharacteristic
322C11⋊#95C2311yescharacteristic
323C11⋊#95C2311yescharacteristic
324C11⋊#95C2311yescharacteristic
325C11⋊#95C2311yescharacteristic
326C11⋊#95C2311yescharacteristic
327C11⋊#95C2311yescharacteristic
328C11⋊#95C2311yescharacteristic
329C11⋊#95C2311yescharacteristic
330C11⋊#95C2311yescharacteristic
331C11⋊#95C2311yescharacteristic
332C11⋊#95C2311yescharacteristic
333C11⋊#95C2311yescharacteristic
334C11⋊#95C2311yescharacteristic
335C11⋊#95C2311yescharacteristic
336C11⋊#95C2311yescharacteristic
337C11⋊#95C2311yescharacteristic
338C11⋊#95C2311yescharacteristic
339C11⋊#95C2311yescharacteristic
340C11⋊#95C2311yescharacteristic
341C11⋊#95C2311yescharacteristic
342C11⋊#95C2311yescharacteristic
343C11⋊#95C2311yescharacteristic
344C11⋊#95C2311yescharacteristic
345C11⋊#95C2311yescharacteristic
346C11⋊#95C2311yescharacteristic
347C11⋊#95C2311yescharacteristic
348C11⋊#95C2311yescharacteristic
349C11⋊#95C2311yescharacteristic
350C11⋊#95C2311yescharacteristic
351#37007—111nomaximal, Sylow
352C24×C11C2411yescharacteristic
353C24×C11C2411yescharacteristic
354C24×C11C2411yescharacteristic
355C2×Q8×C11—22no—
356C2×Q8×C11—22no—
357C2×Q8×C11—22no—
358C2×Q8×C11—41no—
359C2×Q8×C11—41no—
360C2×Q8×C11—41no—
361C2×D4×C11—22no—
362C2×D4×C11—22no—
363C2×D4×C11—41no—
364C2×D4×C11—41no—
365C2×D4×C11—41no—
366C2×D4×C11—41no—
367C2×D4×C11—41no—
368C2×D4×C11—41no—
369C2×D4×C11—41no—
370C22×C4×C11—41no—
371C22×C4×C11—41no—
372C22×C4×C11—41no—
373C22×C4×C11C2411yescharacteristic
374C22×C4×C11C2411yescharacteristic
375C22×C4×C11C2411yescharacteristic
376C22×C4×C11C2411yescharacteristic
377C22×C4×C11C2411yescharacteristic
378C22×C4×C11C2411yescharacteristic
379C22×C4×C11C2411yescharacteristic
380C22×C4×C11C2411yescharacteristic
381C22×C4×C11C2411yescharacteristic
382C22×C4×C11C2411yescharacteristic
383C22×C4×C11C2411yescharacteristic
384C22×C4×C11C2411yescharacteristic
385C22×Dic11—22no—
386C22×Dic11—41no—
387C22×Dic11—41no—
388C22×Dic11—41no—
389C22×Dic11—41no—
390C22×Dic11—41no—
391C22×Dic11C2411yescharacteristic
392C22×Dic11C2411yescharacteristic
393C22×Dic11C2411yescharacteristic
394C22×Dic11C2411yescharacteristic
395C22×Dic11C2411yescharacteristic
396C22×Dic11C2411yescharacteristic
397C22×Dic11C2411yescharacteristic
398C22×Dic11C2411yescharacteristic
399C22×Dic11C2411yescharacteristic
400C22×Dic11C2411yescharacteristic
401C22×Dic11C2411yescharacteristic
402C22×Dic11C2411yescharacteristic
403C22×Dic11C2411yescharacteristic
404C22×Dic11C2411yescharacteristic
405C22×Dic11C2411yescharacteristic
406C22×Dic11C2411yescharacteristic
407C2×Dic22—22no—
408C2×Dic22—41no—
409C2×Dic22—41no—
410C2×Dic22—41no—
411C2×Dic22—41no—
412C2×Dic22—41no—
413C11×C4⋊C4—41no—
414C11×C4⋊C4—41no—
415C11×C4⋊C4—41no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—41no—
422C11×C22⋊C4—41no—
423C11×C22⋊C4—41no—
424C11×C22⋊C4—41no—
425C11×C22⋊C4—41no—
426C11×C22⋊C4—41no—
427C11×C22⋊C4—41no—
428C11×C22⋊C4—41no—
429C11×C22⋊C4—41no—
430C42×C11—22no—
431C42×C11—41no—
432C22⋊Dic11—22no—
433C22⋊Dic11—22no—
434C22⋊Dic11—22no—
435C22⋊Dic11—22no—
436C22⋊Dic11—22no—
437C22⋊Dic11—41no—
438C22⋊Dic11—41no—
439C22⋊Dic11—41no—
440C22⋊Dic11—41no—
441C22⋊Dic11—41no—
442C22⋊Dic11—41no—
443C22⋊Dic11—41no—
444C22⋊Dic11—41no—
445C22⋊Dic11—41no—
446C22⋊Dic11—41no—
447C22⋊Dic11—41no—
448C22⋊Dic11—41no—
449C22⋊Dic11—41no—
450C22⋊Dic11—41no—
451C22⋊Dic11—41no—
452C22⋊Dic11—41no—
453C22⋊Dic11—41no—
454C4⋊Dic11—22no—
455C4⋊Dic11—22no—
456C4⋊Dic11—22no—
457C4⋊Dic11—22no—
458C4⋊Dic11—41no—
459C4⋊Dic11—41no—
460C4⋊Dic11—41no—
461C4⋊Dic11—41no—
462C4⋊Dic11—41no—
463C4⋊Dic11—41no—
464C4⋊Dic11—41no—
465C4⋊Dic11—41no—
466Dic11⋊C4—22no—
467Dic11⋊C4—22no—
468Dic11⋊C4—22no—
469Dic11⋊C4—22no—
470Dic11⋊C4—22no—
471Dic11⋊C4—22no—
472Dic11⋊C4—41no—
473Dic11⋊C4—41no—
474Dic11⋊C4—41no—
475Dic11⋊C4—41no—
476Dic11⋊C4—41no—
477Dic11⋊C4—41no—
478Dic11⋊C4—41no—
479Dic11⋊C4—41no—
480Dic11⋊C4—41no—
481Dic11⋊C4—41no—
482Dic11⋊C4—41no—
483Dic11⋊C4—41no—
484Dic11⋊C4—41no—
485Dic11⋊C4—41no—
486C4×Dic11—22no—
487C4×Dic11—22no—
488C4×Dic11—22no—
489C4×Dic11—22no—
490C4×Dic11—41no—
491C4×Dic11—41no—
492C4×Dic11—41no—
493C4×Dic11—41no—
494C4×Dic11—41no—
495C4×Dic11—41no—
496C4×Dic11—41no—
497C4×Dic11—41no—
498C4×Dic11—41no—
499C4×Dic11#4114yes—
500#2865—111no—
501#2861—111no—
502#2799—111no—
503#2797—111no—
504#2793—111no—
505#2784—111no—
506#2779—111no—
507#2775—111no—
508#2765—111no—
509#2759—111no—
510#2750—111no—
511#2740—111no—
512#2720—111no—
513#2716—111no—
514#2715—111no—
515#2713—111no—
516#2712D1111yescharacteristic
517#2700—111no—
518#2651—111no—
519#2650—111no—
520#2610—111no—
521#2605—111no—
522#2599—111no—
523#2577—111no—
524#2560—111no—
525#2545—111no—
526#2527—111no—
527#2526—111no—
528#2337—111no—
529#2314—111no—
530#2295—111no—
531C23×C11—21no—
532C23×C11—21no—
533C23×C11—21no—
534C23×C11—21no—
535C23×C11—21no—
536C23×C11—21no—
537C23×C11—21no—
538C23×C11—21no—
539C23×C11—21no—
540C23×C11—21no—
541C23×C11—21no—
542C23×C11—21no—
543C23×C11—21no—
544C23×C11—21no—
545C23×C11—21no—
546C23×C11—21no—
547C23×C11—21no—
548C23×C11—21no—
549C23×C11—21no—
550C23×C11—21no—
551C23×C11—21no—
552C23×C11C2511yescharacteristic
553Q8×C11—44no—
554Q8×C11—82no—
555D4×C11—82no—
556D4×C11—82no—
557D4×C11—82no—
558C2×C4×C11—21no—
559C2×C4×C11—21no—
560C2×C4×C11—21no—
561C2×C4×C11—21no—
562C2×C4×C11—21no—
563C2×C4×C11—21no—
564C2×C4×C11—21no—
565C2×C4×C11—21no—
566C2×C4×C11—21no—
567C2×C4×C11—21no—
568C2×C4×C11—21no—
569C2×C4×C11—21no—
570C2×C4×C11—21no—
571C2×C4×C11—21no—
572C2×C4×C11—21no—
573C2×C4×C11—21no—
574C2×C4×C11—21no—
575C2×C4×C11—21no—
576C2×C4×C11—21no—
577C2×C4×C11—21no—
578C2×C4×C11—21no—
579C2×C4×C11—21no—
580C2×C4×C11—21no—
581C2×C4×C11—21no—
582C2×C4×C11—21no—
583C2×C4×C11—21no—
584C2×C4×C11—21no—
585C2×C4×C11—21no—
586C2×C4×C11—21no—
587C2×C4×C11—21no—
588C2×C4×C11—21no—
589C2×C4×C11—21no—
590C2×C4×C11—21no—
591C2×C4×C11—82no—
592C2×C4×C11C2×#4112yes—
593C2×C4×C11H(5,𝔽2)12yes—
594C2×C4×C112−1+412yes—
595C2×Dic11—21no—
596C2×Dic11—21no—
597C2×Dic11—21no—
598C2×Dic11—21no—
599C2×Dic11—21no—
600C2×Dic11—21no—
601C2×Dic11—21no—
602C2×Dic11—21no—
603C2×Dic11—21no—
604C2×Dic11—21no—
605C2×Dic11—21no—
606C2×Dic11—21no—
607C2×Dic11—21no—
608C2×Dic11—21no—
609C2×Dic11—21no—
610C2×Dic11—21no—
611C2×Dic11—21no—
612C2×Dic11—21no—
613C2×Dic11—21no—
614C2×Dic11—21no—
615C2×Dic11—21no—
616C2×Dic11—21no—
617C2×Dic11—21no—
618C2×Dic11—21no—
619C2×Dic11—21no—
620C2×Dic11—21no—
621C2×Dic11—21no—
622C2×Dic11—21no—
623C2×Dic11—21no—
624C2×Dic11—21no—
625C2×Dic11—21no—
626C2×Dic11—21no—
627C2×Dic11—21no—
628C2×Dic11—21no—
629C2×Dic11—21no—
630C2×Dic11—21no—
631C2×Dic11—21no—
632C2×Dic11—21no—
633C2×Dic11—21no—
634C2×Dic11—21no—
635C2×Dic11—21no—
636C2×Dic11—21no—
637C2×Dic11—21no—
638C2×Dic11—21no—
639C2×Dic11—21no—
640C2×Dic11—21no—
641C2×Dic11—44no—
642C2×Dic11—82no—
643C2×Dic11C2×#4112yes—
644C2×Dic11C2×#4112yes—
645Dic22—82no—
646Dic22—82no—
647C2×C4⋊Q8—111no—
648C2×#126—111no—
649C2×#125—111no—
650C2×#124—111no—
651C2×#124C2×D1111yescharacteristic
652C2×#124C2×D1111yescharacteristic
653C2×C22⋊Q8—111no—
654C2×C4×Q8—111no—
655C2×#117—111no—
656#401—111no—
657#400—111no—
658#400—111no—
659#400—111no—
660#400—111no—
661#400—111no—
662#400—111no—
663#400—111no—
664#400—111no—
665#399—111no—
666#398—111no—
667#398—111no—
668#398—111no—
669#398—111no—
670#398—111no—
671#397—111no—
672#397—111no—
673#397—111no—
674#397—111no—
675#397—111no—
676#397—111no—
677#397—111no—
678#397—111no—
679#397—111no—
680#397C2×D1111yescharacteristic
681#396—111no—
682#396—111no—
683#396—111no—
684#396—111no—
685#396—111no—
686#396—111no—
687#396—111no—
688#395—111no—
689#395—111no—
690#395—111no—
691#395—111no—
692#395—111no—
693#394—111no—
694#394—111no—
695#394—111no—
696#394C2×D1111yescharacteristic
697#394C2×D1111yescharacteristic
698#393—111no—
699#393—111no—
700#393—111no—
701#393C2×D1111yescharacteristic
702#393C2×D1111yescharacteristic
703#392C2×D1111yescharacteristic
704#391—111no—
705#391—111no—
706#391—111no—
707#391—111no—
708#391—111no—
709#391—111no—
710#391—111no—
711#391—111no—
712#391—111no—
713#391C2×D1111yescharacteristic
714#391C2×D1111yescharacteristic
715#390—111no—
716#390—111no—
717#390—111no—
718#390—111no—
719#389—111no—
720#389—111no—
721#389—111no—
722#388—111no—
723#388—111no—
724#388—111no—
725#388—111no—
726#388—111no—
727#388—111no—
728#388—111no—
729#388—111no—
730#388—111no—
731#388—111no—
732#388—111no—
733#388—111no—
734#388—111no—
735#388—111no—
736#388—111no—
737#388—111no—
738#388—111no—
739#388—111no—
740#388—111no—
741#388—111no—
742#388—111no—
743#388—111no—
744#388—111no—
745#388—111no—
746#388—111no—
747#388C2×D1111yescharacteristic
748#388C2×D1111yescharacteristic
749#387—111no—
750#387—111no—
751#387—111no—
752#387—111no—
753#387—111no—
754#387—111no—
755#387—111no—
756#387—111no—
757#387—111no—
758#387—111no—
759#387—111no—
760#387—111no—
761#387—111no—
762#387—111no—
763#387—111no—
764#387—111no—
765#387—111no—
766#387—111no—
767#387—111no—
768#387—111no—
769#387—111no—
770#387—111no—
771#387—111no—
772#386—111no—
773#386—111no—
774#386—111no—
775#386—111no—
776#386C2×D1111yescharacteristic
777#386C2×D1111yescharacteristic
778#385—111no—
779#385—111no—
780#385—111no—
781#385—111no—
782#385—111no—
783#385C2×D1111yescharacteristic
784#384—111no—
785#383—111no—
786#383—111no—
787#382—111no—
788#381—111no—
789#381—111no—
790#380—111no—
791#380—111no—
792#380—111no—
793C4×C4⋊C4—111no—
794C4×C4⋊C4—111no—
795C4×C4⋊C4—111no—
796C4×C4⋊C4—111no—
797C4×C22⋊C4—111no—
798C4×C22⋊C4—111no—
799#376—111no—
800#376—111no—
801C43—111no—
802C22×C11—41no—
803C22×C11—41no—
804C22×C11—41no—
805C22×C11—41no—
806C22×C11—41no—
807C22×C11—41no—
808C22×C11—41no—
809C22×C11—41no—
810C22×C11—41no—
811C22×C11—41no—
812C22×C11—41no—
813C22×C11—41no—
814C22×C11—41no—
815C22×C11—41no—
816C22×C11—41no—
817C22×C11—41no—
818C22×C11—41no—
819C22×C11—41no—
820C22×C11—41no—
821C22×C11—41no—
822C22×C11—41no—
823C22×C11C22×#4111yescharacteristic
824C22×C11C2×H(5,𝔽2)11yescharacteristic
825C22×C11C2×2−1+411yescharacteristic
826C22×C11#58511yescharacteristic
827C22×C11#58511yescharacteristic
828C22×C11#58511yescharacteristic
829C22×C11#58511yescharacteristic
830C4×C11—22no—
831C4×C11—22no—
832C4×C11—22no—
833C4×C11—41no—
834C4×C11—41no—
835C4×C11—41no—
836C4×C11—41no—
837C4×C11—41no—
838C4×C11—41no—
839C4×C11—41no—
840C4×C11—41no—
841C4×C11—41no—
842Dic11—22no—
843Dic11—22no—
844Dic11—41no—
845Dic11—41no—
846Dic11—41no—
847Dic11—41no—
848Dic11—41no—
849Dic11—41no—
850Dic11—41no—
851Dic11—41no—
852Dic11—41no—
853Dic11—41no—
854Dic11—41no—
855Dic11—41no—
856Dic11—41no—
857Dic11—41no—
858C22×Q8—111no—
859C22×Q8—111no—
860C22×Q8C22×D1111yescharacteristic
861C22×Q8C22×D1111yescharacteristic
862C22×D4C22×D1111yescharacteristic
863C22×D4C22×D1111yescharacteristic
864C22×D4C22×D1111yescharacteristic
865C23×C4—111no—
866C23×C4—111no—
867C23×C4C22×D1111yescharacteristic
868C4⋊Q8—442no—
869#126—442no—
870#125—442no—
871#124—42no—
872#124—42no—
873#124—224no—
874C22⋊Q8—442no—
875C4×Q8—224no—
876#117—224no—
877C2×C4⋊C4—111no—
878C2×C4⋊C4—111no—
879C2×C4⋊C4—111no—
880C2×C4⋊C4—111no—
881C2×C4⋊C4—111no—
882C2×C4⋊C4—111no—
883C2×C4⋊C4—111no—
884C2×C4⋊C4—111no—
885C2×C4⋊C4—111no—
886C2×C4⋊C4—111no—
887C2×C4⋊C4—111no—
888C2×C4⋊C4—111no—
889C2×C4⋊C4—111no—
890C2×C4⋊C4—111no—
891C2×C4⋊C4—111no—
892C2×C4⋊C4—111no—
893C2×C4⋊C4—111no—
894C2×C4⋊C4—111no—
895C2×C4⋊C4—111no—
896C2×C4⋊C4—111no—
897C2×C4⋊C4—111no—
898C2×C4⋊C4—111no—
899C2×C4⋊C4—111no—
900C2×C4⋊C4—111no—
901C2×C4⋊C4—111no—
902C2×C4⋊C4—111no—
903C2×C4⋊C4—111no—
904C2×C4⋊C4—111no—
905C2×C4⋊C4—111no—
906C2×C4⋊C4—111no—
907C2×C4⋊C4—111no—
908C2×C4⋊C4—111no—
909C2×C4⋊C4C22×D1111yescharacteristic
910C2×C4⋊C4C22×D1111yescharacteristic
911C2×C4⋊C4C22×D1111yescharacteristic
912C2×C22⋊C4—111no—
913C2×C22⋊C4—111no—
914C2×C22⋊C4—111no—
915C2×C22⋊C4—111no—
916C2×C22⋊C4—111no—
917C2×C22⋊C4—111no—
918C2×C22⋊C4—111no—
919C2×C22⋊C4—111no—
920C2×C22⋊C4—111no—
921C2×C22⋊C4—111no—
922C2×C22⋊C4—111no—
923C2×C22⋊C4—111no—
924C2×C22⋊C4—111no—
925C2×C22⋊C4—111no—
926C2×C22⋊C4—111no—
927C2×C22⋊C4—111no—
928C2×C22⋊C4—111no—
929C2×C22⋊C4—111no—
930C2×C22⋊C4—111no—
931C2×C22⋊C4—111no—
932C2×C22⋊C4—111no—
933C2×C22⋊C4—111no—
934C2×C22⋊C4C22×D1111yescharacteristic
935C2×C22⋊C4C22×D1111yescharacteristic
936C2×C22⋊C4C22×D1111yescharacteristic
937C2×C22⋊C4C22×D1111yescharacteristic
938C2×C22⋊C4C22×D1111yescharacteristic
939C2×C22⋊C4C22×D1111yescharacteristic
940C2×C22⋊C4C22×D1111yescharacteristic
941C2×C22⋊C4C22×D1111yescharacteristic
942C2×C22⋊C4C22×D1111yescharacteristic
943C2×C22⋊C4C22×D1111yescharacteristic
944C2×C22⋊C4C22×D1111yescharacteristic
945C2×C22⋊C4C22×D1111yescharacteristic
946C2×C22⋊C4C22×D1111yescharacteristic
947C2×C22⋊C4C22×D1111yescharacteristic
948C2×C42—111no—
949C2×C42—111no—
950C2×C42—111no—
951C2×C42—111no—
952C2×C42—111no—
953C2×C42—111no—
954C2×C42—111no—
955C2×C42—111no—
956C2×C42—111no—
957C2×C42—111no—
958C2×C42—111no—
959C2×C42—111no—
960C2×C42—111no—
961C2×C42—111no—
962C2×C42C22×D1111yescharacteristic
963C2×C42C22×D1111yescharacteristic
964#95—111no—
965#95—111no—
966#95—111no—
967#95—111no—
968#95—111no—
969#95—111no—
970#95—111no—
971#95—111no—
972#95—111no—
973#95—111no—
974#95—111no—
975#95—111no—
976#95—111no—
977#95—111no—
978#95—111no—
979#95—111no—
980#95—111no—
981#95—111no—
982#95—111no—
983#95—111no—
984#95—111no—
985#95—111no—
986#95—111no—
987#95—111no—
988#95—111no—
989#95—111no—
990#95—111no—
991#95—111no—
992#95—111no—
993#95—111no—
994#95—111no—
995#95—111no—
996#95—111no—
997#95—111no—
998#95—111no—
999#95—111no—
1000#95—111no—
1001#95—111no—
1002#95—111no—
1003#95—111no—
1004#95—111no—
1005#95—111no—
1006#95—111no—
1007#95—111no—
1008#95—111no—
1009#95—111no—
1010#95—111no—
1011#95—111no—
1012#95C22×D1111yescharacteristic
1013#95C22×D1111yescharacteristic
1014#95C22×D1111yescharacteristic
1015#95C22×D1111yescharacteristic
1016#95C22×D1111yescharacteristic
1017#95C22×D1111yescharacteristic
1018#95C22×D1111yescharacteristic
1019#95C22×D1111yescharacteristic
1020#95C22×D1111yescharacteristic
1021#95C22×D1111yescharacteristic
1022C2×C11—81no—
1023C2×C11—81no—
1024C2×C11—81no—
1025C2×C11#345511yescharacteristic
1026C2×C11#349411yescharacteristic
1027C2×C11#350711yescharacteristic
1028C2×C11#355111yescharacteristic
1029C2×C11#356111yescharacteristic
1030C2×C11#356511yescharacteristic
1031C2×C11#356811yescharacteristic
1032C24C23×D1111yescharacteristic
1033C24C23×D1111yescharacteristic
1034C24C23×D1111yescharacteristic
1035C2×Q8—22no—
1036C2×Q8—22no—
1037C2×Q8—22no—
1038C2×Q8—41no—
1039C2×Q8—41no—
1040C2×Q8—41no—
1041C2×Q8—222no—
1042C2×Q8—441no—
1043C2×Q8—441no—
1044C2×Q8—441no—
1045C2×Q8—441no—
1046C2×Q8—441no—
1047C2×D4—22no—
1048C2×D4—22no—
1049C2×D4—41no—
1050C2×D4—41no—
1051C2×D4—41no—
1052C2×D4—41no—
1053C2×D4—41no—
1054C2×D4—41no—
1055C2×D4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—111no—
1060C22×C4—111no—
1061C22×C4—111no—
1062C22×C4—111no—
1063C22×C4—111no—
1064C22×C4—111no—
1065C22×C4—111no—
1066C22×C4—111no—
1067C22×C4—111no—
1068C22×C4—111no—
1069C22×C4—111no—
1070C22×C4—111no—
1071C22×C4—111no—
1072C22×C4—111no—
1073C22×C4—111no—
1074C22×C4—111no—
1075C22×C4—222no—
1076C22×C4—441no—
1077C22×C4—441no—
1078C22×C4—441no—
1079C22×C4—441no—
1080C22×C4—441no—
1081C22×C4C23×D1111yescharacteristic
1082C22×C4C23×D1111yescharacteristic
1083C22×C4C23×D1111yescharacteristic
1084C22×C4C23×D1111yescharacteristic
1085C22×C4C23×D1111yescharacteristic
1086C22×C4C23×D1111yescharacteristic
1087C22×C4C23×D1111yescharacteristic
1088C22×C4C23×D1111yescharacteristic
1089C22×C4C23×D1111yescharacteristic
1090C22×C4C23×D1111yescharacteristic
1091C22×C4C23×D1111yescharacteristic
1092C22×C4C23×D1111yescharacteristic
1093C4⋊C4—41no—
1094C4⋊C4—41no—
1095C4⋊C4—41no—
1096C4⋊C4—222no—
1097C4⋊C4—222no—
1098C4⋊C4—222no—
1099C4⋊C4—222no—
1100C4⋊C4—222no—
1101C4⋊C4—222no—
1102C4⋊C4—222no—
1103C4⋊C4—222no—
1104C4⋊C4—222no—
1105C4⋊C4—222no—
1106C4⋊C4—441no—
1107C4⋊C4—441no—
1108C4⋊C4—441no—
1109C4⋊C4—441no—
1110C4⋊C4—441no—
1111C4⋊C4—441no—
1112C4⋊C4—441no—
1113C4⋊C4—441no—
1114C4⋊C4—441no—
1115C4⋊C4—441no—
1116C4⋊C4—441no—
1117C4⋊C4—441no—
1118C4⋊C4—441no—
1119C4⋊C4—441no—
1120C4⋊C4—441no—
1121C4⋊C4—441no—
1122C4⋊C4—441no—
1123C4⋊C4—441no—
1124C4⋊C4—441no—
1125C4⋊C4—441no—
1126C4⋊C4—441no—
1127C4⋊C4—441no—
1128C22⋊C4—22no—
1129C22⋊C4—22no—
1130C22⋊C4—22no—
1131C22⋊C4—22no—
1132C22⋊C4—22no—
1133C22⋊C4—41no—
1134C22⋊C4—41no—
1135C22⋊C4—41no—
1136C22⋊C4—41no—
1137C22⋊C4—41no—
1138C22⋊C4—41no—
1139C22⋊C4—41no—
1140C22⋊C4—41no—
1141C22⋊C4—41no—
1142C22⋊C4—222no—
1143C22⋊C4—222no—
1144C22⋊C4—222no—
1145C22⋊C4—222no—
1146C22⋊C4—222no—
1147C22⋊C4—441no—
1148C22⋊C4—441no—
1149C22⋊C4—441no—
1150C22⋊C4—441no—
1151C22⋊C4—441no—
1152C22⋊C4—441no—
1153C22⋊C4—441no—
1154C22⋊C4—441no—
1155C22⋊C4—441no—
1156C22⋊C4—441no—
1157C22⋊C4—441no—
1158C22⋊C4—441no—
1159C22⋊C4—441no—
1160C22⋊C4—441no—
1161C22⋊C4—441no—
1162C22⋊C4—441no—
1163C22⋊C4—441no—
1164C42—22no—
1165C42—41no—
1166C42—114no—
1167C42—222no—
1168C42—222no—
1169C42—222no—
1170C42—222no—
1171C42—441no—
1172C42—441no—
1173C42—441no—
1174C42—441no—
1175C42—441no—
1176C42—441no—
1177C42—441no—
1178C42—441no—
1179C42—441no—
1180C11#3700711yescharacteristic, complemented, Sylow
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23—21no—
1202C23C24×D1111yescharacteristic
1203Q8—44no—
1204Q8—82no—
1205Q8—882no—
1206Q8—882no—
1207D4—82no—
1208D4—82no—
1209D4—82no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—82no—
1244C2×C4—112no—
1245C2×C4—112no—
1246C2×C4—221no—
1247C2×C4—221no—
1248C2×C4—221no—
1249C2×C4—221no—
1250C2×C4—221no—
1251C2×C4—221no—
1252C2×C4—221no—
1253C2×C4—221no—
1254C2×C4—221no—
1255C2×C4—221no—
1256C2×C4—221no—
1257C2×C4—221no—
1258C2×C4—221no—
1259C2×C4—221no—
1260C2×C4—221no—
1261C2×C4—221no—
1262C2×C4—221no—
1263C2×C4—221no—
1264C2×C4—221no—
1265C2×C4—221no—
1266C2×C4—221no—
1267C2×C4—221no—
1268C2×C4—221no—
1269C2×C4—221no—
1270C2×C4—221no—
1271C2×C4—221no—
1272C2×C4—221no—
1273C2×C4—221no—
1274C2×C4—221no—
1275C2×C4—221no—
1276C2×C4—221no—
1277C2×C4—221no—
1278C2×C4—221no—
1279C2×C4—221no—
1280C2×C4—221no—
1281C2×C4—221no—
1282C2×C4—221no—
1283C2×C4—221no—
1284C2×C4—221no—
1285C2×C4—221no—
1286C2×C4—221no—
1287C2×C4—221no—
1288C2×C4—221no—
1289C2×C4—221no—
1290C2×C4—221no—
1291C2×C4—221no—
1292C2×C4—444no—
1293C2×C4—882no—
1294C2×C4#6703712yes—
1295C2×C4#41×D1112yes—
1296C2×C4#6704312yes—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22C2×#6703711yescharacteristic
1319C22C2×#41×D1111yescharacteristic
1320C22C2×#6704311yescharacteristic
1321C22#1062345511yescharacteristic
1322C22#1062345511yescharacteristic
1323C22#1062345511yescharacteristic
1324C22#1062345711yescharacteristic
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—222no—
1338C4—222no—
1339C4—441no—
1340C4—441no—
1341C4—441no—
1342C4—441no—
1343C4—441no—
1344C4—441no—
1345C4—441no—
1346C4—441no—
1347C4—441no—
1348C4—441no—
1349C4—441no—
1350C4—441no—
1351C4—441no—
1352C4—441no—
1353C2—81no—
1354C2—81no—
1355C2—81no—
1356C2#1308200311yescharacteristic
1357C2#1308233811yescharacteristic
1358C2#1308247311yescharacteristic
1359C2#1308303411yescharacteristic
1360C2#1308317511yescharacteristic
1361C2#1308326711yescharacteristic
1362C2#1308331011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2712C2
prime radicalC11×#392C22
hypercenter#2712D11
hypocenterC11#37007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2712

Complements

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

NH ≅ G/Ntype
1. #13077004C2semidirect
2. #13076986C2semidirect
3. #13076502C2semidirect
5. #13076424C2semidirect
6. #13076314C2semidirect
7. #13076242C2semidirect
8. #13076194C2semidirect
9. #13076055C2semidirect
10. #13075986C2semidirect
11. #13075856C2semidirect
12. #13075720C2semidirect
13. #13075500C2semidirect
14. #13075435C2semidirect
15. #13075421C2semidirect
16. #13075397C2semidirect
17. #13075208C2semidirect
18. #13074646C2semidirect
19. #13074639C2semidirect
21. #13074262C2semidirect
22. #13074186C2semidirect
23. #13073939C2semidirect
24. #13073753C2semidirect
25. #13073595C2semidirect
26. #13073396C2semidirect
27. #13073392C2semidirect
28. #13071425C2semidirect
29. #13071220C2semidirect
30. #13071091C2semidirect
1180. C11#37007semidirect

Maximal subgroups

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

subgroupindex
#130770042
#130769862
#130765022
#130764752
#130764242
#130763142
#130762422
#130761942
#130760552
#130759862
#130758562
#130757202
#130755002
#130754352
#130754212
#130753972
#130752082
#130746462
#130746392
#130742962
#130742622
#130741862
#130739392
#130737532
#130735952
#130733962
#130733922
#130714252
#130712202
#130710912
C11×#27122
#3700711