Finite Group Databasebeta

← #14967759

Subgroups — #14967759

Order 2816.

1562 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076951C211yesmaximal, characteristic, complemented
2#13076949C211yesmaximal, characteristic
3#13076196C211yesmaximal, characteristic, complemented
4#13076184C211yesmaximal, characteristic, complemented
5#13076125C211yesmaximal, characteristic, complemented
6#13076113C211yesmaximal, characteristic, complemented
7#13076072C211yesmaximal, characteristic, complemented
8#13076069C211yesmaximal, characteristic, complemented
9#13076040C211yesmaximal, characteristic, complemented
10#13076038C211yesmaximal, characteristic, complemented
11#13075984C211yesmaximal, characteristic, complemented
12#13075980C211yesmaximal, characteristic, complemented
13#13075966C211yesmaximal, characteristic, complemented
14#13075957C211yesmaximal, characteristic, complemented
15#13075949C211yesmaximal, characteristic, complemented
16#13075678C211yesmaximal, characteristic, complemented
17#13075672C211yesmaximal, characteristic, complemented
18#13074729C211yesmaximal, characteristic, complemented
19#13074548C211yesmaximal, characteristic
20#13073183C211yesmaximal, characteristic, complemented
21#13073177C211yesmaximal, characteristic, complemented
22#13072949C211yesmaximal, characteristic, complemented
23#13072937C211yesmaximal, characteristic, complemented
24#13072443C211yesmaximal, characteristic, complemented
25#13072437C211yesmaximal, characteristic, complemented
26#13072100C211yesmaximal, characteristic, complemented
27#13072096C211yesmaximal, characteristic, complemented
28#13071343C211yesmaximal, characteristic, complemented
29#13071315C211yesmaximal, characteristic
30D11×#383C211yesmaximal, characteristic, complemented
31C11×#2758C211yesmaximal, characteristic, complemented
32C2×#66999C2211yescharacteristic
33C2×#66949C2211yescharacteristic
34C2×#66949C2211yescharacteristic
35C2×#66948C2211yescharacteristic
36C2×#66947C2211yescharacteristic
37C2×#66947C2211yescharacteristic
38C2×#66946C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×C42×D11C2211yescharacteristic
41C11×#400C2211yescharacteristic
42C11×#400C2211yescharacteristic
43C11×#400C2211yescharacteristic
44C11×#400C2211yescharacteristic
45C11×#400C2211yescharacteristic
46C11×#395C2211yescharacteristic
47C11×#391C2211yescharacteristic
48C11×#391C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#387C2211yescharacteristic
51C11×#387C2211yescharacteristic
52C11×#387C2211yescharacteristic
53C11×#387C2211yescharacteristic
54C11×#383C2211yescharacteristic
55C11×#383C2211yescharacteristic
56#10622844C2211yescharacteristic
57#10622844C2211yescharacteristic
58#10622842C2211yescharacteristic
59#10622607C2211yescharacteristic
60#10622606C2211yescharacteristic
61#10622604C2211yescharacteristic
62#10622603C2211yescharacteristic
63#10622603C2211yescharacteristic
64#10622603C2211yescharacteristic
65#10622603C2211yescharacteristic
66#10622603C2211yescharacteristic
67#10622602C2211yescharacteristic
68#10622602C2211yescharacteristic
69#10622601C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2211yescharacteristic
72#10622600C2211yescharacteristic
73#10622599C2211yescharacteristic
74#10622598C2211yescharacteristic
75#10622597C2211yescharacteristic
76#10622596C2211yescharacteristic
77#10622595C2211yescharacteristic
78#10622595C2211yescharacteristic
79#10622594C2211yescharacteristic
80#10622593C2211yescharacteristic
81#10622592C2211yescharacteristic
82#10622592C2211yescharacteristic
83#10622591C2211yescharacteristic
84#10622591C2211yescharacteristic
85#10622591C2211yescharacteristic
86#10622587C2211yescharacteristic
87#10622586C2211yescharacteristic
88#10622585C2211yescharacteristic
89#10622553C2211yescharacteristic
90#10622553C2211yescharacteristic
91#10622553C2211yescharacteristic
92#10622552C2211yescharacteristic
93C4×(C2×D11)⋊C4C2211yescharacteristic
94#10622550C2211yescharacteristic
95#10622546C2211yescharacteristic
96#10622546C2211yescharacteristic
97#10622546C2211yescharacteristic
98#10622542C2211yescharacteristic
99#10622289C2211yescharacteristic
100#10622288C2211yescharacteristic
101#10622288C2211yescharacteristic
102#10622288C2211yescharacteristic
103#10622288C2211yescharacteristic
104#10622288C2211yescharacteristic
105#10622288C2211yescharacteristic
106#10622288C2211yescharacteristic
107#10622288C2211yescharacteristic
108#10622287C2211yescharacteristic
109#10622287C2211yescharacteristic
110#10622287C2211yescharacteristic
111#10622286C2211yescharacteristic
112#10622286C2211yescharacteristic
113#10622286C2211yescharacteristic
114#10622286C2211yescharacteristic
115#10622285C2211yescharacteristic
116#10622283C2211yescharacteristic
117#10622282C2211yescharacteristic
118#10622282C2211yescharacteristic
119#10622282C2211yescharacteristic
120#10622282C2211yescharacteristic
121#10622282C2211yescharacteristic
122#10622281C2211yescharacteristic
123#10622281C2211yescharacteristic
124#10622281C2211yescharacteristic
125#10622281C2211yescharacteristic
126#10622281C2211yescharacteristic
127#10622281C2211yescharacteristic
128#10622281C2211yescharacteristic
129#10622281C2211yescharacteristic
130#10622280C2211yescharacteristic
131#10622280C2211yescharacteristic
132#10622280C2211yescharacteristic
133#10622279C2211yescharacteristic
134#10622278C2211yescharacteristic
135#10622278C2211yescharacteristic
136#10622278C2211yescharacteristic
137#10622278C2211yescharacteristic
138#10622278C2211yescharacteristic
139#10622278C2211yescharacteristic
140#10622278C2211yescharacteristic
141#10622278C2211yescharacteristic
142#10622278C2211yescharacteristic
143#10622278C2211yescharacteristic
144#10622277C2211yescharacteristic
145#10622277C2211yescharacteristic
146#10622277C2211yescharacteristic
147#10622277C2211yescharacteristic
148D11×#95C2211yescharacteristic
149D11×#95C2211yescharacteristic
150D11×#95C2211yescharacteristic
151D11×#95C2211yescharacteristic
152D11×#95C2211yescharacteristic
153D11×#95C2211yescharacteristic
154C11⋊#401C2211yescharacteristic
155C11⋊#401C2211yescharacteristic
156#10622274C2211yescharacteristic
157#10622274C2211yescharacteristic
158#10622274C2211yescharacteristic
159#10622273C2211yescharacteristic
160#10622273C2211yescharacteristic
161#10622271C2211yescharacteristic
162#10622271C2211yescharacteristic
163#10622270C2211yescharacteristic
164#10622270C2211yescharacteristic
165#10622268C2211yescharacteristic
166#10622268C2211yescharacteristic
167#10622267C2211yescharacteristic
168#10622266C2211yescharacteristic
169#10622266C2211yescharacteristic
170#10622266C2211yescharacteristic
171#10622265C2211yescharacteristic
172#10622264C2211yescharacteristic
173#10622264C2211yescharacteristic
174#10622264C2211yescharacteristic
175#10622264C2211yescharacteristic
176#10622264C2211yescharacteristic
177#10622264C2211yescharacteristic
178#10622264C2211yescharacteristic
179#10622263C2211yescharacteristic
180#10622263C2211yescharacteristic
181#10622260C2211yescharacteristic
182#10622260C2211yescharacteristic
183#10622259C2211yescharacteristic
184#10622259C2211yescharacteristic
185#10622259C2211yescharacteristic
186#10622259C2211yescharacteristic
187C22×Q8×C11C2311yescharacteristic
188C22×D44C2311yescharacteristic
189C22×D44C2311yescharacteristic
190C22×D44C2311yescharacteristic
191C22×C4×D11C2311yescharacteristic
192C22×C4×D11C2311yescharacteristic
193C22×C4×D11C2311yescharacteristic
194C22×C4×D11C2311yescharacteristic
195C22×C4×D11C2311yescharacteristic
196C22×C4×D11C2311yescharacteristic
197C22×C4×D11C2311yescharacteristic
198C22×C4×D11C2311yescharacteristic
199C22×C4×D11C2311yescharacteristic
200C22×Dic22C2311yescharacteristic
201C22×Dic22C2311yescharacteristic
202C2×C11×C4⋊C4C2311yescharacteristic
203C2×C11×C4⋊C4C2311yescharacteristic
204C2×C11×C4⋊C4C2311yescharacteristic
205C2×C11×C4⋊C4C2311yescharacteristic
206C2×C11×C4⋊C4C2311yescharacteristic
207C2×C11×C4⋊C4C2311yescharacteristic
208C2×C11×C4⋊C4C2311yescharacteristic
209C2×C11×C4⋊C4C2311yescharacteristic
210C2×C11×C4⋊C4C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214#66999—42no—
215C2×(C2×D11)⋊C4C2311yescharacteristic
216C2×(C2×D11)⋊C4C2311yescharacteristic
217C2×(C2×D11)⋊C4C2311yescharacteristic
218C2×(C2×D11)⋊C4C2311yescharacteristic
219C2×(C2×D11)⋊C4C2311yescharacteristic
220C2×(C2×D11)⋊C4C2311yescharacteristic
221C2×(C2×D11)⋊C4C2311yescharacteristic
222C2×(C2×D11)⋊C4C2311yescharacteristic
223C2×(C2×D11)⋊C4C2311yescharacteristic
224C2×(C2×D11)⋊C4C2311yescharacteristic
225C2×(C2×D11)⋊C4C2311yescharacteristic
226C2×(C2×D11)⋊C4C2311yescharacteristic
227C2×(C2×D11)⋊C4C2311yescharacteristic
228C2×(C2×D11)⋊C4C2311yescharacteristic
229C2×(C2×D11)⋊C4C2311yescharacteristic
230C2×(C2×D11)⋊C4C2311yescharacteristic
231C2×(C2×D11)⋊C4C2311yescharacteristic
232C2×(C2×D11)⋊C4C2311yescharacteristic
233C2×(C2×D11)⋊C4C2311yescharacteristic
234C2×(C2×D11)⋊C4C2311yescharacteristic
235C2×(C2×D11)⋊C4C2311yescharacteristic
236C2×(C2×D11)⋊C4C2311yescharacteristic
237C2×(C2×D11)⋊C4C2311yescharacteristic
238C2×(C2×D11)⋊C4C2311yescharacteristic
239C2×(C2×D11)⋊C4C2311yescharacteristic
240C2×(C2×D11)⋊C4C2311yescharacteristic
241C2×(C2×D11)⋊C4C2311yescharacteristic
242C2×(C2×D11)⋊C4C2311yescharacteristic
243C2×(C2×D11)⋊C4C2311yescharacteristic
244C2×(C2×D11)⋊C4C2311yescharacteristic
245C2×C4⋊Dic11C2311yescharacteristic
246C2×C4⋊Dic11C2311yescharacteristic
247C2×C4⋊Dic11C2311yescharacteristic
248C2×C4⋊Dic11C2311yescharacteristic
249C2×C4⋊Dic11C2311yescharacteristic
250C2×C4⋊Dic11C2311yescharacteristic
251C2×C4⋊Dic11C2311yescharacteristic
252C2×Dic11⋊C4C2311yescharacteristic
253C2×Dic11⋊C4C2311yescharacteristic
254C2×Dic11⋊C4C2311yescharacteristic
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×C4×Dic11C2311yescharacteristic
269C2×C4×Dic11C2311yescharacteristic
270C2×C4×Dic11C2311yescharacteristic
271C2×C4×Dic11C2311yescharacteristic
272C2×C4×Dic11C2311yescharacteristic
273C2×C4×Dic11C2311yescharacteristic
274C2×C4×Dic11C2311yescharacteristic
275#66949—24no—
276#66949—42no—
277#66948—24no—
278#66947—42no—
279#66947—42no—
280#66946—42no—
281C4×D44—42no—
282C42×D11—24no—
283C11×#95C2311yescharacteristic
284C11×#95C2311yescharacteristic
285C11×#95C2311yescharacteristic
286C11×#95C2311yescharacteristic
287C11×#95C2311yescharacteristic
288C11×#95C2311yescharacteristic
289C11×#95C2311yescharacteristic
290C11×#95C2311yescharacteristic
291C11×#95C2311yescharacteristic
292C11×#95C2311yescharacteristic
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#36980—111nomaximal, Sylow
352C23×D11C2411yescharacteristic
353C23×D11C2411yescharacteristic
354C23×D11C2411yescharacteristic
355C2×Q8×C11—41no—
356C2×Q8×C11—41no—
357C2×Q8×C11—41no—
358C22×C4×C11C2411yescharacteristic
359C22×C4×C11C2411yescharacteristic
360C22×C4×C11C2411yescharacteristic
361C22×C4×C11C2411yescharacteristic
362C22×C4×C11C2411yescharacteristic
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C22×C4×C11C2411yescharacteristic
366C22×C4×C11C2411yescharacteristic
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2411yescharacteristic
369C22×C4×C11C2411yescharacteristic
370C22×C4×C11C2411yescharacteristic
371C22×C4×C11C2411yescharacteristic
372C22×C4×C11C2411yescharacteristic
373C22×Dic11C2411yescharacteristic
374C22×Dic11C2411yescharacteristic
375C22×Dic11C2411yescharacteristic
376C22×Dic11C2411yescharacteristic
377C22×Dic11C2411yescharacteristic
378C22×Dic11C2411yescharacteristic
379C22×Dic11C2411yescharacteristic
380C22×Dic11C2411yescharacteristic
381C22×Dic11C2411yescharacteristic
382C22×Dic11C2411yescharacteristic
383C22×Dic11C2411yescharacteristic
384C22×Dic11C2411yescharacteristic
385C22×Dic11C2411yescharacteristic
386C2×D44—22no—
387C2×D44—22no—
388C2×D44—22no—
389C2×D44—22no—
390C2×D44—22no—
391C2×D44—22no—
392C2×D44—22no—
393C2×D44—41no—
394C2×D44—41no—
395C2×C4×D11—22no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—22no—
399C2×C4×D11—22no—
400C2×C4×D11—22no—
401C2×C4×D11—22no—
402C2×C4×D11—22no—
403C2×C4×D11—41no—
404C2×C4×D11—41no—
405C2×C4×D11—41no—
406C2×C4×D11—41no—
407C2×C4×D11—41no—
408C2×C4×D11—41no—
409C2×C4×D11—41no—
410C2×C4×D11—41no—
411C2×C4×D11—41no—
412C2×C4×D11—41no—
413C2×C4×D11—41no—
414C2×C4×D11—41no—
415C2×C4×D11—41no—
416C2×C4×D11—41no—
417C2×C4×D11—41no—
418C2×C4×D11—41no—
419C2×C4×D11—41no—
420C2×C4×D11—41no—
421C2×C4×D11#4114yes—
422C2×Dic22—22no—
423C2×Dic22—41no—
424C2×Dic22—41no—
425C2×Dic22—41no—
426C2×Dic22—41no—
427C2×Dic22—41no—
428C11×C4⋊C4—22no—
429C11×C4⋊C4—22no—
430C11×C4⋊C4—41no—
431C11×C4⋊C4—41no—
432C11×C4⋊C4—41no—
433C11×C4⋊C4—41no—
434C11×C4⋊C4—41no—
435C11×C4⋊C4—41no—
436C11×C4⋊C4—41no—
437C42×C11—22no—
438C42×C11—41no—
439C42×C11—41no—
440(C2×D11)⋊C4—22no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—22no—
443(C2×D11)⋊C4—22no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—22no—
447(C2×D11)⋊C4—22no—
448(C2×D11)⋊C4—41no—
449(C2×D11)⋊C4—41no—
450(C2×D11)⋊C4—41no—
451(C2×D11)⋊C4—41no—
452(C2×D11)⋊C4—41no—
453(C2×D11)⋊C4—41no—
454(C2×D11)⋊C4—41no—
455(C2×D11)⋊C4—41no—
456(C2×D11)⋊C4—41no—
457(C2×D11)⋊C4—41no—
458(C2×D11)⋊C4—41no—
459(C2×D11)⋊C4—41no—
460(C2×D11)⋊C4—41no—
461(C2×D11)⋊C4—41no—
462(C2×D11)⋊C4—41no—
463(C2×D11)⋊C4—41no—
464(C2×D11)⋊C4—41no—
465(C2×D11)⋊C4—41no—
466(C2×D11)⋊C4—41no—
467(C2×D11)⋊C4—41no—
468(C2×D11)⋊C4—41no—
469(C2×D11)⋊C4—41no—
470C4⋊Dic11—41no—
471C4⋊Dic11—41no—
472C4⋊Dic11—41no—
473C4⋊Dic11—41no—
474C4⋊Dic11—41no—
475C4⋊Dic11—41no—
476C4⋊Dic11—41no—
477Dic11⋊C4—22no—
478Dic11⋊C4—22no—
479Dic11⋊C4—41no—
480Dic11⋊C4—41no—
481Dic11⋊C4—41no—
482Dic11⋊C4—41no—
483Dic11⋊C4—41no—
484Dic11⋊C4—41no—
485Dic11⋊C4—41no—
486Dic11⋊C4—41no—
487Dic11⋊C4—41no—
488Dic11⋊C4—41no—
489Dic11⋊C4—41no—
490Dic11⋊C4—41no—
491Dic11⋊C4—41no—
492Dic11⋊C4—41no—
493C4×Dic11—22no—
494C4×Dic11—22no—
495C4×Dic11—22no—
496C4×Dic11—41no—
497C4×Dic11—41no—
498C4×Dic11—41no—
499C4×Dic11—41no—
500#2855—111no—
501#2854—111no—
502#2775—111no—
503#2775—111no—
504#2770—111no—
505#2770—111no—
506#2766—111no—
507#2766—111no—
508#2764—111no—
509#2764—111no—
510#2759—111no—
511#2759—111no—
512#2758—111no—
513#2758D1111yescharacteristic, complemented
514#2757—111no—
515#2757—111no—
516#2737—111no—
517#2737—111no—
518#2659—111no—
519#2639—111no—
520#2510—111no—
521#2510—111no—
522#2488—111no—
523#2488—111no—
524#2450—111no—
525#2450—111no—
526#2419—111no—
527#2419—111no—
528#2329—111no—
529#2325—111no—
530C2×#383—111no—
531C23×C11C2511yescharacteristic
532C22×D11—21no—
533C22×D11—21no—
534C22×D11—21no—
535C22×D11—21no—
536C22×D11—21no—
537C22×D11—21no—
538C22×D11—21no—
539C22×D11—21no—
540C22×D11—21no—
541C22×D11—21no—
542C22×D11—21no—
543C22×D11—21no—
544C22×D11—21no—
545C22×D11—21no—
546C22×D11—21no—
547C22×D11—21no—
548C22×D11—21no—
549C22×D11—21no—
550C22×D11C2×#4112yes—
551C22×D11H(5,𝔽2)12yes—
552C22×D112−1+412yes—
553Q8×C11—82no—
554C2×C4×C11—21no—
555C2×C4×C11—21no—
556C2×C4×C11—21no—
557C2×C4×C11—21no—
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—21no—
592C2×C4×C11—21no—
593C2×C4×C11—21no—
594C2×C4×C11—21no—
595C2×C4×C11—21no—
596C2×C4×C11—21no—
597C2×C4×C11—21no—
598C2×C4×C11C2×#4112yes—
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×Dic11C2×#4112yes—
638D44—44no—
639D44—44no—
640D44—82no—
641C4×D11—44no—
642C4×D11—44no—
643C4×D11—44no—
644C4×D11—82no—
645C4×D11—82no—
646C4×D11—82no—
647C4×D11—82no—
648C4×D11—82no—
649C4×D11—82no—
650Dic22—82no—
651Dic22—82no—
652C2×#123—111no—
653C2×#123—111no—
654C2×C22⋊Q8—111no—
655C2×C22⋊Q8—111no—
656C2×C22⋊Q8—111no—
657C2×#121—111no—
658C2×C4×D4—111no—
659C2×C4×D4—111no—
660C22×C42—111no—
661#401—111no—
662#401—111no—
663#400—111no—
664#400—111no—
665#400—111no—
666#400—111no—
667#400—111no—
668#400—111no—
669#400—111no—
670#400C2×D1111yescharacteristic
671#400C2×D1111yescharacteristic
672#400C2×D1111yescharacteristic
673#400C2×D1111yescharacteristic
674#400C2×D1111yescharacteristic
675#398—111no—
676#398—111no—
677#398—111no—
678#398—111no—
679#398—111no—
680#398—111no—
681#398—111no—
682#398—111no—
683#397—111no—
684#397—111no—
685#397—111no—
686#397—111no—
687#397—111no—
688#397—111no—
689#397—111no—
690#397—111no—
691#397—111no—
692#397—111no—
693#397—111no—
694#397—111no—
695#396—111no—
696#396—111no—
697#395—111no—
698#395—111no—
699#395—111no—
700#395C2×D1111yescharacteristic
701#394—111no—
702#394—111no—
703#393—111no—
704#393—111no—
705#393—111no—
706#393—111no—
707#393—111no—
708#393—111no—
709#391—111no—
710#391—111no—
711#391—111no—
712#391—111no—
713#391—111no—
714#391—111no—
715#391C2×D1111yescharacteristic
716#391C2×D1111yescharacteristic
717#390—111no—
718#390—111no—
719#389—111no—
720#389—111no—
721#389—111no—
722#389—111no—
723#389—111no—
724#389C2×D1111yescharacteristic
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#387—111no—
740#387—111no—
741#387—111no—
742#387—111no—
743#387—111no—
744#387—111no—
745#387—111no—
746#387—111no—
747#387—111no—
748#387—111no—
749#387—111no—
750#387—111no—
751#387—111no—
752#387—111no—
753#387C2×D1111yescharacteristic
754#387C2×D1111yescharacteristic
755#387C2×D1111yescharacteristic
756#387C2×D1111yescharacteristic
757#386—111no—
758#386—111no—
759#386—111no—
760#386—111no—
761#386—111no—
762#386—111no—
763#386—111no—
764#386—111no—
765#386—111no—
766#386—111no—
767#385—111no—
768#385—111no—
769#385—111no—
770#385—111no—
771#385—111no—
772#385—111no—
773#385—111no—
774#385—111no—
775#385—111no—
776#385—111no—
777#383—111no—
778#383—111no—
779#383—111no—
780#383—111no—
781#383—111no—
782#383—111no—
783#383—111no—
784#383—111no—
785#383C2×D1111yescharacteristic
786#383C2×D1111yescharacteristic
787#382—111no—
788#382—111no—
789#381—111no—
790#381—111no—
791#381—111no—
792#381—111no—
793#380—111no—
794#380—111no—
795#380—111no—
796#380—111no—
797#380—111no—
798#380—111no—
799C4×C22⋊C4—111no—
800C4×C22⋊C4—111no—
801C2×#95—111no—
802C2×#95—111no—
803C2×#95—111no—
804C2×#95—111no—
805C2×#95—111no—
806C2×#95—111no—
807C22×C11C22×#4111yescharacteristic
808C22×C11C2×H(5,𝔽2)11yescharacteristic
809C22×C11C2×2−1+411yescharacteristic
810C22×C11#58511yescharacteristic
811C22×C11#58511yescharacteristic
812C22×C11#58511yescharacteristic
813C22×C11#58511yescharacteristic
814C2×D11—22no—
815C2×D11—22no—
816C2×D11—22no—
817C2×D11—22no—
818C2×D11—22no—
819C2×D11—22no—
820C2×D11—41no—
821C2×D11—41no—
822C2×D11—41no—
823C2×D11—41no—
824C2×D11—41no—
825C2×D11—41no—
826C2×D11—41no—
827C2×D11—41no—
828C2×D11—41no—
829C2×D11—41no—
830C2×D11—41no—
831C2×D11—41no—
832C2×D11—41no—
833C2×D11—41no—
834C2×D11#54214yes—
835C4×C11—22no—
836C4×C11—41no—
837C4×C11—41no—
838C4×C11—41no—
839C4×C11—41no—
840C4×C11—41no—
841C4×C11—41no—
842C4×C11—41no—
843C4×C11—41no—
844C4×C11—41no—
845C4×C11—41no—
846C4×C11—41no—
847C4×C11—41no—
848C4×C11—41no—
849C4×C11—41no—
850Dic11—22no—
851Dic11—41no—
852Dic11—41no—
853Dic11—41no—
854Dic11—41no—
855Dic11—41no—
856Dic11—41no—
857Dic11—41no—
858Dic11—41no—
859Dic11—41no—
860Dic11—41no—
861Dic11—41no—
862Dic11—41no—
863C22×Q8—111no—
864C22×Q8—111no—
865C22×Q8C22×D1111yescharacteristic
866C22×D4—111no—
867C22×D4—111no—
868C22×D4—111no—
869C23×C4—111no—
870C23×C4—111no—
871C23×C4—111no—
872C23×C4—111no—
873C23×C4—111no—
874C23×C4—111no—
875C23×C4—111no—
876C23×C4—111no—
877C23×C4—111no—
878#123—442no—
879#123—442no—
880C22⋊Q8—224no—
881C22⋊Q8—442no—
882C22⋊Q8—442no—
883#121—224no—
884C4×D4—442no—
885C4×D4—442no—
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×C4⋊C4C22×D1111yescharacteristic
913C2×C4⋊C4C22×D1111yescharacteristic
914C2×C4⋊C4C22×D1111yescharacteristic
915C2×C4⋊C4C22×D1111yescharacteristic
916C2×C4⋊C4C22×D1111yescharacteristic
917C2×C4⋊C4C22×D1111yescharacteristic
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⋊C4—111no—
935C2×C22⋊C4—111no—
936C2×C22⋊C4—111no—
937C2×C22⋊C4—111no—
938C2×C22⋊C4—111no—
939C2×C22⋊C4—111no—
940C2×C22⋊C4—111no—
941C2×C22⋊C4—111no—
942C2×C22⋊C4—111no—
943C2×C22⋊C4—111no—
944C2×C22⋊C4—111no—
945C2×C22⋊C4—111no—
946C2×C22⋊C4—111no—
947C2×C22⋊C4—111no—
948C2×C42—111no—
949C2×C42—111no—
950C2×C42—111no—
951C2×C42—111no—
952C2×C42—111no—
953C2×C42—111no—
954C2×C42—111no—
955C2×C42—224no—
956C2×C42C22×D1111yescharacteristic
957C2×C42C22×D1111yescharacteristic
958C2×C42C22×D1111yescharacteristic
959#95—111no—
960#95—111no—
961#95—111no—
962#95—111no—
963#95—111no—
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#95C22×D1111yescharacteristic
1006#95C22×D1111yescharacteristic
1007#95C22×D1111yescharacteristic
1008#95C22×D1111yescharacteristic
1009#95C22×D1111yescharacteristic
1010#95C22×D1111yescharacteristic
1011#95C22×D1111yescharacteristic
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
1022#95C22×D1111yescharacteristic
1023#95C22×D1111yescharacteristic
1024#95C22×D1111yescharacteristic
1025#95C22×D1111yescharacteristic
1026#95C22×D1111yescharacteristic
1027C2×C11C2×#54211yescharacteristic
1028C2×C11#349111yescharacteristic
1029C2×C11#349311yescharacteristic
1030C2×C11#356011yescharacteristic
1031C2×C11#356011yescharacteristic
1032C2×C11#356411yescharacteristic
1033C2×C11#356411yescharacteristic
1034D11—24no—
1035D11—81no—
1036D11—81no—
1037C24—111no—
1038C24—111no—
1039C24—111no—
1040C2×Q8—41no—
1041C2×Q8—41no—
1042C2×Q8—41no—
1043C2×Q8—222no—
1044C2×Q8—441no—
1045C2×Q8—441no—
1046C2×Q8—441no—
1047C2×Q8—441no—
1048C2×Q8—441no—
1049C2×D4—222no—
1050C2×D4—222no—
1051C2×D4—222no—
1052C2×D4—222no—
1053C2×D4—222no—
1054C2×D4—222no—
1055C2×D4—222no—
1056C2×D4—441no—
1057C2×D4—441no—
1058C22×C4—111no—
1059C22×C4—114no—
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—222no—
1073C22×C4—222no—
1074C22×C4—222no—
1075C22×C4—222no—
1076C22×C4—222no—
1077C22×C4—222no—
1078C22×C4—222no—
1079C22×C4—222no—
1080C22×C4—441no—
1081C22×C4—441no—
1082C22×C4—441no—
1083C22×C4—441no—
1084C22×C4—441no—
1085C22×C4—441no—
1086C22×C4—441no—
1087C22×C4—441no—
1088C22×C4—441no—
1089C22×C4—441no—
1090C22×C4—441no—
1091C22×C4—441no—
1092C22×C4—441no—
1093C22×C4—441no—
1094C22×C4—441no—
1095C22×C4—441no—
1096C22×C4—441no—
1097C22×C4—441no—
1098C22×C4C23×D1111yescharacteristic
1099C22×C4C23×D1111yescharacteristic
1100C22×C4C23×D1111yescharacteristic
1101C22×C4C23×D1111yescharacteristic
1102C22×C4C23×D1111yescharacteristic
1103C22×C4C23×D1111yescharacteristic
1104C22×C4C23×D1111yescharacteristic
1105C22×C4C23×D1111yescharacteristic
1106C22×C4C23×D1111yescharacteristic
1107C22×C4C23×D1111yescharacteristic
1108C22×C4C23×D1111yescharacteristic
1109C22×C4C23×D1111yescharacteristic
1110C22×C4C23×D1111yescharacteristic
1111C22×C4C23×D1111yescharacteristic
1112C22×C4C23×D1111yescharacteristic
1113C4⋊C4—22no—
1114C4⋊C4—22no—
1115C4⋊C4—41no—
1116C4⋊C4—41no—
1117C4⋊C4—41no—
1118C4⋊C4—41no—
1119C4⋊C4—41no—
1120C4⋊C4—41no—
1121C4⋊C4—41no—
1122C4⋊C4—222no—
1123C4⋊C4—222no—
1124C4⋊C4—441no—
1125C4⋊C4—441no—
1126C4⋊C4—441no—
1127C4⋊C4—441no—
1128C4⋊C4—441no—
1129C4⋊C4—441no—
1130C4⋊C4—441no—
1131C4⋊C4—441no—
1132C4⋊C4—441no—
1133C4⋊C4—441no—
1134C4⋊C4—441no—
1135C4⋊C4—441no—
1136C4⋊C4—441no—
1137C4⋊C4—441no—
1138C4⋊C4—441no—
1139C4⋊C4—441no—
1140C4⋊C4—441no—
1141C4⋊C4—441no—
1142C4⋊C4—441no—
1143C4⋊C4—441no—
1144C4⋊C4—441no—
1145C22⋊C4—222no—
1146C22⋊C4—222no—
1147C22⋊C4—222no—
1148C22⋊C4—222no—
1149C22⋊C4—222no—
1150C22⋊C4—222no—
1151C22⋊C4—222no—
1152C22⋊C4—222no—
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—
1164C22⋊C4—441no—
1165C22⋊C4—441no—
1166C22⋊C4—441no—
1167C22⋊C4—441no—
1168C22⋊C4—441no—
1169C22⋊C4—441no—
1170C22⋊C4—441no—
1171C22⋊C4—441no—
1172C22⋊C4—441no—
1173C22⋊C4—441no—
1174C22⋊C4—441no—
1175C42—22no—
1176C42—41no—
1177C42—41no—
1178C42—222no—
1179C42—222no—
1180C42—222no—
1181C42—441no—
1182C42—441no—
1183C42—441no—
1184C42—441no—
1185C11#3698011yescharacteristic, complemented, Sylow
1186C23—112no—
1187C23—112no—
1188C23—112no—
1189C23—221no—
1190C23—221no—
1191C23—221no—
1192C23—221no—
1193C23—221no—
1194C23—221no—
1195C23—221no—
1196C23—221no—
1197C23—221no—
1198C23—221no—
1199C23—221no—
1200C23—221no—
1201C23—221no—
1202C23—221no—
1203C23—221no—
1204C23—221no—
1205C23—221no—
1206C23—221no—
1207C23C24×D1111yescharacteristic
1208Q8—82no—
1209Q8—882no—
1210Q8—882no—
1211D4—444no—
1212D4—444no—
1213D4—882no—
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—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—112no—
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—221no—
1293C2×C4—221no—
1294C2×C4—221no—
1295C2×C4—221no—
1296C2×C4—221no—
1297C2×C4—444no—
1298C2×C4—444no—
1299C2×C4—444no—
1300C2×C4—882no—
1301C2×C4—882no—
1302C2×C4—882no—
1303C2×C4—882no—
1304C2×C4—882no—
1305C2×C4—882no—
1306C2×C4#41×D1112yes—
1307C22—114no—
1308C22—222no—
1309C22—222no—
1310C22—222no—
1311C22—222no—
1312C22—222no—
1313C22—222no—
1314C22—441no—
1315C22—441no—
1316C22—441no—
1317C22—441no—
1318C22—441no—
1319C22—441no—
1320C22—441no—
1321C22—441no—
1322C22—441no—
1323C22—441no—
1324C22—441no—
1325C22—441no—
1326C22—441no—
1327C22—441no—
1328C22C2×#41×D1111yescharacteristic
1329C22#1062345311yescharacteristic
1330C22#1062345311yescharacteristic
1331C22D11×H(5,𝔽2)11yescharacteristic
1332C22D11×2−1+411yescharacteristic
1333C22#1062345711yescharacteristic
1334C22#1062345711yescharacteristic
1335C4—22no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—222no—
1351C4—441no—
1352C4—441no—
1353C4—441no—
1354C4—441no—
1355C4—441no—
1356C4—441no—
1357C4—441no—
1358C4—441no—
1359C4—441no—
1360C4—441no—
1361C4—441no—
1362C4—441no—
1363C2—224no—
1364C2—881no—
1365C2—881no—
1366C2D11×#54211yescharacteristic
1367C2#1308231111yescharacteristic
1368C2#1308233011yescharacteristic
1369C2#1308315911yescharacteristic
1370C2#1308316311yescharacteristic
1371C2#1308322911yescharacteristic
1372C2#1308324311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2758C2
prime radicalC2×#66948C22
hypercenter#2758D11
hypocenterC11#36980
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2758

Complements

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

NH ≅ G/Ntype
1. #13076951C2semidirect
3. #13076196C2semidirect
4. #13076184C2semidirect
5. #13076125C2semidirect
6. #13076113C2semidirect
7. #13076072C2semidirect
8. #13076069C2semidirect
9. #13076040C2semidirect
10. #13076038C2semidirect
11. #13075984C2semidirect
12. #13075980C2semidirect
13. #13075966C2semidirect
14. #13075957C2semidirect
15. #13075949C2semidirect
16. #13075678C2semidirect
17. #13075672C2semidirect
18. #13074729C2semidirect
20. #13073183C2semidirect
21. #13073177C2semidirect
22. #13072949C2semidirect
23. #13072937C2semidirect
24. #13072443C2semidirect
25. #13072437C2semidirect
26. #13072100C2semidirect
27. #13072096C2semidirect
28. #13071343C2semidirect
30. D11×#383C2semidirect
31. C11×#2758C2semidirect
513. #2758D11semidirect
1185. C11#36980semidirect

Maximal subgroups

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

subgroupindex
#130769512
#130769492
#130761962
#130761842
#130761252
#130761132
#130760722
#130760692
#130760402
#130760382
#130759842
#130759802
#130759662
#130759572
#130759492
#130756782
#130756722
#130747292
#130745482
#130731832
#130731772
#130729492
#130729372
#130724432
#130724372
#130721002
#130720962
#130713432
#130713152
D11×#3832
C11×#27582
#3698011