Finite Group Databasebeta

← #14961731

Subgroups — #14961731

Order 2816.

1482 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076967C211yesmaximal, characteristic
2#13076927C211yesmaximal, characteristic
3#13076536C211yesmaximal, characteristic, complemented
4#13076534C211yesmaximal, characteristic, complemented
5#13076441C211yesmaximal, characteristic, complemented
6#13076434C211yesmaximal, characteristic, complemented
7#13076375C211yesmaximal, characteristic, complemented
8#13076370C211yesmaximal, characteristic, complemented
9#13076208C211yesmaximal, characteristic, complemented
10#13076206C211yesmaximal, characteristic, complemented
11#13076062C211yesmaximal, characteristic, complemented
12#13075972C211yesmaximal, characteristic, complemented
13#13075965C211yesmaximal, characteristic, complemented
14#13075485C211yesmaximal, characteristic, complemented
15#13075481C211yesmaximal, characteristic, complemented
16#13075404C211yesmaximal, characteristic, complemented
17#13075395C211yesmaximal, characteristic, complemented
18#13074434C211yesmaximal, characteristic
19#13074434C211yesmaximal, characteristic
20#13073124C211yesmaximal, characteristic
21#13073112C211yesmaximal, characteristic
22#13073000C211yesmaximal, characteristic
23#13072998C211yesmaximal, characteristic
24#13072996C211yesmaximal, characteristic
25#13072994C211yesmaximal, characteristic
26#13072758C211yesmaximal, characteristic
27#13072755C211yesmaximal, characteristic
28#13071350C211yesmaximal, characteristic
29#13071343C211yesmaximal, characteristic
30D11×#387C211yesmaximal, characteristic
31C11×#2766C211yesmaximal, characteristic, complemented
32C2×#66949C2211yescharacteristic
33C2×#66949C2211yescharacteristic
34C2×C4⋊C4×D11C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×#66942C2211yescharacteristic
37C2×#66942C2211yescharacteristic
38C2×#66941C2211yescharacteristic
39C2×C42×D11C2211yescharacteristic
40C2×#66923C2211yescharacteristic
41C11×#401C2211yescharacteristic
42C11×#400C2211yescharacteristic
43C11×#400C2211yescharacteristic
44C11×#398C2211yescharacteristic
45C11×#398C2211yescharacteristic
46C11×#398C2211yescharacteristic
47C11×#389C2211yescharacteristic
48C11×#389C2211yescharacteristic
49C11×#387C2211yescharacteristic
50C11×#387C2211yescharacteristic
51C11×#387C2211yescharacteristic
52C11×#387C2211yescharacteristic
53C11×#387C2211yescharacteristic
54C11×#383C2211yescharacteristic
55C11×#382C2211yescharacteristic
56#10622602C2211yescharacteristic
57#10622602C2211yescharacteristic
58#10622602C2211yescharacteristic
59#10622602C2211yescharacteristic
60#10622600C2211yescharacteristic
61#10622600C2211yescharacteristic
62#10622600C2211yescharacteristic
63#10622600C2211yescharacteristic
64#10622599C2211yescharacteristic
65#10622598C2211yescharacteristic
66#10622598C2211yescharacteristic
67#10622598C2211yescharacteristic
68#10622598C2211yescharacteristic
69#10622597C2211yescharacteristic
70#10622597C2211yescharacteristic
71#10622597C2211yescharacteristic
72#10622597C2211yescharacteristic
73#10622597C2211yescharacteristic
74#10622596C2211yescharacteristic
75#10622596C2211yescharacteristic
76#10622596C2211yescharacteristic
77#10622596C2211yescharacteristic
78#10622595C2211yescharacteristic
79#10622594C2211yescharacteristic
80#10622594C2211yescharacteristic
81#10622594C2211yescharacteristic
82#10622594C2211yescharacteristic
83#10622593C2211yescharacteristic
84#10622592C2211yescharacteristic
85#10622592C2211yescharacteristic
86#10622591C2211yescharacteristic
87#10622591C2211yescharacteristic
88#10622591C2211yescharacteristic
89#10622591C2211yescharacteristic
90#10622591C2211yescharacteristic
91#10622589C2211yescharacteristic
92#10622587C2211yescharacteristic
93#10622586C2211yescharacteristic
94#10622585C2211yescharacteristic
95#10622585C2211yescharacteristic
96#10622585C2211yescharacteristic
97C4×(C2×D11)⋊C4C2211yescharacteristic
98C4×(C2×D11)⋊C4C2211yescharacteristic
99#10622550C2211yescharacteristic
100#10622546C2211yescharacteristic
101#10622546C2211yescharacteristic
102#10622546C2211yescharacteristic
103#10622542C2211yescharacteristic
104#10622541C2211yescharacteristic
105#10622541C2211yescharacteristic
106#10622541C2211yescharacteristic
107#10622281C2211yescharacteristic
108#10622281C2211yescharacteristic
109#10622281C2211yescharacteristic
110#10622281C2211yescharacteristic
111#10622281C2211yescharacteristic
112#10622281C2211yescharacteristic
113#10622281C2211yescharacteristic
114#10622281C2211yescharacteristic
115#10622280C2211yescharacteristic
116#10622280C2211yescharacteristic
117#10622279C2211yescharacteristic
118#10622279C2211yescharacteristic
119#10622277C2211yescharacteristic
120#10622277C2211yescharacteristic
121#10622277C2211yescharacteristic
122#10622277C2211yescharacteristic
123D11×#95C2211yescharacteristic
124D11×#95C2211yescharacteristic
125D11×#95C2211yescharacteristic
126D11×#95C2211yescharacteristic
127C11⋊#401C2211yescharacteristic
128C11⋊#401C2211yescharacteristic
129C11⋊#401C2211yescharacteristic
130#10622274C2211yescharacteristic
131#10622274C2211yescharacteristic
132#10622273C2211yescharacteristic
133#10622273C2211yescharacteristic
134#10622273C2211yescharacteristic
135#10622273C2211yescharacteristic
136#10622273C2211yescharacteristic
137#10622273C2211yescharacteristic
138#10622273C2211yescharacteristic
139#10622273C2211yescharacteristic
140#10622273C2211yescharacteristic
141#10622272C2211yescharacteristic
142#10622272C2211yescharacteristic
143#10622272C2211yescharacteristic
144#10622272C2211yescharacteristic
145#10622271C2211yescharacteristic
146#10622271C2211yescharacteristic
147#10622271C2211yescharacteristic
148#10622271C2211yescharacteristic
149#10622271C2211yescharacteristic
150#10622271C2211yescharacteristic
151#10622271C2211yescharacteristic
152#10622270C2211yescharacteristic
153#10622269C2211yescharacteristic
154#10622269C2211yescharacteristic
155#10622268C2211yescharacteristic
156#10622268C2211yescharacteristic
157#10622268C2211yescharacteristic
158#10622268C2211yescharacteristic
159#10622268C2211yescharacteristic
160#10622268C2211yescharacteristic
161#10622268C2211yescharacteristic
162#10622268C2211yescharacteristic
163#10622267C2211yescharacteristic
164#10622267C2211yescharacteristic
165#10622267C2211yescharacteristic
166#10622267C2211yescharacteristic
167#10622266C2211yescharacteristic
168#10622266C2211yescharacteristic
169#10622266C2211yescharacteristic
170#10622266C2211yescharacteristic
171#10622266C2211yescharacteristic
172#10622266C2211yescharacteristic
173#10622266C2211yescharacteristic
174#10622265C2211yescharacteristic
175#10622265C2211yescharacteristic
176#10622265C2211yescharacteristic
177#10622265C2211yescharacteristic
178#10622264C2211yescharacteristic
179#10622264C2211yescharacteristic
180#10622263C2211yescharacteristic
181#10622263C2211yescharacteristic
182#10622260C2211yescharacteristic
183#10622259C2211yescharacteristic
184#10622259C2211yescharacteristic
185#10622259C2211yescharacteristic
186#10622259C2211yescharacteristic
187C22×C4×D11C2311yescharacteristic
188C22×C4×D11C2311yescharacteristic
189C22×C4×D11C2311yescharacteristic
190C22×C4×D11C2311yescharacteristic
191C22×C4×D11C2311yescharacteristic
192C22×C4×D11C2311yescharacteristic
193C22×C4×D11C2311yescharacteristic
194C22×Dic22C2311yescharacteristic
195C22×Dic22C2311yescharacteristic
196C2×C11×C4⋊C4C2311yescharacteristic
197C2×C11×C4⋊C4C2311yescharacteristic
198C2×C11×C4⋊C4C2311yescharacteristic
199C2×C11×C4⋊C4C2311yescharacteristic
200C2×C11×C4⋊C4C2311yescharacteristic
201C2×C11×C4⋊C4C2311yescharacteristic
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×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×(C2×D11)⋊C4C2311yescharacteristic
212C2×(C2×D11)⋊C4C2311yescharacteristic
213C2×(C2×D11)⋊C4C2311yescharacteristic
214C2×(C2×D11)⋊C4C2311yescharacteristic
215C2×(C2×D11)⋊C4C2311yescharacteristic
216C2×(C2×D11)⋊C4C2311yescharacteristic
217C2×(C2×D11)⋊C4C2311yescharacteristic
218C2×(C2×D11)⋊C4C2311yescharacteristic
219C2×C4⋊Dic11C2311yescharacteristic
220C2×C4⋊Dic11C2311yescharacteristic
221C2×C4⋊Dic11C2311yescharacteristic
222C2×C4⋊Dic11C2311yescharacteristic
223C2×C4⋊Dic11C2311yescharacteristic
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×Dic11⋊C4C2311yescharacteristic
234C2×Dic11⋊C4C2311yescharacteristic
235C2×Dic11⋊C4C2311yescharacteristic
236C2×Dic11⋊C4C2311yescharacteristic
237C2×Dic11⋊C4C2311yescharacteristic
238C2×Dic11⋊C4C2311yescharacteristic
239C2×Dic11⋊C4C2311yescharacteristic
240C2×Dic11⋊C4C2311yescharacteristic
241C2×Dic11⋊C4C2311yescharacteristic
242C2×Dic11⋊C4C2311yescharacteristic
243C2×Dic11⋊C4C2311yescharacteristic
244C2×Dic11⋊C4C2311yescharacteristic
245C2×Dic11⋊C4C2311yescharacteristic
246C2×Dic11⋊C4C2311yescharacteristic
247C2×Dic11⋊C4C2311yescharacteristic
248C2×Dic11⋊C4C2311yescharacteristic
249C2×Dic11⋊C4C2311yescharacteristic
250C2×Dic11⋊C4C2311yescharacteristic
251C2×Dic11⋊C4C2311yescharacteristic
252C2×Dic11⋊C4C2311yescharacteristic
253C2×Dic11⋊C4C2311yescharacteristic
254C2×Dic11⋊C4C2311yescharacteristic
255C2×Dic11⋊C4C2311yescharacteristic
256C2×Dic11⋊C4C2311yescharacteristic
257C2×C4×Dic11C2311yescharacteristic
258C2×C4×Dic11C2311yescharacteristic
259C2×C4×Dic11C2311yescharacteristic
260C2×C4×Dic11C2311yescharacteristic
261C2×C4×Dic11C2311yescharacteristic
262C2×C4×Dic11C2311yescharacteristic
263C2×C4×Dic11C2311yescharacteristic
264C2×C4×Dic11C2311yescharacteristic
265C2×C4×Dic11C2311yescharacteristic
266#66949—24no—
267#66949—24no—
268C4⋊C4×D11—24no—
269C4⋊C4×D11—42no—
270#66942—42no—
271#66942—42no—
272#66941—42no—
273C42×D11—42no—
274#66923—42no—
275C11×#95C2311yescharacteristic
276C11×#95C2311yescharacteristic
277C11×#95C2311yescharacteristic
278C11×#95C2311yescharacteristic
279C11×#95C2311yescharacteristic
280C11×#95C2311yescharacteristic
281C11×#95C2311yescharacteristic
282C11×#95C2311yescharacteristic
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#36762—111nomaximal, Sylow
352C23×D11C2411yescharacteristic
353C22×C4×C11C2411yescharacteristic
354C22×C4×C11C2411yescharacteristic
355C22×C4×C11C2411yescharacteristic
356C22×C4×C11C2411yescharacteristic
357C22×C4×C11C2411yescharacteristic
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×Dic11C2411yescharacteristic
369C22×Dic11C2411yescharacteristic
370C22×Dic11C2411yescharacteristic
371C22×Dic11C2411yescharacteristic
372C22×Dic11C2411yescharacteristic
373C22×Dic11C2411yescharacteristic
374C22×Dic11C2411yescharacteristic
375C22×Dic11C2411yescharacteristic
376C22×Dic11C2411yescharacteristic
377C22×Dic11C2411yescharacteristic
378C22×Dic11C2411yescharacteristic
379C22×Dic11C2411yescharacteristic
380C22×Dic11C2411yescharacteristic
381C22×Dic11C2411yescharacteristic
382C22×Dic11C2411yescharacteristic
383C2×C4×D11—22no—
384C2×C4×D11—22no—
385C2×C4×D11—22no—
386C2×C4×D11—22no—
387C2×C4×D11—22no—
388C2×C4×D11—22no—
389C2×C4×D11—22no—
390C2×C4×D11—22no—
391C2×C4×D11—22no—
392C2×C4×D11—22no—
393C2×C4×D11—41no—
394C2×C4×D11—41no—
395C2×C4×D11—41no—
396C2×C4×D11—41no—
397C2×C4×D11—41no—
398C2×C4×D11—41no—
399C2×C4×D11—41no—
400C2×C4×D11—41no—
401C2×C4×D11—41no—
402C2×C4×D11—41no—
403C2×C4×D11#4114yes—
404C2×Dic22—22no—
405C2×Dic22—22no—
406C2×Dic22—41no—
407C2×Dic22—41no—
408C2×Dic22—41no—
409C2×Dic22—41no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4—22no—
414C11×C4⋊C4—22no—
415C11×C4⋊C4—41no—
416C11×C4⋊C4—41no—
417C11×C4⋊C4—41no—
418C11×C4⋊C4—41no—
419C11×C4⋊C4—41no—
420C11×C4⋊C4—41no—
421C11×C4⋊C4—41no—
422C42×C11—22no—
423C42×C11—41no—
424C42×C11—41no—
425(C2×D11)⋊C4—22no—
426(C2×D11)⋊C4—22no—
427(C2×D11)⋊C4—22no—
428(C2×D11)⋊C4—22no—
429(C2×D11)⋊C4—22no—
430(C2×D11)⋊C4—22no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—22no—
433C4⋊Dic11—22no—
434C4⋊Dic11—22no—
435C4⋊Dic11—22no—
436C4⋊Dic11—22no—
437C4⋊Dic11—41no—
438C4⋊Dic11—41no—
439C4⋊Dic11—41no—
440C4⋊Dic11—41no—
441C4⋊Dic11—41no—
442C4⋊Dic11—41no—
443C4⋊Dic11—41no—
444C4⋊Dic11—41no—
445C4⋊Dic11—41no—
446C4⋊Dic11—41no—
447Dic11⋊C4—22no—
448Dic11⋊C4—22no—
449Dic11⋊C4—22no—
450Dic11⋊C4—22no—
451Dic11⋊C4—22no—
452Dic11⋊C4—22no—
453Dic11⋊C4—22no—
454Dic11⋊C4—22no—
455Dic11⋊C4—22no—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—41no—
459Dic11⋊C4—41no—
460Dic11⋊C4—41no—
461Dic11⋊C4—41no—
462Dic11⋊C4—41no—
463Dic11⋊C4—41no—
464Dic11⋊C4—41no—
465Dic11⋊C4—41no—
466Dic11⋊C4—41no—
467Dic11⋊C4—41no—
468Dic11⋊C4—41no—
469Dic11⋊C4—41no—
470Dic11⋊C4—41no—
471C4×Dic11—22no—
472C4×Dic11—41no—
473C4×Dic11—41no—
474C4×Dic11—41no—
475C4×Dic11—41no—
476C4×Dic11—41no—
477C4×Dic11—41no—
478C4×Dic11—41no—
479C4×Dic11—41no—
480#2857—111no—
481#2851—111no—
482#2802—111no—
483#2802—111no—
484#2794—111no—
485#2794—111no—
486#2789—111no—
487#2789—111no—
488#2776—111no—
489#2776—111no—
490#2766—111no—
491#2766D1111yescharacteristic, complemented
492#2758—111no—
493#2758—111no—
494#2719—111no—
495#2719—111no—
496#2713—111no—
497#2713—111no—
498#2627—111no—
499#2627—111no—
500#2505—111no—
501#2505—111no—
502#2493—111no—
503#2493—111no—
504#2493—111no—
505#2493—111no—
506#2473—111no—
507#2473—111no—
508#2329—111no—
509#2329—111no—
510C2×#387—111no—
511C23×C11C2511yescharacteristic
512C22×D11—21no—
513C22×D11—21no—
514C22×D11—21no—
515C22×D11—21no—
516C22×D11C2×#4112yes—
517C22×D112−1+412yes—
518C22×D112−1+412yes—
519C2×C4×C11—21no—
520C2×C4×C11—21no—
521C2×C4×C11—21no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—21no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—21no—
532C2×C4×C11—21no—
533C2×C4×C11—21no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—21no—
548C2×C4×C11—21no—
549C2×C4×C11—21no—
550C2×C4×C11—21no—
551C2×C4×C11—21no—
552C2×C4×C11—21no—
553C2×C4×C11—21no—
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×C11C2×#4112yes—
563C2×C4×C11H(5,𝔽2)12yes—
564C2×Dic11—21no—
565C2×Dic11—21no—
566C2×Dic11—21no—
567C2×Dic11—21no—
568C2×Dic11—21no—
569C2×Dic11—21no—
570C2×Dic11—21no—
571C2×Dic11—21no—
572C2×Dic11—21no—
573C2×Dic11—21no—
574C2×Dic11—21no—
575C2×Dic11—21no—
576C2×Dic11—21no—
577C2×Dic11—21no—
578C2×Dic11—21no—
579C2×Dic11—21no—
580C2×Dic11—21no—
581C2×Dic11—21no—
582C2×Dic11—21no—
583C2×Dic11—21no—
584C2×Dic11—21no—
585C2×Dic11—21no—
586C2×Dic11—21no—
587C2×Dic11—21no—
588C2×Dic11—21no—
589C2×Dic11—21no—
590C2×Dic11—21no—
591C2×Dic11—21no—
592C2×Dic11—21no—
593C2×Dic11—21no—
594C2×Dic11—21no—
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×Dic11C2×#4112yes—
608C2×Dic112−1+412yes—
609C4×D11—44no—
610C4×D11—44no—
611C4×D11—44no—
612C4×D11—44no—
613C4×D11—44no—
614C4×D11—82no—
615C4×D11—82no—
616Dic22—82no—
617Dic22—82no—
618C2×C4⋊Q8—111no—
619C2×#125—111no—
620C2×#125—111no—
621C2×#125—111no—
622C2×C22⋊Q8—111no—
623C2×C22⋊Q8—111no—
624C22×C4⋊C4—111no—
625C22×C4⋊C4—111no—
626C22×C42—111no—
627#401—111no—
628#401—111no—
629#401—111no—
630#401C2×D1111yescharacteristic
631#400—111no—
632#400—111no—
633#400—111no—
634#400—111no—
635#400—111no—
636#400—111no—
637#400—111no—
638#400—111no—
639#400—111no—
640#400—111no—
641#400—111no—
642#400—111no—
643#400—111no—
644#400—111no—
645#400—111no—
646#400—111no—
647#400—111no—
648#400—111no—
649#400—111no—
650#400—111no—
651#400—111no—
652#400—111no—
653#400C2×D1111yescharacteristic
654#400C2×D1111yescharacteristic
655#398—111no—
656#398—111no—
657#398—111no—
658#398—111no—
659#398—111no—
660#398—111no—
661#398—111no—
662#398—111no—
663#398—111no—
664#398—111no—
665#398—111no—
666#398—111no—
667#398—111no—
668#398C2×D1111yescharacteristic
669#398C2×D1111yescharacteristic
670#398C2×D1111yescharacteristic
671#395—111no—
672#395—111no—
673#395—111no—
674#395—111no—
675#391—111no—
676#391—111no—
677#391—111no—
678#391—111no—
679#391—111no—
680#391—111no—
681#389—111no—
682#389—111no—
683#389—111no—
684#389—111no—
685#389—111no—
686#389—111no—
687#389—111no—
688#389—111no—
689#389—111no—
690#389—111no—
691#389—111no—
692#389—111no—
693#389C2×D1111yescharacteristic
694#389C2×D1111yescharacteristic
695#387—111no—
696#387—111no—
697#387—111no—
698#387—111no—
699#387—111no—
700#387—111no—
701#387—111no—
702#387—111no—
703#387—111no—
704#387—111no—
705#387—111no—
706#387—111no—
707#387—111no—
708#387—111no—
709#387—111no—
710#387—111no—
711#387—111no—
712#387—111no—
713#387—111no—
714#387—111no—
715#387—111no—
716#387—111no—
717#387—111no—
718#387—111no—
719#387—111no—
720#387—111no—
721#387—111no—
722#387—111no—
723#387—111no—
724#387—111no—
725#387—111no—
726#387—111no—
727#387—111no—
728#387—111no—
729#387—111no—
730#387C2×D1111yescharacteristic
731#387C2×D1111yescharacteristic
732#387C2×D1111yescharacteristic
733#387C2×D1111yescharacteristic
734#387C2×D1111yescharacteristic
735#385—111no—
736#385—111no—
737#385—111no—
738#385—111no—
739#385—111no—
740#385—111no—
741#385—111no—
742#385—111no—
743#385—111no—
744#385—111no—
745#385—111no—
746#385—111no—
747#384—111no—
748#383—111no—
749#383—111no—
750#383—111no—
751#383C2×D1111yescharacteristic
752#382—111no—
753#382—111no—
754#382C2×D1111yescharacteristic
755#381—111no—
756#381—111no—
757#381—111no—
758#381—111no—
759#380—111no—
760#380—111no—
761#380—111no—
762#380—111no—
763#380—111no—
764#380—111no—
765C4×C22⋊C4—111no—
766C4×C22⋊C4—111no—
767C4×C22⋊C4—111no—
768C4×C22⋊C4—111no—
769C2×#95—111no—
770C2×#95—111no—
771C2×#95—111no—
772C2×#95—111no—
773C22×C11C22×#4111yescharacteristic
774C22×C11C2×H(5,𝔽2)11yescharacteristic
775C22×C11C2×2−1+411yescharacteristic
776C22×C11C2×2−1+411yescharacteristic
777C22×C11C2×2−1+411yescharacteristic
778C22×C11#58511yescharacteristic
779C22×C11#58511yescharacteristic
780C2×D11—22no—
781C2×D11—22no—
782C2×D11—22no—
783C2×D11—22no—
784C2×D11—22no—
785C2×D11—22no—
786C2×D11#54114yes—
787C4×C11—22no—
788C4×C11—22no—
789C4×C11—41no—
790C4×C11—41no—
791C4×C11—41no—
792C4×C11—41no—
793C4×C11—41no—
794C4×C11—41no—
795C4×C11—41no—
796C4×C11—41no—
797C4×C11—41no—
798C4×C11—41no—
799C4×C11—41no—
800C4×C11—41no—
801C4×C11—41no—
802Dic11—22no—
803Dic11—22no—
804Dic11—41no—
805Dic11—41no—
806Dic11—41no—
807Dic11—41no—
808Dic11—41no—
809Dic11—41no—
810Dic11—41no—
811Dic11—41no—
812Dic11—41no—
813Dic11—41no—
814Dic11—41no—
815Dic11—41no—
816Dic11—41no—
817C22×Q8—111no—
818C22×Q8—111no—
819C23×C4—111no—
820C23×C4—111no—
821C23×C4—111no—
822C23×C4—111no—
823C23×C4—111no—
824C23×C4—111no—
825C23×C4—111no—
826C4⋊Q8—442no—
827#125—442no—
828#125—442no—
829#125—442no—
830C22⋊Q8—224no—
831C22⋊Q8—224no—
832C2×C4⋊C4—111no—
833C2×C4⋊C4—111no—
834C2×C4⋊C4—111no—
835C2×C4⋊C4—111no—
836C2×C4⋊C4—111no—
837C2×C4⋊C4—111no—
838C2×C4⋊C4—111no—
839C2×C4⋊C4—111no—
840C2×C4⋊C4—111no—
841C2×C4⋊C4—111no—
842C2×C4⋊C4—111no—
843C2×C4⋊C4—111no—
844C2×C4⋊C4—111no—
845C2×C4⋊C4—111no—
846C2×C4⋊C4—111no—
847C2×C4⋊C4—111no—
848C2×C4⋊C4—111no—
849C2×C4⋊C4—111no—
850C2×C4⋊C4—111no—
851C2×C4⋊C4—111no—
852C2×C4⋊C4—111no—
853C2×C4⋊C4—111no—
854C2×C4⋊C4—111no—
855C2×C4⋊C4—111no—
856C2×C4⋊C4—111no—
857C2×C4⋊C4—111no—
858C2×C4⋊C4—111no—
859C2×C4⋊C4—111no—
860C2×C4⋊C4—111no—
861C2×C4⋊C4—111no—
862C2×C4⋊C4—111no—
863C2×C4⋊C4—111no—
864C2×C4⋊C4—111no—
865C2×C4⋊C4—111no—
866C2×C4⋊C4—111no—
867C2×C4⋊C4—111no—
868C2×C4⋊C4—111no—
869C2×C4⋊C4—111no—
870C2×C4⋊C4—224no—
871C2×C4⋊C4—442no—
872C2×C4⋊C4C22×D1111yescharacteristic
873C2×C4⋊C4C22×D1111yescharacteristic
874C2×C4⋊C4C22×D1111yescharacteristic
875C2×C4⋊C4C22×D1111yescharacteristic
876C2×C4⋊C4C22×D1111yescharacteristic
877C2×C4⋊C4C22×D1111yescharacteristic
878C2×C4⋊C4C22×D1111yescharacteristic
879C2×C4⋊C4C22×D1111yescharacteristic
880C2×C4⋊C4C22×D1111yescharacteristic
881C2×C4⋊C4C22×D1111yescharacteristic
882C2×C4⋊C4C22×D1111yescharacteristic
883C2×C4⋊C4C22×D1111yescharacteristic
884C2×C22⋊C4—111no—
885C2×C22⋊C4—111no—
886C2×C22⋊C4—111no—
887C2×C22⋊C4—111no—
888C2×C22⋊C4—111no—
889C2×C22⋊C4—111no—
890C2×C22⋊C4—111no—
891C2×C22⋊C4—111no—
892C2×C42—111no—
893C2×C42—111no—
894C2×C42—111no—
895C2×C42—111no—
896C2×C42—111no—
897C2×C42—111no—
898C2×C42—111no—
899C2×C42—111no—
900C2×C42—111no—
901C2×C42—442no—
902C2×C42C22×D1111yescharacteristic
903C2×C42C22×D1111yescharacteristic
904C2×C42C22×D1111yescharacteristic
905#95—111no—
906#95—111no—
907#95—111no—
908#95—111no—
909#95—111no—
910#95—111no—
911#95—111no—
912#95—111no—
913#95—111no—
914#95—111no—
915#95—111no—
916#95—111no—
917#95—111no—
918#95—111no—
919#95—111no—
920#95—111no—
921#95—111no—
922#95—111no—
923#95—111no—
924#95—111no—
925#95—111no—
926#95—111no—
927#95—111no—
928#95—111no—
929#95—111no—
930#95—111no—
931#95—111no—
932#95—111no—
933#95—111no—
934#95—111no—
935#95—111no—
936#95—111no—
937#95—111no—
938#95—111no—
939#95—111no—
940#95—111no—
941#95—111no—
942#95—111no—
943#95—111no—
944#95—111no—
945#95—111no—
946#95—111no—
947#95—111no—
948#95—111no—
949#95—111no—
950#95—111no—
951#95—111no—
952#95—111no—
953#95—111no—
954#95—111no—
955#95—111no—
956#95—111no—
957#95—111no—
958#95—111no—
959#95—111no—
960#95—111no—
961#95C22×D1111yescharacteristic
962#95C22×D1111yescharacteristic
963#95C22×D1111yescharacteristic
964#95C22×D1111yescharacteristic
965#95C22×D1111yescharacteristic
966#95C22×D1111yescharacteristic
967#95C22×D1111yescharacteristic
968#95C22×D1111yescharacteristic
969#95C22×D1111yescharacteristic
970#95C22×D1111yescharacteristic
971#95C22×D1111yescharacteristic
972#95C22×D1111yescharacteristic
973#95C22×D1111yescharacteristic
974#95C22×D1111yescharacteristic
975#95C22×D1111yescharacteristic
976#95C22×D1111yescharacteristic
977#95C22×D1111yescharacteristic
978#95C22×D1111yescharacteristic
979#95C22×D1111yescharacteristic
980#95C22×D1111yescharacteristic
981C2×C11C2×#54111yescharacteristic
982C2×C11#350511yescharacteristic
983C2×C11#350711yescharacteristic
984C2×C11#353511yescharacteristic
985C2×C11#353811yescharacteristic
986C2×C11#356311yescharacteristic
987C2×C11#356411yescharacteristic
988D11—24no—
989C24—111no—
990C2×Q8—222no—
991C2×Q8—222no—
992C2×Q8—441no—
993C2×Q8—441no—
994C2×Q8—441no—
995C2×Q8—441no—
996C22×C4—111no—
997C22×C4—111no—
998C22×C4—114no—
999C22×C4—111no—
1000C22×C4—111no—
1001C22×C4—111no—
1002C22×C4—111no—
1003C22×C4—111no—
1004C22×C4—111no—
1005C22×C4—111no—
1006C22×C4—111no—
1007C22×C4—111no—
1008C22×C4—111no—
1009C22×C4—111no—
1010C22×C4—111no—
1011C22×C4—111no—
1012C22×C4—222no—
1013C22×C4—222no—
1014C22×C4—222no—
1015C22×C4—222no—
1016C22×C4—222no—
1017C22×C4—222no—
1018C22×C4—222no—
1019C22×C4—222no—
1020C22×C4—222no—
1021C22×C4—222no—
1022C22×C4—441no—
1023C22×C4—441no—
1024C22×C4—441no—
1025C22×C4—441no—
1026C22×C4—441no—
1027C22×C4—441no—
1028C22×C4—441no—
1029C22×C4—441no—
1030C22×C4—441no—
1031C22×C4—441no—
1032C22×C4C23×D1111yescharacteristic
1033C22×C4C23×D1111yescharacteristic
1034C22×C4C23×D1111yescharacteristic
1035C22×C4C23×D1111yescharacteristic
1036C22×C4C23×D1111yescharacteristic
1037C22×C4C23×D1111yescharacteristic
1038C22×C4C23×D1111yescharacteristic
1039C22×C4C23×D1111yescharacteristic
1040C22×C4C23×D1111yescharacteristic
1041C22×C4C23×D1111yescharacteristic
1042C22×C4C23×D1111yescharacteristic
1043C22×C4C23×D1111yescharacteristic
1044C22×C4C23×D1111yescharacteristic
1045C22×C4C23×D1111yescharacteristic
1046C22×C4C23×D1111yescharacteristic
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—222no—
1060C4⋊C4—222no—
1061C4⋊C4—222no—
1062C4⋊C4—222no—
1063C4⋊C4—222no—
1064C4⋊C4—222no—
1065C4⋊C4—222no—
1066C4⋊C4—222no—
1067C4⋊C4—222no—
1068C4⋊C4—222no—
1069C4⋊C4—222no—
1070C4⋊C4—222no—
1071C4⋊C4—222no—
1072C4⋊C4—222no—
1073C4⋊C4—222no—
1074C4⋊C4—441no—
1075C4⋊C4—441no—
1076C4⋊C4—441no—
1077C4⋊C4—441no—
1078C4⋊C4—441no—
1079C4⋊C4—441no—
1080C4⋊C4—441no—
1081C4⋊C4—441no—
1082C4⋊C4—441no—
1083C4⋊C4—441no—
1084C4⋊C4—441no—
1085C4⋊C4—441no—
1086C4⋊C4—441no—
1087C4⋊C4—441no—
1088C4⋊C4—441no—
1089C4⋊C4—441no—
1090C4⋊C4—441no—
1091C4⋊C4—441no—
1092C4⋊C4—441no—
1093C4⋊C4—441no—
1094C4⋊C4—441no—
1095C4⋊C4—441no—
1096C4⋊C4—441no—
1097C22⋊C4—222no—
1098C22⋊C4—222no—
1099C22⋊C4—222no—
1100C22⋊C4—222no—
1101C22⋊C4—222no—
1102C22⋊C4—222no—
1103C22⋊C4—222no—
1104C22⋊C4—222no—
1105C42—22no—
1106C42—41no—
1107C42—41no—
1108C42—222no—
1109C42—441no—
1110C42—441no—
1111C42—441no—
1112C42—441no—
1113C42—441no—
1114C42—441no—
1115C42—441no—
1116C42—441no—
1117C11#3676211yescharacteristic, complemented, Sylow
1118C23—112no—
1119C23—112no—
1120C23—112no—
1121C23—221no—
1122C23—221no—
1123C23—221no—
1124C23—221no—
1125C23C24×D1111yescharacteristic
1126Q8—882no—
1127Q8—882no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—112no—
1172C2×C4—112no—
1173C2×C4—221no—
1174C2×C4—221no—
1175C2×C4—221no—
1176C2×C4—221no—
1177C2×C4—221no—
1178C2×C4—221no—
1179C2×C4—221no—
1180C2×C4—221no—
1181C2×C4—221no—
1182C2×C4—221no—
1183C2×C4—221no—
1184C2×C4—221no—
1185C2×C4—221no—
1186C2×C4—221no—
1187C2×C4—221no—
1188C2×C4—221no—
1189C2×C4—221no—
1190C2×C4—221no—
1191C2×C4—221no—
1192C2×C4—221no—
1193C2×C4—221no—
1194C2×C4—221no—
1195C2×C4—221no—
1196C2×C4—221no—
1197C2×C4—221no—
1198C2×C4—221no—
1199C2×C4—221no—
1200C2×C4—221no—
1201C2×C4—221no—
1202C2×C4—221no—
1203C2×C4—221no—
1204C2×C4—221no—
1205C2×C4—221no—
1206C2×C4—221no—
1207C2×C4—221no—
1208C2×C4—221no—
1209C2×C4—221no—
1210C2×C4—221no—
1211C2×C4—221no—
1212C2×C4—221no—
1213C2×C4—221no—
1214C2×C4—221no—
1215C2×C4—221no—
1216C2×C4—444no—
1217C2×C4—444no—
1218C2×C4—444no—
1219C2×C4—444no—
1220C2×C4—444no—
1221C2×C4—882no—
1222C2×C4—882no—
1223C2×C4#41×D1112yes—
1224C2×C4#6704212yes—
1225C22—114no—
1226C22—222no—
1227C22—222no—
1228C22—222no—
1229C22—222no—
1230C22—222no—
1231C22—222no—
1232C22C2×#41×D1111yescharacteristic
1233C22C2×#6704211yescharacteristic
1234C22#1062345311yescharacteristic
1235C22#1062345511yescharacteristic
1236C22D11×2−1+411yescharacteristic
1237C22D11×2−1+411yescharacteristic
1238C22D11×2−1+411yescharacteristic
1239C4—22no—
1240C4—22no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—222no—
1255C4—222no—
1256C4—441no—
1257C4—441no—
1258C4—441no—
1259C4—441no—
1260C4—441no—
1261C4—441no—
1262C4—441no—
1263C4—441no—
1264C4—441no—
1265C4—441no—
1266C4—441no—
1267C4—441no—
1268C4—441no—
1269C2—224no—
1270C2D11×#54111yescharacteristic
1271C2#1308244511yescharacteristic
1272C2#1308247511yescharacteristic
1273C2#1308282811yescharacteristic
1274C2#1308286411yescharacteristic
1275C2#1308321611yescharacteristic
1276C2#1308324111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2766C2
prime radicalC23×D11C24
hypercenter#2766D11
hypocenterC11#36762
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2766

Complements

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

NH ≅ G/Ntype
3. #13076536C2semidirect
4. #13076534C2semidirect
5. #13076441C2semidirect
6. #13076434C2semidirect
7. #13076375C2semidirect
8. #13076370C2semidirect
9. #13076208C2semidirect
10. #13076206C2semidirect
11. #13076062C2semidirect
12. #13075972C2semidirect
13. #13075965C2semidirect
14. #13075485C2semidirect
15. #13075481C2semidirect
16. #13075404C2semidirect
17. #13075395C2semidirect
31. C11×#2766C2semidirect
491. #2766D11semidirect
1117. C11#36762semidirect

Maximal subgroups

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

subgroupindex
#130769672
#130769272
#130765362
#130765342
#130764412
#130764342
#130763752
#130763702
#130762082
#130762062
#130760622
#130759722
#130759652
#130754852
#130754812
#130754042
#130753952
#130744342
#130731242
#130731122
#130730002
#130729982
#130729962
#130729942
#130727582
#130727552
#130713502
#130713432
D11×#3872
C11×#27662
#3676211