Finite Group Databasebeta

← #14962308

Subgroups — #14962308

Order 2816.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076929C211yesmaximal, characteristic
2#13076924C211yesmaximal, characteristic, complemented
3#13076302C211yesmaximal, characteristic, complemented
4#13076301C211yesmaximal, characteristic, complemented
5#13076210C211yesmaximal, characteristic, complemented
6#13076200C211yesmaximal, characteristic, complemented
7#13076142C211yesmaximal, characteristic, complemented
8#13076111C211yesmaximal, characteristic, complemented
9#13076073C211yesmaximal, characteristic, complemented
10#13076069C211yesmaximal, characteristic, complemented
11#13076021C211yesmaximal, characteristic, complemented
12#13076017C211yesmaximal, characteristic, complemented
13#13075820C211yesmaximal, characteristic, complemented
14#13075764C211yesmaximal, characteristic, complemented
15#13075563C211yesmaximal, characteristic, complemented
16#13075479C211yesmaximal, characteristic, complemented
17#13075087C211yesmaximal, characteristic, complemented
18#13075065C211yesmaximal, characteristic, complemented
19#13074588C211yesmaximal, characteristic, complemented
20#13074571C211yesmaximal, characteristic
21#13073993C211yesmaximal, characteristic, complemented
22#13073960C211yesmaximal, characteristic
23#13073178C211yesmaximal, characteristic
24#13073117C211yesmaximal, characteristic, complemented
25#13073111C211yesmaximal, characteristic, complemented
26#13072337C211yesmaximal, characteristic, complemented
27#13072064C211yesmaximal, characteristic
28#13071344C211yesmaximal, characteristic, complemented
29#13071242C211yesmaximal, characteristic
30C2×#10622266C211yesmaximal, characteristic, complemented
31C11×#2510C211yesmaximal, characteristic
32C2×D4×Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C2×#66943C2211yescharacteristic
37C2×#66942C2211yescharacteristic
38C2×#66932C2211yescharacteristic
39C2×#66931C2211yescharacteristic
40C2×#66931C2211yescharacteristic
41C11×#401C2211yescharacteristic
42C11×#400C2211yescharacteristic
43C11×#397C2211yescharacteristic
44C11×#397C2211yescharacteristic
45C11×#388C2211yescharacteristic
46C11×#388C2211yescharacteristic
47C11×#387C2211yescharacteristic
48C11×#386C2211yescharacteristic
49C11×#386C2211yescharacteristic
50C11×#386C2211yescharacteristic
51C11×#385C2211yescharacteristic
52C11×#383C2211yescharacteristic
53C11×#380C2211yescharacteristic
54C4×C11×C22⋊C4C2211yescharacteristic
55C2×C11×#95C2211yescharacteristic
56#10622833C2211yescharacteristic
57#10622833C2211yescharacteristic
58#10622833C2211yescharacteristic
59#10622825C2211yescharacteristic
60#10622823C2211yescharacteristic
61#10622823C2211yescharacteristic
62#10622823C2211yescharacteristic
63#10622823C2211yescharacteristic
64C4×C22⋊Dic11C2211yescharacteristic
65C2×C11⋊#95C2211yescharacteristic
66C2×C11⋊#95C2211yescharacteristic
67C2×C11⋊#95C2211yescharacteristic
68#10622598C2211yescharacteristic
69#10622598C2211yescharacteristic
70#10622598C2211yescharacteristic
71#10622597C2211yescharacteristic
72#10622597C2211yescharacteristic
73#10622597C2211yescharacteristic
74#10622596C2211yescharacteristic
75#10622596C2211yescharacteristic
76#10622595C2211yescharacteristic
77#10622595C2211yescharacteristic
78#10622593C2211yescharacteristic
79#10622590C2211yescharacteristic
80#10622586C2211yescharacteristic
81#10622585C2211yescharacteristic
82#10622566C2211yescharacteristic
83#10622566C2211yescharacteristic
84#10622565C2211yescharacteristic
85#10622565C2211yescharacteristic
86#10622565C2211yescharacteristic
87#10622564C2211yescharacteristic
88#10622564C2211yescharacteristic
89#10622563C2211yescharacteristic
90#10622563C2211yescharacteristic
91#10622563C2211yescharacteristic
92#10622563C2211yescharacteristic
93#10622563C2211yescharacteristic
94#10622563C2211yescharacteristic
95#10622561C2211yescharacteristic
96#10622561C2211yescharacteristic
97#10622561C2211yescharacteristic
98#10622561C2211yescharacteristic
99#10622561C2211yescharacteristic
100#10622559C2211yescharacteristic
101#10622559C2211yescharacteristic
102#10622559C2211yescharacteristic
103#10622558C2211yescharacteristic
104#10622558C2211yescharacteristic
105#10622557C2211yescharacteristic
106#10622557C2211yescharacteristic
107#10622557C2211yescharacteristic
108#10622556C2211yescharacteristic
109#10622555C2211yescharacteristic
110#10622555C2211yescharacteristic
111#10622555C2211yescharacteristic
112#10622555C2211yescharacteristic
113#10622555C2211yescharacteristic
114C22⋊C4×Dic11C2211yescharacteristic
115#10622549C2211yescharacteristic
116#10622546C2211yescharacteristic
117#10622546C2211yescharacteristic
118#10622546C2211yescharacteristic
119#10622546C2211yescharacteristic
120#10622542C2211yescharacteristic
121#10622541C2211yescharacteristic
122#10622541C2211yescharacteristic
123C11⋊#401C2211yescharacteristic
124C11⋊#401C2211yescharacteristic
125#10622274C2211yescharacteristic
126#10622274C2211yescharacteristic
127#10622274C2211yescharacteristic
128#10622273C2211yescharacteristic
129#10622273C2211yescharacteristic
130#10622273C2211yescharacteristic
131#10622273C2211yescharacteristic
132#10622272C2211yescharacteristic
133#10622272C2211yescharacteristic
134#10622272C2211yescharacteristic
135#10622272C2211yescharacteristic
136#10622271C2211yescharacteristic
137#10622271C2211yescharacteristic
138#10622271C2211yescharacteristic
139#10622271C2211yescharacteristic
140#10622271C2211yescharacteristic
141#10622271C2211yescharacteristic
142#10622270C2211yescharacteristic
143#10622270C2211yescharacteristic
144#10622270C2211yescharacteristic
145#10622270C2211yescharacteristic
146#10622270C2211yescharacteristic
147#10622269C2211yescharacteristic
148#10622269C2211yescharacteristic
149#10622268C2211yescharacteristic
150#10622268C2211yescharacteristic
151#10622268C2211yescharacteristic
152#10622268C2211yescharacteristic
153#10622268C2211yescharacteristic
154#10622268C2211yescharacteristic
155#10622268C2211yescharacteristic
156#10622267C2211yescharacteristic
157#10622267C2211yescharacteristic
158#10622267C2211yescharacteristic
159#10622267C2211yescharacteristic
160#10622266C2211yescharacteristic
161#10622266C2211yescharacteristic
162#10622266C2211yescharacteristic
163#10622266C2211yescharacteristic
164#10622266C2211yescharacteristic
165#10622266C2211yescharacteristic
166#10622266C2211yescharacteristic
167#10622266C2211yescharacteristic
168#10622266C2211yescharacteristic
169#10622266C2211yescharacteristic
170#10622266C2211yescharacteristic
171#10622265C2211yescharacteristic
172#10622265C2211yescharacteristic
173#10622264C2211yescharacteristic
174#10622264C2211yescharacteristic
175#10622264C2211yescharacteristic
176#10622263C2211yescharacteristic
177#10622263C2211yescharacteristic
178#10622263C2211yescharacteristic
179#10622260C2211yescharacteristic
180#10622260C2211yescharacteristic
181#10622260C2211yescharacteristic
182#10622260C2211yescharacteristic
183#10622260C2211yescharacteristic
184#10622260C2211yescharacteristic
185#10622259C2211yescharacteristic
186#10622259C2211yescharacteristic
187C22×D4×C11C2311yescharacteristic
188C23×C4×C11C2311yescharacteristic
189C23×C4×C11C2311yescharacteristic
190C23×C4×C11C2311yescharacteristic
191C23×Dic11C2311yescharacteristic
192C23×Dic11C2311yescharacteristic
193C23×Dic11C2311yescharacteristic
194C23×Dic11C2311yescharacteristic
195C23×Dic11C2311yescharacteristic
196C22×Dic22C2311yescharacteristic
197C2×C11×C4⋊C4C2311yescharacteristic
198C2×C11×C4⋊C4C2311yescharacteristic
199C2×C11×C4⋊C4C2311yescharacteristic
200C2×C11×C4⋊C4C2311yescharacteristic
201C2×C11×C22⋊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×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C22⋊Dic11C2311yescharacteristic
213C2×C22⋊Dic11C2311yescharacteristic
214C2×C22⋊Dic11C2311yescharacteristic
215C2×C22⋊Dic11C2311yescharacteristic
216C2×C22⋊Dic11C2311yescharacteristic
217C2×C22⋊Dic11C2311yescharacteristic
218C2×C22⋊Dic11C2311yescharacteristic
219C2×C22⋊Dic11C2311yescharacteristic
220C2×C22⋊Dic11C2311yescharacteristic
221C2×C22⋊Dic11C2311yescharacteristic
222C2×C22⋊Dic11C2311yescharacteristic
223D4×Dic11—24no—
224C2×C4⋊Dic11—24no—
225C2×C4⋊Dic11C2311yescharacteristic
226C2×C4⋊Dic11C2311yescharacteristic
227C2×C4⋊Dic11C2311yescharacteristic
228C2×C4⋊Dic11C2311yescharacteristic
229C2×C4⋊Dic11C2311yescharacteristic
230C2×C4⋊Dic11C2311yescharacteristic
231C2×C4⋊Dic11C2311yescharacteristic
232C2×C4⋊Dic11C2311yescharacteristic
233C2×C4⋊Dic11C2311yescharacteristic
234C2×C4⋊Dic11C2311yescharacteristic
235C2×C4⋊Dic11C2311yescharacteristic
236C2×C4⋊Dic11C2311yescharacteristic
237C2×C4⋊Dic11C2311yescharacteristic
238C2×C4⋊Dic11C2311yescharacteristic
239C2×C4⋊Dic11C2311yescharacteristic
240C2×C4⋊Dic11C2311yescharacteristic
241C2×Dic11⋊C4—42no—
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×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×Dic11—42no—
269C2×C4×Dic11C2311yescharacteristic
270C2×C4×Dic11C2311yescharacteristic
271C2×C4×Dic11C2311yescharacteristic
272C2×C4×Dic11C2311yescharacteristic
273C2×C4×Dic11C2311yescharacteristic
274C2×C4×Dic11C2311yescharacteristic
275C2×C4×Dic11C2311yescharacteristic
276C2×C4×Dic11C2311yescharacteristic
277C2×C4×Dic11C2311yescharacteristic
278#66943—42no—
279#66942—42no—
280#66932—42no—
281#66931—24no—
282#66931—42no—
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#36782—111nomaximal, Sylow
352C24×C11C2411yescharacteristic
353C24×C11C2411yescharacteristic
354C2×D4×C11—22no—
355C2×D4×C11—22no—
356C2×D4×C11—22no—
357C22×C4×C11—22no—
358C22×C4×C11—22no—
359C22×C4×C11—22no—
360C22×C4×C11—22no—
361C22×C4×C11—41no—
362C22×C4×C11—41no—
363C22×C4×C11—41no—
364C22×C4×C11—41no—
365C22×C4×C11—41no—
366C22×C4×C11C2411yescharacteristic
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2411yescharacteristic
369C22×C4×C11C2411yescharacteristic
370C22×C4×C11C2411yescharacteristic
371C22×C4×C11C2411yescharacteristic
372C22×C4×C11C2411yescharacteristic
373C22×C4×C11C2411yescharacteristic
374C22×C4×C11C2411yescharacteristic
375C22×C4×C11C2411yescharacteristic
376C22×C4×C11C2411yescharacteristic
377C22×C4×C11C2411yescharacteristic
378C22×C4×C11C2411yescharacteristic
379C22×Dic11—22no—
380C22×Dic11—22no—
381C22×Dic11—22no—
382C22×Dic11—22no—
383C22×Dic11—41no—
384C22×Dic11—41no—
385C22×Dic11—41no—
386C22×Dic11—41no—
387C22×Dic11—41no—
388C22×Dic11—41no—
389C22×Dic11—41no—
390C22×Dic11—41no—
391C22×Dic11—41no—
392C22×Dic11—41no—
393C22×Dic11#4114yes—
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
407C22×Dic11C2411yescharacteristic
408C22×Dic11C2411yescharacteristic
409C22×Dic11C2411yescharacteristic
410C2×Dic22—22no—
411C2×Dic22—41no—
412C2×Dic22—41no—
413C11×C4⋊C4—22no—
414C11×C4⋊C4—41no—
415C11×C4⋊C4—41no—
416C11×C4⋊C4—41no—
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—
426C42×C11—41no—
427C42×C11—41no—
428C22⋊Dic11—22no—
429C22⋊Dic11—22no—
430C22⋊Dic11—22no—
431C22⋊Dic11—22no—
432C22⋊Dic11—22no—
433C22⋊Dic11—41no—
434C22⋊Dic11—41no—
435C22⋊Dic11—41no—
436C22⋊Dic11—41no—
437C22⋊Dic11—41no—
438C22⋊Dic11—41no—
439C4⋊Dic11—22no—
440C4⋊Dic11—22no—
441C4⋊Dic11—22no—
442C4⋊Dic11—22no—
443C4⋊Dic11—22no—
444C4⋊Dic11—22no—
445C4⋊Dic11—22no—
446C4⋊Dic11—41no—
447C4⋊Dic11—41no—
448C4⋊Dic11—41no—
449C4⋊Dic11—41no—
450C4⋊Dic11—41no—
451C4⋊Dic11—41no—
452C4⋊Dic11—41no—
453C4⋊Dic11—41no—
454C4⋊Dic11—41no—
455Dic11⋊C4—22no—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459Dic11⋊C4—22no—
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—
471Dic11⋊C4—41no—
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—
481C4×Dic11—22no—
482C4×Dic11—22no—
483C4×Dic11—22no—
484C4×Dic11—41no—
485C4×Dic11—41no—
486C4×Dic11—41no—
487C4×Dic11—41no—
488C4×Dic11—41no—
489C4×Dic11—41no—
490#2852—111no—
491#2851—111no—
492#2783—111no—
493#2783—111no—
494#2776—111no—
495#2776—111no—
496#2772—111no—
497#2769—111no—
498#2766—111no—
499#2766—111no—
500#2762—111no—
501#2762—111no—
502#2747—111no—
503#2744—111no—
504#2725—111no—
505#2719—111no—
506#2690—111no—
507#2689—111no—
508#2646—111no—
509#2643—111no—
510#2583—111no—
511#2579—111no—
512#2510—111no—
513#2510D1111yescharacteristic
514#2505—111no—
515#2505—111no—
516#2442—111no—
517#2417—111no—
518#2329—111no—
519#2318—111no—
520C2×#387—111no—
521C23×C11—21no—
522C23×C11—21no—
523C23×C11—21no—
524C23×C11—21no—
525C23×C11—21no—
526C23×C11—21no—
527C23×C11—21no—
528C23×C11—21no—
529C23×C11—21no—
530C23×C11—21no—
531C23×C11—21no—
532C23×C11C2×#4112yes—
533C23×C112−1+412yes—
534C23×C112−1+412yes—
535C23×C11C2511yescharacteristic
536D4×C11—44no—
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×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—44no—
576C2×C4×C11—44no—
577C2×C4×C11—82no—
578C2×C4×C11H(5,𝔽2)12yes—
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×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—44no—
626C2×Dic11—44no—
627C2×Dic11—44no—
628C2×Dic11—82no—
629C2×Dic11—82no—
630C2×Dic11C2×#4112yes—
631C2×Dic11C2×#4112yes—
632Dic22—82no—
633C2×#126—111no—
634C2×#125—111no—
635C2×#125—111no—
636C2×C22⋊Q8—111no—
637C2×C22⋊Q8—111no—
638C2×C4×D4—111no—
639C22×C4⋊C4—111no—
640C22×C4⋊C4—111no—
641C22×C42—111no—
642#401—111no—
643#401—111no—
644#401C2×D1111yescharacteristic
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#400—111no—
654#400—111no—
655#400—111no—
656#400—111no—
657#400—111no—
658#400—111no—
659#400—111no—
660#400—111no—
661#400C2×D1111yescharacteristic
662#398—111no—
663#398—111no—
664#398—111no—
665#398—111no—
666#398—111no—
667#398—111no—
668#398—111no—
669#398—111no—
670#398—111no—
671#398—111no—
672#398—111no—
673#398—111no—
674#398—111no—
675#398—111no—
676#397—111no—
677#397—111no—
678#397—111no—
679#397—111no—
680#397—111no—
681#397C2×D1111yescharacteristic
682#397C2×D1111yescharacteristic
683#396—111no—
684#396—111no—
685#396—111no—
686#396—111no—
687#396—111no—
688#395—111no—
689#395—111no—
690#391—111no—
691#391—111no—
692#391—111no—
693#389—111no—
694#389—111no—
695#389—111no—
696#389—111no—
697#389—111no—
698#389—111no—
699#389—111no—
700#389—111no—
701#389—111no—
702#389—111no—
703#389—111no—
704#389—111no—
705#389—111no—
706#388—111no—
707#388—111no—
708#388—111no—
709#388—111no—
710#388—111no—
711#388—111no—
712#388—111no—
713#388C2×D1111yescharacteristic
714#388C2×D1111yescharacteristic
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#387—111no—
731#387—111no—
732#387—111no—
733#387—111no—
734#387—111no—
735#387—111no—
736#387—111no—
737#387—111no—
738#387—111no—
739#387—111no—
740#387—111no—
741#387—111no—
742#387—111no—
743#387C2×D1111yescharacteristic
744#386—111no—
745#386—111no—
746#386—111no—
747#386C2×D1111yescharacteristic
748#386C2×D1111yescharacteristic
749#386C2×D1111yescharacteristic
750#385—111no—
751#385—111no—
752#385—111no—
753#385—111no—
754#385—111no—
755#385—111no—
756#385—111no—
757#385—111no—
758#385—111no—
759#385—111no—
760#385—111no—
761#385—111no—
762#385—111no—
763#385C2×D1111yescharacteristic
764#383—111no—
765#383—111no—
766#383—111no—
767#383C2×D1111yescharacteristic
768#382—111no—
769#382—111no—
770#382—111no—
771#382—111no—
772#382—111no—
773#381—111no—
774#380—111no—
775#380—111no—
776#380—111no—
777#380—111no—
778#380—111no—
779#380—111no—
780#380C2×D1111yescharacteristic
781C4×C22⋊C4—111no—
782C4×C22⋊C4—111no—
783C4×C22⋊C4C2×D1111yescharacteristic
784C2×#95—111no—
785C2×#95—111no—
786C2×#95—111no—
787C2×#95C2×D1111yescharacteristic
788C22×C11—22no—
789C22×C11—22no—
790C22×C11—22no—
791C22×C11—22no—
792C22×C11—22no—
793C22×C11—22no—
794C22×C11—41no—
795C22×C11—41no—
796C22×C11—41no—
797C22×C11—41no—
798C22×C11—41no—
799C22×C11—41no—
800C22×C11—41no—
801C22×C11#54114yes—
802C22×C11C22×#4111yescharacteristic
803C22×C11C2×H(5,𝔽2)11yescharacteristic
804C22×C11C2×2−1+411yescharacteristic
805C22×C11C2×2−1+411yescharacteristic
806C22×C11#58511yescharacteristic
807C22×C11#58511yescharacteristic
808C22×C11#58511yescharacteristic
809C4×C11—22no—
810C4×C11—41no—
811C4×C11—41no—
812C4×C11—41no—
813C4×C11—41no—
814C4×C11—41no—
815C4×C11—41no—
816C4×C11—41no—
817C4×C11—41no—
818C4×C11—41no—
819C4×C11—41no—
820C4×C11—41no—
821C4×C11—41no—
822Dic11—22no—
823Dic11—22no—
824Dic11—41no—
825Dic11—41no—
826Dic11—41no—
827Dic11—41no—
828Dic11—41no—
829Dic11—41no—
830Dic11—41no—
831Dic11—41no—
832Dic11—41no—
833Dic11—41no—
834Dic11—41no—
835Dic11—41no—
836Dic11—41no—
837Dic11—41no—
838C22×Q8—111no—
839C22×D4C22×D1111yescharacteristic
840C23×C4—111no—
841C23×C4—111no—
842C23×C4—111no—
843C23×C4—111no—
844C23×C4—111no—
845C23×C4C22×D1111yescharacteristic
846C23×C4C22×D1111yescharacteristic
847C23×C4C22×D1111yescharacteristic
848#126—442no—
849#125—442no—
850#125—442no—
851C22⋊Q8—224no—
852C22⋊Q8—442no—
853C4×D4—224no—
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—111no—
871C2×C4⋊C4—111no—
872C2×C4⋊C4—111no—
873C2×C4⋊C4—111no—
874C2×C4⋊C4—111no—
875C2×C4⋊C4—111no—
876C2×C4⋊C4—111no—
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—224no—
897C2×C4⋊C4—442no—
898C2×C4⋊C4C22×D1111yescharacteristic
899C2×C4⋊C4C22×D1111yescharacteristic
900C2×C4⋊C4C22×D1111yescharacteristic
901C2×C4⋊C4C22×D1111yescharacteristic
902C2×C22⋊C4—111no—
903C2×C22⋊C4—111no—
904C2×C22⋊C4—111no—
905C2×C22⋊C4—111no—
906C2×C22⋊C4—111no—
907C2×C22⋊C4—111no—
908C2×C22⋊C4—111no—
909C2×C22⋊C4—111no—
910C2×C22⋊C4—111no—
911C2×C22⋊C4—111no—
912C2×C22⋊C4—111no—
913C2×C22⋊C4C22×D1111yescharacteristic
914C2×C22⋊C4C22×D1111yescharacteristic
915C2×C22⋊C4C22×D1111yescharacteristic
916C2×C22⋊C4C22×D1111yescharacteristic
917C2×C22⋊C4C22×D1111yescharacteristic
918C2×C22⋊C4C22×D1111yescharacteristic
919C2×C22⋊C4C22×D1111yescharacteristic
920C2×C22⋊C4C22×D1111yescharacteristic
921C2×C22⋊C4C22×D1111yescharacteristic
922C2×C42—111no—
923C2×C42—111no—
924C2×C42—111no—
925C2×C42—111no—
926C2×C42—111no—
927C2×C42—111no—
928C2×C42—111no—
929C2×C42—111no—
930C2×C42—111no—
931C2×C42—442no—
932C2×C42C22×D1111yescharacteristic
933C2×C42C22×D1111yescharacteristic
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#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#95C22×D1111yescharacteristic
987#95C22×D1111yescharacteristic
988#95C22×D1111yescharacteristic
989#95C22×D1111yescharacteristic
990#95C22×D1111yescharacteristic
991#95C22×D1111yescharacteristic
992#95C22×D1111yescharacteristic
993#95C22×D1111yescharacteristic
994#95C22×D1111yescharacteristic
995#95C22×D1111yescharacteristic
996#95C22×D1111yescharacteristic
997#95C22×D1111yescharacteristic
998#95C22×D1111yescharacteristic
999#95C22×D1111yescharacteristic
1000#95C22×D1111yescharacteristic
1001#95C22×D1111yescharacteristic
1002C2×C11—24no—
1003C2×C11—81no—
1004C2×C11C2×#54111yescharacteristic
1005C2×C11#349311yescharacteristic
1006C2×C11#350511yescharacteristic
1007C2×C11#353511yescharacteristic
1008C2×C11#354111yescharacteristic
1009C2×C11#355311yescharacteristic
1010C2×C11#356411yescharacteristic
1011C24C23×D1111yescharacteristic
1012C24C23×D1111yescharacteristic
1013C2×Q8—222no—
1014C2×Q8—441no—
1015C2×Q8—441no—
1016C2×D4—22no—
1017C2×D4—22no—
1018C2×D4—22no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—111no—
1029C22×C4—111no—
1030C22×C4—114no—
1031C22×C4—111no—
1032C22×C4—111no—
1033C22×C4—111no—
1034C22×C4—111no—
1035C22×C4—111no—
1036C22×C4—111no—
1037C22×C4—111no—
1038C22×C4—111no—
1039C22×C4—111no—
1040C22×C4—111no—
1041C22×C4—111no—
1042C22×C4—111no—
1043C22×C4—111no—
1044C22×C4—111no—
1045C22×C4—222no—
1046C22×C4—222no—
1047C22×C4—222no—
1048C22×C4—222no—
1049C22×C4—441no—
1050C22×C4—441no—
1051C22×C4—441no—
1052C22×C4—441no—
1053C22×C4—441no—
1054C22×C4—441no—
1055C22×C4—441no—
1056C22×C4—441no—
1057C22×C4—441no—
1058C22×C4—441no—
1059C22×C4C23×D1111yescharacteristic
1060C22×C4C23×D1111yescharacteristic
1061C22×C4C23×D1111yescharacteristic
1062C22×C4C23×D1111yescharacteristic
1063C22×C4C23×D1111yescharacteristic
1064C22×C4C23×D1111yescharacteristic
1065C22×C4C23×D1111yescharacteristic
1066C22×C4C23×D1111yescharacteristic
1067C22×C4C23×D1111yescharacteristic
1068C22×C4C23×D1111yescharacteristic
1069C22×C4C23×D1111yescharacteristic
1070C22×C4C23×D1111yescharacteristic
1071C22×C4C23×D1111yescharacteristic
1072C4⋊C4—22no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—222no—
1077C4⋊C4—222no—
1078C4⋊C4—222no—
1079C4⋊C4—222no—
1080C4⋊C4—222no—
1081C4⋊C4—222no—
1082C4⋊C4—222no—
1083C4⋊C4—222no—
1084C4⋊C4—222no—
1085C4⋊C4—222no—
1086C4⋊C4—222no—
1087C4⋊C4—222no—
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—
1097C4⋊C4—441no—
1098C4⋊C4—441no—
1099C4⋊C4—441no—
1100C4⋊C4—441no—
1101C4⋊C4—441no—
1102C4⋊C4—441no—
1103C4⋊C4—441no—
1104C4⋊C4—441no—
1105C4⋊C4—441no—
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—
1118C22⋊C4—22no—
1119C22⋊C4—22no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—222no—
1128C22⋊C4—222no—
1129C22⋊C4—222no—
1130C22⋊C4—222no—
1131C22⋊C4—222no—
1132C22⋊C4—441no—
1133C22⋊C4—441no—
1134C22⋊C4—441no—
1135C22⋊C4—441no—
1136C22⋊C4—441no—
1137C22⋊C4—441no—
1138C42—41no—
1139C42—41no—
1140C42—222no—
1141C42—222no—
1142C42—222no—
1143C42—441no—
1144C42—441no—
1145C42—441no—
1146C42—441no—
1147C42—441no—
1148C42—441no—
1149C11#3678211yescharacteristic, complemented, Sylow
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23#41×D1112yes—
1162C23#6704312yes—
1163C23#6704312yes—
1164C23C24×D1111yescharacteristic
1165Q8—882no—
1166D4—44no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—44no—
1206C2×C4—44no—
1207C2×C4—82no—
1208C2×C4—112no—
1209C2×C4—112no—
1210C2×C4—221no—
1211C2×C4—221no—
1212C2×C4—221no—
1213C2×C4—221no—
1214C2×C4—221no—
1215C2×C4—221no—
1216C2×C4—221no—
1217C2×C4—221no—
1218C2×C4—221no—
1219C2×C4—221no—
1220C2×C4—221no—
1221C2×C4—221no—
1222C2×C4—221no—
1223C2×C4—221no—
1224C2×C4—221no—
1225C2×C4—221no—
1226C2×C4—221no—
1227C2×C4—221no—
1228C2×C4—221no—
1229C2×C4—221no—
1230C2×C4—221no—
1231C2×C4—221no—
1232C2×C4—221no—
1233C2×C4—221no—
1234C2×C4—221no—
1235C2×C4—221no—
1236C2×C4—221no—
1237C2×C4—221no—
1238C2×C4—221no—
1239C2×C4—221no—
1240C2×C4—221no—
1241C2×C4—221no—
1242C2×C4—221no—
1243C2×C4—221no—
1244C2×C4—221no—
1245C2×C4—221no—
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—444no—
1257C2×C4—444no—
1258C2×C4—444no—
1259C2×C4—882no—
1260C2×C4—882no—
1261C2×C4#6704212yes—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22#1062323214yes—
1276C22C2×#41×D1111yescharacteristic
1277C22C2×#6704211yescharacteristic
1278C22C2×#6704311yescharacteristic
1279C22C2×#6704311yescharacteristic
1280C22#1062345311yescharacteristic
1281C22#1062345511yescharacteristic
1282C22#1062345511yescharacteristic
1283C4—22no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—222no—
1297C4—222no—
1298C4—441no—
1299C4—441no—
1300C4—441no—
1301C4—441no—
1302C4—441no—
1303C4—441no—
1304C4—441no—
1305C4—441no—
1306C4—441no—
1307C4—441no—
1308C4—441no—
1309C4—441no—
1310C4—441no—
1311C4—441no—
1312C2—24no—
1313C2—81no—
1314C2C2×#1062323211yescharacteristic
1315C2#1308233111yescharacteristic
1316C2#1308245111yescharacteristic
1317C2#1308282111yescharacteristic
1318C2#1308290311yescharacteristic
1319C2#1308306411yescharacteristic
1320C2#1308322811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2510C2
prime radicalC22×D4×C11C23
hypercenter#2510D11
hypocenterC11#36782
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2510

Complements

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

NH ≅ G/Ntype
2. #13076924C2semidirect
3. #13076302C2semidirect
4. #13076301C2semidirect
5. #13076210C2semidirect
6. #13076200C2semidirect
7. #13076142C2semidirect
8. #13076111C2semidirect
9. #13076073C2semidirect
10. #13076069C2semidirect
11. #13076021C2semidirect
12. #13076017C2semidirect
13. #13075820C2semidirect
14. #13075764C2semidirect
15. #13075563C2semidirect
16. #13075479C2semidirect
17. #13075087C2semidirect
18. #13075065C2semidirect
19. #13074588C2semidirect
21. #13073993C2semidirect
24. #13073117C2semidirect
25. #13073111C2semidirect
26. #13072337C2semidirect
28. #13071344C2semidirect
30. C2×#10622266C2semidirect
1149. C11#36782semidirect

Maximal subgroups

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

subgroupindex
#130769292
#130769242
#130763022
#130763012
#130762102
#130762002
#130761422
#130761112
#130760732
#130760692
#130760212
#130760172
#130758202
#130757642
#130755632
#130754792
#130750872
#130750652
#130745882
#130745712
#130739932
#130739602
#130731782
#130731172
#130731112
#130723372
#130720642
#130713442
#130712422
C2×#106222662
C11×#25102
#3678211