Finite Group Databasebeta

← #14967783

Subgroups — #14967783

Order 2816.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076950C211yesmaximal, characteristic, complemented
2#13076939C211yesmaximal, characteristic
3#13076213C211yesmaximal, characteristic, complemented
4#13076129C211yesmaximal, characteristic, complemented
5#13076090C211yesmaximal, characteristic, complemented
6#13076075C211yesmaximal, characteristic, complemented
7#13076069C211yesmaximal, characteristic, complemented
8#13076045C211yesmaximal, characteristic, complemented
9#13076036C211yesmaximal, characteristic, complemented
10#13076018C211yesmaximal, characteristic, complemented
11#13076001C211yesmaximal, characteristic
12#13075917C211yesmaximal, characteristic, complemented
13#13075902C211yesmaximal, characteristic, complemented
14#13075794C211yesmaximal, characteristic
15#13075764C211yesmaximal, characteristic, complemented
16#13075756C211yesmaximal, characteristic
17#13075710C211yesmaximal, characteristic
18#13075680C211yesmaximal, characteristic, complemented
19#13074812C211yesmaximal, characteristic, complemented
20#13074767C211yesmaximal, characteristic
21#13074122C211yesmaximal, characteristic, complemented
22#13074084C211yesmaximal, characteristic, complemented
23#13074082C211yesmaximal, characteristic, complemented
24#13073907C211yesmaximal, characteristic, complemented
25#13073493C211yesmaximal, characteristic, complemented
26#13073450C211yesmaximal, characteristic, complemented
27#13073433C211yesmaximal, characteristic, complemented
28#13073420C211yesmaximal, characteristic, complemented
29#13071406C211yesmaximal, characteristic
30#13071010C211yesmaximal, characteristic, complemented
31C11×#2332C211yesmaximal, characteristic, complemented
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×#66982C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C11×#391C2211yescharacteristic
36C11×#391C2211yescharacteristic
37C11×#388C2211yescharacteristic
38C11×#388C2211yescharacteristic
39C11×#388C2211yescharacteristic
40C11×#388C2211yescharacteristic
41C11×#387C2211yescharacteristic
42C11×#387C2211yescharacteristic
43C11×#387C2211yescharacteristic
44C11×#387C2211yescharacteristic
45C11×#381C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4C2211yescharacteristic
49#10622844C2211yescharacteristic
50#10622843C2211yescharacteristic
51#10622843C2211yescharacteristic
52#10622842C2211yescharacteristic
53#10622825C2211yescharacteristic
54C4×C22⋊Dic11C2211yescharacteristic
55#10622607C2211yescharacteristic
56#10622607C2211yescharacteristic
57#10622605C2211yescharacteristic
58#10622605C2211yescharacteristic
59#10622603C2211yescharacteristic
60#10622603C2211yescharacteristic
61#10622602C2211yescharacteristic
62#10622599C2211yescharacteristic
63#10622597C2211yescharacteristic
64#10622597C2211yescharacteristic
65#10622597C2211yescharacteristic
66#10622595C2211yescharacteristic
67#10622595C2211yescharacteristic
68#10622595C2211yescharacteristic
69#10622594C2211yescharacteristic
70#10622594C2211yescharacteristic
71#10622593C2211yescharacteristic
72#10622593C2211yescharacteristic
73#10622593C2211yescharacteristic
74#10622591C2211yescharacteristic
75#10622591C2211yescharacteristic
76#10622591C2211yescharacteristic
77#10622591C2211yescharacteristic
78#10622591C2211yescharacteristic
79#10622586C2211yescharacteristic
80#10622586C2211yescharacteristic
81#10622585C2211yescharacteristic
82#10622585C2211yescharacteristic
83#10622572C2211yescharacteristic
84#10622572C2211yescharacteristic
85#10622571C2211yescharacteristic
86#10622571C2211yescharacteristic
87#10622570C2211yescharacteristic
88#10622569C2211yescharacteristic
89#10622565C2211yescharacteristic
90#10622565C2211yescharacteristic
91#10622563C2211yescharacteristic
92#10622563C2211yescharacteristic
93#10622562C2211yescharacteristic
94#10622562C2211yescharacteristic
95#10622561C2211yescharacteristic
96#10622561C2211yescharacteristic
97#10622559C2211yescharacteristic
98#10622559C2211yescharacteristic
99#10622558C2211yescharacteristic
100#10622557C2211yescharacteristic
101#10622556C2211yescharacteristic
102#10622556C2211yescharacteristic
103#10622556C2211yescharacteristic
104#10622556C2211yescharacteristic
105#10622555C2211yescharacteristic
106#10622555C2211yescharacteristic
107#10622553C2211yescharacteristic
108#10622553C2211yescharacteristic
109#10622553C2211yescharacteristic
110#10622553C2211yescharacteristic
111#10622553C2211yescharacteristic
112C4×(C2×D11)⋊C4C2211yescharacteristic
113#10622550C2211yescharacteristic
114#10622549C2211yescharacteristic
115#10622546C2211yescharacteristic
116#10622546C2211yescharacteristic
117#10622546C2211yescharacteristic
118#10622546C2211yescharacteristic
119#10622546C2211yescharacteristic
120#10622546C2211yescharacteristic
121#10622546C2211yescharacteristic
122#10622546C2211yescharacteristic
123#10622545C2211yescharacteristic
124#10622545C2211yescharacteristic
125C4×Dic11⋊C4C2211yescharacteristic
126C4×Dic11⋊C4C2211yescharacteristic
127C4×Dic11⋊C4C2211yescharacteristic
128#10622541C2211yescharacteristic
129#10622541C2211yescharacteristic
130#10622541C2211yescharacteristic
131#10622288C2211yescharacteristic
132#10622288C2211yescharacteristic
133#10622288C2211yescharacteristic
134#10622288C2211yescharacteristic
135#10622287C2211yescharacteristic
136#10622283C2211yescharacteristic
137#10622283C2211yescharacteristic
138#10622283C2211yescharacteristic
139#10622283C2211yescharacteristic
140#10622283C2211yescharacteristic
141#10622281C2211yescharacteristic
142#10622281C2211yescharacteristic
143#10622280C2211yescharacteristic
144#10622277C2211yescharacteristic
145C11⋊#401C2211yescharacteristic
146C11⋊#401C2211yescharacteristic
147#10622274C2211yescharacteristic
148#10622274C2211yescharacteristic
149#10622273C2211yescharacteristic
150#10622273C2211yescharacteristic
151#10622273C2211yescharacteristic
152#10622272C2211yescharacteristic
153#10622272C2211yescharacteristic
154#10622272C2211yescharacteristic
155#10622271C2211yescharacteristic
156#10622271C2211yescharacteristic
157#10622271C2211yescharacteristic
158#10622271C2211yescharacteristic
159#10622270C2211yescharacteristic
160#10622270C2211yescharacteristic
161#10622270C2211yescharacteristic
162#10622270C2211yescharacteristic
163#10622270C2211yescharacteristic
164#10622268C2211yescharacteristic
165#10622268C2211yescharacteristic
166#10622268C2211yescharacteristic
167#10622268C2211yescharacteristic
168#10622267C2211yescharacteristic
169#10622267C2211yescharacteristic
170#10622266C2211yescharacteristic
171#10622266C2211yescharacteristic
172#10622266C2211yescharacteristic
173#10622266C2211yescharacteristic
174#10622266C2211yescharacteristic
175#10622265C2211yescharacteristic
176#10622265C2211yescharacteristic
177#10622264C2211yescharacteristic
178#10622264C2211yescharacteristic
179#10622263C2211yescharacteristic
180#10622263C2211yescharacteristic
181#10622263C2211yescharacteristic
182#10622263C2211yescharacteristic
183#10622260C2211yescharacteristic
184#10622260C2211yescharacteristic
185#10622260C2211yescharacteristic
186#10622260C2211yescharacteristic
187C22×Q8×C11C2311yescharacteristic
188C23×C4×C11C2311yescharacteristic
189C22×C22⋊D11C2311yescharacteristic
190C23×Dic11C2311yescharacteristic
191C23×Dic11C2311yescharacteristic
192C22×C4×D11C2311yescharacteristic
193C11×C22⋊Q8—24no—
194C2×C11×C4⋊C4C2311yescharacteristic
195C2×C11×C4⋊C4C2311yescharacteristic
196C2×C11×C4⋊C4C2311yescharacteristic
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×C42×C11C2311yescharacteristic
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C22⋊Dic11C2311yescharacteristic
214C2×C22⋊Dic11C2311yescharacteristic
215C2×C22⋊Dic11C2311yescharacteristic
216C2×C22⋊Dic11C2311yescharacteristic
217C2×C22⋊Dic11C2311yescharacteristic
218#66982—24no—
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×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×C4⋊Dic11C2311yescharacteristic
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×C4×Dic11—24no—
268C2×C4×Dic11C2311yescharacteristic
269C2×C4×Dic11C2311yescharacteristic
270C2×C4×Dic11C2311yescharacteristic
271C2×C4×Dic11C2311yescharacteristic
272C2×C4×Dic11C2311yescharacteristic
273C2×C4×Dic11C2311yescharacteristic
274C2×C4×Dic11C2311yescharacteristic
275C2×C4×Dic11C2311yescharacteristic
276C2×C4×Dic11C2311yescharacteristic
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
345#36981—111nomaximal, Sylow
346C24×C11C2411yescharacteristic
347C23×D11C2411yescharacteristic
348C2×Q8×C11—22no—
349C2×Q8×C11—41no—
350C2×Q8×C11—41no—
351C22×C4×C11—41no—
352C22×C4×C11—41no—
353C22×C4×C11#4114yes—
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
368C2×C22⋊D11—22no—
369C2×C22⋊D11—41no—
370C2×C22⋊D11—41no—
371C22×Dic11—22no—
372C22×Dic11—22no—
373C22×Dic11—22no—
374C22×Dic11—41no—
375C22×Dic11—41no—
376C22×Dic11—41no—
377C22×Dic11C2411yescharacteristic
378C22×Dic11C2411yescharacteristic
379C22×Dic11C2411yescharacteristic
380C22×Dic11C2411yescharacteristic
381C22×Dic11C2411yescharacteristic
382C22×Dic11C2411yescharacteristic
383C22×Dic11C2411yescharacteristic
384C22×Dic11C2411yescharacteristic
385C22×Dic11C2411yescharacteristic
386C22×Dic11C2411yescharacteristic
387C22×Dic11C2411yescharacteristic
388C22×Dic11C2411yescharacteristic
389C22×Dic11C2411yescharacteristic
390C22×Dic11C2411yescharacteristic
391C22×Dic11C2411yescharacteristic
392C2×C4×D11—41no—
393C2×C4×D11—41no—
394C2×C4×D11—41no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—41no—
399C11×C4⋊C4—41no—
400C11×C4⋊C4—41no—
401C11×C4⋊C4—41no—
402C11×C22⋊C4—22no—
403C11×C22⋊C4—22no—
404C11×C22⋊C4—41no—
405C11×C22⋊C4—41no—
406C11×C22⋊C4—41no—
407C11×C22⋊C4—41no—
408C42×C11—41no—
409C42×C11—41no—
410C42×C11—41no—
411C42×C11—41no—
412C42×C11—41no—
413C42×C11—41no—
414C22⋊Dic11—22no—
415C22⋊Dic11—41no—
416C22⋊Dic11—41no—
417C22⋊Dic11—41no—
418C22⋊Dic11—41no—
419(C2×D11)⋊C4—22no—
420(C2×D11)⋊C4—22no—
421(C2×D11)⋊C4—22no—
422(C2×D11)⋊C4—41no—
423(C2×D11)⋊C4—41no—
424(C2×D11)⋊C4—41no—
425(C2×D11)⋊C4—41no—
426(C2×D11)⋊C4—41no—
427(C2×D11)⋊C4—41no—
428(C2×D11)⋊C4—41no—
429(C2×D11)⋊C4—41no—
430(C2×D11)⋊C4—41no—
431(C2×D11)⋊C4—41no—
432C4⋊Dic11—22no—
433C4⋊Dic11—41no—
434C4⋊Dic11—41no—
435C4⋊Dic11—41no—
436C4⋊Dic11—41no—
437C4⋊Dic11—41no—
438C4⋊Dic11—41no—
439C4⋊Dic11—41no—
440C4⋊Dic11—41no—
441C4⋊Dic11—41no—
442Dic11⋊C4—22no—
443Dic11⋊C4—22no—
444Dic11⋊C4—22no—
445Dic11⋊C4—22no—
446Dic11⋊C4—41no—
447Dic11⋊C4—41no—
448Dic11⋊C4—41no—
449Dic11⋊C4—41no—
450Dic11⋊C4—41no—
451Dic11⋊C4—41no—
452Dic11⋊C4—41no—
453Dic11⋊C4—41no—
454Dic11⋊C4—41no—
455Dic11⋊C4—41no—
456Dic11⋊C4—41no—
457Dic11⋊C4—41no—
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—
467C4×Dic11—22no—
468C4×Dic11—22no—
469C4×Dic11—22no—
470C4×Dic11—22no—
471C4×Dic11—41no—
472C4×Dic11—41no—
473C4×Dic11—41no—
474C4×Dic11—41no—
475C4×Dic11—41no—
476#2855—111no—
477#2853—111no—
478#2777—111no—
479#2771—111no—
480#2768—111no—
481#2767—111no—
482#2766—111no—
483#2765—111no—
484#2764—111no—
485#2762—111no—
486#2761—111no—
487#2755—111no—
488#2754—111no—
489#2746—111no—
490#2744—111no—
491#2743—111no—
492#2740—111no—
493#2738—111no—
494#2667—111no—
495#2663—111no—
496#2594—111no—
497#2590—111no—
498#2590—111no—
499#2575—111no—
500#2533—111no—
501#2530—111no—
502#2529—111no—
503#2528—111no—
504#2335—111no—
505#2332D1111yescharacteristic, complemented
506#2283—111no—
507C23×C11—21no—
508C23×C11—21no—
509C23×C11—21no—
510C23×C11—21no—
511C23×C11—21no—
512C23×C11—21no—
513C23×C11C2×#4112yes—
514C23×C11C2511yescharacteristic
515C22×D11—21no—
516C22×D11—21no—
517C22×D11—21no—
518C22×D11—21no—
519C22×D11—21no—
520C22×D11—21no—
521C22×D11—21no—
522Q8×C11—82no—
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×C11—21no—
563C2×C4×C11—44no—
564C2×C4×C11C2×#4112yes—
565C2×C4×C11C2×#4112yes—
566C22⋊D11—82no—
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×Dic11—21no—
608C2×Dic11—21no—
609C2×Dic11—21no—
610C2×Dic11—21no—
611C2×Dic11—44no—
612C2×Dic11—44no—
613C2×Dic112−1+412yes—
614C4×D11—82no—
615C2×#123—111no—
616C2×C22⋊Q8C2×D1111yescharacteristic
617C22×C42—111no—
618#401—111no—
619#401—111no—
620#400—111no—
621#400—111no—
622#400—111no—
623#400—111no—
624#400—111no—
625#400—111no—
626#400—111no—
627#400—111no—
628#400—111no—
629#400—111no—
630#400—111no—
631#400—111no—
632#400—111no—
633#400—111no—
634#399—111no—
635#399—111no—
636#399—111no—
637#399—111no—
638#398—111no—
639#398—111no—
640#398—111no—
641#398—111no—
642#398—111no—
643#398—111no—
644#398—111no—
645#398—111no—
646#398—111no—
647#398—111no—
648#398—111no—
649#398—111no—
650#398—111no—
651#397—111no—
652#397—111no—
653#397—111no—
654#397—111no—
655#397—111no—
656#397—111no—
657#397—111no—
658#396—111no—
659#396—111no—
660#396—111no—
661#396—111no—
662#395—111no—
663#394—111no—
664#394—111no—
665#393—111no—
666#391—111no—
667#391—111no—
668#391C2×D1111yescharacteristic
669#391C2×D1111yescharacteristic
670#390—111no—
671#389—111no—
672#389—111no—
673#389—111no—
674#389—111no—
675#389—111no—
676#389—111no—
677#389—111no—
678#389—111no—
679#389—111no—
680#389—111no—
681#389—111no—
682#388—111no—
683#388—111no—
684#388—111no—
685#388—111no—
686#388—111no—
687#388—111no—
688#388—111no—
689#388—111no—
690#388—111no—
691#388—111no—
692#388—111no—
693#388—111no—
694#388—111no—
695#388—111no—
696#388C2×D1111yescharacteristic
697#388C2×D1111yescharacteristic
698#388C2×D1111yescharacteristic
699#388C2×D1111yescharacteristic
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#387C2×D1111yescharacteristic
729#387C2×D1111yescharacteristic
730#387C2×D1111yescharacteristic
731#387C2×D1111yescharacteristic
732#386—111no—
733#386—111no—
734#386—111no—
735#385—111no—
736#385—111no—
737#385—111no—
738#385—111no—
739#385—111no—
740#385—111no—
741#385—111no—
742#383—111no—
743#383—111no—
744#383—111no—
745#382—111no—
746#382—111no—
747#382—111no—
748#382—111no—
749#382—111no—
750#381—111no—
751#381—111no—
752#381—111no—
753#381—111no—
754#381—111no—
755#381C2×D1111yescharacteristic
756#380—111no—
757#380—111no—
758#380—111no—
759#380—111no—
760C4×C4⋊C4—111no—
761C4×C4⋊C4—111no—
762C4×C4⋊C4—111no—
763C4×C4⋊C4C2×D1111yescharacteristic
764C4×C4⋊C4C2×D1111yescharacteristic
765C4×C22⋊C4—111no—
766C4×C22⋊C4—111no—
767C4×C22⋊C4C2×D1111yescharacteristic
768#376—111no—
769#376—111no—
770C22×C11—22no—
771C22×C11—22no—
772C22×C11—22no—
773C22×C11—41no—
774C22×C11—41no—
775C22×C11—41no—
776C22×C11—41no—
777C22×C11C22×#4111yescharacteristic
778C22×C11C2×2−1+411yescharacteristic
779C22×C11#58511yescharacteristic
780C22×C11#58511yescharacteristic
781C22×C11#58511yescharacteristic
782C22×C11#58511yescharacteristic
783C22×C11#58511yescharacteristic
784C2×D11—41no—
785C2×D11—41no—
786C2×D11—41no—
787C2×D11—41no—
788C2×D11—41no—
789C2×D11—41no—
790C2×D11—41no—
791C4×C11—22no—
792C4×C11—22no—
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—
802C4×C11—41no—
803C4×C11—41no—
804C4×C11—41no—
805Dic11—22no—
806Dic11—41no—
807Dic11—41no—
808Dic11—41no—
809Dic11—41no—
810Dic11—41no—
811Dic11—41no—
812Dic11—41no—
813Dic11—41no—
814Dic11—41no—
815Dic11—41no—
816Dic11—41no—
817Dic11—41no—
818Dic11—41no—
819Dic11—41no—
820C22×Q8C22×D1111yescharacteristic
821C22×D4—111no—
822C23×C4—111no—
823C23×C4—111no—
824C23×C4—111no—
825C23×C4C22×D1111yescharacteristic
826#123—224no—
827C22⋊Q8—24no—
828C2×C4⋊C4—111no—
829C2×C4⋊C4—111no—
830C2×C4⋊C4—111no—
831C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
864C2×C4⋊C4C22×D1111yescharacteristic
865C2×C4⋊C4C22×D1111yescharacteristic
866C2×C4⋊C4C22×D1111yescharacteristic
867C2×C4⋊C4C22×D1111yescharacteristic
868C2×C4⋊C4C22×D1111yescharacteristic
869C2×C4⋊C4C22×D1111yescharacteristic
870C2×C22⋊C4—111no—
871C2×C22⋊C4—111no—
872C2×C22⋊C4—111no—
873C2×C22⋊C4—111no—
874C2×C22⋊C4—111no—
875C2×C22⋊C4—111no—
876C2×C22⋊C4—111no—
877C2×C22⋊C4—111no—
878C2×C22⋊C4—111no—
879C2×C22⋊C4—111no—
880C2×C22⋊C4—111no—
881C2×C22⋊C4—111no—
882C2×C22⋊C4—111no—
883C2×C22⋊C4—111no—
884C2×C22⋊C4—111no—
885C2×C22⋊C4—111no—
886C2×C22⋊C4—111no—
887C2×C22⋊C4—111no—
888C2×C22⋊C4C22×D1111yescharacteristic
889C2×C22⋊C4C22×D1111yescharacteristic
890C2×C22⋊C4C22×D1111yescharacteristic
891C2×C22⋊C4C22×D1111yescharacteristic
892C2×C22⋊C4C22×D1111yescharacteristic
893C2×C22⋊C4C22×D1111yescharacteristic
894C2×C42—111no—
895C2×C42—111no—
896C2×C42—111no—
897C2×C42—111no—
898C2×C42—111no—
899C2×C42—111no—
900C2×C42—111no—
901C2×C42—111no—
902C2×C42—111no—
903C2×C42—224no—
904C2×C42C22×D1111yescharacteristic
905C2×C42C22×D1111yescharacteristic
906C2×C42C22×D1111yescharacteristic
907C2×C42C22×D1111yescharacteristic
908C2×C42C22×D1111yescharacteristic
909C2×C42C22×D1111yescharacteristic
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#95—111no—
962#95—111no—
963#95—111no—
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
978C2×C11—42no—
979C2×C11#345511yescharacteristic
980C2×C11#349111yescharacteristic
981C2×C11#349511yescharacteristic
982C2×C11#355711yescharacteristic
983C2×C11#356511yescharacteristic
984C2×C11#356611yescharacteristic
985C2×C11#356711yescharacteristic
986D11—81no—
987C24—111no—
988C24C23×D1111yescharacteristic
989C2×Q8—22no—
990C2×Q8—41no—
991C2×Q8—41no—
992C2×D4—222no—
993C2×D4—441no—
994C2×D4—441no—
995C22×C4—41no—
996C22×C4—41no—
997C22×C4—111no—
998C22×C4—111no—
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—441no—
1016C22×C4—441no—
1017C22×C4—441no—
1018C22×C4—441no—
1019C22×C4—441no—
1020C22×C4—441no—
1021C22×C4#433914yes—
1022C22×C4C23×D1111yescharacteristic
1023C22×C4C23×D1111yescharacteristic
1024C22×C4C23×D1111yescharacteristic
1025C22×C4C23×D1111yescharacteristic
1026C22×C4C23×D1111yescharacteristic
1027C22×C4C23×D1111yescharacteristic
1028C22×C4C23×D1111yescharacteristic
1029C22×C4C23×D1111yescharacteristic
1030C22×C4C23×D1111yescharacteristic
1031C22×C4C23×D1111yescharacteristic
1032C22×C4C23×D1111yescharacteristic
1033C22×C4C23×D1111yescharacteristic
1034C22×C4C23×D1111yescharacteristic
1035C22×C4C23×D1111yescharacteristic
1036C4⋊C4—22no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—222no—
1044C4⋊C4—222no—
1045C4⋊C4—222no—
1046C4⋊C4—222no—
1047C4⋊C4—222no—
1048C4⋊C4—441no—
1049C4⋊C4—441no—
1050C4⋊C4—441no—
1051C4⋊C4—441no—
1052C4⋊C4—441no—
1053C4⋊C4—441no—
1054C4⋊C4—441no—
1055C4⋊C4—441no—
1056C4⋊C4—441no—
1057C4⋊C4—441no—
1058C4⋊C4—441no—
1059C4⋊C4—441no—
1060C4⋊C4—441no—
1061C4⋊C4—441no—
1062C4⋊C4—441no—
1063C4⋊C4—441no—
1064C4⋊C4—441no—
1065C4⋊C4—441no—
1066C4⋊C4—441no—
1067C4⋊C4—441no—
1068C4⋊C4—441no—
1069C4⋊C4—441no—
1070C4⋊C4—441no—
1071C4⋊C4—441no—
1072C4⋊C4—441no—
1073C4⋊C4—441no—
1074C4⋊C4—441no—
1075C4⋊C4—441no—
1076C4⋊C4—441no—
1077C4⋊C4—441no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—222no—
1085C22⋊C4—222no—
1086C22⋊C4—222no—
1087C22⋊C4—222no—
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⋊C4—441no—
1099C22⋊C4—441no—
1100C22⋊C4—441no—
1101C22⋊C4—441no—
1102C42—41no—
1103C42—41no—
1104C42—41no—
1105C42—41no—
1106C42—41no—
1107C42—41no—
1108C42—222no—
1109C42—222no—
1110C42—222no—
1111C42—222no—
1112C42—441no—
1113C42—441no—
1114C42—441no—
1115C42—441no—
1116C42—441no—
1117C11#3698111yescharacteristic, complemented, Sylow
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—221no—
1125C23—221no—
1126C23—221no—
1127C23—221no—
1128C23—221no—
1129C23—221no—
1130C23—221no—
1131C23C2×#433912yes—
1132C23C24×D1111yescharacteristic
1133Q8—82no—
1134D4—882no—
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—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—44no—
1176C2×C4—112no—
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—221no—
1217C2×C4—221no—
1218C2×C4—221no—
1219C2×C4—221no—
1220C2×C4—221no—
1221C2×C4—444no—
1222C2×C4—444no—
1223C2×C4—882no—
1224C2×C4C2×#433912yes—
1225C2×C4C2×#433912yes—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—441no—
1234C22—441no—
1235C22—441no—
1236C22—441no—
1237C22—441no—
1238C22—441no—
1239C22—441no—
1240C22C22×#433911yescharacteristic
1241C22#1062345311yescharacteristic
1242C22#1062345311yescharacteristic
1243C22#1062345511yescharacteristic
1244C22#1062345511yescharacteristic
1245C22D11×2−1+411yescharacteristic
1246C22#1062345711yescharacteristic
1247C4—22no—
1248C4—22no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—222no—
1262C4—441no—
1263C4—441no—
1264C4—441no—
1265C4—441no—
1266C4—441no—
1267C4—441no—
1268C4—441no—
1269C4—441no—
1270C4—441no—
1271C4—441no—
1272C4—441no—
1273C4—441no—
1274C4—441no—
1275C4—441no—
1276C2—42no—
1277C2—881no—
1278C2#1308200111yescharacteristic
1279C2#1308230911yescharacteristic
1280C2#1308235811yescharacteristic
1281C2#1308311411yescharacteristic
1282C2#1308326011yescharacteristic
1283C2#1308329611yescharacteristic
1284C2#1308330211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2332C2
prime radicalC22×C22⋊D11C23
hypercenter#2332D11
hypocenterC11#36981
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2332

Complements

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

NH ≅ G/Ntype
1. #13076950C2semidirect
3. #13076213C2semidirect
4. #13076129C2semidirect
5. #13076090C2semidirect
6. #13076075C2semidirect
7. #13076069C2semidirect
8. #13076045C2semidirect
9. #13076036C2semidirect
10. #13076018C2semidirect
12. #13075917C2semidirect
13. #13075902C2semidirect
15. #13075764C2semidirect
18. #13075680C2semidirect
19. #13074812C2semidirect
21. #13074122C2semidirect
22. #13074084C2semidirect
23. #13074082C2semidirect
24. #13073907C2semidirect
25. #13073493C2semidirect
26. #13073450C2semidirect
27. #13073433C2semidirect
28. #13073420C2semidirect
30. #13071010C2semidirect
31. C11×#2332C2semidirect
505. #2332D11semidirect
1117. C11#36981semidirect

Maximal subgroups

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

subgroupindex
#130769502
#130769392
#130762132
#130761292
#130760902
#130760752
#130760692
#130760452
#130760362
#130760182
#130760012
#130759172
#130759022
#130757942
#130757642
#130757562
#130757102
#130756802
#130748122
#130747672
#130741222
#130740842
#130740822
#130739072
#130734932
#130734502
#130734332
#130734202
#130714062
#130710102
C11×#23322
#3698111