Finite Group Databasebeta

← C2×C11×#2590 #14612032

Subgroups — C2×C11×#2590 #14612032

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2590C2116yesmaximal, direct product factor
2C2×C11×#400C211yesmaximal, characteristic
3C2×C11×#398C211yesmaximal, characteristic
4C2×C11×#398C211yesmaximal, characteristic
5C2×C11×#398C211yesmaximal, characteristic
6C2×C11×#389C211yesmaximal, characteristic
7C2×C11×#389C211yesmaximal, characteristic
8C2×C11×#389C211yesmaximal, characteristic
9C2×C11×#387C211yesmaximal, characteristic
10C2×C11×#387C211yesmaximal, characteristic
11C2×C11×#387C211yesmaximal, characteristic
12C2×C11×#387C211yesmaximal, characteristic
13C2×C11×#387C211yesmaximal, characteristic
14C2×C11×#387C211yesmaximal, characteristic
15C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
16C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C42×C11C2211yescharacteristic
32C22×C42×C11C2211yescharacteristic
33C22×C42×C11C2211yescharacteristic
34C22×C42×C11C2211yescharacteristic
35C22×C42×C11C2211yescharacteristic
36C11×#400C2218yes—
37C11×#398C2218yes—
38C11×#398C2218yes—
39C11×#398C2218yes—
40C11×#389C2218yes—
41C11×#389C2218yes—
42C11×#389C2218yes—
43C11×#387C2218yes—
44C11×#387C2218yes—
45C11×#387C2218yes—
46C11×#387C2218yes—
47C11×#387C2218yes—
48C11×#387C2218yes—
49C4×C11×C4⋊C4C2218yes—
50C4×C11×C4⋊C4C2218yes—
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59C2×C11×#95C2211yescharacteristic
60C2×C11×#95C2211yescharacteristic
61C2×C11×#95C2211yescharacteristic
62C2×C11×#95C2211yescharacteristic
63C2×C11×#95C2211yescharacteristic
64C2×C11×#95C2211yescharacteristic
65C2×C11×#95C2211yescharacteristic
66C2×C11×#95C2211yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4—24no—
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4—24no—
92C2×C11×C4⋊C4—42no—
93C2×C11×C4⋊C4—42no—
94C2×C11×C4⋊C4—42no—
95C2×C11×C4⋊C4Q818yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2314yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C42×C11—24no—
111C2×C42×C11—24no—
112C2×C42×C11—42no—
113C2×C42×C11—42no—
114C2×C42×C11—42no—
115C2×C42×C11C2314yes—
116C2×C42×C11C2314yes—
117C2×C42×C11C2314yes—
118C2×C42×C11C2314yes—
119C2×C42×C11C2314yes—
120C11×#95C2314yes—
121C11×#95C2314yes—
122C11×#95C2314yes—
123C11×#95C2314yes—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11×#95C2314yes—
127C11×#95C2314yes—
128C11×#95C2314yes—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11×#95C2314yes—
135C11×#95C2314yes—
136C2×#2590C1111yesmaximal, characteristic, direct product factor, Sylow
137C24×C11C2411yescharacteristic
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11C2×Q814yes—
177C22×C4×C11C2×Q814yes—
178C22×C4×C11C2×Q814yes—
179C22×C4×C11#4114yes—
180C22×C4×C11#4114yes—
181C22×C4×C11#4114yes—
182C22×C4×C11#4114yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C11×C4⋊C4—28no—
199C11×C4⋊C4—28no—
200C11×C4⋊C4—28no—
201C11×C4⋊C4—28no—
202C11×C4⋊C4—28no—
203C11×C4⋊C4—28no—
204C11×C4⋊C4—28no—
205C11×C4⋊C4—28no—
206C11×C4⋊C4—28no—
207C11×C4⋊C4—28no—
208C11×C4⋊C4—44no—
209C11×C4⋊C4—44no—
210C11×C4⋊C4—44no—
211C11×C4⋊C4C2×Q8116yes—
212C42×C11—28no—
213C42×C11—28no—
214C42×C11—44no—
215C42×C11—44no—
216C42×C11—44no—
217#2590C2×C11116yesdirect product factor
218C2×#400C2×C1111yescharacteristic
219C2×#398C2×C1111yescharacteristic
220C2×#398C2×C1111yescharacteristic
221C2×#398C2×C1111yescharacteristic
222C2×#389C2×C1111yescharacteristic
223C2×#389C2×C1111yescharacteristic
224C2×#389C2×C1111yescharacteristic
225C2×#387C2×C1111yescharacteristic
226C2×#387C2×C1111yescharacteristic
227C2×#387C2×C1111yescharacteristic
228C2×#387C2×C1111yescharacteristic
229C2×#387C2×C1111yescharacteristic
230C2×#387C2×C1111yescharacteristic
231C2×C4×C4⋊C4C2×C1111yescharacteristic
232C2×C4×C4⋊C4C2×C1111yescharacteristic
233C23×C11C22×Q812yes—
234C23×C11C2×#4112yes—
235C23×C11C2×#4112yes—
236C23×C11C2×#4112yes—
237C23×C11C2×#4112yes—
238C23×C11H(5,𝔽2)12yes—
239C23×C112−1+412yes—
240C23×C11C2511yescharacteristic
241C2×C4×C11—28no—
242C2×C4×C11—28no—
243C2×C4×C11—28no—
244C2×C4×C11—28no—
245C2×C4×C11—28no—
246C2×C4×C11—28no—
247C2×C4×C11—28no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—44no—
287C2×C4×C11—44no—
288C2×C4×C11—44no—
289C2×C4×C11—44no—
290C2×C4×C11—44no—
291C2×C4×C11—44no—
292C2×C4×C11—44no—
293C2×C4×C11—44no—
294C2×C4×C11C22×Q814yes—
295C2×C4×C11C22×Q814yes—
296C2×C4×C11C22×Q814yes—
297C2×C4×C11C2×#4114yes—
298C2×C4×C11C2×#4114yes—
299C2×C4×C11C2×#4114yes—
300C2×C4×C11C2×#4114yes—
301C22×C4⋊C4C22×C1111yescharacteristic
302C22×C4⋊C4C22×C1111yescharacteristic
303C22×C4⋊C4C22×C1111yescharacteristic
304C22×C4⋊C4C22×C1111yescharacteristic
305C22×C4⋊C4C22×C1111yescharacteristic
306C22×C4⋊C4C22×C1111yescharacteristic
307C22×C4⋊C4C22×C1111yescharacteristic
308C22×C4⋊C4C22×C1111yescharacteristic
309C22×C4⋊C4C22×C1111yescharacteristic
310C22×C4⋊C4C22×C1111yescharacteristic
311C22×C4⋊C4C22×C1111yescharacteristic
312C22×C4⋊C4C22×C1111yescharacteristic
313C22×C4⋊C4C22×C1111yescharacteristic
314C22×C4⋊C4C22×C1111yescharacteristic
315C22×C42C22×C1111yescharacteristic
316C22×C42C22×C1111yescharacteristic
317C22×C42C22×C1111yescharacteristic
318C22×C42C22×C1111yescharacteristic
319C22×C42C22×C1111yescharacteristic
320#400C22×C1118yes—
321#398C22×C1118yes—
322#398C22×C1118yes—
323#398C22×C1118yes—
324#389C22×C1118yes—
325#389C22×C1118yes—
326#389C22×C1118yes—
327#387C22×C1118yes—
328#387C22×C1118yes—
329#387C22×C1118yes—
330#387C22×C1118yes—
331#387C22×C1118yes—
332#387C22×C1118yes—
333C4×C4⋊C4C22×C1118yes—
334C4×C4⋊C4C22×C1118yes—
335C2×#95C22×C1111yescharacteristic
336C2×#95C22×C1111yescharacteristic
337C2×#95C22×C1111yescharacteristic
338C2×#95C22×C1111yescharacteristic
339C2×#95C22×C1111yescharacteristic
340C2×#95C22×C1111yescharacteristic
341C2×#95C22×C1111yescharacteristic
342C2×#95C22×C1111yescharacteristic
343C2×#95C22×C1111yescharacteristic
344C2×#95C22×C1111yescharacteristic
345C2×#95C22×C1111yescharacteristic
346C2×#95C22×C1111yescharacteristic
347C2×#95C22×C1111yescharacteristic
348C2×#95C22×C1111yescharacteristic
349C2×#95C22×C1111yescharacteristic
350C2×#95C22×C1111yescharacteristic
351C22×C11#52914yes—
352C22×C11#53314yes—
353C22×C11#53914yes—
354C22×C11#55214yes—
355C22×C11#55314yes—
356C22×C11#55414yes—
357C22×C11#55714yes—
358C22×C11C23×Q811yescharacteristic
359C22×C11C22×#4111yescharacteristic
360C22×C11C22×#4111yescharacteristic
361C22×C11C22×#4111yescharacteristic
362C22×C11C22×#4111yescharacteristic
363C22×C11C2×H(5,𝔽2)11yescharacteristic
364C22×C11C2×2−1+411yescharacteristic
365C4×C11—24no—
366C4×C11—24no—
367C4×C11—24no—
368C4×C11—24no—
369C4×C11—24no—
370C4×C11—24no—
371C4×C11—24no—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—42no—
380C23×C4C23×C1111yescharacteristic
381C23×C4C23×C1111yescharacteristic
382C23×C4C23×C1111yescharacteristic
383C23×C4C23×C1111yescharacteristic
384C23×C4C23×C1111yescharacteristic
385C23×C4C23×C1111yescharacteristic
386C23×C4C23×C1111yescharacteristic
387C23×C4C23×C1111yescharacteristic
388C23×C4C23×C1111yescharacteristic
389C23×C4C23×C1111yescharacteristic
390C23×C4C23×C1111yescharacteristic
391C23×C4C23×C1111yescharacteristic
392C23×C4C23×C1111yescharacteristic
393C23×C4C23×C1111yescharacteristic
394C23×C4C23×C1111yescharacteristic
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4Q8×C1118yes—
409C2×C4⋊C4C23×C1114yes—
410C2×C4⋊C4C23×C1114yes—
411C2×C4⋊C4C23×C1114yes—
412C2×C4⋊C4C23×C1114yes—
413C2×C4⋊C4C23×C1114yes—
414C2×C4⋊C4C23×C1114yes—
415C2×C4⋊C4C23×C1114yes—
416C2×C4⋊C4C23×C1114yes—
417C2×C4⋊C4C23×C1114yes—
418C2×C4⋊C4C23×C1114yes—
419C2×C4⋊C4C23×C1114yes—
420C2×C4⋊C4C23×C1114yes—
421C2×C4⋊C4C23×C1114yes—
422C2×C4⋊C4C23×C1114yes—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42C23×C1114yes—
429C2×C42C23×C1114yes—
430C2×C42C23×C1114yes—
431C2×C42C23×C1114yes—
432C2×C42C23×C1114yes—
433#95C23×C1114yes—
434#95C23×C1114yes—
435#95C23×C1114yes—
436#95C23×C1114yes—
437#95C23×C1114yes—
438#95C23×C1114yes—
439#95C23×C1114yes—
440#95C23×C1114yes—
441#95C23×C1114yes—
442#95C23×C1114yes—
443#95C23×C1114yes—
444#95C23×C1114yes—
445#95C23×C1114yes—
446#95C23×C1114yes—
447#95C23×C1114yes—
448#95C23×C1114yes—
449C2×C11#259018yesdirect product factor
450C2×C11C2×#52911yescharacteristic
451C2×C11C2×#53311yescharacteristic
452C2×C11C2×#53911yescharacteristic
453C2×C11C2×#55211yescharacteristic
454C2×C11C2×#55311yescharacteristic
455C2×C11C2×#55411yescharacteristic
456C2×C11C2×#55711yescharacteristic
457C24C24×C1111yescharacteristic
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4C2×Q8×C1114yes—
497C22×C4C2×Q8×C1114yes—
498C22×C4C2×Q8×C1114yes—
499C22×C4C11×#4114yes—
500C22×C4C11×#4114yes—
501C22×C4C11×#4114yes—
502C22×C4C11×#4114yes—
503C22×C4C24×C1112yes—
504C22×C4C24×C1112yes—
505C22×C4C24×C1112yes—
506C22×C4C24×C1112yes—
507C22×C4C24×C1112yes—
508C22×C4C24×C1112yes—
509C22×C4C24×C1112yes—
510C22×C4C24×C1112yes—
511C22×C4C24×C1112yes—
512C22×C4C24×C1112yes—
513C22×C4C24×C1112yes—
514C22×C4C24×C1112yes—
515C22×C4C24×C1112yes—
516C22×C4C24×C1112yes—
517C22×C4C24×C1112yes—
518C4⋊C4—28no—
519C4⋊C4—28no—
520C4⋊C4—28no—
521C4⋊C4—28no—
522C4⋊C4—28no—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—44no—
529C4⋊C4—44no—
530C4⋊C4—44no—
531C4⋊C4C2×Q8×C11116yes—
532C42—28no—
533C42—28no—
534C42—44no—
535C42—44no—
536C42—44no—
537C11C2×#259011yescharacteristic, direct product factor, Sylow
538C23C22×Q8×C1112yes—
539C23C2×C11×#4112yes—
540C23C2×C11×#4112yes—
541C23C2×C11×#4112yes—
542C23C2×C11×#4112yes—
543C23C11×H(5,𝔽2)12yes—
544C23C11×2−1+412yes—
545C23C25×C1111yescharacteristic
546C2×C4—28no—
547C2×C4—28no—
548C2×C4—28no—
549C2×C4—28no—
550C2×C4—28no—
551C2×C4—28no—
552C2×C4—28no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4C22×Q8×C1114yes—
600C2×C4C22×Q8×C1114yes—
601C2×C4C22×Q8×C1114yes—
602C2×C4C2×C11×#4114yes—
603C2×C4C2×C11×#4114yes—
604C2×C4C2×C11×#4114yes—
605C2×C4C2×C11×#4114yes—
606C22C11×#52914yes—
607C22C11×#53314yes—
608C22C11×#53914yes—
609C22C11×#55214yes—
610C22C11×#55314yes—
611C22C11×#55414yes—
612C22C11×#55714yes—
613C22C23×Q8×C1111yescharacteristic
614C22C22×C11×#4111yescharacteristic
615C22C22×C11×#4111yescharacteristic
616C22C22×C11×#4111yescharacteristic
617C22C22×C11×#4111yescharacteristic
618C22C2×C11×H(5,𝔽2)11yescharacteristic
619C22C2×C11×2−1+411yescharacteristic
620C4—24no—
621C4—24no—
622C4—24no—
623C4—24no—
624C4—24no—
625C4—24no—
626C4—24no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4—42no—
633C4—42no—
634C4—42no—
635C2C11×#259018yesdirect product factor
636C2C2×C11×#52911yescharacteristic
637C2C2×C11×#53311yescharacteristic
638C2C2×C11×#53911yescharacteristic
639C2C2×C11×#55211yescharacteristic
640C2C2×C11×#55311yescharacteristic
641C2C2×C11×#55411yescharacteristic
642C2C2×C11×#55711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C11C24
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2590C2direct (N × H)
136. C2×#2590C11direct (N × H)
217. #2590C2×C11direct (N × H)
449. C2×C11#2590direct (N × H)
537. C11C2×#2590direct (N × H)
635. C2C11×#2590direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25902
C2×C11×#4002
C2×C11×#3982
C2×C11×#3892
C2×C11×#3872
C2×C4×C11×C4⋊C42
C2×#259011