Finite Group Databasebeta

← C2×C11×#2462 #14611879

Subgroups — C2×C11×#2462 #14611879

Order 2816.

2486 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic
2C22×C4×Q8×C11C211yesmaximal, characteristic
3C11×#2462C2116yesmaximal, direct product factor
4C2×C11×#398C211yesmaximal, characteristic
5C2×C11×#398C211yesmaximal, characteristic
6C2×C11×#395C211yesmaximal, characteristic
7C2×C11×#395C211yesmaximal, characteristic
8C2×C11×#389C211yesmaximal, characteristic
9C2×C11×#389C211yesmaximal, characteristic
10C2×C11×#387C211yesmaximal, characteristic
11C2×C11×#387C211yesmaximal, characteristic
12C2×C11×#387C211yesmaximal, characteristic
13C2×C11×#387C211yesmaximal, characteristic
14C2×C11×#387C211yesmaximal, characteristic
15C2×C11×#387C211yesmaximal, characteristic
16C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
17C23×Q8×C11C2211yescharacteristic
18C2×C11×#125—28no—
19C2×C11×#125C2218yes—
20C2×C4×Q8×C11—28no—
21C2×C4×Q8×C11C2218yes—
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×C11×C4⋊C4C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C22×C11×C4⋊C4C2211yescharacteristic
34C22×C11×C4⋊C4C2211yescharacteristic
35C22×C11×C4⋊C4C2211yescharacteristic
36C22×C11×C4⋊C4C2211yescharacteristic
37C22×C42×C11C2211yescharacteristic
38C22×C42×C11C2211yescharacteristic
39C22×C42×C11C2211yescharacteristic
40C22×C42×C11C2211yescharacteristic
41C22×C42×C11C2211yescharacteristic
42C11×#398C2218yes—
43C11×#398C2218yes—
44C11×#395C2218yes—
45C11×#395C2218yes—
46C11×#389C2218yes—
47C11×#389C2218yes—
48C11×#387C2218yes—
49C11×#387C2218yes—
50C11×#387C2218yes—
51C11×#387C2218yes—
52C11×#387C2218yes—
53C11×#387C2218yes—
54C4×C11×C4⋊C4C2218yes—
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
67C2×C11×#95C2211yescharacteristic
68C2×C11×#95C2211yescharacteristic
69C22×Q8×C11—24no—
70C22×Q8×C11—24no—
71C22×Q8×C11—24no—
72C22×Q8×C11C2314yes—
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
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C11×#125—232no—
89C4×Q8×C11—232no—
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4—24no—
92C2×C11×C4⋊C4—24no—
93C2×C11×C4⋊C4—24no—
94C2×C11×C4⋊C4—24no—
95C2×C11×C4⋊C4—24no—
96C2×C11×C4⋊C4—24no—
97C2×C11×C4⋊C4—24no—
98C2×C11×C4⋊C4—24no—
99C2×C11×C4⋊C4—24no—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4D418yes—
104C2×C11×C4⋊C4Q818yescomplemented
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C4⋊C4C2314yes—
119C2×C11×C4⋊C4C2314yes—
120C2×C42×C11—24no—
121C2×C42×C11—24no—
122C2×C42×C11—24no—
123C2×C42×C11—24no—
124C2×C42×C11—24no—
125C2×C42×C11C2314yes—
126C2×C42×C11C2314yes—
127C2×C42×C11C2314yes—
128C2×C42×C11C2314yes—
129C2×C42×C11C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11×#95C2314yes—
135C11×#95C2314yes—
136C11×#95C2314yes—
137C11×#95C2314yes—
138C11×#95C2314yes—
139C11×#95C2314yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C2×#2462C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11C2411yescharacteristic
146C2×Q8×C11—232no—
147C2×Q8×C11—28no—
148C2×Q8×C11—28no—
149C2×Q8×C11—28no—
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×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11C2×D414yes—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2×D414yes—
189C22×C4×C11C2×Q814yes—
190C22×C4×C11C2×Q814yes—
191C22×C4×C11C2×Q814yes—
192C22×C4×C11#4114yes—
193C22×C4×C11#4114yes—
194C22×C4×C11#4114yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C11×C4⋊C4—28no—
211C11×C4⋊C4—28no—
212C11×C4⋊C4—28no—
213C11×C4⋊C4—28no—
214C11×C4⋊C4—28no—
215C11×C4⋊C4—28no—
216C11×C4⋊C4—28no—
217C11×C4⋊C4—28no—
218C11×C4⋊C4—28no—
219C11×C4⋊C4—28no—
220C11×C4⋊C4—28no—
221C11×C4⋊C4—28no—
222C11×C4⋊C4—28no—
223C11×C4⋊C4C2×D4116yes—
224C11×C4⋊C4C2×Q8116yescomplemented
225C42×C11—28no—
226C42×C11—28no—
227C42×C11—28no—
228C42×C11—28no—
229C42×C11—28no—
230C22×#125C2×C1111yescharacteristic
231C22×C4×Q8C2×C1111yescharacteristic
232#2462C2×C11116yesdirect product factor
233C2×#398C2×C1111yescharacteristic
234C2×#398C2×C1111yescharacteristic
235C2×#395C2×C1111yescharacteristic
236C2×#395C2×C1111yescharacteristic
237C2×#389C2×C1111yescharacteristic
238C2×#389C2×C1111yescharacteristic
239C2×#387C2×C1111yescharacteristic
240C2×#387C2×C1111yescharacteristic
241C2×#387C2×C1111yescharacteristic
242C2×#387C2×C1111yescharacteristic
243C2×#387C2×C1111yescharacteristic
244C2×#387C2×C1111yescharacteristic
245C2×C4×C4⋊C4C2×C1111yescharacteristic
246C23×C11C22×D412yes—
247C23×C11C22×Q812yes—
248C23×C11C2×#4112yes—
249C23×C11C2×#4112yes—
250C23×C11C2×#4112yes—
251C23×C112−1+412yes—
252C23×C112−1+412yes—
253C23×C11C2511yescharacteristic
254Q8×C11—232no—
255C2×C4×C11—28no—
256C2×C4×C11—28no—
257C2×C4×C11—28no—
258C2×C4×C11—28no—
259C2×C4×C11—28no—
260C2×C4×C11—28no—
261C2×C4×C11—28no—
262C2×C4×C11—28no—
263C2×C4×C11—28no—
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—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—44no—
301C2×C4×C11—44no—
302C2×C4×C11—44no—
303C2×C4×C11—44no—
304C2×C4×C11—44no—
305C2×C4×C11—44no—
306C2×C4×C11C22×D414yes—
307C2×C4×C11C22×D414yes—
308C2×C4×C11C22×D414yes—
309C2×C4×C11C22×Q814yes—
310C2×C4×C11C22×Q814yes—
311C2×C4×C11C22×Q814yes—
312C2×C4×C11C2×#4114yes—
313C2×C4×C11C2×#4114yes—
314C2×C4×C11C2×#4114yes—
315C23×Q8C22×C1111yescharacteristic
316C2×#125—28no—
317C2×#125C22×C1118yes—
318C2×C4×Q8—28no—
319C2×C4×Q8C22×C1118yes—
320C22×C4⋊C4C22×C1111yescharacteristic
321C22×C4⋊C4C22×C1111yescharacteristic
322C22×C4⋊C4C22×C1111yescharacteristic
323C22×C4⋊C4C22×C1111yescharacteristic
324C22×C4⋊C4C22×C1111yescharacteristic
325C22×C4⋊C4C22×C1111yescharacteristic
326C22×C4⋊C4C22×C1111yescharacteristic
327C22×C4⋊C4C22×C1111yescharacteristic
328C22×C4⋊C4C22×C1111yescharacteristic
329C22×C4⋊C4C22×C1111yescharacteristic
330C22×C4⋊C4C22×C1111yescharacteristic
331C22×C4⋊C4C22×C1111yescharacteristic
332C22×C4⋊C4C22×C1111yescharacteristic
333C22×C4⋊C4C22×C1111yescharacteristic
334C22×C4⋊C4C22×C1111yescharacteristic
335C22×C42C22×C1111yescharacteristic
336C22×C42C22×C1111yescharacteristic
337C22×C42C22×C1111yescharacteristic
338C22×C42C22×C1111yescharacteristic
339C22×C42C22×C1111yescharacteristic
340#398C22×C1118yes—
341#398C22×C1118yes—
342#395C22×C1118yes—
343#395C22×C1118yes—
344#389C22×C1118yes—
345#389C22×C1118yes—
346#387C22×C1118yes—
347#387C22×C1118yes—
348#387C22×C1118yes—
349#387C22×C1118yes—
350#387C22×C1118yes—
351#387C22×C1118yes—
352C4×C4⋊C4C22×C1118yes—
353C2×#95C22×C1111yescharacteristic
354C2×#95C22×C1111yescharacteristic
355C2×#95C22×C1111yescharacteristic
356C2×#95C22×C1111yescharacteristic
357C2×#95C22×C1111yescharacteristic
358C2×#95C22×C1111yescharacteristic
359C2×#95C22×C1111yescharacteristic
360C2×#95C22×C1111yescharacteristic
361C2×#95C22×C1111yescharacteristic
362C2×#95C22×C1111yescharacteristic
363C2×#95C22×C1111yescharacteristic
364C2×#95C22×C1111yescharacteristic
365C2×#95C22×C1111yescharacteristic
366C2×#95C22×C1111yescharacteristic
367C22×C11#52514yes—
368C22×C11#53314yes—
369C22×C11#54114yes—
370C22×C11#54714yes—
371C22×C11D4×Q814yes—
372C22×C11#55214yes—
373C22×C11#55714yes—
374C22×C11C23×D411yescharacteristic
375C22×C11C23×Q811yescharacteristic
376C22×C11C22×#4111yescharacteristic
377C22×C11C22×#4111yescharacteristic
378C22×C11C22×#4111yescharacteristic
379C22×C11C2×2−1+411yescharacteristic
380C22×C11C2×2−1+411yescharacteristic
381C4×C11—24no—
382C4×C11—24no—
383C4×C11—24no—
384C4×C11—24no—
385C4×C11—24no—
386C4×C11—24no—
387C4×C11—24no—
388C4×C11—24no—
389C4×C11—24no—
390C4×C11—42no—
391C4×C11—42no—
392C4×C11—42no—
393C4×C11—42no—
394C4×C11—42no—
395C4×C11—42no—
396C22×Q8—24no—
397C22×Q8—24no—
398C22×Q8—24no—
399C22×Q8C23×C1114yes—
400C23×C4C23×C1111yescharacteristic
401C23×C4C23×C1111yescharacteristic
402C23×C4C23×C1111yescharacteristic
403C23×C4C23×C1111yescharacteristic
404C23×C4C23×C1111yescharacteristic
405C23×C4C23×C1111yescharacteristic
406C23×C4C23×C1111yescharacteristic
407C23×C4C23×C1111yescharacteristic
408C23×C4C23×C1111yescharacteristic
409C23×C4C23×C1111yescharacteristic
410C23×C4C23×C1111yescharacteristic
411C23×C4C23×C1111yescharacteristic
412C23×C4C23×C1111yescharacteristic
413C23×C4C23×C1111yescharacteristic
414C23×C4C23×C1111yescharacteristic
415#125—232no—
416C4×Q8—232no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4D4×C1118yes—
431C2×C4⋊C4Q8×C1118yescomplemented
432C2×C4⋊C4C23×C1114yes—
433C2×C4⋊C4C23×C1114yes—
434C2×C4⋊C4C23×C1114yes—
435C2×C4⋊C4C23×C1114yes—
436C2×C4⋊C4C23×C1114yes—
437C2×C4⋊C4C23×C1114yes—
438C2×C4⋊C4C23×C1114yes—
439C2×C4⋊C4C23×C1114yes—
440C2×C4⋊C4C23×C1114yes—
441C2×C4⋊C4C23×C1114yes—
442C2×C4⋊C4C23×C1114yes—
443C2×C4⋊C4C23×C1114yes—
444C2×C4⋊C4C23×C1114yes—
445C2×C4⋊C4C23×C1114yes—
446C2×C4⋊C4C23×C1114yes—
447C2×C42—24no—
448C2×C42—24no—
449C2×C42—24no—
450C2×C42—24no—
451C2×C42—24no—
452C2×C42C23×C1114yes—
453C2×C42C23×C1114yes—
454C2×C42C23×C1114yes—
455C2×C42C23×C1114yes—
456C2×C42C23×C1114yes—
457#95C23×C1114yes—
458#95C23×C1114yes—
459#95C23×C1114yes—
460#95C23×C1114yes—
461#95C23×C1114yes—
462#95C23×C1114yes—
463#95C23×C1114yes—
464#95C23×C1114yes—
465#95C23×C1114yes—
466#95C23×C1114yes—
467#95C23×C1114yes—
468#95C23×C1114yes—
469#95C23×C1114yes—
470#95C23×C1114yes—
471C2×C11#246218yesdirect product factor
472C2×C11C2×#52511yescharacteristic
473C2×C11C2×#53311yescharacteristic
474C2×C11C2×#54111yescharacteristic
475C2×C11C2×#54711yescharacteristic
476C2×C11C2×D4×Q811yescharacteristic
477C2×C11C2×#55211yescharacteristic
478C2×C11C2×#55711yescharacteristic
479C24C24×C1111yescharacteristic
480C2×Q8—232no—
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—28no—
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×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4C2×D4×C1114yes—
521C22×C4C2×D4×C1114yes—
522C22×C4C2×D4×C1114yes—
523C22×C4C2×Q8×C1114yes—
524C22×C4C2×Q8×C1114yes—
525C22×C4C2×Q8×C1114yes—
526C22×C4C11×#4114yes—
527C22×C4C11×#4114yes—
528C22×C4C11×#4114yes—
529C22×C4C24×C1112yes—
530C22×C4C24×C1112yes—
531C22×C4C24×C1112yes—
532C22×C4C24×C1112yes—
533C22×C4C24×C1112yes—
534C22×C4C24×C1112yes—
535C22×C4C24×C1112yes—
536C22×C4C24×C1112yes—
537C22×C4C24×C1112yes—
538C22×C4C24×C1112yes—
539C22×C4C24×C1112yes—
540C22×C4C24×C1112yes—
541C22×C4C24×C1112yes—
542C22×C4C24×C1112yes—
543C22×C4C24×C1112yes—
544C4⋊C4—28no—
545C4⋊C4—28no—
546C4⋊C4—28no—
547C4⋊C4—28no—
548C4⋊C4—28no—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C4⋊C4—28no—
556C4⋊C4—28no—
557C4⋊C4C2×D4×C11116yes—
558C4⋊C4C2×Q8×C11116yescomplemented
559C42—28no—
560C42—28no—
561C42—28no—
562C42—28no—
563C42—28no—
564C11C2×#246211yescharacteristic, direct product factor, Sylow
565C23C22×D4×C1112yes—
566C23C22×Q8×C1112yes—
567C23C2×C11×#4112yes—
568C23C2×C11×#4112yes—
569C23C2×C11×#4112yes—
570C23C11×2−1+412yes—
571C23C11×2−1+412yes—
572C23C25×C1111yescharacteristic
573Q8—232no—
574C2×C4—28no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—28no—
578C2×C4—28no—
579C2×C4—28no—
580C2×C4—28no—
581C2×C4—28no—
582C2×C4—28no—
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—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4C22×D4×C1114yes—
626C2×C4C22×D4×C1114yes—
627C2×C4C22×D4×C1114yes—
628C2×C4C22×Q8×C1114yes—
629C2×C4C22×Q8×C1114yes—
630C2×C4C22×Q8×C1114yes—
631C2×C4C2×C11×#4114yes—
632C2×C4C2×C11×#4114yes—
633C2×C4C2×C11×#4114yes—
634C22C11×#52514yes—
635C22C11×#53314yes—
636C22C11×#54114yes—
637C22C11×#54714yes—
638C22D4×Q8×C1114yes—
639C22C11×#55214yes—
640C22C11×#55714yes—
641C22C23×D4×C1111yescharacteristic
642C22C23×Q8×C1111yescharacteristic
643C22C22×C11×#4111yescharacteristic
644C22C22×C11×#4111yescharacteristic
645C22C22×C11×#4111yescharacteristic
646C22C2×C11×2−1+411yescharacteristic
647C22C2×C11×2−1+411yescharacteristic
648C4—24no—
649C4—24no—
650C4—24no—
651C4—24no—
652C4—24no—
653C4—24no—
654C4—24no—
655C4—24no—
656C4—24no—
657C4—42no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—42no—
663C2C11×#246218yesdirect product factor
664C2C2×C11×#52511yescharacteristic
665C2C2×C11×#53311yescharacteristic
666C2C2×C11×#54111yescharacteristic
667C2C2×C11×#54711yescharacteristic
668C2C2×D4×Q8×C1111yescharacteristic
669C2C2×C11×#55211yescharacteristic
670C2C2×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
3. C11×#2462C2direct (N × H)
104. C2×C11×C4⋊C4Q8semidirect
144. C2×#2462C11direct (N × H)
224. C11×C4⋊C4C2×Q8semidirect
232. #2462C2×C11direct (N × H)
431. C2×C4⋊C4Q8×C11semidirect
471. C2×C11#2462direct (N × H)
558. C4⋊C4C2×Q8×C11semidirect
564. C11C2×#2462direct (N × H)
663. C2C11×#2462direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C22×C4×Q8×C112
C11×#24622
C2×C11×#3982
C2×C11×#3952
C2×C11×#3892
C2×C11×#3872
C2×C4×C11×C4⋊C42
C2×#246211