Finite Group Databasebeta

← C2×C11×#2477 #14611911

Subgroups — C2×C11×#2477 #14611911

Order 2816.

3070 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C11×#117C211yesmaximal, characteristic, complemented
3C11×#2477C2116yesmaximal, direct product factor
4C2×C11×#400C211yesmaximal, characteristic, complemented
5C2×C11×#397C211yesmaximal, characteristic, complemented
6C2×C11×#394C211yesmaximal, characteristic
7C2×C11×#393C211yesmaximal, characteristic, complemented
8C2×C11×#391C211yesmaximal, characteristic, complemented
9C2×C11×#388C211yesmaximal, characteristic, complemented
10C2×C11×#388C211yesmaximal, characteristic, complemented
11C2×C11×#387C211yesmaximal, characteristic, complemented
12C2×C11×#387C211yesmaximal, characteristic, complemented
13C2×C11×#386C211yesmaximal, characteristic
14C2×C11×#386C211yesmaximal, characteristic
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C2×C11×C22⋊Q8—28no—
22C2×C11×C22⋊Q8C2218yescomplemented
23C2×C11×#117—28no—
24C2×C11×#117C2218yescomplemented
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×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C11×C22⋊C4C2211yescharacteristic
39C22×C11×C22⋊C4C2211yescharacteristic
40C22×C11×C22⋊C4C2211yescharacteristic
41C22×C42×C11C2211yescharacteristic
42C22×C42×C11C2211yescharacteristic
43C22×C42×C11C2211yescharacteristic
44C11×#400C2218yescomplemented
45C11×#397C2218yescomplemented
46C11×#394C2218yes—
47C11×#393C2218yescomplemented
48C11×#391C2218yescomplemented
49C11×#388C2218yescomplemented
50C11×#388C2218yescomplemented
51C11×#387C2218yescomplemented
52C11×#387C2218yescomplemented
53C11×#386C2218yes—
54C11×#386C2218yes—
55C11×#385C2218yescomplemented
56C4×C11×C22⋊C4C2218yescomplemented
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
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C22×Q8×C11—24no—
72C22×Q8×C11—24no—
73C22×Q8×C11—42no—
74C22×Q8×C11C2314yes—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—42no—
78C22×D4×C11C2314yes—
79C23×C4×C11—24no—
80C23×C4×C11—24no—
81C23×C4×C11—24no—
82C23×C4×C11—24no—
83C23×C4×C11—24no—
84C23×C4×C11—42no—
85C23×C4×C11C2314yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2314yes—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C11×C22⋊Q8—232no—
101C11×#117—232no—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4—24no—
104C2×C11×C4⋊C4—24no—
105C2×C11×C4⋊C4—24no—
106C2×C11×C4⋊C4—42no—
107C2×C11×C4⋊C4D418yescomplemented
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×C22⋊C4—24no—
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4—42no—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C11×C22⋊C4C2314yes—
129C2×C11×C22⋊C4C2314yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C11×C22⋊C4C2314yes—
133C2×C11×C22⋊C4C2314yes—
134C2×C42×C11—24no—
135C2×C42×C11—24no—
136C2×C42×C11—42no—
137C2×C42×C11C2314yes—
138C2×C42×C11C2314yes—
139C2×C42×C11C2314yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C2×#2477C1111yesmaximal, characteristic, direct product factor, Sylow
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11#4114yes—
166C24×C11#4114yes—
167C24×C11C2412yes—
168C24×C11C2412yes—
169C24×C11C2411yescharacteristic
170C2×Q8×C11—28no—
171C2×Q8×C11—28no—
172C2×Q8×C11—44no—
173C2×Q8×C11—416no—
174C2×D4×C11—28no—
175C2×D4×C11—28no—
176C2×D4×C11—44no—
177C2×D4×C11—416no—
178C22×C4×C11—232no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—28no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—28no—
191C22×C4×C11—28no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—28no—
217C22×C4×C11—28no—
218C22×C4×C11—44no—
219C22×C4×C11—416no—
220C22×C4×C11C2×D414yes—
221C22×C4×C11C2×D414yes—
222C22×C4×C11C2×D414yes—
223C22×C4×C11#4114yes—
224C22×C4×C11#4114yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C11×C4⋊C4—28no—
239C11×C4⋊C4—28no—
240C11×C4⋊C4—28no—
241C11×C4⋊C4—28no—
242C11×C4⋊C4—44no—
243C11×C4⋊C4C2×D4116yescomplemented
244C11×C22⋊C4—28no—
245C11×C22⋊C4—28no—
246C11×C22⋊C4—28no—
247C11×C22⋊C4—28no—
248C11×C22⋊C4—28no—
249C11×C22⋊C4—28no—
250C11×C22⋊C4—28no—
251C11×C22⋊C4—28no—
252C11×C22⋊C4—28no—
253C11×C22⋊C4—44no—
254C42×C11—28no—
255C42×C11—28no—
256C42×C11—44no—
257C22×C22⋊Q8C2×C1111yescharacteristic, complemented
258C22×#117C2×C1111yescharacteristic, complemented
259#2477C2×C11116yesdirect product factor
260C2×#400C2×C1111yescharacteristic, complemented
261C2×#397C2×C1111yescharacteristic, complemented
262C2×#394C2×C1111yescharacteristic
263C2×#393C2×C1111yescharacteristic, complemented
264C2×#391C2×C1111yescharacteristic, complemented
265C2×#388C2×C1111yescharacteristic, complemented
266C2×#388C2×C1111yescharacteristic, complemented
267C2×#387C2×C1111yescharacteristic, complemented
268C2×#387C2×C1111yescharacteristic, complemented
269C2×#386C2×C1111yescharacteristic
270C2×#386C2×C1111yescharacteristic
271C2×#385C2×C1111yescharacteristic, complemented
272C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
273C23×C11—28no—
274C23×C11—28no—
275C23×C11—28no—
276C23×C11—28no—
277C23×C11—28no—
278C23×C11—28no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—44no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11—44no—
299C23×C11C22×D412yes—
300C23×C11C2×#4114yes—
301C23×C11C2×#4114yes—
302C23×C11C2×#4112yes—
303C23×C11C2×#4112yes—
304C23×C11C2×#4112yes—
305C23×C11C2×#4112yes—
306C23×C11H(5,𝔽2)12yes—
307C23×C112−1+412yes—
308C23×C11C2511yescharacteristic
309Q8×C11—416no—
310D4×C11—416no—
311C2×C4×C11—232no—
312C2×C4×C11—28no—
313C2×C4×C11—28no—
314C2×C4×C11—28no—
315C2×C4×C11—28no—
316C2×C4×C11—28no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—416no—
352C2×C4×C11—44no—
353C2×C4×C11—44no—
354C2×C4×C11—44no—
355C2×C4×C11—44no—
356C2×C4×C11—44no—
357C2×C4×C11—44no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11C22×D414yes—
361C2×C4×C11C22×D414yes—
362C2×C4×C11C22×D414yes—
363C2×C4×C11C2×#4114yes—
364C2×C4×C11C2×#4114yes—
365C23×Q8C22×C1111yescharacteristic
366C23×D4C22×C1111yescharacteristic
367C24×C4C22×C1111yescharacteristic
368C24×C4C22×C1111yescharacteristic
369C2×C22⋊Q8—28no—
370C2×C22⋊Q8C22×C1118yescomplemented
371C2×#117—28no—
372C2×#117C22×C1118yescomplemented
373C22×C4⋊C4C22×C1111yescharacteristic
374C22×C4⋊C4C22×C1111yescharacteristic
375C22×C4⋊C4C22×C1111yescharacteristic
376C22×C4⋊C4C22×C1111yescharacteristic
377C22×C4⋊C4C22×C1111yescharacteristic
378C22×C4⋊C4C22×C1111yescharacteristic
379C22×C22⋊C4C22×C1111yescharacteristic
380C22×C22⋊C4C22×C1111yescharacteristic
381C22×C22⋊C4C22×C1111yescharacteristic
382C22×C22⋊C4C22×C1111yescharacteristic
383C22×C22⋊C4C22×C1111yescharacteristic
384C22×C22⋊C4C22×C1111yescharacteristic
385C22×C22⋊C4C22×C1111yescharacteristic
386C22×C22⋊C4C22×C1111yescharacteristic
387C22×C22⋊C4C22×C1111yescharacteristic
388C22×C22⋊C4C22×C1111yescharacteristic
389C22×C42C22×C1111yescharacteristic
390C22×C42C22×C1111yescharacteristic
391C22×C42C22×C1111yescharacteristic
392#400C22×C1118yescomplemented
393#397C22×C1118yescomplemented
394#394C22×C1118yes—
395#393C22×C1118yescomplemented
396#391C22×C1118yescomplemented
397#388C22×C1118yescomplemented
398#388C22×C1118yescomplemented
399#387C22×C1118yescomplemented
400#387C22×C1118yescomplemented
401#386C22×C1118yes—
402#386C22×C1118yes—
403#385C22×C1118yescomplemented
404C4×C22⋊C4C22×C1118yescomplemented
405C2×#95C22×C1111yescharacteristic
406C2×#95C22×C1111yescharacteristic
407C2×#95C22×C1111yescharacteristic
408C2×#95C22×C1111yescharacteristic
409C2×#95C22×C1111yescharacteristic
410C2×#95C22×C1111yescharacteristic
411C2×#95C22×C1111yescharacteristic
412C2×#95C22×C1111yescharacteristic
413C2×#95C22×C1111yescharacteristic
414C2×#95C22×C1111yescharacteristic
415C2×#95C22×C1111yescharacteristic
416C2×#95C22×C1111yescharacteristic
417C22×C11—24no—
418C22×C11—24no—
419C22×C11—24no—
420C22×C11—24no—
421C22×C11—24no—
422C22×C11—24no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—416no—
432C22×C11—416no—
433C22×C11#52514yes—
434C22×C11#52914yes—
435C22×C11#54214yes—
436C22×C11#54614yes—
437C22×C11#54814yes—
438C22×C11#55114yes—
439C22×C11#55214yes—
440C22×C11C23×D411yescharacteristic
441C22×C11C22×#4111yescharacteristic
442C22×C11C22×#4111yescharacteristic
443C22×C11C22×#4111yescharacteristic
444C22×C11C22×#4111yescharacteristic
445C22×C11C2×H(5,𝔽2)11yescharacteristic
446C22×C11C2×2−1+411yescharacteristic
447C4×C11—24no—
448C4×C11—24no—
449C4×C11—24no—
450C4×C11—24no—
451C4×C11—24no—
452C4×C11—42no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11—42no—
458C4×C11—42no—
459C4×C11—42no—
460C25C23×C1111yescharacteristic
461C25C23×C1111yescharacteristic
462C22×Q8—24no—
463C22×Q8—24no—
464C22×Q8—42no—
465C22×Q8C23×C1114yes—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—42no—
469C22×D4C23×C1114yes—
470C23×C4—24no—
471C23×C4—24no—
472C23×C4—24no—
473C23×C4—24no—
474C23×C4—24no—
475C23×C4—42no—
476C23×C4C23×C1111yescharacteristic
477C23×C4C23×C1111yescharacteristic
478C23×C4C23×C1111yescharacteristic
479C23×C4C23×C1111yescharacteristic
480C23×C4C23×C1111yescharacteristic
481C23×C4C23×C1111yescharacteristic
482C23×C4C23×C1111yescharacteristic
483C23×C4C23×C1111yescharacteristic
484C23×C4C23×C1114yes—
485C23×C4C23×C1114yes—
486C23×C4C23×C1111yescharacteristic
487C23×C4C23×C1111yescharacteristic
488C23×C4C23×C1111yescharacteristic
489C23×C4C23×C1111yescharacteristic
490C23×C4C23×C1111yescharacteristic
491C22⋊Q8—232no—
492#117—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4D4×C1118yescomplemented
499C2×C4⋊C4C23×C1114yes—
500C2×C4⋊C4C23×C1114yes—
501C2×C4⋊C4C23×C1114yes—
502C2×C4⋊C4C23×C1114yes—
503C2×C4⋊C4C23×C1114yes—
504C2×C4⋊C4C23×C1114yes—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4C23×C1114yes—
516C2×C22⋊C4C23×C1114yes—
517C2×C22⋊C4C23×C1114yes—
518C2×C22⋊C4C23×C1114yes—
519C2×C22⋊C4C23×C1114yes—
520C2×C22⋊C4C23×C1114yes—
521C2×C22⋊C4C23×C1114yes—
522C2×C22⋊C4C23×C1114yes—
523C2×C22⋊C4C23×C1114yes—
524C2×C22⋊C4C23×C1114yes—
525C2×C42—24no—
526C2×C42—24no—
527C2×C42—42no—
528C2×C42C23×C1114yes—
529C2×C42C23×C1114yes—
530C2×C42C23×C1114yes—
531#95C23×C1114yes—
532#95C23×C1114yes—
533#95C23×C1114yes—
534#95C23×C1114yes—
535#95C23×C1114yes—
536#95C23×C1114yes—
537#95C23×C1114yes—
538#95C23×C1114yes—
539#95C23×C1114yes—
540#95C23×C1114yes—
541#95C23×C1114yes—
542#95C23×C1114yes—
543C2×C11—44no—
544C2×C11—44no—
545C2×C11#247718yesdirect product factor
546C2×C11C2×#52511yescharacteristic
547C2×C11C2×#52911yescharacteristic
548C2×C11C2×#54211yescharacteristic
549C2×C11C2×#54611yescharacteristic
550C2×C11C2×#54811yescharacteristic
551C2×C11C2×#55111yescharacteristic
552C2×C11C2×#55211yescharacteristic
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24C11×#4114yes—
566C24C11×#4114yes—
567C24C24×C1112yes—
568C24C24×C1112yes—
569C24C24×C1111yescharacteristic
570C2×Q8—28no—
571C2×Q8—28no—
572C2×Q8—44no—
573C2×Q8—416no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—44no—
577C2×D4—416no—
578C22×C4—232no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—44no—
619C22×C4—416no—
620C22×C4C2×D4×C1114yes—
621C22×C4C2×D4×C1114yes—
622C22×C4C2×D4×C1114yes—
623C22×C4C11×#4114yes—
624C22×C4C11×#4114yes—
625C22×C4C24×C1112yes—
626C22×C4C24×C1112yes—
627C22×C4C24×C1112yes—
628C22×C4C24×C1112yes—
629C22×C4C24×C1112yes—
630C22×C4C24×C1112yes—
631C22×C4C24×C1112yes—
632C22×C4C24×C1112yes—
633C22×C4C24×C1112yes—
634C22×C4C24×C1112yes—
635C22×C4C24×C1112yes—
636C22×C4C24×C1112yes—
637C22×C4C24×C1112yes—
638C4⋊C4—28no—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—44no—
643C4⋊C4C2×D4×C11116yescomplemented
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—44no—
654C42—28no—
655C42—28no—
656C42—44no—
657C11C2×#247711yescharacteristic, direct product factor, Sylow
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23C22×D4×C1112yes—
685C23C2×C11×#4114yes—
686C23C2×C11×#4114yes—
687C23C2×C11×#4112yes—
688C23C2×C11×#4112yes—
689C23C2×C11×#4112yes—
690C23C2×C11×#4112yes—
691C23C11×H(5,𝔽2)12yes—
692C23C11×2−1+412yes—
693C23C25×C1111yescharacteristic
694Q8—416no—
695D4—416no—
696C2×C4—232no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4C22×D4×C1114yes—
746C2×C4C22×D4×C1114yes—
747C2×C4C22×D4×C1114yes—
748C2×C4C2×C11×#4114yes—
749C2×C4C2×C11×#4114yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—416no—
765C22—416no—
766C22C11×#52514yes—
767C22C11×#52914yes—
768C22C11×#54214yes—
769C22C11×#54614yes—
770C22C11×#54814yes—
771C22C11×#55114yes—
772C22C11×#55214yes—
773C22C23×D4×C1111yescharacteristic
774C22C22×C11×#4111yescharacteristic
775C22C22×C11×#4111yescharacteristic
776C22C22×C11×#4111yescharacteristic
777C22C22×C11×#4111yescharacteristic
778C22C2×C11×H(5,𝔽2)11yescharacteristic
779C22C2×C11×2−1+411yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—24no—
784C4—24no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—42no—
793C2—44no—
794C2—44no—
795C2C11×#247718yesdirect product factor
796C2C2×C11×#52511yescharacteristic
797C2C2×C11×#52911yescharacteristic
798C2C2×C11×#54211yescharacteristic
799C2C2×C11×#54611yescharacteristic
800C2C2×C11×#54811yescharacteristic
801C2C2×C11×#55111yescharacteristic
802C2C2×C11×#55211yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C22⋊Q8C2semidirect
2. C22×C11×#117C2semidirect
3. C11×#2477C2direct (N × H)
4. C2×C11×#400C2semidirect
5. C2×C11×#397C2semidirect
7. C2×C11×#393C2semidirect
8. C2×C11×#391C2semidirect
9. C2×C11×#388C2semidirect
10. C2×C11×#388C2semidirect
11. C2×C11×#387C2semidirect
12. C2×C11×#387C2semidirect
15. C2×C11×#385C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
22. C2×C11×C22⋊Q8C22semidirect
24. C2×C11×#117C22semidirect
44. C11×#400C22semidirect
45. C11×#397C22semidirect
47. C11×#393C22semidirect
48. C11×#391C22semidirect
49. C11×#388C22semidirect
50. C11×#388C22semidirect
51. C11×#387C22semidirect
52. C11×#387C22semidirect
55. C11×#385C22semidirect
56. C4×C11×C22⋊C4C22semidirect
107. C2×C11×C4⋊C4D4semidirect
152. C2×#2477C11direct (N × H)
243. C11×C4⋊C4C2×D4semidirect
257. C22×C22⋊Q8C2×C11semidirect
258. C22×#117C2×C11semidirect
259. #2477C2×C11direct (N × H)
260. C2×#400C2×C11semidirect
261. C2×#397C2×C11semidirect
263. C2×#393C2×C11semidirect
264. C2×#391C2×C11semidirect
265. C2×#388C2×C11semidirect
266. C2×#388C2×C11semidirect
267. C2×#387C2×C11semidirect
268. C2×#387C2×C11semidirect
271. C2×#385C2×C11semidirect
272. C2×C4×C22⋊C4C2×C11semidirect
370. C2×C22⋊Q8C22×C11semidirect
372. C2×#117C22×C11semidirect
392. #400C22×C11semidirect
393. #397C22×C11semidirect
395. #393C22×C11semidirect
396. #391C22×C11semidirect
397. #388C22×C11semidirect
398. #388C22×C11semidirect
399. #387C22×C11semidirect
400. #387C22×C11semidirect
403. #385C22×C11semidirect
404. C4×C22⋊C4C22×C11semidirect
498. C2×C4⋊C4D4×C11semidirect
545. C2×C11#2477direct (N × H)
643. C4⋊C4C2×D4×C11semidirect
657. C11C2×#2477direct (N × H)
795. C2C11×#2477direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C22×C11×#1172
C11×#24772
C2×C11×#4002
C2×C11×#3972
C2×C11×#3942
C2×C11×#3932
C2×C11×#3912
C2×C11×#3882
C2×C11×#3872
C2×C11×#3862
C2×C11×#3852
C2×C4×C11×C22⋊C42
C2×#247711