Finite Group Databasebeta

← C2×C11×#2461 #14611869

Subgroups — C2×C11×#2461 #14611869

Order 2816.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#124C211yesmaximal, characteristic, complemented
2C22×C11×#123C211yesmaximal, characteristic, complemented
3C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
4C22×C4×D4×C11C211yesmaximal, characteristic, complemented
5C11×#2461C2116yesmaximal, direct product factor
6C2×C11×#396C211yesmaximal, characteristic, complemented
7C2×C11×#395C211yesmaximal, characteristic, complemented
8C2×C11×#394C211yesmaximal, characteristic, complemented
9C2×C11×#392C211yesmaximal, characteristic
10C2×C11×#390C211yesmaximal, characteristic, complemented
11C2×C11×#388C211yesmaximal, characteristic, complemented
12C2×C11×#388C211yesmaximal, characteristic, complemented
13C2×C11×#388C211yesmaximal, characteristic, complemented
14C2×C11×#386C211yesmaximal, characteristic, complemented
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic
21C24×C4×C11C2211yescharacteristic
22C24×C4×C11C2211yescharacteristic
23C2×C11×#124—28no—
24C2×C11×#124C2218yescomplemented
25C2×C11×#123—28no—
26C2×C11×#123C2218yescomplemented
27C2×C11×C22⋊Q8—28no—
28C2×C11×C22⋊Q8C2218yescomplemented
29C2×C4×D4×C11—28no—
30C2×C4×D4×C11C2218yescomplemented
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×C11×C4⋊C4C2211yescharacteristic
38C22×C11×C22⋊C4C2211yescharacteristic
39C22×C11×C22⋊C4C2211yescharacteristic
40C22×C11×C22⋊C4C2211yescharacteristic
41C22×C11×C22⋊C4C2211yescharacteristic
42C22×C11×C22⋊C4C2211yescharacteristic
43C22×C11×C22⋊C4C2211yescharacteristic
44C22×C11×C22⋊C4C2211yescharacteristic
45C22×C11×C22⋊C4C2211yescharacteristic
46C22×C11×C22⋊C4C2211yescharacteristic
47C22×C11×C22⋊C4C2211yescharacteristic
48C22×C11×C22⋊C4C2211yescharacteristic
49C22×C11×C22⋊C4C2211yescharacteristic
50C22×C11×C22⋊C4C2211yescharacteristic
51C22×C42×C11C2211yescharacteristic
52C22×C42×C11C2211yescharacteristic
53C22×C42×C11C2211yescharacteristic
54C11×#396C2218yescomplemented
55C11×#395C2218yescomplemented
56C11×#394C2218yescomplemented
57C11×#392C2218yes—
58C11×#390C2218yescomplemented
59C11×#388C2218yescomplemented
60C11×#388C2218yescomplemented
61C11×#388C2218yescomplemented
62C11×#386C2218yescomplemented
63C11×#385C2218yescomplemented
64C4×C11×C4⋊C4C2218yescomplemented
65C2×C11×#95C2211yescharacteristic
66C2×C11×#95C2211yescharacteristic
67C2×C11×#95C2211yescharacteristic
68C2×C11×#95C2211yescharacteristic
69C2×C11×#95C2211yescharacteristic
70C2×C11×#95C2211yescharacteristic
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C22×Q8×C11—24no—
75C22×Q8×C11—24no—
76C22×Q8×C11—42no—
77C22×Q8×C11C2314yes—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11—24no—
84C22×D4×C11—24no—
85C22×D4×C11—42no—
86C22×D4×C11—42no—
87C22×D4×C11C2314yes—
88C22×D4×C11C2314yes—
89C22×D4×C11C2314yes—
90C23×C4×C11—24no—
91C23×C4×C11—24no—
92C23×C4×C11—24no—
93C23×C4×C11—24no—
94C23×C4×C11—42no—
95C23×C4×C11—42no—
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2314yes—
102C23×C4×C11C2314yes—
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C11×#124—232no—
111C11×#123—232no—
112C11×C22⋊Q8—232no—
113C4×D4×C11—232no—
114C2×C11×C4⋊C4—24no—
115C2×C11×C4⋊C4—24no—
116C2×C11×C4⋊C4—24no—
117C2×C11×C4⋊C4—24no—
118C2×C11×C4⋊C4—24no—
119C2×C11×C4⋊C4—42no—
120C2×C11×C4⋊C4D418yescomplemented
121C2×C11×C4⋊C4C2314yes—
122C2×C11×C4⋊C4C2314yes—
123C2×C11×C4⋊C4C2314yes—
124C2×C11×C4⋊C4C2314yes—
125C2×C11×C4⋊C4C2314yes—
126C2×C11×C4⋊C4C2314yes—
127C2×C11×C4⋊C4C2314yes—
128C2×C11×C22⋊C4—24no—
129C2×C11×C22⋊C4—24no—
130C2×C11×C22⋊C4—24no—
131C2×C11×C22⋊C4—24no—
132C2×C11×C22⋊C4—24no—
133C2×C11×C22⋊C4—24no—
134C2×C11×C22⋊C4—24no—
135C2×C11×C22⋊C4—24no—
136C2×C11×C22⋊C4—24no—
137C2×C11×C22⋊C4—24no—
138C2×C11×C22⋊C4—24no—
139C2×C11×C22⋊C4—24no—
140C2×C11×C22⋊C4D418yescomplemented
141C2×C11×C22⋊C4C2314yes—
142C2×C11×C22⋊C4C2314yes—
143C2×C11×C22⋊C4C2314yes—
144C2×C11×C22⋊C4C2314yes—
145C2×C11×C22⋊C4C2314yes—
146C2×C11×C22⋊C4C2314yes—
147C2×C11×C22⋊C4C2314yes—
148C2×C11×C22⋊C4C2314yes—
149C2×C11×C22⋊C4C2314yes—
150C2×C11×C22⋊C4C2314yes—
151C2×C11×C22⋊C4C2314yes—
152C2×C11×C22⋊C4C2314yes—
153C2×C11×C22⋊C4C2314yes—
154C2×C42×C11—24no—
155C2×C42×C11—24no—
156C2×C42×C11—24no—
157C2×C42×C11C2314yes—
158C2×C42×C11C2314yes—
159C2×C42×C11C2314yes—
160C11×#95C2314yes—
161C11×#95C2314yes—
162C11×#95C2314yes—
163C11×#95C2314yes—
164C11×#95C2314yes—
165C11×#95C2314yes—
166C2×#2461C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11C2×D414yes—
187C24×C11#4114yes—
188C24×C11C2412yes—
189C24×C11C2412yes—
190C24×C11C2412yes—
191C24×C11C2411yescharacteristic
192C2×Q8×C11—28no—
193C2×Q8×C11—28no—
194C2×Q8×C11—44no—
195C2×Q8×C11—416no—
196C2×D4×C11—232no—
197C2×D4×C11—28no—
198C2×D4×C11—28no—
199C2×D4×C11—28no—
200C2×D4×C11—28no—
201C2×D4×C11—28no—
202C2×D4×C11—28no—
203C2×D4×C11—28no—
204C2×D4×C11—44no—
205C2×D4×C11—44no—
206C2×D4×C11—416no—
207C2×D4×C11—416no—
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—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—28no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—28no—
239C22×C4×C11—28no—
240C22×C4×C11—28no—
241C22×C4×C11—44no—
242C22×C4×C11—44no—
243C22×C4×C11—416no—
244C22×C4×C11—416no—
245C22×C4×C11C2×D414yes—
246C22×C4×C11C2×D414yes—
247C22×C4×C11C2×D414yes—
248C22×C4×C11C2×D414yes—
249C22×C4×C11C2×D414yes—
250C22×C4×C11#4114yes—
251C22×C4×C11#4114yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2412yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2412yes—
259C22×C4×C11C2412yes—
260C22×C4×C11C2412yes—
261C22×C4×C11C2412yes—
262C22×C4×C11C2412yes—
263C22×C4×C11C2412yes—
264C11×C4⋊C4—28no—
265C11×C4⋊C4—28no—
266C11×C4⋊C4—28no—
267C11×C4⋊C4—28no—
268C11×C4⋊C4—28no—
269C11×C4⋊C4—44no—
270C11×C4⋊C4C2×D4116yescomplemented
271C11×C22⋊C4—28no—
272C11×C22⋊C4—28no—
273C11×C22⋊C4—28no—
274C11×C22⋊C4—28no—
275C11×C22⋊C4—28no—
276C11×C22⋊C4—28no—
277C11×C22⋊C4—28no—
278C11×C22⋊C4—28no—
279C11×C22⋊C4—28no—
280C11×C22⋊C4—28no—
281C11×C22⋊C4—28no—
282C11×C22⋊C4—28no—
283C11×C22⋊C4C2×D4116yescomplemented
284C42×C11—28no—
285C42×C11—28no—
286C42×C11—28no—
287C22×#124C2×C1111yescharacteristic, complemented
288C22×#123C2×C1111yescharacteristic, complemented
289C22×C22⋊Q8C2×C1111yescharacteristic, complemented
290C22×C4×D4C2×C1111yescharacteristic, complemented
291#2461C2×C11116yesdirect product factor
292C2×#396C2×C1111yescharacteristic, complemented
293C2×#395C2×C1111yescharacteristic, complemented
294C2×#394C2×C1111yescharacteristic, complemented
295C2×#392C2×C1111yescharacteristic
296C2×#390C2×C1111yescharacteristic, complemented
297C2×#388C2×C1111yescharacteristic, complemented
298C2×#388C2×C1111yescharacteristic, complemented
299C2×#388C2×C1111yescharacteristic, complemented
300C2×#386C2×C1111yescharacteristic, complemented
301C2×#385C2×C1111yescharacteristic, complemented
302C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11—44no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11C22×D414yes—
344C23×C11C22×D412yes—
345C23×C11C22×D412yes—
346C23×C11C2×#4114yes—
347C23×C11C2×#4112yes—
348C23×C11C2×#4112yes—
349C23×C11C2×#4112yes—
350C23×C11H(5,𝔽2)12yes—
351C23×C112−1+412yes—
352C23×C11C2511yescharacteristic
353Q8×C11—416no—
354D4×C11—232no—
355D4×C11—416no—
356D4×C11—416no—
357C2×C4×C11—28no—
358C2×C4×C11—28no—
359C2×C4×C11—28no—
360C2×C4×C11—28no—
361C2×C4×C11—28no—
362C2×C4×C11—28no—
363C2×C4×C11—28no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—416no—
394C2×C4×C11—416no—
395C2×C4×C11—44no—
396C2×C4×C11—44no—
397C2×C4×C11—44no—
398C2×C4×C11—44no—
399C2×C4×C11—44no—
400C2×C4×C11C22×D414yes—
401C2×C4×C11C22×D414yes—
402C2×C4×C11C22×D414yes—
403C2×C4×C11C22×D414yes—
404C2×C4×C11C22×D414yes—
405C2×C4×C11C2×#4114yes—
406C2×C4×C11C2×#4114yes—
407C23×Q8C22×C1111yescharacteristic
408C23×D4C22×C1111yescharacteristic
409C23×D4C22×C1111yescharacteristic
410C23×D4C22×C1111yescharacteristic
411C24×C4C22×C1111yescharacteristic
412C24×C4C22×C1111yescharacteristic
413C2×#124—28no—
414C2×#124C22×C1118yescomplemented
415C2×#123—28no—
416C2×#123C22×C1118yescomplemented
417C2×C22⋊Q8—28no—
418C2×C22⋊Q8C22×C1118yescomplemented
419C2×C4×D4—28no—
420C2×C4×D4C22×C1118yescomplemented
421C22×C4⋊C4C22×C1111yescharacteristic
422C22×C4⋊C4C22×C1111yescharacteristic
423C22×C4⋊C4C22×C1111yescharacteristic
424C22×C4⋊C4C22×C1111yescharacteristic
425C22×C4⋊C4C22×C1111yescharacteristic
426C22×C4⋊C4C22×C1111yescharacteristic
427C22×C4⋊C4C22×C1111yescharacteristic
428C22×C22⋊C4C22×C1111yescharacteristic
429C22×C22⋊C4C22×C1111yescharacteristic
430C22×C22⋊C4C22×C1111yescharacteristic
431C22×C22⋊C4C22×C1111yescharacteristic
432C22×C22⋊C4C22×C1111yescharacteristic
433C22×C22⋊C4C22×C1111yescharacteristic
434C22×C22⋊C4C22×C1111yescharacteristic
435C22×C22⋊C4C22×C1111yescharacteristic
436C22×C22⋊C4C22×C1111yescharacteristic
437C22×C22⋊C4C22×C1111yescharacteristic
438C22×C22⋊C4C22×C1111yescharacteristic
439C22×C22⋊C4C22×C1111yescharacteristic
440C22×C22⋊C4C22×C1111yescharacteristic
441C22×C42C22×C1111yescharacteristic
442C22×C42C22×C1111yescharacteristic
443C22×C42C22×C1111yescharacteristic
444#396C22×C1118yescomplemented
445#395C22×C1118yescomplemented
446#394C22×C1118yescomplemented
447#392C22×C1118yes—
448#390C22×C1118yescomplemented
449#388C22×C1118yescomplemented
450#388C22×C1118yescomplemented
451#388C22×C1118yescomplemented
452#386C22×C1118yescomplemented
453#385C22×C1118yescomplemented
454C4×C4⋊C4C22×C1118yescomplemented
455C2×#95C22×C1111yescharacteristic
456C2×#95C22×C1111yescharacteristic
457C2×#95C22×C1111yescharacteristic
458C2×#95C22×C1111yescharacteristic
459C2×#95C22×C1111yescharacteristic
460C2×#95C22×C1111yescharacteristic
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—416no—
476C22×C11—416no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—88no—
485C22×C11#52514yes—
486C22×C11#53214yes—
487C22×C11#54214yes—
488C22×C11D4214yes—
489C22×C11#54714yes—
490C22×C11#54814yes—
491C22×C11#55114yes—
492C22×C11C23×D411yescharacteristic
493C22×C11C23×D411yescharacteristic
494C22×C11C22×#4111yescharacteristic
495C22×C11C22×#4111yescharacteristic
496C22×C11C22×#4111yescharacteristic
497C22×C11C2×H(5,𝔽2)11yescharacteristic
498C22×C11C2×2−1+411yescharacteristic
499C4×C11—24no—
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—24no—
504C4×C11—24no—
505C4×C11—24no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—42no—
511C25C23×C1111yescharacteristic
512C25C23×C1111yescharacteristic
513C25C23×C1111yescharacteristic
514C22×Q8—24no—
515C22×Q8—24no—
516C22×Q8—42no—
517C22×Q8C23×C1114yes—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4—24no—
524C22×D4—24no—
525C22×D4—42no—
526C22×D4—42no—
527C22×D4C23×C1114yes—
528C22×D4C23×C1114yes—
529C22×D4C23×C1114yes—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4—24no—
533C23×C4—24no—
534C23×C4—42no—
535C23×C4—42no—
536C23×C4C23×C1111yescharacteristic
537C23×C4C23×C1111yescharacteristic
538C23×C4C23×C1111yescharacteristic
539C23×C4C23×C1111yescharacteristic
540C23×C4C23×C1111yescharacteristic
541C23×C4C23×C1114yes—
542C23×C4C23×C1114yes—
543C23×C4C23×C1111yescharacteristic
544C23×C4C23×C1111yescharacteristic
545C23×C4C23×C1111yescharacteristic
546C23×C4C23×C1111yescharacteristic
547C23×C4C23×C1111yescharacteristic
548C23×C4C23×C1111yescharacteristic
549C23×C4C23×C1111yescharacteristic
550#124—232no—
551#123—232no—
552C22⋊Q8—232no—
553C4×D4—232no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—24no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4—42no—
560C2×C4⋊C4D4×C1118yescomplemented
561C2×C4⋊C4C23×C1114yes—
562C2×C4⋊C4C23×C1114yes—
563C2×C4⋊C4C23×C1114yes—
564C2×C4⋊C4C23×C1114yes—
565C2×C4⋊C4C23×C1114yes—
566C2×C4⋊C4C23×C1114yes—
567C2×C4⋊C4C23×C1114yes—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4D4×C1118yescomplemented
581C2×C22⋊C4C23×C1114yes—
582C2×C22⋊C4C23×C1114yes—
583C2×C22⋊C4C23×C1114yes—
584C2×C22⋊C4C23×C1114yes—
585C2×C22⋊C4C23×C1114yes—
586C2×C22⋊C4C23×C1114yes—
587C2×C22⋊C4C23×C1114yes—
588C2×C22⋊C4C23×C1114yes—
589C2×C22⋊C4C23×C1114yes—
590C2×C22⋊C4C23×C1114yes—
591C2×C22⋊C4C23×C1114yes—
592C2×C22⋊C4C23×C1114yes—
593C2×C22⋊C4C23×C1114yes—
594C2×C42—24no—
595C2×C42—24no—
596C2×C42—24no—
597C2×C42C23×C1114yes—
598C2×C42C23×C1114yes—
599C2×C42C23×C1114yes—
600#95C23×C1114yes—
601#95C23×C1114yes—
602#95C23×C1114yes—
603#95C23×C1114yes—
604#95C23×C1114yes—
605#95C23×C1114yes—
606C2×C11—44no—
607C2×C11—44no—
608C2×C11—82no—
609C2×C11#246118yesdirect product factor
610C2×C11C2×#52511yescharacteristic
611C2×C11C2×#53211yescharacteristic
612C2×C11C2×#54211yescharacteristic
613C2×C11C2×D4211yescharacteristic
614C2×C11C2×#54711yescharacteristic
615C2×C11C2×#54811yescharacteristic
616C2×C11C2×#55111yescharacteristic
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24C2×D4×C1114yes—
637C24C11×#4114yes—
638C24C24×C1112yes—
639C24C24×C1112yes—
640C24C24×C1112yes—
641C24C24×C1111yescharacteristic
642C2×Q8—28no—
643C2×Q8—28no—
644C2×Q8—44no—
645C2×Q8—416no—
646C2×D4—232no—
647C2×D4—28no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—416no—
657C2×D4—416no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—28no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—28no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—416no—
694C22×C4—416no—
695C22×C4C2×D4×C1114yes—
696C22×C4C2×D4×C1114yes—
697C22×C4C2×D4×C1114yes—
698C22×C4C2×D4×C1114yes—
699C22×C4C2×D4×C1114yes—
700C22×C4C11×#4114yes—
701C22×C4C11×#4114yes—
702C22×C4C24×C1112yes—
703C22×C4C24×C1112yes—
704C22×C4C24×C1112yes—
705C22×C4C24×C1112yes—
706C22×C4C24×C1112yes—
707C22×C4C24×C1112yes—
708C22×C4C24×C1112yes—
709C22×C4C24×C1112yes—
710C22×C4C24×C1112yes—
711C22×C4C24×C1112yes—
712C22×C4C24×C1112yes—
713C22×C4C24×C1112yes—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—28no—
718C4⋊C4—28no—
719C4⋊C4—44no—
720C4⋊C4C2×D4×C11116yescomplemented
721C22⋊C4—28no—
722C22⋊C4—28no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4C2×D4×C11116yescomplemented
734C42—28no—
735C42—28no—
736C42—28no—
737C11C2×#246111yescharacteristic, direct product factor, Sylow
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23C22×D4×C1114yes—
779C23C22×D4×C1112yes—
780C23C22×D4×C1112yes—
781C23C2×C11×#4114yes—
782C23C2×C11×#4112yes—
783C23C2×C11×#4112yes—
784C23C2×C11×#4112yes—
785C23C11×H(5,𝔽2)12yes—
786C23C11×2−1+412yes—
787C23C25×C1111yescharacteristic
788Q8—416no—
789D4—232no—
790D4—416no—
791D4—416no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4C22×D4×C1114yes—
836C2×C4C22×D4×C1114yes—
837C2×C4C22×D4×C1114yes—
838C2×C4C22×D4×C1114yes—
839C2×C4C22×D4×C1114yes—
840C2×C4C2×C11×#4114yes—
841C2×C4C2×C11×#4114yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—416no—
857C22—416no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—88no—
866C22C11×#52514yes—
867C22C11×#53214yes—
868C22C11×#54214yes—
869C22D42×C1114yes—
870C22C11×#54714yes—
871C22C11×#54814yes—
872C22C11×#55114yes—
873C22C23×D4×C1111yescharacteristic
874C22C23×D4×C1111yescharacteristic
875C22C22×C11×#4111yescharacteristic
876C22C22×C11×#4111yescharacteristic
877C22C22×C11×#4111yescharacteristic
878C22C2×C11×H(5,𝔽2)11yescharacteristic
879C22C2×C11×2−1+411yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—42no—
892C2—44no—
893C2—44no—
894C2—82no—
895C2C11×#246118yesdirect product factor
896C2C2×C11×#52511yescharacteristic
897C2C2×C11×#53211yescharacteristic
898C2C2×C11×#54211yescharacteristic
899C2C2×D42×C1111yescharacteristic
900C2C2×C11×#54711yescharacteristic
901C2C2×C11×#54811yescharacteristic
902C2C2×C11×#55111yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC2×C11×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#124C2semidirect
2. C22×C11×#123C2semidirect
3. C22×C11×C22⋊Q8C2semidirect
4. C22×C4×D4×C11C2semidirect
5. C11×#2461C2direct (N × H)
6. C2×C11×#396C2semidirect
7. C2×C11×#395C2semidirect
8. C2×C11×#394C2semidirect
10. C2×C11×#390C2semidirect
11. C2×C11×#388C2semidirect
12. C2×C11×#388C2semidirect
13. C2×C11×#388C2semidirect
14. C2×C11×#386C2semidirect
15. C2×C11×#385C2semidirect
16. C2×C4×C11×C4⋊C4C2semidirect
24. C2×C11×#124C22semidirect
26. C2×C11×#123C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
30. C2×C4×D4×C11C22semidirect
54. C11×#396C22semidirect
55. C11×#395C22semidirect
56. C11×#394C22semidirect
58. C11×#390C22semidirect
59. C11×#388C22semidirect
60. C11×#388C22semidirect
61. C11×#388C22semidirect
62. C11×#386C22semidirect
63. C11×#385C22semidirect
64. C4×C11×C4⋊C4C22semidirect
120. C2×C11×C4⋊C4D4semidirect
140. C2×C11×C22⋊C4D4semidirect
166. C2×#2461C11direct (N × H)
270. C11×C4⋊C4C2×D4semidirect
283. C11×C22⋊C4C2×D4semidirect
287. C22×#124C2×C11semidirect
288. C22×#123C2×C11semidirect
289. C22×C22⋊Q8C2×C11semidirect
290. C22×C4×D4C2×C11semidirect
291. #2461C2×C11direct (N × H)
292. C2×#396C2×C11semidirect
293. C2×#395C2×C11semidirect
294. C2×#394C2×C11semidirect
296. C2×#390C2×C11semidirect
297. C2×#388C2×C11semidirect
298. C2×#388C2×C11semidirect
299. C2×#388C2×C11semidirect
300. C2×#386C2×C11semidirect
301. C2×#385C2×C11semidirect
302. C2×C4×C4⋊C4C2×C11semidirect
414. C2×#124C22×C11semidirect
416. C2×#123C22×C11semidirect
418. C2×C22⋊Q8C22×C11semidirect
420. C2×C4×D4C22×C11semidirect
444. #396C22×C11semidirect
445. #395C22×C11semidirect
446. #394C22×C11semidirect
448. #390C22×C11semidirect
449. #388C22×C11semidirect
450. #388C22×C11semidirect
451. #388C22×C11semidirect
452. #386C22×C11semidirect
453. #385C22×C11semidirect
454. C4×C4⋊C4C22×C11semidirect
560. C2×C4⋊C4D4×C11semidirect
580. C2×C22⋊C4D4×C11semidirect
609. C2×C11#2461direct (N × H)
720. C4⋊C4C2×D4×C11semidirect
733. C22⋊C4C2×D4×C11semidirect
737. C11C2×#2461direct (N × H)
895. C2C11×#2461direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1242
C22×C11×#1232
C22×C11×C22⋊Q82
C22×C4×D4×C112
C11×#24612
C2×C11×#3962
C2×C11×#3952
C2×C11×#3942
C2×C11×#3922
C2×C11×#3902
C2×C11×#3882
C2×C11×#3862
C2×C11×#3852
C2×C4×C11×C4⋊C42
C2×#246111