Finite Group Databasebeta

← C11×#60751 #14637944

Subgroups — C11×#60751 #14637944

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C11×#3196C214yesmaximal, complemented
4C11×#3195C212yesmaximal, complemented
5C11×#3193C212yesmaximal, complemented
6C11×#3190C214yesmaximal, complemented
7C11×#3189C212yesmaximal, complemented
8C11×#3187C212yesmaximal, complemented
9C11×#3095C212yesmaximal, complemented
10C11×#3092C212yesmaximal, complemented
11C11×#3056C214yesmaximal, complemented
12C11×#3007C212yesmaximal, complemented
13C11×#3004C212yesmaximal, complemented
14C2×C11×#407C211yesmaximal, characteristic, complemented
15C22×C11×#41C2211yescharacteristic
16C23×Q8×C11C2211yescharacteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C2×C11×#137C2214yescomplemented
19C22×C11×M16C2212yescomplemented
20C11×#525—21no—
21C11×#525—21no—
22C11×#525—21no—
23C11×#525—21no—
24C11×#525C2212yes—
25C11×#525C2212yes—
26C11×#525C2212yes—
27C11×#525C2212yes—
28C2×C11×#123—21no—
29C2×C11×C22⋊Q8—21no—
30C2×C11×C22⋊Q8—21no—
31C2×C11×C22⋊Q8—21no—
32C2×C11×C22⋊Q8—21no—
33C2×C11×C22⋊Q8—21no—
34C2×C11×C22⋊Q8—21no—
35C2×C11×C22⋊Q8C2212yes—
36C2×C11×C22⋊Q8C2212yes—
37C2×C11×C22⋊Q8C2212yes—
38C2×C11×C22⋊Q8C2211yescharacteristic
39C2×C11×C22⋊Q8C2211yescharacteristic
40C2×C11×C22⋊Q8C2212yescomplemented
41C2×C11×C22⋊Q8C2212yescomplemented
42C2×C11×C22⋊Q8C2212yescomplemented
43C2×C11×#121C2211yescharacteristic
44C2×C11×#121C2211yescharacteristic
45C2×C11×#120—21no—
46C2×C4×D4×C11—21no—
47C2×C4×D4×C11—21no—
48C2×C11×#117C2211yescharacteristic
49C22×C11×C4⋊C4—21no—
50C22×C11×C4⋊C4C2211yescharacteristic, complemented
51C22×C11×C22⋊C4—21no—
52C11×#485C2218yescomplemented
53C11×#484C2214yescomplemented
54C11×#484C2214yescomplemented
55C11×#483C2214yescomplemented
56C11×#483C2214yescomplemented
57C11×#481C2214yescomplemented
58C11×#480C2214yescomplemented
59C11×#470C2218yescomplemented
60C11×#468C2218yescomplemented
61C11×#467C2218yescomplemented
62C11×#465C2218yescomplemented
63C11×#452C2218yescomplemented
64C11×#451C2214yescomplemented
65C11×#451C2214yescomplemented
66C11×#451C2214yescomplemented
67C11×#450C2214yescomplemented
68C11×#448C2214yescomplemented
69C11×#448C2214yescomplemented
70C11×#428C2214yescomplemented
71C11×#419C2214yescomplemented
72C11×#417C2214yescomplemented
73C11×#407C2212yes—
74C11×#407C2212yes—
75C11×#407C2212yescomplemented
76C11×#407C2212yescomplemented
77C2×C11×C22⋊C8C2212yes—
78C2×C11×C22⋊C8C2212yescomplemented
79C25×C11D411yescharacteristic
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41—44no—
83C2×C11×#41C2312yes—
84C2×C11×#41C2312yes—
85C22×Q8×C11—21no—
86C22×Q8×C11—21no—
87C22×Q8×C11—21no—
88C22×Q8×C11—44no—
89C22×Q8×C11C2312yes—
90C22×Q8×C11C2311yescharacteristic
91C22×Q8×C11C2312yes—
92C22×Q8×C11C2312yes—
93C22×D4×C11—21no—
94C22×D4×C11—21no—
95C22×D4×C11—21no—
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C23×C4×C11—21no—
99C23×C4×C11—21no—
100C23×C4×C11—44no—
101C23×C4×C11D411yescharacteristic
102C23×C4×C11D411yescharacteristic
103C23×C4×C11D411yescharacteristic
104C23×C4×C11D411yescharacteristic
105C23×C4×C11D411yescharacteristic
106C23×C4×C11D411yescharacteristic
107C23×C4×C11D411yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C23×C4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C23×C4×C11C2311yescharacteristic
115C11×#137—48no—
116C2×C11×Q16C2318yescomplemented
117C2×C11×SD16C2318yescomplemented
118C2×C11×M16—44no—
119C2×C11×M16C2314yes—
120C2×C11×M16C2314yes—
121C22×C8×C11C2314yes—
122C11×#123—22no—
123C11×#123—22no—
124C11×#123—22no—
125C11×#123—22no—
126C11×C22⋊Q8—22no—
127C11×C22⋊Q8—22no—
128C11×C22⋊Q8—22no—
129C11×C22⋊Q8—22no—
130C11×C22⋊Q8—22no—
131C11×C22⋊Q8—22no—
132C11×C22⋊Q8—22no—
133C11×C22⋊Q8—22no—
134C11×C22⋊Q8—22no—
135C11×C22⋊Q8—22no—
136C11×C22⋊Q8—22no—
137C11×C22⋊Q8—22no—
138C11×C22⋊Q8—21no—
139C11×C22⋊Q8—21no—
140C11×C22⋊Q8—21no—
141C11×C22⋊Q8—21no—
142C11×C22⋊Q8C2314yes—
143C11×C22⋊Q8C2314yes—
144C11×C22⋊Q8C2314yes—
145C11×C22⋊Q8C2314yes—
146C11×C22⋊Q8C2312yes—
147C11×C22⋊Q8C2312yes—
148C11×C22⋊Q8C2312yes—
149C11×C22⋊Q8C2312yes—
150C11×#121—21no—
151C11×#121—21no—
152C11×#121—21no—
153C11×#121—21no—
154C11×#121C2312yes—
155C11×#121C2312yes—
156C11×#121C2312yes—
157C11×#121C2312yes—
158C11×#120—22no—
159C11×#120—22no—
160C11×#120—22no—
161C11×#120—22no—
162C4×D4×C11—22no—
163C4×D4×C11—22no—
164C4×D4×C11—22no—
165C4×D4×C11—22no—
166C4×D4×C11—22no—
167C4×D4×C11—22no—
168C4×D4×C11—22no—
169C4×D4×C11—22no—
170C11×#117—21no—
171C11×#117—21no—
172C11×#117C2312yes—
173C11×#117C2312yes—
174C2×C11×C4⋊C4—22no—
175C2×C11×C4⋊C4—22no—
176C2×C11×C4⋊C4—22no—
177C2×C11×C4⋊C4—22no—
178C2×C11×C4⋊C4—22no—
179C2×C11×C4⋊C4—22no—
180C2×C11×C4⋊C4—21no—
181C2×C11×C4⋊C4—21no—
182C2×C11×C4⋊C4—21no—
183C2×C11×C4⋊C4—21no—
184C2×C11×C4⋊C4—21no—
185C2×C11×C4⋊C4C2312yes—
186C2×C11×C4⋊C4C2312yes—
187C2×C11×C4⋊C4C2312yes—
188C2×C11×C4⋊C4C2311yescharacteristic
189C2×C11×C4⋊C4C2311yescharacteristic
190C2×C11×C22⋊C4—22no—
191C2×C11×C22⋊C4—22no—
192C2×C11×C22⋊C4—22no—
193C2×C11×C22⋊C4—22no—
194C2×C11×C22⋊C4—22no—
195C2×C11×C22⋊C4—22no—
196C2×C11×C22⋊C4—21no—
197C2×C11×C22⋊C4—21no—
198C2×C11×C22⋊C4—21no—
199C2×C11×C22⋊C4—21no—
200C2×C11×C22⋊C4—21no—
201C2×C42×C11—21no—
202C11×#107C2318yescomplemented
203C11×#106C2318yescomplemented
204C11×#103C2318yescomplemented
205C11×#103C2318yescomplemented
206C11×#103C2318yescomplemented
207C11×#102C2318yescomplemented
208C11×C22⋊C8C2314yes—
209C11×C22⋊C8C2314yes—
210C11×C22⋊C8C2314yes—
211C11×C22⋊C8C2314yes—
212#60751C1111yesmaximal, characteristic, direct product factor, Sylow
213C24×C11—24no—
214C24×C11—21no—
215C24×C11—42no—
216C24×C11—42no—
217C24×C11C2×D411yescharacteristic
218C24×C11C2×D411yescharacteristic
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C24×C11C2×D411yescharacteristic
222C24×C11C2×D411yescharacteristic
223C24×C11C2×D411yescharacteristic
224C11×#41—28no—
225C11×#41—44no—
226C11×#41—44no—
227C11×#41—44no—
228C2×Q8×C11—22no—
229C2×Q8×C11—22no—
230C2×Q8×C11—22no—
231C2×Q8×C11—21no—
232C2×Q8×C11—28no—
233C2×Q8×C11—44no—
234C2×Q8×C11—44no—
235C2×Q8×C11—42no—
236C2×Q8×C11—44no—
237C2×Q8×C11—44no—
238C2×Q8×C11—44no—
239C2×Q8×C11C2414yes—
240C2×Q8×C11C2412yes—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—21no—
248C2×D4×C11—42no—
249C2×D4×C11—44no—
250C2×D4×C11—44no—
251C2×D4×C11—44no—
252C2×D4×C11C2412yes—
253C22×C4×C11—24no—
254C22×C4×C11—24no—
255C22×C4×C11—24no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—22no—
259C22×C4×C11—22no—
260C22×C4×C11—22no—
261C22×C4×C11—21no—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—22no—
266C22×C4×C11—22no—
267C22×C4×C11—42no—
268C22×C4×C11—42no—
269C22×C4×C11—42no—
270C22×C4×C11—42no—
271C22×C4×C11—42no—
272C22×C4×C11—42no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11—44no—
279C22×C4×C11—44no—
280C22×C4×C11—44no—
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D411yescharacteristic
283C22×C4×C11C2×D411yescharacteristic
284C22×C4×C11C2×D411yescharacteristic
285C22×C4×C11C2×D411yescharacteristic
286C22×C4×C11C2×D411yescharacteristic
287C22×C4×C11C2×D411yescharacteristic
288C22×C4×C11C2×D411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2×D411yescharacteristic
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2×D411yescharacteristic
299C22×C4×C11C2×D411yescharacteristic
300C22×C4×C11C2×D411yescharacteristic
301C22×C4×C11C2×D411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C11×Q16—48no—
310C11×SD16—48no—
311C11×M16—28no—
312C11×M16—44no—
313C2×C8×C11—44no—
314C2×C8×C11C2418yes—
315C11×C4⋊C4—24no—
316C11×C4⋊C4—24no—
317C11×C4⋊C4—24no—
318C11×C4⋊C4—24no—
319C11×C4⋊C4—22no—
320C11×C4⋊C4—22no—
321C11×C4⋊C4—22no—
322C11×C4⋊C4—22no—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—21no—
327C11×C4⋊C4—21no—
328C11×C4⋊C4C2414yes—
329C11×C4⋊C4C2412yes—
330C11×C4⋊C4C2412yes—
331C11×C22⋊C4—24no—
332C11×C22⋊C4—24no—
333C11×C22⋊C4—24no—
334C11×C22⋊C4—24no—
335C11×C22⋊C4—22no—
336C11×C22⋊C4—22no—
337C11×C22⋊C4—22no—
338C11×C22⋊C4—22no—
339C11×C22⋊C4—22no—
340C11×C22⋊C4—22no—
341C11×C22⋊C4—22no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—22no—
344C11×C22⋊C4—22no—
345C42×C11—22no—
346C42×C11—22no—
347C2×#525C2×C1111yescharacteristic
348C22×C22⋊Q8C2×C1111yescharacteristic, complemented
349#3196C2×C1114yescomplemented
350#3195C2×C1112yescomplemented
351#3193C2×C1112yescomplemented
352#3190C2×C1114yescomplemented
353#3189C2×C1112yescomplemented
354#3187C2×C1112yescomplemented
355#3095C2×C1112yescomplemented
356#3092C2×C1112yescomplemented
357#3056C2×C1114yescomplemented
358#3007C2×C1112yescomplemented
359#3004C2×C1112yescomplemented
360C2×#407C2×C1111yescharacteristic, complemented
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—416no—
383C23×C11—42no—
384C23×C11—42no—
385C23×C11—42no—
386C23×C11#13714yescomplemented
387C23×C11C22×D411yescharacteristic
388C23×C11C22×D411yescharacteristic
389C23×C11C22×D411yescharacteristic
390C23×C11C22×D411yescharacteristic
391C23×C11C22×D411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394Q8×C11—28no—
395Q8×C11—24no—
396Q8×C11—44no—
397Q8×C11—44no—
398Q8×C11—42no—
399Q8×C11—44no—
400D4×C11—24no—
401D4×C11—42no—
402D4×C11—44no—
403D4×C11—44no—
404D4×C11—44no—
405D4×C11—44no—
406D4×C11—44no—
407D4×C11—44no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—24no—
426C2×C4×C11—22no—
427C2×C4×C11—24no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—44no—
441C2×C4×C11—44no—
442C2×C4×C11—44no—
443C2×C4×C11—42no—
444C2×C4×C11—44no—
445C2×C4×C11—44no—
446C2×C4×C11—42no—
447C2×C4×C11—44no—
448C2×C4×C11—42no—
449C2×C4×C11—44no—
450C2×C4×C11—44no—
451C2×C4×C11C22×D411yescharacteristic
452C2×C4×C11C22×D411yescharacteristic
453C2×C4×C11C22×D411yescharacteristic
454C2×C4×C11C22×D411yescharacteristic
455C2×C4×C11C22×D411yescharacteristic
456C2×C4×C11C22×D411yescharacteristic
457C2×C4×C11C22×D411yescharacteristic
458C2×C4×C11H(5,𝔽2)14yes—
459C2×C4×C11C2511yescharacteristic
460C8×C11—28no—
461C22×#41C22×C1111yescharacteristic
462C23×Q8C22×C1111yescharacteristic, complemented
463C24×C4C22×C1111yescharacteristic
464C2×#137C22×C1114yescomplemented
465C22×M16C22×C1112yescomplemented
466#525—21no—
467#525—21no—
468#525—21no—
469#525—21no—
470#525C22×C1112yes—
471#525C22×C1112yes—
472#525C22×C1112yes—
473#525C22×C1112yes—
474C2×#123—21no—
475C2×C22⋊Q8—21no—
476C2×C22⋊Q8—21no—
477C2×C22⋊Q8—21no—
478C2×C22⋊Q8—21no—
479C2×C22⋊Q8—21no—
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8C22×C1112yes—
482C2×C22⋊Q8C22×C1112yes—
483C2×C22⋊Q8C22×C1112yes—
484C2×C22⋊Q8C22×C1111yescharacteristic
485C2×C22⋊Q8C22×C1111yescharacteristic
486C2×C22⋊Q8C22×C1112yescomplemented
487C2×C22⋊Q8C22×C1112yescomplemented
488C2×C22⋊Q8C22×C1112yescomplemented
489C2×#121C22×C1111yescharacteristic
490C2×#121C22×C1111yescharacteristic
491C2×#120—21no—
492C2×C4×D4—21no—
493C2×C4×D4—21no—
494C2×#117C22×C1111yescharacteristic
495C22×C4⋊C4—21no—
496C22×C4⋊C4C22×C1111yescharacteristic, complemented
497C22×C22⋊C4—21no—
498#485C22×C1118yescomplemented
499#484C22×C1114yescomplemented
500#484C22×C1114yescomplemented
501#483C22×C1114yescomplemented
502#483C22×C1114yescomplemented
503#481C22×C1114yescomplemented
504#480C22×C1114yescomplemented
505#470C22×C1118yescomplemented
506#468C22×C1118yescomplemented
507#467C22×C1118yescomplemented
508#465C22×C1118yescomplemented
509#452C22×C1118yescomplemented
510#451C22×C1114yescomplemented
511#451C22×C1114yescomplemented
512#451C22×C1114yescomplemented
513#450C22×C1114yescomplemented
514#448C22×C1114yescomplemented
515#448C22×C1114yescomplemented
516#428C22×C1114yescomplemented
517#419C22×C1114yescomplemented
518#417C22×C1114yescomplemented
519#407C22×C1112yes—
520#407C22×C1112yes—
521#407C22×C1112yescomplemented
522#407C22×C1112yescomplemented
523C2×C22⋊C8C22×C1112yes—
524C2×C22⋊C8C22×C1112yescomplemented
525C22×C11—28no—
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—21no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—21no—
540C22×C11—21no—
541C22×C11—21no—
542C22×C11—44no—
543C22×C11—44no—
544C22×C11—44no—
545C22×C11—44no—
546C22×C11—44no—
547C22×C11—44no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—84no—
552C22×C11#53412yes—
553C22×C11C2×#13712yes—
554C22×C11C2×#13712yes—
555C22×C11C2×#13712yes—
556C22×C11#57512yes—
557C22×C11C23×D411yescharacteristic
558C4×C11—21no—
559C4×C11—21no—
560C4×C11—21no—
561C4×C11—21no—
562C4×C11—21no—
563C4×C11—21no—
564C4×C11—42no—
565C4×C11—44no—
566C4×C11—42no—
567C4×C11—44no—
568C4×C11—42no—
569C4×C11#53412yes—
570C4×C11C2×H(5,𝔽2)12yes—
571C25D4×C1111yescharacteristic
572C2×#41—21no—
573C2×#41—21no—
574C2×#41—44no—
575C2×#41C23×C1112yes—
576C2×#41C23×C1112yes—
577C22×Q8—21no—
578C22×Q8—21no—
579C22×Q8—21no—
580C22×Q8—44no—
581C22×Q8C23×C1112yes—
582C22×Q8C23×C1111yescharacteristic
583C22×Q8C23×C1112yes—
584C22×Q8C23×C1112yes—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4C23×C1111yescharacteristic
589C23×C4—21no—
590C23×C4—21no—
591C23×C4—21no—
592C23×C4—44no—
593C23×C4D4×C1111yescharacteristic
594C23×C4D4×C1111yescharacteristic
595C23×C4D4×C1111yescharacteristic
596C23×C4D4×C1111yescharacteristic
597C23×C4D4×C1111yescharacteristic
598C23×C4D4×C1111yescharacteristic
599C23×C4D4×C1111yescharacteristic
600C23×C4C23×C1111yescharacteristic
601C23×C4C23×C1111yescharacteristic
602C23×C4C23×C1111yescharacteristic
603C23×C4C23×C1111yescharacteristic
604C23×C4C23×C1111yescharacteristic
605C23×C4C23×C1111yescharacteristic
606C23×C4C23×C1111yescharacteristic
607#137—48no—
608C2×Q16C23×C1118yescomplemented
609C2×SD16C23×C1118yescomplemented
610C2×M16—44no—
611C2×M16C23×C1114yes—
612C2×M16C23×C1114yes—
613C22×C8C23×C1114yes—
614#123—22no—
615#123—22no—
616#123—22no—
617#123—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—22no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—22no—
626C22⋊Q8—22no—
627C22⋊Q8—22no—
628C22⋊Q8—22no—
629C22⋊Q8—22no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634C22⋊Q8C23×C1114yes—
635C22⋊Q8C23×C1114yes—
636C22⋊Q8C23×C1114yes—
637C22⋊Q8C23×C1114yes—
638C22⋊Q8C23×C1112yes—
639C22⋊Q8C23×C1112yes—
640C22⋊Q8C23×C1112yes—
641C22⋊Q8C23×C1112yes—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121C23×C1112yes—
647#121C23×C1112yes—
648#121C23×C1112yes—
649#121C23×C1112yes—
650#120—22no—
651#120—22no—
652#120—22no—
653#120—22no—
654C4×D4—22no—
655C4×D4—22no—
656C4×D4—22no—
657C4×D4—22no—
658C4×D4—22no—
659C4×D4—22no—
660C4×D4—22no—
661C4×D4—22no—
662#117—21no—
663#117—21no—
664#117C23×C1112yes—
665#117C23×C1112yes—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4C23×C1112yes—
678C2×C4⋊C4C23×C1112yes—
679C2×C4⋊C4C23×C1112yes—
680C2×C4⋊C4C23×C1111yescharacteristic
681C2×C4⋊C4C23×C1111yescharacteristic
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C42—21no—
694#107C23×C1118yescomplemented
695#106C23×C1118yescomplemented
696#103C23×C1118yescomplemented
697#103C23×C1118yescomplemented
698#103C23×C1118yescomplemented
699#102C23×C1118yescomplemented
700C22⋊C8C23×C1114yes—
701C22⋊C8C23×C1114yes—
702C22⋊C8C23×C1114yes—
703C22⋊C8C23×C1114yes—
704C2×C11—22no—
705C2×C11—22no—
706C2×C11—22no—
707C2×C11—22no—
708C2×C11—22no—
709C2×C11—41no—
710C2×C11—41no—
711C2×C11—82no—
712C2×C11C2×#53411yescharacteristic
713C2×C11C22×#13711yescharacteristic
714C2×C11C2×#57511yescharacteristic
715C24—24no—
716C24—21no—
717C24—42no—
718C24—42no—
719C24C2×D4×C1111yescharacteristic
720C24C2×D4×C1111yescharacteristic
721C24C2×D4×C1111yescharacteristic
722C24C2×D4×C1111yescharacteristic
723C24C2×D4×C1111yescharacteristic
724C24C2×D4×C1111yescharacteristic
725C24C2×D4×C1111yescharacteristic
726#41—28no—
727#41—44no—
728#41—44no—
729#41—44no—
730C2×Q8—22no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—21no—
734C2×Q8—28no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—42no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—44no—
741C2×Q8C24×C1114yes—
742C2×Q8C24×C1112yes—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—21no—
750C2×D4—42no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4C24×C1112yes—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4C2×D4×C1111yescharacteristic
784C22×C4C2×D4×C1111yescharacteristic
785C22×C4C2×D4×C1111yescharacteristic
786C22×C4C2×D4×C1111yescharacteristic
787C22×C4C2×D4×C1111yescharacteristic
788C22×C4C2×D4×C1111yescharacteristic
789C22×C4C2×D4×C1111yescharacteristic
790C22×C4C2×D4×C1111yescharacteristic
791C22×C4C2×D4×C1111yescharacteristic
792C22×C4C2×D4×C1111yescharacteristic
793C22×C4C2×D4×C1111yescharacteristic
794C22×C4C2×D4×C1111yescharacteristic
795C22×C4C2×D4×C1111yescharacteristic
796C22×C4C2×D4×C1111yescharacteristic
797C22×C4C2×D4×C1111yescharacteristic
798C22×C4C2×D4×C1111yescharacteristic
799C22×C4C2×D4×C1111yescharacteristic
800C22×C4C2×D4×C1111yescharacteristic
801C22×C4C2×D4×C1111yescharacteristic
802C22×C4C2×D4×C1111yescharacteristic
803C22×C4C2×D4×C1111yescharacteristic
804C22×C4C24×C1111yescharacteristic
805C22×C4C24×C1111yescharacteristic
806C22×C4C24×C1111yescharacteristic
807C22×C4C24×C1111yescharacteristic
808C22×C4C24×C1111yescharacteristic
809C22×C4C24×C1111yescharacteristic
810C22×C4C24×C1111yescharacteristic
811Q16—48no—
812SD16—48no—
813M16—28no—
814M16—44no—
815C2×C8—44no—
816C2×C8C24×C1118yes—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4C24×C1114yes—
831C4⋊C4C24×C1112yes—
832C4⋊C4C24×C1112yes—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—22no—
840C22⋊C4—22no—
841C22⋊C4—22no—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—22no—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C42—22no—
848C42—22no—
849C11#6075111yescharacteristic, direct product factor, Sylow
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—416no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23C11×#13714yescomplemented
876C23C22×D4×C1111yescharacteristic
877C23C22×D4×C1111yescharacteristic
878C23C22×D4×C1111yescharacteristic
879C23C22×D4×C1111yescharacteristic
880C23C22×D4×C1111yescharacteristic
881C23C22×D4×C1111yescharacteristic
882C23C22×D4×C1111yescharacteristic
883Q8—28no—
884Q8—24no—
885Q8—44no—
886Q8—44no—
887Q8—42no—
888Q8—44no—
889D4—24no—
890D4—42no—
891D4—44no—
892D4—44no—
893D4—44no—
894D4—44no—
895D4—44no—
896D4—44no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—42no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—42no—
936C2×C4—44no—
937C2×C4—42no—
938C2×C4—44no—
939C2×C4—44no—
940C2×C4C22×D4×C1111yescharacteristic
941C2×C4C22×D4×C1111yescharacteristic
942C2×C4C22×D4×C1111yescharacteristic
943C2×C4C22×D4×C1111yescharacteristic
944C2×C4C22×D4×C1111yescharacteristic
945C2×C4C22×D4×C1111yescharacteristic
946C2×C4C22×D4×C1111yescharacteristic
947C2×C4C11×H(5,𝔽2)14yes—
948C2×C4C25×C1111yescharacteristic
949C8—28no—
950C22—28no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—84no—
977C22C11×#53412yes—
978C22C2×C11×#13712yes—
979C22C2×C11×#13712yes—
980C22C2×C11×#13712yes—
981C22C11×#57512yes—
982C22C23×D4×C1111yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—42no—
990C4—44no—
991C4—42no—
992C4—44no—
993C4—42no—
994C4C11×#53412yes—
995C4C2×C11×H(5,𝔽2)12yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—82no—
1004C2C2×C11×#53411yescharacteristic
1005C2C22×C11×#13711yescharacteristic
1006C2C2×C11×#57511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×C22⋊Q8C2semidirect
3. C11×#3196C2semidirect
4. C11×#3195C2semidirect
5. C11×#3193C2semidirect
6. C11×#3190C2semidirect
7. C11×#3189C2semidirect
8. C11×#3187C2semidirect
9. C11×#3095C2semidirect
10. C11×#3092C2semidirect
11. C11×#3056C2semidirect
12. C11×#3007C2semidirect
13. C11×#3004C2semidirect
14. C2×C11×#407C2semidirect
16. C23×Q8×C11C22semidirect
18. C2×C11×#137C22semidirect
19. C22×C11×M16C22semidirect
40. C2×C11×C22⋊Q8C22semidirect
41. C2×C11×C22⋊Q8C22semidirect
42. C2×C11×C22⋊Q8C22semidirect
50. C22×C11×C4⋊C4C22semidirect
52. C11×#485C22semidirect
53. C11×#484C22semidirect
54. C11×#484C22semidirect
55. C11×#483C22semidirect
56. C11×#483C22semidirect
57. C11×#481C22semidirect
58. C11×#480C22semidirect
59. C11×#470C22semidirect
60. C11×#468C22semidirect
61. C11×#467C22semidirect
62. C11×#465C22semidirect
63. C11×#452C22semidirect
64. C11×#451C22semidirect
65. C11×#451C22semidirect
66. C11×#451C22semidirect
67. C11×#450C22semidirect
68. C11×#448C22semidirect
69. C11×#448C22semidirect
70. C11×#428C22semidirect
71. C11×#419C22semidirect
72. C11×#417C22semidirect
75. C11×#407C22semidirect
76. C11×#407C22semidirect
78. C2×C11×C22⋊C8C22semidirect
116. C2×C11×Q16C23semidirect
117. C2×C11×SD16C23semidirect
202. C11×#107C23semidirect
203. C11×#106C23semidirect
204. C11×#103C23semidirect
205. C11×#103C23semidirect
206. C11×#103C23semidirect
207. C11×#102C23semidirect
212. #60751C11direct (N × H)
348. C22×C22⋊Q8C2×C11semidirect
349. #3196C2×C11semidirect
350. #3195C2×C11semidirect
351. #3193C2×C11semidirect
352. #3190C2×C11semidirect
353. #3189C2×C11semidirect
354. #3187C2×C11semidirect
355. #3095C2×C11semidirect
356. #3092C2×C11semidirect
357. #3056C2×C11semidirect
358. #3007C2×C11semidirect
359. #3004C2×C11semidirect
360. C2×#407C2×C11semidirect
386. C23×C11#137semidirect
462. C23×Q8C22×C11semidirect
464. C2×#137C22×C11semidirect
465. C22×M16C22×C11semidirect
486. C2×C22⋊Q8C22×C11semidirect
487. C2×C22⋊Q8C22×C11semidirect
488. C2×C22⋊Q8C22×C11semidirect
496. C22×C4⋊C4C22×C11semidirect
498. #485C22×C11semidirect
499. #484C22×C11semidirect
500. #484C22×C11semidirect
501. #483C22×C11semidirect
502. #483C22×C11semidirect
503. #481C22×C11semidirect
504. #480C22×C11semidirect
505. #470C22×C11semidirect
506. #468C22×C11semidirect
507. #467C22×C11semidirect
508. #465C22×C11semidirect
509. #452C22×C11semidirect
510. #451C22×C11semidirect
511. #451C22×C11semidirect
512. #451C22×C11semidirect
513. #450C22×C11semidirect
514. #448C22×C11semidirect
515. #448C22×C11semidirect
516. #428C22×C11semidirect
517. #419C22×C11semidirect
518. #417C22×C11semidirect
521. #407C22×C11semidirect
522. #407C22×C11semidirect
524. C2×C22⋊C8C22×C11semidirect
608. C2×Q16C23×C11semidirect
609. C2×SD16C23×C11semidirect
694. #107C23×C11semidirect
695. #106C23×C11semidirect
696. #103C23×C11semidirect
697. #103C23×C11semidirect
698. #103C23×C11semidirect
699. #102C23×C11semidirect
849. C11#60751direct (N × H)
875. C23C11×#137semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C22×C11×C22⋊Q82
C11×#31962
C11×#31952
C11×#31932
C11×#31902
C11×#31892
C11×#31872
C11×#30952
C11×#30922
C11×#30562
C11×#30072
C11×#30042
C2×C11×#4072
#6075111