Finite Group Databasebeta

← C11×#34473 #14611666

Subgroups — C11×#34473 #14611666

Order 2816.

2344 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic
2C11×#2377C212yesmaximal, complemented
3C11×#2376C212yesmaximal, complemented
4C11×#2374C212yesmaximal, complemented
5C11×#2365C211yesmaximal, characteristic, complemented
6C11×#2362C211yesmaximal, characteristic, complemented
7C11×#2360C211yesmaximal, characteristic, complemented
8C11×#2357C211yesmaximal, characteristic, complemented
9C11×#2352C211yesmaximal, characteristic, complemented
10C11×#2345C212yesmaximal, complemented
11C11×#2341C211yesmaximal, characteristic, complemented
12C11×#2341C211yesmaximal, characteristic, complemented
13C11×#2335C212yesmaximal, complemented
14C11×#2335C212yesmaximal, complemented
15C11×#2333C212yesmaximal, complemented
16C11×#2327C211yesmaximal, characteristic, complemented
17C11×#2323C211yesmaximal, characteristic, complemented
18C11×#2319C211yesmaximal, characteristic, complemented
19C11×#2313C212yesmaximal, complemented
20C11×#2311C211yesmaximal, characteristic, complemented
21C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
22C11×#2297C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C22×C11×#41C2211yescharacteristic
26C11×#547C4116yescomplemented
27C2×C11×C4⋊Q8C2211yescharacteristic
28C2×C11×#123C2212yes—
29C2×C11×#123C2212yes—
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C11×C22⋊Q8C2211yescharacteristic
32C2×C11×#121C2212yes—
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C4×Q8×C11C2211yescharacteristic
35C2×C4×Q8×C11C2211yescharacteristic
36C2×C4×Q8×C11C2211yescharacteristic
37C2×C4×D4×C11C2211yescharacteristic
38C2×C4×D4×C11C2211yescharacteristic
39C2×C11×#117C2211yescharacteristic
40C2×C11×#117C2211yescharacteristic
41C22×C11×C4⋊C4C2211yescharacteristic
42C22×C11×C4⋊C4C2212yes—
43C22×C42×C11C2211yescharacteristic
44C11×#391C2211yescharacteristic
45C11×#391C2211yescharacteristic
46C11×#391C2211yescharacteristic
47C11×#391C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#390C2212yes—
53C11×#390C2212yes—
54C11×#390C2212yes—
55C11×#390C2212yes—
56C11×#389C2211yescharacteristic
57C11×#389C2211yescharacteristic
58C11×#389C2212yes—
59C11×#389C2212yes—
60C11×#389C2212yes—
61C11×#388C2211yescharacteristic
62C11×#388C2211yescharacteristic
63C11×#388C2212yes—
64C11×#388C2212yes—
65C11×#388C2212yes—
66C11×#388C2212yes—
67C11×#388C2212yes—
68C11×#388C2212yes—
69C11×#388C2212yes—
70C11×#388C2212yes—
71C11×#388C2212yes—
72C11×#387C2211yescharacteristic
73C11×#387C2211yescharacteristic
74C11×#387C2212yes—
75C11×#387C2212yes—
76C11×#387C2212yes—
77C11×#387C2212yes—
78C11×#387C2212yes—
79C11×#387C2212yes—
80C11×#387C2212yes—
81C11×#387C2212yes—
82C11×#387C2212yes—
83C11×#387C2212yes—
84C11×#387C2212yes—
85C11×#386C2211yescharacteristic
86C11×#386C2211yescharacteristic
87C11×#386C2212yes—
88C11×#386C2212yes—
89C11×#386C2212yes—
90C11×#386C2212yes—
91C11×#386C2212yes—
92C11×#385C2211yescharacteristic
93C11×#385C2211yescharacteristic
94C11×#385C2212yes—
95C11×#385C2212yes—
96C11×#382C2211yescharacteristic
97C11×#381C2212yes—
98C11×#381C2212yes—
99C11×#380C2211yescharacteristic
100C11×#380C2212yes—
101C11×#380C2212yes—
102C11×#380C2212yes—
103C11×#380C2212yes—
104C11×#380C2211yescharacteristic
105C11×#380C2212yes—
106C4×C11×C4⋊C4C2211yescharacteristic
107C4×C11×C4⋊C4C2212yes—
108C4×C11×C4⋊C4C2211yescharacteristic
109C4×C11×C4⋊C4C2211yescharacteristic
110C4×C11×C4⋊C4C2211yescharacteristic
111C4×C11×C4⋊C4C2212yes—
112C4×C11×C4⋊C4C2212yes—
113C4×C11×C22⋊C4C2211yescharacteristic
114C4×C11×C22⋊C4C2211yescharacteristic
115C4×C11×C22⋊C4C2212yes—
116C4×C11×C22⋊C4C2212yes—
117C4×C11×C22⋊C4C2212yes—
118C4×C11×C22⋊C4C2212yes—
119C4×C11×C22⋊C4C2212yes—
120C4×C11×C22⋊C4C2212yes—
121C4×C11×C22⋊C4C2212yes—
122C4×C11×C22⋊C4C2212yes—
123C11×#376C2211yescharacteristic
124C2×C11×#41—42no—
125C2×C11×#41—42no—
126C2×C11×#41—42no—
127C2×C11×#41—42no—
128C2×C11×#41C2×C418yescomplemented
129C2×C11×#41C2×C418yescomplemented
130C22×Q8×C11C2311yescharacteristic
131C22×Q8×C11C2311yescharacteristic
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2311yescharacteristic
134C22×D4×C11C2312yes—
135C22×D4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C23×C4×C11C2311yescharacteristic
139C23×C4×C11C2311yescharacteristic
140C23×C4×C11C2312yes—
141C23×C4×C11C2312yes—
142C23×C4×C11C2312yes—
143C23×C4×C11C2312yes—
144C11×C4⋊Q8C2×C418yescomplemented
145C11×#123C2×C4116yescomplemented
146C11×#123C2×C4116yescomplemented
147C11×C22⋊Q8C2×C418yescomplemented
148C11×C22⋊Q8C2×C418yescomplemented
149C11×#121C2×C4116yes—
150C4×Q8×C11—42no—
151C4×Q8×C11—42no—
152C4×Q8×C11—42no—
153C4×Q8×C11—42no—
154C4×D4×C11C2×C418yes—
155C4×D4×C11C2×C418yescomplemented
156C11×#117—42no—
157C11×#117—42no—
158C2×C11×C4⋊C4—42no—
159C2×C11×C4⋊C4C2×C4116yescomplemented
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2312yes—
174C2×C11×C4⋊C4C2312yes—
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2312yes—
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C4⋊C4C2311yescharacteristic
180C2×C11×C4⋊C4C2312yes—
181C2×C11×C22⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2311yescharacteristic
184C2×C11×C22⋊C4C2311yescharacteristic
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2312yes—
192C2×C11×C22⋊C4C2312yes—
193C2×C11×C22⋊C4C2312yes—
194C2×C11×C22⋊C4C2312yes—
195C2×C11×C22⋊C4C2311yescharacteristic
196C2×C11×C22⋊C4C2311yescharacteristic
197C2×C11×C22⋊C4C2311yescharacteristic
198C2×C11×C22⋊C4C2311yescharacteristic
199C2×C11×C22⋊C4C2312yes—
200C2×C11×C22⋊C4C2312yes—
201C2×C11×C22⋊C4C2311yescharacteristic
202C2×C11×C22⋊C4C2312yes—
203C2×C42×C11—42no—
204C2×C42×C11C2311yescharacteristic
205C2×C42×C11C2311yescharacteristic
206C2×C42×C11C2311yescharacteristic
207C2×C42×C11C2311yescharacteristic
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2312yes—
211C2×C42×C11C2312yes—
212C2×C42×C11C2312yes—
213C2×C42×C11C2312yes—
214C2×C42×C11C2312yes—
215C2×C42×C11C2312yes—
216C2×C42×C11C2312yes—
217C2×C42×C11C2312yes—
218C2×C42×C11C2311yescharacteristic
219C11×#95C2311yescharacteristic
220C11×#95C2311yescharacteristic
221C11×#95C2311yescharacteristic
222C11×#95C2311yescharacteristic
223C11×#95C2311yescharacteristic
224C11×#95C2311yescharacteristic
225C11×#95C2312yes—
226C11×#95C2311yescharacteristic
227C11×#95C2312yes—
228C11×#95C2311yescharacteristic
229C11×#95C2311yescharacteristic
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2311yescharacteristic
244C11×#95C2312yes—
245C11×#95C2312yes—
246#34473C1111yesmaximal, characteristic, direct product factor, Sylow
247C24×C11C2411yescharacteristic
248C24×C11C2411yescharacteristic
249C24×C11C2412yes—
250C11×#41—416no—
251C11×#41—416no—
252C2×Q8×C11—22no—
253C2×Q8×C11—22no—
254C2×Q8×C11—22no—
255C2×Q8×C11—22no—
256C2×Q8×C11C22×C414yes—
257C2×Q8×C11C22×C414yes—
258C2×D4×C11—22no—
259C2×D4×C11—22no—
260C2×D4×C11—41no—
261C2×D4×C11—41no—
262C2×D4×C11—42no—
263C2×D4×C11—42no—
264C2×D4×C11—42no—
265C2×D4×C11—42no—
266C2×D4×C11C22×C414yes—
267C2×D4×C11C22×C414yes—
268C2×D4×C11C22×C418yes—
269C2×D4×C11C22×C418yes—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—22no—
274C22×C4×C11—22no—
275C22×C4×C11—41no—
276C22×C4×C11—41no—
277C22×C4×C11—41no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—41no—
281C22×C4×C11—41no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11C22×C414yes—
290C22×C4×C11C22×C414yes—
291C22×C4×C11C22×C418yes—
292C22×C4×C11C22×C418yes—
293C22×C4×C11C22×C418yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2412yes—
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C22×C4×C11C2412yes—
310C22×C4×C11C2412yes—
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2411yescharacteristic
314C11×C4⋊C4—22no—
315C11×C4⋊C4—22no—
316C11×C4⋊C4—22no—
317C11×C4⋊C4—22no—
318C11×C4⋊C4—22no—
319C11×C4⋊C4—42no—
320C11×C4⋊C4—41no—
321C11×C4⋊C4—42no—
322C11×C4⋊C4—42no—
323C11×C4⋊C4—41no—
324C11×C4⋊C4—41no—
325C11×C4⋊C4—42no—
326C11×C4⋊C4—42no—
327C11×C4⋊C4—42no—
328C11×C4⋊C4—42no—
329C11×C4⋊C4C22×C414yes—
330C11×C4⋊C4C22×C418yes—
331C11×C4⋊C4C22×C418yes—
332C11×C4⋊C4C22×C418yes—
333C11×C4⋊C4C22×C414yes—
334C11×C4⋊C4C22×C418yes—
335C11×C22⋊C4—22no—
336C11×C22⋊C4—24no—
337C11×C22⋊C4—41no—
338C11×C22⋊C4—42no—
339C11×C22⋊C4—42no—
340C11×C22⋊C4—42no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—41no—
346C11×C22⋊C4—41no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4—42no—
349C11×C22⋊C4—41no—
350C11×C22⋊C4—41no—
351C11×C22⋊C4—42no—
352C11×C22⋊C4C22×C414yes—
353C11×C22⋊C4C22×C414yes—
354C11×C22⋊C4C22×C418yes—
355C11×C22⋊C4C22×C418yes—
356C11×C22⋊C4C22×C418yes—
357C42×C11—22no—
358C42×C11—22no—
359C42×C11—22no—
360C42×C11—22no—
361C42×C11—41no—
362C42×C11—41no—
363C42×C11—42no—
364C42×C11—42no—
365C42×C11—42no—
366C42×C11—42no—
367C42×C11—42no—
368C42×C11—42no—
369C42×C11—42no—
370C42×C11—42no—
371C42×C11C22×C414yes—
372C2×#547C2×C1111yescharacteristic
373#2377C2×C1112yescomplemented
374#2376C2×C1112yescomplemented
375#2374C2×C1112yescomplemented
376#2365C2×C1111yescharacteristic, complemented
377#2362C2×C1111yescharacteristic, complemented
378#2360C2×C1111yescharacteristic, complemented
379#2357C2×C1111yescharacteristic, complemented
380#2352C2×C1111yescharacteristic, complemented
381#2345C2×C1112yescomplemented
382#2341C2×C1111yescharacteristic, complemented
383#2341C2×C1111yescharacteristic, complemented
384#2335C2×C1112yescomplemented
385#2335C2×C1112yescomplemented
386#2333C2×C1112yescomplemented
387#2327C2×C1111yescharacteristic, complemented
388#2323C2×C1111yescharacteristic, complemented
389#2319C2×C1111yescharacteristic, complemented
390#2313C2×C1112yescomplemented
391#2311C2×C1111yescharacteristic, complemented
392C4×C22⋊Q8C2×C1111yescharacteristic, complemented
393#2297C2×C1111yescharacteristic, complemented
394#2290C2×C1111yescharacteristic, complemented
395C23×C11—21no—
396C23×C11—21no—
397C23×C11—21no—
398C23×C11—21no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—21no—
403C23×C11—21no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—21no—
408C23×C11—21no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11C23×C412yes—
414C23×C11C23×C412yes—
415C23×C11C23×C414yes—
416C23×C11C2511yescharacteristic
417Q8×C11—28no—
418Q8×C11—28no—
419D4×C11—28no—
420D4×C11—44no—
421D4×C11—48no—
422D4×C11—48no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—28no—
440C2×C4×C11—28no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—21no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—22no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—22no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—48no—
475C2×C4×C11—48no—
476C2×C4×C11—48no—
477C2×C4×C11—44no—
478C2×C4×C11—44no—
479C2×C4×C11—84no—
480C2×C4×C11C23×C412yes—
481C2×C4×C11C23×C412yes—
482C2×C4×C11C23×C414yes—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C23×C412yes—
485C2×C4×C11C23×C414yes—
486C2×C4×C11C23×C414yes—
487C2×C4×C11C23×C412yes—
488C2×C4×C11H(5,𝔽2)12yes—
489C2×C4×C11H(5,𝔽2)12yes—
490C2×C4×C112−1+412yes—
491C22×#41C22×C1111yescharacteristic
492C22×#41C22×C1111yescharacteristic
493#547C4×C11116yescomplemented
494C2×C4⋊Q8C22×C1111yescharacteristic
495C2×#123C22×C1112yes—
496C2×#123C22×C1112yes—
497C2×C22⋊Q8C22×C1111yescharacteristic
498C2×C22⋊Q8C22×C1111yescharacteristic
499C2×#121C22×C1112yes—
500C2×C4×Q8C22×C1111yescharacteristic
501C2×C4×Q8C22×C1111yescharacteristic
502C2×C4×Q8C22×C1111yescharacteristic
503C2×C4×Q8C22×C1111yescharacteristic
504C2×C4×D4C22×C1111yescharacteristic
505C2×C4×D4C22×C1111yescharacteristic
506C2×#117C22×C1111yescharacteristic
507C2×#117C22×C1111yescharacteristic
508C22×C4⋊C4C22×C1111yescharacteristic
509C22×C4⋊C4C22×C1112yes—
510C22×C42C22×C1111yescharacteristic
511#391C22×C1111yescharacteristic
512#391C22×C1111yescharacteristic
513#391C22×C1111yescharacteristic
514#391C22×C1111yescharacteristic
515#390C22×C1111yescharacteristic
516#390C22×C1111yescharacteristic
517#390C22×C1111yescharacteristic
518#390C22×C1112yes—
519#390C22×C1112yes—
520#390C22×C1112yes—
521#390C22×C1112yes—
522#390C22×C1111yescharacteristic
523#389C22×C1111yescharacteristic
524#389C22×C1111yescharacteristic
525#389C22×C1112yes—
526#389C22×C1112yes—
527#389C22×C1112yes—
528#388C22×C1112yes—
529#388C22×C1112yes—
530#388C22×C1112yes—
531#388C22×C1112yes—
532#388C22×C1112yes—
533#388C22×C1111yescharacteristic
534#388C22×C1112yes—
535#388C22×C1112yes—
536#388C22×C1112yes—
537#388C22×C1112yes—
538#388C22×C1111yescharacteristic
539#387C22×C1111yescharacteristic
540#387C22×C1112yes—
541#387C22×C1112yes—
542#387C22×C1112yes—
543#387C22×C1112yes—
544#387C22×C1112yes—
545#387C22×C1112yes—
546#387C22×C1112yes—
547#387C22×C1112yes—
548#387C22×C1112yes—
549#387C22×C1112yes—
550#387C22×C1112yes—
551#387C22×C1111yescharacteristic
552#386C22×C1112yes—
553#386C22×C1112yes—
554#386C22×C1111yescharacteristic
555#386C22×C1112yes—
556#386C22×C1112yes—
557#386C22×C1112yes—
558#386C22×C1111yescharacteristic
559#385C22×C1111yescharacteristic
560#385C22×C1112yes—
561#385C22×C1111yescharacteristic
562#385C22×C1112yes—
563#382C22×C1111yescharacteristic
564#381C22×C1112yes—
565#381C22×C1112yes—
566#380C22×C1112yes—
567#380C22×C1112yes—
568#380C22×C1112yes—
569#380C22×C1112yes—
570#380C22×C1111yescharacteristic
571#380C22×C1112yes—
572#380C22×C1111yescharacteristic
573C4×C4⋊C4C22×C1111yescharacteristic
574C4×C4⋊C4C22×C1111yescharacteristic
575C4×C4⋊C4C22×C1112yes—
576C4×C4⋊C4C22×C1112yes—
577C4×C4⋊C4C22×C1112yes—
578C4×C4⋊C4C22×C1111yescharacteristic
579C4×C4⋊C4C22×C1111yescharacteristic
580C4×C22⋊C4C22×C1112yes—
581C4×C22⋊C4C22×C1112yes—
582C4×C22⋊C4C22×C1112yes—
583C4×C22⋊C4C22×C1112yes—
584C4×C22⋊C4C22×C1112yes—
585C4×C22⋊C4C22×C1112yes—
586C4×C22⋊C4C22×C1112yes—
587C4×C22⋊C4C22×C1111yescharacteristic
588C4×C22⋊C4C22×C1111yescharacteristic
589C4×C22⋊C4C22×C1112yes—
590#376C22×C1111yescharacteristic
591C22×C11—22no—
592C22×C11—22no—
593C22×C11—24no—
594C22×C11—24no—
595C22×C11—22no—
596C22×C11—22no—
597C22×C11—24no—
598C22×C11—22no—
599C22×C11—22no—
600C22×C11—41no—
601C22×C11—41no—
602C22×C11—42no—
603C22×C11—41no—
604C22×C11—41no—
605C22×C11—42no—
606C22×C11—41no—
607C22×C11—41no—
608C22×C11—42no—
609C22×C11—41no—
610C22×C11—41no—
611C22×C11—42no—
612C22×C11C24×C411yescharacteristic
613C22×C11C2×H(5,𝔽2)11yescharacteristic
614C22×C11C2×H(5,𝔽2)11yescharacteristic
615C22×C11C2×2−1+411yescharacteristic
616C22×C11#58511yescharacteristic
617C22×C11#58511yescharacteristic
618C22×C11#58511yescharacteristic
619C4×C11—22no—
620C4×C11—22no—
621C4×C11—24no—
622C4×C11—24no—
623C4×C11—22no—
624C4×C11—24no—
625C4×C11—22no—
626C4×C11—22no—
627C4×C11—41no—
628C4×C11—42no—
629C4×C11—41no—
630C4×C11—41no—
631C4×C11—41no—
632C4×C11—41no—
633C4×C11—41no—
634C4×C11—42no—
635C4×C11—41no—
636C4×C11—42no—
637C4×C11—42no—
638C4×C11#51814yes—
639C2×#41—42no—
640C2×#41—42no—
641C2×#41—42no—
642C2×#41—42no—
643C2×#41C2×C4×C1118yescomplemented
644C2×#41C2×C4×C1118yescomplemented
645C22×Q8C23×C1111yescharacteristic
646C22×Q8C23×C1111yescharacteristic
647C22×D4C23×C1111yescharacteristic
648C22×D4C23×C1111yescharacteristic
649C22×D4C23×C1112yes—
650C22×D4C23×C1112yes—
651C23×C4C23×C1111yescharacteristic
652C23×C4C23×C1111yescharacteristic
653C23×C4C23×C1111yescharacteristic
654C23×C4C23×C1112yes—
655C23×C4C23×C1111yescharacteristic
656C23×C4C23×C1112yes—
657C23×C4C23×C1112yes—
658C23×C4C23×C1112yes—
659C4⋊Q8C2×C4×C1118yescomplemented
660#123C2×C4×C11116yescomplemented
661#123C2×C4×C11116yescomplemented
662C22⋊Q8C2×C4×C1118yescomplemented
663C22⋊Q8C2×C4×C1118yescomplemented
664#121C2×C4×C11116yes—
665C4×Q8—42no—
666C4×Q8—42no—
667C4×Q8—42no—
668C4×Q8—42no—
669C4×D4C2×C4×C1118yes—
670C4×D4C2×C4×C1118yescomplemented
671#117—42no—
672#117—42no—
673C2×C4⋊C4—42no—
674C2×C4⋊C4C2×C4×C11116yescomplemented
675C2×C4⋊C4C23×C1111yescharacteristic
676C2×C4⋊C4C23×C1111yescharacteristic
677C2×C4⋊C4C23×C1111yescharacteristic
678C2×C4⋊C4C23×C1111yescharacteristic
679C2×C4⋊C4C23×C1111yescharacteristic
680C2×C4⋊C4C23×C1112yes—
681C2×C4⋊C4C23×C1111yescharacteristic
682C2×C4⋊C4C23×C1111yescharacteristic
683C2×C4⋊C4C23×C1112yes—
684C2×C4⋊C4C23×C1112yes—
685C2×C4⋊C4C23×C1112yes—
686C2×C4⋊C4C23×C1112yes—
687C2×C4⋊C4C23×C1112yes—
688C2×C4⋊C4C23×C1112yes—
689C2×C4⋊C4C23×C1111yescharacteristic
690C2×C4⋊C4C23×C1111yescharacteristic
691C2×C4⋊C4C23×C1112yes—
692C2×C4⋊C4C23×C1112yes—
693C2×C4⋊C4C23×C1112yes—
694C2×C4⋊C4C23×C1111yescharacteristic
695C2×C4⋊C4C23×C1112yes—
696C2×C22⋊C4C23×C1112yes—
697C2×C22⋊C4C23×C1111yescharacteristic
698C2×C22⋊C4C23×C1111yescharacteristic
699C2×C22⋊C4C23×C1111yescharacteristic
700C2×C22⋊C4C23×C1112yes—
701C2×C22⋊C4C23×C1112yes—
702C2×C22⋊C4C23×C1112yes—
703C2×C22⋊C4C23×C1112yes—
704C2×C22⋊C4C23×C1112yes—
705C2×C22⋊C4C23×C1112yes—
706C2×C22⋊C4C23×C1112yes—
707C2×C22⋊C4C23×C1112yes—
708C2×C22⋊C4C23×C1112yes—
709C2×C22⋊C4C23×C1112yes—
710C2×C22⋊C4C23×C1111yescharacteristic
711C2×C22⋊C4C23×C1111yescharacteristic
712C2×C22⋊C4C23×C1111yescharacteristic
713C2×C22⋊C4C23×C1111yescharacteristic
714C2×C22⋊C4C23×C1111yescharacteristic
715C2×C22⋊C4C23×C1112yes—
716C2×C22⋊C4C23×C1112yes—
717C2×C22⋊C4C23×C1112yes—
718C2×C42—42no—
719C2×C42C23×C1111yescharacteristic
720C2×C42C23×C1111yescharacteristic
721C2×C42C23×C1111yescharacteristic
722C2×C42C23×C1111yescharacteristic
723C2×C42C23×C1112yes—
724C2×C42C23×C1112yes—
725C2×C42C23×C1112yes—
726C2×C42C23×C1112yes—
727C2×C42C23×C1112yes—
728C2×C42C23×C1112yes—
729C2×C42C23×C1111yescharacteristic
730C2×C42C23×C1111yescharacteristic
731C2×C42C23×C1112yes—
732C2×C42C23×C1112yes—
733C2×C42C23×C1111yescharacteristic
734#95C23×C1111yescharacteristic
735#95C23×C1111yescharacteristic
736#95C23×C1111yescharacteristic
737#95C23×C1111yescharacteristic
738#95C23×C1111yescharacteristic
739#95C23×C1111yescharacteristic
740#95C23×C1112yes—
741#95C23×C1111yescharacteristic
742#95C23×C1112yes—
743#95C23×C1111yescharacteristic
744#95C23×C1111yescharacteristic
745#95C23×C1112yes—
746#95C23×C1112yes—
747#95C23×C1112yes—
748#95C23×C1112yes—
749#95C23×C1112yes—
750#95C23×C1112yes—
751#95C23×C1112yes—
752#95C23×C1112yes—
753#95C23×C1112yes—
754#95C23×C1112yes—
755#95C23×C1112yes—
756#95C23×C1112yes—
757#95C23×C1112yes—
758#95C23×C1111yescharacteristic
759#95C23×C1112yes—
760#95C23×C1112yes—
761C2×C11—42no—
762C2×C11—42no—
763C2×C11—44no—
764C2×C11C2×#51811yescharacteristic
765C2×C11#342811yescharacteristic
766C2×C11C4×2−1+411yescharacteristic
767C2×C11#353911yescharacteristic
768C2×C11#354111yescharacteristic
769C2×C11#355411yescharacteristic
770C2×C11#356211yescharacteristic
771C24C24×C1111yescharacteristic
772C24C24×C1111yescharacteristic
773C24C24×C1112yes—
774#41—416no—
775#41—416no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8C22×C4×C1114yes—
781C2×Q8C22×C4×C1114yes—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4C22×C4×C1114yes—
791C2×D4C22×C4×C1114yes—
792C2×D4C22×C4×C1118yes—
793C2×D4C22×C4×C1118yes—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—41no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4C22×C4×C1114yes—
814C22×C4C22×C4×C1114yes—
815C22×C4C22×C4×C1118yes—
816C22×C4C22×C4×C1118yes—
817C22×C4C22×C4×C1118yes—
818C22×C4C24×C1111yescharacteristic
819C22×C4C24×C1111yescharacteristic
820C22×C4C24×C1111yescharacteristic
821C22×C4C24×C1112yes—
822C22×C4C24×C1111yescharacteristic
823C22×C4C24×C1111yescharacteristic
824C22×C4C24×C1112yes—
825C22×C4C24×C1112yes—
826C22×C4C24×C1111yescharacteristic
827C22×C4C24×C1111yescharacteristic
828C22×C4C24×C1112yes—
829C22×C4C24×C1111yescharacteristic
830C22×C4C24×C1111yescharacteristic
831C22×C4C24×C1111yescharacteristic
832C22×C4C24×C1112yes—
833C22×C4C24×C1112yes—
834C22×C4C24×C1112yes—
835C22×C4C24×C1111yescharacteristic
836C22×C4C24×C1111yescharacteristic
837C22×C4C24×C1111yescharacteristic
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—42no—
844C4⋊C4—41no—
845C4⋊C4—41no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—42no—
850C4⋊C4—41no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4C22×C4×C1114yes—
854C4⋊C4C22×C4×C1118yes—
855C4⋊C4C22×C4×C1118yes—
856C4⋊C4C22×C4×C1118yes—
857C4⋊C4C22×C4×C1114yes—
858C4⋊C4C22×C4×C1118yes—
859C22⋊C4—24no—
860C22⋊C4—22no—
861C22⋊C4—41no—
862C22⋊C4—41no—
863C22⋊C4—42no—
864C22⋊C4—41no—
865C22⋊C4—42no—
866C22⋊C4—42no—
867C22⋊C4—42no—
868C22⋊C4—42no—
869C22⋊C4—42no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—41no—
873C22⋊C4—41no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4C22×C4×C1114yes—
877C22⋊C4C22×C4×C1114yes—
878C22⋊C4C22×C4×C1118yes—
879C22⋊C4C22×C4×C1118yes—
880C22⋊C4C22×C4×C1118yes—
881C42—22no—
882C42—22no—
883C42—22no—
884C42—22no—
885C42—41no—
886C42—41no—
887C42—42no—
888C42—42no—
889C42—42no—
890C42—42no—
891C42—42no—
892C42—42no—
893C42—42no—
894C42—42no—
895C42C22×C4×C1114yes—
896C11#3447311yescharacteristic, direct product factor, Sylow
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23C23×C4×C1112yes—
916C23C23×C4×C1112yes—
917C23C23×C4×C1114yes—
918C23C25×C1111yescharacteristic
919Q8—28no—
920Q8—28no—
921D4—28no—
922D4—44no—
923D4—48no—
924D4—48no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—28no—
942C2×C4—28no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—48no—
977C2×C4—48no—
978C2×C4—48no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—84no—
982C2×C4C23×C4×C1112yes—
983C2×C4C23×C4×C1112yes—
984C2×C4C23×C4×C1114yes—
985C2×C4C23×C4×C1112yes—
986C2×C4C23×C4×C1112yes—
987C2×C4C23×C4×C1114yes—
988C2×C4C23×C4×C1114yes—
989C2×C4C23×C4×C1112yes—
990C2×C4C11×H(5,𝔽2)12yes—
991C2×C4C11×H(5,𝔽2)12yes—
992C2×C4C11×2−1+412yes—
993C22—22no—
994C22—22no—
995C22—24no—
996C22—24no—
997C22—22no—
998C22—22no—
999C22—24no—
1000C22—22no—
1001C22—22no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—42no—
1014C22C24×C4×C1111yescharacteristic
1015C22C2×C11×H(5,𝔽2)11yescharacteristic
1016C22C2×C11×H(5,𝔽2)11yescharacteristic
1017C22C2×C11×2−1+411yescharacteristic
1018C22C11×#58511yescharacteristic
1019C22C11×#58511yescharacteristic
1020C22C11×#58511yescharacteristic
1021C4—22no—
1022C4—22no—
1023C4—24no—
1024C4—24no—
1025C4—22no—
1026C4—24no—
1027C4—22no—
1028C4—22no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—42no—
1037C4—42no—
1038C4—42no—
1039C4—41no—
1040C4C11×#51814yes—
1041C2—42no—
1042C2—42no—
1043C2—44no—
1044C2C2×C11×#51811yescharacteristic
1045C2C11×#342811yescharacteristic
1046C2C4×C11×2−1+411yescharacteristic
1047C2C11×#353911yescharacteristic
1048C2C11×#354111yescharacteristic
1049C2C11×#355411yescharacteristic
1050C2C11×#356211yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#547C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2377C2semidirect
3. C11×#2376C2semidirect
4. C11×#2374C2semidirect
5. C11×#2365C2semidirect
6. C11×#2362C2semidirect
7. C11×#2360C2semidirect
8. C11×#2357C2semidirect
9. C11×#2352C2semidirect
10. C11×#2345C2semidirect
11. C11×#2341C2semidirect
12. C11×#2341C2semidirect
13. C11×#2335C2semidirect
14. C11×#2335C2semidirect
15. C11×#2333C2semidirect
16. C11×#2327C2semidirect
17. C11×#2323C2semidirect
18. C11×#2319C2semidirect
19. C11×#2313C2semidirect
20. C11×#2311C2semidirect
21. C4×C11×C22⋊Q8C2semidirect
22. C11×#2297C2semidirect
23. C11×#2290C2semidirect
26. C11×#547C4semidirect
128. C2×C11×#41C2×C4semidirect
129. C2×C11×#41C2×C4semidirect
144. C11×C4⋊Q8C2×C4semidirect
145. C11×#123C2×C4semidirect
146. C11×#123C2×C4semidirect
147. C11×C22⋊Q8C2×C4semidirect
148. C11×C22⋊Q8C2×C4semidirect
155. C4×D4×C11C2×C4semidirect
159. C2×C11×C4⋊C4C2×C4semidirect
246. #34473C11direct (N × H)
373. #2377C2×C11semidirect
374. #2376C2×C11semidirect
375. #2374C2×C11semidirect
376. #2365C2×C11semidirect
377. #2362C2×C11semidirect
378. #2360C2×C11semidirect
379. #2357C2×C11semidirect
380. #2352C2×C11semidirect
381. #2345C2×C11semidirect
382. #2341C2×C11semidirect
383. #2341C2×C11semidirect
384. #2335C2×C11semidirect
385. #2335C2×C11semidirect
386. #2333C2×C11semidirect
387. #2327C2×C11semidirect
388. #2323C2×C11semidirect
389. #2319C2×C11semidirect
390. #2313C2×C11semidirect
391. #2311C2×C11semidirect
392. C4×C22⋊Q8C2×C11semidirect
393. #2297C2×C11semidirect
394. #2290C2×C11semidirect
493. #547C4×C11semidirect
643. C2×#41C2×C4×C11semidirect
644. C2×#41C2×C4×C11semidirect
659. C4⋊Q8C2×C4×C11semidirect
660. #123C2×C4×C11semidirect
661. #123C2×C4×C11semidirect
662. C22⋊Q8C2×C4×C11semidirect
663. C22⋊Q8C2×C4×C11semidirect
670. C4×D4C2×C4×C11semidirect
674. C2×C4⋊C4C2×C4×C11semidirect
896. C11#34473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C11×#23772
C11×#23762
C11×#23742
C11×#23652
C11×#23622
C11×#23602
C11×#23572
C11×#23522
C11×#23452
C11×#23412
C11×#23352
C11×#23332
C11×#23272
C11×#23232
C11×#23192
C11×#23132
C11×#23112
C4×C11×C22⋊Q82
C11×#22972
C11×#22902
#3447311