Finite Group Databasebeta

← C11×#34474 #14611667

Subgroups — C11×#34474 #14611667

Order 2816.

2352 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#548C211yesmaximal, characteristic
2C11×#2379C212yesmaximal, complemented
3C11×#2377C212yesmaximal, complemented
4C11×#2368C212yesmaximal, complemented
5C11×#2367C211yesmaximal, characteristic, complemented
6C11×#2363C211yesmaximal, characteristic, complemented
7C11×#2362C211yesmaximal, characteristic, complemented
8C11×#2357C212yesmaximal, complemented
9C11×#2355C211yesmaximal, characteristic, complemented
10C11×#2354C211yesmaximal, characteristic, complemented
11Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C11×#2339C211yesmaximal, characteristic, complemented
13C11×#2337C212yesmaximal, complemented
14C11×#2333C212yesmaximal, complemented
15C11×#2332C212yesmaximal, complemented
16C11×#2326C211yesmaximal, characteristic, complemented
17C11×#2324C211yesmaximal, characteristic, complemented
18C11×#2320C211yesmaximal, characteristic, complemented
19C11×#2318C212yesmaximal, complemented
20C11×#2310C211yesmaximal, characteristic, complemented
21C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
22C11×#2297C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C23×Q8×C11C2211yescharacteristic
26C11×#548C4116yescomplemented
27C2×C11×#124C2212yes—
28C2×C11×#124C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×C22⋊Q8C2212yes—
31C2×C11×#121C2211yescharacteristic
32C2×C11×#121C2212yes—
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C4×Q8×C11C2211yescharacteristic
35C2×C4×Q8×C11C2211yescharacteristic
36C2×C4×D4×C11C2211yescharacteristic
37C2×C4×D4×C11C2211yescharacteristic
38C2×C4×D4×C11C2211yescharacteristic
39C2×C4×D4×C11C2212yes—
40C2×C11×#117C2211yescharacteristic
41C2×C11×#117C2211yescharacteristic
42C2×C11×#117C2211yescharacteristic
43C22×C42×C11C2211yescharacteristic
44C11×#391C2212yes—
45C11×#391C2212yes—
46C11×#391C2211yescharacteristic
47C11×#391C2211yescharacteristic
48C11×#391C2211yescharacteristic
49C11×#391C2212yes—
50C11×#391C2211yescharacteristic
51C11×#391C2211yescharacteristic
52C11×#391C2211yescharacteristic
53C11×#391C2212yes—
54C11×#390C2211yescharacteristic
55C11×#390C2211yescharacteristic
56C11×#390C2212yes—
57C11×#390C2212yes—
58C11×#390C2212yes—
59C11×#389C2211yescharacteristic
60C11×#389C2211yescharacteristic
61C11×#388C2212yes—
62C11×#388C2212yes—
63C11×#388C2212yes—
64C11×#388C2212yes—
65C11×#388C2211yescharacteristic
66C11×#388C2211yescharacteristic
67C11×#388C2212yes—
68C11×#388C2212yes—
69C11×#388C2212yes—
70C11×#388C2212yes—
71C11×#388C2212yes—
72C11×#388C2212yes—
73C11×#387C2211yescharacteristic
74C11×#387C2211yescharacteristic
75C11×#387C2212yes—
76C11×#387C2212yes—
77C11×#387C2212yes—
78C11×#387C2212yes—
79C11×#387C2212yes—
80C11×#387C2212yes—
81C11×#386C2212yes—
82C11×#386C2212yes—
83C11×#386C2211yescharacteristic
84C11×#386C2211yescharacteristic
85C11×#386C2212yes—
86C11×#386C2212yes—
87C11×#386C2212yes—
88C11×#386C2212yes—
89C11×#385C2211yescharacteristic
90C11×#385C2212yes—
91C11×#385C2212yes—
92C11×#385C2212yes—
93C11×#385C2211yescharacteristic
94C11×#385C2212yes—
95C11×#385C2212yes—
96C11×#384C2211yescharacteristic
97C11×#383C2212yes—
98C11×#382C2212yes—
99C11×#382C2212yes—
100C11×#381C2212yes—
101C11×#381C2212yes—
102C11×#381C2212yes—
103C11×#380C2211yescharacteristic
104C11×#380C2212yes—
105C11×#380C2211yescharacteristic
106C4×C11×C4⋊C4C2211yescharacteristic
107C4×C11×C4⋊C4C2211yescharacteristic
108C4×C11×C4⋊C4C2212yes—
109C4×C11×C4⋊C4C2211yescharacteristic
110C4×C11×C4⋊C4C2211yescharacteristic
111C4×C11×C4⋊C4C2212yes—
112C4×C11×C4⋊C4C2212yes—
113C4×C11×C4⋊C4C2212yes—
114C4×C11×C22⋊C4C2211yescharacteristic
115C4×C11×C22⋊C4C2211yescharacteristic
116C4×C11×C22⋊C4C2212yes—
117C4×C11×C22⋊C4C2212yes—
118C4×C11×C22⋊C4C2212yes—
119C4×C11×C22⋊C4C2212yes—
120C4×C11×C22⋊C4C2212yes—
121C4×C11×C22⋊C4C2212yes—
122C11×#376C2211yescharacteristic
123C2×C11×#95C2212yes—
124C2×C11×#41—42no—
125C2×C11×#41—42no—
126C2×C11×#41C2×C418yes—
127C22×Q8×C11—42no—
128C22×Q8×C11—42no—
129C22×Q8×C11C2×C418yescomplemented
130C22×Q8×C11C2311yescharacteristic
131C22×Q8×C11C2311yescharacteristic
132C22×Q8×C11C2312yes—
133C22×D4×C11C2311yescharacteristic
134C22×D4×C11C2311yescharacteristic
135C22×D4×C11C2312yes—
136C22×D4×C11C2312yes—
137C23×C4×C11C2311yescharacteristic
138C23×C4×C11C2311yescharacteristic
139C23×C4×C11C2311yescharacteristic
140C23×C4×C11C2311yescharacteristic
141C23×C4×C11C2312yes—
142C23×C4×C11C2312yes—
143C23×C4×C11C2312yes—
144C23×C4×C11C2312yes—
145C11×#124C2×C418yescomplemented
146C11×#124C2×C4116yescomplemented
147C11×C22⋊Q8C2×C418yescomplemented
148C11×C22⋊Q8C2×C4116yescomplemented
149C11×#121C2×C418yescomplemented
150C11×#121C2×C4116yescomplemented
151C4×Q8×C11—42no—
152C4×Q8×C11—42no—
153C4×Q8×C11C2×C418yescomplemented
154C4×D4×C11—42no—
155C4×D4×C11—42no—
156C4×D4×C11C2×C418yescomplemented
157C4×D4×C11C2×C4116yescomplemented
158C11×#117—42no—
159C11×#117—42no—
160C11×#117—42no—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2312yes—
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⋊C4C2311yescharacteristic
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4C2311yescharacteristic
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2311yescharacteristic
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2311yescharacteristic
190C2×C11×C22⋊C4C2311yescharacteristic
191C2×C11×C22⋊C4C2312yes—
192C2×C11×C22⋊C4C2312yes—
193C2×C11×C22⋊C4C2312yes—
194C2×C11×C22⋊C4C2312yes—
195C2×C11×C22⋊C4C2312yes—
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2312yes—
198C2×C11×C22⋊C4C2311yescharacteristic
199C2×C11×C22⋊C4C2311yescharacteristic
200C2×C11×C22⋊C4C2312yes—
201C2×C42×C11—42no—
202C2×C42×C11C2311yescharacteristic
203C2×C42×C11C2311yescharacteristic
204C2×C42×C11C2311yescharacteristic
205C2×C42×C11C2311yescharacteristic
206C2×C42×C11C2311yescharacteristic
207C2×C42×C11C2311yescharacteristic
208C2×C42×C11C2312yes—
209C2×C42×C11C2312yes—
210C2×C42×C11C2312yes—
211C2×C42×C11C2312yes—
212C2×C42×C11C2312yes—
213C2×C42×C11C2312yes—
214C2×C42×C11C2312yes—
215C2×C42×C11C2311yescharacteristic
216C2×C42×C11C2312yes—
217C11×#95C2311yescharacteristic
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11×#95C2312yes—
221C11×#95C2311yescharacteristic
222C11×#95C2311yescharacteristic
223C11×#95C2311yescharacteristic
224C11×#95C2311yescharacteristic
225C11×#95C2311yescharacteristic
226C11×#95C2311yescharacteristic
227C11×#95C2312yes—
228C11×#95C2311yescharacteristic
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2311yescharacteristic
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246#34474C1111yesmaximal, characteristic, direct product factor, Sylow
247C24×C11C2411yescharacteristic
248C24×C11C2411yescharacteristic
249C24×C11C2412yes—
250C11×#41—416no—
251C2×Q8×C11—22no—
252C2×Q8×C11—22no—
253C2×Q8×C11—22no—
254C2×Q8×C11—22no—
255C2×Q8×C11—42no—
256C2×Q8×C11—42no—
257C2×Q8×C11—416no—
258C2×Q8×C11C22×C414yes—
259C2×Q8×C11C22×C414yes—
260C2×Q8×C11C22×C418yes—
261C2×D4×C11—22no—
262C2×D4×C11—22no—
263C2×D4×C11—41no—
264C2×D4×C11—42no—
265C2×D4×C11—42no—
266C2×D4×C11—41no—
267C2×D4×C11—42no—
268C2×D4×C11—42no—
269C2×D4×C11C22×C414yes—
270C2×D4×C11C22×C414yes—
271C2×D4×C11C22×C418yes—
272C2×D4×C11C22×C418yes—
273C22×C4×C11—22no—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—22no—
278C22×C4×C11—41no—
279C22×C4×C11—41no—
280C22×C4×C11—41no—
281C22×C4×C11—41no—
282C22×C4×C11—41no—
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×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11—42no—
292C22×C4×C11—42no—
293C22×C4×C11C22×C414yes—
294C22×C4×C11C22×C414yes—
295C22×C4×C11C22×C418yes—
296C22×C4×C11C22×C418yes—
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2412yes—
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2412yes—
306C22×C4×C11C2412yes—
307C22×C4×C11C2412yes—
308C22×C4×C11C2412yes—
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2412yes—
313C22×C4×C11C2411yescharacteristic
314C22×C4×C11C2412yes—
315C22×C4×C11C2411yescharacteristic
316C22×C4×C11C2411yescharacteristic
317C11×C4⋊C4—22no—
318C11×C4⋊C4—22no—
319C11×C4⋊C4—22no—
320C11×C4⋊C4—22no—
321C11×C4⋊C4—22no—
322C11×C4⋊C4—42no—
323C11×C4⋊C4—41no—
324C11×C4⋊C4—42no—
325C11×C4⋊C4—42no—
326C11×C4⋊C4—42no—
327C11×C4⋊C4—41no—
328C11×C4⋊C4—41no—
329C11×C4⋊C4—42no—
330C11×C4⋊C4—42no—
331C11×C4⋊C4C22×C414yes—
332C11×C4⋊C4C22×C418yes—
333C11×C4⋊C4C22×C418yes—
334C11×C4⋊C4C22×C414yes—
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—41no—
344C11×C22⋊C4—41no—
345C11×C22⋊C4—41no—
346C11×C22⋊C4—41no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4—42no—
349C11×C22⋊C4—42no—
350C11×C22⋊C4—42no—
351C11×C22⋊C4C22×C414yes—
352C11×C22⋊C4C22×C414yes—
353C11×C22⋊C4C22×C418yes—
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×C11C22×C418yes—
371C42×C11C22×C414yes—
372C2×#548C2×C1111yescharacteristic
373#2379C2×C1112yescomplemented
374#2377C2×C1112yescomplemented
375#2368C2×C1112yescomplemented
376#2367C2×C1111yescharacteristic, complemented
377#2363C2×C1111yescharacteristic, complemented
378#2362C2×C1111yescharacteristic, complemented
379#2357C2×C1112yescomplemented
380#2355C2×C1111yescharacteristic, complemented
381#2354C2×C1111yescharacteristic, complemented
382Q8×C22⋊C4C2×C1111yescharacteristic, complemented
383#2339C2×C1111yescharacteristic, complemented
384#2337C2×C1112yescomplemented
385#2333C2×C1112yescomplemented
386#2332C2×C1112yescomplemented
387#2326C2×C1111yescharacteristic, complemented
388#2324C2×C1111yescharacteristic, complemented
389#2320C2×C1111yescharacteristic, complemented
390#2318C2×C1112yescomplemented
391#2310C2×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—22no—
399C23×C11—22no—
400C23×C11—21no—
401C23×C11—21no—
402C23×C11—22no—
403C23×C11—21no—
404C23×C11—21no—
405C23×C11—21no—
406C23×C11—22no—
407C23×C11—21no—
408C23×C11—22no—
409C23×C11—21no—
410C23×C11—22no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11C23×C412yes—
414C23×C11C23×C414yes—
415C23×C11C23×C412yes—
416C23×C11C2511yescharacteristic
417Q8×C11—28no—
418Q8×C11—28no—
419Q8×C11—48no—
420D4×C11—28no—
421D4×C11—44no—
422D4×C11—48no—
423D4×C11—48no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—21no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—21no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—22no—
437C2×C4×C11—21no—
438C2×C4×C11—22no—
439C2×C4×C11—21no—
440C2×C4×C11—28no—
441C2×C4×C11—28no—
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—21no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—21no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—22no—
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—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—48no—
476C2×C4×C11—48no—
477C2×C4×C11—44no—
478C2×C4×C11—44no—
479C2×C4×C11—84no—
480C2×C4×C11—84no—
481C2×C4×C11C23×C412yes—
482C2×C4×C11C23×C414yes—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C23×C414yes—
485C2×C4×C11C23×C412yes—
486C2×C4×C11C23×C414yes—
487C2×C4×C11C23×C412yes—
488C2×C4×C11C23×C412yes—
489C2×C4×C11H(5,𝔽2)12yes—
490C2×C4×C11H(5,𝔽2)12yes—
491C2×C4×C112−1+412yes—
492C22×#41C22×C1111yescharacteristic
493C23×Q8C22×C1111yescharacteristic
494#548C4×C11116yescomplemented
495C2×#124C22×C1111yescharacteristic
496C2×#124C22×C1112yes—
497C2×C22⋊Q8C22×C1112yes—
498C2×C22⋊Q8C22×C1111yescharacteristic
499C2×#121C22×C1111yescharacteristic
500C2×#121C22×C1112yes—
501C2×C4×Q8C22×C1111yescharacteristic
502C2×C4×Q8C22×C1111yescharacteristic
503C2×C4×Q8C22×C1111yescharacteristic
504C2×C4×D4C22×C1111yescharacteristic
505C2×C4×D4C22×C1111yescharacteristic
506C2×C4×D4C22×C1112yes—
507C2×C4×D4C22×C1111yescharacteristic
508C2×#117C22×C1111yescharacteristic
509C2×#117C22×C1111yescharacteristic
510C2×#117C22×C1111yescharacteristic
511C22×C42C22×C1111yescharacteristic
512#391C22×C1111yescharacteristic
513#391C22×C1111yescharacteristic
514#391C22×C1112yes—
515#391C22×C1111yescharacteristic
516#391C22×C1111yescharacteristic
517#391C22×C1112yes—
518#391C22×C1111yescharacteristic
519#391C22×C1112yes—
520#391C22×C1112yes—
521#391C22×C1111yescharacteristic
522#390C22×C1111yescharacteristic
523#390C22×C1112yes—
524#390C22×C1112yes—
525#390C22×C1112yes—
526#390C22×C1111yescharacteristic
527#389C22×C1111yescharacteristic
528#389C22×C1111yescharacteristic
529#388C22×C1111yescharacteristic
530#388C22×C1112yes—
531#388C22×C1112yes—
532#388C22×C1112yes—
533#388C22×C1112yes—
534#388C22×C1112yes—
535#388C22×C1112yes—
536#388C22×C1112yes—
537#388C22×C1112yes—
538#388C22×C1112yes—
539#388C22×C1112yes—
540#388C22×C1111yescharacteristic
541#387C22×C1112yes—
542#387C22×C1112yes—
543#387C22×C1112yes—
544#387C22×C1112yes—
545#387C22×C1111yescharacteristic
546#387C22×C1112yes—
547#387C22×C1112yes—
548#387C22×C1111yescharacteristic
549#386C22×C1112yes—
550#386C22×C1112yes—
551#386C22×C1111yescharacteristic
552#386C22×C1112yes—
553#386C22×C1112yes—
554#386C22×C1112yes—
555#386C22×C1111yescharacteristic
556#386C22×C1112yes—
557#385C22×C1112yes—
558#385C22×C1112yes—
559#385C22×C1112yes—
560#385C22×C1112yes—
561#385C22×C1111yescharacteristic
562#385C22×C1112yes—
563#385C22×C1111yescharacteristic
564#384C22×C1111yescharacteristic
565#383C22×C1112yes—
566#382C22×C1112yes—
567#382C22×C1112yes—
568#381C22×C1112yes—
569#381C22×C1112yes—
570#381C22×C1112yes—
571#380C22×C1112yes—
572#380C22×C1111yescharacteristic
573#380C22×C1111yescharacteristic
574C4×C4⋊C4C22×C1111yescharacteristic
575C4×C4⋊C4C22×C1111yescharacteristic
576C4×C4⋊C4C22×C1112yes—
577C4×C4⋊C4C22×C1112yes—
578C4×C4⋊C4C22×C1112yes—
579C4×C4⋊C4C22×C1111yescharacteristic
580C4×C4⋊C4C22×C1111yescharacteristic
581C4×C4⋊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
591C2×#95C22×C1112yes—
592C22×C11—22no—
593C22×C11—22no—
594C22×C11—24no—
595C22×C11—22no—
596C22×C11—22no—
597C22×C11—24no—
598C22×C11—22no—
599C22×C11—24no—
600C22×C11—22no—
601C22×C11—41no—
602C22×C11—42no—
603C22×C11—41no—
604C22×C11—41no—
605C22×C11—41no—
606C22×C11—42no—
607C22×C11—41no—
608C22×C11—41no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11—41no—
612C22×C11—41no—
613C22×C11C24×C411yescharacteristic
614C22×C11C2×H(5,𝔽2)11yescharacteristic
615C22×C11C2×H(5,𝔽2)11yescharacteristic
616C22×C11C2×2−1+411yescharacteristic
617C22×C11#58511yescharacteristic
618C22×C11#58511yescharacteristic
619C22×C11#58511yescharacteristic
620C4×C11—22no—
621C4×C11—22no—
622C4×C11—24no—
623C4×C11—24no—
624C4×C11—22no—
625C4×C11—24no—
626C4×C11—22no—
627C4×C11—22no—
628C4×C11—41no—
629C4×C11—41no—
630C4×C11—42no—
631C4×C11—41no—
632C4×C11—41no—
633C4×C11—41no—
634C4×C11—41no—
635C4×C11—42no—
636C4×C11—42no—
637C4×C11—42no—
638C4×C11—41no—
639C4×C11#51814yes—
640C2×#41—42no—
641C2×#41—42no—
642C2×#41C2×C4×C1118yes—
643C22×Q8—42no—
644C22×Q8—42no—
645C22×Q8C2×C4×C1118yescomplemented
646C22×Q8C23×C1111yescharacteristic
647C22×Q8C23×C1111yescharacteristic
648C22×Q8C23×C1112yes—
649C22×D4C23×C1111yescharacteristic
650C22×D4C23×C1112yes—
651C22×D4C23×C1111yescharacteristic
652C22×D4C23×C1112yes—
653C23×C4C23×C1111yescharacteristic
654C23×C4C23×C1111yescharacteristic
655C23×C4C23×C1111yescharacteristic
656C23×C4C23×C1112yes—
657C23×C4C23×C1112yes—
658C23×C4C23×C1111yescharacteristic
659C23×C4C23×C1112yes—
660C23×C4C23×C1112yes—
661#124C2×C4×C1118yescomplemented
662#124C2×C4×C11116yescomplemented
663C22⋊Q8C2×C4×C1118yescomplemented
664C22⋊Q8C2×C4×C11116yescomplemented
665#121C2×C4×C1118yescomplemented
666#121C2×C4×C11116yescomplemented
667C4×Q8—42no—
668C4×Q8—42no—
669C4×Q8C2×C4×C1118yescomplemented
670C4×D4—42no—
671C4×D4—42no—
672C4×D4C2×C4×C1118yescomplemented
673C4×D4C2×C4×C11116yescomplemented
674#117—42no—
675#117—42no—
676#117—42no—
677C2×C4⋊C4C23×C1111yescharacteristic
678C2×C4⋊C4C23×C1111yescharacteristic
679C2×C4⋊C4C23×C1111yescharacteristic
680C2×C4⋊C4C23×C1111yescharacteristic
681C2×C4⋊C4C23×C1111yescharacteristic
682C2×C4⋊C4C23×C1111yescharacteristic
683C2×C4⋊C4C23×C1111yescharacteristic
684C2×C4⋊C4C23×C1112yes—
685C2×C4⋊C4C23×C1112yes—
686C2×C4⋊C4C23×C1111yescharacteristic
687C2×C4⋊C4C23×C1112yes—
688C2×C4⋊C4C23×C1112yes—
689C2×C4⋊C4C23×C1112yes—
690C2×C4⋊C4C23×C1112yes—
691C2×C4⋊C4C23×C1112yes—
692C2×C4⋊C4C23×C1111yescharacteristic
693C2×C4⋊C4C23×C1111yescharacteristic
694C2×C4⋊C4C23×C1112yes—
695C2×C22⋊C4C23×C1111yescharacteristic
696C2×C22⋊C4C23×C1112yes—
697C2×C22⋊C4C23×C1111yescharacteristic
698C2×C22⋊C4C23×C1111yescharacteristic
699C2×C22⋊C4C23×C1112yes—
700C2×C22⋊C4C23×C1112yes—
701C2×C22⋊C4C23×C1112yes—
702C2×C22⋊C4C23×C1112yes—
703C2×C22⋊C4C23×C1111yescharacteristic
704C2×C22⋊C4C23×C1112yes—
705C2×C22⋊C4C23×C1112yes—
706C2×C22⋊C4C23×C1112yes—
707C2×C22⋊C4C23×C1111yescharacteristic
708C2×C22⋊C4C23×C1111yescharacteristic
709C2×C22⋊C4C23×C1112yes—
710C2×C22⋊C4C23×C1112yes—
711C2×C22⋊C4C23×C1111yescharacteristic
712C2×C22⋊C4C23×C1112yes—
713C2×C22⋊C4C23×C1111yescharacteristic
714C2×C22⋊C4C23×C1112yes—
715C2×C22⋊C4C23×C1112yes—
716C2×C22⋊C4C23×C1112yes—
717C2×C42—42no—
718C2×C42C23×C1111yescharacteristic
719C2×C42C23×C1111yescharacteristic
720C2×C42C23×C1111yescharacteristic
721C2×C42C23×C1111yescharacteristic
722C2×C42C23×C1112yes—
723C2×C42C23×C1112yes—
724C2×C42C23×C1112yes—
725C2×C42C23×C1112yes—
726C2×C42C23×C1112yes—
727C2×C42C23×C1111yescharacteristic
728C2×C42C23×C1111yescharacteristic
729C2×C42C23×C1112yes—
730C2×C42C23×C1112yes—
731C2×C42C23×C1111yescharacteristic
732C2×C42C23×C1112yes—
733#95C23×C1111yescharacteristic
734#95C23×C1112yes—
735#95C23×C1112yes—
736#95C23×C1112yes—
737#95C23×C1111yescharacteristic
738#95C23×C1111yescharacteristic
739#95C23×C1111yescharacteristic
740#95C23×C1111yescharacteristic
741#95C23×C1111yescharacteristic
742#95C23×C1111yescharacteristic
743#95C23×C1112yes—
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×C1111yescharacteristic
754#95C23×C1112yes—
755#95C23×C1112yes—
756#95C23×C1112yes—
757#95C23×C1112yes—
758#95C23×C1112yes—
759#95C23×C1112yes—
760#95C23×C1112yes—
761#95C23×C1111yescharacteristic
762C2×C11—42no—
763C2×C11—42no—
764C2×C11—44no—
765C2×C11C2×#51811yescharacteristic
766C2×C11#342811yescharacteristic
767C2×C11C4×2−1+411yescharacteristic
768C2×C11#354011yescharacteristic
769C2×C11#354111yescharacteristic
770C2×C11#355411yescharacteristic
771C2×C11#356211yescharacteristic
772C24C24×C1111yescharacteristic
773C24C24×C1111yescharacteristic
774C24C24×C1112yes—
775#41—416no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—416no—
783C2×Q8C22×C4×C1114yes—
784C2×Q8C22×C4×C1114yes—
785C2×Q8C22×C4×C1118yes—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—41no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—41no—
794C2×D4C22×C4×C1114yes—
795C2×D4C22×C4×C1114yes—
796C2×D4C22×C4×C1118yes—
797C2×D4C22×C4×C1118yes—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4C22×C4×C1114yes—
819C22×C4C22×C4×C1114yes—
820C22×C4C22×C4×C1118yes—
821C22×C4C22×C4×C1118yes—
822C22×C4C24×C1111yescharacteristic
823C22×C4C24×C1111yescharacteristic
824C22×C4C24×C1111yescharacteristic
825C22×C4C24×C1111yescharacteristic
826C22×C4C24×C1111yescharacteristic
827C22×C4C24×C1112yes—
828C22×C4C24×C1111yescharacteristic
829C22×C4C24×C1111yescharacteristic
830C22×C4C24×C1112yes—
831C22×C4C24×C1112yes—
832C22×C4C24×C1112yes—
833C22×C4C24×C1112yes—
834C22×C4C24×C1111yescharacteristic
835C22×C4C24×C1111yescharacteristic
836C22×C4C24×C1111yescharacteristic
837C22×C4C24×C1112yes—
838C22×C4C24×C1111yescharacteristic
839C22×C4C24×C1112yes—
840C22×C4C24×C1111yescharacteristic
841C22×C4C24×C1111yescharacteristic
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—41no—
848C4⋊C4—41no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—42no—
852C4⋊C4—41no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4C22×C4×C1114yes—
857C4⋊C4C22×C4×C1118yes—
858C4⋊C4C22×C4×C1118yes—
859C4⋊C4C22×C4×C1114yes—
860C22⋊C4—22no—
861C22⋊C4—24no—
862C22⋊C4—41no—
863C22⋊C4—41no—
864C22⋊C4—42no—
865C22⋊C4—42no—
866C22⋊C4—42no—
867C22⋊C4—42no—
868C22⋊C4—41no—
869C22⋊C4—42no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—42no—
874C22⋊C4—41no—
875C22⋊C4—41no—
876C22⋊C4C22×C4×C1114yes—
877C22⋊C4C22×C4×C1114yes—
878C22⋊C4C22×C4×C1118yes—
879C22⋊C4C22×C4×C1118yes—
880C22⋊C4C22×C4×C1118yes—
881C22⋊C4C22×C4×C1118yes—
882C42—22no—
883C42—22no—
884C42—22no—
885C42—22no—
886C42—41no—
887C42—41no—
888C42—42no—
889C42—42no—
890C42—42no—
891C42—42no—
892C42—42no—
893C42—42no—
894C42—42no—
895C42C22×C4×C1118yes—
896C42C22×C4×C1114yes—
897C11#3447411yescharacteristic, direct product factor, Sylow
898C23—21no—
899C23—21no—
900C23—21no—
901C23—22no—
902C23—22no—
903C23—21no—
904C23—21no—
905C23—22no—
906C23—21no—
907C23—21no—
908C23—21no—
909C23—22no—
910C23—21no—
911C23—22no—
912C23—21no—
913C23—22no—
914C23—21no—
915C23—21no—
916C23C23×C4×C1112yes—
917C23C23×C4×C1114yes—
918C23C23×C4×C1112yes—
919C23C25×C1111yescharacteristic
920Q8—28no—
921Q8—28no—
922Q8—48no—
923D4—28no—
924D4—44no—
925D4—48no—
926D4—48no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—28no—
944C2×C4—28no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—48no—
979C2×C4—48no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4—84no—
983C2×C4—84no—
984C2×C4C23×C4×C1112yes—
985C2×C4C23×C4×C1114yes—
986C2×C4C23×C4×C1112yes—
987C2×C4C23×C4×C1114yes—
988C2×C4C23×C4×C1112yes—
989C2×C4C23×C4×C1114yes—
990C2×C4C23×C4×C1112yes—
991C2×C4C23×C4×C1112yes—
992C2×C4C11×H(5,𝔽2)12yes—
993C2×C4C11×H(5,𝔽2)12yes—
994C2×C4C11×2−1+412yes—
995C22—22no—
996C22—22no—
997C22—24no—
998C22—22no—
999C22—22no—
1000C22—24no—
1001C22—22no—
1002C22—24no—
1003C22—22no—
1004C22—41no—
1005C22—42no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—42no—
1010C22—41no—
1011C22—41no—
1012C22—42no—
1013C22—42no—
1014C22—41no—
1015C22—41no—
1016C22C24×C4×C1111yescharacteristic
1017C22C2×C11×H(5,𝔽2)11yescharacteristic
1018C22C2×C11×H(5,𝔽2)11yescharacteristic
1019C22C2×C11×2−1+411yescharacteristic
1020C22C11×#58511yescharacteristic
1021C22C11×#58511yescharacteristic
1022C22C11×#58511yescharacteristic
1023C4—22no—
1024C4—22no—
1025C4—24no—
1026C4—24no—
1027C4—22no—
1028C4—24no—
1029C4—22no—
1030C4—22no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—42no—
1035C4—41no—
1036C4—41no—
1037C4—41no—
1038C4—42no—
1039C4—41no—
1040C4—42no—
1041C4—42no—
1042C4C11×#51814yes—
1043C2—42no—
1044C2—42no—
1045C2—44no—
1046C2C2×C11×#51811yescharacteristic
1047C2C11×#342811yescharacteristic
1048C2C4×C11×2−1+411yescharacteristic
1049C2C11×#354011yescharacteristic
1050C2C11×#354111yescharacteristic
1051C2C11×#355411yescharacteristic
1052C2C11×#356211yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#548C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2379C2semidirect
3. C11×#2377C2semidirect
4. C11×#2368C2semidirect
5. C11×#2367C2semidirect
6. C11×#2363C2semidirect
7. C11×#2362C2semidirect
8. C11×#2357C2semidirect
9. C11×#2355C2semidirect
10. C11×#2354C2semidirect
11. Q8×C11×C22⋊C4C2semidirect
12. C11×#2339C2semidirect
13. C11×#2337C2semidirect
14. C11×#2333C2semidirect
15. C11×#2332C2semidirect
16. C11×#2326C2semidirect
17. C11×#2324C2semidirect
18. C11×#2320C2semidirect
19. C11×#2318C2semidirect
20. C11×#2310C2semidirect
21. C4×C11×C22⋊Q8C2semidirect
22. C11×#2297C2semidirect
23. C11×#2290C2semidirect
26. C11×#548C4semidirect
129. C22×Q8×C11C2×C4semidirect
145. C11×#124C2×C4semidirect
146. C11×#124C2×C4semidirect
147. C11×C22⋊Q8C2×C4semidirect
148. C11×C22⋊Q8C2×C4semidirect
149. C11×#121C2×C4semidirect
150. C11×#121C2×C4semidirect
153. C4×Q8×C11C2×C4semidirect
156. C4×D4×C11C2×C4semidirect
157. C4×D4×C11C2×C4semidirect
246. #34474C11direct (N × H)
373. #2379C2×C11semidirect
374. #2377C2×C11semidirect
375. #2368C2×C11semidirect
376. #2367C2×C11semidirect
377. #2363C2×C11semidirect
378. #2362C2×C11semidirect
379. #2357C2×C11semidirect
380. #2355C2×C11semidirect
381. #2354C2×C11semidirect
382. Q8×C22⋊C4C2×C11semidirect
383. #2339C2×C11semidirect
384. #2337C2×C11semidirect
385. #2333C2×C11semidirect
386. #2332C2×C11semidirect
387. #2326C2×C11semidirect
388. #2324C2×C11semidirect
389. #2320C2×C11semidirect
390. #2318C2×C11semidirect
391. #2310C2×C11semidirect
392. C4×C22⋊Q8C2×C11semidirect
393. #2297C2×C11semidirect
394. #2290C2×C11semidirect
494. #548C4×C11semidirect
645. C22×Q8C2×C4×C11semidirect
661. #124C2×C4×C11semidirect
662. #124C2×C4×C11semidirect
663. C22⋊Q8C2×C4×C11semidirect
664. C22⋊Q8C2×C4×C11semidirect
665. #121C2×C4×C11semidirect
666. #121C2×C4×C11semidirect
669. C4×Q8C2×C4×C11semidirect
672. C4×D4C2×C4×C11semidirect
673. C4×D4C2×C4×C11semidirect
897. C11#34474direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5482
C11×#23792
C11×#23772
C11×#23682
C11×#23672
C11×#23632
C11×#23622
C11×#23572
C11×#23552
C11×#23542
Q8×C11×C22⋊C42
C11×#23392
C11×#23372
C11×#23332
C11×#23322
C11×#23262
C11×#23242
C11×#23202
C11×#23182
C11×#23102
C4×C11×C22⋊Q82
C11×#22972
C11×#22902
#3447411