Finite Group Databasebeta

← C11×#34472 #14611665

Subgroups — C11×#34472 #14611665

Order 2816.

2480 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#548C211yesmaximal, characteristic
2C11×#2379C212yesmaximal, complemented
3C11×#2378C212yesmaximal, complemented
4C11×#2367C211yesmaximal, characteristic, complemented
5C11×#2364C212yesmaximal, complemented
6C11×#2361C211yesmaximal, characteristic, complemented
7C11×#2360C211yesmaximal, characteristic, complemented
8C11×#2355C211yesmaximal, characteristic, complemented
9C11×#2349C212yesmaximal, complemented
10D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C11×#2339C211yesmaximal, characteristic, complemented
13C11×#2337C212yesmaximal, complemented
14C11×#2329C212yesmaximal, complemented
15C11×#2326C211yesmaximal, characteristic, complemented
16C11×#2325C212yesmaximal, complemented
17C11×#2323C211yesmaximal, characteristic, complemented
18C11×#2320C211yesmaximal, characteristic, complemented
19C11×#2318C212yesmaximal, complemented
20C11×#2311C211yesmaximal, characteristic, complemented
21C4×C11×#121C211yesmaximal, characteristic, complemented
22C2×C11×#391C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C23×Q8×C11C2211yescharacteristic
26C11×#548C4116yescomplemented
27C2×C11×#124C2212yes—
28C2×C11×#124C2211yescharacteristic
29C2×C11×C22⋊Q8C2212yes—
30C2×C11×C22⋊Q8C2211yescharacteristic
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×C11C2212yes—
38C2×C4×D4×C11C2212yes—
39C2×C4×D4×C11C2212yes—
40C2×C4×D4×C11C2211yescharacteristic
41C2×C4×D4×C11C2211yescharacteristic
42C2×C4×D4×C11C2212yes—
43C2×C11×#117C2211yescharacteristic
44C22×C11×C4⋊C4C2211yescharacteristic
45C22×C11×C4⋊C4C2211yescharacteristic
46C22×C42×C11C2211yescharacteristic
47C11×#391C2212yes—
48C11×#391C2212yes—
49C11×#391C2212yes—
50C11×#391C2211yescharacteristic
51C11×#391C2211yescharacteristic
52C11×#391C2212yes—
53C11×#391C2211yescharacteristic
54C11×#391C2211yescharacteristic
55C11×#391C2211yescharacteristic
56C11×#391C2211yescharacteristic
57C11×#390C2211yescharacteristic
58C11×#390C2211yescharacteristic
59C11×#389C2212yes—
60C11×#389C2212yes—
61C11×#389C2211yescharacteristic
62C11×#389C2211yescharacteristic
63C11×#389C2212yes—
64C11×#388C2212yes—
65C11×#388C2212yes—
66C11×#388C2212yes—
67C11×#388C2212yes—
68C11×#388C2211yescharacteristic
69C11×#388C2212yes—
70C11×#388C2212yes—
71C11×#388C2211yescharacteristic
72C11×#388C2212yes—
73C11×#388C2212yes—
74C11×#387C2211yescharacteristic
75C11×#387C2212yes—
76C11×#387C2212yes—
77C11×#387C2212yes—
78C11×#387C2211yescharacteristic
79C11×#387C2212yes—
80C11×#387C2212yes—
81C11×#387C2212yes—
82C11×#386C2212yes—
83C11×#386C2212yes—
84C11×#386C2211yescharacteristic
85C11×#386C2211yescharacteristic
86C11×#386C2212yes—
87C11×#386C2212yes—
88C11×#386C2212yes—
89C11×#386C2212yes—
90C11×#385C2212yes—
91C11×#385C2212yes—
92C11×#385C2212yes—
93C11×#385C2212yes—
94C11×#385C2211yescharacteristic
95C11×#385C2211yescharacteristic
96C11×#385C2212yes—
97C11×#385C2212yes—
98C11×#385C2212yes—
99C11×#384C2211yescharacteristic
100C11×#383C2212yes—
101C11×#382C2212yes—
102C11×#382C2212yes—
103C11×#381C2212yes—
104C11×#380C2212yes—
105C11×#380C2211yescharacteristic
106C11×#380C2212yes—
107C11×#380C2211yescharacteristic
108C11×#380C2212yes—
109C4×C11×C4⋊C4C2211yescharacteristic
110C4×C11×C4⋊C4C2211yescharacteristic
111C4×C11×C4⋊C4C2211yescharacteristic
112C4×C11×C4⋊C4C2211yescharacteristic
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—
120C11×#376C2211yescharacteristic
121C2×C11×#95C2212yes—
122C2×C11×#95C2212yes—
123C2×C11×#95C2212yes—
124C2×C11×#41—42no—
125C2×C11×#41—42no—
126C2×C11×#41C2×C418yescomplemented
127C22×Q8×C11—42no—
128C22×Q8×C11—42no—
129C22×Q8×C11C2×C418yescomplemented
130C22×Q8×C11C2311yescharacteristic
131C22×Q8×C11C2311yescharacteristic
132C22×Q8×C11C2312yes—
133C22×D4×C11C2312yes—
134C22×D4×C11C2311yescharacteristic
135C22×D4×C11C2311yescharacteristic
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—
145C23×C4×C11C2312yes—
146C23×C4×C11C2312yes—
147C11×#124C2×C418yescomplemented
148C11×#124C2×C4116yescomplemented
149C11×C22⋊Q8C2×C418yescomplemented
150C11×C22⋊Q8C2×C4116yescomplemented
151C11×#121C2×C418yescomplemented
152C11×#121C2×C4116yescomplemented
153C4×Q8×C11—42no—
154C4×Q8×C11—42no—
155C4×Q8×C11C2×C418yescomplemented
156C4×D4×C11—42no—
157C4×D4×C11—42no—
158C4×D4×C11—44no—
159C4×D4×C11—44no—
160C4×D4×C11—44no—
161C4×D4×C11C2×C418yescomplemented
162C4×D4×C11C2×C4116yescomplemented
163C11×#117—42no—
164C2×C11×C4⋊C4—42no—
165C2×C11×C4⋊C4—42no—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C4⋊C4C2312yes—
176C2×C11×C4⋊C4C2312yes—
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2311yescharacteristic
179C2×C11×C4⋊C4C2312yes—
180C2×C11×C4⋊C4C2312yes—
181C2×C11×C4⋊C4C2312yes—
182C2×C11×C4⋊C4C2311yescharacteristic
183C2×C11×C4⋊C4C2312yes—
184C2×C11×C4⋊C4C2311yescharacteristic
185C2×C11×C4⋊C4C2312yes—
186C2×C11×C22⋊C4C2311yescharacteristic
187C2×C11×C22⋊C4C2311yescharacteristic
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2311yescharacteristic
190C2×C11×C22⋊C4C2311yescharacteristic
191C2×C11×C22⋊C4C2311yescharacteristic
192C2×C11×C22⋊C4C2312yes—
193C2×C11×C22⋊C4C2312yes—
194C2×C11×C22⋊C4C2311yescharacteristic
195C2×C11×C22⋊C4C2312yes—
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2312yes—
198C2×C11×C22⋊C4C2312yes—
199C2×C11×C22⋊C4C2312yes—
200C2×C11×C22⋊C4C2312yes—
201C2×C11×C22⋊C4C2312yes—
202C2×C11×C22⋊C4C2312yes—
203C2×C11×C22⋊C4C2311yescharacteristic
204C2×C11×C22⋊C4C2311yescharacteristic
205C2×C11×C22⋊C4C2312yes—
206C2×C42×C11—42no—
207C2×C42×C11C2311yescharacteristic
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2312yes—
214C2×C42×C11C2312yes—
215C2×C42×C11C2312yes—
216C2×C42×C11C2312yes—
217C2×C42×C11C2312yes—
218C2×C42×C11C2311yescharacteristic
219C2×C42×C11C2312yes—
220C11×#95C2311yescharacteristic
221C11×#95C2312yes—
222C11×#95C2312yes—
223C11×#95C2312yes—
224C11×#95C2312yes—
225C11×#95C2312yes—
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2311yescharacteristic
232C11×#95C2311yescharacteristic
233C11×#95C2311yescharacteristic
234C11×#95C2311yescharacteristic
235C11×#95C2311yescharacteristic
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2311yescharacteristic
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2311yescharacteristic
243C11×#95C2311yescharacteristic
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11×#95C2311yescharacteristic
249#34472C1111yesmaximal, characteristic, direct product factor, Sylow
250C24×C11C2411yescharacteristic
251C24×C11C2412yes—
252C24×C11C2411yescharacteristic
253C11×#41—416no—
254C2×Q8×C11—22no—
255C2×Q8×C11—22no—
256C2×Q8×C11—22no—
257C2×Q8×C11—22no—
258C2×Q8×C11—42no—
259C2×Q8×C11—42no—
260C2×Q8×C11—416no—
261C2×Q8×C11C22×C414yes—
262C2×Q8×C11C22×C414yes—
263C2×Q8×C11C22×C418yes—
264C2×D4×C11—24no—
265C2×D4×C11—22no—
266C2×D4×C11—24no—
267C2×D4×C11—22no—
268C2×D4×C11—22no—
269C2×D4×C11—22no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11C22×C414yes—
273C2×D4×C11C22×C418yes—
274C2×D4×C11C22×C414yes—
275C2×D4×C11C22×C418yes—
276C22×C4×C11—22no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—24no—
283C22×C4×C11—22no—
284C22×C4×C11—24no—
285C22×C4×C11—41no—
286C22×C4×C11—41no—
287C22×C4×C11—41no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11—42no—
292C22×C4×C11—42no—
293C22×C4×C11—42no—
294C22×C4×C11—42no—
295C22×C4×C11—42no—
296C22×C4×C11—42no—
297C22×C4×C11—42no—
298C22×C4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11—42no—
301C22×C4×C11—42no—
302C22×C4×C11C22×C414yes—
303C22×C4×C11C22×C414yes—
304C22×C4×C11C22×C418yes—
305C22×C4×C11C22×C418yes—
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2412yes—
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2412yes—
314C22×C4×C11C2412yes—
315C22×C4×C11C2411yescharacteristic
316C22×C4×C11C2412yes—
317C22×C4×C11C2412yes—
318C22×C4×C11C2411yescharacteristic
319C22×C4×C11C2411yescharacteristic
320C22×C4×C11C2412yes—
321C22×C4×C11C2411yescharacteristic
322C22×C4×C11C2412yes—
323C22×C4×C11C2411yescharacteristic
324C22×C4×C11C2411yescharacteristic
325C22×C4×C11C2411yescharacteristic
326C11×C4⋊C4—22no—
327C11×C4⋊C4—22no—
328C11×C4⋊C4—22no—
329C11×C4⋊C4—22no—
330C11×C4⋊C4—22no—
331C11×C4⋊C4—42no—
332C11×C4⋊C4—42no—
333C11×C4⋊C4—41no—
334C11×C4⋊C4—42no—
335C11×C4⋊C4—41no—
336C11×C4⋊C4—41no—
337C11×C4⋊C4—42no—
338C11×C4⋊C4—42no—
339C11×C4⋊C4—42no—
340C11×C4⋊C4—42no—
341C11×C4⋊C4—42no—
342C11×C4⋊C4C22×C414yes—
343C11×C4⋊C4C22×C418yes—
344C11×C4⋊C4C22×C418yes—
345C11×C4⋊C4C22×C414yes—
346C11×C22⋊C4—22no—
347C11×C22⋊C4—24no—
348C11×C22⋊C4—22no—
349C11×C22⋊C4—22no—
350C11×C22⋊C4—42no—
351C11×C22⋊C4—42no—
352C11×C22⋊C4—41no—
353C11×C22⋊C4—41no—
354C11×C22⋊C4—41no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4—42no—
358C11×C22⋊C4—42no—
359C11×C22⋊C4—42no—
360C11×C22⋊C4C22×C414yes—
361C11×C22⋊C4C22×C414yes—
362C11×C22⋊C4C22×C418yes—
363C11×C22⋊C4C22×C418yes—
364C11×C22⋊C4C22×C418yes—
365C11×C22⋊C4C22×C418yes—
366C42×C11—22no—
367C42×C11—22no—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—41no—
371C42×C11—41no—
372C42×C11—42no—
373C42×C11—42no—
374C42×C11—42no—
375C42×C11—42no—
376C42×C11—42no—
377C42×C11C22×C418yes—
378C42×C11C22×C414yes—
379C2×#548C2×C1111yescharacteristic
380#2379C2×C1112yescomplemented
381#2378C2×C1112yescomplemented
382#2367C2×C1111yescharacteristic, complemented
383#2364C2×C1112yescomplemented
384#2361C2×C1111yescharacteristic, complemented
385#2360C2×C1111yescharacteristic, complemented
386#2355C2×C1111yescharacteristic, complemented
387#2349C2×C1112yescomplemented
388D4×C4⋊C4C2×C1111yescharacteristic, complemented
389Q8×C22⋊C4C2×C1111yescharacteristic, complemented
390#2339C2×C1111yescharacteristic, complemented
391#2337C2×C1112yescomplemented
392#2329C2×C1112yescomplemented
393#2326C2×C1111yescharacteristic, complemented
394#2325C2×C1112yescomplemented
395#2323C2×C1111yescharacteristic, complemented
396#2320C2×C1111yescharacteristic, complemented
397#2318C2×C1112yescomplemented
398#2311C2×C1111yescharacteristic, complemented
399C4×#121C2×C1111yescharacteristic, complemented
400C2×#391C2×C1111yescharacteristic, complemented
401#2290C2×C1111yescharacteristic, complemented
402C23×C11—21no—
403C23×C11—21no—
404C23×C11—21no—
405C23×C11—21no—
406C23×C11—21no—
407C23×C11—22no—
408C23×C11—21no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11—22no—
414C23×C11—21no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—21no—
418C23×C11C23×C412yes—
419C23×C11C23×C414yes—
420C23×C11C23×C412yes—
421C23×C11H(5,𝔽2)12yes—
422C23×C112−1+412yes—
423C23×C11C2511yescharacteristic
424Q8×C11—28no—
425Q8×C11—28no—
426Q8×C11—48no—
427D4×C11—28no—
428D4×C11—216no—
429D4×C11—28no—
430D4×C11—48no—
431C2×C4×C11—21no—
432C2×C4×C11—22no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—21no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—22no—
446C2×C4×C11—21no—
447C2×C4×C11—28no—
448C2×C4×C11—28no—
449C2×C4×C11—21no—
450C2×C4×C11—21no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—21no—
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—22no—
462C2×C4×C11—22no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—48no—
483C2×C4×C11—48no—
484C2×C4×C11—44no—
485C2×C4×C11—44no—
486C2×C4×C11—84no—
487C2×C4×C11—84no—
488C2×C4×C11—84no—
489C2×C4×C11—84no—
490C2×C4×C11C23×C412yes—
491C2×C4×C11C23×C414yes—
492C2×C4×C11C23×C412yes—
493C2×C4×C11C23×C414yes—
494C2×C4×C11C23×C412yes—
495C2×C4×C11C23×C414yes—
496C2×C4×C11C23×C412yes—
497C2×C4×C11C23×C412yes—
498C2×C4×C11H(5,𝔽2)12yes—
499C2×C4×C11H(5,𝔽2)12yes—
500C2×C4×C112−1+412yes—
501C22×#41C22×C1111yescharacteristic
502C23×Q8C22×C1111yescharacteristic
503#548C4×C11116yescomplemented
504C2×#124C22×C1111yescharacteristic
505C2×#124C22×C1112yes—
506C2×C22⋊Q8C22×C1111yescharacteristic
507C2×C22⋊Q8C22×C1112yes—
508C2×#121C22×C1112yes—
509C2×#121C22×C1111yescharacteristic
510C2×C4×Q8C22×C1111yescharacteristic
511C2×C4×Q8C22×C1111yescharacteristic
512C2×C4×Q8C22×C1111yescharacteristic
513C2×C4×D4C22×C1112yes—
514C2×C4×D4C22×C1112yes—
515C2×C4×D4C22×C1111yescharacteristic
516C2×C4×D4C22×C1111yescharacteristic
517C2×C4×D4C22×C1112yes—
518C2×C4×D4C22×C1112yes—
519C2×C4×D4C22×C1111yescharacteristic
520C2×#117C22×C1111yescharacteristic
521C22×C4⋊C4C22×C1111yescharacteristic
522C22×C4⋊C4C22×C1111yescharacteristic
523C22×C42C22×C1111yescharacteristic
524#391C22×C1111yescharacteristic
525#391C22×C1111yescharacteristic
526#391C22×C1111yescharacteristic
527#391C22×C1111yescharacteristic
528#391C22×C1112yes—
529#391C22×C1112yes—
530#391C22×C1112yes—
531#391C22×C1111yescharacteristic
532#391C22×C1111yescharacteristic
533#391C22×C1112yes—
534#390C22×C1111yescharacteristic
535#390C22×C1111yescharacteristic
536#389C22×C1111yescharacteristic
537#389C22×C1111yescharacteristic
538#389C22×C1112yes—
539#389C22×C1112yes—
540#389C22×C1112yes—
541#388C22×C1112yes—
542#388C22×C1112yes—
543#388C22×C1112yes—
544#388C22×C1112yes—
545#388C22×C1112yes—
546#388C22×C1112yes—
547#388C22×C1111yescharacteristic
548#388C22×C1112yes—
549#388C22×C1112yes—
550#388C22×C1111yescharacteristic
551#387C22×C1112yes—
552#387C22×C1112yes—
553#387C22×C1112yes—
554#387C22×C1112yes—
555#387C22×C1112yes—
556#387C22×C1111yescharacteristic
557#387C22×C1112yes—
558#387C22×C1111yescharacteristic
559#386C22×C1112yes—
560#386C22×C1112yes—
561#386C22×C1112yes—
562#386C22×C1112yes—
563#386C22×C1111yescharacteristic
564#386C22×C1112yes—
565#386C22×C1112yes—
566#386C22×C1111yescharacteristic
567#385C22×C1111yescharacteristic
568#385C22×C1112yes—
569#385C22×C1112yes—
570#385C22×C1112yes—
571#385C22×C1112yes—
572#385C22×C1112yes—
573#385C22×C1112yes—
574#385C22×C1112yes—
575#385C22×C1111yescharacteristic
576#384C22×C1111yescharacteristic
577#383C22×C1112yes—
578#382C22×C1112yes—
579#382C22×C1112yes—
580#381C22×C1112yes—
581#380C22×C1112yes—
582#380C22×C1112yes—
583#380C22×C1111yescharacteristic
584#380C22×C1112yes—
585#380C22×C1111yescharacteristic
586C4×C4⋊C4C22×C1111yescharacteristic
587C4×C4⋊C4C22×C1111yescharacteristic
588C4×C4⋊C4C22×C1112yes—
589C4×C4⋊C4C22×C1111yescharacteristic
590C4×C4⋊C4C22×C1111yescharacteristic
591C4×C22⋊C4C22×C1112yes—
592C4×C22⋊C4C22×C1112yes—
593C4×C22⋊C4C22×C1112yes—
594C4×C22⋊C4C22×C1112yes—
595C4×C22⋊C4C22×C1111yescharacteristic
596C4×C22⋊C4C22×C1111yescharacteristic
597#376C22×C1111yescharacteristic
598C2×#95C22×C1112yes—
599C2×#95C22×C1112yes—
600C2×#95C22×C1112yes—
601C22×C11—22no—
602C22×C11—22no—
603C22×C11—22no—
604C22×C11—22no—
605C22×C11—22no—
606C22×C11—22no—
607C22×C11—22no—
608C22×C11—24no—
609C22×C11—22no—
610C22×C11—24no—
611C22×C11—22no—
612C22×C11—24no—
613C22×C11—42no—
614C22×C11—41no—
615C22×C11—41no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—41no—
619C22×C11—41no—
620C22×C11—42no—
621C22×C11#52014yes—
622C22×C11C24×C411yescharacteristic
623C22×C11C2×H(5,𝔽2)11yescharacteristic
624C22×C11C2×H(5,𝔽2)11yescharacteristic
625C22×C11C2×H(5,𝔽2)11yescharacteristic
626C22×C11C2×2−1+411yescharacteristic
627C22×C11C2×2−1+411yescharacteristic
628C22×C11#58511yescharacteristic
629C4×C11—22no—
630C4×C11—22no—
631C4×C11—24no—
632C4×C11—24no—
633C4×C11—24no—
634C4×C11—22no—
635C4×C11—22no—
636C4×C11—22no—
637C4×C11—41no—
638C4×C11—41no—
639C4×C11—42no—
640C4×C11—41no—
641C4×C11—41no—
642C4×C11—41no—
643C4×C11—41no—
644C4×C11—42no—
645C4×C11—41no—
646C4×C11—42no—
647C4×C11—42no—
648C4×C11#51814yes—
649C2×#41—42no—
650C2×#41—42no—
651C2×#41C2×C4×C1118yescomplemented
652C22×Q8—42no—
653C22×Q8—42no—
654C22×Q8C2×C4×C1118yescomplemented
655C22×Q8C23×C1111yescharacteristic
656C22×Q8C23×C1111yescharacteristic
657C22×Q8C23×C1112yes—
658C22×D4C23×C1111yescharacteristic
659C22×D4C23×C1112yes—
660C22×D4C23×C1111yescharacteristic
661C22×D4C23×C1112yes—
662C23×C4C23×C1111yescharacteristic
663C23×C4C23×C1111yescharacteristic
664C23×C4C23×C1111yescharacteristic
665C23×C4C23×C1112yes—
666C23×C4C23×C1112yes—
667C23×C4C23×C1111yescharacteristic
668C23×C4C23×C1112yes—
669C23×C4C23×C1112yes—
670C23×C4C23×C1112yes—
671C23×C4C23×C1112yes—
672#124C2×C4×C1118yescomplemented
673#124C2×C4×C11116yescomplemented
674C22⋊Q8C2×C4×C1118yescomplemented
675C22⋊Q8C2×C4×C11116yescomplemented
676#121C2×C4×C1118yescomplemented
677#121C2×C4×C11116yescomplemented
678C4×Q8—42no—
679C4×Q8—42no—
680C4×Q8C2×C4×C1118yescomplemented
681C4×D4—42no—
682C4×D4—42no—
683C4×D4—44no—
684C4×D4—44no—
685C4×D4—44no—
686C4×D4C2×C4×C1118yescomplemented
687C4×D4C2×C4×C11116yescomplemented
688#117—42no—
689C2×C4⋊C4—42no—
690C2×C4⋊C4—42no—
691C2×C4⋊C4C23×C1111yescharacteristic
692C2×C4⋊C4C23×C1111yescharacteristic
693C2×C4⋊C4C23×C1111yescharacteristic
694C2×C4⋊C4C23×C1111yescharacteristic
695C2×C4⋊C4C23×C1111yescharacteristic
696C2×C4⋊C4C23×C1112yes—
697C2×C4⋊C4C23×C1112yes—
698C2×C4⋊C4C23×C1111yescharacteristic
699C2×C4⋊C4C23×C1111yescharacteristic
700C2×C4⋊C4C23×C1112yes—
701C2×C4⋊C4C23×C1112yes—
702C2×C4⋊C4C23×C1112yes—
703C2×C4⋊C4C23×C1112yes—
704C2×C4⋊C4C23×C1112yes—
705C2×C4⋊C4C23×C1111yescharacteristic
706C2×C4⋊C4C23×C1112yes—
707C2×C4⋊C4C23×C1112yes—
708C2×C4⋊C4C23×C1111yescharacteristic
709C2×C4⋊C4C23×C1111yescharacteristic
710C2×C4⋊C4C23×C1112yes—
711C2×C22⋊C4C23×C1112yes—
712C2×C22⋊C4C23×C1111yescharacteristic
713C2×C22⋊C4C23×C1111yescharacteristic
714C2×C22⋊C4C23×C1111yescharacteristic
715C2×C22⋊C4C23×C1111yescharacteristic
716C2×C22⋊C4C23×C1111yescharacteristic
717C2×C22⋊C4C23×C1112yes—
718C2×C22⋊C4C23×C1112yes—
719C2×C22⋊C4C23×C1112yes—
720C2×C22⋊C4C23×C1112yes—
721C2×C22⋊C4C23×C1112yes—
722C2×C22⋊C4C23×C1112yes—
723C2×C22⋊C4C23×C1112yes—
724C2×C22⋊C4C23×C1111yescharacteristic
725C2×C22⋊C4C23×C1111yescharacteristic
726C2×C22⋊C4C23×C1112yes—
727C2×C22⋊C4C23×C1111yescharacteristic
728C2×C22⋊C4C23×C1112yes—
729C2×C22⋊C4C23×C1112yes—
730C2×C22⋊C4C23×C1112yes—
731C2×C42—42no—
732C2×C42C23×C1111yescharacteristic
733C2×C42C23×C1111yescharacteristic
734C2×C42C23×C1111yescharacteristic
735C2×C42C23×C1111yescharacteristic
736C2×C42C23×C1112yes—
737C2×C42C23×C1112yes—
738C2×C42C23×C1112yes—
739C2×C42C23×C1112yes—
740C2×C42C23×C1112yes—
741C2×C42C23×C1111yescharacteristic
742C2×C42C23×C1111yescharacteristic
743C2×C42C23×C1111yescharacteristic
744C2×C42C23×C1112yes—
745#95C23×C1111yescharacteristic
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×C1111yescharacteristic
757#95C23×C1111yescharacteristic
758#95C23×C1111yescharacteristic
759#95C23×C1111yescharacteristic
760#95C23×C1111yescharacteristic
761#95C23×C1112yes—
762#95C23×C1112yes—
763#95C23×C1111yescharacteristic
764#95C23×C1112yes—
765#95C23×C1112yes—
766#95C23×C1112yes—
767#95C23×C1111yescharacteristic
768#95C23×C1111yescharacteristic
769#95C23×C1112yes—
770#95C23×C1112yes—
771#95C23×C1112yes—
772#95C23×C1112yes—
773#95C23×C1111yescharacteristic
774C2×C11—24no—
775C2×C11—42no—
776C2×C11—44no—
777C2×C11C2×#51811yescharacteristic
778C2×C11C2×#52011yescharacteristic
779C2×C11C4×2−1+411yescharacteristic
780C2×C11#353611yescharacteristic
781C2×C11#354111yescharacteristic
782C2×C11#355211yescharacteristic
783C2×C11#355811yescharacteristic
784C24C24×C1111yescharacteristic
785C24C24×C1112yes—
786C24C24×C1111yescharacteristic
787#41—416no—
788C2×Q8—22no—
789C2×Q8—22no—
790C2×Q8—22no—
791C2×Q8—22no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—416no—
795C2×Q8C22×C4×C1114yes—
796C2×Q8C22×C4×C1114yes—
797C2×Q8C22×C4×C1118yes—
798C2×D4—24no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—24no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4C22×C4×C1114yes—
807C2×D4C22×C4×C1118yes—
808C2×D4C22×C4×C1114yes—
809C2×D4C22×C4×C1118yes—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—24no—
817C22×C4—22no—
818C22×C4—24no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—41no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4C22×C4×C1114yes—
837C22×C4C22×C4×C1114yes—
838C22×C4C22×C4×C1118yes—
839C22×C4C22×C4×C1118yes—
840C22×C4C24×C1111yescharacteristic
841C22×C4C24×C1111yescharacteristic
842C22×C4C24×C1111yescharacteristic
843C22×C4C24×C1111yescharacteristic
844C22×C4C24×C1111yescharacteristic
845C22×C4C24×C1112yes—
846C22×C4C24×C1111yescharacteristic
847C22×C4C24×C1112yes—
848C22×C4C24×C1112yes—
849C22×C4C24×C1111yescharacteristic
850C22×C4C24×C1112yes—
851C22×C4C24×C1112yes—
852C22×C4C24×C1111yescharacteristic
853C22×C4C24×C1111yescharacteristic
854C22×C4C24×C1112yes—
855C22×C4C24×C1111yescharacteristic
856C22×C4C24×C1112yes—
857C22×C4C24×C1111yescharacteristic
858C22×C4C24×C1111yescharacteristic
859C22×C4C24×C1111yescharacteristic
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—41no—
868C4⋊C4—41no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—41no—
875C4⋊C4—42no—
876C4⋊C4C22×C4×C1114yes—
877C4⋊C4C22×C4×C1118yes—
878C4⋊C4C22×C4×C1118yes—
879C4⋊C4C22×C4×C1114yes—
880C22⋊C4—22no—
881C22⋊C4—24no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—41no—
885C22⋊C4—41no—
886C22⋊C4—42no—
887C22⋊C4—42no—
888C22⋊C4—42no—
889C22⋊C4—42no—
890C22⋊C4—42no—
891C22⋊C4—42no—
892C22⋊C4—42no—
893C22⋊C4—41no—
894C22⋊C4C22×C4×C1114yes—
895C22⋊C4C22×C4×C1114yes—
896C22⋊C4C22×C4×C1118yes—
897C22⋊C4C22×C4×C1118yes—
898C22⋊C4C22×C4×C1118yes—
899C22⋊C4C22×C4×C1118yes—
900C42—22no—
901C42—22no—
902C42—22no—
903C42—22no—
904C42—41no—
905C42—41no—
906C42—42no—
907C42—42no—
908C42—42no—
909C42—42no—
910C42—42no—
911C42C22×C4×C1118yes—
912C42C22×C4×C1114yes—
913C11#3447211yescharacteristic, direct product factor, Sylow
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—22no—
920C23—21no—
921C23—22no—
922C23—22no—
923C23—21no—
924C23—21no—
925C23—22no—
926C23—21no—
927C23—22no—
928C23—22no—
929C23—21no—
930C23C23×C4×C1112yes—
931C23C23×C4×C1114yes—
932C23C23×C4×C1112yes—
933C23C11×H(5,𝔽2)12yes—
934C23C11×2−1+412yes—
935C23C25×C1111yescharacteristic
936Q8—28no—
937Q8—28no—
938Q8—48no—
939D4—28no—
940D4—216no—
941D4—28no—
942D4—48no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—28no—
960C2×C4—28no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—48no—
995C2×C4—48no—
996C2×C4—44no—
997C2×C4—44no—
998C2×C4—84no—
999C2×C4—84no—
1000C2×C4—84no—
1001C2×C4—84no—
1002C2×C4C23×C4×C1112yes—
1003C2×C4C23×C4×C1114yes—
1004C2×C4C23×C4×C1112yes—
1005C2×C4C23×C4×C1114yes—
1006C2×C4C23×C4×C1112yes—
1007C2×C4C23×C4×C1114yes—
1008C2×C4C23×C4×C1112yes—
1009C2×C4C23×C4×C1112yes—
1010C2×C4C11×H(5,𝔽2)12yes—
1011C2×C4C11×H(5,𝔽2)12yes—
1012C2×C4C11×2−1+412yes—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—24no—
1021C22—22no—
1022C22—24no—
1023C22—22no—
1024C22—24no—
1025C22—42no—
1026C22—41no—
1027C22—41no—
1028C22—42no—
1029C22—42no—
1030C22—41no—
1031C22—41no—
1032C22—42no—
1033C22C11×#52014yes—
1034C22C24×C4×C1111yescharacteristic
1035C22C2×C11×H(5,𝔽2)11yescharacteristic
1036C22C2×C11×H(5,𝔽2)11yescharacteristic
1037C22C2×C11×H(5,𝔽2)11yescharacteristic
1038C22C2×C11×2−1+411yescharacteristic
1039C22C2×C11×2−1+411yescharacteristic
1040C22C11×#58511yescharacteristic
1041C4—22no—
1042C4—22no—
1043C4—24no—
1044C4—24no—
1045C4—24no—
1046C4—22no—
1047C4—22no—
1048C4—22no—
1049C4—41no—
1050C4—42no—
1051C4—41no—
1052C4—41no—
1053C4—41no—
1054C4—41no—
1055C4—41no—
1056C4—41no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4C11×#51814yes—
1061C2—24no—
1062C2—42no—
1063C2—44no—
1064C2C2×C11×#51811yescharacteristic
1065C2C2×C11×#52011yescharacteristic
1066C2C4×C11×2−1+411yescharacteristic
1067C2C11×#353611yescharacteristic
1068C2C11×#354111yescharacteristic
1069C2C11×#355211yescharacteristic
1070C2C11×#355811yescharacteristic
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×#2378C2semidirect
4. C11×#2367C2semidirect
5. C11×#2364C2semidirect
6. C11×#2361C2semidirect
7. C11×#2360C2semidirect
8. C11×#2355C2semidirect
9. C11×#2349C2semidirect
10. D4×C11×C4⋊C4C2semidirect
11. Q8×C11×C22⋊C4C2semidirect
12. C11×#2339C2semidirect
13. C11×#2337C2semidirect
14. C11×#2329C2semidirect
15. C11×#2326C2semidirect
16. C11×#2325C2semidirect
17. C11×#2323C2semidirect
18. C11×#2320C2semidirect
19. C11×#2318C2semidirect
20. C11×#2311C2semidirect
21. C4×C11×#121C2semidirect
22. C2×C11×#391C2semidirect
23. C11×#2290C2semidirect
26. C11×#548C4semidirect
126. C2×C11×#41C2×C4semidirect
129. C22×Q8×C11C2×C4semidirect
147. C11×#124C2×C4semidirect
148. C11×#124C2×C4semidirect
149. C11×C22⋊Q8C2×C4semidirect
150. C11×C22⋊Q8C2×C4semidirect
151. C11×#121C2×C4semidirect
152. C11×#121C2×C4semidirect
155. C4×Q8×C11C2×C4semidirect
161. C4×D4×C11C2×C4semidirect
162. C4×D4×C11C2×C4semidirect
249. #34472C11direct (N × H)
380. #2379C2×C11semidirect
381. #2378C2×C11semidirect
382. #2367C2×C11semidirect
383. #2364C2×C11semidirect
384. #2361C2×C11semidirect
385. #2360C2×C11semidirect
386. #2355C2×C11semidirect
387. #2349C2×C11semidirect
388. D4×C4⋊C4C2×C11semidirect
389. Q8×C22⋊C4C2×C11semidirect
390. #2339C2×C11semidirect
391. #2337C2×C11semidirect
392. #2329C2×C11semidirect
393. #2326C2×C11semidirect
394. #2325C2×C11semidirect
395. #2323C2×C11semidirect
396. #2320C2×C11semidirect
397. #2318C2×C11semidirect
398. #2311C2×C11semidirect
399. C4×#121C2×C11semidirect
400. C2×#391C2×C11semidirect
401. #2290C2×C11semidirect
503. #548C4×C11semidirect
651. C2×#41C2×C4×C11semidirect
654. C22×Q8C2×C4×C11semidirect
672. #124C2×C4×C11semidirect
673. #124C2×C4×C11semidirect
674. C22⋊Q8C2×C4×C11semidirect
675. C22⋊Q8C2×C4×C11semidirect
676. #121C2×C4×C11semidirect
677. #121C2×C4×C11semidirect
680. C4×Q8C2×C4×C11semidirect
686. C4×D4C2×C4×C11semidirect
687. C4×D4C2×C4×C11semidirect
913. C11#34472direct (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×#23782
C11×#23672
C11×#23642
C11×#23612
C11×#23602
C11×#23552
C11×#23492
D4×C11×C4⋊C42
Q8×C11×C22⋊C42
C11×#23392
C11×#23372
C11×#23292
C11×#23262
C11×#23252
C11×#23232
C11×#23202
C11×#23182
C11×#23112
C4×C11×#1212
C2×C11×#3912
C11×#22902
#3447211