Finite Group Databasebeta

← C11×#34467 #14611660

Subgroups — C11×#34467 #14611660

Order 2816.

2248 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic
2C11×#2379C212yesmaximal, complemented
3C11×#2377C212yesmaximal, complemented
4C11×#2367C212yesmaximal, complemented
5C11×#2365C211yesmaximal, characteristic, complemented
6C11×#2363C211yesmaximal, characteristic, complemented
7C11×#2361C211yesmaximal, characteristic, complemented
8C11×#2352C211yesmaximal, characteristic, complemented
9C11×#2349C211yesmaximal, characteristic, complemented
10C11×#2347C211yesmaximal, characteristic, complemented
11C11×#2346C211yesmaximal, characteristic, complemented
12C11×#2343C212yesmaximal, complemented
13C11×#2337C212yesmaximal, complemented
14C11×#2331C211yesmaximal, characteristic, complemented
15C11×#2326C212yesmaximal, complemented
16C11×#2325C212yesmaximal, complemented
17C11×#2324C211yesmaximal, characteristic, complemented
18C11×#2319C211yesmaximal, characteristic, complemented
19C11×#2317C211yesmaximal, characteristic, complemented
20C11×#2314C212yesmaximal, complemented
21C4×C11×#121C211yesmaximal, characteristic, complemented
22C11×#2296C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic, complemented
24C11×#555C4116yescomplemented
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#124C2212yes—
27C2×C11×#124C2212yes—
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2212yes—
31C2×C4×Q8×C11C2212yes—
32C2×C4×D4×C11C2212yes—
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C2×C4×D4×C11C2212yes—
36C2×C4×D4×C11C2211yescharacteristic
37C2×C4×D4×C11C2211yescharacteristic
38C2×C11×#117C2211yescharacteristic
39C2×C11×#117C2211yescharacteristic
40C2×C11×#117C2211yescharacteristic
41C2×C11×#117C2212yes—
42C2×C11×#117C2211yescharacteristic
43C22×C11×C4⋊C4C2211yescharacteristic
44C22×C42×C11C2211yescharacteristic
45C11×#391C2212yes—
46C11×#391C2212yes—
47C11×#391C2212yes—
48C11×#390C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#390C2212yes—
51C11×#390C2212yes—
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#389C2211yescharacteristic
55C11×#389C2211yescharacteristic
56C11×#389C2211yescharacteristic
57C11×#389C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#389C2211yescharacteristic
60C11×#388C2212yes—
61C11×#388C2212yes—
62C11×#388C2212yes—
63C11×#388C2212yes—
64C11×#388C2211yescharacteristic
65C11×#388C2211yescharacteristic
66C11×#388C2212yes—
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×#386C2212yes—
81C11×#386C2212yes—
82C11×#386C2211yescharacteristic
83C11×#386C2211yescharacteristic
84C11×#386C2212yes—
85C11×#386C2212yes—
86C11×#386C2212yes—
87C11×#385C2211yescharacteristic
88C11×#385C2212yes—
89C11×#385C2212yes—
90C11×#385C2212yes—
91C11×#385C2211yescharacteristic
92C11×#385C2212yes—
93C11×#385C2212yes—
94C11×#385C2212yes—
95C11×#385C2212yes—
96C11×#385C2212yes—
97C11×#384C2212yes—
98C11×#383C2212yes—
99C11×#382C2212yes—
100C11×#382C2212yes—
101C11×#382C2211yescharacteristic
102C11×#381C2212yes—
103C11×#380C2211yescharacteristic
104C11×#380C2212yes—
105C11×#380C2212yes—
106C11×#380C2211yescharacteristic
107C4×C11×C4⋊C4C2211yescharacteristic
108C4×C11×C4⋊C4C2212yes—
109C4×C11×C4⋊C4C2212yes—
110C4×C11×C4⋊C4C2211yescharacteristic
111C4×C11×C4⋊C4C2212yes—
112C4×C11×C4⋊C4C2211yescharacteristic
113C4×C11×C4⋊C4C2211yescharacteristic
114C4×C11×C4⋊C4C2211yescharacteristic
115C4×C11×C4⋊C4C2211yescharacteristic
116C4×C11×C22⋊C4C2211yescharacteristic
117C4×C11×C22⋊C4C2211yescharacteristic
118C4×C11×C22⋊C4C2212yes—
119C4×C11×C22⋊C4C2212yes—
120C4×C11×C22⋊C4C2212yes—
121C11×#376C2211yescharacteristic
122C11×#376C2212yes—
123C2×C11×#95C2212yes—
124C22×Q8×C11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2312yes—
135C23×C4×C11C2312yes—
136C23×C4×C11C2312yes—
137C11×C4⋊Q8C2×C418yescomplemented
138C11×#124C2×C4116yescomplemented
139C11×#124C2×C4116yescomplemented
140C11×#121C2×C418yescomplemented
141C11×#121C2×C418yescomplemented
142C11×#121C2×C4116yescomplemented
143C4×Q8×C11—44no—
144C4×D4×C11—42no—
145C4×D4×C11—42no—
146C4×D4×C11—44no—
147C4×D4×C11—44no—
148C4×D4×C11C2×C418yescomplemented
149C4×D4×C11C2×C418yescomplemented
150C11×#117—42no—
151C11×#117—42no—
152C11×#117C2×C418yescomplemented
153C11×#117C2×C418yescomplemented
154C11×#117C2×C4116yescomplemented
155C2×C11×C4⋊C4—42no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2311yescharacteristic
186C2×C11×C22⋊C4C2311yescharacteristic
187C2×C11×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2311yescharacteristic
198C2×C11×C22⋊C4C2311yescharacteristic
199C2×C11×C22⋊C4C2312yes—
200C2×C42×C11—42no—
201C2×C42×C11C2311yescharacteristic
202C2×C42×C11C2311yescharacteristic
203C2×C42×C11C2311yescharacteristic
204C2×C42×C11C2312yes—
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×C11C2311yescharacteristic
215C2×C42×C11C2312yes—
216C11×#95C2311yescharacteristic
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11×#95C2311yescharacteristic
221C11×#95C2311yescharacteristic
222C11×#95C2312yes—
223C11×#95C2311yescharacteristic
224C11×#95C2312yes—
225C11×#95C2311yescharacteristic
226C11×#95C2311yescharacteristic
227C11×#95C2311yescharacteristic
228C11×#95C2312yes—
229C11×#95C2311yescharacteristic
230C11×#95C2311yescharacteristic
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2311yescharacteristic
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243#34467C1111yesmaximal, characteristic, direct product factor, Sylow
244C24×C11C2411yescharacteristic
245C24×C11C2411yescharacteristic
246C24×C11C2412yes—
247C2×Q8×C11—42no—
248C2×Q8×C11—42no—
249C2×Q8×C11C22×C418yes—
250C2×D4×C11—22no—
251C2×D4×C11—22no—
252C2×D4×C11—42no—
253C2×D4×C11—42no—
254C2×D4×C11—42no—
255C2×D4×C11—42no—
256C2×D4×C11—41no—
257C2×D4×C11—41no—
258C2×D4×C11C22×C414yes—
259C2×D4×C11C22×C414yes—
260C2×D4×C11C22×C418yes—
261C2×D4×C11C22×C418yes—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—22no—
266C22×C4×C11—22no—
267C22×C4×C11—24no—
268C22×C4×C11—41no—
269C22×C4×C11—41no—
270C22×C4×C11—42no—
271C22×C4×C11—42no—
272C22×C4×C11—41no—
273C22×C4×C11—41no—
274C22×C4×C11—41no—
275C22×C4×C11—42no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11C22×C414yes—
284C22×C4×C11C22×C414yes—
285C22×C4×C11C22×C418yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2412yes—
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2412yes—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C11×C4⋊C4—22no—
307C11×C4⋊C4—22no—
308C11×C4⋊C4—22no—
309C11×C4⋊C4—24no—
310C11×C4⋊C4—22no—
311C11×C4⋊C4—22no—
312C11×C4⋊C4—42no—
313C11×C4⋊C4—42no—
314C11×C4⋊C4—42no—
315C11×C4⋊C4—42no—
316C11×C4⋊C4—42no—
317C11×C4⋊C4—42no—
318C11×C4⋊C4—41no—
319C11×C4⋊C4—41no—
320C11×C4⋊C4—41no—
321C11×C4⋊C4—42no—
322C11×C4⋊C4—42no—
323C11×C4⋊C4C22×C414yes—
324C11×C4⋊C4C22×C414yes—
325C11×C4⋊C4C22×C418yes—
326C11×C4⋊C4C22×C414yes—
327C11×C4⋊C4C22×C414yes—
328C11×C22⋊C4—22no—
329C11×C22⋊C4—41no—
330C11×C22⋊C4—41no—
331C11×C22⋊C4—42no—
332C11×C22⋊C4—42no—
333C11×C22⋊C4—42no—
334C11×C22⋊C4—41no—
335C11×C22⋊C4—41no—
336C11×C22⋊C4—41no—
337C11×C22⋊C4—42no—
338C11×C22⋊C4—42no—
339C11×C22⋊C4—42no—
340C11×C22⋊C4—42no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4C22×C418yes—
344C11×C22⋊C4C22×C418yes—
345C11×C22⋊C4C22×C418yes—
346C11×C22⋊C4C22×C418yes—
347C11×C22⋊C4C22×C414yes—
348C11×C22⋊C4C22×C414yes—
349C11×C22⋊C4C22×C418yes—
350C42×C11—22no—
351C42×C11—22no—
352C42×C11—22no—
353C42×C11—24no—
354C42×C11—22no—
355C42×C11—41no—
356C42×C11—41no—
357C42×C11—42no—
358C42×C11—42no—
359C42×C11—42no—
360C42×C11—42no—
361C42×C11—42no—
362C42×C11C22×C418yes—
363C42×C11C22×C418yes—
364C42×C11C22×C414yes—
365C2×#555C2×C1111yescharacteristic
366#2379C2×C1112yescomplemented
367#2377C2×C1112yescomplemented
368#2367C2×C1112yescomplemented
369#2365C2×C1111yescharacteristic, complemented
370#2363C2×C1111yescharacteristic, complemented
371#2361C2×C1111yescharacteristic, complemented
372#2352C2×C1111yescharacteristic, complemented
373#2349C2×C1111yescharacteristic, complemented
374#2347C2×C1111yescharacteristic, complemented
375#2346C2×C1111yescharacteristic, complemented
376#2343C2×C1112yescomplemented
377#2337C2×C1112yescomplemented
378#2331C2×C1111yescharacteristic, complemented
379#2326C2×C1112yescomplemented
380#2325C2×C1112yescomplemented
381#2324C2×C1111yescharacteristic, complemented
382#2319C2×C1111yescharacteristic, complemented
383#2317C2×C1111yescharacteristic, complemented
384#2314C2×C1112yescomplemented
385C4×#121C2×C1111yescharacteristic, complemented
386#2296C2×C1111yescharacteristic, complemented
387#2290C2×C1111yescharacteristic, complemented
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—21no—
391C23×C11—21no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—21no—
395C23×C11—21no—
396C23×C11—22no—
397C23×C11—21no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—21no—
401C23×C11—21no—
402C23×C11—21no—
403C23×C11—21no—
404C23×C11—21no—
405C23×C11—22no—
406C23×C11C23×C412yes—
407C23×C11C23×C412yes—
408C23×C11C23×C414yes—
409C23×C11C2511yescharacteristic
410Q8×C11—48no—
411D4×C11—28no—
412D4×C11—44no—
413D4×C11—48no—
414D4×C11—48no—
415C2×C4×C11—21no—
416C2×C4×C11—22no—
417C2×C4×C11—21no—
418C2×C4×C11—22no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—21no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—28no—
432C2×C4×C11—28no—
433C2×C4×C11—22no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—21no—
446C2×C4×C11—22no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—22no—
450C2×C4×C11—21no—
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—21no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—22no—
466C2×C4×C11—48no—
467C2×C4×C11—44no—
468C2×C4×C11—44no—
469C2×C4×C11—84no—
470C2×C4×C11—84no—
471C2×C4×C11—84no—
472C2×C4×C11C23×C412yes—
473C2×C4×C11C23×C412yes—
474C2×C4×C11C23×C414yes—
475C2×C4×C11C23×C412yes—
476C2×C4×C11C23×C414yes—
477C2×C4×C11C23×C414yes—
478C2×C4×C11C23×C412yes—
479C2×C4×C11C23×C412yes—
480C2×C4×C11H(5,𝔽2)12yes—
481C2×C4×C11H(5,𝔽2)12yes—
482C2×C4×C112−1+412yes—
483#555C4×C11116yescomplemented
484C2×C4⋊Q8C22×C1111yescharacteristic
485C2×#124C22×C1112yes—
486C2×#124C22×C1112yes—
487C2×#121C22×C1111yescharacteristic
488C2×#121C22×C1112yes—
489C2×#121C22×C1111yescharacteristic
490C2×C4×Q8C22×C1112yes—
491C2×C4×D4C22×C1111yescharacteristic
492C2×C4×D4C22×C1112yes—
493C2×C4×D4C22×C1112yes—
494C2×C4×D4C22×C1111yescharacteristic
495C2×C4×D4C22×C1111yescharacteristic
496C2×C4×D4C22×C1111yescharacteristic
497C2×#117C22×C1111yescharacteristic
498C2×#117C22×C1111yescharacteristic
499C2×#117C22×C1112yes—
500C2×#117C22×C1111yescharacteristic
501C2×#117C22×C1111yescharacteristic
502C22×C4⋊C4C22×C1111yescharacteristic
503C22×C42C22×C1111yescharacteristic
504#391C22×C1112yes—
505#391C22×C1112yes—
506#391C22×C1112yes—
507#390C22×C1111yescharacteristic
508#390C22×C1111yescharacteristic
509#390C22×C1112yes—
510#390C22×C1112yes—
511#389C22×C1111yescharacteristic
512#389C22×C1111yescharacteristic
513#389C22×C1111yescharacteristic
514#389C22×C1111yescharacteristic
515#389C22×C1111yescharacteristic
516#389C22×C1111yescharacteristic
517#389C22×C1111yescharacteristic
518#389C22×C1111yescharacteristic
519#388C22×C1112yes—
520#388C22×C1112yes—
521#388C22×C1112yes—
522#388C22×C1112yes—
523#388C22×C1112yes—
524#388C22×C1112yes—
525#388C22×C1112yes—
526#388C22×C1112yes—
527#388C22×C1112yes—
528#388C22×C1112yes—
529#388C22×C1111yescharacteristic
530#388C22×C1112yes—
531#388C22×C1111yescharacteristic
532#387C22×C1111yescharacteristic
533#387C22×C1112yes—
534#387C22×C1112yes—
535#387C22×C1112yes—
536#387C22×C1112yes—
537#387C22×C1112yes—
538#387C22×C1111yescharacteristic
539#386C22×C1112yes—
540#386C22×C1111yescharacteristic
541#386C22×C1112yes—
542#386C22×C1112yes—
543#386C22×C1112yes—
544#386C22×C1111yescharacteristic
545#386C22×C1112yes—
546#385C22×C1112yes—
547#385C22×C1112yes—
548#385C22×C1112yes—
549#385C22×C1112yes—
550#385C22×C1111yescharacteristic
551#385C22×C1112yes—
552#385C22×C1112yes—
553#385C22×C1112yes—
554#385C22×C1112yes—
555#385C22×C1111yescharacteristic
556#384C22×C1112yes—
557#383C22×C1112yes—
558#382C22×C1112yes—
559#382C22×C1112yes—
560#382C22×C1111yescharacteristic
561#381C22×C1112yes—
562#380C22×C1112yes—
563#380C22×C1112yes—
564#380C22×C1111yescharacteristic
565#380C22×C1111yescharacteristic
566C4×C4⋊C4C22×C1112yes—
567C4×C4⋊C4C22×C1112yes—
568C4×C4⋊C4C22×C1111yescharacteristic
569C4×C4⋊C4C22×C1111yescharacteristic
570C4×C4⋊C4C22×C1111yescharacteristic
571C4×C4⋊C4C22×C1111yescharacteristic
572C4×C4⋊C4C22×C1112yes—
573C4×C4⋊C4C22×C1111yescharacteristic
574C4×C4⋊C4C22×C1111yescharacteristic
575C4×C22⋊C4C22×C1112yes—
576C4×C22⋊C4C22×C1112yes—
577C4×C22⋊C4C22×C1112yes—
578C4×C22⋊C4C22×C1111yescharacteristic
579C4×C22⋊C4C22×C1111yescharacteristic
580#376C22×C1111yescharacteristic
581#376C22×C1112yes—
582C2×#95C22×C1112yes—
583C22×C11—22no—
584C22×C11—22no—
585C22×C11—24no—
586C22×C11—24no—
587C22×C11—22no—
588C22×C11—22no—
589C22×C11—22no—
590C22×C11—22no—
591C22×C11—24no—
592C22×C11—41no—
593C22×C11—42no—
594C22×C11—41no—
595C22×C11—41no—
596C22×C11—41no—
597C22×C11—42no—
598C22×C11—41no—
599C22×C11—41no—
600C22×C11—42no—
601C22×C11—41no—
602C22×C11—41no—
603C22×C11—42no—
604C22×C11C24×C411yescharacteristic
605C22×C11C2×H(5,𝔽2)11yescharacteristic
606C22×C11C2×H(5,𝔽2)11yescharacteristic
607C22×C11C2×2−1+411yescharacteristic
608C22×C11#58511yescharacteristic
609C22×C11#58511yescharacteristic
610C22×C11#58511yescharacteristic
611C4×C11—22no—
612C4×C11—22no—
613C4×C11—22no—
614C4×C11—24no—
615C4×C11—24no—
616C4×C11—24no—
617C4×C11—22no—
618C4×C11—22no—
619C4×C11—41no—
620C4×C11—41no—
621C4×C11—42no—
622C4×C11—41no—
623C4×C11—41no—
624C4×C11—41no—
625C4×C11—42no—
626C4×C11—42no—
627C4×C11—42no—
628C4×C11—41no—
629C4×C11—41no—
630C4×C11#52014yes—
631C22×Q8C23×C1112yes—
632C22×D4C23×C1111yescharacteristic
633C22×D4C23×C1112yes—
634C22×D4C23×C1112yes—
635C22×D4C23×C1111yescharacteristic
636C23×C4C23×C1111yescharacteristic
637C23×C4C23×C1111yescharacteristic
638C23×C4C23×C1112yes—
639C23×C4C23×C1111yescharacteristic
640C23×C4C23×C1112yes—
641C23×C4C23×C1112yes—
642C23×C4C23×C1111yescharacteristic
643C23×C4C23×C1112yes—
644C4⋊Q8C2×C4×C1118yescomplemented
645#124C2×C4×C11116yescomplemented
646#124C2×C4×C11116yescomplemented
647#121C2×C4×C1118yescomplemented
648#121C2×C4×C1118yescomplemented
649#121C2×C4×C11116yescomplemented
650C4×Q8—44no—
651C4×D4—42no—
652C4×D4—42no—
653C4×D4—44no—
654C4×D4—44no—
655C4×D4C2×C4×C1118yescomplemented
656C4×D4C2×C4×C1118yescomplemented
657#117—42no—
658#117—42no—
659#117C2×C4×C1118yescomplemented
660#117C2×C4×C1118yescomplemented
661#117C2×C4×C11116yescomplemented
662C2×C4⋊C4—42no—
663C2×C4⋊C4C23×C1111yescharacteristic
664C2×C4⋊C4C23×C1111yescharacteristic
665C2×C4⋊C4C23×C1111yescharacteristic
666C2×C4⋊C4C23×C1112yes—
667C2×C4⋊C4C23×C1111yescharacteristic
668C2×C4⋊C4C23×C1111yescharacteristic
669C2×C4⋊C4C23×C1112yes—
670C2×C4⋊C4C23×C1111yescharacteristic
671C2×C4⋊C4C23×C1111yescharacteristic
672C2×C4⋊C4C23×C1112yes—
673C2×C4⋊C4C23×C1112yes—
674C2×C4⋊C4C23×C1112yes—
675C2×C4⋊C4C23×C1112yes—
676C2×C4⋊C4C23×C1112yes—
677C2×C4⋊C4C23×C1112yes—
678C2×C4⋊C4C23×C1111yescharacteristic
679C2×C4⋊C4C23×C1112yes—
680C2×C4⋊C4C23×C1111yescharacteristic
681C2×C4⋊C4C23×C1111yescharacteristic
682C2×C4⋊C4C23×C1111yescharacteristic
683C2×C4⋊C4C23×C1111yescharacteristic
684C2×C4⋊C4C23×C1112yes—
685C2×C22⋊C4C23×C1111yescharacteristic
686C2×C22⋊C4C23×C1111yescharacteristic
687C2×C22⋊C4C23×C1112yes—
688C2×C22⋊C4C23×C1111yescharacteristic
689C2×C22⋊C4C23×C1112yes—
690C2×C22⋊C4C23×C1112yes—
691C2×C22⋊C4C23×C1112yes—
692C2×C22⋊C4C23×C1112yes—
693C2×C22⋊C4C23×C1112yes—
694C2×C22⋊C4C23×C1112yes—
695C2×C22⋊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×C1111yescharacteristic
705C2×C22⋊C4C23×C1112yes—
706C2×C22⋊C4C23×C1111yescharacteristic
707C2×C42—42no—
708C2×C42C23×C1111yescharacteristic
709C2×C42C23×C1111yescharacteristic
710C2×C42C23×C1112yes—
711C2×C42C23×C1111yescharacteristic
712C2×C42C23×C1111yescharacteristic
713C2×C42C23×C1112yes—
714C2×C42C23×C1112yes—
715C2×C42C23×C1112yes—
716C2×C42C23×C1112yes—
717C2×C42C23×C1112yes—
718C2×C42C23×C1111yescharacteristic
719C2×C42C23×C1111yescharacteristic
720C2×C42C23×C1112yes—
721C2×C42C23×C1112yes—
722C2×C42C23×C1111yescharacteristic
723#95C23×C1111yescharacteristic
724#95C23×C1112yes—
725#95C23×C1112yes—
726#95C23×C1112yes—
727#95C23×C1111yescharacteristic
728#95C23×C1111yescharacteristic
729#95C23×C1112yes—
730#95C23×C1111yescharacteristic
731#95C23×C1112yes—
732#95C23×C1111yescharacteristic
733#95C23×C1111yescharacteristic
734#95C23×C1111yescharacteristic
735#95C23×C1112yes—
736#95C23×C1111yescharacteristic
737#95C23×C1111yescharacteristic
738#95C23×C1112yes—
739#95C23×C1112yes—
740#95C23×C1112yes—
741#95C23×C1111yescharacteristic
742#95C23×C1112yes—
743#95C23×C1112yes—
744#95C23×C1112yes—
745#95C23×C1112yes—
746#95C23×C1112yes—
747#95C23×C1112yes—
748#95C23×C1112yes—
749#95C23×C1112yes—
750C2×C11—42no—
751C2×C11—42no—
752C2×C11—44no—
753C2×C11C2×#52011yescharacteristic
754C2×C11#342811yescharacteristic
755C2×C11C4×H(5,𝔽2)11yescharacteristic
756C2×C11#354011yescharacteristic
757C2×C11#354211yescharacteristic
758C2×C11#354711yescharacteristic
759C2×C11#356511yescharacteristic
760C24C24×C1111yescharacteristic
761C24C24×C1111yescharacteristic
762C24C24×C1112yes—
763C2×Q8—42no—
764C2×Q8—42no—
765C2×Q8C22×C4×C1118yes—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4C22×C4×C1114yes—
775C2×D4C22×C4×C1114yes—
776C2×D4C22×C4×C1118yes—
777C2×D4C22×C4×C1118yes—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—24no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4—41no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4C22×C4×C1114yes—
800C22×C4C22×C4×C1114yes—
801C22×C4C22×C4×C1118yes—
802C22×C4C24×C1111yescharacteristic
803C22×C4C24×C1111yescharacteristic
804C22×C4C24×C1112yes—
805C22×C4C24×C1111yescharacteristic
806C22×C4C24×C1111yescharacteristic
807C22×C4C24×C1111yescharacteristic
808C22×C4C24×C1112yes—
809C22×C4C24×C1112yes—
810C22×C4C24×C1111yescharacteristic
811C22×C4C24×C1112yes—
812C22×C4C24×C1111yescharacteristic
813C22×C4C24×C1111yescharacteristic
814C22×C4C24×C1111yescharacteristic
815C22×C4C24×C1111yescharacteristic
816C22×C4C24×C1112yes—
817C22×C4C24×C1112yes—
818C22×C4C24×C1111yescharacteristic
819C22×C4C24×C1112yes—
820C22×C4C24×C1111yescharacteristic
821C22×C4C24×C1111yescharacteristic
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—24no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—42no—
829C4⋊C4—41no—
830C4⋊C4—41no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—41no—
839C4⋊C4C22×C4×C1114yes—
840C4⋊C4C22×C4×C1114yes—
841C4⋊C4C22×C4×C1118yes—
842C4⋊C4C22×C4×C1114yes—
843C4⋊C4C22×C4×C1114yes—
844C22⋊C4—22no—
845C22⋊C4—41no—
846C22⋊C4—41no—
847C22⋊C4—42no—
848C22⋊C4—42no—
849C22⋊C4—42no—
850C22⋊C4—42no—
851C22⋊C4—42no—
852C22⋊C4—42no—
853C22⋊C4—41no—
854C22⋊C4—41no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—41no—
859C22⋊C4C22×C4×C1118yes—
860C22⋊C4C22×C4×C1118yes—
861C22⋊C4C22×C4×C1118yes—
862C22⋊C4C22×C4×C1118yes—
863C22⋊C4C22×C4×C1114yes—
864C22⋊C4C22×C4×C1114yes—
865C22⋊C4C22×C4×C1118yes—
866C42—22no—
867C42—22no—
868C42—22no—
869C42—24no—
870C42—22no—
871C42—41no—
872C42—41no—
873C42—42no—
874C42—42no—
875C42—42no—
876C42—42no—
877C42—42no—
878C42C22×C4×C1118yes—
879C42C22×C4×C1118yes—
880C42C22×C4×C1114yes—
881C11#3446711yescharacteristic, direct product factor, Sylow
882C23—21no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—22no—
887C23—22no—
888C23—21no—
889C23—21no—
890C23—22no—
891C23—21no—
892C23—22no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23C23×C4×C1112yes—
901C23C23×C4×C1112yes—
902C23C23×C4×C1114yes—
903C23C25×C1111yescharacteristic
904Q8—48no—
905D4—28no—
906D4—44no—
907D4—48no—
908D4—48no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—48no—
961C2×C4—44no—
962C2×C4—44no—
963C2×C4—84no—
964C2×C4—84no—
965C2×C4—84no—
966C2×C4C23×C4×C1112yes—
967C2×C4C23×C4×C1112yes—
968C2×C4C23×C4×C1114yes—
969C2×C4C23×C4×C1112yes—
970C2×C4C23×C4×C1114yes—
971C2×C4C23×C4×C1114yes—
972C2×C4C23×C4×C1112yes—
973C2×C4C23×C4×C1112yes—
974C2×C4C11×H(5,𝔽2)12yes—
975C2×C4C11×H(5,𝔽2)12yes—
976C2×C4C11×2−1+412yes—
977C22—22no—
978C22—22no—
979C22—24no—
980C22—24no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—24no—
986C22—41no—
987C22—42no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—41no—
994C22—42no—
995C22—41no—
996C22—41no—
997C22—42no—
998C22C24×C4×C1111yescharacteristic
999C22C2×C11×H(5,𝔽2)11yescharacteristic
1000C22C2×C11×H(5,𝔽2)11yescharacteristic
1001C22C2×C11×2−1+411yescharacteristic
1002C22C11×#58511yescharacteristic
1003C22C11×#58511yescharacteristic
1004C22C11×#58511yescharacteristic
1005C4—22no—
1006C4—22no—
1007C4—22no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—22no—
1012C4—22no—
1013C4—41no—
1014C4—41no—
1015C4—41no—
1016C4—42no—
1017C4—41no—
1018C4—42no—
1019C4—42no—
1020C4—41no—
1021C4—42no—
1022C4—41no—
1023C4—41no—
1024C4C11×#52014yes—
1025C2—42no—
1026C2—42no—
1027C2—44no—
1028C2C2×C11×#52011yescharacteristic
1029C2C11×#342811yescharacteristic
1030C2C4×C11×H(5,𝔽2)11yescharacteristic
1031C2C11×#354011yescharacteristic
1032C2C11×#354211yescharacteristic
1033C2C11×#354711yescharacteristic
1034C2C11×#356511yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#555C2
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×#2367C2semidirect
5. C11×#2365C2semidirect
6. C11×#2363C2semidirect
7. C11×#2361C2semidirect
8. C11×#2352C2semidirect
9. C11×#2349C2semidirect
10. C11×#2347C2semidirect
11. C11×#2346C2semidirect
12. C11×#2343C2semidirect
13. C11×#2337C2semidirect
14. C11×#2331C2semidirect
15. C11×#2326C2semidirect
16. C11×#2325C2semidirect
17. C11×#2324C2semidirect
18. C11×#2319C2semidirect
19. C11×#2317C2semidirect
20. C11×#2314C2semidirect
21. C4×C11×#121C2semidirect
22. C11×#2296C2semidirect
23. C11×#2290C2semidirect
24. C11×#555C4semidirect
137. C11×C4⋊Q8C2×C4semidirect
138. C11×#124C2×C4semidirect
139. C11×#124C2×C4semidirect
140. C11×#121C2×C4semidirect
141. C11×#121C2×C4semidirect
142. C11×#121C2×C4semidirect
148. C4×D4×C11C2×C4semidirect
149. C4×D4×C11C2×C4semidirect
152. C11×#117C2×C4semidirect
153. C11×#117C2×C4semidirect
154. C11×#117C2×C4semidirect
243. #34467C11direct (N × H)
366. #2379C2×C11semidirect
367. #2377C2×C11semidirect
368. #2367C2×C11semidirect
369. #2365C2×C11semidirect
370. #2363C2×C11semidirect
371. #2361C2×C11semidirect
372. #2352C2×C11semidirect
373. #2349C2×C11semidirect
374. #2347C2×C11semidirect
375. #2346C2×C11semidirect
376. #2343C2×C11semidirect
377. #2337C2×C11semidirect
378. #2331C2×C11semidirect
379. #2326C2×C11semidirect
380. #2325C2×C11semidirect
381. #2324C2×C11semidirect
382. #2319C2×C11semidirect
383. #2317C2×C11semidirect
384. #2314C2×C11semidirect
385. C4×#121C2×C11semidirect
386. #2296C2×C11semidirect
387. #2290C2×C11semidirect
483. #555C4×C11semidirect
644. C4⋊Q8C2×C4×C11semidirect
645. #124C2×C4×C11semidirect
646. #124C2×C4×C11semidirect
647. #121C2×C4×C11semidirect
648. #121C2×C4×C11semidirect
649. #121C2×C4×C11semidirect
655. C4×D4C2×C4×C11semidirect
656. C4×D4C2×C4×C11semidirect
659. #117C2×C4×C11semidirect
660. #117C2×C4×C11semidirect
661. #117C2×C4×C11semidirect
881. C11#34467direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C11×#23792
C11×#23772
C11×#23672
C11×#23652
C11×#23632
C11×#23612
C11×#23522
C11×#23492
C11×#23472
C11×#23462
C11×#23432
C11×#23372
C11×#23312
C11×#23262
C11×#23252
C11×#23242
C11×#23192
C11×#23172
C11×#23142
C4×C11×#1212
C11×#22962
C11×#22902
#3446711