Finite Group Databasebeta

← C11×#35038 #14612231

Subgroups — C11×#35038 #14612231

Order 2816.

2100 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2861C211yesmaximal, characteristic, complemented
2C11×#2860C211yesmaximal, characteristic, complemented
3C11×#2856C211yesmaximal, characteristic, complemented
4C11×#2855C211yesmaximal, characteristic, complemented
5C11×#2648C212yesmaximal, complemented
6C11×#2635C212yesmaximal, complemented
7C11×#2595C212yesmaximal, complemented
8C11×#2559C212yesmaximal, complemented
9C11×#2511C211yesmaximal, characteristic, complemented
10C11×#2490C211yesmaximal, characteristic, complemented
11C11×#2467C212yesmaximal, complemented
12C11×#2456C212yesmaximal, complemented
13C11×#2445C211yesmaximal, characteristic, complemented
14C11×#2441C211yesmaximal, characteristic, complemented
15C11×#2431C211yesmaximal, characteristic, complemented
16C11×#2427C211yesmaximal, characteristic, complemented
17C11×#2414C211yesmaximal, characteristic, complemented
18C11×#2407C211yesmaximal, characteristic, complemented
19C11×#2335C212yesmaximal, complemented
20C11×#2333C212yesmaximal, complemented
21C4×C11×#121C211yesmaximal, characteristic, complemented
22C11×#2297C211yesmaximal, characteristic, complemented
23C42×D4×C11C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C2×C11×#126C2212yes—
27C2×C11×#125C2211yescharacteristic
28C2×C11×#124C2211yescharacteristic
29C2×C11×#123C2212yes—
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C11×#121C2212yes—
32C2×C11×#121C2211yescharacteristic
33C2×C11×#121C2211yescharacteristic
34C2×C11×#121C2211yescharacteristic
35C2×C11×#121C2212yes—
36C2×C4×D4×C11C2211yescharacteristic
37C2×C4×D4×C11C2211yescharacteristic
38C2×C4×D4×C11C2211yescharacteristic
39C2×C4×D4×C11C2211yescharacteristic
40C2×C4×D4×C11C2212yes—
41C2×C11×#117C2211yescharacteristic
42C22×C42×C11C2211yescharacteristic
43C22×C42×C11C2211yescharacteristic
44C11×#400C2212yes—
45C11×#400C2212yes—
46C11×#399C2212yes—
47C11×#397C2212yes—
48C11×#397C2212yes—
49C11×#396C2212yes—
50C11×#394C2212yes—
51C11×#394C2212yes—
52C11×#394C2212yes—
53C11×#394C2212yes—
54C11×#394C2212yes—
55C11×#394C2212yes—
56C11×#392C2212yes—
57C11×#392C2212yes—
58C11×#392C2212yes—
59C11×#392C2212yes—
60C11×#391C2211yescharacteristic
61C11×#391C2211yescharacteristic
62C11×#391C2211yescharacteristic
63C11×#391C2211yescharacteristic
64C11×#390C2212yes—
65C11×#390C2211yescharacteristic
66C11×#390C2211yescharacteristic
67C11×#390C2212yes—
68C11×#390C2211yescharacteristic
69C11×#390C2211yescharacteristic
70C11×#390C2212yes—
71C11×#390C2212yes—
72C11×#390C2211yescharacteristic
73C11×#390C2211yescharacteristic
74C11×#389C2211yescharacteristic
75C11×#389C2211yescharacteristic
76C11×#389C2211yescharacteristic
77C11×#389C2212yes—
78C11×#389C2211yescharacteristic
79C11×#388C2212yes—
80C11×#388C2212yes—
81C11×#388C2212yes—
82C11×#388C2212yes—
83C11×#388C2212yes—
84C11×#388C2212yes—
85C11×#388C2212yes—
86C11×#388C2212yes—
87C11×#388C2212yes—
88C11×#388C2212yes—
89C11×#387C2212yes—
90C11×#387C2212yes—
91C11×#387C2212yes—
92C11×#387C2212yes—
93C11×#387C2212yes—
94C11×#386C2212yes—
95C11×#386C2212yes—
96C11×#386C2212yes—
97C11×#386C2212yes—
98C11×#386C2212yes—
99C11×#386C2212yes—
100C11×#386C2212yes—
101C11×#386C2212yes—
102C11×#385C2212yes—
103C11×#385C2212yes—
104C11×#384C2211yescharacteristic
105C11×#381C2212yes—
106C11×#380C2211yescharacteristic
107C11×#380C2211yescharacteristic
108C11×#380C2212yes—
109C4×C11×C4⋊C4C2211yescharacteristic
110C4×C11×C4⋊C4C2211yescharacteristic
111C4×C11×C4⋊C4C2211yescharacteristic
112C4×C11×C4⋊C4C2211yescharacteristic
113C4×C11×C22⋊C4C2211yescharacteristic
114C4×C11×C22⋊C4C2211yescharacteristic
115C4×C11×C22⋊C4C2211yescharacteristic
116C4×C11×C22⋊C4C2211yescharacteristic
117C4×C11×C22⋊C4C2211yescharacteristic
118C4×C11×C22⋊C4C2211yescharacteristic
119C4×C11×C22⋊C4C2212yes—
120C4×C11×C22⋊C4C2212yes—
121C4×C11×C22⋊C4C2212yes—
122C43×C11C2211yescharacteristic
123C2×C11×#41—24no—
124C2×C11×#41—42no—
125C2×C11×#41—42no—
126C22×Q8×C11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C22×D4×C11C2312yes—
132C22×D4×C11C2312yes—
133C22×D4×C11C2312yes—
134C22×D4×C11C2312yes—
135C22×D4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C23×C4×C11C2311yescharacteristic
139C23×C4×C11C2311yescharacteristic
140C23×C4×C11C2311yescharacteristic
141C23×C4×C11C2312yes—
142C23×C4×C11C2312yes—
143C23×C4×C11C2311yescharacteristic
144C11×#127—42no—
145C11×#126—44no—
146C11×#125—42no—
147C11×#124—42no—
148C11×#123—28no—
149C11×C22⋊Q8—42no—
150C11×#121—24no—
151C11×#121—28no—
152C11×#121—44no—
153C11×#121—42no—
154C11×#121—42no—
155C4×D4×C11—24no—
156C4×D4×C11—24no—
157C4×D4×C11—24no—
158C4×D4×C11—42no—
159C4×D4×C11—44no—
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⋊C4C2312yes—
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⋊C4C2312yes—
176C2×C11×C4⋊C4C2312yes—
177C2×C11×C4⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C11×C22⋊C4C2311yescharacteristic
181C2×C11×C22⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4C2311yescharacteristic
183C2×C11×C22⋊C4C2311yescharacteristic
184C2×C11×C22⋊C4C2312yes—
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⋊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⋊C4C2312yes—
204C2×C11×C22⋊C4C2312yes—
205C2×C11×C22⋊C4C2312yes—
206C2×C42×C11—42no—
207C2×C42×C11—42no—
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214C2×C42×C11C2311yescharacteristic
215C2×C42×C11C2311yescharacteristic
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2311yescharacteristic
218C2×C42×C11C2311yescharacteristic
219C2×C42×C11C2311yescharacteristic
220C2×C42×C11C2311yescharacteristic
221C2×C42×C11C2312yes—
222C2×C42×C11C2312yes—
223C11×#95C2311yescharacteristic
224C11×#95C2311yescharacteristic
225C11×#95C2311yescharacteristic
226C11×#95C2311yescharacteristic
227C11×#95C2311yescharacteristic
228C11×#95C2311yescharacteristic
229C11×#95C2312yes—
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×#95C2312yes—
244#35038C1111yesmaximal, characteristic, direct product factor, Sylow
245C24×C11C2412yes—
246C24×C11C2412yes—
247C24×C11C2411yescharacteristic
248C24×C11C2411yescharacteristic
249C11×#41—416no—
250C2×Q8×C11—22no—
251C2×Q8×C11—22no—
252C2×Q8×C11—22no—
253C2×D4×C11—22no—
254C2×D4×C11—22no—
255C2×D4×C11—24no—
256C2×D4×C11—24no—
257C2×D4×C11—24no—
258C2×D4×C11—24no—
259C2×D4×C11—22no—
260C2×D4×C11—22no—
261C2×D4×C11—22no—
262C2×D4×C11—24no—
263C2×D4×C11—24no—
264C2×D4×C11—22no—
265C2×D4×C11—22no—
266C2×D4×C11—22no—
267C2×D4×C11—22no—
268C2×D4×C11—42no—
269C2×D4×C11—42no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11—42no—
273C2×D4×C11—42no—
274C2×D4×C11—42no—
275C2×D4×C11—42no—
276C2×D4×C11—42no—
277C2×D4×C11—42no—
278C2×D4×C11—42no—
279C2×D4×C11—42no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—24no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—24no—
292C22×C4×C11—41no—
293C22×C4×C11—41no—
294C22×C4×C11—41no—
295C22×C4×C11—41no—
296C22×C4×C11—41no—
297C22×C4×C11—41no—
298C22×C4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11—42no—
301C22×C4×C11—42no—
302C22×C4×C11#4114yes—
303C22×C4×C11#4114yescomplemented
304C22×C4×C11C2412yes—
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2412yes—
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2412yes—
311C22×C4×C11C2412yes—
312C22×C4×C11C2412yes—
313C22×C4×C11C2412yes—
314C22×C4×C11C2411yescharacteristic
315C22×C4×C11C2411yescharacteristic
316C22×C4×C11C2411yescharacteristic
317C22×C4×C11C2411yescharacteristic
318C22×C4×C11C2411yescharacteristic
319C22×C4×C11C2411yescharacteristic
320C22×C4×C11C2411yescharacteristic
321C22×C4×C11C2411yescharacteristic
322C22×C4×C11C2411yescharacteristic
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—24no—
326C11×C4⋊C4—22no—
327C11×C4⋊C4—24no—
328C11×C4⋊C4—22no—
329C11×C4⋊C4—22no—
330C11×C4⋊C4—22no—
331C11×C4⋊C4—24no—
332C11×C4⋊C4—22no—
333C11×C4⋊C4—42no—
334C11×C4⋊C4—42no—
335C11×C4⋊C4—42no—
336C11×C4⋊C4—42no—
337C11×C4⋊C4—42no—
338C11×C4⋊C4—42no—
339C11×C4⋊C4#4114yescomplemented
340C11×C22⋊C4—22no—
341C11×C22⋊C4—22no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—22no—
344C11×C22⋊C4—22no—
345C11×C22⋊C4—22no—
346C11×C22⋊C4—24no—
347C11×C22⋊C4—24no—
348C11×C22⋊C4—24no—
349C11×C22⋊C4—24no—
350C11×C22⋊C4—24no—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4—42no—
358C11×C22⋊C4—42no—
359C11×C22⋊C4—42no—
360C11×C22⋊C4—42no—
361C11×C22⋊C4—42no—
362C11×C22⋊C4—42no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4—42no—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—22no—
372C42×C11—22no—
373C42×C11—22no—
374C42×C11—22no—
375C42×C11—22no—
376C42×C11—41no—
377C42×C11—41no—
378C42×C11—41no—
379C42×C11—41no—
380C42×C11—41no—
381C42×C11—42no—
382C42×C11—42no—
383#2861C2×C1111yescharacteristic, complemented
384#2860C2×C1111yescharacteristic, complemented
385#2856C2×C1111yescharacteristic, complemented
386#2855C2×C1111yescharacteristic, complemented
387#2648C2×C1112yescomplemented
388#2635C2×C1112yescomplemented
389#2595C2×C1112yescomplemented
390#2559C2×C1112yescomplemented
391#2511C2×C1111yescharacteristic, complemented
392#2490C2×C1111yescharacteristic, complemented
393#2467C2×C1112yescomplemented
394#2456C2×C1112yescomplemented
395#2445C2×C1111yescharacteristic, complemented
396#2441C2×C1111yescharacteristic, complemented
397#2431C2×C1111yescharacteristic, complemented
398#2427C2×C1111yescharacteristic, complemented
399#2414C2×C1111yescharacteristic, complemented
400#2407C2×C1111yescharacteristic, complemented
401#2335C2×C1112yescomplemented
402#2333C2×C1112yescomplemented
403C4×#121C2×C1111yescharacteristic, complemented
404#2297C2×C1111yescharacteristic, complemented
405C42×D4C2×C1111yescharacteristic, complemented
406C23×C11—21no—
407C23×C11—21no—
408C23×C11—21no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11—21no—
414C23×C11—21no—
415C23×C11—21no—
416C23×C11—21no—
417C23×C11—21no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—22no—
428C23×C11—22no—
429C23×C11—22no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11C2×#4112yes—
433C23×C11C2×#4112yes—
434C23×C11C2511yescharacteristic
435Q8×C11—44no—
436D4×C11—28no—
437D4×C11—48no—
438D4×C11—48no—
439D4×C11—44no—
440D4×C11—44no—
441D4×C11—84no—
442D4×C11—84no—
443D4×C11—84no—
444D4×C11—84no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
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—21no—
458C2×C4×C11—21no—
459C2×C4×C11—28no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—22no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—44no—
494C2×C4×C11—44no—
495C2×C4×C11—44no—
496C2×C4×C11—44no—
497C2×C4×C11—48no—
498C2×C4×C11—44no—
499C2×C4×C11—84no—
500C2×C4×C11C2×#4112yes—
501C2×C4×C11C2×#4112yes—
502C2×C4×C11C2×#4112yes—
503C2×C4×C11C2×#4112yes—
504C2×C4×C11C2×#4112yes—
505C2×C4×C11C2×#4112yes—
506C2×C4×C11C2×#4112yes—
507C2×C4×C11H(5,𝔽2)12yes—
508C2×C4×C11H(5,𝔽2)12yes—
509C2×C4×C11H(5,𝔽2)12yes—
510C22×#41C22×C1111yescharacteristic
511C2×#127C22×C1111yescharacteristic
512C2×#126C22×C1112yes—
513C2×#125C22×C1111yescharacteristic
514C2×#124C22×C1111yescharacteristic
515C2×#123C22×C1112yes—
516C2×C22⋊Q8C22×C1111yescharacteristic
517C2×#121C22×C1112yes—
518C2×#121C22×C1111yescharacteristic
519C2×#121C22×C1111yescharacteristic
520C2×#121C22×C1111yescharacteristic
521C2×#121C22×C1112yes—
522C2×C4×D4C22×C1111yescharacteristic
523C2×C4×D4C22×C1111yescharacteristic
524C2×C4×D4C22×C1111yescharacteristic
525C2×C4×D4C22×C1111yescharacteristic
526C2×C4×D4C22×C1112yes—
527C2×#117C22×C1111yescharacteristic
528C22×C42C22×C1111yescharacteristic
529C22×C42C22×C1111yescharacteristic
530#400C22×C1112yes—
531#400C22×C1112yes—
532#399C22×C1112yes—
533#397C22×C1112yes—
534#397C22×C1112yes—
535#396C22×C1112yes—
536#394C22×C1112yes—
537#394C22×C1112yes—
538#394C22×C1112yes—
539#394C22×C1112yes—
540#394C22×C1112yes—
541#394C22×C1112yes—
542#392C22×C1112yes—
543#392C22×C1112yes—
544#392C22×C1112yes—
545#392C22×C1112yes—
546#391C22×C1111yescharacteristic
547#391C22×C1111yescharacteristic
548#391C22×C1111yescharacteristic
549#391C22×C1111yescharacteristic
550#390C22×C1112yes—
551#390C22×C1112yes—
552#390C22×C1112yes—
553#390C22×C1112yes—
554#390C22×C1111yescharacteristic
555#390C22×C1111yescharacteristic
556#390C22×C1111yescharacteristic
557#390C22×C1111yescharacteristic
558#390C22×C1111yescharacteristic
559#390C22×C1111yescharacteristic
560#389C22×C1112yes—
561#389C22×C1111yescharacteristic
562#389C22×C1111yescharacteristic
563#389C22×C1111yescharacteristic
564#389C22×C1111yescharacteristic
565#388C22×C1112yes—
566#388C22×C1112yes—
567#388C22×C1112yes—
568#388C22×C1112yes—
569#388C22×C1112yes—
570#388C22×C1112yes—
571#388C22×C1112yes—
572#388C22×C1112yes—
573#388C22×C1112yes—
574#388C22×C1112yes—
575#387C22×C1112yes—
576#387C22×C1112yes—
577#387C22×C1112yes—
578#387C22×C1112yes—
579#387C22×C1112yes—
580#386C22×C1112yes—
581#386C22×C1112yes—
582#386C22×C1112yes—
583#386C22×C1112yes—
584#386C22×C1112yes—
585#386C22×C1112yes—
586#386C22×C1112yes—
587#386C22×C1112yes—
588#385C22×C1112yes—
589#385C22×C1112yes—
590#384C22×C1111yescharacteristic
591#381C22×C1112yes—
592#380C22×C1112yes—
593#380C22×C1111yescharacteristic
594#380C22×C1111yescharacteristic
595C4×C4⋊C4C22×C1111yescharacteristic
596C4×C4⋊C4C22×C1111yescharacteristic
597C4×C4⋊C4C22×C1111yescharacteristic
598C4×C4⋊C4C22×C1111yescharacteristic
599C4×C22⋊C4C22×C1111yescharacteristic
600C4×C22⋊C4C22×C1112yes—
601C4×C22⋊C4C22×C1112yes—
602C4×C22⋊C4C22×C1112yes—
603C4×C22⋊C4C22×C1111yescharacteristic
604C4×C22⋊C4C22×C1111yescharacteristic
605C4×C22⋊C4C22×C1111yescharacteristic
606C4×C22⋊C4C22×C1111yescharacteristic
607C4×C22⋊C4C22×C1111yescharacteristic
608C43C22×C1111yescharacteristic
609C22×C11—22no—
610C22×C11—22no—
611C22×C11—22no—
612C22×C11—22no—
613C22×C11—22no—
614C22×C11—22no—
615C22×C11—41no—
616C22×C11—41no—
617C22×C11—41no—
618C22×C11—41no—
619C22×C11—41no—
620C22×C11—41no—
621C22×C11—41no—
622C22×C11—41no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11—42no—
627C22×C11—42no—
628C22×C11—42no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11C22×#4111yescharacteristic
638C22×C11C22×#4111yescharacteristic
639C22×C11C22×#4111yescharacteristic
640C22×C11C2×H(5,𝔽2)11yescharacteristic
641C22×C11C2×H(5,𝔽2)11yescharacteristic
642C22×C11C2×H(5,𝔽2)11yescharacteristic
643C22×C11#58511yescharacteristic
644C4×C11—22no—
645C4×C11—22no—
646C4×C11—22no—
647C4×C11—22no—
648C4×C11—22no—
649C4×C11—22no—
650C4×C11—22no—
651C4×C11—41no—
652C4×C11—42no—
653C4×C11—41no—
654C4×C11—42no—
655C4×C11—41no—
656C4×C11—41no—
657C4×C11—42no—
658C4×C11—42no—
659C4×C11—41no—
660C4×C11—42no—
661C4×C11—42no—
662C4×C11#53814yes—
663C2×#41—24no—
664C2×#41—42no—
665C2×#41—42no—
666C22×Q8C23×C1111yescharacteristic
667C22×D4C23×C1111yescharacteristic
668C22×D4C23×C1111yescharacteristic
669C22×D4C23×C1111yescharacteristic
670C22×D4C23×C1112yes—
671C22×D4C23×C1112yes—
672C22×D4C23×C1112yes—
673C22×D4C23×C1112yes—
674C22×D4C23×C1112yes—
675C22×D4C23×C1112yes—
676C23×C4C23×C1111yescharacteristic
677C23×C4C23×C1111yescharacteristic
678C23×C4C23×C1111yescharacteristic
679C23×C4C23×C1111yescharacteristic
680C23×C4C23×C1112yes—
681C23×C4C23×C1111yescharacteristic
682C23×C4C23×C1112yes—
683C23×C4C23×C1111yescharacteristic
684#127—42no—
685#126—44no—
686#125—42no—
687#124—42no—
688#123—28no—
689C22⋊Q8—42no—
690#121—24no—
691#121—28no—
692#121—44no—
693#121—42no—
694#121—42no—
695C4×D4—24no—
696C4×D4—24no—
697C4×D4—24no—
698C4×D4—42no—
699C4×D4—44no—
700#117—42no—
701C2×C4⋊C4C23×C1111yescharacteristic
702C2×C4⋊C4C23×C1111yescharacteristic
703C2×C4⋊C4C23×C1111yescharacteristic
704C2×C4⋊C4C23×C1112yes—
705C2×C4⋊C4C23×C1111yescharacteristic
706C2×C4⋊C4C23×C1111yescharacteristic
707C2×C4⋊C4C23×C1111yescharacteristic
708C2×C4⋊C4C23×C1111yescharacteristic
709C2×C4⋊C4C23×C1112yes—
710C2×C4⋊C4C23×C1112yes—
711C2×C4⋊C4C23×C1112yes—
712C2×C4⋊C4C23×C1112yes—
713C2×C4⋊C4C23×C1112yes—
714C2×C4⋊C4C23×C1112yes—
715C2×C4⋊C4C23×C1112yes—
716C2×C4⋊C4C23×C1112yes—
717C2×C4⋊C4C23×C1111yescharacteristic
718C2×C22⋊C4C23×C1112yes—
719C2×C22⋊C4C23×C1111yescharacteristic
720C2×C22⋊C4C23×C1111yescharacteristic
721C2×C22⋊C4C23×C1111yescharacteristic
722C2×C22⋊C4C23×C1111yescharacteristic
723C2×C22⋊C4C23×C1111yescharacteristic
724C2×C22⋊C4C23×C1111yescharacteristic
725C2×C22⋊C4C23×C1112yes—
726C2×C22⋊C4C23×C1112yes—
727C2×C22⋊C4C23×C1112yes—
728C2×C22⋊C4C23×C1112yes—
729C2×C22⋊C4C23×C1112yes—
730C2×C22⋊C4C23×C1112yes—
731C2×C22⋊C4C23×C1112yes—
732C2×C22⋊C4C23×C1112yes—
733C2×C22⋊C4C23×C1112yes—
734C2×C22⋊C4C23×C1112yes—
735C2×C22⋊C4C23×C1112yes—
736C2×C22⋊C4C23×C1112yes—
737C2×C22⋊C4C23×C1112yes—
738C2×C22⋊C4C23×C1112yes—
739C2×C22⋊C4C23×C1112yes—
740C2×C22⋊C4C23×C1112yes—
741C2×C22⋊C4C23×C1112yes—
742C2×C22⋊C4C23×C1112yes—
743C2×C22⋊C4C23×C1112yes—
744C2×C22⋊C4C23×C1112yes—
745C2×C22⋊C4C23×C1112yes—
746C2×C42—42no—
747C2×C42—42no—
748C2×C42C23×C1111yescharacteristic
749C2×C42C23×C1111yescharacteristic
750C2×C42C23×C1111yescharacteristic
751C2×C42C23×C1111yescharacteristic
752C2×C42C23×C1111yescharacteristic
753C2×C42C23×C1111yescharacteristic
754C2×C42C23×C1111yescharacteristic
755C2×C42C23×C1111yescharacteristic
756C2×C42C23×C1112yes—
757C2×C42C23×C1112yes—
758C2×C42C23×C1111yescharacteristic
759C2×C42C23×C1111yescharacteristic
760C2×C42C23×C1111yescharacteristic
761C2×C42C23×C1111yescharacteristic
762C2×C42C23×C1111yescharacteristic
763#95C23×C1111yescharacteristic
764#95C23×C1111yescharacteristic
765#95C23×C1111yescharacteristic
766#95C23×C1111yescharacteristic
767#95C23×C1111yescharacteristic
768#95C23×C1111yescharacteristic
769#95C23×C1112yes—
770#95C23×C1112yes—
771#95C23×C1112yes—
772#95C23×C1112yes—
773#95C23×C1112yes—
774#95C23×C1112yes—
775#95C23×C1112yes—
776#95C23×C1112yes—
777#95C23×C1112yes—
778#95C23×C1112yes—
779#95C23×C1112yes—
780#95C23×C1112yes—
781#95C23×C1112yes—
782#95C23×C1112yes—
783#95C23×C1112yes—
784C2×C11—42no—
785C2×C11—42no—
786C2×C11—82no—
787C2×C11—82no—
788C2×C11#344411yescharacteristic
789C2×C11C2×#53811yescharacteristic
790C2×C11#346011yescharacteristic
791C2×C11#350511yescharacteristic
792C2×C11#350811yescharacteristic
793C2×C11#351711yescharacteristic
794C2×C11#351911yescharacteristic
795C24C24×C1112yes—
796C24C24×C1112yes—
797C24C24×C1111yescharacteristic
798C24C24×C1111yescharacteristic
799#41—416no—
800C2×Q8—22no—
801C2×Q8—22no—
802C2×Q8—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—24no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—24no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4C11×#4114yes—
853C22×C4C11×#4114yescomplemented
854C22×C4C24×C1112yes—
855C22×C4C24×C1111yescharacteristic
856C22×C4C24×C1112yes—
857C22×C4C24×C1111yescharacteristic
858C22×C4C24×C1111yescharacteristic
859C22×C4C24×C1111yescharacteristic
860C22×C4C24×C1112yes—
861C22×C4C24×C1112yes—
862C22×C4C24×C1112yes—
863C22×C4C24×C1112yes—
864C22×C4C24×C1111yescharacteristic
865C22×C4C24×C1111yescharacteristic
866C22×C4C24×C1111yescharacteristic
867C22×C4C24×C1111yescharacteristic
868C22×C4C24×C1111yescharacteristic
869C22×C4C24×C1111yescharacteristic
870C22×C4C24×C1111yescharacteristic
871C22×C4C24×C1111yescharacteristic
872C22×C4C24×C1111yescharacteristic
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4C11×#4114yescomplemented
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—24no—
897C22⋊C4—24no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—42no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C42—22no—
919C42—22no—
920C42—22no—
921C42—22no—
922C42—22no—
923C42—22no—
924C42—22no—
925C42—22no—
926C42—41no—
927C42—41no—
928C42—41no—
929C42—41no—
930C42—42no—
931C42—42no—
932C42—41no—
933C11#3503811yescharacteristic, direct product factor, Sylow
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23C2×C11×#4112yes—
961C23C2×C11×#4112yes—
962C23C25×C1111yescharacteristic
963Q8—44no—
964D4—28no—
965D4—48no—
966D4—48no—
967D4—44no—
968D4—44no—
969D4—84no—
970D4—84no—
971D4—84no—
972D4—84no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—28no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—44no—
1022C2×C4—44no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—48no—
1026C2×C4—44no—
1027C2×C4—84no—
1028C2×C4C2×C11×#4112yes—
1029C2×C4C2×C11×#4112yes—
1030C2×C4C2×C11×#4112yes—
1031C2×C4C2×C11×#4112yes—
1032C2×C4C2×C11×#4112yes—
1033C2×C4C2×C11×#4112yes—
1034C2×C4C2×C11×#4112yes—
1035C2×C4C11×H(5,𝔽2)12yes—
1036C2×C4C11×H(5,𝔽2)12yes—
1037C2×C4C11×H(5,𝔽2)12yes—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22C22×C11×#4111yescharacteristic
1067C22C22×C11×#4111yescharacteristic
1068C22C22×C11×#4111yescharacteristic
1069C22C2×C11×H(5,𝔽2)11yescharacteristic
1070C22C2×C11×H(5,𝔽2)11yescharacteristic
1071C22C2×C11×H(5,𝔽2)11yescharacteristic
1072C22C11×#58511yescharacteristic
1073C4—22no—
1074C4—22no—
1075C4—22no—
1076C4—22no—
1077C4—22no—
1078C4—22no—
1079C4—22no—
1080C4—42no—
1081C4—41no—
1082C4—42no—
1083C4—41no—
1084C4—41no—
1085C4—42no—
1086C4—42no—
1087C4—41no—
1088C4—41no—
1089C4—42no—
1090C4—42no—
1091C4C11×#53814yes—
1092C2—42no—
1093C2—42no—
1094C2—82no—
1095C2—82no—
1096C2C11×#344411yescharacteristic
1097C2C2×C11×#53811yescharacteristic
1098C2C11×#346011yescharacteristic
1099C2C11×#350511yescharacteristic
1100C2C11×#350811yescharacteristic
1101C2C11×#351711yescharacteristic
1102C2C11×#351911yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2861C2semidirect
2. C11×#2860C2semidirect
3. C11×#2856C2semidirect
4. C11×#2855C2semidirect
5. C11×#2648C2semidirect
6. C11×#2635C2semidirect
7. C11×#2595C2semidirect
8. C11×#2559C2semidirect
9. C11×#2511C2semidirect
10. C11×#2490C2semidirect
11. C11×#2467C2semidirect
12. C11×#2456C2semidirect
13. C11×#2445C2semidirect
14. C11×#2441C2semidirect
15. C11×#2431C2semidirect
16. C11×#2427C2semidirect
17. C11×#2414C2semidirect
18. C11×#2407C2semidirect
19. C11×#2335C2semidirect
20. C11×#2333C2semidirect
21. C4×C11×#121C2semidirect
22. C11×#2297C2semidirect
23. C42×D4×C11C2semidirect
244. #35038C11direct (N × H)
303. C22×C4×C11#41semidirect
339. C11×C4⋊C4#41semidirect
383. #2861C2×C11semidirect
384. #2860C2×C11semidirect
385. #2856C2×C11semidirect
386. #2855C2×C11semidirect
387. #2648C2×C11semidirect
388. #2635C2×C11semidirect
389. #2595C2×C11semidirect
390. #2559C2×C11semidirect
391. #2511C2×C11semidirect
392. #2490C2×C11semidirect
393. #2467C2×C11semidirect
394. #2456C2×C11semidirect
395. #2445C2×C11semidirect
396. #2441C2×C11semidirect
397. #2431C2×C11semidirect
398. #2427C2×C11semidirect
399. #2414C2×C11semidirect
400. #2407C2×C11semidirect
401. #2335C2×C11semidirect
402. #2333C2×C11semidirect
403. C4×#121C2×C11semidirect
404. #2297C2×C11semidirect
405. C42×D4C2×C11semidirect
853. C22×C4C11×#41semidirect
889. C4⋊C4C11×#41semidirect
933. C11#35038direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28612
C11×#28602
C11×#28562
C11×#28552
C11×#26482
C11×#26352
C11×#25952
C11×#25592
C11×#25112
C11×#24902
C11×#24672
C11×#24562
C11×#24452
C11×#24412
C11×#24312
C11×#24272
C11×#24142
C11×#24072
C11×#23352
C11×#23332
C4×C11×#1212
C11×#22972
C42×D4×C112
#3503811