Finite Group Databasebeta

← C11×#36698 #14613891

Subgroups — C11×#36698 #14613891

Order 2816.

1484 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2844C211yesmaximal, characteristic, complemented
2C11×#2838C214yesmaximal, complemented
3C11×#2836C214yesmaximal, complemented
4C11×#2833C212yesmaximal, complemented
5C11×#2830C212yesmaximal
6C11×#2822C211yesmaximal, characteristic, complemented
7C11×#2820C212yesmaximal
8C11×#2401C214yesmaximal, complemented
9C11×#2399C212yesmaximal, complemented
10C11×#2396C214yesmaximal, complemented
11C11×#2395C212yesmaximal
12C4×C11×#125C212yesmaximal, complemented
13C4×C11×#124C211yesmaximal, characteristic
14C2×C11×#125C2212yes—
15C2×C11×#124C2211yescharacteristic
16C2×C4×Q8×C11C2212yes—
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2212yes—
20C11×#401C2214yes—
21C11×#400C2212yes—
22C11×#400C2214yes—
23C11×#400C2214yes—
24C11×#400C2214yes—
25C11×#400C2214yes—
26C11×#399C2212yes—
27C11×#399C2214yes—
28C11×#398C2212yes—
29C11×#398C2214yes—
30C11×#398C2214yes—
31C11×#398C2212yes—
32C11×#398C2212yes—
33C11×#398C2214yes—
34C11×#397C2212yes—
35C11×#397C2214yes—
36C11×#397C2214yes—
37C11×#397C2214yes—
38C11×#397C2214yes—
39C11×#396C2214yes—
40C11×#396C2214yes—
41C11×#396C2214yes—
42C11×#395C2214yes—
43C11×#395C2214yes—
44C11×#395C2212yes—
45C11×#395C2212yes—
46C11×#394C2214yes—
47C11×#393C2214yes—
48C11×#391C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#389C2212yes—
51C11×#389C2212yes—
52C11×#388C2214yes—
53C11×#387C2214yes—
54C11×#387C2214yes—
55C11×#382C2211yescharacteristic
56C11×#382C2212yes—
57C4×C11×C4⋊C4C2214yes—
58C4×C11×C4⋊C4C2212yes—
59C4×C11×C4⋊C4C2214yes—
60C4×C11×C4⋊C4C2214yes—
61C4×C11×C4⋊C4C2212yes—
62C4×C11×C22⋊C4C2214yes—
63C4×C11×C22⋊C4C2212yes—
64C4×C11×C22⋊C4C2214yes—
65C11×#376C2212yes—
66C43×C11C2211yescharacteristic
67C22×Q8×C11C2311yescharacteristic
68C22×Q8×C11C2312yes—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11C2312yes—
71C11×#125—28no—
72C11×#124—24no—
73C4×Q8×C11—44no—
74C4×Q8×C11—42no—
75C4×D4×C11—42no—
76C11×#117—44no—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C11×C22⋊C4C2314yes—
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C11×C22⋊C4C2312yes—
101C2×C42×C11C2312yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2314yes—
104C2×C42×C11C2312yes—
105C2×C42×C11C2314yes—
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2312yes—
108C2×C42×C11C2311yescharacteristic
109C11×#95C2314yes—
110C11×#95C2312yes—
111C11×#95C2312yes—
112C11×#95C2314yes—
113C11×#95C2314yes—
114C11×#95C2314yes—
115C11×#95C2314yes—
116C11×#95C2312yes—
117C11×#95C2312yes—
118C11×#95C2314yes—
119C11×#95C2314yes—
120C11×#95C2314yes—
121C11×#95C2314yes—
122C11×#95C2314yes—
123C11×#95C2314yes—
124C11×#95C2314yes—
125C11×#95C2314yes—
126#36698C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11C2412yes—
128C2×Q8×C11—22no—
129C2×Q8×C11—41no—
130C2×Q8×C11—42no—
131C2×Q8×C11—41no—
132C2×Q8×C11—44no—
133C2×D4×C11—22no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C22×C4×C11—24no—
137C22×C4×C11—28no—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C11×C4⋊C4—28no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—44no—
157C11×C4⋊C4—44no—
158C11×C4⋊C4—44no—
159C11×C4⋊C4—44no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—41no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—44no—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—44no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—42no—
174C42×C11—28no—
175C42×C11—22no—
176C42×C11—24no—
177C42×C11—24no—
178C42×C11—28no—
179C42×C11—42no—
180C42×C11—41no—
181C42×C11#4114yes—
182#2844C2×C1111yescharacteristic, complemented
183#2838C2×C1114yescomplemented
184#2836C2×C1114yescomplemented
185#2833C2×C1112yescomplemented
186#2830C2×C1112yes—
187#2822C2×C1111yescharacteristic, complemented
188#2820C2×C1112yes—
189#2401C2×C1114yescomplemented
190#2399C2×C1112yescomplemented
191#2396C2×C1114yescomplemented
192#2395C2×C1112yes—
193C4×#125C2×C1112yescomplemented
194C4×#124C2×C1111yescharacteristic
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11C2511yescharacteristic
201Q8×C11—44no—
202Q8×C11—48no—
203D4×C11—44no—
204C2×C4×C11—21no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—48no—
233C2×C4×C11C2×#4114yes—
234C2×C4×C11C2×#4112yes—
235C2×C4×C11H(5,𝔽2)12yes—
236C2×C4×C112−1+414yes—
237C2×#125C22×C1112yes—
238C2×#124C22×C1111yescharacteristic
239C2×C4×Q8C22×C1112yes—
240C2×C4×Q8C22×C1111yescharacteristic
241C2×C4×D4C22×C1111yescharacteristic
242C2×#117C22×C1112yes—
243#401C22×C1114yes—
244#400C22×C1114yes—
245#400C22×C1114yes—
246#400C22×C1114yes—
247#400C22×C1112yes—
248#400C22×C1114yes—
249#399C22×C1114yes—
250#399C22×C1112yes—
251#398C22×C1112yes—
252#398C22×C1112yes—
253#398C22×C1114yes—
254#398C22×C1114yes—
255#398C22×C1112yes—
256#398C22×C1114yes—
257#397C22×C1114yes—
258#397C22×C1114yes—
259#397C22×C1114yes—
260#397C22×C1112yes—
261#397C22×C1114yes—
262#396C22×C1114yes—
263#396C22×C1114yes—
264#396C22×C1114yes—
265#395C22×C1114yes—
266#395C22×C1112yes—
267#395C22×C1112yes—
268#395C22×C1114yes—
269#394C22×C1114yes—
270#393C22×C1114yes—
271#391C22×C1111yescharacteristic
272#390C22×C1111yescharacteristic
273#389C22×C1112yes—
274#389C22×C1112yes—
275#388C22×C1114yes—
276#387C22×C1114yes—
277#387C22×C1114yes—
278#382C22×C1112yes—
279#382C22×C1111yescharacteristic
280C4×C4⋊C4C22×C1114yes—
281C4×C4⋊C4C22×C1112yes—
282C4×C4⋊C4C22×C1114yes—
283C4×C4⋊C4C22×C1112yes—
284C4×C4⋊C4C22×C1114yes—
285C4×C22⋊C4C22×C1114yes—
286C4×C22⋊C4C22×C1112yes—
287C4×C22⋊C4C22×C1114yes—
288#376C22×C1112yes—
289C43C22×C1111yescharacteristic
290C22×C11—42no—
291C22×C11—44no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—44no—
295C22×C11C22×#4111yescharacteristic
296C22×C11C2×H(5,𝔽2)11yescharacteristic
297C22×C11C2×2−1+412yes—
298C22×C11#58511yescharacteristic
299C22×C11#58512yes—
300C4×C11—22no—
301C4×C11—24no—
302C4×C11—44no—
303C4×C11—42no—
304C4×C11—44no—
305C4×C11—42no—
306C4×C11—41no—
307C4×C11—44no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—44no—
311C4×C11#56314yes—
312C22×Q8C23×C1111yescharacteristic
313C22×Q8C23×C1112yes—
314C22×D4C23×C1111yescharacteristic
315C23×C4C23×C1112yes—
316#125—28no—
317#124—24no—
318C4×Q8—44no—
319C4×Q8—42no—
320C4×D4—42no—
321#117—44no—
322C2×C4⋊C4C23×C1114yes—
323C2×C4⋊C4C23×C1114yes—
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1112yes—
326C2×C4⋊C4C23×C1112yes—
327C2×C4⋊C4C23×C1112yes—
328C2×C4⋊C4C23×C1111yescharacteristic
329C2×C4⋊C4C23×C1111yescharacteristic
330C2×C4⋊C4C23×C1112yes—
331C2×C4⋊C4C23×C1114yes—
332C2×C4⋊C4C23×C1112yes—
333C2×C4⋊C4C23×C1112yes—
334C2×C4⋊C4C23×C1112yes—
335C2×C4⋊C4C23×C1114yes—
336C2×C4⋊C4C23×C1114yes—
337C2×C4⋊C4C23×C1114yes—
338C2×C4⋊C4C23×C1114yes—
339C2×C22⋊C4C23×C1114yes—
340C2×C22⋊C4C23×C1114yes—
341C2×C22⋊C4C23×C1112yes—
342C2×C22⋊C4C23×C1114yes—
343C2×C22⋊C4C23×C1114yes—
344C2×C22⋊C4C23×C1114yes—
345C2×C22⋊C4C23×C1114yes—
346C2×C42C23×C1114yes—
347C2×C42C23×C1111yescharacteristic
348C2×C42C23×C1112yes—
349C2×C42C23×C1112yes—
350C2×C42C23×C1114yes—
351C2×C42C23×C1111yescharacteristic
352C2×C42C23×C1112yes—
353C2×C42C23×C1111yescharacteristic
354#95C23×C1114yes—
355#95C23×C1112yes—
356#95C23×C1112yes—
357#95C23×C1114yes—
358#95C23×C1114yes—
359#95C23×C1114yes—
360#95C23×C1114yes—
361#95C23×C1112yes—
362#95C23×C1112yes—
363#95C23×C1114yes—
364#95C23×C1114yes—
365#95C23×C1114yes—
366#95C23×C1114yes—
367#95C23×C1114yes—
368#95C23×C1114yes—
369#95C23×C1114yes—
370#95C23×C1114yes—
371C2×C11—82no—
372C2×C11#346011yescharacteristic
373C2×C11#346112yes—
374C2×C11C2×#56311yescharacteristic
375C2×C11#352911yescharacteristic
376C2×C11#353112yes—
377C24C24×C1112yes—
378C2×Q8—22no—
379C2×Q8—41no—
380C2×Q8—42no—
381C2×Q8—41no—
382C2×Q8—44no—
383C2×D4—22no—
384C2×D4—41no—
385C2×D4—41no—
386C22×C4—24no—
387C22×C4—28no—
388C22×C4C24×C1112yes—
389C22×C4C24×C1112yes—
390C22×C4C24×C1114yes—
391C22×C4C24×C1114yes—
392C22×C4C24×C1112yes—
393C22×C4C24×C1114yes—
394C22×C4C24×C1112yes—
395C22×C4C24×C1111yescharacteristic
396C22×C4C24×C1114yes—
397C22×C4C24×C1112yes—
398C22×C4C24×C1111yescharacteristic
399C22×C4C24×C1111yescharacteristic
400C4⋊C4—28no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—28no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—44no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—44no—
414C4⋊C4—44no—
415C4⋊C4—44no—
416C4⋊C4—44no—
417C22⋊C4—28no—
418C22⋊C4—44no—
419C22⋊C4—42no—
420C22⋊C4—44no—
421C22⋊C4—44no—
422C22⋊C4—44no—
423C22⋊C4—44no—
424C42—28no—
425C42—22no—
426C42—24no—
427C42—24no—
428C42—28no—
429C42—42no—
430C42—41no—
431C42C11×#4114yes—
432C11#3669811yescharacteristic, direct product factor, Sylow
433C23—22no—
434C23—22no—
435C23—24no—
436C23—24no—
437C23—22no—
438C23C25×C1111yescharacteristic
439Q8—44no—
440Q8—48no—
441D4—44no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—48no—
471C2×C4C2×C11×#4114yes—
472C2×C4C2×C11×#4112yes—
473C2×C4C11×H(5,𝔽2)12yes—
474C2×C4C11×2−1+414yes—
475C22—42no—
476C22—44no—
477C22—42no—
478C22—42no—
479C22—44no—
480C22C22×C11×#4111yescharacteristic
481C22C2×C11×H(5,𝔽2)11yescharacteristic
482C22C2×C11×2−1+412yes—
483C22C11×#58511yescharacteristic
484C22C11×#58512yes—
485C4—22no—
486C4—24no—
487C4—42no—
488C4—44no—
489C4—44no—
490C4—42no—
491C4—44no—
492C4—42no—
493C4—41no—
494C4—42no—
495C4—44no—
496C4C11×#56314yes—
497C2—82no—
498C2C11×#346011yescharacteristic
499C2C11×#346112yes—
500C2C2×C11×#56311yescharacteristic
501C2C11×#352911yescharacteristic
502C2C11×#353112yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC22×D4×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2844C2semidirect
2. C11×#2838C2semidirect
3. C11×#2836C2semidirect
4. C11×#2833C2semidirect
6. C11×#2822C2semidirect
8. C11×#2401C2semidirect
9. C11×#2399C2semidirect
10. C11×#2396C2semidirect
12. C4×C11×#125C2semidirect
126. #36698C11direct (N × H)
182. #2844C2×C11semidirect
183. #2838C2×C11semidirect
184. #2836C2×C11semidirect
185. #2833C2×C11semidirect
187. #2822C2×C11semidirect
189. #2401C2×C11semidirect
190. #2399C2×C11semidirect
191. #2396C2×C11semidirect
193. C4×#125C2×C11semidirect
432. C11#36698direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28442
C11×#28382
C11×#28362
C11×#28332
C11×#28302
C11×#28222
C11×#28202
C11×#24012
C11×#23992
C11×#23962
C11×#23952
C4×C11×#1252
C4×C11×#1242
#3669811