Finite Group Databasebeta

← C11×#34313 #14611506

Subgroups — C11×#34313 #14611506

Order 2816.

3276 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#550C211yesmaximal, characteristic
2C2×C11×#520C212yesmaximal, complemented
3C11×#2366C213yesmaximal, complemented
4C11×#2361C216yesmaximal, complemented
5Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6D4×C11×C4⋊C4C213yesmaximal, complemented
7C11×#2341C212yesmaximal, complemented
8C11×#2324C216yesmaximal, complemented
9C4×C11×#127C213yesmaximal, complemented
10C11×#2293C213yesmaximal, complemented
11C42×Q8×C11C211yesmaximal, characteristic, complemented
12C22×C11×#41C2212yes—
13C11×#550C4116yescomplemented
14C2×C11×#127C2213yes—
15C2×C11×#121C2216yes—
16C11×#520—216no—
17C2×C4×Q8×C11C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2216yes—
22C2×C4×D4×C11C2216yes—
23C2×C4×D4×C11C2216yes—
24C2×C4×D4×C11C2216yes—
25C2×C4×D4×C11C2213yes—
26C2×C11×#117C2216yes—
27C22×C11×C4⋊C4C2216yes—
28C11×#390C2213yes—
29C11×#390C2213yes—
30C11×#390C2216yes—
31C11×#390C2216yes—
32C11×#390C2216yes—
33C11×#389C2211yescharacteristic
34C11×#389C2213yes—
35C11×#389C2216yes—
36C11×#388C2216yes—
37C11×#388C2216yes—
38C11×#386C22112yes—
39C11×#385C22112yes—
40C11×#384C2213yes—
41C11×#380C2216yes—
42C4×C11×C4⋊C4C2213yes—
43C4×C11×C4⋊C4C2213yes—
44C4×C11×C4⋊C4C2213yes—
45C4×C11×C4⋊C4C2213yes—
46C4×C11×C22⋊C4C2216yes—
47C43×C11C2213yes—
48C2×C11×#41—28no—
49C2×C11×#41—28no—
50C2×C11×#41C2×C4116yescomplemented
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11C2313yes—
53C22×D4×C11C2316yes—
54C22×D4×C11C2316yes—
55C23×C4×C11C2316yes—
56C23×C4×C11C23112yes—
57C11×#127C2×C4124yescomplemented
58C11×#121C2×C4148yescomplemented
59C4×Q8×C11—28no—
60C4×Q8×C11—24no—
61C4×Q8×C11C2×C418yescomplemented
62C4×Q8×C11D418yescomplemented
63C4×D4×C11—224no—
64C4×D4×C11—224no—
65C4×D4×C11—412no—
66C4×D4×C11—412no—
67C4×D4×C11C2×C4124yescomplemented
68C11×#117—224no—
69C2×C11×C4⋊C4—224no—
70C2×C11×C4⋊C4C2316yes—
71C2×C11×C4⋊C4C2316yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2313yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2313yes—
76C2×C11×C4⋊C4C2316yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2313yes—
79C2×C11×C4⋊C4C2313yes—
80C2×C11×C22⋊C4C2316yes—
81C2×C11×C22⋊C4C2316yes—
82C2×C11×C22⋊C4C2316yes—
83C2×C11×C22⋊C4C2316yes—
84C2×C11×C22⋊C4C23112yes—
85C2×C11×C22⋊C4C2316yes—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2313yes—
88C2×C42×C11C2313yes—
89C2×C42×C11C2313yes—
90C2×C42×C11C2316yes—
91C2×C42×C11C2313yes—
92C2×C42×C11C2313yes—
93C2×C42×C11C2313yes—
94C11×#95C2312yes—
95C11×#95C2316yes—
96C11×#95C2316yes—
97C11×#95C2316yes—
98#34313C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11C2416yes—
100C11×#41—264no—
101C2×Q8×C11C22×C414yes—
102C2×Q8×C11C2×D414yes—
103C2×Q8×C11#4114yes—
104C2×D4×C11—212no—
105C2×D4×C11—212no—
106C2×D4×C11—26no—
107C2×D4×C11—26no—
108C2×D4×C11—46no—
109C2×D4×C11—46no—
110C2×D4×C11C22×C4112yes—
111C2×D4×C11C22×C4124yes—
112C2×D4×C11C22×C4124yes—
113C22×C4×C11—212no—
114C22×C4×C11—212no—
115C22×C4×C11—224no—
116C22×C4×C11—412no—
117C22×C4×C11—412no—
118C22×C4×C11C22×C4124yes—
119C22×C4×C11C2412yes—
120C22×C4×C11C2413yes—
121C22×C4×C11C2416yes—
122C22×C4×C11C2413yes—
123C22×C4×C11C2412yes—
124C22×C4×C11C2413yes—
125C22×C4×C11C2411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×C4×C11C2413yes—
128C22×C4×C11C2411yescharacteristic
129C11×C4⋊C4—212no—
130C11×C4⋊C4—212no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—26no—
133C11×C4⋊C4—26no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—46no—
136C11×C4⋊C4C22×C414yes—
137C11×C4⋊C4C22×C4112yes—
138C11×C4⋊C4C2×D4112yes—
139C11×C22⋊C4—212no—
140C11×C22⋊C4—212no—
141C11×C22⋊C4—212no—
142C11×C22⋊C4—46no—
143C11×C22⋊C4—412no—
144C11×C22⋊C4C22×C4124yes—
145C42×C11—212no—
146C42×C11—26no—
147C42×C11—26no—
148C42×C11—26no—
149C42×C11—22no—
150C42×C11—43no—
151C42×C11C22×C4112yes—
152C42×C11C2×D4112yes—
153C2×#550C2×C1111yescharacteristic
154C2×#520C2×C1112yescomplemented
155#2366C2×C1113yescomplemented
156#2361C2×C1116yescomplemented
157Q8×C4⋊C4C2×C1111yescharacteristic, complemented
158D4×C4⋊C4C2×C1113yescomplemented
159#2341C2×C1112yescomplemented
160#2324C2×C1116yescomplemented
161C4×#127C2×C1113yescomplemented
162#2293C2×C1113yescomplemented
163C42×Q8C2×C1111yescharacteristic, complemented
164C23×C11—26no—
165C23×C11—26no—
166C23×C11—26no—
167C23×C11—26no—
168C23×C11—26no—
169C23×C11—26no—
170C23×C11C23×C4112yes—
171C23×C11C2511yescharacteristic
172Q8×C11C4×D4116yescomplemented
173D4×C11—248no—
174D4×C11—224no—
175D4×C11—424no—
176C2×C4×C11—22no—
177C2×C4×C11—21no—
178C2×C4×C11—22no—
179C2×C4×C11—23no—
180C2×C4×C11—23no—
181C2×C4×C11—23no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—23no—
186C2×C4×C11—248no—
187C2×C4×C11—22no—
188C2×C4×C11—26no—
189C2×C4×C11—23no—
190C2×C4×C11—23no—
191C2×C4×C11—26no—
192C2×C4×C11—26no—
193C2×C4×C11—22no—
194C2×C4×C11—23no—
195C2×C4×C11—22no—
196C2×C4×C11—824no—
197C2×C4×C11C23×C416yes—
198C2×C4×C11C23×C414yes—
199C2×C4×C11C23×C416yes—
200C2×C4×C11C23×C412yes—
201C2×C4×C11C22×D412yes—
202C2×C4×C11C22×D416yes—
203C2×C4×C11C22×D416yes—
204C2×C4×C11C2×#4116yes—
205C2×C4×C11H(5,𝔽2)12yes—
206C2×C4×C11H(5,𝔽2)12yes—
207C2×C4×C112−1+412yes—
208C22×#41C22×C1112yes—
209#550C4×C11116yescomplemented
210C2×#127C22×C1113yes—
211C2×#121C22×C1116yes—
212#520—216no—
213C2×C4×Q8C22×C1111yescharacteristic
214C2×C4×Q8C22×C1112yes—
215C2×C4×Q8C22×C1111yescharacteristic
216C2×C4×Q8C22×C1111yescharacteristic
217C2×C4×D4C22×C1116yes—
218C2×C4×D4C22×C1116yes—
219C2×C4×D4C22×C1116yes—
220C2×C4×D4C22×C1116yes—
221C2×C4×D4C22×C1113yes—
222C2×#117C22×C1116yes—
223C22×C4⋊C4C22×C1116yes—
224#390C22×C1113yes—
225#390C22×C1116yes—
226#390C22×C1116yes—
227#390C22×C1116yes—
228#390C22×C1113yes—
229#389C22×C1116yes—
230#389C22×C1113yes—
231#389C22×C1111yescharacteristic
232#388C22×C1116yes—
233#388C22×C1116yes—
234#386C22×C11112yes—
235#385C22×C11112yes—
236#384C22×C1113yes—
237#380C22×C1116yes—
238C4×C4⋊C4C22×C1113yes—
239C4×C4⋊C4C22×C1113yes—
240C4×C4⋊C4C22×C1113yes—
241C4×C4⋊C4C22×C1113yes—
242C4×C22⋊C4C22×C1116yes—
243C43C22×C1113yes—
244C22×C11—212no—
245C22×C11—212no—
246C22×C11—212no—
247C22×C11—46no—
248C22×C11—46no—
249C22×C11—46no—
250C22×C11—46no—
251C22×C11C24×C411yescharacteristic
252C22×C11C23×D411yescharacteristic
253C22×C11C22×#4111yescharacteristic
254C22×C11C2×H(5,𝔽2)11yescharacteristic
255C22×C11C2×H(5,𝔽2)11yescharacteristic
256C22×C11C2×2−1+411yescharacteristic
257C22×C11#58511yescharacteristic
258C4×C11—24no—
259C4×C11—26no—
260C4×C11—22no—
261C4×C11—26no—
262C4×C11—22no—
263C4×C11—42no—
264C4×C11—46no—
265C4×C11—43no—
266C4×C11C2×C4×D4112yes—
267C4×C11#52014yescomplemented
268C2×#41—28no—
269C2×#41—28no—
270C2×#41C2×C4×C11116yescomplemented
271C22×Q8C23×C1111yescharacteristic
272C22×D4C23×C1113yes—
273C22×D4C23×C1116yes—
274C22×D4C23×C1116yes—
275C23×C4C23×C1116yes—
276C23×C4C23×C11112yes—
277#127C2×C4×C11124yescomplemented
278#121C2×C4×C11148yescomplemented
279C4×Q8—28no—
280C4×Q8—24no—
281C4×Q8C2×C4×C1118yescomplemented
282C4×Q8D4×C1118yescomplemented
283C4×D4—224no—
284C4×D4—224no—
285C4×D4—412no—
286C4×D4—412no—
287C4×D4C2×C4×C11124yescomplemented
288#117—224no—
289C2×C4⋊C4—224no—
290C2×C4⋊C4C23×C1116yes—
291C2×C4⋊C4C23×C1116yes—
292C2×C4⋊C4C23×C1112yes—
293C2×C4⋊C4C23×C1113yes—
294C2×C4⋊C4C23×C1113yes—
295C2×C4⋊C4C23×C1111yescharacteristic
296C2×C4⋊C4C23×C1116yes—
297C2×C4⋊C4C23×C1111yescharacteristic
298C2×C4⋊C4C23×C1113yes—
299C2×C4⋊C4C23×C1113yes—
300C2×C22⋊C4C23×C1116yes—
301C2×C22⋊C4C23×C1116yes—
302C2×C22⋊C4C23×C1116yes—
303C2×C22⋊C4C23×C11112yes—
304C2×C22⋊C4C23×C1116yes—
305C2×C22⋊C4C23×C1116yes—
306C2×C42C23×C1116yes—
307C2×C42C23×C1113yes—
308C2×C42C23×C1113yes—
309C2×C42C23×C1113yes—
310C2×C42C23×C1111yescharacteristic
311C2×C42C23×C1113yes—
312C2×C42C23×C1113yes—
313C2×C42C23×C1113yes—
314#95C23×C1112yes—
315#95C23×C1116yes—
316#95C23×C1116yes—
317#95C23×C1116yes—
318C2×C11—412no—
319C2×C11C22×C4×D411yescharacteristic
320C2×C11C2×#52011yescharacteristic
321C2×C11C4×H(5,𝔽2)11yescharacteristic
322C2×C11#349711yescharacteristic
323C2×C11#349811yescharacteristic
324C2×C11#351711yescharacteristic
325C2×C11#352211yescharacteristic
326C24C24×C1116yes—
327#41—264no—
328C2×Q8C22×C4×C1114yes—
329C2×Q8C2×D4×C1114yes—
330C2×Q8C11×#4114yes—
331C2×D4—212no—
332C2×D4—212no—
333C2×D4—26no—
334C2×D4—26no—
335C2×D4—46no—
336C2×D4—46no—
337C2×D4C22×C4×C11112yes—
338C2×D4C22×C4×C11124yes—
339C2×D4C22×C4×C11124yes—
340C22×C4—212no—
341C22×C4—212no—
342C22×C4—224no—
343C22×C4—412no—
344C22×C4—412no—
345C22×C4C22×C4×C11124yes—
346C22×C4C24×C1112yes—
347C22×C4C24×C1113yes—
348C22×C4C24×C1116yes—
349C22×C4C24×C1113yes—
350C22×C4C24×C1112yes—
351C22×C4C24×C1113yes—
352C22×C4C24×C1111yescharacteristic
353C22×C4C24×C1111yescharacteristic
354C22×C4C24×C1113yes—
355C22×C4C24×C1111yescharacteristic
356C4⋊C4—212no—
357C4⋊C4—212no—
358C4⋊C4—24no—
359C4⋊C4—26no—
360C4⋊C4—26no—
361C4⋊C4—22no—
362C4⋊C4—46no—
363C4⋊C4C22×C4×C1114yes—
364C4⋊C4C22×C4×C11112yes—
365C4⋊C4C2×D4×C11112yes—
366C22⋊C4—212no—
367C22⋊C4—212no—
368C22⋊C4—212no—
369C22⋊C4—412no—
370C22⋊C4—46no—
371C22⋊C4C22×C4×C11124yes—
372C42—212no—
373C42—26no—
374C42—26no—
375C42—26no—
376C42—22no—
377C42—43no—
378C42C22×C4×C11112yes—
379C42C2×D4×C11112yes—
380C11#3431311yescharacteristic, direct product factor, Sylow
381C23—26no—
382C23—26no—
383C23—26no—
384C23—26no—
385C23—26no—
386C23—26no—
387C23C23×C4×C11112yes—
388C23C25×C1111yescharacteristic
389Q8C4×D4×C11116yescomplemented
390D4—248no—
391D4—224no—
392D4—424no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—23no—
397C2×C4—23no—
398C2×C4—23no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—23no—
403C2×C4—248no—
404C2×C4—22no—
405C2×C4—26no—
406C2×C4—23no—
407C2×C4—23no—
408C2×C4—26no—
409C2×C4—26no—
410C2×C4—22no—
411C2×C4—23no—
412C2×C4—22no—
413C2×C4—824no—
414C2×C4C23×C4×C1116yes—
415C2×C4C23×C4×C1114yes—
416C2×C4C23×C4×C1116yes—
417C2×C4C23×C4×C1112yes—
418C2×C4C22×D4×C1112yes—
419C2×C4C22×D4×C1116yes—
420C2×C4C22×D4×C1116yes—
421C2×C4C2×C11×#4116yes—
422C2×C4C11×H(5,𝔽2)12yes—
423C2×C4C11×H(5,𝔽2)12yes—
424C2×C4C11×2−1+412yes—
425C22—212no—
426C22—212no—
427C22—212no—
428C22—46no—
429C22—46no—
430C22—46no—
431C22—46no—
432C22C24×C4×C1111yescharacteristic
433C22C23×D4×C1111yescharacteristic
434C22C22×C11×#4111yescharacteristic
435C22C2×C11×H(5,𝔽2)11yescharacteristic
436C22C2×C11×H(5,𝔽2)11yescharacteristic
437C22C2×C11×2−1+411yescharacteristic
438C22C11×#58511yescharacteristic
439C4—24no—
440C4—26no—
441C4—22no—
442C4—26no—
443C4—22no—
444C4—42no—
445C4—46no—
446C4—43no—
447C4C2×C4×D4×C11112yes—
448C4C11×#52014yescomplemented
449C2—412no—
450C2C22×C4×D4×C1111yescharacteristic
451C2C2×C11×#52011yescharacteristic
452C2C4×C11×H(5,𝔽2)11yescharacteristic
453C2C11×#349711yescharacteristic
454C2C11×#349811yescharacteristic
455C2C11×#351711yescharacteristic
456C2C11×#352211yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#550C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#520C2semidirect
3. C11×#2366C2semidirect
4. C11×#2361C2semidirect
5. Q8×C11×C4⋊C4C2semidirect
6. D4×C11×C4⋊C4C2semidirect
7. C11×#2341C2semidirect
8. C11×#2324C2semidirect
9. C4×C11×#127C2semidirect
10. C11×#2293C2semidirect
11. C42×Q8×C11C2semidirect
13. C11×#550C4semidirect
50. C2×C11×#41C2×C4semidirect
57. C11×#127C2×C4semidirect
58. C11×#121C2×C4semidirect
61. C4×Q8×C11C2×C4semidirect
62. C4×Q8×C11D4semidirect
67. C4×D4×C11C2×C4semidirect
98. #34313C11direct (N × H)
154. C2×#520C2×C11semidirect
155. #2366C2×C11semidirect
156. #2361C2×C11semidirect
157. Q8×C4⋊C4C2×C11semidirect
158. D4×C4⋊C4C2×C11semidirect
159. #2341C2×C11semidirect
160. #2324C2×C11semidirect
161. C4×#127C2×C11semidirect
162. #2293C2×C11semidirect
163. C42×Q8C2×C11semidirect
172. Q8×C11C4×D4semidirect
209. #550C4×C11semidirect
267. C4×C11#520semidirect
270. C2×#41C2×C4×C11semidirect
277. #127C2×C4×C11semidirect
278. #121C2×C4×C11semidirect
281. C4×Q8C2×C4×C11semidirect
282. C4×Q8D4×C11semidirect
287. C4×D4C2×C4×C11semidirect
380. C11#34313direct (N × H)
389. Q8C4×D4×C11semidirect
448. C4C11×#520semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5502
C2×C11×#5202
C11×#23662
C11×#23612
Q8×C11×C4⋊C42
D4×C11×C4⋊C42
C11×#23412
C11×#23242
C4×C11×#1272
C11×#22932
C42×Q8×C112
#3431311