Finite Group Databasebeta

← C11×#34485 #14611678

Subgroups — C11×#34485 #14611678

Order 2816.

2340 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic
2C11×#2379C214yesmaximal, complemented
3C11×#2369C211yesmaximal, characteristic, complemented
4C11×#2361C214yesmaximal, complemented
5D4×C11×C4⋊C4C212yesmaximal, complemented
6C11×#2346C214yesmaximal, complemented
7C11×#2326C214yesmaximal, complemented
8C11×#2324C214yesmaximal, complemented
9C11×#2317C214yesmaximal, complemented
10C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
11C11×#2293C212yesmaximal, complemented
12C11×#555C4116yescomplemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#124C2214yes—
15C2×C11×#121C2214yes—
16C2×C4×Q8×C11C2212yes—
17C2×C4×D4×C11C2214yes—
18C2×C4×D4×C11C2214yes—
19C2×C4×D4×C11C2212yes—
20C2×C11×#117C2214yes—
21C2×C11×#117C2214yes—
22C22×C11×C4⋊C4C2214yes—
23C11×#391C2212yes—
24C11×#391C2214yes—
25C11×#390C2212yes—
26C11×#390C2212yes—
27C11×#390C2214yes—
28C11×#389C2212yes—
29C11×#389C2212yes—
30C11×#389C2214yes—
31C11×#389C2214yes—
32C11×#389C2214yes—
33C11×#388C2214yes—
34C11×#388C2218yes—
35C11×#388C2214yes—
36C11×#388C2218yes—
37C11×#386C2218yes—
38C11×#385C2218yes—
39C11×#385C2218yes—
40C11×#385C2218yes—
41C11×#384C2211yescharacteristic
42C11×#384C2214yes—
43C11×#382C2218yes—
44C11×#380C2214yes—
45C4×C11×C4⋊C4C2212yes—
46C4×C11×C4⋊C4C2214yes—
47C4×C11×C4⋊C4C2214yes—
48C4×C11×C22⋊C4C2214yes—
49C11×#376C2214yes—
50C43×C11C2211yescharacteristic
51C22×Q8×C11C2312yes—
52C22×D4×C11C2312yes—
53C22×D4×C11C2314yes—
54C23×C4×C11C2314yes—
55C23×C4×C11C2318yes—
56C11×C4⋊Q8C2×C418yescomplemented
57C11×#124C2×C4132yescomplemented
58C11×#121C2×C4132yescomplemented
59C4×Q8×C11—44no—
60C4×D4×C11—48no—
61C4×D4×C11—48no—
62C4×D4×C11C2×C4116yescomplemented
63C11×#117—48no—
64C11×#117C2×C4132yescomplemented
65C2×C11×C4⋊C4—48no—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2318yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2314yes—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C42×C11C2312yes—
85C2×C42×C11C2312yes—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2314yes—
88C2×C42×C11C2314yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2314yes—
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2314yes—
93C11×#95C2314yes—
94C11×#95C2318yes—
95C11×#95C2314yes—
96C11×#95C2318yes—
97C11×#95C2318yes—
98C11×#95C2314yes—
99#34485C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11C2414yes—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11C22×C418yes—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—44no—
107C2×D4×C11—44no—
108C2×D4×C11C22×C418yes—
109C2×D4×C11C22×C4116yes—
110C22×C4×C11—28no—
111C22×C4×C11—28no—
112C22×C4×C11—48no—
113C22×C4×C11—48no—
114C22×C4×C11—48no—
115C22×C4×C11C22×C4116yes—
116C22×C4×C11C2414yes—
117C22×C4×C11C2412yes—
118C22×C4×C11C2414yes—
119C22×C4×C11C2414yes—
120C22×C4×C11C2411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×C4×C11C2414yes—
123C22×C4×C11C2414yes—
124C22×C4×C11C2411yescharacteristic
125C22×C4×C11C2412yes—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—28no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—48no—
130C11×C4⋊C4—44no—
131C11×C4⋊C4—44no—
132C11×C4⋊C4—44no—
133C11×C4⋊C4—44no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4C22×C418yes—
136C11×C4⋊C4C22×C4116yes—
137C11×C22⋊C4—28no—
138C11×C22⋊C4—44no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—44no—
141C11×C22⋊C4—48no—
142C11×C22⋊C4C22×C4132yes—
143C11×C22⋊C4C22×C4116yes—
144C42×C11—24no—
145C42×C11—28no—
146C42×C11—28no—
147C42×C11—22no—
148C42×C11—24no—
149C42×C11—44no—
150C42×C11—41no—
151C42×C11C22×C4116yes—
152C42×C11C22×C414yes—
153C2×#555C2×C1111yescharacteristic
154#2379C2×C1114yescomplemented
155#2369C2×C1111yescharacteristic, complemented
156#2361C2×C1114yescomplemented
157D4×C4⋊C4C2×C1112yescomplemented
158#2346C2×C1114yescomplemented
159#2326C2×C1114yescomplemented
160#2324C2×C1114yescomplemented
161#2317C2×C1114yescomplemented
162C4×C4⋊Q8C2×C1111yescharacteristic, complemented
163#2293C2×C1112yescomplemented
164C23×C11—24no—
165C23×C11—24no—
166C23×C11—24no—
167C23×C11—24no—
168C23×C11—24no—
169C23×C11—24no—
170C23×C11C23×C418yes—
171C23×C11C2511yescharacteristic
172Q8×C11—48no—
173D4×C11—216no—
174D4×C11—416no—
175C2×C4×C11—24no—
176C2×C4×C11—21no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—21no—
182C2×C4×C11—232no—
183C2×C4×C11—24no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—21no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—28no—
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—816no—
197C2×C4×C11C23×C418yes—
198C2×C4×C11C23×C412yes—
199C2×C4×C11C23×C418yes—
200C2×C4×C11C23×C414yes—
201C2×C4×C11H(5,𝔽2)12yes—
202C2×C4×C11H(5,𝔽2)14yes—
203C2×C4×C112−1+414yes—
204#555C4×C11116yescomplemented
205C2×C4⋊Q8C22×C1111yescharacteristic
206C2×#124C22×C1114yes—
207C2×#121C22×C1114yes—
208C2×C4×Q8C22×C1112yes—
209C2×C4×D4C22×C1114yes—
210C2×C4×D4C22×C1114yes—
211C2×C4×D4C22×C1112yes—
212C2×#117C22×C1114yes—
213C2×#117C22×C1114yes—
214C22×C4⋊C4C22×C1114yes—
215#391C22×C1112yes—
216#391C22×C1114yes—
217#390C22×C1114yes—
218#390C22×C1112yes—
219#390C22×C1112yes—
220#389C22×C1114yes—
221#389C22×C1112yes—
222#389C22×C1114yes—
223#389C22×C1114yes—
224#389C22×C1112yes—
225#388C22×C1118yes—
226#388C22×C1114yes—
227#388C22×C1118yes—
228#388C22×C1114yes—
229#386C22×C1118yes—
230#385C22×C1118yes—
231#385C22×C1118yes—
232#385C22×C1118yes—
233#384C22×C1111yescharacteristic
234#384C22×C1114yes—
235#382C22×C1118yes—
236#380C22×C1114yes—
237C4×C4⋊C4C22×C1114yes—
238C4×C4⋊C4C22×C1114yes—
239C4×C4⋊C4C22×C1112yes—
240C4×C22⋊C4C22×C1114yes—
241#376C22×C1114yes—
242C43C22×C1111yescharacteristic
243C22×C11—28no—
244C22×C11—28no—
245C22×C11—28no—
246C22×C11—44no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11—44no—
250C22×C11C24×C411yescharacteristic
251C22×C11C2×H(5,𝔽2)12yes—
252C22×C11C2×H(5,𝔽2)11yescharacteristic
253C22×C11C2×2−1+412yes—
254C22×C11#58511yescharacteristic
255C4×C11—28no—
256C4×C11—28no—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—44no—
260C4×C11—42no—
261C4×C11—41no—
262C4×C11—44no—
263C4×C11—44no—
264C4×C11#52018yes—
265C22×Q8C23×C1112yes—
266C22×D4C23×C1112yes—
267C22×D4C23×C1114yes—
268C23×C4C23×C1114yes—
269C23×C4C23×C1118yes—
270C4⋊Q8C2×C4×C1118yescomplemented
271#124C2×C4×C11132yescomplemented
272#121C2×C4×C11132yescomplemented
273C4×Q8—44no—
274C4×D4—48no—
275C4×D4—48no—
276C4×D4C2×C4×C11116yescomplemented
277#117—48no—
278#117C2×C4×C11132yescomplemented
279C2×C4⋊C4—48no—
280C2×C4⋊C4C23×C1112yes—
281C2×C4⋊C4C23×C1114yes—
282C2×C4⋊C4C23×C1112yes—
283C2×C4⋊C4C23×C1118yes—
284C2×C4⋊C4C23×C1114yes—
285C2×C4⋊C4C23×C1114yes—
286C2×C4⋊C4C23×C1114yes—
287C2×C4⋊C4C23×C1112yes—
288C2×C4⋊C4C23×C1114yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1114yes—
291C2×C22⋊C4C23×C1114yes—
292C2×C22⋊C4C23×C1114yes—
293C2×C22⋊C4C23×C1114yes—
294C2×C22⋊C4C23×C1118yes—
295C2×C22⋊C4C23×C1114yes—
296C2×C22⋊C4C23×C1118yes—
297C2×C22⋊C4C23×C1114yes—
298C2×C42C23×C1112yes—
299C2×C42C23×C1114yes—
300C2×C42C23×C1114yes—
301C2×C42C23×C1111yescharacteristic
302C2×C42C23×C1112yes—
303C2×C42C23×C1111yescharacteristic
304C2×C42C23×C1114yes—
305C2×C42C23×C1114yes—
306C2×C42C23×C1111yescharacteristic
307#95C23×C1114yes—
308#95C23×C1118yes—
309#95C23×C1114yes—
310#95C23×C1118yes—
311#95C23×C1118yes—
312#95C23×C1114yes—
313C2×C11—48no—
314C2×C11C2×#52012yes—
315C2×C11C4×H(5,𝔽2)11yescharacteristic
316C2×C11#354411yescharacteristic
317C2×C11#354712yes—
318C2×C11#354911yescharacteristic
319C24C24×C1114yes—
320C2×Q8—42no—
321C2×Q8—42no—
322C2×Q8C22×C4×C1118yes—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—44no—
326C2×D4—44no—
327C2×D4C22×C4×C1118yes—
328C2×D4C22×C4×C11116yes—
329C22×C4—28no—
330C22×C4—28no—
331C22×C4—48no—
332C22×C4—48no—
333C22×C4—48no—
334C22×C4C22×C4×C11116yes—
335C22×C4C24×C1114yes—
336C22×C4C24×C1112yes—
337C22×C4C24×C1114yes—
338C22×C4C24×C1114yes—
339C22×C4C24×C1111yescharacteristic
340C22×C4C24×C1111yescharacteristic
341C22×C4C24×C1114yes—
342C22×C4C24×C1114yes—
343C22×C4C24×C1111yescharacteristic
344C22×C4C24×C1112yes—
345C4⋊C4—24no—
346C4⋊C4—28no—
347C4⋊C4—24no—
348C4⋊C4—48no—
349C4⋊C4—44no—
350C4⋊C4—44no—
351C4⋊C4—44no—
352C4⋊C4—44no—
353C4⋊C4—42no—
354C4⋊C4C22×C4×C1118yes—
355C4⋊C4C22×C4×C11116yes—
356C22⋊C4—28no—
357C22⋊C4—44no—
358C22⋊C4—44no—
359C22⋊C4—48no—
360C22⋊C4—44no—
361C22⋊C4C22×C4×C11132yes—
362C22⋊C4C22×C4×C11116yes—
363C42—24no—
364C42—28no—
365C42—28no—
366C42—22no—
367C42—24no—
368C42—44no—
369C42—41no—
370C42C22×C4×C11116yes—
371C42C22×C4×C1114yes—
372C11#3448511yescharacteristic, direct product factor, Sylow
373C23—24no—
374C23—24no—
375C23—24no—
376C23—24no—
377C23—24no—
378C23—24no—
379C23C23×C4×C1118yes—
380C23C25×C1111yescharacteristic
381Q8—48no—
382D4—216no—
383D4—416no—
384C2×C4—24no—
385C2×C4—21no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—21no—
391C2×C4—232no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—21no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—28no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—816no—
406C2×C4C23×C4×C1118yes—
407C2×C4C23×C4×C1112yes—
408C2×C4C23×C4×C1118yes—
409C2×C4C23×C4×C1114yes—
410C2×C4C11×H(5,𝔽2)12yes—
411C2×C4C11×H(5,𝔽2)14yes—
412C2×C4C11×2−1+414yes—
413C22—28no—
414C22—28no—
415C22—28no—
416C22—44no—
417C22—44no—
418C22—44no—
419C22—44no—
420C22C24×C4×C1111yescharacteristic
421C22C2×C11×H(5,𝔽2)12yes—
422C22C2×C11×H(5,𝔽2)11yescharacteristic
423C22C2×C11×2−1+412yes—
424C22C11×#58511yescharacteristic
425C4—28no—
426C4—28no—
427C4—22no—
428C4—22no—
429C4—44no—
430C4—42no—
431C4—44no—
432C4—44no—
433C4—41no—
434C4C11×#52018yes—
435C2—48no—
436C2C2×C11×#52012yes—
437C2C4×C11×H(5,𝔽2)11yescharacteristic
438C2C11×#354411yescharacteristic
439C2C11×#354712yes—
440C2C11×#354911yescharacteristic
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×#2369C2semidirect
4. C11×#2361C2semidirect
5. D4×C11×C4⋊C4C2semidirect
6. C11×#2346C2semidirect
7. C11×#2326C2semidirect
8. C11×#2324C2semidirect
9. C11×#2317C2semidirect
10. C4×C11×C4⋊Q8C2semidirect
11. C11×#2293C2semidirect
12. C11×#555C4semidirect
56. C11×C4⋊Q8C2×C4semidirect
57. C11×#124C2×C4semidirect
58. C11×#121C2×C4semidirect
62. C4×D4×C11C2×C4semidirect
64. C11×#117C2×C4semidirect
99. #34485C11direct (N × H)
154. #2379C2×C11semidirect
155. #2369C2×C11semidirect
156. #2361C2×C11semidirect
157. D4×C4⋊C4C2×C11semidirect
158. #2346C2×C11semidirect
159. #2326C2×C11semidirect
160. #2324C2×C11semidirect
161. #2317C2×C11semidirect
162. C4×C4⋊Q8C2×C11semidirect
163. #2293C2×C11semidirect
204. #555C4×C11semidirect
270. C4⋊Q8C2×C4×C11semidirect
271. #124C2×C4×C11semidirect
272. #121C2×C4×C11semidirect
276. C4×D4C2×C4×C11semidirect
278. #117C2×C4×C11semidirect
372. C11#34485direct (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×#23692
C11×#23612
D4×C11×C4⋊C42
C11×#23462
C11×#23262
C11×#23242
C11×#23172
C4×C11×C4⋊Q82
C11×#22932
#3448511