Finite Group Databasebeta

← C11×#34547 #14611740

Subgroups — C11×#34547 #14611740

Order 2816.

2938 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×#41C212yesmaximal, complemented
2C11×#2399C211yesmaximal, characteristic, complemented
3C11×#2398C212yesmaximal, complemented
4C11×#2397C211yesmaximal, characteristic, complemented
5C11×#2396C214yesmaximal, complemented
6C11×#2395C214yesmaximal, complemented
7C11×#2392C214yesmaximal, complemented
8C11×#2392C214yesmaximal, complemented
9C11×#2388C214yesmaximal, complemented
10C42×D4×C11C214yesmaximal, complemented
11C4×C11×#117C211yesmaximal, characteristic, complemented
12C22×C11×#41C2212yes—
13C4×C11×#41—216no—
14C2×C4×Q8×C11C2212yes—
15C2×C4×Q8×C11C2212yes—
16C2×C4×D4×C11C2218yes—
17C2×C4×D4×C11C2214yes—
18C2×C4×D4×C11C2214yes—
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2214yes—
21C2×C4×D4×C11C2212yes—
22C2×C11×#117C2212yes—
23C2×C11×#117C2214yes—
24C2×C11×#117C2212yes—
25C22×C42×C11C2214yes—
26C22×C42×C11C2211yescharacteristic
27C11×#400C2214yes—
28C11×#399C2214yes—
29C11×#398C2214yes—
30C11×#398C2214yes—
31C11×#397C2214yes—
32C11×#397C2214yes—
33C11×#396C2218yes—
34C11×#395C2214yes—
35C11×#394C2218yes—
36C11×#394C2214yes—
37C11×#394C2214yes—
38C11×#393C2214yes—
39C11×#392C2214yes—
40C11×#392C2214yes—
41C4×C11×C4⋊C4C2214yes—
42C4×C11×C4⋊C4C2214yes—
43C4×C11×C4⋊C4C2218yes—
44C4×C11×C22⋊C4C2214yes—
45C4×C11×C22⋊C4C2218yes—
46C4×C11×C22⋊C4C2218yes—
47C4×C11×C22⋊C4C2218yes—
48C11×#376C2211yescharacteristic
49C11×#376C2211yescharacteristic
50C43×C11C2212yes—
51C2×C11×#41—28no—
52C2×C11×#41—216no—
53C22×Q8×C11C2312yes—
54C22×D4×C11C2314yes—
55C22×D4×C11C2312yes—
56C22×D4×C11C2314yes—
57C23×C4×C11C2314yes—
58C23×C4×C11C2314yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2314yes—
62C4×Q8×C11—28no—
63C4×Q8×C11—28no—
64C4×D4×C11—216no—
65C4×D4×C11—216no—
66C4×D4×C11—232no—
67C4×D4×C11—28no—
68C4×D4×C11—28no—
69C4×D4×C11—216no—
70C11×#117—28no—
71C11×#117—216no—
72C11×#117—28no—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2318yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2318yes—
85C2×C11×C22⋊C4C2318yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C42×C11—216no—
88C2×C42×C11D418yescomplemented
89C2×C42×C11C2314yes—
90C2×C42×C11C2314yes—
91C2×C42×C11C2314yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2318yes—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2312yes—
96C2×C42×C11C2312yes—
97C2×C42×C11C2311yescharacteristic
98C11×#95C2314yes—
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11×#95C2318yes—
102C11×#95C2314yes—
103C11×#95C2318yes—
104#34547C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11C2411yescharacteristic
106C24×C11C2414yes—
107C11×#41—264no—
108C2×Q8×C11—24no—
109C2×Q8×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—216no—
112C2×D4×C11—28no—
113C2×D4×C11—28no—
114C2×D4×C11—24no—
115C2×D4×C11—28no—
116C2×D4×C11—28no—
117C22×C4×C11—28no—
118C22×C4×C11—24no—
119C22×C4×C11—28no—
120C22×C4×C11—28no—
121C22×C4×C11—28no—
122C22×C4×C11—28no—
123C22×C4×C11—216no—
124C22×C4×C11—216no—
125C22×C4×C11C2×D418yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11#41116yescomplemented
128C22×C4×C11C2414yes—
129C22×C4×C11C2414yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2411yescharacteristic
133C22×C4×C11C2414yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2411yescharacteristic
137C11×C4⋊C4—28no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—216no—
143C11×C4⋊C4—28no—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—216no—
146C11×C22⋊C4—28no—
147C11×C22⋊C4—28no—
148C11×C22⋊C4—28no—
149C11×C22⋊C4—216no—
150C11×C22⋊C4—216no—
151C42×C11—28no—
152C42×C11—28no—
153C42×C11—28no—
154C42×C11—24no—
155C42×C11—216no—
156C42×C11C2×D414yes—
157C42×C11C2×D418yes—
158C42×C11C2×D414yes—
159C42×C11#4118yescomplemented
160C2×C4×#41C2×C1112yescomplemented
161#2399C2×C1111yescharacteristic, complemented
162#2398C2×C1112yescomplemented
163#2397C2×C1111yescharacteristic, complemented
164#2396C2×C1114yescomplemented
165#2395C2×C1114yescomplemented
166#2392C2×C1114yescomplemented
167#2392C2×C1114yescomplemented
168#2388C2×C1114yescomplemented
169C42×D4C2×C1114yescomplemented
170C4×#117C2×C1111yescharacteristic, complemented
171C23×C11—24no—
172C23×C11—22no—
173C23×C11—28no—
174C23×C11—28no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11C22×D412yes—
178C23×C11C2×#4118yes—
179C23×C11C2511yescharacteristic
180Q8×C11—216no—
181D4×C11—232no—
182D4×C11—216no—
183D4×C11—232no—
184C2×C4×C11—24no—
185C2×C4×C11—28no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—216no—
190C2×C4×C11—232no—
191C2×C4×C11—28no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—28no—
195C2×C4×C11—24no—
196C2×C4×C11—28no—
197C2×C4×C11—28no—
198C2×C4×C11—416no—
199C2×C4×C11—416no—
200C2×C4×C11C22×D412yes—
201C2×C4×C11C22×D414yes—
202C2×C4×C11C22×D414yes—
203C2×C4×C11C22×D412yes—
204C2×C4×C11C2×#4118yes—
205C2×C4×C11C2×#4118yes—
206C2×C4×C11C2×#4118yes—
207C2×C4×C11C2×#4114yes—
208C22×#41C22×C1112yes—
209C4×#41—216no—
210C2×C4×Q8C22×C1112yes—
211C2×C4×Q8C22×C1112yes—
212C2×C4×D4C22×C1118yes—
213C2×C4×D4C22×C1114yes—
214C2×C4×D4C22×C1114yes—
215C2×C4×D4C22×C1112yes—
216C2×C4×D4C22×C1114yes—
217C2×C4×D4C22×C1112yes—
218C2×#117C22×C1112yes—
219C2×#117C22×C1114yes—
220C2×#117C22×C1112yes—
221C22×C42C22×C1114yes—
222C22×C42C22×C1111yescharacteristic
223#400C22×C1114yes—
224#399C22×C1114yes—
225#398C22×C1114yes—
226#398C22×C1114yes—
227#397C22×C1114yes—
228#397C22×C1114yes—
229#396C22×C1118yes—
230#395C22×C1114yes—
231#394C22×C1118yes—
232#394C22×C1114yes—
233#394C22×C1114yes—
234#393C22×C1114yes—
235#392C22×C1114yes—
236#392C22×C1114yes—
237C4×C4⋊C4C22×C1114yes—
238C4×C4⋊C4C22×C1114yes—
239C4×C4⋊C4C22×C1118yes—
240C4×C22⋊C4C22×C1114yes—
241C4×C22⋊C4C22×C1118yes—
242C4×C22⋊C4C22×C1118yes—
243C4×C22⋊C4C22×C1118yes—
244#376C22×C1111yescharacteristic
245#376C22×C1111yescharacteristic
246C43C22×C1112yes—
247C22×C11—24no—
248C22×C11—28no—
249C22×C11—22no—
250C22×C11—216no—
251C22×C11—44no—
252C22×C11—44no—
253C22×C11—44no—
254C22×C11—48no—
255C22×C11C23×D411yescharacteristic
256C22×C11C22×#4114yes—
257C22×C11C22×#4112yes—
258C4×C11—24no—
259C4×C11—28no—
260C4×C11—22no—
261C4×C11—28no—
262C4×C11—44no—
263C4×C11—44no—
264C4×C11—44no—
265C4×C11#52518yes—
266C4×C11#53214yes—
267C2×#41—28no—
268C2×#41—216no—
269C22×Q8C23×C1112yes—
270C22×D4C23×C1114yes—
271C22×D4C23×C1112yes—
272C22×D4C23×C1114yes—
273C23×C4C23×C1114yes—
274C23×C4C23×C1114yes—
275C23×C4C23×C1111yescharacteristic
276C23×C4C23×C1112yes—
277C23×C4C23×C1114yes—
278C4×Q8—28no—
279C4×Q8—28no—
280C4×D4—216no—
281C4×D4—216no—
282C4×D4—232no—
283C4×D4—28no—
284C4×D4—28no—
285C4×D4—216no—
286#117—28no—
287#117—216no—
288#117—28no—
289C2×C4⋊C4C23×C1114yes—
290C2×C4⋊C4C23×C1114yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C4⋊C4C23×C1112yes—
293C2×C4⋊C4C23×C1114yes—
294C2×C4⋊C4C23×C1118yes—
295C2×C4⋊C4C23×C1114yes—
296C2×C22⋊C4C23×C1114yes—
297C2×C22⋊C4C23×C1114yes—
298C2×C22⋊C4C23×C1114yes—
299C2×C22⋊C4C23×C1114yes—
300C2×C22⋊C4C23×C1118yes—
301C2×C22⋊C4C23×C1118yes—
302C2×C22⋊C4C23×C1118yes—
303C2×C42—216no—
304C2×C42D4×C1118yescomplemented
305C2×C42C23×C1114yes—
306C2×C42C23×C1112yes—
307C2×C42C23×C1114yes—
308C2×C42C23×C1114yes—
309C2×C42C23×C1118yes—
310C2×C42C23×C1112yes—
311C2×C42C23×C1111yescharacteristic
312C2×C42C23×C1111yescharacteristic
313C2×C42C23×C1112yes—
314#95C23×C1114yes—
315#95C23×C1114yes—
316#95C23×C1114yes—
317#95C23×C1118yes—
318#95C23×C1114yes—
319#95C23×C1118yes—
320C2×C11—42no—
321C2×C11—48no—
322C2×C11C2×#52512yes—
323C2×C11C2×#53211yescharacteristic
324C2×C11#344414yes—
325C24C24×C1111yescharacteristic
326C24C24×C1114yes—
327#41—264no—
328C2×Q8—24no—
329C2×Q8—28no—
330C2×D4—28no—
331C2×D4—216no—
332C2×D4—28no—
333C2×D4—28no—
334C2×D4—24no—
335C2×D4—28no—
336C2×D4—28no—
337C22×C4—28no—
338C22×C4—24no—
339C22×C4—28no—
340C22×C4—28no—
341C22×C4—28no—
342C22×C4—28no—
343C22×C4—216no—
344C22×C4—216no—
345C22×C4C2×D4×C1118yes—
346C22×C4C2×D4×C1114yes—
347C22×C4C11×#41116yescomplemented
348C22×C4C24×C1114yes—
349C22×C4C24×C1114yes—
350C22×C4C24×C1114yes—
351C22×C4C24×C1112yes—
352C22×C4C24×C1111yescharacteristic
353C22×C4C24×C1114yes—
354C22×C4C24×C1114yes—
355C22×C4C24×C1112yes—
356C22×C4C24×C1111yescharacteristic
357C4⋊C4—28no—
358C4⋊C4—28no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—28no—
362C4⋊C4—216no—
363C4⋊C4—28no—
364C22⋊C4—28no—
365C22⋊C4—216no—
366C22⋊C4—28no—
367C22⋊C4—28no—
368C22⋊C4—28no—
369C22⋊C4—216no—
370C22⋊C4—216no—
371C42—28no—
372C42—28no—
373C42—28no—
374C42—24no—
375C42—216no—
376C42C2×D4×C1114yes—
377C42C2×D4×C1118yes—
378C42C2×D4×C1114yes—
379C42C11×#4118yescomplemented
380C11#3454711yescharacteristic, direct product factor, Sylow
381C23—24no—
382C23—22no—
383C23—28no—
384C23—28no—
385C23—24no—
386C23—24no—
387C23C22×D4×C1112yes—
388C23C2×C11×#4118yes—
389C23C25×C1111yescharacteristic
390Q8—216no—
391D4—232no—
392D4—216no—
393D4—232no—
394C2×C4—24no—
395C2×C4—28no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—216no—
400C2×C4—232no—
401C2×C4—28no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—28no—
405C2×C4—24no—
406C2×C4—28no—
407C2×C4—28no—
408C2×C4—416no—
409C2×C4—416no—
410C2×C4C22×D4×C1112yes—
411C2×C4C22×D4×C1114yes—
412C2×C4C22×D4×C1114yes—
413C2×C4C22×D4×C1112yes—
414C2×C4C2×C11×#4118yes—
415C2×C4C2×C11×#4118yes—
416C2×C4C2×C11×#4118yes—
417C2×C4C2×C11×#4114yes—
418C22—24no—
419C22—28no—
420C22—22no—
421C22—216no—
422C22—44no—
423C22—44no—
424C22—44no—
425C22—48no—
426C22C23×D4×C1111yescharacteristic
427C22C22×C11×#4114yes—
428C22C22×C11×#4112yes—
429C4—24no—
430C4—28no—
431C4—22no—
432C4—28no—
433C4—44no—
434C4—44no—
435C4—44no—
436C4C11×#52518yes—
437C4C11×#53214yes—
438C2—42no—
439C2—48no—
440C2C2×C11×#52512yes—
441C2C2×C11×#53211yescharacteristic
442C2C11×#344414yes—
subgroupG/H
centerC2×C42×C11C23
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×C11×#41C2semidirect
2. C11×#2399C2semidirect
3. C11×#2398C2semidirect
4. C11×#2397C2semidirect
5. C11×#2396C2semidirect
6. C11×#2395C2semidirect
7. C11×#2392C2semidirect
8. C11×#2392C2semidirect
9. C11×#2388C2semidirect
10. C42×D4×C11C2semidirect
11. C4×C11×#117C2semidirect
88. C2×C42×C11D4semidirect
104. #34547C11direct (N × H)
127. C22×C4×C11#41semidirect
159. C42×C11#41semidirect
160. C2×C4×#41C2×C11semidirect
161. #2399C2×C11semidirect
162. #2398C2×C11semidirect
163. #2397C2×C11semidirect
164. #2396C2×C11semidirect
165. #2395C2×C11semidirect
166. #2392C2×C11semidirect
167. #2392C2×C11semidirect
168. #2388C2×C11semidirect
169. C42×D4C2×C11semidirect
170. C4×#117C2×C11semidirect
304. C2×C42D4×C11semidirect
347. C22×C4C11×#41semidirect
379. C42C11×#41semidirect
380. C11#34547direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×#412
C11×#23992
C11×#23982
C11×#23972
C11×#23962
C11×#23952
C11×#23922
C11×#23882
C42×D4×C112
C4×C11×#1172
#3454711