Finite Group Databasebeta

← C11×#60715 #14637908

Subgroups — C11×#60715 #14637908

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3509C212yesmaximal
2C11×#3185C214yesmaximal, complemented
3C11×#3177C218yesmaximal, complemented
4C11×#3170C214yesmaximal, complemented
5C11×#3160C211yesmaximal, characteristic, complemented
6C2×C11×#494C211yesmaximal, characteristic, complemented
7C11×#3139C212yesmaximal, complemented
8C11×#3059C214yesmaximal
9C11×#2950C214yesmaximal, complemented
10C4×C11×#131C211yesmaximal, characteristic
11C22×C11×Q16C2214yes—
12C2×C11×#131C2212yes—
13C11×#557—24no—
14C11×#556—24no—
15C11×#552—28no—
16C11×#541C2218yes—
17C11×#536C2214yes—
18C11×#533C2218yes—
19C11×#533C2212yes—
20C2×C11×C4⋊Q8C2212yes—
21C11×#519C2214yes—
22C4×C11×#41C2211yescharacteristic
23C11×#500C2212yes—
24C11×#499C2214yes—
25C11×#498C2212yes—
26C11×#494C2212yes—
27C11×#494C2214yes—
28C11×#494C2212yes—
29C11×#491C2218yes—
30C11×#487C2218yes—
31C11×#470C22116yes—
32C11×#467C22116yes—
33C11×#441C22116yes—
34C4×C11×Q16C22116yes—
35C11×#427C2214yes—
36C11×#419C2218yes—
37C11×#405C2214yes—
38C11×#405C2212yes—
39C4×C11×M16C2212yes—
40C4×C11×M16C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C2×C4×C8×C11C2212yes—
43C2×C11×#41C2311yescharacteristic
44C22×Q8×C11C2314yes—
45C2×C11×Q16—216no—
46C2×C11×Q16C2318yes—
47C2×C11×Q16C2318yes—
48C11×#131—28no—
49C2×C11×M16C2312yes—
50C2×C11×M16C2314yes—
51C22×C8×C11C2314yes—
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—24no—
55C11×C4⋊Q8C2314yes—
56C11×C4⋊Q8C2314yes—
57C11×C4⋊Q8C2314yes—
58C11×#126—216no—
59C11×#125—216no—
60C11×#125—28no—
61C11×#125C2314yes—
62C11×#124—24no—
63C11×#123—28no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—28no—
66C11×C22⋊Q8C23116yes—
67C4×Q8×C11—28no—
68C4×Q8×C11—28no—
69C4×Q8×C11—24no—
70C4×Q8×C11D412yes—
71C4×Q8×C11C23116yes—
72C4×D4×C11D414yes—
73C4×D4×C11D412yes—
74C11×#117—28no—
75C11×#117—28no—
76C11×#117C2314yes—
77C11×#117C2311yescharacteristic
78C11×#117C2312yes—
79C2×C11×C4⋊C4—24no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2312yes—
82C11×#107C2318yes—
83C11×#106C2318yes—
84C11×#103C23132yes—
85C11×#97C2312yes—
86C11×#97C2314yes—
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2312yes—
89C4×C8×C11C2311yescharacteristic
90C4×C8×C11C2312yes—
91C4×C8×C11C2314yes—
92#60715C1111yesmaximal, characteristic, direct product factor, Sylow
93C11×#41—24no—
94C2×Q8×C11—24no—
95C2×Q8×C11—24no—
96C2×Q8×C11—216no—
97C2×Q8×C11C2×D411yescharacteristic
98C2×Q8×C11C2418yes—
99C2×D4×C11C2×D412yes—
100C2×D4×C11C2×D411yescharacteristic
101C22×C4×C11—24no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D414yes—
104C22×C4×C11C2412yes—
105C22×C4×C11C2411yescharacteristic
106C11×Q16—216no—
107C11×Q16—216no—
108C11×M16—28no—
109C11×M16—24no—
110C2×C8×C11—28no—
111C2×C8×C11#4118yes—
112C2×C8×C11C2414yes—
113C2×C8×C11C2412yes—
114C2×C8×C11C2412yes—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—216no—
119C11×C4⋊C4—28no—
120C11×C4⋊C4—216no—
121C11×C4⋊C4C2×D412yes—
122C11×C4⋊C4C2×D414yes—
123C11×C4⋊C4C2418yes—
124C11×C22⋊C4—24no—
125C11×C22⋊C4—216no—
126C11×C22⋊C4C2×D412yes—
127C11×C22⋊C4C2×D414yes—
128C42×C11—216no—
129C42×C11—24no—
130C42×C11C2×D414yes—
131C42×C11C2×D412yes—
132C42×C11C2411yescharacteristic
133C42×C11C2412yes—
134C42×C11C2411yescharacteristic
135#3509C2×C1112yes—
136#3185C2×C1114yescomplemented
137#3177C2×C1118yescomplemented
138#3170C2×C1114yescomplemented
139#3160C2×C1111yescharacteristic, complemented
140C2×#494C2×C1111yescharacteristic, complemented
141#3139C2×C1112yescomplemented
142#3059C2×C1114yes—
143#2950C2×C1114yescomplemented
144C4×#131C2×C1111yescharacteristic
145C23×C11C22×D412yes—
146C23×C11C22×D411yescharacteristic
147Q8×C11—22no—
148Q8×C11—216no—
149Q8×C11—48no—
150Q8×C11—48no—
151D4×C11—24no—
152D4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—28no—
155C2×C4×C11—24no—
156C2×C4×C11—28no—
157C2×C4×C11—28no—
158C2×C4×C11—48no—
159C2×C4×C11C22×D414yes—
160C2×C4×C11C22×D412yes—
161C2×C4×C11C22×D412yes—
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×D412yes—
164C2×C4×C11C2×#4114yes—
165C2×C4×C11C2511yescharacteristic
166C8×C11—24no—
167C8×C11C2×#4114yes—
168C8×C11C2×#4114yes—
169C22×Q16C22×C1114yes—
170C2×#131C22×C1112yes—
171#557—24no—
172#556—24no—
173#552—28no—
174#541C22×C1118yes—
175#536C22×C1114yes—
176#533C22×C1118yes—
177#533C22×C1112yes—
178C2×C4⋊Q8C22×C1112yes—
179#519C22×C1114yes—
180C4×#41C22×C1111yescharacteristic
181#500C22×C1112yes—
182#499C22×C1114yes—
183#498C22×C1112yes—
184#494C22×C1112yes—
185#494C22×C1114yes—
186#494C22×C1112yes—
187#491C22×C1118yes—
188#487C22×C1118yes—
189#470C22×C11116yes—
190#467C22×C11116yes—
191#441C22×C11116yes—
192C4×Q16C22×C11116yes—
193#427C22×C1114yes—
194#419C22×C1118yes—
195#405C22×C1114yes—
196#405C22×C1112yes—
197C4×M16C22×C1111yescharacteristic
198C4×M16C22×C1112yes—
199C2×C4×C8C22×C1111yescharacteristic
200C2×C4×C8C22×C1112yes—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—24no—
204C22×C11#53212yes—
205C22×C11C23×D411yescharacteristic
206C4×C11—22no—
207C4×C11—24no—
208C4×C11—22no—
209C4×C11—48no—
210C4×C11—48no—
211C4×C11#53212yes—
212C4×C11#57814yes—
213C4×C11C22×#4112yes—
214C2×#41C23×C1111yescharacteristic
215C22×Q8C23×C1114yes—
216C2×Q16—216no—
217C2×Q16C23×C1118yes—
218C2×Q16C23×C1118yes—
219#131—28no—
220C2×M16C23×C1112yes—
221C2×M16C23×C1114yes—
222C22×C8C23×C1114yes—
223C22×C8C23×C1112yes—
224C4⋊Q8—24no—
225C4⋊Q8—24no—
226C4⋊Q8C23×C1114yes—
227C4⋊Q8C23×C1114yes—
228C4⋊Q8C23×C1114yes—
229#126—216no—
230#125—216no—
231#125—28no—
232#125C23×C1114yes—
233#124—24no—
234#123—28no—
235C22⋊Q8—24no—
236C22⋊Q8—28no—
237C22⋊Q8C23×C11116yes—
238C4×Q8—28no—
239C4×Q8—28no—
240C4×Q8—24no—
241C4×Q8D4×C1112yes—
242C4×Q8C23×C11116yes—
243C4×D4D4×C1114yes—
244C4×D4D4×C1112yes—
245#117—28no—
246#117—28no—
247#117C23×C1114yes—
248#117C23×C1111yescharacteristic
249#117C23×C1112yes—
250C2×C4⋊C4—24no—
251C2×C42C23×C1111yescharacteristic
252C2×C42C23×C1112yes—
253#107C23×C1118yes—
254#106C23×C1118yes—
255#103C23×C11132yes—
256#97C23×C1114yes—
257#97C23×C1112yes—
258C4×C8C23×C1111yescharacteristic
259C4×C8C23×C1112yes—
260C4×C8C23×C1111yescharacteristic
261C4×C8C23×C1114yes—
262C4×C8C23×C1112yes—
263C2×C11—22no—
264C2×C11—42no—
265C2×C11C2×#53211yescharacteristic
266C2×C11C2×#57812yes—
267#41—24no—
268C2×Q8—24no—
269C2×Q8—24no—
270C2×Q8—216no—
271C2×Q8C2×D4×C1111yescharacteristic
272C2×Q8C24×C1118yes—
273C2×D4C2×D4×C1112yes—
274C2×D4C2×D4×C1111yescharacteristic
275C22×C4—24no—
276C22×C4C2×D4×C1112yes—
277C22×C4C2×D4×C1114yes—
278C22×C4C24×C1112yes—
279C22×C4C24×C1111yescharacteristic
280Q16—216no—
281Q16—216no—
282M16—24no—
283M16—28no—
284C2×C8—28no—
285C2×C8C11×#4118yes—
286C2×C8C24×C1114yes—
287C2×C8C24×C1112yes—
288C2×C8C24×C1112yes—
289C4⋊C4—28no—
290C4⋊C4—28no—
291C4⋊C4—24no—
292C4⋊C4—216no—
293C4⋊C4—28no—
294C4⋊C4—216no—
295C4⋊C4C2×D4×C1112yes—
296C4⋊C4C2×D4×C1114yes—
297C4⋊C4C24×C1118yes—
298C22⋊C4—24no—
299C22⋊C4—216no—
300C22⋊C4C2×D4×C1112yes—
301C22⋊C4C2×D4×C1114yes—
302C42—216no—
303C42—24no—
304C42C2×D4×C1114yes—
305C42C2×D4×C1112yes—
306C42C24×C1111yescharacteristic
307C42C24×C1112yes—
308C42C24×C1111yescharacteristic
309C11#6071511yescharacteristic, direct product factor, Sylow
310C23C22×D4×C1112yes—
311C23C22×D4×C1111yescharacteristic
312Q8—22no—
313Q8—216no—
314Q8—48no—
315Q8—48no—
316D4—24no—
317D4—22no—
318C2×C4—24no—
319C2×C4—28no—
320C2×C4—24no—
321C2×C4—28no—
322C2×C4—28no—
323C2×C4—48no—
324C2×C4C22×D4×C1114yes—
325C2×C4C22×D4×C1112yes—
326C2×C4C22×D4×C1112yes—
327C2×C4C22×D4×C1111yescharacteristic
328C2×C4C22×D4×C1112yes—
329C2×C4C2×C11×#4114yes—
330C2×C4C25×C1111yescharacteristic
331C8—24no—
332C8C2×C11×#4114yes—
333C8C2×C11×#4114yes—
334C22—22no—
335C22—22no—
336C22—24no—
337C22C11×#53212yes—
338C22C23×D4×C1111yescharacteristic
339C4—22no—
340C4—24no—
341C4—22no—
342C4—48no—
343C4—48no—
344C4C11×#53212yes—
345C4C11×#57814yes—
346C4C22×C11×#4112yes—
347C2—22no—
348C2—42no—
349C2C2×C11×#53211yescharacteristic
350C2C2×C11×#57812yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3185C2semidirect
3. C11×#3177C2semidirect
4. C11×#3170C2semidirect
5. C11×#3160C2semidirect
6. C2×C11×#494C2semidirect
7. C11×#3139C2semidirect
9. C11×#2950C2semidirect
92. #60715C11direct (N × H)
136. #3185C2×C11semidirect
137. #3177C2×C11semidirect
138. #3170C2×C11semidirect
139. #3160C2×C11semidirect
140. C2×#494C2×C11semidirect
141. #3139C2×C11semidirect
143. #2950C2×C11semidirect
309. C11#60715direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35092
C11×#31852
C11×#31772
C11×#31702
C11×#31602
C2×C11×#4942
C11×#31392
C11×#30592
C11×#29502
C4×C11×#1312
#6071511