Finite Group Databasebeta

← C11×#60627 #14637820

Subgroups — C11×#60627 #14637820

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3504C211yesmaximal, characteristic, complemented
2C11×#3499C211yesmaximal, characteristic
3C11×#3142C213yesmaximal, complemented
4C11×#3139C213yesmaximal, complemented
5C11×#3137C2112yesmaximal, complemented
6C11×#3135C213yesmaximal, complemented
7C2×C11×#491C213yesmaximal, complemented
8C11×#2898C214yesmaximal, complemented
9C11×#2875C211yesmaximal, characteristic, complemented
10C2×C11×2−1+4C2212yes—
11C2×C11×#131C2212yes—
12C11×#557—22no—
13C11×#554—26no—
14D4×Q8×C11—22no—
15C11×#547—26no—
16C11×#544C2216yes—
17C11×#536C2216yes—
18C11×#533C2213yes—
19C11×#532C2213yes—
20C2×C11×C4⋊Q8C2213yes—
21C2×C11×#125C2213yes—
22C11×#520C2212yes—
23C4×C11×#41C2211yescharacteristic
24C11×#491C2213yes—
25C11×#491C22112yes—
26C11×#491C2216yes—
27C11×#491C2213yes—
28C11×#490C2211yescharacteristic
29C11×#490C2213yes—
30C11×#489C22112yes—
31C11×#488C22112yes—
32C11×#487C22112yes—
33C11×#419C22112yes—
34C11×#417C22112yes—
35C11×#416C22112yes—
36C2×C11×#103C22112yes—
37C11×#405C2216yes—
38C4×C11×M16C2213yes—
39C2×C11×#97C2213yes—
40C11×2−1+4—216no—
41C2×C11×#41—26no—
42C2×C11×#41C2316yes—
43C2×C11×#41C2311yescharacteristic
44C22×Q8×C11—22no—
45C22×Q8×C11C2316yes—
46C11×#131—28no—
47C2×C11×M16C2316yes—
48C22×C8×C11C2316yes—
49C11×C4⋊Q8—26no—
50C11×C4⋊Q8—26no—
51C11×C4⋊Q8C2313yes—
52C11×C4⋊Q8C2316yes—
53C11×C4⋊Q8C2316yes—
54C11×#127C2311yescharacteristic
55C11×#125—26no—
56C11×#125—26no—
57C11×#125C2313yes—
58C11×#125C2311yescharacteristic
59C11×#125C2316yes—
60C11×#124C2316yes—
61C11×#123—212no—
62C11×C22⋊Q8—26no—
63C11×C22⋊Q8—212no—
64C11×C22⋊Q8—212no—
65C11×#121—26no—
66C4×Q8×C11—22no—
67C4×Q8×C11—26no—
68C4×Q8×C11D412yes—
69C4×D4×C11—26no—
70C4×D4×C11—26no—
71C4×D4×C11D416yes—
72C11×#117C2316yes—
73C11×#117C2313yes—
74C2×C11×C4⋊C4—26no—
75C2×C11×C4⋊C4—26no—
76C2×C11×C4⋊C4C2316yes—
77C2×C42×C11C2313yes—
78C11×#103C23112yes—
79C11×#103C23112yes—
80C11×#103C23124yes—
81C11×#102C2314yes—
82C11×#102C23112yes—
83C11×#97C2316yes—
84C11×#97C2311yescharacteristic
85C11×#97C2313yes—
86C4×C8×C11C2316yes—
87#60627C1111yesmaximal, characteristic, direct product factor, Sylow
88C11×#41—224no—
89C11×#41—424no—
90C11×#41#4118yes—
91C2×Q8×C11—26no—
92C2×Q8×C11—26no—
93C2×Q8×C11—224no—
94C2×Q8×C11—48no—
95C2×Q8×C11C2×D411yescharacteristic
96C2×Q8×C11C2416yes—
97C2×D4×C11—26no—
98C2×D4×C11—22no—
99C2×D4×C11C2×D413yes—
100C2×D4×C11C2412yes—
101C22×C4×C11—26no—
102C22×C4×C11—26no—
103C22×C4×C11—26no—
104C22×C4×C11C2×D416yes—
105C22×C4×C11C2413yes—
106C11×M16—212no—
107C2×C8×C11—212no—
108C2×C8×C11C2416yes—
109C2×C8×C11C2412yes—
110C11×C4⋊C4—26no—
111C11×C4⋊C4—26no—
112C11×C4⋊C4—212no—
113C11×C4⋊C4—212no—
114C11×C4⋊C4—26no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—26no—
117C11×C4⋊C4C2×D416yes—
118C11×C4⋊C4C2416yes—
119C11×C4⋊C4C2412yes—
120C11×C22⋊C4—26no—
121C11×C22⋊C4—212no—
122C11×C22⋊C4C2×D416yes—
123C42×C11—26no—
124C42×C11C2×D416yes—
125C42×C11C2413yes—
126C42×C11C2411yescharacteristic
127#3504C2×C1111yescharacteristic, complemented
128#3499C2×C1111yescharacteristic
129#3142C2×C1113yescomplemented
130#3139C2×C1113yescomplemented
131#3137C2×C11112yescomplemented
132#3135C2×C1113yescomplemented
133C2×#491C2×C1113yescomplemented
134#2898C2×C1114yescomplemented
135#2875C2×C1111yescharacteristic, complemented
136C23×C11—22no—
137C23×C11C22×D413yes—
138Q8×C11—212no—
139Q8×C11—412no—
140Q8×C11—86no—
141Q8×C11#12414yes—
142D4×C11—24no—
143D4×C11—44no—
144D4×C11—412no—
145D4×C11#124112yes—
146C2×C4×C11—22no—
147C2×C4×C11—26no—
148C2×C4×C11—26no—
149C2×C4×C11—46no—
150C2×C4×C11—412no—
151C2×C4×C11—412no—
152C2×C4×C11—86no—
153C2×C4×C11C22×D412yes—
154C2×C4×C11C22×D416yes—
155C2×C4×C11C22×D413yes—
156C2×C4×C11C2×#41112yes—
157C2×C4×C11C2511yescharacteristic
158C8×C11—22no—
159C8×C11—26no—
160C2×2−1+4C22×C1112yes—
161C2×#131C22×C1112yes—
162#557—22no—
163#554—26no—
164D4×Q8—22no—
165#547—26no—
166#544C22×C1116yes—
167#536C22×C1116yes—
168#533C22×C1113yes—
169#532C22×C1113yes—
170C2×C4⋊Q8C22×C1113yes—
171C2×#125C22×C1113yes—
172#520C22×C1112yes—
173C4×#41C22×C1111yescharacteristic
174#491C22×C1113yes—
175#491C22×C11112yes—
176#491C22×C1116yes—
177#491C22×C1113yes—
178#490C22×C1111yescharacteristic
179#490C22×C1113yes—
180#489C22×C11112yes—
181#488C22×C11112yes—
182#487C22×C11112yes—
183#419C22×C11112yes—
184#417C22×C11112yes—
185#416C22×C11112yes—
186C2×#103C22×C11112yes—
187#405C22×C1116yes—
188C4×M16C22×C1113yes—
189C2×#97C22×C1113yes—
190C22×C11—26no—
191C22×C11—44no—
192C22×C11—42no—
193C22×C11C2×#12416yes—
194C22×C11C23×D411yescharacteristic
195C4×C11—22no—
196C4×C11—26no—
197C4×C11—46no—
198C4×C11—42no—
199C4×C11—46no—
200C4×C11C2×#12416yes—
201C4×C11C22×#4112yes—
2022−1+4—216no—
203C2×#41—26no—
204C2×#41C23×C1116yes—
205C2×#41C23×C1111yescharacteristic
206C22×Q8—22no—
207C22×Q8C23×C1116yes—
208#131—28no—
209C2×M16C23×C1116yes—
210C22×C8C23×C1116yes—
211C4⋊Q8—26no—
212C4⋊Q8—26no—
213C4⋊Q8C23×C1113yes—
214C4⋊Q8C23×C1116yes—
215C4⋊Q8C23×C1116yes—
216#127C23×C1111yescharacteristic
217#125—26no—
218#125—26no—
219#125C23×C1113yes—
220#125C23×C1116yes—
221#125C23×C1111yescharacteristic
222#124C23×C1116yes—
223#123—212no—
224C22⋊Q8—26no—
225C22⋊Q8—212no—
226C22⋊Q8—212no—
227#121—26no—
228C4×Q8—22no—
229C4×Q8—26no—
230C4×Q8D4×C1112yes—
231C4×D4—26no—
232C4×D4—26no—
233C4×D4D4×C1116yes—
234#117C23×C1116yes—
235#117C23×C1113yes—
236C2×C4⋊C4—26no—
237C2×C4⋊C4—26no—
238C2×C4⋊C4C23×C1116yes—
239C2×C42C23×C1113yes—
240#103C23×C11112yes—
241#103C23×C11124yes—
242#103C23×C11112yes—
243#102C23×C1114yes—
244#102C23×C11112yes—
245#97C23×C1111yescharacteristic
246#97C23×C1113yes—
247#97C23×C1116yes—
248C4×C8C23×C1116yes—
249C2×C11—26no—
250C2×C11—82no—
251C2×C11C22×#12411yescharacteristic
252C2×C11#358612yes—
253#41—224no—
254#41—424no—
255#41C11×#4118yes—
256C2×Q8—26no—
257C2×Q8—26no—
258C2×Q8—224no—
259C2×Q8—48no—
260C2×Q8C2×D4×C1111yescharacteristic
261C2×Q8C24×C1116yes—
262C2×D4—26no—
263C2×D4—22no—
264C2×D4C2×D4×C1113yes—
265C2×D4C24×C1112yes—
266C22×C4—26no—
267C22×C4—26no—
268C22×C4—26no—
269C22×C4C2×D4×C1116yes—
270C22×C4C24×C1113yes—
271M16—212no—
272C2×C8—212no—
273C2×C8C24×C1116yes—
274C2×C8C24×C1112yes—
275C4⋊C4—26no—
276C4⋊C4—26no—
277C4⋊C4—212no—
278C4⋊C4—212no—
279C4⋊C4—26no—
280C4⋊C4—22no—
281C4⋊C4—26no—
282C4⋊C4C2×D4×C1116yes—
283C4⋊C4C24×C1116yes—
284C4⋊C4C24×C1112yes—
285C22⋊C4—26no—
286C22⋊C4—212no—
287C22⋊C4C2×D4×C1116yes—
288C42—26no—
289C42C2×D4×C1116yes—
290C42C24×C1113yes—
291C42C24×C1111yescharacteristic
292C11#6062711yescharacteristic, direct product factor, Sylow
293C23—22no—
294C23C22×D4×C1113yes—
295Q8—212no—
296Q8—412no—
297Q8—86no—
298Q8C11×#12414yes—
299D4—24no—
300D4—44no—
301D4—412no—
302D4C11×#124112yes—
303C2×C4—22no—
304C2×C4—26no—
305C2×C4—26no—
306C2×C4—46no—
307C2×C4—412no—
308C2×C4—412no—
309C2×C4—86no—
310C2×C4C22×D4×C1112yes—
311C2×C4C22×D4×C1116yes—
312C2×C4C22×D4×C1113yes—
313C2×C4C2×C11×#41112yes—
314C2×C4C25×C1111yescharacteristic
315C8—22no—
316C8—26no—
317C22—26no—
318C22—42no—
319C22—44no—
320C22C2×C11×#12416yes—
321C22C23×D4×C1111yescharacteristic
322C4—22no—
323C4—26no—
324C4—46no—
325C4—46no—
326C4—42no—
327C4C2×C11×#12416yes—
328C4C22×C11×#4112yes—
329C2—26no—
330C2—82no—
331C2C22×C11×#12411yescharacteristic
332C2C11×#358612yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3499C2
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
1. C11×#3504C2semidirect
3. C11×#3142C2semidirect
4. C11×#3139C2semidirect
5. C11×#3137C2semidirect
6. C11×#3135C2semidirect
7. C2×C11×#491C2semidirect
8. C11×#2898C2semidirect
9. C11×#2875C2semidirect
87. #60627C11direct (N × H)
127. #3504C2×C11semidirect
129. #3142C2×C11semidirect
130. #3139C2×C11semidirect
131. #3137C2×C11semidirect
132. #3135C2×C11semidirect
133. C2×#491C2×C11semidirect
134. #2898C2×C11semidirect
135. #2875C2×C11semidirect
292. C11#60627direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35042
C11×#34992
C11×#31422
C11×#31392
C11×#31372
C11×#31352
C2×C11×#4912
C11×#28982
C11×#28752
#6062711