Finite Group Databasebeta

← C11×#9552 #14586745

Subgroups — C11×#9552 #14586745

Order 2816.

366 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#100C211yesmaximal, characteristic
2C11×#1565C211yesmaximal, characteristic, complemented
3C11×#1478C211yesmaximal, characteristic
4C2×C11×D4⋊C8C211yesmaximal, characteristic
5C11×#1451C211yesmaximal, characteristic, complemented
6C11×#1283C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#100C411yescharacteristic
13C2×C11×#100C411yescharacteristic
14C4×C11×M16C2211yescharacteristic
15C4×C11×M16C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C11×#343C411yescharacteristic
18C11×#343C411yescharacteristic
19C11×#335—21no—
20C11×#334—21no—
21C11×D4⋊C8—21no—
22C11×D4⋊C8—21no—
23C11×D4⋊C8—21no—
24C11×D4⋊C8—21no—
25C11×#322—21no—
26C11×#322—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11—21no—
29C2×C11×M16C2×C411yescharacteristic
30C2×C11×M16C2×C411yescharacteristic
31C2×C11×M16C2×C411yescharacteristic
32C2×C11×M16C2×C411yescharacteristic
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C11×C4⋊C8—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8D411yescharacteristic
46C11×C4⋊C8D411yescharacteristic
47C11×#100—22no—
48C11×#100—22no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×#97—21no—
52C11×#97—21no—
53C4×C8×C11—21no—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56C4×C8×C11—21no—
57C4×C8×C11—21no—
58C4×C8×C11D411yescharacteristic
59C4×C8×C11D411yescharacteristic
60#9552C1111yesmaximal, characteristic, direct product factor, Sylow
61C24×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11M1612yes—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—81no—
72C22×C4×C11—81no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C11×M16—21no—
77C11×M16—21no—
78C11×M16—21no—
79C11×M16—21no—
80C11×M16—21no—
81C11×M16—21no—
82C11×M16—21no—
83C11×M16M1612yes—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—42no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—81no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104C4×#100C2×C1111yescharacteristic
105#1565C2×C1111yescharacteristic, complemented
106#1478C2×C1111yescharacteristic
107C2×D4⋊C8C2×C1111yescharacteristic
108#1451C2×C1111yescharacteristic, complemented
109#1283C2×C1111yescharacteristic, complemented
110#1278C2×C1111yescharacteristic, complemented
111C23×C11—22no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—81no—
115C23×C11—81no—
116C23×C11#11711yescharacteristic
117D4×C11—22no—
118D4×C11—22no—
119D4×C11—41no—
120D4×C11—41no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—82no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11#12611yescharacteristic
135C2×C4×C11C2×M1611yescharacteristic
136C2×C4×C11C2×M1611yescharacteristic
137C2×C4×C11#13111yescharacteristic
138C2×C4×C11#13111yescharacteristic
139C8×C11—22no—
140C8×C11—22no—
141C8×C11—41no—
142C8×C11—41no—
143C8×C11—41no—
144C8×C11—41no—
145C8×C11—41no—
146C8×C11—41no—
147C8×C11—81no—
148C8×C11—81no—
149C2×C4×D4C22×C1111yescharacteristic
150#431C22×C1111yescharacteristic
151#431C22×C1111yescharacteristic
152C2×C4⋊C8C22×C1111yescharacteristic
153C2×#100C4×C1111yescharacteristic
154C2×#100C4×C1111yescharacteristic
155C4×M16C22×C1111yescharacteristic
156C4×M16C22×C1111yescharacteristic
157C2×C4×C8C22×C1111yescharacteristic
158#343C4×C1111yescharacteristic
159#343C4×C1111yescharacteristic
160#335—21no—
161#334—21no—
162D4⋊C8—21no—
163D4⋊C8—21no—
164D4⋊C8—21no—
165D4⋊C8—21no—
166#322—21no—
167#322—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—42no—
171C22×C11—82no—
172C22×C11—82no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11#38811yescharacteristic
176C22×C11#43211yescharacteristic
177C22×C11#43311yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—81no—
182C4×C11#43511yescharacteristic
183C4×C11#43511yescharacteristic
184C4×C11#43511yescharacteristic
185C4×C11#43611yescharacteristic
186C4×C11#47111yescharacteristic
187C4×C11#47211yescharacteristic
188C22×D4C2×C4×C1111yescharacteristic
189C23×C4—21no—
190C2×M16C2×C4×C1111yescharacteristic
191C2×M16C2×C4×C1111yescharacteristic
192C2×M16C2×C4×C1111yescharacteristic
193C2×M16C2×C4×C1111yescharacteristic
194C22×C8—21no—
195C22×C8—21no—
196C4×D4—21no—
197C4×D4—21no—
198C4×D4—21no—
199C4×D4—21no—
200C2×C4⋊C4C2×C4×C1111yescharacteristic
201C2×C22⋊C4—21no—
202C2×C42C23×C1111yescharacteristic
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8D4×C1111yescharacteristic
207C4⋊C8D4×C1111yescharacteristic
208#100—22no—
209#100—22no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212#97—21no—
213#97—21no—
214C4×C8—21no—
215C4×C8—21no—
216C4×C8—21no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8D4×C1111yescharacteristic
220C4×C8D4×C1111yescharacteristic
221C2×C11—21no—
222C2×C11—21no—
223C2×C11—82no—
224C2×C11#192411yescharacteristic
225C2×C11#193111yescharacteristic
226C2×C11#193211yescharacteristic
227C24—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4C11×M1612yes—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4C22×C4×C1111yescharacteristic
240C22×C4C11×#4111yescharacteristic
241C22×C4C11×#4111yescharacteristic
242M16—21no—
243M16—21no—
244M16—21no—
245M16—21no—
246M16—21no—
247M16—21no—
248M16—21no—
249M16C11×M1612yes—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—42no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—81no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C42C2×D4×C1111yescharacteristic
267C42C2×D4×C1111yescharacteristic
268C42C11×#4111yescharacteristic
269C42C11×#4111yescharacteristic
270C11#955211yescharacteristic, direct product factor, Sylow
271C23—22no—
272C23—41no—
273C23—41no—
274C23—81no—
275C23—81no—
276C23C11×#11711yescharacteristic
277D4—22no—
278D4—22no—
279D4—41no—
280D4—41no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—82no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4C4×D4×C1111yescharacteristic
290C2×C4C4×D4×C1111yescharacteristic
291C2×C4C11×#12111yescharacteristic
292C2×C4C11×#12311yescharacteristic
293C2×C4C11×#12411yescharacteristic
294C2×C4C11×#12611yescharacteristic
295C2×C4C2×C11×M1611yescharacteristic
296C2×C4C2×C11×M1611yescharacteristic
297C2×C4C11×#13111yescharacteristic
298C2×C4C11×#13111yescharacteristic
299C8—22no—
300C8—22no—
301C8—41no—
302C8—41no—
303C8—41no—
304C8—41no—
305C8—41no—
306C8—41no—
307C8—81no—
308C8—81no—
309C22—21no—
310C22—21no—
311C22—42no—
312C22—82no—
313C22—82no—
314C22—81no—
315C22—81no—
316C22C11×#38811yescharacteristic
317C22C11×#43211yescharacteristic
318C22C11×#43311yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—81no—
323C4C11×#43511yescharacteristic
324C4C11×#43511yescharacteristic
325C4C11×#43511yescharacteristic
326C4C11×#43611yescharacteristic
327C4C11×#47111yescharacteristic
328C4C11×#47211yescharacteristic
329C2—21no—
330C2—21no—
331C2—82no—
332C2C11×#192411yescharacteristic
333C2C11×#193111yescharacteristic
334C2C11×#193211yescharacteristic
subgroupG/H
centerC2×C4×C11#121
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
socleC22×C11#388
prime radicalC22×D4×C11C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1565C2semidirect
5. C11×#1451C2semidirect
6. C11×#1283C2semidirect
7. C11×#1278C2semidirect
60. #9552C11direct (N × H)
105. #1565C2×C11semidirect
108. #1451C2×C11semidirect
109. #1283C2×C11semidirect
110. #1278C2×C11semidirect
270. C11#9552direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×#1002
C11×#15652
C11×#14782
C2×C11×D4⋊C82
C11×#14512
C11×#12832
C11×#12782
#955211