Finite Group Databasebeta

← C11×#21948 #14599141

Subgroups — C11×#21948 #14599141

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#407C212yesmaximal
2C22×C11×C22⋊C8C211yesmaximal, characteristic
3C11×#1855C218yesmaximal, complemented
4C11×#1810C214yesmaximal, complemented
5C24×C4×C11C2211yescharacteristic
6C22×C11×M16C2214yes—
7C23×C8×C11C2212yes—
8C2×C11×#108C2218yescomplemented
9C11×#407—22no—
10C11×#407—22no—
11C11×#407C2214yes—
12C11×#407C2214yes—
13C2×C11×C22⋊C8—22no—
14C2×C11×C22⋊C8—22no—
15C2×C11×C22⋊C8C414yes—
16C2×C11×C22⋊C8C412yes—
17C2×C11×C22⋊C8C412yes—
18C2×C11×C22⋊C8C2214yes—
19C11×#341C2218yescomplemented
20C25×C11Q811yescharacteristic
21C23×C4×C11—44no—
22C23×C4×C11C2×C412yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D412yes—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11Q811yescharacteristic
29C23×C4×C11Q812yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C2×C11×M16—24no—
33C2×C11×M16—48no—
34C2×C11×M16C2318yes—
35C22×C8×C11—24no—
36C22×C8×C11—44no—
37C22×C8×C11C2×C414yes—
38C22×C8×C11C2×C414yes—
39C22×C8×C11C2314yes—
40C11×#108—48no—
41C11×C22⋊C8—24no—
42C11×C22⋊C8—24no—
43C11×C22⋊C8—24no—
44C11×C22⋊C8—24no—
45C11×C22⋊C8C2×C418yes—
46C11×C22⋊C8C2×C418yes—
47#21948C1111yesmaximal, characteristic, direct product factor, Sylow
48C24×C11—24no—
49C24×C11—42no—
50C24×C11—42no—
51C24×C11C4⋊C412yes—
52C24×C11C4⋊C411yescharacteristic
53C24×C11C4⋊C411yescharacteristic
54C24×C11C2×Q811yescharacteristic
55C24×C11C2×Q812yes—
56C22×C4×C11—24no—
57C22×C4×C11—28no—
58C22×C4×C11—42no—
59C22×C4×C11—44no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—44no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—44no—
66C22×C4×C11C4⋊C412yes—
67C22×C4×C11C4⋊C412yes—
68C22×C4×C11C4⋊C411yescharacteristic
69C22×C4×C11C4⋊C412yes—
70C22×C4×C11C4⋊C412yes—
71C22×C4×C11C4⋊C411yescharacteristic
72C22×C4×C11C4⋊C412yes—
73C22×C4×C11C22×C412yes—
74C22×C4×C11C22×C412yes—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×D412yes—
81C22×C4×C11C2×Q812yes—
82C22×C4×C11C2×Q811yescharacteristic
83C22×C4×C11C2411yescharacteristic
84C11×M16—216no—
85C11×M16—48no—
86C2×C8×C11—28no—
87C2×C8×C11—28no—
88C2×C8×C11—44no—
89C2×C8×C11—44no—
90C2×C8×C11—48no—
91C2×C8×C11C22×C418yes—
92C2×#407C2×C1112yes—
93C22×C22⋊C8C2×C1111yescharacteristic
94#1855C2×C1118yescomplemented
95#1810C2×C1114yescomplemented
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11—24no—
100C23×C11—24no—
101C23×C11—22no—
102C23×C11—24no—
103C23×C11—24no—
104C23×C11—41no—
105C23×C11—42no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—42no—
110C23×C11—416no—
111C23×C11#10814yescomplemented
112C23×C11C2×C4⋊C412yes—
113C23×C11C2×C4⋊C412yes—
114C23×C11C2×C4⋊C411yescharacteristic
115C23×C11C2×C4⋊C411yescharacteristic
116C23×C11C22×Q811yescharacteristic
117C2×C4×C11—22no—
118C2×C4×C11—24no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—24no—
122C2×C4×C11—24no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11C2×C4⋊C412yes—
135C2×C4×C11C2×C4⋊C412yes—
136C2×C4×C11C2×C4⋊C411yescharacteristic
137C2×C4×C11C2×C4⋊C411yescharacteristic
138C2×C4×C11C23×C411yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×C4×C11H(5,𝔽2)14yes—
141C8×C11—28no—
142C8×C11—48no—
143C24×C4C22×C1111yescharacteristic
144C22×M16C22×C1114yes—
145C23×C8C22×C1112yes—
146C2×#108C22×C1118yescomplemented
147#407—22no—
148#407—22no—
149#407C22×C1114yes—
150#407C22×C1114yes—
151C2×C22⋊C8—22no—
152C2×C22⋊C8—22no—
153C2×C22⋊C8C4×C1114yes—
154C2×C22⋊C8C4×C1112yes—
155C2×C22⋊C8C4×C1112yes—
156C2×C22⋊C8C22×C1114yes—
157#341C22×C1118yescomplemented
158C22×C11—28no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—22no—
166C22×C11—21no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—22no—
170C22×C11—44no—
171C22×C11—48no—
172C22×C11—48no—
173C22×C11—44no—
174C22×C11C2×#10812yes—
175C22×C11C2×#10814yes—
176C22×C11#43012yes—
177C22×C11C22×C4⋊C411yescharacteristic
178C22×C11#54312yes—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11#51812yes—
184C4×C11#53412yes—
185C25Q8×C1111yescharacteristic
186C23×C4—44no—
187C23×C4C2×C4×C1112yes—
188C23×C4C2×C4×C1111yescharacteristic
189C23×C4C2×C4×C1111yescharacteristic
190C23×C4D4×C1111yescharacteristic
191C23×C4D4×C1112yes—
192C23×C4D4×C1111yescharacteristic
193C23×C4Q8×C1111yescharacteristic
194C23×C4Q8×C1112yes—
195C23×C4C23×C1111yescharacteristic
196C23×C4C23×C1112yes—
197C2×M16—24no—
198C2×M16—48no—
199C2×M16C23×C1118yes—
200C22×C8—24no—
201C22×C8—44no—
202C22×C8C2×C4×C1114yes—
203C22×C8C2×C4×C1114yes—
204C22×C8C23×C1114yes—
205#108—48no—
206C22⋊C8—24no—
207C22⋊C8—24no—
208C22⋊C8—24no—
209C22⋊C8—24no—
210C22⋊C8C2×C4×C1118yes—
211C22⋊C8C2×C4×C1118yes—
212C2×C11—22no—
213C2×C11—22no—
214C2×C11—22no—
215C2×C11—24no—
216C2×C11—42no—
217C2×C11#231511yescharacteristic
218C2×C11C22×#10811yescharacteristic
219C2×C11C2×#43011yescharacteristic
220C24—24no—
221C24—42no—
222C24—42no—
223C24C11×C4⋊C412yes—
224C24C11×C4⋊C411yescharacteristic
225C24C11×C4⋊C411yescharacteristic
226C24C2×Q8×C1111yescharacteristic
227C24C2×Q8×C1112yes—
228C22×C4—24no—
229C22×C4—28no—
230C22×C4—42no—
231C22×C4—44no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—44no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—44no—
238C22×C4C11×C4⋊C412yes—
239C22×C4C11×C4⋊C412yes—
240C22×C4C11×C4⋊C411yescharacteristic
241C22×C4C11×C4⋊C412yes—
242C22×C4C11×C4⋊C412yes—
243C22×C4C11×C4⋊C411yescharacteristic
244C22×C4C11×C4⋊C412yes—
245C22×C4C22×C4×C1112yes—
246C22×C4C22×C4×C1112yes—
247C22×C4C22×C4×C1111yescharacteristic
248C22×C4C22×C4×C1111yescharacteristic
249C22×C4C2×D4×C1111yescharacteristic
250C22×C4C2×D4×C1111yescharacteristic
251C22×C4C2×D4×C1112yes—
252C22×C4C2×D4×C1112yes—
253C22×C4C2×Q8×C1111yescharacteristic
254C22×C4C2×Q8×C1112yes—
255C22×C4C24×C1111yescharacteristic
256M16—216no—
257M16—48no—
258C2×C8—28no—
259C2×C8—28no—
260C2×C8—44no—
261C2×C8—44no—
262C2×C8—48no—
263C2×C8C22×C4×C1118yes—
264C11#2194811yescharacteristic, direct product factor, Sylow
265C23—22no—
266C23—22no—
267C23—22no—
268C23—24no—
269C23—24no—
270C23—22no—
271C23—24no—
272C23—24no—
273C23—41no—
274C23—42no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—42no—
279C23—416no—
280C23C11×#10814yescomplemented
281C23C2×C11×C4⋊C412yes—
282C23C2×C11×C4⋊C412yes—
283C23C2×C11×C4⋊C411yescharacteristic
284C23C2×C11×C4⋊C411yescharacteristic
285C23C22×Q8×C1111yescharacteristic
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×C11×C4⋊C412yes—
304C2×C4C2×C11×C4⋊C412yes—
305C2×C4C2×C11×C4⋊C411yescharacteristic
306C2×C4C2×C11×C4⋊C411yescharacteristic
307C2×C4C23×C4×C1111yescharacteristic
308C2×C4C22×D4×C1111yescharacteristic
309C2×C4C11×H(5,𝔽2)14yes—
310C8—28no—
311C8—48no—
312C22—28no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—44no—
325C22—48no—
326C22—48no—
327C22—44no—
328C22C2×C11×#10812yes—
329C22C2×C11×#10814yes—
330C22C11×#43012yes—
331C22C22×C11×C4⋊C411yescharacteristic
332C22C11×#54312yes—
333C4—21no—
334C4—21no—
335C4—22no—
336C4—22no—
337C4C11×#51812yes—
338C4C11×#53412yes—
339C2—22no—
340C2—22no—
341C2—22no—
342C2—24no—
343C2—42no—
344C2C11×#231511yescharacteristic
345C2C22×C11×#10811yescharacteristic
346C2C2×C11×#43011yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C22×C4⋊C4
prime radicalC25×C11Q8
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1855C2semidirect
4. C11×#1810C2semidirect
8. C2×C11×#108C22semidirect
19. C11×#341C22semidirect
47. #21948C11direct (N × H)
94. #1855C2×C11semidirect
95. #1810C2×C11semidirect
111. C23×C11#108semidirect
146. C2×#108C22×C11semidirect
157. #341C22×C11semidirect
264. C11#21948direct (N × H)
280. C23C11×#108semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4072
C22×C11×C22⋊C82
C11×#18552
C11×#18102
#2194811