Finite Group Databasebeta

← C11×#21949 #14599142

Subgroups — C11×#21949 #14599142

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#407C212yesmaximal
2C2×C11×#407C211yesmaximal, characteristic
3C11×#1855C218yesmaximal, complemented
4C11×#1811C214yesmaximal, complemented
5C24×C4×C11C2211yescharacteristic
6C22×C11×M16C2214yes—
7C22×C11×M16C2212yes—
8C2×C11×#108C2218yescomplemented
9C11×#407—22no—
10C11×#407—22no—
11C11×#407C412yes—
12C11×#407C414yes—
13C11×#407C412yes—
14C11×#407C2214yes—
15C11×#407C2214yes—
16C2×C11×C22⋊C8—22no—
17C2×C11×C22⋊C8—22no—
18C2×C11×C22⋊C8C2214yes—
19C11×#341C2218yescomplemented
20C25×C11Q811yescharacteristic
21C23×C4×C11—44no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11C2×C412yes—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D412yes—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11Q812yes—
29C23×C4×C11Q811yescharacteristic
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C2×C11×M16—24no—
33C2×C11×M16—44no—
34C2×C11×M16—48no—
35C2×C11×M16C2×C414yes—
36C2×C11×M16C2×C414yes—
37C2×C11×M16C2318yes—
38C22×C8×C11—24no—
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#21949C1111yesmaximal, characteristic, direct product factor, Sylow
48C24×C11—42no—
49C24×C11—44no—
50C24×C11C4⋊C411yescharacteristic
51C24×C11C4⋊C412yes—
52C24×C11C4⋊C411yescharacteristic
53C24×C11C2×Q812yes—
54C24×C11C2×Q811yescharacteristic
55C22×C4×C11—24no—
56C22×C4×C11—28no—
57C22×C4×C11—42no—
58C22×C4×C11—44no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11—44no—
62C22×C4×C11—42no—
63C22×C4×C11—44no—
64C22×C4×C11—42no—
65C22×C4×C11C4⋊C411yescharacteristic
66C22×C4×C11C4⋊C412yes—
67C22×C4×C11C4⋊C412yes—
68C22×C4×C11C4⋊C411yescharacteristic
69C22×C4×C11C4⋊C412yes—
70C22×C4×C11C4⋊C412yes—
71C22×C4×C11C4⋊C412yes—
72C22×C4×C11C22×C412yes—
73C22×C4×C11C22×C412yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×Q812yes—
81C22×C4×C11C2×Q811yescharacteristic
82C22×C4×C11C2411yescharacteristic
83C11×M16—216no—
84C11×M16—44no—
85C11×M16—44no—
86C11×M16—48no—
87C2×C8×C11—28no—
88C2×C8×C11—28no—
89C2×C8×C11—48no—
90C2×C8×C11C22×C418yes—
91C2×#407C2×C1112yes—
92C2×#407C2×C1111yescharacteristic
93#1855C2×C1118yescomplemented
94#1811C2×C1114yescomplemented
95C23×C11—24no—
96C23×C11—22no—
97C23×C11—24no—
98C23×C11—24no—
99C23×C11—24no—
100C23×C11—41no—
101C23×C11—42no—
102C23×C11—41no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11—416no—
108C23×C11C2×C4⋊C412yes—
109C23×C11C2×C4⋊C411yescharacteristic
110C23×C11C2×C4⋊C411yescharacteristic
111C23×C11C2×C4⋊C412yes—
112C23×C11C22×Q811yescharacteristic
113C2×C4×C11—22no—
114C2×C4×C11—24no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—24no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11C2×C4⋊C412yes—
131C2×C4×C11C2×C4⋊C412yes—
132C2×C4×C11C2×C4⋊C411yescharacteristic
133C2×C4×C11C2×C4⋊C411yescharacteristic
134C2×C4×C11C23×C411yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11H(5,𝔽2)14yes—
137C8×C11—28no—
138C8×C11—48no—
139C24×C4C22×C1111yescharacteristic
140C22×M16C22×C1114yes—
141C22×M16C22×C1112yes—
142C2×#108C22×C1118yescomplemented
143#407—22no—
144#407—22no—
145#407C4×C1112yes—
146#407C4×C1114yes—
147#407C4×C1112yes—
148#407C22×C1114yes—
149#407C22×C1114yes—
150C2×C22⋊C8—22no—
151C2×C22⋊C8—22no—
152C2×C22⋊C8C22×C1114yes—
153#341C22×C1118yescomplemented
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—48no—
165C22×C11—44no—
166C22×C11—44no—
167C22×C11—48no—
168C22×C11—44no—
169C22×C11#43014yes—
170C22×C11C22×C4⋊C411yescharacteristic
171C22×C11#54312yes—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11#51812yes—
177C4×C11#53412yes—
178C25Q8×C1111yescharacteristic
179C23×C4—44no—
180C23×C4C2×C4×C1111yescharacteristic
181C23×C4C2×C4×C1112yes—
182C23×C4C2×C4×C1111yescharacteristic
183C23×C4D4×C1111yescharacteristic
184C23×C4D4×C1112yes—
185C23×C4D4×C1111yescharacteristic
186C23×C4Q8×C1112yes—
187C23×C4Q8×C1111yescharacteristic
188C23×C4C23×C1112yes—
189C23×C4C23×C1111yescharacteristic
190C2×M16—24no—
191C2×M16—44no—
192C2×M16—48no—
193C2×M16C2×C4×C1114yes—
194C2×M16C2×C4×C1114yes—
195C2×M16C23×C1118yes—
196C22×C8—24no—
197C22×C8C23×C1114yes—
198#108—48no—
199C22⋊C8—24no—
200C22⋊C8—24no—
201C22⋊C8—24no—
202C22⋊C8—24no—
203C22⋊C8C2×C4×C1118yes—
204C22⋊C8C2×C4×C1118yes—
205C2×C11—22no—
206C2×C11—24no—
207C2×C11—41no—
208C2×C11—42no—
209C2×C11—41no—
210C2×C11#231511yescharacteristic
211C2×C11C2×#43012yes—
212C24—42no—
213C24—44no—
214C24C11×C4⋊C411yescharacteristic
215C24C11×C4⋊C412yes—
216C24C11×C4⋊C411yescharacteristic
217C24C2×Q8×C1112yes—
218C24C2×Q8×C1111yescharacteristic
219C22×C4—24no—
220C22×C4—28no—
221C22×C4—42no—
222C22×C4—44no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—44no—
226C22×C4—42no—
227C22×C4—44no—
228C22×C4—42no—
229C22×C4C11×C4⋊C411yescharacteristic
230C22×C4C11×C4⋊C412yes—
231C22×C4C11×C4⋊C412yes—
232C22×C4C11×C4⋊C411yescharacteristic
233C22×C4C11×C4⋊C412yes—
234C22×C4C11×C4⋊C412yes—
235C22×C4C11×C4⋊C412yes—
236C22×C4C22×C4×C1112yes—
237C22×C4C22×C4×C1112yes—
238C22×C4C22×C4×C1111yescharacteristic
239C22×C4C22×C4×C1111yescharacteristic
240C22×C4C2×D4×C1111yescharacteristic
241C22×C4C2×D4×C1111yescharacteristic
242C22×C4C2×D4×C1112yes—
243C22×C4C2×D4×C1112yes—
244C22×C4C2×Q8×C1112yes—
245C22×C4C2×Q8×C1111yescharacteristic
246C22×C4C24×C1111yescharacteristic
247M16—216no—
248M16—44no—
249M16—44no—
250M16—48no—
251C2×C8—28no—
252C2×C8—28no—
253C2×C8—48no—
254C2×C8C22×C4×C1118yes—
255C11#2194911yescharacteristic, direct product factor, Sylow
256C23—24no—
257C23—22no—
258C23—24no—
259C23—24no—
260C23—24no—
261C23—41no—
262C23—42no—
263C23—41no—
264C23—42no—
265C23—42no—
266C23—42no—
267C23—42no—
268C23—416no—
269C23C2×C11×C4⋊C412yes—
270C23C2×C11×C4⋊C411yescharacteristic
271C23C2×C11×C4⋊C411yescharacteristic
272C23C2×C11×C4⋊C412yes—
273C23C22×Q8×C1111yescharacteristic
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—24no—
281C2×C4—24no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4C2×C11×C4⋊C412yes—
292C2×C4C2×C11×C4⋊C412yes—
293C2×C4C2×C11×C4⋊C411yescharacteristic
294C2×C4C2×C11×C4⋊C411yescharacteristic
295C2×C4C23×C4×C1111yescharacteristic
296C2×C4C22×D4×C1111yescharacteristic
297C2×C4C11×H(5,𝔽2)14yes—
298C8—28no—
299C8—48no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—48no—
311C22—44no—
312C22—44no—
313C22—48no—
314C22—44no—
315C22C11×#43014yes—
316C22C22×C11×C4⋊C411yescharacteristic
317C22C11×#54312yes—
318C4—21no—
319C4—21no—
320C4—22no—
321C4—22no—
322C4C11×#51812yes—
323C4C11×#53412yes—
324C2—22no—
325C2—24no—
326C2—41no—
327C2—42no—
328C2—41no—
329C2C11×#231511yescharacteristic
330C2C2×C11×#43012yes—
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×#1811C2semidirect
8. C2×C11×#108C22semidirect
19. C11×#341C22semidirect
47. #21949C11direct (N × H)
93. #1855C2×C11semidirect
94. #1811C2×C11semidirect
142. C2×#108C22×C11semidirect
153. #341C22×C11semidirect
255. C11#21949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4072
C11×#18552
C11×#18112
#2194911