Finite Group Databasebeta

← C2×C11×#1944 #14598346

Subgroups — C2×C11×#1944 #14598346

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#107C211yesmaximal, characteristic
2C22×C11×#106C211yesmaximal, characteristic
3C22×C11×#97C211yesmaximal, characteristic
4C2×C11×#389C212yesmaximal
5C11×#1944C218yesmaximal, direct product factor
6C2×C11×#340C212yesmaximal
7C23×C8×C11C2211yescharacteristic
8C23×C8×C11C2211yescharacteristic
9C22×C11×C4⋊C4—22no—
10C22×C11×C4⋊C4C2212yes—
11C22×C11×C4⋊C4C2212yes—
12C22×C42×C11C2211yescharacteristic
13C2×C11×#107—24no—
14C2×C11×#107C2214yes—
15C2×C11×#106C418yescomplemented
16C2×C11×#106C2214yes—
17C2×C11×#97—24no—
18C2×C11×#97C2214yes—
19C11×#389—24no—
20C11×#389C2218yes—
21C2×C11×#95—22no—
22C11×#340C2218yes—
23C23×C4×C11—22no—
24C23×C4×C11—22no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C8×C11—22no—
29C22×C8×C11—22no—
30C22×C8×C11C2×C414yes—
31C22×C8×C11D414yes—
32C22×C8×C11Q814yes—
33C22×C8×C11Q814yes—
34C22×C8×C11C2312yes—
35C22×C8×C11C2312yes—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—24no—
38C2×C11×C4⋊C4—24no—
39C2×C11×C4⋊C4—24no—
40C2×C11×C4⋊C4—28no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—48no—
43C2×C11×C4⋊C4C2×C418yes—
44C2×C11×C4⋊C4C2314yes—
45C2×C11×C4⋊C4C2314yes—
46C2×C42×C11—22no—
47C2×C42×C11—22no—
48C2×C42×C11D412yes—
49C2×C42×C11C2312yes—
50C11×#107—28no—
51C11×#106C2×C4116yescomplemented
52C11×#97—28no—
53C11×#95—28no—
54C2×#1944C1111yesmaximal, characteristic, direct product factor, Sylow
55C24×C11C2×D411yescharacteristic
56C22×C4×C11—28no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—24no—
60C22×C4×C11—24no—
61C22×C4×C11—24no—
62C22×C4×C11—24no—
63C22×C4×C11—44no—
64C22×C4×C11—44no—
65C22×C4×C11—44no—
66C22×C4×C11—44no—
67C22×C4×C11—44no—
68C22×C4×C11C22×C412yes—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×Q812yes—
74C22×C4×C11C2×Q812yes—
75C22×C4×C11#4112yes—
76C22×C4×C11#4112yes—
77C22×C4×C11C2411yescharacteristic
78C2×C8×C11—28no—
79C2×C8×C11—22no—
80C2×C8×C11—22no—
81C2×C8×C11C4⋊C4116yescomplemented
82C2×C8×C11C22×C414yes—
83C2×C8×C11C2×D414yes—
84C2×C8×C11C2×Q814yes—
85C2×C8×C11C2×Q814yes—
86C11×C4⋊C4—28no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—416no—
91C11×C4⋊C4—44no—
92C11×C4⋊C4C22×C418yes—
93C42×C11—24no—
94C42×C11—22no—
95C42×C11—22no—
96C22×#107C2×C1111yescharacteristic
97C22×#106C2×C1111yescharacteristic
98C22×#97C2×C1111yescharacteristic
99C2×#389C2×C1112yes—
100#1944C2×C1118yesdirect product factor
101C2×#340C2×C1112yes—
102C23×C11C4×D412yes—
103C23×C11#12112yes—
104C23×C11C4⋊Q812yes—
105C23×C11AGL(1,ℤ/8)14yes—
106C23×C11#13714yes—
107C23×C11C22×D411yescharacteristic
108C2×C4×C11—28no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—24no—
112C2×C4×C11—24no—
113C2×C4×C11—44no—
114C2×C4×C11—44no—
115C2×C4×C11—416no—
116C2×C4×C11—44no—
117C2×C4×C11—44no—
118C2×C4×C11—44no—
119C2×C4×C11—44no—
120C2×C4×C11—44no—
121C2×C4×C11—88no—
122C2×C4×C11C2×C4⋊C414yes—
123C2×C4×C11C4×D412yes—
124C2×C4×C11C4×Q814yes—
125C2×C4×C11#12112yes—
126C2×C4×C11C22⋊Q814yes—
127C2×C4×C11#12514yes—
128C2×C4×C11C4⋊Q812yes—
129C2×C4×C11C23×C411yescharacteristic
130C2×C4×C11C22×D411yescharacteristic
131C2×C4×C11C22×Q811yescharacteristic
132C2×C4×C11C22×Q811yescharacteristic
133C2×C4×C11C2×#4111yescharacteristic
134C2×C4×C11C2×#4111yescharacteristic
135C8×C11—24no—
136C8×C11C2×C4⋊C418yescomplemented
137C23×C8C22×C1111yescharacteristic
138C23×C8C22×C1111yescharacteristic
139C22×C4⋊C4—22no—
140C22×C4⋊C4C22×C1112yes—
141C22×C4⋊C4C22×C1112yes—
142C22×C42C22×C1111yescharacteristic
143C2×#107—24no—
144C2×#107C22×C1114yes—
145C2×#106C4×C1118yescomplemented
146C2×#106C22×C1114yes—
147C2×#97—24no—
148C2×#97C22×C1114yes—
149#389—24no—
150#389C22×C1118yes—
151C2×#95—22no—
152#340C22×C1118yes—
153C22×C11#38914yes—
154C22×C11#44018yes—
155C22×C11#46914yes—
156C22×C11#47014yes—
157C22×C11#50118yes—
158C22×C11C2×C4×D411yescharacteristic
159C22×C11C2×#12111yescharacteristic
160C22×C11C2×C4⋊Q811yescharacteristic
161C22×C11C2×AGL(1,ℤ/8)12yes—
162C22×C11C2×#13712yes—
163C4×C11—48no—
164C4×C11—42no—
165C4×C11—42no—
166C4×C11—84no—
167C4×C11#38914yes—
168C4×C11C22×C4⋊C411yescharacteristic
169C4×C11C2×C4×Q811yescharacteristic
170C4×C11C2×C22⋊Q811yescharacteristic
171C4×C11C2×#12511yescharacteristic
172C23×C4—22no—
173C23×C4—22no—
174C23×C4D4×C1111yescharacteristic
175C23×C4D4×C1111yescharacteristic
176C23×C4C23×C1111yescharacteristic
177C22×C8—22no—
178C22×C8—22no—
179C22×C8C2×C4×C1114yes—
180C22×C8D4×C1114yes—
181C22×C8Q8×C1114yes—
182C22×C8Q8×C1114yes—
183C22×C8C23×C1112yes—
184C22×C8C23×C1112yes—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—28no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—48no—
192C2×C4⋊C4C2×C4×C1118yes—
193C2×C4⋊C4C23×C1114yes—
194C2×C4⋊C4C23×C1114yes—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42D4×C1112yes—
198C2×C42C23×C1112yes—
199#107—28no—
200#106C2×C4×C11116yescomplemented
201#97—28no—
202#95—28no—
203C2×C11#194418yesdirect product factor
204C2×C11C2×#38911yescharacteristic
205C2×C11C2×#44012yes—
206C2×C11C2×#46911yescharacteristic
207C2×C11C2×#47011yescharacteristic
208C2×C11C2×#50112yes—
209C24C2×D4×C1111yescharacteristic
210C22×C4—28no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—44no—
218C22×C4—44no—
219C22×C4—44no—
220C22×C4—44no—
221C22×C4—44no—
222C22×C4C22×C4×C1112yes—
223C22×C4C2×D4×C1112yes—
224C22×C4C2×D4×C1112yes—
225C22×C4C2×D4×C1112yes—
226C22×C4C2×D4×C1111yescharacteristic
227C22×C4C2×Q8×C1112yes—
228C22×C4C2×Q8×C1112yes—
229C22×C4C11×#4112yes—
230C22×C4C11×#4112yes—
231C22×C4C24×C1111yescharacteristic
232C2×C8—28no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8C11×C4⋊C4116yescomplemented
236C2×C8C22×C4×C1114yes—
237C2×C8C2×D4×C1114yes—
238C2×C8C2×Q8×C1114yes—
239C2×C8C2×Q8×C1114yes—
240C4⋊C4—28no—
241C4⋊C4—24no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—416no—
245C4⋊C4—44no—
246C4⋊C4C22×C4×C1118yes—
247C42—24no—
248C42—22no—
249C42—22no—
250C11C2×#194411yescharacteristic, direct product factor, Sylow
251C23C4×D4×C1112yes—
252C23C11×#12112yes—
253C23C11×C4⋊Q812yes—
254C23C11×AGL(1,ℤ/8)14yes—
255C23C11×#13714yes—
256C23C22×D4×C1111yescharacteristic
257C2×C4—28no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—416no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—88no—
271C2×C4C2×C11×C4⋊C414yes—
272C2×C4C4×D4×C1112yes—
273C2×C4C4×Q8×C1114yes—
274C2×C4C11×#12112yes—
275C2×C4C11×C22⋊Q814yes—
276C2×C4C11×#12514yes—
277C2×C4C11×C4⋊Q812yes—
278C2×C4C23×C4×C1111yescharacteristic
279C2×C4C22×D4×C1111yescharacteristic
280C2×C4C22×Q8×C1111yescharacteristic
281C2×C4C22×Q8×C1111yescharacteristic
282C2×C4C2×C11×#4111yescharacteristic
283C2×C4C2×C11×#4111yescharacteristic
284C8—24no—
285C8C2×C11×C4⋊C418yescomplemented
286C22C11×#38914yes—
287C22C11×#44018yes—
288C22C11×#46914yes—
289C22C11×#47014yes—
290C22C11×#50118yes—
291C22C2×C4×D4×C1111yescharacteristic
292C22C2×C11×#12111yescharacteristic
293C22C2×C11×C4⋊Q811yescharacteristic
294C22C2×C11×AGL(1,ℤ/8)12yes—
295C22C2×C11×#13712yes—
296C4—48no—
297C4—42no—
298C4—42no—
299C4—84no—
300C4C11×#38914yes—
301C4C22×C11×C4⋊C411yescharacteristic
302C4C2×C4×Q8×C1111yescharacteristic
303C4C2×C11×C22⋊Q811yescharacteristic
304C4C2×C11×#12511yescharacteristic
305C2C11×#194418yesdirect product factor
306C2C2×C11×#38911yescharacteristic
307C2C2×C11×#44012yes—
308C2C2×C11×#46911yescharacteristic
309C2C2×C11×#47011yescharacteristic
310C2C2×C11×#50112yes—
subgroupG/H
center, socle, prime radicalC24×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#1944C2direct (N × H)
15. C2×C11×#106C4semidirect
51. C11×#106C2×C4semidirect
54. C2×#1944C11direct (N × H)
81. C2×C8×C11C4⋊C4semidirect
100. #1944C2×C11direct (N × H)
136. C8×C11C2×C4⋊C4semidirect
145. C2×#106C4×C11semidirect
200. #106C2×C4×C11semidirect
203. C2×C11#1944direct (N × H)
235. C2×C8C11×C4⋊C4semidirect
250. C11C2×#1944direct (N × H)
285. C8C2×C11×C4⋊C4semidirect
305. C2C11×#1944direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1072
C22×C11×#1062
C22×C11×#972
C2×C11×#3892
C11×#19442
C2×C11×#3402
C2×#194411