Finite Group Databasebeta

← C2×C11×#1988 #14598502

Subgroups — C2×C11×#1988 #14598502

Order 2816.

1510 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic
2C22×C11×C4⋊C8C211yesmaximal, characteristic
3C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1988C218yesmaximal, direct product factor
5C2×C11×#340C214yesmaximal
6C23×Q8×C11—21no—
7C23×C8×C11C2212yes—
8C2×C11×C4⋊Q8—22no—
9C2×C11×C4⋊Q8—24no—
10C2×C11×C4⋊Q8C418yescomplemented
11C2×C11×C4⋊Q8C2214yes—
12C22×C11×C4⋊C4—21no—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2212yes—
15C22×C42×C11—21no—
16C22×C42×C11C2211yescharacteristic
17C2×C11×C4⋊C8—24no—
18C2×C11×C4⋊C8C2214yes—
19C4×C11×C4⋊C4—22no—
20C4×C11×C4⋊C4C2214yes—
21C2×C11×#95—21no—
22C11×#340C22116yes—
23C22×Q8×C11—28no—
24C22×Q8×C11—24no—
25C22×Q8×C11—44no—
26C22×Q8×C11—44no—
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C22×C8×C11—24no—
33C22×C8×C11—28no—
34C22×C8×C11C2314yes—
35C11×C4⋊Q8—216no—
36C11×C4⋊Q8—28no—
37C11×C4⋊Q8C2×C4116yescomplemented
38C2×C11×C4⋊C4—28no—
39C2×C11×C4⋊C4—24no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—24no—
43C2×C11×C4⋊C4—24no—
44C2×C11×C4⋊C4C2×C418yes—
45C2×C11×C4⋊C4Q818yescomplemented
46C2×C11×C4⋊C4C2314yes—
47C2×C11×C4⋊C4C2314yes—
48C2×C42×C11—24no—
49C2×C42×C11—44no—
50C2×C42×C11C2×C414yes—
51C2×C42×C11D412yes—
52C2×C42×C11D414yes—
53C2×C42×C11C2312yes—
54C11×C4⋊C8—28no—
55C11×#95—24no—
56C2×#1988C1111yesmaximal, characteristic, direct product factor, Sylow
57C24×C11C2×D411yescharacteristic
58C2×Q8×C11—216no—
59C2×Q8×C11—432no—
60C2×Q8×C11—48no—
61C2×Q8×C11—48no—
62C22×C4×C11—24no—
63C22×C4×C11—28no—
64C22×C4×C11—28no—
65C22×C4×C11—24no—
66C22×C4×C11—24no—
67C22×C4×C11—44no—
68C22×C4×C11—44no—
69C22×C4×C11—44no—
70C22×C4×C11—44no—
71C22×C4×C11C22⋊C414yes—
72C22×C4×C11C22⋊C414yes—
73C22×C4×C11D814yes—
74C22×C4×C11SD1614yes—
75C22×C4×C11C22×C412yes—
76C22×C4×C11C2×D412yes—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×Q814yes—
81C22×C4×C11#4114yes—
82C22×C4×C11C2411yescharacteristic
83C2×C8×C11—24no—
84C2×C8×C11—28no—
85C2×C8×C11—48no—
86C11×C4⋊C4—216no—
87C11×C4⋊C4—28no—
88C11×C4⋊C4—28no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4C22×C418yes—
92C11×C4⋊C4C2×Q818yescomplemented
93C42×C11—48no—
94C42×C11C22⋊C418yes—
95C42×C11C22×C414yes—
96C42×C11C2×D414yes—
97C22×C4⋊Q8C2×C1111yescharacteristic
98C22×C4⋊C8C2×C1111yescharacteristic
99C2×C4×C4⋊C4C2×C1111yescharacteristic
100#1988C2×C1118yesdirect product factor
101C2×#340C2×C1114yes—
102C23×C11C2×C22⋊C412yes—
103C23×C11C22⋊Q814yes—
104C23×C11C2×D812yes—
105C23×C11C2×SD1612yes—
106C23×C11#13714yes—
107C23×C11C22×D411yescharacteristic
108Q8×C11—432no—
109C2×C4×C11—24no—
110C2×C4×C11—28no—
111C2×C4×C11—28no—
112C2×C4×C11—28no—
113C2×C4×C11—44no—
114C2×C4×C11—44no—
115C2×C4×C11—44no—
116C2×C4×C11—44no—
117C2×C4×C11—416no—
118C2×C4×C11—416no—
119C2×C4×C11#102116yes—
120C2×C4×C11C2×C22⋊C414yes—
121C2×C4×C11C2×C22⋊C412yes—
122C2×C4×C11C2×C22⋊C414yes—
123C2×C4×C11C4×Q818yes—
124C2×C4×C11C22⋊Q814yes—
125C2×C4×C11#12414yes—
126C2×C4×C11C4⋊Q814yes—
127C2×C4×C11C2×D814yes—
128C2×C4×C11C2×SD1614yes—
129C2×C4×C11C23×C411yescharacteristic
130C2×C4×C11C22×D411yescharacteristic
131C2×C4×C11C22×Q812yes—
132C2×C4×C11C2×#4112yes—
133C8×C11—44no—
134C23×Q8—21no—
135C23×C8C22×C1112yes—
136C2×C4⋊Q8—22no—
137C2×C4⋊Q8—24no—
138C2×C4⋊Q8C4×C1118yescomplemented
139C2×C4⋊Q8C22×C1114yes—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C22×C1112yes—
142C22×C4⋊C4C22×C1112yes—
143C22×C42—21no—
144C22×C42C22×C1111yescharacteristic
145C2×C4⋊C8—24no—
146C2×C4⋊C8C22×C1114yes—
147C4×C4⋊C4—22no—
148C4×C4⋊C4C22×C1114yes—
149C2×#95—21no—
150#340C22×C11116yes—
151C22×C11#39114yes—
152C22×C11C2×#10214yes—
153C22×C11#41914yes—
154C22×C11#47418yes—
155C22×C11#47518yes—
156C22×C11C22×C22⋊C411yescharacteristic
157C22×C11C2×C22⋊Q812yes—
158C22×C11C22×D811yescharacteristic
159C22×C11C22×SD1611yescharacteristic
160C22×C11C2×#13712yes—
161C4×C11—24no—
162C4×C11—48no—
163C4×C11—48no—
164C4×C11#39114yes—
165C4×C11C2×#10218yes—
166C4×C11C2×C4×Q812yes—
167C4×C11C2×#12411yescharacteristic
168C4×C11C2×C4⋊Q811yescharacteristic
169C22×Q8—28no—
170C22×Q8—24no—
171C22×Q8—44no—
172C22×Q8—44no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4D4×C1111yescharacteristic
176C23×C4D4×C1111yescharacteristic
177C23×C4C23×C1111yescharacteristic
178C22×C8—24no—
179C22×C8—28no—
180C22×C8C23×C1114yes—
181C4⋊Q8—216no—
182C4⋊Q8—28no—
183C4⋊Q8C2×C4×C11116yescomplemented
184C2×C4⋊C4—28no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4C2×C4×C1118yes—
191C2×C4⋊C4Q8×C1118yescomplemented
192C2×C4⋊C4C23×C1114yes—
193C2×C4⋊C4C23×C1114yes—
194C2×C42—24no—
195C2×C42—44no—
196C2×C42C2×C4×C1114yes—
197C2×C42D4×C1112yes—
198C2×C42D4×C1114yes—
199C2×C42C23×C1112yes—
200C4⋊C8—28no—
201#95—24no—
202C2×C11#198818yesdirect product factor
203C2×C11C2×#39111yescharacteristic
204C2×C11C22×#10211yescharacteristic
205C2×C11C2×#41911yescharacteristic
206C2×C11C2×#47412yes—
207C2×C11C2×#47512yes—
208C24C2×D4×C1111yescharacteristic
209C2×Q8—216no—
210C2×Q8—432no—
211C2×Q8—48no—
212C2×Q8—48no—
213C22×C4—24no—
214C22×C4—28no—
215C22×C4—28no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—44no—
219C22×C4—44no—
220C22×C4—44no—
221C22×C4—44no—
222C22×C4C11×C22⋊C414yes—
223C22×C4C11×C22⋊C414yes—
224C22×C4C11×D814yes—
225C22×C4C11×SD1614yes—
226C22×C4C22×C4×C1112yes—
227C22×C4C2×D4×C1112yes—
228C22×C4C2×D4×C1111yescharacteristic
229C22×C4C2×D4×C1112yes—
230C22×C4C2×D4×C1112yes—
231C22×C4C2×Q8×C1114yes—
232C22×C4C11×#4114yes—
233C22×C4C24×C1111yescharacteristic
234C2×C8—24no—
235C2×C8—28no—
236C2×C8—48no—
237C4⋊C4—216no—
238C4⋊C4—28no—
239C4⋊C4—28no—
240C4⋊C4—24no—
241C4⋊C4—24no—
242C4⋊C4C22×C4×C1118yes—
243C4⋊C4C2×Q8×C1118yescomplemented
244C42—48no—
245C42C11×C22⋊C418yes—
246C42C22×C4×C1114yes—
247C42C2×D4×C1114yes—
248C11C2×#198811yescharacteristic, direct product factor, Sylow
249C23C2×C11×C22⋊C412yes—
250C23C11×C22⋊Q814yes—
251C23C2×C11×D812yes—
252C23C2×C11×SD1612yes—
253C23C11×#13714yes—
254C23C22×D4×C1111yescharacteristic
255Q8—432no—
256C2×C4—28no—
257C2×C4—24no—
258C2×C4—28no—
259C2×C4—28no—
260C2×C4—416no—
261C2×C4—44no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—416no—
266C2×C4C11×#102116yes—
267C2×C4C2×C11×C22⋊C414yes—
268C2×C4C2×C11×C22⋊C412yes—
269C2×C4C2×C11×C22⋊C414yes—
270C2×C4C4×Q8×C1118yes—
271C2×C4C11×C22⋊Q814yes—
272C2×C4C11×#12414yes—
273C2×C4C11×C4⋊Q814yes—
274C2×C4C2×C11×D814yes—
275C2×C4C2×C11×SD1614yes—
276C2×C4C23×C4×C1111yescharacteristic
277C2×C4C22×D4×C1111yescharacteristic
278C2×C4C22×Q8×C1112yes—
279C2×C4C2×C11×#4112yes—
280C8—44no—
281C22C11×#39114yes—
282C22C2×C11×#10214yes—
283C22C11×#41914yes—
284C22C11×#47418yes—
285C22C11×#47518yes—
286C22C22×C11×C22⋊C411yescharacteristic
287C22C2×C11×C22⋊Q812yes—
288C22C22×C11×D811yescharacteristic
289C22C22×C11×SD1611yescharacteristic
290C22C2×C11×#13712yes—
291C4—24no—
292C4—48no—
293C4—48no—
294C4C11×#39114yes—
295C4C2×C11×#10218yes—
296C4C2×C4×Q8×C1112yes—
297C4C2×C11×#12411yescharacteristic
298C4C2×C11×C4⋊Q811yescharacteristic
299C2C11×#198818yesdirect product factor
300C2C2×C11×#39111yescharacteristic
301C2C22×C11×#10211yescharacteristic
302C2C2×C11×#41911yescharacteristic
303C2C2×C11×#47412yes—
304C2C2×C11×#47512yes—
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
4. C11×#1988C2direct (N × H)
10. C2×C11×C4⋊Q8C4semidirect
37. C11×C4⋊Q8C2×C4semidirect
45. C2×C11×C4⋊C4Q8semidirect
56. C2×#1988C11direct (N × H)
92. C11×C4⋊C4C2×Q8semidirect
100. #1988C2×C11direct (N × H)
138. C2×C4⋊Q8C4×C11semidirect
183. C4⋊Q8C2×C4×C11semidirect
191. C2×C4⋊C4Q8×C11semidirect
202. C2×C11#1988direct (N × H)
243. C4⋊C4C2×Q8×C11semidirect
248. C11C2×#1988direct (N × H)
299. C2C11×#1988direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C22×C11×C4⋊C82
C2×C4×C11×C4⋊C42
C11×#19882
C2×C11×#3402
C2×#198811