Finite Group Databasebeta

← C2×C11×#2032 #14600666

Subgroups — C2×C11×#2032 #14600666

Order 2816.

1434 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×#543C211yesmaximal, characteristic, complemented
2C22×C11×#99C213yesmaximal
3C11×#2032C218yesmaximal, direct product factor
4C2×C11×#342C213yesmaximal, complemented
5C23×D4×C11C2211yescharacteristic
6C11×#543—26no—
7C11×#543C2214yescomplemented
8C2×C11×C22⋊Q8—26no—
9C22×C11×C22⋊C4C2213yes—
10C22×C11×C22⋊C4C2213yes—
11C2×C11×#99—26no—
12C2×C11×#99—26no—
13C2×C11×#99C22112yes—
14C11×#342C22112yescomplemented
15C25×C11Q811yescharacteristic, complemented
16C25×C11C2311yescharacteristic
17C22×Q8×C11—22no—
18C22×D4×C11—23no—
19C22×D4×C11—23no—
20C22×D4×C11—23no—
21C22×D4×C11—23no—
22C22×D4×C11Q812yescomplemented
23C22×D4×C11C2312yes—
24C23×C4×C11—23no—
25C23×C4×C11—23no—
26C23×C4×C11Q811yescharacteristic, complemented
27C11×C22⋊Q8—224no—
28C11×C22⋊Q8—224no—
29C2×C11×C4⋊C4—26no—
30C2×C11×C22⋊C4—23no—
31C2×C11×C22⋊C4—23no—
32C2×C11×C22⋊C4—23no—
33C2×C11×C22⋊C4—23no—
34C2×C11×C22⋊C4—23no—
35C2×C11×C22⋊C4—23no—
36C2×C11×C22⋊C4—23no—
37C2×C11×C22⋊C4—23no—
38C2×C11×C22⋊C4D416yes—
39C2×C11×C22⋊C4D416yes—
40C2×C11×C22⋊C4C2316yes—
41C2×C11×C22⋊C4C2316yes—
42C11×#99—224no—
43C2×#2032C1111yesmaximal, characteristic, direct product factor, Sylow
44C24×C11—23no—
45C24×C11—23no—
46C24×C11—82no—
47C24×C11—82no—
48C24×C11C2×D413yes—
49C24×C11C2×D413yes—
50C24×C11C2×Q811yescharacteristic
51C24×C11C2×Q811yescharacteristic
52C24×C11C2×Q812yescomplemented
53C24×C11#4113yes—
54C24×C11#4113yes—
55C24×C11C2411yescharacteristic
56C2×Q8×C11—28no—
57C2×Q8×C11—84no—
58C2×D4×C11—26no—
59C2×D4×C11—26no—
60C2×D4×C11—26no—
61C2×D4×C11—26no—
62C2×D4×C11—43no—
63C2×D4×C11—41no—
64C2×D4×C11—43no—
65C2×D4×C11—43no—
66C2×D4×C11—43no—
67C2×D4×C11—43no—
68C22×C4×C11—26no—
69C22×C4×C11—23no—
70C22×C4×C11—23no—
71C22×C4×C11—26no—
72C22×C4×C11—26no—
73C22×C4×C11—26no—
74C22×C4×C11—43no—
75C22×C4×C11—43no—
76C22×C4×C11—86no—
77C22×C4×C11—86no—
78C22×C4×C11C2×Q812yescomplemented
79C11×C4⋊C4—224no—
80C11×C22⋊C4—26no—
81C11×C22⋊C4—26no—
82C11×C22⋊C4—26no—
83C11×C22⋊C4—26no—
84C11×C22⋊C4—26no—
85C11×C22⋊C4—43no—
86C11×C22⋊C4—43no—
87C11×C22⋊C4C2×D4112yes—
88C2×#543C2×C1111yescharacteristic, complemented
89C22×#99C2×C1113yes—
90#2032C2×C1118yesdirect product factor
91C2×#342C2×C1113yescomplemented
92C23×C11—26no—
93C23×C11—46no—
94C23×C11—46no—
95C23×C11—42no—
96C23×C11—43no—
97C23×C11—41no—
98C23×C11—86no—
99C23×C11—83no—
100C23×C11—81no—
101C23×C11—83no—
102C23×C11—81no—
103C23×C11—82no—
104C23×C11—86no—
105C23×C11#12011yescharacteristic
106C23×C11#12013yes—
107C23×C11C22⋊Q813yes—
108C23×C11C22⋊Q813yes—
109C23×C11C22⋊Q813yes—
110C23×C11C22⋊Q813yes—
111C23×C11#12413yes—
112C23×C11#12413yes—
113C23×C11#12413yes—
114C23×C11#12413yes—
115C23×C11C22×D413yes—
116C23×C11C22×Q811yescharacteristic
117C23×C11C2×#4113yes—
118Q8×C11—88no—
119D4×C11—42no—
120D4×C11—46no—
121D4×C11—42no—
122D4×C11—46no—
123C2×C4×C11—212no—
124C2×C4×C11—26no—
125C2×C4×C11—412no—
126C2×C4×C11—43no—
127C2×C4×C11—41no—
128C2×C4×C11—46no—
129C2×C4×C11—86no—
130C2×C4×C11—86no—
131C2×C4×C11—86no—
132C2×C4×C11—86no—
133C2×C4×C11—86no—
134C23×D4C22×C1111yescharacteristic
135#543—26no—
136#543C22×C1114yescomplemented
137C2×C22⋊Q8—26no—
138C22×C22⋊C4C22×C1113yes—
139C22×C22⋊C4C22×C1113yes—
140C2×#99—26no—
141C2×#99—26no—
142C2×#99C22×C11112yes—
143#342C22×C11112yescomplemented
144C22×C11—22no—
145C22×C11—26no—
146C22×C11—26no—
147C22×C11—43no—
148C22×C11—43no—
149C22×C11—43no—
150C22×C11—43no—
151C22×C11—43no—
152C22×C11—41no—
153C22×C11—43no—
154C22×C11—43no—
155C22×C11—43no—
156C22×C11—43no—
157C22×C11—42no—
158C22×C11—86no—
159C22×C11—86no—
160C22×C11—82no—
161C22×C11#39313yes—
162C22×C11#39311yescharacteristic
163C22×C11#39313yes—
164C22×C11#39311yescharacteristic
165C22×C11C2×#12011yescharacteristic
166C22×C11C2×C22⋊Q813yes—
167C22×C11C2×#12413yes—
168C4×C11—412no—
169C4×C11—42no—
170C4×C11—86no—
171C25Q8×C1111yescharacteristic, complemented
172C25C23×C1111yescharacteristic
173C22×Q8—22no—
174C22×D4—23no—
175C22×D4—23no—
176C22×D4—23no—
177C22×D4—23no—
178C22×D4Q8×C1112yescomplemented
179C22×D4C23×C1112yes—
180C23×C4—23no—
181C23×C4—23no—
182C23×C4Q8×C1111yescharacteristic, complemented
183C22⋊Q8—224no—
184C22⋊Q8—224no—
185C2×C4⋊C4—26no—
186C2×C22⋊C4—23no—
187C2×C22⋊C4—23no—
188C2×C22⋊C4—23no—
189C2×C22⋊C4—23no—
190C2×C22⋊C4—23no—
191C2×C22⋊C4—23no—
192C2×C22⋊C4—23no—
193C2×C22⋊C4—23no—
194C2×C22⋊C4D4×C1116yes—
195C2×C22⋊C4D4×C1116yes—
196C2×C22⋊C4C23×C1116yes—
197C2×C22⋊C4C23×C1116yes—
198#99—224no—
199C2×C11—21no—
200C2×C11—23no—
201C2×C11—23no—
202C2×C11—23no—
203C2×C11—21no—
204C2×C11—23no—
205C2×C11—82no—
206C2×C11#203212yesdirect product factor
207C2×C11C2×#39311yescharacteristic
208C24—23no—
209C24—23no—
210C24—82no—
211C24—82no—
212C24C2×D4×C1113yes—
213C24C2×D4×C1113yes—
214C24C2×Q8×C1111yescharacteristic
215C24C2×Q8×C1111yescharacteristic
216C24C2×Q8×C1112yescomplemented
217C24C11×#4113yes—
218C24C11×#4113yes—
219C24C24×C1111yescharacteristic
220C2×Q8—28no—
221C2×Q8—84no—
222C2×D4—26no—
223C2×D4—26no—
224C2×D4—26no—
225C2×D4—26no—
226C2×D4—41no—
227C2×D4—43no—
228C2×D4—43no—
229C2×D4—43no—
230C2×D4—43no—
231C2×D4—43no—
232C22×C4—26no—
233C22×C4—23no—
234C22×C4—23no—
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—26no—
238C22×C4—43no—
239C22×C4—43no—
240C22×C4—86no—
241C22×C4—86no—
242C22×C4C2×Q8×C1112yescomplemented
243C4⋊C4—224no—
244C22⋊C4—26no—
245C22⋊C4—26no—
246C22⋊C4—26no—
247C22⋊C4—26no—
248C22⋊C4—26no—
249C22⋊C4—43no—
250C22⋊C4—43no—
251C22⋊C4C2×D4×C11112yes—
252C11C2×#203211yescharacteristic, direct product factor, Sylow
253C23—26no—
254C23—46no—
255C23—46no—
256C23—42no—
257C23—43no—
258C23—41no—
259C23—86no—
260C23—83no—
261C23—81no—
262C23—83no—
263C23—81no—
264C23—82no—
265C23—86no—
266C23C11×#12011yescharacteristic
267C23C11×#12013yes—
268C23C11×C22⋊Q813yes—
269C23C11×C22⋊Q813yes—
270C23C11×C22⋊Q813yes—
271C23C11×C22⋊Q813yes—
272C23C11×#12413yes—
273C23C11×#12413yes—
274C23C11×#12413yes—
275C23C11×#12413yes—
276C23C22×D4×C1113yes—
277C23C22×Q8×C1111yescharacteristic
278C23C2×C11×#4113yes—
279Q8—88no—
280D4—42no—
281D4—46no—
282D4—42no—
283D4—46no—
284C2×C4—212no—
285C2×C4—26no—
286C2×C4—412no—
287C2×C4—43no—
288C2×C4—41no—
289C2×C4—46no—
290C2×C4—86no—
291C2×C4—86no—
292C2×C4—86no—
293C2×C4—86no—
294C2×C4—86no—
295C22—22no—
296C22—26no—
297C22—26no—
298C22—43no—
299C22—43no—
300C22—43no—
301C22—43no—
302C22—43no—
303C22—41no—
304C22—43no—
305C22—43no—
306C22—43no—
307C22—43no—
308C22—42no—
309C22—86no—
310C22—86no—
311C22—82no—
312C22C11×#39313yes—
313C22C11×#39311yescharacteristic
314C22C11×#39313yes—
315C22C11×#39311yescharacteristic
316C22C2×C11×#12011yescharacteristic
317C22C2×C11×C22⋊Q813yes—
318C22C2×C11×#12413yes—
319C4—412no—
320C4—42no—
321C4—86no—
322C2—21no—
323C2—23no—
324C2—23no—
325C2—23no—
326C2—21no—
327C2—23no—
328C2—82no—
329C2C11×#203212yesdirect product factor
330C2C2×C11×#39311yescharacteristic
subgroupG/H
center, socleC22×C11#393
commutator, Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#543C2semidirect
3. C11×#2032C2direct (N × H)
4. C2×C11×#342C2semidirect
7. C11×#543C22semidirect
14. C11×#342C22semidirect
15. C25×C11Q8semidirect
22. C22×D4×C11Q8semidirect
26. C23×C4×C11Q8semidirect
43. C2×#2032C11direct (N × H)
52. C24×C11C2×Q8semidirect
78. C22×C4×C11C2×Q8semidirect
88. C2×#543C2×C11semidirect
90. #2032C2×C11direct (N × H)
91. C2×#342C2×C11semidirect
136. #543C22×C11semidirect
143. #342C22×C11semidirect
171. C25Q8×C11semidirect
178. C22×D4Q8×C11semidirect
182. C23×C4Q8×C11semidirect
206. C2×C11#2032direct (N × H)
216. C24C2×Q8×C11semidirect
242. C22×C4C2×Q8×C11semidirect
252. C11C2×#2032direct (N × H)
329. C2C11×#2032direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5432
C22×C11×#992
C11×#20322
C2×C11×#3422
C2×#203211