Finite Group Databasebeta

← C2×C11×#2634 #14611793

Subgroups — C2×C11×#2634 #14611793

Order 2816.

2286 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
1C22×C11×#125C211yesmaximal, characteristic
2C22×C4×Q8×C11C211yesmaximal, characteristic
3C11×#2634C2116yesmaximal, direct product factor
4C2×C11×#400C212yesmaximal
5C2×C11×#400C212yesmaximal
6C2×C11×#398C212yesmaximal
7C2×C11×#395C212yesmaximal
8C2×C11×#387C214yesmaximal
9C2×C11×#383C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C2×C11×#125—28no—
12C2×C11×#125C2218yes—
13C2×C4×Q8×C11—28no—
14C2×C4×Q8×C11C2218yes—
15C22×C11×C4⋊C4C2214yes—
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×C42×C11C2212yes—
23C22×C42×C11C2211yescharacteristic
24C11×#400C22116yes—
25C11×#400C22116yes—
26C11×#398C22116yes—
27C11×#395C22116yes—
28C11×#387C22132yes—
29C11×#383C2218yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2214yes—
32C2×C11×#95C2212yes—
33C2×C11×#95C2214yes—
34C2×C11×#95C2214yes—
35C2×C11×#95C2212yes—
36C22×Q8×C11—24no—
37C22×Q8×C11—28no—
38C22×Q8×C11C2314yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2314yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C11×#125—232no—
48C4×Q8×C11—232no—
49C2×C11×C4⋊C4—28no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—28no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—28no—
55C2×C11×C4⋊C4—216no—
56C2×C11×C4⋊C4C2318yes—
57C2×C11×C4⋊C4C2314yes—
58C2×C11×C4⋊C4C2318yes—
59C2×C11×C4⋊C4C23116yes—
60C2×C11×C4⋊C4C2318yes—
61C2×C11×C4⋊C4C2314yes—
62C2×C11×C4⋊C4C2314yes—
63C2×C42×C11—28no—
64C2×C42×C11D418yes—
65C2×C42×C11C2318yes—
66C2×C42×C11C2314yes—
67C11×#95C2318yes—
68C11×#95C2318yes—
69C11×#95C2318yes—
70C11×#95C23116yes—
71C11×#95C23116yes—
72C11×#95C23116yes—
73C2×#2634C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11C2411yescharacteristic
75C2×Q8×C11—232no—
76C2×Q8×C11—28no—
77C2×Q8×C11—216no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—28no—
87C22×C4×C11—28no—
88C22×C4×C11—28no—
89C22×C4×C11—28no—
90C22×C4×C11—28no—
91C22×C4×C11—28no—
92C22×C4×C11C2×D414yes—
93C22×C4×C11C2×D414yes—
94C22×C4×C11C2×D414yes—
95C22×C4×C11#4118yes—
96C22×C4×C11C2418yes—
97C22×C4×C11C2414yes—
98C22×C4×C11C2414yes—
99C22×C4×C11C2414yes—
100C22×C4×C11C2412yes—
101C22×C4×C11C2412yes—
102C22×C4×C11C2412yes—
103C22×C4×C11C2414yes—
104C11×C4⋊C4—216no—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—216no—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—28no—
109C11×C4⋊C4—216no—
110C11×C4⋊C4—232no—
111C42×C11—216no—
112C42×C11C2×D4116yes—
113C22×#125C2×C1111yescharacteristic
114C22×C4×Q8C2×C1111yescharacteristic
115#2634C2×C11116yesdirect product factor
116C2×#400C2×C1112yes—
117C2×#400C2×C1112yes—
118C2×#398C2×C1112yes—
119C2×#395C2×C1112yes—
120C2×#387C2×C1114yes—
121C2×#383C2×C1111yescharacteristic
122C23×C11C22×D412yes—
123C23×C11C2×#4114yes—
124C23×C112−1+414yes—
125C23×C112−1+414yes—
126C23×C11C2511yescharacteristic
127Q8×C11—232no—
128C2×C4×C11—28no—
129C2×C4×C11—216no—
130C2×C4×C11—28no—
131C2×C4×C11—28no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—28no—
141C2×C4×C11—28no—
142C2×C4×C11—28no—
143C2×C4×C11—28no—
144C2×C4×C11—28no—
145C2×C4×C11—28no—
146C2×C4×C11—48no—
147C2×C4×C11—48no—
148C2×C4×C11—48no—
149C2×C4×C11—416no—
150C2×C4×C11C22×D414yes—
151C2×C4×C11C22×D414yes—
152C2×C4×C11C22×D414yes—
153C2×C4×C11C2×#4118yes—
154C23×Q8C22×C1111yescharacteristic
155C2×#125—28no—
156C2×#125C22×C1118yes—
157C2×C4×Q8—28no—
158C2×C4×Q8C22×C1118yes—
159C22×C4⋊C4C22×C1114yes—
160C22×C4⋊C4C22×C1112yes—
161C22×C4⋊C4C22×C1111yescharacteristic
162C22×C4⋊C4C22×C1112yes—
163C22×C4⋊C4C22×C1111yescharacteristic
164C22×C4⋊C4C22×C1111yescharacteristic
165C22×C4⋊C4C22×C1112yes—
166C22×C42C22×C1112yes—
167C22×C42C22×C1111yescharacteristic
168#400C22×C11116yes—
169#400C22×C11116yes—
170#398C22×C11116yes—
171#395C22×C11116yes—
172#387C22×C11132yes—
173#383C22×C1118yes—
174C2×#95C22×C1112yes—
175C2×#95C22×C1114yes—
176C2×#95C22×C1112yes—
177C2×#95C22×C1114yes—
178C2×#95C22×C1114yes—
179C2×#95C22×C1112yes—
180C22×C11#52514yes—
181C22×C11#53614yes—
182C22×C11#53614yes—
183C22×C11#541116yes—
184C22×C11C23×D411yescharacteristic
185C22×C11C22×#4112yes—
186C22×C11C2×2−1+412yes—
187C22×C11C2×2−1+412yes—
188C4×C11—24no—
189C4×C11—28no—
190C4×C11—24no—
191C4×C11—24no—
192C4×C11—44no—
193C4×C11—44no—
194C4×C11—44no—
195C4×C11—48no—
196C22×Q8—24no—
197C22×Q8—28no—
198C22×Q8C23×C1114yes—
199C23×C4C23×C1112yes—
200C23×C4C23×C1112yes—
201C23×C4C23×C1112yes—
202C23×C4C23×C1114yes—
203C23×C4C23×C1111yescharacteristic
204C23×C4C23×C1111yescharacteristic
205C23×C4C23×C1111yescharacteristic
206C23×C4C23×C1112yes—
207#125—232no—
208C4×Q8—232no—
209C2×C4⋊C4—28no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—28no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—28no—
215C2×C4⋊C4—216no—
216C2×C4⋊C4C23×C1118yes—
217C2×C4⋊C4C23×C1114yes—
218C2×C4⋊C4C23×C1118yes—
219C2×C4⋊C4C23×C1118yes—
220C2×C4⋊C4C23×C1114yes—
221C2×C4⋊C4C23×C1114yes—
222C2×C4⋊C4C23×C11116yes—
223C2×C42—28no—
224C2×C42D4×C1118yes—
225C2×C42C23×C1118yes—
226C2×C42C23×C1114yes—
227#95C23×C1118yes—
228#95C23×C1118yes—
229#95C23×C1118yes—
230#95C23×C11116yes—
231#95C23×C11116yes—
232#95C23×C11116yes—
233C2×C11#263418yesdirect product factor
234C2×C11C2×#52511yescharacteristic
235C2×C11C2×#53611yescharacteristic
236C2×C11C2×#53611yescharacteristic
237C2×C11C2×#54114yes—
238C24C24×C1111yescharacteristic
239C2×Q8—232no—
240C2×Q8—28no—
241C2×Q8—216no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—28no—
251C22×C4—28no—
252C22×C4—28no—
253C22×C4—28no—
254C22×C4—28no—
255C22×C4—28no—
256C22×C4C2×D4×C1114yes—
257C22×C4C2×D4×C1114yes—
258C22×C4C2×D4×C1114yes—
259C22×C4C11×#4118yes—
260C22×C4C24×C1118yes—
261C22×C4C24×C1114yes—
262C22×C4C24×C1114yes—
263C22×C4C24×C1114yes—
264C22×C4C24×C1112yes—
265C22×C4C24×C1112yes—
266C22×C4C24×C1112yes—
267C22×C4C24×C1114yes—
268C4⋊C4—216no—
269C4⋊C4—28no—
270C4⋊C4—216no—
271C4⋊C4—28no—
272C4⋊C4—28no—
273C4⋊C4—216no—
274C4⋊C4—232no—
275C42—216no—
276C42C2×D4×C11116yes—
277C11C2×#263411yescharacteristic, direct product factor, Sylow
278C23C22×D4×C1112yes—
279C23C2×C11×#4114yes—
280C23C11×2−1+414yes—
281C23C11×2−1+414yes—
282C23C25×C1111yescharacteristic
283Q8—232no—
284C2×C4—28no—
285C2×C4—216no—
286C2×C4—28no—
287C2×C4—28no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—28no—
297C2×C4—28no—
298C2×C4—28no—
299C2×C4—28no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—48no—
303C2×C4—48no—
304C2×C4—48no—
305C2×C4—416no—
306C2×C4C22×D4×C1114yes—
307C2×C4C22×D4×C1114yes—
308C2×C4C22×D4×C1114yes—
309C2×C4C2×C11×#4118yes—
310C22C11×#52514yes—
311C22C11×#53614yes—
312C22C11×#53614yes—
313C22C11×#541116yes—
314C22C23×D4×C1111yescharacteristic
315C22C22×C11×#4112yes—
316C22C2×C11×2−1+412yes—
317C22C2×C11×2−1+412yes—
318C4—24no—
319C4—28no—
320C4—24no—
321C4—24no—
322C4—44no—
323C4—44no—
324C4—44no—
325C4—48no—
326C2C11×#263418yesdirect product factor
327C2C2×C11×#52511yescharacteristic
328C2C2×C11×#53611yescharacteristic
329C2C2×C11×#53611yescharacteristic
330C2C2×C11×#54114yes—
subgroupG/H
center, socle, prime radicalC24×C11C24
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2634C2direct (N × H)
73. C2×#2634C11direct (N × H)
115. #2634C2×C11direct (N × H)
233. C2×C11#2634direct (N × H)
277. C11C2×#2634direct (N × H)
326. C2C11×#2634direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C22×C4×Q8×C112
C11×#26342
C2×C11×#4002
C2×C11×#3982
C2×C11×#3952
C2×C11×#3872
C2×C11×#3832
C2×#263411