Finite Group Databasebeta

← C2×C11×#2629 #14611805

Subgroups — C2×C11×#2629 #14611805

Order 2816.

2614 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic, complemented
2C22×C11×#117C211yesmaximal, characteristic
3C11×#2629C2116yesmaximal, direct product factor
4C2×C11×#398C214yesmaximal, complemented
5C2×C11×#396C214yesmaximal
6C2×C11×#389C212yesmaximal, complemented
7C2×C11×#384C211yesmaximal, characteristic, complemented
8C2×C11×#380C212yesmaximal
9C24×C4×C11C2211yescharacteristic
10C2×C11×#125—28no—
11C2×C11×#125C2218yescomplemented
12C2×C11×#117—28no—
13C2×C11×#117C2218yes—
14C22×C11×C4⋊C4C2214yes—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C4⋊C4C2214yes—
19C22×C11×C4⋊C4C2214yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2214yes—
22C22×C42×C11C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C11×#398C22132yescomplemented
25C11×#396C22132yes—
26C11×#389C22116yescomplemented
27C11×#384C2218yescomplemented
28C11×#380C22116yes—
29C2×C11×#95C2214yes—
30C2×C11×#95C2214yes—
31C25×C11C2311yescharacteristic
32C23×C4×C11—24no—
33C23×C4×C11—24no—
34C23×C4×C11Q818yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2314yes—
37C23×C4×C11C2314yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2314yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C11×#125—232no—
43C11×#117—232no—
44C2×C11×C4⋊C4—28no—
45C2×C11×C4⋊C4—216no—
46C2×C11×C4⋊C4—28no—
47C2×C11×C4⋊C4—28no—
48C2×C11×C4⋊C4—48no—
49C2×C11×C4⋊C4—48no—
50C2×C11×C4⋊C4C2318yes—
51C2×C11×C4⋊C4C2318yes—
52C2×C11×C4⋊C4C2318yes—
53C2×C11×C4⋊C4C23116yes—
54C2×C11×C4⋊C4C23116yes—
55C2×C11×C4⋊C4C23116yes—
56C2×C11×C22⋊C4—28no—
57C2×C11×C22⋊C4—48no—
58C2×C11×C22⋊C4C2318yes—
59C2×C11×C22⋊C4C23116yes—
60C2×C42×C11—24no—
61C2×C42×C11D418yes—
62C2×C42×C11C2314yes—
63C2×C42×C11C2314yes—
64C11×#95C23116yes—
65C11×#95C23116yes—
66C2×#2629C1111yesmaximal, characteristic, direct product factor, Sylow
67C24×C11—22no—
68C24×C11—22no—
69C24×C11—24no—
70C24×C11—24no—
71C24×C11C2×Q814yes—
72C24×C11C2412yes—
73C24×C11C2411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—232no—
79C22×C4×C11—28no—
80C22×C4×C11—28no—
81C22×C4×C11—24no—
82C22×C4×C11—28no—
83C22×C4×C11—28no—
84C22×C4×C11—28no—
85C22×C4×C11—28no—
86C22×C4×C11—24no—
87C22×C4×C11—28no—
88C22×C4×C11—24no—
89C22×C4×C11—28no—
90C22×C4×C11C2×D418yes—
91C22×C4×C11C2×D414yes—
92C22×C4×C11C2×Q814yes—
93C22×C4×C11C2×Q8116yes—
94C22×C4×C11C2×Q814yes—
95C22×C4×C11#4114yes—
96C22×C4×C11C2414yes—
97C22×C4×C11C2418yes—
98C22×C4×C11C2418yes—
99C22×C4×C11C2414yes—
100C22×C4×C11C2412yes—
101C22×C4×C11C2412yes—
102C11×C4⋊C4—216no—
103C11×C4⋊C4—232no—
104C11×C4⋊C4—216no—
105C11×C4⋊C4—216no—
106C11×C4⋊C4—416no—
107C11×C4⋊C4—416no—
108C11×C22⋊C4—216no—
109C11×C22⋊C4—416no—
110C42×C11—28no—
111C42×C11C2×D4116yes—
112C22×#125C2×C1111yescharacteristic, complemented
113C22×#117C2×C1111yescharacteristic
114#2629C2×C11116yesdirect product factor
115C2×#398C2×C1114yescomplemented
116C2×#396C2×C1114yes—
117C2×#389C2×C1112yescomplemented
118C2×#384C2×C1111yescharacteristic, complemented
119C2×#380C2×C1112yes—
120C23×C11—28no—
121C23×C11—216no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—24no—
125C23×C11—24no—
126C23×C11—48no—
127C23×C11—44no—
128C23×C11—44no—
129C23×C11C22×D412yes—
130C23×C11C22×Q814yes—
131C23×C11C22×Q812yes—
132C23×C11C2×#4112yes—
133C23×C11H(5,𝔽2)14yes—
134C23×C112−1+414yes—
135C23×C11C2511yescharacteristic
136C2×C4×C11—28no—
137C2×C4×C11—216no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—232no—
143C2×C4×C11—24no—
144C2×C4×C11—28no—
145C2×C4×C11—28no—
146C2×C4×C11—28no—
147C2×C4×C11—28no—
148C2×C4×C11—24no—
149C2×C4×C11—28no—
150C2×C4×C11—24no—
151C2×C4×C11—28no—
152C2×C4×C11—48no—
153C2×C4×C11—416no—
154C2×C4×C11—416no—
155C2×C4×C11C22⋊Q8116yes—
156C2×C4×C11C22×D418yes—
157C2×C4×C11C22×D414yes—
158C2×C4×C11C22×Q814yes—
159C2×C4×C11C22×Q814yes—
160C2×C4×C11C2×#4114yes—
161C24×C4C22×C1111yescharacteristic
162C2×#125—28no—
163C2×#125C22×C1118yescomplemented
164C2×#117—28no—
165C2×#117C22×C1118yes—
166C22×C4⋊C4C22×C1114yes—
167C22×C4⋊C4C22×C1112yes—
168C22×C4⋊C4C22×C1112yes—
169C22×C4⋊C4C22×C1112yes—
170C22×C4⋊C4C22×C1114yes—
171C22×C4⋊C4C22×C1114yes—
172C22×C22⋊C4C22×C1112yes—
173C22×C22⋊C4C22×C1114yes—
174C22×C42C22×C1111yescharacteristic
175C22×C42C22×C1111yescharacteristic
176#398C22×C11132yescomplemented
177#396C22×C11132yes—
178#389C22×C11116yescomplemented
179#384C22×C1118yescomplemented
180#380C22×C11116yes—
181C2×#95C22×C1114yes—
182C2×#95C22×C1114yes—
183C22×C11—24no—
184C22×C11—28no—
185C22×C11—416no—
186C22×C11—44no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11C2×C22⋊Q814yes—
190C22×C11#53718yes—
191C22×C11#54014yes—
192C22×C11#54114yes—
193C22×C11#54418yes—
194C22×C11C23×D411yescharacteristic
195C22×C11C23×Q811yescharacteristic
196C22×C11C22×#4111yescharacteristic
197C22×C11C2×H(5,𝔽2)12yes—
198C22×C11C2×2−1+412yes—
199C4×C11—24no—
200C4×C11—28no—
201C4×C11—44no—
202C4×C11—48no—
203C4×C11—48no—
204C4×C11C2×C22⋊Q818yes—
205C25C23×C1111yescharacteristic
206C23×C4—24no—
207C23×C4—24no—
208C23×C4Q8×C1118yes—
209C23×C4C23×C1114yes—
210C23×C4C23×C1114yes—
211C23×C4C23×C1112yes—
212C23×C4C23×C1112yes—
213C23×C4C23×C1111yescharacteristic
214C23×C4C23×C1114yes—
215C23×C4C23×C1111yescharacteristic
216#125—232no—
217#117—232no—
218C2×C4⋊C4—28no—
219C2×C4⋊C4—216no—
220C2×C4⋊C4—28no—
221C2×C4⋊C4—28no—
222C2×C4⋊C4—48no—
223C2×C4⋊C4—48no—
224C2×C4⋊C4C23×C1118yes—
225C2×C4⋊C4C23×C1118yes—
226C2×C4⋊C4C23×C11116yes—
227C2×C4⋊C4C23×C1118yes—
228C2×C4⋊C4C23×C11116yes—
229C2×C4⋊C4C23×C11116yes—
230C2×C22⋊C4—28no—
231C2×C22⋊C4—48no—
232C2×C22⋊C4C23×C1118yes—
233C2×C22⋊C4C23×C11116yes—
234C2×C42—24no—
235C2×C42D4×C1118yes—
236C2×C42C23×C1114yes—
237C2×C42C23×C1114yes—
238#95C23×C11116yes—
239#95C23×C11116yes—
240C2×C11—44no—
241C2×C11#262918yesdirect product factor
242C2×C11C22×C22⋊Q811yescharacteristic
243C2×C11C2×#53712yes—
244C2×C11C2×#54011yescharacteristic
245C2×C11C2×#54111yescharacteristic
246C2×C11C2×#54412yes—
247C24—22no—
248C24—22no—
249C24—24no—
250C24—24no—
251C24C2×Q8×C1114yes—
252C24C24×C1112yes—
253C24C24×C1111yescharacteristic
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—232no—
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—28no—
264C22×C4—28no—
265C22×C4—28no—
266C22×C4—24no—
267C22×C4—28no—
268C22×C4—28no—
269C22×C4—24no—
270C22×C4C2×D4×C1118yes—
271C22×C4C2×D4×C1114yes—
272C22×C4C2×Q8×C1114yes—
273C22×C4C2×Q8×C11116yes—
274C22×C4C2×Q8×C1114yes—
275C22×C4C11×#4114yes—
276C22×C4C24×C1114yes—
277C22×C4C24×C1118yes—
278C22×C4C24×C1118yes—
279C22×C4C24×C1114yes—
280C22×C4C24×C1112yes—
281C22×C4C24×C1112yes—
282C4⋊C4—216no—
283C4⋊C4—232no—
284C4⋊C4—216no—
285C4⋊C4—216no—
286C4⋊C4—416no—
287C4⋊C4—416no—
288C22⋊C4—216no—
289C22⋊C4—416no—
290C42—28no—
291C42C2×D4×C11116yes—
292C11C2×#262911yescharacteristic, direct product factor, Sylow
293C23—28no—
294C23—216no—
295C23—22no—
296C23—22no—
297C23—24no—
298C23—24no—
299C23—48no—
300C23—44no—
301C23—44no—
302C23C22×D4×C1112yes—
303C23C22×Q8×C1114yes—
304C23C22×Q8×C1112yes—
305C23C2×C11×#4112yes—
306C23C11×H(5,𝔽2)14yes—
307C23C11×2−1+414yes—
308C23C25×C1111yescharacteristic
309C2×C4—28no—
310C2×C4—216no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—232no—
316C2×C4—24no—
317C2×C4—28no—
318C2×C4—28no—
319C2×C4—28no—
320C2×C4—28no—
321C2×C4—24no—
322C2×C4—28no—
323C2×C4—24no—
324C2×C4—28no—
325C2×C4—48no—
326C2×C4—416no—
327C2×C4—416no—
328C2×C4C11×C22⋊Q8116yes—
329C2×C4C22×D4×C1118yes—
330C2×C4C22×D4×C1114yes—
331C2×C4C22×Q8×C1114yes—
332C2×C4C22×Q8×C1114yes—
333C2×C4C2×C11×#4114yes—
334C22—24no—
335C22—28no—
336C22—44no—
337C22—42no—
338C22—42no—
339C22—416no—
340C22C2×C11×C22⋊Q814yes—
341C22C11×#53718yes—
342C22C11×#54014yes—
343C22C11×#54114yes—
344C22C11×#54418yes—
345C22C23×D4×C1111yescharacteristic
346C22C23×Q8×C1111yescharacteristic
347C22C22×C11×#4111yescharacteristic
348C22C2×C11×H(5,𝔽2)12yes—
349C22C2×C11×2−1+412yes—
350C4—24no—
351C4—28no—
352C4—44no—
353C4—48no—
354C4—48no—
355C4C2×C11×C22⋊Q818yes—
356C2—44no—
357C2C11×#262918yesdirect product factor
358C2C22×C11×C22⋊Q811yescharacteristic
359C2C2×C11×#53712yes—
360C2C2×C11×#54011yescharacteristic
361C2C2×C11×#54111yescharacteristic
362C2C2×C11×#54412yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#125C2semidirect
3. C11×#2629C2direct (N × H)
4. C2×C11×#398C2semidirect
6. C2×C11×#389C2semidirect
7. C2×C11×#384C2semidirect
11. C2×C11×#125C22semidirect
24. C11×#398C22semidirect
26. C11×#389C22semidirect
27. C11×#384C22semidirect
66. C2×#2629C11direct (N × H)
112. C22×#125C2×C11semidirect
114. #2629C2×C11direct (N × H)
115. C2×#398C2×C11semidirect
117. C2×#389C2×C11semidirect
118. C2×#384C2×C11semidirect
163. C2×#125C22×C11semidirect
176. #398C22×C11semidirect
178. #389C22×C11semidirect
179. #384C22×C11semidirect
241. C2×C11#2629direct (N × H)
292. C11C2×#2629direct (N × H)
357. C2C11×#2629direct (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×C11×#1172
C11×#26292
C2×C11×#3982
C2×C11×#3962
C2×C11×#3892
C2×C11×#3842
C2×C11×#3802
C2×#262911