Finite Group Databasebeta

← C11×#23823 #14601016

Subgroups — C11×#23823 #14601016

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×C4⋊Q8C211yesmaximal, characteristic
2C4×C11×C4⋊Q8C211yesmaximal, characteristic
3C11×#2099C212yesmaximal
4C11×#2072C212yesmaximal
5C11×#2043C212yesmaximal
6C11×#2024C212yesmaximal
7C11×#1763C214yesmaximal
8C11×#1745C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11—21no—
12C2×C4×Q8×C11C2212yes—
13C2×C11×#103C2214yes—
14C2×C11×#103C2214yes—
15C2×C11×#97C2212yes—
16C11×#391—21no—
17C11×#391C2212yes—
18C11×#389—21no—
19C11×#389—21no—
20C11×#389—21no—
21C11×#389C2212yes—
22C11×#384C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C4×C11×C4⋊C4—21no—
25C4×C11×C4⋊C4—21no—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2212yes—
28C43×C11C2211yescharacteristic
29C11×#340C2214yes—
30C11×#340C2214yes—
31C11×#336C2212yes—
32C11×#336C2212yes—
33C22×Q8×C11—21no—
34C22×Q8×C11C2312yes—
35C22×C8×C11C2314yes—
36C11×C4⋊Q8—24no—
37C11×C4⋊Q8—24no—
38C4×Q8×C11—28no—
39C4×Q8×C11—44no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2312yes—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11D411yescharacteristic
55C2×C42×C11D411yescharacteristic
56C2×C42×C11D411yescharacteristic
57C2×C42×C11D411yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C11×#103—28no—
62C11×#103—28no—
63C11×#97—24no—
64C11×#95—22no—
65C11×#95—22no—
66C11×#95—22no—
67C11×#95—22no—
68#23823C1111yesmaximal, characteristic, direct product factor, Sylow
69C2×Q8×C11—24no—
70C2×Q8×C11—22no—
71C2×Q8×C11—24no—
72C2×Q8×C11—24no—
73C2×Q8×C11—42no—
74C2×Q8×C11—42no—
75C2×Q8×C11#4114yes—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2411yescharacteristic
87C2×C8×C11—24no—
88C2×C8×C11—24no—
89C2×C8×C11—24no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—44no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—44no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4#4114yes—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11—44no—
110C42×C11—44no—
111C42×C11#4114yes—
112C4×C4⋊Q8C2×C1111yescharacteristic
113C4×C4⋊Q8C2×C1111yescharacteristic
114#2099C2×C1112yes—
115#2072C2×C1112yes—
116#2043C2×C1112yes—
117#2024C2×C1112yes—
118#1763C2×C1114yes—
119#1745C2×C1111yescharacteristic
120C23×C11C22×D411yescharacteristic
121Q8×C11—28no—
122Q8×C11—48no—
123Q8×C11—44no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11#12412yes—
149C2×C4×C11#12412yes—
150C2×C4×C11AGL(1,ℤ/8)12yes—
151C2×C4×C11#13712yes—
152C2×C4×C11#13712yes—
153C2×C4×C11#13712yes—
154C2×C4×C11C2×#4112yes—
155C2×C4×C11C2×#4112yes—
156C2×C4×C11C2×#4112yes—
157C8×C11—44no—
158C2×C4⋊Q8C22×C1111yescharacteristic
159C2×C4⋊Q8C22×C1111yescharacteristic
160C2×C4×Q8—21no—
161C2×C4×Q8C22×C1112yes—
162C2×#103C22×C1114yes—
163C2×#103C22×C1114yes—
164C2×#97C22×C1112yes—
165#391—21no—
166#391C22×C1112yes—
167#389—21no—
168#389—21no—
169#389—21no—
170#389C22×C1112yes—
171#384C22×C1111yescharacteristic
172#384C22×C1111yescharacteristic
173C4×C4⋊C4—21no—
174C4×C4⋊C4—21no—
175C4×C4⋊C4—21no—
176C4×C4⋊C4C22×C1112yes—
177C43C22×C1111yescharacteristic
178#340C22×C1114yes—
179#340C22×C1114yes—
180#336C22×C1112yes—
181#336C22×C1112yes—
182C22×C11#52511yescharacteristic
183C22×C11#52511yescharacteristic
184C22×C11C2×#12411yescharacteristic
185C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
186C22×C11C2×#13711yescharacteristic
187C22×C11C2×#13711yescharacteristic
188C22×C11C2×#13711yescharacteristic
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—22no—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—44no—
196C4×C11—44no—
197C4×C11—82no—
198C4×C11—82no—
199C4×C11#52914yes—
200C22×Q8—21no—
201C22×Q8C23×C1112yes—
202C22×C8C23×C1114yes—
203C4⋊Q8—24no—
204C4⋊Q8—24no—
205C4×Q8—28no—
206C4×Q8—44no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C23×C1112yes—
217C2×C4⋊C4C23×C1112yes—
218C2×C4⋊C4C23×C1112yes—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42D4×C1111yescharacteristic
222C2×C42D4×C1111yescharacteristic
223C2×C42D4×C1111yescharacteristic
224C2×C42D4×C1111yescharacteristic
225C2×C42C23×C1111yescharacteristic
226C2×C42C23×C1111yescharacteristic
227C2×C42C23×C1111yescharacteristic
228#103—28no—
229#103—28no—
230#97—24no—
231#95—22no—
232#95—22no—
233#95—22no—
234#95—22no—
235C2×C11#239811yescharacteristic
236C2×C11#311011yescharacteristic
237C2×C11#311211yescharacteristic
238C2×C11#311311yescharacteristic
239C2×C11#311311yescharacteristic
240C2×C11#313911yescharacteristic
241C2×C11#314111yescharacteristic
242C2×Q8—24no—
243C2×Q8—22no—
244C2×Q8—24no—
245C2×Q8—24no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8C11×#4114yes—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4C2×D4×C1111yescharacteristic
254C22×C4C2×D4×C1111yescharacteristic
255C22×C4C2×D4×C1111yescharacteristic
256C22×C4C2×D4×C1111yescharacteristic
257C22×C4C2×D4×C1111yescharacteristic
258C22×C4C2×D4×C1111yescharacteristic
259C22×C4C24×C1111yescharacteristic
260C2×C8—24no—
261C2×C8—24no—
262C2×C8—24no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—22no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—42no—
270C4⋊C4—44no—
271C4⋊C4—44no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4C11×#4114yes—
276C42—22no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—22no—
282C42—44no—
283C42—44no—
284C42C11×#4114yes—
285C11#2382311yescharacteristic, direct product factor, Sylow
286C23C22×D4×C1111yescharacteristic
287Q8—28no—
288Q8—48no—
289Q8—44no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4C11×#12412yes—
315C2×C4C11×#12412yes—
316C2×C4C11×AGL(1,ℤ/8)12yes—
317C2×C4C11×#13712yes—
318C2×C4C11×#13712yes—
319C2×C4C11×#13712yes—
320C2×C4C2×C11×#4112yes—
321C2×C4C2×C11×#4112yes—
322C2×C4C2×C11×#4112yes—
323C8—44no—
324C22C11×#52511yescharacteristic
325C22C11×#52511yescharacteristic
326C22C2×C11×#12411yescharacteristic
327C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
328C22C2×C11×#13711yescharacteristic
329C22C2×C11×#13711yescharacteristic
330C22C2×C11×#13711yescharacteristic
331C4—22no—
332C4—22no—
333C4—22no—
334C4—22no—
335C4—22no—
336C4—22no—
337C4—44no—
338C4—44no—
339C4—82no—
340C4—82no—
341C4C11×#52914yes—
342C2C11×#239811yescharacteristic
343C2C11×#311011yescharacteristic
344C2C11×#311211yescharacteristic
345C2C11×#311311yescharacteristic
346C2C11×#311311yescharacteristic
347C2C11×#313911yescharacteristic
348C2C11×#314111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
68. #23823C11direct (N × H)
285. C11#23823direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×C4⋊Q82
C11×#20992
C11×#20722
C11×#20432
C11×#20242
C11×#17632
C11×#17452
#2382311