Finite Group Databasebeta

← C11×#19058 #14596251

Subgroups — C11×#19058 #14596251

Order 2816.

840 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic
2C11×#3237C212yesmaximal, complemented
3C11×#3135C211yesmaximal, characteristic
4C11×#1664C218yesmaximal, complemented
5C11×#1536C211yesmaximal, characteristic
6C11×#1531C212yesmaximal, complemented
7C11×#563C2214yes—
8C11×#559—21no—
9Q82×C11—21no—
10C11×#556—22no—
11D4×Q8×C11—22no—
12C11×#542—24no—
13C11×#536—22no—
14C11×#533C2211yescharacteristic
15C11×#533C2212yes—
16C11×#532C2211yescharacteristic
17C11×#501C2214yes—
18C11×#491—21no—
19C11×#491C2214yes—
20C11×#490—21no—
21C11×#489C2214yes—
22C11×#485—24no—
23C11×#477—22no—
24C11×#475—22no—
25C11×#432C2212yes—
26C11×#416—22no—
27C2×C11×#97C2211yescharacteristic
28C11×#330C2218yes—
29C11×#329C2214yes—
30C2×C11×#41D412yes—
31C22×Q8×C11—22no—
32C22×C8×C11—21no—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8—24no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D412yes—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8C2312yes—
39C11×#127D411yescharacteristic
40C11×#126—28no—
41C11×#125—21no—
42C11×#125C2314yes—
43C11×#124—24no—
44C11×#124—24no—
45C11×#124C2312yes—
46C11×#123—24no—
47C11×#123—24no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—28no—
52C11×C22⋊Q8—22no—
53C11×#121—22no—
54C4×Q8×C11—24no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C11×#117—22no—
61C11×#117—21no—
62C11×#117D414yes—
63C2×C42×C11C2311yescharacteristic
64C11×#107—24no—
65C11×#106—24no—
66C11×C4⋊C8—22no—
67C11×#103—24no—
68C11×#103—24no—
69C11×#103—24no—
70C11×#102—24no—
71C11×C22⋊C8—22no—
72C11×#97—21no—
73C11×#97C2312yes—
74C11×#97C2314yes—
75#19058C1111yesmaximal, characteristic, direct product factor, Sylow
76C11×#41—44no—
77C2×Q8×C11—24no—
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11—22no—
81C2×Q8×C11—84no—
82C2×Q8×C11C2×D412yes—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11C2×D412yes—
86C22×C4×C11—24no—
87C22×C4×C11—22no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D412yes—
90C2×C8×C11—22no—
91C2×C8×C11—24no—
92C2×C8×C11—42no—
93C11×C4⋊C4—28no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4C2×D414yes—
103C11×C4⋊C4C2×D414yes—
104C11×C22⋊C4—24no—
105C11×C22⋊C4—28no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—41no—
109C42×C11—24no—
110C42×C11—24no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D412yes—
114C42×C11C2411yescharacteristic
115#3550C2×C1111yescharacteristic
116#3237C2×C1112yescomplemented
117#3135C2×C1111yescharacteristic
118#1664C2×C1118yescomplemented
119#1536C2×C1111yescharacteristic
120#1531C2×C1112yescomplemented
121C23×C11—22no—
122C23×C11#12011yescharacteristic
123Q8×C11—42no—
124Q8×C11—44no—
125Q8×C11—44no—
126Q8×C11—44no—
127Q8×C11—84no—
128D4×C11—42no—
129D4×C11—44no—
130D4×C11—82no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—22no—
134C2×C4×C11—24no—
135C2×C4×C11—42no—
136C2×C4×C11—44no—
137C2×C4×C11—42no—
138C2×C4×C11—84no—
139C2×C4×C11#12012yes—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11C22×D412yes—
142C2×C4×C11C22×D411yescharacteristic
143C8×C11—44no—
144C8×C11—42no—
145#563C22×C1114yes—
146#559—21no—
147Q82—21no—
148#556—22no—
149D4×Q8—22no—
150#542—24no—
151#536—22no—
152#533C22×C1111yescharacteristic
153#533C22×C1112yes—
154#532C22×C1111yescharacteristic
155#501C22×C1114yes—
156#491—21no—
157#491C22×C1114yes—
158#490—21no—
159#489C22×C1114yes—
160#485—24no—
161#477—22no—
162#475—22no—
163#432C22×C1112yes—
164#416—22no—
165C2×#97C22×C1111yescharacteristic
166#330C22×C1118yes—
167#329C22×C1114yes—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—42no—
171C22×C11—44no—
172C22×C11C2×#12011yescharacteristic
173C4×C11—21no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—42no—
177C4×C11—44no—
178C4×C11—44no—
179C4×C11—82no—
180C4×C11#45512yes—
181C2×#41D4×C1112yes—
182C22×Q8—22no—
183C22×C8—21no—
184C4⋊Q8—24no—
185C4⋊Q8—24no—
186C4⋊Q8D4×C1111yescharacteristic
187C4⋊Q8D4×C1112yes—
188C4⋊Q8D4×C1112yes—
189C4⋊Q8C23×C1112yes—
190#127D4×C1111yescharacteristic
191#126—28no—
192#125—21no—
193#125C23×C1114yes—
194#124—24no—
195#124—24no—
196#124C23×C1112yes—
197#123—24no—
198#123—24no—
199C22⋊Q8—24no—
200C22⋊Q8—22no—
201C22⋊Q8—22no—
202C22⋊Q8—28no—
203C22⋊Q8—22no—
204#121—22no—
205C4×Q8—24no—
206C4×Q8—22no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×D4—24no—
210C4×D4—22no—
211#117—22no—
212#117—21no—
213#117D4×C1114yes—
214C2×C42C23×C1111yescharacteristic
215#107—24no—
216#106—24no—
217C4⋊C8—22no—
218#103—24no—
219#103—24no—
220#103—24no—
221#102—24no—
222C22⋊C8—22no—
223#97—21no—
224#97C23×C1114yes—
225#97C23×C1112yes—
226C2×C11—41no—
227C2×C11—82no—
228C2×C11C2×#45511yescharacteristic
229C2×C11#302012yes—
230#41—44no—
231C2×Q8—24no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—84no—
236C2×Q8C2×D4×C1112yes—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4C2×D4×C1112yes—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4C2×D4×C1111yescharacteristic
243C22×C4C2×D4×C1112yes—
244C2×C8—22no—
245C2×C8—24no—
246C2×C8—42no—
247C4⋊C4—28no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—42no—
256C4⋊C4C2×D4×C1114yes—
257C4⋊C4C2×D4×C1114yes—
258C22⋊C4—24no—
259C22⋊C4—28no—
260C22⋊C4—24no—
261C22⋊C4—24no—
262C22⋊C4—41no—
263C42—24no—
264C42—24no—
265C42—41no—
266C42C2×D4×C1111yescharacteristic
267C42C2×D4×C1112yes—
268C42C24×C1111yescharacteristic
269C11#1905811yescharacteristic, direct product factor, Sylow
270C23—22no—
271C23C11×#12011yescharacteristic
272Q8—42no—
273Q8—44no—
274Q8—44no—
275Q8—44no—
276Q8—84no—
277D4—42no—
278D4—44no—
279D4—82no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—84no—
288C2×C4C11×#12012yes—
289C2×C4C11×#12011yescharacteristic
290C2×C4C22×D4×C1112yes—
291C2×C4C22×D4×C1111yescharacteristic
292C8—42no—
293C8—44no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—44no—
298C22C2×C11×#12011yescharacteristic
299C4—21no—
300C4—22no—
301C4—22no—
302C4—42no—
303C4—44no—
304C4—44no—
305C4—82no—
306C4C11×#45512yes—
307C2—41no—
308C2—82no—
309C2C2×C11×#45511yescharacteristic
310C2C11×#302012yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3237C2semidirect
4. C11×#1664C2semidirect
6. C11×#1531C2semidirect
75. #19058C11direct (N × H)
116. #3237C2×C11semidirect
118. #1664C2×C11semidirect
120. #1531C2×C11semidirect
269. C11#19058direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35502
C11×#32372
C11×#31352
C11×#16642
C11×#15362
C11×#15312
#1905811