Finite Group Databasebeta

← C11×#19078 #14596271

Subgroups — C11×#19078 #14596271

Order 2816.

944 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3165C212yesmaximal, complemented
3C11×#3152C211yesmaximal, characteristic
4C11×#1660C218yesmaximal, complemented
5C11×#1526C212yesmaximal, complemented
6C11×#1525C211yesmaximal, characteristic
7C2×C11×#137—22no—
8C11×#563C2214yes—
9C11×#559—21no—
10Q82×C11—21no—
11C11×#556—22no—
12D4×Q8×C11—22no—
13C11×#542—24no—
14C11×#536—22no—
15C11×#533C2212yes—
16C11×#532C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C11×#501C2218yes—
19C11×#500—22no—
20C11×#498—22no—
21C11×#497C2214yes—
22C11×#494—21no—
23C11×#492—21no—
24C11×#428—24no—
25C4×C11×M16C2211yescharacteristic
26C4×C11×M16C2212yes—
27C11×#330C2218yes—
28C11×#329C2214yes—
29C2×C11×#41D412yes—
30C22×Q8×C11—22no—
31C22×Q8×C11—21no—
32C11×#137—48no—
33C2×C11×Q16—24no—
34C2×C11×SD16—24no—
35C2×C11×M16—22no—
36C2×C11×M16—21no—
37C11×C4⋊Q8—24no—
38C11×C4⋊Q8—24no—
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D411yescharacteristic
42C11×C4⋊Q8D412yes—
43C11×C4⋊Q8D412yes—
44C11×C4⋊Q8C2312yes—
45C11×#127D411yescharacteristic
46C11×#126—28no—
47C11×#125C2314yes—
48C11×#124—24no—
49C11×#124—24no—
50C11×#124C2312yes—
51C11×#123—24no—
52C11×#123—24no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—28no—
57C11×#121—22no—
58C4×Q8×C11—24no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×D4×C11—24no—
62C4×D4×C11—22no—
63C11×#117—22no—
64C11×#117D414yes—
65C2×C11×C4⋊C4—22no—
66C2×C42×C11C2311yescharacteristic
67C11×#107—28no—
68C11×#106—28no—
69C11×#97C2314yes—
70C11×#97C2312yes—
71C4×C8×C11—21no—
72C4×C8×C11—22no—
73#19078C1111yesmaximal, characteristic, direct product factor, Sylow
74C11×#41—44no—
75C2×Q8×C11—24no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—22no—
79C2×Q8×C11—44no—
80C2×Q8×C11—41no—
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×C11—41no—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D411yescharacteristic
91C11×Q16—48no—
92C11×SD16—48no—
93C11×M16—28no—
94C11×M16—24no—
95C2×C8×C11—24no—
96C2×C8×C11—22no—
97C11×C4⋊C4—28no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4C2×D414yes—
106C11×C4⋊C4C2×D414yes—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—28no—
109C11×C22⋊C4—24no—
110C11×C22⋊C4—24no—
111C42×C11—24no—
112C42×C11—24no—
113C42×C11C2×D412yes—
114C42×C11C2×D411yescharacteristic
115C42×C11C2411yescharacteristic
116#3550C2×C1111yescharacteristic
117#3165C2×C1112yescomplemented
118#3152C2×C1111yescharacteristic
119#1660C2×C1118yescomplemented
120#1526C2×C1112yescomplemented
121#1525C2×C1111yescharacteristic
122C23×C11—22no—
123C23×C11#12011yescharacteristic
124Q8×C11—42no—
125Q8×C11—44no—
126Q8×C11—44no—
127Q8×C11—44no—
128Q8×C11—84no—
129Q8×C11—82no—
130D4×C11—42no—
131D4×C11—44no—
132D4×C11—82no—
133C2×C4×C11—22no—
134C2×C4×C11—24no—
135C2×C4×C11—24no—
136C2×C4×C11—22no—
137C2×C4×C11—24no—
138C2×C4×C11—44no—
139C2×C4×C11—42no—
140C2×C4×C11—84no—
141C2×C4×C11—82no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12012yes—
144C2×C4×C11C22×D412yes—
145C2×C4×C11C22×D411yescharacteristic
146C8×C11—28no—
147C8×C11—24no—
148C2×#137—22no—
149#563C22×C1114yes—
150#559—21no—
151Q82—21no—
152#556—22no—
153D4×Q8—22no—
154#542—24no—
155#536—22no—
156#533C22×C1112yes—
157#532C22×C1111yescharacteristic
158C2×C4⋊Q8C22×C1111yescharacteristic
159#501C22×C1118yes—
160#500—22no—
161#498—22no—
162#497C22×C1114yes—
163#494—21no—
164#492—21no—
165#428—24no—
166C4×M16C22×C1111yescharacteristic
167C4×M16C22×C1112yes—
168#330C22×C1118yes—
169#329C22×C1114yes—
170C22×C11—21no—
171C22×C11—22no—
172C22×C11—42no—
173C22×C11—44no—
174C22×C11C2×#12011yescharacteristic
175C4×C11—21no—
176C4×C11—22no—
177C4×C11—42no—
178C4×C11—44no—
179C4×C11—44no—
180C4×C11—82no—
181C4×C11#45312yes—
182C4×C11#45614yes—
183C2×#41D4×C1112yes—
184C22×Q8—22no—
185C22×Q8—21no—
186#137—48no—
187C2×Q16—24no—
188C2×SD16—24no—
189C2×M16—21no—
190C2×M16—22no—
191C4⋊Q8—24no—
192C4⋊Q8—24no—
193C4⋊Q8—22no—
194C4⋊Q8—21no—
195C4⋊Q8D4×C1111yescharacteristic
196C4⋊Q8D4×C1112yes—
197C4⋊Q8D4×C1112yes—
198C4⋊Q8C23×C1112yes—
199#127D4×C1111yescharacteristic
200#126—28no—
201#125C23×C1114yes—
202#124—24no—
203#124—24no—
204#124C23×C1112yes—
205#123—24no—
206#123—24no—
207C22⋊Q8—24no—
208C22⋊Q8—22no—
209C22⋊Q8—22no—
210C22⋊Q8—28no—
211#121—22no—
212C4×Q8—24no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×D4—24no—
216C4×D4—22no—
217#117—22no—
218#117D4×C1114yes—
219C2×C4⋊C4—22no—
220C2×C42C23×C1111yescharacteristic
221#107—28no—
222#106—28no—
223#97C23×C1114yes—
224#97C23×C1112yes—
225C4×C8—21no—
226C4×C8—22no—
227C2×C11—41no—
228C2×C11—82no—
229C2×C11C2×#45311yescharacteristic
230C2×C11C2×#45612yes—
231#41—44no—
232C2×Q8—24no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—44no—
237C2×Q8—41no—
238C2×Q8—84no—
239C2×Q8C2×D4×C1112yes—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4C2×D4×C1112yes—
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4C2×D4×C1112yes—
247C22×C4C2×D4×C1111yescharacteristic
248Q16—48no—
249SD16—48no—
250M16—24no—
251M16—28no—
252C2×C8—24no—
253C2×C8—22no—
254C4⋊C4—28no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—42no—
262C4⋊C4C2×D4×C1114yes—
263C4⋊C4C2×D4×C1114yes—
264C22⋊C4—24no—
265C22⋊C4—28no—
266C22⋊C4—24no—
267C22⋊C4—24no—
268C42—24no—
269C42—24no—
270C42C2×D4×C1112yes—
271C42C2×D4×C1111yescharacteristic
272C42C24×C1111yescharacteristic
273C11#1907811yescharacteristic, direct product factor, Sylow
274C23—22no—
275C23C11×#12011yescharacteristic
276Q8—42no—
277Q8—44no—
278Q8—44no—
279Q8—44no—
280Q8—84no—
281Q8—82no—
282D4—42no—
283D4—44no—
284D4—82no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—84no—
293C2×C4—82no—
294C2×C4C11×#12011yescharacteristic
295C2×C4C11×#12012yes—
296C2×C4C22×D4×C1112yes—
297C2×C4C22×D4×C1111yescharacteristic
298C8—24no—
299C8—28no—
300C22—21no—
301C22—22no—
302C22—42no—
303C22—44no—
304C22C2×C11×#12011yescharacteristic
305C4—21no—
306C4—22no—
307C4—42no—
308C4—44no—
309C4—44no—
310C4—82no—
311C4C11×#45312yes—
312C4C11×#45614yes—
313C2—41no—
314C2—82no—
315C2C2×C11×#45311yescharacteristic
316C2C2×C11×#45612yes—
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×#3165C2semidirect
4. C11×#1660C2semidirect
5. C11×#1526C2semidirect
73. #19078C11direct (N × H)
117. #3165C2×C11semidirect
119. #1660C2×C11semidirect
120. #1526C2×C11semidirect
273. C11#19078direct (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×#31652
C11×#31522
C11×#16602
C11×#15262
C11×#15252
#1907811