Finite Group Databasebeta

← C11×#10078 #14587271

Subgroups — C11×#10078 #14587271

Order 2816.

780 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C2×C11×#496C212yesmaximal, complemented
2C11×#2819C211yesmaximal, characteristic, complemented
3C11×#1961C211yesmaximal, characteristic, complemented
4C2×C11×#329C212yesmaximal, complemented
5C11×#1295C211yesmaximal, characteristic, complemented
6C22×C11×SD16—22no—
7C22×C11×D8—22no—
8C2×C11×#127C2211yescharacteristic
9C2×C11×#124C2212yes—
10C11×#496—24no—
11C11×#496—24no—
12C2×C11×#102—22no—
13C2×C11×#97C2211yescharacteristic
14C2×C11×#97C2212yes—
15C11×#394—22no—
16C11×#393—22no—
17C11×#392—22no—
18C11×#382C2211yescharacteristic
19C11×#329—24no—
20C22×Q8×C11D412yes—
21C22×D4×C11—22no—
22C22×D4×C11—21no—
23C22×D4×C11—22no—
24C22×D4×C11D412yes—
25C2×C11×SD16—28no—
26C2×C11×SD16—48no—
27C2×C11×D8—28no—
28C2×C11×D8—48no—
29C22×C8×C11—22no—
30C22×C8×C11—21no—
31C11×#127—22no—
32C11×#127—21no—
33C11×#127D412yescomplemented
34C11×#124—22no—
35C11×#124—22no—
36C11×#124—22no—
37C11×#124—22no—
38C2×C11×C4⋊C4D412yes—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—24no—
42C2×C42×C11C2311yescharacteristic
43C11×#102—44no—
44C11×#97—22no—
45C11×#97—22no—
46C11×#97D414yescomplemented
47C11×#95—22no—
48C11×#95—22no—
49#10078C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11—22no—
51C24×C11—41no—
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—44no—
55C2×D4×C11—22no—
56C2×D4×C11—24no—
57C2×D4×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—44no—
60C2×D4×C11—42no—
61C2×D4×C11—44no—
62C2×D4×C11—44no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11—41no—
66C2×D4×C11—84no—
67C2×D4×C11—82no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D411yescharacteristic
72C11×SD16—416no—
73C11×D8—416no—
74C2×C8×C11—28no—
75C2×C8×C11—22no—
76C2×C8×C11—24no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C11×C4⋊C4—42no—
80C11×C22⋊C4—42no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C11×C22⋊C4—84no—
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D412yes—
87C42×C11#4111yescharacteristic
88C2×#496C2×C1112yescomplemented
89#2819C2×C1111yescharacteristic, complemented
90#1961C2×C1111yescharacteristic, complemented
91C2×#329C2×C1112yescomplemented
92#1295C2×C1111yescharacteristic, complemented
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—44no—
96C23×C11—44no—
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—84no—
100C23×C11—81no—
101C23×C11—81no—
102C23×C11#12011yescharacteristic
103Q8×C11—44no—
104Q8×C11—82no—
105D4×C11—44no—
106D4×C11—44no—
107D4×C11—44no—
108D4×C11—44no—
109D4×C11—82no—
110D4×C11—84no—
111D4×C11—82no—
112D4×C11—88no—
113C2×C4×C11—21no—
114C2×C4×C11—24no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11—44no—
118C2×C4×C11—44no—
119C2×C4×C11—42no—
120C2×C4×C11#12012yes—
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12112yes—
123C2×C4×C11#12711yescharacteristic
124C8×C11—28no—
125C8×C11—42no—
126C22×SD16—22no—
127C22×D8—22no—
128C2×#127C22×C1111yescharacteristic
129C2×#124C22×C1112yes—
130#496—24no—
131#496—24no—
132C2×#102—22no—
133C2×#97C22×C1111yescharacteristic
134C2×#97C22×C1112yes—
135#394—22no—
136#393—22no—
137#392—22no—
138#382C22×C1111yescharacteristic
139#329—24no—
140C22×C11—84no—
141C22×C11—84no—
142C22×C11—84no—
143C22×C11—82no—
144C22×C11—82no—
145C22×C11—82no—
146C22×C11—82no—
147C22×C11—162no—
148C22×C11—162no—
149C22×C11#39211yescharacteristic
150C22×C11#45311yescharacteristic
151C22×C11#45314yes—
152C22×C11#45411yescharacteristic
153C4×C11—22no—
154C4×C11—22no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—82no—
158C4×C11—82no—
159C22×Q8D4×C1112yes—
160C22×D4—22no—
161C22×D4—22no—
162C22×D4—21no—
163C22×D4D4×C1112yes—
164C2×SD16—28no—
165C2×SD16—48no—
166C2×D8—28no—
167C2×D8—48no—
168C22×C8—22no—
169C22×C8—21no—
170#127—22no—
171#127—21no—
172#127D4×C1112yescomplemented
173#124—22no—
174#124—22no—
175#124—22no—
176#124—22no—
177C2×C4⋊C4D4×C1112yes—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—24no—
181C2×C42C23×C1111yescharacteristic
182#102—44no—
183#97—22no—
184#97—22no—
185#97D4×C1114yescomplemented
186#95—22no—
187#95—22no—
188C2×C11—162no—
189C2×C11—162no—
190C2×C11#165512yes—
191C2×C11#165612yes—
192C2×C11#200212yes—
193C2×C11#200611yescharacteristic
194C24—22no—
195C24—41no—
196C2×Q8—22no—
197C2×Q8—22no—
198C2×Q8—44no—
199C2×D4—22no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—44no—
204C2×D4—42no—
205C2×D4—44no—
206C2×D4—44no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—41no—
210C2×D4—84no—
211C2×D4—82no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4C2×D4×C1112yes—
215C22×C4C2×D4×C1111yescharacteristic
216SD16—416no—
217D8—416no—
218C2×C8—28no—
219C2×C8—24no—
220C2×C8—22no—
221C2×C8—41no—
222C2×C8—41no—
223C4⋊C4—42no—
224C22⋊C4—42no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—84no—
229C42C2×D4×C1111yescharacteristic
230C42C2×D4×C1112yes—
231C42C11×#4111yescharacteristic
232C11#1007811yescharacteristic, direct product factor, Sylow
233C23—42no—
234C23—42no—
235C23—44no—
236C23—44no—
237C23—42no—
238C23—42no—
239C23—84no—
240C23—81no—
241C23—81no—
242C23C11×#12011yescharacteristic
243Q8—44no—
244Q8—82no—
245D4—44no—
246D4—44no—
247D4—44no—
248D4—44no—
249D4—82no—
250D4—84no—
251D4—82no—
252D4—88no—
253C2×C4—21no—
254C2×C4—24no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4C11×#12012yes—
261C2×C4C11×#12111yescharacteristic
262C2×C4C11×#12112yes—
263C2×C4C11×#12711yescharacteristic
264C8—28no—
265C8—42no—
266C22—84no—
267C22—84no—
268C22—84no—
269C22—82no—
270C22—82no—
271C22—82no—
272C22—82no—
273C22—162no—
274C22—162no—
275C22C11×#39211yescharacteristic
276C22C11×#45311yescharacteristic
277C22C11×#45314yes—
278C22C11×#45411yescharacteristic
279C4—22no—
280C4—22no—
281C4—21no—
282C4—21no—
283C4—82no—
284C4—82no—
285C2—162no—
286C2—162no—
287C2C11×#165512yes—
288C2C11×#165612yes—
289C2C11×#200212yes—
290C2C11×#200611yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#496C2semidirect
2. C11×#2819C2semidirect
3. C11×#1961C2semidirect
4. C2×C11×#329C2semidirect
5. C11×#1295C2semidirect
33. C11×#127D4semidirect
46. C11×#97D4semidirect
49. #10078C11direct (N × H)
88. C2×#496C2×C11semidirect
89. #2819C2×C11semidirect
90. #1961C2×C11semidirect
91. C2×#329C2×C11semidirect
92. #1295C2×C11semidirect
172. #127D4×C11semidirect
185. #97D4×C11semidirect
232. C11#10078direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4962
C11×#28192
C11×#19612
C2×C11×#3292
C11×#12952
#1007811