Finite Group Databasebeta

← C11×#7830 #14585023

Subgroups — C11×#7830 #14585023

Order 2816.

494 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2733C211yesmaximal, characteristic
2C11×#2095C211yesmaximal, characteristic, complemented
3C11×#2094C212yesmaximal, complemented
4C11×#1272C211yesmaximal, characteristic, complemented
5C11×#1270C212yesmaximal, complemented
6C2×C11×#124—21no—
7C2×C11×#107—21no—
8C2×C11×#106—22no—
9C2×C11×#103—21no—
10C2×C11×#102—22no—
11C11×#394—21no—
12C11×#392—22no—
13C11×#391C2211yescharacteristic
14C11×#390C2212yes—
15C11×#388—22no—
16C11×#384C2211yescharacteristic
17C11×#336C2211yescharacteristic
18C11×#336C2212yes—
19C22×Q8×C11D411yescharacteristic
20C22×D4×C11—21no—
21C22×D4×C11—21no—
22C22×D4×C11D412yes—
23C22×C8×C11—22no—
24C22×C8×C11—21no—
25C11×#124—42no—
26C11×#124—42no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4D412yes—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C11×#107—42no—
38C11×#106—44no—
39C11×#103—42no—
40C11×#102—44no—
41C11×#95—21no—
42C11×#95—22no—
43#7830C1111yesmaximal, characteristic, direct product factor, Sylow
44C24×C11—22no—
45C2×Q8×C11—21no—
46C2×Q8×C11—41no—
47C2×Q8×C11—41no—
48C2×Q8×C11SD1612yes—
49C2×D4×C11—22no—
50C2×D4×C11—22no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—42no—
54C2×D4×C11—81no—
55C2×D4×C11—81no—
56C2×D4×C11—82no—
57C2×D4×C11—81no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C2×C8×C11—24no—
65C2×C8×C11—22no—
66C2×C8×C11—42no—
67C2×C8×C11—41no—
68C2×C8×C11—42no—
69C2×C8×C11—41no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—41no—
76C11×C22⋊C4—44no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—42no—
81C11×C22⋊C4—82no—
82C42×C11—41no—
83C42×C11—42no—
84#2733C2×C1111yescharacteristic
85#2095C2×C1111yescharacteristic, complemented
86#2094C2×C1112yescomplemented
87#1272C2×C1111yescharacteristic, complemented
88#1270C2×C1112yescomplemented
89C23×C11—42no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11#12011yescharacteristic
97Q8×C11—42no—
98Q8×C11—81no—
99D4×C11—44no—
100D4×C11—82no—
101D4×C11—84no—
102D4×C11—84no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—81no—
116C2×C4×C11—82no—
117C2×C4×C11C2×SD1611yescharacteristic
118C2×C4×C11#13512yes—
119C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C11#13712yes—
121C8×C11—42no—
122C8×C11—44no—
123C2×#124—21no—
124C2×#107—21no—
125C2×#106—22no—
126C2×#103—21no—
127C2×#102—22no—
128#394—21no—
129#392—22no—
130#391C22×C1111yescharacteristic
131#390C22×C1112yes—
132#388—22no—
133#384C22×C1111yescharacteristic
134#336C22×C1112yes—
135#336C22×C1111yescharacteristic
136C22×C11—82no—
137C22×C11—82no—
138C22×C11—82no—
139C22×C11—82no—
140C22×C11—82no—
141C22×C11—82no—
142C22×C11—82no—
143C22×C11#45011yescharacteristic
144C22×C11#45212yes—
145C22×C11#45311yescharacteristic
146C22×C11#45312yes—
147C22×C11#45811yescharacteristic
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—22no—
151C4×C11—22no—
152C4×C11—42no—
153C4×C11—82no—
154C4×C11—81no—
155C4×C11—161no—
156C22×Q8D4×C1111yescharacteristic
157C22×D4—21no—
158C22×D4—21no—
159C22×D4D4×C1112yes—
160C22×C8—22no—
161C22×C8—21no—
162#124—42no—
163#124—42no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4D4×C1112yes—
167C2×C4⋊C4D4×C1111yescharacteristic
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—22no—
172C2×C42—21no—
173C2×C42C23×C1111yescharacteristic
174#107—42no—
175#106—44no—
176#103—42no—
177#102—44no—
178#95—21no—
179#95—22no—
180C2×C11—162no—
181C2×C11#161311yescharacteristic
182C2×C11#161812yes—
183C2×C11#163112yes—
184C2×C11#163411yescharacteristic
185C2×C11#165511yescharacteristic
186C24—22no—
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8C11×SD1612yes—
191C2×D4—22no—
192C2×D4—22no—
193C2×D4—42no—
194C2×D4—42no—
195C2×D4—42no—
196C2×D4—81no—
197C2×D4—81no—
198C2×D4—82no—
199C2×D4—81no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—41no—
204C22×C4C2×D4×C1111yescharacteristic
205C22×C4C2×D4×C1112yes—
206C2×C8—24no—
207C2×C8—22no—
208C2×C8—42no—
209C2×C8—41no—
210C2×C8—42no—
211C2×C8—41no—
212C4⋊C4—42no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—42no—
217C4⋊C4—41no—
218C22⋊C4—44no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—82no—
224C42—41no—
225C42—42no—
226C11#783011yescharacteristic, direct product factor, Sylow
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23C11×#12011yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—44no—
238D4—82no—
239D4—84no—
240D4—84no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—81no—
254C2×C4—82no—
255C2×C4C2×C11×SD1611yescharacteristic
256C2×C4C11×#13512yes—
257C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
258C2×C4C11×#13712yes—
259C8—42no—
260C8—44no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22C11×#45011yescharacteristic
269C22C11×#45212yes—
270C22C11×#45311yescharacteristic
271C22C11×#45312yes—
272C22C11×#45811yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—82no—
279C4—81no—
280C4—161no—
281C2—162no—
282C2C11×#161311yescharacteristic
283C2C11×#161812yes—
284C2C11×#163112yes—
285C2C11×#163411yescharacteristic
286C2C11×#165511yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#2733C2
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2095C2semidirect
3. C11×#2094C2semidirect
4. C11×#1272C2semidirect
5. C11×#1270C2semidirect
43. #7830C11direct (N × H)
85. #2095C2×C11semidirect
86. #2094C2×C11semidirect
87. #1272C2×C11semidirect
88. #1270C2×C11semidirect
226. C11#7830direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#27332
C11×#20952
C11×#20942
C11×#12722
C11×#12702
#783011