Finite Group Databasebeta

← #14643029

Subgroups — #14643029

Order 2816.

422 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 83 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
1#13076562C211yesmaximal, characteristic
2#13070144C211yesmaximal, characteristic
3#13070026C212yesmaximal, complemented
4#13066441C212yesmaximal, complemented
5C11×#1270C211yesmaximal, characteristic
6C11×#390C2211yescharacteristic
7#10622833—21no—
8C2×#66896—21no—
9C2×#66880—22no—
10#10622599—21no—
11C2×#66871—21no—
12#10622563—22no—
13#10622560—22no—
14#10622548C2211yescharacteristic
15#10622542C2212yes—
16C11×#336C2212yes—
17#10622189—22no—
18#10622162C2211yescharacteristic
19C22×D4×C11D411yescharacteristic
20C23×Dic11—21no—
21C22×Dic22D412yes—
22C22×C8×C11—22no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C11×C22⋊C4—22no—
25C2×C42×C11C2311yescharacteristic
26C2×C22⋊Dic11—21no—
27C2×C22⋊Dic11—22no—
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—22no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11D412yes—
32C22×C11⋊C8—21no—
33#66896—42no—
34C11⋊#95—21no—
35C11⋊#95—22no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38#66880—44no—
39#66871—42no—
40#7821—111nomaximal, Sylow
41C24×C11—21no—
42C2×D4×C11—21no—
43C2×D4×C11—41no—
44C2×D4×C11—41no—
45C2×D4×C11Q1612yes—
46C22×C4×C11—21no—
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11C2×D412yes—
49C22×Dic11—22no—
50C22×Dic11—22no—
51C22×Dic11—41no—
52C22×Dic11—81no—
53C22×Dic11—82no—
54C2×Dic22—22no—
55C2×Dic22—22no—
56C2×Dic22—42no—
57C2×Dic22—42no—
58C2×C8×C11—42no—
59C2×C8×C11—42no—
60C2×C8×C11—42no—
61C11×C4⋊C4—41no—
62C11×C22⋊C4—42no—
63C11×C22⋊C4—42no—
64C42×C11—41no—
65C22⋊Dic11—82no—
66C22⋊Dic11—81no—
67C4⋊Dic11—42no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C4⋊Dic11—81no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—41no—
75C2×C11⋊C8—41no—
76#2804—111no—
77#2093—111no—
78#2072—112no—
79#1272—112no—
80#1270D1111yescharacteristic
81C23×C11—22no—
82C23×C11—42no—
83C23×C11—41no—
84C23×C11—42no—
85C23×C11—41no—
86C23×C11#12011yescharacteristic
87D4×C11—42no—
88D4×C11—81no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—42no—
94C2×C4×C11—41no—
95C2×C4×C11C2×Q1611yescharacteristic
96C2×C4×C11#13512yes—
97C2×C4×C11AGL(1,ℤ/8)12yes—
98C2×C4×C11#13711yescharacteristic
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—84no—
106C2×Dic11—82no—
107C2×Dic11—81no—
108Dic22—44no—
109Dic22—82no—
110C8×C11—82no—
111C11⋊C8—42no—
112C2×#107—221no—
113C2×#103—222no—
114C2×#102—221no—
115#400—221no—
116#393—222no—
117#391—112no—
118#390C2×D1111yescharacteristic
119#386—221no—
120#385—222no—
121#384—111no—
122#340—222no—
123#336—111no—
124#336C2×D1112yes—
125C22×C11—42no—
126C22×C11—44no—
127C22×C11—82no—
128C22×C11—81no—
129C22×C11—81no—
130C22×C11#44912yes—
131C22×C11#45111yescharacteristic
132C22×C11#45311yescharacteristic
133C22×C11#45512yes—
134C22×C11#45811yescharacteristic
135C4×C11—22no—
136C4×C11—22no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—81no—
140Dic11—82no—
141Dic11—82no—
142Dic11—161no—
143C22×Q8—112no—
144C22×D4D4411yescharacteristic
145C23×C4—221no—
146C22×C8—22no—
147C22×C8—221no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—221no—
150C2×C4⋊C4—222no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4D4411yescharacteristic
153C2×C22⋊C4—22no—
154C2×C22⋊C4—222no—
155C2×C22⋊C4—221no—
156C2×C42C22×D1111yescharacteristic
157#107—442no—
158#103—444no—
159#102—442no—
160#95—222no—
161#95—221no—
162#95—222no—
163#95—222no—
164C2×C11—82no—
165C2×C11#161212yes—
166C2×C11#161411yescharacteristic
167C2×C11#162011yescharacteristic
168C2×C11#164412yes—
169C2×C11#165911yescharacteristic
170C24—21no—
171C2×Q8—222no—
172C2×Q8—222no—
173C2×Q8—442no—
174C2×Q8—442no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4Dic4412yes—
179C22×C4—21no—
180C22×C4—222no—
181C22×C4—222no—
182C22×C4—441no—
183C22×C4—881no—
184C22×C4—882no—
185C22×C4C2×D4411yescharacteristic
186C22×C4D4×D1112yes—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—222no—
191C2×C8—441no—
192C2×C8—441no—
193C4⋊C4—41no—
194C4⋊C4—442no—
195C4⋊C4—441no—
196C4⋊C4—441no—
197C4⋊C4—442no—
198C4⋊C4—442no—
199C4⋊C4—881no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C22⋊C4—881no—
203C22⋊C4—882no—
204C42—41no—
205C11#782111yescharacteristic, complemented, Sylow
206C23—22no—
207C23—41no—
208C23—41no—
209C23—42no—
210C23—42no—
211C23#6693511yescharacteristic
212Q8—444no—
213Q8—882no—
214D4—42no—
215D4—81no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—442no—
223C2×C4—442no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—884no—
229C2×C4—881no—
230C2×C4—882no—
231C2×C4C2×Dic4411yescharacteristic
232C2×C4#6696211yescharacteristic
233C2×C4#6696412yes—
234C2×C4#6696912yes—
235C8—82no—
236C8—442no—
237C22—44no—
238C22—42no—
239C22—82no—
240C22—81no—
241C22—81no—
242C22#1062235211yescharacteristic
243C22#1062235511yescharacteristic
244C22#1062236011yescharacteristic
245C22#1062239412yes—
246C22#1062243812yes—
247C4—22no—
248C4—22no—
249C4—21no—
250C4—21no—
251C4—81no—
252C4—882no—
253C4—882no—
254C4—1761no—
255C2—82no—
256C2#1306763112yes—
257C2#1306764311yescharacteristic
258C2#1306767611yescharacteristic
259C2#1306783312yes—
260C2#1306792311yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#1270D11
hypocenterC11#7821
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
3. #13070026C2semidirect
4. #13066441C2semidirect
205. C11#7821semidirect

Maximal subgroups

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

subgroupindex
#130765622
#130701442
#130700262
#130664412
C11×#12702
#782111