Finite Group Databasebeta

← #14658507

Subgroups — #14658507

Order 2816.

402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 123 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#13068744C211yesmaximal, characteristic, complemented
2#13068616C212yesmaximal
3#13066500C212yesmaximal, complemented
4#13066451C211yesmaximal, characteristic, complemented
5C11×#1954C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×C11×C4⋊C8C2211yescharacteristic
8C2×C11×C22⋊C8—22no—
9C2×C4×C8×C11C2211yescharacteristic
10C2×#66896—22no—
11#10622548C2212yes—
12C2×C4⋊(C11⋊C8)C2212yes—
13#10622189—22no—
14#10622167—22no—
15C22×D4×C11D411yescharacteristic
16C23×C4×C11—21no—
17C22×C8×C11—21no—
18C22×C8×C11D412yes—
19C4×D4×C11—22no—
20C4×D4×C11—22no—
21C2×C11×C4⋊C4D411yescharacteristic
22C2×C11×C22⋊C4—21no—
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11—22no—
25C2×C4⋊Dic11—22no—
26C2×C4⋊Dic11—22no—
27C22×C11⋊C8—22no—
28C11×C4⋊C8—22no—
29C11×C22⋊C8—44no—
30C4×C8×C11—22no—
31#66896—44no—
32C4⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—22no—
34#10621—111nomaximal, Sylow
35C24×C11—21no—
36C2×D4×C11—22no—
37C2×D4×C11—21no—
38C2×D4×C11—22no—
39C2×D4×C11D812yes—
40C22×C4×C11—21no—
41C22×C4×C11—41no—
42C22×C4×C11—41no—
43C22×C4×C11—42no—
44C22×C4×C11—42no—
45C22×C4×C11C2×D411yescharacteristic
46C22×C4×C11C2×D411yescharacteristic
47C22×C4×C11#4111yescharacteristic
48C22×Dic11—42no—
49C2×C8×C11—22no—
50C2×C8×C11—22no—
51C2×C8×C11—22no—
52C2×C8×C11—41no—
53C2×C8×C11—42no—
54C11×C4⋊C4—22no—
55C11×C22⋊C4—42no—
56C42×C11#4112yes—
57C42×C11#4112yes—
58C4⋊Dic11—42no—
59C4⋊Dic11—42no—
60C4⋊Dic11—42no—
61C4⋊Dic11—42no—
62C4⋊Dic11—82no—
63C2×C11⋊C8—42no—
64C2×C11⋊C8—42no—
65C2×C11⋊C8—42no—
66#1954D1111yescharacteristic
67#1834—111no—
68#1802—112no—
69#1296—112no—
70#1277—111no—
71C23×C11—22no—
72C23×C11—41no—
73C23×C11—42no—
74C23×C11—41no—
75C23×C11—42no—
76C23×C11#12111yescharacteristic
77D4×C11—24no—
78D4×C11—42no—
79C2×C4×C11—22no—
80C2×C4×C11—41no—
81C2×C4×C11—42no—
82C2×C4×C11—82no—
83C2×C4×C11—81no—
84C2×C4×C11—81no—
85C2×C4×C11#12312yes—
86C2×C4×C11#12311yescharacteristic
87C2×C4×C11#12411yescharacteristic
88C2×C4×C11#12612yes—
89C2×C4×C11C2×D811yescharacteristic
90C2×C4×C11#13511yescharacteristic
91C2×C4×C11#13512yes—
92C2×C4×C11AGL(1,ℤ/8)12yes—
93C2×C4×C11#13712yes—
94C2×Dic11—82no—
95C2×Dic11—82no—
96C2×Dic11—82no—
97C8×C11—42no—
98C8×C11—81no—
99C11⋊C8—82no—
100C2×C4×D4C2×D1111yescharacteristic
101C2×C4⋊C8—112no—
102C2×C4⋊C8C2×D1111yescharacteristic
103C2×#102—222no—
104C2×C22⋊C8—22no—
105C2×C4×C8C2×D1111yescharacteristic
106#384—112no—
107#340—222no—
108#340—222no—
109C22×C11—42no—
110C22×C11—44no—
111C22×C11—81no—
112C22×C11—81no—
113C22×C11—82no—
114C22×C11#39711yescharacteristic
115C22×C11#46312yes—
116C22×C11#46611yescharacteristic
117C22×C11#47011yescharacteristic
118C22×C11#47112yes—
119C4×C11—22no—
120C4×C11—81no—
121C4×C11#48012yes—
122C4×C11#48212yes—
123C4×C11#48512yes—
124C4×C11#48811yescharacteristic
125C4×C11#49011yescharacteristic
126Dic11—162no—
127C22×D4D4411yescharacteristic
128C23×C4—21no—
129C22×C8—21no—
130C22×C8—222no—
131C22×C8C22⋊D1112yes—
132C4×D4—22no—
133C4×D4—22no—
134C2×C4⋊C4—222no—
135C2×C4⋊C4—222no—
136C2×C4⋊C4—222no—
137C2×C4⋊C4D4411yescharacteristic
138C2×C22⋊C4—21no—
139C2×C42C22×D1111yescharacteristic
140C4⋊C8—22no—
141C4⋊C8—222no—
142C4⋊C8—222no—
143#102—444no—
144C22⋊C8—44no—
145C4×C8—22no—
146C2×C11—82no—
147C2×C11#168112yes—
148C2×C11#170312yes—
149C2×C11#207311yescharacteristic
150C2×C11#207511yescharacteristic
151C2×C11#207911yescharacteristic
152C24—21no—
153C2×D4—22no—
154C2×D4—21no—
155C2×D4—22no—
156C2×D4D8812yes—
157C22×C4—21no—
158C22×C4—42no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—42no—
162C22×C4—442no—
163C22×C4C2×D4411yescharacteristic
164C22×C4#433911yescharacteristic
165C22×C4C2×C22⋊D1111yescharacteristic
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—42no—
170C2×C8—41no—
171C2×C8—442no—
172C2×C8—442no—
173C2×C8—442no—
174C4⋊C4—22no—
175C4⋊C4—442no—
176C4⋊C4—442no—
177C4⋊C4—442no—
178C4⋊C4—442no—
179C4⋊C4—882no—
180C22⋊C4—42no—
181C42#434112yes—
182C42#434112yes—
183C11#1062111yescharacteristic, complemented, Sylow
184C23—22no—
185C23—41no—
186C23—42no—
187C23—41no—
188C23—42no—
189C23#6698311yescharacteristic
190D4—24no—
191D4—42no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—882no—
199C2×C4—882no—
200C2×C4—882no—
201C2×C4#6693212yes—
202C2×C4#6693912yes—
203C2×C4C2×D8811yescharacteristic
204C2×C4#6695711yescharacteristic
205C2×C4#6696212yes—
206C2×C4#6698512yes—
207C2×C4#6698811yescharacteristic
208C2×C4#6698911yescharacteristic
209C2×C4#6700312yes—
210C8—42no—
211C8—81no—
212C8—882no—
213C22—44no—
214C22—42no—
215C22—82no—
216C22—81no—
217C22—81no—
218C22#1062256611yescharacteristic
219C22#1062262912yes—
220C22#1062272811yescharacteristic
221C22#1062275011yescharacteristic
222C22#1062275412yes—
223C4—22no—
224C4—81no—
225C4—1762no—
226C4#1062233612yes—
227C4#1062234912yes—
228C4#1062264812yes—
229C4#1062266911yescharacteristic
230C4#1062268411yescharacteristic
231C2—82no—
232C2#1306805312yes—
233C2#1306819112yes—
234C2#1307002911yescharacteristic
235C2#1307003911yescharacteristic
236C2#1307006111yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1954C2
socleC23×C11#121
prime radicalC22×D4×C11D4
hypercenter#1954D11
hypocenterC11#10621
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. #13068744C2semidirect
3. #13066500C2semidirect
4. #13066451C2semidirect
183. C11#10621semidirect

Maximal subgroups

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

subgroupindex
#130687442
#130686162
#130665002
#130664512
C11×#19542
#1062111