Finite Group Databasebeta

← #13069751

Subgroups — #13069751

Order 1408.

326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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×#66941C211yesmaximal, characteristic, complemented
2C2×#66885C211yesmaximal, characteristic
3#10622601C211yesmaximal, characteristic
4C2×#66873C211yesmaximal, characteristic
5C11×#340C211yesmaximal, characteristic, complemented
6#10622188C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D44C2211yescharacteristic
9C22×Dic22—21no—
10C22×C8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×(C2×D11)⋊C4—21no—
14C2×(C2×D11)⋊C4—21no—
15C2×C4⋊Dic11C2211yescharacteristic
16C2×Dic11⋊C4—21no—
17C2×C4×Dic11C2211yescharacteristic
18C22×C11⋊C8C2211yescharacteristic
19#66941—22no—
20#66941—22no—
21#66885—22no—
22#66873—22no—
23C23×D11—21no—
24C22×C4×C11—21no—
25C22×C4×C11—21no—
26C22×C4×C11C2311yescharacteristic
27C22×Dic11—21no—
28C22×Dic11D411yescharacteristic
29C22×Dic11D411yescharacteristic
30C2×D44—21no—
31C2×D44—21no—
32C2×D44—21no—
33C2×D44—21no—
34C2×D44—21no—
35C2×D44Q812yescomplemented
36C2×Dic22—24no—
37C2×Dic22—42no—
38C2×Dic22—42no—
39C2×C8×C11—21no—
40C2×C8×C11—21no—
41C2×C8×C11—21no—
42C11×C4⋊C4—21no—
43C11×C4⋊C4—21no—
44C11×C4⋊C4—21no—
45C11×C4⋊C4D412yes—
46(C2×D11)⋊C4—42no—
47(C2×D11)⋊C4—42no—
48C4⋊Dic11—21no—
49C4⋊Dic11D412yes—
50Dic11⋊C4—24no—
51C4×Dic11—21no—
52C4×Dic11—21no—
53C2×C11⋊C8—21no—
54C2×C11⋊C8—21no—
55C2×C11⋊C8—21no—
56#2023—111nomaximal, Sylow
57C23×C11C2×D411yescharacteristic
58C22×D11—22no—
59C22×D11—41no—
60C22×D11—41no—
61C22×D11—41no—
62C22×D11—41no—
63C22×D11—41no—
64C22×D11—41no—
65C2×C4×C11—22no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11—41no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×Q811yescharacteristic
74C2×C4×C11#4111yescharacteristic
75C2×C4×C11#4111yescharacteristic
76C2×C4×C11#4111yescharacteristic
77C2×Dic11—21no—
78C2×Dic11—21no—
79C2×Dic11—21no—
80C2×Dic11—21no—
81C2×Dic11—22no—
82C2×Dic11—41no—
83C2×Dic11—41no—
84C2×Dic11D812yes—
85C2×Dic11SD1612yes—
86D44—22no—
87D44—22no—
88D44—41no—
89D44—41no—
90Dic22—48no—
91C8×C11—41no—
92C11⋊C8—41no—
93C2×C4⋊Q8—111no—
94C2×#102—111no—
95C2×#102—111no—
96#390—111no—
97#340—111no—
98#340D1111yescharacteristic, complemented
99#336—111no—
100C22×C11#12011yescharacteristic
101C22×C11C22⋊Q811yescharacteristic
102C22×C11#12411yescharacteristic
103C22×C11C2×D811yescharacteristic
104C22×C11C2×SD1611yescharacteristic
105C22×C11AGL(1,ℤ/8)11yescharacteristic
106C22×C11#13711yescharacteristic
107C2×D11—42no—
108C2×D11—42no—
109C2×D11—42no—
110C2×D11—81no—
111C2×D11—81no—
112C2×D11—81no—
113C2×D11—81no—
114C4×C11—42no—
115C4×C11—81no—
116C4×C11C22⋊Q811yescharacteristic
117C4×C11C22⋊Q811yescharacteristic
118C4×C11#12411yescharacteristic
119C4×C11#12411yescharacteristic
120Dic11—22no—
121Dic11—22no—
122Dic11—42no—
123C22×Q8—221no—
124C22×D4—111no—
125C22×C8—111no—
126C22×C8C2×D1111yescharacteristic
127C4⋊Q8—222no—
128C4⋊Q8—222no—
129C2×C4⋊C4—111no—
130C2×C4⋊C4—221no—
131C2×C4⋊C4C2×D1111yescharacteristic
132C2×C4⋊C4C2×D1111yescharacteristic
133C2×C22⋊C4—221no—
134C2×C22⋊C4—221no—
135C2×C42—111no—
136#102—222no—
137#102—222no—
138C2×C11#39311yescharacteristic
139C2×C11#44711yescharacteristic
140C2×C11#44811yescharacteristic
141C2×C11#47411yescharacteristic
142C2×C11#47611yescharacteristic
143C2×C11#48611yescharacteristic
144C2×C11#48911yescharacteristic
145D11—82no—
146C24—221no—
147C2×Q8—224no—
148C2×Q8—442no—
149C2×Q8—442no—
150C2×D4—112no—
151C2×D4—221no—
152C2×D4—221no—
153C2×D4—221no—
154C2×D4—221no—
155C2×D4—221no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—111no—
159C22×C4—111no—
160C22×C4—221no—
161C22×C4C22×D1111yescharacteristic
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—221no—
166C2×C8—221no—
167C2×C8—221no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—112no—
172C4⋊C4—224no—
173C4⋊C4—221no—
174C4⋊C4D4412yes—
175C22⋊C4—442no—
176C22⋊C4—442no—
177C42—221no—
178C42—221no—
179C11#202311yescharacteristic, complemented, Sylow
180C23—222no—
181C23—441no—
182C23—441no—
183C23—441no—
184C23—441no—
185C23—441no—
186C23—441no—
187C23D4×D1111yescharacteristic
188Q8—448no—
189D4—222no—
190D4—222no—
191D4—441no—
192D4—441no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—112no—
200C2×C4—112no—
201C2×C4—221no—
202C2×C4—221no—
203C2×C4—221no—
204C2×C4—221no—
205C2×C4—222no—
206C2×C4—441no—
207C2×C4—441no—
208C2×C4C2×D4411yescharacteristic
209C2×C4#433911yescharacteristic
210C2×C4#433911yescharacteristic
211C2×C4D4×D1111yescharacteristic
212C2×C4#434111yescharacteristic
213C2×C4Q8×D1111yescharacteristic
214C8—41no—
215C8—441no—
216C22—442no—
217C22—442no—
218C22—442no—
219C22—881no—
220C22—881no—
221C22—881no—
222C22—881no—
223C22#6693511yescharacteristic
224C22#6693811yescharacteristic
225C22#6694911yescharacteristic
226C22D8×D1111yescharacteristic
227C22SD16×D1111yescharacteristic
228C22#6696711yescharacteristic
229C22#6697111yescharacteristic
230C4—42no—
231C4—81no—
232C4—222no—
233C4—222no—
234C4—442no—
235C4#6692811yescharacteristic
236C4#6693811yescharacteristic
237C4#6694911yescharacteristic
238C4#6695011yescharacteristic
239C2—882no—
240C2#1062228611yescharacteristic
241C2#1062237311yescharacteristic
242C2#1062238611yescharacteristic
243C2#1062240811yescharacteristic
244C2#1062241911yescharacteristic
245C2#1062248311yescharacteristic
246C2#1062250311yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#340C2
socleC23×C11C2×D4
prime radicalC22×D44C22
hypercenter#340D11
hypocenterC11#2023
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C2×#66941C2semidirect
5. C11×#340C2semidirect
6. #10622188C2semidirect
7. #10622167C2semidirect
35. C2×D44Q8semidirect
98. #340D11semidirect
179. C11#2023semidirect

Maximal subgroups

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

subgroupindex
C2×#669412
C2×#668852
#106226012
C2×#668732
C11×#3402
#106221882
#106221672
#202311