Finite Group Databasebeta

← #13069750

Subgroups — #13069750

Order 1408.

326 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 89 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×C11×#102C211yesmaximal, characteristic
3#10622834C211yesmaximal, characteristic
4C2×#66896C211yesmaximal, characteristic
5#10622189C211yesmaximal, characteristic, complemented
6#10622188C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×Dic22—21no—
10C22×C8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C22⋊Dic11—21no—
13C2×C22⋊Dic11—21no—
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×Dic11⋊C4—21no—
17C2×C4×Dic11C2211yescharacteristic
18C22×C11⋊C8C2211yescharacteristic
19#66941—22no—
20#66941—22no—
21C11×#102—22no—
22#66896—22no—
23C24×C11—21no—
24C2×D4×C11—21no—
25C2×D4×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11Q812yescomplemented
30C22×C4×C11—21no—
31C22×C4×C11C2311yescharacteristic
32C22×Dic11—21no—
33C22×Dic11—21no—
34C22×Dic11D411yescharacteristic
35C22×Dic11D411yescharacteristic
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⋊C4D412yes—
44C22⋊Dic11—42no—
45C22⋊Dic11—42no—
46C4⋊Dic11—21no—
47C4⋊Dic11—21no—
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×C11—22no—
58C23×C11—41no—
59C23×C11—41no—
60C23×C11—41no—
61C23×C11—41no—
62C23×C11—41no—
63C23×C11—41no—
64C23×C11C2×D411yescharacteristic
65D4×C11—22no—
66D4×C11—22no—
67D4×C11—41no—
68D4×C11—41no—
69C2×C4×C11—22no—
70C2×C4×C11—41no—
71C2×C4×C11—41no—
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×Q811yescharacteristic
75C2×C4×C11#4111yescharacteristic
76C2×C4×C11#4111yescharacteristic
77C2×C4×C11#4111yescharacteristic
78C2×Dic11—21no—
79C2×Dic11—21no—
80C2×Dic11—21no—
81C2×Dic11—21no—
82C2×Dic11—22no—
83C2×Dic11—41no—
84C2×Dic11—41no—
85C2×Dic11—41no—
86C2×Dic11—41no—
87C2×Dic11—41no—
88C2×Dic11D812yes—
89C2×Dic11SD1612yes—
90Dic22—48no—
91C8×C11—41no—
92C11⋊C8—41no—
93C2×C4⋊Q8—111no—
94C2×#102—111no—
95C2×#102D1111yescharacteristic
96#390—111no—
97#340—111no—
98#340—111no—
99#336—111no—
100C22×C11—42no—
101C22×C11—42no—
102C22×C11—42no—
103C22×C11—81no—
104C22×C11—81no—
105C22×C11—81no—
106C22×C11—81no—
107C22×C11#12011yescharacteristic
108C22×C11C22⋊Q811yescharacteristic
109C22×C11#12411yescharacteristic
110C22×C11C2×D811yescharacteristic
111C22×C11C2×SD1611yescharacteristic
112C22×C11AGL(1,ℤ/8)11yescharacteristic
113C22×C11#13711yescharacteristic
114C4×C11—42no—
115C4×C11C22⋊Q811yescharacteristic
116C4×C11C22⋊Q811yescharacteristic
117C4×C11#12411yescharacteristic
118C4×C11#12411yescharacteristic
119Dic11—22no—
120Dic11—22no—
121Dic11—42no—
122Dic11—81no—
123C22×Q8—221no—
124C22×D4C2×D1111yescharacteristic
125C22×C8—111no—
126C22×C8C2×D1111yescharacteristic
127C4⋊Q8—222no—
128C4⋊Q8—222no—
129C2×C4⋊C4—111no—
130C2×C4⋊C4—111no—
131C2×C4⋊C4—221no—
132C2×C4⋊C4C2×D1111yescharacteristic
133C2×C22⋊C4—221no—
134C2×C22⋊C4—221no—
135C2×C42—111no—
136#102—22no—
137#102—222no—
138C2×C11—82no—
139C2×C11#39311yescharacteristic
140C2×C11#44711yescharacteristic
141C2×C11#44811yescharacteristic
142C2×C11#47411yescharacteristic
143C2×C11#47611yescharacteristic
144C2×C11#48611yescharacteristic
145C2×C11#48911yescharacteristic
146C24—21no—
147C2×Q8—224no—
148C2×Q8—442no—
149C2×Q8—442no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4Dic2212yescomplemented
156C22×C4—21no—
157C22×C4—111no—
158C22×C4—111no—
159C22×C4—221no—
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—112no—
170C4⋊C4—224no—
171C4⋊C4—221no—
172C4⋊C4—221no—
173C4⋊C4—221no—
174C4⋊C4C22⋊D1112yes—
175C22⋊C4—442no—
176C22⋊C4—442no—
177C42—221no—
178C42—221no—
179C11#202311yescharacteristic, complemented, Sylow
180C23—22no—
181C23—41no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23D4×D1111yescharacteristic
188Q8—448no—
189D4—22no—
190D4—22no—
191D4—41no—
192D4—41no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—112no—
197C2×C4—112no—
198C2×C4—221no—
199C2×C4—221no—
200C2×C4—221no—
201C2×C4—221no—
202C2×C4—222no—
203C2×C4—441no—
204C2×C4—441no—
205C2×C4—441no—
206C2×C4—441no—
207C2×C4—441no—
208C2×C4C2×Dic2211yescharacteristic
209C2×C4#433911yescharacteristic
210C2×C4D4×D1111yescharacteristic
211C2×C4#434111yescharacteristic
212C2×C4#434111yescharacteristic
213C2×C4C2×C22⋊D1111yescharacteristic
214C8—41no—
215C8—441no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—81no—
220C22—81no—
221C22—81no—
222C22—81no—
223C22#6693111yescharacteristic
224C22#6693811yescharacteristic
225C22D8×D1111yescharacteristic
226C22#6696411yescharacteristic
227C22SD16×D1111yescharacteristic
228C22#6696811yescharacteristic
229C22#6699011yescharacteristic
230C4—42no—
231C4—222no—
232C4—222no—
233C4—442no—
234C4—881no—
235C4#6693111yescharacteristic
236C4#6693811yescharacteristic
237C4#6697711yescharacteristic
238C4#6698911yescharacteristic
239C2—82no—
240C2#1062237211yescharacteristic
241C2#1062237311yescharacteristic
242C2#1062237411yescharacteristic
243C2#1062237811yescharacteristic
244C2#1062256011yescharacteristic
245C2#1062276911yescharacteristic
246C2#1062278311yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#102C2
socleC23×C11C2×D4
prime radicalC22×D4×C11C22
hypercenterC2×#102D11
hypocenterC11#2023
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#66941C2semidirect
5. #10622189C2semidirect
6. #10622188C2semidirect
7. #10622167C2semidirect
29. C2×D4×C11Q8semidirect
155. C2×D4Dic22semidirect
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×C11×#1022
#106228342
C2×#668962
#106221892
#106221882
#106221672
#202311