Finite Group Databasebeta

← #13069813

Subgroups — #13069813

Order 1408.

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

normal subgroups only

This group has 316 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×#66977C211yesmaximal, characteristic
2C2×C11×C22⋊C8C211yesmaximal, characteristic
3#10622825C211yesmaximal, characteristic
4C2×#66881C211yesmaximal, characteristic, complemented
5C2×#66880C211yesmaximal, characteristic, complemented
6C2×#66880C211yesmaximal, characteristic, complemented
7#10622189C211yesmaximal, characteristic, complemented
8C23×C4×C11C2211yescharacteristic
9C22×Dic22C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C2×C22⋊Dic11—21no—
13C2×C22⋊Dic11—21no—
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17#66977—22no—
18#66977—22no—
19C2×Dic11⋊C4—21no—
20C11×C22⋊C8—22no—
21C11⋊#95—21no—
22#66881—22no—
23#66880—22no—
24#66880—22no—
25C24×C11D411yescharacteristic
26C22×C4×C11—21no—
27C22×C4×C11—21no—
28C22×C4×C11—21no—
29C22×C4×C11—21no—
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11D411yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×Dic11—21no—
35C22×Dic11—21no—
36C22×Dic11—21no—
37C22×Dic11—21no—
38C2×Dic22—21no—
39C2×Dic22—21no—
40C2×Dic22—21no—
41C2×Dic22—21no—
42C2×Dic22—21no—
43C2×Dic22D412yes—
44C2×C8×C11—21no—
45C2×C8×C11—21no—
46C2×C8×C11—21no—
47C2×C8×C11—21no—
48C2×C8×C11—21no—
49C2×C8×C11D412yes—
50C22⋊Dic11—24no—
51C22⋊Dic11—42no—
52C4⋊Dic11—21no—
53C4⋊Dic11—21no—
54C4⋊Dic11—21no—
55C4⋊Dic11—21no—
56C4⋊Dic11—21no—
57C4⋊Dic11D412yes—
58Dic11⋊C4—24no—
59#2035—111nomaximal, Sylow
60C23×C11—21no—
61C23×C11—21no—
62C23×C11—21no—
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—21no—
66C23×C11SD1612yes—
67C23×C11C2×D411yescharacteristic
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—41no—
72C2×C4×C11—41no—
73C2×C4×C11—41no—
74C2×C4×C11—41no—
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11#4111yescharacteristic
79C2×C4×C11#4111yescharacteristic
80C2×C4×C11#4111yescharacteristic
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—41no—
84C2×Dic11—41no—
85C2×Dic11—41no—
86C2×Dic11—41no—
87C2×Dic11—41no—
88C2×Dic11—41no—
89C2×Dic11—41no—
90C2×Dic11—41no—
91C2×Dic11—41no—
92C2×Dic11—41no—
93Dic22—22no—
94Dic22—22no—
95Dic22—41no—
96Dic22—41no—
97C8×C11—22no—
98C8×C11—41no—
99C2×C22⋊Q8—111no—
100C2×#106—111no—
101C2×#103—111no—
102C2×#103—111no—
103C2×C22⋊C8D1111yescharacteristic
104#380—111no—
105#340—111no—
106C22×C11—22no—
107C22×C11—22no—
108C22×C11—22no—
109C22×C11—41no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11#12011yescharacteristic
114C22×C11#12111yescharacteristic
115C22×C11#12311yescharacteristic
116C22×C11C2×SD1611yescharacteristic
117C22×C11#13511yescharacteristic
118C22×C11#13711yescharacteristic
119C22×C11#13711yescharacteristic
120C4×C11—41no—
121C4×C11#12111yescharacteristic
122C4×C11#12111yescharacteristic
123C4×C11#12311yescharacteristic
124C4×C11#12411yescharacteristic
125Dic11—42no—
126Dic11—42no—
127Dic11—81no—
128Dic11—81no—
129C22×Q8—111no—
130C23×C4C2×D1111yescharacteristic
131C22×C8C2×D1111yescharacteristic
132C22×C8C2×D1111yescharacteristic
133C22⋊Q8—222no—
134C22⋊Q8—222no—
135C2×C4⋊C4—111no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4—111no—
138C2×C4⋊C4—221no—
139C2×C22⋊C4—221no—
140C2×C22⋊C4—221no—
141#106—222no—
142#103—222no—
143#103—222no—
144C22⋊C8—22no—
145#95—221no—
146C2×C11—42no—
147C2×C11#39411yescharacteristic
148C2×C11#44811yescharacteristic
149C2×C11#45211yescharacteristic
150C2×C11#46511yescharacteristic
151C2×C11#47011yescharacteristic
152C2×C11#48311yescharacteristic
153C2×C11#48511yescharacteristic
154C24D4411yescharacteristic
155C2×Q8—112no—
156C2×Q8—221no—
157C2×Q8—221no—
158C2×Q8—221no—
159C2×Q8—221no—
160C2×Q8—221no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—221no—
168C22×C4—221no—
169C22×C4—221no—
170C22×C4—221no—
171C22×C4D4411yescharacteristic
172C22×C4C22×D1111yescharacteristic
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8C22⋊D1112yes—
179C4⋊C4—112no—
180C4⋊C4—224no—
181C4⋊C4—221no—
182C4⋊C4—221no—
183C4⋊C4—221no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C22⋊C4—224no—
187C22⋊C4—442no—
188C11#203511yescharacteristic, complemented, Sylow
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23#431412yes—
196C23C2×D4411yescharacteristic
197Q8—222no—
198Q8—222no—
199Q8—441no—
200Q8—441no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—441no—
211C2×C4—441no—
212C2×C4—441no—
213C2×C4—441no—
214C2×C4—441no—
215C2×C4—441no—
216C2×C4—441no—
217C2×C4—441no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4#433911yescharacteristic
221C2×C4D4×D1111yescharacteristic
222C2×C4D4×D1111yescharacteristic
223C2×C4#434111yescharacteristic
224C2×C4#434111yescharacteristic
225C2×C4C2×C22⋊D1111yescharacteristic
226C8—22no—
227C8—41no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22#6693511yescharacteristic
236C22#6693911yescharacteristic
237C22C2×#431411yescharacteristic
238C22#6695711yescharacteristic
239C22#6696211yescharacteristic
240C22#6696211yescharacteristic
241C22#6698311yescharacteristic
242C4—41no—
243C4—442no—
244C4—442no—
245C4—881no—
246C4—881no—
247C4#6693611yescharacteristic
248C4#6693811yescharacteristic
249C4#6699111yescharacteristic
250C4#6699211yescharacteristic
251C2—42no—
252C2#1062233411yescharacteristic
253C2#1062233611yescharacteristic
254C2#1062234611yescharacteristic
255C2#1062235111yescharacteristic
256C2#1062257411yescharacteristic
257C2#1062272711yescharacteristic
258C2#1062275011yescharacteristic
subgroupG/H
centerC23C2×D44
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×C22⋊C8C2
socleC23×C11C2×D4
prime radicalC24×C11D4
hypercenterC2×C22⋊C8D11
hypocenterC11#2035
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#66881C2semidirect
5. C2×#66880C2semidirect
6. C2×#66880C2semidirect
7. #10622189C2semidirect
188. C11#2035semidirect

Maximal subgroups

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

subgroupindex
C2×#669772
C2×C11×C22⋊C82
#106228252
C2×#668812
C2×#668802
#106221892
#203511