Finite Group Databasebeta

← #13068950

Subgroups — #13068950

Order 1408.

402 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 113 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×C4×D4×C11C211yesmaximal, characteristic
2C22×#4324C211yesmaximal, characteristic
3C2×#66896C211yesmaximal, characteristic
4C2×#66874C211yesmaximal, characteristic, complemented
5#10622542C211yesmaximal, characteristic, complemented
6#10622167C211yesmaximal, characteristic, complemented
7#10622162C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C23×C4×C11—21no—
10C22×Dic22C2211yescharacteristic
11C4×D4×C11—22no—
12C4×D4×C11—22no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4—21no—
15C2×C42×C11C2211yescharacteristic
16C2×#4324—22no—
17C2×#4324—22no—
18C2×#4324C414yescomplemented
19C2×C4⋊Dic11C2211yescharacteristic
20C22×C11⋊C8C2211yescharacteristic
21C22×C11⋊C8C2211yescharacteristic
22#66896—22no—
23C11⋊#95—21no—
24C11⋊#95—21no—
25#66874—22no—
26C24×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11C2×C412yes—
31C2×D4×C11D412yes—
32C2×D4×C11D412yes—
33C22×C4×C11—24no—
34C22×C4×C11—21no—
35C22×C4×C11—42no—
36C22×C4×C11—42no—
37C22×C4×C11D411yescharacteristic
38C22×C4×C11D411yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×Dic11—21no—
41C22×Dic11—21no—
42C2×Dic22—21no—
43C2×Dic22—21no—
44C2×Dic22—21no—
45C2×Dic22—21no—
46C2×Dic22—21no—
47C2×Dic22C2×C412yescomplemented
48C11×C4⋊C4—21no—
49C11×C4⋊C4D412yes—
50C11×C22⋊C4—24no—
51C42×C11—21no—
52C42×C11—21no—
53#4324—28no—
54C4⋊Dic11—21no—
55C4⋊Dic11—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58C2×C11⋊C8—21no—
59C2×C11⋊C8—21no—
60C2×C11⋊C8—21no—
61C2×C11⋊C8C2×C412yescomplemented
62#1877—111nomaximal, Sylow
63C23×C11—22no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—41no—
67C23×C11—41no—
68C23×C11—41no—
69C23×C11—41no—
70C23×C11C2×D411yescharacteristic
71D4×C11—22no—
72D4×C11—22no—
73D4×C11—22no—
74D4×C11C22⋊C414yes—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—48no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11SD1612yescomplemented
85C2×C4×C11C22×C411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11#4111yescharacteristic
90C2×C4×C11#4111yescharacteristic
91C2×Dic11—22no—
92C2×Dic11—41no—
93C2×Dic11—41no—
94C2×Dic11—41no—
95C2×Dic11—41no—
96C2×Dic11—41no—
97Dic22—22no—
98Dic22—22no—
99Dic22—41no—
100Dic22—41no—
101C11⋊C8—22no—
102C11⋊C8—41no—
103C22×SD16—111no—
104C2×C4×D4D1111yescharacteristic
105C2×#103—111no—
106C2×#102—111no—
107#391—111no—
108#340—111no—
109#336—111no—
110C22×C11—24no—
111C22×C11—42no—
112C22×C11—42no—
113C22×C11—42no—
114C22×C11—42no—
115C22×C11—42no—
116C22×C11—42no—
117C22×C11C4×D411yescharacteristic
118C22×C11#12011yescharacteristic
119C22×C11#12111yescharacteristic
120C22×C11C2×SD1611yescharacteristic
121C22×C11#13511yescharacteristic
122C22×C11AGL(1,ℤ/8)11yescharacteristic
123C22×C11#13711yescharacteristic
124C4×C11—22no—
125C4×C11—42no—
126C4×C11—41no—
127C4×C11C2×C22⋊C411yescharacteristic
128C4×C11C4×D411yescharacteristic
129C4×C11#12111yescharacteristic
130C4×C11#12311yescharacteristic
131Dic11—42no—
132Dic11—81no—
133C22×Q8—111no—
134C22×D4C2×D1111yescharacteristic
135C23×C4—21no—
136C2×SD16—114no—
137C2×SD16—222no—
138C2×SD16—222no—
139C22×C8—111no—
140C22×C8—111no—
141C4×D4—22no—
142C4×D4—22no—
143C2×C4⋊C4—111no—
144C2×C4⋊C4C2×D1111yescharacteristic
145C2×C22⋊C4—21no—
146C2×C42C2×D1111yescharacteristic
147#103—222no—
148#102—222no—
149#95—221no—
150#95—221no—
151C2×C11—44no—
152C2×C11#38611yescharacteristic
153C2×C11C4×SD1611yescharacteristic
154C2×C11#44011yescharacteristic
155C2×C11#45011yescharacteristic
156C2×C11#45211yescharacteristic
157C2×C11#46111yescharacteristic
158C2×C11#46311yescharacteristic
159C24—21no—
160C2×Q8—112no—
161C2×Q8—221no—
162C2×Q8—221no—
163C2×Q8—221no—
164C2×Q8—221no—
165C2×Q8—221no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4C4×D1112yes—
170C2×D4D4412yes—
171C2×D4C22⋊D1112yes—
172C22×C4—24no—
173C22×C4—21no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—221no—
177C22×C4—221no—
178C22×C4C22⋊D1111yescharacteristic
179C22×C4C22⋊D1111yescharacteristic
180C22×C4C22×D1111yescharacteristic
181SD16—228no—
182C2×C8—112no—
183C2×C8—221no—
184C2×C8—221no—
185C2×C8—221no—
186C2×C8—221no—
187C2×C8—221no—
188C4⋊C4—21no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4C22⋊D1112yes—
192C22⋊C4—24no—
193C42—21no—
194C42—21no—
195C11#187711yescharacteristic, complemented, Sylow
196C23—22no—
197C23—22no—
198C23—22no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23C2×C22⋊D1111yescharacteristic
204Q8—222no—
205Q8—222no—
206Q8—441no—
207Q8—441no—
208D4—22no—
209D4—22no—
210D4—22no—
211D4(C2×D11)⋊C414yes—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—48no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—222no—
222C2×C4—441no—
223C2×C4—441no—
224C2×C4—441no—
225C2×C4—441no—
226C2×C4—441no—
227C2×C4#432412yescomplemented
228C2×C4C2×C4×D1111yescharacteristic
229C2×C4C2×D4411yescharacteristic
230C2×C4#433911yescharacteristic
231C2×C4#433911yescharacteristic
232C2×C4C2×C22⋊D1111yescharacteristic
233C2×C4C2×C22⋊D1111yescharacteristic
234C8—222no—
235C8—441no—
236C22—24no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22C4×C22⋊D1111yescharacteristic
244C22#6698311yescharacteristic
245C22#6698511yescharacteristic
246C22C2×#432411yescharacteristic
247C22#6700311yescharacteristic
248C22#6700411yescharacteristic
249C22#6700611yescharacteristic
250C4—22no—
251C4—42no—
252C4—41no—
253C4—442no—
254C4—881no—
255C4C2×(C2×D11)⋊C411yescharacteristic
256C4C4×C22⋊D1111yescharacteristic
257C4#6698211yescharacteristic
258C4#6698311yescharacteristic
259C2—44no—
260C2#1062262911yescharacteristic
261C2C4×#432411yescharacteristic
262C2#1062263111yescharacteristic
263C2#1062263211yescharacteristic
264C2#1062282611yescharacteristic
265C2#1062283111yescharacteristic
266C2#1062285211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC2×C4×D4×C11C2
socleC23×C11C2×D4
prime radicalC22×D4×C11C22
cosocleC22×C4×C11C23
hypercenterC2×C4×D4D11
hypocenterC11#1877
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
4. C2×#66874C2semidirect
5. #10622542C2semidirect
6. #10622167C2semidirect
7. #10622162C2semidirect
18. C2×#4324C4semidirect
47. C2×Dic22C2×C4semidirect
61. C2×C11⋊C8C2×C4semidirect
84. C2×C4×C11SD16semidirect
195. C11#1877semidirect
227. C2×C4#4324semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
C22×#43242
C2×#668962
C2×#668742
#106225422
#106221672
#106221622
#187711