Finite Group Databasebeta

← #13078413

Subgroups — #13078413

Order 1408.

440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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
2#10623001C211yesmaximal, characteristic, complemented
3#10622828C212yesmaximal
4#10622622C214yesmaximal, complemented
5#10622621C212yesmaximal, complemented
6#10622620C212yesmaximal, complemented
7#10622577C212yesmaximal, complemented
8#10622537C211yesmaximal, characteristic, complemented
9C22×D4×C11C2211yescharacteristic
10C23×C4×C11—21no—
11C4×D4×C11—21no—
12C4×D4×C11—21no—
13C4×D4×C11C2212yes—
14C4×D4×C11C2212yes—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4—21no—
17C2×C42×C11C2211yescharacteristic
18#66979C2212yes—
19#66977—21no—
20#66977—21no—
21C2×#4318C2212yes—
22#66923C2212yescomplemented
23#66922C2211yescharacteristic, complemented
24#66922C2211yescharacteristic, complemented
25C4×Dic22—21no—
26C4×Dic22—21no—
27#66896C2214yes—
28#66896C2214yes—
29#66872C2214yescomplemented
30#66871C2214yescomplemented
31C4⋊(C11⋊C8)C2212yescomplemented
32C4⋊(C11⋊C8)C2212yescomplemented
33C24×C11—21no—
34C2×D4×C11—21no—
35C2×D4×C11—22no—
36C2×D4×C11Q814yescomplemented
37C2×D4×C11C2312yes—
38C22×C4×C11—21no—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11—44no—
42C22×C4×C11D411yescharacteristic
43C22×C4×C11D411yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C2×Dic22—21no—
46C2×Dic22—21no—
47C11×C4⋊C4—21no—
48C11×C4⋊C4C2312yes—
49C11×C22⋊C4—22no—
50C11×C22⋊C4—22no—
51C42×C11D411yescharacteristic
52C42×C11D411yescharacteristic
53C42×C11C2311yescharacteristic
54C42×C11C2311yescharacteristic
55C22⋊Dic11—22no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11C2312yes—
59C4⋊Dic11C2312yes—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62C4×Dic11—22no—
63#4318—24no—
64C2×C11⋊C8C2314yes—
65#3077—111nomaximal, Sylow
66C23×C11—24no—
67C23×C11—22no—
68C23×C11—42no—
69C23×C11—42no—
70C23×C11C2×D411yescharacteristic
71D4×C11—24no—
72D4×C11—22no—
73D4×C11C2×Q814yes—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—41no—
77C2×C4×C11—44no—
78C2×C4×C11—42no—
79C2×C4×C11—44no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×Q812yes—
86C2×C4×C11#4112yes—
87C2×C4×C11C2411yescharacteristic
88C2×Dic11—22no—
89C2×Dic11—22no—
90Dic22—42no—
91Dic22—42no—
92C11⋊C8—24no—
93#533—111no—
94C2×C4×D4D1111yescharacteristic
95#478—114no—
96#476—112no—
97#474—112no—
98#428—112no—
99#423—111no—
100#418—112no—
101C22×C11—21no—
102C22×C11—21no—
103C22×C11—24no—
104C22×C11—48no—
105C22×C11—42no—
106C22×C11—42no—
107C22×C11C22⋊Q812yes—
108C22×C11C22×D411yescharacteristic
109C4×C11—21no—
110C4×C11—21no—
111C4×C11—21no—
112C4×C11—42no—
113C4×C11C22⋊Q812yes—
114C4×C11AGL(1,ℤ/8)12yes—
115C4×C11C22×Q811yescharacteristic
116C4×C11C2×#4111yescharacteristic
117Dic11—42no—
118Dic11—42no—
119C22×D4C2×D1111yescharacteristic
120C23×C4—21no—
121C2×M16—112no—
122C4⋊Q8—111no—
123C4⋊Q8—111no—
124#125—112no—
125C22⋊Q8—221no—
126C22⋊Q8—221no—
127C4×Q8—221no—
128C4×Q8—221no—
129C4×D4—21no—
130C4×D4—21no—
131C4×D4C2×D1112yes—
132C4×D4C2×D1112yes—
133#117—112no—
134C2×C4⋊C4C2×D1111yescharacteristic
135C2×C22⋊C4—21no—
136C2×C42C2×D1111yescharacteristic
137#107—114no—
138#106—114no—
139C4⋊C8—112no—
140C4⋊C8—112no—
141#102—114no—
142#102—114no—
143C2×C11—22no—
144C2×C11—44no—
145C2×C11C2×C22⋊Q811yescharacteristic
146C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C11#57511yescharacteristic
148C24—21no—
149C2×Q8—221no—
150C2×Q8—221no—
151C2×D4—22no—
152C2×D4—21no—
153C2×D4Dic2214yescomplemented
154C2×D4C22×D1112yes—
155C22×C4—21no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—44no—
159C22×C4C22⋊D1111yescharacteristic
160C22×C4C22⋊D1111yescharacteristic
161C22×C4C22×D1111yescharacteristic
162M16—224no—
163C2×C8—114no—
164C4⋊C4—21no—
165C4⋊C4—112no—
166C4⋊C4—112no—
167C4⋊C4—222no—
168C4⋊C4—222no—
169C4⋊C4—221no—
170C4⋊C4—221no—
171C4⋊C4C22×D1112yes—
172C22⋊C4—22no—
173C22⋊C4—22no—
174C22⋊C4—222no—
175C42—222no—
176C42C22⋊D1111yescharacteristic
177C42C22⋊D1111yescharacteristic
178C42C22×D1111yescharacteristic
179C42C22×D1111yescharacteristic
180C11#307711yescharacteristic, complemented, Sylow
181C23—24no—
182C23—22no—
183C23—42no—
184C23—42no—
185C23C2×C22⋊D1111yescharacteristic
186Q8—442no—
187Q8—442no—
188D4—24no—
189D4—22no—
190D4C2×Dic2214yes—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—44no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4C2×Dic2212yes—
200C2×C4#433912yes—
201C2×C4C2×C22⋊D1111yescharacteristic
202C2×C4C2×C22⋊D1111yescharacteristic
203C2×C4C2×C22⋊D1111yescharacteristic
204C2×C4C2×C22⋊D1111yescharacteristic
205C2×C4C2×C22⋊D1111yescharacteristic
206C2×C4C23×D1111yescharacteristic
207C8—224no—
208C22—21no—
209C22—21no—
210C22—24no—
211C22—48no—
212C22—42no—
213C22—42no—
214C22#6697712yes—
215C22C22×C22⋊D1111yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—442no—
221C4—442no—
222C4#6697712yes—
223C4#6698512yes—
224C4C22×Dic2211yescharacteristic
225C4C2×#433911yescharacteristic
226C2—22no—
227C2—44no—
228C2C2×#6697711yescharacteristic
229C2C2×#6698511yescharacteristic
230C2#1062335311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C4×D4×C11C2
socleC22×C11C22×D4
prime radicalC22×D4×C11C22
hypercenterC2×C4×D4D11
hypocenterC11#3077
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #10623001C2semidirect
4. #10622622C2semidirect
5. #10622621C2semidirect
6. #10622620C2semidirect
7. #10622577C2semidirect
8. #10622537C2semidirect
22. #66923C22semidirect
23. #66922C22semidirect
24. #66922C22semidirect
29. #66872C22semidirect
30. #66871C22semidirect
31. C4⋊(C11⋊C8)C22semidirect
32. C4⋊(C11⋊C8)C22semidirect
36. C2×D4×C11Q8semidirect
153. C2×D4Dic22semidirect
180. C11#3077semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
#106230012
#106228282
#106226222
#106226212
#106226202
#106225772
#106225372
#307711