Finite Group Databasebeta

← #13130705

Subgroups — #13130705

Order 1664.

308 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C4×Q8×D13C211yesmaximal, characteristic
2C2×#88117C212yesmaximal
3#11719059C211yesmaximal, characteristic
4D13⋊(C4⋊C8)C211yesmaximal, characteristic
5#11718246C212yesmaximal
6C2×Q8×D13C2211yescharacteristic
7C2×C4⋊#261—21no—
8C2×C4⋊#261—21no—
9C2×C4⋊#261C2212yes—
10C2×D13⋊C8C2212yes—
11C4×Q8×C13C411yescharacteristic, complemented
12Q8×Dic13C411yescharacteristic, complemented
13C4⋊C4×D13—21no—
14C4⋊C4×D13C2211yescharacteristic
15#88141—21no—
16#88141C411yescharacteristic, complemented
17C42×D13—21no—
18C42×D13C2211yescharacteristic
19C4×Dic26—21no—
20C4×Dic26C411yescharacteristic, complemented
21#88117—24no—
22#88112—21no—
23C4⋊#1057—21no—
24C22×#261—22no—
25C2×Q8×C13C2×C411yescharacteristic
26Q8×D13—21no—
27Q8×D13—21no—
28Q8×D13D412yes—
29Q8×D13Q812yes—
30C2×C4×D13—21no—
31C2×C4×D13—21no—
32C2×C4×D13D411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×C4×D13C2311yescharacteristic
35C2×Dic26—21no—
36C2×Dic26C2×C411yescharacteristic
37C2×#1057—22no—
38C4⋊#261—22no—
39C4⋊#261—22no—
40C4⋊#261—42no—
41C4⋊#261—42no—
42D13⋊C8—22no—
43D13⋊C8—22no—
44C13×C4⋊C4—21no—
45C13×C4⋊C4C2×C411yescharacteristic
46C42×C13—21no—
47C42×C13C2×C411yescharacteristic
48C4⋊Dic13—21no—
49C4⋊Dic13C2×C411yescharacteristic
50#6101—21no—
51#6101—21no—
52#6101—21no—
53C4×Dic13—21no—
54C4×Dic13—21no—
55C4×Dic13—21no—
56C4×Dic13C2×C411yescharacteristic
57C4×Dic13D411yescharacteristic
58C4×Dic13D411yescharacteristic
59#1803—131nomaximal, Sylow
60C22×D13C2×D411yescharacteristic
61C2×#261—42no—
62C2×#261—42no—
63C2×#261—42no—
64Q8×C13—21no—
65Q8×C13C4⋊C412yescomplemented
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13C22⋊C411yescharacteristic
69C2×C4×C13C22⋊C411yescharacteristic
70C2×C4×C13C22×C411yescharacteristic
71C2×Dic13—21no—
72C2×Dic13—21no—
73C2×Dic13C22⋊C411yescharacteristic
74C2×Dic13C22⋊C411yescharacteristic
75C2×Dic13C2×D411yescharacteristic
76C4×D13—22no—
77C4×D13—22no—
78C4×D13—21no—
79C4×D13—21no—
80C4×D13—41no—
81C4×D13—41no—
82C4×D13SD1612yes—
83C4×D13Q1612yes—
84C4×D13C2×D411yescharacteristic
85C4×D13C2×Q811yescharacteristic
86C4×D13#4111yescharacteristic
87C4×D13#4111yescharacteristic
88Dic26—21no—
89Dic26—22no—
90Dic26—22no—
91Dic26C4⋊C412yescomplemented
92#1057—42no—
93C2×C4×Q8—131no—
94C2×C4⋊C8—131no—
95C2×#103—132no—
96#384—131no—
97#340—132no—
98C22×C13C2×C22⋊C411yescharacteristic
99C2×D13#12111yescharacteristic
100C2×D13C22⋊Q811yescharacteristic
101C2×D13C2×SD1611yescharacteristic
102C2×D13C2×Q1611yescharacteristic
103C2×D13AGL(1,ℤ/8)11yescharacteristic
104C2×D13#13711yescharacteristic
105#261—82no—
106C4×C13—22no—
107C4×C13—21no—
108C4×C13—41no—
109C4×C13#10312yescomplemented
110C4×C13C2×C4⋊C411yescharacteristic
111C4×C13#11711yescharacteristic
112Dic13—22no—
113Dic13—21no—
114Dic13—41no—
115Dic13#10312yescomplemented
116Dic13#12111yescharacteristic
117Dic13C22⋊Q811yescharacteristic
118C22×Q8—131no—
119C22×C8—132no—
120C4×Q8—131no—
121C4×Q8—131no—
122C4×Q8—131no—
123C4×Q8—261no—
124C4×Q8—261no—
125C4×Q8#26111yescharacteristic, complemented
126C2×C4⋊C4—131no—
127C2×C4⋊C4—132no—
128C2×C4⋊C4—261no—
129C2×C4⋊C4—261no—
130C2×C4⋊C4—261no—
131C2×C42—131no—
132C2×C42—261no—
133C4⋊C8—261no—
134C4⋊C8—261no—
135#103—264no—
136C2×C13#38011yescharacteristic
137C2×C13C2×#10311yescharacteristic
138C2×C13#41711yescharacteristic
139D13#46011yescharacteristic
140D13#46211yescharacteristic
141D13#47511yescharacteristic
142D13#47711yescharacteristic
143C2×Q8—132no—
144C2×Q8—132no—
145C2×Q8—131no—
146C2×Q8—261no—
147C2×Q8—261no—
148C2×Q8—261no—
149C2×Q8C2×#26111yescharacteristic
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—261no—
154C22×C4—261no—
155C22×C4—262no—
156C2×C8—262no—
157C2×C8—262no—
158C2×C8—262no—
159C4⋊C4—21no—
160C4⋊C4—131no—
161C4⋊C4—261no—
162C4⋊C4—261no—
163C4⋊C4—261no—
164C4⋊C4—262no—
165C4⋊C4—262no—
166C4⋊C4—261no—
167C4⋊C4—522no—
168C4⋊C4—522no—
169C4⋊C4C2×#26111yescharacteristic
170C42—21no—
171C42—131no—
172C42—131no—
173C42—131no—
174C42—261no—
175C42—261no—
176C42—261no—
177C42C2×#26111yescharacteristic
178C13#180311yescharacteristic, complemented, Sylow
179C23—131no—
180Q8—21no—
181Q8—132no—
182Q8—262no—
183Q8—262no—
184Q8—261no—
185Q8C4⋊#26112yescomplemented
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—132no—
191C2×C4—132no—
192C2×C4—131no—
193C2×C4—131no—
194C2×C4—131no—
195C2×C4—131no—
196C2×C4—131no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—261no—
202C2×C4—261no—
203C2×C4—521no—
204C2×C4—521no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4C22⋊#26111yescharacteristic
209C2×C4C22⋊#26111yescharacteristic
210C2×C4C22×#26111yescharacteristic
211C8—522no—
212C22—131no—
213C22—131no—
214C22—131no—
215C22—131no—
216C22—131no—
217C22—131no—
218C22C2×C22⋊#26111yescharacteristic
219C4—22no—
220C4—21no—
221C4—41no—
222C4—131no—
223C4—131no—
224C4—132no—
225C4—262no—
226C4—261no—
227C4—521no—
228C4—1042no—
229C4#8811712yescomplemented
230C4C2×C4⋊#26111yescharacteristic
231C4#8823711yescharacteristic
232C2—131no—
233C2—131no—
234C2—131no—
235C2—131no—
236C2#1171913611yescharacteristic
237C2C2×#8811711yescharacteristic
238C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×Q8×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C2×D4
cosocleC2×C4×D13C23
hypercenterC4×Q8#261
hypocenterC13#1803
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
11. C4×Q8×C13C4semidirect
12. Q8×Dic13C4semidirect
16. #88141C4semidirect
20. C4×Dic26C4semidirect
65. Q8×C13C4⋊C4semidirect
91. Dic26C4⋊C4semidirect
109. C4×C13#103semidirect
115. Dic13#103semidirect
125. C4×Q8#261semidirect
178. C13#1803semidirect
185. Q8C4⋊#261semidirect
229. C4#88117semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D132
C2×#881172
#117190592
D13⋊(C4⋊C8)2
#117182462
#180313