Finite Group Databasebeta

← #13130167

Subgroups — #13130167

Order 1664.

246 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 68 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
1#41×Dic13C211yesmaximal, characteristic
2#11719130C211yesmaximal, characteristic, complemented
3#11719125C211yesmaximal, characteristic, complemented
4Q8⋊#1057C212yesmaximal, complemented
5D4⋊#1057C212yesmaximal, complemented
6C2×C13×#41C411yescharacteristic
7Q8×Dic13C411yescharacteristic
8Q8×Dic13C2211yescharacteristic
9D4×Dic13—21no—
10D4×Dic13—21no—
11D4×Dic13C411yescharacteristic
12D4×Dic13C2211yescharacteristic
13#88180—21no—
14#88180C411yescharacteristic
15C2×C4×Dic13—21no—
16C2×C4×Dic13C2211yescharacteristic
17C22⋊#1057—21no—
18C22⋊#1057—21no—
19#88112—21no—
20#88110—21no—
21C4⋊#1057C2212yes—
22C4×#1057C2212yes—
23C13×#41—22no—
24C13×#41—22no—
25C2×Q8×C13C2×C411yescharacteristic
26C2×D4×C13—21no—
27C2×D4×C13C2×C411yescharacteristic
28C22×C4×C13—21no—
29C22×C4×C13C2×C411yescharacteristic
30C22×Dic13—21no—
31C22×Dic13—21no—
32C22×Dic13D411yescharacteristic
33C22×Dic13D411yescharacteristic
34C2×#1057—22no—
35C2×#1057—22no—
36C22⋊Dic13—21no—
37C22⋊Dic13—21no—
38C22⋊Dic13—21no—
39C4⋊Dic13—21no—
40C4⋊Dic13—21no—
41C4⋊Dic13C2×C411yescharacteristic
42C4⋊Dic13C2×C411yescharacteristic
43C4×Dic13—21no—
44C4×Dic13—21no—
45C4×Dic13—21no—
46C4×Dic13C2×C411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13D411yescharacteristic
49C4×Dic13C2311yescharacteristic
50#1488—131nomaximal, Sylow
51C23×C13—21no—
52C23×C13C22⋊C411yescharacteristic
53Q8×C13—21no—
54Q8×C13M1612yes—
55D4×C13—24no—
56D4×C13—21no—
57D4×C13M1612yes—
58C2×C4×C13—24no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13C22⋊C411yescharacteristic
63C2×C4×C13C22×C411yescharacteristic
64C2×Dic13—22no—
65C2×Dic13—21no—
66C2×Dic13—21no—
67C2×Dic13—41no—
68C2×Dic13—42no—
69C2×Dic13—42no—
70C2×Dic13C22⋊C411yescharacteristic
71C2×Dic13C22⋊C411yescharacteristic
72C2×Dic13C2×D411yescharacteristic
73C2×Dic13C2×D411yescharacteristic
74#1057—42no—
75#1057—42no—
76C4×#41—131no—
77#432—131no—
78#431—131no—
79Q8⋊C8—132no—
80D4⋊C8—132no—
81C22×C13—21no—
82C22×C13—22no—
83C22×C13—21no—
84C22×C13—21no—
85C22×C13—41no—
86C22×C13—41no—
87C22×C13C2×C22⋊C411yescharacteristic
88C4×C13—21no—
89C4×C13—22no—
90C4×C13C2×M1611yescharacteristic
91C4×C13C2×M1611yescharacteristic
92Dic13—21no—
93Dic13—21no—
94Dic13—21no—
95Dic13—41no—
96Dic13—41no—
97Dic13#13512yes—
98C2×#41#26111yescharacteristic
99C4×Q8—131no—
100C4×Q8—131no—
101C4×D4—131no—
102C4×D4—131no—
103C4×D4—261no—
104C4×D4—261no—
105#117—131no—
106#117—261no—
107C2×C42—131no—
108C2×C42—261no—
109C4⋊C8—132no—
110C4⋊C8—261no—
111C22⋊C8—261no—
112C22⋊C8—261no—
113#97—261no—
114C4×C8—132no—
115C2×C13—41no—
116C2×C13—42no—
117C2×C13#40711yescharacteristic
118C2×C13#41611yescharacteristic
119C2×C13#42111yescharacteristic
120#41—22no—
121#41—22no—
122C2×Q8C2×#26111yescharacteristic
123C2×D4—21no—
124C2×D4C2×#26111yescharacteristic
125C22×C4—21no—
126C22×C4—131no—
127C22×C4—131no—
128C22×C4—261no—
129C22×C4—261no—
130C22×C4C2×#26111yescharacteristic
131C2×C8—262no—
132C2×C8—262no—
133C4⋊C4—131no—
134C4⋊C4—131no—
135C4⋊C4—261no—
136C4⋊C4—261no—
137C22⋊C4—261no—
138C22⋊C4—261no—
139C22⋊C4—261no—
140C42—131no—
141C42—131no—
142C42—131no—
143C42—131no—
144C42—261no—
145C42—261no—
146C42—261no—
147C13#148811yescharacteristic, complemented, Sylow
148C23—21no—
149C23C22⋊#26111yescharacteristic
150Q8—21no—
151Q8#612212yes—
152D4—24no—
153D4—21no—
154D4#612212yes—
155C2×C4—24no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—131no—
160C2×C4—131no—
161C2×C4—131no—
162C2×C4—131no—
163C2×C4—262no—
164C2×C4—261no—
165C2×C4—261no—
166C2×C4—522no—
167C2×C4—521no—
168C2×C4—522no—
169C2×C4C22⋊#26111yescharacteristic
170C2×C4C22×#26111yescharacteristic
171C8—522no—
172C8—522no—
173C22—21no—
174C22—22no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22C2×C22⋊#26111yescharacteristic
180C4—21no—
181C4—22no—
182C4—132no—
183C4—261no—
184C4—261no—
185C4—261no—
186C4—521no—
187C4—521no—
188C4C2×#612211yescharacteristic
189C4C2×#612211yescharacteristic
190C2—41no—
191C2—42no—
192C2#1171916511yescharacteristic
193C2#1171916611yescharacteristic
194C2#1171916911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
Fitting, prime radicalC2×C13×#41C4
socleC22×C13C2×C22⋊C4
cosocleC4×Dic13C23
hypercenterC2×#41#261
hypocenterC13#1488
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11719130C2semidirect
3. #11719125C2semidirect
4. Q8⋊#1057C2semidirect
5. D4⋊#1057C2semidirect
147. C13#1488semidirect

Maximal subgroups

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

subgroupindex
#41×Dic132
#117191302
#117191252
Q8⋊#10572
D4⋊#10572
#148813