Finite Group Databasebeta

← #16777177

Subgroups — #16777177

Order 3328.

286 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 102 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
1D13⋊(C4⋊C16)C211yesmaximal, characteristic
2C8×C4⋊#261C211yesmaximal, characteristic
3C4×C16×D13C211yesmaximal, characteristic
4C2×C8×#261—21no—
5C2×D13⋊C16—21no—
6C4×C4⋊#261C411yescharacteristic
7D13⋊(C4⋊C8)C411yescharacteristic
8C2×C16×D13—21no—
9C4×C8×D13C2211yescharacteristic
10(C2×#261)⋊C8—21no—
11#11718260—21no—
12C4⋊#6092C412yescomplemented
13C4×C13×C16C411yescharacteristic, complemented
14C16×Dic13—21no—
15C4×#6090C411yescharacteristic, complemented
16C2×C4⋊#261C812yes—
17C2×C4×#261—21no—
18C2×D13⋊C8—21no—
19C2×C8×D13D411yescharacteristic
20C2×C8×D13D411yescharacteristic
21C42×D13C2×C411yescharacteristic
22(C2×#261)⋊C4—21no—
23#88112—21no—
24C4⋊#1057C812yes—
25C2×#6092—22no—
26C8×#261—41no—
27C8×#261—41no—
28D13⋊C16—41no—
29D13⋊C16—41no—
30C2×C13×C16—21no—
31C4×C8×C13C2×C411yescharacteristic
32C8×Dic13D411yescharacteristic
33C8×Dic13Q811yescharacteristic
34C2×#6090—21no—
35C4×#1055C2×C411yescharacteristic
36C16×D13—22no—
37C16×D13—22no—
38#7167—131nomaximal, Sylow
39C22×#261—22no—
40C2×C4×D13C22⋊C411yescharacteristic
41C2×C4×D13C2×C811yescharacteristic
42C2×C4×D13M1611yescharacteristic
43C2×#1057—22no—
44C4⋊#261—22no—
45C4⋊#261C1614yescomplemented
46C4×#261—41no—
47C4×#261—41no—
48D13⋊C8—41no—
49D13⋊C8—41no—
50C2×C8×C13C22⋊C411yescharacteristic
51C2×C8×C13C4⋊C411yescharacteristic
52C42×C13C4211yescharacteristic
53C4×Dic13C4⋊C411yescharacteristic
54C4×Dic13C2×C811yescharacteristic
55C4×Dic13M1611yescharacteristic
56C2×#1055C22⋊C411yescharacteristic
57C2×#1055C4⋊C411yescharacteristic
58C8×D13—21no—
59C8×D13—21no—
60C8×D13D811yescharacteristic
61C8×D13SD1611yescharacteristic
62C8×D13SD1611yescharacteristic
63C8×D13Q1611yescharacteristic
64#6092—42no—
65C13×C16—22no—
66#6090—22no—
67C2×C4⋊C16—131no—
68C2×C4×C16—131no—
69C8×C4⋊C4—131no—
70C22×D13C22⋊C811yescharacteristic
71C2×#261—24no—
72C2×#261—42no—
73C2×#261—42no—
74C2×C4×C13#9511yescharacteristic
75C2×C4×C13C4×C811yescharacteristic
76C2×C4×C13#9711yescharacteristic
77C2×Dic13C22⋊C811yescharacteristic
78C2×Dic13C4⋊C811yescharacteristic
79C2×Dic13C4⋊C811yescharacteristic
80C4×D13—22no—
81C4×D13#10211yescharacteristic
82C4×D13#10311yescharacteristic
83C4×D13#10411yescharacteristic
84C4×D13#10411yescharacteristic
85C4×D13C2×C1612yes—
86C4×D13M3212yes—
87#1057—42no—
88C8×C13—21no—
89C8×C13#10611yescharacteristic
90C8×C13#10711yescharacteristic
91#1055—21no—
92#1055#10211yescharacteristic
93#1055#10311yescharacteristic
94C22×C16—261no—
95C22×C16—261no—
96C2×C4⋊C8—131no—
97C2×C4×C8—131no—
98C2×C4×C8—261no—
99C4×C4⋊C4—131no—
100C4⋊C16—132no—
101C4⋊C16—261no—
102C4×C16—131no—
103C4×C16—261no—
104C4×C16#26111yescharacteristic, complemented
105#336—261no—
106C22×C13#33611yescharacteristic
107C2×D13D4⋊C811yescharacteristic
108C2×D13Q8⋊C811yescharacteristic
109C2×D13C22⋊C1612yes—
110C2×D13#35012yes—
111#261—44no—
112C4×C13—21no—
113C4×C13#33911yescharacteristic
114C4×C13#34011yescharacteristic
115C4×C13C4×C1611yescharacteristic
116C4×C13#34611yescharacteristic
117Dic13—21no—
118Dic13D4⋊C811yescharacteristic
119Dic13Q8⋊C811yescharacteristic
120Dic13C4⋊C1612yes—
121C22×C8—131no—
122C22×C8—131no—
123C22×C8—261no—
124C2×C4⋊C4—132no—
125C2×C42—131no—
126C2×C42—261no—
127C2×C16—21no—
128C2×C16—262no—
129C2×C16—262no—
130C2×C16—261no—
131C2×C16—262no—
132C2×C16—521no—
133C2×C16—521no—
134C4⋊C8—132no—
135C4⋊C8—261no—
136C4×C8—131no—
137C4×C8—131no—
138C4×C8—131no—
139C4×C8—521no—
140C4×C8—521no—
141C4×C8C2×#26111yescharacteristic
142#95—261no—
143C2×C13#127911yescharacteristic
144C2×C13#137411yescharacteristic
145C2×C13#137911yescharacteristic
146D13D4⋊C1612yes—
147D13Q8⋊C1612yes—
148C22×C4—131no—
149C22×C4—131no—
150C22×C4—131no—
151C22×C4—262no—
152C2×C8—131no—
153C2×C8—131no—
154C2×C8—131no—
155C2×C8—131no—
156C2×C8—131no—
157C2×C8—131no—
158C2×C8—261no—
159C2×C8—261no—
160C2×C8—262no—
161C2×C8—521no—
162C2×C8—521no—
163C2×C8C4⋊#26111yescharacteristic
164C2×C8C22⋊#26111yescharacteristic
165C4⋊C4—134no—
166C4⋊C4—262no—
167C42—131no—
168C42—131no—
169C42—131no—
170C42—521no—
171C42—521no—
172C42C4×#26111yescharacteristic
173C16—22no—
174C16—262no—
175C16—522no—
176C13#716711yescharacteristic, complemented, Sylow
177C23—131no—
178C2×C4—131no—
179C2×C4—131no—
180C2×C4—132no—
181C2×C4—132no—
182C2×C4—131no—
183C2×C4—131no—
184C2×C4—131no—
185C2×C4—131no—
186C2×C4—131no—
187C2×C4—262no—
188C2×C4—264no—
189C2×C4—522no—
190C2×C4—522no—
191C2×C4C8×#26111yescharacteristic
192C2×C4#8810011yescharacteristic
193C2×C4(C2×#261)⋊C411yescharacteristic
194C8—21no—
195C8—131no—
196C8—131no—
197C8—261no—
198C8—522no—
199C8#8810111yescharacteristic
200C8#8810211yescharacteristic
201C22—132no—
202C22—132no—
203C22—131no—
204C22—131no—
205C22(C2×#261)⋊C811yescharacteristic
206C4—21no—
207C4—132no—
208C4—131no—
209C4—131no—
210C4—261no—
211C4—524no—
212C4C16×#26111yescharacteristic
213C4#1171821611yescharacteristic
214C4#1171823411yescharacteristic
215C4#1171826511yescharacteristic
216C2—132no—
217C2—132no—
218C2#1312967111yescharacteristic
219C2(C2×#261)⋊C1611yescharacteristic
220C2#1312988911yescharacteristic
subgroupG/H
centerC2×C8C4⋊#261
commutatorC4×C13C4×C16
FrattiniC4×C8C2×#261
FittingC4×C13×C16C4
socleC22×C13#336
prime radicalC22×D13C22⋊C8
cosocleC4×C8×D13C22
hypercenterC4×C16#261
hypocenterC13#7167
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C4×C16

Complements

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

NH ≅ G/Ntype
12. C4⋊#6092C4semidirect
13. C4×C13×C16C4semidirect
15. C4×#6090C4semidirect
45. C4⋊#261C16semidirect
104. C4×C16#261semidirect
176. C13#7167semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C4⋊C16)2
C8×C4⋊#2612
C4×C16×D132
#716713