Finite Group Databasebeta

← #16791165

Subgroups — #16791165

Order 3328.

330 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 106 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×#11718214C212yesmaximal, complemented
2#13129950C212yesmaximal, complemented
3C22⋊#88036C212yesmaximal, complemented
4C22×C16×D13C211yesmaximal, characteristic
5C22×C8×D13C411yescharacteristic
6C22×C13×C16C411yescharacteristic
7C22×#6090C2211yescharacteristic
8C2×C16×D13—24no—
9C2×C16×D13C411yescharacteristic
10C2×C16×D13C411yescharacteristic
11C2×C16×D13C2211yescharacteristic
12C2×C16×D13C2211yescharacteristic
13C2×#88036C2214yescomplemented
14#11718214—24no—
15C22×C4×D13C811yescharacteristic
16C22×C8×C13C2×C411yescharacteristic
17C22×#1055C811yescharacteristic
18C2×C8×D13—22no—
19C2×C8×D13—22no—
20C2×C8×D13C811yescharacteristic
21C2×C8×D13C811yescharacteristic
22C2×C8×D13C2×C411yescharacteristic
23C2×C8×D13C2×C411yescharacteristic
24C2×C13×C16—22no—
25C2×C13×C16C2×C411yescharacteristic
26C2×C13×C16C2×C411yescharacteristic
27C2×#6090—22no—
28C2×#6090C2×C411yescharacteristic
29C2×#6090C2311yescharacteristic
30C16×D13—22no—
31C16×D13—22no—
32C16×D13—22no—
33C16×D13D414yes—
34#88036—24no—
35#13553—131nomaximal, Sylow
36C23×D13C1611yescharacteristic
37C22×C4×C13C2×C811yescharacteristic
38C22×Dic13C1611yescharacteristic
39C2×C4×D13—22no—
40C2×C4×D13—22no—
41C2×C4×D13C1611yescharacteristic
42C2×C4×D13C1611yescharacteristic
43C2×C4×D13C2×C811yescharacteristic
44C2×C4×D13C2×C811yescharacteristic
45C2×C8×C13—21no—
46C2×C8×C13—21no—
47C2×C8×C13C2×C811yescharacteristic
48C2×C8×C13C22×C411yescharacteristic
49C2×#1055—22no—
50C2×#1055C2×C811yescharacteristic
51C2×#1055C2×C811yescharacteristic
52C8×D13—22no—
53C8×D13—21no—
54C8×D13—21no—
55C8×D13—22no—
56C8×D13C22⋊C412yes—
57C8×D13M1612yes—
58C13×C16—21no—
59C13×C16C22⋊C412yes—
60#6090—21no—
61#6090C2×D412yes—
62C23×C16—131no—
63C2×M64—132no—
64C22⋊C32—132no—
65C22⋊C32—132no—
66C23×C13C2×C1611yescharacteristic
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C22×D13C2×C1611yescharacteristic
71C22×D13C2×C1611yescharacteristic
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13C2×C1611yescharacteristic
75C2×C4×C13C22×C811yescharacteristic
76C2×Dic13—22no—
77C2×Dic13C2×C1611yescharacteristic
78C2×Dic13C2×C1611yescharacteristic
79C4×D13—22no—
80C4×D13—21no—
81C4×D13—21no—
82C4×D13—22no—
83C4×D13C22⋊C812yes—
84C4×D13M3212yes—
85C8×C13—21no—
86C8×C13C2×C22⋊C411yescharacteristic
87C8×C13C2×M1611yescharacteristic
88#1055—21no—
89#1055C22⋊C812yes—
90C23×C8—131no—
91C22×C16—131no—
92C22×C16—131no—
93C22×C16—131no—
94C22×C16—131no—
95C22×C16—131no—
96C22×C16—264no—
97C22×C16#26111yescharacteristic
98M64—264no—
99C2×C32—134no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13M6412yescomplemented
103C22×C13C22×C1611yescharacteristic
104C2×D13—28no—
105C2×D13—21no—
106C2×D13—21no—
107C2×D13—21no—
108C2×D13—21no—
109C2×D13C22⋊C1612yes—
110C2×D13M6412yescomplemented
111C4×C13—21no—
112C4×C13C2×C22⋊C811yescharacteristic
113C4×C13C2×M3211yescharacteristic
114Dic13—21no—
115Dic13C22⋊C1612yes—
116C23×C4—131no—
117C22×C8—131no—
118C22×C8—131no—
119C22×C8—131no—
120C22×C8—131no—
121C22×C8—131no—
122C22×C8—262no—
123C22×C8—262no—
124C22×C8C2×#26111yescharacteristic
125C2×C16—22no—
126C2×C16—131no—
127C2×C16—134no—
128C2×C16—131no—
129C2×C16—262no—
130C2×C16—262no—
131C2×C16—262no—
132C2×C16—262no—
133C2×C16C2×#26111yescharacteristic
134C2×C16C2×#26111yescharacteristic
135C32—264no—
136C2×C13—22no—
137C2×C13C2×C22⋊C1611yescharacteristic
138C2×C13C2×M6411yescharacteristic
139C2×C13C2×M6411yescharacteristic
140D13—22no—
141D13—22no—
142C24—131no—
143C22×C4—131no—
144C22×C4—131no—
145C22×C4—131no—
146C22×C4—131no—
147C22×C4—131no—
148C22×C4—262no—
149C22×C4—262no—
150C22×C4D13⋊C811yescharacteristic
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—131no—
154C2×C8—132no—
155C2×C8—132no—
156C2×C8—131no—
157C2×C8—262no—
158C2×C8—262no—
159C2×C8—262no—
160C2×C8—261no—
161C2×C8—261no—
162C2×C8D13⋊C811yescharacteristic
163C2×C8C22×#26111yescharacteristic
164C16—21no—
165C16—132no—
166C16—261no—
167C16C22⋊#26112yes—
168C13#1355311yescharacteristic, complemented, Sylow
169C23—131no—
170C23—131no—
171C23—262no—
172C23—262no—
173C23—262no—
174C23D13⋊C1611yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—131no—
178C2×C4—132no—
179C2×C4—132no—
180C2×C4—131no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—261no—
185C2×C4—261no—
186C2×C4D13⋊C1611yescharacteristic
187C2×C4C2×D13⋊C811yescharacteristic
188C8—21no—
189C8—132no—
190C8—261no—
191C8D13⋊M1611yescharacteristic
192C8C2×C22⋊#26111yescharacteristic
193C22—21no—
194C22—21no—
195C22—132no—
196C22—132no—
197C22—268no—
198C22—261no—
199C22—261no—
200C22—261no—
201C22—261no—
202C22#1171821412yescomplemented
203C22C2×D13⋊C1611yescharacteristic
204C4—21no—
205C4—132no—
206C4—261no—
207C4D13⋊M3211yescharacteristic
208C4D13⋊(C22⋊C8)11yescharacteristic
209C2—22no—
210C2—262no—
211C2—262no—
212C2D13⋊(C22⋊C16)11yescharacteristic
213C2D13⋊M6411yescharacteristic
214C2C2×#1171821411yescharacteristic
subgroupG/H
center, FrattiniC2×C8C22×#261
commutator, socleC22×C13C22×C16
FittingC22×C13×C16C4
prime radicalC23×D13C16
cosocleC2×#6090C23
hypercenterC22×C16#261
hypocenterC13#13553
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
1. C2×#11718214C2semidirect
2. #13129950C2semidirect
3. C22⋊#88036C2semidirect
13. C2×#88036C22semidirect
102. C22×C13M64semidirect
110. C2×D13M64semidirect
168. C13#13553semidirect
202. C22#11718214semidirect

Maximal subgroups

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

subgroupindex
C2×#117182142
#131299502
C22⋊#880362
C22×C16×D132
#1355313