Finite Group Databasebeta

← #13130695

Subgroups — #13130695

Order 1664.

312 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 92 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×#88146C211yesmaximal, characteristic
2C2×#88112C211yesmaximal, characteristic, complemented
3C2×#88111C212yesmaximal
4C2×C4⋊#1057C211yesmaximal, characteristic, complemented
5#11718290C212yesmaximal, complemented
6C22×C4×D13C2211yescharacteristic
7C22×#1057C2212yes—
8C22×#1057C2212yes—
9C2×C13×C4⋊C4C411yescharacteristic
10C2×#6103C411yescharacteristic
11C2×#6103C411yescharacteristic
12C2×C4⋊Dic13C411yescharacteristic
13C2×C4×Dic13C2211yescharacteristic
14C2×C4×Dic13C2211yescharacteristic
15#88146—22no—
16#88146—22no—
17#88112—22no—
18#88111—24no—
19C4⋊#1057—22no—
20C23×D13C2×C411yescharacteristic
21C22×C4×C13C2×C411yescharacteristic
22C22×C4×C13C2×C411yescharacteristic
23C22×C4×C13C2×C411yescharacteristic
24C22×Dic13C2×C411yescharacteristic
25C22×Dic13C2×C411yescharacteristic
26C22×Dic13C2311yescharacteristic
27C2×C4×D13—21no—
28C2×C4×D13—21no—
29C2×C4×D13—21no—
30C2×C4×D13—21no—
31C2×C4×D13D412yes—
32C2×C4×D13Q812yes—
33C2×#1057—22no—
34C2×#1057—22no—
35C2×#1057—22no—
36C2×#1057—22no—
37C2×#1057—22no—
38C2×#1057—22no—
39C13×C4⋊C4—22no—
40#6103—22no—
41#6103—22no—
42C4⋊Dic13—22no—
43C4×Dic13—21no—
44C4×Dic13—21no—
45C4×Dic13D412yes—
46C4×Dic13D412yes—
47#1798—131nomaximal, Sylow
48C23×C13C22×C411yescharacteristic
49C22×D13—21no—
50C22×D13—21no—
51C22×D13—22no—
52C22×D13—22no—
53C22×D13C4⋊C412yes—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—22no—
57C2×C4×C13—21no—
58C2×C4×C13—22no—
59C2×C4×C13C22⋊C412yes—
60C2×C4×C13C4⋊C412yes—
61C2×Dic13—22no—
62C2×Dic13—21no—
63C2×Dic13—22no—
64C2×Dic13C22⋊C412yes—
65C2×Dic13C2×D411yescharacteristic
66C2×Dic13C2×D411yescharacteristic
67C2×Dic13C2×D411yescharacteristic
68C2×Dic13C2×Q811yescharacteristic
69C2×Dic13#4111yescharacteristic
70C2×Dic13#4111yescharacteristic
71C4×D13—22no—
72C4×D13—22no—
73C4×D13—22no—
74C4×D13—22no—
75#1057—42no—
76#1057—42no—
77C2×#117—131no—
78C2×C4⋊C8—131no—
79C2×C4⋊C8—131no—
80C2×C22⋊C8—132no—
81#336—132no—
82C22×C13C2×C22⋊C411yescharacteristic
83C22×C13C2×C4⋊C411yescharacteristic
84C22×C13#11711yescharacteristic
85C22×C13#13112yes—
86C22×C13#13112yes—
87C2×D13—22no—
88C2×D13—24no—
89C2×D13—41no—
90C2×D13—41no—
91C2×D13—42no—
92C4×C13—22no—
93C4×C13—22no—
94C4×C13—41no—
95Dic13—22no—
96Dic13—41no—
97Dic13#12111yescharacteristic
98Dic13#12111yescharacteristic
99Dic13C22⋊Q811yescharacteristic
100Dic13C22⋊Q811yescharacteristic
101C23×C4—131no—
102C22×C8—132no—
103C22×C8—132no—
104#117—262no—
105#117—262no—
106C2×C4⋊C4—131no—
107C2×C4⋊C4#26111yescharacteristic
108C2×C22⋊C4—131no—
109C2×C22⋊C4—131no—
110C2×C42—131no—
111C2×C42—131no—
112C4⋊C8—262no—
113C4⋊C8—262no—
114C22⋊C8—264no—
115C2×C13#38011yescharacteristic
116C2×C13#40811yescharacteristic
117C2×C13#40811yescharacteristic
118C2×C13#42412yes—
119C2×C13#43312yes—
120D13—42no—
121C24—131no—
122C22×C4—131no—
123C22×C4—131no—
124C22×C4—132no—
125C22×C4—132no—
126C22×C4—131no—
127C22×C4—261no—
128C22×C4—261no—
129C22×C4—261no—
130C22×C4—261no—
131C22×C4C2×#26111yescharacteristic
132C22×C4C2×#26111yescharacteristic
133C22×C4C2×#26111yescharacteristic
134C2×C8—262no—
135C2×C8—262no—
136C2×C8—262no—
137C2×C8—262no—
138C2×C8—262no—
139C2×C8—262no—
140C4⋊C4—22no—
141C4⋊C4—262no—
142C22⋊C4—262no—
143C22⋊C4—262no—
144C42—132no—
145C42—132no—
146C42—261no—
147C42—261no—
148C13#179811yescharacteristic, complemented, Sylow
149C23—132no—
150C23—261no—
151C23—262no—
152C23—262no—
153C23—261no—
154C23C22×#26111yescharacteristic
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—131no—
161C2×C4—131no—
162C2×C4—131no—
163C2×C4—131no—
164C2×C4—131no—
165C2×C4—131no—
166C2×C4—132no—
167C2×C4—262no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4—262no—
173C2×C4—261no—
174C2×C4C4⋊#26112yes—
175C2×C4C22⋊#26112yes—
176C8—522no—
177C8—522no—
178C22—264no—
179C22—262no—
180C22—522no—
181C22—521no—
182C22—521no—
183C22C2×C4⋊#26111yescharacteristic
184C22#8823711yescharacteristic
185C22#8823812yes—
186C22#8824012yes—
187C22C2×C22⋊#26111yescharacteristic
188C4—22no—
189C4—22no—
190C4—41no—
191C4—131no—
192C4—131no—
193C4—131no—
194C4—131no—
195C4—262no—
196C4—521no—
197C2—522no—
198C2#1171907712yes—
199C2#1171907912yes—
200C2#1171913611yescharacteristic
201C2#1171914611yescharacteristic
202C2#1171915911yescharacteristic
subgroupG/H
center, FrattiniC23C22×#261
commutator, socleC23×C13C22×C4
FittingC2×C13×C4⋊C4C4
prime radicalC23×D13C2×C4
cosocleC22×Dic13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1798
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#88112C2semidirect
4. C2×C4⋊#1057C2semidirect
5. #11718290C2semidirect
148. C13#1798semidirect

Maximal subgroups

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

subgroupindex
C2×#881462
C2×#881122
C2×#881112
C2×C4⋊#10572
#117182902
#179813