Finite Group Databasebeta

← #13131098

Subgroups — #13131098

Order 1664.

234 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 54 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#11719521C211yesmaximal, characteristic
2#11719132C211yesmaximal, characteristic
3#11719116C211yesmaximal, characteristic
4#11718288C214yesmaximal, complemented
5C22×Q8×C13C411yescharacteristic, complemented
6C2×#6127C2211yescharacteristic
7#88237—21no—
8D13⋊M16—21no—
9#88201—21no—
10#88200—21no—
11#88200—21no—
12#88198—21no—
13#88183C412yescomplemented
14#88183C2212yes—
15#88180C411yescharacteristic, complemented
16#88121C2212yes—
17#88119C2212yes—
18#88113—21no—
19#88107—21no—
20C2×Q8×C13—21no—
21C2×Q8×C13—21no—
22C2×Q8×C13—41no—
23C2×Q8×C13—41no—
24C22×C4×C13C2×C412yes—
25C22×C4×C13C2×C411yescharacteristic
26C2×C22⋊D13C2×C411yescharacteristic
27C2×C22⋊D13C2311yescharacteristic
28#6127—41no—
29#6127—41no—
30C2×D52D411yescharacteristic
31C2×C4×D13D411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×Dic26D411yescharacteristic
34C22⋊#261—22no—
35#6122—22no—
36C4⋊#261—41no—
37C4×#261—41no—
38#6118—41no—
39D13⋊C8—41no—
40C22⋊Dic13C2×C412yes—
41#6103—22no—
42#6103—22no—
43C4⋊Dic13—21no—
44#6101—22no—
45#6101—22no—
46C4×Dic13—21no—
47#2123—131nomaximal, Sylow
48C23×C13C22×C411yescharacteristic
49C22×D13C22⋊C411yescharacteristic
50C22×D13C2×D411yescharacteristic
51C2×#261—42no—
52Q8×C13—42no—
53Q8×C13—41no—
54Q8×C13—41no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—22no—
58C2×C4×C13—42no—
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22⋊C411yescharacteristic
61C22⋊D13—41no—
62C22⋊D13—41no—
63C2×Dic13—22no—
64C2×Dic13C22⋊C411yescharacteristic
65C2×Dic13C2×D411yescharacteristic
66D52—41no—
67C4×D13—21no—
68C4×D13—21no—
69C4×D13—21no—
70C4×D13—21no—
71Dic26—41no—
72#1057—42no—
73#536—131no—
74#413—131no—
75#410—131no—
76#352—134no—
77C22×C13—21no—
78C22×C13—41no—
79C22×C13C2×C22⋊C411yescharacteristic
80C2×D13—21no—
81C2×D13—21no—
82C2×D13—41no—
83C2×D13—41no—
84#261—82no—
85C4×C13—21no—
86C4×C13—42no—
87C4×C13#9911yescharacteristic
88C4×C13#9911yescharacteristic
89Dic13—21no—
90Dic13—21no—
91Dic13—42no—
92C2×#41—131no—
93C22×Q8#26111yescharacteristic, complemented
94C2×M16—261no—
95C4⋊Q8—261no—
96#124—261no—
97#123—132no—
98#123—132no—
99C22⋊Q8—261no—
100C22⋊Q8—261no—
101#117—131no—
102#117—261no—
103#101—261no—
104#100—132no—
105#99—132no—
106#99—261no—
107C2×C13—21no—
108C2×C13—41no—
109C2×C13C2×#9911yescharacteristic
110D13—41no—
111D13—41no—
112#41—521no—
113#41—521no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—41no—
117C2×Q8—41no—
118C2×Q8—131no—
119C2×D4—131no—
120C2×D4—131no—
121C2×D4—131no—
122C22×C4—131no—
123C22×C4—131no—
124C22×C4C2×#26112yes—
125C22×C4C2×#26111yescharacteristic
126M16—262no—
127M16—521no—
128C2×C8—521no—
129C4⋊C4—262no—
130C4⋊C4—262no—
131C4⋊C4—261no—
132C4⋊C4—521no—
133C22⋊C4—132no—
134C22⋊C4—262no—
135C22⋊C4—262no—
136C22⋊C4—262no—
137C42—261no—
138C42—521no—
139C13#212311yescharacteristic, complemented, Sylow
140C23—131no—
141C23—131no—
142C23C22×#26111yescharacteristic
143Q8—42no—
144Q8—41no—
145Q8—41no—
146Q8—521no—
147D4—521no—
148D4—521no—
149D4—521no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—131no—
155C2×C4—131no—
156C2×C4—261no—
157C2×C4—261no—
158C2×C4—261no—
159C2×C4—261no—
160C2×C4—262no—
161C2×C4—522no—
162C2×C4C22⋊#26111yescharacteristic
163C2×C4C22⋊#26111yescharacteristic
164C8—522no—
165C22—21no—
166C22—41no—
167C22—261no—
168C22—261no—
169C22—521no—
170C22—521no—
171C22C2×C22⋊#26111yescharacteristic
172C4—21no—
173C4—42no—
174C4—261no—
175C4—261no—
176C4—522no—
177C4—1042no—
178C4#8811911yescharacteristic
179C4#8811911yescharacteristic
180C2—21no—
181C2—41no—
182C2—521no—
183C2—521no—
184C2C2×#8811911yescharacteristic
subgroupG/H
centerC2C2×#88119
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC22×Q8×C13C4
socleC2×C13C2×#99
prime radicalC2×#6127C22
cosocleC2×C22⋊D13C23
hypercenterC22×Q8#261
hypocenterC13#2123
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #11718288C2semidirect
5. C22×Q8×C13C4semidirect
13. #88183C4semidirect
15. #88180C4semidirect
93. C22×Q8#261semidirect
139. C13#2123semidirect

Maximal subgroups

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

subgroupindex
#117195212
#117191322
#117191162
#117182882
#212313