Finite Group Databasebeta

← #13130323

Subgroups — #13130323

Order 1664.

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

normal subgroups only

This group has 200 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#11719329C211yesmaximal, characteristic
2#11719130C211yesmaximal, characteristic, complemented
3#11719128C211yesmaximal, characteristic, complemented
4#11718299C212yesmaximal, complemented
5#11718242C212yesmaximal, complemented
6C13×C22⋊Q8C411yescharacteristic
7#88201C2211yescharacteristic
8Q8×Dic13C411yescharacteristic
9#88184C411yescharacteristic
10C2×C4×Dic13C2211yescharacteristic
11#88152—21no—
12#88147C411yescharacteristic
13#88146—21no—
14#88144C2211yescharacteristic
15#88140—21no—
16#88135—21no—
17C22⋊#1057—21no—
18C22⋊#1057—21no—
19#88112—21no—
20#88110C2212yes—
21#88110C2212yes—
22C4⋊#1057—21no—
23C2×Q8×C13C2×C411yescharacteristic
24C22×C4×C13C2×C411yescharacteristic
25C2×C22⋊D13—21no—
26C22×Dic13D411yescharacteristic
27C22×Dic13D411yescharacteristic
28C2×D52C2×C411yescharacteristic
29C2×C4×D13—21no—
30C2×#1057—22no—
31C2×#1057—22no—
32C13×C4⋊C4—21no—
33C13×C4⋊C4C2×C411yescharacteristic
34C13×C22⋊C4—21no—
35#6103—21no—
36#6103—21no—
37#6103—21no—
38#6103—21no—
39C4⋊Dic13—21no—
40C4⋊Dic13—21no—
41C4⋊Dic13C2×C411yescharacteristic
42#6101—21no—
43C4×Dic13—21no—
44C4×Dic13C2×C411yescharacteristic
45C4×Dic13D411yescharacteristic
46C4×Dic13D411yescharacteristic
47C4×Dic13C2311yescharacteristic
48#1535—131nomaximal, Sylow
49C23×C13C22⋊C411yescharacteristic
50C22×D13—21no—
51Q8×C13—41no—
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13—41no—
55C2×C4×C13C22⋊C411yescharacteristic
56C2×C4×C13C22×C411yescharacteristic
57C22⋊D13—42no—
58C2×Dic13—21no—
59C2×Dic13—41no—
60C2×Dic13—41no—
61C2×Dic13C22⋊C411yescharacteristic
62C2×Dic13C22⋊C411yescharacteristic
63C2×Dic13C2×D411yescharacteristic
64C2×Dic13C2×D411yescharacteristic
65D52—41no—
66C4×D13—42no—
67#1057—42no—
68#1057—42no—
69#529—131no—
70#432—131no—
71#432—131no—
72#330—132no—
73#329—132no—
74C22×C13—21no—
75C22×C13—21no—
76C22×C13—21no—
77C22×C13C2×C22⋊C411yescharacteristic
78C2×D13—41no—
79C2×D13—41no—
80C2×D13—41no—
81C4×C13—21no—
82C4×C13—21no—
83C4×C13—41no—
84C4×C13—41no—
85Dic13—21no—
86Dic13—21no—
87Dic13—21no—
88Dic13—21no—
89Dic13—41no—
90#126—261no—
91#125—131no—
92#124—131no—
93#123—261no—
94C22⋊Q8#26111yescharacteristic
95#121—131no—
96C4×Q8—131no—
97C4×D4—131no—
98C4×D4—261no—
99#117—261no—
100C2×C42—131no—
101C4⋊C8—261no—
102C4⋊C8—261no—
103C22⋊C8—261no—
104C22⋊C8—261no—
105#97—132no—
106#97—132no—
107C2×C13—41no—
108C2×C13#41311yescharacteristic
109C2×C13#42111yescharacteristic
110C2×C13#42111yescharacteristic
111D13—81no—
112C2×Q8C2×#26111yescharacteristic
113C2×D4—131no—
114C2×D4—261no—
115C22×C4—131no—
116C22×C4—131no—
117C22×C4—261no—
118C22×C4C2×#26111yescharacteristic
119C2×C8—262no—
120C2×C8—262no—
121C4⋊C4—21no—
122C4⋊C4—131no—
123C4⋊C4—261no—
124C4⋊C4—261no—
125C4⋊C4—261no—
126C4⋊C4C2×#26111yescharacteristic
127C22⋊C4—21no—
128C22⋊C4—261no—
129C22⋊C4—261no—
130C22⋊C4—261no—
131C22⋊C4—261no—
132C42—131no—
133C42—131no—
134C42—131no—
135C42—131no—
136C42—261no—
137C13#153511yescharacteristic, complemented, Sylow
138C23—261no—
139C23C22⋊#26111yescharacteristic
140Q8—41no—
141D4—521no—
142D4—522no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—131no—
147C2×C4—131no—
148C2×C4—131no—
149C2×C4—131no—
150C2×C4—261no—
151C2×C4—522no—
152C2×C4—521no—
153C2×C4—521no—
154C2×C4C22⋊#26111yescharacteristic
155C2×C4C22×#26111yescharacteristic
156C8—522no—
157C8—522no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—521no—
162C22—521no—
163C22—521no—
164C22C2×C22⋊#26111yescharacteristic
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—261no—
170C4—261no—
171C4—261no—
172C4—261no—
173C4—521no—
174C2—41no—
175C2—1041no—
176C2#1171914811yescharacteristic
177C2#1171915511yescharacteristic
178C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C22⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radical#88184C4
cosocleC4×Dic13C23
hypercenterC22⋊Q8#261
hypocenterC13#1535
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11719130C2semidirect
3. #11719128C2semidirect
4. #11718299C2semidirect
5. #11718242C2semidirect
137. C13#1535semidirect

Maximal subgroups

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

subgroupindex
#117193292
#117191302
#117191282
#117182992
#117182422
#153513