Finite Group Databasebeta

← #13130165

Subgroups — #13130165

Order 1664.

248 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C4×Q8×D13C211yesmaximal, characteristic
2#11719052C211yesmaximal, characteristic
3#11719051C211yesmaximal, characteristic
4Q8⋊#1057C212yesmaximal, complemented
5#11718244C212yesmaximal, complemented
6C2×Q8×D13C411yescharacteristic
7C2×#6118—21no—
8C4×Q8×C13C411yescharacteristic
9Q8×Dic13C2211yescharacteristic
10C4⋊C4×D13—21no—
11C4⋊C4×D13C411yescharacteristic
12#88141—21no—
13#88141C2211yescharacteristic
14C42×D13—21no—
15C42×D13C2211yescharacteristic
16C4×Dic26—21no—
17C4×Dic26C411yescharacteristic
18#88111—21no—
19C4⋊#1057—21no—
20C4⋊#1057—21no—
21C4⋊#1057C2212yes—
22C4×#1057C2212yes—
23C2×Q8×C13C2×C411yescharacteristic
24Q8×D13—22no—
25Q8×D13—22no—
26C2×C4×D13—21no—
27C2×C4×D13—21no—
28C2×C4×D13C2×C411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×C4×D13D411yescharacteristic
31C2×Dic26—21no—
32C2×Dic26C2×C411yescharacteristic
33C2×#1057—22no—
34C2×#1057—22no—
35#6118—42no—
36C13×C4⋊C4—21no—
37C13×C4⋊C4C2×C411yescharacteristic
38C42×C13—21no—
39C42×C13C2×C411yescharacteristic
40C4⋊Dic13—21no—
41C4⋊Dic13C2×C411yescharacteristic
42#6101—21no—
43#6101—21no—
44#6101—21no—
45C4×Dic13—21no—
46C4×Dic13—21no—
47C4×Dic13—21no—
48C4×Dic13D411yescharacteristic
49C4×Dic13D411yescharacteristic
50C4×Dic13C2311yescharacteristic
51#1487—131nomaximal, Sylow
52C22×D13C22⋊C411yescharacteristic
53Q8×C13—21no—
54Q8×C13M1612yescomplemented
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22⋊C411yescharacteristic
59C2×C4×C13C22×C411yescharacteristic
60C2×Dic13—21no—
61C2×Dic13—21no—
62C2×Dic13C22⋊C411yescharacteristic
63C2×Dic13C2×D411yescharacteristic
64C2×Dic13C2×D411yescharacteristic
65C4×D13—24no—
66C4×D13—21no—
67C4×D13—21no—
68C4×D13—41no—
69C4×D13—42no—
70C4×D13SD1612yes—
71C4×D13Q1612yes—
72Dic26—24no—
73Dic26—21no—
74Dic26M1612yescomplemented
75#1057—42no—
76#1057—42no—
77C2×C4×Q8—131no—
78#431—131no—
79#423—131no—
80Q8⋊C8—132no—
81Q8⋊C8—132no—
82C22×C13C2×C22⋊C411yescharacteristic
83C2×D13—21no—
84C2×D13—21no—
85C2×D13#10312yes—
86C4×C13—22no—
87C4×C13—21no—
88C4×C13—41no—
89C4×C13#10312yes—
90C4×C13C2×M1611yescharacteristic
91C4×C13C2×M1611yescharacteristic
92Dic13—21no—
93Dic13—22no—
94Dic13—21no—
95Dic13—41no—
96Dic13C2×SD1611yescharacteristic
97Dic13C2×Q1611yescharacteristic
98C22×Q8—131no—
99C2×M16—261no—
100C4×Q8—131no—
101C4×Q8—131no—
102C4×Q8—131no—
103C4×Q8—261no—
104C4×Q8—261no—
105C4×Q8#26111yescharacteristic
106C2×C4⋊C4—131no—
107C2×C4⋊C4—261no—
108C2×C42—131no—
109C2×C42—261no—
110C4⋊C8—132no—
111C4⋊C8—261no—
112C4⋊C8—261no—
113C22⋊C8—261no—
114C4×C8—132no—
115C2×C13#40711yescharacteristic
116C2×C13C2×#10311yescharacteristic
117C2×C13#42111yescharacteristic
118D13—22no—
119C2×Q8—131no—
120C2×Q8—261no—
121C2×Q8—262no—
122C2×Q8—262no—
123C2×Q8C2×#26111yescharacteristic
124C22×C4—131no—
125C22×C4—131no—
126C22×C4—131no—
127C22×C4—261no—
128C22×C4—261no—
129M16—522no—
130C2×C8—262no—
131C2×C8—262no—
132C4⋊C4—21no—
133C4⋊C4—131no—
134C4⋊C4—261no—
135C4⋊C4—261no—
136C4⋊C4—261no—
137C4⋊C4—261no—
138C4⋊C4C2×#26111yescharacteristic
139C42—21no—
140C42—131no—
141C42—131no—
142C42—131no—
143C42—261no—
144C42—261no—
145C42—261no—
146C42C2×#26111yescharacteristic
147C13#148711yescharacteristic, complemented, Sylow
148C23—131no—
149Q8—21no—
150Q8—132no—
151Q8—264no—
152Q8—261no—
153Q8#611812yescomplemented
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—131no—
157C2×C4—132no—
158C2×C4—132no—
159C2×C4—131no—
160C2×C4—131no—
161C2×C4—264no—
162C2×C4—261no—
163C2×C4—261no—
164C2×C4—261no—
165C2×C4—261no—
166C2×C4—521no—
167C2×C4—522no—
168C2×C4C22⋊#26111yescharacteristic
169C2×C4C22⋊#26111yescharacteristic
170C2×C4C22×#26111yescharacteristic
171C8—522no—
172C8—522no—
173C22—132no—
174C22—261no—
175C22—261no—
176C22C2×C22⋊#26111yescharacteristic
177C4—22no—
178C4—21no—
179C4—41no—
180C4—131no—
181C4—131no—
182C4—261no—
183C4—262no—
184C4—261no—
185C4—521no—
186C4#8811712yes—
187C4C2×#611811yescharacteristic
188C4D13⋊M1611yescharacteristic
189C2—262no—
190C2#1171912711yescharacteristic
191C2C2×#8811711yescharacteristic
192C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×Q8×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C22⋊C4
cosocleC4×Dic13C23
hypercenterC4×Q8#261
hypocenterC13#1487
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
4. Q8⋊#1057C2semidirect
5. #11718244C2semidirect
54. Q8×C13M16semidirect
74. Dic26M16semidirect
147. C13#1487semidirect
153. Q8#6118semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D132
#117190522
#117190512
Q8⋊#10572
#117182442
#148713