Finite Group Databasebeta

← #13130193

Subgroups — #13130193

Order 1664.

216 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 60 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#11719129C211yesmaximal, characteristic, complemented
3#11719119C211yesmaximal, characteristic, complemented
4Q8⋊#1057C212yesmaximal, complemented
5#11718243C212yesmaximal, complemented
6C2×#6122—21no—
7C13×C22⋊Q8C411yescharacteristic
8#88201C411yescharacteristic
9Q8×Dic13C2211yescharacteristic
10#88184C411yescharacteristic
11C2×C4×Dic13C2211yescharacteristic
12#88152—21no—
13#88147C2211yescharacteristic
14#88146—21no—
15#88144C411yescharacteristic
16#88140—21no—
17#88135—21no—
18C22⋊#1057—21no—
19#88112—21no—
20C4⋊#1057—21no—
21C4⋊#1057C2212yes—
22C4×#1057C2212yes—
23C2×Q8×C13C2×C411yescharacteristic
24C22×C4×C13C2×C411yescharacteristic
25C2×C22⋊D13—21no—
26C22×Dic13D411yescharacteristic
27C22×Dic13D411yescharacteristic
28C2×D52C2×C411yescharacteristic
29C2×C4×D13—21no—
30#6122—42no—
31C2×#1057—22no—
32C2×#1057—22no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4C2×C411yescharacteristic
35C13×C22⋊C4—21no—
36#6103—21no—
37#6103—21no—
38#6103—21no—
39#6103—21no—
40C4⋊Dic13—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13C2×C411yescharacteristic
43#6101—21no—
44C4×Dic13—21no—
45C4×Dic13C2×C411yescharacteristic
46C4×Dic13D411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13C2311yescharacteristic
49#1495—131nomaximal, Sylow
50C23×C13C22⋊C411yescharacteristic
51C22×D13—21no—
52Q8×C13—22no—
53C2×C4×C13—22no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13C22⋊C411yescharacteristic
57C2×C4×C13C22×C411yescharacteristic
58C22⋊D13—42no—
59C2×Dic13—21no—
60C2×Dic13—21no—
61C2×Dic13—21no—
62C2×Dic13—41no—
63C2×Dic13C22⋊C411yescharacteristic
64C2×Dic13C22⋊C411yescharacteristic
65C2×Dic13C2×D411yescharacteristic
66C2×Dic13C2×D411yescharacteristic
67D52—22no—
68C4×D13—41no—
69C4×D13—41no—
70#1057—42no—
71#1057—42no—
72#529—131no—
73#431—131no—
74#423—131no—
75Q8⋊C8—132no—
76D4⋊C8—132no—
77C22×C13—21no—
78C22×C13—21no—
79C22×C13—21no—
80C22×C13C2×C22⋊C411yescharacteristic
81C2×D13—41no—
82C2×D13—41no—
83C2×D13—41no—
84C4×C13—21no—
85C4×C13—41no—
86C4×C13—41no—
87C4×C13#13112yes—
88Dic13—21no—
89Dic13—21no—
90Dic13—21no—
91Dic13—41no—
92Dic13AGL(1,ℤ/8)11yescharacteristic
93Dic13#13711yescharacteristic
94C2×M16—261no—
95#126—261no—
96#125—131no—
97#124—131no—
98#123—261no—
99C22⋊Q8#26111yescharacteristic
100#121—131no—
101C4×Q8—131no—
102C4×D4—131no—
103C4×D4—261no—
104#117—261no—
105C2×C42—131no—
106C4⋊C8—132no—
107C4⋊C8—261no—
108C4⋊C8—261no—
109C22⋊C8—261no—
110C4×C8—132no—
111C2×C13—41no—
112C2×C13#40811yescharacteristic
113C2×C13#41711yescharacteristic
114C2×C13#42111yescharacteristic
115D13—81no—
116C2×Q8C2×#26111yescharacteristic
117C2×D4—131no—
118C2×D4—261no—
119C22×C4—131no—
120C22×C4—131no—
121C22×C4—261no—
122C22×C4C2×#26111yescharacteristic
123M16—522no—
124C2×C8—262no—
125C2×C8—262no—
126C4⋊C4—21no—
127C4⋊C4—131no—
128C4⋊C4—261no—
129C4⋊C4—261no—
130C4⋊C4—261no—
131C4⋊C4C2×#26111yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—261no—
134C22⋊C4—261no—
135C22⋊C4—261no—
136C22⋊C4—261no—
137C42—131no—
138C42—131no—
139C42—131no—
140C42—131no—
141C42—261no—
142C13#149511yescharacteristic, complemented, Sylow
143C23—261no—
144C23C22⋊#26111yescharacteristic
145Q8—22no—
146D4—262no—
147D4—522no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—131no—
152C2×C4—131no—
153C2×C4—131no—
154C2×C4—131no—
155C2×C4—261no—
156C2×C4—261no—
157C2×C4—261no—
158C2×C4—521no—
159C2×C4—521no—
160C2×C4—521no—
161C2×C4C22⋊#26111yescharacteristic
162C2×C4C22×#26111yescharacteristic
163C8—522no—
164C8—522no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—521no—
169C22—521no—
170C22—521no—
171C22C2×C22⋊#26111yescharacteristic
172C4—21no—
173C4—41no—
174C4—41no—
175C4—131no—
176C4—131no—
177C4—261no—
178C4—261no—
179C4—261no—
180C4—521no—
181C4#8823812yes—
182C2—41no—
183C2—1041no—
184C2#1171914611yescharacteristic
185C2#1171915511yescharacteristic
186C2#1171916411yescharacteristic
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#1495
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11719129C2semidirect
3. #11719119C2semidirect
4. Q8⋊#1057C2semidirect
5. #11718243C2semidirect
142. C13#1495semidirect

Maximal subgroups

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

subgroupindex
#117193292
#117191292
#117191192
Q8⋊#10572
#117182432
#149513