Finite Group Databasebeta

← #13130746

Subgroups — #13130746

Order 1664.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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#11719227C211yesmaximal, characteristic
2#11719132C211yesmaximal, characteristic
3#11719116C211yesmaximal, characteristic
4#11718235C212yesmaximal, complemented
5#11718234C212yesmaximal, complemented
6C2×#6127C2211yescharacteristic
7#88237C2212yes—
8D13⋊M16C2212yes—
9C13×#117C411yescharacteristic, complemented
10C2×C4×Dic13C411yescharacteristic, complemented
11#88147—21no—
12#88141—21no—
13#88135—21no—
14#88135—21no—
15#88126C411yescharacteristic, complemented
16#88126C2211yescharacteristic
17C42×D13C411yescharacteristic, complemented
18C42×D13C2211yescharacteristic
19#88121—21no—
20#88119—21no—
21#88113—21no—
22#88107—21no—
23C22×C4×C13C2×C411yescharacteristic
24C2×C22⋊D13D411yescharacteristic
25C2×C22⋊D13D411yescharacteristic
26C22×Dic13—21no—
27#6127—22no—
28#6127—22no—
29C2×D52D411yescharacteristic
30C2×C4×D13—21no—
31C2×C4×D13—21no—
32C2×C4×D13C2×C411yescharacteristic
33C2×C4×D13C2311yescharacteristic
34C2×Dic26D411yescharacteristic
35C22⋊#261—22no—
36#6122—22no—
37C4⋊#261—22no—
38C4×#261—22no—
39#6118—22no—
40D13⋊C8—22no—
41C13×C4⋊C4—21no—
42C13×C22⋊C4—21no—
43C42×C13C2×C411yescharacteristic
44C42×C13C2×C411yescharacteristic
45#6103—21no—
46#6103—21no—
47#6101—21no—
48#6101—21no—
49C4×Dic13—21no—
50C4×Dic13—21no—
51C4×Dic13—21no—
52C4×Dic13C2×C411yescharacteristic
53C4×Dic13C2×C411yescharacteristic
54#1827—131nomaximal, Sylow
55C23×C13C22⋊C411yescharacteristic
56C22×D13C22⋊C411yescharacteristic
57C22×D13C2×D411yescharacteristic
58C2×#261—42no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13C22⋊C411yescharacteristic
64C2×C4×C13C22×C411yescharacteristic
65C22⋊D13—22no—
66C22⋊D13—22no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—42no—
70C2×Dic13C22⋊C411yescharacteristic
71C2×Dic13C2×D411yescharacteristic
72D52—22no—
73C4×D13—21no—
74C4×D13—21no—
75C4×D13—42no—
76C4×D13—42no—
77C4×D13#4112yes—
78C4×D13#4112yes—
79Dic26—22no—
80#1057—42no—
81C4×#41—131no—
82#413—131no—
83#410—131no—
84#339—132no—
85H(3,ℤ/4)—132no—
86C22×C13—21no—
87C22×C13—41no—
88C22×C13C2×C22⋊C411yescharacteristic
89C2×D13—21no—
90C2×D13—41no—
91C2×D13—41no—
92C2×D13#12312yes—
93#261—82no—
94C4×C13—21no—
95C4×C13—41no—
96C4×C13—41no—
97C4×C13#11711yescharacteristic
98C4×C13#11711yescharacteristic
99Dic13—22no—
100Dic13—21no—
101Dic13—41no—
102Dic13#12312yes—
103C2×#41—131no—
104C2×M16—132no—
105C4×Q8—261no—
106C4×D4—261no—
107C4×D4—261no—
108C4×D4—261no—
109#117—131no—
110#117—131no—
111#117—132no—
112#117#26111yescharacteristic, complemented
113C2×C42—131no—
114C2×C42—131no—
115C2×C42—131no—
116#101—261no—
117#100—261no—
118#99—261no—
119#99—261no—
120C2×C13—21no—
121C2×C13—41no—
122C2×C13#38111yescharacteristic
123D13—22no—
124D13—41no—
125#41—262no—
126#41—262no—
127C2×Q8—131no—
128C2×D4—131no—
129C2×D4—131no—
130C2×D4—131no—
131C22×C4—131no—
132C22×C4—131no—
133C22×C4—261no—
134C22×C4—261no—
135C22×C4—261no—
136C22×C4C2×#26111yescharacteristic
137M16—262no—
138M16—262no—
139C2×C8—262no—
140C4⋊C4—21no—
141C4⋊C4—261no—
142C4⋊C4—261no—
143C4⋊C4—262no—
144C22⋊C4—21no—
145C22⋊C4—261no—
146C22⋊C4—261no—
147C22⋊C4—262no—
148C42—131no—
149C42—131no—
150C42—261no—
151C42—261no—
152C42—262no—
153C42—261no—
154C42C2×#26111yescharacteristic
155C42C2×#26111yescharacteristic
156C13#182711yescharacteristic, complemented, Sylow
157C23—131no—
158C23—131no—
159C23C22⋊#26111yescharacteristic
160Q8—262no—
161D4—262no—
162D4—262no—
163D4—262no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—131no—
169C2×C4—132no—
170C2×C4—132no—
171C2×C4—131no—
172C2×C4—261no—
173C2×C4—261no—
174C2×C4—261no—
175C2×C4—261no—
176C2×C4—522no—
177C2×C4—522no—
178C2×C4—522no—
179C2×C4—522no—
180C2×C4C22⋊#26111yescharacteristic
181C2×C4C22×#26111yescharacteristic
182C8—522no—
183C22—21no—
184C22—41no—
185C22—132no—
186C22—261no—
187C22—521no—
188C22—521no—
189C22C2×C22⋊#26111yescharacteristic
190C4—21no—
191C4—41no—
192C4—41no—
193C4—132no—
194C4—262no—
195C4—261no—
196C4—521no—
197C4—1042no—
198C4#8823711yescharacteristic
199C4#8823711yescharacteristic
200C2—21no—
201C2—41no—
202C2—262no—
203C2—521no—
204C2#1171913511yescharacteristic
subgroupG/H
centerC4#88237
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#117C4
socleC2×C13#381
prime radicalC2×#6127C22
cosocleC2×C4×D13C23
hypercenter#117#261
hypocenterC13#1827
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C42 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #11718235C2semidirect
5. #11718234C2semidirect
9. C13×#117C4semidirect
10. C2×C4×Dic13C4semidirect
15. #88126C4semidirect
17. C42×D13C4semidirect
112. #117#261semidirect
156. C13#1827semidirect

Maximal subgroups

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

subgroupindex
#117192272
#117191322
#117191162
#117182352
#117182342
#182713