Finite Group Databasebeta

← #13130921

Subgroups — #13130921

Order 1664.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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#11719153C211yesmaximal, characteristic
2C2×#88117C211yesmaximal, characteristic
3#11719099C211yesmaximal, characteristic
4#11719098C211yesmaximal, characteristic
5D13×#101C211yesmaximal, characteristic
6#11718273C211yesmaximal, characteristic
7#11718271C211yesmaximal, characteristic
8C2×Q8×D13C2211yescharacteristic
9#88237C2211yescharacteristic
10C2×C4⋊#261C2211yescharacteristic
11D13⋊M16C2211yescharacteristic
12C2×D13⋊C8C2211yescharacteristic
13M16×D13C2211yescharacteristic
14M16×D13C2211yescharacteristic
15#88117—21no—
16#88117—21no—
17#88117—21no—
18#88117—21no—
19#88102—21no—
20#88101—21no—
21#88100—21no—
22C8×#261—21no—
23C13×#101C411yescharacteristic, complemented
24#88076C411yescharacteristic, complemented
25#88064C411yescharacteristic, complemented
26#88064C411yescharacteristic, complemented
27C22×#261—21no—
28C2×Q8×C13C2×C411yescharacteristic
29Q8×D13—21no—
30Q8×D13—21no—
31Q8×D13—21no—
32Q8×D13—21no—
33C2×C4×D13—21no—
34C2×C4×D13C2311yescharacteristic
35C2×Dic26—21no—
36C2×Dic26C2×C411yescharacteristic
37C22⋊#261—21no—
38#6122—21no—
39C2×#1057—21no—
40C4⋊#261—21no—
41C4⋊#261—21no—
42C4⋊#261D411yescharacteristic
43C4⋊#261D411yescharacteristic
44C4×#261—21no—
45#6118—21no—
46D13⋊C8—21no—
47D13⋊C8—21no—
48D13⋊C8D411yescharacteristic
49D13⋊C8D411yescharacteristic
50C13×M16C2×C411yescharacteristic
51C13×M16C2×C411yescharacteristic
52#6099C2×C411yescharacteristic
53#6099C2×C411yescharacteristic
54#6094—21no—
55#6094—21no—
56C8×D13—21no—
57C8×D13—21no—
58#1930—131nomaximal, Sylow
59C22×D13#4111yescharacteristic
60C2×#261—21no—
61C2×#261—21no—
62C2×#261—41no—
63C2×#261—81no—
64Q8×C13—21no—
65Q8×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13C22×C411yescharacteristic
68C2×Dic13—21no—
69C2×Dic13#4111yescharacteristic
70C4×D13—41no—
71C4×D13—41no—
72C4×D13C2×D411yescharacteristic
73C4×D13C2×D411yescharacteristic
74C4×D13#4111yescharacteristic
75C4×D13#4111yescharacteristic
76Dic26—21no—
77Dic26—21no—
78Dic26—41no—
79Dic26—41no—
80#1057—21no—
81#1057—21no—
82#1057—41no—
83C8×C13—21no—
84C8×C13—21no—
85#1055—21no—
86#1055—21no—
87#428—131no—
88#419—131no—
89C2×#103—131no—
90C2×#101—131no—
91#405—131no—
92#343—131no—
93#341—131no—
94C22×C13#11711yescharacteristic
95C2×D13—21no—
96C2×D13—21no—
97C2×D13#12111yescharacteristic
98C2×D13#12611yescharacteristic
99#261—41no—
100#261—41no—
101#261—81no—
102C4×C13—41no—
103C4×C13C4×D411yescharacteristic
104C4×C13C4×D411yescharacteristic
105Dic13—41no—
106Dic13#12311yescharacteristic
107Dic13#12411yescharacteristic
108C22×Q8—131no—
109C2×M16—131no—
110C2×M16—131no—
111C2×M16—131no—
112C22×C8—131no—
113#117—131no—
114C2×C4⋊C4—131no—
115#107—261no—
116#106—261no—
117#103—261no—
118#103—261no—
119#103—261no—
120#103—261no—
121#101—131no—
122#101—131no—
123#101—131no—
124#101#26111yescharacteristic, complemented
125#97—261no—
126C4×C8—261no—
127C2×C13—21no—
128C2×C13#38811yescharacteristic
129D13—21no—
130D13#47111yescharacteristic
131D13#47311yescharacteristic
132C2×Q8—131no—
133C2×Q8—261no—
134C2×Q8—261no—
135C2×Q8—261no—
136C2×Q8—261no—
137C2×Q8—261no—
138C2×Q8C2×#26111yescharacteristic
139C22×C4—131no—
140C22×C4—261no—
141C22×C4—261no—
142M16—131no—
143M16—131no—
144M16—261no—
145M16—261no—
146M16—261no—
147M16—261no—
148M16C2×#26111yescharacteristic
149M16C2×#26111yescharacteristic
150C2×C8—131no—
151C2×C8—131no—
152C2×C8—261no—
153C2×C8—261no—
154C2×C8—261no—
155C2×C8—261no—
156C2×C8—261no—
157C4⋊C4—131no—
158C4⋊C4—131no—
159C4⋊C4—261no—
160C4⋊C4—261no—
161C22⋊C4—261no—
162C42—261no—
163C13#193011yescharacteristic, complemented, Sylow
164C23—131no—
165Q8—21no—
166Q8—21no—
167Q8—261no—
168Q8—261no—
169Q8—521no—
170Q8—521no—
171C2×C4—21no—
172C2×C4—131no—
173C2×C4—131no—
174C2×C4—131no—
175C2×C4—131no—
176C2×C4—131no—
177C2×C4—261no—
178C2×C4—261no—
179C2×C4—261no—
180C2×C4—521no—
181C2×C4—521no—
182C2×C4—521no—
183C2×C4—1041no—
184C2×C4C22×#26111yescharacteristic
185C8—21no—
186C8—21no—
187C8—261no—
188C8—261no—
189C8—261no—
190C8—261no—
191C8—521no—
192C22—131no—
193C22—131no—
194C22—261no—
195C22—261no—
196C22#8823711yescharacteristic
197C4—41no—
198C4—131no—
199C4—131no—
200C4—521no—
201C4—521no—
202C4—521no—
203C4—1041no—
204C4D4×#26111yescharacteristic
205C4D4×#26111yescharacteristic
206C2—21no—
207C2—131no—
208C2—131no—
209C2—261no—
210C2#1171907111yescharacteristic
subgroupG/H
centerC2#11719071
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#101C4
socleC2×C13#388
prime radicalC22×D13#41
cosocleC2×C4×D13C23
hypercenter#101#261
hypocenterC13#1930
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
23. C13×#101C4semidirect
24. #88076C4semidirect
25. #88064C4semidirect
26. #88064C4semidirect
124. #101#261semidirect
163. C13#1930semidirect

Maximal subgroups

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

subgroupindex
#117191532
C2×#881172
#117190992
#117190982
D13×#1012
#117182732
#117182712
#193013