Finite Group Databasebeta

← #13116009

Subgroups — #13116009

Order 1664.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#11719175C211yesmaximal, characteristic, complemented
2#11718800C211yesmaximal, characteristic
3#11718667C211yesmaximal, characteristic
4C2×#88045C211yesmaximal, characteristic
5C13×#339C211yesmaximal, characteristic, complemented
6#11718148C211yesmaximal, characteristic, complemented
7#11718123C211yesmaximal, characteristic, complemented
8C2×#6127C2211yescharacteristic
9C2×C13×M16C2211yescharacteristic
10C13×#117C2211yescharacteristic
11C2×C42×C13C2211yescharacteristic
12#88180C2211yescharacteristic
13#88180C2211yescharacteristic
14#88178—22no—
15C2×#6099C2211yescharacteristic
16#88124—21no—
17#88123—21no—
18C4×Dic26—22no—
19#88065—22no—
20#88046—22no—
21#88045—21no—
22#88045—21no—
23C22×C4×C13—21no—
24C22×C4×C13C2311yescharacteristic
25C2×C22⋊D13—21no—
26#6127—21no—
27#6127—21no—
28#6127—21no—
29#6127—21no—
30C2×D52Q811yescharacteristic, complemented
31C2×C4×D13—21no—
32C2×Dic26—22no—
33C2×Dic26Q811yescharacteristic, complemented
34C13×M16—21no—
35C13×M16—21no—
36C2×C8×C13—21no—
37C13×C4⋊C4—21no—
38C13×C22⋊C4—21no—
39C42×C13—21no—
40C42×C13—21no—
41C42×C13D411yescharacteristic
42C42×C13D411yescharacteristic
43C22⋊Dic13—21no—
44C22⋊Dic13D412yes—
45C4⋊Dic13—22no—
46C4⋊Dic13—21no—
47C4⋊Dic13—21no—
48#6101—24no—
49C4×Dic13—21no—
50C4×Dic13D412yes—
51#6099—21no—
52#6099—21no—
53C2×#1055—21no—
54#2031—131nomaximal, Sylow
55C23×C13C2×D411yescharacteristic
56C22×D13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—42no—
60C2×C4×C13—41no—
61C2×C4×C13C2×D411yescharacteristic
62C2×C4×C13C2×D411yescharacteristic
63C2×C4×C13C2×Q811yescharacteristic
64C2×C4×C13#4111yescharacteristic
65C2×C4×C13#4111yescharacteristic
66C2×C4×C13#4111yescharacteristic
67C22⋊D13—41no—
68C22⋊D13—41no—
69C2×Dic13—22no—
70C2×Dic13—22no—
71C2×Dic13—21no—
72D52—21no—
73D52—21no—
74C4×D13—41no—
75C4×D13—41no—
76Dic26—21no—
77Dic26—21no—
78Dic26—44no—
79C8×C13—41no—
80#1055—41no—
81#533—131no—
82#421—131no—
83C2×#104—131no—
84#410—131no—
85#344—131no—
86#339D1311yescharacteristic, complemented
87H(3,ℤ/4)—131no—
88C22×C13—41no—
89C22×C13#12011yescharacteristic
90C22×C13C22⋊Q811yescharacteristic
91C22×C13#12411yescharacteristic
92C2×D13—41no—
93C2×D13—81no—
94C4×C13—22no—
95C4×C13—41no—
96C4×C13—81no—
97C4×C13C22⋊Q811yescharacteristic
98C4×C13C22⋊Q811yescharacteristic
99C4×C13#12411yescharacteristic
100C4×C13#12411yescharacteristic
101Dic13—42no—
102Dic13—42no—
103Dic13—41no—
104C2×#41—131no—
105C2×M16—131no—
106C2×M16C2×D1311yescharacteristic
107C4⋊Q8—261no—
108#125—261no—
109C22⋊Q8—262no—
110C4×Q8—262no—
111#117—131no—
112#117—131no—
113#117C2×D1311yescharacteristic
114C2×C42C2×D1311yescharacteristic
115#104—262no—
116#104—261no—
117#104—261no—
118#99—262no—
119C2×C13—21no—
120C2×C13—21no—
121C2×C13—21no—
122C2×C13#39311yescharacteristic
123D13—81no—
124#41—261no—
125#41—261no—
126#41—261no—
127#41—261no—
128C2×Q8—131no—
129C2×Q8—262no—
130C2×D4—131no—
131C2×D4—261no—
132C22×C4—21no—
133C22×C4—261no—
134C22×C4C22×D1311yescharacteristic
135M16—21no—
136M16—21no—
137M16—261no—
138M16—261no—
139C2×C8—21no—
140C2×C8—261no—
141C4⋊C4—21no—
142C4⋊C4—264no—
143C4⋊C4—262no—
144C4⋊C4—261no—
145C4⋊C4—261no—
146C22⋊C4—21no—
147C22⋊C4—132no—
148C22⋊C4—261no—
149C42—21no—
150C42—21no—
151C42—132no—
152C42—261no—
153C42D5211yescharacteristic
154C42D5211yescharacteristic
155C13#203111yescharacteristic, complemented, Sylow
156C23—261no—
157C23D4×D1311yescharacteristic
158Q8—261no—
159Q8—261no—
160Q8—524no—
161D4—261no—
162D4—261no—
163D4—521no—
164D4—521no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—261no—
172C2×C4—521no—
173C2×C4—521no—
174C2×C4C2×D5211yescharacteristic
175C2×C4#612711yescharacteristic
176C2×C4#612711yescharacteristic
177C2×C4D4×D1311yescharacteristic
178C2×C4#612911yescharacteristic
179C2×C4Q8×D1311yescharacteristic
180C8—41no—
181C8—521no—
182C22—41no—
183C22—521no—
184C22—1041no—
185C22#8813611yescharacteristic
186C22#8813911yescharacteristic
187C22#8815011yescharacteristic
188C4—22no—
189C4—41no—
190C4—81no—
191C4—522no—
192C4—522no—
193C4—521no—
194C4#8812911yescharacteristic
195C4#8813911yescharacteristic
196C4#8815011yescharacteristic
197C4#8815111yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—1041no—
202C2#1171833411yescharacteristic
subgroupG/H
centerC4#88139
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#339C2
socleC2×C13#393
prime radicalC2×#6127C22
hypercenter#339D13
hypocenterC13#2031
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #11719175C2semidirect
5. C13×#339C2semidirect
6. #11718148C2semidirect
7. #11718123C2semidirect
30. C2×D52Q8semidirect
33. C2×Dic26Q8semidirect
86. #339D13semidirect
155. C13#2031semidirect

Maximal subgroups

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

subgroupindex
#117191752
#117188002
#117186672
C2×#880452
C13×#3392
#117181482
#117181232
#203113