Finite Group Databasebeta

← #16777318

Subgroups — #16777318

Order 3328.

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

normal subgroups only

This group has 248 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#13131073C211yesmaximal, characteristic
2#13130591C211yesmaximal, characteristic
3#13116451C211yesmaximal, characteristic
4C2×#88155C2211yescharacteristic
5#11719132C411yescharacteristic
6#11719116C411yescharacteristic
7#11719089—21no—
8D13⋊M32—21no—
9C2×C13×M32C411yescharacteristic, complemented
10C22×#6090C411yescharacteristic, complemented
11#11718284C412yescomplemented
12#11718266—21no—
13#11718263—21no—
14#11718099—21no—
15#11718099—21no—
16C2×#6127C2×C411yescharacteristic
17#88237—21no—
18D13⋊M16—21no—
19C22×C8×C13C2×C411yescharacteristic
20C2×#6099C2×C411yescharacteristic
21#88155—41no—
22#88155—41no—
23C2×#6094D411yescharacteristic
24C2×#6094Q811yescharacteristic
25C2×C8×D13D411yescharacteristic
26C2×C8×D13D411yescharacteristic
27#88121—21no—
28#88119—21no—
29#88113C812yes—
30#88107C812yes—
31#88106—22no—
32#88100—41no—
33C8×#261—41no—
34#88098—41no—
35D13⋊C16—41no—
36C13×M32—41no—
37C2×C13×C16—21no—
38C2×#6090—21no—
39C2×#6090—41no—
40#7208—131nomaximal, Sylow
41C22×C4×C13C4211yescharacteristic
42C2×C22⋊D13M1611yescharacteristic
43C2×C22⋊D13M1611yescharacteristic
44#6127—41no—
45#6127—41no—
46C2×D52C2×C811yescharacteristic
47C2×C4×D13C22⋊C411yescharacteristic
48C2×C4×D13C4⋊C411yescharacteristic
49C2×Dic26C2×C811yescharacteristic
50C22⋊#261—22no—
51#6122—22no—
52C4⋊#261—41no—
53C4×#261—41no—
54#6118—41no—
55D13⋊C8—41no—
56C2×C8×C13—21no—
57C2×C8×C13—21no—
58C2×C8×C13C22⋊C411yescharacteristic
59C2×C8×C13C4⋊C411yescharacteristic
60#6099—41no—
61C2×#1055C22⋊C411yescharacteristic
62C2×#1055C4⋊C411yescharacteristic
63#6094—41no—
64#6094—41no—
65C8×D13—21no—
66C8×D13—21no—
67C8×D13—21no—
68C8×D13—21no—
69#6092—42no—
70C13×C16—41no—
71#6090—41no—
72#2115—131no—
73#2113—131no—
74#1757—131no—
75C23×C13#9711yescharacteristic
76C22×D13C22⋊C811yescharacteristic
77C22×D13C4⋊C811yescharacteristic
78C2×#261—42no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13#9511yescharacteristic
82C2×C4×C13C4×C811yescharacteristic
83C22⋊D13—41no—
84C22⋊D13—41no—
85C2×Dic13C22⋊C811yescharacteristic
86C2×Dic13C4⋊C811yescharacteristic
87D52—41no—
88C4×D13—21no—
89C4×D13—21no—
90C4×D13—21no—
91C4×D13—21no—
92Dic26—41no—
93#1057—42no—
94C8×C13—21no—
95C8×C13#9911yescharacteristic
96C8×C13#9911yescharacteristic
97#1055—21no—
98#1055—21no—
99C2×#131—131no—
100C2×M32—261no—
101C2×M32#26111yescharacteristic, complemented
102C22×C16—131no—
103#413—131no—
104#410—131no—
105#405—261no—
106#349—132no—
107#349—261no—
108C22⋊C16—261no—
109C22⋊C16—261no—
110#344—261no—
111C22×C13—21no—
112C22×C13—41no—
113C22×C13#33611yescharacteristic
114C2×D13—21no—
115C2×D13—21no—
116C2×D13—41no—
117C2×D13—41no—
118#261—82no—
119C4×C13—21no—
120C4×C13#34211yescharacteristic
121C4×C13#34411yescharacteristic
122Dic13—21no—
123Dic13—21no—
124C2×#41—131no—
125#131—521no—
126#131—521no—
127C2×M16—131no—
128C2×M16—131no—
129C2×M16—131no—
130C2×M16—261no—
131C22×C8—131no—
132C22×C8—131no—
133C22×C8C2×#26111yescharacteristic
134#117—261no—
135M32—41no—
136M32—262no—
137M32—521no—
138C2×C16—21no—
139C2×C16—261no—
140C2×C16—521no—
141C2×C16—521no—
142#101—132no—
143#100—261no—
144#99—132no—
145#99—261no—
146#97—521no—
147C4×C8—521no—
148C2×C13—21no—
149C2×C13—41no—
150C2×C13#128211yescharacteristic
151D13—41no—
152D13—41no—
153#41—521no—
154#41—521no—
155C2×Q8—131no—
156C2×D4—131no—
157C2×D4—131no—
158C2×D4—131no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4C4×#26111yescharacteristic
162M16—262no—
163M16—521no—
164M16—521no—
165M16—521no—
166M16—521no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—131no—
170C2×C8—131no—
171C2×C8—261no—
172C2×C8—261no—
173C2×C8—261no—
174C2×C8—261no—
175C2×C8—521no—
176C2×C8C4⋊#26111yescharacteristic
177C2×C8C22⋊#26111yescharacteristic
178C4⋊C4—521no—
179C22⋊C4—262no—
180C42—521no—
181C16—41no—
182C16—522no—
183C16—521no—
184C13#720811yescharacteristic, complemented, Sylow
185C23—131no—
186C23—131no—
187C23#8810011yescharacteristic
188Q8—521no—
189D4—521no—
190D4—521no—
191D4—521no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—131no—
195C2×C4—131no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—522no—
201C2×C4C8×#26111yescharacteristic
202C2×C4(C2×#261)⋊C411yescharacteristic
203C8—21no—
204C8—261no—
205C8—261no—
206C8—522no—
207C8#8810711yescharacteristic
208C8#8811911yescharacteristic
209C22—21no—
210C22—41no—
211C22—261no—
212C22—261no—
213C22—521no—
214C22—521no—
215C22(C2×#261)⋊C811yescharacteristic
216C4—21no—
217C4—261no—
218C4—261no—
219C4—1042no—
220C4#1171826611yescharacteristic
221C4#1171828911yescharacteristic
222C2—21no—
223C2—41no—
224C2—521no—
225C2—521no—
226C2#1312967811yescharacteristic
subgroupG/H
centerC8#88119
commutatorC2×C4×C13C4×C8
FrattiniC22×C8C2×#261
FittingC2×C13×M32C4
socleC2×C13#1282
prime radicalC2×#6127C2×C4
cosocleC2×#88155C22
hypercenterC2×M32#261
hypocenterC13#7208
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
9. C2×C13×M32C4semidirect
10. C22×#6090C4semidirect
11. #11718284C4semidirect
101. C2×M32#261semidirect
184. C13#7208semidirect

Maximal subgroups

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

subgroupindex
#131310732
#131305912
#131164512
#720813