Finite Group Databasebeta

← #16787055

Subgroups — #16787055

Order 3328.

284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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#13131206C212yesmaximal, complemented
2#13129783C212yesmaximal, complemented
3#13129768C212yesmaximal
4#13123471C211yesmaximal, characteristic
5C2×#88180C411yescharacteristic
6C13×#407C411yescharacteristic
7#11718868C2211yescharacteristic
8#11718779C411yescharacteristic
9#11718779C2211yescharacteristic
10M16×Dic13C411yescharacteristic
11M16×Dic13C2211yescharacteristic
12#11718381—22no—
13#11718381—22no—
14#11718284C2214yes—
15#11718262—22no—
16#11718261—22no—
17C23×C4×C13C2×C411yescharacteristic
18C2×C13×M16C2×C411yescharacteristic
19C2×C13×M16C2×C411yescharacteristic
20C2×C22⋊Dic13—21no—
21#88180—21no—
22#88180—21no—
23#88180—22no—
24C2×C4⋊Dic13—21no—
25C2×C4×Dic13C2×C411yescharacteristic
26C2×C4×Dic13C2×C411yescharacteristic
27C2×#6099C2×C411yescharacteristic
28C2×#6099C2311yescharacteristic
29#88106—24no—
30C13×C22⋊C8—22no—
31C22⋊#1055—22no—
32#88055—21no—
33#88055D412yes—
34#88054—22no—
35#88054—22no—
36C8×Dic13—21no—
37C8×Dic13D412yes—
38#11522—131nomaximal, Sylow
39C24×C13M1611yescharacteristic
40C22×C4×C13—21no—
41C22×C4×C13—21no—
42C22×C4×C13—41no—
43C22×C4×C13—41no—
44C22×C4×C13M1611yescharacteristic
45C22×C4×C13C22×C411yescharacteristic
46C22×Dic13—21no—
47C22×Dic13—21no—
48C13×M16—41no—
49C13×M16—41no—
50C2×C8×C13—21no—
51C2×C8×C13C22⋊C412yes—
52C22⋊Dic13—22no—
53C22⋊Dic13—22no—
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56C4×Dic13—21no—
57C4×Dic13—21no—
58C4×Dic13C22⋊C411yescharacteristic
59C4×Dic13C22⋊C411yescharacteristic
60C4×Dic13M1612yes—
61#6099—41no—
62#6099—41no—
63C2×#1055—21no—
64C2×#1055C2×D412yes—
65#6092—44no—
66#2921—131no—
67#2165—132no—
68#1327—132no—
69#1320—132no—
70C23×C13—21no—
71C23×C13—41no—
72C23×C13—81no—
73C23×C13C2×M1611yescharacteristic
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—42no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—41no—
81C2×C4×C13C2×C22⋊C411yescharacteristic
82C2×C4×C13C2×M1611yescharacteristic
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—22no—
86C2×Dic13—81no—
87C2×Dic13—81no—
88C8×C13—22no—
89C8×C13—41no—
90#1055—22no—
91#1055—41no—
92C2×#117—131no—
93#433—262no—
94#433—262no—
95#423—131no—
96#423—131no—
97#407—131no—
98#407#26111yescharacteristic
99C4×M16—131no—
100C4×M16—131no—
101#364—262no—
102#349—134no—
103#347—262no—
104C22×C13—21no—
105C22×C13—41no—
106C22×C13—42no—
107C22×C13—41no—
108C22×C13—82no—
109C22×C13#40711yescharacteristic
110C4×C13—21no—
111C4×C13—41no—
112C4×C13#41011yescharacteristic
113C4×C13#41311yescharacteristic
114Dic13—41no—
115Dic13—41no—
116Dic13—42no—
117C23×C4C2×#26111yescharacteristic
118C2×M16—131no—
119C2×M16—131no—
120C2×M16C2×#26111yescharacteristic
121C2×M16C2×#26111yescharacteristic
122#117—262no—
123#117—261no—
124#117—261no—
125C2×C4⋊C4—261no—
126C2×C22⋊C4—261no—
127C2×C42—131no—
128C2×C42—131no—
129M32—264no—
130C4⋊C8—262no—
131C4⋊C8—262no—
132C22⋊C8—22no—
133C22⋊C8—262no—
134#97—132no—
135#97—261no—
136C4×C8—132no—
137C4×C8—261no—
138C2×C13—21no—
139C2×C13—41no—
140C2×C13—81no—
141C2×C13#146411yescharacteristic
142C24#611811yescharacteristic
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—261no—
148C22×C4—261no—
149C22×C4#611811yescharacteristic
150C22×C4C22×#26111yescharacteristic
151M16—41no—
152M16—41no—
153M16—521no—
154M16—521no—
155C2×C8—21no—
156C2×C8—132no—
157C2×C8—261no—
158C2×C8C22⋊#26112yes—
159C4⋊C4—262no—
160C4⋊C4—262no—
161C22⋊C4—262no—
162C22⋊C4—262no—
163C42—132no—
164C42—131no—
165C42—131no—
166C42—261no—
167C42—261no—
168C16—524no—
169C13#1152211yescharacteristic, complemented, Sylow
170C23—21no—
171C23—41no—
172C23—81no—
173C23C2×#611811yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—262no—
182C2×C4—261no—
183C2×C4—261no—
184C2×C4—1041no—
185C2×C4—1041no—
186C2×C4D13⋊M1611yescharacteristic
187C2×C4C2×C22⋊#26111yescharacteristic
188C8—22no—
189C8—41no—
190C8—262no—
191C8—521no—
192C22—21no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—82no—
197C22#1171912711yescharacteristic
198C4—21no—
199C4—41no—
200C4—521no—
201C4—521no—
202C4—522no—
203C4#1171914211yescharacteristic
204C4#1171914811yescharacteristic
205C2—21no—
206C2—41no—
207C2—81no—
208C2#1313008811yescharacteristic
subgroupG/H
centerC4#11719142
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#407C4
socleC2×C13#1464
prime radicalC24×C13M16
cosocleC2×#6099C23
hypercenter#407#261
hypocenterC13#11522
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #13131206C2semidirect
2. #13129783C2semidirect
169. C13#11522semidirect

Maximal subgroups

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

subgroupindex
#131312062
#131297832
#131297682
#131234712
#1152213