Finite Group Databasebeta

← #16787059

Subgroups — #16787059

Order 3328.

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

normal subgroups only

This group has 280 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#13129785C212yesmaximal, complemented
3#13129770C212yesmaximal
4#13123483C211yesmaximal, characteristic
5#41×Dic13C411yescharacteristic
6C13×#408C411yescharacteristic
7#11718895C2211yescharacteristic
8#11718780C411yescharacteristic
9M16×Dic13C2211yescharacteristic
10#11718763C2211yescharacteristic
11C2×#88055C411yescharacteristic
12#11718381—22no—
13#11718380—22no—
14#11718284C2214yes—
15#11718262—22no—
16#11718261—22no—
17C2×C13×#41C2×C411yescharacteristic
18C2×C13×M16C2×C411yescharacteristic
19C22×C8×C13C2×C411yescharacteristic
20Q8×Dic13—21no—
21D4×Dic13—21no—
22D4×Dic13—22no—
23#88180—21no—
24#88180C2×C411yescharacteristic
25C2×C4×Dic13—21no—
26C2×C4×Dic13C2×C411yescharacteristic
27C2×#6099C2311yescharacteristic
28C22×#1055C2×C411yescharacteristic
29#88106—24no—
30C13×C22⋊C8—22no—
31C22⋊#1055—22no—
32#88055—21no—
33#88055—21no—
34#88055D412yes—
35#88054—22no—
36#88054—22no—
37C8×Dic13D412yes—
38#11523—131nomaximal, Sylow
39C13×#41—41no—
40C13×#41—41no—
41C2×Q8×C13M1611yescharacteristic
42C2×D4×C13—21no—
43C2×D4×C13M1611yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13C22×C411yescharacteristic
46C22×Dic13—22no—
47C22×Dic13—21no—
48C13×M16—41no—
49C2×C8×C13—21no—
50C2×C8×C13—41no—
51C2×C8×C13C22⋊C412yes—
52C22⋊Dic13—22no—
53C22⋊Dic13M1612yes—
54C4⋊Dic13—22no—
55C4⋊Dic13—21no—
56C4×Dic13—22no—
57C4×Dic13—21no—
58C4×Dic13—21no—
59C4×Dic13C22⋊C411yescharacteristic
60C4×Dic13C22⋊C411yescharacteristic
61#6099—41no—
62C2×#1055—21no—
63C2×#1055—41no—
64C2×#1055C2×D412yes—
65#6092—44no—
66#2923—131no—
67#2165—132no—
68#1328—132no—
69#1321—132no—
70C23×C13—21no—
71C23×C13C2×M1611yescharacteristic
72Q8×C13—41no—
73D4×C13—41no—
74D4×C13—42no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13C2×C22⋊C411yescharacteristic
81C2×C4×C13C2×M1611yescharacteristic
82C2×Dic13—21no—
83C2×Dic13—22no—
84C2×Dic13—21no—
85C2×Dic13—81no—
86C2×Dic13—82no—
87C8×C13—22no—
88C8×C13—41no—
89#1055—22no—
90#1055—41no—
91C4×#41—131no—
92#433—262no—
93#432—262no—
94#424—131no—
95#424—131no—
96#408—131no—
97#408#26111yescharacteristic
98C4×M16—131no—
99C2×#97—131no—
100#364—262no—
101#349—134no—
102#347—262no—
103C22×C13—21no—
104C22×C13—41no—
105C22×C13—42no—
106C22×C13—41no—
107C22×C13#40711yescharacteristic
108C4×C13—21no—
109C4×C13—41no—
110C4×C13#41011yescharacteristic
111C4×C13#41311yescharacteristic
112Dic13—42no—
113Dic13—41no—
114Dic13—41no—
115C2×#41C2×#26111yescharacteristic
116C2×M16—131no—
117C2×M16C2×#26111yescharacteristic
118C22×C8—131no—
119C22×C8C2×#26111yescharacteristic
120C4×Q8—261no—
121C4×D4—262no—
122C4×D4—261no—
123#117—131no—
124#117—261no—
125C2×C42—131no—
126C2×C42—261no—
127M32—264no—
128C4⋊C8—262no—
129C4⋊C8—262no—
130C22⋊C8—22no—
131C22⋊C8—262no—
132#97—132no—
133#97—261no—
134#97—261no—
135C4×C8—132no—
136C2×C13—21no—
137C2×C13—41no—
138C2×C13—81no—
139C2×C13#146411yescharacteristic
140#41—41no—
141#41—41no—
142C2×Q8#611811yescharacteristic
143C2×D4—21no—
144C2×D4#611811yescharacteristic
145C22×C4—21no—
146C22×C4—262no—
147C22×C4—261no—
148C22×C4C22×#26111yescharacteristic
149M16—41no—
150M16—521no—
151C2×C8—21no—
152C2×C8—41no—
153C2×C8—132no—
154C2×C8—261no—
155C2×C8—521no—
156C2×C8C22⋊#26112yes—
157C4⋊C4—262no—
158C4⋊C4—261no—
159C22⋊C4—132no—
160C22⋊C4—262no—
161C42—131no—
162C42—131no—
163C42—262no—
164C42—261no—
165C42—261no—
166C16—524no—
167C13#1152311yescharacteristic, complemented, Sylow
168C23—21no—
169C23D13⋊M1611yescharacteristic
170Q8—41no—
171D4—41no—
172D4—42no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—261no—
179C2×C4—261no—
180C2×C4—262no—
181C2×C4—1041no—
182C2×C4—1042no—
183C2×C4C2×#611811yescharacteristic
184C2×C4C2×C22⋊#26111yescharacteristic
185C8—22no—
186C8—41no—
187C8—262no—
188C8—521no—
189C22—21no—
190C22—41no—
191C22—42no—
192C22—41no—
193C22#1171912711yescharacteristic
194C4—21no—
195C4—41no—
196C4—521no—
197C4—522no—
198C4—521no—
199C4#1171914211yescharacteristic
200C4#1171914811yescharacteristic
201C2—21no—
202C2—41no—
203C2—81no—
204C2#1313008811yescharacteristic
subgroupG/H
centerC4#11719142
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#408C4
socleC2×C13#1464
prime radicalC2×C13×#41C2×C4
cosocleC2×#6099C23
hypercenter#408#261
hypocenterC13#11523
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #13131206C2semidirect
2. #13129785C2semidirect
167. C13#11523semidirect

Maximal subgroups

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

subgroupindex
#131312062
#131297852
#131297702
#131234832
#1152313