Finite Group Databasebeta

← #16777507

Subgroups — #16777507

Order 3328.

218 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 54 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#13131053C211yesmaximal, characteristic
2#13130759C211yesmaximal, characteristic
3D13×#347C211yesmaximal, characteristic
4D13⋊M32—21no—
5#11719060C411yescharacteristic
6#11719059C411yescharacteristic
7D13×M32—21no—
8D13×#97C2211yescharacteristic
9#11718265—21no—
10#11718265—21no—
11#11718262—21no—
12#11718232C412yescomplemented
13C13×#347C411yescharacteristic, complemented
14#11718104—21no—
15#11718058C411yescharacteristic, complemented
16C2×C4⋊#261—21no—
17C2×C4⋊#261—21no—
18C2×C4⋊#261—41no—
19C2×C8×D13D411yescharacteristic
20C2×C8×D13D411yescharacteristic
21C42×D13C2×C411yescharacteristic
22(C2×#261)⋊C4—41no—
23#88106—22no—
24#88098—22no—
25D13⋊C16—22no—
26C13×M32—21no—
27C13×#97C2×C411yescharacteristic
28#88055D411yescharacteristic
29#88055Q811yescharacteristic
30#88052—21no—
31#88043C2×C411yescharacteristic
32#88038—22no—
33C16×D13—22no—
34#7266—131nomaximal, Sylow
35C22×#261—41no—
36C22×#261—41no—
37C2×C4×D13—21no—
38C2×C4×D13C22⋊C411yescharacteristic
39C4⋊#261—41no—
40C4⋊#261—41no—
41C4⋊#261—41no—
42C4⋊#261—41no—
43C4⋊#261—82no—
44C2×C8×C13C22⋊C411yescharacteristic
45C2×C8×C13C4⋊C411yescharacteristic
46C42×C13C4211yescharacteristic
47C4×Dic13—21no—
48C4×Dic13C4⋊C411yescharacteristic
49C2×#1055C22⋊C411yescharacteristic
50C2×#1055C4⋊C411yescharacteristic
51C8×D13—21no—
52C8×D13—21no—
53C8×D13—21no—
54C8×D13—21no—
55#6092—24no—
56C13×C16—22no—
57#6090—22no—
58C2×#347—131no—
59C2×#347—131no—
60#1836—131no—
61C22×D13#10011yescharacteristic
62C2×#261—82no—
63C2×#261—81no—
64C2×#261—81no—
65C2×#261—81no—
66C2×#261—81no—
67C2×C4×C13—21no—
68C2×C4×C13#9511yescharacteristic
69C2×Dic13—21no—
70C2×Dic13#10111yescharacteristic
71C4×D13—41no—
72C4×D13—41no—
73C4×D13#10411yescharacteristic
74C4×D13#10411yescharacteristic
75C4×D13#10411yescharacteristic
76C4×D13#10411yescharacteristic
77C8×C13—21no—
78C8×C13—21no—
79#1055—21no—
80#1055—21no—
81C2×M32—261no—
82C2×M32—261no—
83C2×#97—131no—
84#384—131no—
85#382—131no—
86#347—132no—
87#347—131no—
88#347—261no—
89#347—261no—
90#347#26111yescharacteristic, complemented
91#340—261no—
92#340—261no—
93C22×C13#34311yescharacteristic
94C2×D13—21no—
95C2×D13—21no—
96C2×D13#32911yescharacteristic
97C2×D13#32911yescharacteristic
98#261—161no—
99#261—161no—
100C4×C13—41no—
101C4×C13#33911yescharacteristic
102C4×C13#33911yescharacteristic
103Dic13—41no—
104Dic13#33011yescharacteristic
105Dic13#33011yescharacteristic
106C22×C8—131no—
107C22×C8—131no—
108C2×C4⋊C4—261no—
109C2×C4⋊C4—261no—
110C2×C4⋊C4—521no—
111C2×C42—131no—
112M32—21no—
113M32—262no—
114M32—262no—
115M32—262no—
116M32—261no—
117C2×C16—262no—
118C2×C16—262no—
119#97—131no—
120#97—131no—
121#97—131no—
122#97C2×#26111yescharacteristic
123#95—521no—
124C2×C13—21no—
125C2×C13#129511yescharacteristic
126D13—21no—
127D13#135511yescharacteristic
128D13#135611yescharacteristic
129C22×C4—131no—
130C22×C4—261no—
131C22×C4—521no—
132C22×C4—521no—
133C2×C8—131no—
134C2×C8—131no—
135C2×C8—261no—
136C2×C8—261no—
137C2×C8—261no—
138C2×C8—261no—
139C2×C8C4⋊#26111yescharacteristic
140C2×C8C22⋊#26111yescharacteristic
141C4⋊C4—521no—
142C4⋊C4—521no—
143C4⋊C4—521no—
144C4⋊C4—521no—
145C4⋊C4—1042no—
146C42—131no—
147C42—261no—
148C42C4×#26111yescharacteristic
149C16—22no—
150C16—262no—
151C16—264no—
152C13#726611yescharacteristic, complemented, Sylow
153C23—131no—
154C2×C4—21no—
155C2×C4—131no—
156C2×C4—131no—
157C2×C4—131no—
158C2×C4—131no—
159C2×C4—131no—
160C2×C4—261no—
161C2×C4—521no—
162C2×C4—521no—
163C2×C4—1041no—
164C2×C4—1041no—
165C2×C4—1042no—
166C2×C4—1041no—
167C2×C4—1041no—
168C2×C4(C2×#261)⋊C411yescharacteristic
169C8—21no—
170C8—21no—
171C8—261no—
172C8—261no—
173C22—131no—
174C22—131no—
175C22—261no—
176C22—261no—
177C22#1171827111yescharacteristic
178C4—41no—
179C4—131no—
180C4—131no—
181C4—521no—
182C4—2081no—
183C4—2081no—
184C4#1171823411yescharacteristic
185C4#1171827211yescharacteristic
186C2—21no—
187C2—131no—
188C2—131no—
189C2—261no—
190C2#1312971311yescharacteristic
subgroupG/H
centerC2#13129713
commutatorC42×C13C42
Frattini#97C2×#261
FittingC13×#347C4
socleC2×C13#1295
prime radicalC22×D13#100
cosocleD13×#97C22
hypercenter#347#261
hypocenterC13#7266
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #347

Complements

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

NH ≅ G/Ntype
12. #11718232C4semidirect
13. C13×#347C4semidirect
15. #11718058C4semidirect
90. #347#261semidirect
152. C13#7266semidirect

Maximal subgroups

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

subgroupindex
#131310532
#131307592
D13×#3472
#726613