Finite Group Databasebeta

← #28378373

Subgroups — #28378373

Order 13952.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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#20296047C211yesmaximal, characteristic, complemented
2C4×#13182038C211yesmaximal, characteristic, complemented
3#20295874C214yesmaximal, complemented
4C2×#16812661C211yesmaximal, characteristic
5C2×#13182038—21no—
6C4⋊#11724786C2212yescomplemented
7C22⋊#11724786—21no—
8#16812754—21no—
9#16812754—21no—
10C4×#11724786C2212yescomplemented
11C22×D436C411yescharacteristic
12C22×C4×D109—21no—
13#16812661—21no—
14#16812661—21no—
15#16812661C412yes—
16#16812661C2212yes—
17C2×#13182006—21no—
18C2×C4×Dic109C2211yescharacteristic
19C2×C4⋊C4×C109C411yescharacteristic
20#13182038—24no—
21C2×#11724786—22no—
22C2×#11724786—22no—
23C23×D109—21no—
24C2×D436—21no—
25C2×D436—24no—
26C2×D436C2×C412yes—
27C22×Dic109D411yescharacteristic
28C22×Dic109D411yescharacteristic
29C2×C4×D109—22no—
30C2×C4×D109—22no—
31C2×C4×D109—44no—
32#13182006—22no—
33#13182006—22no—
34C4×Dic109C2×C411yescharacteristic
35C4×Dic109D411yescharacteristic
36C4×Dic109D411yescharacteristic
37C4×Dic109C2311yescharacteristic
38C22×C4×C109—21no—
39C22×C4×C109C2×C411yescharacteristic
40C4⋊C4×C109—21no—
41C4⋊C4×C109C2×C412yes—
42C23×C109C22⋊C411yescharacteristic
43C22×D109—24no—
44C22×D109—22no—
45C22×D109—42no—
46C22×D109—42no—
47C2×C4×C109—22no—
48C2×C4×C109—22no—
49C2×C4×C109—42no—
50C2×C4×C109C22⋊C411yescharacteristic
51C2×C4×C109C22×C411yescharacteristic
52C2×Dic109—22no—
53C2×Dic109—22no—
54C2×Dic109C22⋊C411yescharacteristic
55C2×Dic109C22⋊C411yescharacteristic
56C2×Dic109C2×D411yescharacteristic
57C2×Dic109C2×D411yescharacteristic
58D436—24no—
59D436—22no—
60D436M1614yescomplemented
61C4×D109—44no—
62C4×D109—44no—
63#11724786—24no—
64#11724786—42no—
65C22×C109—21no—
66C22×C109—21no—
67C22×C109#10412yes—
68C22×C109C2×C22⋊C411yescharacteristic
69C2×D109—24no—
70C2×D109—48no—
71C2×D109—42no—
72C2×D109—42no—
73C4×C109—21no—
74C4×C109—42no—
75C4×C109C2×M1612yes—
76Dic109—21no—
77Dic109—21no—
78Dic109—21no—
79Dic109AGL(1,ℤ/8)12yes—
80C2×C109—22no—
81C2×C109#40711yescharacteristic
82C2×C109#41811yescharacteristic
83C2×C109C2×#10411yescharacteristic
84D109—44no—
85#1490—1091nomaximal, Sylow
86C109#149011yescharacteristic, complemented, Sylow
87C2×C4×D4—1091no—
88#432—1091no—
89C4×M16—1091no—
90D4⋊C8—1094no—
91C22×D4—1091no—
92C23×C4—2181no—
93C2×M16—2181no—
94C4×D4—1092no—
95C4×D4—1092no—
96C4×D4—2181no—
97C4×D4—2181no—
98C2×C4⋊C4#8913711yescharacteristic
99C2×C22⋊C4—2181no—
100C2×C42—1091no—
101C4⋊C8—1092no—
102C22⋊C8—2181no—
103#97—2181no—
104#97—2181no—
105C4×C8—1092no—
106C24—2181no—
107C2×D4—1092no—
108C2×D4—2184no—
109C2×D4—2181no—
110C22×C4—21no—
111C22×C4—1091no—
112C22×C4—1091no—
113C22×C4—4364no—
114C22×C4—2182no—
115C22×C4—2182no—
116C22×C4C2×#8913711yescharacteristic
117M16—2184no—
118C2×C8—2182no—
119C2×C8—2182no—
120C4⋊C4—21no—
121C4⋊C4C2×#8913712yes—
122C22⋊C4—2182no—
123C22⋊C4—2182no—
124C42—1091no—
125C42—1091no—
126C42—1091no—
127C42—1091no—
128C23—4362no—
129C23—4362no—
130C23—2184no—
131C23—2182no—
132C23C22⋊#8913711yescharacteristic
133D4—1094no—
134D4—2184no—
135D4—2182no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—1091no—
140C2×C4—1091no—
141C2×C4—1091no—
142C2×C4—1091no—
143C2×C4—4364no—
144C2×C4—4364no—
145C2×C4—2182no—
146C2×C4—2182no—
147C2×C4C22⋊#8913711yescharacteristic
148C2×C4C22×#8913711yescharacteristic
149C8—4362no—
150C8—2184no—
151C22—21no—
152C22—21no—
153C22—4368no—
154C22—4362no—
155C22—4362no—
156C22—2184no—
157C22#1681276412yes—
158C22C2×C22⋊#8913711yescharacteristic
159C4—21no—
160C4—42no—
161C4—1092no—
162C4—2181no—
163C4—2181no—
164C4—2181no—
165C4D109⋊M1612yes—
166C2—22no—
167C2—4364no—
168C2#2029599811yescharacteristic
169C2#2029601811yescharacteristic
170C2C2×#1681276411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC2×C4⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×D436C4
cosocleC4×Dic109C23
hypercenterC2×C4⋊C4#89137
hypocenterC109#1490
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #20296047C2semidirect
2. C4×#13182038C2semidirect
3. #20295874C2semidirect
6. C4⋊#11724786C22semidirect
10. C4×#11724786C22semidirect
60. D436M16semidirect
86. C109#1490semidirect

Maximal subgroups

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

subgroupindex
#202960472
C4×#131820382
#202958742
C2×#168126612
#1490109