Finite Group Databasebeta

← #28378333

Subgroups — #28378333

Order 13952.

312 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 84 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#20296042C211yesmaximal, characteristic, complemented
2#20296042C211yesmaximal, characteristic, complemented
3#20295874C214yesmaximal, complemented
4C2×#16812661C211yesmaximal, characteristic
5C4⋊#11724786—21no—
6C4⋊#11724786C2212yescomplemented
7C22⋊#11724786—21no—
8C22⋊#11724786—21no—
9C4×#11724786—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
20C2×#11724786—22no—
21C2×#11724786—22no—
22C23×D109—21no—
23C2×D436—21no—
24C2×D436—22no—
25C2×D436C814yescomplemented
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—42no—
49C2×C4×C109C22⋊C411yescharacteristic
50C2×C4×C109C2×C812yes—
51C2×C4×C109M1612yes—
52C2×C4×C109C22×C411yescharacteristic
53C2×Dic109—22no—
54C2×Dic109—41no—
55C2×Dic109C22⋊C411yescharacteristic
56C2×Dic109C22⋊C411yescharacteristic
57C2×Dic109C2×D411yescharacteristic
58C2×Dic109C2×D411yescharacteristic
59D436—24no—
60D436—22no—
61D436C2×C814yes—
62C4×D109—44no—
63C4×D109—44no—
64#11724786—42no—
65#11724786—42no—
66C22×C109—21no—
67C22×C109—21no—
68C22×C109C22⋊C812yes—
69C22×C109C2×C22⋊C411yescharacteristic
70C2×D109—24no—
71C2×D109—48no—
72C2×D109—42no—
73C2×D109—42no—
74C4×C109—42no—
75C4×C109C22⋊C812yes—
76C4×C109C22×C811yescharacteristic
77C4×C109C2×M1611yescharacteristic
78Dic109—21no—
79Dic109—21no—
80Dic109—21no—
81Dic109AGL(1,ℤ/8)12yes—
82C2×C109—22no—
83C2×C109C2×C22⋊C811yescharacteristic
84C2×C109#41811yescharacteristic
85C2×C109#42111yescharacteristic
86D109—44no—
87#1478—1091nomaximal, Sylow
88C109#147811yescharacteristic, complemented, Sylow
89C2×C4×D4—1091no—
90#431—1091no—
91#431—1091no—
92D4⋊C8—1094no—
93C22×D4—1091no—
94C23×C4—2181no—
95C4×D4—1092no—
96C4×D4—1092no—
97C4×D4—2181no—
98C4×D4—2181no—
99C2×C4⋊C4#8913711yescharacteristic
100C2×C22⋊C4—2181no—
101C2×C42—1091no—
102C4⋊C8—1092no—
103C4⋊C8—2181no—
104C22⋊C8—2181no—
105C22⋊C8—2181no—
106C4×C8—1092no—
107C4×C8—2181no—
108C24—2181no—
109C2×D4—1094no—
110C2×D4—1092no—
111C2×D4—2181no—
112C2×D4—2182no—
113C22×C4—21no—
114C22×C4—1091no—
115C22×C4—1091no—
116C22×C4—4364no—
117C22×C4—2182no—
118C22×C4—2182no—
119C22×C4C2×#8913711yescharacteristic
120C2×C8—2182no—
121C2×C8—2182no—
122C4⋊C4—21no—
123C4⋊C4C2×#8913712yes—
124C22⋊C4—2182no—
125C22⋊C4—2182no—
126C42—1091no—
127C42—1091no—
128C42—1091no—
129C42—1091no—
130C23—4362no—
131C23—4362no—
132C23—2184no—
133C23—2182no—
134C23C22⋊#8913711yescharacteristic
135D4—1094no—
136D4—2184no—
137D4—2182no—
138C2×C4—22no—
139C2×C4—42no—
140C2×C4—1091no—
141C2×C4—1091no—
142C2×C4—1091no—
143C2×C4—1091no—
144C2×C4—4364no—
145C2×C4—4364no—
146C2×C4—4361no—
147C2×C4—2182no—
148C2×C4C22⋊#8913711yescharacteristic
149C2×C4D109⋊C812yes—
150C2×C4#1318203912yes—
151C2×C4C22×#8913711yescharacteristic
152C8—4362no—
153C8—4362no—
154C22—21no—
155C22—21no—
156C22—4368no—
157C22—4362no—
158C22—4362no—
159C22—2184no—
160C22#1681275612yes—
161C22C2×C22⋊#8913711yescharacteristic
162C4—42no—
163C4—1092no—
164C4—2181no—
165C4—2181no—
166C4—2181no—
167C4#1681275612yes—
168C4C2×D109⋊C811yescharacteristic
169C4C2×#1318203911yescharacteristic
170C2—22no—
171C2—4364no—
172C2C2×#1681275611yescharacteristic
173C2#2029601811yescharacteristic
174C2#2029602511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC4×C109C22×C8
FrattiniC2×C4C22×#89137
FittingC2×C4⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×D436C4
cosocleC4×Dic109C23
hypercenterC2×C4⋊C4#89137
hypocenterC109#1478
LCSG ▷ 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. #20296042C2semidirect
2. #20296042C2semidirect
3. #20295874C2semidirect
6. C4⋊#11724786C22semidirect
10. C4×#11724786C22semidirect
25. C2×D436C8semidirect
88. C109#1478semidirect

Maximal subgroups

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

subgroupindex
#202960422
#202958742
C2×#168126612
#1478109