Finite Group Databasebeta

← #28378359

Subgroups — #28378359

Order 13952.

312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 74 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#20296043C211yesmaximal, characteristic, complemented
2#20296029C211yesmaximal, characteristic, complemented
3#20295874C214yesmaximal, complemented
4C2×#16812661C211yesmaximal, characteristic
5C2×#13182038—21no—
6#16812766—21no—
7#16812766—21no—
8C4⋊#11724786C2212yescomplemented
9C22⋊#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
20#13182038—42no—
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—42no—
32C2×C4×D109—42no—
33#13182006—22no—
34#13182006—22no—
35C4×Dic109C2×C411yescharacteristic
36C4×Dic109D411yescharacteristic
37C4×Dic109D411yescharacteristic
38C4×Dic109C2311yescharacteristic
39C22×C4×C109—21no—
40C22×C4×C109C2×C411yescharacteristic
41C4⋊C4×C109—21no—
42C4⋊C4×C109C2×C412yes—
43C23×C109C22⋊C411yescharacteristic
44C22×D109—24no—
45C22×D109—22no—
46C22×D109—42no—
47C22×D109—42no—
48C2×C4×C109—22no—
49C2×C4×C109—22no—
50C2×C4×C109—42no—
51C2×C4×C109C22⋊C411yescharacteristic
52C2×C4×C109C22×C411yescharacteristic
53C2×Dic109—41no—
54C2×Dic109C22⋊C411yescharacteristic
55C2×Dic109C22⋊C411yescharacteristic
56C2×Dic109D812yes—
57C2×Dic109SD1612yes—
58C2×Dic109C2×D411yescharacteristic
59C2×Dic109C2×D411yescharacteristic
60D436—24no—
61D436—22no—
62D436M1614yescomplemented
63C4×D109—44no—
64C4×D109—42no—
65C4×D109—42no—
66#11724786—42no—
67#11724786—42no—
68C22×C109—21no—
69C22×C109—21no—
70C22×C109#10212yes—
71C22×C109C2×C22⋊C411yescharacteristic
72C2×D109—24no—
73C2×D109—48no—
74C2×D109—42no—
75C2×D109—42no—
76C4×C109—21no—
77C4×C109—42no—
78C4×C109C2×M1612yes—
79Dic109—21no—
80Dic109—21no—
81Dic109#10212yes—
82Dic109C2×D811yescharacteristic
83Dic109C2×SD1611yescharacteristic
84C2×C109—22no—
85C2×C109#40711yescharacteristic
86C2×C109C2×#10211yescharacteristic
87C2×C109#42111yescharacteristic
88D109—44no—
89#1486—1091nomaximal, Sylow
90C109#148611yescharacteristic, complemented, Sylow
91C2×C4×D4—1091no—
92#431—1091no—
93#423—1091no—
94D4⋊C8—1094no—
95C22×D4—1091no—
96C23×C4—2181no—
97C2×M16—2181no—
98C4×D4—1092no—
99C4×D4—1092no—
100C4×D4—2181no—
101C4×D4—2181no—
102C2×C4⋊C4#8913711yescharacteristic
103C2×C22⋊C4—2181no—
104C2×C42—1091no—
105C4⋊C8—1092no—
106C4⋊C8—2181no—
107C4⋊C8—2181no—
108C22⋊C8—2181no—
109C4×C8—1092no—
110C24—2181no—
111C2×D4—1092no—
112C2×D4—2184no—
113C2×D4—2181no—
114C22×C4—21no—
115C22×C4—1091no—
116C22×C4—1091no—
117C22×C4—4362no—
118C22×C4—4362no—
119C22×C4—2182no—
120C22×C4—2182no—
121C22×C4C2×#8913711yescharacteristic
122M16—4362no—
123C2×C8—2182no—
124C2×C8—2182no—
125C4⋊C4—21no—
126C4⋊C4C2×#8913712yes—
127C22⋊C4—2182no—
128C22⋊C4—2182no—
129C42—1091no—
130C42—1091no—
131C42—1091no—
132C42—1091no—
133C23—4362no—
134C23—4362no—
135C23—2184no—
136C23—2182no—
137C23C22⋊#8913711yescharacteristic
138D4—1094no—
139D4—2184no—
140D4—2182no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—1092no—
145C2×C4—1092no—
146C2×C4—1091no—
147C2×C4—1091no—
148C2×C4—1091no—
149C2×C4—1091no—
150C2×C4—4362no—
151C2×C4—4364no—
152C2×C4—4362no—
153C2×C4—4361no—
154C2×C4C22⋊#8913711yescharacteristic
155C2×C4C22×#8913711yescharacteristic
156C8—4362no—
157C8—4362no—
158C22—21no—
159C22—21no—
160C22—4368no—
161C22—4362no—
162C22—4362no—
163C22—2184no—
164C22#1681276112yes—
165C22C2×C22⋊#8913711yescharacteristic
166C4—21no—
167C4—42no—
168C4—1091no—
169C4—1092no—
170C4—1091no—
171C4—2181no—
172C4—2181no—
173C4D109⋊M1612yes—
174C2—22no—
175C2—4364no—
176C2#2029599811yescharacteristic
177C2C2×#1681276111yescharacteristic
178C2#2029602511yescharacteristic
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#1486
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. #20296043C2semidirect
2. #20296029C2semidirect
3. #20295874C2semidirect
8. C4⋊#11724786C22semidirect
10. C4×#11724786C22semidirect
62. D436M16semidirect
90. C109#1486semidirect

Maximal subgroups

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

subgroupindex
#202960432
#202960292
#202958742
C2×#168126612
#1486109