Finite Group Databasebeta

← #22627105

Subgroups — #22627105

Order 9344.

236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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#17989706C212yesmaximal, complemented
2#17989686C212yesmaximal, complemented
3#17989685C212yesmaximal, complemented
4C2×D73⋊M16C211yesmaximal, characteristic
5#14556688—22no—
6#14556687C2214yescomplemented
7#14556686—22no—
8C2×#11924038C411yescharacteristic
9C2×#11924038C2211yescharacteristic
10D73⋊M16—22no—
11D73⋊M16—22no—
12C2×#11924037C411yescharacteristic
13C2×#11924037C2211yescharacteristic
14C2×#11924036C411yescharacteristic
15C2×#11924036C2211yescharacteristic
16C22×C4×D73C411yescharacteristic
17#11924040—24no—
18#11924038—22no—
19#11924038—22no—
20#11924037—22no—
21#11924037—22no—
22#11924036—21no—
23#11924036—21no—
24#11924036D412yes—
25#11924036D412yes—
26C2×#10596833C2×C411yescharacteristic
27C2×#10596833C2×C411yescharacteristic
28C2×#10596833C2×C411yescharacteristic
29C2×#10596833C2311yescharacteristic
30C23×D73C811yescharacteristic
31C22×Dic73C2×C411yescharacteristic
32C2×C4×D73—21no—
33C2×C4×D73—21no—
34C2×C4×D73—21no—
35C2×C4×D73—21no—
36C2×C4×D73C811yescharacteristic
37C2×C4×D73C811yescharacteristic
38C2×C4×D73C2×C411yescharacteristic
39C2×C4×D73C2×C411yescharacteristic
40C22×C4×C73C811yescharacteristic
41C23×C73C2×C811yescharacteristic
42C22×D73—21no—
43C22×D73—21no—
44C22×D73—42no—
45C22×D73C2×C811yescharacteristic
46C22×D73C2×C811yescharacteristic
47C2×C4×C73—21no—
48C2×C4×C73—21no—
49C2×C4×C73C2×C811yescharacteristic
50C2×C4×C73C2×C811yescharacteristic
51C2×Dic73—21no—
52C2×Dic73—21no—
53C2×Dic73C2×C811yescharacteristic
54C2×Dic73C22×C411yescharacteristic
55C4×D73—21no—
56C4×D73—21no—
57C4×D73—21no—
58C4×D73—21no—
59C4×D73—21no—
60C4×D73—21no—
61C4×D73C22⋊C411yescharacteristic
62C4×D73C22⋊C411yescharacteristic
63C4×D73M1611yescharacteristic
64C4×D73M1611yescharacteristic
65#10596833—21no—
66#10596833—21no—
67#10596833C22⋊C412yes—
68#10596833C2×D412yes—
69C22×C73—21no—
70C22×C73—41no—
71C22×C73C22×C811yescharacteristic
72C2×D73—22no—
73C2×D73—21no—
74C2×D73—42no—
75C2×D73—42no—
76C2×D73—41no—
77C2×D73C22⋊C811yescharacteristic
78C2×D73C22⋊C811yescharacteristic
79C4×C73—21no—
80C4×C73C22⋊C811yescharacteristic
81C4×C73C22⋊C811yescharacteristic
82Dic73—21no—
83Dic73C2×C22⋊C411yescharacteristic
84Dic73C2×M1611yescharacteristic
85C2×C73—21no—
86C2×C73—41no—
87C2×C73C2×C22⋊C811yescharacteristic
88D73—21no—
89D73—41no—
90D73#34912yescomplemented
91C2×#349—731nomaximal, Sylow
92C73C2×#34911yescharacteristic, complemented, Sylow
93C22×M16—731no—
94C2×M32—732no—
95#349—732no—
96#349—732no—
97C23×C4—731no—
98C2×M16—731no—
99C2×M16—731no—
100C2×M16—731no—
101C2×M16—731no—
102C2×M16—1462no—
103C2×M16—1462no—
104C22×C8—731no—
105C22×C8—731no—
106M32—734no—
107M32—1462no—
108C2×C16—1462no—
109C24—731no—
110C22×C4—731no—
111C22×C4—731no—
112C22×C4—731no—
113C22×C4—731no—
114C22×C4—731no—
115C22×C4—1461no—
116C22×C4—1461no—
117C22×C4—1461no—
118C22×C4—1461no—
119C22×C4#1059684211yescharacteristic
120M16—1462no—
121M16—1462no—
122M16—1462no—
123M16—1462no—
124C2×C8—731no—
125C2×C8—731no—
126C2×C8—732no—
127C2×C8—732no—
128C2×C8—731no—
129C2×C8—731no—
130C2×C8—1461no—
131C2×C8—1461no—
132C16—1464no—
133C23—2922no—
134C23—731no—
135C23—731no—
136C23—1461no—
137C23—1461no—
138C23C2×#1059684211yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—731no—
142C2×C4—731no—
143C2×C4—731no—
144C2×C4—731no—
145C2×C4—731no—
146C2×C4—731no—
147C2×C4—1461no—
148C2×C4—1461no—
149C2×C4—1461no—
150C2×C4—1461no—
151C2×C4—1461no—
152C2×C4—1461no—
153C2×C4—1461no—
154C2×C4—1461no—
155C2×C4C2×#1059684211yescharacteristic
156C2×C4C2×#1059684211yescharacteristic
157C8—732no—
158C8—732no—
159C8—1461no—
160C8—1461no—
161C22—21no—
162C22—41no—
163C22—2921no—
164C22—2922no—
165C22—2922no—
166C22—731no—
167C22—731no—
168C22—1462no—
169C22—1461no—
170C22C22×#1059684211yescharacteristic
171C4—21no—
172C4—731no—
173C4—731no—
174C4—1461no—
175C4C22⋊#1059684211yescharacteristic
176C4C22⋊#1059684211yescharacteristic
177C2—21no—
178C2—41no—
179C2—2921no—
180C2—732no—
181C2—1461no—
182C2C2×C22⋊#1059684211yescharacteristic
subgroupG/H
centerC4C22⋊#10596842
commutatorC22×C73C22×C8
FrattiniC22C22×#10596842
FittingC22×C4×C73C8
socleC2×C73C2×C22⋊C8
hypercenterC22×C4#10596842
hypocenterC73C2×#349
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #17989706C2semidirect
2. #17989686C2semidirect
3. #17989685C2semidirect
6. #14556687C22semidirect
90. D73#349semidirect
92. C73C2×#349semidirect