Finite Group Databasebeta

← #22626165

Subgroups — #22626165

Order 9344.

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

normal subgroups only

This group has 236 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#17989643C212yesmaximal, complemented
2#17989484C212yesmaximal, complemented
3#17989483C212yesmaximal, complemented
4C2×M16×D73C211yesmaximal, characteristic
5#14556666—22no—
6#14556665C2214yescomplemented
7#14556664—22no—
8C22×C4×D73C411yescharacteristic
9C2×#11924012C2211yescharacteristic
10C2×#11924011C411yescharacteristic
11C2×#11924011C2211yescharacteristic
12M16×D73—22no—
13M16×D73—22no—
14C2×C8×D73C411yescharacteristic
15C2×C8×D73C2211yescharacteristic
16C2×M16×C73C411yescharacteristic
17#11924031—24no—
18C23×D73C811yescharacteristic
19C22×Dic73C811yescharacteristic
20C2×C4×D73—21no—
21C2×C4×D73—21no—
22C2×C4×D73—21no—
23C2×C4×D73—21no—
24C2×C4×D73C811yescharacteristic
25C2×C4×D73C811yescharacteristic
26C2×C4×D73C2×C411yescharacteristic
27C2×C4×D73C2×C411yescharacteristic
28#11924012—22no—
29#11924011—22no—
30#11924011—22no—
31C2×#10596831C2×C411yescharacteristic
32C2×#10596831C2311yescharacteristic
33C8×D73—21no—
34C8×D73—21no—
35C8×D73D412yes—
36C8×D73D412yes—
37C22×C4×C73C2×C411yescharacteristic
38M16×C73—22no—
39C2×C8×C73C2×C411yescharacteristic
40C2×C8×C73C2×C411yescharacteristic
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×C73C22×C411yescharacteristic
51C2×Dic73—21no—
52C2×Dic73—21no—
53C2×Dic73C2×C811yescharacteristic
54C2×Dic73C2×C811yescharacteristic
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
65C8×C73—21no—
66C8×C73C22⋊C412yes—
67#10596831—21no—
68#10596831C2×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×C73C2×C22⋊C411yescharacteristic
81C4×C73C2×M1611yescharacteristic
82Dic73—21no—
83Dic73C22⋊C811yescharacteristic
84Dic73C22⋊C811yescharacteristic
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—1462no—
102C2×M16—1462no—
103C2×M16#6440811yescharacteristic
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×C4C2×#6440811yescharacteristic
120M16—22no—
121M16—1462no—
122M16—1462no—
123M16—1462no—
124C2×C8—731no—
125C2×C8—732no—
126C2×C8—732no—
127C2×C8—731no—
128C2×C8—1461no—
129C2×C8—1461no—
130C2×C8C2×#6440811yescharacteristic
131C2×C8C2×#6440811yescharacteristic
132C16—1464no—
133C23—2922no—
134C23—731no—
135C23—731no—
136C23—1461no—
137C23—1461no—
138C23#1192403611yescharacteristic
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×C4#1192403611yescharacteristic
156C2×C4C22×#6440811yescharacteristic
157C8—21no—
158C8—732no—
159C8—1461no—
160C8C22⋊#6440812yes—
161C22—21no—
162C22—41no—
163C22—2921no—
164C22—2922no—
165C22—2922no—
166C22—731no—
167C22—731no—
168C22—1462no—
169C22—1461no—
170C22C2×#1192403611yescharacteristic
171C4—21no—
172C4—731no—
173C4—731no—
174C4—1461no—
175C4C2×C22⋊#6440811yescharacteristic
176C4D73⋊M1611yescharacteristic
177C2—21no—
178C2—41no—
179C2—2921no—
180C2—732no—
181C2—1461no—
182C2#1798955511yescharacteristic
subgroupG/H
centerC4C2×C22⋊#64408
commutatorC22×C73C22×C8
FrattiniC2×C4C22×#64408
FittingC2×M16×C73C4
socleC2×C73C2×C22⋊C8
hypercenterC2×M16#64408
hypocenterC73C2×#349
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #17989643C2semidirect
2. #17989484C2semidirect
3. #17989483C2semidirect
6. #14556665C22semidirect
90. D73#349semidirect
92. C73C2×#349semidirect