Finite Group Databasebeta

← #22626940

Subgroups — #22626940

Order 9344.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×C22⋊#10596842C212yesmaximal
2C2×(C2×#64408)⋊C4C211yesmaximal, characteristic
3C22×#10596842—22no—
4C22⋊#10596842—22no—
5C22⋊#10596842C414yescomplemented
6C23×#64408C411yescharacteristic
7C23×#64408C2211yescharacteristic
8(C2×#64408)⋊C4—22no—
9C22×C4×D73C411yescharacteristic
10C2×#10596842—24no—
11C2×#10596842—42no—
12C2×#10596842—42no—
13C22×#64408—21no—
14C22×#64408—21no—
15C22×#64408—41no—
16C22×#64408—41no—
17C22×#64408—41no—
18C22×#64408—41no—
19C22×#64408C812yescomplemented
20C22×#64408C2×C412yes—
21C22×#64408D412yes—
22C22×#64408D411yescharacteristic
23C22×#64408Q811yescharacteristic
24C23×D73C2×C411yescharacteristic
25C22×Dic73C811yescharacteristic, complemented
26C2×C4×D73—21no—
27C2×C4×D73—21no—
28C2×C4×D73—41no—
29C2×C4×D73—41no—
30C22×C4×C73C811yescharacteristic, complemented
31C23×C73C2×C811yescharacteristic
32C22×D73—21no—
33C22×D73—21no—
34C22×D73—21no—
35C22×D73—21no—
36C22×D73C4211yescharacteristic
37C22×D73C22⋊C411yescharacteristic
38C22×D73C4⋊C411yescharacteristic
39C22×D73C2×C811yescharacteristic
40C22×D73M1611yescharacteristic
41C22×D73M1611yescharacteristic
42C2×#64408—22no—
43C2×#64408—22no—
44C2×#64408—22no—
45C2×#64408—42no—
46C2×#64408—41no—
47C2×#64408—41no—
48C2×#64408—42no—
49C2×#64408—41no—
50C2×#64408—41no—
51C2×#64408—42no—
52C2×#64408C22⋊C412yes—
53C2×#64408C4⋊C412yes—
54#10596842—44no—
55C2×C4×C73—21no—
56C2×C4×C73—41no—
57C2×Dic73—21no—
58C2×Dic73—41no—
59C4×D73—42no—
60C4×D73—41no—
61C4×D73—41no—
62C22×C73—21no—
63C22×C73—21no—
64C22×C73C4×C811yescharacteristic
65C22×C73C22⋊C811yescharacteristic
66C22×C73C4⋊C811yescharacteristic
67C2×D73—21no—
68C2×D73—21no—
69C2×D73—21no—
70C2×D73—21no—
71C2×D73—21no—
72C2×D73—21no—
73C2×D73—21no—
74C2×D73—21no—
75C2×D73—21no—
76C2×D73—21no—
77C2×D73#9511yescharacteristic
78C2×D73#9711yescharacteristic
79C2×D73C22⋊C811yescharacteristic
80C2×D73#9911yescharacteristic
81C2×D73#9911yescharacteristic
82C2×D73#10011yescharacteristic
83C2×D73#10111yescharacteristic
84C2×D73C4⋊C811yescharacteristic
85#64408—22no—
86#64408—22no—
87#64408—42no—
88C4×C73—41no—
89Dic73—41no—
90C2×C73—21no—
91C2×C73—21no—
92C2×C73#32311yescharacteristic
93C2×C73#32411yescharacteristic
94C2×C73#33611yescharacteristic
95D73—21no—
96D73—21no—
97D73#32311yescharacteristic
98D73#32411yescharacteristic
99D73#34211yescharacteristic
100D73#34311yescharacteristic
101#1280—731nomaximal, Sylow
102C73#128011yescharacteristic, complemented, Sylow
103C2×C22⋊C8—732no—
104C2×#95—731no—
105C23×C4—731no—
106C23×C4—731no—
107C23×C4—731no—
108C22×C8—1462no—
109C22⋊C8—734no—
110C22⋊C8—1462no—
111#95—1462no—
112C24—731no—
113C22×C4—2921no—
114C22×C4—2921no—
115C22×C4—2921no—
116C22×C4—2921no—
117C22×C4—2921no—
118C22×C4—2921no—
119C22×C4—732no—
120C22×C4—731no—
121C22×C4—731no—
122C22×C4—732no—
123C22×C4—731no—
124C22×C4—732no—
125C22×C4—1461no—
126C22×C4—1461no—
127C22×C4—1461no—
128C22×C4—1461no—
129C22×C4#1059684211yescharacteristic, complemented
130C2×C8—2922no—
131C2×C8—2922no—
132C2×C8—1464no—
133C23—731no—
134C23—731no—
135C23—731no—
136C23—731no—
137C23—731no—
138C23—731no—
139C23—1461no—
140C23—1461no—
141C23—1461no—
142C23—1461no—
143C23C2×#1059684211yescharacteristic
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—2921no—
147C2×C4—2921no—
148C2×C4—2922no—
149C2×C4—2921no—
150C2×C4—2921no—
151C2×C4—2922no—
152C2×C4—2921no—
153C2×C4—2922no—
154C2×C4—2921no—
155C2×C4—2922no—
156C2×C4—2921no—
157C2×C4—732no—
158C2×C4—732no—
159C2×C4—1462no—
160C2×C4—1461no—
161C2×C4—1462no—
162C2×C4—1462no—
163C8—2924no—
164C22—21no—
165C22—21no—
166C22—731no—
167C22—731no—
168C22—731no—
169C22—731no—
170C22—731no—
171C22—731no—
172C22—731no—
173C22—731no—
174C22—1461no—
175C22—1461no—
176C22—1461no—
177C22—1461no—
178C22—1461no—
179C22—1461no—
180C22—1461no—
181C22—1461no—
182C22—1461no—
183C22—1461no—
184C22C4×#1059684211yescharacteristic
185C22C22⋊#1059684211yescharacteristic
186C22C4⋊#1059684211yescharacteristic
187C4—41no—
188C4—2922no—
189C4—2921no—
190C4—1462no—
191C4—1462no—
192C2—21no—
193C2—21no—
194C2—731no—
195C2—731no—
196C2—731no—
197C2—731no—
198C2—1461no—
199C2—1461no—
200C2#1798967211yescharacteristic
201C2#1798967311yescharacteristic
202C2(C2×#10596842)⋊C411yescharacteristic
subgroupG/H
centerC22C22⋊#10596842
commutatorC22×C73C4×C8
FrattiniC23C2×#10596842
FittingC22×C4×C73C8
socleC22×C73C22⋊C8
hypercenterC22×C4#10596842
hypocenterC73#1280
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
5. C22⋊#10596842C4semidirect
19. C22×#64408C8semidirect
25. C22×Dic73C8semidirect
30. C22×C4×C73C8semidirect
102. C73#1280semidirect
129. C22×C4#10596842semidirect