Finite Group Databasebeta

← #22627043

Subgroups — #22627043

Order 9344.

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

normal subgroups only

This group has 264 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#17989700C212yesmaximal, complemented
2#17989673C212yesmaximal, complemented
3#17989672C212yesmaximal
4C2×#14556670C211yesmaximal, characteristic
5C4⋊#10596842—22no—
6C22⋊#10596842C2214yes—
7C4×#10596842—22no—
8#14556670—22no—
9#14556670—22no—
10C2×C4⋊#64408C411yescharacteristic
11C2×C4⋊#64408C2211yescharacteristic
12C2×C22⋊#64408C411yescharacteristic
13C2×C22⋊#64408C2211yescharacteristic
14C2×C4×#64408C411yescharacteristic
15C2×C4×#64408C2211yescharacteristic
16C22×C4×D73C411yescharacteristic
17C2×#10596842—24no—
18C22×#64408C2×C411yescharacteristic
19C22×#64408C2×C411yescharacteristic
20C22×#64408C2×C411yescharacteristic
21C22×#64408C2311yescharacteristic
22C4⋊#64408—22no—
23C4⋊#64408—22no—
24C22⋊#64408—22no—
25C22⋊#64408—22no—
26C4×#64408—21no—
27C4×#64408—21no—
28C4×#64408D412yes—
29C4×#64408D412yes—
30C23×D73C2×C411yescharacteristic
31C22×Dic73C811yescharacteristic, complemented
32C2×C4×D73—21no—
33C2×C4×D73—21no—
34C2×C4×D73—21no—
35C2×C4×D73—21no—
36C2×C4×D73C811yescharacteristic, complemented
37C2×C4×D73C811yescharacteristic, complemented
38C2×C4×D73C2×C411yescharacteristic
39C2×C4×D73C2×C411yescharacteristic
40C22×C4×C73C811yescharacteristic, complemented
41C23×C73C2×C811yescharacteristic
42C22×D73—21no—
43C22×D73—21no—
44C22×D73—41no—
45C22×D73—41no—
46C22×D73C2×C811yescharacteristic
47C22×D73C22×C411yescharacteristic
48C2×#64408—21no—
49C2×#64408—21no—
50C2×#64408—41no—
51C2×#64408—41no—
52C2×#64408—41no—
53C2×#64408—41no—
54C2×#64408C22⋊C412yes—
55C2×#64408C2×D412yes—
56#10596842—44no—
57C2×C4×C73—21no—
58C2×C4×C73—21no—
59C2×C4×C73C2×C811yescharacteristic
60C2×C4×C73C2×C811yescharacteristic
61C2×Dic73—21no—
62C2×Dic73—21no—
63C2×Dic73C2×C811yescharacteristic
64C2×Dic73C2×C811yescharacteristic
65C4×D73—21no—
66C4×D73—21no—
67C4×D73—21no—
68C4×D73—21no—
69C4×D73—21no—
70C4×D73—21no—
71C4×D73C22⋊C411yescharacteristic
72C4×D73C22⋊C411yescharacteristic
73C4×D73M1611yescharacteristic
74C4×D73M1611yescharacteristic
75C22×C73—21no—
76C22×C73—41no—
77C22×C73C22×C811yescharacteristic
78C2×D73—21no—
79C2×D73—21no—
80C2×D73—21no—
81C2×D73—42no—
82C2×D73—41no—
83C2×D73—41no—
84C2×D73—41no—
85C2×D73C2×C22⋊C411yescharacteristic
86C2×D73C2×M1611yescharacteristic
87#64408—22no—
88#64408—22no—
89#64408—41no—
90#64408—41no—
91C4×C73—21no—
92C4×C73C22⋊C811yescharacteristic
93C4×C73C22⋊C811yescharacteristic
94Dic73—21no—
95Dic73C22⋊C811yescharacteristic
96Dic73C22⋊C811yescharacteristic
97C2×C73—21no—
98C2×C73—41no—
99C2×C73C2×C22⋊C811yescharacteristic
100D73—21no—
101D73—41no—
102D73#41011yescharacteristic
103D73#41311yescharacteristic
104#1458—731nomaximal, Sylow
105C73#145811yescharacteristic, complemented, Sylow
106C2×#117—731no—
107#431—732no—
108#324—732no—
109#323—732no—
110C23×C4—731no—
111#117—1462no—
112#117—1462no—
113C2×C4⋊C4—731no—
114C2×C4⋊C4—731no—
115C2×C22⋊C4—731no—
116C2×C22⋊C4—731no—
117C2×C42—731no—
118C2×C42—731no—
119C4⋊C8—1462no—
120C22⋊C8—734no—
121C4×C8—1462no—
122C24—731no—
123C22×C4—731no—
124C22×C4—731no—
125C22×C4—731no—
126C22×C4—731no—
127C22×C4—731no—
128C22×C4—731no—
129C22×C4—731no—
130C22×C4—731no—
131C22×C4—731no—
132C22×C4—1461no—
133C22×C4—1461no—
134C22×C4—1461no—
135C22×C4—1461no—
136C22×C4#1059684211yescharacteristic, complemented
137C2×C8—1464no—
138C4⋊C4—1462no—
139C4⋊C4—1462no—
140C22⋊C4—1462no—
141C22⋊C4—1462no—
142C42—732no—
143C42—732no—
144C42—1461no—
145C42—1461no—
146C23—2921no—
147C23—2921no—
148C23—731no—
149C23—731no—
150C23—1461no—
151C23—1461no—
152C23C2×#1059684211yescharacteristic
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—2921no—
156C2×C4—2921no—
157C2×C4—2921no—
158C2×C4—2921no—
159C2×C4—731no—
160C2×C4—731no—
161C2×C4—731no—
162C2×C4—731no—
163C2×C4—731no—
164C2×C4—732no—
165C2×C4—732no—
166C2×C4—731no—
167C2×C4—1461no—
168C2×C4—1461no—
169C2×C4—1461no—
170C2×C4—1461no—
171C2×C4—1461no—
172C2×C4—1461no—
173C2×C4—1461no—
174C2×C4—1461no—
175C2×C4—1461no—
176C2×C4—1461no—
177C2×C4C2×#1059684211yescharacteristic
178C2×C4C2×#1059684211yescharacteristic
179C8—2924no—
180C22—21no—
181C22—41no—
182C22—2921no—
183C22—2921no—
184C22—2921no—
185C22—2922no—
186C22—731no—
187C22—731no—
188C22—1461no—
189C22—1461no—
190C22—1461no—
191C22C22×#1059684211yescharacteristic
192C4—21no—
193C4—2921no—
194C4—2921no—
195C4—731no—
196C4—731no—
197C4—1462no—
198C4—1462no—
199C4—1461no—
200C4C22⋊#1059684211yescharacteristic
201C4C22⋊#1059684211yescharacteristic
202C2—21no—
203C2—41no—
204C2—2921no—
205C2—731no—
206C2—731no—
207C2—1461no—
208C2C2×C22⋊#1059684211yescharacteristic
subgroupG/H
centerC4C22⋊#10596842
commutatorC22×C73C22×C8
FrattiniC22C22×#10596842
FittingC22×C4×C73C8
socleC2×C73C2×C22⋊C8
hypercenterC22×C4#10596842
hypocenterC73#1458
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. #17989700C2semidirect
2. #17989673C2semidirect
31. C22×Dic73C8semidirect
36. C2×C4×D73C8semidirect
37. C2×C4×D73C8semidirect
40. C22×C4×C73C8semidirect
105. C73#1458semidirect
136. C22×C4#10596842semidirect