Finite Group Databasebeta

← #22608554

Subgroups — #22608554

Order 9344.

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

normal subgroups only

This group has 248 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
1C2×#14556579C211yesmaximal, characteristic
2#17988644C211yesmaximal, characteristic, complemented
3#17988326C214yesmaximal, complemented
4#432×C73C211yesmaximal, characteristic, complemented
5C22×Dic146C411yescharacteristic
6C22×D292C411yescharacteristic
7#14556579—21no—
8#14556579—21no—
9#14556579C412yes—
10#14556579C2212yes—
11C2×#11924005—21no—
12C2×#11924005—21no—
13C4⋊#10596831—21no—
14C22⋊#10596831—21no—
15#14556502C2212yescomplemented
16C2×C42×C73C2211yescharacteristic
17C4⋊C8×C73—21no—
18C22⋊C8×C73—21no—
19#97×C73C2212yescomplemented
20C23×D73—21no—
21C2×Dic146—21no—
22C2×Dic146—42no—
23C2×Dic146C2×C412yes—
24C2×D292—21no—
25C2×D292—42no—
26C2×D292C2×C412yes—
27C22×Dic73—21no—
28C2×#10596831—22no—
29#11924005—22no—
30#11924005—22no—
31#11924005—22no—
32#11924005—22no—
33C22×C4×C73C2×C411yescharacteristic
34C22×C4×C73D411yescharacteristic
35C22×C4×C73D411yescharacteristic
36C2×C8×C73—22no—
37C42×C73C2×C411yescharacteristic
38C42×C73D411yescharacteristic
39C42×C73D411yescharacteristic
40C42×C73C2311yescharacteristic
41C23×C73C22⋊C411yescharacteristic
42C22×D73—22no—
43C22×D73—42no—
44C22×D73—42no—
45C22×D73—42no—
46C2×C4×C73—22no—
47C2×C4×C73—41no—
48C2×C4×C73—41no—
49C2×C4×C73C22⋊C411yescharacteristic
50C2×C4×C73C22⋊C411yescharacteristic
51C2×C4×C73C22⋊C411yescharacteristic
52C2×C4×C73C22×C411yescharacteristic
53C2×C4×C73C2×D411yescharacteristic
54C2×C4×C73C2×D411yescharacteristic
55C2×Dic73—22no—
56C2×Dic73—42no—
57D292—42no—
58D292—42no—
59Dic146—42no—
60Dic146—42no—
61C8×C73—42no—
62#10596831—42no—
63C22×C73—21no—
64C22×C73—21no—
65C22×C73#10012yes—
66C22×C73C2×C22⋊C411yescharacteristic
67C2×D73—42no—
68C2×D73—42no—
69C2×D73—42no—
70C2×D73—84no—
71C4×C73—21no—
72C4×C73—21no—
73C4×C73—21no—
74C4×C73—21no—
75C4×C73—21no—
76C4×C73—21no—
77Dic73—42no—
78C2×C73—22no—
79C2×C73C2×#10011yescharacteristic
80C2×C73#42111yescharacteristic
81C2×C73#42111yescharacteristic
82D73—82no—
83#1533—731nomaximal, Sylow
84C73#153311yescharacteristic, complemented, Sylow
85C2×#124—731no—
86#432—731no—
87#432D7311yescharacteristic, complemented
88#329—734no—
89C22×Q8—731no—
90C22×D4—731no—
91#124—732no—
92#124—732no—
93#124—1461no—
94#124—1461no—
95C2×C22⋊C4—1461no—
96C2×C22⋊C4—1461no—
97C2×C42C2×D7311yescharacteristic
98C4⋊C8—21no—
99C4⋊C8—1461no—
100C22⋊C8—21no—
101C22⋊C8—1461no—
102#97—732no—
103#97C2×D7312yescomplemented
104C24—1461no—
105C2×Q8—2922no—
106C2×Q8—732no—
107C2×Q8—1461no—
108C2×D4—2922no—
109C2×D4—732no—
110C2×D4—1461no—
111C22×C4—1461no—
112C22×C4C4×D7311yescharacteristic
113C22×C4D29211yescharacteristic
114C22×C4C22⋊D7311yescharacteristic
115C2×C8—22no—
116C2×C8—1462no—
117C22⋊C4—1462no—
118C22⋊C4—1462no—
119C22⋊C4—1462no—
120C22⋊C4—1462no—
121C42C4×D7311yescharacteristic
122C42D29211yescharacteristic
123C42C22⋊D7311yescharacteristic
124C42C22×D7311yescharacteristic
125C23—2922no—
126C23—2922no—
127C23—2922no—
128C23—1462no—
129C23#1192400511yescharacteristic
130Q8—2922no—
131Q8—2922no—
132D4—2922no—
133D4—2922no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—2922no—
138C2×C4—1462no—
139C2×C4#1192400511yescharacteristic
140C2×C4#1192400511yescharacteristic
141C2×C4#1192400511yescharacteristic
142C2×C4C2×C4×D7311yescharacteristic
143C2×C4C2×C22⋊D7311yescharacteristic
144C2×C4C2×D29211yescharacteristic
145C8—42no—
146C8—2922no—
147C22—21no—
148C22—21no—
149C22—2922no—
150C22—2922no—
151C22—2922no—
152C22—5844no—
153C22#1455650712yes—
154C22C2×#1192400511yescharacteristic
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—2922no—
162C2—22no—
163C2—5842no—
164C2C2×#1455650711yescharacteristic
165C2#1798860311yescharacteristic
166C2#1798860511yescharacteristic
subgroupG/H
centerC22C2×#11924005
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#432×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#432D73
hypocenterC73#1533
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #17988644C2semidirect
3. #17988326C2semidirect
4. #432×C73C2semidirect
15. #14556502C22semidirect
19. #97×C73C22semidirect
84. C73#1533semidirect
87. #432D73semidirect
103. #97C2×D73semidirect