Finite Group Databasebeta

← #22625394

Subgroups — #22625394

Order 9344.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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#17989610C211yesmaximal, characteristic
2C4×#11924038C211yesmaximal, characteristic
3#17989444C212yesmaximal, complemented
4#17989444C212yesmaximal, complemented
5#125×D73C211yesmaximal, characteristic
6C2×#11924038—21no—
7#14556658—21no—
8#14556648—21no—
9#14556646C2212yes—
10#14556646C2212yes—
11C4×#10596833—21no—
12#14556583C411yescharacteristic
13#14556582C2211yescharacteristic
14#14556582C2211yescharacteristic
15#14556581—21no—
16#14556581—21no—
17C4⋊C4×D73—21no—
18C4⋊C4×D73—21no—
19C4⋊C4×D73C411yescharacteristic
20C4⋊C4×D73C411yescharacteristic
21C42×D73C2211yescharacteristic
22#125×C73C411yescharacteristic
23#11924038—24no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26C2×C4×D73—21no—
27C2×C4×D73—21no—
28C2×C4×D73C2×C411yescharacteristic
29C2×C4×D73D411yescharacteristic
30C2×C4×D73D411yescharacteristic
31C4⋊Dic73—21no—
32C4⋊Dic73—21no—
33C4⋊Dic73C2×C411yescharacteristic
34C4⋊Dic73C2×C411yescharacteristic
35#11924007—21no—
36#11924007—21no—
37#11924007—21no—
38#11924007—21no—
39#11924007—21no—
40#11924007—21no—
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73C2311yescharacteristic
44C4⋊C4×C73—21no—
45C4⋊C4×C73—21no—
46C4⋊C4×C73C2×C411yescharacteristic
47C4⋊C4×C73C2×C411yescharacteristic
48C42×C73C2×C411yescharacteristic
49C22×D73C22⋊C411yescharacteristic
50C2×C4×C73—21no—
51C2×C4×C73—21no—
52C2×C4×C73C22⋊C411yescharacteristic
53C2×C4×C73C22⋊C411yescharacteristic
54C2×C4×C73C22×C411yescharacteristic
55C2×Dic73—21no—
56C2×Dic73—21no—
57C2×Dic73C22⋊C411yescharacteristic
58C2×Dic73C2×D411yescharacteristic
59C2×Dic73C2×D411yescharacteristic
60C4×D73—22no—
61C4×D73—22no—
62C4×D73—41no—
63C4×D73—42no—
64C4×D73—42no—
65#10596833—24no—
66#10596833—42no—
67C22×C73C2×C22⋊C411yescharacteristic
68C2×D73—21no—
69C2×D73—21no—
70C2×D73#10412yes—
71C4×C73—21no—
72C4×C73—21no—
73C4×C73—21no—
74C4×C73—41no—
75C4×C73—41no—
76Dic73—21no—
77Dic73—21no—
78Dic73—41no—
79Dic73—41no—
80Dic73#10112yes—
81C2×C73C2×#10111yescharacteristic
82C2×C73C2×#10411yescharacteristic
83C2×C73#42111yescharacteristic
84D73—22no—
85#1528—731nomaximal, Sylow
86C73#152811yescharacteristic, complemented, Sylow
87C2×#125—731no—
88#432—731no—
89C4×M16—731no—
90#330—732no—
91#330—732no—
92C2×M16—1461no—
93#125—731no—
94#125—731no—
95#125—731no—
96#125—1461no—
97#125—1461no—
98#125#6440811yescharacteristic
99C2×C4⋊C4—731no—
100C2×C4⋊C4—731no—
101C2×C4⋊C4—1461no—
102C2×C4⋊C4—1461no—
103C2×C42—731no—
104C4⋊C8—1461no—
105C22⋊C8—1461no—
106#97—732no—
107#97—732no—
108C4×C8—1461no—
109C22×C4—731no—
110C22×C4—731no—
111C22×C4—731no—
112C22×C4—1461no—
113C22×C4—1461no—
114M16—1464no—
115C2×C8—1462no—
116C2×C8—1462no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—731no—
120C4⋊C4—731no—
121C4⋊C4—1461no—
122C4⋊C4—1461no—
123C4⋊C4—1461no—
124C4⋊C4—1461no—
125C4⋊C4—1461no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4C2×#6440811yescharacteristic
130C4⋊C4C2×#6440811yescharacteristic
131C42—731no—
132C42—731no—
133C42—731no—
134C42C2×#6440811yescharacteristic
135C23—731no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—2921no—
139C2×C4—2922no—
140C2×C4—2922no—
141C2×C4—731no—
142C2×C4—731no—
143C2×C4—731no—
144C2×C4—1462no—
145C2×C4—1462no—
146C2×C4—1461no—
147C2×C4—1461no—
148C2×C4C22⋊#6440811yescharacteristic
149C2×C4C22⋊#6440811yescharacteristic
150C2×C4C22×#6440811yescharacteristic
151C8—2922no—
152C8—1464no—
153C22—732no—
154C22—1461no—
155C22—1461no—
156C22C2×C22⋊#6440811yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4—2921no—
163C4—2921no—
164C4—732no—
165C4—1461no—
166C4—1461no—
167C2—1462no—
168C2D73⋊#10111yescharacteristic
169C2D73⋊#10411yescharacteristic
170C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#125×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#125#64408
hypocenterC73#1528
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #17989444C2semidirect
4. #17989444C2semidirect
86. C73#1528semidirect