Finite Group Databasebeta

← #22625403

Subgroups — #22625403

Order 9344.

212 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989607C211yesmaximal, characteristic
2C2×#14556646C211yesmaximal, characteristic
3#17989444C212yesmaximal, complemented
4#17989444C212yesmaximal, complemented
5#17989140C211yesmaximal, characteristic
6C22×#10596833—21no—
7#14556658—21no—
8C22⋊#10596833—21no—
9#14556646—21no—
10#14556646C2212yes—
11#14556646C2212yes—
12#14556590C411yescharacteristic
13#14556590C411yescharacteristic
14#14556582C2211yescharacteristic
15#14556582C2211yescharacteristic
16#14556568—21no—
17#14556568—21no—
18C4×Dic146—21no—
19C4×Dic146—21no—
20#14556550C411yescharacteristic
21C2×C4×Dic73C2211yescharacteristic
22#117×C73C411yescharacteristic
23C2×#10596833—24no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26C2×Dic146—21no—
27C2×Dic146—21no—
28C22×Dic73D411yescharacteristic
29C22×Dic73D411yescharacteristic
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C4⋊Dic73C2×C411yescharacteristic
33C4⋊Dic73C2×C411yescharacteristic
34#11924007—21no—
35#11924007—21no—
36#11924007—21no—
37#11924007—21no—
38C22⋊Dic73—21no—
39C4×Dic73—21no—
40C4×Dic73C2×C411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73C2311yescharacteristic
44C22×C4×C73C2×C411yescharacteristic
45C4⋊C4×C73C2×C411yescharacteristic
46C4⋊C4×C73C2×C411yescharacteristic
47C22⋊C4×C73—21no—
48C42×C73—21no—
49C23×C73C22⋊C411yescharacteristic
50C2×C4×C73—22no—
51C2×C4×C73—21no—
52C2×C4×C73—21no—
53C2×C4×C73C22⋊C411yescharacteristic
54C2×C4×C73C22×C411yescharacteristic
55C2×Dic73—22no—
56C2×Dic73—21no—
57C2×Dic73—21no—
58C2×Dic73—41no—
59C2×Dic73C22⋊C411yescharacteristic
60C2×Dic73C22⋊C411yescharacteristic
61C2×Dic73C2×D411yescharacteristic
62C2×Dic73C2×D411yescharacteristic
63Dic146—42no—
64Dic146—42no—
65#10596833—24no—
66#10596833—42no—
67C22×C73—21no—
68C22×C73—21no—
69C22×C73#10112yes—
70C22×C73C2×C22⋊C411yescharacteristic
71C4×C73—21no—
72C4×C73—21no—
73C4×C73—41no—
74C4×C73—41no—
75Dic73—21no—
76Dic73—21no—
77Dic73—21no—
78Dic73—41no—
79Dic73—41no—
80Dic73#10412yes—
81C2×C73—22no—
82C2×C73C2×#10111yescharacteristic
83C2×C73C2×#10411yescharacteristic
84C2×C73#42111yescharacteristic
85#1531—731nomaximal, Sylow
86C73#153111yescharacteristic, complemented, Sylow
87#533—731no—
88#432—731no—
89C2×#97—731no—
90#330—732no—
91#330—732no—
92C22×C8—1461no—
93C4⋊Q8—731no—
94C4⋊Q8—731no—
95#125—731no—
96#125—731no—
97C22⋊Q8—1461no—
98C22⋊Q8—1461no—
99C4×Q8—1461no—
100C4×Q8—1461no—
101#117—731no—
102#117#6440811yescharacteristic
103C2×C42—731no—
104C4⋊C8—1461no—
105C22⋊C8—1461no—
106#97—732no—
107#97—732no—
108#97—1461no—
109C2×Q8—1461no—
110C2×Q8—1461no—
111C22×C4—731no—
112C22×C4—731no—
113C22×C4C2×#6440811yescharacteristic
114C2×C8—1462no—
115C2×C8—1462no—
116C2×C8—1464no—
117C4⋊C4—731no—
118C4⋊C4—731no—
119C4⋊C4—1461no—
120C4⋊C4—1461no—
121C4⋊C4—1461no—
122C4⋊C4—1461no—
123C4⋊C4—1461no—
124C4⋊C4—1461no—
125C4⋊C4C2×#6440811yescharacteristic
126C4⋊C4C2×#6440811yescharacteristic
127C22⋊C4—21no—
128C22⋊C4—1461no—
129C42—21no—
130C42—731no—
131C42—731no—
132C42—731no—
133C42—731no—
134C42—1461no—
135C23C22⋊#6440811yescharacteristic
136Q8—2922no—
137Q8—2922no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—2921no—
142C2×C4—731no—
143C2×C4—731no—
144C2×C4—731no—
145C2×C4—731no—
146C2×C4—1461no—
147C2×C4—1461no—
148C2×C4—1462no—
149C2×C4C22⋊#6440811yescharacteristic
150C2×C4C22×#6440811yescharacteristic
151C8—2922no—
152C8—1464no—
153C22—21no—
154C22—21no—
155C22#1455665212yes—
156C22C2×C22⋊#6440811yescharacteristic
157C4—21no—
158C4—21no—
159C4—41no—
160C4—41no—
161C4—2921no—
162C4—2921no—
163C4—732no—
164C4—1461no—
165C4—1461no—
166C4—1461no—
167C2—22no—
168C2C2×#1455665211yescharacteristic
169C2D73⋊#10411yescharacteristic
170C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#117×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#117#64408
hypocenterC73#1531
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #17989444C2semidirect
4. #17989444C2semidirect
86. C73#1531semidirect