Finite Group Databasebeta

← #22625452

Subgroups — #22625452

Order 9344.

208 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 62 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×#14556658C211yesmaximal, characteristic
3#17989446C212yesmaximal, complemented
4#17989446C212yesmaximal, complemented
5#17989140C211yesmaximal, characteristic
6C22×#10596833—21no—
7#14556658—21no—
8#14556658C2212yes—
9#14556658C2212yes—
10C22⋊#10596833—21no—
11#14556646—21no—
12#14556590C2211yescharacteristic
13#14556590C2211yescharacteristic
14#14556582C411yescharacteristic
15#14556582C411yescharacteristic
16#14556568—21no—
17#14556568—21no—
18C4×Dic146—21no—
19C4×Dic146—21no—
20#14556550C411yescharacteristic
21C2×C4×Dic73C2211yescharacteristic
22#117×C73C411yescharacteristic
23C2×#10596833—22no—
24C2×#10596833—22no—
25C2×#10596833—42no—
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—21no—
59C2×Dic73—21no—
60C2×Dic73C22⋊C411yescharacteristic
61C2×Dic73C22⋊C411yescharacteristic
62C2×Dic73C2×D411yescharacteristic
63C2×Dic73C2×D411yescharacteristic
64Dic146—42no—
65Dic146—41no—
66Dic146—41no—
67#10596833—42no—
68#10596833—42no—
69C22×C73—21no—
70C22×C73—21no—
71C22×C73#10112yes—
72C22×C73C2×C22⋊C411yescharacteristic
73C4×C73—21no—
74C4×C73—21no—
75C4×C73—41no—
76C4×C73—41no—
77Dic73—21no—
78Dic73—21no—
79Dic73—41no—
80Dic73—41no—
81Dic73#13512yes—
82Dic73AGL(1,ℤ/8)11yescharacteristic
83Dic73#13711yescharacteristic
84C2×C73—22no—
85C2×C73C2×#10111yescharacteristic
86C2×C73#41611yescharacteristic
87C2×C73#41711yescharacteristic
88#1552—731nomaximal, Sylow
89C73#155211yescharacteristic, complemented, Sylow
90#533—731no—
91#432—731no—
92C2×C4⋊C8—731no—
93#332—732no—
94#332—732no—
95C22×C8—1461no—
96C4⋊Q8—731no—
97C4⋊Q8—731no—
98#125—731no—
99#125—731no—
100C22⋊Q8—1461no—
101C22⋊Q8—1461no—
102C4×Q8—1461no—
103C4×Q8—1461no—
104#117—731no—
105#117#6440811yescharacteristic
106C2×C42—731no—
107C4⋊C8—732no—
108C4⋊C8—732no—
109C4⋊C8—1461no—
110C22⋊C8—1461no—
111#97—1461no—
112C2×Q8—1461no—
113C2×Q8—1461no—
114C22×C4—731no—
115C22×C4—731no—
116C22×C4C2×#6440811yescharacteristic
117C2×C8—2922no—
118C2×C8—1462no—
119C2×C8—1462no—
120C4⋊C4—731no—
121C4⋊C4—731no—
122C4⋊C4—1461no—
123C4⋊C4—1461no—
124C4⋊C4—1461no—
125C4⋊C4—1461no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4C2×#6440811yescharacteristic
129C4⋊C4C2×#6440811yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—1461no—
132C42—21no—
133C42—731no—
134C42—731no—
135C42—731no—
136C42—731no—
137C42—1461no—
138C23C22⋊#6440811yescharacteristic
139Q8—2922no—
140Q8—2921no—
141Q8—2921no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—731no—
146C2×C4—731no—
147C2×C4—731no—
148C2×C4—731no—
149C2×C4—1461no—
150C2×C4—1461no—
151C2×C4—1461no—
152C2×C4—1462no—
153C2×C4—1461no—
154C2×C4C22⋊#6440811yescharacteristic
155C2×C4C22×#6440811yescharacteristic
156C8—2922no—
157C8—2922no—
158C22—21no—
159C22—21no—
160C22#1455665212yes—
161C22C2×C22⋊#6440811yescharacteristic
162C4—21no—
163C4—21no—
164C4—41no—
165C4—41no—
166C4—2921no—
167C4—2921no—
168C4—732no—
169C4—731no—
170C4—731no—
171C4—1461no—
172C4—1461no—
173C2—22no—
174C2C2×#1455665211yescharacteristic
175C2#1798957711yescharacteristic
176C2#1798957811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#117×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#117#64408
hypocenterC73#1552
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. #17989446C2semidirect
4. #17989446C2semidirect
89. C73#1552semidirect