Finite Group Databasebeta

← #22625467

Subgroups — #22625467

Order 9344.

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

normal subgroups only

This group has 202 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#17989607C211yesmaximal, characteristic
2#17989590C211yesmaximal, characteristic
3#17989447C212yesmaximal, complemented
4#17989446C212yesmaximal, complemented
5#17989139C211yesmaximal, characteristic
6C2×#11924037—21no—
7#14556658C2212yes—
8#14556658C2212yes—
9C4⋊#10596833—21no—
10C22⋊#10596833—21no—
11#14556646—21no—
12#14556590C2211yescharacteristic
13#14556589C2211yescharacteristic
14#14556581—21no—
15#14556570C411yescharacteristic
16#14556568—21no—
17Q8×Dic73C411yescharacteristic
18#14556556—21no—
19#14556556C411yescharacteristic
20#14556547—21no—
21C2×C4×Dic73C2211yescharacteristic
22C22⋊Q8×C73C411yescharacteristic
23#11924037—42no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26C2×Dic146—21no—
27C2×Dic146C2×C411yescharacteristic
28C22×Dic73D411yescharacteristic
29C22×Dic73D411yescharacteristic
30C4⋊Dic73—21no—
31C4⋊Dic73C2×C411yescharacteristic
32#11924007—21no—
33#11924007—21no—
34#11924007—21no—
35#11924007—21no—
36#11924007—21no—
37C22⋊Dic73—21no—
38C4×Dic73—21no—
39C4×Dic73—21no—
40C4×Dic73C2×C411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73C2311yescharacteristic
44C2×Q8×C73C2×C411yescharacteristic
45C22×C4×C73C2×C411yescharacteristic
46C4⋊C4×C73—21no—
47C4⋊C4×C73C2×C411yescharacteristic
48C22⋊C4×C73—21no—
49C23×C73C22⋊C411yescharacteristic
50Q8×C73—41no—
51C2×C4×C73—21no—
52C2×C4×C73—21no—
53C2×C4×C73—41no—
54C2×C4×C73C22⋊C411yescharacteristic
55C2×C4×C73C22×C411yescharacteristic
56C2×Dic73—21no—
57C2×Dic73—21no—
58C2×Dic73—22no—
59C2×Dic73—21no—
60C2×Dic73—21no—
61C2×Dic73C22⋊C411yescharacteristic
62C2×Dic73C22⋊C411yescharacteristic
63C2×Dic73C2×D411yescharacteristic
64C2×Dic73C2×D411yescharacteristic
65Dic146—41no—
66Dic146—41no—
67Dic146—41no—
68#10596833—42no—
69#10596833—42no—
70C22×C73—21no—
71C22×C73—21no—
72C22×C73—21no—
73C22×C73C2×C22⋊C411yescharacteristic
74C4×C73—21no—
75C4×C73—21no—
76C4×C73—41no—
77C4×C73—41no—
78Dic73—21no—
79Dic73—21no—
80Dic73—41no—
81Dic73—41no—
82Dic73AGL(1,ℤ/8)11yescharacteristic
83Dic73#13711yescharacteristic
84Dic73#13712yes—
85C2×C73—41no—
86C2×C73#41311yescharacteristic
87C2×C73#41711yescharacteristic
88C2×C73#41911yescharacteristic
89#1559—731nomaximal, Sylow
90C73#155911yescharacteristic, complemented, Sylow
91#533—731no—
92#432—731no—
93#423—731no—
94#333—732no—
95#332—732no—
96C2×M16—1461no—
97C4⋊Q8—731no—
98C4⋊Q8—731no—
99#125—1461no—
100C22⋊Q8—731no—
101C22⋊Q8—1461no—
102C22⋊Q8#6440811yescharacteristic
103C4×Q8—731no—
104C4×Q8—731no—
105C4×Q8—1461no—
106#117—1461no—
107C2×C42—731no—
108C4⋊C8—732no—
109C4⋊C8—732no—
110C4⋊C8—1461no—
111C22⋊C8—1461no—
112#97—1461no—
113C2×Q8—731no—
114C2×Q8—1461no—
115C2×Q8C2×#6440811yescharacteristic
116C22×C4—731no—
117C22×C4—731no—
118C22×C4C2×#6440811yescharacteristic
119M16—2922no—
120C2×C8—1462no—
121C2×C8—1462no—
122C4⋊C4—21no—
123C4⋊C4—731no—
124C4⋊C4—1461no—
125C4⋊C4—1461no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C4⋊C4C2×#6440811yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—1461no—
133C42—731no—
134C42—731no—
135C42—731no—
136C42—731no—
137C42—1461no—
138C42—1461no—
139C23C22⋊#6440811yescharacteristic
140Q8—41no—
141Q8—2921no—
142Q8—2921no—
143Q8—2921no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—731no—
148C2×C4—731no—
149C2×C4—731no—
150C2×C4—731no—
151C2×C4—1461no—
152C2×C4—1461no—
153C2×C4—1461no—
154C2×C4—1461no—
155C2×C4—1462no—
156C2×C4C22⋊#6440811yescharacteristic
157C2×C4C22×#6440811yescharacteristic
158C8—2922no—
159C8—2922no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22C2×C22⋊#6440811yescharacteristic
164C4—21no—
165C4—21no—
166C4—41no—
167C4—41no—
168C4—2921no—
169C4—2921no—
170C4—731no—
171C4—731no—
172C4—732no—
173C4—1461no—
174C4—1461no—
175C2—41no—
176C2#1798957411yescharacteristic
177C2#1798957811yescharacteristic
178C2#1798958011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22⋊Q8#64408
hypocenterC73#1559
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #17989447C2semidirect
4. #17989446C2semidirect
90. C73#1559semidirect