Finite Group Databasebeta

← #22625449

Subgroups — #22625449

Order 9344.

216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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#17989590C211yesmaximal, characteristic
2C2×#14556658C211yesmaximal, characteristic
3#17989447C212yesmaximal, complemented
4#17989446C212yesmaximal, complemented
5#17989139C211yesmaximal, characteristic
6C2×#11924037—21no—
7C22×#10596833—21no—
8#14556658—21no—
9#14556658C2212yes—
10#14556658C2212yes—
11C4⋊#10596833—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×#10596833—42no—
27C2×Dic146—21no—
28C2×Dic146C2×C411yescharacteristic
29C22×Dic73D411yescharacteristic
30C22×Dic73D411yescharacteristic
31C4⋊Dic73—21no—
32C4⋊Dic73C2×C411yescharacteristic
33#11924007—21no—
34#11924007—21no—
35#11924007—21no—
36#11924007—21no—
37#11924007—21no—
38C22⋊Dic73—21no—
39C4×Dic73—21no—
40C4×Dic73—21no—
41C4×Dic73C2×C411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73C2311yescharacteristic
45C2×Q8×C73C2×C411yescharacteristic
46C22×C4×C73C2×C411yescharacteristic
47C4⋊C4×C73—21no—
48C4⋊C4×C73C2×C411yescharacteristic
49C22⋊C4×C73—21no—
50C23×C73C22⋊C411yescharacteristic
51Q8×C73—41no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—41no—
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22×C411yescharacteristic
57C2×Dic73—21no—
58C2×Dic73—21no—
59C2×Dic73—21no—
60C2×Dic73—21no—
61C2×Dic73C22⋊C411yescharacteristic
62C2×Dic73C22⋊C411yescharacteristic
63C2×Dic73SD1612yes—
64C2×Dic73Q1612yes—
65C2×Dic73C2×D411yescharacteristic
66C2×Dic73C2×D411yescharacteristic
67Dic146—41no—
68Dic146—41no—
69Dic146—41no—
70#10596833—42no—
71#10596833—42no—
72C22×C73—21no—
73C22×C73—21no—
74C22×C73#10312yes—
75C22×C73C2×C22⋊C411yescharacteristic
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—41no—
79C4×C73—41no—
80Dic73—21no—
81Dic73—41no—
82Dic73—41no—
83Dic73#10312yes—
84Dic73C2×SD1611yescharacteristic
85Dic73C2×Q1611yescharacteristic
86Dic73AGL(1,ℤ/8)11yescharacteristic
87Dic73#13711yescharacteristic
88C2×C73—22no—
89C2×C73#41311yescharacteristic
90C2×C73C2×#10311yescharacteristic
91C2×C73#41711yescharacteristic
92#1550—731nomaximal, Sylow
93C73#155011yescharacteristic, complemented, Sylow
94#533—731no—
95#423—731no—
96C2×C4⋊C8—731no—
97#333—732no—
98#332—732no—
99C2×M16—1461no—
100C22×C8—1461no—
101C4⋊Q8—731no—
102C4⋊Q8—731no—
103#125—1461no—
104C22⋊Q8—731no—
105C22⋊Q8—1461no—
106C22⋊Q8#6440811yescharacteristic
107C4×Q8—731no—
108C4×Q8—731no—
109C4×Q8—1461no—
110#117—1461no—
111C2×C42—731no—
112C4⋊C8—732no—
113C4⋊C8—732no—
114C4⋊C8—1461no—
115C4⋊C8—1461no—
116C2×Q8—731no—
117C2×Q8—1461no—
118C2×Q8C2×#6440811yescharacteristic
119C22×C4—731no—
120C22×C4—731no—
121C22×C4C2×#6440811yescharacteristic
122M16—2922no—
123C2×C8—2922no—
124C2×C8—1462no—
125C2×C8—1462no—
126C4⋊C4—21no—
127C4⋊C4—731no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4—1461no—
132C4⋊C4—1461no—
133C4⋊C4—1461no—
134C4⋊C4C2×#6440811yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—1461no—
137C42—731no—
138C42—731no—
139C42—731no—
140C42—731no—
141C42—1461no—
142C42—1461no—
143C23C22⋊#6440811yescharacteristic
144Q8—41no—
145Q8—2921no—
146Q8—2921no—
147Q8—2921no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—732no—
152C2×C4—732no—
153C2×C4—731no—
154C2×C4—731no—
155C2×C4—731no—
156C2×C4—731no—
157C2×C4—1461no—
158C2×C4—1461no—
159C2×C4—1461no—
160C2×C4—1461no—
161C2×C4C22⋊#6440811yescharacteristic
162C2×C4C22×#6440811yescharacteristic
163C8—2922no—
164C8—2922no—
165C22—21no—
166C22—21no—
167C22#1455665412yes—
168C22C2×C22⋊#6440811yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—2921no—
174C4—2921no—
175C4—731no—
176C4—732no—
177C4—731no—
178C4—731no—
179C4—731no—
180C4—1461no—
181C2—22no—
182C2#1798957411yescharacteristic
183C2C2×#1455665411yescharacteristic
184C2#1798957811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22⋊Q8#64408
hypocenterC73#1550
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
93. C73#1550semidirect