Finite Group Databasebeta

← #22620478

Subgroups — #22620478

Order 9344.

380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#14556591C211yesmaximal, characteristic
2#17988997C214yesmaximal, complemented
3#17988990C212yesmaximal, complemented
4#17988983C212yesmaximal, complemented
5#17988630C214yesmaximal
6C4×#11924012C211yesmaximal, characteristic
7#533×C73C211yesmaximal, characteristic
8C22×Dic146—21no—
9C2×#11924012C2212yes—
10#14556591—21no—
11#14556591—21no—
12#14556591C2212yes—
13#14556591C2212yes—
14C2×C4⋊Dic73—21no—
15C2×C4⋊Dic73C2212yes—
16#14556524C2218yes—
17#14556522C2218yes—
18#14556502C2212yes—
19C4×#10596831C2212yes—
20C4⋊Q8×C73C2211yescharacteristic
21C4⋊Q8×C73C2211yescharacteristic
22#125×C73C2212yes—
23C22⋊Q8×C73—21no—
24C22⋊Q8×C73—21no—
25C4×Q8×C73—21no—
26C4×Q8×C73—21no—
27#117×C73C2212yes—
28C2×C42×C73C2211yescharacteristic
29C2×Dic146—22no—
30C2×Dic146—22no—
31C2×Dic146—44no—
32C22×Dic73—22no—
33#11924012Q818yescomplemented
34C2×#10596831C2314yes—
35C4⋊Dic73—22no—
36C4⋊Dic73—22no—
37C4⋊Dic73—22no—
38C4⋊Dic73C2314yes—
39C2×Q8×C73—21no—
40C2×Q8×C73—21no—
41C22×C4×C73D411yescharacteristic
42C22×C4×C73D411yescharacteristic
43C22×C4×C73C2311yescharacteristic
44C4⋊C4×C73—22no—
45C4⋊C4×C73—22no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73—21no—
48C4⋊C4×C73C2312yes—
49C4⋊C4×C73C2312yes—
50C22⋊C4×C73—22no—
51C42×C73—22no—
52C42×C73D411yescharacteristic
53C42×C73D411yescharacteristic
54C42×C73C2311yescharacteristic
55C42×C73C2311yescharacteristic
56C23×C73C2×D411yescharacteristic
57Q8×C73—42no—
58Q8×C73—42no—
59C2×C4×C73—22no—
60C2×C4×C73—22no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73C2×D411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×Q814yes—
69C2×C4×C73C2411yescharacteristic
70C2×Dic73—24no—
71C2×Dic73—44no—
72Dic146—44no—
73Dic146—44no—
74#10596831C2×Q818yescomplemented
75C22×C73—21no—
76C22×C73—21no—
77C22×C73C4⋊Q812yes—
78C22×C73C22×D411yescharacteristic
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—42no—
82C4×C73—42no—
83C4×C73C4⋊Q812yes—
84C4×C73AGL(1,ℤ/8)12yes—
85C4×C73#13712yes—
86C4×C73C22×Q812yes—
87Dic73—44no—
88C2×C73—22no—
89C2×C73C2×C4⋊Q811yescharacteristic
90C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
91C2×C73C2×#13711yescharacteristic
92#3165—731nomaximal, Sylow
93C73#316511yescharacteristic, complemented, Sylow
94#533D7311yescharacteristic
95C2×C4⋊Q8—731no—
96#501—734no—
97#500—732no—
98#498—732no—
99#428—734no—
100C4×M16—731no—
101C22×Q8—1461no—
102C2×M16—732no—
103C4⋊Q8—732no—
104C4⋊Q8—732no—
105C4⋊Q8—1461no—
106C4⋊Q8—1461no—
107C4⋊Q8C2×D7311yescharacteristic
108C4⋊Q8C2×D7311yescharacteristic
109#125C2×D7312yes—
110C22⋊Q8—21no—
111C22⋊Q8—21no—
112C4×Q8—21no—
113C4×Q8—21no—
114#117C2×D7312yes—
115C2×C4⋊C4—732no—
116C2×C4⋊C4—1461no—
117C2×C42C2×D7311yescharacteristic
118#107—738no—
119#106—738no—
120#97—732no—
121C4×C8—732no—
122C2×Q8—21no—
123C2×Q8—21no—
124C2×Q8—2924no—
125C2×Q8—1462no—
126C2×Q8—1462no—
127C22×C4—1462no—
128C22×C4C22⋊D7311yescharacteristic
129C22×C4C22⋊D7311yescharacteristic
130C22×C4C22×D7311yescharacteristic
131M16—738no—
132C2×C8—734no—
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—734no—
138C4⋊C4—1462no—
139C4⋊C4—1462no—
140C4⋊C4—1462no—
141C4⋊C4C22×D7312yes—
142C4⋊C4C22×D7312yes—
143C22⋊C4—22no—
144C42—22no—
145C42C22⋊D7311yescharacteristic
146C42C22⋊D7311yescharacteristic
147C42C22×D7311yescharacteristic
148C42C22×D7311yescharacteristic
149C23C2×C22⋊D7311yescharacteristic
150Q8—42no—
151Q8—42no—
152Q8—2924no—
153Q8—2924no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—2924no—
159C2×C4—1464no—
160C2×C4C2×C22⋊D7311yescharacteristic
161C2×C4C2×C22⋊D7311yescharacteristic
162C2×C4C2×C22⋊D7311yescharacteristic
163C2×C4C2×C22⋊D7311yescharacteristic
164C2×C4C2×C22⋊D7311yescharacteristic
165C2×C4Q8×D7314yes—
166C2×C4C23×D7311yescharacteristic
167C8—738no—
168C22—21no—
169C22—21no—
170C22#1455658912yes—
171C22C22×C22⋊D7311yescharacteristic
172C4—21no—
173C4—21no—
174C4—42no—
175C4—42no—
176C4—2924no—
177C4#1455658912yes—
178C4#1455661612yes—
179C4#1455662112yes—
180C4C2×Q8×D7312yes—
181C2—22no—
182C2C2×#1455658911yescharacteristic
183C2C2×#1455661611yescharacteristic
184C2C2×#1455662111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#533×C73C2
socleC22×C73C22×D4
hypercenter#533D73
hypocenterC73#3165
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #17988997C2semidirect
3. #17988990C2semidirect
4. #17988983C2semidirect
33. #11924012Q8semidirect
74. #10596831C2×Q8semidirect
93. C73#3165semidirect