Finite Group Databasebeta

← #22620477

Subgroups — #22620477

Order 9344.

380 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 173 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#17989144C211yesmaximal, characteristic
2C2×#14556591C211yesmaximal, characteristic
3#17988996C214yesmaximal, complemented
4#17988992C212yesmaximal, complemented
5#17988985C212yesmaximal, complemented
6#17988629C214yesmaximal
7C4×M16×C73C211yesmaximal, characteristic
8C22×Dic146—21no—
9#14556591—21no—
10#14556591—21no—
11#14556591C2212yes—
12#14556591C2212yes—
13#14556591C2211yescharacteristic
14#14556591C2211yescharacteristic
15#14556583C2212yes—
16#14556570—21no—
17#14556570—21no—
18C4×Dic146—21no—
19C4×Dic146—21no—
20#14556550C2212yes—
21C2×C4⋊Dic73—21no—
22C2×C4⋊Dic73C2212yes—
23#14556525C2218yes—
24#14556523C2218yes—
25C2×M16×C73C2212yes—
26C2×C42×C73C2211yescharacteristic
27#97×C73C2212yes—
28C4×C8×C73C2212yes—
29C2×Dic146—21no—
30C2×Dic146—21no—
31C2×Dic146—22no—
32C2×Dic146—22no—
33C2×Dic146—44no—
34C22×Dic73—22no—
35C4⋊Dic73—22no—
36C4⋊Dic73—22no—
37C4⋊Dic73—22no—
38C4⋊Dic73—21no—
39C4⋊Dic73—21no—
40C4⋊Dic73C2312yes—
41C4⋊Dic73C2314yes—
42C4⋊Dic73C2312yes—
43#11924007—22no—
44#11924007—22no—
45C22⋊Dic73—22no—
46C4×Dic73—22no—
47C22×C4×C73D411yescharacteristic
48C22×C4×C73D411yescharacteristic
49C22×C4×C73C2311yescharacteristic
50M16×C73Q818yescomplemented
51C2×C8×C73C2314yes—
52C42×C73D411yescharacteristic
53C42×C73D411yescharacteristic
54C42×C73C2311yescharacteristic
55C42×C73C2311yescharacteristic
56C23×C73C2×D411yescharacteristic
57C2×C4×C73—22no—
58C2×C4×C73—22no—
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73C2×D411yescharacteristic
64C2×C4×C73C2×Q814yes—
65C2×C4×C73C2411yescharacteristic
66C2×Dic73—22no—
67C2×Dic73—22no—
68C2×Dic73—24no—
69C2×Dic73—44no—
70Dic146—44no—
71Dic146—42no—
72Dic146—44no—
73Dic146—42no—
74C8×C73C2×Q818yescomplemented
75C22×C73—21no—
76C22×C73—21no—
77C22×C73C4⋊Q812yes—
78C22×C73C22×D411yescharacteristic
79C4×C73—21no—
80C4×C73—21no—
81C4×C73C4⋊Q812yes—
82C4×C73AGL(1,ℤ/8)12yes—
83C4×C73#13712yes—
84C4×C73C22×Q812yes—
85Dic73—44no—
86Dic73—42no—
87Dic73—42no—
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#533—731no—
95C2×C4⋊Q8—731no—
96#501—734no—
97#500—732no—
98#498—732no—
99#428—734no—
100C4×M16D7311yescharacteristic
101C22×Q8—1461no—
102C2×M16C2×D7312yes—
103C4⋊Q8—732no—
104C4⋊Q8—732no—
105C4⋊Q8—731no—
106C4⋊Q8—731no—
107C4⋊Q8—1461no—
108C4⋊Q8—1461no—
109#125—732no—
110C22⋊Q8—1461no—
111C22⋊Q8—1461no—
112C4×Q8—1461no—
113C4×Q8—1461no—
114#117—732no—
115C2×C4⋊C4—732no—
116C2×C4⋊C4—1461no—
117C2×C42C2×D7311yescharacteristic
118#107—738no—
119#106—738no—
120#97C2×D7312yes—
121C4×C8C2×D7312yes—
122C2×Q8—2924no—
123C2×Q8—1461no—
124C2×Q8—1461no—
125C2×Q8—1462no—
126C2×Q8—1462no—
127C22×C4—1462no—
128C22×C4D29211yescharacteristic
129C22×C4D29211yescharacteristic
130C22×C4C22×D7311yescharacteristic
131M16Dic14618yescomplemented
132C2×C8C22×D7314yes—
133C4⋊C4—732no—
134C4⋊C4—734no—
135C4⋊C4—732no—
136C4⋊C4—1462no—
137C4⋊C4—1462no—
138C4⋊C4—1462no—
139C4⋊C4—1462no—
140C4⋊C4—1462no—
141C4⋊C4—1461no—
142C4⋊C4—1461no—
143C22⋊C4—1462no—
144C42—1462no—
145C42D29211yescharacteristic
146C42D29211yescharacteristic
147C42C22×D7311yescharacteristic
148C42C22×D7311yescharacteristic
149C23C2×D29211yescharacteristic
150Q8—2924no—
151Q8—2924no—
152Q8—2922no—
153Q8—2922no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—2924no—
157C2×C4—1462no—
158C2×C4—1462no—
159C2×C4—1464no—
160C2×C4C2×D29211yescharacteristic
161C2×C4C2×D29211yescharacteristic
162C2×C4C2×D29211yescharacteristic
163C2×C4C2×D29211yescharacteristic
164C2×C4C2×D29211yescharacteristic
165C2×C4C2×Dic14614yes—
166C2×C4C23×D7311yescharacteristic
167C8C2×Dic14618yescomplemented
168C22—21no—
169C22—21no—
170C22#1455659112yes—
171C22C22×D29211yescharacteristic
172C4—21no—
173C4—21no—
174C4—2924no—
175C4—2922no—
176C4—2922no—
177C4#1455659112yes—
178C4#1455661912yes—
179C4#1455662412yes—
180C4C22×Dic14612yes—
181C2—22no—
182C2C2×#1455659111yescharacteristic
183C2C2×#1455661911yescharacteristic
184C2C2×#1455662411yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×M16×C73C2
socleC22×C73C22×D4
hypercenterC4×M16D73
hypocenterC73#3165
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #17988996C2semidirect
4. #17988992C2semidirect
5. #17988985C2semidirect
50. M16×C73Q8semidirect
74. C8×C73C2×Q8semidirect
93. C73#3165semidirect
131. M16Dic146semidirect
167. C8C2×Dic146semidirect