Finite Group Databasebeta

← #22614218

Subgroups — #22614218

Order 9344.

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

normal subgroups only

This group has 512 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×#14556550C211yesmaximal, characteristic
2#17988526C212yesmaximal, complemented
3#17988517C212yesmaximal, complemented
4#17988468C214yesmaximal, complemented
5#17988460C212yesmaximal
6#17988450C212yesmaximal
7#17988450C211yesmaximal, characteristic
8C22×C4⋊C4×C73C211yesmaximal, characteristic
9#14556550—24no—
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007C2214yes—
13C2×C22⋊Dic73C2212yes—
14C2×C22⋊Dic73C2212yes—
15C2×C4×Dic73C2212yes—
16#14556498C2212yes—
17#14556498C2214yes—
18#14556498C2214yes—
19#14556498C2212yes—
20#14556498C2214yes—
21C23×C4×C73C2211yescharacteristic
22C23×C4×C73C2211yescharacteristic
23C23×C4×C73C2211yescharacteristic
24C2×C4⋊C4×C73—24no—
25C2×C4⋊C4×C73C2212yes—
26C2×C4⋊C4×C73C2212yes—
27C22×Dic73C2314yes—
28C22×Dic73C2312yes—
29C22×Dic73C2312yes—
30C4⋊Dic73—22no—
31C4⋊Dic73—22no—
32#11924007—28no—
33C22⋊Dic73—24no—
34C22⋊Dic73—24no—
35C4×Dic73—24no—
36C24×C73C2311yescharacteristic
37C22×C4×C73—22no—
38C22×C4×C73—24no—
39C22×C4×C73—24no—
40C22×C4×C73—22no—
41C22×C4×C73—24no—
42C22×C4×C73D414yes—
43C22×C4×C73C2312yes—
44C22×C4×C73C2311yescharacteristic
45C22×C4×C73C2311yescharacteristic
46C22×C4×C73C2312yes—
47C4⋊C4×C73—24no—
48C4⋊C4×C73—24no—
49C23×C73—22no—
50C23×C73—22no—
51C23×C73C2×D412yes—
52C23×C73#4114yes—
53C23×C73C2411yescharacteristic
54C2×C4×C73—28no—
55C2×C4×C73—28no—
56C2×C4×C73—22no—
57C2×C4×C73—22no—
58C2×C4×C73—22no—
59C2×C4×C73—22no—
60C2×C4×C73—22no—
61C2×C4×C73—24no—
62C2×C4×C73—44no—
63C2×C4×C73C2×D412yes—
64C2×C4×C73C2×D412yes—
65C2×C4×C73#4114yes—
66C2×Dic73—22no—
67C2×Dic73—22no—
68C2×Dic73—24no—
69C2×Dic73—24no—
70C2×Dic73—24no—
71C2×Dic73—24no—
72C2×Dic73—24no—
73C22×C73—22no—
74C22×C73—22no—
75C22×C73—28no—
76C22×C73#12314yes—
77C22×C73C22×D411yescharacteristic
78C22×C73C2×#4112yes—
79C22×C73C2×#4112yes—
80C22×C732−1+412yes—
81C4×C73—22no—
82C4×C73—22no—
83C4×C73—24no—
84C4×C73—42no—
85Dic73—42no—
86Dic73—42no—
87Dic73—44no—
88C2×C73—24no—
89C2×C73C2×#12311yescharacteristic
90C2×C73#52511yescharacteristic
91C2×C73#53611yescharacteristic
92C2×C73#55214yes—
93#2484—731nomaximal, Sylow
94C73#248411yescharacteristic, complemented, Sylow
95C2×#117—731no—
96C22×C4⋊C4D7311yescharacteristic
97#400—732no—
98#398—732no—
99#387—734no—
100#385—732no—
101#381—731no—
102#381—732no—
103C23×C4C2×D7311yescharacteristic
104C23×C4C2×D7311yescharacteristic
105C23×C4C2×D7311yescharacteristic
106#117—1464no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4—731no—
109C2×C4⋊C4—731no—
110C2×C4⋊C4—734no—
111C2×C4⋊C4C2×D7312yes—
112C2×C4⋊C4C2×D7312yes—
113C2×C22⋊C4—732no—
114C2×C22⋊C4—732no—
115C2×C42—732no—
116#95—732no—
117#95—734no—
118#95—734no—
119#95—732no—
120#95—734no—
121C24C22×D7311yescharacteristic
122C22×C4—22no—
123C22×C4—24no—
124C22×C4—24no—
125C22×C4—22no—
126C22×C4—24no—
127C22×C4—734no—
128C22×C4—732no—
129C22×C4—732no—
130C22×C4C22⋊D7314yes—
131C22×C4C22×D7312yes—
132C22×C4C22×D7311yescharacteristic
133C22×C4C22×D7311yescharacteristic
134C22×C4C22×D7312yes—
135C4⋊C4—24no—
136C4⋊C4—24no—
137C4⋊C4—1462no—
138C4⋊C4—1462no—
139C4⋊C4—1468no—
140C22⋊C4—1464no—
141C22⋊C4—1464no—
142C42—1464no—
143C23—22no—
144C23—22no—
145C23C2×C22⋊D7312yes—
146C23#1192402714yes—
147C23C23×D7311yescharacteristic
148C2×C4—28no—
149C2×C4—28no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—24no—
156C2×C4—44no—
157C2×C4—1462no—
158C2×C4—1462no—
159C2×C4—1464no—
160C2×C4—1464no—
161C2×C4—1464no—
162C2×C4—1464no—
163C2×C4—1464no—
164C2×C4C2×C22⋊D7312yes—
165C2×C4C2×C22⋊D7312yes—
166C2×C4#1192402814yes—
167C22—22no—
168C22—28no—
169C22—22no—
170C22#1455657214yes—
171C22C22×C22⋊D7311yescharacteristic
172C22C2×#1192402712yes—
173C22C2×#1192402812yes—
174C22#1455663912yes—
175C4—22no—
176C4—22no—
177C4—24no—
178C4—42no—
179C4—2922no—
180C4—2924no—
181C4—2922no—
182C2—24no—
183C2C2×#1455657211yescharacteristic
184C2#1798909811yescharacteristic
185C2#1798916111yescharacteristic
186C2#1798927214yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC22×C4⋊C4×C73C2
hypercenterC22×C4⋊C4D73
hypocenterC73#2484
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #17988526C2semidirect
3. #17988517C2semidirect
4. #17988468C2semidirect
94. C73#2484semidirect