Finite Group Databasebeta

← #22615744

Subgroups — #22615744

Order 9344.

508 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14556570C211yesmaximal, characteristic
2#17988526C212yesmaximal, complemented
3#17988520C214yesmaximal, complemented
4#17988507C212yesmaximal, complemented
5#17988460C212yesmaximal
6#17988450C212yesmaximal
7#17988447C211yesmaximal, characteristic
8C22×C4⋊C4×C73C211yesmaximal, characteristic
9C22×Dic146C2211yescharacteristic
10#14556570—24no—
11C2×C4⋊Dic73C2211yescharacteristic
12C2×C4⋊Dic73C2212yes—
13C2×#11924007C2212yes—
14C2×#11924007C2214yes—
15C2×C22⋊Dic73C2212yes—
16C2×C22⋊Dic73C2212yes—
17#14556498C2212yes—
18#14556498C2214yes—
19#14556498C2214yes—
20#14556498C2214yes—
21C23×C4×C73C2211yescharacteristic
22C23×C4×C73C2211yescharacteristic
23C23×C4×C73C2211yescharacteristic
24C2×C4⋊C4×C73—24no—
25C2×C4⋊C4×C73C2212yes—
26C2×C4⋊C4×C73C2212yes—
27C2×Dic146—22no—
28C2×Dic146—42no—
29C22×Dic73C2312yes—
30C22×Dic73C2314yes—
31C22×Dic73C2312yes—
32C4⋊Dic73—22no—
33C4⋊Dic73—42no—
34#11924007—24no—
35#11924007—44no—
36C22⋊Dic73—24no—
37C22⋊Dic73—24no—
38C24×C73C2311yescharacteristic
39C22×C4×C73—22no—
40C22×C4×C73—22no—
41C22×C4×C73—22no—
42C22×C4×C73—42no—
43C22×C4×C73—42no—
44C22×C4×C73D414yes—
45C22×C4×C73Q814yescomplemented
46C22×C4×C73C2312yes—
47C22×C4×C73C2311yescharacteristic
48C22×C4×C73C2311yescharacteristic
49C22×C4×C73C2312yes—
50C4⋊C4×C73—24no—
51C4⋊C4×C73—24no—
52C23×C73—22no—
53C23×C73—22no—
54C23×C73C2×D412yes—
55C23×C73C2×Q812yes—
56C23×C73#4112yes—
57C23×C73C2411yescharacteristic
58C2×C4×C73—28no—
59C2×C4×C73—22no—
60C2×C4×C73—22no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—22no—
64C2×C4×C73—24no—
65C2×C4×C73—44no—
66C2×C4×C73—44no—
67C2×C4×C73C2×D412yes—
68C2×C4×C73C2×D412yes—
69C2×C4×C73C2×Q814yes—
70C2×Dic73—22no—
71C2×Dic73—22no—
72C2×Dic73—24no—
73C2×Dic73—24no—
74C2×Dic73—24no—
75C2×Dic73—24no—
76C2×Dic73—24no—
77Dic146—44no—
78C22×C73—22no—
79C22×C73—22no—
80C22×C73—24no—
81C22×C73—24no—
82C22×C73C22⋊Q814yes—
83C22×C73C22×D411yescharacteristic
84C22×C73C22×Q811yescharacteristic
85C22×C73C2×#4111yescharacteristic
86C22×C73H(5,𝔽2)12yes—
87C22×C732−1+412yes—
88C4×C73—24no—
89C4×C73—22no—
90C4×C73—22no—
91C4×C73—42no—
92Dic73—42no—
93Dic73—42no—
94Dic73—44no—
95C2×C73—24no—
96C2×C73C2×C22⋊Q811yescharacteristic
97C2×C73#53411yescharacteristic
98C2×C73#53611yescharacteristic
99C2×C73#53912yes—
100C2×C73#54412yes—
101#2627—731nomaximal, Sylow
102C73#262711yescharacteristic, complemented, Sylow
103C2×C22⋊Q8—731no—
104C22×C4⋊C4D7311yescharacteristic
105#400—732no—
106#398—734no—
107#395—732no—
108#385—732no—
109#381—732no—
110#380—731no—
111C22×Q8—731no—
112C23×C4C2×D7311yescharacteristic
113C23×C4C2×D7311yescharacteristic
114C23×C4C2×D7311yescharacteristic
115C22⋊Q8—1464no—
116C2×C4⋊C4—24no—
117C2×C4⋊C4—732no—
118C2×C4⋊C4—734no—
119C2×C4⋊C4—732no—
120C2×C4⋊C4—731no—
121C2×C4⋊C4C2×D7312yes—
122C2×C4⋊C4C2×D7312yes—
123C2×C22⋊C4—732no—
124C2×C22⋊C4—732no—
125#95—732no—
126#95—734no—
127#95—734no—
128#95—734no—
129C24C22×D7311yescharacteristic
130C2×Q8—2922no—
131C2×Q8—1462no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—42no—
136C22×C4—42no—
137C22×C4—732no—
138C22×C4—734no—
139C22×C4—732no—
140C22×C4Dic14614yescomplemented
141C22×C4C22⋊D7314yes—
142C22×C4C22×D7312yes—
143C22×C4C22×D7311yescharacteristic
144C22×C4C22×D7311yescharacteristic
145C22×C4C22×D7312yes—
146C4⋊C4—24no—
147C4⋊C4—24no—
148C4⋊C4—2924no—
149C4⋊C4—2922no—
150C4⋊C4—1464no—
151C4⋊C4—1462no—
152C22⋊C4—1464no—
153C22⋊C4—1464no—
154C23—22no—
155C23—22no—
156C23C2×C22⋊D7312yes—
157C23C2×Dic14612yes—
158C23#1192402812yes—
159C23C23×D7311yescharacteristic
160Q8—2924no—
161C2×C4—28no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—44no—
169C2×C4—44no—
170C2×C4—1462no—
171C2×C4—1462no—
172C2×C4—1464no—
173C2×C4—1464no—
174C2×C4—1464no—
175C2×C4—1464no—
176C2×C4—1464no—
177C2×C4C2×C22⋊D7312yes—
178C2×C4C2×C22⋊D7312yes—
179C2×C4C2×Dic14614yes—
180C22—22no—
181C22—22no—
182C22—24no—
183C22—24no—
184C22#1455657014yes—
185C22C22×C22⋊D7311yescharacteristic
186C22C22×Dic14611yescharacteristic
187C22C2×#1192402811yescharacteristic
188C22#1455663612yes—
189C22#1455663912yes—
190C4—22no—
191C4—22no—
192C4—24no—
193C4—42no—
194C4—2922no—
195C4—2922no—
196C4—2924no—
197C2—24no—
198C2C2×#1455657011yescharacteristic
199C2#1798914611yescharacteristic
200C2#1798916111yescharacteristic
201C2#1798918412yes—
202C2#1798921812yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC22×C4⋊C4×C73C2
hypercenterC22×C4⋊C4D73
hypocenterC73#2627
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. #17988520C2semidirect
4. #17988507C2semidirect
45. C22×C4×C73Q8semidirect
102. C73#2627semidirect
140. C22×C4Dic146semidirect