Finite Group Databasebeta

← #22620856

Subgroups — #22620856

Order 9344.

428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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#17989137C211yesmaximal, characteristic
2#17988961C212yesmaximal, complemented
3#17988937C212yesmaximal, complemented
4#17988789C214yesmaximal, complemented
5#17988726C214yesmaximal, complemented
6#17988640C211yesmaximal, characteristic, complemented
7C2×C4⋊Q8×C73C211yesmaximal, characteristic, complemented
8C2×#11924028—21no—
9C2×#11924015C2218yes—
10#14556591C2211yescharacteristic
11#14556588C2211yescharacteristic
12#14556579—21no—
13#14556565—21no—
14#14556565C2212yes—
15C4×D292—21no—
16C4×D292C2212yes—
17C4⋊#10596831C2212yes—
18#14556515C2218yes—
19C22⋊#10596831C2212yes—
20C4×#10596831C2212yes—
21C22×Q8×C73C2212yes—
22C4⋊Q8×C73—21no—
23C4⋊Q8×C73—21no—
24C4⋊Q8×C73C2212yes—
25C4⋊Q8×C73C2212yes—
26C2×C4⋊C4×C73—21no—
27C2×C4⋊C4×C73—21no—
28C2×C42×C73C2211yescharacteristic
29#11924028—44no—
30C2×Dic146—21no—
31C2×D292—21no—
32C2×D292—21no—
33C2×D292C2312yes—
34C2×C22⋊D73—22no—
35C2×C4×D73—22no—
36#11924015—48no—
37C2×#10596831C2314yes—
38C4⋊Dic73—21no—
39C4⋊Dic73C2312yes—
40#11924005—22no—
41#11924005—22no—
42C2×Q8×C73—22no—
43C2×Q8×C73—44no—
44C2×Q8×C73C2314yes—
45C22×C4×C73—22no—
46C22×C4×C73D411yescharacteristic
47C22×C4×C73D411yescharacteristic
48C22×C4×C73C2311yescharacteristic
49C4⋊C4×C73—22no—
50C4⋊C4×C73—22no—
51C4⋊C4×C73—22no—
52C4⋊C4×C73—22no—
53C42×C73D411yescharacteristic
54C42×C73D411yescharacteristic
55C42×C73C2311yescharacteristic
56C42×C73C2311yescharacteristic
57C23×C73C2×D411yescharacteristic
58C22×D73—22no—
59Q8×C73—28no—
60Q8×C73—44no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—24no—
64C2×C4×C73—44no—
65C2×C4×C73SD1614yescomplemented
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2411yescharacteristic
72C22⋊D73—44no—
73C2×Dic73—22no—
74D292—24no—
75D292—42no—
76D292—42no—
77C4×D73—44no—
78Dic146—42no—
79#10596831—24no—
80C22×C73—21no—
81C22×C73—21no—
82C22×C73C2×SD1612yes—
83C22×C73C22×D411yescharacteristic
84C2×D73—42no—
85C2×D73—42no—
86C2×D73—42no—
87C4×C73—21no—
88C4×C73—21no—
89C4×C73—44no—
90C4×C73C2×SD1612yes—
91C4×C73C2×SD1612yes—
92C4×C73#13712yes—
93C4×C73H(5,𝔽2)12yes—
94Dic73—42no—
95C2×C73—22no—
96C2×C73#53511yescharacteristic
97C2×C73C22×SD1611yescharacteristic
98C2×C73C2×#13711yescharacteristic
99D73—82no—
100#3206—731nomaximal, Sylow
101C73#320611yescharacteristic, complemented, Sylow
102#532—731no—
103C2×C4⋊Q8D7311yescharacteristic, complemented
104#492—732no—
105#487—732no—
106#461—734no—
107#448—734no—
108#431—731no—
109C2×#41—1461no—
110C22×Q8C2×D7312yes—
111C2×SD16—738no—
112C4⋊Q8—21no—
113C4⋊Q8—21no—
114C4⋊Q8—731no—
115C4⋊Q8C2×D7312yes—
116C4⋊Q8C2×D7312yes—
117#127—731no—
118#124—1461no—
119#121—732no—
120#121—1461no—
121C4×D4—732no—
122C4×D4—1461no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C42C2×D7311yescharacteristic
126C4⋊C8—732no—
127#103—738no—
128C22⋊C8—732no—
129C4×C8—732no—
130#41—2924no—
131C2×Q8—22no—
132C2×Q8—44no—
133C2×Q8—1461no—
134C2×Q8C22×D7314yes—
135C2×D4—732no—
136C2×D4—1462no—
137C2×D4—1461no—
138C2×D4—1461no—
139C22×C4—22no—
140C22×C4—1462no—
141C22×C4C22⋊D7311yescharacteristic
142C22×C4C22⋊D7311yescharacteristic
143C22×C4C22×D7311yescharacteristic
144SD16—2928no—
145C2×C8—734no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—732no—
151C4⋊C4—1461no—
152C22⋊C4—1462no—
153C22⋊C4—1462no—
154C42C22⋊D7311yescharacteristic
155C42C22⋊D7311yescharacteristic
156C42C22×D7311yescharacteristic
157C42C22×D7311yescharacteristic
158C23—1462no—
159C23C2×C22⋊D7311yescharacteristic
160Q8—28no—
161Q8—44no—
162Q8—2922no—
163D4—2924no—
164D4—2922no—
165D4—2922no—
166D4—1464no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—44no—
171C2×C4—2924no—
172C2×C4—1462no—
173C2×C4#1192401514yescomplemented
174C2×C4C2×C22⋊D7311yescharacteristic
175C2×C4C2×C22⋊D7311yescharacteristic
176C2×C4C2×C22⋊D7311yescharacteristic
177C2×C4C2×C22⋊D7311yescharacteristic
178C2×C4C2×C22⋊D7311yescharacteristic
179C2×C4C23×D7311yescharacteristic
180C8—1464no—
181C22—21no—
182C22—21no—
183C22—2922no—
184C22—2922no—
185C22—2922no—
186C22C2×#1192401512yes—
187C22C22×C22⋊D7311yescharacteristic
188C4—21no—
189C4—21no—
190C4—44no—
191C4—2922no—
192C4C2×#1192401512yes—
193C4C2×#1192401512yes—
194C4#1455662212yes—
195C4#1455663612yes—
196C2—22no—
197C2—5842no—
198C2#1798915411yescharacteristic
199C2C22×#1192401511yescharacteristic
200C2C2×#1455662211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×C4⋊Q8×C73C2
socleC22×C73C22×D4
hypercenterC2×C4⋊Q8D73
hypocenterC73#3206
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #17988961C2semidirect
3. #17988937C2semidirect
4. #17988789C2semidirect
5. #17988726C2semidirect
6. #17988640C2semidirect
7. C2×C4⋊Q8×C73C2semidirect
65. C2×C4×C73SD16semidirect
101. C73#3206semidirect
103. C2×C4⋊Q8D73semidirect
173. C2×C4#11924015semidirect