Finite Group Databasebeta

← #22620853

Subgroups — #22620853

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
1C2×#14556591C211yesmaximal, characteristic, complemented
2#17988959C212yesmaximal, complemented
3#17988939C212yesmaximal, complemented
4#17988792C214yesmaximal, complemented
5#17988725C214yesmaximal, complemented
6#17988640C211yesmaximal, characteristic, complemented
7#532×C73C211yesmaximal, characteristic
8C22×Dic146C2212yes—
9C2×#11924016C2218yes—
10#14556591—21no—
11#14556591—21no—
12#14556591C2212yes—
13#14556591C2212yes—
14C2×C4⋊Dic73—21no—
15C2×C4⋊Dic73—21no—
16C4⋊#10596831C2212yes—
17#14556514C2218yes—
18C22⋊#10596831C2212yes—
19C4×#10596831C2212yes—
20C2×#41×C73—21no—
21C4⋊Q8×C73C2211yescharacteristic
22#127×C73C2211yescharacteristic
23#124×C73—21no—
24#121×C73—21no—
25#121×C73C2212yes—
26C4×D4×C73—21no—
27C4×D4×C73C2212yes—
28C2×C42×C73C2211yescharacteristic
29C2×Dic146—22no—
30C2×Dic146—44no—
31C2×Dic146C2314yes—
32C22×Dic73—22no—
33#11924016—48no—
34C2×#10596831C2314yes—
35C4⋊Dic73—22no—
36C4⋊Dic73—22no—
37C4⋊Dic73—22no—
38C4⋊Dic73—22no—
39#41×C73—44no—
40C2×Q8×C73—21no—
41C2×D4×C73—22no—
42C2×D4×C73—21no—
43C2×D4×C73—21no—
44C2×D4×C73C2312yes—
45C22×C4×C73—22no—
46C22×C4×C73D411yescharacteristic
47C22×C4×C73D411yescharacteristic
48C22×C4×C73C2311yescharacteristic
49C4⋊C4×C73—21no—
50C4⋊C4×C73C2312yes—
51C22⋊C4×C73—22no—
52C22⋊C4×C73—22no—
53C42×C73D411yescharacteristic
54C42×C73D411yescharacteristic
55C42×C73C2311yescharacteristic
56C42×C73C2311yescharacteristic
57C23×C73—22no—
58C23×C73C2×D411yescharacteristic
59Q8×C73—42no—
60D4×C73—24no—
61D4×C73—44no—
62D4×C73—42no—
63D4×C73—42no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—44no—
68C2×C4×C73SD1614yescomplemented
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2411yescharacteristic
75C2×Dic73—24no—
76C2×Dic73—44no—
77Dic146—28no—
78Dic146—44no—
79#10596831—24no—
80C22×C73—21no—
81C22×C73—21no—
82C22×C73—42no—
83C22×C73—42no—
84C22×C73—42no—
85C22×C73C2×SD1612yes—
86C22×C73C22×D411yescharacteristic
87C4×C73—21no—
88C4×C73—21no—
89C4×C73—42no—
90C4×C73C2×SD1612yes—
91C4×C73C2×SD1612yes—
92C4×C73#13712yes—
93C4×C73H(5,𝔽2)12yes—
94Dic73—44no—
95C2×C73—22no—
96C2×C73—82no—
97C2×C73#53511yescharacteristic
98C2×C73C22×SD1611yescharacteristic
99C2×C73C2×#13711yescharacteristic
100#3206—731nomaximal, Sylow
101C73#320611yescharacteristic, complemented, Sylow
102#532D7311yescharacteristic
103C2×C4⋊Q8—731no—
104#492—732no—
105#487—732no—
106#461—734no—
107#448—734no—
108#431—731no—
109C2×#41—21no—
110C22×Q8—732no—
111C2×SD16—738no—
112C4⋊Q8—732no—
113C4⋊Q8—732no—
114C4⋊Q8—1461no—
115C4⋊Q8—1461no—
116C4⋊Q8C2×D7311yescharacteristic
117#127C2×D7311yescharacteristic
118#124—21no—
119#121—21no—
120#121C2×D7312yes—
121C4×D4—21no—
122C4×D4C2×D7312yes—
123C2×C4⋊C4—1461no—
124C2×C4⋊C4—1461no—
125C2×C42C2×D7311yescharacteristic
126C4⋊C8—732no—
127#103—738no—
128C22⋊C8—732no—
129C4×C8—732no—
130#41—44no—
131C2×Q8—21no—
132C2×Q8—2924no—
133C2×Q8—734no—
134C2×Q8—1462no—
135C2×D4—22no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4C22×D7312yes—
139C22×C4—22no—
140C22×C4—1462no—
141C22×C4C22⋊D7311yescharacteristic
142C22×C4C22⋊D7311yescharacteristic
143C22×C4C22×D7311yescharacteristic
144SD16—2928no—
145C2×C8—734no—
146C4⋊C4—21no—
147C4⋊C4—1462no—
148C4⋊C4—1462no—
149C4⋊C4—1462no—
150C4⋊C4—1462no—
151C4⋊C4C22×D7312yes—
152C22⋊C4—22no—
153C22⋊C4—22no—
154C42C22⋊D7311yescharacteristic
155C42C22⋊D7311yescharacteristic
156C42C22×D7311yescharacteristic
157C42C22×D7311yescharacteristic
158C23—22no—
159C23C2×C22⋊D7311yescharacteristic
160Q8—42no—
161Q8—2924no—
162Q8—1468no—
163D4—24no—
164D4—44no—
165D4—42no—
166D4—42no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—44no—
171C2×C4—2924no—
172C2×C4—1464no—
173C2×C4#1192401614yescomplemented
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—42no—
184C22—42no—
185C22—42no—
186C22C2×#1192401612yes—
187C22C22×C22⋊D7311yescharacteristic
188C4—21no—
189C4—21no—
190C4—42no—
191C4—2924no—
192C4C2×#1192401612yes—
193C4C2×#1192401612yes—
194C4#1455662112yes—
195C4#1455663712yes—
196C2—22no—
197C2—82no—
198C2#1798915111yescharacteristic
199C2C22×#1192401611yescharacteristic
200C2C2×#1455662111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#532×C73C2
socleC22×C73C22×D4
hypercenter#532D73
hypocenterC73#3206
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#14556591C2semidirect
2. #17988959C2semidirect
3. #17988939C2semidirect
4. #17988792C2semidirect
5. #17988725C2semidirect
6. #17988640C2semidirect
68. C2×C4×C73SD16semidirect
101. C73#3206semidirect
173. C2×C4#11924016semidirect