Finite Group Databasebeta

← #22620467

Subgroups — #22620467

Order 9344.

340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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#17989218C212yesmaximal
2#17988995C214yesmaximal, complemented
3#17988991C212yesmaximal, complemented
4#17988988C212yesmaximal, complemented
5#17988627C212yesmaximal
6#17988625C211yesmaximal, characteristic
7#17988542C211yesmaximal, characteristic
8C2×#107×C73C211yesmaximal, characteristic
9C2×#11924012C2211yescharacteristic
10#14556590—22no—
11#14556590C2214yes—
12#14556582—22no—
13#14556582C2214yes—
14#14556570—24no—
15#14556550C2212yes—
16#14556550C2211yescharacteristic
17#14556525C2211yescharacteristic
18#14556525C2211yescharacteristic
19#14556524C2214yes—
20#14556523C2212yes—
21#14556522C2214yes—
22#14556501C2212yes—
23C8×Dic73C2212yes—
24C22×C8×C73C2211yescharacteristic
25C2×C4⋊C4×C73C2212yes—
26#107×C73C2212yes—
27#107×C73C2212yes—
28C2×Dic146—24no—
29#11924012Q814yescomplemented
30C2×#10596831C2312yes—
31C4⋊Dic73—24no—
32C4⋊Dic73D411yescharacteristic
33C4⋊Dic73D411yescharacteristic
34C4⋊Dic73C2312yes—
35C4⋊Dic73C2312yes—
36#11924007—24no—
37#11924007—24no—
38C22⋊Dic73—22no—
39C22⋊Dic73D412yes—
40C4×Dic73—22no—
41C4×Dic73C2312yes—
42C22×C4×C73—22no—
43C22×C4×C73C2311yescharacteristic
44C2×C8×C73Q814yescomplemented
45C2×C8×C73C2311yescharacteristic
46C2×C8×C73C2311yescharacteristic
47C4⋊C4×C73—22no—
48C4⋊C4×C73C2314yes—
49C23×C73C2×D411yescharacteristic
50C2×C4×C73—24no—
51C2×C4×C73—82no—
52C2×C4×C73C2×D411yescharacteristic
53C2×C4×C73C2×Q812yes—
54C2×C4×C73C2×Q812yes—
55C2×C4×C73C2411yescharacteristic
56C2×Dic73—22no—
57C2×Dic73—22no—
58C2×Dic73C2×D412yes—
59C2×Dic73C2×D412yes—
60Dic146—84no—
61C8×C73C2×Q812yes—
62C8×C73C2×Q812yes—
63#10596831C2×Q814yes—
64C22×C73—21no—
65C22×C73—21no—
66C22×C73C4⋊Q812yes—
67C22×C73C22×D411yescharacteristic
68C4×C73—44no—
69C4×C73C4⋊Q812yes—
70C4×C73C22×Q811yescharacteristic
71C4×C73C22×Q811yescharacteristic
72Dic73—22no—
73Dic73—22no—
74Dic73—42no—
75Dic73—42no—
76C2×C73—22no—
77C2×C73C2×C4⋊Q811yescharacteristic
78C2×C73#57611yescharacteristic
79C2×C73#57811yescharacteristic
80#3164—731nomaximal, Sylow
81C73#316411yescharacteristic, complemented, Sylow
82#544—732no—
83#501—734no—
84#500—732no—
85#499—732no—
86#428—732no—
87#427—731no—
88C2×#107D7311yescharacteristic
89#405—731no—
90C2×M16—731no—
91C22×C8C2×D7311yescharacteristic
92C4⋊Q8—734no—
93C4⋊Q8—1462no—
94#125—734no—
95#125—1462no—
96C22⋊Q8—1464no—
97#117—731no—
98#117—732no—
99C2×C4⋊C4C2×D7312yes—
100#107—731no—
101#107—731no—
102#107—734no—
103#107C2×D7312yes—
104#107C2×D7312yes—
105#106—732no—
106#106—734no—
107#97—732no—
108C4×C8—732no—
109C2×Q8—1464no—
110C22×C4—22no—
111C22×C4C22×D7311yescharacteristic
112M16—734no—
113C2×C8—732no—
114C2×C8Dic14614yescomplemented
115C2×C8C22×D7311yescharacteristic
116C2×C8C22×D7311yescharacteristic
117C4⋊C4—22no—
118C4⋊C4—731no—
119C4⋊C4—731no—
120C4⋊C4—732no—
121C4⋊C4—732no—
122C4⋊C4—1464no—
123C4⋊C4—1464no—
124C4⋊C4—1464no—
125C4⋊C4C22×D7314yes—
126C22⋊C4—732no—
127C22⋊C4—1462no—
128C42—732no—
129C42—1462no—
130C23D4×D7311yescharacteristic
131Q8—5844no—
132C2×C4—24no—
133C2×C4—82no—
134C2×C4—732no—
135C2×C4—732no—
136C2×C4—1462no—
137C2×C4—1462no—
138C2×C4D4×D7311yescharacteristic
139C2×C4Q8×D7312yes—
140C2×C4C2×Dic14612yes—
141C2×C4C23×D7311yescharacteristic
142C8—734no—
143C8C2×Dic14612yes—
144C8C2×Dic14612yes—
145C22—21no—
146C22—21no—
147C22#1455659012yes—
148C22C2×D4×D7311yescharacteristic
149C4—44no—
150C4—2922no—
151C4—2922no—
152C4—1462no—
153C4—1462no—
154C4#1455659012yes—
155C4C2×Q8×D7311yescharacteristic
156C4C22×Dic14611yescharacteristic
157C2—22no—
158C2C2×#1455659011yescharacteristic
159C2#1798938811yescharacteristic
160C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#107×C73C2
socleC22×C73C22×D4
hypercenterC2×#107D73
hypocenterC73#3164
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #17988995C2semidirect
3. #17988991C2semidirect
4. #17988988C2semidirect
29. #11924012Q8semidirect
44. C2×C8×C73Q8semidirect
81. C73#3164semidirect
114. C2×C8Dic146semidirect