Finite Group Databasebeta

← #22609816

Subgroups — #22609816

Order 9344.

224 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14556526C211yesmaximal, characteristic
2#17988623C211yesmaximal, characteristic
3#17988542C211yesmaximal, characteristic
4C2×#14556501C211yesmaximal, characteristic
5#17988348C211yesmaximal, characteristic
6#17988346C211yesmaximal, characteristic
7#405×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9C22×#10596831C2211yescharacteristic
10#14556550C2211yescharacteristic
11C2×C4×Dic73C2211yescharacteristic
12#14556526C414yescomplemented
13#14556524C412yescomplemented
14#14556522C412yescomplemented
15#14556501—21no—
16#14556501C414yescomplemented
17C8×Dic73—21no—
18C2×M16×C73C2211yescharacteristic
19C22×C8×C73C2211yescharacteristic
20#117×C73C2211yescharacteristic
21#97×C73—21no—
22C4×C8×C73—21no—
23C22×Dic73—21no—
24#11924012—21no—
25#11924012C2×C412yes—
26C2×#10596831—21no—
27C2×#10596831C2×C412yes—
28C2×#10596831C2×C411yescharacteristic
29C2×#10596831C2×C411yescharacteristic
30C2×#10596831C2×C412yes—
31C4⋊Dic73C2×C412yes—
32C22⋊Dic73—21no—
33C4×Dic73—21no—
34C4×Dic73—21no—
35C4×Dic73C2×C412yes—
36C22×C4×C73C2311yescharacteristic
37M16×C73—21no—
38M16×C73C2×C412yes—
39C2×C8×C73—21no—
40C2×C8×C73C2×C412yes—
41C2×C8×C73D411yescharacteristic
42C2×C8×C73D411yescharacteristic
43C2×C8×C73Q812yes—
44C4⋊C4×C73C2×C412yes—
45C22⋊C4×C73—21no—
46C42×C73—21no—
47C23×C73#4111yescharacteristic
48C2×C4×C73—22no—
49C2×C4×C73C22×C411yescharacteristic
50C2×C4×C73C22×C411yescharacteristic
51C2×C4×C73C22×C411yescharacteristic
52C2×C4×C73C2×D411yescharacteristic
53C2×C4×C73C2×Q811yescharacteristic
54C2×C4×C73#4111yescharacteristic
55C2×Dic73—22no—
56C2×Dic73—22no—
57C2×Dic73—42no—
58C8×C73—22no—
59C8×C73C4⋊C412yes—
60C8×C73C4⋊C412yes—
61#10596831—22no—
62#10596831C4212yes—
63#10596831C4212yes—
64C22×C73—22no—
65C22×C73#11711yescharacteristic
66C22×C73C4×D411yescharacteristic
67C22×C73C4×Q811yescharacteristic
68C4×C73—42no—
69C4×C73C2×C4211yescharacteristic
70C4×C73C2×C4⋊C411yescharacteristic
71C4×C73C4×D411yescharacteristic
72C4×C73C4×Q811yescharacteristic
73Dic73—42no—
74Dic73—42no—
75C2×C73—21no—
76C2×C73—21no—
77C2×C73C4×C4⋊C411yescharacteristic
78C2×C73#44412yes—
79#1773—731nomaximal, Sylow
80C73#177311yescharacteristic, complemented, Sylow
81C2×#108—731no—
82#427—731no—
83#405—731no—
84#405D7311yescharacteristic
85C2×#97—731no—
86#339—731no—
87#339—731no—
88C2×M16—731no—
89C2×M16C2×D7311yescharacteristic
90C22×C8—731no—
91C22×C8C2×D7311yescharacteristic
92#117—731no—
93#117C2×D7311yescharacteristic
94C2×C42—731no—
95#108—734no—
96#107—732no—
97#106—732no—
98#97—21no—
99#97—734no—
100#97—1461no—
101C4×C8—21no—
102C4×C8—1461no—
103C22×C4—1461no—
104C22×C4C22×D7311yescharacteristic
105M16—21no—
106M16—732no—
107M16—1461no—
108M16C4×D7312yes—
109C2×C8—21no—
110C2×C8—732no—
111C2×C8—731no—
112C2×C8—731no—
113C2×C8—732no—
114C2×C8—1461no—
115C2×C8Dic14612yes—
116C2×C8C4×D7312yes—
117C2×C8C22⋊D7311yescharacteristic
118C2×C8C22⋊D7311yescharacteristic
119C4⋊C4—732no—
120C4⋊C4C4×D7312yes—
121C22⋊C4—21no—
122C22⋊C4—1461no—
123C42—21no—
124C42—732no—
125C42—1461no—
126C42—1461no—
127C23#1192402811yescharacteristic
128C2×C4—22no—
129C2×C4—2922no—
130C2×C4—1462no—
131C2×C4—1462no—
132C2×C4C2×C4×D7311yescharacteristic
133C2×C4C2×C4×D7311yescharacteristic
134C2×C4C2×C4×D7311yescharacteristic
135C2×C4C2×C22⋊D7311yescharacteristic
136C2×C4C2×Dic14611yescharacteristic
137C2×C4#1192402811yescharacteristic
138C8—22no—
139C8—732no—
140C8—732no—
141C8—1462no—
142C8#1192400712yes—
143C8#1192400712yes—
144C22—22no—
145C22#1455654811yescharacteristic
146C22C4×C22⋊D7311yescharacteristic
147C22C4×Dic14611yescharacteristic
148C4—42no—
149C4—2922no—
150C4—2922no—
151C4C42×D7311yescharacteristic
152C4C2×#1192400711yescharacteristic
153C4C4×C22⋊D7311yescharacteristic
154C4C4×Dic14611yescharacteristic
155C2—21no—
156C2—21no—
157C2C4×#1192400711yescharacteristic
158C2#1798870712yes—
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC4×C73C2×C42
FrattiniC22×C4C22×D73
Fitting#405×C73C2
socleC22×C73C4×D4
hypercenter#405D73
hypocenterC73#1773
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
12. #14556526C4semidirect
13. #14556524C4semidirect
14. #14556522C4semidirect
16. #14556501C4semidirect
80. C73#1773semidirect