Finite Group Databasebeta

← #22608604

Subgroups — #22608604

Order 9344.

240 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 93 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
2#17988640C211yesmaximal, characteristic
3#17988334C214yesmaximal, complemented
4#423×C73C211yesmaximal, characteristic
5C22×Dic146—21no—
6#14556591—21no—
7#14556591—21no—
8#14556591C412yes—
9#14556591C2212yes—
10C2×C4⋊Dic73—21no—
11C2×C4⋊Dic73C412yes—
12C4⋊#10596831C2212yes—
13C22⋊#10596831—21no—
14C4×#10596831—21no—
15C2×M16×C73—21no—
16C2×C42×C73C2211yescharacteristic
17C4⋊C8×C73—21no—
18C4⋊C8×C73C2212yes—
19C2×Dic146—22no—
20C2×Dic146—22no—
21C2×Dic146—42no—
22C2×Dic146—42no—
23C22×Dic73—22no—
24C2×#10596831—22no—
25C4⋊Dic73—22no—
26C4⋊Dic73—22no—
27C4⋊Dic73—22no—
28C4⋊Dic73C2×C414yes—
29C22×C4×C73C2×C411yescharacteristic
30C22×C4×C73D411yescharacteristic
31C22×C4×C73D411yescharacteristic
32M16×C73—42no—
33C2×C8×C73—22no—
34C42×C73C2×C411yescharacteristic
35C42×C73D411yescharacteristic
36C42×C73D411yescharacteristic
37C42×C73C2311yescharacteristic
38C23×C73C22⋊C411yescharacteristic
39C2×C4×C73—22no—
40C2×C4×C73—22no—
41C2×C4×C73C22⋊C411yescharacteristic
42C2×C4×C73C22⋊C411yescharacteristic
43C2×C4×C73C22⋊C411yescharacteristic
44C2×C4×C73D812yes—
45C2×C4×C73SD1612yes—
46C2×C4×C73C22×C411yescharacteristic
47C2×C4×C73C2×D411yescharacteristic
48C2×C4×C73C2×D411yescharacteristic
49C2×Dic73—24no—
50C2×Dic73—44no—
51Dic146—44no—
52Dic146—42no—
53Dic146—42no—
54C8×C73—42no—
55#10596831—42no—
56C22×C73—21no—
57C22×C73—21no—
58C22×C73#10212yes—
59C22×C73C2×C22⋊C411yescharacteristic
60C4×C73—21no—
61C4×C73—21no—
62C4×C73#10112yes—
63C4×C73#10212yes—
64C4×C73C2×D811yescharacteristic
65C4×C73C2×SD1611yescharacteristic
66C4×C73#13712yes—
67Dic73—44no—
68C2×C73—22no—
69C2×C73C2×#10111yescharacteristic
70C2×C73C2×#10211yescharacteristic
71C2×C73#41911yescharacteristic
72#1546—731nomaximal, Sylow
73C73#154611yescharacteristic, complemented, Sylow
74C2×C4⋊Q8—731no—
75#431—731no—
76#423D7311yescharacteristic
77#332—734no—
78C22×Q8—1461no—
79C2×M16—21no—
80C4⋊Q8—732no—
81C4⋊Q8—732no—
82C4⋊Q8—1461no—
83C4⋊Q8—1461no—
84C2×C4⋊C4—732no—
85C2×C4⋊C4—1461no—
86C2×C42C2×D7311yescharacteristic
87C4⋊C8—21no—
88C4⋊C8—732no—
89C4⋊C8C2×D7312yes—
90C22⋊C8—1461no—
91C4×C8—1461no—
92C2×Q8—2922no—
93C2×Q8—2922no—
94C2×Q8—1462no—
95C2×Q8—1462no—
96C22×C4—1462no—
97C22×C4C4×D7311yescharacteristic
98C22×C4D29211yescharacteristic
99C22×C4C22⋊D7311yescharacteristic
100M16—42no—
101C2×C8—22no—
102C2×C8—1462no—
103C4⋊C4—734no—
104C4⋊C4—1462no—
105C4⋊C4—1462no—
106C4⋊C4—1462no—
107C42C4×D7311yescharacteristic
108C42D29211yescharacteristic
109C42C22⋊D7311yescharacteristic
110C42C22×D7311yescharacteristic
111C23#1192400511yescharacteristic
112Q8—2924no—
113Q8—2922no—
114Q8—2922no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—2924no—
118C2×C4—1464no—
119C2×C4#1192400511yescharacteristic
120C2×C4#1192400511yescharacteristic
121C2×C4#1192400511yescharacteristic
122C2×C4#1192401312yes—
123C2×C4#1192401512yes—
124C2×C4C2×C4×D7311yescharacteristic
125C2×C4C2×C22⋊D7311yescharacteristic
126C2×C4C2×D29211yescharacteristic
127C8—42no—
128C8—2922no—
129C22—21no—
130C22—21no—
131C22#1455651112yes—
132C22C2×#1192400511yescharacteristic
133C4—21no—
134C4—21no—
135C4—2924no—
136C4#1455650912yes—
137C4#1455651112yes—
138C4C2×#1192401311yescharacteristic
139C4C2×#1192401511yescharacteristic
140C4#1455662412yes—
141C2—22no—
142C2C2×#1455650911yescharacteristic
143C2C2×#1455651111yescharacteristic
144C2#1798859711yescharacteristic
subgroupG/H
centerC22C2×#11924005
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#423×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#423D73
hypocenterC73#1546
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
3. #17988334C2semidirect
73. C73#1546semidirect