Finite Group Databasebeta

← #22612201

Subgroups — #22612201

Order 9344.

178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic584C211yesmaximal, characteristic, complemented
2C2×#14556537C211yesmaximal, characteristic, complemented
3C2×#14556535C211yesmaximal, characteristic
4#17988970C211yesmaximal, characteristic
5#17988965C211yesmaximal, characteristic, complemented
6#17988362C211yesmaximal, characteristic, complemented
7C2×SD32×C73C211yesmaximal, characteristic
8C2×Dic292C2211yescharacteristic
9C2×Dic292C2211yescharacteristic
10C2×#11924018—21no—
11C2×#11924016—21no—
12#14556589—21no—
13#14556578—21no—
14Dic584—22no—
15#14556537—22no—
16#14556535—22no—
17C2×#11924003C2211yescharacteristic
18C8×Dic73C2211yescharacteristic
19C2×Q16×C73C2211yescharacteristic
20C2×D8×C73C2211yescharacteristic
21SD32×C73—22no—
22C2×C16×C73C2211yescharacteristic
23C2×Dic146—21no—
24C2×Dic146—21no—
25Dic292—21no—
26Dic292—21no—
27Dic292—21no—
28Dic292—21no—
29#11924018—42no—
30#11924016—42no—
31C2×#10596831D411yescharacteristic
32#11924007—42no—
33C22⋊Dic73—42no—
34C4×Dic73D411yescharacteristic
35#11924003D412yes—
36C2×Q8×C73—21no—
37C2×D4×C73—21no—
38Q16×C73—21no—
39Q16×C73—21no—
40D8×C73—21no—
41D8×C73—21no—
42C2×C8×C73C2311yescharacteristic
43C16×C73D412yes—
44C23×C73—41no—
45Q8×C73—41no—
46Q8×C73—41no—
47D4×C73—41no—
48D4×C73—41no—
49C2×C4×C73—41no—
50C2×C4×C73C2×D411yescharacteristic
51C2×Dic73—41no—
52C2×Dic73—41no—
53C2×Dic73D812yes—
54Dic146—41no—
55Dic146—41no—
56Dic146—41no—
57Dic146—41no—
58C8×C73C2×D411yescharacteristic
59C8×C73C2×D411yescharacteristic
60#10596831D812yes—
61C22×C73—81no—
62C22×C73—82no—
63C22×C73C2×D811yescharacteristic
64C4×C73—81no—
65C4×C73#12711yescharacteristic
66C4×C73C2×D811yescharacteristic
67Dic73—22no—
68Dic73—81no—
69Dic73—81no—
70C2×C73—161no—
71C2×C73#49311yescharacteristic
72C2×C73#51012yes—
73#2251—731nomaximal, Sylow
74C73#225111yescharacteristic, complemented, Sylow
75C2×Q32—731no—
76C2×Q32—731no—
77C2×SD32—731no—
78C2×SD32D7311yescharacteristic
79#495—731no—
80#494—731no—
81#346—731no—
82C2×Q16—731no—
83C2×Q16—731no—
84C2×Q16—1461no—
85C2×Q16C2×D7311yescharacteristic
86C2×SD16—1461no—
87C2×D8C2×D7311yescharacteristic
88C4⋊Q8—1461no—
89#124—1461no—
90Q32—1462no—
91Q32—1462no—
92SD32—22no—
93SD32—1462no—
94C2×C16—731no—
95C2×C16C2×D7311yescharacteristic
96C4×C8—731no—
97C2×Q8—21no—
98C2×Q8—1461no—
99C2×Q8—1461no—
100C2×D4—21no—
101Q16—21no—
102Q16—21no—
103Q16—2922no—
104Q16—1461no—
105Q16—1461no—
106Q16—1461no—
107Q16—1461no—
108SD16—2922no—
109D8—21no—
110D8—21no—
111C2×C8—731no—
112C2×C8C22×D7311yescharacteristic
113C4⋊C4—2922no—
114C22⋊C4—2922no—
115C42—731no—
116C16—732no—
117C16C22⋊D7312yes—
118C23—41no—
119Q8—41no—
120Q8—41no—
121Q8—2921no—
122Q8—2921no—
123Q8—2921no—
124Q8—2921no—
125D4—41no—
126D4—41no—
127C2×C4—41no—
128C2×C4—2921no—
129C2×C4—2921no—
130C2×C4—732no—
131C2×C4D4×D7311yescharacteristic
132C8—732no—
133C8D4×D7311yescharacteristic
134C8C2×C22⋊D7311yescharacteristic
135C22—81no—
136C22—82no—
137C22D8×D7311yescharacteristic
138C4—81no—
139C4—5841no—
140C4—5841no—
141C4—1462no—
142C4#1455658711yescharacteristic
143C4D8×D7311yescharacteristic
144C2—161no—
145C2#1798896211yescharacteristic
146C2#1798902612yes—
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC2×SD32×C73C2
socleC22×C73C2×D8
hypercenterC2×SD32D73
hypocenterC73#2251
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×Dic584C2semidirect
2. C2×#14556537C2semidirect
5. #17988965C2semidirect
6. #17988362C2semidirect
74. C73#2251semidirect