Finite Group Databasebeta

← #22608975

Subgroups — #22608975

Order 9344.

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

normal subgroups only

This group has 202 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
1#17989218C211yesmaximal, characteristic
2#17988923C212yesmaximal
3#17988526C211yesmaximal, characteristic
4#17988325C212yesmaximal
5#324×C73C211yesmaximal, characteristic
6#14556590—22no—
7#14556582—22no—
8#14556570—21no—
9#14556570C2212yes—
10#14556550—21no—
11C2×C4⋊Dic73C2211yescharacteristic
12#14556525—22no—
13#14556516—22no—
14#14556498—21no—
15#14556498—21no—
16#14556498C2211yescharacteristic
17C2×C4⋊C4×C73C2211yescharacteristic
18C22⋊C8×C73C2212yes—
19C2×Dic146—21no—
20C2×Dic146D412yes—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C4⋊Dic73—21no—
24C4⋊Dic73—21no—
25C4⋊Dic73—21no—
26C4⋊Dic73—22no—
27C4⋊Dic73D412yes—
28#11924007—22no—
29#11924007—22no—
30C22⋊Dic73—22no—
31C4×Dic73—22no—
32C22×C4×C73D411yescharacteristic
33C22×C4×C73D411yescharacteristic
34C22×C4×C73C2311yescharacteristic
35C2×C8×C73—22no—
36C4⋊C4×C73—22no—
37C23×C73C2×D411yescharacteristic
38C2×C4×C73—21no—
39C2×C4×C73—21no—
40C2×C4×C73—21no—
41C2×C4×C73—41no—
42C2×C4×C73—41no—
43C2×C4×C73Q1612yes—
44C2×C4×C73C2×D412yes—
45C2×Dic73—22no—
46C2×Dic73—22no—
47C2×Dic73—41no—
48C2×Dic73—41no—
49C2×Dic73—42no—
50C2×Dic73—41no—
51C2×Dic73—41no—
52Dic146—42no—
53Dic146—81no—
54C8×C73—42no—
55C22×C73—21no—
56C22×C73—21no—
57C22×C73#12011yescharacteristic
58C22×C73C2×Q1611yescharacteristic
59C22×C73#13711yescharacteristic
60C4×C73—22no—
61C4×C73—22no—
62C4×C73—41no—
63Dic73—42no—
64Dic73—42no—
65Dic73—81no—
66Dic73—81no—
67C2×C73—21no—
68C2×C73—21no—
69C2×C73#45111yescharacteristic
70C2×C73#45411yescharacteristic
71C2×C73#45811yescharacteristic
72#1617—731nomaximal, Sylow
73C73#161711yescharacteristic, complemented, Sylow
74#544—731no—
75#484—732no—
76#400—731no—
77#328—732no—
78#324D7311yescharacteristic
79C4⋊Q8—1462no—
80#125—1462no—
81C22⋊Q8—732no—
82C22⋊Q8—1461no—
83#117—1461no—
84C2×C4⋊C4—731no—
85C2×C4⋊C4C2×D7311yescharacteristic
86#107—1462no—
87#103—1462no—
88C22⋊C8C2×D7312yes—
89#95—731no—
90#95—1461no—
91#95—1461no—
92C2×Q8—732no—
93C2×Q8—1461no—
94C22×C4—1461no—
95C22×C4—1461no—
96C22×C4D29211yescharacteristic
97C22×C4D29211yescharacteristic
98C22×C4C22×D7311yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—732no—
102C4⋊C4—1462no—
103C4⋊C4—1461no—
104C4⋊C4—1461no—
105C4⋊C4—1461no—
106C4⋊C4—1462no—
107C4⋊C4—1462no—
108C22⋊C4—1462no—
109C42—1462no—
110C23C2×D29211yescharacteristic
111Q8—2922no—
112Q8—5841no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—2921no—
119C2×C4—2921no—
120C2×C4—2922no—
121C2×C4—2921no—
122C2×C4—2921no—
123C2×C4—1462no—
124C2×C4—1462no—
125C2×C4Dic29212yes—
126C2×C4D4×D7312yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1455656111yescharacteristic
131C22C2×Dic29211yescharacteristic
132C22#1455662411yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—2922no—
137C4—2922no—
138C4—5841no—
139C4—5841no—
140C2—21no—
141C2—21no—
142C2#1798874511yescharacteristic
143C2#1798876211yescharacteristic
144C2#1798877811yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#324×C73C2
socleC22×C73#120
hypercenter#324D73
hypocenterC73#1617
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
73. C73#1617semidirect