Finite Group Databasebeta

← #22608941

Subgroups — #22608941

Order 9344.

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

normal subgroups only

This group has 210 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#17988918C212yesmaximal
3#17988517C211yesmaximal, characteristic
4#17988325C212yesmaximal
5#324×C73C211yesmaximal, characteristic
6#14556590—22no—
7#14556582—22no—
8#14556570—21no—
9#14556570C2212yes—
10#14556550—21no—
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007—21no—
13#14556523—22no—
14#14556516—22no—
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—
30#11924007—42no—
31C22⋊Dic73—22no—
32C4×Dic73—22no—
33C22×C4×C73D411yescharacteristic
34C22×C4×C73D411yescharacteristic
35C22×C4×C73C2311yescharacteristic
36C2×C8×C73—22no—
37C4⋊C4×C73—22no—
38C23×C73C2×D411yescharacteristic
39C2×C4×C73—21no—
40C2×C4×C73—21no—
41C2×C4×C73—21no—
42C2×C4×C73—41no—
43C2×C4×C73—41no—
44C2×C4×C73SD1612yes—
45C2×C4×C73C2×D412yes—
46C2×Dic73—22no—
47C2×Dic73—22no—
48C2×Dic73—22no—
49C2×Dic73—41no—
50C2×Dic73—41no—
51C2×Dic73—41no—
52C2×Dic73—41no—
53C2×Dic73—41no—
54Dic146—42no—
55Dic146—81no—
56C8×C73—42no—
57C22×C73—21no—
58C22×C73—21no—
59C22×C73#12011yescharacteristic
60C22×C73C2×SD1611yescharacteristic
61C22×C73#13711yescharacteristic
62C4×C73—22no—
63C4×C73—22no—
64C4×C73—41no—
65Dic73—42no—
66Dic73—42no—
67Dic73—42no—
68Dic73—81no—
69C2×C73—21no—
70C2×C73—21no—
71C2×C73#44811yescharacteristic
72C2×C73#45611yescharacteristic
73C2×C73#45811yescharacteristic
74#1611—731nomaximal, Sylow
75C73#161111yescharacteristic, complemented, Sylow
76#544—731no—
77#483—732no—
78#398—731no—
79#328—732no—
80#324D7311yescharacteristic
81C4⋊Q8—1462no—
82#125—1462no—
83C22⋊Q8—732no—
84C22⋊Q8—1461no—
85#117—1461no—
86C2×C4⋊C4—731no—
87C2×C4⋊C4—1461no—
88C2×C4⋊C4C2×D7311yescharacteristic
89#106—1462no—
90#103—1462no—
91C22⋊C8C2×D7312yes—
92#95—731no—
93#95—1461no—
94C2×Q8—732no—
95C2×Q8—1461no—
96C22×C4—1461no—
97C22×C4—1461no—
98C22×C4D29211yescharacteristic
99C22×C4D29211yescharacteristic
100C22×C4C22×D7311yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—2922no—
104C4⋊C4—732no—
105C4⋊C4—1462no—
106C4⋊C4—1461no—
107C4⋊C4—1461no—
108C4⋊C4—1461no—
109C4⋊C4—1462no—
110C4⋊C4—1462no—
111C22⋊C4—1462no—
112C42—1462no—
113C23C2×D29211yescharacteristic
114Q8—2922no—
115Q8—5841no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—2921no—
122C2×C4—2921no—
123C2×C4—2921no—
124C2×C4—2921no—
125C2×C4—2921no—
126C2×C4—1462no—
127C2×C4—1462no—
128C2×C4—1462no—
129C2×C4#1192401712yes—
130C2×C4D4×D7312yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#1455656111yescharacteristic
135C22C2×#1192401711yescharacteristic
136C22#1455662411yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—2922no—
141C4—2922no—
142C4—2922no—
143C4—5841no—
144C2—21no—
145C2—21no—
146C2#1798872811yescharacteristic
147C2#1798877211yescharacteristic
148C2#1798877811yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#324×C73C2
socleC22×C73#120
hypercenter#324D73
hypocenterC73#1611
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
75. C73#1611semidirect