Finite Group Databasebeta

← #22609243

Subgroups — #22609243

Order 9344.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#17989337C211yesmaximal, characteristic
2#17988996C212yesmaximal, complemented
3#17988982C211yesmaximal, characteristic
4#17988328C212yesmaximal, complemented
5#329×C73C211yesmaximal, characteristic
6C2×#11924018—21no—
7C2×#11924016—21no—
8#14556591C2211yescharacteristic
9#14556589—21no—
10#14556584—22no—
11#14556583C2212yes—
12#14556572—21no—
13#14556568—22no—
14#14556525—22no—
15#14556523—22no—
16#14556502C2211yescharacteristic
17#124×C73C2211yescharacteristic
18#97×C73C2212yes—
19C2×Dic146—21no—
20C2×Dic146—21no—
21C22×Dic73—21no—
22#11924018—42no—
23#11924016—42no—
24C2×#10596831—21no—
25C4⋊Dic73—22no—
26C4⋊Dic73D412yes—
27C4⋊Dic73D412yes—
28#11924007—22no—
29#11924007—22no—
30#11924007—22no—
31C22⋊Dic73—22no—
32C22⋊Dic73—21no—
33C4×Dic73—21no—
34C2×Q8×C73D411yescharacteristic
35C2×D4×C73D411yescharacteristic
36C2×C8×C73—22no—
37C22⋊C4×C73—22no—
38C42×C73C2311yescharacteristic
39C23×C73—21no—
40Q8×C73—41no—
41D4×C73—41no—
42C2×C4×C73—21no—
43C2×C4×C73C2×D412yes—
44C2×C4×C73C2×D411yescharacteristic
45C2×Dic73—22no—
46C2×Dic73—22no—
47C2×Dic73—41no—
48C2×Dic73—81no—
49Dic146—41no—
50Dic146—41no—
51Dic146—81no—
52C8×C73—24no—
53#10596831—22no—
54C22×C73—41no—
55C22×C73—42no—
56C22×C73#12011yescharacteristic
57C4×C73—21no—
58C4×C73—22no—
59C4×C73—41no—
60Dic73—42no—
61Dic73—42no—
62Dic73—81no—
63C2×C73—81no—
64C2×C73#45311yescharacteristic
65C2×C73#45612yes—
66#1660—731nomaximal, Sylow
67C73#166011yescharacteristic, complemented, Sylow
68#563—731no—
69#501—732no—
70#497—731no—
71#330—732no—
72#329D7311yescharacteristic
73C2×Q16—1461no—
74C2×SD16—1461no—
75C4⋊Q8—731no—
76C4⋊Q8—1461no—
77#126—1462no—
78#125—732no—
79#124C2×D7311yescharacteristic
80#123—1461no—
81C22⋊Q8—1462no—
82#107—1462no—
83#106—1462no—
84#97—731no—
85#97C2×D7312yes—
86C2×Q8—1461no—
87C2×Q8—1461no—
88C2×Q8D29211yescharacteristic
89C2×D4D29211yescharacteristic
90C22×C4—1461no—
91Q16—2922no—
92SD16—2922no—
93C2×C8—22no—
94C2×C8—1461no—
95C4⋊C4—732no—
96C4⋊C4—732no—
97C4⋊C4—1462no—
98C4⋊C4—1462no—
99C4⋊C4—1462no—
100C4⋊C4—1462no—
101C22⋊C4—22no—
102C22⋊C4—1462no—
103C22⋊C4—1461no—
104C42—1461no—
105C42C22×D7311yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—2921no—
109Q8—2921no—
110Q8—5841no—
111D4—41no—
112C2×C4—21no—
113C2×C4—2921no—
114C2×C4—5841no—
115C2×C4—1462no—
116C2×C4—1462no—
117C2×C4D4×D7312yes—
118C2×C4C2×D29211yescharacteristic
119C8—24no—
120C8—1462no—
121C22—41no—
122C22—42no—
123C22#1455656111yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—2922no—
128C4—2922no—
129C4—5841no—
130C2—81no—
131C2#1798875711yescharacteristic
132C2#1798877112yes—
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#329×C73C2
socleC22×C73#120
hypercenter#329D73
hypocenterC73#1660
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #17988996C2semidirect
4. #17988328C2semidirect
67. C73#1660semidirect