Finite Group Databasebeta

← #22609261

Subgroups — #22609261

Order 9344.

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

normal subgroups only

This group has 172 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
1C73⋊#564C211yesmaximal, characteristic
2#17988997C211yesmaximal, characteristic
3#17988996C211yesmaximal, characteristic
4#17988956C211yesmaximal, characteristic
5#17988328C211yesmaximal, characteristic
6#17988328C211yesmaximal, characteristic
7#330×C73C211yesmaximal, characteristic
8#14556591C2211yescharacteristic
9#14556583C2211yescharacteristic
10#14556583C2211yescharacteristic
11#14556582—21no—
12#14556582—21no—
13#14556581—21no—
14#14556581—21no—
15#14556581—21no—
16#14556581—21no—
17#14556525—21no—
18#14556524—21no—
19#14556523—21no—
20#14556522—21no—
21#14556516—21no—
22#14556516—21no—
23#14556502C2211yescharacteristic
24#125×C73C2211yescharacteristic
25#97×C73C2211yescharacteristic
26#97×C73C2211yescharacteristic
27C2×Dic146—21no—
28C2×#10596831—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C4⋊Dic73—21no—
33C4⋊Dic73D411yescharacteristic
34C4⋊Dic73D411yescharacteristic
35C4⋊Dic73D411yescharacteristic
36C4⋊Dic73D411yescharacteristic
37#11924007—21no—
38#11924007—21no—
39#11924007—21no—
40#11924007—21no—
41#11924007—21no—
42#11924007—21no—
43#11924007—21no—
44#11924007—21no—
45C4×Dic73—21no—
46C4×Dic73—21no—
47C2×C8×C73—21no—
48C2×C8×C73—21no—
49C4⋊C4×C73—21no—
50C4⋊C4×C73—21no—
51C4⋊C4×C73D411yescharacteristic
52C4⋊C4×C73D411yescharacteristic
53C42×C73C2311yescharacteristic
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73C2×D411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×Dic73—21no—
60C2×Dic73—21no—
61C2×Dic73—21no—
62C2×Dic73—21no—
63C2×Dic73—41no—
64Dic146—42no—
65C8×C73—22no—
66C8×C73—41no—
67#10596831—22no—
68C22×C73#12011yescharacteristic
69C4×C73—21no—
70C4×C73—21no—
71C4×C73—21no—
72C4×C73—41no—
73C4×C73—41no—
74Dic73—41no—
75Dic73—41no—
76Dic73—41no—
77Dic73—41no—
78Dic73—81no—
79C2×C73#45411yescharacteristic
80C2×C73#45611yescharacteristic
81C2×C73#45611yescharacteristic
82#1663—731nomaximal, Sylow
83C73#166311yescharacteristic, complemented, Sylow
84#564—731no—
85#501—731no—
86#501—731no—
87#491—731no—
88#330—731no—
89#330—731no—
90#330D7311yescharacteristic
91C4⋊Q8—731no—
92#125—731no—
93#125—731no—
94#125—1461no—
95#125—1461no—
96#125—1461no—
97#125—1461no—
98#125—1461no—
99#125—1461no—
100#125C2×D7311yescharacteristic
101#107—1461no—
102#107—1461no—
103#106—1461no—
104#106—1461no—
105#103—1461no—
106#103—1461no—
107#97—731no—
108#97C2×D7311yescharacteristic
109#97C2×D7311yescharacteristic
110C2×Q8—1461no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—1461no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—731no—
117C4⋊C4—731no—
118C4⋊C4—731no—
119C4⋊C4—731no—
120C4⋊C4—1461no—
121C4⋊C4—1461no—
122C4⋊C4—1461no—
123C4⋊C4—1461no—
124C4⋊C4—1461no—
125C4⋊C4—1461no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4—1461no—
132C4⋊C4D29211yescharacteristic
133C4⋊C4D29211yescharacteristic
134C42—1461no—
135C42—1461no—
136C42C22×D7311yescharacteristic
137Q8—2922no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—2921no—
141C2×C4—1461no—
142C2×C4—1461no—
143C2×C4—1461no—
144C2×C4—1461no—
145C2×C4D4×D7311yescharacteristic
146C2×C4D4×D7311yescharacteristic
147C2×C4C2×D29211yescharacteristic
148C8—22no—
149C8—41no—
150C8—1462no—
151C22#1455656111yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—2921no—
158C4—2921no—
159C4—2921no—
160C4—2921no—
161C4—5841no—
162C2#1798876111yescharacteristic
163C2#1798877111yescharacteristic
164C2#1798877211yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#330×C73C2
socleC22×C73#120
hypercenter#330D73
hypocenterC73#1663
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
83. C73#1663semidirect