Finite Group Databasebeta

← #22609262

Subgroups — #22609262

Order 9344.

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

normal subgroups only

This group has 184 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#17989341C211yesmaximal, characteristic
2#17988993C211yesmaximal, characteristic, complemented
3#17988949C211yesmaximal, characteristic
4#17988329C211yesmaximal, characteristic, complemented
5#17988328C211yesmaximal, characteristic, complemented
6#17988326C211yesmaximal, characteristic
7#491×C73C211yesmaximal, characteristic, complemented
8#14556590—21no—
9#14556586—21no—
10#14556586—21no—
11#14556583C2211yescharacteristic
12#14556579C2211yescharacteristic
13#14556576—21no—
14#14556571—21no—
15#14556569—21no—
16#14556524—21no—
17#14556522—21no—
18#14556514—21no—
19#14556511—21no—
20#14556502C2211yescharacteristic
21#14556502C2211yescharacteristic
22C4⋊Q8×C73C2211yescharacteristic
23#125×C73C2211yescharacteristic
24#103×C73—21no—
25#103×C73—21no—
26#97×C73C2211yescharacteristic
27C2×Dic146—21no—
28C2×Dic146D411yescharacteristic
29C2×D292D411yescharacteristic
30C2×C4×D73—21no—
31C2×#10596831—21no—
32C2×#10596831—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73D411yescharacteristic
35C4⋊Dic73D411yescharacteristic
36#11924007—21no—
37#11924007—21no—
38#11924007—21no—
39#11924005—21no—
40#11924005—21no—
41#11924005—21no—
42#11924005—21no—
43#11924005—21no—
44C4×Dic73—21no—
45C2×Q8×C73—21no—
46C2×C8×C73—21no—
47C4⋊C4×C73—21no—
48C4⋊C4×C73—21no—
49C4⋊C4×C73—21no—
50C4⋊C4×C73—21no—
51C4⋊C4×C73D411yescharacteristic
52C4⋊C4×C73D411yescharacteristic
53C42×C73C2311yescharacteristic
54C22×D73—21no—
55Q8×C73—42no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—41no—
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C2×Dic73—21no—
63C2×Dic73—21no—
64C2×Dic73—21no—
65D292—41no—
66C4×D73—81no—
67Dic146—41no—
68Dic146—81no—
69C8×C73—41no—
70#10596831—22no—
71#10596831—41no—
72C22×C73#12011yescharacteristic
73C2×D73—41no—
74C2×D73—41no—
75C2×D73—41no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—21no—
79C4×C73—41no—
80C4×C73—41no—
81C4×C73—81no—
82Dic73—41no—
83Dic73—41no—
84Dic73—41no—
85C2×C73#45411yescharacteristic
86C2×C73#45511yescharacteristic
87C2×C73#45611yescharacteristic
88D73—81no—
89#1664—731nomaximal, Sylow
90C73#166411yescharacteristic, complemented, Sylow
91#563—731no—
92#501—731no—
93#491D7311yescharacteristic, complemented
94#489—731no—
95#330—731no—
96#330—731no—
97#329—731no—
98C4⋊Q8—1461no—
99C4⋊Q8C2×D7311yescharacteristic
100#126—1461no—
101#126—1461no—
102#125—731no—
103#125C2×D7311yescharacteristic
104#124—731no—
105#123—1461no—
106C22⋊Q8—1461no—
107C22⋊Q8—1461no—
108#107—1461no—
109#106—1461no—
110#103—21no—
111#103—21no—
112#103—1461no—
113#102—1461no—
114#97—731no—
115#97—731no—
116#97C2×D7311yescharacteristic
117C2×Q8—21no—
118C2×Q8—731no—
119C2×Q8—1461no—
120C2×D4—731no—
121C22×C4—1461no—
122C2×C8—21no—
123C2×C8—1461no—
124C2×C8—1461no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—731no—
130C4⋊C4—731no—
131C4⋊C4—1461no—
132C4⋊C4—1461no—
133C4⋊C4—1461no—
134C4⋊C4—1461no—
135C4⋊C4C22⋊D7311yescharacteristic
136C4⋊C4C22⋊D7311yescharacteristic
137C22⋊C4—1461no—
138C22⋊C4—1461no—
139C22⋊C4—1461no—
140C22⋊C4—1461no—
141C22⋊C4—1461no—
142C42—1461no—
143C42C22×D7311yescharacteristic
144C23—1461no—
145Q8—42no—
146Q8—2921no—
147Q8—5841no—
148D4—2921no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—5841no—
153C2×C4—1461no—
154C2×C4—1461no—
155C2×C4—1461no—
156C2×C4D4×D7311yescharacteristic
157C2×C4D4×D7311yescharacteristic
158C2×C4C2×C22⋊D7311yescharacteristic
159C8—41no—
160C8—2921no—
161C8—1462no—
162C22—2921no—
163C22—2921no—
164C22—2921no—
165C22#1455655911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—2921no—
173C4—2921no—
174C4—2921no—
175C2—5841no—
176C2#1798875911yescharacteristic
177C2#1798876311yescharacteristic
178C2#1798876811yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#491×C73C2
socleC22×C73#120
hypercenter#491D73
hypocenterC73#1664
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #17988993C2semidirect
4. #17988329C2semidirect
5. #17988328C2semidirect
7. #491×C73C2semidirect
90. C73#1664semidirect
93. #491D73semidirect