Finite Group Databasebeta

← #22609266

Subgroups — #22609266

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#17988996C211yesmaximal, characteristic, complemented
3#17988957C211yesmaximal, characteristic, complemented
4#17988947C211yesmaximal, characteristic
5#17988328C211yesmaximal, characteristic, complemented
6#17988326C211yesmaximal, characteristic
7#330×C73C211yesmaximal, characteristic, complemented
8#14556591C2211yescharacteristic
9#14556590—21no—
10#14556586—21no—
11#14556586—21no—
12#14556583C2211yescharacteristic
13#14556579C2211yescharacteristic
14#14556576—21no—
15#14556571—21no—
16#14556569—21no—
17#14556525—21no—
18#14556523—21no—
19#14556516—21no—
20#14556514—21no—
21#14556514—21no—
22#14556513—21no—
23#14556502C2211yescharacteristic
24#125×C73C2211yescharacteristic
25#97×C73C2211yescharacteristic
26#97×C73C2211yescharacteristic
27C2×Dic146—21no—
28C2×Dic146—21no—
29C2×Dic146D411yescharacteristic
30C2×D292D411yescharacteristic
31C2×C4×D73—21no—
32C2×#10596831—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73D411yescharacteristic
37C4⋊Dic73D411yescharacteristic
38#11924007—21no—
39#11924007—21no—
40#11924007—21no—
41#11924005—21no—
42#11924005—21no—
43#11924005—21no—
44#11924005—21no—
45#11924005—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
54C22×D73—21no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C2×Dic73—21no—
61C2×Dic73—21no—
62C2×Dic73—21no—
63C2×Dic73—41no—
64D292—41no—
65C4×D73—81no—
66Dic146—41no—
67Dic146—42no—
68Dic146—81no—
69C8×C73—22no—
70C8×C73—41no—
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—
81Dic73—41no—
82Dic73—41no—
83Dic73—41no—
84Dic73—81no—
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#491—731no—
94#489—731no—
95#330—731no—
96#330D7311yescharacteristic, complemented
97#329—731no—
98C4⋊Q8—731no—
99C4⋊Q8—1461no—
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—1461no—
111#103—1461no—
112#103—1461no—
113#102—1461no—
114#97—731no—
115#97C2×D7311yescharacteristic
116#97C2×D7311yescharacteristic
117C2×Q8—731no—
118C2×Q8—1461no—
119C2×Q8—1461no—
120C2×D4—731no—
121C22×C4—1461no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—1461no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—731no—
128C4⋊C4—731no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4—1461no—
132C4⋊C4—1461no—
133C4⋊C4—1461no—
134C4⋊C4—1461no—
135C4⋊C4D29211yescharacteristic
136C4⋊C4D29211yescharacteristic
137C22⋊C4—1461no—
138C22⋊C4—1461no—
139C22⋊C4—1461no—
140C22⋊C4—1461no—
141C22⋊C4—1461no—
142C42—1461no—
143C42C22×D7311yescharacteristic
144C23—1461no—
145Q8—2921no—
146Q8—2922no—
147Q8—5841no—
148D4—2921no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—2921no—
152C2×C4—5841no—
153C2×C4—1461no—
154C2×C4—1461no—
155C2×C4—1461no—
156C2×C4D4×D7311yescharacteristic
157C2×C4D4×D7311yescharacteristic
158C2×C4C2×D29211yescharacteristic
159C8—22no—
160C8—41no—
161C8—2921no—
162C22—2921no—
163C22—2921no—
164C22—2921no—
165C22#1455656111yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—2921no—
172C4—2921no—
173C4—2921no—
174C4—5841no—
175C2—5841no—
176C2#1798876211yescharacteristic
177C2#1798876611yescharacteristic
178C2#1798877111yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#330×C73C2
socleC22×C73#120
hypercenter#330D73
hypocenterC73#1664
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #17988996C2semidirect
3. #17988957C2semidirect
5. #17988328C2semidirect
7. #330×C73C2semidirect
90. C73#1664semidirect
96. #330D73semidirect