Finite Group Databasebeta

← #22615800

Subgroups — #22615800

Order 9344.

512 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×C4×D292C211yesmaximal, characteristic
2#17988522C212yesmaximal, complemented
3#17988517C212yesmaximal, complemented
4#17988513C212yesmaximal, complemented
5#17988504C212yesmaximal
6#17988458C214yesmaximal, complemented
7#17988455C211yesmaximal, characteristic, complemented
8C2×#125×C73C211yesmaximal, characteristic, complemented
9C22×D292C2211yescharacteristic
10C22×C4×D73C2212yes—
11C4×D292—24no—
12C2×C4⋊Dic73C2211yescharacteristic
13C2×#11924007C2214yes—
14C2×#11924005C2214yes—
15C2×#11924005C2212yes—
16C2×#11924005C2214yes—
17#14556498C2212yes—
18#14556498C2212yes—
19#14556498C2212yes—
20#14556498C2214yes—
21#125×C73—24no—
22C2×C4⋊C4×C73C2212yes—
23C2×C4⋊C4×C73C2212yes—
24C2×C4⋊C4×C73C2211yescharacteristic
25C2×C4⋊C4×C73C2211yescharacteristic
26C2×C42×C73C2211yescharacteristic
27C23×D73C2312yes—
28C2×D292—24no—
29C2×D292—22no—
30C22×Dic73C2314yes—
31C22×Dic73C2312yes—
32C2×C4×D73—24no—
33C2×C4×D73—44no—
34C4⋊Dic73—22no—
35#11924007—44no—
36#11924005—28no—
37#11924005—24no—
38#11924005—44no—
39C22×C4×C73C2312yes—
40C22×C4×C73C2312yes—
41C22×C4×C73C2311yescharacteristic
42C22×C4×C73C2311yescharacteristic
43C22×C4×C73C2311yescharacteristic
44C4⋊C4×C73—22no—
45C4⋊C4×C73—22no—
46C4⋊C4×C73—24no—
47C4⋊C4×C73—24no—
48C42×C73D414yes—
49C23×C73C2411yescharacteristic
50C22×D73—22no—
51C22×D73—22no—
52C22×D73—24no—
53C22×D73—24no—
54C22×D73#4114yes—
55C2×C4×C73—22no—
56C2×C4×C73—22no—
57C2×C4×C73—22no—
58C2×C4×C73—22no—
59C2×C4×C73—22no—
60C2×C4×C73—24no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73C2×D412yes—
64C2×C4×C73C2×D412yes—
65C2×C4×C73C2×D412yes—
66C2×Dic73—22no—
67C2×Dic73—24no—
68C2×Dic73—24no—
69C2×Dic73—24no—
70C2×Dic73—24no—
71D292—28no—
72C4×D73—48no—
73C22×C73C22×D411yescharacteristic
74C22×C73C2×#4112yes—
75C22×C73H(5,𝔽2)12yes—
76C22×C732−1+412yes—
77C2×D73—24no—
78C2×D73—28no—
79C2×D73—42no—
80C2×D73—42no—
81C2×D73—44no—
82C4×C73—22no—
83C4×C73—22no—
84C4×C73—22no—
85C4×C73—42no—
86C4×C73—42no—
87Dic73—42no—
88Dic73—44no—
89C2×C73#52511yescharacteristic
90C2×C73#53511yescharacteristic
91C2×C73#53611yescharacteristic
92C2×C73#53914yes—
93D73—44no—
94#2633—731nomaximal, Sylow
95C73#263311yescharacteristic, complemented, Sylow
96C2×#125D7311yescharacteristic, complemented
97C2×C4×D4—731no—
98#399—732no—
99#398—732no—
100#397—732no—
101#394—732no—
102#385—734no—
103#383—731no—
104C22×D4—731no—
105C23×C4—732no—
106#125—24no—
107C4×D4—1464no—
108C2×C4⋊C4—734no—
109C2×C4⋊C4—731no—
110C2×C4⋊C4C2×D7312yes—
111C2×C4⋊C4C2×D7312yes—
112C2×C4⋊C4C2×D7311yescharacteristic
113C2×C4⋊C4C2×D7311yescharacteristic
114C2×C22⋊C4—734no—
115C2×C22⋊C4—732no—
116C2×C22⋊C4—734no—
117C2×C42C2×D7311yescharacteristic
118#95—732no—
119#95—732no—
120#95—732no—
121#95—734no—
122C24—732no—
123C2×D4—1464no—
124C2×D4—1462no—
125C22×C4—2924no—
126C22×C4—734no—
127C22×C4—732no—
128C22×C4—1464no—
129C22×C4C22×D7312yes—
130C22×C4C22×D7312yes—
131C22×C4C22×D7311yescharacteristic
132C22×C4C22×D7311yescharacteristic
133C22×C4C22×D7311yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—24no—
137C4⋊C4—24no—
138C4⋊C4—2924no—
139C4⋊C4—1462no—
140C22⋊C4—2924no—
141C22⋊C4—1468no—
142C22⋊C4—1464no—
143C42C22⋊D7314yes—
144C23—734no—
145C23—1462no—
146C23—1462no—
147C23—1464no—
148C23—1464no—
149C23C23×D7311yescharacteristic
150D4—1468no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—2928no—
160C2×C4—1462no—
161C2×C4—1464no—
162C2×C4—1464no—
163C2×C4—1464no—
164C2×C4—1464no—
165C2×C4C2×C22⋊D7312yes—
166C2×C4C2×C22⋊D7312yes—
167C2×C4C2×C22⋊D7312yes—
168C22—2922no—
169C22—2922no—
170C22—2924no—
171C22—1468no—
172C22—1464no—
173C22C22×C22⋊D7311yescharacteristic
174C22#41×D7312yes—
175C22#1455663712yes—
176C22#1455663912yes—
177C4—22no—
178C4—22no—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—2922no—
183C4—2924no—
184C2—2924no—
185C2#1798909411yescharacteristic
186C2#1798915111yescharacteristic
187C2#1798916111yescharacteristic
188C2#1798918514yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#125×C73C2
hypercenterC2×#125D73
hypocenterC73#2633
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #17988522C2semidirect
3. #17988517C2semidirect
4. #17988513C2semidirect
6. #17988458C2semidirect
7. #17988455C2semidirect
8. C2×#125×C73C2semidirect
95. C73#2633semidirect
96. C2×#125D73semidirect