Finite Group Databasebeta

← #22625625

Subgroups — #22625625

Order 9344.

372 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C22×#11924038C211yesmaximal, characteristic
2C2×D73⋊M16C211yesmaximal, characteristic
3#17989463C214yesmaximal, complemented
4C2×M16×D73C211yesmaximal, characteristic
5C2×#11924038—21no—
6C2×#11924038—22no—
7C2×#11924038C414yes—
8C2×#11924038C2212yes—
9C2×#11924038C2212yes—
10D73⋊M16—22no—
11D73⋊M16C414yes—
12C2×#11924037—21no—
13C2×#11924036—21no—
14C22×#10596833—21no—
15C22×C4×D73C2211yescharacteristic
16C2×#11924012C411yescharacteristic
17C2×#11924011C412yes—
18M16×D73—22no—
19M16×D73—22no—
20C2×C8×D73C2212yes—
21C2×M16×C73C411yescharacteristic
22#11924038—24no—
23#11924038—22no—
24#11924038—22no—
25#11924038C2×C414yes—
26#11924038C2×C414yes—
27#11924037—24no—
28#11924036—24no—
29C2×#10596833—24no—
30C2×#10596833—22no—
31C2×#10596833—22no—
32C23×D73Q811yescharacteristic
33C22×Dic73D411yescharacteristic
34C2×C4×D73C2×C411yescharacteristic
35C2×C4×D73C2×C412yes—
36C2×C4×D73C2×C412yes—
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D412yes—
39C2×C4×D73D412yes—
40C2×C4×D73Q811yescharacteristic
41C2×C4×D73C2311yescharacteristic
42#11924012—22no—
43#11924011—24no—
44C2×#10596831C2×C412yes—
45C8×D73—22no—
46C8×D73—22no—
47C22×C4×C73C2×C411yescharacteristic
48M16×C73—22no—
49C2×C8×C73C2×C412yes—
50C23×C73C4⋊C411yescharacteristic
51C22×D73—42no—
52C22×D73C4⋊C411yescharacteristic
53C22×D73C4⋊C412yes—
54C22×D73C4⋊C412yes—
55C22×D73C2×Q811yescharacteristic
56C2×C4×C73C4212yes—
57C2×C4×C73C22⋊C412yes—
58C2×C4×C73C4⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C2×Dic73C22⋊C412yes—
61C2×Dic73C22⋊C412yes—
62C2×Dic73C4⋊C411yescharacteristic
63C2×Dic73C2×D411yescharacteristic
64C4×D73C4212yes—
65C4×D73C22⋊C412yes—
66C4×D73C22⋊C412yes—
67C4×D73C22⋊C412yes—
68C4×D73C4⋊C412yes—
69C4×D73C4⋊C412yes—
70C4×D73C22×C411yescharacteristic
71C4×D73C22×C411yescharacteristic
72C4×D73C2×D411yescharacteristic
73C4×D73C2×D411yescharacteristic
74#10596833—24no—
75#10596833—24no—
76C8×C73—22no—
77#10596831—22no—
78C22×C73—22no—
79C22×C73#9512yes—
80C22×C73C2×C4⋊C411yescharacteristic
81C2×D73—22no—
82C2×D73—22no—
83C2×D73—42no—
84C2×D73—42no—
85C2×D73#9512yes—
86C2×D73C2×C4⋊C411yescharacteristic
87C2×D73C2×C4⋊C411yescharacteristic
88C4×C73#9512yes—
89C4×C73C2×C4211yescharacteristic
90C4×C73C2×C22⋊C411yescharacteristic
91Dic73#9512yes—
92Dic73C2×C22⋊C411yescharacteristic
93Dic73C2×C22⋊C411yescharacteristic
94C2×C73—22no—
95C2×C73C2×#9511yescharacteristic
96C2×C73#43012yes—
97D73—22no—
98D73—21no—
99D73—21no—
100#1738—731nomaximal, Sylow
101C73#173811yescharacteristic, complemented, Sylow
102C22×M16—731no—
103C22×M16—731no—
104C22×M16—731no—
105#341—734no—
106C23×C4—731no—
107C2×M16—731no—
108C2×M16—732no—
109C2×M16—734no—
110C2×M16—734no—
111C2×M16—732no—
112C2×M16—732no—
113C2×M16—1462no—
114C2×M16—1462no—
115C2×M16—1461no—
116C2×M16—1462no—
117C2×M16—1462no—
118C2×M16—1461no—
119C2×M16#6440811yescharacteristic
120C22×C8—732no—
121C22×C8—1461no—
122C22×C8—1461no—
123C24—731no—
124C22×C4—731no—
125C22×C4—732no—
126C22×C4—732no—
127C22×C4—732no—
128C22×C4—732no—
129C22×C4—731no—
130C22×C4—731no—
131C22×C4—731no—
132C22×C4—731no—
133C22×C4C2×#6440811yescharacteristic
134M16—22no—
135M16—734no—
136M16—734no—
137M16—1464no—
138M16—1464no—
139M16—1464no—
140M16—1462no—
141M16—1462no—
142M16—1462no—
143C2×C8—732no—
144C2×C8—1462no—
145C2×C8—1462no—
146C2×C8—1464no—
147C2×C8—1462no—
148C2×C8—1462no—
149C2×C8—1464no—
150C2×C8C2×#6440812yes—
151C23—2922no—
152C23—732no—
153C23—732no—
154C23—731no—
155C23—731no—
156C23C4⋊#6440811yescharacteristic
157C2×C4—732no—
158C2×C4—732no—
159C2×C4—731no—
160C2×C4—731no—
161C2×C4—732no—
162C2×C4—732no—
163C2×C4—732no—
164C2×C4—732no—
165C2×C4—731no—
166C2×C4—731no—
167C2×C4—732no—
168C2×C4—731no—
169C2×C4—731no—
170C2×C4—732no—
171C2×C4C4×#6440812yes—
172C2×C4C22⋊#6440812yes—
173C2×C4C4⋊#6440811yescharacteristic
174C2×C4C22×#6440811yescharacteristic
175C8—22no—
176C8—1464no—
177C8—1464no—
178C8—1462no—
179C22—22no—
180C22—2922no—
181C22—2922no—
182C22—732no—
183C22—731no—
184C22—731no—
185C22—1462no—
186C22—1462no—
187C22(C2×#64408)⋊C412yes—
188C22C2×C4⋊#6440811yescharacteristic
189C4—731no—
190C4—731no—
191C4—732no—
192C4(C2×#64408)⋊C412yes—
193C4C2×C4×#6440811yescharacteristic
194C4C2×C22⋊#6440811yescharacteristic
195C2—22no—
196C2—1462no—
197C2—1461no—
198C2—1461no—
199C2C2×(C2×#64408)⋊C411yescharacteristic
200C2#1798960212yes—
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC4×C73C2×C42
FrattiniC2×C4C22×#64408
FittingC2×M16×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC2×M16#64408
hypocenterC73#1738
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #17989463C2semidirect
101. C73#1738semidirect