Finite Group Databasebeta

← #22625834

Subgroups — #22625834

Order 9344.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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#17989555C211yesmaximal, characteristic
2#17989529C211yesmaximal, characteristic
3#17989460C214yesmaximal, complemented
4C2×C4⋊C4×D73C211yesmaximal, characteristic
5C2×#11924036C2212yes—
6C2×C4⋊#64408C2212yes—
7C2×C22⋊#64408—21no—
8#14556648—21no—
9C22⋊#10596833—21no—
10(C2×#64408)⋊C4—21no—
11C22×C4×D73—21no—
12C22×C4×D73C2211yescharacteristic
13C2×C4⋊Dic73C411yescharacteristic, complemented
14C2×#11924007—21no—
15C4⋊C4×D73—21no—
16C4⋊C4×D73—21no—
17C4⋊C4×D73C412yescomplemented
18C4⋊C4×D73C2212yes—
19C2×C4⋊C4×C73C411yescharacteristic, complemented
20C22×#64408—22no—
21#11924036—24no—
22C2×#10596833—22no—
23C4⋊#64408—24no—
24C22⋊#64408—42no—
25C23×D73D411yescharacteristic
26C22×Dic73—21no—
27C22×Dic73D411yescharacteristic
28C2×C4×D73—24no—
29C2×C4×D73—22no—
30C2×C4×D73—22no—
31C2×C4×D73—42no—
32C2×C4×D73—42no—
33C2×C4×D73C2×C411yescharacteristic
34C2×C4×D73D411yescharacteristic
35C2×C4×D73D411yescharacteristic
36C2×C4×D73C2311yescharacteristic
37C4⋊Dic73—21no—
38C4⋊Dic73C2×C412yes—
39#11924007—22no—
40#11924007—22no—
41C22×C4×C73—21no—
42C22×C4×C73C2×C411yescharacteristic
43C4⋊C4×C73—21no—
44C4⋊C4×C73C2×C412yes—
45C23×C73C22⋊C411yescharacteristic
46C22×D73—22no—
47C22×D73—22no—
48C22×D73C22⋊C411yescharacteristic
49C22×D73D812yes—
50C22×D73SD1612yes—
51C22×D73C2×D411yescharacteristic
52C2×#64408—42no—
53C2×#64408—42no—
54C2×#64408—42no—
55C2×C4×C73—22no—
56C2×C4×C73—22no—
57C2×C4×C73—42no—
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C2×Dic73—22no—
61C2×Dic73—22no—
62C2×Dic73—42no—
63C2×Dic73C22⋊C411yescharacteristic
64C2×Dic73C2×D411yescharacteristic
65C4×D73—22no—
66C4×D73—22no—
67C4×D73—22no—
68C4×D73—44no—
69C4×D73—42no—
70C4×D73—42no—
71C4×D73#4114yes—
72#10596833—42no—
73C22×C73—21no—
74C22×C73—21no—
75C22×C73#10212yes—
76C22×C73C2×C22⋊C411yescharacteristic
77C2×D73—21no—
78C2×D73—21no—
79C2×D73—24no—
80C2×D73—24no—
81C2×D73#10212yes—
82C2×D73#12312yes—
83C2×D73C2×D811yescharacteristic
84C2×D73C2×SD1611yescharacteristic
85C2×D73#13712yes—
86#64408—82no—
87C4×C73—21no—
88C4×C73—42no—
89C4×C73#11712yes—
90Dic73—21no—
91Dic73—42no—
92Dic73#12312yes—
93C2×C73—22no—
94C2×C73#38111yescharacteristic
95C2×C73C2×#10211yescharacteristic
96C2×C73#41911yescharacteristic
97D73—22no—
98D73#48012yes—
99D73#48312yes—
100#1823—731nomaximal, Sylow
101C73#182311yescharacteristic, complemented, Sylow
102C22×C4⋊C4—731no—
103C2×C22⋊C8—731no—
104#380—731no—
105#340—734no—
106C23×C4—731no—
107C23×C4—1461no—
108C22×C8—732no—
109C2×C4⋊C4—731no—
110C2×C4⋊C4—732no—
111C2×C4⋊C4—732no—
112C2×C4⋊C4—732no—
113C2×C4⋊C4—1461no—
114C2×C4⋊C4—1461no—
115C2×C4⋊C4—1461no—
116C2×C4⋊C4#6440811yescharacteristic, complemented
117C2×C22⋊C4—1461no—
118C22⋊C8—1461no—
119C22⋊C8—1461no—
120#95—1461no—
121C24—731no—
122C22×C4—21no—
123C22×C4—2922no—
124C22×C4—2922no—
125C22×C4—731no—
126C22×C4—731no—
127C22×C4—731no—
128C22×C4—731no—
129C22×C4—731no—
130C22×C4—1462no—
131C22×C4—1462no—
132C22×C4—1464no—
133C22×C4—1462no—
134C22×C4—1461no—
135C22×C4C2×#6440811yescharacteristic
136C2×C8—1462no—
137C2×C8—1464no—
138C4⋊C4—21no—
139C4⋊C4—732no—
140C4⋊C4—1462no—
141C4⋊C4—1462no—
142C4⋊C4—1464no—
143C4⋊C4—1461no—
144C4⋊C4C2×#6440812yes—
145C22⋊C4—2922no—
146C23—731no—
147C23—732no—
148C23—732no—
149C23—731no—
150C23—1462no—
151C23—1462no—
152C23C22⋊#6440811yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—2922no—
157C2×C4—2922no—
158C2×C4—2924no—
159C2×C4—2922no—
160C2×C4—2922no—
161C2×C4—2922no—
162C2×C4—2922no—
163C2×C4—731no—
164C2×C4—734no—
165C2×C4—731no—
166C2×C4—1462no—
167C2×C4—1462no—
168C2×C4—1462no—
169C2×C4—1462no—
170C2×C4—1462no—
171C2×C4C22⋊#6440811yescharacteristic
172C2×C4C22×#6440811yescharacteristic
173C8—2922no—
174C22—21no—
175C22—21no—
176C22—732no—
177C22—731no—
178C22—731no—
179C22—732no—
180C22—732no—
181C22—1464no—
182C22—1464no—
183C22—1461no—
184C22—1461no—
185C22#1455665312yes—
186C22C2×C22⋊#6440811yescharacteristic
187C4—21no—
188C4—42no—
189C4—2922no—
190C4—5842no—
191C4—732no—
192C4—1461no—
193C4#1455667012yes—
194C2—22no—
195C2—732no—
196C2—732no—
197C2—1462no—
198C2#1798953011yescharacteristic
199C2C2×#1455665311yescharacteristic
200C2#1798958011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×C4⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73#1823
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #17989460C2semidirect
13. C2×C4⋊Dic73C4semidirect
17. C4⋊C4×D73C4semidirect
19. C2×C4⋊C4×C73C4semidirect
101. C73#1823semidirect
116. C2×C4⋊C4#64408semidirect