Finite Group Databasebeta

← #22625367

Subgroups — #22625367

Order 9344.

340 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 70 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, complemented
2#17989529C211yesmaximal, characteristic, complemented
3#17989438C214yesmaximal, complemented
4C2×#14556562C211yesmaximal, characteristic
5C2×#11924036—21no—
6C2×C4⋊#64408—21no—
7C2×C22⋊#64408—21no—
8#14556648C2212yescomplemented
9C22⋊#10596833—21no—
10(C2×#64408)⋊C4C2212yescomplemented
11C22×C22⋊D73—21no—
12C22×C4×D73C2211yescharacteristic
13#14556562—21no—
14#14556562—21no—
15#14556562C412yescomplemented
16#14556562C2212yes—
17C2×C4⋊Dic73C411yescharacteristic, complemented
18C2×C22⋊Dic73—21no—
19C22×D4×C73C411yescharacteristic, complemented
20C22×#64408—22no—
21#11924036—42no—
22C2×#10596833—22no—
23C4⋊#64408—42no—
24C22⋊#64408—42no—
25C23×D73D411yescharacteristic
26C2×C22⋊D73—22no—
27C2×C22⋊D73—22no—
28C2×C22⋊D73—42no—
29C2×C22⋊D73—42no—
30C22×Dic73—21no—
31C22×Dic73D411yescharacteristic
32C2×C4×D73—42no—
33C2×C4×D73C2×C411yescharacteristic
34C2×C4×D73D411yescharacteristic
35C2×C4×D73D411yescharacteristic
36C2×C4×D73C2311yescharacteristic
37C4⋊Dic73—21no—
38C4⋊Dic73C2×C412yes—
39C22⋊Dic73—22no—
40C22⋊Dic73—22no—
41C24×C73—21no—
42C2×D4×C73—21no—
43C2×D4×C73—42no—
44C2×D4×C73C2×C412yes—
45C22×C4×C73C2×C411yescharacteristic
46C23×C73—22no—
47C23×C73—42no—
48C23×C73—42no—
49C23×C73—42no—
50C23×C73C22⋊C411yescharacteristic
51C22×D73—41no—
52C22×D73—41no—
53C22×D73C22⋊C411yescharacteristic
54C22×D73D812yes—
55C22×D73SD1612yes—
56C22×D73C2×D411yescharacteristic
57C2×#64408—42no—
58C2×#64408—42no—
59C2×#64408—42no—
60D4×C73—42no—
61D4×C73—42no—
62C2×C4×C73—22no—
63C2×C4×C73C22⋊C411yescharacteristic
64C2×C4×C73C22×C411yescharacteristic
65C22⋊D73—44no—
66C22⋊D73—42no—
67C22⋊D73—42no—
68C2×Dic73—22no—
69C2×Dic73—41no—
70C2×Dic73—42no—
71C2×Dic73C22⋊C411yescharacteristic
72C2×Dic73C2×D411yescharacteristic
73C4×D73—22no—
74C4×D73—22no—
75C4×D73—41no—
76C4×D73—41no—
77#10596833—42no—
78C22×C73—21no—
79C22×C73—21no—
80C22×C73—42no—
81C22×C73—42no—
82C22×C73—42no—
83C22×C73—84no—
84C22×C73#10212yes—
85C22×C73C2×C22⋊C411yescharacteristic
86C2×D73—21no—
87C2×D73—21no—
88C2×D73—21no—
89C2×D73—21no—
90C2×D73—42no—
91C2×D73—42no—
92C2×D73#10212yes—
93C2×D73C2×D811yescharacteristic
94C2×D73C2×SD1611yescharacteristic
95#64408—82no—
96C4×C73—21no—
97C4×C73#9912yes—
98Dic73—21no—
99Dic73—21no—
100Dic73—42no—
101C2×C73—22no—
102C2×C73—82no—
103C2×C73C2×#9911yescharacteristic
104C2×C73C2×#10211yescharacteristic
105C2×C73#42111yescharacteristic
106D73—21no—
107D73—22no—
108D73—21no—
109#1519—731nomaximal, Sylow
110C73#151911yescharacteristic, complemented, Sylow
111C2×#121—731no—
112C2×C22⋊C8—731no—
113#380—731no—
114#327—734no—
115C22×D4—1461no—
116C22×D4#6440811yescharacteristic, complemented
117C23×C4—731no—
118C22×C8—1461no—
119#121—732no—
120#121—732no—
121#121—1461no—
122#121—1461no—
123C2×C4⋊C4—731no—
124C2×C4⋊C4—1461no—
125C2×C22⋊C4—1461no—
126C2×C22⋊C4—1461no—
127C22⋊C8—732no—
128C22⋊C8—1461no—
129#95—732no—
130C24—21no—
131C24—731no—
132C2×D4—21no—
133C2×D4—42no—
134C2×D4—2922no—
135C2×D4—2922no—
136C2×D4—1462no—
137C2×D4—1462no—
138C2×D4C2×#6440812yes—
139C22×C4—2922no—
140C22×C4—731no—
141C22×C4—731no—
142C22×C4—731no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—1462no—
146C22×C4—1461no—
147C22×C4C2×#6440811yescharacteristic
148C2×C8—2922no—
149C2×C8—1462no—
150C4⋊C4—2922no—
151C4⋊C4—732no—
152C4⋊C4—1461no—
153C22⋊C4—2922no—
154C22⋊C4—1462no—
155C22⋊C4—1462no—
156C23—22no—
157C23—42no—
158C23—42no—
159C23—42no—
160C23—2921no—
161C23—2921no—
162C23—732no—
163C23—732no—
164C23—731no—
165C23—731no—
166C23C22⋊#6440811yescharacteristic
167D4—42no—
168D4—42no—
169D4—2922no—
170D4—2924no—
171D4—2922no—
172C2×C4—22no—
173C2×C4—2921no—
174C2×C4—2921no—
175C2×C4—2922no—
176C2×C4—2922no—
177C2×C4—2922no—
178C2×C4—2922no—
179C2×C4—2921no—
180C2×C4—731no—
181C2×C4—731no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4C22⋊#6440811yescharacteristic
186C2×C4C22×#6440811yescharacteristic
187C8—2922no—
188C22—21no—
189C22—21no—
190C22—42no—
191C22—42no—
192C22—42no—
193C22—84no—
194C22—2922no—
195C22—2922no—
196C22—731no—
197C22—732no—
198C22—731no—
199C22—1461no—
200C22—1461no—
201C22—1461no—
202C22—1461no—
203C22#1455665312yes—
204C22C2×C22⋊#6440811yescharacteristic
205C4—21no—
206C4—2922no—
207C4—5842no—
208C4—1461no—
209C4—1461no—
210C4#1455664912yes—
211C2—22no—
212C2—82no—
213C2—1461no—
214C2—1462no—
215C2—1461no—
216C2C2×#1455664911yescharacteristic
217C2C2×#1455665311yescharacteristic
218C2#1798958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×D4#64408
hypocenterC73#1519
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #17989555C2semidirect
2. #17989529C2semidirect
3. #17989438C2semidirect
8. #14556648C22semidirect
10. (C2×#64408)⋊C4C22semidirect
15. #14556562C4semidirect
17. C2×C4⋊Dic73C4semidirect
19. C22×D4×C73C4semidirect
110. C73#1519semidirect
116. C22×D4#64408semidirect