Finite Group Databasebeta

← #22617632

Subgroups — #22617632

Order 9344.

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

normal subgroups only

This group has 472 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
1#17988526C211yesmaximal, characteristic, complemented
2#17988510C212yesmaximal, complemented
3#17988507C211yesmaximal, characteristic, complemented
4#17988499C212yesmaximal, complemented
5#17988471C212yesmaximal, complemented
6#17988467C212yesmaximal
7#17988459C212yesmaximal, complemented
8#17988445C212yesmaximal, complemented
9#390×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C23×Dic73C2212yes—
12C2×C4⋊Dic73C2211yescharacteristic
13C2×#11924007C2212yes—
14C2×#11924007C2212yes—
15C2×#11924007C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C22⋊Dic73C2212yes—
19#14556498C2211yescharacteristic
20#14556498C2212yes—
21#14556498C2211yescharacteristic
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26C22×D4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2212yes—
30C2×C42×C73C2211yescharacteristic
31C2×Dic146—41no—
32C2×Dic146—42no—
33C22×Dic73—24no—
34C22×Dic73—42no—
35C22×Dic73—42no—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C4⋊Dic73—41no—
41#11924007—24no—
42#11924007—42no—
43#11924007—42no—
44C22⋊Dic73—24no—
45C22⋊Dic73—42no—
46C22⋊Dic73—42no—
47C24×C73C2312yes—
48C2×D4×C73—41no—
49C2×D4×C73—41no—
50C2×D4×C73Q814yescomplemented
51C22×C4×C73C2312yes—
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2311yescharacteristic
54C22×C4×C73C2311yescharacteristic
55C4⋊C4×C73—41no—
56C22⋊C4×C73—42no—
57C22⋊C4×C73—42no—
58C42×C73—41no—
59C23×C73—22no—
60C23×C73—22no—
61C23×C73—22no—
62C23×C73—22no—
63C23×C73—22no—
64C23×C73—22no—
65C23×C73C2×Q814yes—
66C23×C73C2411yescharacteristic
67D4×C73—44no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73C2×Q812yes—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73—48no—
90C2×Dic73#4114yes—
91Dic146—44no—
92C22×C73—24no—
93C22×C73—24no—
94C22×C73—24no—
95C22×C73—42no—
96C22×C73—42no—
97C22×C73—42no—
98C22×C73—42no—
99C22×C73C22×Q811yescharacteristic
100C22×C73C2×#4112yes—
101C22×C73H(5,𝔽2)11yescharacteristic
102C22×C73H(5,𝔽2)12yes—
103C22×C73H(5,𝔽2)11yescharacteristic
104C4×C73—22no—
105C4×C73—42no—
106C4×C73—41no—
107C4×C73—41no—
108Dic73—24no—
109Dic73—42no—
110Dic73—42no—
111Dic73—42no—
112C2×C73—44no—
113C2×C73#53812yes—
114C2×C73#54311yescharacteristic
115C2×C73#55412yes—
116C2×C73#55511yescharacteristic
117C2×C73#56011yescharacteristic
118#2784—731nomaximal, Sylow
119C73#278411yescharacteristic, complemented, Sylow
120#400—731no—
121#396—732no—
122#395—731no—
123#393—732no—
124#390D7311yescharacteristic
125#387—732no—
126#386—732no—
127#385—732no—
128#380—732no—
129C22×Q8—731no—
130C22×D4C2×D7311yescharacteristic
131C23×C4—732no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4—731no—
135C2×C4⋊C4—732no—
136C2×C4⋊C4C2×D7311yescharacteristic
137C2×C22⋊C4—732no—
138C2×C22⋊C4—732no—
139C2×C22⋊C4—732no—
140C2×C22⋊C4C2×D7312yes—
141C2×C22⋊C4C2×D7312yes—
142C2×C42C2×D7311yescharacteristic
143#95—731no—
144#95—732no—
145#95—731no—
146#95—732no—
147#95—732no—
148#95—732no—
149#95—732no—
150C24C22×D7312yes—
151C2×Q8—2922no—
152C2×Q8—2921no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4Dic14614yescomplemented
156C22×C4—2922no—
157C22×C4—2922no—
158C22×C4—732no—
159C22×C4—732no—
160C22×C4—732no—
161C22×C4—732no—
162C22×C4—1464no—
163C22×C4C22×D7311yescharacteristic
164C22×C4C22×D7312yes—
165C22×C4C22×D7311yescharacteristic
166C22×C4C22×D7311yescharacteristic
167C4⋊C4—41no—
168C4⋊C4—2922no—
169C4⋊C4—2922no—
170C4⋊C4—2921no—
171C4⋊C4—1464no—
172C22⋊C4—42no—
173C22⋊C4—42no—
174C22⋊C4—2922no—
175C22⋊C4—2922no—
176C22⋊C4—1464no—
177C42—41no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23C2×Dic14614yes—
185C23C23×D7311yescharacteristic
186Q8—2924no—
187D4—44no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—2928no—
198C2×C4—734no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4—1462no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4—1462no—
207C2×C4—1462no—
208C2×C4—1462no—
209C2×C4—1462no—
210C2×C4C2×Dic14612yes—
211C22—24no—
212C22—24no—
213C22—24no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22C22×Dic14611yescharacteristic
219C22#41×D7312yes—
220C22#1455663611yescharacteristic
221C22#1455663612yes—
222C22#1455663611yescharacteristic
223C4—22no—
224C4—42no—
225C4—41no—
226C4—41no—
227C4—2922no—
228C4—2922no—
229C4—2922no—
230C4—1464no—
231C2—44no—
232C2#1798916912yes—
233C2#1798921311yescharacteristic
234C2#1798929612yes—
235C2#1798929911yescharacteristic
236C2#1798932411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#390×C73C2
hypercenter#390D73
hypocenterC73#2784
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #17988526C2semidirect
2. #17988510C2semidirect
3. #17988507C2semidirect
4. #17988499C2semidirect
5. #17988471C2semidirect
7. #17988459C2semidirect
8. #17988445C2semidirect
50. C2×D4×C73Q8semidirect
119. C73#2784semidirect
155. C2×D4Dic146semidirect