Finite Group Databasebeta

← #22617764

Subgroups — #22617764

Order 9344.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#17988501C212yesmaximal
4#17988480C212yesmaximal, complemented
5#17988475C212yesmaximal, complemented
6#17988475C212yesmaximal, complemented
7#17988469C212yesmaximal, complemented
8#17988456C211yesmaximal, characteristic, complemented
9#394×C73C211yesmaximal, characteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007C2212yes—
13C2×#11924007C2212yes—
14C2×#11924007C2212yes—
15C2×C22⋊Dic73C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C22⋊Dic73C2212yes—
19C2×C4×Dic73C2211yescharacteristic
20C2×C4×Dic73C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2211yescharacteristic
25#14556498C2212yes—
26C22×D4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2212yes—
30#95×C73C2211yescharacteristic
31C22×Dic73C2312yes—
32C22×Dic73C2312yes—
33C22×Dic73C2312yes—
34C22×Dic73C2312yes—
35C4⋊Dic73—41no—
36C4⋊Dic73—41no—
37#11924007—24no—
38#11924007—42no—
39#11924007—42no—
40C22⋊Dic73—24no—
41C22⋊Dic73—24no—
42C22⋊Dic73—42no—
43C22⋊Dic73—42no—
44C4×Dic73—22no—
45C4×Dic73—42no—
46C24×C73C2312yes—
47C2×D4×C73—41no—
48C2×D4×C73—42no—
49C22×C4×C73C2312yes—
50C22×C4×C73C2311yescharacteristic
51C22×C4×C73C2311yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C4⋊C4×C73—41no—
54C22⋊C4×C73—24no—
55C22⋊C4×C73—42no—
56C23×C73—22no—
57C23×C73—22no—
58C23×C73—22no—
59C23×C73—22no—
60C23×C73—22no—
61C23×C73—22no—
62C23×C73—22no—
63C23×C73C2411yescharacteristic
64D4×C73—44no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73#4112yes—
75C2×Dic73—22no—
76C2×Dic73—22no—
77C2×Dic73—22no—
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#4114yes—
87C22×C73—42no—
88C22×C73—42no—
89C22×C73—42no—
90C22×C73—42no—
91C22×C73—42no—
92C22×C73—42no—
93C22×C73—42no—
94C22×C73C2×#4112yes—
95C22×C73C2×#4111yescharacteristic
96C22×C73H(5,𝔽2)11yescharacteristic
97C22×C73H(5,𝔽2)12yes—
98C22×C732−1+411yescharacteristic
99C4×C73—22no—
100C4×C73—42no—
101C4×C73—41no—
102C4×C73—41no—
103Dic73—24no—
104Dic73—42no—
105Dic73—42no—
106Dic73—42no—
107C2×C73—82no—
108C2×C73#53911yescharacteristic
109C2×C73#54212yes—
110C2×C73#55312yes—
111C2×C73#55511yescharacteristic
112C2×C73#56011yescharacteristic
113#2795—731nomaximal, Sylow
114C73#279511yescharacteristic, complemented, Sylow
115#400—731no—
116#396—732no—
117#394—732no—
118#394D7311yescharacteristic
119#388—732no—
120#388—732no—
121#388—732no—
122#387—732no—
123#384—731no—
124C22×D4C2×D7311yescharacteristic
125C2×C4⋊C4—732no—
126C2×C4⋊C4—732no—
127C2×C4⋊C4—731no—
128C2×C4⋊C4—731no—
129C2×C4⋊C4—732no—
130C2×C4⋊C4C2×D7311yescharacteristic
131C2×C22⋊C4—732no—
132C2×C22⋊C4—732no—
133C2×C22⋊C4—732no—
134C2×C22⋊C4—732no—
135C2×C22⋊C4C2×D7312yes—
136C2×C22⋊C4C2×D7312yes—
137C2×C42—732no—
138C2×C42—731no—
139#95—732no—
140#95—732no—
141#95—732no—
142#95—731no—
143#95—732no—
144#95C2×D7311yescharacteristic
145C24C22×D7312yes—
146C2×D4—41no—
147C2×D4—42no—
148C22×C4—732no—
149C22×C4—732no—
150C22×C4—732no—
151C22×C4—732no—
152C22×C4C22×D7312yes—
153C22×C4C22×D7311yescharacteristic
154C22×C4C22×D7311yescharacteristic
155C22×C4C22×D7311yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—2922no—
158C4⋊C4—2922no—
159C4⋊C4—2921no—
160C4⋊C4—2921no—
161C4⋊C4—1464no—
162C22⋊C4—24no—
163C22⋊C4—42no—
164C22⋊C4—2922no—
165C22⋊C4—2922no—
166C22⋊C4—1464no—
167C22⋊C4—1464no—
168C42—2922no—
169C42—1462no—
170C23—22no—
171C23—22no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23C23×D7311yescharacteristic
178D4—44no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—734no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1462no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4#1192402712yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22#41×D7312yes—
209C22C2×#1192402711yescharacteristic
210C22#1455663611yescharacteristic
211C22#1455663612yes—
212C22#1455663811yescharacteristic
213C4—22no—
214C4—42no—
215C4—41no—
216C4—41no—
217C4—2922no—
218C4—2922no—
219C4—2922no—
220C4—1464no—
221C2—82no—
222C2#1798918211yescharacteristic
223C2#1798920512yes—
224C2#1798928412yes—
225C2#1798929911yescharacteristic
226C2#1798932611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2795
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #17988526C2semidirect
2. #17988510C2semidirect
4. #17988480C2semidirect
5. #17988475C2semidirect
6. #17988475C2semidirect
7. #17988469C2semidirect
8. #17988456C2semidirect
114. C73#2795semidirect