Finite Group Databasebeta

← #22617609

Subgroups — #22617609

Order 9344.

448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 125 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#17988527C212yesmaximal, complemented
2#17988526C211yesmaximal, characteristic, complemented
3#17988515C212yesmaximal, complemented
4#17988475C212yesmaximal, complemented
5#17988467C212yesmaximal
6#17988462C212yesmaximal, complemented
7#17988462C212yesmaximal, complemented
8#17988452C211yesmaximal, characteristic, complemented
9#394×C73C211yesmaximal, characteristic
10C23×Dic73C2212yes—
11C2×C4⋊Dic73C2211yescharacteristic
12C2×C4⋊Dic73C2211yescharacteristic
13C2×C4⋊Dic73C2212yes—
14C2×#11924007C2212yes—
15C2×C22⋊Dic73C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C4×Dic73C2211yescharacteristic
19#14556498C2212yes—
20#14556498C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26C22×D4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2212yes—
30#95×C73C2211yescharacteristic
31C22×Dic73—42no—
32C22×Dic73—42no—
33C22×Dic73—42no—
34C22×Dic73C2312yes—
35C22×Dic73C2312yes—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C4⋊Dic73—41no—
39C4⋊Dic73—41no—
40C4⋊Dic73—42no—
41#11924007—42no—
42C22⋊Dic73—24no—
43C22⋊Dic73—42no—
44C22⋊Dic73—42no—
45C4×Dic73—22no—
46C24×C73C2312yes—
47C2×D4×C73—24no—
48C2×D4×C73—41no—
49C22×C4×C73C2312yes—
50C22×C4×C73C2311yescharacteristic
51C22×C4×C73C2311yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C4⋊C4×C73—41no—
54C22⋊C4×C73—24no—
55C22⋊C4×C73—24no—
56C23×C73—22no—
57C23×C73—22no—
58C23×C73—22no—
59C23×C73—22no—
60C23×C73—22no—
61C23×C73—22no—
62C23×C73#4114yes—
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—22no—
87C2×Dic73—48no—
88C22×C73—24no—
89C22×C73—24no—
90C22×C73—24no—
91C22×C73—42no—
92C22×C73—42no—
93C22×C73—42no—
94C22×C73—42no—
95C22×C73C2×#4112yes—
96C22×C73C2×#4111yescharacteristic
97C22×C73H(5,𝔽2)11yescharacteristic
98C22×C73H(5,𝔽2)12yes—
99C22×C732−1+411yescharacteristic
100C4×C73—22no—
101C4×C73—41no—
102C4×C73—41no—
103C4×C73—42no—
104Dic73—42no—
105Dic73—42no—
106Dic73—42no—
107Dic73—42no—
108C2×C73—44no—
109C2×C73#53912yes—
110C2×C73#53911yescharacteristic
111C2×C73#55111yescharacteristic
112C2×C73#55312yes—
113C2×C73H(3,𝔽4)11yescharacteristic
114#2782—731nomaximal, Sylow
115C73#278211yescharacteristic, complemented, Sylow
116#400—731no—
117#400—732no—
118#397—732no—
119#394D7311yescharacteristic
120#388—732no—
121#386—732no—
122#385—732no—
123#385—732no—
124#382—731no—
125C22×D4C2×D7311yescharacteristic
126C23×C4—732no—
127C2×C4⋊C4—731no—
128C2×C4⋊C4—731no—
129C2×C4⋊C4—732no—
130C2×C4⋊C4—732no—
131C2×C4⋊C4C2×D7311yescharacteristic
132C2×C22⋊C4—732no—
133C2×C22⋊C4—732no—
134C2×C22⋊C4—732no—
135C2×C22⋊C4C2×D7312yes—
136C2×C22⋊C4C2×D7312yes—
137C2×C42—731no—
138#95—732no—
139#95—732no—
140#95—732no—
141#95—732no—
142#95—732no—
143#95—732no—
144#95—731no—
145#95C2×D7311yescharacteristic
146C24C22×D7312yes—
147C2×D4—24no—
148C2×D4—41no—
149C22×C4—2922no—
150C22×C4—2922no—
151C22×C4—2922no—
152C22×C4—732no—
153C22×C4—732no—
154C22×C4—732no—
155C22×C4—732no—
156C22×C4C22×D7311yescharacteristic
157C22×C4C22×D7311yescharacteristic
158C22×C4C22×D7312yes—
159C22×C4C22×D7311yescharacteristic
160C4⋊C4—41no—
161C4⋊C4—2922no—
162C4⋊C4—2921no—
163C4⋊C4—2921no—
164C4⋊C4—2922no—
165C22⋊C4—24no—
166C22⋊C4—24no—
167C22⋊C4—2922no—
168C22⋊C4—2922no—
169C22⋊C4—1464no—
170C42—1462no—
171C23—22no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23#1192402714yes—
178C23C23×D7311yescharacteristic
179D4—44no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—2928no—
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—1462no—
201C2×C4—1462no—
202C2×C4#1192402712yes—
203C22—24no—
204C22—24no—
205C22—24no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22C2×#1192402712yes—
211C22C2×#1192402711yescharacteristic
212C22#1455663611yescharacteristic
213C22#1455663712yes—
214C22#1455663811yescharacteristic
215C4—22no—
216C4—41no—
217C4—41no—
218C4—42no—
219C4—2922no—
220C4—2922no—
221C4—2922no—
222C4—2922no—
223C2—44no—
224C2#1798918112yes—
225C2#1798918211yescharacteristic
226C2#1798926811yescharacteristic
227C2#1798928912yes—
228C2#1798932911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2782
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #17988527C2semidirect
2. #17988526C2semidirect
3. #17988515C2semidirect
4. #17988475C2semidirect
6. #17988462C2semidirect
7. #17988462C2semidirect
8. #17988452C2semidirect
115. C73#2782semidirect