Finite Group Databasebeta

← #22617146

Subgroups — #22617146

Order 9344.

464 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 141 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#17988523C212yesmaximal, complemented
2#17988519C212yesmaximal, complemented
3#17988510C212yesmaximal, complemented
4#17988490C211yesmaximal, characteristic
5#17988470C212yesmaximal, complemented
6#17988467C211yesmaximal, characteristic
7#17988462C212yesmaximal, complemented
8#17988447C212yesmaximal, complemented
9#386×C73C211yesmaximal, characteristic
10C23×Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2212yes—
12C2×C4⋊Dic73C2212yes—
13C2×C4⋊Dic73C2212yes—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2212yes—
20C2×C22⋊Dic73C2211yescharacteristic
21C2×C4×Dic73C2211yescharacteristic
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26C22×D4×C73C2211yescharacteristic
27C23×C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2211yescharacteristic
30#95×C73C2212yes—
31C22×Dic73—42no—
32C22×Dic73—41no—
33C22×Dic73C2312yes—
34C22×Dic73C2312yes—
35C22×Dic73C2312yes—
36C22×Dic73C2312yes—
37C4⋊Dic73—24no—
38C4⋊Dic73—42no—
39C4⋊Dic73—41no—
40C4⋊Dic73—42no—
41#11924007—42no—
42#11924007—42no—
43C22⋊Dic73—42no—
44C22⋊Dic73—42no—
45C22⋊Dic73—41no—
46C22⋊Dic73—42no—
47C4×Dic73—41no—
48C24×C73C2311yescharacteristic
49C24×C73C2311yescharacteristic
50C2×D4×C73—41no—
51C2×D4×C73—41no—
52C2×D4×C73Q814yes—
53C22×C4×C73—24no—
54C22×C4×C73—41no—
55C22×C4×C73C2312yes—
56C22×C4×C73C2311yescharacteristic
57C22×C4×C73C2312yes—
58C22⋊C4×C73—24no—
59C22⋊C4×C73—41no—
60C23×C73—22no—
61C23×C73—22no—
62C23×C73—21no—
63C23×C73—21no—
64C23×C73—21no—
65C23×C73—21no—
66C23×C73—22no—
67C23×C73—22no—
68C23×C73C2×Q812yes—
69C23×C73C2×Q812yes—
70C23×C73C2411yescharacteristic
71D4×C73—44no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—44no—
80C2×C4×C73C2×Q812yes—
81C2×C4×C73#4114yes—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—44no—
95C22×C73—22no—
96C22×C73—22no—
97C22×C73—24no—
98C22×C73—24no—
99C22×C73—42no—
100C22×C73—42no—
101C22×C73—41no—
102C22×C73—41no—
103C22×C73—41no—
104C22×C73—41no—
105C22×C73C22×Q811yescharacteristic
106C22×C73C2×#4112yes—
107C22×C73H(5,𝔽2)11yescharacteristic
108C22×C73H(5,𝔽2)11yescharacteristic
109C22×C73H(5,𝔽2)12yes—
110C4×C73—22no—
111C4×C73—24no—
112C4×C73—42no—
113Dic73—42no—
114Dic73—42no—
115Dic73—42no—
116Dic73—42no—
117C2×C73—42no—
118C2×C73—42no—
119C2×C73#54012yes—
120C2×C73#54311yescharacteristic
121C2×C73#55111yescharacteristic
122C2×C73#55412yes—
123C2×C73#56011yescharacteristic
124#2748—731nomaximal, Sylow
125C73#274811yescharacteristic, complemented, Sylow
126#399—732no—
127#398—732no—
128#396—732no—
129#390—731no—
130#387—732no—
131#386—731no—
132#386D7311yescharacteristic
133#385—732no—
134#380—732no—
135C22×D4C2×D7311yescharacteristic
136C23×C4—731no—
137C23×C4C2×D7311yescharacteristic
138C2×C4⋊C4—732no—
139C2×C4⋊C4—732no—
140C2×C4⋊C4—732no—
141C2×C4⋊C4—732no—
142C2×C4⋊C4—731no—
143C2×C4⋊C4—732no—
144C2×C22⋊C4—732no—
145C2×C22⋊C4—732no—
146C2×C22⋊C4—732no—
147C2×C22⋊C4—731no—
148C2×C22⋊C4C2×D7312yes—
149C2×C22⋊C4C2×D7311yescharacteristic
150C2×C42—731no—
151#95—732no—
152#95—732no—
153#95—732no—
154#95—732no—
155#95C2×D7312yes—
156C24C22×D7311yescharacteristic
157C24C22×D7311yescharacteristic
158C2×D4—41no—
159C2×D4—41no—
160C2×D4Dic14614yes—
161C22×C4—24no—
162C22×C4—41no—
163C22×C4—2921no—
164C22×C4—2922no—
165C22×C4—732no—
166C22×C4—732no—
167C22×C4—732no—
168C22×C4—732no—
169C22×C4C22×D7312yes—
170C22×C4C22×D7311yescharacteristic
171C22×C4C22×D7312yes—
172C4⋊C4—2922no—
173C4⋊C4—2922no—
174C4⋊C4—2922no—
175C4⋊C4—2921no—
176C4⋊C4—2922no—
177C4⋊C4—1464no—
178C22⋊C4—24no—
179C22⋊C4—41no—
180C22⋊C4—2921no—
181C22⋊C4—2922no—
182C22⋊C4—2922no—
183C22⋊C4—2922no—
184C42—2921no—
185C23—22no—
186C23—22no—
187C23—21no—
188C23—21no—
189C23—21no—
190C23—21no—
191C23—22no—
192C23—22no—
193C23C2×Dic14612yes—
194C23C2×Dic14612yes—
195C23C23×D7311yescharacteristic
196D4—44no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—44no—
205C2×C4—2924no—
206C2×C4—1462no—
207C2×C4—1462no—
208C2×C4—1462no—
209C2×C4—1462no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4—1462no—
213C2×C4—1462no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4C2×Dic14612yes—
219C2×C4#1192402714yes—
220C22—22no—
221C22—22no—
222C22—24no—
223C22—24no—
224C22—42no—
225C22—42no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22C22×Dic14611yescharacteristic
231C22C2×#1192402712yes—
232C22#1455663611yescharacteristic
233C22#1455663611yescharacteristic
234C22#1455663712yes—
235C4—22no—
236C4—24no—
237C4—42no—
238C4—2922no—
239C4—2922no—
240C4—2922no—
241C4—2922no—
242C2—42no—
243C2—42no—
244C2#1798919012yes—
245C2#1798921311yescharacteristic
246C2#1798926811yescharacteristic
247C2#1798929412yes—
248C2#1798932711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#386×C73C2
hypercenter#386D73
hypocenterC73#2748
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. #17988523C2semidirect
2. #17988519C2semidirect
3. #17988510C2semidirect
5. #17988470C2semidirect
7. #17988462C2semidirect
8. #17988447C2semidirect
125. C73#2748semidirect