Finite Group Databasebeta

← #22616304

Subgroups — #22616304

Order 9344.

592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#14556570C212yesmaximal, complemented
2C2×#14556568C212yesmaximal, complemented
3#17988510C212yesmaximal, complemented
4#17988510C212yesmaximal, complemented
5#17988508C212yesmaximal, complemented
6#17988490C211yesmaximal, characteristic
7#17988484C212yesmaximal, complemented
8#17988467C211yesmaximal, characteristic
9#386×C73C211yesmaximal, characteristic
10C22×Dic146C2212yes—
11C23×Dic73C2211yescharacteristic
12#14556570—28no—
13#14556568—28no—
14C2×C4⋊Dic73C2212yes—
15C2×C4⋊Dic73C2212yes—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×#11924007C2212yes—
20C2×#11924007C2212yes—
21C2×C22⋊Dic73C2212yes—
22C2×C22⋊Dic73C2212yes—
23C2×C22⋊Dic73C2212yes—
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C4×Dic73C2211yescharacteristic
26#14556498C2212yes—
27#14556498C2212yes—
28C22×D4×C73C2211yescharacteristic
29C23×C4×C73C2211yescharacteristic
30C2×C22⋊C4×C73C2212yes—
31C2×C22⋊C4×C73C2211yescharacteristic
32#95×C73C2212yes—
33C2×Dic146—24no—
34C2×Dic146—24no—
35C2×Dic146—42no—
36C22×Dic73—24no—
37C22×Dic73—41no—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C22×Dic73C2312yes—
42C4⋊Dic73—24no—
43C4⋊Dic73—24no—
44C4⋊Dic73—41no—
45#11924007—24no—
46#11924007—24no—
47#11924007—42no—
48#11924007D418yescomplemented
49C22⋊Dic73—24no—
50C22⋊Dic73—24no—
51C22⋊Dic73—24no—
52C22⋊Dic73—41no—
53C4×Dic73—41no—
54C24×C73C2311yescharacteristic
55C24×C73C2311yescharacteristic
56C2×D4×C73—41no—
57C2×D4×C73—41no—
58C2×D4×C73Q814yescomplemented
59C22×C4×C73—24no—
60C22×C4×C73—41no—
61C22×C4×C73C2312yes—
62C22×C4×C73C2312yes—
63C22×C4×C73C2311yescharacteristic
64C22⋊C4×C73—24no—
65C22⋊C4×C73—41no—
66C23×C73—22no—
67C23×C73—22no—
68C23×C73—21no—
69C23×C73—21no—
70C23×C73—21no—
71C23×C73—21no—
72C23×C73—22no—
73C23×C73—22no—
74C23×C73C2×Q812yes—
75C23×C73C2×Q812yes—
76C23×C73C2411yescharacteristic
77D4×C73—44no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73—44no—
86C2×C4×C73C2×D414yes—
87C2×C4×C73C2×Q812yes—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—44no—
99C2×Dic73C2×D414yes—
100C2×Dic73C2×D414yes—
101Dic146—48no—
102C22×C73—22no—
103C22×C73—22no—
104C22×C73—24no—
105C22×C73—24no—
106C22×C73—42no—
107C22×C73—42no—
108C22×C73—41no—
109C22×C73—41no—
110C22×C73—41no—
111C22×C73—41no—
112C22×C73C22×D412yes—
113C22×C73C22×Q811yescharacteristic
114C22×C73H(5,𝔽2)11yescharacteristic
115C22×C73H(5,𝔽2)11yescharacteristic
116C22×C732−1+412yes—
117C4×C73—22no—
118C4×C73—24no—
119C4×C73—42no—
120Dic73—24no—
121Dic73—24no—
122Dic73—42no—
123Dic73—42no—
124C2×C73—42no—
125C2×C73—42no—
126C2×C73#53712yes—
127C2×C73#54311yescharacteristic
128C2×C73D4211yescharacteristic
129C2×C73D4×Q812yes—
130C2×C73#56311yescharacteristic
131#2683—731nomaximal, Sylow
132C73#268311yescharacteristic, complemented, Sylow
133C2×C22⋊Q8—732no—
134C2×C22⋊Q8—732no—
135#396—732no—
136#396—732no—
137#395—732no—
138#390—731no—
139#389—732no—
140#386—731no—
141#386D7311yescharacteristic
142C22×Q8—732no—
143C22×D4C2×D7311yescharacteristic
144C23×C4—731no—
145C23×C4C2×D7311yescharacteristic
146C22⋊Q8—1468no—
147C22⋊Q8—1468no—
148C2×C4⋊C4—732no—
149C2×C4⋊C4—731no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4—732no—
152C2×C4⋊C4—732no—
153C2×C4⋊C4—732no—
154C2×C4⋊C4—732no—
155C2×C22⋊C4—731no—
156C2×C22⋊C4—732no—
157C2×C22⋊C4—732no—
158C2×C22⋊C4—732no—
159C2×C22⋊C4C2×D7312yes—
160C2×C22⋊C4C2×D7311yescharacteristic
161C2×C42—731no—
162#95—732no—
163#95—732no—
164#95C2×D7312yes—
165C24C22×D7311yescharacteristic
166C24C22×D7311yescharacteristic
167C2×Q8—2922no—
168C2×Q8—1464no—
169C2×Q8—1464no—
170C2×D4—41no—
171C2×D4—41no—
172C2×D4Dic14614yescomplemented
173C22×C4—24no—
174C22×C4—41no—
175C22×C4—2921no—
176C22×C4—732no—
177C22×C4—732no—
178C22×C4—732no—
179C22×C4—732no—
180C22×C4—1464no—
181C22×C4C22×D7312yes—
182C22×C4C22×D7312yes—
183C22×C4C22×D7311yescharacteristic
184C4⋊C4—2922no—
185C4⋊C4—2921no—
186C4⋊C4—738no—
187C4⋊C4—1464no—
188C4⋊C4—1464no—
189C4⋊C4—1464no—
190C4⋊C4—1464no—
191C22⋊C4—24no—
192C22⋊C4—41no—
193C22⋊C4—2921no—
194C22⋊C4—1464no—
195C22⋊C4—1464no—
196C22⋊C4—1464no—
197C42—2921no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23—21no—
203C23—21no—
204C23—22no—
205C23—22no—
206C23C2×Dic14612yes—
207C23C2×Dic14612yes—
208C23C23×D7311yescharacteristic
209Q8—2928no—
210D4—44no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—2924no—
220C2×C4—734no—
221C2×C4—734no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1462no—
227C2×C4—1462no—
228C2×C4—1462no—
229C2×C4—1462no—
230C2×C4—1462no—
231C2×C4—1462no—
232C2×C4D4×D7314yes—
233C2×C4C2×Dic14612yes—
234C22—22no—
235C22—22no—
236C22—24no—
237C22—24no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22C2×D4×D7312yes—
245C22C22×Dic14611yescharacteristic
246C22#1455663611yescharacteristic
247C22#1455663611yescharacteristic
248C22#1455663812yes—
249C4—22no—
250C4—24no—
251C4—42no—
252C4—2922no—
253C4—2922no—
254C4—1464no—
255C4—1464no—
256C2—42no—
257C2—42no—
258C2#1798916612yes—
259C2#1798921311yescharacteristic
260C2#1798921911yescharacteristic
261C2D4×Dic14612yes—
262C2#1798934011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#386×C73C2
hypercenter#386D73
hypocenterC73#2683
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#14556570C2semidirect
2. C2×#14556568C2semidirect
3. #17988510C2semidirect
4. #17988510C2semidirect
5. #17988508C2semidirect
7. #17988484C2semidirect
48. #11924007D4semidirect
58. C2×D4×C73Q8semidirect
132. C73#2683semidirect
172. C2×D4Dic146semidirect