Finite Group Databasebeta

← #22617874

Subgroups — #22617874

Order 9344.

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

normal subgroups only

This group has 480 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#17988529C212yesmaximal, complemented
2#17988499C212yesmaximal, complemented
3#17988499C212yesmaximal, complemented
4#17988491C212yesmaximal, complemented
5#17988490C211yesmaximal, characteristic
6#17988467C211yesmaximal, characteristic
7#17988460C212yesmaximal, complemented
8#17988459C212yesmaximal, complemented
9#386×C73C211yesmaximal, characteristic
10C22×Dic146C2212yes—
11C23×Dic73C2211yescharacteristic
12C2×C4⋊Dic73C2211yescharacteristic
13C2×#11924007C2212yes—
14C2×#11924007C2212yes—
15C2×C22⋊Dic73C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C22⋊Dic73C2211yescharacteristic
19C2×C4×Dic73C2211yescharacteristic
20#14556498C2212yes—
21#14556498C2212yes—
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—
31C2×Dic146—24no—
32C2×Dic146—42no—
33C2×Dic146—42no—
34C22×Dic73—42no—
35C22×Dic73—41no—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C4⋊Dic73—41no—
41#11924007—42no—
42#11924007—42no—
43C22⋊Dic73—24no—
44C22⋊Dic73—24no—
45C22⋊Dic73—42no—
46C22⋊Dic73—41no—
47C4×Dic73—41no—
48C24×C73C2311yescharacteristic
49C24×C73C2311yescharacteristic
50C2×D4×C73—41no—
51C2×D4×C73—41no—
52C2×D4×C73Q814yescomplemented
53C22×C4×C73—42no—
54C22×C4×C73—41no—
55C22×C4×C73C2312yes—
56C22×C4×C73C2312yes—
57C22×C4×C73C2311yescharacteristic
58C22⋊C4×C73—42no—
59C22⋊C4×C73—41no—
60C23×C73—22no—
61C23×C73—22no—
62C23×C73—21no—
63C23×C73—22no—
64C23×C73—21no—
65C23×C73—22no—
66C23×C73—21no—
67C23×C73—21no—
68C23×C73C2×Q812yes—
69C23×C73C2×Q812yes—
70C23×C73C2411yescharacteristic
71D4×C73—44no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—44no—
81C2×C4×C73C2×Q812yes—
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—44no—
94C2×Dic73#4114yes—
95Dic146—48no—
96C22×C73—22no—
97C22×C73—22no—
98C22×C73—24no—
99C22×C73—24no—
100C22×C73—42no—
101C22×C73—42no—
102C22×C73—41no—
103C22×C73—41no—
104C22×C73—41no—
105C22×C73—41no—
106C22×C73C22×Q811yescharacteristic
107C22×C73C2×#4112yes—
108C22×C73H(5,𝔽2)11yescharacteristic
109C22×C73H(5,𝔽2)12yes—
110C22×C73H(5,𝔽2)11yescharacteristic
111C4×C73—22no—
112C4×C73—42no—
113C4×C73—42no—
114Dic73—24no—
115Dic73—42no—
116Dic73—42no—
117Dic73—42no—
118C2×C73—42no—
119C2×C73—42no—
120C2×C73#53812yes—
121C2×C73#54311yescharacteristic
122C2×C73#55412yes—
123C2×C73#55911yescharacteristic
124C2×C73H(3,𝔽4)11yescharacteristic
125#2804—731nomaximal, Sylow
126C73#280411yescharacteristic, complemented, Sylow
127#400—732no—
128#393—732no—
129#393—732no—
130#391—732no—
131#390—731no—
132#386—731no—
133#386D7311yescharacteristic
134#385—732no—
135#385—732no—
136C22×Q8—732no—
137C22×D4C2×D7311yescharacteristic
138C23×C4—731no—
139C23×C4C2×D7311yescharacteristic
140C2×C4⋊C4—732no—
141C2×C4⋊C4—732no—
142C2×C4⋊C4—731no—
143C2×C22⋊C4—732no—
144C2×C22⋊C4—731no—
145C2×C22⋊C4—732no—
146C2×C22⋊C4—732no—
147C2×C22⋊C4C2×D7312yes—
148C2×C22⋊C4C2×D7311yescharacteristic
149C2×C42—731no—
150#95—732no—
151#95—732no—
152#95—732no—
153#95—732no—
154#95—732no—
155#95—732no—
156#95C2×D7312yes—
157C24C22×D7311yescharacteristic
158C24C22×D7311yescharacteristic
159C2×Q8—2922no—
160C2×Q8—2922no—
161C2×Q8—1464no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4Dic14614yescomplemented
165C22×C4—42no—
166C22×C4—41no—
167C22×C4—2922no—
168C22×C4—2921no—
169C22×C4—732no—
170C22×C4—732no—
171C22×C4—732no—
172C22×C4—732no—
173C22×C4C22×D7312yes—
174C22×C4C22×D7312yes—
175C22×C4C22×D7311yescharacteristic
176C4⋊C4—2922no—
177C4⋊C4—2922no—
178C4⋊C4—2921no—
179C22⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—2922no—
182C22⋊C4—2921no—
183C22⋊C4—1464no—
184C22⋊C4—1464no—
185C42—2921no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—21no—
190C23—22no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23C2×Dic14612yes—
195C23C2×Dic14612yes—
196C23C23×D7311yescharacteristic
197Q8—2928no—
198D4—44no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—44no—
208C2×C4—2924no—
209C2×C4—734no—
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×C4—1462no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4C2×Dic14612yes—
222C22—22no—
223C22—22no—
224C22—24no—
225C22—24no—
226C22—42no—
227C22—42no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22C22×Dic14611yescharacteristic
233C22#41×D7312yes—
234C22#1455663611yescharacteristic
235C22#1455663612yes—
236C22#1455663611yescharacteristic
237C4—22no—
238C4—42no—
239C4—42no—
240C4—2922no—
241C4—2922no—
242C4—2922no—
243C4—1464no—
244C2—42no—
245C2—42no—
246C2#1798916912yes—
247C2#1798921311yescharacteristic
248C2#1798929612yes—
249C2#1798932111yescharacteristic
250C2#1798933011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#386×C73C2
hypercenter#386D73
hypocenterC73#2804
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. #17988529C2semidirect
2. #17988499C2semidirect
3. #17988499C2semidirect
4. #17988491C2semidirect
7. #17988460C2semidirect
8. #17988459C2semidirect
52. C2×D4×C73Q8semidirect
126. C73#2804semidirect
164. C2×D4Dic146semidirect