Finite Group Databasebeta

← #22617308

Subgroups — #22617308

Order 9344.

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

normal subgroups only

This group has 520 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
1C73⋊#401C212yesmaximal, complemented
2#17988500C212yesmaximal, complemented
3#17988499C211yesmaximal, characteristic, complemented
4#17988496C211yesmaximal, characteristic
5#17988466C212yesmaximal, complemented
6#17988465C212yesmaximal, complemented
7#17988463C212yesmaximal, complemented
8#17988449C212yesmaximal, complemented
9#381×C73C211yesmaximal, characteristic, complemented
10C22×Dic146C2211yescharacteristic
11C22×D292C2211yescharacteristic
12C22×C22⋊D73C2212yes—
13C22×C4×D73C2212yes—
14C2×C22⋊Dic73C2212yes—
15C2×#11924005C2212yes—
16C2×#11924005C2212yes—
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19#14556498C2211yescharacteristic
20#14556498C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26C23×C4×C73C2211yescharacteristic
27C2×C22⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2211yescharacteristic
29#95×C73C2212yes—
30#95×C73C2212yes—
31C23×D73C2312yes—
32C2×Dic146—41no—
33C2×Dic146—42no—
34C2×D292—24no—
35C2×D292—41no—
36C2×C22⋊D73—24no—
37C2×C22⋊D73—24no—
38C2×C22⋊D73—42no—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C22×Dic73C2312yes—
42C2×C4×D73—24no—
43C2×C4×D73—42no—
44C2×C4×D73—42no—
45C22⋊Dic73—42no—
46#11924005—42no—
47#11924005—42no—
48#11924005—42no—
49#11924005—42no—
50C24×C73C2311yescharacteristic
51C22×C4×C73—22no—
52C22×C4×C73—41no—
53C22×C4×C73—41no—
54C22×C4×C73C2311yescharacteristic
55C22×C4×C73C2312yes—
56C22×C4×C73C2311yescharacteristic
57C22×C4×C73C2312yes—
58C22⋊C4×C73—41no—
59C22⋊C4×C73—41no—
60C23×C73—22no—
61C23×C73—21no—
62C23×C73—21no—
63C23×C73—22no—
64C23×C73#4112yes—
65C23×C73C2411yescharacteristic
66C22×D73—22no—
67C22×D73—22no—
68C22×D73—22no—
69C22×D73—22no—
70C22×D73—22no—
71C22×D73—22no—
72C22×D73#4114yes—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—44no—
84C22⋊D73—48no—
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—
94D292—44no—
95C4×D73—48no—
96Dic146—44no—
97C22×C73—22no—
98C22×C73—24no—
99C22×C73—42no—
100C22×C73—41no—
101C22×C73—41no—
102C22×C73C2×#4112yes—
103C22×C73C2×#4111yescharacteristic
104C22×C73H(5,𝔽2)11yescharacteristic
105C22×C73H(5,𝔽2)11yescharacteristic
106C22×C73H(5,𝔽2)12yes—
107C2×D73—24no—
108C2×D73—24no—
109C2×D73—24no—
110C2×D73—42no—
111C2×D73—42no—
112C2×D73—42no—
113C2×D73—42no—
114C4×C73—42no—
115C4×C73—42no—
116C4×C73—41no—
117C4×C73—41no—
118Dic73—42no—
119Dic73—42no—
120Dic73—42no—
121C2×C73—42no—
122C2×C73#53812yes—
123C2×C73#53811yescharacteristic
124C2×C73#55112yes—
125C2×C73#55111yescharacteristic
126C2×C73#56011yescharacteristic
127D73—44no—
128#2760—731nomaximal, Sylow
129C73#276011yescharacteristic, complemented, Sylow
130#401—732no—
131#393—731no—
132#393—732no—
133#392—731no—
134#386—732no—
135#386—732no—
136#386—732no—
137#381—732no—
138#381D7311yescharacteristic, complemented
139C22×Q8—731no—
140C22×D4—732no—
141C22×D4—731no—
142C23×C4—732no—
143C23×C4C2×D7311yescharacteristic
144C2×C22⋊C4—732no—
145C2×C22⋊C4—732no—
146C2×C22⋊C4—732no—
147C2×C22⋊C4—732no—
148C2×C22⋊C4—732no—
149C2×C22⋊C4C2×D7311yescharacteristic
150C2×C22⋊C4C2×D7311yescharacteristic
151#95—731no—
152#95—732no—
153#95—732no—
154#95—732no—
155#95—732no—
156#95—732no—
157#95—731no—
158#95C2×D7312yes—
159#95C2×D7312yes—
160C24—732no—
161C24C22×D7311yescharacteristic
162C2×Q8—2921no—
163C2×Q8—2922no—
164C2×D4—2921no—
165C2×D4—2922no—
166C2×D4—1464no—
167C2×D4—1464no—
168C2×D4—1464no—
169C22×C4—22no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—2922no—
173C22×C4—2922no—
174C22×C4—732no—
175C22×C4—732no—
176C22×C4—732no—
177C22×C4—1464no—
178C22×C4C22×D7311yescharacteristic
179C22×C4C22×D7312yes—
180C22×C4C22×D7312yes—
181C22×C4C22×D7311yescharacteristic
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—2922no—
185C22⋊C4—2922no—
186C22⋊C4—2922no—
187C22⋊C4—2922no—
188C22⋊C4—2922no—
189C23—22no—
190C23—21no—
191C23—21no—
192C23—22no—
193C23—734no—
194C23—1462no—
195C23—1462no—
196C23—1462no—
197C23—1462no—
198C23—1462no—
199C23—1462no—
200C23#1192402812yes—
201C23C23×D7311yescharacteristic
202Q8—2924no—
203D4—2924no—
204D4—2928no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—44no—
216C2×C4—2928no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4—1462no—
226C22—22no—
227C22—24no—
228C22—42no—
229C22—41no—
230C22—41no—
231C22—2922no—
232C22—2922no—
233C22—2922no—
234C22—2922no—
235C22—1464no—
236C22—1464no—
237C22—1464no—
238C22#41×D7312yes—
239C22C2×#1192402811yescharacteristic
240C22#1455663611yescharacteristic
241C22#1455663611yescharacteristic
242C22#1455663712yes—
243C4—42no—
244C4—42no—
245C4—41no—
246C4—41no—
247C4—2922no—
248C4—2922no—
249C4—2922no—
250C2—42no—
251C2—2924no—
252C2#1798917312yes—
253C2#1798917511yescharacteristic
254C2#1798926112yes—
255C2#1798926511yescharacteristic
256C2#1798932711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#381×C73C2
hypercenter#381D73
hypocenterC73#2760
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C73⋊#401C2semidirect
2. #17988500C2semidirect
3. #17988499C2semidirect
5. #17988466C2semidirect
6. #17988465C2semidirect
7. #17988463C2semidirect
8. #17988449C2semidirect
9. #381×C73C2semidirect
129. C73#2760semidirect
138. #381D73semidirect