Finite Group Databasebeta

← #22616973

Subgroups — #22616973

Order 9344.

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

normal subgroups only

This group has 552 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
1#17988516C212yesmaximal, complemented
2#17988512C211yesmaximal, characteristic, complemented
3#17988509C212yesmaximal, complemented
4#17988477C212yesmaximal, complemented
5#17988477C212yesmaximal, complemented
6#17988475C212yesmaximal, complemented
7#17988442C212yesmaximal
8#17988442C211yesmaximal, characteristic
9#399×C73C211yesmaximal, characteristic, complemented
10C24×D73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic, complemented
12C2×#11924007C2212yescomplemented
13C2×C22⋊Dic73C2212yes—
14C2×C22⋊Dic73C2211yescharacteristic
15C2×#11924005C2212yes—
16C2×#11924005C2212yes—
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×C4×Dic73C2212yescomplemented
22#14556498C2212yescomplemented
23#14556498C2212yescomplemented
24#14556498C2211yescharacteristic, complemented
25#14556498C2212yescomplemented
26C2×C4⋊C4×C73C2211yescharacteristic, complemented
27C2×C4⋊C4×C73C2212yescomplemented
28C2×C22⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2211yescharacteristic
30#95×C73C2211yescharacteristic, complemented
31C23×D73—22no—
32C23×D73—24no—
33C23×D73—41no—
34C23×D73—42no—
35C23×D73—41no—
36C23×D73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C4⋊Dic73—41no—
41#11924007—42no—
42C22⋊Dic73—24no—
43C22⋊Dic73—41no—
44#11924005—24no—
45#11924005—24no—
46#11924005—42no—
47#11924005—42no—
48#11924005—42no—
49#11924005—42no—
50C4×Dic73—42no—
51C24×C73C2311yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2312yes—
54C22×C4×C73C2312yes—
55C22×C4×C73C2311yescharacteristic
56C4⋊C4×C73—41no—
57C4⋊C4×C73—42no—
58C22⋊C4×C73—42no—
59C22⋊C4×C73—41no—
60C23×C73—22no—
61C23×C73—21no—
62C23×C73—22no—
63C23×C73—21no—
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—44no—
73C22×D73—48no—
74C22×D73—48no—
75C22×D73—44no—
76C22×D73—44no—
77C22×D73#4114yes—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
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—
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)12yes—
105C22×C73H(5,𝔽2)11yescharacteristic
106C22×C73H(5,𝔽2)11yescharacteristic
107C2×D73—24no—
108C2×D73—24no—
109C2×D73—24no—
110C2×D73—416no—
111C2×D73—42no—
112C2×D73—42no—
113C2×D73—42no—
114C2×D73—42no—
115C4×C73—42no—
116C4×C73—41no—
117C4×C73—42no—
118C4×C73—41no—
119Dic73—42no—
120Dic73—42no—
121Dic73—42no—
122C2×C73—42no—
123C2×C73#53812yes—
124C2×C73#53811yescharacteristic
125C2×C73#55112yes—
126C2×C73#55111yescharacteristic
127C2×C73#56011yescharacteristic
128D73—44no—
129#2735—731nomaximal, Sylow
130C73#273511yescharacteristic, complemented, Sylow
131#399D7311yescharacteristic, complemented
132#397—731no—
133#397—732no—
134#396—732no—
135#388—732no—
136#388—732no—
137#388—732no—
138#379—731no—
139#379—732no—
140C25—731no—
141C2×C4⋊C4—732no—
142C2×C4⋊C4—731no—
143C2×C4⋊C4C2×D7311yescharacteristic, complemented
144C2×C4⋊C4C2×D7312yescomplemented
145C2×C22⋊C4—731no—
146C2×C22⋊C4—732no—
147C2×C22⋊C4—732no—
148C2×C22⋊C4—732no—
149C2×C22⋊C4—732no—
150C2×C22⋊C4—732no—
151C2×C22⋊C4—732no—
152C2×C22⋊C4—732no—
153C2×C22⋊C4C2×D7312yes—
154C2×C22⋊C4C2×D7311yescharacteristic
155C2×C42—732no—
156#95—732no—
157#95—731no—
158#95—732no—
159#95—732no—
160#95C2×D7311yescharacteristic, complemented
161C24—2921no—
162C24—2922no—
163C24—2921no—
164C24—732no—
165C24—1464no—
166C24—1462no—
167C24C22×D7311yescharacteristic
168C22×C4—732no—
169C22×C4—732no—
170C22×C4—732no—
171C22×C4C22×D7311yescharacteristic
172C22×C4C22×D7312yes—
173C22×C4C22×D7312yes—
174C22×C4C22×D7311yescharacteristic
175C4⋊C4—41no—
176C4⋊C4—42no—
177C4⋊C4—2922no—
178C4⋊C4—2921no—
179C22⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—2922no—
182C22⋊C4—2922no—
183C22⋊C4—2922no—
184C22⋊C4—2922no—
185C22⋊C4—2921no—
186C22⋊C4—1464no—
187C22⋊C4—1464no—
188C22⋊C4—1464no—
189C42—2922no—
190C23—22no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23—2924no—
195C23—2928no—
196C23—2924no—
197C23—2928no—
198C23—2924no—
199C23—734no—
200C23—1462no—
201C23—1462no—
202C23—1462no—
203C23—1462no—
204C23—1462no—
205C23—1462no—
206C23#1192402912yes—
207C23C23×D7311yescharacteristic
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1462no—
227C22—22no—
228C22—24no—
229C22—42no—
230C22—41no—
231C22—41no—
232C22—29216no—
233C22—2922no—
234C22—2922no—
235C22—2922no—
236C22—2922no—
237C22—1464no—
238C22—1464no—
239C22—1464no—
240C22#41×D7312yes—
241C22C2×#1192402911yescharacteristic
242C22#1455663612yes—
243C22#1455663611yescharacteristic
244C22#1455663711yescharacteristic
245C4—42no—
246C4—41no—
247C4—42no—
248C4—41no—
249C4—2922no—
250C4—2922no—
251C4—2922no—
252C2—42no—
253C2—2924no—
254C2#1798917312yes—
255C2#1798917711yescharacteristic
256C2#1798926412yes—
257C2#1798926511yescharacteristic
258C2#1798932411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2735
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #17988516C2semidirect
2. #17988512C2semidirect
3. #17988509C2semidirect
4. #17988477C2semidirect
5. #17988477C2semidirect
6. #17988475C2semidirect
9. #399×C73C2semidirect
11. C2×C4⋊Dic73C22semidirect
12. C2×#11924007C22semidirect
21. C2×C4×Dic73C22semidirect
22. #14556498C22semidirect
23. #14556498C22semidirect
24. #14556498C22semidirect
25. #14556498C22semidirect
26. C2×C4⋊C4×C73C22semidirect
27. C2×C4⋊C4×C73C22semidirect
30. #95×C73C22semidirect
130. C73#2735semidirect
131. #399D73semidirect
143. C2×C4⋊C4C2×D73semidirect
144. C2×C4⋊C4C2×D73semidirect
160. #95C2×D73semidirect