Finite Group Databasebeta

← #22618054

Subgroups — #22618054

Order 9344.

508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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#17988526C211yesmaximal, characteristic, complemented
2#17988514C212yesmaximal, complemented
3#17988503C212yesmaximal, complemented
4#17988503C212yesmaximal, complemented
5#17988496C212yesmaximal, complemented
6#17988495C212yesmaximal, complemented
7#17988488C211yesmaximal, characteristic, complemented
8#17988480C212yesmaximal, complemented
9#394×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11C22×C22⋊D73C2212yes—
12C22×C22⋊D73C2212yes—
13C2×C4⋊Dic73C2212yes—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×C22⋊Dic73C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×C4×Dic73C2211yescharacteristic
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26C22×D4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2212yes—
30#95×C73C2211yescharacteristic
31C23×D73C2312yes—
32C2×D292—22no—
33C2×D292—41no—
34C2×D292—41no—
35C2×C22⋊D73—42no—
36C2×C22⋊D73—42no—
37C2×C22⋊D73—42no—
38C2×C22⋊D73—42no—
39C2×C22⋊D73—42no—
40C2×C22⋊D73—42no—
41C22×Dic73C2312yes—
42C22×Dic73C2312yes—
43C22×Dic73C2312yes—
44C4⋊Dic73—42no—
45C4⋊Dic73—41no—
46C22⋊Dic73—42no—
47C22⋊Dic73—42no—
48#11924005—42no—
49#11924005—42no—
50#11924005—42no—
51#11924005—42no—
52C4×Dic73—41no—
53C24×C73C2312yes—
54C2×D4×C73—41no—
55C2×D4×C73—42no—
56C22×C4×C73C2312yes—
57C22×C4×C73C2311yescharacteristic
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2311yescharacteristic
60C4⋊C4×C73—41no—
61C22⋊C4×C73—24no—
62C22⋊C4×C73—42no—
63C23×C73—22no—
64C23×C73—22no—
65C23×C73—22no—
66C23×C73—22no—
67C23×C73—22no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73C2411yescharacteristic
71C22×D73—22no—
72C22×D73—22no—
73C22×D73—22no—
74C22×D73—22no—
75C22×D73—22no—
76C22×D73—22no—
77C22×D73—22no—
78D4×C73—44no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73#4112yes—
89C22⋊D73—48no—
90C22⋊D73—48no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100D292—44no—
101C22×C73—42no—
102C22×C73—42no—
103C22×C73—42no—
104C22×C73—42no—
105C22×C73—42no—
106C22×C73—42no—
107C22×C73—42no—
108C22×C73C2×#4111yescharacteristic
109C22×C73H(5,𝔽2)11yescharacteristic
110C22×C73H(5,𝔽2)12yes—
111C22×C73H(5,𝔽2)11yescharacteristic
112C22×C73H(5,𝔽2)12yes—
113C2×D73—42no—
114C2×D73—42no—
115C2×D73—42no—
116C2×D73—42no—
117C2×D73—42no—
118C2×D73—42no—
119C2×D73—42no—
120C4×C73—22no—
121C4×C73—42no—
122C4×C73—41no—
123C4×C73—41no—
124Dic73—42no—
125Dic73—42no—
126Dic73—42no—
127C2×C73—82no—
128C2×C73#53811yescharacteristic
129C2×C73#54012yes—
130C2×C73#56011yescharacteristic
131C2×C73#56012yes—
132C2×C73H(3,𝔽4)11yescharacteristic
133D73—82no—
134#2828—731nomaximal, Sylow
135C73#282811yescharacteristic, complemented, Sylow
136#400—731no—
137#397—732no—
138#394—732no—
139#394—732no—
140#394D7311yescharacteristic, complemented
141#392—732no—
142#392—732no—
143#390—731no—
144#388—732no—
145C22×D4—732no—
146C22×D4—732no—
147C22×D4—731no—
148C22×D4C2×D7311yescharacteristic
149C2×C4⋊C4—732no—
150C2×C4⋊C4—731no—
151C2×C4⋊C4C2×D7311yescharacteristic
152C2×C22⋊C4—732no—
153C2×C22⋊C4—732no—
154C2×C22⋊C4—732no—
155C2×C22⋊C4—732no—
156C2×C22⋊C4—732no—
157C2×C22⋊C4—732no—
158C2×C22⋊C4C2×D7312yes—
159C2×C22⋊C4C2×D7312yes—
160C2×C42—731no—
161#95—732no—
162#95—732no—
163#95—732no—
164#95—731no—
165#95C2×D7311yescharacteristic
166C24—732no—
167C24C22×D7312yes—
168C2×D4—42no—
169C2×D4—41no—
170C2×D4—2921no—
171C2×D4—2921no—
172C2×D4—2922no—
173C2×D4—2922no—
174C2×D4—2922no—
175C2×D4—2922no—
176C2×D4—2922no—
177C2×D4—2922no—
178C2×D4—1462no—
179C22×C4—732no—
180C22×C4—732no—
181C22×C4—732no—
182C22×C4C22×D7311yescharacteristic
183C22×C4C22×D7312yes—
184C22×C4C22×D7311yescharacteristic
185C22×C4C22×D7311yescharacteristic
186C4⋊C4—41no—
187C4⋊C4—2921no—
188C4⋊C4—2922no—
189C22⋊C4—24no—
190C22⋊C4—42no—
191C22⋊C4—2922no—
192C22⋊C4—2922no—
193C22⋊C4—2922no—
194C22⋊C4—2922no—
195C22⋊C4—2922no—
196C22⋊C4—2922no—
197C42—2921no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—1462no—
206C23—1462no—
207C23—1462no—
208C23—1462no—
209C23—1462no—
210C23—1462no—
211C23—1462no—
212C23C23×D7311yescharacteristic
213D4—44no—
214D4—2924no—
215D4—2928no—
216D4—2928no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—1462no—
227C2×C4—1462no—
228C2×C4—1462no—
229C2×C4—1462no—
230C2×C4—1462no—
231C2×C4—1462no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4#1192402712yes—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—2922no—
244C22—2922no—
245C22—2922no—
246C22—2922no—
247C22—2922no—
248C22—2922no—
249C22—2922no—
250C22C2×#1192402711yescharacteristic
251C22#1455663611yescharacteristic
252C22#1455663612yes—
253C22#1455663711yescharacteristic
254C22#1455663712yes—
255C4—22no—
256C4—42no—
257C4—41no—
258C4—41no—
259C4—2922no—
260C4—2922no—
261C4—2922no—
262C2—82no—
263C2—5842no—
264C2#1798917411yescharacteristic
265C2#1798919012yes—
266C2#1798932611yescharacteristic
267C2#1798932712yes—
268C2#1798932911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2828
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #17988526C2semidirect
2. #17988514C2semidirect
3. #17988503C2semidirect
4. #17988503C2semidirect
5. #17988496C2semidirect
6. #17988495C2semidirect
7. #17988488C2semidirect
8. #17988480C2semidirect
9. #394×C73C2semidirect
135. C73#2828semidirect
140. #394D73semidirect