Finite Group Databasebeta

← #22616439

Subgroups — #22616439

Order 9344.

568 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556572C212yesmaximal, complemented
2#17988528C212yesmaximal, complemented
3#17988512C211yesmaximal, characteristic, complemented
4#17988510C212yesmaximal, complemented
5#17988467C212yesmaximal, complemented
6#17988467C212yesmaximal, complemented
7#17988459C211yesmaximal, characteristic, complemented
8#17988445C212yesmaximal, complemented
9#392×C73C211yesmaximal, characteristic
10C23×Dic73C2212yes—
11C23×Dic73C2211yescharacteristic
12#14556572—28no—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×#11924007C2212yes—
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2212yes—
20C2×C22⋊Dic73C2212yes—
21C2×C22⋊Dic73C2211yescharacteristic
22#14556498C2211yescharacteristic
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26#14556498C2212yes—
27C22×D4×C73C2211yescharacteristic
28C22×D4×C73C2212yes—
29C2×C22⋊C4×C73C2212yes—
30C2×C22⋊C4×C73C2211yescharacteristic
31#95×C73C2211yescharacteristic
32C22×Dic73—24no—
33C22×Dic73—24no—
34C22×Dic73—42no—
35C22×Dic73—41no—
36C22×Dic73—42no—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C4⋊Dic73—41no—
42#11924007—24no—
43#11924007—24no—
44#11924007—42no—
45C22⋊Dic73—24no—
46C22⋊Dic73—24no—
47C22⋊Dic73—42no—
48C22⋊Dic73—42no—
49C22⋊Dic73D414yescomplemented
50C24×C73C2311yescharacteristic
51C24×C73C2312yes—
52C2×D4×C73—24no—
53C2×D4×C73—24no—
54C2×D4×C73—24no—
55C2×D4×C73—41no—
56C2×D4×C73—42no—
57C22×C4×C73C2311yescharacteristic
58C22×C4×C73C2312yes—
59C22×C4×C73C2311yescharacteristic
60C22⋊C4×C73—42no—
61C22⋊C4×C73—41no—
62C23×C73—22no—
63C23×C73—22no—
64C23×C73—22no—
65C23×C73—22no—
66C23×C73—21no—
67C23×C73—22no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73—21no—
71C23×C73—22no—
72C23×C73C2×D412yes—
73C23×C73#4114yes—
74C23×C73C2411yescharacteristic
75D4×C73—48no—
76D4×C73—44no—
77C2×C4×C73—22no—
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×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—22no—
94C2×Dic73—22no—
95C2×Dic73—48no—
96C2×Dic73—44no—
97C2×Dic73C2×D414yes—
98C22×C73—22no—
99C22×C73—24no—
100C22×C73—24no—
101C22×C73—24no—
102C22×C73—24no—
103C22×C73—42no—
104C22×C73—42no—
105C22×C73—42no—
106C22×C73—42no—
107C22×C73—41no—
108C22×C73—41no—
109C22×C73—42no—
110C22×C73C22×D411yescharacteristic
111C22×C73C2×#4112yes—
112C22×C73H(5,𝔽2)11yescharacteristic
113C22×C73H(5,𝔽2)12yes—
114C22×C732−1+411yescharacteristic
115C4×C73—42no—
116C4×C73—41no—
117C4×C73—41no—
118Dic73—24no—
119Dic73—42no—
120Dic73—42no—
121Dic73—42no—
122C2×C73—42no—
123C2×C73—44no—
124C2×C73#53711yescharacteristic
125C2×C73#53912yes—
126C2×C73#54612yes—
127C2×C73#55111yescharacteristic
128C2×C73#56011yescharacteristic
129#2693—731nomaximal, Sylow
130C73#269311yescharacteristic, complemented, Sylow
131C2×#123—732no—
132#400—732no—
133#397—731no—
134#396—732no—
135#392D7311yescharacteristic
136#386—732no—
137#386—732no—
138#385—731no—
139#380—732no—
140C22×D4C2×D7312yes—
141C22×D4C2×D7311yescharacteristic
142C23×C4—731no—
143C23×C4—732no—
144#123—1468no—
145C2×C4⋊C4—732no—
146C2×C4⋊C4—731no—
147C2×C4⋊C4—732no—
148C2×C4⋊C4—732no—
149C2×C22⋊C4—732no—
150C2×C22⋊C4—732no—
151C2×C22⋊C4—731no—
152C2×C22⋊C4—732no—
153C2×C22⋊C4—732no—
154C2×C22⋊C4C2×D7312yes—
155C2×C22⋊C4C2×D7311yescharacteristic
156#95—731no—
157#95—732no—
158#95—732no—
159#95—732no—
160#95—732no—
161#95C2×D7311yescharacteristic
162C24C22×D7311yescharacteristic
163C24C22×D7312yes—
164C2×D4—24no—
165C2×D4—24no—
166C2×D4—24no—
167C2×D4—41no—
168C2×D4—42no—
169C22×C4—2921no—
170C22×C4—2922no—
171C22×C4—2922no—
172C22×C4—732no—
173C22×C4—732no—
174C22×C4—732no—
175C22×C4—732no—
176C22×C4—1464no—
177C22×C4—1464no—
178C22×C4C22×D7311yescharacteristic
179C22×C4C22×D7312yes—
180C22×C4C22×D7311yescharacteristic
181C4⋊C4—2922no—
182C4⋊C4—2921no—
183C4⋊C4—1464no—
184C4⋊C4—1464no—
185C22⋊C4—42no—
186C22⋊C4—41no—
187C22⋊C4—2922no—
188C22⋊C4—2922no—
189C22⋊C4—734no—
190C22⋊C4—1464no—
191C22⋊C4—1464no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—21no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—22no—
202C23D4×D7312yes—
203C23#1192402714yes—
204C23C23×D7311yescharacteristic
205D4—48no—
206D4—44no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—2924no—
215C2×C4—2928no—
216C2×C4—734no—
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—
226C2×C4—1462no—
227C2×C4—1462no—
228C22—22no—
229C22—24no—
230C22—24no—
231C22—24no—
232C22—24no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—41no—
238C22—41no—
239C22—42no—
240C22C2×D4×D7311yescharacteristic
241C22C2×#1192402712yes—
242C22#1455663611yescharacteristic
243C22#1455663612yes—
244C22#1455663811yescharacteristic
245C4—42no—
246C4—41no—
247C4—41no—
248C4—2922no—
249C4—2922no—
250C4—2922no—
251C4—1464no—
252C2—42no—
253C2—44no—
254C2#1798916411yescharacteristic
255C2#1798918212yes—
256C2#1798922412yes—
257C2#1798926811yescharacteristic
258C2#1798932411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2693
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14556572C2semidirect
2. #17988528C2semidirect
3. #17988512C2semidirect
4. #17988510C2semidirect
5. #17988467C2semidirect
6. #17988467C2semidirect
7. #17988459C2semidirect
8. #17988445C2semidirect
49. C22⋊Dic73D4semidirect
130. C73#2693semidirect