Finite Group Databasebeta

← #22613813

Subgroups — #22613813

Order 9344.

660 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14556576C212yesmaximal, complemented
2C2×C4×C22⋊D73C212yesmaximal, complemented
3#17988523C211yesmaximal, characteristic, complemented
4#17988502C212yesmaximal, complemented
5#17988496C211yesmaximal, characteristic
6#17988482C212yesmaximal, complemented
7#17988476C212yesmaximal, complemented
8#17988461C212yesmaximal, complemented
9#385×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11C22×C22⋊D73C2212yes—
12C22×C4×D73C2212yes—
13#14556576—28no—
14C4×C22⋊D73—28no—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×#11924007C2212yes—
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×C22⋊Dic73C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23C2×#11924005C2212yes—
24C2×C4×Dic73C2212yes—
25#14556498C2212yes—
26#14556498C2211yescharacteristic
27#14556498C2211yescharacteristic
28C23×C4×C73C2211yescharacteristic
29C2×C4⋊C4×C73C2212yes—
30C2×C22⋊C4×C73C2211yescharacteristic
31C2×C22⋊C4×C73C2211yescharacteristic
32#95×C73C2212yes—
33C23×D73C2312yes—
34C2×D292—24no—
35C2×D292—41no—
36C2×C22⋊D73—24no—
37C2×C22⋊D73—24no—
38C2×C22⋊D73—24no—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C22×Dic73C2312yes—
42C2×C4×D73—24no—
43C2×C4×D73—24no—
44C2×C4×D73—42no—
45C4⋊Dic73—41no—
46#11924007—24no—
47#11924007—24no—
48#11924007—24no—
49C22⋊Dic73—24no—
50#11924005—24no—
51#11924005—24no—
52#11924005—24no—
53#11924005D418yescomplemented
54C4×Dic73—24no—
55C24×C73C2311yescharacteristic
56C22×C4×C73—24no—
57C22×C4×C73—41no—
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2312yes—
60C22×C4×C73C2311yescharacteristic
61C22×C4×C73C2312yes—
62C4⋊C4×C73—24no—
63C22⋊C4×C73—22no—
64C22⋊C4×C73—41no—
65C23×C73—22no—
66C23×C73—22no—
67C23×C73—21no—
68C23×C73—21no—
69C23×C73#4112yes—
70C23×C73C2411yescharacteristic
71C22×D73—22no—
72C22×D73—22no—
73C22×D73—22no—
74C22×D73—22no—
75C22×D73—22no—
76C22×D73—22no—
77C22×D73C2×D414yes—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—44no—
88C2×C4×C73C2×D414yes—
89C22⋊D73—216no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73C2×D414yes—
98C2×Dic73#4114yes—
99D292—44no—
100C4×D73—48no—
101C22×C73—24no—
102C22×C73—22no—
103C22×C73—41no—
104C22×C73—42no—
105C22×C73—41no—
106C22×C73C22×D412yes—
107C22×C73C2×#4112yes—
108C22×C73C2×#4111yescharacteristic
109C22×C73H(5,𝔽2)11yescharacteristic
110C22×C732−1+411yescharacteristic
111C2×D73—24no—
112C2×D73—24no—
113C2×D73—24no—
114C2×D73—42no—
115C2×D73—42no—
116C2×D73—42no—
117C2×D73—42no—
118C4×C73—24no—
119C4×C73—42no—
120C4×C73—41no—
121C4×C73—41no—
122Dic73—24no—
123Dic73—24no—
124Dic73—42no—
125C2×C73—42no—
126C2×C73#52512yes—
127C2×C73#53911yescharacteristic
128C2×C73D4211yescharacteristic
129C2×C73#54712yes—
130C2×C73#55911yescharacteristic
131D73—44no—
132#2455—731nomaximal, Sylow
133C73#245511yescharacteristic, complemented, Sylow
134C2×#123—732no—
135C2×C4×D4—732no—
136#399—731no—
137#394—732no—
138#392—731no—
139#389—732no—
140#388—732no—
141#385—732no—
142#385D7311yescharacteristic, complemented
143C22×D4—732no—
144C22×D4—731no—
145C23×C4—732no—
146C23×C4C2×D7311yescharacteristic
147#123—1468no—
148C4×D4—1468no—
149C2×C4⋊C4—731no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4—732no—
152C2×C4⋊C4—732no—
153C2×C4⋊C4C2×D7312yes—
154C2×C22⋊C4—732no—
155C2×C22⋊C4—732no—
156C2×C22⋊C4—732no—
157C2×C22⋊C4—732no—
158C2×C22⋊C4—732no—
159C2×C22⋊C4C2×D7311yescharacteristic
160C2×C22⋊C4C2×D7311yescharacteristic
161C2×C42—732no—
162#95—732no—
163#95—731no—
164#95—731no—
165#95C2×D7312yes—
166C24—732no—
167C24C22×D7311yescharacteristic
168C2×D4—2921no—
169C2×D4—1464no—
170C2×D4—1464no—
171C2×D4—1464no—
172C2×D4—1464no—
173C22×C4—24no—
174C22×C4—41no—
175C22×C4—2922no—
176C22×C4—732no—
177C22×C4—732no—
178C22×C4—732no—
179C22×C4—1464no—
180C22×C4—1464no—
181C22×C4C22×D7311yescharacteristic
182C22×C4C22×D7312yes—
183C22×C4C22×D7311yescharacteristic
184C22×C4C22×D7312yes—
185C4⋊C4—24no—
186C4⋊C4—2921no—
187C4⋊C4—1464no—
188C4⋊C4—1464no—
189C4⋊C4—1464no—
190C22⋊C4—22no—
191C22⋊C4—41no—
192C22⋊C4—738no—
193C22⋊C4—1464no—
194C22⋊C4—1464no—
195C22⋊C4—1464no—
196C22⋊C4—1464no—
197C42—1464no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23—734no—
203C23—1462no—
204C23—1462no—
205C23—1462no—
206C23—1462no—
207C23—1462no—
208C23—1462no—
209C23#1192402812yes—
210C23C23×D7311yescharacteristic
211D4—2924no—
212D4—14616no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—44no—
223C2×C4—2928no—
224C2×C4—734no—
225C2×C4—734no—
226C2×C4—1462no—
227C2×C4—1462no—
228C2×C4—1462no—
229C2×C4—1462no—
230C2×C4—1462no—
231C2×C4—1462no—
232C2×C4—1462no—
233C2×C4D4×D7314yes—
234C22—22no—
235C22—24no—
236C22—41no—
237C22—42no—
238C22—41no—
239C22—2922no—
240C22—2922no—
241C22—2922no—
242C22—2922no—
243C22—1464no—
244C22—1464no—
245C22—1464no—
246C22C2×D4×D7312yes—
247C22#41×D7312yes—
248C22C2×#1192402811yescharacteristic
249C22#1455663611yescharacteristic
250C22#1455663911yescharacteristic
251C4—24no—
252C4—41no—
253C4—41no—
254C4—42no—
255C4—2922no—
256C4—1464no—
257C4—1464no—
258C2—42no—
259C2—2924no—
260C2#1798909612yes—
261C2#1798918411yescharacteristic
262C2#1798921911yescharacteristic
263C2#1798923912yes—
264C2#1798932111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2455
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14556576C2semidirect
2. C2×C4×C22⋊D73C2semidirect
3. #17988523C2semidirect
4. #17988502C2semidirect
6. #17988482C2semidirect
7. #17988476C2semidirect
8. #17988461C2semidirect
9. #385×C73C2semidirect
53. #11924005D4semidirect
133. C73#2455semidirect
142. #385D73semidirect