Finite Group Databasebeta

← #22615831

Subgroups — #22615831

Order 9344.

562 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14556586C211yesmaximal, characteristic, complemented
2C2×#14556553C211yesmaximal, characteristic, complemented
3#17988522C211yesmaximal, characteristic, complemented
4#17988511C212yesmaximal, complemented
5#17988505C212yesmaximal, complemented
6#17988504C211yesmaximal, characteristic, complemented
7#17988497C211yesmaximal, characteristic
8#17988465C212yesmaximal, complemented
9#17988461C212yesmaximal, complemented
10#17988451C211yesmaximal, characteristic, complemented
11#400×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×D292C2212yes—
14C22×C4×D73C2212yes—
15#14556586—24no—
16#14556553—24no—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007C2211yescharacteristic
19C2×#11924007C2212yes—
20C2×#11924007C2212yes—
21C2×#11924005C2212yes—
22C2×#11924005C2211yescharacteristic
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28C2×#11924005C2212yes—
29C2×C4×Dic73C2211yescharacteristic
30#14556498C2212yes—
31#14556498C2211yescharacteristic
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34#95×C73C2211yescharacteristic
35#95×C73C2212yes—
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C23×D73C2312yes—
39C2×D292—24no—
40C2×D292—22no—
41C2×D292—24no—
42C2×D292—42no—
43C2×D292—42no—
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C2×C4×D73—24no—
49C2×C4×D73—42no—
50C2×C4×D73—42no—
51C4⋊Dic73—22no—
52#11924007—22no—
53#11924007—42no—
54#11924007—42no—
55#11924005—24no—
56#11924005—22no—
57#11924005—24no—
58#11924005—22no—
59#11924005—22no—
60#11924005—42no—
61#11924005—42no—
62#11924005—42no—
63C4×Dic73D414yescomplemented
64C22×C4×C73C2312yes—
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2311yescharacteristic
67C22×C4×C73C2312yes—
68C22×C4×C73C2311yescharacteristic
69C4⋊C4×C73—22no—
70C4⋊C4×C73—22no—
71C23×C73C2411yescharacteristic
72C22×D73—22no—
73C22×D73—22no—
74C22×D73—22no—
75C22×D73—22no—
76C22×D73—22no—
77C22×D73—22no—
78C22×D73—21no—
79C22×D73—22no—
80C22×D73—22no—
81C22×D73—21no—
82C22×D73—21no—
83C22×D73#4114yes—
84C2×C4×C73—22no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—21no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—21no—
96C2×C4×C73C2×D412yes—
97C2×Dic73—21no—
98C2×Dic73—22no—
99C2×Dic73—21no—
100C2×Dic73—21no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73C2×D412yes—
106C2×Dic73C2×D412yes—
107D292—28no—
108D292—48no—
109C4×D73—48no—
110C22×C73C22×D411yescharacteristic
111C22×C73C2×#4112yes—
112C22×C73H(5,𝔽2)12yes—
113C22×C73H(5,𝔽2)11yescharacteristic
114C22×C732−1+411yescharacteristic
115C2×D73—24no—
116C2×D73—24no—
117C2×D73—24no—
118C2×D73—42no—
119C2×D73—42no—
120C2×D73—42no—
121C2×D73—42no—
122C2×D73—41no—
123C2×D73—41no—
124C2×D73—41no—
125C2×D73—42no—
126C2×D73—42no—
127C4×C73—22no—
128C4×C73—41no—
129C4×C73—42no—
130C4×C73—41no—
131C4×C73—42no—
132Dic73—22no—
133Dic73—22no—
134Dic73—41no—
135Dic73—42no—
136C2×C73#52511yescharacteristic
137C2×C73#53511yescharacteristic
138C2×C73#53711yescharacteristic
139C2×C73#53812yes—
140C2×C73#53912yes—
141D73—44no—
142D73—81no—
143#2636—731nomaximal, Sylow
144C73#263611yescharacteristic, complemented, Sylow
145C2×#126—731no—
146C2×C4×D4—731no—
147#400D7311yescharacteristic, complemented
148#399—731no—
149#396—732no—
150#394—731no—
151#394—732no—
152#392—731no—
153#386—732no—
154#385—732no—
155#382—731no—
156C22×D4—732no—
157C22×D4—731no—
158C23×C4—732no—
159#126—1464no—
160C4×D4—1464no—
161C2×C4⋊C4—732no—
162C2×C4⋊C4—732no—
163C2×C4⋊C4—731no—
164C2×C4⋊C4—731no—
165C2×C4⋊C4C2×D7311yescharacteristic
166C2×C4⋊C4C2×D7311yescharacteristic
167C2×C22⋊C4—732no—
168C2×C22⋊C4—732no—
169C2×C22⋊C4—732no—
170C2×C22⋊C4—732no—
171C2×C22⋊C4—731no—
172C2×C22⋊C4—731no—
173C2×C22⋊C4—731no—
174C2×C22⋊C4—732no—
175C2×C42—731no—
176#95—732no—
177#95—731no—
178#95C2×D7311yescharacteristic
179#95C2×D7312yes—
180#95C2×D7312yes—
181C24—732no—
182C24—731no—
183C2×D4—2922no—
184C2×D4—2922no—
185C2×D4—1464no—
186C2×D4—1464no—
187C2×D4—1462no—
188C22×C4—2922no—
189C22×C4—2922no—
190C22×C4—731no—
191C22×C4—731no—
192C22×C4—732no—
193C22×C4—731no—
194C22×C4—1464no—
195C22×C4C22×D7312yes—
196C22×C4C22×D7311yescharacteristic
197C22×C4C22×D7311yescharacteristic
198C22×C4C22×D7312yes—
199C22×C4C22×D7311yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—2922no—
203C4⋊C4—2922no—
204C4⋊C4—1462no—
205C4⋊C4—1462no—
206C22⋊C4—2922no—
207C22⋊C4—2922no—
208C22⋊C4—2922no—
209C22⋊C4—1464no—
210C22⋊C4—1462no—
211C22⋊C4—1462no—
212C22⋊C4—1464no—
213C22⋊C4—1462no—
214C42—734no—
215C23—734no—
216C23—1461no—
217C23—1462no—
218C23—1462no—
219C23—1461no—
220C23—1461no—
221C23—1462no—
222C23—1462no—
223C23—1462no—
224C23—1462no—
225C23—1462no—
226C23—1462no—
227C23C23×D7311yescharacteristic
228D4—2928no—
229D4—1468no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—2928no—
243C2×C4—732no—
244C2×C4—732no—
245C2×C4—1461no—
246C2×C4—1462no—
247C2×C4—1462no—
248C2×C4—1462no—
249C2×C4—1462no—
250C2×C4—1461no—
251C2×C4—1462no—
252C2×C4—1461no—
253C2×C4D4×D7312yes—
254C22—2922no—
255C22—2922no—
256C22—2922no—
257C22—2922no—
258C22—2921no—
259C22—2921no—
260C22—2922no—
261C22—2922no—
262C22—2921no—
263C22—1464no—
264C22—1464no—
265C22—1464no—
266C22C2×D4×D7311yescharacteristic
267C22#41×D7312yes—
268C22#1455663712yes—
269C22#1455663711yescharacteristic
270C22#1455663911yescharacteristic
271C4—22no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—41no—
276C4—2921no—
277C4—2922no—
278C4—1462no—
279C4—1462no—
280C2—2924no—
281C2—5841no—
282C2#1798909511yescharacteristic
283C2#1798915511yescharacteristic
284C2#1798916711yescharacteristic
285C2#1798917612yes—
286C2#1798918512yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2636
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14556586C2semidirect
2. C2×#14556553C2semidirect
3. #17988522C2semidirect
4. #17988511C2semidirect
5. #17988505C2semidirect
6. #17988504C2semidirect
8. #17988465C2semidirect
9. #17988461C2semidirect
10. #17988451C2semidirect
11. #400×C73C2semidirect
63. C4×Dic73D4semidirect
144. C73#2636semidirect
147. #400D73semidirect