Finite Group Databasebeta

← #22615551

Subgroups — #22615551

Order 9344.

582 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556584C211yesmaximal, characteristic, complemented
2C2×D4×Dic73C211yesmaximal, characteristic, complemented
3#17988519C211yesmaximal, characteristic, complemented
4#17988512C211yesmaximal, characteristic, complemented
5#17988501C211yesmaximal, characteristic, complemented
6#17988490C212yesmaximal, complemented
7#17988475C212yesmaximal, complemented
8#17988467C212yesmaximal, complemented
9#17988462C212yesmaximal, complemented
10#17988432C211yesmaximal, characteristic, complemented
11#392×C73C211yesmaximal, characteristic
12C23×Dic73C2212yes—
13#14556584—24no—
14D4×Dic73—24no—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2212yes—
18C2×#11924007C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×C22⋊Dic73C2211yescharacteristic
21C2×C22⋊Dic73C2212yes—
22C2×C22⋊Dic73C2212yes—
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2212yes—
25C2×C22⋊Dic73C2212yes—
26C2×C4×Dic73C2212yes—
27C2×C4×Dic73C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2211yescharacteristic
30#14556498C2212yes—
31#14556498C2212yes—
32C22×D4×C73C2211yescharacteristic
33C22×D4×C73C2212yes—
34C2×C22⋊C4×C73C2212yes—
35C2×C22⋊C4×C73C2211yescharacteristic
36#95×C73C2211yescharacteristic
37C22×Dic73—24no—
38C22×Dic73—42no—
39C22×Dic73—42no—
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2311yescharacteristic
46C4⋊Dic73—22no—
47C4⋊Dic73—22no—
48C4⋊Dic73—42no—
49#11924007—22no—
50#11924007—22no—
51C22⋊Dic73—24no—
52C22⋊Dic73—24no—
53C22⋊Dic73—22no—
54C22⋊Dic73—22no—
55C22⋊Dic73—42no—
56C22⋊Dic73—42no—
57C4×Dic73—24no—
58C4×Dic73D414yescomplemented
59C24×C73C2311yescharacteristic
60C24×C73C2312yes—
61C2×D4×C73—24no—
62C2×D4×C73—24no—
63C2×D4×C73—22no—
64C2×D4×C73—24no—
65C2×D4×C73—42no—
66C22×C4×C73C2311yescharacteristic
67C22×C4×C73C2311yescharacteristic
68C22×C4×C73C2312yes—
69C22⋊C4×C73—22no—
70C22⋊C4×C73—24no—
71C23×C73—22no—
72C23×C73—22no—
73C23×C73—22no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73—22no—
77C23×C73—21no—
78C23×C73—22no—
79C23×C73—22no—
80C23×C73—21no—
81C23×C73—21no—
82C23×C73#4114yes—
83C23×C73C2411yescharacteristic
84D4×C73—28no—
85D4×C73—48no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—21no—
90C2×C4×C73—22no—
91C2×C4×C73C2×D412yes—
92C2×C4×C73#4114yes—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—21no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—21no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—21no—
106C2×Dic73—22no—
107C2×Dic73—48no—
108C2×Dic73C2×D412yes—
109C2×Dic73C2×D412yes—
110C22×C73—24no—
111C22×C73—24no—
112C22×C73—24no—
113C22×C73—42no—
114C22×C73—42no—
115C22×C73—42no—
116C22×C73—42no—
117C22×C73—41no—
118C22×C73—41no—
119C22×C73—41no—
120C22×C73—42no—
121C22×C73—42no—
122C22×C73C22×D411yescharacteristic
123C22×C73C2×#4112yes—
124C22×C73C2×#4112yes—
125C22×C73H(5,𝔽2)11yescharacteristic
126C22×C73H(5,𝔽2)11yescharacteristic
127C4×C73—22no—
128C4×C73—24no—
129C4×C73—41no—
130Dic73—22no—
131Dic73—22no—
132Dic73—41no—
133Dic73—41no—
134Dic73—42no—
135Dic73—42no—
136C2×C73—44no—
137C2×C73—81no—
138C2×C73#52511yescharacteristic
139C2×C73#53211yescharacteristic
140C2×C73#53511yescharacteristic
141C2×C73#55112yes—
142C2×C73#55312yes—
143#2603—731nomaximal, Sylow
144C73#260311yescharacteristic, complemented, Sylow
145C2×#126—731no—
146C2×C4×D4—731no—
147#398—731no—
148#397—731no—
149#394—731no—
150#392D7311yescharacteristic
151#390—732no—
152#388—732no—
153#386—732no—
154#385—732no—
155#376—731no—
156C22×D4C2×D7311yescharacteristic
157C22×D4C2×D7312yes—
158C23×C4—732no—
159#126—1464no—
160C4×D4—1464no—
161C2×C4⋊C4—732no—
162C2×C4⋊C4—731no—
163C2×C4⋊C4—731no—
164C2×C4⋊C4—731no—
165C2×C4⋊C4—731no—
166C2×C22⋊C4—732no—
167C2×C22⋊C4—732no—
168C2×C22⋊C4—732no—
169C2×C22⋊C4—731no—
170C2×C22⋊C4—731no—
171C2×C22⋊C4—732no—
172C2×C22⋊C4C2×D7311yescharacteristic
173C2×C22⋊C4C2×D7312yes—
174C2×C42—731no—
175C2×C42—732no—
176#95—732no—
177#95—731no—
178#95—732no—
179#95—732no—
180#95C2×D7311yescharacteristic
181C24C22×D7311yescharacteristic
182C24C22×D7312yes—
183C2×D4—24no—
184C2×D4—24no—
185C2×D4—22no—
186C2×D4—24no—
187C2×D4—42no—
188C22×C4—2922no—
189C22×C4—2922no—
190C22×C4—731no—
191C22×C4—731no—
192C22×C4—732no—
193C22×C4—731no—
194C22×C4—732no—
195C22×C4—731no—
196C22×C4—1464no—
197C22×C4C22×D7311yescharacteristic
198C22×C4C22×D7311yescharacteristic
199C22×C4C22×D7312yes—
200C4⋊C4—2922no—
201C4⋊C4—1462no—
202C4⋊C4—1462no—
203C4⋊C4—1462no—
204C4⋊C4—1462no—
205C22⋊C4—22no—
206C22⋊C4—24no—
207C22⋊C4—2922no—
208C22⋊C4—2922no—
209C22⋊C4—1464no—
210C22⋊C4—1462no—
211C22⋊C4—1462no—
212C22⋊C4—1464no—
213C42—734no—
214C42—1464no—
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—22no—
224C23—21no—
225C23—21no—
226C23#1192402714yes—
227C23C23×D7311yescharacteristic
228D4—28no—
229D4—48no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—2928no—
236C2×C4—732no—
237C2×C4—732no—
238C2×C4—1461no—
239C2×C4—1461no—
240C2×C4—1462no—
241C2×C4—1462no—
242C2×C4—1462no—
243C2×C4—1462no—
244C2×C4—1461no—
245C2×C4—1462no—
246C2×C4—1461no—
247C2×C4—1462no—
248C2×C4—1462no—
249C2×C4—1462no—
250C2×C4—1461no—
251C2×C4—1461no—
252C2×C4D4×D7312yes—
253C2×C4#1192402714yes—
254C22—24no—
255C22—24no—
256C22—24no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—41no—
262C22—41no—
263C22—42no—
264C22—42no—
265C22—41no—
266C22C2×D4×D7311yescharacteristic
267C22C2×#1192402712yes—
268C22C2×#1192402712yes—
269C22#1455663611yescharacteristic
270C22#1455663711yescharacteristic
271C4—24no—
272C4—22no—
273C4—41no—
274C4—2922no—
275C4—2921no—
276C4—2922no—
277C4—2921no—
278C4—1462no—
279C4—1462no—
280C2—44no—
281C2—81no—
282C2#1798909311yescharacteristic
283C2#1798913511yescharacteristic
284C2#1798915311yescharacteristic
285C2#1798926812yes—
286C2#1798928912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2603
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14556584C2semidirect
2. C2×D4×Dic73C2semidirect
3. #17988519C2semidirect
4. #17988512C2semidirect
5. #17988501C2semidirect
6. #17988490C2semidirect
7. #17988475C2semidirect
8. #17988467C2semidirect
9. #17988462C2semidirect
10. #17988432C2semidirect
58. C4×Dic73D4semidirect
144. C73#2603semidirect