Finite Group Databasebeta

← #22616492

Subgroups — #22616492

Order 9344.

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

normal subgroups only

This group has 680 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×#14556572C211yesmaximal, characteristic, complemented
2#17988515C212yesmaximal, complemented
3#17988510C212yesmaximal, complemented
4#17988501C212yesmaximal, complemented
5#17988490C211yesmaximal, characteristic, complemented
6#17988481C212yesmaximal, complemented
7#17988467C212yesmaximal, complemented
8#17988443C212yesmaximal, complemented
9C2×#120×C73C211yesmaximal, characteristic
10C23×Dic73C2211yescharacteristic, complemented
11#14556572—24no—
12C2×C4⋊Dic73C2211yescharacteristic, complemented
13C2×#11924007C2212yescomplemented
14C2×#11924007C2212yescomplemented
15C2×C22⋊Dic73C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2212yes—
20C2×C22⋊Dic73C2212yes—
21C2×C22⋊Dic73C2211yescharacteristic, complemented
22C2×C22⋊Dic73C2212yescomplemented
23C2×C4×Dic73C2211yescharacteristic, complemented
24#14556498C2212yescomplemented
25#14556498C2212yescomplemented
26#14556498C2212yescomplemented
27C25×C73C2211yescharacteristic
28C22×D4×C73C2212yes—
29C22×D4×C73C2211yescharacteristic
30#120×C73—24no—
31C2×C22⋊C4×C73C2212yes—
32C2×C22⋊C4×C73C2211yescharacteristic
33C22×Dic73—22no—
34C22×Dic73—41no—
35C22×Dic73—41no—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C4⋊Dic73—41no—
41#11924007—24no—
42#11924007—42no—
43C22⋊Dic73—24no—
44C22⋊Dic73—22no—
45C22⋊Dic73—24no—
46C22⋊Dic73—42no—
47C22⋊Dic73—42no—
48C22⋊Dic73—42no—
49C22⋊Dic73—42no—
50C22⋊Dic73—42no—
51C4×Dic73—41no—
52C24×C73—22no—
53C24×C73—24no—
54C24×C73—41no—
55C24×C73—42no—
56C24×C73—41no—
57C24×C73C2311yescharacteristic
58C24×C73C2311yescharacteristic
59C24×C73C2312yes—
60C2×D4×C73—24no—
61C2×D4×C73—24no—
62C2×D4×C73—41no—
63C2×D4×C73—41no—
64C2×D4×C73—42no—
65C2×D4×C73D414yes—
66C22×C4×C73C2312yes—
67C22×C4×C73C2311yescharacteristic
68C22⋊C4×C73—22no—
69C22⋊C4×C73—24no—
70C23×C73—22no—
71C23×C73—22no—
72C23×C73—22no—
73C23×C73—22no—
74C23×C73—21no—
75C23×C73—21no—
76C23×C73—22no—
77C23×C73—22no—
78C23×C73—21no—
79C23×C73—21no—
80C23×C73—22no—
81C23×C73—22no—
82C23×C73—22no—
83C23×C73—22no—
84C23×C73—48no—
85C23×C73—44no—
86C23×C73—44no—
87C23×C73—48no—
88C23×C73—44no—
89C23×C73C2×D412yes—
90C23×C73C2×D412yes—
91C23×C73#4114yes—
92C23×C73C2411yescharacteristic
93D4×C73—44no—
94D4×C73—48no—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73C2×D412yes—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—44no—
114C22×C73—22no—
115C22×C73—22no—
116C22×C73—24no—
117C22×C73—24no—
118C22×C73—24no—
119C22×C73—24no—
120C22×C73—24no—
121C22×C73—416no—
122C22×C73—42no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73—42no—
126C22×C73—42no—
127C22×C73—41no—
128C22×C73—41no—
129C22×C73—41no—
130C22×C73—41no—
131C22×C73—42no—
132C22×C73C22×D411yescharacteristic
133C22×C73C2×#4112yes—
134C22×C73H(5,𝔽2)11yescharacteristic
135C22×C73H(5,𝔽2)11yescharacteristic
136C22×C73H(5,𝔽2)12yes—
137C4×C73—22no—
138C4×C73—42no—
139Dic73—42no—
140Dic73—42no—
141Dic73—42no—
142Dic73—42no—
143C2×C73—42no—
144C2×C73—42no—
145C2×C73—44no—
146C2×C73#53411yescharacteristic
147C2×C73#53812yes—
148C2×C73#54612yes—
149C2×C73#55111yescharacteristic
150C2×C73#56011yescharacteristic
151#2697—731nomaximal, Sylow
152C73#269711yescharacteristic, complemented, Sylow
153C2×#123—731no—
154C2×#120D7311yescharacteristic
155#397—732no—
156#396—732no—
157#394—732no—
158#390—731no—
159#388—732no—
160#386—732no—
161#379—732no—
162C25C2×D7311yescharacteristic
163C22×D4C2×D7312yes—
164C22×D4C2×D7311yescharacteristic
165C23×C4—731no—
166#123—1464no—
167#120—24no—
168C2×C4⋊C4—732no—
169C2×C4⋊C4—731no—
170C2×C4⋊C4—732no—
171C2×C22⋊C4—732no—
172C2×C22⋊C4—732no—
173C2×C22⋊C4—732no—
174C2×C22⋊C4—732no—
175C2×C22⋊C4—732no—
176C2×C22⋊C4—732no—
177C2×C22⋊C4—731no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4C2×D7312yes—
180C2×C22⋊C4C2×D7311yescharacteristic
181C2×C42—731no—
182#95—732no—
183#95—732no—
184#95—732no—
185C24—22no—
186C24—24no—
187C24—42no—
188C24—41no—
189C24—41no—
190C24C22×D7311yescharacteristic
191C24C22×D7311yescharacteristic
192C24C22×D7312yes—
193C2×D4—24no—
194C2×D4—24no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—42no—
198C2×D4C22⋊D7314yes—
199C22×C4—2921no—
200C22×C4—2921no—
201C22×C4—732no—
202C22×C4—732no—
203C22×C4—732no—
204C22×C4—732no—
205C22×C4—1462no—
206C22×C4C22×D7312yes—
207C22×C4C22×D7311yescharacteristic
208C4⋊C4—2922no—
209C4⋊C4—2921no—
210C4⋊C4—1464no—
211C22⋊C4—22no—
212C22⋊C4—24no—
213C22⋊C4—2922no—
214C22⋊C4—2922no—
215C22⋊C4—2922no—
216C22⋊C4—2922no—
217C22⋊C4—2922no—
218C22⋊C4—1462no—
219C22⋊C4—1464no—
220C22⋊C4—1464no—
221C42—2921no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—48no—
237C23—44no—
238C23—44no—
239C23—48no—
240C23—44no—
241C23C2×C22⋊D7312yes—
242C23C2×C22⋊D7312yes—
243C23#1192402714yes—
244C23C23×D7311yescharacteristic
245D4—44no—
246D4—48no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—2924no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4—1462no—
257C2×C4—1462no—
258C2×C4—1462no—
259C2×C4—1462no—
260C2×C4—1462no—
261C2×C4—1462no—
262C2×C4—1462no—
263C2×C4—1462no—
264C2×C4—1462no—
265C2×C4C2×C22⋊D7312yes—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—24no—
270C22—24no—
271C22—24no—
272C22—24no—
273C22—416no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—42no—
283C22—41no—
284C22C22×C22⋊D7311yescharacteristic
285C22C2×#1192402712yes—
286C22#1455663611yescharacteristic
287C22#1455663611yescharacteristic
288C22#1455663612yes—
289C4—22no—
290C4—42no—
291C4—2922no—
292C4—2922no—
293C4—2922no—
294C4—2922no—
295C2—42no—
296C2—44no—
297C2—42no—
298C2#1798914611yescharacteristic
299C2#1798917212yes—
300C2#1798923112yes—
301C2#1798926811yescharacteristic
302C2#1798932611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#120×C73C2
hypercenterC2×#120D73
hypocenterC73#2697
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14556572C2semidirect
2. #17988515C2semidirect
3. #17988510C2semidirect
4. #17988501C2semidirect
5. #17988490C2semidirect
6. #17988481C2semidirect
7. #17988467C2semidirect
8. #17988443C2semidirect
10. C23×Dic73C22semidirect
12. C2×C4⋊Dic73C22semidirect
13. C2×#11924007C22semidirect
14. C2×#11924007C22semidirect
21. C2×C22⋊Dic73C22semidirect
22. C2×C22⋊Dic73C22semidirect
23. C2×C4×Dic73C22semidirect
24. #14556498C22semidirect
25. #14556498C22semidirect
26. #14556498C22semidirect
152. C73#2697semidirect