Finite Group Databasebeta

← #22618220

Subgroups — #22618220

Order 9344.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C4×D73C211yesmaximal, characteristic, complemented
2C2×#14556572C211yesmaximal, characteristic, complemented
3C2×#14556559C211yesmaximal, characteristic
4#17988463C214yesmaximal, complemented
5#17988458C214yesmaximal, complemented
6#17988450C211yesmaximal, characteristic, complemented
7#17988448C211yesmaximal, characteristic, complemented
8#17988442C211yesmaximal, characteristic, complemented
9C2×#123×C73C211yesmaximal, characteristic, complemented
10C24×D73C2211yescharacteristic
11C22×C22⋊D73C2212yes—
12C23×Dic73C2211yescharacteristic
13C22×C4×D73—24no—
14C22×C4×D73—24no—
15C22×C4×D73—24no—
16C22×C4×D73C2214yes—
17#14556572—24no—
18#14556559—24no—
19C2×#11924007C2212yescomplemented
20C2×C22⋊Dic73C2211yescharacteristic
21C2×C22⋊Dic73C2211yescharacteristic
22C2×C22⋊Dic73C2212yescomplemented
23C2×#11924005C2214yes—
24C2×#11924005C2212yes—
25#14556498C2214yescomplemented
26#14556498C2214yescomplemented
27C22×D4×C73C2211yescharacteristic
28C23×C4×C73C2211yescharacteristic
29#123×C73—24no—
30C2×C4⋊C4×C73C2212yescomplemented
31C2×C22⋊C4×C73C2211yescharacteristic
32C2×C22⋊C4×C73C2212yescomplemented
33C23×D73—22no—
34C23×D73—22no—
35C23×D73—28no—
36C23×D73D414yes—
37C23×D73C2312yes—
38C2×C22⋊D73—24no—
39C2×C22⋊D73—28no—
40C22×Dic73—22no—
41C22×Dic73—22no—
42C22×Dic73D414yescomplemented
43C22×Dic73C2312yes—
44C22×Dic73C2312yes—
45C22×Dic73C2312yes—
46C2×C4×D73—232no—
47C2×C4×D73—28no—
48C2×C4×D73—28no—
49C2×C4×D73—28no—
50#11924007—24no—
51C22⋊Dic73—22no—
52C22⋊Dic73—22no—
53C22⋊Dic73—24no—
54#11924005—24no—
55#11924005—28no—
56C24×C73C2311yescharacteristic
57C24×C73C2311yescharacteristic
58C2×D4×C73—22no—
59C2×D4×C73—22no—
60C2×D4×C73—22no—
61C22×C4×C73—22no—
62C22×C4×C73—22no—
63C22×C4×C73D414yescomplemented
64C22×C4×C73C2312yes—
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2312yes—
67C4⋊C4×C73—24no—
68C22⋊C4×C73—22no—
69C22⋊C4×C73—24no—
70C23×C73—24no—
71C23×C73—21no—
72C23×C73—21no—
73C23×C73—21no—
74C23×C73—24no—
75C23×C73C2×D412yes—
76C23×C73C2×D412yes—
77C23×C73C2×D412yes—
78C23×C73C2411yescharacteristic
79C22×D73—216no—
80C22×D73—216no—
81C22×D73—28no—
82C22×D73—22no—
83C22×D73—22no—
84C22×D73—24no—
85C22×D73—216no—
86C22×D73C2×D414yes—
87C22×D73#4118yes—
88D4×C73—44no—
89C2×C4×C73—28no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—21no—
96C2×C4×C73—24no—
97C2×C4×C73C2×D414yes—
98C22⋊D73—48no—
99C2×Dic73—28no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—24no—
105C2×Dic73—24no—
106C2×Dic73C2×D414yes—
107C4×D73—232no—
108C22×C73—24no—
109C22×C73—24no—
110C22×C73—24no—
111C22×C73—41no—
112C22×C73—42no—
113C22×C73—42no—
114C22×C73—42no—
115C22×C73#12014yes—
116C22×C73C22×D411yescharacteristic
117C22×C73C22×D411yescharacteristic
118C22×C73C22×D411yescharacteristic
119C22×C73C2×#4114yes—
120C2×D73—232no—
121C2×D73—24no—
122C2×D73—24no—
123C2×D73—28no—
124C2×D73—28no—
125C2×D73#12318yescomplemented
126C4×C73—24no—
127C4×C73—41no—
128C4×C73—42no—
129Dic73—24no—
130Dic73—42no—
131Dic73—42no—
132C2×C73—24no—
133C2×C73—81no—
134C2×C73C2×#12011yescharacteristic
135C2×C73C2×#12312yes—
136C2×C73#52512yes—
137C2×C73#52512yes—
138D73—28no—
139#2849—731nomaximal, Sylow
140C73#284911yescharacteristic, complemented, Sylow
141C24×C4—731no—
142C2×#123—731no—
143C2×#123D7311yescharacteristic, complemented
144C2×#120—731no—
145#386—734no—
146#385—734no—
147#381—731no—
148#381—731no—
149#379—731no—
150C25—731no—
151C22×D4—732no—
152C22×D4C2×D7311yescharacteristic
153C23×C4—731no—
154C23×C4—734no—
155C23×C4—1464no—
156C23×C4—1464no—
157C23×C4—1464no—
158C23×C4C2×D7311yescharacteristic
159#123—24no—
160#123—1464no—
161#120—1464no—
162C2×C4⋊C4—732no—
163C2×C4⋊C4C2×D7312yescomplemented
164C2×C22⋊C4—731no—
165C2×C22⋊C4—731no—
166C2×C22⋊C4—732no—
167C2×C22⋊C4—732no—
168C2×C22⋊C4—734no—
169C2×C22⋊C4C2×D7311yescharacteristic
170C2×C22⋊C4C2×D7312yescomplemented
171#95—734no—
172#95—734no—
173C24—732no—
174C24—734no—
175C24—1468no—
176C24—1462no—
177C24—1462no—
178C24C22×D7311yescharacteristic
179C24C22×D7311yescharacteristic
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—1464no—
184C2×D4—1468no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—734no—
188C22×C4—732no—
189C22×C4—732no—
190C22×C4—732no—
191C22×C4—1468no—
192C22×C4—1468no—
193C22×C4—14632no—
194C22×C4—1462no—
195C22×C4—1462no—
196C22×C4—1468no—
197C22×C4C22⋊D7314yescomplemented
198C22×C4C22×D7312yes—
199C22×C4C22×D7311yescharacteristic
200C22×C4C22×D7312yes—
201C4⋊C4—24no—
202C4⋊C4—1464no—
203C22⋊C4—22no—
204C22⋊C4—24no—
205C22⋊C4—1468no—
206C22⋊C4—1464no—
207C22⋊C4—1464no—
208C22⋊C4—1462no—
209C22⋊C4—1462no—
210C23—24no—
211C23—21no—
212C23—21no—
213C23—21no—
214C23—24no—
215C23—734no—
216C23—738no—
217C23—14616no—
218C23—14616no—
219C23—14616no—
220C23—1468no—
221C23—1462no—
222C23—1462no—
223C23—1464no—
224C23D4×D7312yes—
225C23D4×D7312yes—
226C23C2×C22⋊D7312yes—
227C23C23×D7311yescharacteristic
228D4—44no—
229D4—2928no—
230C2×C4—28no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—24no—
238C2×C4—734no—
239C2×C4—14632no—
240C2×C4—1462no—
241C2×C4—1462no—
242C2×C4—1464no—
243C2×C4—1464no—
244C2×C4—1468no—
245C2×C4—1462no—
246C2×C4—1462no—
247C2×C4C2×C22⋊D7314yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—738no—
256C22—14632no—
257C22—1464no—
258C22—1464no—
259C22—1468no—
260C22—1468no—
261C22#1455655914yes—
262C22C2×D4×D7311yescharacteristic
263C22C2×D4×D7311yescharacteristic
264C22C22×C22⋊D7311yescharacteristic
265C22#41×D7314yes—
266C4—24no—
267C4—41no—
268C4—42no—
269C4—2922no—
270C4—2922no—
271C4—1464no—
272C2—24no—
273C2—81no—
274C2—1468no—
275C2C2×#1455655911yescharacteristic
276C2#123×D7312yes—
277C2#1798909412yes—
278C2#1798909512yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#123×C73C2
hypercenterC2×#123D73
hypocenterC73#2849
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C23×C4×D73C2semidirect
2. C2×#14556572C2semidirect
4. #17988463C2semidirect
5. #17988458C2semidirect
6. #17988450C2semidirect
7. #17988448C2semidirect
8. #17988442C2semidirect
9. C2×#123×C73C2semidirect
19. C2×#11924007C22semidirect
22. C2×C22⋊Dic73C22semidirect
25. #14556498C22semidirect
26. #14556498C22semidirect
30. C2×C4⋊C4×C73C22semidirect
32. C2×C22⋊C4×C73C22semidirect
42. C22×Dic73D4semidirect
63. C22×C4×C73D4semidirect
125. C2×D73#123semidirect
140. C73#2849semidirect
143. C2×#123D73semidirect
163. C2×C4⋊C4C2×D73semidirect
170. C2×C22⋊C4C2×D73semidirect
197. C22×C4C22⋊D73semidirect