Finite Group Databasebeta

← #22622176

Subgroups — #22622176

Order 9344.

460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#17989302C211yesmaximal, characteristic, complemented
2#17989222C211yesmaximal, characteristic, complemented
3#17988933C211yesmaximal, characteristic, complemented
4#17988910C212yesmaximal, complemented
5#17988878C211yesmaximal, characteristic, complemented
6#17988837C212yesmaximal, complemented
7#17988719C212yesmaximal, complemented
8C4×#11924013C211yesmaximal, characteristic, complemented
9#17988664C211yesmaximal, characteristic, complemented
10#17988590C212yesmaximal, complemented
11#459×C73C211yesmaximal, characteristic, complemented
12C2×D4×D73—21no—
13C2×D4×D73C2212yes—
14C2×#11924013C2211yescharacteristic
15C2×#11924011C2212yescomplemented
16#14556591C2211yescharacteristic, complemented
17#14556577—22no—
18#14556565—21no—
19#14556562—21no—
20#14556562C2212yes—
21#14556562C2212yescomplemented
22#14556559—22no—
23C4×D292C2211yescharacteristic
24C4×D292C2211yescharacteristic
25#14556550—21no—
26#14556549C2212yescomplemented
27#14556524C2211yescharacteristic, complemented
28#14556523C2212yescomplemented
29#14556513C2212yes—
30#14556512C2212yescomplemented
31#14556512C2211yescharacteristic, complemented
32#14556512C2212yescomplemented
33#14556511C2211yescharacteristic
34#14556503C2212yescomplemented
35C4×#10596831C2211yescharacteristic, complemented
36C2×D8×C73C2212yescomplemented
37#127×C73C2211yescharacteristic
38C4×D4×C73C2211yescharacteristic, complemented
39C4⋊C8×C73C2211yescharacteristic, complemented
40#102×C73C2212yescomplemented
41C23×D73—22no—
42C2×Dic146—21no—
43C2×D292D411yescharacteristic
44C2×D292C2311yescharacteristic
45C2×C22⋊D73—22no—
46C2×C22⋊D73—22no—
47C2×C22⋊D73—22no—
48D4×D73—24no—
49D4×D73—42no—
50D4×D73—44no—
51C2×C4×D73—21no—
52C2×C4×D73C2312yes—
53#11924013—22no—
54#11924011—42no—
55C2×#10596831C2311yescharacteristic
56C2×#10596831C2311yescharacteristic
57C4⋊Dic73—21no—
58C4⋊Dic73D411yescharacteristic
59C4⋊Dic73C2312yes—
60C4⋊Dic73C2311yescharacteristic
61C22⋊Dic73—22no—
62C22⋊Dic73—22no—
63#11924005—22no—
64#11924005—21no—
65#11924005D412yes—
66C4×Dic73—22no—
67C2×D4×C73—21no—
68C2×D4×C73—21no—
69C2×D4×C73C2312yes—
70C2×D4×C73C2311yescharacteristic
71C22×C4×C73—21no—
72D8×C73—42no—
73C2×C8×C73C2312yes—
74C4⋊C4×C73C2311yescharacteristic
75C22⋊C4×C73—21no—
76C42×C73C2311yescharacteristic
77C23×C73—21no—
78C23×C73—22no—
79C22×D73—21no—
80C22×D73—44no—
81C22×D73—44no—
82C22×D73—82no—
83C22×D73C2×D412yes—
84D4×C73—21no—
85D4×C73—22no—
86D4×C73—21no—
87D4×C73—22no—
88D4×C73—42no—
89D4×C73—81no—
90C2×C4×C73—21no—
91C2×C4×C73—42no—
92C2×C4×C73C2×D411yescharacteristic
93C2×C4×C73C2×D411yescharacteristic
94C2×C4×C73C2411yescharacteristic
95C22⋊D73—44no—
96C22⋊D73—44no—
97C22⋊D73—82no—
98C2×Dic73—22no—
99C2×Dic73—21no—
100C2×Dic73C2×D412yes—
101D292—22no—
102D292—21no—
103D292#4112yes—
104C4×D73—22no—
105C4×D73—22no—
106C4×D73—42no—
107Dic146—81no—
108C8×C73—22no—
109#10596831—21no—
110#10596831—21no—
111C22×C73—42no—
112C22×C73—41no—
113C22×C73—42no—
114C22×C73—41no—
115C22×C73—41no—
116C22×C73—42no—
117C22×C73C22×D411yescharacteristic
118C2×D73—22no—
119C2×D73—22no—
120C2×D73—22no—
121C2×D73—22no—
122C2×D73—41no—
123C2×D73—41no—
124C2×D73—88no—
125C4×C73—21no—
126C4×C73—41no—
127C4×C73AGL(1,ℤ/8)12yes—
128C4×C73C2×#4111yescharacteristic
129C4×C73H(5,𝔽2)11yescharacteristic
130Dic73—22no—
131Dic73—41no—
132Dic73—42no—
133C2×C73—82no—
134C2×C73—81no—
135C2×C73#54611yescharacteristic
136C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C73#57611yescharacteristic
138D73—42no—
139D73—42no—
140#3325—731nomaximal, Sylow
141C73#332511yescharacteristic, complemented, Sylow
142#555—731no—
143D42—731no—
144#486—731no—
145#482—732no—
146#476—731no—
147#469—732no—
148#459D7311yescharacteristic, complemented
149#447—732no—
150C4×D8—731no—
151#436—731no—
152#418—732no—
153C22×D4—732no—
154C22×D4—1461no—
155C2×D8—731no—
156C2×D8C2×D7312yescomplemented
157C2×M16—732no—
158C4⋊Q8—731no—
159#127C2×D7311yescharacteristic
160#124—1462no—
161#121—732no—
162#121—732no—
163#121—1461no—
164#121—1461no—
165#120—1462no—
166C4×D4—731no—
167C4×D4—731no—
168C4×D4C2×D7311yescharacteristic, complemented
169#117—732no—
170#117—1461no—
171#107—731no—
172#106—732no—
173C4⋊C8C2×D7311yescharacteristic, complemented
174#102—732no—
175#102—731no—
176#102—732no—
177#102—732no—
178#102—731no—
179#102C2×D7312yescomplemented
180C22⋊C8—732no—
181C4×C8—731no—
182C24—1462no—
183C2×Q8—1461no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—2924no—
187C2×D4—2922no—
188C2×D4—731no—
189C2×D4—731no—
190C2×D4—1462no—
191C2×D4—1464no—
192C2×D4—1462no—
193C2×D4—1462no—
194C2×D4C22×D7312yes—
195C2×D4C22×D7311yescharacteristic
196C22×C4—21no—
197C22×C4—732no—
198C22×C4—1461no—
199D8—42no—
200D8—1462no—
201M16—2922no—
202C2×C8—731no—
203C2×C8—731no—
204C2×C8C22×D7312yes—
205C4⋊C4—731no—
206C4⋊C4—732no—
207C4⋊C4—731no—
208C4⋊C4—1461no—
209C4⋊C4C22×D7311yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—732no—
212C22⋊C4—1462no—
213C22⋊C4—1462no—
214C22⋊C4—1462no—
215C22⋊C4—1461no—
216C42—1462no—
217C42C22×D7311yescharacteristic
218C23—21no—
219C23—22no—
220C23—2924no—
221C23—2924no—
222C23—5842no—
223C23—732no—
224C23—1461no—
225Q8—5841no—
226D4—21no—
227D4—22no—
228D4—21no—
229D4—22no—
230D4—42no—
231D4—81no—
232D4—2924no—
233D4—2924no—
234D4—5842no—
235D4—732no—
236D4—1462no—
237D4—1461no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—2922no—
241C2×C4—732no—
242C2×C4—1462no—
243C2×C4—1461no—
244C2×C4—1462no—
245C2×C4—1462no—
246C2×C4D4×D7311yescharacteristic
247C2×C4D4×D7311yescharacteristic
248C2×C4C23×D7311yescharacteristic
249C8—22no—
250C8—1461no—
251C8—1461no—
252C22—42no—
253C22—41no—
254C22—42no—
255C22—41no—
256C22—41no—
257C22—42no—
258C22—2921no—
259C22—2921no—
260C22—5848no—
261C22—1462no—
262C22—1462no—
263C22—1462no—
264C22—1462no—
265C22C2×D4×D7311yescharacteristic
266C4—21no—
267C4—41no—
268C4—2922no—
269C4—2921no—
270C4—1462no—
271C4#1455661512yes—
272C4#41×D7311yescharacteristic
273C4#1455663611yescharacteristic
274C2—82no—
275C2—81no—
276C2—2922no—
277C2—2922no—
278C2#1798923411yescharacteristic
279C2C2×#1455661511yescharacteristic
280C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#459×C73C2
socleC22×C73C22×D4
hypercenter#459D73
hypocenterC73#3325
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #17989302C2semidirect
2. #17989222C2semidirect
3. #17988933C2semidirect
4. #17988910C2semidirect
5. #17988878C2semidirect
6. #17988837C2semidirect
7. #17988719C2semidirect
8. C4×#11924013C2semidirect
9. #17988664C2semidirect
10. #17988590C2semidirect
11. #459×C73C2semidirect
15. C2×#11924011C22semidirect
16. #14556591C22semidirect
21. #14556562C22semidirect
26. #14556549C22semidirect
27. #14556524C22semidirect
28. #14556523C22semidirect
30. #14556512C22semidirect
31. #14556512C22semidirect
32. #14556512C22semidirect
34. #14556503C22semidirect
35. C4×#10596831C22semidirect
36. C2×D8×C73C22semidirect
38. C4×D4×C73C22semidirect
39. C4⋊C8×C73C22semidirect
40. #102×C73C22semidirect
141. C73#3325semidirect
148. #459D73semidirect
156. C2×D8C2×D73semidirect
168. C4×D4C2×D73semidirect
173. C4⋊C8C2×D73semidirect
179. #102C2×D73semidirect