Finite Group Databasebeta

← #22622174

Subgroups — #22622174

Order 9344.

460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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
2D4×D292C211yesmaximal, characteristic, complemented
3#17988934C211yesmaximal, characteristic, complemented
4#17988912C212yesmaximal, complemented
5#17988878C211yesmaximal, characteristic, complemented
6#17988840C212yesmaximal, complemented
7#17988783C211yesmaximal, characteristic, complemented
8#17988723C212yesmaximal, complemented
9C4×D584C211yesmaximal, characteristic, complemented
10#17988593C212yesmaximal, complemented
11#436×C73C211yesmaximal, characteristic, complemented
12C22×D292C2212yes—
13C2×D4×D73—21no—
14C2×D584C2211yescharacteristic
15C2×D584C2212yescomplemented
16#14556591C2211yescharacteristic, complemented
17#14556588C2211yescharacteristic
18#14556577—22no—
19#14556566—21no—
20#14556565C2212yes—
21#14556565C2212yescomplemented
22#14556562—21no—
23#14556561—22no—
24C4×D292C2211yescharacteristic
25C4×D292C2211yescharacteristic, complemented
26#14556550C2212yescomplemented
27#14556549—21no—
28#14556525C2211yescharacteristic, complemented
29#14556523C2212yescomplemented
30#14556513C2212yes—
31#14556513C2211yescharacteristic
32#14556513C2212yescomplemented
33#14556513C2212yescomplemented
34#14556513C2211yescharacteristic, complemented
35#14556513C2212yescomplemented
36C2×M16×C73C2212yescomplemented
37C4×D4×C73C2211yescharacteristic
38C4⋊C8×C73C2211yescharacteristic, complemented
39C22⋊C8×C73C2212yescomplemented
40C4×C8×C73C2211yescharacteristic, complemented
41C23×D73—22no—
42C2×Dic146—21no—
43C2×D292—24no—
44C2×D292—22no—
45C2×D292—21no—
46C2×D292—21no—
47C2×D292—42no—
48C2×D292C2312yes—
49C2×D292C2311yescharacteristic
50C2×D292C2311yescharacteristic
51C2×C22⋊D73—22no—
52C2×C22⋊D73—22no—
53D4×D73—44no—
54C2×C4×D73—21no—
55C2×C4×D73—21no—
56D584—22no—
57D584—42no—
58C4⋊Dic73—21no—
59C4⋊Dic73C2312yes—
60C4⋊Dic73C2311yescharacteristic
61C4⋊Dic73C2311yescharacteristic
62C22⋊Dic73—22no—
63#11924005—22no—
64#11924005—21no—
65#11924005—21no—
66#11924005—22no—
67C4×Dic73—22no—
68C2×D4×C73D411yescharacteristic
69C22×C4×C73C2312yes—
70M16×C73—42no—
71C2×C8×C73C2311yescharacteristic
72C2×C8×C73C2311yescharacteristic
73C2×C8×C73C2312yes—
74C4⋊C4×C73D411yescharacteristic
75C22⋊C4×C73D412yes—
76C42×C73C2311yescharacteristic
77C23×C73C2×D412yes—
78C22×D73—21no—
79C22×D73—21no—
80C22×D73—22no—
81C22×D73—44no—
82C22×D73—44no—
83C22×D73—82no—
84D4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D412yes—
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2411yescharacteristic
91C22⋊D73—44no—
92C22⋊D73—82no—
93C2×Dic73—21no—
94C2×Dic73—22no—
95C2×Dic73—21no—
96D292—21no—
97D292—22no—
98D292—21no—
99D292—21no—
100D292—22no—
101D292—44no—
102D292—42no—
103D292—81no—
104D292#4112yes—
105C4×D73—42no—
106C4×D73—42no—
107Dic146—81no—
108C8×C73—21no—
109C8×C73—21no—
110C8×C73—22no—
111C22×C73—22no—
112C22×C73—22no—
113C22×C73—22no—
114C22×C73C22×D411yescharacteristic
115C2×D73—22no—
116C2×D73—41no—
117C2×D73—41no—
118C2×D73—42no—
119C2×D73—41no—
120C2×D73—41no—
121C2×D73—42no—
122C2×D73—42no—
123C2×D73—41no—
124C2×D73—88no—
125C4×C73—22no—
126C4×C73—21no—
127C4×C73AGL(1,ℤ/8)12yes—
128C4×C73C2×#4111yescharacteristic
129C4×C73H(5,𝔽2)11yescharacteristic
130Dic73—41no—
131Dic73—41no—
132Dic73—42no—
133C2×C73—42no—
134C2×C73#54611yescharacteristic
135C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C73#57611yescharacteristic
137D73—42no—
138D73—81no—
139D73—82no—
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#459—731no—
149#447—732no—
150C4×D8—731no—
151#436D7311yescharacteristic, complemented
152#418—732no—
153C22×D4—732no—
154C22×D4—1461no—
155C2×D8—732no—
156C2×D8—731no—
157C2×M16C2×D7312yescomplemented
158C4⋊Q8—731no—
159#127—731no—
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
169#117—732no—
170#117—1461no—
171#107—731no—
172#106—732no—
173C4⋊C8C2×D7311yescharacteristic, complemented
174#102—731no—
175#102—732no—
176#102—732no—
177#102—732no—
178#102—731no—
179#102—732no—
180C22⋊C8C2×D7312yescomplemented
181C4×C8C2×D7311yescharacteristic, complemented
182C24—1462no—
183C2×Q8—1461no—
184C2×D4—2922no—
185C2×D4—2924no—
186C2×D4—731no—
187C2×D4—732no—
188C2×D4—731no—
189C2×D4—1464no—
190C2×D4—1462no—
191C2×D4—1462no—
192C2×D4—1462no—
193C2×D4—1461no—
194C2×D4—1461no—
195C2×D4D29211yescharacteristic
196C22×C4—1461no—
197C22×C4—1461no—
198C22×C4C22×D7312yes—
199D8—2922no—
200D8—1462no—
201M16—42no—
202C2×C8C22×D7311yescharacteristic
203C2×C8C22×D7311yescharacteristic
204C2×C8C22×D7312yes—
205C4⋊C4—732no—
206C4⋊C4—731no—
207C4⋊C4—731no—
208C4⋊C4—1461no—
209C4⋊C4D29211yescharacteristic
210C22⋊C4—1462no—
211C22⋊C4—1462no—
212C22⋊C4—1461no—
213C22⋊C4—1461no—
214C22⋊C4—1462no—
215C22⋊C4D29212yes—
216C42—1462no—
217C42C22×D7311yescharacteristic
218C23—2924no—
219C23—2924no—
220C23—5842no—
221C23—1461no—
222C23—1462no—
223C23—1461no—
224C23C2×D29212yes—
225Q8—5841no—
226D4—22no—
227D4—2924no—
228D4—2924no—
229D4—2922no—
230D4—5841no—
231D4—5842no—
232D4—732no—
233D4—1461no—
234D4—1462no—
235D4—1461no—
236D4—1462no—
237D4—1461no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—2922no—
241C2×C4—2922no—
242C2×C4—1461no—
243C2×C4—1462no—
244C2×C4—1461no—
245C2×C4C2×D29212yes—
246C2×C4C2×D29211yescharacteristic
247C2×C4C2×D29211yescharacteristic
248C2×C4C23×D7311yescharacteristic
249C8—21no—
250C8—21no—
251C8—22no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—2921no—
256C22—2921no—
257C22—2921no—
258C22—2922no—
259C22—2921no—
260C22—2922no—
261C22—2922no—
262C22—2921no—
263C22—5848no—
264C22—1462no—
265C22C22×D29211yescharacteristic
266C4—21no—
267C4—22no—
268C4—2921no—
269C4—2921no—
270C4—2922no—
271C4#1455661912yes—
272C4#41×D7311yescharacteristic
273C4#1455663611yescharacteristic
274C2—42no—
275C2—2922no—
276C2—5842no—
277C2—5841no—
278C2#1798923211yescharacteristic
279C2C2×#1455661911yescharacteristic
280C2#1798939211yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#436×C73C2
socleC22×C73C22×D4
hypercenter#436D73
hypocenterC73#3325
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #17989302C2semidirect
2. D4×D292C2semidirect
3. #17988934C2semidirect
4. #17988912C2semidirect
5. #17988878C2semidirect
6. #17988840C2semidirect
7. #17988783C2semidirect
8. #17988723C2semidirect
9. C4×D584C2semidirect
10. #17988593C2semidirect
11. #436×C73C2semidirect
15. C2×D584C22semidirect
16. #14556591C22semidirect
21. #14556565C22semidirect
25. C4×D292C22semidirect
26. #14556550C22semidirect
28. #14556525C22semidirect
29. #14556523C22semidirect
32. #14556513C22semidirect
33. #14556513C22semidirect
34. #14556513C22semidirect
35. #14556513C22semidirect
36. C2×M16×C73C22semidirect
38. C4⋊C8×C73C22semidirect
39. C22⋊C8×C73C22semidirect
40. C4×C8×C73C22semidirect
141. C73#3325semidirect
151. #436D73semidirect
157. C2×M16C2×D73semidirect
173. C4⋊C8C2×D73semidirect
180. C22⋊C8C2×D73semidirect
181. C4×C8C2×D73semidirect