Finite Group Databasebeta

← #22620952

Subgroups — #22620952

Order 9344.

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

normal subgroups only

This group has 490 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
1C2×#14556587C211yesmaximal, characteristic, complemented
2#17989123C211yesmaximal, characteristic, complemented
3#17988973C212yesmaximal, complemented
4#17988950C212yesmaximal, complemented
5#17988785C212yesmaximal, complemented
6#17988781C212yesmaximal, complemented
7#17988737C211yesmaximal, characteristic, complemented
8#17988723C211yesmaximal, characteristic, complemented
9#17988721C211yesmaximal, characteristic, complemented
10#17988641C211yesmaximal, characteristic, complemented
11#450×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×C22⋊D73—21no—
14C22×C22⋊D73—21no—
15C2×#11924015C2212yescomplemented
16C2×D584C2212yescomplemented
17C2×#11924013C2212yescomplemented
18#14556587—21no—
19#14556587—21no—
20#14556587C2212yes—
21#14556587C2212yes—
22#14556586—21no—
23#14556582C2211yescharacteristic, complemented
24#14556580C2211yescharacteristic, complemented
25#14556575—21no—
26#14556565C2211yescharacteristic
27Q8×Dic73C2211yescharacteristic, complemented
28#14556553C2211yescharacteristic, complemented
29#14556551—21no—
30#14556549—21no—
31C2×C4×Dic73C2211yescharacteristic
32#14556520C2212yescomplemented
33#14556513C2212yescomplemented
34#14556512C2212yescomplemented
35#14556511C2212yescomplemented
36C22⋊#10596831C2211yescharacteristic
37#14556501C2212yescomplemented
38C22×D4×C73C2211yescharacteristic
39C2×SD16×C73C2212yescomplemented
40C22⋊Q8×C73C2211yescharacteristic
41#102×C73C2212yescomplemented
42C22⋊C8×C73C2211yescharacteristic
43C23×D73—21no—
44C2×D292—21no—
45C2×D292—42no—
46C2×D292C2312yes—
47C2×D292C2311yescharacteristic
48C2×C22⋊D73—21no—
49C2×C22⋊D73—22no—
50C2×C22⋊D73—22no—
51C2×C22⋊D73—22no—
52C2×C22⋊D73—22no—
53C2×C22⋊D73—44no—
54C2×C22⋊D73—44no—
55C22×Dic73D411yescharacteristic
56C22×Dic73D411yescharacteristic
57C2×C4×D73—21no—
58#11924015—42no—
59D584—42no—
60#11924013—42no—
61C2×#10596831C2312yes—
62C4⋊Dic73—21no—
63C4⋊Dic73—21no—
64C4⋊Dic73C2311yescharacteristic
65#11924007—21no—
66#11924005—21no—
67#11924005—21no—
68#11924005—21no—
69#11924005—21no—
70C4×Dic73—21no—
71C4×Dic73D411yescharacteristic
72C4×Dic73D411yescharacteristic
73C4×Dic73C2311yescharacteristic
74C4×Dic73C2311yescharacteristic
75C24×C73—21no—
76C2×Q8×C73C2311yescharacteristic
77C2×D4×C73—21no—
78C2×D4×C73—42no—
79C2×D4×C73C2312yes—
80C22×C4×C73C2311yescharacteristic
81SD16×C73—42no—
82C2×C8×C73C2312yes—
83C4⋊C4×C73—21no—
84C4⋊C4×C73C2311yescharacteristic
85C22⋊C4×C73—21no—
86C23×C73—22no—
87C23×C73—42no—
88C23×C73—42no—
89C23×C73—42no—
90C23×C73C2×D411yescharacteristic
91C22×D73—21no—
92C22×D73—22no—
93C22×D73—42no—
94C22×D73—42no—
95C22×D73—42no—
96Q8×C73—22no—
97D4×C73—22no—
98D4×C73—22no—
99D4×C73—42no—
100C2×C4×C73—22no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73C2×D411yescharacteristic
104C2×C4×C73C2411yescharacteristic
105C22⋊D73—44no—
106C22⋊D73—44no—
107C22⋊D73—44no—
108C22⋊D73—42no—
109C22⋊D73—44no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—21no—
113C2×Dic73C2×D411yescharacteristic
114C2×Dic73C2×D411yescharacteristic
115C2×Dic73C2×D411yescharacteristic
116C2×Dic73C2×D411yescharacteristic
117D292—22no—
118D292—22no—
119D292—22no—
120D292—42no—
121C4×D73—42no—
122C8×C73—22no—
123#10596831—22no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73—42no—
127C22×C73—42no—
128C22×C73—42no—
129C22×C73—84no—
130C22×C73AGL(1,ℤ/8)12yes—
131C22×C73C22×D411yescharacteristic
132C2×D73—42no—
133C2×D73—41no—
134C2×D73—41no—
135C2×D73—42no—
136C2×D73—42no—
137C2×D73—41no—
138C2×D73—84no—
139C4×C73—21no—
140C4×C73—41no—
141C4×C73—41no—
142C4×C73H(5,𝔽2)12yes—
143Dic73—21no—
144Dic73—21no—
145Dic73—21no—
146Dic73—41no—
147Dic73AGL(1,ℤ/8)12yes—
148C2×C73—22no—
149C2×C73—82no—
150C2×C73#53511yescharacteristic
151C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
152C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
153D73—81no—
154D73—82no—
155#3217—731nomaximal, Sylow
156C73#321711yescharacteristic, complemented, Sylow
157C2×#127—731no—
158#529—731no—
159#496—732no—
160#490—732no—
161#460—732no—
162#459—732no—
163#450—731no—
164#450D7311yescharacteristic, complemented
165#447—731no—
166#447—731no—
167#432—731no—
168C22×D4—731no—
169C22×D4—1461no—
170C22×D4—1461no—
171C22×D4C2×D7311yescharacteristic
172C2×SD16—732no—
173C2×SD16C2×D7312yescomplemented
174C2×D8—732no—
175C2×D8—732no—
176#127—732no—
177#127—732no—
178#127—1461no—
179#127—1461no—
180#126—1461no—
181#125—731no—
182#124—731no—
183#123—1461no—
184C22⋊Q8C2×D7311yescharacteristic
185#121—731no—
186C4×Q8—731no—
187C4×D4—731no—
188C4×D4—1461no—
189#117—1461no—
190C2×C42—731no—
191C4⋊C8—732no—
192#102—732no—
193#102—732no—
194#102—732no—
195#102C2×D7312yescomplemented
196C22⋊C8—731no—
197C22⋊C8C2×D7311yescharacteristic
198#97—732no—
199C24—21no—
200C24—1461no—
201C2×Q8C22×D7311yescharacteristic
202C2×D4—21no—
203C2×D4—42no—
204C2×D4—2922no—
205C2×D4—2924no—
206C2×D4—2924no—
207C2×D4—732no—
208C2×D4—731no—
209C2×D4—1462no—
210C2×D4—1462no—
211C2×D4—1462no—
212C2×D4—1462no—
213C2×D4—1461no—
214C2×D4—1461no—
215C2×D4C22×D7312yes—
216C22×C4—731no—
217C22×C4—731no—
218C22×C4—1461no—
219C22×C4C22×D7311yescharacteristic
220SD16—42no—
221SD16—2922no—
222D8—2922no—
223D8—2922no—
224C2×C8—732no—
225C2×C8C22×D7312yes—
226C4⋊C4—21no—
227C4⋊C4—731no—
228C4⋊C4—1461no—
229C4⋊C4—1461no—
230C4⋊C4—1461no—
231C4⋊C4C22×D7311yescharacteristic
232C22⋊C4—21no—
233C22⋊C4—1461no—
234C22⋊C4—1461no—
235C22⋊C4—1461no—
236C22⋊C4—1461no—
237C42—731no—
238C42—731no—
239C42—731no—
240C42—731no—
241C42—1461no—
242C23—22no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—2922no—
247C23—2922no—
248C23—2922no—
249C23—1461no—
250C23—1462no—
251C23D4×D7311yescharacteristic
252Q8—22no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—2922no—
257D4—2922no—
258D4—2924no—
259D4—2924no—
260D4—2924no—
261D4—2924no—
262D4—1462no—
263D4—1462no—
264D4—1462no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—2922no—
269C2×C4—731no—
270C2×C4—731no—
271C2×C4—731no—
272C2×C4—731no—
273C2×C4—1461no—
274C2×C4—1462no—
275C2×C4—1462no—
276C2×C4D4×D7311yescharacteristic
277C2×C4C23×D7311yescharacteristic
278C8—22no—
279C8—1462no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—2922no—
287C22—2921no—
288C22—2921no—
289C22—2922no—
290C22—2922no—
291C22—2921no—
292C22—5844no—
293C22#1455661812yes—
294C22C2×D4×D7311yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—2921no—
299C4—732no—
300C4—1461no—
301C4—1461no—
302C4—1461no—
303C4#1455663612yes—
304C2—22no—
305C2—82no—
306C2—5842no—
307C2—5841no—
308C2#1798915211yescharacteristic
309C2AGL(1,ℤ/8)×D7311yescharacteristic
310C2C2×#1455661811yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#450×C73C2
socleC22×C73C22×D4
hypercenter#450D73
hypocenterC73#3217
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#14556587C2semidirect
2. #17989123C2semidirect
3. #17988973C2semidirect
4. #17988950C2semidirect
5. #17988785C2semidirect
6. #17988781C2semidirect
7. #17988737C2semidirect
8. #17988723C2semidirect
9. #17988721C2semidirect
10. #17988641C2semidirect
11. #450×C73C2semidirect
15. C2×#11924015C22semidirect
16. C2×D584C22semidirect
17. C2×#11924013C22semidirect
23. #14556582C22semidirect
24. #14556580C22semidirect
27. Q8×Dic73C22semidirect
28. #14556553C22semidirect
32. #14556520C22semidirect
33. #14556513C22semidirect
34. #14556512C22semidirect
35. #14556511C22semidirect
37. #14556501C22semidirect
39. C2×SD16×C73C22semidirect
41. #102×C73C22semidirect
156. C73#3217semidirect
164. #450D73semidirect
173. C2×SD16C2×D73semidirect
195. #102C2×D73semidirect