Finite Group Databasebeta

← #22620848

Subgroups — #22620848

Order 9344.

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

normal subgroups only

This group has 532 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#17989134C211yesmaximal, characteristic, complemented
2#127×D73C211yesmaximal, characteristic, complemented
3#17988962C212yesmaximal, complemented
4#17988932C212yesmaximal, complemented
5#17988783C211yesmaximal, characteristic, complemented
6#17988782C211yesmaximal, characteristic, complemented
7#17988779C211yesmaximal, characteristic, complemented
8#17988722C212yesmaximal, complemented
9#17988719C212yesmaximal, complemented
10#17988639C211yesmaximal, characteristic, complemented
11#459×C73C211yesmaximal, characteristic, complemented
12C2×#11924028—21no—
13C2×D4×D73—21no—
14C2×D4×D73—21no—
15C2×D4×D73C2212yes—
16C2×D584C2212yescomplemented
17C2×#11924013C2212yescomplemented
18C2×#11924013C2212yescomplemented
19#14556590C2211yescharacteristic, complemented
20#14556588C2211yescharacteristic
21#14556587—21no—
22#14556587—21no—
23#14556587C2212yes—
24#14556587C2211yescharacteristic, complemented
25#14556577—21no—
26#14556566C2211yescharacteristic
27#14556564—21no—
28#14556562C2211yescharacteristic
29C4×D292C2211yescharacteristic, complemented
30C4×C22⋊D73—21no—
31C42×D73C2211yescharacteristic
32C4⋊#10596831C2211yescharacteristic, complemented
33#14556513C2212yescomplemented
34#14556512C2212yescomplemented
35#14556511C2212yescomplemented
36#14556503C2212yes—
37C8×Dic73C2212yescomplemented
38C2×D8×C73C2212yescomplemented
39#127×C73C2211yescharacteristic
40C4×D4×C73C2211yescharacteristic, complemented
41C4⋊C8×C73C2211yescharacteristic, complemented
42#102×C73C2212yescomplemented
43C23×D73—22no—
44#11924028—44no—
45C2×Dic146—21no—
46C2×D292—21no—
47C2×D292—21no—
48C2×D292—21no—
49C2×D292C2312yes—
50C2×D292C2311yescharacteristic
51C2×C22⋊D73—21no—
52C2×C22⋊D73—21no—
53C2×C22⋊D73—21no—
54C2×C22⋊D73—22no—
55C2×C22⋊D73—22no—
56C2×C22⋊D73—22no—
57D4×D73—42no—
58D4×D73—42no—
59D4×D73—44no—
60D4×D73—44no—
61C2×C4×D73—21no—
62C2×C4×D73D411yescharacteristic
63C2×C4×D73D411yescharacteristic
64C2×C4×D73C2311yescharacteristic
65D584—42no—
66#11924013—42no—
67#11924013—42no—
68C2×#10596831C2312yes—
69C4⋊Dic73C2311yescharacteristic
70#11924007—21no—
71C22⋊Dic73—21no—
72#11924005—21no—
73#11924005—21no—
74C4×Dic73D411yescharacteristic
75C4×Dic73D411yescharacteristic
76C4×Dic73C2311yescharacteristic
77C2×D4×C73—21no—
78C2×D4×C73—21no—
79C2×D4×C73C2312yes—
80C2×D4×C73C2311yescharacteristic
81C22×C4×C73—21no—
82D8×C73—42no—
83C2×C8×C73C2312yes—
84C4⋊C4×C73C2311yescharacteristic
85C22⋊C4×C73—21no—
86C42×C73C2311yescharacteristic
87C23×C73—21no—
88C23×C73—22no—
89C22×D73—21no—
90C22×D73—22no—
91C22×D73—44no—
92C22×D73—44no—
93C22×D73—44no—
94C22×D73C2×D411yescharacteristic
95D4×C73—21no—
96D4×C73—22no—
97D4×C73—21no—
98D4×C73—22no—
99D4×C73—42no—
100D4×C73—42no—
101C2×C4×C73—21no—
102C2×C4×C73—42no—
103C2×C4×C73C2×D411yescharacteristic
104C2×C4×C73C2×D411yescharacteristic
105C2×C4×C73C2411yescharacteristic
106C22⋊D73—44no—
107C22⋊D73—42no—
108C22⋊D73—44no—
109C22⋊D73—42no—
110C22⋊D73—44no—
111C22⋊D73—42no—
112C2×Dic73—21no—
113C2×Dic73C2×D411yescharacteristic
114C2×Dic73C2×D411yescharacteristic
115C2×Dic73C2×D411yescharacteristic
116D292—21no—
117D292—22no—
118D292—21no—
119D292—22no—
120D292—42no—
121D292—42no—
122D292—42no—
123C4×D73—21no—
124C4×D73—21no—
125C4×D73—22no—
126C4×D73—42no—
127C4×D73D814yescomplemented
128Dic146—42no—
129C8×C73—22no—
130#10596831—22no—
131C22×C73—42no—
132C22×C73—41no—
133C22×C73—41no—
134C22×C73—42no—
135C22×C73—42no—
136C22×C73—41no—
137C22×C73C22×D411yescharacteristic
138C2×D73—21no—
139C2×D73—21no—
140C2×D73—42no—
141C2×D73—41no—
142C2×D73—41no—
143C2×D73—42no—
144C2×D73—42no—
145C2×D73—41no—
146C2×D73—88no—
147C2×D73C2×D812yes—
148C4×C73—21no—
149C4×C73—41no—
150C4×C73C2×D812yes—
151C4×C73H(5,𝔽2)11yescharacteristic
152C4×C73H(5,𝔽2)11yescharacteristic
153Dic73—21no—
154Dic73—41no—
155Dic73C2×D812yes—
156Dic73AGL(1,ℤ/8)12yes—
157C2×C73—82no—
158C2×C73—81no—
159C2×C73#53511yescharacteristic
160C2×C73C22×D811yescharacteristic
161C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
162D73—22no—
163D73—81no—
164D73—82no—
165#3205—731nomaximal, Sylow
166C73#320511yescharacteristic, complemented, Sylow
167#532—731no—
168C2×#127—731no—
169#493—732no—
170#486—732no—
171#459—731no—
172#459—731no—
173#459—731no—
174#459D7311yescharacteristic, complemented
175#447—732no—
176#447—732no—
177#431—731no—
178C2×#41—1461no—
179C22×D4—732no—
180C22×D4—1461no—
181C22×D4—1461no—
182C2×D8—732no—
183C2×D8—732no—
184C2×D8—732no—
185C2×D8C2×D7312yescomplemented
186C4⋊Q8—731no—
187#127—732no—
188#127—731no—
189#127—731no—
190#127—1461no—
191#127—1461no—
192#127C2×D7311yescharacteristic
193#124—1461no—
194#121—731no—
195#121—731no—
196#121—1461no—
197C4×D4—731no—
198C4×D4—1461no—
199C4×D4C2×D7311yescharacteristic, complemented
200C2×C42—731no—
201C4⋊C8—731no—
202C4⋊C8C2×D7311yescharacteristic, complemented
203#102—732no—
204#102—732no—
205#102—732no—
206#102C2×D7312yescomplemented
207C22⋊C8—732no—
208C4×C8—732no—
209C24—1462no—
210#41—2924no—
211C2×Q8—1461no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—2924no—
215C2×D4—2922no—
216C2×D4—2922no—
217C2×D4—2924no—
218C2×D4—732no—
219C2×D4—731no—
220C2×D4—1461no—
221C2×D4—1461no—
222C2×D4—1461no—
223C2×D4—1462no—
224C2×D4—1462no—
225C2×D4—1462no—
226C2×D4—1461no—
227C2×D4—1461no—
228C2×D4—1461no—
229C2×D4C22×D7312yes—
230C2×D4C22×D7311yescharacteristic
231C22×C4—21no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—731no—
235C22×C4—1461no—
236D8—42no—
237D8—2922no—
238D8—2922no—
239D8—2922no—
240C2×C8—732no—
241C2×C8C22×D7312yes—
242C4⋊C4—731no—
243C4⋊C4—1461no—
244C4⋊C4C22×D7311yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—1461no—
247C22⋊C4—1461no—
248C22⋊C4—1461no—
249C42—731no—
250C42—731no—
251C42—731no—
252C42C22×D7311yescharacteristic
253C23—21no—
254C23—22no—
255C23—2924no—
256C23—2924no—
257C23—2924no—
258C23—731no—
259C23—1461no—
260C23—1462no—
261Q8—2922no—
262D4—21no—
263D4—22no—
264D4—21no—
265D4—22no—
266D4—42no—
267D4—42no—
268D4—2922no—
269D4—2922no—
270D4—2922no—
271D4—2924no—
272D4—2924no—
273D4—2922no—
274D4—2922no—
275D4—2924no—
276D4—2922no—
277D4—1461no—
278D4—1462no—
279D4—1461no—
280D4—1462no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—2922no—
284C2×C4—731no—
285C2×C4—731no—
286C2×C4—734no—
287C2×C4—731no—
288C2×C4—1462no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4D4×D7311yescharacteristic
293C2×C4D4×D7311yescharacteristic
294C2×C4C23×D7311yescharacteristic
295C8—22no—
296C8—1462no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—2922no—
304C22—2921no—
305C22—2921no—
306C22—2922no—
307C22—2922no—
308C22—2921no—
309C22—5848no—
310C22—732no—
311C22—1461no—
312C22—1461no—
313C22C2×D4×D7311yescharacteristic
314C4—21no—
315C4—41no—
316C4—2921no—
317C4—732no—
318C4—732no—
319C4—1461no—
320C4D8×D7312yes—
321C4#1455663611yescharacteristic
322C4#1455663711yescharacteristic
323C2—82no—
324C2—81no—
325C2—5842no—
326C2—5841no—
327C2—1462no—
328C2#1798915311yescharacteristic
329C2C2×D8×D7311yescharacteristic
330C2AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#459×C73C2
socleC22×C73C22×D4
hypercenter#459D73
hypocenterC73#3205
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. #17989134C2semidirect
2. #127×D73C2semidirect
3. #17988962C2semidirect
4. #17988932C2semidirect
5. #17988783C2semidirect
6. #17988782C2semidirect
7. #17988779C2semidirect
8. #17988722C2semidirect
9. #17988719C2semidirect
10. #17988639C2semidirect
11. #459×C73C2semidirect
16. C2×D584C22semidirect
17. C2×#11924013C22semidirect
18. C2×#11924013C22semidirect
19. #14556590C22semidirect
24. #14556587C22semidirect
29. C4×D292C22semidirect
32. C4⋊#10596831C22semidirect
33. #14556513C22semidirect
34. #14556512C22semidirect
35. #14556511C22semidirect
37. C8×Dic73C22semidirect
38. C2×D8×C73C22semidirect
40. C4×D4×C73C22semidirect
41. C4⋊C8×C73C22semidirect
42. #102×C73C22semidirect
127. C4×D73D8semidirect
166. C73#3205semidirect
174. #459D73semidirect
185. C2×D8C2×D73semidirect
199. C4×D4C2×D73semidirect
202. C4⋊C8C2×D73semidirect
206. #102C2×D73semidirect