Finite Group Databasebeta

← #22622069

Subgroups — #22622069

Order 9344.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989290C211yesmaximal, characteristic, complemented
2D4×D292C211yesmaximal, characteristic, complemented
3#17988953C211yesmaximal, characteristic, complemented
4#17988914C211yesmaximal, characteristic, complemented
5#17988907C211yesmaximal, characteristic, complemented
6#17988841C211yesmaximal, characteristic, complemented
7#17988824C211yesmaximal, characteristic, complemented
8#17988783C211yesmaximal, characteristic, complemented
9#17988722C211yesmaximal, characteristic, complemented
10#17988722C211yesmaximal, characteristic, complemented
11#17988697C211yesmaximal, characteristic, complemented
12#17988657C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic, complemented
14#102×D73C211yesmaximal, characteristic, complemented
15#478×C73C211yesmaximal, characteristic, complemented
16C22×D292—21no—
17C2×D4×D73C2211yescharacteristic
18C2×D4×D73C2211yescharacteristic
19C2×D584C2211yescharacteristic, complemented
20C2×D584C2211yescharacteristic, complemented
21C2×#11924013C2211yescharacteristic
22C2×#11924011C2211yescharacteristic, complemented
23C2×C8×D73C2211yescharacteristic, complemented
24#14556588C2211yescharacteristic
25#14556586—21no—
26#14556576—21no—
27#14556566—21no—
28#14556566C2211yescharacteristic
29#14556566C2211yescharacteristic
30#14556566C2211yescharacteristic, complemented
31#14556566C2211yescharacteristic, complemented
32#14556565—21no—
33#14556561—21no—
34#14556561—21no—
35C4×D292C2211yescharacteristic
36C4×D292C2211yescharacteristic, complemented
37#14556553—21no—
38#14556549C2211yescharacteristic, complemented
39C4⋊C4×D73C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41#14556513C2211yescharacteristic, complemented
42#14556513C2211yescharacteristic, complemented
43#14556512C2211yescharacteristic
44#14556511C2211yescharacteristic, complemented
45#14556511C2211yescharacteristic, complemented
46#14556511C2211yescharacteristic, complemented
47#14556511C2211yescharacteristic, complemented
48#14556511C2211yescharacteristic, complemented
49#14556503C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic, complemented
51#14556502C2211yescharacteristic, complemented
52#125×C73C2211yescharacteristic, complemented
53C4×D4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56C4⋊C8×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C23×D73—21no—
60C23×D73—21no—
61C2×D292—21no—
62C2×D292—21no—
63C2×D292—21no—
64C2×D292—21no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292—44no—
68C2×D292D411yescharacteristic
69C2×D292C2311yescharacteristic
70C2×D292C2311yescharacteristic
71C2×D292C2311yescharacteristic
72C2×C22⋊D73—21no—
73C2×C22⋊D73—21no—
74D4×D73—22no—
75D4×D73—22no—
76D4×D73—41no—
77D4×D73—41no—
78C2×C4×D73—21no—
79C2×C4×D73—21no—
80C2×C4×D73C2311yescharacteristic
81C2×C4×D73C2311yescharacteristic
82D584—41no—
83D584—41no—
84#11924013—22no—
85#11924011—41no—
86C2×#10596831C2311yescharacteristic
87C2×#10596831C2311yescharacteristic
88C8×D73—41no—
89C4⋊Dic73D411yescharacteristic
90C4⋊Dic73C2311yescharacteristic
91#11924007—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005D411yescharacteristic
99#11924005D411yescharacteristic
100C4×Dic73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73—21no—
106C4⋊C4×C73—21no—
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C42×C73C2311yescharacteristic
112C23×C73—21no—
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—42no—
117C22×D73—42no—
118C22×D73—42no—
119C22×D73—42no—
120C22×D73—81no—
121C22×D73—81no—
122C22×D73C2×D411yescharacteristic
123C22×D73C2×D411yescharacteristic
124D4×C73—21no—
125D4×C73#4112yes—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—42no—
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2411yescharacteristic
133C22⋊D73—42no—
134C22⋊D73—42no—
135C2×Dic73—21no—
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138D292—22no—
139D292—21no—
140D292—21no—
141D292—21no—
142D292—21no—
143D292—21no—
144D292—21no—
145D292—42no—
146D292—42no—
147D292—42no—
148D292—42no—
149D292—81no—
150D292—81no—
151C4×D73—21no—
152C4×D73—21no—
153C4×D73—21no—
154C4×D73—21no—
155C4×D73—81no—
156C4×D73—81no—
157C8×C73—21no—
158C8×C73—21no—
159#10596831—21no—
160#10596831—21no—
161C22×C73—22no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73C22×D411yescharacteristic
165C2×D73—21no—
166C2×D73—21no—
167C2×D73—21no—
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—41no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—41no—
177C2×D73—41no—
178C2×D73—41no—
179C2×D73—84no—
180C2×D73—84no—
181C2×D73AGL(1,ℤ/8)12yes—
182C4×C73—21no—
183C4×C73—21no—
184C4×C73—41no—
185C4×C73—41no—
186C4×C73—41no—
187C4×C73C2×#4111yescharacteristic
188C4×C73H(5,𝔽2)11yescharacteristic
189Dic73—21no—
190Dic73—21no—
191Dic73—41no—
192C2×C73—42no—
193C2×C73#54611yescharacteristic
194C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C73#57611yescharacteristic
196D73—22no—
197D73—41no—
198D73—81no—
199D73—81no—
200D73—81no—
201#3318—731nomaximal, Sylow
202C73#331811yescharacteristic, complemented, Sylow
203#553—731no—
204D42—731no—
205#490—731no—
206#482—731no—
207#481—731no—
208#478D7311yescharacteristic, complemented
209#469—731no—
210#466—731no—
211#459—731no—
212#447—731no—
213#447—731no—
214#442—731no—
215#435—731no—
216#418—731no—
217C2×#102—731no—
218C22×D4—731no—
219C22×D4—731no—
220C22×D4—1461no—
221C2×D8—731no—
222C2×D8—731no—
223C2×D8—731no—
224C2×M16—731no—
225C22×C8—731no—
226#127—731no—
227#126—1461no—
228#125C2×D7311yescharacteristic, complemented
229#123—1461no—
230#121—731no—
231#121—731no—
232#121—731no—
233#121—731no—
234#121—1461no—
235#121—1461no—
236#120—1461no—
237#120—1461no—
238C4×D4—731no—
239C4×D4—731no—
240C4×D4—1461no—
241C4×D4C2×D7311yescharacteristic
242#117—731no—
243C2×C4⋊C4—731no—
244#107C2×D7311yescharacteristic, complemented
245#106—731no—
246#106C2×D7311yescharacteristic, complemented
247C4⋊C8C2×D7311yescharacteristic, complemented
248#102—731no—
249#102—731no—
250#102—731no—
251#102—731no—
252#102—731no—
253#102—731no—
254#102—731no—
255#102—731no—
256#102C2×D7311yescharacteristic
257#102C2×D7311yescharacteristic
258C22⋊C8—731no—
259C22⋊C8—731no—
260#97—731no—
261C24—1461no—
262C24—1461no—
263C2×D4—2924no—
264C2×D4—2921no—
265C2×D4—2921no—
266C2×D4—731no—
267C2×D4—731no—
268C2×D4—731no—
269C2×D4—731no—
270C2×D4—1461no—
271C2×D4—1461no—
272C2×D4—1461no—
273C2×D4—1461no—
274C2×D4—1461no—
275C2×D4—1461no—
276C2×D4—1462no—
277C2×D4—1462no—
278C2×D4—1461no—
279C2×D4—1461no—
280C2×D4C22×D7311yescharacteristic
281C22×C4—21no—
282C22×C4—731no—
283C22×C4—731no—
284C22×C4—1461no—
285C22×C4—1461no—
286D8—2921no—
287D8—2921no—
288D8—1462no—
289M16—2921no—
290C2×C8—2921no—
291C2×C8—731no—
292C2×C8—731no—
293C2×C8C22×D7311yescharacteristic
294C2×C8C22×D7311yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—731no—
298C4⋊C4—731no—
299C4⋊C4—1461no—
300C4⋊C4C22×D7311yescharacteristic
301C4⋊C4C22×D7311yescharacteristic
302C4⋊C4C22×D7311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—731no—
305C22⋊C4—731no—
306C22⋊C4—1461no—
307C22⋊C4—1461no—
308C22⋊C4—1461no—
309C22⋊C4—1461no—
310C22⋊C4—1461no—
311C22⋊C4—1461no—
312C42—1461no—
313C42C22×D7311yescharacteristic
314C23—21no—
315C23—2922no—
316C23—2922no—
317C23—2922no—
318C23—2922no—
319C23—5841no—
320C23—5841no—
321C23—731no—
322C23—731no—
323C23—1461no—
324C23—1461no—
325C23—1461no—
326D4—21no—
327D4—2922no—
328D4—2922no—
329D4—2922no—
330D4—2922no—
331D4—2922no—
332D4—2922no—
333D4—5841no—
334D4—5841no—
335D4—1462no—
336D4—1461no—
337D4—1461no—
338D4—1461no—
339D4—1461no—
340D4—1461no—
341D4—1461no—
342D4#1192402912yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—5841no—
348C2×C4—5841no—
349C2×C4—731no—
350C2×C4—731no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4D4×D7311yescharacteristic
357C2×C4D4×D7311yescharacteristic
358C2×C4C23×D7311yescharacteristic
359C8—21no—
360C8—21no—
361C8—1461no—
362C8—1461no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—2921no—
367C22—2921no—
368C22—2921no—
369C22—2921no—
370C22—2921no—
371C22—2921no—
372C22—2921no—
373C22—2921no—
374C22—2921no—
375C22—5844no—
376C22—5844no—
377C22—732no—
378C22—1461no—
379C22—1461no—
380C22—1461no—
381C22—1461no—
382C22—1461no—
383C22C2×D4×D7311yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—2921no—
390C4—1461no—
391C4—1461no—
392C4C2×#1192402911yescharacteristic
393C4#1455663711yescharacteristic
394C2—42no—
395C2—2921no—
396C2—5841no—
397C2—5841no—
398C2—5841no—
399C2—1462no—
400C2#1798922811yescharacteristic
401C2AGL(1,ℤ/8)×D7311yescharacteristic
402C2#1798938911yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#478×C73C2
socleC22×C73C22×D4
hypercenter#478D73
hypocenterC73#3318
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #17989290C2semidirect
2. D4×D292C2semidirect
3. #17988953C2semidirect
4. #17988914C2semidirect
5. #17988907C2semidirect
6. #17988841C2semidirect
7. #17988824C2semidirect
8. #17988783C2semidirect
9. #17988722C2semidirect
10. #17988722C2semidirect
11. #17988697C2semidirect
12. #17988657C2semidirect
13. #17988590C2semidirect
14. #102×D73C2semidirect
15. #478×C73C2semidirect
19. C2×D584C22semidirect
20. C2×D584C22semidirect
22. C2×#11924011C22semidirect
23. C2×C8×D73C22semidirect
30. #14556566C22semidirect
31. #14556566C22semidirect
36. C4×D292C22semidirect
38. #14556549C22semidirect
39. C4⋊C4×D73C22semidirect
40. #14556522C22semidirect
41. #14556513C22semidirect
42. #14556513C22semidirect
44. #14556511C22semidirect
45. #14556511C22semidirect
46. #14556511C22semidirect
47. #14556511C22semidirect
48. #14556511C22semidirect
49. #14556503C22semidirect
50. #14556503C22semidirect
51. #14556502C22semidirect
52. #125×C73C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
56. C4⋊C8×C73C22semidirect
202. C73#3318semidirect
208. #478D73semidirect
228. #125C2×D73semidirect
244. #107C2×D73semidirect
246. #106C2×D73semidirect
247. C4⋊C8C2×D73semidirect