Finite Group Databasebeta

← #22622071

Subgroups — #22622071

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
2#17989222C211yesmaximal, characteristic, complemented
3#17988910C211yesmaximal, characteristic, complemented
4#17988904C211yesmaximal, characteristic, complemented
5#17988884C211yesmaximal, characteristic, complemented
6#17988839C211yesmaximal, characteristic, complemented
7#17988822C211yesmaximal, characteristic, complemented
8#17988779C211yesmaximal, characteristic, complemented
9#17988722C211yesmaximal, characteristic, complemented
10#17988722C211yesmaximal, characteristic, complemented
11#17988700C211yesmaximal, characteristic, complemented
12#17988660C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic, complemented
14#102×D73C211yesmaximal, characteristic, complemented
15#490×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73—21no—
17C2×D4×D73C2211yescharacteristic
18C2×D4×D73C2211yescharacteristic
19C2×D584C2211yescharacteristic
20C2×#11924013C2211yescharacteristic, complemented
21C2×#11924013C2211yescharacteristic, complemented
22C2×#11924011C2211yescharacteristic, complemented
23C2×C8×D73C2211yescharacteristic, complemented
24#14556586—21no—
25#14556576—21no—
26#14556566—21no—
27#14556566C2211yescharacteristic, complemented
28#14556566C2211yescharacteristic, complemented
29#14556562—21no—
30#14556562C2211yescharacteristic
31#14556562C2211yescharacteristic
32#14556559—21no—
33#14556559—21no—
34C4×D292C2211yescharacteristic
35C4×D292C2211yescharacteristic
36C4×D292C2211yescharacteristic, complemented
37#14556553—21no—
38#14556549C2211yescharacteristic, complemented
39C4⋊C4×D73C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556523C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43C4⋊#10596831C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic, complemented
46#14556512C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic, complemented
48#14556511C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556503C2211yescharacteristic, complemented
52#127×C73C2211yescharacteristic
53#125×C73C2211yescharacteristic, complemented
54#102×C73C2211yescharacteristic, complemented
55#102×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic, complemented
58#97×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C23×D73—21no—
61C2×D292—21no—
62C2×D292—21no—
63C2×D292D411yescharacteristic
64C2×D292C2311yescharacteristic
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70D4×D73—22no—
71D4×D73—22no—
72D4×D73—41no—
73D4×D73—41no—
74D4×D73—44no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77C2×C4×D73—21no—
78C2×C4×D73C2311yescharacteristic
79C2×C4×D73C2311yescharacteristic
80D584—22no—
81#11924013—41no—
82#11924013—41no—
83#11924011—41no—
84C2×#10596831C2311yescharacteristic
85C2×#10596831C2311yescharacteristic
86C8×D73—41no—
87C4⋊Dic73D411yescharacteristic
88C4⋊Dic73C2311yescharacteristic
89C4⋊Dic73C2311yescharacteristic
90#11924007—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—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×C73—21no—
102C2×D4×C73—21no—
103C2×D4×C73C2311yescharacteristic
104C2×D4×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73—21no—
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C42×C73C2311yescharacteristic
112C23×C73—21no—
113C23×C73—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—21no—
126D4×C73—21no—
127D4×C73—21no—
128D4×C73—42no—
129D4×C73—81no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73C2×D411yescharacteristic
133C2×C4×C73C2×D411yescharacteristic
134C2×C4×C73C2411yescharacteristic
135C22⋊D73—42no—
136C22⋊D73—42no—
137C22⋊D73—42no—
138C22⋊D73—42no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143D292—22no—
144D292—21no—
145D292—21no—
146D292—21no—
147D292—42no—
148D292—81no—
149D292#4112yes—
150C4×D73—21no—
151C4×D73—21no—
152C4×D73—21no—
153C4×D73—21no—
154C4×D73—42no—
155C4×D73—81no—
156C4×D73—81no—
157C8×C73—21no—
158C8×C73—21no—
159#10596831—21no—
160#10596831—21no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73C22×D411yescharacteristic
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—22no—
172C2×D73—21no—
173C2×D73—21no—
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×C73C2×#4111yescharacteristic
187C4×C73H(5,𝔽2)11yescharacteristic
188Dic73—21no—
189Dic73—21no—
190Dic73—41no—
191Dic73—41no—
192C2×C73—81no—
193C2×C73—81no—
194C2×C73#54611yescharacteristic
195C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C73#57611yescharacteristic
197D73—22no—
198D73—41no—
199D73—42no—
200D73—81no—
201#3318—731nomaximal, Sylow
202C73#331811yescharacteristic, complemented, Sylow
203#553—731no—
204D42—731no—
205#490D7311yescharacteristic, complemented
206#482—731no—
207#481—731no—
208#478—731no—
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#127C2×D7311yescharacteristic
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—731no—
241C4×D4—1461no—
242#117—731no—
243C2×C4⋊C4—731no—
244#107—731no—
245#106—731no—
246#106—731no—
247C4⋊C8—731no—
248#102—731no—
249#102—731no—
250#102—731no—
251#102—731no—
252#102—731no—
253#102—731no—
254#102C2×D7311yescharacteristic, complemented
255#102C2×D7311yescharacteristic, complemented
256#102C2×D7311yescharacteristic, complemented
257#102C2×D7311yescharacteristic, complemented
258C22⋊C8—731no—
259C22⋊C8—731no—
260#97C2×D7311yescharacteristic, complemented
261C24—1461no—
262C24—1461no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—2924no—
266C2×D4—2921no—
267C2×D4—2921no—
268C2×D4—731no—
269C2×D4—731no—
270C2×D4—731no—
271C2×D4—1461no—
272C2×D4—1461no—
273C2×D4—1461no—
274C2×D4—1461no—
275C2×D4—1462no—
276C2×D4—1462no—
277C2×D4—1461no—
278C2×D4—1461no—
279C2×D4C22×D7311yescharacteristic
280C2×D4C22×D7311yescharacteristic
281C22×C4—731no—
282C22×C4—731no—
283C22×C4—1461no—
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—731no—
300C4⋊C4—1461no—
301C4⋊C4C22×D7311yescharacteristic
302C4⋊C4C22×D7311yescharacteristic
303C22⋊C4—731no—
304C22⋊C4—731no—
305C22⋊C4—1461no—
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—21no—
316C23—2922no—
317C23—2922no—
318C23—2922no—
319C23—2922no—
320C23—5841no—
321C23—5841no—
322C23—731no—
323C23—731no—
324C23—1461no—
325C23—1461no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—81no—
332D4—2922no—
333D4—2922no—
334D4—2922no—
335D4—2922no—
336D4—2922no—
337D4—5841no—
338D4—732no—
339D4—1462no—
340D4—1461no—
341D4—1461no—
342D4—1461no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—2922no—
346C2×C4—5841no—
347C2×C4—5841no—
348C2×C4—731no—
349C2×C4—731no—
350C2×C4—1461no—
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—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—2921no—
370C22—2921no—
371C22—2921no—
372C22—2921no—
373C22—2921no—
374C22—5844no—
375C22—5844no—
376C22—732no—
377C22—1461no—
378C22—1461no—
379C22—1462no—
380C22—1461no—
381C22—1461no—
382C22—1461no—
383C22C2×D4×D7311yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—2921no—
389C4—2921no—
390C4—1461no—
391C4—1461no—
392C4#41×D7311yescharacteristic
393C4#1455663711yescharacteristic
394C2—81no—
395C2—81no—
396C2—2922no—
397C2—2921no—
398C2—5841no—
399C2—1462no—
400C2#1798923011yescharacteristic
401C2AGL(1,ℤ/8)×D7311yescharacteristic
402C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#490×C73C2
socleC22×C73C22×D4
hypercenter#490D73
hypocenterC73#3318
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #17989290C2semidirect
2. #17989222C2semidirect
3. #17988910C2semidirect
4. #17988904C2semidirect
5. #17988884C2semidirect
6. #17988839C2semidirect
7. #17988822C2semidirect
8. #17988779C2semidirect
9. #17988722C2semidirect
10. #17988722C2semidirect
11. #17988700C2semidirect
12. #17988660C2semidirect
13. #17988590C2semidirect
14. #102×D73C2semidirect
15. #490×C73C2semidirect
20. C2×#11924013C22semidirect
21. C2×#11924013C22semidirect
22. C2×#11924011C22semidirect
23. C2×C8×D73C22semidirect
27. #14556566C22semidirect
28. #14556566C22semidirect
36. C4×D292C22semidirect
38. #14556549C22semidirect
39. C4⋊C4×D73C22semidirect
40. #14556524C22semidirect
41. #14556523C22semidirect
42. #14556522C22semidirect
43. C4⋊#10596831C22semidirect
45. #14556513C22semidirect
46. #14556512C22semidirect
47. #14556512C22semidirect
50. #14556503C22semidirect
51. #14556503C22semidirect
53. #125×C73C22semidirect
54. #102×C73C22semidirect
55. #102×C73C22semidirect
56. #102×C73C22semidirect
57. #102×C73C22semidirect
58. #97×C73C22semidirect
202. C73#3318semidirect
205. #490D73semidirect
228. #125C2×D73semidirect
254. #102C2×D73semidirect
255. #102C2×D73semidirect
256. #102C2×D73semidirect
257. #102C2×D73semidirect
260. #97C2×D73semidirect