Finite Group Databasebeta

← #22622155

Subgroups — #22622155

Order 9344.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989308C211yesmaximal, characteristic, complemented
2D4×C22⋊D73C211yesmaximal, characteristic
3#17988932C211yesmaximal, characteristic, complemented
4#17988912C211yesmaximal, characteristic, complemented
5#17988910C211yesmaximal, characteristic, complemented
6#17988865C211yesmaximal, characteristic, complemented
7#17988835C211yesmaximal, characteristic, complemented
8#17988830C211yesmaximal, characteristic, complemented
9#17988785C211yesmaximal, characteristic, complemented
10#17988736C211yesmaximal, characteristic, complemented
11SD16×Dic73C211yesmaximal, characteristic, complemented
12#17988662C211yesmaximal, characteristic, complemented
13#17988592C211yesmaximal, characteristic, complemented
14#17988590C211yesmaximal, characteristic, complemented
15#450×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73—21no—
17C2×D4×D73C2211yescharacteristic
18C2×#11924015C2211yescharacteristic, complemented
19C2×#11924012C2211yescharacteristic, complemented
20C2×#11924011C2211yescharacteristic, complemented
21#14556590C2211yescharacteristic, complemented
22#14556587C2211yescharacteristic
23#14556586—21no—
24#14556584—21no—
25#14556577—21no—
26#14556567C2211yescharacteristic, complemented
27#14556565C2211yescharacteristic
28#14556563—21no—
29#14556562C2211yescharacteristic
30#14556560—21no—
31#14556559—21no—
32Q8×Dic73C2211yescharacteristic, complemented
33#14556556—21no—
34D4×Dic73C2211yescharacteristic
35C4×C22⋊D73C2211yescharacteristic
36#14556550C2211yescharacteristic, complemented
37#14556549C2211yescharacteristic, complemented
38#14556525C2211yescharacteristic, complemented
39#14556524C2211yescharacteristic, complemented
40#14556523C2211yescharacteristic, complemented
41#14556520C2211yescharacteristic, complemented
42#14556515C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic, complemented
45#14556512C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic, complemented
48#14556512C2211yescharacteristic, complemented
49#14556511C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C22×D4×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic, complemented
55C22⋊Q8×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C2×Dic146—21no—
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—44no—
68C2×C22⋊D73D411yescharacteristic
69D4×D73—22no—
70D4×D73—41no—
71C22×Dic73—21no—
72C2×C4×D73C2311yescharacteristic
73#11924015—41no—
74#11924012—41no—
75#11924011—41no—
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007D411yescharacteristic
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73D411yescharacteristic
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005D411yescharacteristic
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C24×C73—21no—
98C2×Q8×C73C2311yescharacteristic
99C2×D4×C73—22no—
100C2×D4×C73—21no—
101C2×D4×C73—41no—
102C2×D4×C73C2311yescharacteristic
103C2×D4×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105SD16×C73—22no—
106SD16×C73—41no—
107C2×C8×C73C2311yescharacteristic
108C2×C8×C73C2311yescharacteristic
109C4⋊C4×C73—21no—
110C4⋊C4×C73C2311yescharacteristic
111C22⋊C4×C73—21no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—42no—
115C23×C73—42no—
116C23×C73—81no—
117C23×C73C2×D411yescharacteristic
118C22×D73—21no—
119C22×D73—42no—
120C22×D73—42no—
121C22×D73—81no—
122C22×D73C2×D411yescharacteristic
123Q8×C73—21no—
124Q8×C73—21no—
125D4×C73—21no—
126D4×C73—21no—
127D4×C73—21no—
128D4×C73—42no—
129D4×C73#4112yes—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73C2×D411yescharacteristic
135C2×C4×C73C2411yescharacteristic
136C22⋊D73—22no—
137C22⋊D73—42no—
138C22⋊D73—42no—
139C22⋊D73—42no—
140C22⋊D73—42no—
141C22⋊D73—81no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—42no—
146C2×Dic73C2×D411yescharacteristic
147C2×Dic73C2×D411yescharacteristic
148C2×Dic73C2×D411yescharacteristic
149D292—21no—
150D292—21no—
151C4×D73—21no—
152C4×D73—21no—
153Dic146—42no—
154C8×C73—21no—
155C8×C73—21no—
156#10596831—21no—
157#10596831—21no—
158C22×C73—22no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—84no—
168C22×C73C22×D411yescharacteristic
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—21no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—41no—
175C2×D73—84no—
176C4×C73—21no—
177C4×C73—41no—
178C4×C73—41no—
179C4×C73C2×#4111yescharacteristic
180C4×C73H(5,𝔽2)11yescharacteristic
181Dic73—21no—
182Dic73—21no—
183Dic73—41no—
184Dic73—41no—
185Dic73—41no—
186Dic73AGL(1,ℤ/8)12yes—
187C2×C73—42no—
188C2×C73—41no—
189C2×C73—81no—
190C2×C73#54611yescharacteristic
191C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C73#57711yescharacteristic
193D73—41no—
194D73—81no—
195#3324—731nomaximal, Sylow
196C73#332411yescharacteristic, complemented, Sylow
197#556—731no—
198D42—731no—
199#486—731no—
200#482—731no—
201#482—731no—
202#474—731no—
203#468—731no—
204#468—731no—
205#460—731no—
206#450—731no—
207#450D7311yescharacteristic, complemented
208C4×SD16—731no—
209#436—731no—
210#418—731no—
211#418—731no—
212C22×D4—731no—
213C22×D4—1461no—
214C22×D4C2×D7311yescharacteristic
215C2×SD16—731no—
216C2×SD16C2×D7311yescharacteristic
217C2×SD16C2×D7311yescharacteristic, complemented
218C2×M16—731no—
219C2×M16—731no—
220C4⋊Q8—731no—
221#127—731no—
222#126—1461no—
223#126—1461no—
224#124—1461no—
225C22⋊Q8—731no—
226C22⋊Q8C2×D7311yescharacteristic, complemented
227#121—731no—
228#121—731no—
229#121—1461no—
230#120—1461no—
231#120—1461no—
232C4×Q8—731no—
233C4×Q8—1461no—
234C4×D4—731no—
235C4×D4—731no—
236#117—731no—
237#117—731no—
238#107—731no—
239#107—731no—
240#106—731no—
241C4⋊C8—731no—
242#103—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247#102—731no—
248#102—731no—
249#102—731no—
250#102C2×D7311yescharacteristic
251#102C2×D7311yescharacteristic, complemented
252C22⋊C8—731no—
253C22⋊C8C2×D7311yescharacteristic, complemented
254C4×C8—731no—
255C24—21no—
256C24—1461no—
257C2×Q8—1461no—
258C2×Q8C22×D7311yescharacteristic
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—2924no—
263C2×D4—2921no—
264C2×D4—731no—
265C2×D4—731no—
266C2×D4—1461no—
267C2×D4—1461no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4—1462no—
272C2×D4C22×D7311yescharacteristic
273C2×D4C22×D7311yescharacteristic
274C22×C4—731no—
275C22×C4—1461no—
276C22×C4C22×D7311yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—2921no—
280M16—2921no—
281M16—2921no—
282C2×C8—731no—
283C2×C8—731no—
284C2×C8C22×D7311yescharacteristic
285C2×C8C22×D7311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—731no—
288C4⋊C4—731no—
289C4⋊C4—731no—
290C4⋊C4—731no—
291C4⋊C4—1461no—
292C4⋊C4—1461no—
293C4⋊C4—1461no—
294C4⋊C4C22×D7311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—731no—
297C22⋊C4—731no—
298C22⋊C4—1461no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C42—731no—
305C42—1461no—
306C42—1461no—
307C42—1461no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—2922no—
314C23—2922no—
315C23—5841no—
316C23—731no—
317C23—1461no—
318C23D4×D7311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—2922no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—2922no—
327D4—2922no—
328D4—2922no—
329D4—2922no—
330D4—5841no—
331D4—1462no—
332D4—1461no—
333D4—1461no—
334D4#1192402712yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—2922no—
340C2×C4—731no—
341C2×C4—731no—
342C2×C4—731no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4D4×D7311yescharacteristic
349C2×C4C23×D7311yescharacteristic
350C8—21no—
351C8—21no—
352C8—1461no—
353C8—1461no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—2921no—
365C22—2921no—
366C22—2921no—
367C22—5844no—
368C22—1461no—
369C22—1461no—
370C22—1461no—
371C22C2×D4×D7311yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—2921no—
376C4—2921no—
377C4—2921no—
378C4—732no—
379C4—1461no—
380C4—1461no—
381C4C2×#1192402711yescharacteristic
382C4#1455663611yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—2921no—
387C2—5841no—
388C2#1798922411yescharacteristic
389C2AGL(1,ℤ/8)×D7311yescharacteristic
390C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#450×C73C2
socleC22×C73C22×D4
hypercenter#450D73
hypocenterC73#3324
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. #17989308C2semidirect
3. #17988932C2semidirect
4. #17988912C2semidirect
5. #17988910C2semidirect
6. #17988865C2semidirect
7. #17988835C2semidirect
8. #17988830C2semidirect
9. #17988785C2semidirect
10. #17988736C2semidirect
11. SD16×Dic73C2semidirect
12. #17988662C2semidirect
13. #17988592C2semidirect
14. #17988590C2semidirect
15. #450×C73C2semidirect
18. C2×#11924015C22semidirect
19. C2×#11924012C22semidirect
20. C2×#11924011C22semidirect
21. #14556590C22semidirect
26. #14556567C22semidirect
32. Q8×Dic73C22semidirect
36. #14556550C22semidirect
37. #14556549C22semidirect
38. #14556525C22semidirect
39. #14556524C22semidirect
40. #14556523C22semidirect
41. #14556520C22semidirect
42. #14556515C22semidirect
43. #14556513C22semidirect
44. #14556513C22semidirect
47. #14556512C22semidirect
48. #14556512C22semidirect
49. #14556511C22semidirect
50. #14556503C22semidirect
51. C8×Dic73C22semidirect
54. C2×SD16×C73C22semidirect
55. C22⋊Q8×C73C22semidirect
57. #102×C73C22semidirect
58. C22⋊C8×C73C22semidirect
196. C73#3324semidirect
207. #450D73semidirect
217. C2×SD16C2×D73semidirect
226. C22⋊Q8C2×D73semidirect
251. #102C2×D73semidirect
253. C22⋊C8C2×D73semidirect