Finite Group Databasebeta

← #22619983

Subgroups — #22619983

Order 9344.

454 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989122C211yesmaximal, characteristic, complemented
2C4×D4×D73C211yesmaximal, characteristic, complemented
3#17988924C211yesmaximal, characteristic, complemented
4#17988907C211yesmaximal, characteristic, complemented
5#17988884C211yesmaximal, characteristic, complemented
6#17988803C211yesmaximal, characteristic, complemented
7#17988802C211yesmaximal, characteristic, complemented
8#17988739C211yesmaximal, characteristic, complemented
9#17988722C211yesmaximal, characteristic
10#17988678C211yesmaximal, characteristic, complemented
11#17988674C211yesmaximal, characteristic, complemented
12#17988669C211yesmaximal, characteristic, complemented
13#17988667C211yesmaximal, characteristic, complemented
14#17988639C211yesmaximal, characteristic, complemented
15#478×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73C2211yescharacteristic
17C22×C4×D73—21no—
18C2×#11924017C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×D584C2211yescharacteristic
21C2×#11924013C2211yescharacteristic
22#14556586—21no—
23#14556579C2211yescharacteristic, complemented
24#14556576—21no—
25#14556571C2211yescharacteristic
26#14556566C2211yescharacteristic
27#14556556C2211yescharacteristic, complemented
28C4×D292C2211yescharacteristic
29D4×Dic73C2211yescharacteristic
30#14556553—21no—
31#14556553C2211yescharacteristic
32#14556553C2211yescharacteristic, complemented
33C4×C22⋊D73—21no—
34#14556551—21no—
35#14556549—21no—
36C4⋊C4×D73C2211yescharacteristic
37C22⋊C4×D73—21no—
38C42×D73C2211yescharacteristic
39#14556524C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41C4⋊#10596831C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556514C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic, complemented
45#14556511C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic, complemented
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50C8×Dic73C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, 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—
60C2×Dic146C2311yescharacteristic
61C2×D292—21no—
62C2×D292C2311yescharacteristic
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65D4×D73—22no—
66D4×D73—22no—
67C22×Dic73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73—44no—
73C2×C4×D73D411yescharacteristic
74C2×C4×D73D411yescharacteristic
75C2×C4×D73C2311yescharacteristic
76#11924017—22no—
77#11924016—22no—
78D584—22no—
79#11924013—22no—
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84#11924007—21no—
85#11924007—21no—
86C22⋊Dic73—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94C4×Dic73—21no—
95C4×Dic73D411yescharacteristic
96C4×Dic73D411yescharacteristic
97C4×Dic73C2311yescharacteristic
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73—21no—
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73—21no—
103C4⋊C4×C73—21no—
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C22⋊C4×C73—21no—
108C42×C73C2311yescharacteristic
109C23×C73—21no—
110C22×D73—24no—
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—42no—
114C22×D73—42no—
115C22×D73C2×D411yescharacteristic
116D4×C73—21no—
117D4×C73#4112yes—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—42no—
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2411yescharacteristic
125C22⋊D73—24no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—42no—
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132D292—21no—
133D292—21no—
134D292—21no—
135D292—42no—
136D292#4112yes—
137C4×D73—22no—
138C4×D73—21no—
139C4×D73—21no—
140C4×D73—22no—
141C4×D73—42no—
142C4×D73—42no—
143C4×D73—42no—
144C4×D73—42no—
145Dic146—21no—
146Dic146—21no—
147C8×C73—21no—
148C8×C73—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—22no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73C22×D411yescharacteristic
155C2×D73—21no—
156C2×D73—21no—
157C2×D73—22no—
158C2×D73—48no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—41no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73#13512yes—
165C4×C73—21no—
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73C2×#4111yescharacteristic
171C4×C73C2×#4111yescharacteristic
172Dic73—21no—
173Dic73—21no—
174Dic73—41no—
175Dic73—41no—
176Dic73AGL(1,ℤ/8)12yes—
177C2×C73—42no—
178C2×C73#52511yescharacteristic
179C2×C73C2×#13511yescharacteristic
180C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
181D73—22no—
182D73—42no—
183D73—81no—
184#3105—731nomaximal, Sylow
185C73#310511yescharacteristic, complemented, Sylow
186#529—731no—
187C2×C4×D4—731no—
188#484—731no—
189#481—731no—
190#478—731no—
191#478D7311yescharacteristic, complemented
192#463—731no—
193#463—731no—
194#450—731no—
195#447—731no—
196C4×SD16—731no—
197C4×SD16—731no—
198C4×D8—731no—
199C4×D8—731no—
200#431—731no—
201C22×D4—731no—
202C23×C4—1461no—
203C2×SD16—731no—
204C2×SD16—731no—
205C2×D8—731no—
206C2×D8—731no—
207#126—1461no—
208#125C2×D7311yescharacteristic, complemented
209#124—731no—
210#123—1461no—
211C22⋊Q8—731no—
212#121—731no—
213C4×Q8—731no—
214C4×D4—731no—
215C4×D4—731no—
216C4×D4—731no—
217C4×D4—731no—
218C4×D4—1461no—
219C4×D4—1461no—
220C4×D4—1461no—
221C4×D4C2×D7311yescharacteristic
222#117—1461no—
223C2×C4⋊C4—731no—
224C2×C22⋊C4—1461no—
225C2×C42—731no—
226#107—731no—
227#107C2×D7311yescharacteristic, complemented
228#106—731no—
229#106C2×D7311yescharacteristic, complemented
230C4⋊C8—731no—
231C4⋊C8C2×D7311yescharacteristic, complemented
232#103—731no—
233#103—731no—
234#102—731no—
235#102—731no—
236#102—731no—
237#102—731no—
238#102C2×D7311yescharacteristic
239#102C2×D7311yescharacteristic
240C22⋊C8—731no—
241C22⋊C8—731no—
242C4×C8—731no—
243C4×C8—731no—
244C24—1461no—
245C2×Q8—731no—
246C2×D4—731no—
247C2×D4—731no—
248C2×D4—1461no—
249C2×D4—1461no—
250C2×D4—1462no—
251C2×D4—1462no—
252C2×D4C22×D7311yescharacteristic
253C22×C4—21no—
254C22×C4—2924no—
255C22×C4—731no—
256C22×C4—731no—
257C22×C4—731no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4—1461no—
263SD16—1462no—
264SD16—1462no—
265D8—1462no—
266D8—1462no—
267C2×C8—731no—
268C2×C8—731no—
269C2×C8C22×D7311yescharacteristic
270C2×C8C22×D7311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—731no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4C22×D7311yescharacteristic
278C4⋊C4C22×D7311yescharacteristic
279C4⋊C4C22×D7311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C42—731no—
290C42—731no—
291C42—731no—
292C42—1461no—
293C42C22×D7311yescharacteristic
294C23—21no—
295C23—2922no—
296C23—2922no—
297C23—731no—
298C23—1464no—
299C23—1461no—
300C23—1461no—
301Q8—1461no—
302Q8—1461no—
303D4—21no—
304D4—2922no—
305D4—732no—
306D4—1464no—
307D4—1461no—
308D4—1461no—
309D4—1461no—
310D4#1192402912yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—2922no—
316C2×C4—2922no—
317C2×C4—2922no—
318C2×C4—2922no—
319C2×C4—2922no—
320C2×C4—731no—
321C2×C4—731no—
322C2×C4—731no—
323C2×C4—1462no—
324C2×C4—1462no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4D4×D7311yescharacteristic
330C2×C4D4×D7311yescharacteristic
331C2×C4C23×D7311yescharacteristic
332C8—21no—
333C8—21no—
334C8—1461no—
335C8—1461no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—2928no—
340C22—2921no—
341C22—2921no—
342C22—2921no—
343C22—2921no—
344C22—2921no—
345C22—732no—
346C22—1462no—
347C22—1461no—
348C22—1461no—
349C22C2×D4×D7311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—2921no—
356C4—2921no—
357C4—732no—
358C4—1461no—
359C4—1461no—
360C4#41×D7311yescharacteristic
361C4C2×#1192402911yescharacteristic
362C2—42no—
363C2—2922no—
364C2—5841no—
365C2—1462no—
366C2#1798910011yescharacteristic
367C2#135×D7311yescharacteristic
368C2AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#478×C73C2
socleC22×C73C22×D4
hypercenter#478D73
hypocenterC73#3105
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. #17989122C2semidirect
2. C4×D4×D73C2semidirect
3. #17988924C2semidirect
4. #17988907C2semidirect
5. #17988884C2semidirect
6. #17988803C2semidirect
7. #17988802C2semidirect
8. #17988739C2semidirect
10. #17988678C2semidirect
11. #17988674C2semidirect
12. #17988669C2semidirect
13. #17988667C2semidirect
14. #17988639C2semidirect
15. #478×C73C2semidirect
23. #14556579C22semidirect
27. #14556556C22semidirect
32. #14556553C22semidirect
39. #14556524C22semidirect
40. #14556522C22semidirect
41. C4⋊#10596831C22semidirect
42. #14556516C22semidirect
43. #14556514C22semidirect
44. #14556513C22semidirect
47. #14556511C22semidirect
50. C8×Dic73C22semidirect
51. C8×Dic73C22semidirect
52. #125×C73C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
56. C4⋊C8×C73C22semidirect
185. C73#3105semidirect
191. #478D73semidirect
208. #125C2×D73semidirect
227. #107C2×D73semidirect
229. #106C2×D73semidirect
231. C4⋊C8C2×D73semidirect