Finite Group Databasebeta

← #22620068

Subgroups — #22620068

Order 9344.

450 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#17989116C211yesmaximal, characteristic, complemented
2C4×D4×D73C211yesmaximal, characteristic, complemented
3#17988916C211yesmaximal, characteristic, complemented
4#17988899C211yesmaximal, characteristic, complemented
5#17988888C211yesmaximal, characteristic, complemented
6#17988887C211yesmaximal, characteristic, complemented
7#17988799C211yesmaximal, characteristic, complemented
8#17988736C211yesmaximal, characteristic, complemented
9#17988719C211yesmaximal, characteristic
10#17988699C211yesmaximal, characteristic, complemented
11#17988696C211yesmaximal, characteristic, complemented
12#17988690C211yesmaximal, characteristic, complemented
13#17988688C211yesmaximal, characteristic, complemented
14#17988643C211yesmaximal, characteristic, complemented
15#463×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73C2211yescharacteristic
17C22×C4×D73—21no—
18C2×#11924015C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20#14556584—21no—
21#14556583C2211yescharacteristic, complemented
22#14556573—21no—
23#14556567C2211yescharacteristic
24#14556562C2211yescharacteristic
25Q8×Dic73C2211yescharacteristic, complemented
26C4×D292C2211yescharacteristic
27D4×Dic73C2211yescharacteristic
28D4×Dic73C2211yescharacteristic, complemented
29#14556553C2211yescharacteristic
30C4×C22⋊D73—21no—
31#14556551—21no—
32#14556551—21no—
33#14556547—21no—
34C4⋊C4×D73C2211yescharacteristic
35C22⋊C4×D73—21no—
36C42×D73C2211yescharacteristic
37#14556525C2211yescharacteristic, complemented
38#14556524C2211yescharacteristic, complemented
39#14556523C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41C4⋊#10596831C2211yescharacteristic, complemented
42#14556515C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556512C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic, complemented
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic, complemented
51#14556501C2211yescharacteristic, complemented
52C2×SD16×C73C2211yescharacteristic
53C2×D8×C73C2211yescharacteristic
54#124×C73C2211yescharacteristic, complemented
55C4×D4×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58#102×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C2×D292C2311yescharacteristic
61C2×C22⋊D73—21no—
62C2×C22⋊D73—21no—
63D4×D73—22no—
64D4×D73—22no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—44no—
71C2×C4×D73D411yescharacteristic
72C2×C4×D73D411yescharacteristic
73C2×C4×D73C2311yescharacteristic
74#11924015—22no—
75#11924013—22no—
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92C4×Dic73—21no—
93C4×Dic73D411yescharacteristic
94C4×Dic73D411yescharacteristic
95C4×Dic73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73—21no—
100SD16×C73—22no—
101D8×C73—22no—
102C2×C8×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C42×C73C2311yescharacteristic
109C23×C73—21no—
110C23×C73—21no—
111C22×D73—24no—
112C22×D73—21no—
113C22×D73—42no—
114C22×D73—42no—
115C22×D73C2×D411yescharacteristic
116Q8×C73—21no—
117Q8×C73—21no—
118D4×C73—21no—
119D4×C73—21no—
120D4×C73—21no—
121D4×C73#4112yes—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—42no—
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2411yescharacteristic
128C22⋊D73—24no—
129C22⋊D73—42no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—42no—
134C2×Dic73—42no—
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138D292—21no—
139D292#4112yes—
140C4×D73—22no—
141C4×D73—21no—
142C4×D73—21no—
143C4×D73—41no—
144C4×D73—42no—
145C4×D73—42no—
146C4×D73—42no—
147C8×C73—21no—
148C8×C73—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—22no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73C22×D411yescharacteristic
158C2×D73—21no—
159C2×D73—21no—
160C2×D73—22no—
161C2×D73—48no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73AGL(1,ℤ/8)12yes—
165C4×C73—21no—
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73C2×#4111yescharacteristic
170C4×C73C2×#4111yescharacteristic
171Dic73—21no—
172Dic73—21no—
173Dic73—21no—
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177C2×C73—42no—
178C2×C73—81no—
179C2×C73#52511yescharacteristic
180C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C73#57511yescharacteristic
182D73—22no—
183D73—42no—
184#3114—731nomaximal, Sylow
185C73#311411yescharacteristic, complemented, Sylow
186#529—731no—
187C2×C4×D4—731no—
188#483—731no—
189#480—731no—
190#478—731no—
191#478—731no—
192#463—731no—
193#463D7311yescharacteristic, complemented
194#450—731no—
195#447—731no—
196#442—731no—
197#442—731no—
198#440—731no—
199#440—731no—
200#432—731no—
201C22×D4—731no—
202C23×C4—1461no—
203C2×SD16—731no—
204C2×SD16C2×D7311yescharacteristic
205C2×D8—731no—
206C2×D8C2×D7311yescharacteristic
207#126—1461no—
208#125—731no—
209#124C2×D7311yescharacteristic, complemented
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#107—731no—
228#106—731no—
229#106—731no—
230C4⋊C8—731no—
231C4⋊C8C2×D7311yescharacteristic, complemented
232#103—731no—
233#103C2×D7311yescharacteristic, complemented
234#102—731no—
235#102—731no—
236#102—731no—
237#102—731no—
238#102—731no—
239#102C2×D7311yescharacteristic, complemented
240C22⋊C8—731no—
241C22⋊C8—731no—
242#97—731no—
243#97—731no—
244C24—1461no—
245C2×Q8C22×D7311yescharacteristic
246C2×D4—731no—
247C2×D4—1461no—
248C2×D4—1462no—
249C2×D4—1461no—
250C2×D4—1462no—
251C2×D4C22×D7311yescharacteristic
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—22no—
264SD16—1462no—
265D8—22no—
266D8—1462no—
267C2×C8—731no—
268C2×C8—731no—
269C2×C8C22×D7311yescharacteristic
270C2×C8C22×D7311yescharacteristic
271C4⋊C4—731no—
272C4⋊C4—731no—
273C4⋊C4—731no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4C22×D7311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
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—21no—
296C23—2922no—
297C23—2922no—
298C23—731no—
299C23—1464no—
300C23—1461no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—2922no—
307D4—732no—
308D4—1464no—
309D4—1461no—
310D4#1192402712yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—2922no—
315C2×C4—2921no—
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—1461no—
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—41no—
340C22—41no—
341C22—41no—
342C22—2928no—
343C22—2921no—
344C22—2921no—
345C22—732no—
346C22—1462no—
347C22—1461no—
348C22—1461no—
349C22C2×D4×D7311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—2921no—
355C4—2921no—
356C4—2921no—
357C4—1461no—
358C4—1461no—
359C4—1461no—
360C4#41×D7311yescharacteristic
361C4C2×#1192402711yescharacteristic
362C2—42no—
363C2—81no—
364C2—2922no—
365C2—1462no—
366C2#1798909711yescharacteristic
367C2AGL(1,ℤ/8)×D7311yescharacteristic
368C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#463×C73C2
socleC22×C73C22×D4
hypercenter#463D73
hypocenterC73#3114
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #17989116C2semidirect
2. C4×D4×D73C2semidirect
3. #17988916C2semidirect
4. #17988899C2semidirect
5. #17988888C2semidirect
6. #17988887C2semidirect
7. #17988799C2semidirect
8. #17988736C2semidirect
10. #17988699C2semidirect
11. #17988696C2semidirect
12. #17988690C2semidirect
13. #17988688C2semidirect
14. #17988643C2semidirect
15. #463×C73C2semidirect
21. #14556583C22semidirect
25. Q8×Dic73C22semidirect
28. D4×Dic73C22semidirect
37. #14556525C22semidirect
38. #14556524C22semidirect
39. #14556523C22semidirect
40. #14556522C22semidirect
41. C4⋊#10596831C22semidirect
42. #14556515C22semidirect
47. #14556512C22semidirect
50. #14556501C22semidirect
51. #14556501C22semidirect
54. #124×C73C22semidirect
56. C4⋊C8×C73C22semidirect
57. #103×C73C22semidirect
58. #102×C73C22semidirect
185. C73#3114semidirect
193. #463D73semidirect
209. #124C2×D73semidirect
231. C4⋊C8C2×D73semidirect
233. #103C2×D73semidirect
239. #102C2×D73semidirect