Finite Group Databasebeta

← #22620282

Subgroups — #22620282

Order 9344.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989214C211yesmaximal, characteristic, complemented
2#17989155C211yesmaximal, characteristic
3#17988952C211yesmaximal, characteristic, complemented
4#17988950C211yesmaximal, characteristic, complemented
5#17988948C211yesmaximal, characteristic, complemented
6#17988943C211yesmaximal, characteristic, complemented
7#17988941C211yesmaximal, characteristic, complemented
8#17988935C211yesmaximal, characteristic, complemented
9#17988932C211yesmaximal, characteristic, complemented
10#17988590C211yesmaximal, characteristic, complemented
11#17988587C211yesmaximal, characteristic, complemented
12#17988582C211yesmaximal, characteristic, complemented
13#102×D73C211yesmaximal, characteristic, complemented
14#17988544C211yesmaximal, characteristic, complemented
15#489×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20#14556590C2211yescharacteristic, complemented
21#14556589—21no—
22#14556588C2211yescharacteristic
23#14556587C2211yescharacteristic
24#14556583C2211yescharacteristic, complemented
25#14556582C2211yescharacteristic, complemented
26#14556581—21no—
27#14556580C2211yescharacteristic
28#14556569—21no—
29#14556567—21no—
30#14556564—21no—
31#14556564—21no—
32#14556561—21no—
33#14556561—21no—
34#14556549C2211yescharacteristic
35#14556548C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic
37#14556515C2211yescharacteristic, complemented
38#14556515C2211yescharacteristic, complemented
39#14556513C2211yescharacteristic
40#14556513C2211yescharacteristic
41#14556513C2211yescharacteristic, complemented
42#14556513C2211yescharacteristic, complemented
43#14556512C2211yescharacteristic
44#14556512C2211yescharacteristic
45#14556511C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic, complemented
48#14556511C2211yescharacteristic, complemented
49#14556501C2211yescharacteristic, complemented
50C4×#10596831C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C4⋊Q8×C73C2211yescharacteristic, complemented
53#124×C73C2211yescharacteristic
54#103×C73C2211yescharacteristic, complemented
55#103×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924029—22no—
61#11924029—22no—
62C2×Dic146—21no—
63C2×D292—21no—
64C2×D292—21no—
65C2×D292—21no—
66C2×D292C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71D4×D73—22no—
72D4×D73—22no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73C2311yescharacteristic
76#11924011—22no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C8×D73—22no—
80C4⋊Dic73—21no—
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88#11924007D411yescharacteristic
89#11924007D411yescharacteristic
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005D411yescharacteristic
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73—21no—
98C2×Q8×C73C2311yescharacteristic
99C2×D4×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C22×D73—21no—
110C22×D73—21no—
111C22×D73—42no—
112C22×D73—81no—
113C22×D73—81no—
114C22×D73C2×D411yescharacteristic
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—81no—
118D4×C73—21no—
119D4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2411yescharacteristic
126C22⋊D73—42no—
127C22⋊D73—81no—
128C22⋊D73—81no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73C2×D411yescharacteristic
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134D292—21no—
135D292—21no—
136D292—21no—
137D292—21no—
138D292—42no—
139D292—81no—
140D292—81no—
141C4×D73—42no—
142C4×D73—81no—
143C4×D73#4112yes—
144C4×D73#4112yes—
145Dic146—81no—
146C8×C73—21no—
147C8×C73—21no—
148#10596831—21no—
149#10596831—21no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73C22×D411yescharacteristic
154C2×D73—21no—
155C2×D73—21no—
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—41no—
162C2×D73—84no—
163C2×D73#12412yes—
164C4×C73—21no—
165C4×C73—21no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73C2×#4111yescharacteristic
170C4×C73C2×#4111yescharacteristic
171Dic73—21no—
172Dic73—21no—
173Dic73—41no—
174Dic73—41no—
175Dic73#12412yes—
176C2×C73—81no—
177C2×C73C2×#12411yescharacteristic
178C2×C73#57611yescharacteristic
179C2×C73#57711yescharacteristic
180D73—22no—
181D73—81no—
182D73—81no—
183#3136—731nomaximal, Sylow
184C73#313611yescharacteristic, complemented, Sylow
185#544—731no—
186#535—731no—
187#490—731no—
188#490—731no—
189#489—731no—
190#489D7311yescharacteristic, complemented
191#488—731no—
192#488—731no—
193#486—731no—
194#486—731no—
195#418—731no—
196#417—731no—
197#416—731no—
198C2×#102—731no—
199#405—731no—
200C2×#41—731no—
201C22×D4—731no—
202C2×M16—731no—
203C22×C8—731no—
204C4⋊Q8—731no—
205C4⋊Q8—1461no—
206C4⋊Q8C2×D7311yescharacteristic, complemented
207#127—731no—
208#127—731no—
209#125—731no—
210#125—731no—
211#125—1461no—
212#124—731no—
213#124C2×D7311yescharacteristic
214C22⋊Q8—1461no—
215C22⋊Q8—1461no—
216#121—1461no—
217#121—1461no—
218#120—1461no—
219#120—1461no—
220#117—731no—
221#117—731no—
222C2×C4⋊C4—731no—
223#103—731no—
224#103—731no—
225#103C2×D7311yescharacteristic, complemented
226#103C2×D7311yescharacteristic, complemented
227#102—731no—
228#102—731no—
229#102—731no—
230#102—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#102—731no—
235#102—731no—
236#102—731no—
237#102C2×D7311yescharacteristic
238#102C2×D7311yescharacteristic
239#97—731no—
240#97C2×D7311yescharacteristic, complemented
241C4×C8—731no—
242C4×C8—731no—
243C24—1461no—
244#41—1462no—
245#41—1462no—
246C2×Q8—21no—
247C2×Q8—1461no—
248C2×Q8C22×D7311yescharacteristic
249C2×D4—731no—
250C2×D4—731no—
251C2×D4—1461no—
252C2×D4—1462no—
253C2×D4—1462no—
254C2×D4—1461no—
255C2×D4—1461no—
256C2×D4—1461no—
257C2×D4—1461no—
258C2×D4—1461no—
259C2×D4C22×D7311yescharacteristic
260C22×C4—731no—
261C22×C4—1461no—
262C22×C4—1461no—
263M16—1462no—
264C2×C8—731no—
265C2×C8—731no—
266C2×C8—1462no—
267C2×C8C22×D7311yescharacteristic
268C2×C8C22×D7311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—731no—
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⋊C4—1461no—
280C4⋊C4C22×D7311yescharacteristic
281C4⋊C4C22×D7311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—731no—
285C22⋊C4—731no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C42—731no—
290C42—1461no—
291C42C22×D7311yescharacteristic
292C23—21no—
293C23—2922no—
294C23—5841no—
295C23—5841no—
296C23—731no—
297C23—1461no—
298C23—1461no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—5841no—
303D4—21no—
304D4—21no—
305D4—2922no—
306D4—2922no—
307D4—5841no—
308D4—5841no—
309D4—5841no—
310D4—5841no—
311D4—1461no—
312D4—1461no—
313D4—1461no—
314D4—1461no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2922no—
319C2×C4—5841no—
320C2×C4—731no—
321C2×C4—732no—
322C2×C4—732no—
323C2×C4—731no—
324C2×C4—731no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4D4×D7311yescharacteristic
328C2×C4D4×D7311yescharacteristic
329C2×C4C23×D7311yescharacteristic
330C8—21no—
331C8—21no—
332C8—1461no—
333C8—1461no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2921no—
338C22—2921no—
339C22—2921no—
340C22—2921no—
341C22—2921no—
342C22—2921no—
343C22—5844no—
344C22—732no—
345C22—1461no—
346C22—1461no—
347C22C2×D4×D7311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2921no—
354C4—2921no—
355C4—732no—
356C4—1461no—
357C4—1461no—
358C4#41×D7311yescharacteristic
359C4#41×D7311yescharacteristic
360C2—81no—
361C2—5841no—
362C2—5841no—
363C2—1462no—
364C2#124×D7311yescharacteristic
365C2#1798939111yescharacteristic
366C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#489×C73C2
socleC22×C73C22×D4
hypercenter#489D73
hypocenterC73#3136
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #17989214C2semidirect
3. #17988952C2semidirect
4. #17988950C2semidirect
5. #17988948C2semidirect
6. #17988943C2semidirect
7. #17988941C2semidirect
8. #17988935C2semidirect
9. #17988932C2semidirect
10. #17988590C2semidirect
11. #17988587C2semidirect
12. #17988582C2semidirect
13. #102×D73C2semidirect
14. #17988544C2semidirect
15. #489×C73C2semidirect
20. #14556590C22semidirect
24. #14556583C22semidirect
25. #14556582C22semidirect
37. #14556515C22semidirect
38. #14556515C22semidirect
41. #14556513C22semidirect
42. #14556513C22semidirect
47. #14556511C22semidirect
48. #14556511C22semidirect
49. #14556501C22semidirect
50. C4×#10596831C22semidirect
51. C8×Dic73C22semidirect
52. C4⋊Q8×C73C22semidirect
54. #103×C73C22semidirect
55. #103×C73C22semidirect
58. #97×C73C22semidirect
184. C73#3136semidirect
190. #489D73semidirect
206. C4⋊Q8C2×D73semidirect
225. #103C2×D73semidirect
226. #103C2×D73semidirect
240. #97C2×D73semidirect