Finite Group Databasebeta

← #22620897

Subgroups — #22620897

Order 9344.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989122C211yesmaximal, characteristic, complemented
2#124×D73C211yesmaximal, characteristic, complemented
3#17988971C211yesmaximal, characteristic, complemented
4#17988969C211yesmaximal, characteristic, complemented
5#17988944C211yesmaximal, characteristic, complemented
6#17988812C211yesmaximal, characteristic, complemented
7#17988808C211yesmaximal, characteristic, complemented
8#17988805C211yesmaximal, characteristic, complemented
9#17988801C211yesmaximal, characteristic, complemented
10#17988744C211yesmaximal, characteristic, complemented
11#17988739C211yesmaximal, characteristic, complemented
12#17988727C211yesmaximal, characteristic, complemented
13#17988722C211yesmaximal, characteristic
14#17988638C211yesmaximal, characteristic, complemented
15#488×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×Dic292C2211yescharacteristic, complemented
19C2×#11924018C2211yescharacteristic, complemented
20C2×#11924017C2211yescharacteristic
21C2×#11924017C2211yescharacteristic, complemented
22C2×#11924016C2211yescharacteristic
23C2×#11924015C2211yescharacteristic, complemented
24C2×D584C2211yescharacteristic
25C2×#11924013C2211yescharacteristic
26#14556586—21no—
27#14556580C2211yescharacteristic
28#14556579C2211yescharacteristic
29#14556579C2211yescharacteristic, complemented
30#14556578C2211yescharacteristic
31#14556577—21no—
32#14556577—21no—
33#14556576—21no—
34#14556571C2211yescharacteristic
35#14556566C2211yescharacteristic
36#14556556C2211yescharacteristic, complemented
37#14556553—21no—
38#14556553C2211yescharacteristic, complemented
39#14556549—21no—
40C22⋊C4×D73—21no—
41C22⋊C4×D73—21no—
42C42×D73C2211yescharacteristic
43#14556520C2211yescharacteristic, complemented
44#14556520C2211yescharacteristic, complemented
45#14556514C2211yescharacteristic, complemented
46#14556514C2211yescharacteristic, complemented
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic
51C4×#10596831C2211yescharacteristic, complemented
52#125×C73C2211yescharacteristic, complemented
53#124×C73C2211yescharacteristic
54#103×C73C2211yescharacteristic, complemented
55#103×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C2×Dic146—21no—
61C2×Dic146C2311yescharacteristic
62C2×Dic146C2311yescharacteristic
63Q8×D73—41no—
64Q8×D73—41no—
65C2×D292—21no—
66C2×D292C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69D4×D73—41no—
70D4×D73—41no—
71C2×C4×D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73D411yescharacteristic
74C2×C4×D73D411yescharacteristic
75C2×C4×D73C2311yescharacteristic
76Dic292—41no—
77#11924018—41no—
78#11924017—41no—
79#11924017—41no—
80#11924016—41no—
81#11924015—41no—
82D584—41no—
83#11924013—41no—
84C2×#10596831C2311yescharacteristic
85C2×#10596831C2311yescharacteristic
86C4⋊Dic73—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99C4×Dic73—21no—
100C4×Dic73D411yescharacteristic
101C4×Dic73D411yescharacteristic
102C4×Dic73C2311yescharacteristic
103C2×Q8×C73C2311yescharacteristic
104C2×D4×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73—21no—
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C22⋊C4×C73—21no—
112C22⋊C4×C73—21no—
113C42×C73C2311yescharacteristic
114C23×C73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—42no—
118C22×D73—42no—
119C22×D73—42no—
120C22×D73C2×D411yescharacteristic
121Q8×C73—21no—
122Q8×C73—21no—
123D4×C73—21no—
124D4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2411yescharacteristic
131C22⋊D73—42no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137D292—21no—
138D292—21no—
139D292—21no—
140D292—21no—
141D292—42no—
142C4×D73—22no—
143C4×D73—21no—
144C4×D73—21no—
145C4×D73—41no—
146C4×D73—42no—
147C4×D73—42no—
148Dic146—21no—
149Dic146—21no—
150Dic146—21no—
151Dic146—21no—
152Dic146—42no—
153C8×C73—21no—
154C8×C73—21no—
155#10596831—21no—
156#10596831—21no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73C22×D411yescharacteristic
161C2×D73—21no—
162C2×D73—21no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—84no—
170C2×D73#13512yes—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73—41no—
176C4×C73H(5,𝔽2)11yescharacteristic
177C4×C73H(5,𝔽2)11yescharacteristic
178Dic73—21no—
179Dic73—21no—
180Dic73—21no—
181Dic73—41no—
182Dic73—41no—
183C2×C73—81no—
184C2×C73#53511yescharacteristic
185C2×C73C2×#13511yescharacteristic
186C2×C73#57511yescharacteristic
187D73—22no—
188D73—81no—
189D73—81no—
190#3211—731nomaximal, Sylow
191C73#321111yescharacteristic, complemented, Sylow
192#529—731no—
193C2×#124—731no—
194#495—731no—
195#495—731no—
196#488—731no—
197#488D7311yescharacteristic, complemented
198#464—731no—
199#464—731no—
200#463—731no—
201#463—731no—
202#451—731no—
203#450—731no—
204#448—731no—
205#447—731no—
206#431—731no—
207C22×Q8—731no—
208C22×D4—731no—
209C2×Q16—731no—
210C2×Q16—731no—
211C2×SD16—731no—
212C2×SD16—731no—
213C2×SD16—731no—
214C2×SD16—731no—
215C2×D8—731no—
216C2×D8—731no—
217#126—1461no—
218#125C2×D7311yescharacteristic, complemented
219#124—731no—
220#124—731no—
221#124—731no—
222#124—731no—
223#124—1461no—
224#124—1461no—
225#124C2×D7311yescharacteristic
226#123—1461no—
227C22⋊Q8—731no—
228#121—731no—
229C4×Q8—731no—
230C4×D4—731no—
231C4×D4—1461no—
232#117—1461no—
233C2×C22⋊C4—1461no—
234C2×C22⋊C4—1461no—
235C2×C42—731no—
236C4⋊C8—731no—
237C4⋊C8—731no—
238#103—731no—
239#103—731no—
240#103C2×D7311yescharacteristic, complemented
241#103C2×D7311yescharacteristic, complemented
242#102—731no—
243#102—731no—
244#102C2×D7311yescharacteristic
245#102C2×D7311yescharacteristic
246C22⋊C8—731no—
247C22⋊C8—731no—
248C4×C8—731no—
249C4×C8C2×D7311yescharacteristic, complemented
250C24—1461no—
251C2×Q8—2921no—
252C2×Q8—2921no—
253C2×Q8—731no—
254C2×Q8—731no—
255C2×Q8—1461no—
256C2×Q8C22×D7311yescharacteristic
257C2×D4—2921no—
258C2×D4—2921no—
259C2×D4—731no—
260C2×D4—731no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4C22×D7311yescharacteristic
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—1461no—
268C22×C4—1461no—
269Q16—2921no—
270Q16—2921no—
271SD16—2921no—
272SD16—2921no—
273SD16—2921no—
274SD16—2921no—
275D8—2921no—
276D8—2921no—
277C2×C8—731no—
278C2×C8—731no—
279C2×C8C22×D7311yescharacteristic
280C2×C8C22×D7311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—1461no—
284C4⋊C4—1461no—
285C4⋊C4C22×D7311yescharacteristic
286C4⋊C4C22×D7311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C22⋊C4—1461no—
300C42—731no—
301C42—731no—
302C42—731no—
303C42—1461no—
304C42C22×D7311yescharacteristic
305C23—21no—
306C23—2922no—
307C23—2922no—
308C23—2922no—
309C23—731no—
310C23—1461no—
311C23—1461no—
312Q8—21no—
313Q8—21no—
314Q8—2922no—
315Q8—1461no—
316Q8—1461no—
317Q8—1461no—
318Q8—1461no—
319D4—21no—
320D4—21no—
321D4—2922no—
322D4—2922no—
323D4—1461no—
324D4—1461no—
325D4—1461no—
326D4—1461no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2921no—
331C2×C4—2922no—
332C2×C4—2922no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—731no—
336C2×C4—1462no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4D4×D7311yescharacteristic
342C2×C4D4×D7311yescharacteristic
343C2×C4C23×D7311yescharacteristic
344C8—21no—
345C8—21no—
346C8—1461no—
347C8—1461no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—2921no—
352C22—2921no—
353C22—2921no—
354C22—2921no—
355C22—2921no—
356C22—2921no—
357C22—5844no—
358C22—732no—
359C22—1461no—
360C22—1461no—
361C22C2×D4×D7311yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—2921no—
368C4—2921no—
369C4—1461no—
370C4—1461no—
371C4—1461no—
372C4#1455663711yescharacteristic
373C4#1455663711yescharacteristic
374C2—81no—
375C2—5841no—
376C2—5841no—
377C2—1462no—
378C2#1798915511yescharacteristic
379C2#135×D7311yescharacteristic
380C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#488×C73C2
socleC22×C73C22×D4
hypercenter#488D73
hypocenterC73#3211
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #17989122C2semidirect
2. #124×D73C2semidirect
3. #17988971C2semidirect
4. #17988969C2semidirect
5. #17988944C2semidirect
6. #17988812C2semidirect
7. #17988808C2semidirect
8. #17988805C2semidirect
9. #17988801C2semidirect
10. #17988744C2semidirect
11. #17988739C2semidirect
12. #17988727C2semidirect
14. #17988638C2semidirect
15. #488×C73C2semidirect
18. C2×Dic292C22semidirect
19. C2×#11924018C22semidirect
21. C2×#11924017C22semidirect
23. C2×#11924015C22semidirect
29. #14556579C22semidirect
36. #14556556C22semidirect
38. #14556553C22semidirect
43. #14556520C22semidirect
44. #14556520C22semidirect
45. #14556514C22semidirect
46. #14556514C22semidirect
51. C4×#10596831C22semidirect
52. #125×C73C22semidirect
54. #103×C73C22semidirect
55. #103×C73C22semidirect
58. C4×C8×C73C22semidirect
191. C73#3211semidirect
197. #488D73semidirect
218. #125C2×D73semidirect
240. #103C2×D73semidirect
241. #103C2×D73semidirect
249. C4×C8C2×D73semidirect