Finite Group Databasebeta

← #22621002

Subgroups — #22621002

Order 9344.

396 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#17989195C211yesmaximal, characteristic, complemented
2#17989150C211yesmaximal, characteristic
3#17988978C211yesmaximal, characteristic, complemented
4#17988958C211yesmaximal, characteristic, complemented
5#17988950C211yesmaximal, characteristic, complemented
6#17988940C211yesmaximal, characteristic, complemented
7#17988810C211yesmaximal, characteristic, complemented
8#17988809C211yesmaximal, characteristic, complemented
9#17988784C211yesmaximal, characteristic, complemented
10#17988750C211yesmaximal, characteristic, complemented
11#17988746C211yesmaximal, characteristic, complemented
12#17988739C211yesmaximal, characteristic, complemented
13#17988736C211yesmaximal, characteristic, complemented
14#17988647C211yesmaximal, characteristic, complemented
15#460×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×Dic292C2211yescharacteristic, complemented
19C2×#11924018C2211yescharacteristic, complemented
20C2×#11924017C2211yescharacteristic
21C2×#11924016C2211yescharacteristic
22C2×#11924016C2211yescharacteristic, complemented
23C2×#11924015C2211yescharacteristic
24#14556589C2211yescharacteristic, complemented
25#14556587C2211yescharacteristic
26#14556586—21no—
27#14556585—21no—
28#14556583—21no—
29#14556582C2211yescharacteristic, complemented
30#14556581—21no—
31#14556579C2211yescharacteristic
32#14556578C2211yescharacteristic
33#14556571C2211yescharacteristic
34#14556567C2211yescharacteristic
35#14556563—21no—
36#14556563—21no—
37#14556559—21no—
38#14556559—21no—
39C4×Dic146C2211yescharacteristic, complemented
40#14556548C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556514C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic
45#14556512C2211yescharacteristic
46#14556512C2211yescharacteristic, complemented
47#14556511C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C2×SD16×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic, complemented
54#127×C73C2211yescharacteristic
55C4×Q8×C73C2211yescharacteristic, complemented
56C4⋊C8×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924027—41no—
61#11924027—41no—
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69D4×D73—41no—
70D4×D73—41no—
71C22×Dic73—21no—
72C2×C4×D73C2311yescharacteristic
73Dic292—41no—
74#11924018—41no—
75#11924017—41no—
76#11924016—41no—
77#11924016—41no—
78#11924015—41no—
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C4⋊Dic73—21no—
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89#11924007D411yescharacteristic
90#11924007D411yescharacteristic
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005D411yescharacteristic
98#11924005D411yescharacteristic
99C4×Dic73—21no—
100C4×Dic73C2311yescharacteristic
101C2×Q8×C73C2311yescharacteristic
102C2×D4×C73—21no—
103C2×D4×C73—21no—
104C2×D4×C73C2311yescharacteristic
105C2×D4×C73C2311yescharacteristic
106SD16×C73—41no—
107SD16×C73—41no—
108C2×C8×C73C2311yescharacteristic
109C2×C8×C73C2311yescharacteristic
110C4⋊C4×C73—21no—
111C4⋊C4×C73C2311yescharacteristic
112C42×C73—21no—
113C42×C73C2311yescharacteristic
114C23×C73—21no—
115C23×C73—21no—
116C22×D73—21no—
117C22×D73—42no—
118C22×D73—81no—
119C22×D73—81no—
120C22×D73C2×D411yescharacteristic
121Q8×C73—21no—
122Q8×C73—21no—
123D4×C73—21no—
124D4×C73—21no—
125D4×C73—21no—
126D4×C73—21no—
127D4×C73—81no—
128D4×C73—81no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2×D411yescharacteristic
133C2×C4×C73C2411yescharacteristic
134C22⋊D73—42no—
135C22⋊D73—42no—
136C22⋊D73—81no—
137C22⋊D73—81no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—42no—
142C2×Dic73C2×D411yescharacteristic
143C2×Dic73C2×D411yescharacteristic
144C2×Dic73C2×D411yescharacteristic
145D292—21no—
146D292—21no—
147C4×D73—21no—
148C4×D73—21no—
149Dic146—21no—
150Dic146—21no—
151Dic146—21no—
152Dic146—21no—
153C8×C73—21no—
154C8×C73—21no—
155#10596831—21no—
156#10596831—21no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73C22×D411yescharacteristic
164C2×D73—21no—
165C2×D73—21no—
166C2×D73—21no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—84no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73H(5,𝔽2)11yescharacteristic
176C4×C73H(5,𝔽2)11yescharacteristic
177Dic73—21no—
178Dic73—21no—
179Dic73—21no—
180Dic73—41no—
181Dic73—41no—
182Dic73—41no—
183C2×C73—81no—
184C2×C73—81no—
185C2×C73#53511yescharacteristic
186C2×C73#57711yescharacteristic
187C2×C73#57711yescharacteristic
188D73—41no—
189D73—81no—
190#3222—731nomaximal, Sylow
191C73#322211yescharacteristic, complemented, Sylow
192#541—731no—
193#535—731no—
194#497—731no—
195#492—731no—
196#490—731no—
197#488—731no—
198#464—731no—
199#464—731no—
200#460—731no—
201#460D7311yescharacteristic, complemented
202#452—731no—
203#452—731no—
204#450—731no—
205#450—731no—
206#433—731no—
207C2×#41—731no—
208C22×D4—731no—
209C2×Q16—731no—
210C2×Q16—731no—
211C2×SD16—731no—
212C2×SD16—731no—
213C2×SD16—731no—
214C2×SD16—731no—
215C2×SD16C2×D7311yescharacteristic
216C2×SD16C2×D7311yescharacteristic, complemented
217C4⋊Q8—731no—
218#127—731no—
219#127C2×D7311yescharacteristic
220#126—1461no—
221#126—1461no—
222#125—731no—
223#125—1461no—
224#125—1461no—
225#124—731no—
226#124—731no—
227C22⋊Q8—731no—
228C22⋊Q8—731no—
229#121—1461no—
230#121—1461no—
231#120—1461no—
232#120—1461no—
233C4×Q8—731no—
234C4×Q8C2×D7311yescharacteristic, complemented
235#117—731no—
236C4⋊C8—731no—
237C4⋊C8C2×D7311yescharacteristic, complemented
238#103—731no—
239#103—731no—
240#102—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244#102C2×D7311yescharacteristic
245#102C2×D7311yescharacteristic, complemented
246C22⋊C8—731no—
247C22⋊C8—731no—
248#97—731no—
249C4×C8—731no—
250C24—1461no—
251#41—2921no—
252#41—2921no—
253C2×Q8—731no—
254C2×Q8—731no—
255C2×Q8C22×D7311yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—2921no—
259C2×D4—2921no—
260C2×D4—731no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1461no—
265C2×D4C22×D7311yescharacteristic
266C2×D4C22×D7311yescharacteristic
267C22×C4—731no—
268C22×C4—1461no—
269Q16—2921no—
270Q16—2921no—
271SD16—41no—
272SD16—41no—
273SD16—2921no—
274SD16—2921no—
275SD16—2921no—
276SD16—2921no—
277C2×C8—731no—
278C2×C8—731no—
279C2×C8C22×D7311yescharacteristic
280C2×C8C22×D7311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—731no—
283C4⋊C4—731no—
284C4⋊C4—731no—
285C4⋊C4—1461no—
286C4⋊C4—1461no—
287C4⋊C4—1461no—
288C4⋊C4—1461no—
289C4⋊C4—1461no—
290C4⋊C4—1461no—
291C4⋊C4—1461no—
292C4⋊C4C22×D7311yescharacteristic
293C22⋊C4—731no—
294C22⋊C4—731no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C42—21no—
302C42—731no—
303C42—1461no—
304C42C22×D7311yescharacteristic
305C23—21no—
306C23—21no—
307C23—2922no—
308C23—5841no—
309C23—5841no—
310C23—731no—
311C23—1461no—
312Q8—21no—
313Q8—21no—
314Q8—1461no—
315Q8—1461no—
316Q8—1461no—
317Q8—1461no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—81no—
323D4—81no—
324D4—2922no—
325D4—2922no—
326D4—5841no—
327D4—5841no—
328D4—1461no—
329D4—1461no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—2922no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—731no—
336C2×C4—1461no—
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—41no—
352C22—41no—
353C22—41no—
354C22—2921no—
355C22—2921no—
356C22—2921no—
357C22—5844no—
358C22—1461no—
359C22—1461no—
360C22—1461no—
361C22C2×D4×D7311yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—2921no—
367C4—2921no—
368C4—2921no—
369C4—1461no—
370C4—1461no—
371C4—1461no—
372C4#1455663611yescharacteristic
373C4#1455663711yescharacteristic
374C2—81no—
375C2—81no—
376C2—2921no—
377C2—5841no—
378C2#1798915311yescharacteristic
379C2#1798939311yescharacteristic
380C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#460×C73C2
socleC22×C73C22×D4
hypercenter#460D73
hypocenterC73#3222
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #17989195C2semidirect
3. #17988978C2semidirect
4. #17988958C2semidirect
5. #17988950C2semidirect
6. #17988940C2semidirect
7. #17988810C2semidirect
8. #17988809C2semidirect
9. #17988784C2semidirect
10. #17988750C2semidirect
11. #17988746C2semidirect
12. #17988739C2semidirect
13. #17988736C2semidirect
14. #17988647C2semidirect
15. #460×C73C2semidirect
18. C2×Dic292C22semidirect
19. C2×#11924018C22semidirect
22. C2×#11924016C22semidirect
24. #14556589C22semidirect
29. #14556582C22semidirect
39. C4×Dic146C22semidirect
41. C4⋊#10596831C22semidirect
42. #14556516C22semidirect
43. #14556514C22semidirect
46. #14556512C22semidirect
50. #14556501C22semidirect
51. C8×Dic73C22semidirect
53. C2×SD16×C73C22semidirect
55. C4×Q8×C73C22semidirect
56. C4⋊C8×C73C22semidirect
58. #102×C73C22semidirect
191. C73#3222semidirect
201. #460D73semidirect
216. C2×SD16C2×D73semidirect
234. C4×Q8C2×D73semidirect
237. C4⋊C8C2×D73semidirect
245. #102C2×D73semidirect