Finite Group Databasebeta

← #34056513

Subgroups — #34056513

Order 19072.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750330C211yesmaximal, characteristic, complemented
2#23750259C211yesmaximal, characteristic
3#23749970C211yesmaximal, characteristic, complemented
4#23749945C211yesmaximal, characteristic, complemented
5#23749914C211yesmaximal, characteristic, complemented
6#23749855C211yesmaximal, characteristic, complemented
7#23749852C211yesmaximal, characteristic, complemented
8#23749824C211yesmaximal, characteristic, complemented
9#23749778C211yesmaximal, characteristic, complemented
10#23749777C211yesmaximal, characteristic, complemented
11#23749712C211yesmaximal, characteristic, complemented
12#23749688C211yesmaximal, characteristic, complemented
13C2×#18011831C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15#481×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C2×D4×D149—21no—
18C2×D4×D149C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558725C2211yescharacteristic, complemented
21C2×#14558724C2211yescharacteristic, complemented
22C22×#11924746C2211yescharacteristic, complemented
23C2×C8×D149C2211yescharacteristic, complemented
24#18011910C2211yescharacteristic, complemented
25#18011907C2211yescharacteristic
26#18011901—21no—
27#18011891C2211yescharacteristic, complemented
28#18011890—21no—
29#18011890C2211yescharacteristic, complemented
30#18011889—21no—
31#18011886C2211yescharacteristic
32#18011884—21no—
33#18011881—21no—
34#18011879—21no—
35#18011876C2211yescharacteristic, complemented
36#18011873C2211yescharacteristic
37C4×C22⋊D149—21no—
38C4×C22⋊D149C2211yescharacteristic
39C4⋊C4×D149C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011834C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic
44#18011833C2211yescharacteristic, complemented
45#18011832C2211yescharacteristic, complemented
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic, complemented
49#18011831C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52#121×C149C2211yescharacteristic
53C2×C4⋊C4×C149C2211yescharacteristic, complemented
54#106×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C23×D149—21no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×D596—22no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—41no—
67C2×D596C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149D411yescharacteristic
73D4×D149—22no—
74D4×D149—41no—
75D4×D149—44no—
76C2×C4×D149—21no—
77C2×C4×D149—21no—
78C2×C4×D149C2311yescharacteristic
79#14558725—22no—
80#14558725—41no—
81#14558724—41no—
82C2×#11924746—41no—
83C2×#11924746C2311yescharacteristic
84C2×#11924746C2311yescharacteristic
85C8×D149—41no—
86C4⋊Dic149—21no—
87C4⋊Dic149C2311yescharacteristic
88#14558715—21no—
89#14558715—21no—
90#14558715—21no—
91#14558715—21no—
92#14558715D411yescharacteristic
93C22⋊Dic149—21no—
94C22⋊Dic149D411yescharacteristic
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713D411yescharacteristic
99C4×Dic149—21no—
100C4×Dic149C2311yescharacteristic
101C2×D4×C149—21no—
102C2×D4×C149C2311yescharacteristic
103C22×C4×C149—21no—
104C22×C4×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—42no—
115C22×D149—42no—
116C22×D149—42no—
117C22×D149—42no—
118C22×D149—81no—
119C22×D149—81no—
120C22×D149C2×D411yescharacteristic
121Dic298—21no—
122Dic298—21no—
123Dic298—81no—
124D596—21no—
125D596—21no—
126D596—21no—
127D596—42no—
128D596—42no—
129D596#4112yes—
130C22⋊D149—42no—
131C22⋊D149—42no—
132C22⋊D149—81no—
133C22⋊D149SD1614yescomplemented
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149C2×D411yescharacteristic
137C2×Dic149C2×D411yescharacteristic
138C2×Dic149C2×D411yescharacteristic
139C4×D149—21no—
140C4×D149—21no—
141C4×D149—42no—
142C4×D149—81no—
143#11924746—21no—
144#11924746—21no—
145C23×C149—21no—
146C23×C149C2×D411yescharacteristic
147D4×C149—21no—
148D4×C149—21no—
149D4×C149—42no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—81no—
156C2×C4×C149C2×D411yescharacteristic
157C2×C4×C149C2411yescharacteristic
158C8×C149—21no—
159C8×C149—21no—
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—41no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149C2×SD1612yes—
166C22×C149C22×D411yescharacteristic
167C2×D149—21no—
168C2×D149—21no—
169C2×D149—22no—
170C2×D149—41no—
171C2×D149—41no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—84no—
176C2×D149—84no—
177C2×D149C2×SD1612yes—
178C4×C149—21no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149—41no—
182C4×C149C2×#4111yescharacteristic
183C4×C149H(5,𝔽2)11yescharacteristic
184Dic149—21no—
185Dic149—21no—
186Dic149—41no—
187Dic149—41no—
188Dic149C2×SD1612yes—
189C2×C149—22no—
190C2×C149—81no—
191C2×C149#54611yescharacteristic
192C2×C149C22×SD1611yescharacteristic
193C2×C149#57611yescharacteristic
194D149—22no—
195D149—42no—
196D149—81no—
197C149#329511yescharacteristic, complemented, Sylow
198#3295—1491nomaximal, Sylow
199#554—1491no—
200D42—1491no—
201#486—1491no—
202#481—1491no—
203#481D14911yescharacteristic, complemented
204#476—1491no—
205#465—1491no—
206#465—1491no—
207#460—1491no—
208#450—1491no—
209#450—1491no—
210C4×SD16—1491no—
211C8×D4—1491no—
212C2×#102—1491no—
213C2×#102—1491no—
214C22×D4—2981no—
215C22×D4—1491no—
216C22×D4—1491no—
217C2×SD16—1491no—
218C2×SD16—1491no—
219C2×SD16—1491no—
220C22×C8—1491no—
221C22×C8—1491no—
222C4⋊Q8—1491no—
223#127—1491no—
224#125—2981no—
225C22⋊Q8—2981no—
226C22⋊Q8—2981no—
227C22⋊Q8—1491no—
228C22⋊Q8—1491no—
229#121—2981no—
230#121—1491no—
231#121C2×D14911yescharacteristic
232#120—2981no—
233#120—2981no—
234C4×Q8—1491no—
235C4×D4—2981no—
236C4×D4—1491no—
237C4×D4—1491no—
238C2×C4⋊C4—1491no—
239C2×C4⋊C4C2×D14911yescharacteristic, complemented
240#106—1491no—
241#106C2×D14911yescharacteristic, complemented
242#106C2×D14911yescharacteristic, complemented
243C4⋊C8—1491no—
244#103—1491no—
245#102—1491no—
246#102—1491no—
247#102—1491no—
248#102—1491no—
249#102—1491no—
250#102—1491no—
251#102—1491no—
252#102C2×D14911yescharacteristic, complemented
253#102C2×D14911yescharacteristic, complemented
254C22⋊C8—1491no—
255C22⋊C8C2×D14911yescharacteristic, complemented
256C4×C8—1491no—
257C24—2981no—
258C24—2981no—
259C2×Q8—2981no—
260C2×Q8—1491no—
261C2×D4—21no—
262C2×D4—2982no—
263C2×D4—2981no—
264C2×D4—2982no—
265C2×D4—2981no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—5961no—
270C2×D4—5961no—
271C2×D4—5964no—
272C2×D4—1491no—
273C2×D4—1491no—
274C2×D4—1491no—
275C2×D4C22×D14911yescharacteristic
276C22×C4—21no—
277C22×C4—2981no—
278C22×C4—2981no—
279C22×C4—1491no—
280C22×C4C22×D14911yescharacteristic
281SD16—2982no—
282SD16—5961no—
283SD16—5961no—
284C2×C8—5961no—
285C2×C8—5961no—
286C2×C8—1491no—
287C2×C8—1491no—
288C2×C8C22×D14911yescharacteristic
289C2×C8C22×D14911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—2981no—
292C4⋊C4—2981no—
293C4⋊C4—2981no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4C22×D14911yescharacteristic
299C4⋊C4C22×D14911yescharacteristic
300C4⋊C4C22×D14911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—1491no—
307C22⋊C4—1491no—
308C42—2981no—
309C42—1491no—
310C23—21no—
311C23—2981no—
312C23—2981no—
313C23—5962no—
314C23—5962no—
315C23—5962no—
316C23—5962no—
317C23—1491no—
318C23—11921no—
319C23—11921no—
320C23D4×D14911yescharacteristic
321Q8—2981no—
322Q8—2981no—
323Q8—11921no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—2981no—
328D4—2981no—
329D4—2981no—
330D4—5962no—
331D4—5962no—
332D4—5962no—
333D4—5962no—
334D4—1494no—
335D4—1492no—
336D4—11921no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—81no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—5962no—
348C2×C4—1491no—
349C2×C4—1491no—
350C2×C4—1491no—
351C2×C4—11921no—
352C2×C4D4×D14911yescharacteristic
353C2×C4C23×D14911yescharacteristic
354C8—21no—
355C8—21no—
356C8—2981no—
357C8—2981no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—2981no—
364C22—2981no—
365C22—2982no—
366C22—5961no—
367C22—5961no—
368C22—5961no—
369C22—5961no—
370C22—5961no—
371C22—1492no—
372C22—11924no—
373C22—11924no—
374C22SD16×D14912yes—
375C22C2×D4×D14911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2981no—
381C4—2981no—
382C4—5961no—
383C4—5961no—
384C4—1492no—
385C4#41×D14911yescharacteristic
386C4#1801195711yescharacteristic
387C2—22no—
388C2—81no—
389C2—2982no—
390C2—5962no—
391C2—11921no—
392C2#2375026711yescharacteristic
393C2C2×SD16×D14911yescharacteristic
394C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#481×C149C2
socleC22×C149C22×D4
prime radical#23750259C2
hypercenter#481D149
hypocenterC149#3295
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #23750330C2semidirect
3. #23749970C2semidirect
4. #23749945C2semidirect
5. #23749914C2semidirect
6. #23749855C2semidirect
7. #23749852C2semidirect
8. #23749824C2semidirect
9. #23749778C2semidirect
10. #23749777C2semidirect
11. #23749712C2semidirect
12. #23749688C2semidirect
13. C2×#18011831C2semidirect
14. #102×D149C2semidirect
15. #481×C149C2semidirect
20. C2×#14558725C22semidirect
21. C2×#14558724C22semidirect
22. C22×#11924746C22semidirect
23. C2×C8×D149C22semidirect
24. #18011910C22semidirect
27. #18011891C22semidirect
29. #18011890C22semidirect
35. #18011876C22semidirect
39. C4⋊C4×D149C22semidirect
40. #18011842C22semidirect
41. #18011840C22semidirect
42. #18011834C22semidirect
44. #18011833C22semidirect
45. #18011832C22semidirect
48. #18011831C22semidirect
49. #18011831C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
53. C2×C4⋊C4×C149C22semidirect
54. #106×C149C22semidirect
55. #106×C149C22semidirect
56. #102×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
133. C22⋊D149SD16semidirect
197. C149#3295semidirect
203. #481D149semidirect
239. C2×C4⋊C4C2×D149semidirect
241. #106C2×D149semidirect
242. #106C2×D149semidirect
252. #102C2×D149semidirect
253. #102C2×D149semidirect
255. C22⋊C8C2×D149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237503302
#237502592
#237499702
#237499452
#237499142
#237498552
#237498522
#237498242
#237497782
#237497772
#237497122
#237496882
C2×#180118312
#102×D1492
#481×C1492
#3295149