Finite Group Databasebeta

← #34056931

Subgroups — #34056931

Order 19072.

460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750338C211yesmaximal, characteristic, complemented
2#23750259C211yesmaximal, characteristic, complemented
3#23749970C211yesmaximal, characteristic, complemented
4#23749952C211yesmaximal, characteristic, complemented
5#23749914C211yesmaximal, characteristic, complemented
6#23749879C211yesmaximal, characteristic, complemented
7#23749876C211yesmaximal, characteristic, complemented
8#23749819C211yesmaximal, characteristic, complemented
9#23749761C211yesmaximal, characteristic, complemented
10#23749760C211yesmaximal, characteristic, complemented
11#23749707C211yesmaximal, characteristic, complemented
12#23749700C211yesmaximal, characteristic, complemented
13#23749629C211yesmaximal, characteristic, complemented
14#23749628C211yesmaximal, characteristic, complemented
15#482×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C2×D4×D149—21no—
18C2×D4×D149C2211yescharacteristic
19C2×D1192C2211yescharacteristic
20C2×D1192C2211yescharacteristic, complemented
21C2×#14558721C2211yescharacteristic, complemented
22C2×#14558720C2211yescharacteristic, complemented
23C2×#14558719C2211yescharacteristic, complemented
24#18011910C2211yescharacteristic, complemented
25#18011907C2211yescharacteristic
26#18011899—21no—
27#18011897—21no—
28#18011886C2211yescharacteristic
29#18011886C2211yescharacteristic, complemented
30#18011885C2211yescharacteristic, complemented
31#18011884—21no—
32#18011884—21no—
33#18011881—21no—
34#18011879—21no—
35#18011873C2211yescharacteristic
36#18011873C2211yescharacteristic, complemented
37C4×C22⋊D149C2211yescharacteristic
38#18011869C2211yescharacteristic, complemented
39#18011868—21no—
40#18011842C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011833C2211yescharacteristic
43#18011833C2211yescharacteristic, complemented
44#18011832C2211yescharacteristic, complemented
45#18011831C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic, complemented
49#18011831C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52#121×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic, complemented
54#107×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×D596—22no—
63C2×D596—21no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—41no—
67C2×D596C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×D596C2311yescharacteristic
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149—21no—
74C2×C22⋊D149D411yescharacteristic
75D4×D149—22no—
76D4×D149—41no—
77D4×D149—44no—
78C2×C4×D149—21no—
79C2×C4×D149—21no—
80C2×C4×D149C2311yescharacteristic
81D1192—22no—
82D1192—41no—
83#14558721—41no—
84#14558720—41no—
85#14558719—41no—
86C2×#11924746C2311yescharacteristic
87C2×#11924746C2311yescharacteristic
88C4⋊Dic149C2311yescharacteristic
89#14558715—21no—
90#14558715D411yescharacteristic
91C22⋊Dic149D411yescharacteristic
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
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×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C22⋊C4×C149—21no—
111C42×C149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—21no—
115C22×D149—42no—
116C22×D149—42no—
117C22×D149—42no—
118C22×D149—42no—
119C22×D149—81no—
120C22×D149—81no—
121C22×D149C2×D411yescharacteristic
122Dic298—81no—
123D596—21no—
124D596—21no—
125D596—21no—
126D596—21no—
127D596—21no—
128D596—42no—
129D596—42no—
130D596—81no—
131D596#4112yes—
132C22⋊D149—22no—
133C22⋊D149—42no—
134C22⋊D149—42no—
135C22⋊D149—81no—
136C22⋊D149—81no—
137C2×Dic149—21no—
138C2×Dic149C2×D411yescharacteristic
139C2×Dic149C2×D411yescharacteristic
140C2×Dic149C2×D411yescharacteristic
141C4×D149—21no—
142C4×D149—21no—
143C4×D149—42no—
144C4×D149—42no—
145#11924746—21no—
146#11924746—21no—
147C23×C149—21no—
148C23×C149C2×D411yescharacteristic
149D4×C149—21no—
150D4×C149—21no—
151D4×C149—42no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2411yescharacteristic
159C8×C149—21no—
160C8×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149C22×D411yescharacteristic
168C2×D149—21no—
169C2×D149—22no—
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
178C2×D149—41no—
179C2×D149—41no—
180C2×D149—84no—
181C2×D149—84no—
182C4×C149—21no—
183C4×C149—41no—
184C4×C149—41no—
185C4×C149—41no—
186C4×C149C2×#4111yescharacteristic
187C4×C149H(5,𝔽2)11yescharacteristic
188Dic149—21no—
189Dic149—21no—
190Dic149—41no—
191Dic149AGL(1,ℤ/8)12yes—
192C2×C149—41no—
193C2×C149—81no—
194C2×C149#54611yescharacteristic
195C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C149#57611yescharacteristic
197D149—41no—
198D149—42no—
199D149—81no—
200D149—81no—
201C149#332511yescharacteristic, complemented, Sylow
202#3325—1491nomaximal, Sylow
203#555—1491no—
204D42—1491no—
205#486—1491no—
206#482—1491no—
207#482D14911yescharacteristic, complemented
208#476—1491no—
209#469—1491no—
210#469—1491no—
211#459—1491no—
212#447—1491no—
213#447—1491no—
214C4×D8—1491no—
215#436—1491no—
216#418—1491no—
217#418—1491no—
218C22×D4—2981no—
219C22×D4—1491no—
220C22×D4—1491no—
221C2×D8—1491no—
222C2×D8—1491no—
223C2×D8—1491no—
224C2×M16—1491no—
225C2×M16—1491no—
226C4⋊Q8—1491no—
227#127—1491no—
228#124—2981no—
229#124—2981no—
230#121—2981no—
231#121—2981no—
232#121—1491no—
233#121—1491no—
234#121—1491no—
235#121C2×D14911yescharacteristic
236#120—2981no—
237#120—2981no—
238C4×D4—1491no—
239C4×D4—1491no—
240C4×D4—1491no—
241#117—2981no—
242#117—1491no—
243#117C2×D14911yescharacteristic, complemented
244#107C2×D14911yescharacteristic, complemented
245#106—1491no—
246#106C2×D14911yescharacteristic, complemented
247C4⋊C8—1491no—
248#102—1491no—
249#102—1491no—
250#102—1491no—
251#102—1491no—
252#102—1491no—
253#102—1491no—
254#102—1491no—
255#102—1491no—
256#102C2×D14911yescharacteristic, complemented
257#102C2×D14911yescharacteristic, complemented
258C22⋊C8—1491no—
259C22⋊C8C2×D14911yescharacteristic, complemented
260C4×C8—1491no—
261C24—2981no—
262C24—2981no—
263C2×Q8—2981no—
264C2×D4—21no—
265C2×D4—2982no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2982no—
269C2×D4—2981no—
270C2×D4—2981no—
271C2×D4—2981no—
272C2×D4—2981no—
273C2×D4—2981no—
274C2×D4—5961no—
275C2×D4—5961no—
276C2×D4—5964no—
277C2×D4—1491no—
278C2×D4—1491no—
279C2×D4—1491no—
280C2×D4—1491no—
281C2×D4C22×D14911yescharacteristic
282C22×C4—2981no—
283C22×C4—2981no—
284C22×C4—1491no—
285C22×C4C22×D14911yescharacteristic
286D8—2982no—
287D8—5961no—
288D8—5961no—
289M16—5961no—
290M16—5961no—
291C2×C8—1491no—
292C2×C8—1491no—
293C2×C8C22×D14911yescharacteristic
294C2×C8C22×D14911yescharacteristic
295C4⋊C4—2981no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4C22×D14911yescharacteristic
299C4⋊C4C22×D14911yescharacteristic
300C4⋊C4C22×D14911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—1491no—
310C22⋊C4—1491no—
311C42—21no—
312C42—2981no—
313C42—1491no—
314C23—21no—
315C23—2981no—
316C23—2981no—
317C23—2981no—
318C23—5962no—
319C23—5962no—
320C23—5962no—
321C23—5962no—
322C23—1491no—
323C23—11921no—
324C23—11921no—
325C23D4×D14911yescharacteristic
326Q8—11921no—
327D4—21no—
328D4—21no—
329D4—42no—
330D4—2982no—
331D4—2981no—
332D4—2981no—
333D4—2981no—
334D4—2981no—
335D4—2981no—
336D4—5962no—
337D4—5962no—
338D4—5962no—
339D4—5962no—
340D4—1492no—
341D4—11921no—
342D4—11921no—
343D4—11921no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—2981no—
350C2×C4—2981no—
351C2×C4—2981no—
352C2×C4—5962no—
353C2×C4—5962no—
354C2×C4—1491no—
355C2×C4—1491no—
356C2×C4—1491no—
357C2×C4D4×D14911yescharacteristic
358C2×C4C23×D14911yescharacteristic
359C8—21no—
360C8—21no—
361C8—2981no—
362C8—2981no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—2981no—
370C22—2981no—
371C22—2981no—
372C22—2982no—
373C22—5961no—
374C22—5961no—
375C22—5961no—
376C22—5961no—
377C22—5961no—
378C22—5961no—
379C22—5961no—
380C22—5961no—
381C22—11924no—
382C22—11924no—
383C22C2×D4×D14911yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—2981no—
389C4—2981no—
390C4—5961no—
391C4—1492no—
392C4#41×D14911yescharacteristic
393C4#1801195711yescharacteristic
394C2—41no—
395C2—81no—
396C2—5961no—
397C2—5962no—
398C2—11921no—
399C2—11921no—
400C2#2375026711yescharacteristic
401C2AGL(1,ℤ/8)×D14911yescharacteristic
402C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#482×C149C2
socleC22×C149C22×D4
hypercenter#482D149
hypocenterC149#3325
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23750338C2semidirect
2. #23750259C2semidirect
3. #23749970C2semidirect
4. #23749952C2semidirect
5. #23749914C2semidirect
6. #23749879C2semidirect
7. #23749876C2semidirect
8. #23749819C2semidirect
9. #23749761C2semidirect
10. #23749760C2semidirect
11. #23749707C2semidirect
12. #23749700C2semidirect
13. #23749629C2semidirect
14. #23749628C2semidirect
15. #482×C149C2semidirect
20. C2×D1192C22semidirect
21. C2×#14558721C22semidirect
22. C2×#14558720C22semidirect
23. C2×#14558719C22semidirect
24. #18011910C22semidirect
29. #18011886C22semidirect
30. #18011885C22semidirect
36. #18011873C22semidirect
38. #18011869C22semidirect
40. #18011842C22semidirect
41. #18011840C22semidirect
43. #18011833C22semidirect
44. #18011832C22semidirect
47. #18011831C22semidirect
48. #18011831C22semidirect
49. #18011831C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
53. #117×C149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. #102×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
201. C149#3325semidirect
207. #482D149semidirect
243. #117C2×D149semidirect
244. #107C2×D149semidirect
246. #106C2×D149semidirect
256. #102C2×D149semidirect
257. #102C2×D149semidirect
259. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503382
#237502592
#237499702
#237499522
#237499142
#237498792
#237498762
#237498192
#237497612
#237497602
#237497072
#237497002
#237496292
#237496282
#482×C1492
#3325149