Finite Group Databasebeta

← #34056926

Subgroups — #34056926

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#23750339C211yesmaximal, characteristic, complemented
2D4×C22⋊D149C211yesmaximal, characteristic, complemented
3#23749970C211yesmaximal, characteristic, complemented
4#23749950C211yesmaximal, characteristic, complemented
5#23749947C211yesmaximal, characteristic, complemented
6#23749913C211yesmaximal, characteristic, complemented
7#23749876C211yesmaximal, characteristic, complemented
8#23749875C211yesmaximal, characteristic, complemented
9#23749818C211yesmaximal, characteristic, complemented
10#23749757C211yesmaximal, characteristic, complemented
11D8×Dic149C211yesmaximal, characteristic, complemented
12#23749700C211yesmaximal, characteristic, complemented
13#23749630C211yesmaximal, characteristic, complemented
14#23749628C211yesmaximal, characteristic, complemented
15#447×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149—21no—
17C2×D4×D149C2211yescharacteristic
18C2×#14558721C2211yescharacteristic, complemented
19C2×#14558720C2211yescharacteristic, complemented
20C2×#14558719C2211yescharacteristic, complemented
21#18011910C2211yescharacteristic, complemented
22#18011907C2211yescharacteristic
23#18011898—21no—
24#18011897—21no—
25#18011885C2211yescharacteristic
26#18011883—21no—
27#18011883—21no—
28#18011882C2211yescharacteristic
29#18011882C2211yescharacteristic, complemented
30#18011880—21no—
31#18011879—21no—
32D4×Dic149C2211yescharacteristic
33D4×Dic149C2211yescharacteristic, complemented
34C4×C22⋊D149C2211yescharacteristic
35#18011870C2211yescharacteristic, complemented
36#18011869C2211yescharacteristic, complemented
37#18011867—21no—
38#18011845C2211yescharacteristic, complemented
39#18011843C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011833C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic, complemented
44#18011832C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic, complemented
47#18011832C2211yescharacteristic, complemented
48#18011832C2211yescharacteristic, complemented
49#18011831C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C22×D4×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54C2×D8×C149C2211yescharacteristic, complemented
55#121×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×Dic298—21no—
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—44no—
69C2×C22⋊D149D411yescharacteristic
70D4×D149—22no—
71D4×D149—41no—
72C22×Dic149—21no—
73C22×Dic149—21no—
74C2×C4×D149C2311yescharacteristic
75#14558721—41no—
76#14558720—41no—
77#14558719—41no—
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149D411yescharacteristic
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C24×C149—21no—
98C2×D4×C149—22no—
99C2×D4×C149—21no—
100C2×D4×C149—21no—
101C2×D4×C149—41no—
102C2×D4×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104C2×D4×C149C2311yescharacteristic
105C22×C4×C149C2311yescharacteristic
106D8×C149—22no—
107D8×C149—41no—
108C2×C8×C149C2311yescharacteristic
109C2×C8×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22×D149—21no—
113C22×D149—42no—
114C22×D149—42no—
115C22×D149—81no—
116C22×D149C2×D411yescharacteristic
117Dic298—81no—
118D596—21no—
119D596—21no—
120C22⋊D149—22no—
121C22⋊D149—42no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C22⋊D149—81no—
126C22⋊D149—81no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—42no—
131C2×Dic149—42no—
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C2×Dic149C2×D411yescharacteristic
135C4×D149—21no—
136C4×D149—21no—
137#11924746—21no—
138#11924746—21no—
139C23×C149—21no—
140C23×C149—21no—
141C23×C149—21no—
142C23×C149—42no—
143C23×C149—42no—
144C23×C149—81no—
145C23×C149C2×D411yescharacteristic
146D4×C149—21no—
147D4×C149—21no—
148D4×C149—21no—
149D4×C149—21no—
150D4×C149—21no—
151D4×C149—42no—
152D4×C149—81no—
153D4×C149#4112yes—
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—22no—
163C22×C149—21no—
164C22×C149—21no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149—84no—
174C22×C149C22×D411yescharacteristic
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—21no—
178C2×D149—41no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—84no—
182C4×C149—21no—
183C4×C149—41no—
184C4×C149C2×#4111yescharacteristic
185C4×C149H(5,𝔽2)11yescharacteristic
186Dic149—21no—
187Dic149—21no—
188Dic149—41no—
189Dic149—41no—
190Dic149—41no—
191Dic149AGL(1,ℤ/8)12yes—
192C2×C149—42no—
193C2×C149—41no—
194C2×C149—81no—
195C2×C149—81no—
196C2×C149#54611yescharacteristic
197C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C149#57611yescharacteristic
199D149—41no—
200D149—81no—
201C149#332511yescharacteristic, complemented, Sylow
202#3325—1491nomaximal, Sylow
203#555—1491no—
204D42—1491no—
205#486—1491no—
206#482—1491no—
207#482—1491no—
208#476—1491no—
209#469—1491no—
210#469—1491no—
211#459—1491no—
212#447—1491no—
213#447D14911yescharacteristic, complemented
214C4×D8—1491no—
215#436—1491no—
216#418—1491no—
217#418—1491no—
218C22×D4—2981no—
219C22×D4—1491no—
220C22×D4C2×D14911yescharacteristic
221C2×D8—1491no—
222C2×D8C2×D14911yescharacteristic
223C2×D8C2×D14911yescharacteristic, complemented
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, complemented
236#120—2981no—
237#120—2981no—
238C4×D4—1491no—
239C4×D4—1491no—
240C4×D4—1491no—
241#117—2981no—
242#117—1491no—
243#117—1491no—
244#107—1491no—
245#106—1491no—
246#106—1491no—
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
257#102C2×D14911yescharacteristic, complemented
258C22⋊C8—1491no—
259C22⋊C8C2×D14911yescharacteristic, complemented
260C4×C8—1491no—
261C24—21no—
262C24—2981no—
263C2×Q8—2981no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—2982no—
269C2×D4—2981no—
270C2×D4—2981no—
271C2×D4—2981no—
272C2×D4—2981no—
273C2×D4—2981no—
274C2×D4—2981no—
275C2×D4—5961no—
276C2×D4—5964no—
277C2×D4—1491no—
278C2×D4—1491no—
279C2×D4C22×D14911yescharacteristic
280C2×D4C22×D14911yescharacteristic
281C2×D4C22×D14911yescharacteristic
282C22×C4—2981no—
283C22×C4—2981no—
284C22×C4—1491no—
285C22×C4C22×D14911yescharacteristic
286D8—22no—
287D8—41no—
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⋊C4—1491no—
299C4⋊C4—1491no—
300C4⋊C4C22×D14911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—2981no—
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—2981no—
312C42—2981no—
313C42—1491no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—2981no—
321C23—5962no—
322C23—5962no—
323C23—1491no—
324C23—11921no—
325C23D4×D14911yescharacteristic
326Q8—11921no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—2982no—
335D4—2981no—
336D4—2981no—
337D4—5962no—
338D4—5962no—
339D4—5962no—
340D4—5962no—
341D4—11921no—
342D4—11921no—
343D4#1455873512yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—2981no—
348C2×C4—2981no—
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—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—84no—
376C22—2981no—
377C22—2981no—
378C22—2981no—
379C22—5961no—
380C22—5961no—
381C22—5961no—
382C22—11924no—
383C22C2×D4×D14911yescharacteristic
384C4—21no—
385C4—41no—
386C4—2981no—
387C4—2981no—
388C4—5961no—
389C4—5961no—
390C4—5961no—
391C4—1492no—
392C4C2×#1455873511yescharacteristic
393C4#1801195611yescharacteristic
394C2—41no—
395C2—42no—
396C2—81no—
397C2—81no—
398C2—5961no—
399C2—11921no—
400C2#2375026211yescharacteristic
401C2AGL(1,ℤ/8)×D14911yescharacteristic
402C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#447×C149C2
socleC22×C149C22×D4
hypercenter#447D149
hypocenterC149#3325
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #23750339C2semidirect
2. D4×C22⋊D149C2semidirect
3. #23749970C2semidirect
4. #23749950C2semidirect
5. #23749947C2semidirect
6. #23749913C2semidirect
7. #23749876C2semidirect
8. #23749875C2semidirect
9. #23749818C2semidirect
10. #23749757C2semidirect
11. D8×Dic149C2semidirect
12. #23749700C2semidirect
13. #23749630C2semidirect
14. #23749628C2semidirect
15. #447×C149C2semidirect
18. C2×#14558721C22semidirect
19. C2×#14558720C22semidirect
20. C2×#14558719C22semidirect
21. #18011910C22semidirect
29. #18011882C22semidirect
33. D4×Dic149C22semidirect
35. #18011870C22semidirect
36. #18011869C22semidirect
38. #18011845C22semidirect
39. #18011843C22semidirect
40. #18011842C22semidirect
41. #18011840C22semidirect
42. #18011833C22semidirect
43. #18011833C22semidirect
46. #18011832C22semidirect
47. #18011832C22semidirect
48. #18011832C22semidirect
49. #18011831C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
54. C2×D8×C149C22semidirect
55. #121×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
201. C149#3325semidirect
213. #447D149semidirect
223. C2×D8C2×D149semidirect
235. #121C2×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
#237503392
D4×C22⋊D1492
#237499702
#237499502
#237499472
#237499132
#237498762
#237498752
#237498182
#237497572
D8×Dic1492
#237497002
#237496302
#237496282
#447×C1492
#3325149