Finite Group Databasebeta

← #482×D149 #34054571

Subgroups — #482×D149 #34054571

Order 19072.

468 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D149C211yesmaximal, characteristic
2#117×D149C211yesmaximal, characteristic, complemented
3#23749952C211yesmaximal, characteristic, complemented
4#23749951C211yesmaximal, characteristic, complemented
5#23749950C211yesmaximal, characteristic, complemented
6#23749949C211yesmaximal, characteristic, complemented
7#23749948C211yesmaximal, characteristic, complemented
8#23749947C211yesmaximal, characteristic, complemented
9#23749946C211yesmaximal, characteristic, complemented
10#107×D149C211yesmaximal, characteristic, complemented
11#106×D149C211yesmaximal, characteristic, complemented
12#102×D149C211yesmaximal, characteristic, complemented
13#102×D149C211yesmaximal, characteristic, complemented
14C22⋊C8×D149C211yesmaximal, characteristic, complemented
15#482×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149—21no—
17C2×D4×D149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19C2×C8×D149C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21#18011886C2211yescharacteristic
22#18011885C2211yescharacteristic
23#18011884—21no—
24#18011883—21no—
25#18011882C2211yescharacteristic
26#18011870C2211yescharacteristic, complemented
27#18011869C2211yescharacteristic, complemented
28#18011869C2211yescharacteristic, complemented
29#18011868—21no—
30#18011867—21no—
31C4⋊C4×D149C2211yescharacteristic
32C4⋊C4×D149C2211yescharacteristic
33C4⋊C4×D149C2211yescharacteristic
34C22⋊C4×D149—21no—
35C22⋊C4×D149—21no—
36C42×D149—21no—
37#18011845C2211yescharacteristic, complemented
38#18011844C2211yescharacteristic, complemented
39#18011844C2211yescharacteristic, complemented
40#18011843C2211yescharacteristic, complemented
41#18011842C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic, complemented
45#18011832C2211yescharacteristic, complemented
46#18011832C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic, 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×D149D411yescharacteristic
61C2×D596—21no—
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66D4×D149—22no—
67D4×D149—22no—
68D4×D149—44no—
69C22×Dic149D411yescharacteristic
70C2×C4×D149—22no—
71C2×C4×D149—22no—
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149D411yescharacteristic
76C2×C4×D149D411yescharacteristic
77C2×C4×D149C2311yescharacteristic
78C2×C4×D149C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C2×#11924746C2311yescharacteristic
81C8×D149—22no—
82C8×D149—22no—
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85C4⋊Dic149C2311yescharacteristic
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C4×Dic149—21no—
98C2×D4×C149—21no—
99C2×D4×C149C2311yescharacteristic
100C22×C4×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C42×C149—21no—
109C22×D149—22no—
110C22×D149—22no—
111C22×D149—22no—
112C22×D149—21no—
113C22×D149—42no—
114C22×D149—42no—
115C22×D149—42no—
116C22×D149C2×D411yescharacteristic
117C22×D149C2×D411yescharacteristic
118D596—21no—
119D596—21no—
120D596—42no—
121C22⋊D149—42no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C2×Dic149—22no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C4×D149—22no—
131C4×D149—21no—
132C4×D149—21no—
133C4×D149—22no—
134C4×D149—42no—
135C4×D149—42no—
136C4×D149—42no—
137C4×D149#4112yes—
138C4×D149#4112yes—
139#11924746—21no—
140#11924746—21no—
141C23×C149—21no—
142C23×C149C2×D411yescharacteristic
143D4×C149—21no—
144D4×C149—21no—
145D4×C149—42no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2411yescharacteristic
153C8×C149—21no—
154C8×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149—21no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149C22×D411yescharacteristic
162C2×D149—21no—
163C2×D149—21no—
164C2×D149—21no—
165C2×D149—44no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—84no—
170C2×D149#12312yes—
171C2×D149#13512yes—
172C2×D149AGL(1,ℤ/8)12yes—
173C4×C149—21no—
174C4×C149—41no—
175C4×C149—41no—
176C4×C149—41no—
177C4×C149C2×#4111yescharacteristic
178C4×C149C2×#4111yescharacteristic
179Dic149—21no—
180Dic149—41no—
181Dic149—41no—
182Dic149—41no—
183Dic149#12312yes—
184C2×C149—41no—
185C2×C149—81no—
186C2×C149C2×#12311yescharacteristic
187C2×C149C2×#13511yescharacteristic
188C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
189D149—41no—
190D149—81no—
191D149#48214yesdirect product factor
192C149C2×#48211yescharacteristic, complemented, Sylow
193C2×#482—1491nomaximal, Sylow
194C2×#121—1491no—
195C2×#117—1491no—
196#482—1491no—
197#482—1491no—
198#482—1491no—
199#482—1491no—
200#482—1491no—
201#482—1491no—
202#482—1491no—
203#482D14911yescharacteristic, direct product factor
204C2×#107—1491no—
205C2×#106—1491no—
206C2×#102—1491no—
207C2×#102—1491no—
208C2×C22⋊C8—1491no—
209C22×D4—2981no—
210C22×D4—1491no—
211C23×C4—1491no—
212C22×C8—1491no—
213C22×C8—1491no—
214#121—2981no—
215#121—2981no—
216#121—1491no—
217#121—1491no—
218#121—1491no—
219#121C2×D14911yescharacteristic
220#117—2981no—
221#117—2981no—
222#117—1491no—
223#117—1491no—
224#117—1491no—
225#117C2×D14911yescharacteristic, complemented
226C2×C4⋊C4—1491no—
227C2×C4⋊C4—1491no—
228C2×C4⋊C4—1491no—
229C2×C22⋊C4—2981no—
230C2×C22⋊C4—2981no—
231C2×C42—2981no—
232#107—1491no—
233#107—1491no—
234#107—1491no—
235#107C2×D14911yescharacteristic, complemented
236#106—1491no—
237#106—1491no—
238#106—1491no—
239#106C2×D14911yescharacteristic, complemented
240#102—1491no—
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102C2×D14911yescharacteristic, complemented
247#102C2×D14911yescharacteristic, complemented
248C22⋊C8—1491no—
249C22⋊C8—1491no—
250C22⋊C8—1491no—
251C22⋊C8C2×D14911yescharacteristic, complemented
252C24—2981no—
253C24—1491no—
254C2×D4—21no—
255C2×D4—2981no—
256C2×D4—2981no—
257C2×D4—2981no—
258C2×D4—2982no—
259C2×D4—2982no—
260C2×D4—2981no—
261C2×D4—5964no—
262C2×D4—1491no—
263C2×D4C22×D14911yescharacteristic
264C22×C4—2982no—
265C22×C4—2982no—
266C22×C4—2981no—
267C22×C4—2981no—
268C22×C4—2981no—
269C22×C4—1491no—
270C22×C4—1491no—
271C22×C4—1491no—
272C22×C4—1491no—
273C22×C4—1491no—
274C22×C4C22×D14911yescharacteristic
275C2×C8—2982no—
276C2×C8—2982no—
277C2×C8—1491no—
278C2×C8—1491no—
279C2×C8C22×D14911yescharacteristic
280C2×C8C22×D14911yescharacteristic
281C4⋊C4—2981no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—1491no—
285C4⋊C4—1491no—
286C4⋊C4—1491no—
287C4⋊C4C22×D14911yescharacteristic
288C4⋊C4C22×D14911yescharacteristic
289C4⋊C4C22×D14911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C42—21no—
299C42—2981no—
300C42—2981no—
301C42—2981no—
302C23—21no—
303C23—2982no—
304C23—2982no—
305C23—2982no—
306C23—2981no—
307C23—5962no—
308C23—5962no—
309C23—5962no—
310C23—1491no—
311C23—1491no—
312C23D4×D14911yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—2981no—
317D4—2981no—
318D4—5962no—
319D4—5962no—
320D4—5962no—
321D4—5962no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—2982no—
328C2×C4—2982no—
329C2×C4—2982no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—5962no—
336C2×C4—5962no—
337C2×C4—5962no—
338C2×C4—1491no—
339C2×C4—1491no—
340C2×C4—1492no—
341C2×C4—1492no—
342C2×C4D4×D14911yescharacteristic
343C2×C4C23×D14911yescharacteristic
344C8—21no—
345C8—21no—
346C8—2981no—
347C8—2981no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—2981no—
355C22—2981no—
356C22—2981no—
357C22—5964no—
358C22—5961no—
359C22—5961no—
360C22—5961no—
361C22—1492no—
362C22—1492no—
363C22—1492no—
364C22—11924no—
365C22C2×D4×D14911yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—2981no—
371C4—5961no—
372C4—5961no—
373C4—5961no—
374C4—1492no—
375C4#41×D14911yescharacteristic
376C4#41×D14911yescharacteristic
377C2—41no—
378C2—81no—
379C2—5961no—
380C2—1494no—
381C2—11921no—
382C2#123×D14911yescharacteristic
383C2#135×D14911yescharacteristic
384C2AGL(1,ℤ/8)×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#482×C149C2
socleC22×C149C22×D4
prime radical#121×D149C2
hypercenter#482D149
hypocenterC149C2×#482
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
2. #117×D149C2semidirect
3. #23749952C2semidirect
4. #23749951C2semidirect
5. #23749950C2semidirect
6. #23749949C2semidirect
7. #23749948C2semidirect
8. #23749947C2semidirect
9. #23749946C2semidirect
10. #107×D149C2semidirect
11. #106×D149C2semidirect
12. #102×D149C2semidirect
13. #102×D149C2semidirect
14. C22⋊C8×D149C2semidirect
15. #482×C149C2semidirect
26. #18011870C22semidirect
27. #18011869C22semidirect
28. #18011869C22semidirect
37. #18011845C22semidirect
38. #18011844C22semidirect
39. #18011844C22semidirect
40. #18011843C22semidirect
41. #18011842C22semidirect
42. #18011842C22semidirect
43. #18011833C22semidirect
44. #18011833C22semidirect
45. #18011832C22semidirect
46. #18011832C22semidirect
47. #18011831C22semidirect
48. #18011831C22semidirect
49. C22⋊#11924746C22semidirect
50. #18011823C22semidirect
51. #18011823C22semidirect
53. #117×C149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. #102×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
191. D149#482direct (N × H)
192. C149C2×#482semidirect
203. #482D149direct (N × H)
225. #117C2×D149semidirect
235. #107C2×D149semidirect
239. #106C2×D149semidirect
246. #102C2×D149semidirect
247. #102C2×D149semidirect
251. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#121×D1492
#117×D1492
#237499522
#237499512
#237499502
#237499492
#237499482
#237499472
#237499462
#107×D1492
#106×D1492
#102×D1492
C22⋊C8×D1492
#482×C1492
C2×#482149