Finite Group Databasebeta

← #34056508

Subgroups — #34056508

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#23750333C211yesmaximal, characteristic, complemented
2D4×C22⋊D149C211yesmaximal, characteristic
3#23749970C211yesmaximal, characteristic, complemented
4#23749944C211yesmaximal, characteristic, complemented
5#23749942C211yesmaximal, characteristic, complemented
6#23749913C211yesmaximal, characteristic, complemented
7#23749856C211yesmaximal, characteristic, complemented
8#23749851C211yesmaximal, characteristic, complemented
9#23749823C211yesmaximal, characteristic, complemented
10#23749774C211yesmaximal, characteristic, complemented
11SD16×Dic149C211yesmaximal, characteristic, complemented
12#23749688C211yesmaximal, characteristic, complemented
13C2×#18011832C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15#450×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149—21no—
17C2×D4×D149C2211yescharacteristic
18C2×#14558723C2211yescharacteristic, complemented
19C22×#11924746C2211yescharacteristic, complemented
20C2×C8×D149C2211yescharacteristic, complemented
21#18011910C2211yescharacteristic, complemented
22#18011907C2211yescharacteristic
23#18011901—21no—
24#18011891—21no—
25#18011888—21no—
26#18011887C2211yescharacteristic, complemented
27#18011885C2211yescharacteristic
28#18011883—21no—
29#18011882C2211yescharacteristic
30#18011880—21no—
31#18011879—21no—
32Q8×Dic149C2211yescharacteristic, complemented
33D4×Dic149C2211yescharacteristic
34C4×C22⋊D149C2211yescharacteristic
35#18011871—21no—
36C2×C4⋊Dic149C2211yescharacteristic, complemented
37C4⋊C4×D149C2211yescharacteristic, complemented
38#18011843C2211yescharacteristic, complemented
39#18011843C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011835C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic, complemented
45#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic, complemented
48#18011832C2211yescharacteristic, complemented
49#18011831C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C22×D4×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic, complemented
55C22⋊Q8×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—44no—
68C2×C22⋊D149D411yescharacteristic
69D4×D149—22no—
70D4×D149—41no—
71C22×Dic149—21no—
72C22×Dic149—21no—
73C2×C4×D149—21no—
74C2×C4×D149C2311yescharacteristic
75#14558723—41no—
76C2×#11924746—41no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C8×D149—41no—
80C4⋊Dic149—21no—
81C4⋊Dic149—21no—
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715D411yescharacteristic
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149D411yescharacteristic
92#14558713—21no—
93#14558713—21no—
94#14558713D411yescharacteristic
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C24×C149—21no—
98C2×Q8×C149C2311yescharacteristic
99C2×D4×C149—22no—
100C2×D4×C149—21no—
101C2×D4×C149—41no—
102C2×D4×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105SD16×C149—22no—
106SD16×C149—41no—
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C4⋊C4×C149—21no—
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—42no—
121C22⋊D149—42no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C22⋊D149—81no—
125C22⋊D149SD1614yescomplemented
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—42no—
130C2×Dic149—81no—
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—81no—
137#11924746—21no—
138#11924746—21no—
139C23×C149—21no—
140C23×C149—21no—
141C23×C149—42no—
142C23×C149—42no—
143C23×C149—81no—
144C23×C149C2×D411yescharacteristic
145Q8×C149—21no—
146Q8×C149—21no—
147D4×C149—21no—
148D4×C149—21no—
149D4×C149—21no—
150D4×C149—42no—
151D4×C149#4112yes—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149C2×D411yescharacteristic
157C2×C4×C149C2411yescharacteristic
158C8×C149—21no—
159C8×C149—21no—
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—22no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—41no—
168C22×C149—84no—
169C22×C149C2×SD1612yes—
170C22×C149C22×D411yescharacteristic
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—84no—
177C2×D149C2×SD1612yes—
178C4×C149—21no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149C2×#4111yescharacteristic
182C4×C149H(5,𝔽2)11yescharacteristic
183Dic149—21no—
184Dic149—21no—
185Dic149—41no—
186Dic149—41no—
187Dic149—41no—
188Dic149C2×SD1612yes—
189C2×C149—22no—
190C2×C149—42no—
191C2×C149—81no—
192C2×C149#54611yescharacteristic
193C2×C149C22×SD1611yescharacteristic
194C2×C149#57611yescharacteristic
195D149—22no—
196D149—81no—
197C149#329511yescharacteristic, complemented, Sylow
198#3295—1491nomaximal, Sylow
199#554—1491no—
200D42—1491no—
201#486—1491no—
202#481—1491no—
203#481—1491no—
204#476—1491no—
205#465—1491no—
206#465—1491no—
207#460—1491no—
208#450—1491no—
209#450D14911yescharacteristic, complemented
210C4×SD16—1491no—
211C8×D4—1491no—
212C2×#102—1491no—
213C2×#102—1491no—
214C22×D4—2981no—
215C22×D4—1491no—
216C22×D4C2×D14911yescharacteristic
217C2×SD16—1491no—
218C2×SD16C2×D14911yescharacteristic
219C2×SD16C2×D14911yescharacteristic, complemented
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⋊Q8C2×D14911yescharacteristic, complemented
229#121—2981no—
230#121—1491no—
231#121—1491no—
232#120—2981no—
233#120—2981no—
234C4×Q8—1491no—
235C4×D4—2981no—
236C4×D4—1491no—
237C4×D4—1491no—
238C2×C4⋊C4—1491no—
239C2×C4⋊C4—1491no—
240#106—1491no—
241#106—1491no—
242#106—1491no—
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
253#102C2×D14911yescharacteristic, complemented
254C22⋊C8—1491no—
255C22⋊C8C2×D14911yescharacteristic, complemented
256C4×C8—1491no—
257C24—21no—
258C24—2981no—
259C2×Q8—2981no—
260C2×Q8C22×D14911yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—2982no—
265C2×D4—2981no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—5961no—
271C2×D4—5964no—
272C2×D4—1491no—
273C2×D4—1491no—
274C2×D4C22×D14911yescharacteristic
275C2×D4C22×D14911yescharacteristic
276C22×C4—2981no—
277C22×C4—2981no—
278C22×C4—2981no—
279C22×C4—1491no—
280C22×C4C22×D14911yescharacteristic
281SD16—22no—
282SD16—41no—
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⋊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—1491no—
307C22⋊C4—1491no—
308C42—2981no—
309C42—1491no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—2981no—
316C23—5962no—
317C23—5962no—
318C23—1491no—
319C23—11921no—
320C23D4×D14911yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—11921no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—2981no—
329D4—2981no—
330D4—5962no—
331D4—5962no—
332D4—5962no—
333D4—5962no—
334D4—1494no—
335D4—11921no—
336D4#1455873512yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—5962no—
347C2×C4—1491no—
348C2×C4—1491no—
349C2×C4—1491no—
350C2×C4—11921no—
351C2×C4—11921no—
352C2×C4D4×D14911yescharacteristic
353C2×C4C23×D14911yescharacteristic
354C8—21no—
355C8—21no—
356C8—2981no—
357C8—2981no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—2981no—
368C22—2981no—
369C22—5961no—
370C22—5961no—
371C22—5961no—
372C22—1492no—
373C22—11924no—
374C22SD16×D14912yes—
375C22C2×D4×D14911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—2981no—
380C4—2981no—
381C4—5961no—
382C4—5961no—
383C4—5961no—
384C4—1492no—
385C4C2×#1455873511yescharacteristic
386C4#1801195611yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—2982no—
391C2—11921no—
392C2#2375026211yescharacteristic
393C2C2×SD16×D14911yescharacteristic
394C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#450×C149C2
socleC22×C149C22×D4
prime radicalD4×C22⋊D149C2
hypercenter#450D149
hypocenterC149#3295
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23750333C2semidirect
3. #23749970C2semidirect
4. #23749944C2semidirect
5. #23749942C2semidirect
6. #23749913C2semidirect
7. #23749856C2semidirect
8. #23749851C2semidirect
9. #23749823C2semidirect
10. #23749774C2semidirect
11. SD16×Dic149C2semidirect
12. #23749688C2semidirect
13. C2×#18011832C2semidirect
14. #102×D149C2semidirect
15. #450×C149C2semidirect
18. C2×#14558723C22semidirect
19. C22×#11924746C22semidirect
20. C2×C8×D149C22semidirect
21. #18011910C22semidirect
26. #18011887C22semidirect
32. Q8×Dic149C22semidirect
36. C2×C4⋊Dic149C22semidirect
37. C4⋊C4×D149C22semidirect
38. #18011843C22semidirect
39. #18011843C22semidirect
40. #18011842C22semidirect
41. #18011840C22semidirect
42. #18011835C22semidirect
43. #18011833C22semidirect
44. #18011833C22semidirect
47. #18011832C22semidirect
48. #18011832C22semidirect
49. #18011831C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
54. C2×SD16×C149C22semidirect
55. C22⋊Q8×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
125. C22⋊D149SD16semidirect
197. C149#3295semidirect
209. #450D149semidirect
219. C2×SD16C2×D149semidirect
228. C22⋊Q8C2×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
#237503332
D4×C22⋊D1492
#237499702
#237499442
#237499422
#237499132
#237498562
#237498512
#237498232
#237497742
SD16×Dic1492
#237496882
C2×#180118322
#102×D1492
#450×C1492
#3295149