Finite Group Databasebeta

← #34056925

Subgroups — #34056925

Order 19072.

448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750348C211yesmaximal, characteristic, complemented
2#23750260C211yesmaximal, characteristic
3#23749971C211yesmaximal, characteristic, complemented
4#23749947C212yesmaximal, complemented
5#23749906C211yesmaximal, characteristic, complemented
6#23749868C212yesmaximal, complemented
7#23749774C212yesmaximal, complemented
8C4×#14558723C211yesmaximal, characteristic, complemented
9#23749702C211yesmaximal, characteristic, complemented
10#23749628C212yesmaximal, complemented
11#460×C149C211yesmaximal, characteristic, complemented
12C2×D4×D149—21no—
13C2×D4×D149C2212yes—
14C2×#14558723C2211yescharacteristic
15C2×#14558719C2212yescomplemented
16#18011911C2211yescharacteristic, complemented
17#18011906—22no—
18#18011899—21no—
19#18011887C2212yescomplemented
20#18011882—21no—
21#18011882C2212yes—
22#18011879—22no—
23C4×Dic298—21no—
24C4×D596C2211yescharacteristic
25C4×D596C2211yescharacteristic
26#18011869C2212yescomplemented
27#18011845C2212yescomplemented
28#18011842C2211yescharacteristic, complemented
29#18011835C2211yescharacteristic, complemented
30#18011833C2212yes—
31#18011832C2212yescomplemented
32#18011832C2212yescomplemented
33#18011831C2211yescharacteristic
34#18011823C2212yescomplemented
35C4×#11924746C2211yescharacteristic, complemented
36C2×SD16×C149C2212yescomplemented
37#127×C149C2211yescharacteristic
38C4×Q8×C149C2211yescharacteristic, complemented
39C4⋊C8×C149C2211yescharacteristic, complemented
40#102×C149C2212yescomplemented
41C23×D149—22no—
42C2×Dic298—21no—
43C2×D596D411yescharacteristic
44C2×D596C2311yescharacteristic
45C2×C22⋊D149—22no—
46C2×C22⋊D149—22no—
47D4×D149—24no—
48D4×D149—42no—
49D4×D149—44no—
50C2×C4×D149—21no—
51C2×C4×D149C2312yes—
52#14558723—22no—
53#14558719—42no—
54C2×#11924746C2311yescharacteristic
55C2×#11924746C2311yescharacteristic
56C4⋊Dic149—21no—
57C4⋊Dic149D411yescharacteristic
58C4⋊Dic149C2312yes—
59C4⋊Dic149C2311yescharacteristic
60#14558715—22no—
61C22⋊Dic149—22no—
62#14558713—22no—
63#14558713—22no—
64#14558713—21no—
65#14558713D412yes—
66C4×Dic149—22no—
67C2×Q8×C149C2311yescharacteristic
68C2×D4×C149—21no—
69C2×D4×C149—21no—
70C2×D4×C149C2312yes—
71SD16×C149—42no—
72C2×C8×C149C2312yes—
73C4⋊C4×C149—21no—
74C4⋊C4×C149C2311yescharacteristic
75C42×C149—21no—
76C42×C149C2311yescharacteristic
77C22×D149—21no—
78C22×D149—44no—
79C22×D149—44no—
80C22×D149—82no—
81C22×D149C2×D412yes—
82Dic298—42no—
83D596—22no—
84D596—21no—
85D596#4112yes—
86C22⋊D149—44no—
87C22⋊D149—44no—
88C2×Dic149—21no—
89C2×Dic149—22no—
90C2×Dic149C2×D412yes—
91C4×D149—22no—
92C4×D149—22no—
93C4×D149—42no—
94#11924746—21no—
95#11924746—21no—
96C23×C149—22no—
97Q8×C149—21no—
98Q8×C149—21no—
99D4×C149—22no—
100D4×C149—22no—
101D4×C149—42no—
102D4×C149—81no—
103C2×C4×C149—21no—
104C2×C4×C149—21no—
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2411yescharacteristic
108C8×C149—22no—
109C22×C149—42no—
110C22×C149—42no—
111C22×C149—42no—
112C22×C149C22×D411yescharacteristic
113C2×D149—22no—
114C2×D149—22no—
115C2×D149—22no—
116C2×D149—22no—
117C2×D149—41no—
118C2×D149—41no—
119C2×D149—88no—
120C4×C149—21no—
121C4×C149—41no—
122C4×C149—41no—
123C4×C149AGL(1,ℤ/8)12yes—
124C4×C149C2×#4111yescharacteristic
125C4×C149H(5,𝔽2)11yescharacteristic
126Dic149—22no—
127Dic149—41no—
128Dic149—42no—
129C2×C149—82no—
130C2×C149#54611yescharacteristic
131C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C149#57711yescharacteristic
133D149—42no—
134D149—42no—
135C149#332411yescharacteristic, complemented, Sylow
136#3324—1491nomaximal, Sylow
137#556—1491no—
138D42—1491no—
139#486—1491no—
140#482—1492no—
141#474—1491no—
142#468—1492no—
143#460D14911yescharacteristic, complemented
144#450—1492no—
145C4×SD16—1491no—
146#436—1491no—
147#418—1492no—
148C22×D4—2981no—
149C22×D4—1492no—
150C2×SD16—1491no—
151C2×SD16C2×D14912yescomplemented
152C2×M16—1492no—
153C4⋊Q8—1491no—
154#127C2×D14911yescharacteristic
155#126—2982no—
156#124—2981no—
157C22⋊Q8—1492no—
158#121—2981no—
159#121—1492no—
160#120—2982no—
161C4×Q8—2981no—
162C4×Q8C2×D14911yescharacteristic, complemented
163C4×D4—1491no—
164C4×D4—1491no—
165#117—1492no—
166#107—1492no—
167#106—1491no—
168C4⋊C8C2×D14911yescharacteristic, complemented
169#103—1491no—
170#102—1492no—
171#102—1492no—
172#102—1492no—
173#102—1491no—
174#102C2×D14912yescomplemented
175C22⋊C8—1492no—
176C4×C8—1491no—
177C24—2982no—
178C2×Q8—2981no—
179C2×Q8C22×D14911yescharacteristic
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—2984no—
183C2×D4—2982no—
184C2×D4—2982no—
185C2×D4—5962no—
186C2×D4—5964no—
187C2×D4—1491no—
188C2×D4—1491no—
189C2×D4C22×D14912yes—
190C22×C4—2981no—
191C22×C4—1492no—
192SD16—42no—
193SD16—2982no—
194M16—5962no—
195C2×C8—1491no—
196C2×C8—1491no—
197C2×C8C22×D14912yes—
198C4⋊C4—21no—
199C4⋊C4—2982no—
200C4⋊C4—2981no—
201C4⋊C4—1492no—
202C4⋊C4—1491no—
203C4⋊C4—1491no—
204C4⋊C4C22×D14911yescharacteristic
205C22⋊C4—2982no—
206C22⋊C4—2982no—
207C22⋊C4—2982no—
208C22⋊C4—2981no—
209C22⋊C4—1492no—
210C42—21no—
211C42—2982no—
212C42C22×D14911yescharacteristic
213C23—22no—
214C23—2981no—
215C23—5964no—
216C23—5964no—
217C23—1492no—
218C23—11922no—
219Q8—21no—
220Q8—21no—
221Q8—5962no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—81no—
226D4—2982no—
227D4—2981no—
228D4—5964no—
229D4—5964no—
230D4—1492no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—2982no—
234C2×C4—2982no—
235C2×C4—2982no—
236C2×C4—2981no—
237C2×C4—5962no—
238C2×C4—1492no—
239C2×C4D4×D14911yescharacteristic
240C2×C4D4×D14911yescharacteristic
241C2×C4C23×D14911yescharacteristic
242C8—22no—
243C8—2981no—
244C8—2981no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—2982no—
249C22—2982no—
250C22—2982no—
251C22—2982no—
252C22—5961no—
253C22—5961no—
254C22—11928no—
255C22C2×D4×D14911yescharacteristic
256C4—21no—
257C4—41no—
258C4—41no—
259C4—2982no—
260C4—5961no—
261C4—5962no—
262C4#1801193812yes—
263C4#41×D14911yescharacteristic
264C4#1801195611yescharacteristic
265C2—82no—
266C2—5962no—
267C2—5962no—
268C2#2375027211yescharacteristic
269C2C2×#1801193811yescharacteristic
270C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#460×C149C2
socleC22×C149C22×D4
prime radical#23750260C2
hypercenter#460D149
hypocenterC149#3324
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #23750348C2semidirect
3. #23749971C2semidirect
4. #23749947C2semidirect
5. #23749906C2semidirect
6. #23749868C2semidirect
7. #23749774C2semidirect
8. C4×#14558723C2semidirect
9. #23749702C2semidirect
10. #23749628C2semidirect
11. #460×C149C2semidirect
15. C2×#14558719C22semidirect
16. #18011911C22semidirect
19. #18011887C22semidirect
26. #18011869C22semidirect
27. #18011845C22semidirect
28. #18011842C22semidirect
29. #18011835C22semidirect
31. #18011832C22semidirect
32. #18011832C22semidirect
34. #18011823C22semidirect
35. C4×#11924746C22semidirect
36. C2×SD16×C149C22semidirect
38. C4×Q8×C149C22semidirect
39. C4⋊C8×C149C22semidirect
40. #102×C149C22semidirect
135. C149#3324semidirect
143. #460D149semidirect
151. C2×SD16C2×D149semidirect
162. C4×Q8C2×D149semidirect
168. C4⋊C8C2×D149semidirect
174. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503482
#237502602
#237499712
#237499472
#237499062
#237498682
#237497742
C4×#145587232
#237497022
#237496282
#460×C1492
#3324149