Finite Group Databasebeta

← #34055478

Subgroups — #34055478

Order 19072.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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#23750135C212yesmaximal, complemented
2#23749968C212yesmaximal, complemented
3#23749947C212yesmaximal, complemented
4#23749866C211yesmaximal, characteristic, complemented
5#23749852C212yesmaximal, complemented
6#23749788C212yesmaximal, complemented
7#23749767C212yesmaximal, complemented
8C2×#18011823C211yesmaximal, characteristic, complemented
9#466×C149C211yesmaximal, characteristic, complemented
10C2×#14558735C2212yes—
11C22×C4×D149C2211yescharacteristic
12C2×Dic596C2211yescharacteristic, complemented
13C2×#14558724C2212yescomplemented
14C22×#11924746C2211yescharacteristic
15#18011893—22no—
16#18011891C2212yes—
17#18011890C2212yes—
18#18011882C2212yes—
19#18011879—22no—
20D4×Dic149—22no—
21#18011871—22no—
22#18011869C2212yes—
23#18011845C2211yescharacteristic, complemented
24#18011842C2212yescomplemented
25#18011836C2212yescomplemented
26#18011834C2212yescomplemented
27#18011832C2212yescomplemented
28#18011823C2212yes—
29#18011823C2212yes—
30C2×D8×C149C2211yescharacteristic, complemented
31C22×C8×C149C2211yescharacteristic
32#121×C149C2212yes—
33#107×C149C2211yescharacteristic, complemented
34#102×C149C2212yescomplemented
35C23×D149D411yescharacteristic
36#14558735—42no—
37#14558735—42no—
38C2×Dic298C2312yes—
39C2×C22⋊D149—22no—
40C2×C22⋊D149—22no—
41C22×Dic149—22no—
42C22×Dic149D411yescharacteristic
43C2×C4×D149—41no—
44C2×C4×D149—41no—
45C2×C4×D149D412yes—
46C2×C4×D149C2312yes—
47Dic596—41no—
48#14558724—42no—
49C2×#11924746—41no—
50C2×#11924746C2312yes—
51C4⋊Dic149—22no—
52C4⋊Dic149C2312yes—
53#14558715—22no—
54C22⋊Dic149—22no—
55C22⋊Dic149—22no—
56#14558713—22no—
57#14558713—22no—
58C4×Dic149—22no—
59C2×D4×C149—22no—
60C2×D4×C149C2312yes—
61C22×C4×C149C2311yescharacteristic
62D8×C149—41no—
63C2×C8×C149—41no—
64C2×C8×C149C2311yescharacteristic
65C2×C8×C149C2311yescharacteristic
66C4⋊C4×C149C2312yes—
67C22⋊C4×C149—22no—
68C22×D149—22no—
69C22×D149—41no—
70C22×D149—41no—
71C22×D149C2×D412yes—
72Dic298—22no—
73Dic298—22no—
74C22⋊D149—44no—
75C22⋊D149—44no—
76C2×Dic149—22no—
77C2×Dic149—22no—
78C2×Dic149—41no—
79C2×Dic149—44no—
80C2×Dic149C2×D412yes—
81C4×D149—22no—
82C4×D149—22no—
83C4×D149—42no—
84#11924746—22no—
85C23×C149—22no—
86C23×C149C2×D411yescharacteristic
87D4×C149—22no—
88D4×C149—22no—
89D4×C149—44no—
90C2×C4×C149—21no—
91C2×C4×C149—21no—
92C2×C4×C149—22no—
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2411yescharacteristic
95C8×C149—21no—
96C8×C149—21no—
97C22×C149—21no—
98C22×C149—21no—
99C22×C149—42no—
100C22×C149—42no—
101C22×C149—42no—
102C22×C149#13512yes—
103C22×C149C22×D411yescharacteristic
104C2×D149—22no—
105C2×D149—22no—
106C2×D149—22no—
107C2×D149—44no—
108C4×C149—21no—
109C4×C149—42no—
110C4×C149H(5,𝔽2)11yescharacteristic
111C4×C149H(5,𝔽2)11yescharacteristic
112Dic149—22no—
113Dic149—42no—
114Dic149—42no—
115C2×C149—22no—
116C2×C149—82no—
117C2×C149#53411yescharacteristic
118C2×C149C2×#13511yescharacteristic
119C2×C149#57511yescharacteristic
120D149—42no—
121C149#319111yescharacteristic, complemented, Sylow
122#3191—1491nomaximal, Sylow
123#525—1492no—
124#485—1492no—
125#482—1492no—
126#467—1491no—
127#466D14911yescharacteristic, complemented
128#465—1492no—
129#452—1492no—
130#449—1492no—
131C2×C22⋊C8—1491no—
132C2×#41—1492no—
133C23×C4—1491no—
134C2×Q16—1491no—
135C2×SD16—1492no—
136C2×D8C2×D14911yescharacteristic, complemented
137C22×C8—1491no—
138C22×C8C2×D14911yescharacteristic
139#123—2982no—
140C22⋊Q8—1492no—
141C22⋊Q8—1492no—
142#121—1492no—
143#121C2×D14912yes—
144#120—2982no—
145C4×D4—2982no—
146C4×D4—2982no—
147#117—1492no—
148#107—1491no—
149#107C2×D14911yescharacteristic, complemented
150#106—1492no—
151#103—1492no—
152#103—1492no—
153#102—1492no—
154#102C2×D14912yescomplemented
155C22⋊C8—1492no—
156C22⋊C8—1492no—
157C24—1491no—
158#41—5962no—
159#41—5962no—
160C2×Q8—1492no—
161C2×D4—22no—
162C2×D4—2982no—
163C2×D4—2982no—
164C2×D4C22×D14912yes—
165C22×C4—2982no—
166C22×C4—5961no—
167C22×C4—5961no—
168C22×C4—1492no—
169C22×C4—1491no—
170C22×C4—1492no—
171C22×C4C22×D14911yescharacteristic
172Q16—5961no—
173SD16—5962no—
174D8—41no—
175C2×C8—41no—
176C2×C8—5961no—
177C2×C8—1492no—
178C2×C8C22×D14911yescharacteristic
179C2×C8C22×D14911yescharacteristic
180C4⋊C4—2982no—
181C4⋊C4—2982no—
182C4⋊C4—1492no—
183C4⋊C4C22×D14912yes—
184C22⋊C4—22no—
185C22⋊C4—2982no—
186C22⋊C4—2982no—
187C22⋊C4—2982no—
188C22⋊C4—2982no—
189C42—2982no—
190C23—22no—
191C23—2982no—
192C23—5961no—
193C23—5961no—
194C23—1492no—
195C23D4×D14911yescharacteristic
196Q8—2982no—
197Q8—2982no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—5964no—
202D4—5964no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—2982no—
207C2×C4—2982no—
208C2×C4—2982no—
209C2×C4—2982no—
210C2×C4—5962no—
211C2×C4—5961no—
212C2×C4—5964no—
213C2×C4—1492no—
214C2×C4D4×D14911yescharacteristic
215C2×C4C23×D14911yescharacteristic
216C8—21no—
217C8—21no—
218C8—2982no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—2982no—
225C22—2982no—
226C22—2982no—
227C22—5964no—
228C22#1801193012yes—
229C22C2×D4×D14911yescharacteristic
230C4—21no—
231C4—42no—
232C4—2982no—
233C4—5962no—
234C4—5962no—
235C4#1801195611yescharacteristic
236C4#1801195711yescharacteristic
237C2—22no—
238C2—82no—
239C2—5962no—
240C2#2375018311yescharacteristic
241C2C2×#1801193011yescharacteristic
242C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#466×C149C2
socleC22×C149C22×D4
hypercenter#466D149
hypocenterC149#3191
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #23750135C2semidirect
2. #23749968C2semidirect
3. #23749947C2semidirect
4. #23749866C2semidirect
5. #23749852C2semidirect
6. #23749788C2semidirect
7. #23749767C2semidirect
8. C2×#18011823C2semidirect
9. #466×C149C2semidirect
12. C2×Dic596C22semidirect
13. C2×#14558724C22semidirect
23. #18011845C22semidirect
24. #18011842C22semidirect
25. #18011836C22semidirect
26. #18011834C22semidirect
27. #18011832C22semidirect
30. C2×D8×C149C22semidirect
33. #107×C149C22semidirect
34. #102×C149C22semidirect
121. C149#3191semidirect
127. #466D149semidirect
136. C2×D8C2×D149semidirect
149. #107C2×D149semidirect
154. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501352
#237499682
#237499472
#237498662
#237498522
#237497882
#237497672
C2×#180118232
#466×C1492
#3191149