Finite Group Databasebeta

← #34061450

Subgroups — #34061450

Order 19072.

528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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#23750692C212yesmaximal, complemented
2#23750666C214yesmaximal, complemented
3D8×#10597010C214yesmaximal, complemented
4#23750635C211yesmaximal, characteristic, complemented
5#23750617C212yesmaximal, complemented
6#23750588C211yesmaximal, characteristic, complemented
7C2×D8×D149C211yesmaximal, characteristic
8D149⋊M16C2211yescharacteristic
9D4×#10597010—24no—
10D4×#10597010C2218yescomplemented
11#18011990C2212yes—
12#18011990C2211yescharacteristic
13C2×C22⋊#10597010—24no—
14#18011980C2212yescomplemented
15#18011979C2212yescomplemented
16#18011973C2218yescomplemented
17#18011965C2212yescomplemented
18C8×#10597010C2212yescomplemented
19C2×D4×D149C2212yes—
20C2×D1192C411yescharacteristic, complemented
21C2×#14558721C412yescomplemented
22D8×D149C412yescomplemented
23D8×D149C412yescomplemented
24D8×D149C2212yes—
25D8×D149C2212yes—
26C2×C8×D149C2211yescharacteristic
27C2×D8×C149C411yescharacteristic, complemented
28C22×#10597010—28no—
29#14558746—21no—
30#14558745—21no—
31D149⋊C8C2312yes—
32C4⋊#10597010D412yes—
33C4⋊#10597010C2314yes—
34C22⋊#10597010—28no—
35C22⋊#10597010—22no—
36C22⋊#10597010D412yes—
37C4×#10597010—22no—
38C4×#10597010C2312yes—
39C23×D149—22no—
40C2×D596C2×C412yescomplemented
41C2×C22⋊D149—22no—
42D4×D149—22no—
43D4×D149—22no—
44D4×D149C2×C414yescomplemented
45D4×D149C2314yes—
46C2×C4×D149C2311yescharacteristic
47D1192C2×C412yescomplemented
48D1192C2×C412yescomplemented
49#14558721C2×C414yescomplemented
50#14558721C2×C414yescomplemented
51C2×#11924746C2×C411yescharacteristic, complemented
52C8×D149C2×C411yescharacteristic, complemented
53C8×D149C2×C411yescharacteristic, complemented
54C8×D149C2311yescharacteristic
55C8×D149C2311yescharacteristic
56C2×D4×C149C2×C412yescomplemented
57D8×C149C2×C412yescomplemented
58D8×C149C2×C412yescomplemented
59C2×C8×C149C2×C411yescharacteristic, complemented
60C2×#10597010—24no—
61C2×#10597010—88no—
62C2×#10597010C2×D414yes—
63#11924753—22no—
64C22×D149—22no—
65C22×D149—24no—
66C22×D149—24no—
67C22×D149—84no—
68C22×D149C2×D411yescharacteristic
69D596—22no—
70D596C22×C414yes—
71C22⋊D149—24no—
72C22⋊D149—24no—
73C2×Dic149#4111yescharacteristic
74C4×D149C22×C411yescharacteristic
75C4×D149C2×D411yescharacteristic
76C4×D149#4111yescharacteristic
77C4×D149C2411yescharacteristic
78#11924746C22×C411yescharacteristic
79#11924746C22×C411yescharacteristic
80C23×C149—22no—
81D4×C149—22no—
82D4×C149C22×C414yes—
83C2×C4×C149C22×C411yescharacteristic
84C8×C149C22×C411yescharacteristic
85C8×C149C22×C411yescharacteristic
86C22×C149—24no—
87C22×C149—82no—
88C22×C149C4×D411yescharacteristic
89C2×D149—22no—
90C2×D149—24no—
91C2×D149—48no—
92C2×D149—84no—
93C2×D149—82no—
94C2×D149C4×D411yescharacteristic
95C2×D149C22×D411yescharacteristic
96#10597010—24no—
97#10597010—44no—
98C4×C149C4×D411yescharacteristic
99C4×C149C23×C411yescharacteristic
100Dic149C4×D411yescharacteristic
101Dic149C2×#4111yescharacteristic
102C2×C149—21no—
103C2×C149—44no—
104C2×C149C2×C4×D411yescharacteristic
105D149—21no—
106D149—44no—
107D149#57612yes—
108C149#294811yescharacteristic, complemented, Sylow
109#2948—1491nomaximal, Sylow
110C22×D8—1491no—
111#518—1492no—
112#442—1494no—
113C4×D8—1494no—
114#427—1491no—
115#418—1492no—
116#405—1491no—
117C22×D4—1492no—
118C2×D8—1492no—
119C2×D8—1492no—
120C2×D8—1492no—
121C2×D8—1492no—
122C2×D8—1492no—
123C2×D8—1491no—
124C2×D8#1059701011yescharacteristic, complemented
125C2×M16—1491no—
126C22×C8—1491no—
127C4×D4—2984no—
128C4×D4—1498no—
129#117—1492no—
130#117—1491no—
131C2×C22⋊C4—2984no—
132#107—1492no—
133#106—1492no—
134#102—1498no—
135#97—1492no—
136C4×C8—1492no—
137C24—2982no—
138C2×D4—2982no—
139C2×D4—2982no—
140C2×D4—2982no—
141C2×D4—1494no—
142C2×D4—1494no—
143C2×D4—1492no—
144C2×D4C2×#1059701012yescomplemented
145C22×C4—2988no—
146C22×C4—1491no—
147D8—1494no—
148D8—1494no—
149D8—1492no—
150D8—1492no—
151D8C2×#1059701012yescomplemented
152D8C2×#1059701012yescomplemented
153M16—2981no—
154M16—2981no—
155C2×C8—1492no—
156C2×C8—1491no—
157C2×C8—1491no—
158C2×C8—1491no—
159C2×C8—1491no—
160C2×C8—1491no—
161C2×C8C2×#1059701011yescharacteristic, complemented
162C4⋊C4—1494no—
163C4⋊C4—1492no—
164C22⋊C4—2982no—
165C22⋊C4—2988no—
166C22⋊C4—1492no—
167C42—2982no—
168C42—1492no—
169C23—22no—
170C23—2984no—
171C23—2984no—
172C23—2982no—
173C23—1491no—
174C23—11924no—
175D4—22no—
176D4—2984no—
177D4—2984no—
178D4—2982no—
179D4—1494no—
180D4C22×#1059701014yes—
181C2×C4—2984no—
182C2×C4—1494no—
183C2×C4—1491no—
184C2×C4—1491no—
185C2×C4—1491no—
186C2×C4—1491no—
187C2×C4—1491no—
188C2×C4—11928no—
189C2×C4C22×#1059701011yescharacteristic
190C8—2982no—
191C8—1491no—
192C8—1491no—
193C8C22×#1059701011yescharacteristic
194C8C22×#1059701011yescharacteristic
195C22—24no—
196C22—82no—
197C22—2982no—
198C22—2984no—
199C22—5968no—
200C22—1491no—
201C22—1491no—
202C22—11922no—
203C22—11924no—
204C22D4×#1059701011yescharacteristic
205C4—2984no—
206C4—5964no—
207C4—1491no—
208C4—1491no—
209C4D4×#1059701011yescharacteristic
210C4C23×#1059701011yescharacteristic
211C2—21no—
212C2—44no—
213C2—2981no—
214C2—5964no—
215C2—1492no—
216C2C2×D4×#1059701011yescharacteristic
subgroupG/H
centerC2C2×D4×#10597010
commutatorC4×C149C23×C4
FrattiniC4C23×#10597010
FittingC2×D8×C149C4
socleC2×C149C2×C4×D4
prime radicalC2×D8×D149C2
cosocleC4×D149C24
hypercenterC2×D8#10597010
hypocenterC149#2948
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #23750692C2semidirect
2. #23750666C2semidirect
3. D8×#10597010C2semidirect
4. #23750635C2semidirect
5. #23750617C2semidirect
6. #23750588C2semidirect
10. D4×#10597010C22semidirect
14. #18011980C22semidirect
15. #18011979C22semidirect
16. #18011973C22semidirect
17. #18011965C22semidirect
18. C8×#10597010C22semidirect
20. C2×D1192C4semidirect
21. C2×#14558721C4semidirect
22. D8×D149C4semidirect
23. D8×D149C4semidirect
27. C2×D8×C149C4semidirect
40. C2×D596C2×C4semidirect
44. D4×D149C2×C4semidirect
47. D1192C2×C4semidirect
48. D1192C2×C4semidirect
49. #14558721C2×C4semidirect
50. #14558721C2×C4semidirect
51. C2×#11924746C2×C4semidirect
52. C8×D149C2×C4semidirect
53. C8×D149C2×C4semidirect
56. C2×D4×C149C2×C4semidirect
57. D8×C149C2×C4semidirect
58. D8×C149C2×C4semidirect
59. C2×C8×C149C2×C4semidirect
108. C149#2948semidirect
124. C2×D8#10597010semidirect
144. C2×D4C2×#10597010semidirect
151. D8C2×#10597010semidirect
152. D8C2×#10597010semidirect
161. C2×C8C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506922
#237506662
D8×#105970102
#237506352
#237506172
#237505882
C2×D8×D1492
#2948149