Finite Group Databasebeta

← #34060096

Subgroups — #34060096

Order 19072.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750597C211yesmaximal, characteristic, complemented
2#23750568C211yesmaximal, characteristic, complemented
3#23750476C214yesmaximal, complemented
4C2×#18011882C211yesmaximal, characteristic
5C2×#14558745—21no—
6C2×C22⋊#10597010—21no—
7#18011968—21no—
8#18011968C2212yescomplemented
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4C2212yescomplemented
11C22×C22⋊D149—21no—
12C22×C4×D149C2211yescharacteristic
13#18011882—21no—
14#18011882—21no—
15#18011882C412yescomplemented
16#18011882C2212yes—
17C2×C4⋊Dic149C411yescharacteristic, complemented
18C2×C22⋊Dic149—21no—
19C22×D4×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21#14558745—42no—
22C2×#11924753—22no—
23C22⋊#10597010—42no—
24C23×D149D411yescharacteristic
25C2×C22⋊D149—22no—
26C2×C22⋊D149—22no—
27C2×C22⋊D149—44no—
28C22×Dic149—21no—
29C22×Dic149D411yescharacteristic
30C2×C4×D149—42no—
31C2×C4×D149C2×C411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149D411yescharacteristic
34C2×C4×D149C2311yescharacteristic
35C4⋊Dic149—21no—
36C4⋊Dic149C2×C412yes—
37C22⋊Dic149—22no—
38C22⋊Dic149—22no—
39C24×C149—21no—
40C2×D4×C149—21no—
41C2×D4×C149—42no—
42C2×D4×C149C2×C412yes—
43C22×C4×C149C2×C411yescharacteristic
44C2×#10597010—42no—
45C2×#10597010—42no—
46C2×#10597010—42no—
47#11924753—42no—
48C22×D149—22no—
49C22×D149—22no—
50C22×D149—41no—
51C22×D149C22⋊C411yescharacteristic
52C22×D149C2×D411yescharacteristic
53C22⋊D149—44no—
54C22⋊D149—44no—
55C2×Dic149—22no—
56C2×Dic149—22no—
57C2×Dic149—42no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C4×D149—41no—
61C4×D149—41no—
62C4×D149—41no—
63C4×D149—41no—
64C23×C149—22no—
65C23×C149—42no—
66C23×C149—42no—
67C23×C149—42no—
68C23×C149C22⋊C411yescharacteristic
69D4×C149—42no—
70D4×C149—42no—
71C2×C4×C149—22no—
72C2×C4×C149C22⋊C411yescharacteristic
73C2×C4×C149C22×C411yescharacteristic
74C22×C149—21no—
75C22×C149—21no—
76C22×C149—42no—
77C22×C149—42no—
78C22×C149—42no—
79C22×C149—84no—
80C22×C149#9912yes—
81C22×C149C2×C22⋊C411yescharacteristic
82C2×D149—21no—
83C2×D149—21no—
84C2×D149—21no—
85C2×D149—21no—
86C2×D149—21no—
87C2×D149—44no—
88C2×D149AGL(1,ℤ/8)12yes—
89#10597010—82no—
90C4×C149—21no—
91C4×C149—21no—
92Dic149—21no—
93Dic149—21no—
94Dic149—42no—
95C2×C149—22no—
96C2×C149—82no—
97C2×C149C2×#9911yescharacteristic
98C2×C149#41811yescharacteristic
99C2×C149#42111yescharacteristic
100D149—22no—
101D149—41no—
102C149#151011yescharacteristic, complemented, Sylow
103#1510—1491nomaximal, Sylow
104C2×#121—1491no—
105#407—1491no—
106#381—1491no—
107#327—1494no—
108C22×D4—2981no—
109C22×D4#1059701011yescharacteristic, complemented
110C23×C4—1491no—
111C2×M16—2981no—
112#121—2981no—
113#121—2981no—
114#121—1492no—
115#121—1492no—
116C2×C4⋊C4—1491no—
117C2×C22⋊C4—2981no—
118C2×C22⋊C4—2981no—
119C22⋊C8—2981no—
120C22⋊C8—1492no—
121#95—2981no—
122#95—1492no—
123C24—21no—
124C24—1491no—
125C2×D4—21no—
126C2×D4—42no—
127C2×D4—2982no—
128C2×D4—2982no—
129C2×D4—5964no—
130C2×D4C2×#1059701012yes—
131C22×C4—2981no—
132C22×C4—2982no—
133C22×C4—5962no—
134C22×C4—1491no—
135C22×C4—1491no—
136C22×C4—1491no—
137C22×C4—1491no—
138C22×C4—1491no—
139C22×C4C2×#1059701011yescharacteristic
140M16—5962no—
141C2×C8—2982no—
142C4⋊C4—2981no—
143C4⋊C4—1492no—
144C22⋊C4—2982no—
145C22⋊C4—2982no—
146C22⋊C4—5962no—
147C23—22no—
148C23—42no—
149C23—42no—
150C23—42no—
151C23—2982no—
152C23—2982no—
153C23—5961no—
154C23—1491no—
155C23—1491no—
156C23C22⋊#1059701011yescharacteristic
157D4—42no—
158D4—42no—
159D4—5964no—
160D4—5964no—
161C2×C4—22no—
162C2×C4—2982no—
163C2×C4—2982no—
164C2×C4—5961no—
165C2×C4—5961no—
166C2×C4—5961no—
167C2×C4—5961no—
168C2×C4—5962no—
169C2×C4—5962no—
170C2×C4—5962no—
171C2×C4—5962no—
172C2×C4—1491no—
173C2×C4—1491no—
174C2×C4C22⋊#1059701011yescharacteristic
175C2×C4C22×#1059701011yescharacteristic
176C8—5962no—
177C22—21no—
178C22—21no—
179C22—42no—
180C22—42no—
181C22—42no—
182C22—84no—
183C22—2981no—
184C22—2981no—
185C22—2981no—
186C22—2981no—
187C22—2981no—
188C22—5964no—
189C22—1492no—
190C22#1801196912yes—
191C22C2×C22⋊#1059701011yescharacteristic
192C4—21no—
193C4—21no—
194C4—2981no—
195C4—2981no—
196C4—5962no—
197C4—11922no—
198C2—22no—
199C2—82no—
200C2—2982no—
201C2—5961no—
202C2C2×#1801196911yescharacteristic
203C2#2375061711yescharacteristic
204C2#2375062311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#18011882C2
cosocleC2×C4×D149C23
hypercenterC22×D4#10597010
hypocenterC149#1510
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #23750597C2semidirect
2. #23750568C2semidirect
3. #23750476C2semidirect
8. #18011968C22semidirect
10. (C2×#10597010)⋊C4C22semidirect
15. #18011882C4semidirect
17. C2×C4⋊Dic149C4semidirect
19. C22×D4×C149C4semidirect
102. C149#1510semidirect
109. C22×D4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505972
#237505682
#237504762
C2×#180118822
#1510149