Finite Group Databasebeta

← #34060032

Subgroups — #34060032

Order 19072.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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#23750646C211yesmaximal, characteristic, complemented
2C4×#14558745C211yesmaximal, characteristic, complemented
3#23750473C214yesmaximal, complemented
4C2×#18011873C211yesmaximal, characteristic
5C2×#14558745—21no—
6C4⋊#11924753C2212yescomplemented
7C22⋊#11924753—21no—
8#18011966—21no—
9#18011966—21no—
10C4×#11924753C2212yescomplemented
11C22×D596C411yescharacteristic
12C22×C4×D149—21no—
13#18011873—21no—
14#18011873—21no—
15#18011873C412yes—
16#18011873C2212yes—
17C2×#14558713—21no—
18C2×C4×Dic149C2211yescharacteristic
19C2×C4⋊C4×C149C411yescharacteristic
20#14558745—24no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C23×D149—21no—
24C2×D596—24no—
25C2×D596—21no—
26C2×D596C2×C412yes—
27C22×Dic149D411yescharacteristic
28C22×Dic149D411yescharacteristic
29C2×C4×D149—22no—
30C2×C4×D149—22no—
31C2×C4×D149—44no—
32#14558713—22no—
33#14558713—22no—
34C4×Dic149C2×C411yescharacteristic
35C4×Dic149D411yescharacteristic
36C4×Dic149D411yescharacteristic
37C4×Dic149C2311yescharacteristic
38C22×C4×C149—21no—
39C22×C4×C149C2×C411yescharacteristic
40C4⋊C4×C149—21no—
41C4⋊C4×C149C2×C412yes—
42#11924753—24no—
43#11924753—42no—
44C22×D149—24no—
45C22×D149—22no—
46C22×D149—42no—
47C22×D149—42no—
48D596—24no—
49D596—22no—
50D596M1614yescomplemented
51C2×Dic149—22no—
52C2×Dic149—22no—
53C2×Dic149C22⋊C411yescharacteristic
54C2×Dic149C22⋊C411yescharacteristic
55C2×Dic149C2×D411yescharacteristic
56C2×Dic149C2×D411yescharacteristic
57C4×D149—44no—
58C4×D149—44no—
59C23×C149C22⋊C411yescharacteristic
60C2×C4×C149—22no—
61C2×C4×C149—22no—
62C2×C4×C149—42no—
63C2×C4×C149C22⋊C411yescharacteristic
64C2×C4×C149C22×C411yescharacteristic
65C22×C149—21no—
66C22×C149—21no—
67C22×C149#10412yes—
68C22×C149C2×C22⋊C411yescharacteristic
69C2×D149—24no—
70C2×D149—48no—
71C2×D149—42no—
72C2×D149—42no—
73C4×C149—21no—
74C4×C149—42no—
75C4×C149C2×M1612yes—
76Dic149—21no—
77Dic149—21no—
78Dic149—21no—
79Dic149AGL(1,ℤ/8)12yes—
80C2×C149—22no—
81C2×C149#40711yescharacteristic
82C2×C149#41811yescharacteristic
83C2×C149C2×#10411yescharacteristic
84D149—44no—
85C149#149011yescharacteristic, complemented, Sylow
86#1490—1491nomaximal, Sylow
87C2×C4×D4—1491no—
88#432—1491no—
89C4×M16—1491no—
90D4⋊C8—1494no—
91C22×D4—1491no—
92C23×C4—2981no—
93C2×M16—2981no—
94C4×D4—2981no—
95C4×D4—2981no—
96C4×D4—1492no—
97C4×D4—1492no—
98C2×C4⋊C4#1059701011yescharacteristic
99C2×C22⋊C4—2981no—
100C2×C42—1491no—
101C4⋊C8—1492no—
102C22⋊C8—2981no—
103#97—2981no—
104#97—2981no—
105C4×C8—1492no—
106C24—2981no—
107C2×D4—2984no—
108C2×D4—2981no—
109C2×D4—1492no—
110C22×C4—21no—
111C22×C4—2982no—
112C22×C4—2982no—
113C22×C4—5964no—
114C22×C4—1491no—
115C22×C4—1491no—
116C22×C4C2×#1059701011yescharacteristic
117M16—2984no—
118C2×C8—2982no—
119C2×C8—2982no—
120C4⋊C4—21no—
121C4⋊C4C2×#1059701012yes—
122C22⋊C4—2982no—
123C22⋊C4—2982no—
124C42—1491no—
125C42—1491no—
126C42—1491no—
127C42—1491no—
128C23—2984no—
129C23—2982no—
130C23—5962no—
131C23—5962no—
132C23C22⋊#1059701011yescharacteristic
133D4—2984no—
134D4—2982no—
135D4—1494no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—2982no—
140C2×C4—2982no—
141C2×C4—5964no—
142C2×C4—5964no—
143C2×C4—1491no—
144C2×C4—1491no—
145C2×C4—1491no—
146C2×C4—1491no—
147C2×C4C22⋊#1059701011yescharacteristic
148C2×C4C22×#1059701011yescharacteristic
149C8—2984no—
150C8—5962no—
151C22—21no—
152C22—21no—
153C22—2984no—
154C22—5968no—
155C22—5962no—
156C22—5962no—
157C22#1801197612yes—
158C22C2×C22⋊#1059701011yescharacteristic
159C4—21no—
160C4—42no—
161C4—2981no—
162C4—2981no—
163C4—2981no—
164C4—1492no—
165C4D149⋊M1612yes—
166C2—22no—
167C2—5964no—
168C2#2375059711yescharacteristic
169C2#2375061711yescharacteristic
170C2C2×#1801197611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D596C4
cosocleC4×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1490
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #23750646C2semidirect
2. C4×#14558745C2semidirect
3. #23750473C2semidirect
6. C4⋊#11924753C22semidirect
10. C4×#11924753C22semidirect
50. D596M16semidirect
85. C149#1490semidirect

Maximal subgroups

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

subgroupindex
#237506462
C4×#145587452
#237504732
C2×#180118732
#1490149