Finite Group Databasebeta

← #34060011

Subgroups — #34060011

Order 19072.

262 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 64 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#23750644C211yesmaximal, characteristic, complemented
2C4×#14558746C211yesmaximal, characteristic, complemented
3D4⋊#11924753C214yesmaximal, complemented
4#23750173C211yesmaximal, characteristic
5C2×#14558746—21no—
6C4⋊#11924753C2212yes—
7#18011968—21no—
8#18011966—21no—
9C4×#11924753—21no—
10C4×#11924753C2212yes—
11C2×#14558735—21no—
12#18011911C411yescharacteristic
13#18011898—21no—
14#18011882—21no—
15#18011882C412yes—
16D4×Dic149—21no—
17D4×Dic149C2212yes—
18C42×D149C2211yescharacteristic
19#127×C149C411yescharacteristic
20#14558746—24no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23#14558735—44no—
24C2×Dic298—21no—
25C2×C22⋊D149—22no—
26C22×Dic149—22no—
27C2×C4×D149C2×C411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C4⋊Dic149—21no—
31C4⋊Dic149C2×C412yes—
32C22⋊Dic149—22no—
33C22⋊Dic149—22no—
34C4×Dic149D411yescharacteristic
35C4×Dic149D411yescharacteristic
36C4×Dic149C2311yescharacteristic
37C2×D4×C149—21no—
38C2×D4×C149—21no—
39C2×D4×C149C2×C412yes—
40C42×C149C2×C411yescharacteristic
41#11924753—24no—
42#11924753—42no—
43C22×D149C22⋊C411yescharacteristic
44Dic298—42no—
45C22⋊D149—44no—
46C2×Dic149—22no—
47C2×Dic149—44no—
48C2×Dic149C22⋊C411yescharacteristic
49C2×Dic149C2×D411yescharacteristic
50C2×Dic149C2×D411yescharacteristic
51C4×D149—22no—
52C4×D149—22no—
53C4×D149—22no—
54C23×C149—22no—
55D4×C149—24no—
56D4×C149—42no—
57D4×C149—42no—
58C2×C4×C149C22⋊C411yescharacteristic
59C2×C4×C149C22⋊C411yescharacteristic
60C2×C4×C149C22×C411yescharacteristic
61C22×C149—42no—
62C22×C149—42no—
63C22×C149—42no—
64C22×C149C2×C22⋊C411yescharacteristic
65C2×D149—21no—
66C2×D149—21no—
67C2×D149—21no—
68C4×C149—21no—
69C4×C149#10412yes—
70C4×C149#13112yes—
71Dic149—21no—
72Dic149—21no—
73Dic149—42no—
74Dic149AGL(1,ℤ/8)12yes—
75C2×C149—82no—
76C2×C149#40811yescharacteristic
77C2×C149#41811yescharacteristic
78C2×C149C2×#10411yescharacteristic
79D149—41no—
80C149#148411yescharacteristic, complemented, Sylow
81#1484—1491nomaximal, Sylow
82#532—1491no—
83#431—1491no—
84C4×M16—1491no—
85D4⋊C8—1494no—
86C2×#41—2981no—
87C2×M16—2981no—
88C4⋊Q8—1491no—
89#127#1059701011yescharacteristic
90#124—2981no—
91#121—2981no—
92#121—1492no—
93C4×D4—2981no—
94C4×D4—1492no—
95C2×C42—1491no—
96C4⋊C8—1492no—
97C22⋊C8—2981no—
98#97—2981no—
99C4×C8—2981no—
100C4×C8—1492no—
101#41—5964no—
102C2×Q8—2981no—
103C2×D4—21no—
104C2×D4—21no—
105C2×D4—2982no—
106C2×D4C2×#1059701012yes—
107C22×C4—2982no—
108C22×C4—1491no—
109C22×C4—1491no—
110C22×C4—1491no—
111M16—2984no—
112C2×C8—2982no—
113C2×C8—2982no—
114C4⋊C4—2981no—
115C4⋊C4—1492no—
116C22⋊C4—2982no—
117C22⋊C4—2982no—
118C42—1491no—
119C42—1491no—
120C42—1491no—
121C42C2×#1059701011yescharacteristic
122C23—22no—
123C23—1491no—
124Q8—5962no—
125D4—24no—
126D4—42no—
127D4—42no—
128D4—5964no—
129C2×C4—2982no—
130C2×C4—2982no—
131C2×C4—2982no—
132C2×C4—2982no—
133C2×C4—5964no—
134C2×C4—1491no—
135C2×C4—1491no—
136C2×C4—1491no—
137C2×C4C22⋊#1059701011yescharacteristic
138C2×C4C22⋊#1059701011yescharacteristic
139C2×C4C22×#1059701011yescharacteristic
140C8—2984no—
141C8—5962no—
142C22—42no—
143C22—42no—
144C22—42no—
145C22—2981no—
146C22—2981no—
147C22—2981no—
148C22C2×C22⋊#1059701011yescharacteristic
149C4—21no—
150C4—2981no—
151C4—2981no—
152C4—5962no—
153C4—1492no—
154C4#1801197512yes—
155C4#1801199812yes—
156C2—82no—
157C2—5961no—
158C2#2375059911yescharacteristic
159C2#2375061711yescharacteristic
160C2C2×#1801197511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750173C2
cosocleC4×Dic149C23
hypercenter#127#10597010
hypocenterC149#1484
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #23750644C2semidirect
2. C4×#14558746C2semidirect
3. D4⋊#11924753C2semidirect
80. C149#1484semidirect

Maximal subgroups

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

subgroupindex
#237506442
C4×#145587462
D4⋊#119247532
#237501732
#1484149