Finite Group Databasebeta

← #34059997

Subgroups — #34059997

Order 19072.

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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
2D149⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3D4⋊#11924753C214yesmaximal, complemented
4#23750173C211yesmaximal, characteristic
5C2×D149⋊C8—21no—
6#18011978—21no—
7C4⋊#11924753—21no—
8C4⋊#11924753C2212yes—
9#18011968—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
20D149⋊C8—42no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23#14558735—42no—
24#14558735—42no—
25C2×Dic298—21no—
26C2×C22⋊D149—22no—
27C22×Dic149—22no—
28C2×C4×D149C2×C411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C4⋊Dic149—21no—
32C4⋊Dic149C2×C412yes—
33C22⋊Dic149—22no—
34C22⋊Dic149—22no—
35C4×Dic149D411yescharacteristic
36C4×Dic149D411yescharacteristic
37C4×Dic149C2311yescharacteristic
38C2×D4×C149—21no—
39C2×D4×C149—21no—
40C2×D4×C149C2×C412yes—
41C42×C149C2×C411yescharacteristic
42#11924753—42no—
43#11924753—42no—
44C22×D149C22⋊C411yescharacteristic
45Dic298—42no—
46C22⋊D149—44no—
47C2×Dic149—22no—
48C2×Dic149—42no—
49C2×Dic149—42no—
50C2×Dic149C22⋊C411yescharacteristic
51C2×Dic149C2×D411yescharacteristic
52C2×Dic149C2×D411yescharacteristic
53C4×D149—22no—
54C4×D149—41no—
55C4×D149D812yes—
56C4×D149SD1612yes—
57C23×C149—22no—
58D4×C149—24no—
59D4×C149—42no—
60D4×C149—42no—
61C2×C4×C149C22⋊C411yescharacteristic
62C2×C4×C149C22⋊C411yescharacteristic
63C2×C4×C149C22×C411yescharacteristic
64C22×C149—42no—
65C22×C149—42no—
66C22×C149—42no—
67C22×C149C2×C22⋊C411yescharacteristic
68C2×D149—21no—
69C2×D149—21no—
70C2×D149#10212yes—
71C4×C149—21no—
72C4×C149#10212yes—
73C4×C149#13112yes—
74Dic149—21no—
75Dic149—21no—
76Dic149—42no—
77Dic149C2×D811yescharacteristic
78Dic149C2×SD1611yescharacteristic
79C2×C149—82no—
80C2×C149#40811yescharacteristic
81C2×C149C2×#10211yescharacteristic
82C2×C149#42111yescharacteristic
83D149—22no—
84C149#148011yescharacteristic, complemented, Sylow
85#1480—1491nomaximal, Sylow
86#532—1491no—
87#431—1491no—
88C2×C4⋊C8—1491no—
89D4⋊C8—1494no—
90C2×#41—2981no—
91C22×C8—2981no—
92C4⋊Q8—1491no—
93#127#1059701011yescharacteristic
94#124—2981no—
95#121—2981no—
96#121—1492no—
97C4×D4—2981no—
98C4×D4—1492no—
99C2×C42—1491no—
100C4⋊C8—2981no—
101C4⋊C8—2981no—
102C4⋊C8—1492no—
103C22⋊C8—2981no—
104C4×C8—1492no—
105#41—5962no—
106#41—5962no—
107C2×Q8—2981no—
108C2×D4—21no—
109C2×D4—21no—
110C2×D4—2982no—
111C2×D4C2×#1059701012yes—
112C22×C4—2982no—
113C22×C4—1491no—
114C22×C4—1491no—
115C22×C4—1491no—
116C2×C8—2982no—
117C2×C8—2982no—
118C2×C8—5962no—
119C4⋊C4—2981no—
120C4⋊C4—1492no—
121C22⋊C4—2982no—
122C22⋊C4—2982no—
123C42—1491no—
124C42—1491no—
125C42—1491no—
126C42C2×#1059701011yescharacteristic
127C23—22no—
128C23—1491no—
129Q8—5962no—
130D4—24no—
131D4—42no—
132D4—42no—
133D4—5964no—
134C2×C4—2982no—
135C2×C4—2982no—
136C2×C4—5961no—
137C2×C4—5962no—
138C2×C4—5962no—
139C2×C4—1491no—
140C2×C4—1491no—
141C2×C4—1491no—
142C2×C4—1492no—
143C2×C4—1492no—
144C2×C4C22⋊#1059701011yescharacteristic
145C2×C4C22⋊#1059701011yescharacteristic
146C2×C4C22×#1059701011yescharacteristic
147C8—5962no—
148C8—5962no—
149C22—42no—
150C22—42no—
151C22—42no—
152C22—2981no—
153C22—2981no—
154C22—1492no—
155C22C2×C22⋊#1059701011yescharacteristic
156C4—21no—
157C4—2981no—
158C4—2981no—
159C4—5962no—
160C4—1491no—
161C4—1491no—
162C4#1801197312yes—
163C4#1801199812yes—
164C2—82no—
165C2—2982no—
166C2#2375059911yescharacteristic
167C2C2×#1801197311yescharacteristic
168C2#2375062311yescharacteristic
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#1480
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. D149⋊(C4⋊C8)C2semidirect
3. D4⋊#11924753C2semidirect
84. C149#1480semidirect

Maximal subgroups

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

subgroupindex
#237506442
D149⋊(C4⋊C8)2
D4⋊#119247532
#237501732
#1480149