Finite Group Databasebeta

← #34060154

Subgroups — #34060154

Order 19072.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750648C211yesmaximal, characteristic
2C4×#14558746C211yesmaximal, characteristic
3#23750482C212yesmaximal, complemented
4#23750482C212yesmaximal, complemented
5#125×D149C211yesmaximal, characteristic
6C2×#14558746—21no—
7#18011978—21no—
8#18011968—21no—
9#18011966C2212yes—
10#18011966C2212yes—
11C4×#11924753—21no—
12#18011903C411yescharacteristic
13#18011902C2211yescharacteristic
14#18011902C2211yescharacteristic
15#18011901—21no—
16#18011901—21no—
17C4⋊C4×D149—21no—
18C4⋊C4×D149—21no—
19C4⋊C4×D149C411yescharacteristic
20C4⋊C4×D149C411yescharacteristic
21C42×D149C2211yescharacteristic
22#125×C149C411yescharacteristic
23#14558746—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×C4×D149—21no—
27C2×C4×D149—21no—
28C2×C4×D149C2×C411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C4⋊Dic149—21no—
32C4⋊Dic149—21no—
33C4⋊Dic149C2×C411yescharacteristic
34C4⋊Dic149C2×C411yescharacteristic
35#14558715—21no—
36#14558715—21no—
37#14558715—21no—
38#14558715—21no—
39#14558715—21no—
40#14558715—21no—
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149C2311yescharacteristic
44C4⋊C4×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149C2×C411yescharacteristic
47C4⋊C4×C149C2×C411yescharacteristic
48C42×C149C2×C411yescharacteristic
49#11924753—24no—
50#11924753—42no—
51C22×D149C22⋊C411yescharacteristic
52C2×Dic149—21no—
53C2×Dic149—21no—
54C2×Dic149C22⋊C411yescharacteristic
55C2×Dic149C2×D411yescharacteristic
56C2×Dic149C2×D411yescharacteristic
57C4×D149—22no—
58C4×D149—22no—
59C4×D149—41no—
60C4×D149—42no—
61C4×D149—42no—
62C2×C4×C149—21no—
63C2×C4×C149—21no—
64C2×C4×C149C22⋊C411yescharacteristic
65C2×C4×C149C22⋊C411yescharacteristic
66C2×C4×C149C22×C411yescharacteristic
67C22×C149C2×C22⋊C411yescharacteristic
68C2×D149—21no—
69C2×D149—21no—
70C2×D149#10412yes—
71C4×C149—21no—
72C4×C149—21no—
73C4×C149—21no—
74C4×C149—41no—
75C4×C149—41no—
76Dic149—21no—
77Dic149—21no—
78Dic149—41no—
79Dic149—41no—
80Dic149#10112yes—
81C2×C149C2×#10111yescharacteristic
82C2×C149C2×#10411yescharacteristic
83C2×C149#42111yescharacteristic
84D149—22no—
85C149#152811yescharacteristic, complemented, Sylow
86#1528—1491nomaximal, Sylow
87C2×#125—1491no—
88#432—1491no—
89C4×M16—1491no—
90#330—1492no—
91#330—1492no—
92C2×M16—2981no—
93#125—2981no—
94#125—2981no—
95#125—1491no—
96#125—1491no—
97#125—1491no—
98#125#1059701011yescharacteristic
99C2×C4⋊C4—2981no—
100C2×C4⋊C4—2981no—
101C2×C4⋊C4—1491no—
102C2×C4⋊C4—1491no—
103C2×C42—1491no—
104C4⋊C8—2981no—
105C22⋊C8—2981no—
106#97—1492no—
107#97—1492no—
108C4×C8—2981no—
109C22×C4—2981no—
110C22×C4—2981no—
111C22×C4—1491no—
112C22×C4—1491no—
113C22×C4—1491no—
114M16—2984no—
115C2×C8—2982no—
116C2×C8—2982no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—2981no—
120C4⋊C4—2981no—
121C4⋊C4—2981no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C4⋊C4—2981no—
125C4⋊C4—2981no—
126C4⋊C4—2981no—
127C4⋊C4—1491no—
128C4⋊C4—1491no—
129C4⋊C4C2×#1059701011yescharacteristic
130C4⋊C4C2×#1059701011yescharacteristic
131C42—1491no—
132C42—1491no—
133C42—1491no—
134C42C2×#1059701011yescharacteristic
135C23—1491no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—2982no—
139C2×C4—2982no—
140C2×C4—2981no—
141C2×C4—2981no—
142C2×C4—5961no—
143C2×C4—5962no—
144C2×C4—5962no—
145C2×C4—1491no—
146C2×C4—1491no—
147C2×C4—1491no—
148C2×C4C22⋊#1059701011yescharacteristic
149C2×C4C22⋊#1059701011yescharacteristic
150C2×C4C22×#1059701011yescharacteristic
151C8—2984no—
152C8—5962no—
153C22—2981no—
154C22—2981no—
155C22—1492no—
156C22C2×C22⋊#1059701011yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4—2981no—
163C4—2981no—
164C4—5961no—
165C4—5961no—
166C4—1492no—
167C2—2982no—
168C2D149⋊#10111yescharacteristic
169C2D149⋊#10411yescharacteristic
170C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#125×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenter#125#10597010
hypocenterC149#1528
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #23750482C2semidirect
4. #23750482C2semidirect
85. C149#1528semidirect

Maximal subgroups

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

subgroupindex
#237506482
C4×#145587462
#237504822
#125×D1492
#1528149