Finite Group Databasebeta

← #34060179

Subgroups — #34060179

Order 19072.

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

normal subgroups only

This group has 238 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#23750646C212yesmaximal, complemented
2#23750481C212yesmaximal, complemented
3#23750480C212yesmaximal, complemented
4#23750171C211yesmaximal, characteristic
5C4⋊#11924753—22no—
6C22⋊#11924753—22no—
7#18011966C2214yes—
8C2×#14558736C411yescharacteristic
9#18011909C411yescharacteristic
10#18011907C411yescharacteristic
11#18011900C2211yescharacteristic
12#18011898C2211yescharacteristic
13#18011883—22no—
14C4×C22⋊D149—22no—
15C2×C4×Dic149C2211yescharacteristic
16C2×#41×C149C411yescharacteristic
17C2×#11924753—24no—
18#14558736—42no—
19C2×Dic298C2×C411yescharacteristic
20C2×D596C2×C411yescharacteristic
21C2×C22⋊D149—22no—
22C2×C22⋊D149—21no—
23C22×Dic149D412yes—
24C2×C4×D149—21no—
25#14558715—22no—
26C22⋊Dic149—22no—
27#14558713—22no—
28C4×Dic149C2×C411yescharacteristic
29C4×Dic149D412yes—
30C4×Dic149C2311yescharacteristic
31#41×C149—42no—
32C2×Q8×C149C2×C411yescharacteristic
33C2×D4×C149—21no—
34C2×D4×C149C2×C411yescharacteristic
35C22×C4×C149—21no—
36C22×C4×C149C2×C411yescharacteristic
37#11924753—44no—
38C22×D149—21no—
39Dic298—41no—
40D596—41no—
41C22⋊D149—44no—
42C22⋊D149—42no—
43C2×Dic149—21no—
44C2×Dic149—42no—
45C2×Dic149C22⋊C412yes—
46C2×Dic149C2×D412yes—
47C4×D149—42no—
48C23×C149—21no—
49C23×C149C22⋊C411yescharacteristic
50Q8×C149—41no—
51D4×C149—41no—
52D4×C149—42no—
53C2×C4×C149—22no—
54C2×C4×C149—21no—
55C2×C4×C149—42no—
56C2×C4×C149C22⋊C411yescharacteristic
57C2×C4×C149C22×C411yescharacteristic
58C22×C149—21no—
59C22×C149—22no—
60C22×C149—41no—
61C22×C149—42no—
62C22×C149C2×C22⋊C411yescharacteristic
63C2×D149—41no—
64C2×D149—42no—
65C4×C149—21no—
66C4×C149—41no—
67C4×C149#10012yes—
68Dic149—22no—
69Dic149—22no—
70Dic149—41no—
71C2×C149—41no—
72C2×C149—81no—
73C2×C149C2×#10011yescharacteristic
74C2×C149#42112yes—
75D149—81no—
76C149#153611yescharacteristic, complemented, Sylow
77#1536—1491nomaximal, Sylow
78#532—1491no—
79#432—1492no—
80#329—1492no—
81#329—1492no—
82C2×#41—1491no—
83C2×#41#1059701011yescharacteristic
84C4⋊Q8—1491no—
85#127—1491no—
86#124—1491no—
87#124—1491no—
88#121—2982no—
89C4×D4—2982no—
90C2×C42—1491no—
91C4⋊C8—2982no—
92C22⋊C8—2982no—
93#97—1494no—
94#41—42no—
95#41—5962no—
96C2×Q8—1491no—
97C2×Q8C2×#1059701011yescharacteristic
98C2×D4—21no—
99C2×D4—2981no—
100C2×D4—2982no—
101C2×D4—1491no—
102C2×D4C2×#1059701011yescharacteristic
103C22×C4—21no—
104C22×C4—2981no—
105C22×C4—1492no—
106C22×C4C2×#1059701011yescharacteristic
107C2×C8—2984no—
108C4⋊C4—2982no—
109C22⋊C4—2982no—
110C22⋊C4—2982no—
111C42—1492no—
112C42—1491no—
113C42—1491no—
114C23—21no—
115C23—2981no—
116C23C22⋊#1059701011yescharacteristic
117Q8—41no—
118Q8—5961no—
119D4—41no—
120D4—42no—
121D4—5961no—
122D4—5964no—
123D4—5962no—
124C2×C4—22no—
125C2×C4—21no—
126C2×C4—42no—
127C2×C4—2981no—
128C2×C4—5962no—
129C2×C4—5962no—
130C2×C4—1492no—
131C2×C4—1492no—
132C2×C4C22⋊#1059701011yescharacteristic
133C2×C4C22×#1059701011yescharacteristic
134C8—5964no—
135C22—21no—
136C22—22no—
137C22—41no—
138C22—42no—
139C22—5961no—
140C22—5962no—
141C22C2×C22⋊#1059701011yescharacteristic
142C4—21no—
143C4—41no—
144C4—2982no—
145C4—2982no—
146C4—5961no—
147C4#1801197112yes—
148C2—41no—
149C2—81no—
150C2—11921no—
151C2C2×#1801197111yescharacteristic
152C2#2375062212yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×#41×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750171C2
cosocleC4×Dic149C23
hypercenterC2×#41#10597010
hypocenterC149#1536
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23750646C2semidirect
2. #23750481C2semidirect
3. #23750480C2semidirect
76. C149#1536semidirect

Maximal subgroups

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

subgroupindex
#237506462
#237504812
#237504802
#237501712
#1536149