Finite Group Databasebeta

← #34060975

Subgroups — #34060975

Order 19072.

238 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 54 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#23750604C212yesmaximal
2#23750532C214yesmaximal, complemented
3#23750201C211yesmaximal, characteristic
4#18011990—22no—
5#18011970C2214yes—
6#18011969—22no—
7C2×#14558736C2211yescharacteristic
8C22×Dic298C411yescharacteristic, complemented
9#18011911C412yescomplemented
10#18011899C2212yes—
11#18011895—22no—
12#18011891—22no—
13#117×C149C411yescharacteristic, complemented
14C4⋊#10597010—42no—
15C22⋊#10597010—24no—
16C4×#10597010—42no—
17#14558736—42no—
18C2×Dic298—21no—
19C2×Dic298—42no—
20C2×Dic298C2×C412yes—
21C2×Dic298C2×C411yescharacteristic
22C2×D596C2311yescharacteristic
23C2×C22⋊D149D412yes—
24C22×Dic149—21no—
25C2×C4×D149D412yes—
26C4⋊Dic149—24no—
27#14558713—24no—
28C22×C4×C149C2×C411yescharacteristic
29C4⋊C4×C149—21no—
30C22⋊C4×C149—21no—
31C42×C149C2×C412yes—
32C2×#10597010—44no—
33C22×D149C2×D412yes—
34Dic298—41no—
35Dic298—42no—
36Dic298—42no—
37D596—41no—
38C22⋊D149—42no—
39C2×Dic149—22no—
40C2×Dic149—42no—
41C2×Dic149C22⋊C412yes—
42C4×D149—22no—
43C4×D149—22no—
44C23×C149C22⋊C411yescharacteristic
45C2×C4×C149—22no—
46C2×C4×C149—22no—
47C2×C4×C149C22⋊C411yescharacteristic
48C2×C4×C149C22×C411yescharacteristic
49C22×C149—21no—
50C22×C149—41no—
51C22×C149C2×C22⋊C411yescharacteristic
52C2×D149—22no—
53C2×D149—42no—
54#10597010—84no—
55C4×C149—21no—
56C4×C149—42no—
57C4×C149#9912yes—
58Dic149—22no—
59Dic149—42no—
60C2×C149—21no—
61C2×C149—41no—
62C2×C149C2×#9911yescharacteristic
63D149—42no—
64C149#212911yescharacteristic, complemented, Sylow
65#2129—1491nomaximal, Sylow
66#536—1491no—
67#410—1492no—
68#354—1494no—
69C2×#41—1491no—
70C22×Q8—1491no—
71C4⋊Q8—1492no—
72#124—1492no—
73#123—2982no—
74C22⋊Q8—2982no—
75#117—2982no—
76#117#1059701011yescharacteristic, complemented
77#99—2982no—
78#99—1494no—
79#41—5962no—
80C2×Q8—2981no—
81C2×Q8—5962no—
82C2×Q8—1492no—
83C2×Q8—1491no—
84C2×D4—1492no—
85C2×D4—1491no—
86C22×C4—2981no—
87C22×C4—1492no—
88C22×C4C2×#1059701011yescharacteristic
89C4⋊C4—21no—
90C4⋊C4—2984no—
91C4⋊C4—5962no—
92C22⋊C4—21no—
93C22⋊C4—2984no—
94C22⋊C4—2984no—
95C42—5962no—
96C42C2×#1059701012yes—
97C23—1492no—
98C23C22⋊#1059701011yescharacteristic
99Q8—5961no—
100Q8—5962no—
101Q8—5962no—
102D4—5961no—
103D4—5962no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—2982no—
107C2×C4—2982no—
108C2×C4—2982no—
109C2×C4—5962no—
110C2×C4—5964no—
111C2×C4—1492no—
112C2×C4C22⋊#1059701011yescharacteristic
113C2×C4C22×#1059701011yescharacteristic
114C22—21no—
115C22—41no—
116C22—2982no—
117C22—5962no—
118C22C2×C22⋊#1059701011yescharacteristic
119C4—21no—
120C4—42no—
121C4—2982no—
122C4—5962no—
123C4—11924no—
124C4#1801197012yes—
125C2—21no—
126C2—41no—
127C2—5962no—
128C2C2×#1801197011yescharacteristic
subgroupG/H
centerC2C2×#18011970
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#117×C149C4
socleC2×C149C2×#99
prime radicalC2×#14558736C22
cosocleC2×D596C23
hypercenter#117#10597010
hypocenterC149#2129
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #23750532C2semidirect
8. C22×Dic298C4semidirect
9. #18011911C4semidirect
13. #117×C149C4semidirect
64. C149#2129semidirect
76. #117#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506042
#237505322
#237502012
#2129149