Finite Group Databasebeta

← #34060182

Subgroups — #34060182

Order 19072.

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

normal subgroups only

This group has 194 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
2#23750482C214yesmaximal, complemented
3#23750178C211yesmaximal, characteristic
4C4⋊#11924753—22no—
5C22⋊#11924753—22no—
6#18011966C2214yes—
7#18011910C412yes—
8#18011902C2212yes—
9#18011888—22no—
10C4×Dic298—22no—
11#18011870C411yescharacteristic
12C2×C4×Dic149C2211yescharacteristic
13#117×C149C411yescharacteristic
14C2×#11924753—24no—
15C2×Dic298—22no—
16C22×Dic149D412yes—
17C4⋊Dic149—22no—
18C4⋊Dic149C2×C412yes—
19#14558715—22no—
20#14558715—22no—
21C22⋊Dic149—21no—
22C4×Dic149—21no—
23C4×Dic149C2×C411yescharacteristic
24C4×Dic149D412yes—
25C4×Dic149C2311yescharacteristic
26C22×C4×C149C2×C411yescharacteristic
27C4⋊C4×C149C2×C412yes—
28C22⋊C4×C149—21no—
29C42×C149—21no—
30#11924753—44no—
31Dic298—44no—
32C2×Dic149—22no—
33C2×Dic149—42no—
34C2×Dic149C22⋊C412yes—
35C2×Dic149C2×D412yes—
36C23×C149C22⋊C411yescharacteristic
37C2×C4×C149—22no—
38C2×C4×C149—22no—
39C2×C4×C149C22⋊C411yescharacteristic
40C2×C4×C149C22×C411yescharacteristic
41C22×C149—21no—
42C22×C149—22no—
43C22×C149C2×C22⋊C411yescharacteristic
44C4×C149—21no—
45C4×C149—42no—
46C4×C149#10112yes—
47Dic149—22no—
48Dic149—22no—
49Dic149—42no—
50C2×C149—41no—
51C2×C149C2×#10111yescharacteristic
52C2×C149#42112yes—
53C149#153711yescharacteristic, complemented, Sylow
54#1537—1491nomaximal, Sylow
55#533—1491no—
56#432—1492no—
57#330—1494no—
58C4⋊Q8—1492no—
59#125—1492no—
60C22⋊Q8—2982no—
61C4×Q8—2982no—
62#117—1491no—
63#117#1059701011yescharacteristic
64C2×C42—1491no—
65C4⋊C8—2982no—
66C22⋊C8—2982no—
67#97—1494no—
68C2×Q8—2982no—
69C22×C4—1492no—
70C22×C4C2×#1059701011yescharacteristic
71C2×C8—2984no—
72C4⋊C4—2982no—
73C4⋊C4—2982no—
74C4⋊C4—2982no—
75C4⋊C4—1492no—
76C4⋊C4C2×#1059701012yes—
77C22⋊C4—21no—
78C22⋊C4—2981no—
79C42—21no—
80C42—2981no—
81C42—1492no—
82C42—1491no—
83C42—1491no—
84C23C22⋊#1059701011yescharacteristic
85Q8—5964no—
86C2×C4—22no—
87C2×C4—22no—
88C2×C4—2982no—
89C2×C4—5962no—
90C2×C4—1492no—
91C2×C4—1492no—
92C2×C4C22⋊#1059701011yescharacteristic
93C2×C4C22×#1059701011yescharacteristic
94C8—5964no—
95C22—21no—
96C22—22no—
97C22C2×C22⋊#1059701011yescharacteristic
98C4—21no—
99C4—42no—
100C4—2982no—
101C4—2982no—
102C4—5962no—
103C4#1801197212yes—
104C2—41no—
105C2C2×#1801197211yescharacteristic
106C2#2375062212yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#117×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenter#117#10597010
hypocenterC149#1537
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #23750482C2semidirect
53. C149#1537semidirect

Maximal subgroups

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

subgroupindex
#237506462
#237504822
#237501782
#1537149