Finite Group Databasebeta

← #34060603

Subgroups — #34060603

Order 19072.

296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×#18011970C212yesmaximal
2#23750502C214yesmaximal, complemented
3#23750099C211yesmaximal, characteristic
4C2×C22⋊#10597010C2214yes—
5#18011970—22no—
6#18011970—22no—
7C22×D596C2211yescharacteristic
8C4×D596—22no—
9#18011873—22no—
10#18011870C411yescharacteristic, complemented
11C22⋊C4×D149C412yescomplemented
12C22⋊C4×D149C2212yes—
13#117×C149C411yescharacteristic, complemented
14C22×#10597010—24no—
15C22⋊#10597010—24no—
16C22⋊#10597010—24no—
17C23×D149C2×C411yescharacteristic
18C23×D149C2311yescharacteristic
19C2×D596—24no—
20C2×D596D412yes—
21C2×D596D412yes—
22C2×C4×D149—22no—
23C2×C4×D149—22no—
24C4⋊Dic149—21no—
25C22⋊Dic149C2×C412yes—
26#14558713—22no—
27#14558713—22no—
28C4×Dic149—21no—
29C22×C4×C149C2×C411yescharacteristic
30C4⋊C4×C149—21no—
31C22⋊C4×C149C2×C412yes—
32C42×C149—21no—
33C2×#10597010—44no—
34C2×#10597010—84no—
35C22×D149—22no—
36C22×D149—81no—
37C22×D149—81no—
38C22×D149C22⋊C412yes—
39C22×D149C2×D412yes—
40C22×D149#4114yes—
41D596—24no—
42D596—24no—
43C2×Dic149—22no—
44C4×D149—82no—
45C4×D149—82no—
46C23×C149C22×C411yescharacteristic
47C2×C4×C149—22no—
48C2×C4×C149—22no—
49C2×C4×C149C22⋊C411yescharacteristic
50C2×C4×C149C22⋊C411yescharacteristic
51C22×C149—41no—
52C22×C149C2×C22⋊C411yescharacteristic
53C22×C149#11712yes—
54C2×D149—22no—
55C2×D149—42no—
56C2×D149—44no—
57C2×D149—42no—
58C2×D149—82no—
59C2×D149#12314yes—
60#10597010—84no—
61C4×C149—21no—
62C4×C149—21no—
63C4×C149—42no—
64Dic149—42no—
65C2×C149—21no—
66C2×C149—22no—
67C2×C149#38111yescharacteristic
68D149—24no—
69D149—42no—
70C149#182811yescharacteristic, complemented, Sylow
71#1828—1491nomaximal, Sylow
72#518—1491no—
73C2×#99—1492no—
74#342—1494no—
75C22×D4—1491no—
76C4×D4—2982no—
77C4×D4—2982no—
78#117—1491no—
79#117#1059701011yescharacteristic, complemented
80C2×C22⋊C4—1494no—
81C2×C22⋊C4—1492no—
82C2×C22⋊C4—1492no—
83#99—2982no—
84#99—2982no—
85C24—1491no—
86C24—1491no—
87C2×D4—2984no—
88C2×D4—1492no—
89C2×D4—1492no—
90C22×C4—2982no—
91C22×C4—2982no—
92C22×C4—2984no—
93C22×C4C2×#1059701011yescharacteristic
94C4⋊C4—21no—
95C4⋊C4—2981no—
96C22⋊C4—2982no—
97C22⋊C4—2982no—
98C22⋊C4—2984no—
99C22⋊C4—2984no—
100C22⋊C4—1492no—
101C22⋊C4C2×#1059701012yes—
102C42—21no—
103C42—2981no—
104C23—2982no—
105C23—1492no—
106C23—1492no—
107C23—1494no—
108C23—11921no—
109C23—11921no—
110C23C22×#1059701011yescharacteristic
111D4—2984no—
112D4—2984no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—2982no—
116C2×C4—5964no—
117C2×C4—11922no—
118C2×C4—11922no—
119C2×C4—11924no—
120C2×C4C22⋊#1059701011yescharacteristic
121C2×C4C22⋊#1059701011yescharacteristic
122C22—41no—
123C22—2982no—
124C22—5962no—
125C22—5964no—
126C22—5962no—
127C22—1494no—
128C22—11922no—
129C22C2×C22⋊#1059701011yescharacteristic
130C22#1801199012yes—
131C4—21no—
132C4—21no—
133C4—42no—
134C4—5962no—
135C4—11924no—
136C2—21no—
137C2—22no—
138C2—2984no—
139C2—5962no—
140C2#2375056811yescharacteristic
subgroupG/H
centerC2#23750568
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
Fitting#117×C149C4
socleC2×C149#381
prime radicalC22×D596C22
cosocleC23×D149C23
hypercenter#117#10597010
hypocenterC149#1828
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #23750502C2semidirect
10. #18011870C4semidirect
11. C22⋊C4×D149C4semidirect
13. #117×C149C4semidirect
70. C149#1828semidirect
79. #117#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119702
#237505022
#237500992
#1828149