Finite Group Databasebeta

← #34060874

Subgroups — #34060874

Order 19072.

260 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 78 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#23750584C211yesmaximal, characteristic
2#23750571C211yesmaximal, characteristic
3#23750498C214yesmaximal
4#125×D149C211yesmaximal, characteristic
5C2×D149⋊C8C2212yes—
6C2×C4⋊#10597010—22no—
7C2×C4⋊#10597010C2212yes—
8#18011966—22no—
9#18011903C411yescharacteristic, complemented
10#18011902C412yescomplemented
11#18011901—22no—
12C4⋊C4×D149—22no—
13C4⋊C4×D149C2212yes—
14C42×D149C2211yescharacteristic
15#125×C149C411yescharacteristic, complemented
16C22×#10597010—22no—
17D149⋊C8—22no—
18D149⋊C8Q814yes—
19C2×#11924753—22no—
20C4⋊#10597010—24no—
21C4⋊#10597010—44no—
22C2×C4×D149—22no—
23C2×C4×D149D412yes—
24C2×C4×D149C2311yescharacteristic
25C4⋊Dic149—22no—
26C4⋊Dic149C2×C412yes—
27#14558715—22no—
28#14558715—22no—
29#14558715—22no—
30C4×Dic149C2×C411yescharacteristic
31C4×Dic149D412yes—
32C4⋊C4×C149—22no—
33C4⋊C4×C149C2×C412yes—
34C42×C149C2×C411yescharacteristic
35C2×#10597010—42no—
36C2×#10597010—44no—
37#11924753—24no—
38C22×D149C2×D411yescharacteristic
39C2×Dic149—22no—
40C2×Dic149C22⋊C412yes—
41C2×Dic149C2×D411yescharacteristic
42C4×D149—22no—
43C4×D149—22no—
44C4×D149—42no—
45C4×D149—42no—
46C4×D149C2×Q812yes—
47C4×D149#4112yes—
48C2×C4×C149—22no—
49C2×C4×C149C22⋊C412yes—
50C2×C4×C149C22×C411yescharacteristic
51C22×C149C2×C22⋊C411yescharacteristic
52C2×D149#12411yescharacteristic
53C2×D149C4⋊Q811yescharacteristic
54C2×D149AGL(1,ℤ/8)12yes—
55C2×D149#13712yes—
56#10597010—82no—
57C4×C149—22no—
58C4×C149—42no—
59C4×C149C4×Q812yes—
60Dic149—22no—
61Dic149—42no—
62Dic149C22⋊Q812yes—
63C2×C149#39111yescharacteristic
64C2×C149#41712yes—
65D149#49011yescharacteristic
66D149#49111yescharacteristic
67D149#50112yes—
68C149#199211yescharacteristic, complemented, Sylow
69#1992—1491nomaximal, Sylow
70C2×#125—1491no—
71C2×#97—1491no—
72#384—1491no—
73#340—1494no—
74C22×C8—1492no—
75#125—2982no—
76#125—1492no—
77#125—1491no—
78#125#1059701011yescharacteristic, complemented
79C2×C4⋊C4—2982no—
80C2×C4⋊C4—2982no—
81C2×C4⋊C4—1492no—
82C2×C4⋊C4—1492no—
83C2×C42—1491no—
84#97—2982no—
85C22×C4—2982no—
86C22×C4—2982no—
87C22×C4—1492no—
88C22×C4—1491no—
89C2×C8—2982no—
90C2×C8—2982no—
91C2×C8—1494no—
92C4⋊C4—22no—
93C4⋊C4—2982no—
94C4⋊C4—2982no—
95C4⋊C4—2982no—
96C4⋊C4—2982no—
97C4⋊C4—2984no—
98C4⋊C4—5964no—
99C4⋊C4—1492no—
100C4⋊C4C2×#1059701012yes—
101C42—1492no—
102C42—1491no—
103C42C2×#1059701011yescharacteristic
104C23—1491no—
105C2×C4—22no—
106C2×C4—2982no—
107C2×C4—2982no—
108C2×C4—2982no—
109C2×C4—5962no—
110C2×C4—5962no—
111C2×C4—5962no—
112C2×C4—5964no—
113C2×C4—1492no—
114C2×C4—1491no—
115C2×C4—1492no—
116C2×C4—1492no—
117C2×C4C22⋊#1059701012yes—
118C2×C4C22×#1059701011yescharacteristic
119C8—2984no—
120C22—1491no—
121C22—1491no—
122C22—1492no—
123C22—1492no—
124C22C2×C22⋊#1059701011yescharacteristic
125C4—22no—
126C4—42no—
127C4—2982no—
128C4—5962no—
129C4—1492no—
130C4—11922no—
131C4Q8×#1059701012yes—
132C2—1491no—
133C2—1491no—
134C2—1492no—
135C2(C2×#10597010)⋊Q811yescharacteristic
136C2#2375061612yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#125×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenter#125#10597010
hypocenterC149#1992
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. #18011903C4semidirect
10. #18011902C4semidirect
15. #125×C149C4semidirect
68. C149#1992semidirect
78. #125#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505842
#237505712
#237504982
#125×D1492
#1992149