Finite Group Databasebeta

← #34060827

Subgroups — #34060827

Order 19072.

320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 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#23750630C211yesmaximal, characteristic, complemented
2C2×#18011976C214yesmaximal, complemented
3#23750561C211yesmaximal, characteristic, complemented
4#23750176C211yesmaximal, characteristic
5C2×#14558746C2212yes—
6C2×C4×#10597010C2212yes—
7#18011978—22no—
8#18011976—28no—
9(C2×#10597010)⋊C4—22no—
10C2×#14558737C2212yes—
11#18011908C411yescharacteristic, complemented
12#18011900C412yescomplemented
13#18011886—22no—
14#18011873—22no—
15C42×D149C2211yescharacteristic
16C4⋊Q8×C149C411yescharacteristic, complemented
17C22×#10597010—22no—
18#14558746—24no—
19C2×#11924753—22no—
20C4×#10597010—22no—
21C4×#10597010D414yescomplemented
22#14558737—24no—
23#14558737—24no—
24C2×D596—22no—
25C2×D596—22no—
26C2×D596C2×C412yes—
27C2×C4×D149—22no—
28C2×C4×D149D412yes—
29C2×C4×D149C2311yescharacteristic
30#14558713—24no—
31C4×Dic149C2×C411yescharacteristic
32C4×Dic149D412yes—
33C2×Q8×C149C2×C412yes—
34C4⋊C4×C149—22no—
35C42×C149C2×C411yescharacteristic
36C2×#10597010—24no—
37C2×#10597010—44no—
38#11924753—42no—
39C22×D149—22no—
40C22×D149C2×D411yescharacteristic
41D596—24no—
42D596—44no—
43D596—44no—
44C2×Dic149C22⋊C412yes—
45C2×Dic149C2×D411yescharacteristic
46C4×D149—42no—
47C4×D149—42no—
48C4×D149—42no—
49C4×D149C2×D412yes—
50C4×D149#4112yes—
51Q8×C149—24no—
52C2×C4×C149—22no—
53C2×C4×C149C22⋊C412yes—
54C2×C4×C149C22×C411yescharacteristic
55C22×C149C2×C22⋊C411yescharacteristic
56C2×D149—22no—
57C2×D149—42no—
58C2×D149—44no—
59C2×D149#12112yes—
60#10597010—44no—
61C4×C149—22no—
62C4×C149—42no—
63C4×C149C4×D412yes—
64Dic149—22no—
65Dic149#12411yescharacteristic
66Dic149#12711yescharacteristic
67C2×C149#39011yescharacteristic
68C2×C149#42112yes—
69D149—22no—
70D149—82no—
71C149#196311yescharacteristic, complemented, Sylow
72#1963—1491nomaximal, Sylow
73#532—1491no—
74#423—1491no—
75C2×#104—1494no—
76#376—1491no—
77C2×#41—1492no—
78C2×M16—1492no—
79C4⋊Q8#1059701011yescharacteristic, complemented
80#127—1491no—
81#124—1492no—
82#121—2982no—
83C4×D4—2982no—
84C2×C42—1492no—
85C2×C42—1491no—
86C4⋊C8—2982no—
87#104—2988no—
88#95—2982no—
89#41—2984no—
90#41—2984no—
91C2×Q8C2×#1059701012yes—
92C2×D4—2982no—
93C2×D4—2982no—
94C2×D4—1492no—
95C22×C4—2982no—
96C22×C4—2982no—
97C22×C4—1492no—
98C22×C4—1491no—
99M16—2984no—
100C2×C8—2982no—
101C4⋊C4—22no—
102C22⋊C4—2984no—
103C42—2982no—
104C42—1494no—
105C42—1492no—
106C42—1491no—
107C42C2×#1059701011yescharacteristic
108C23—2982no—
109C23—1491no—
110Q8—24no—
111D4—2984no—
112D4—5964no—
113D4—5964no—
114C2×C4—22no—
115C2×C4—2984no—
116C2×C4—5962no—
117C2×C4—5962no—
118C2×C4—5962no—
119C2×C4—5964no—
120C2×C4—1492no—
121C2×C4—1491no—
122C2×C4—1492no—
123C2×C4—1492no—
124C2×C4C22⋊#1059701012yes—
125C2×C4C22×#1059701011yescharacteristic
126C8—5962no—
127C22—2982no—
128C22—5962no—
129C22—5964no—
130C22—1492no—
131C22C2×C22⋊#1059701011yescharacteristic
132C4—22no—
133C4—42no—
134C4—2982no—
135C4—5964no—
136C4—1491no—
137C4—1491no—
138C4D4×#1059701012yes—
139C2—2982no—
140C2—11922no—
141C2#2375057711yescharacteristic
142C2#2375062412yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750176C2
cosocleC2×C4×D149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1963
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #23750630C2semidirect
2. C2×#18011976C2semidirect
3. #23750561C2semidirect
11. #18011908C4semidirect
12. #18011900C4semidirect
16. C4⋊Q8×C149C4semidirect
21. C4×#10597010D4semidirect
71. C149#1963semidirect
79. C4⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506302
C2×#180119762
#237505612
#237501762
#1963149