Finite Group Databasebeta

← #34060125

Subgroups — #34060125

Order 19072.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750643C211yesmaximal, characteristic
2#23750569C211yesmaximal, characteristic
3#23750479C214yesmaximal
4#23750180C211yesmaximal, characteristic
5C2×C4⋊#10597010—21no—
6#18011978—21no—
7#18011968C2212yes—
8C4×#11924753—21no—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4C2212yes—
11#18011911C411yescharacteristic, complemented
12#18011902—21no—
13#18011891—21no—
14#18011887C2212yes—
15Q8×Dic149C412yescomplemented
16#18011876—21no—
17#18011869—21no—
18C42×D149C2211yescharacteristic
19C4⋊Q8×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21C2×#11924753—22no—
22C4⋊#10597010—42no—
23C2×Dic298—21no—
24C2×C4×D149D411yescharacteristic
25C2×C4×D149D411yescharacteristic
26C2×C4×D149C2311yescharacteristic
27C4⋊Dic149—22no—
28C4⋊Dic149—21no—
29C4⋊Dic149C2×C412yes—
30#14558715—22no—
31#14558713—22no—
32C4×Dic149—22no—
33C4×Dic149C2×C411yescharacteristic
34C4×Dic149D411yescharacteristic
35C4×Dic149D411yescharacteristic
36C2×Q8×C149C2×C412yes—
37C4⋊C4×C149—21no—
38C4⋊C4×C149—21no—
39C42×C149C2×C411yescharacteristic
40C2×#10597010—42no—
41C2×#10597010—42no—
42C2×#10597010—42no—
43#11924753—42no—
44C22×D149C2×D411yescharacteristic
45Dic298—42no—
46C2×Dic149—22no—
47C2×Dic149C22⋊C411yescharacteristic
48C2×Dic149C22⋊C411yescharacteristic
49C2×Dic149C2×D411yescharacteristic
50C4×D149—41no—
51C4×D149—41no—
52C4×D149SD1612yes—
53C4×D149Q1612yes—
54Q8×C149—42no—
55C2×C4×C149—22no—
56C2×C4×C149C22⋊C411yescharacteristic
57C2×C4×C149C22⋊C411yescharacteristic
58C2×C4×C149C22×C411yescharacteristic
59C22×C149C2×C22⋊C411yescharacteristic
60C2×D149—21no—
61C2×D149—21no—
62C2×D149C2×SD1611yescharacteristic
63C2×D149C2×Q1611yescharacteristic
64#10597010—82no—
65C4×C149—21no—
66C4×C149—21no—
67C4×C149—42no—
68C4×C149#10312yes—
69Dic149—21no—
70Dic149—21no—
71Dic149—42no—
72Dic149#10312yes—
73C2×C149#41011yescharacteristic
74C2×C149C2×#10311yescharacteristic
75C2×C149#42111yescharacteristic
76D149—21no—
77D149—21no—
78C149#151811yescharacteristic, complemented, Sylow
79#1518—1491nomaximal, Sylow
80#533—1491no—
81#431—1491no—
82#382—1491no—
83#328—1494no—
84C4⋊Q8—1491no—
85C4⋊Q8#1059701011yescharacteristic, complemented
86#125—2981no—
87C22⋊Q8—2981no—
88C22⋊Q8—1492no—
89C4×Q8—2981no—
90C4×Q8—1492no—
91#117—2981no—
92C2×C4⋊C4—2981no—
93C2×C42—1491no—
94C4⋊C8—2981no—
95C22⋊C8—1492no—
96C4×C8—2981no—
97#95—2981no—
98#95—1492no—
99C2×Q8—2981no—
100C2×Q8C2×#1059701012yes—
101C22×C4—2982no—
102C22×C4—1491no—
103C22×C4—1491no—
104C22×C4—1491no—
105C2×C8—2982no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—2982no—
109C4⋊C4—2982no—
110C4⋊C4—2981no—
111C4⋊C4—5962no—
112C4⋊C4—1492no—
113C22⋊C4—2982no—
114C42—2982no—
115C42—1491no—
116C42—1491no—
117C42—1491no—
118C42C2×#1059701011yescharacteristic
119C23—1491no—
120Q8—42no—
121Q8—5962no—
122C2×C4—22no—
123C2×C4—2982no—
124C2×C4—5961no—
125C2×C4—5961no—
126C2×C4—5962no—
127C2×C4—5962no—
128C2×C4—5962no—
129C2×C4—1491no—
130C2×C4—1491no—
131C2×C4—1491no—
132C2×C4—1492no—
133C2×C4—1492no—
134C2×C4C22⋊#1059701011yescharacteristic
135C2×C4C22⋊#1059701011yescharacteristic
136C2×C4C22×#1059701011yescharacteristic
137C8—5962no—
138C22—2981no—
139C22—2981no—
140C22—1491no—
141C22—1491no—
142C22C2×C22⋊#1059701011yescharacteristic
143C4—21no—
144C4—21no—
145C4—42no—
146C4—2981no—
147C4—2981no—
148C4—5962no—
149C4—1492no—
150C4—11922no—
151C4#1801197412yes—
152C2—2981no—
153C2—2981no—
154C2#2375060511yescharacteristic
155C2C2×#1801197411yescharacteristic
156C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1518
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #18011911C4semidirect
15. Q8×Dic149C4semidirect
19. C4⋊Q8×C149C4semidirect
78. C149#1518semidirect
85. C4⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506432
#237505692
#237504792
#237501802
#1518149