Finite Group Databasebeta

← #34060075

Subgroups — #34060075

Order 19072.

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

normal subgroups only

This group has 240 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#23750644C211yesmaximal, characteristic
2C4×C4⋊#10597010C211yesmaximal, characteristic
3#23750479C214yesmaximal
4#23750180C211yesmaximal, characteristic
5C2×C4⋊#10597010—21no—
6C2×C4×#10597010—21no—
7C4⋊#11924753—21no—
8#18011968C2212yes—
9C4×#11924753—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—24no—
23C4×#10597010—42no—
24C2×Dic298—21no—
25C2×C4×D149D411yescharacteristic
26C2×C4×D149D411yescharacteristic
27C2×C4×D149C2311yescharacteristic
28C4⋊Dic149—22no—
29C4⋊Dic149—21no—
30C4⋊Dic149C2×C412yes—
31#14558715—22no—
32#14558713—22no—
33C4×Dic149—22no—
34C4×Dic149C2×C411yescharacteristic
35C4×Dic149D411yescharacteristic
36C4×Dic149D411yescharacteristic
37C2×Q8×C149C2×C412yes—
38C4⋊C4×C149—21no—
39C4⋊C4×C149—21no—
40C42×C149C2×C411yescharacteristic
41C2×#10597010—24no—
42C2×#10597010—42no—
43C2×#10597010—42no—
44#11924753—42no—
45C22×D149C2×D411yescharacteristic
46Dic298—42no—
47C2×Dic149—22no—
48C2×Dic149C22⋊C411yescharacteristic
49C2×Dic149C22⋊C411yescharacteristic
50C2×Dic149C2×D411yescharacteristic
51C4×D149—22no—
52C4×D149—41no—
53C4×D149SD1612yes—
54C4×D149Q1612yes—
55Q8×C149—42no—
56C2×C4×C149—22no—
57C2×C4×C149C22⋊C411yescharacteristic
58C2×C4×C149C22⋊C411yescharacteristic
59C2×C4×C149C22×C411yescharacteristic
60C22×C149C2×C22⋊C411yescharacteristic
61C2×D149—21no—
62C2×D149—21no—
63C2×D149C2×SD1611yescharacteristic
64C2×D149C2×Q1611yescharacteristic
65#10597010—44no—
66C4×C149—21no—
67C4×C149—42no—
68C4×C149#10312yes—
69C4×C149#10412yes—
70Dic149—21no—
71Dic149—21no—
72Dic149—42no—
73Dic149#10312yes—
74C2×C149#41011yescharacteristic
75C2×C149C2×#10311yescharacteristic
76C2×C149C2×#10411yescharacteristic
77D149—21no—
78D149—21no—
79C149#150311yescharacteristic, complemented, Sylow
80#1503—1491nomaximal, Sylow
81#533—1491no—
82#431—1491no—
83C4×C4⋊C4—1491no—
84#328—1494no—
85C4⋊Q8—1491no—
86C4⋊Q8#1059701011yescharacteristic, complemented
87#125—2981no—
88C22⋊Q8—2981no—
89C22⋊Q8—1492no—
90C4×Q8—2981no—
91C4×Q8—1492no—
92#117—2981no—
93C2×C4⋊C4—2981no—
94C2×C42—2981no—
95C2×C42—1491no—
96C4⋊C8—2981no—
97C22⋊C8—1492no—
98C4×C8—2981no—
99#95—1492no—
100C2×Q8—2981no—
101C2×Q8C2×#1059701012yes—
102C22×C4—2982no—
103C22×C4—1491no—
104C22×C4—1491no—
105C22×C4—1491no—
106C2×C8—2982no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—2982no—
110C4⋊C4—2982no—
111C4⋊C4—2984no—
112C4⋊C4—2981no—
113C4⋊C4—1492no—
114C22⋊C4—2982no—
115C42—2982no—
116C42—5962no—
117C42—1491no—
118C42—1491no—
119C42—1491no—
120C42C2×#1059701011yescharacteristic
121C23—1491no—
122Q8—42no—
123Q8—5962no—
124C2×C4—22no—
125C2×C4—2982no—
126C2×C4—2984no—
127C2×C4—2982no—
128C2×C4—5961no—
129C2×C4—5962no—
130C2×C4—5962no—
131C2×C4—1491no—
132C2×C4—1491no—
133C2×C4—1491no—
134C2×C4—1492no—
135C2×C4—1492no—
136C2×C4C22⋊#1059701011yescharacteristic
137C2×C4C22⋊#1059701011yescharacteristic
138C2×C4C22×#1059701011yescharacteristic
139C8—5962no—
140C22—2981no—
141C22—2981no—
142C22—1491no—
143C22—1491no—
144C22C2×C22⋊#1059701011yescharacteristic
145C4—21no—
146C4—42no—
147C4—2981no—
148C4—2981no—
149C4—5964no—
150C4—5962no—
151C4—1492no—
152C4#1801197412yes—
153C4#1801197612yes—
154C2—2981no—
155C2—2981no—
156C2#2375060511yescharacteristic
157C2C2×#1801197411yescharacteristic
158C2C2×#1801197611yescharacteristic
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#1503
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
79. C149#1503semidirect
86. C4⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506442
C4×C4⋊#105970102
#237504792
#237501802
#1503149