Finite Group Databasebeta

← #34060054

Subgroups — #34060054

Order 19072.

202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750647C211yesmaximal, characteristic
2#23750643C211yesmaximal, characteristic
3Q8⋊#11924753C214yesmaximal, complemented
4#23750180C211yesmaximal, characteristic
5#18011978—21no—
6C4⋊#11924753C2212yes—
7#18011968—21no—
8#18011968—21no—
9#18011966—21no—
10C4×#11924753C2212yes—
11#18011911C411yescharacteristic
12#18011902—21no—
13#18011891—21no—
14#18011887C412yes—
15Q8×Dic149C2212yes—
16#18011876—21no—
17#18011869—21no—
18C42×D149C2211yescharacteristic
19C4⋊Q8×C149C411yescharacteristic
20C2×#11924753—22no—
21C2×#11924753—22no—
22C2×Dic298—21no—
23C2×C4×D149C2×C411yescharacteristic
24C2×C4×D149D411yescharacteristic
25C2×C4×D149D411yescharacteristic
26C4⋊Dic149—22no—
27C4⋊Dic149—21no—
28C4⋊Dic149C2×C412yes—
29#14558715—22no—
30#14558713—22no—
31C4×Dic149—22no—
32C4×Dic149D411yescharacteristic
33C4×Dic149D411yescharacteristic
34C4×Dic149C2311yescharacteristic
35C2×Q8×C149C2×C412yes—
36C4⋊C4×C149—21no—
37C4⋊C4×C149—21no—
38C42×C149C2×C411yescharacteristic
39#11924753—42no—
40#11924753—42no—
41C22×D149C22⋊C411yescharacteristic
42Dic298—42no—
43C2×Dic149—22no—
44C2×Dic149C22⋊C411yescharacteristic
45C2×Dic149C2×D411yescharacteristic
46C2×Dic149C2×D411yescharacteristic
47C4×D149—22no—
48C4×D149—22no—
49C4×D149—41no—
50Q8×C149—24no—
51C2×C4×C149—22no—
52C2×C4×C149C22⋊C411yescharacteristic
53C2×C4×C149C22⋊C411yescharacteristic
54C2×C4×C149C22×C411yescharacteristic
55C22×C149C2×C22⋊C411yescharacteristic
56C2×D149—21no—
57C2×D149—21no—
58C2×D149—21no—
59C4×C149—21no—
60C4×C149—21no—
61C4×C149—42no—
62C4×C149#13112yes—
63Dic149—21no—
64Dic149—21no—
65Dic149—42no—
66Dic149#13712yes—
67C2×C149#40811yescharacteristic
68C2×C149#41911yescharacteristic
69C2×C149#42111yescharacteristic
70D149—41no—
71C149#149711yescharacteristic, complemented, Sylow
72#1497—1491nomaximal, Sylow
73#533—1491no—
74#432—1491no—
75#431—1491no—
76Q8⋊C8—1494no—
77C4⋊Q8—1491no—
78C4⋊Q8#1059701011yescharacteristic
79#125—2981no—
80C22⋊Q8—2981no—
81C22⋊Q8—1492no—
82C4×Q8—2981no—
83C4×Q8—1492no—
84#117—2981no—
85C2×C42—1491no—
86C4⋊C8—2981no—
87C4⋊C8—1492no—
88C22⋊C8—2981no—
89C22⋊C8—2981no—
90#97—2981no—
91C4×C8—1492no—
92C2×Q8—2981no—
93C2×Q8C2×#1059701012yes—
94C22×C4—1491no—
95C22×C4—1491no—
96C22×C4—1491no—
97C2×C8—2982no—
98C2×C8—2982no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—2982no—
102C4⋊C4—2982no—
103C4⋊C4—2981no—
104C4⋊C4—1492no—
105C22⋊C4—2982no—
106C42—2982no—
107C42—1491no—
108C42—1491no—
109C42—1491no—
110C42C2×#1059701011yescharacteristic
111C23—1491no—
112Q8—24no—
113Q8—5962no—
114C2×C4—22no—
115C2×C4—2982no—
116C2×C4—2982no—
117C2×C4—2982no—
118C2×C4—5961no—
119C2×C4—1491no—
120C2×C4—1491no—
121C2×C4—1491no—
122C2×C4C22⋊#1059701011yescharacteristic
123C2×C4C22⋊#1059701011yescharacteristic
124C2×C4C22×#1059701011yescharacteristic
125C8—5962no—
126C8—5962no—
127C22—2981no—
128C22—2981no—
129C22—2981no—
130C22C2×C22⋊#1059701011yescharacteristic
131C4—21no—
132C4—21no—
133C4—42no—
134C4—2981no—
135C4—2981no—
136C4—5962no—
137C4—1492no—
138C4#1801199812yes—
139C2—5961no—
140C2#2375059911yescharacteristic
141C2#2375061811yescharacteristic
142C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1497
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
3. Q8⋊#11924753C2semidirect
71. C149#1497semidirect

Maximal subgroups

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

subgroupindex
#237506472
#237506432
Q8⋊#119247532
#237501802
#1497149