Finite Group Databasebeta

← #34060205

Subgroups — #34060205

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#23750643C211yesmaximal, characteristic
2#23750630C211yesmaximal, characteristic
3#23750485C214yesmaximal, complemented
4C4⋊Q8×D149C211yesmaximal, characteristic
5C2×#14558746—21no—
6#18011978—21no—
7#18011978C2212yes—
8#18011978C2212yes—
9#18011968—21no—
10C4×#11924753—21no—
11C2×Q8×D149C412yes—
12#18011911C411yescharacteristic
13#18011910—21no—
14#18011910—21no—
15#18011909C2212yes—
16C4⋊C4×D149—21no—
17C4⋊C4×D149—21no—
18C42×D149C2211yescharacteristic
19C4⋊Q8×C149C411yescharacteristic
20#14558746—42no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C2×Dic298—22no—
24C2×Dic298C2×C412yes—
25Q8×D149—44no—
26C2×C4×D149—22no—
27C2×C4×D149C2×C411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C4⋊Dic149—21no—
31C4⋊Dic149—21no—
32#14558715—22no—
33#14558715—22no—
34C4×Dic149D411yescharacteristic
35C4×Dic149D411yescharacteristic
36C4×Dic149C2311yescharacteristic
37C2×Q8×C149C2×C412yes—
38C4⋊C4×C149—21no—
39C4⋊C4×C149—21no—
40C42×C149C2×C411yescharacteristic
41#11924753—42no—
42#11924753—42no—
43C22×D149C22⋊C411yescharacteristic
44Dic298—44no—
45Dic298—42no—
46C2×Dic149—22no—
47C2×Dic149C22⋊C411yescharacteristic
48C2×Dic149C2×D411yescharacteristic
49C2×Dic149C2×D411yescharacteristic
50C4×D149—22no—
51C4×D149—22no—
52C4×D149—44no—
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×D149#10312yes—
64C4×C149—21no—
65C4×C149—21no—
66C4×C149—42no—
67C4×C149#10312yes—
68Dic149—42no—
69Dic149#10012yes—
70Dic149C2×SD1611yescharacteristic
71Dic149C2×Q1611yescharacteristic
72Dic149#13712yes—
73C2×C149C2×#10011yescharacteristic
74C2×C149C2×#10311yescharacteristic
75C2×C149#41911yescharacteristic
76D149—22no—
77C149#154811yescharacteristic, complemented, Sylow
78#1548—1491nomaximal, Sylow
79C2×C4⋊Q8—1491no—
80#431—1491no—
81#423—1491no—
82#333—1494no—
83C22×Q8—1492no—
84C2×M16—2981no—
85C4⋊Q8—2981no—
86C4⋊Q8—2981no—
87C4⋊Q8—1492no—
88C4⋊Q8—1491no—
89C4⋊Q8#1059701011yescharacteristic
90C2×C4⋊C4—2981no—
91C2×C4⋊C4—2981no—
92C2×C42—1491no—
93C4⋊C8—2981no—
94C4⋊C8—1492no—
95C4⋊C8—1492no—
96C22⋊C8—2981no—
97C4×C8—2981no—
98C2×Q8—2982no—
99C2×Q8—5964no—
100C2×Q8—1492no—
101C2×Q8C2×#1059701012yes—
102C22×C4—2982no—
103C22×C4—1491no—
104C22×C4—1491no—
105C22×C4—1491no—
106M16—5962no—
107C2×C8—2982no—
108C2×C8—2982no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—2982no—
112C4⋊C4—2982no—
113C4⋊C4—2981no—
114C4⋊C4—2981no—
115C42—1491no—
116C42—1491no—
117C42—1491no—
118C42C2×#1059701011yescharacteristic
119C23—1491no—
120Q8—42no—
121Q8—5962no—
122Q8—5964no—
123C2×C4—22no—
124C2×C4—2982no—
125C2×C4—2982no—
126C2×C4—2982no—
127C2×C4—5964no—
128C2×C4—1491no—
129C2×C4—1491no—
130C2×C4—1491no—
131C2×C4—1492no—
132C2×C4—1492no—
133C2×C4C22⋊#1059701011yescharacteristic
134C2×C4C22⋊#1059701011yescharacteristic
135C2×C4C22×#1059701011yescharacteristic
136C8—5962no—
137C8—5962no—
138C22—2981no—
139C22—2981no—
140C22—1492no—
141C22C2×C22⋊#1059701011yescharacteristic
142C4—21no—
143C4—21no—
144C4—42no—
145C4—5962no—
146C4—1492no—
147C4—1491no—
148C4—1491no—
149C4—1492no—
150C4#1801197412yes—
151C2—2982no—
152C2D149⋊#10011yescharacteristic
153C2C2×#1801197411yescharacteristic
154C2#2375061811yescharacteristic
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#1548
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
3. #23750485C2semidirect
77. C149#1548semidirect

Maximal subgroups

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

subgroupindex
#237506432
#237506302
#237504852
C4⋊Q8×D1492
#1548149