Finite Group Databasebeta

← #34060206

Subgroups — #34060206

Order 19072.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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#23750642C211yesmaximal, characteristic
2#23750628C211yesmaximal, characteristic
3#23750484C214yesmaximal, complemented
4C2×#18011910C211yesmaximal, characteristic
5C2×#14558745—21no—
6#18011978C2212yes—
7#18011978C2212yes—
8C4⋊#11924753—21no—
9C22⋊#11924753—21no—
10C4×#11924753—21no—
11C22×Dic298—21no—
12#18011910—21no—
13#18011910—21no—
14#18011910C412yes—
15#18011910C2212yes—
16C2×C4⋊Dic149C411yescharacteristic
17C2×#14558715—21no—
18C2×C4×Dic149C2211yescharacteristic
19C2×C4⋊C4×C149C411yescharacteristic
20#14558745—42no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C2×Dic298—22no—
24C2×Dic298—22no—
25C2×Dic298—44no—
26C22×Dic149—21no—
27C22×Dic149D411yescharacteristic
28C22×Dic149D411yescharacteristic
29C4⋊Dic149—21no—
30C4⋊Dic149C2×C412yes—
31#14558715—22no—
32#14558715—22no—
33C4×Dic149C2×C411yescharacteristic
34C4×Dic149D411yescharacteristic
35C4×Dic149D411yescharacteristic
36C4×Dic149C2311yescharacteristic
37C22×C4×C149—21no—
38C22×C4×C149C2×C411yescharacteristic
39C4⋊C4×C149—21no—
40C4⋊C4×C149C2×C412yes—
41#11924753—42no—
42#11924753—42no—
43Dic298—44no—
44Dic298—44no—
45C2×Dic149—22no—
46C2×Dic149—22no—
47C2×Dic149—42no—
48C2×Dic149C22⋊C411yescharacteristic
49C2×Dic149C22⋊C411yescharacteristic
50C2×Dic149SD1612yes—
51C2×Dic149Q1612yes—
52C2×Dic149C2×D411yescharacteristic
53C2×Dic149C2×D411yescharacteristic
54C23×C149C22⋊C411yescharacteristic
55C2×C4×C149—22no—
56C2×C4×C149—22no—
57C2×C4×C149—42no—
58C2×C4×C149C22⋊C411yescharacteristic
59C2×C4×C149C22×C411yescharacteristic
60C22×C149—21no—
61C22×C149—21no—
62C22×C149#10312yes—
63C22×C149C2×C22⋊C411yescharacteristic
64C4×C149—21no—
65C4×C149—42no—
66C4×C149#10112yes—
67Dic149—21no—
68Dic149—42no—
69Dic149#10312yes—
70Dic149C2×SD1611yescharacteristic
71Dic149C2×Q1611yescharacteristic
72Dic149AGL(1,ℤ/8)12yes—
73C2×C149—22no—
74C2×C149C2×#10111yescharacteristic
75C2×C149C2×#10311yescharacteristic
76C2×C149#41811yescharacteristic
77C149#154911yescharacteristic, complemented, Sylow
78#1549—1491nomaximal, Sylow
79C2×C4⋊Q8—1491no—
80#431—1491no—
81#423—1491no—
82#332—1494no—
83C22×Q8—2981no—
84C2×M16—2981no—
85C4⋊Q8—2981no—
86C4⋊Q8—2981no—
87C4⋊Q8—1492no—
88C4⋊Q8—1492no—
89C2×C4⋊C4—2981no—
90C2×C4⋊C4—1491no—
91C2×C4⋊C4#1059701011yescharacteristic
92C2×C42—1491no—
93C4⋊C8—2981no—
94C4⋊C8—1492no—
95C4⋊C8—1492no—
96C22⋊C8—2981no—
97C4×C8—2981no—
98C2×Q8—2982no—
99C2×Q8—2982no—
100C2×Q8—5964no—
101C22×C4—21no—
102C22×C4—2981no—
103C22×C4—1491no—
104C22×C4—1491no—
105C22×C4C2×#1059701011yescharacteristic
106M16—5962no—
107C2×C8—2982no—
108C2×C8—2982no—
109C4⋊C4—21no—
110C4⋊C4—2982no—
111C4⋊C4—2982no—
112C4⋊C4—2981no—
113C4⋊C4—1492no—
114C4⋊C4C2×#1059701012yes—
115C42—1491no—
116C42—1491no—
117C42—1491no—
118C42—1491no—
119C23C22⋊#1059701011yescharacteristic
120Q8—5964no—
121Q8—5964no—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—42no—
125C2×C4—2982no—
126C2×C4—2982no—
127C2×C4—5962no—
128C2×C4—1491no—
129C2×C4—1492no—
130C2×C4—1492no—
131C2×C4—1491no—
132C2×C4—1491no—
133C2×C4—1491no—
134C2×C4C22⋊#1059701011yescharacteristic
135C2×C4C22×#1059701011yescharacteristic
136C8—5962no—
137C8—5962no—
138C22—21no—
139C22—21no—
140C22#1801197412yes—
141C22C2×C22⋊#1059701011yescharacteristic
142C4—21no—
143C4—42no—
144C4—2981no—
145C4—5962no—
146C4—1491no—
147C4—1492no—
148C4—1491no—
149C4—1492no—
150C4#1801197212yes—
151C2—22no—
152C2C2×#1801197211yescharacteristic
153C2C2×#1801197411yescharacteristic
154C2#2375061711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1549
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #23750484C2semidirect
77. C149#1549semidirect

Maximal subgroups

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

subgroupindex
#237506422
#237506282
#237504842
C2×#180119102
#1549149