Finite Group Databasebeta

← #34060021

Subgroups — #34060021

Order 19072.

248 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 74 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#23750475C214yesmaximal, complemented
4C2×#18011876C211yesmaximal, characteristic
5C2×#14558745—21no—
6#18011978—21no—
7#18011978—21no—
8C4⋊#11924753C2212yes—
9C22⋊#11924753—21no—
10C4×#11924753C2212yes—
11C22×Dic298C411yescharacteristic
12#18011876—21no—
13#18011876—21no—
14#18011876C412yes—
15#18011876C2212yes—
16C2×#14558715—21no—
17C2×C4×Dic149—21no—
18C2×C4×Dic149C2211yescharacteristic
19C2×C4⋊C4×C149C411yescharacteristic
20#14558745—42no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C2×Dic298—24no—
24C2×Dic298—21no—
25C2×Dic298C2×C412yes—
26C22×Dic149—21no—
27C22×Dic149D411yescharacteristic
28C22×Dic149D411yescharacteristic
29#14558715—22no—
30#14558715—22no—
31C4×Dic149—22no—
32C4×Dic149—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—24no—
44Dic298—22no—
45Dic298M1614yescomplemented
46C2×Dic149—24no—
47C2×Dic149—22no—
48C2×Dic149—41no—
49C2×Dic149C22⋊C411yescharacteristic
50C2×Dic149C22⋊C411yescharacteristic
51C2×Dic149SD1612yes—
52C2×Dic149Q1612yes—
53C2×Dic149C2×D411yescharacteristic
54C2×Dic149C2×D411yescharacteristic
55C23×C149C22⋊C411yescharacteristic
56C2×C4×C149—22no—
57C2×C4×C149—22no—
58C2×C4×C149—42no—
59C2×C4×C149C22⋊C411yescharacteristic
60C2×C4×C149C22×C411yescharacteristic
61C22×C149—21no—
62C22×C149—21no—
63C22×C149#10312yes—
64C22×C149C2×C22⋊C411yescharacteristic
65C4×C149—21no—
66C4×C149—42no—
67C4×C149C2×M1612yes—
68Dic149—24no—
69Dic149—21no—
70Dic149—21no—
71Dic149#10312yes—
72Dic149C2×SD1611yescharacteristic
73Dic149C2×Q1611yescharacteristic
74C2×C149—22no—
75C2×C149#40711yescharacteristic
76C2×C149C2×#10311yescharacteristic
77C2×C149#42111yescharacteristic
78C149#148711yescharacteristic, complemented, Sylow
79#1487—1491nomaximal, Sylow
80C2×C4×Q8—1491no—
81#431—1491no—
82#423—1491no—
83Q8⋊C8—1494no—
84C22×Q8—1491no—
85C2×M16—2981no—
86C4×Q8—2981no—
87C4×Q8—2981no—
88C4×Q8—1492no—
89C4×Q8—1492no—
90C2×C4⋊C4—2981no—
91C2×C4⋊C4#1059701011yescharacteristic
92C2×C42—2981no—
93C2×C42—1491no—
94C4⋊C8—2981no—
95C4⋊C8—2981no—
96C4⋊C8—1492no—
97C22⋊C8—2981no—
98C4×C8—1492no—
99C2×Q8—2984no—
100C2×Q8—2981no—
101C2×Q8—1492no—
102C22×C4—21no—
103C22×C4—2981no—
104C22×C4—1491no—
105C22×C4—1491no—
106C22×C4C2×#1059701011yescharacteristic
107M16—5962no—
108C2×C8—2982no—
109C2×C8—2982no—
110C4⋊C4—21no—
111C4⋊C4—2982no—
112C4⋊C4—2982no—
113C4⋊C4C2×#1059701012yes—
114C42—2982no—
115C42—2982no—
116C42—1491no—
117C42—1491no—
118C42—1491no—
119C42—1491no—
120C23C22⋊#1059701011yescharacteristic
121Q8—2984no—
122Q8—2982no—
123Q8—1494no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—42no—
127C2×C4—2984no—
128C2×C4—2982no—
129C2×C4—5961no—
130C2×C4—1491no—
131C2×C4—1491no—
132C2×C4—1492no—
133C2×C4—1492no—
134C2×C4—1491no—
135C2×C4—1491no—
136C2×C4C22⋊#1059701011yescharacteristic
137C2×C4C22×#1059701011yescharacteristic
138C8—5962no—
139C8—5962no—
140C22—21no—
141C22—21no—
142C22#1801197412yes—
143C22C2×C22⋊#1059701011yescharacteristic
144C4—21no—
145C4—42no—
146C4—2984no—
147C4—2981no—
148C4—2981no—
149C4—1491no—
150C4—1492no—
151C4—1491no—
152C4D149⋊M1612yes—
153C2—22no—
154C2#2375059711yescharacteristic
155C2C2×#1801197411yescharacteristic
156C2#2375062311yescharacteristic
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#1487
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #23750475C2semidirect
45. Dic298M16semidirect
78. C149#1487semidirect

Maximal subgroups

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

subgroupindex
#237506422
#237506282
#237504752
C2×#180118762
#1487149