Finite Group Databasebeta

← #34060834

Subgroups — #34060834

Order 19072.

292 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 76 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#23750628C211yesmaximal, characteristic
2C2×#18011972C214yesmaximal
3C4×#14558745C211yesmaximal, characteristic
4C2×#18011910C211yesmaximal, characteristic
5C2×#14558745C2212yes—
6C2×#14558745C2212yes—
7#18011978—21no—
8C4⋊#11924753—21no—
9#18011972—28no—
10#18011966—21no—
11C4×#11924753—21no—
12C22×Dic298C2212yes—
13#18011910—21no—
14#18011910—21no—
15#18011910—21no—
16#18011910—21no—
17C2×C4⋊Dic149C411yescharacteristic
18C2×#14558715C412yes—
19C2×C4×Dic149C2211yescharacteristic
20C2×C4⋊C4×C149C411yescharacteristic
21#14558745—24no—
22#14558745—22no—
23#14558745D414yes—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×Dic298—22no—
27C2×Dic298—22no—
28C2×Dic298—24no—
29C2×Dic298—24no—
30C22×Dic149C2×C412yes—
31C22×Dic149C2×C411yescharacteristic
32C22×Dic149C2311yescharacteristic
33C4⋊Dic149—21no—
34C4⋊Dic149—21no—
35#14558715—22no—
36#14558715—22no—
37C4×Dic149D411yescharacteristic
38C4×Dic149D411yescharacteristic
39C4×Dic149D411yescharacteristic
40C4×Dic149D411yescharacteristic
41C22×C4×C149C2×C412yes—
42C22×C4×C149C2×C411yescharacteristic
43C4⋊C4×C149—21no—
44C4⋊C4×C149—21no—
45#11924753—24no—
46#11924753—42no—
47Dic298—44no—
48Dic298—42no—
49Dic298—42no—
50C2×Dic149—22no—
51C2×Dic149—22no—
52C2×Dic149—24no—
53C2×Dic149C22⋊C411yescharacteristic
54C2×Dic149C22⋊C411yescharacteristic
55C2×Dic149C2×D411yescharacteristic
56C2×Dic149C2×D412yes—
57C2×Dic149C2×D411yescharacteristic
58C2×Dic149#4112yes—
59C23×C149C22×C411yescharacteristic
60C2×C4×C149—22no—
61C2×C4×C149—22no—
62C2×C4×C149—24no—
63C2×C4×C149C22⋊C411yescharacteristic
64C2×C4×C149C22⋊C411yescharacteristic
65C22×C149—21no—
66C22×C149—21no—
67C22×C149C2×C22⋊C411yescharacteristic
68C22×C149C4×D412yes—
69C4×C149—21no—
70C4×C149—42no—
71C4×C149#10112yescomplemented
72Dic149—21no—
73Dic149—42no—
74Dic149#10112yescomplemented
75Dic149#12112yes—
76Dic149#12411yescharacteristic
77Dic149#12711yescharacteristic
78C2×C149—22no—
79C2×C149#39011yescharacteristic
80C2×C149C2×#10111yescharacteristic
81C2×C149C2×#10111yescharacteristic
82C149#196611yescharacteristic, complemented, Sylow
83#1966—1491nomaximal, Sylow
84C2×C4⋊Q8—1491no—
85#423—1491no—
86C2×#101—1494no—
87C4×M16—1491no—
88C22×Q8—1492no—
89C2×M16—1492no—
90C2×M16—1492no—
91C4⋊Q8—2981no—
92C4⋊Q8—2981no—
93C4⋊Q8—2981no—
94C4⋊Q8—2981no—
95C2×C4⋊C4—1492no—
96C2×C4⋊C4—1491no—
97C2×C4⋊C4#1059701011yescharacteristic
98C2×C42—1491no—
99C4⋊C8—2981no—
100C4⋊C8—2981no—
101#101—2988no—
102#97—2981no—
103C4×C8—2981no—
104C2×Q8—2984no—
105C2×Q8—2982no—
106C2×Q8—2982no—
107C2×Q8—2984no—
108C22×C4—1492no—
109C22×C4—1491no—
110C22×C4—1491no—
111C22×C4C2×#1059701012yes—
112C22×C4C2×#1059701011yescharacteristic
113M16—2982no—
114M16—2984no—
115M16—1494no—
116C2×C8—2982no—
117C2×C8—2982no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—2982no—
121C4⋊C4—2982no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C42—1491no—
125C42—1491no—
126C42—1491no—
127C42—1491no—
128C23C22×#1059701011yescharacteristic
129Q8—5964no—
130Q8—5962no—
131Q8—5962no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—2982no—
136C2×C4—2982no—
137C2×C4—2984no—
138C2×C4—1491no—
139C2×C4—1491no—
140C2×C4—1491no—
141C2×C4—1491no—
142C2×C4—1492no—
143C2×C4—1492no—
144C2×C4C22⋊#1059701011yescharacteristic
145C2×C4C22⋊#1059701011yescharacteristic
146C8—2984no—
147C8—5962no—
148C22—21no—
149C22—21no—
150C22C2×C22⋊#1059701011yescharacteristic
151C22D4×#1059701012yes—
152C4—21no—
153C4—42no—
154C4—2981no—
155C4—5962no—
156C4—1492no—
157C4—1491no—
158C4—1491no—
159C4—1492no—
160C4#1801197212yescomplemented
161C2—22no—
162C2#2375057711yescharacteristic
163C2C2×#1801197211yescharacteristic
164C2D149⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutator, prime radicalC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
cosocleC22×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1966
LCSG ▷ C23×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
71. C4×C149#101semidirect
74. Dic149#101semidirect
82. C149#1966semidirect
160. C4#18011972semidirect

Maximal subgroups

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

subgroupindex
#237506282
C2×#180119722
C4×#145587452
C2×#180119102
#1966149