Finite Group Databasebeta

← #34060983

Subgroups — #34060983

Order 19072.

250 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 52 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#23750612C212yesmaximal, complemented
2#23750536C212yesmaximal, complemented
3#23750533C212yesmaximal, complemented
4#23750173C211yesmaximal, characteristic
5C2×#14558745—22no—
6#18011972C2214yes—
7#18011971—22no—
8C2×#14558735C411yescharacteristic
9C2×#14558735C2211yescharacteristic
10#18011911C2211yescharacteristic
11#18011898C411yescharacteristic
12#18011898C2211yescharacteristic
13#18011882—22no—
14D4×Dic149—22no—
15C42×D149C411yescharacteristic
16#127×C149C411yescharacteristic
17#14558745—24no—
18#14558745—42no—
19C2×#11924753—42no—
20#14558735—41no—
21#14558735—41no—
22#14558735—41no—
23#14558735—41no—
24C2×Dic298C2×C411yescharacteristic
25C2×Dic298C2311yescharacteristic
26C2×C22⋊D149—21no—
27C2×C22⋊D149D412yes—
28C22×Dic149—21no—
29C22×Dic149D412yes—
30C2×C4×D149—21no—
31C2×C4×D149C2×C411yescharacteristic
32C4⋊Dic149—22no—
33C22⋊Dic149—22no—
34C22⋊Dic149—22no—
35C4×Dic149—21no—
36C4×Dic149C2×C411yescharacteristic
37C2×D4×C149—22no—
38C2×D4×C149C2×C411yescharacteristic
39C2×D4×C149C2×C411yescharacteristic
40C42×C149C2×C411yescharacteristic
41#11924753—44no—
42C22×D149C22⋊C411yescharacteristic
43Dic298—41no—
44Dic298—41no—
45C22⋊D149—42no—
46C22⋊D149—42no—
47C2×Dic149—22no—
48C2×Dic149—22no—
49C2×Dic149—21no—
50C2×Dic149—21no—
51C2×Dic149—41no—
52C2×Dic149—41no—
53C2×Dic149C22⋊C411yescharacteristic
54C2×Dic149C2×D412yes—
55C4×D149—21no—
56C4×D149—21no—
57C4×D149—42no—
58C23×C149—21no—
59C23×C149C22⋊C412yes—
60D4×C149—41no—
61D4×C149—41no—
62D4×C149—44no—
63C2×C4×C149—21no—
64C2×C4×C149C22×C411yescharacteristic
65C22×C149—22no—
66C22×C149—42no—
67C22×C149—42no—
68C22×C149—41no—
69C22×C149C2×C22⋊C411yescharacteristic
70C2×D149—21no—
71C2×D149—41no—
72C4×C149—22no—
73C4×C149—21no—
74Dic149—22no—
75Dic149—41no—
76Dic149—41no—
77Dic149#9911yescharacteristic
78Dic149#9911yescharacteristic
79C2×C149—21no—
80C2×C149—42no—
81C2×C149—81no—
82C2×C149C2×#9911yescharacteristic
83D149—41no—
84C149#213211yescharacteristic, complemented, Sylow
85#2132—1491nomaximal, Sylow
86#532—1491no—
87#413—1492no—
88#356—1492no—
89#355—1492no—
90C2×#41—1491no—
91C2×#41—1491no—
92C2×M16—2982no—
93C4⋊Q8—1491no—
94#127#1059701011yescharacteristic
95#124—1491no—
96#124—1491no—
97#121—2982no—
98C4×D4—2982no—
99C2×C42—1491no—
100#101—1494no—
101#100—2982no—
102#41—5961no—
103#41—5961no—
104#41—5961no—
105#41—5961no—
106C2×Q8—1491no—
107C2×Q8—1491no—
108C2×D4—22no—
109C2×D4—2981no—
110C2×D4—1492no—
111C2×D4C2×#1059701011yescharacteristic
112C2×D4C2×#1059701011yescharacteristic
113C22×C4—2981no—
114C22×C4—2981no—
115C22×C4—1492no—
116C22×C4—1491no—
117M16—2984no—
118M16—5962no—
119C2×C8—5962no—
120C4⋊C4—2982no—
121C22⋊C4—2982no—
122C22⋊C4—2982no—
123C42—2981no—
124C42—1491no—
125C42C2×#1059701011yescharacteristic
126C23—21no—
127C23—1491no—
128C23C22⋊#1059701012yes—
129Q8—5961no—
130Q8—5961no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—5962no—
135D4—5962no—
136C2×C4—21no—
137C2×C4—2981no—
138C2×C4—2981no—
139C2×C4—2982no—
140C2×C4—2982no—
141C2×C4—2981no—
142C2×C4—2981no—
143C2×C4—5962no—
144C2×C4—5961no—
145C2×C4—5961no—
146C2×C4—1492no—
147C2×C4—1491no—
148C2×C4C22×#1059701011yescharacteristic
149C8—5964no—
150C22—22no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22—2981no—
155C22—5961no—
156C22C2×C22⋊#1059701011yescharacteristic
157C4—22no—
158C4—21no—
159C4—2982no—
160C4—5961no—
161C4—5961no—
162C4—1491no—
163C4—1491no—
164C2—21no—
165C2—42no—
166C2—81no—
167C2—5961no—
168C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC2×C149C2×#99
prime radical#23750173C2
cosocleC2×Dic298C23
hypercenter#127#10597010
hypocenterC149#2132
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #23750612C2semidirect
2. #23750536C2semidirect
3. #23750533C2semidirect
84. C149#2132semidirect

Maximal subgroups

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

subgroupindex
#237506122
#237505362
#237505332
#237501732
#2132149