Finite Group Databasebeta

← #34060195

Subgroups — #34060195

Order 19072.

246 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750643C212yesmaximal, complemented
2#23750485C212yesmaximal, complemented
3#23750483C212yesmaximal, complemented
4#23750174C211yesmaximal, characteristic
5#18011978C2214yes—
6#18011968—22no—
7C4×#11924753—22no—
8C2×#14558737C411yescharacteristic
9C2×#14558735C411yescharacteristic
10#18011909C2211yescharacteristic
11#18011907C2211yescharacteristic
12#18011899C411yescharacteristic
13#18011884—22no—
14#18011871—22no—
15C42×D149C2211yescharacteristic
16#124×C149C411yescharacteristic
17C2×#11924753—24no—
18#14558737—42no—
19#14558735—42no—
20C2×Dic298C2×C411yescharacteristic
21C2×D596—21no—
22C2×D596C2×C411yescharacteristic
23C2×C22⋊D149—21no—
24C2×C22⋊D149—22no—
25C22×Dic149—21no—
26C2×C4×D149—21no—
27C2×C4×D149C2×C411yescharacteristic
28C2×C4×D149D412yes—
29#14558715—22no—
30#14558713—22no—
31C4×Dic149D412yes—
32C4×Dic149C2311yescharacteristic
33C2×Q8×C149C2×C411yescharacteristic
34C2×D4×C149C2×C411yescharacteristic
35C22⋊C4×C149—22no—
36C42×C149C2×C411yescharacteristic
37#11924753—44no—
38C22×D149—21no—
39C22×D149C22⋊C411yescharacteristic
40Dic298—41no—
41D596—41no—
42D596—42no—
43C22⋊D149—42no—
44C22⋊D149—44no—
45C2×Dic149—21no—
46C2×Dic149—42no—
47C2×Dic149C22⋊C411yescharacteristic
48C2×Dic149C2×D412yes—
49C4×D149—22no—
50C4×D149—24no—
51C4×D149—42no—
52C23×C149—21no—
53Q8×C149—41no—
54D4×C149—41no—
55C2×C4×C149—21no—
56C2×C4×C149C22⋊C412yes—
57C2×C4×C149C22×C411yescharacteristic
58C22×C149—41no—
59C22×C149—42no—
60C22×C149C2×C22⋊C411yescharacteristic
61C2×D149—21no—
62C2×D149—22no—
63C2×D149—41no—
64C2×D149—42no—
65C4×C149—21no—
66C4×C149—22no—
67C4×C149—41no—
68Dic149—41no—
69Dic149#10012yes—
70Dic149#13514yes—
71C2×C149—81no—
72C2×C149C2×#10011yescharacteristic
73C2×C149#41612yes—
74D149—41no—
75D149—81no—
76C149#154311yescharacteristic, complemented, Sylow
77#1543—1491nomaximal, Sylow
78#532—1491no—
79#431—1492no—
80#333—1492no—
81#331—1492no—
82C2×#41—1491no—
83C2×#41—1491no—
84C4⋊Q8—1491no—
85#127—1491no—
86#124—1491no—
87#124#1059701011yescharacteristic
88#121—2982no—
89C4×D4—2982no—
90C2×C42—1491no—
91C4⋊C8—1494no—
92C22⋊C8—2982no—
93C4×C8—2982no—
94#41—5962no—
95#41—5962no—
96C2×Q8—1491no—
97C2×Q8C2×#1059701011yescharacteristic
98C2×D4—2981no—
99C2×D4—2981no—
100C2×D4—2982no—
101C2×D4—1491no—
102C2×D4C2×#1059701011yescharacteristic
103C22×C4—2981no—
104C22×C4—2981no—
105C22×C4—1492no—
106C22×C4—1491no—
107C2×C8—2984no—
108C4⋊C4—2982no—
109C22⋊C4—22no—
110C22⋊C4—2982no—
111C42—1492no—
112C42—1491no—
113C42C2×#1059701011yescharacteristic
114C23—21no—
115C23—2981no—
116C23—1491no—
117Q8—41no—
118Q8—5961no—
119D4—41no—
120D4—5961no—
121D4—5962no—
122D4—5962no—
123D4—5964no—
124C2×C4—21no—
125C2×C4—2984no—
126C2×C4—2982no—
127C2×C4—2981no—
128C2×C4—5962no—
129C2×C4—5962no—
130C2×C4—1491no—
131C2×C4—1492no—
132C2×C4C22⋊#1059701012yes—
133C2×C4C22×#1059701011yescharacteristic
134C8—5964no—
135C22—41no—
136C22—42no—
137C22—2981no—
138C22—2982no—
139C22—5961no—
140C22—5962no—
141C22C2×C22⋊#1059701011yescharacteristic
142C4—21no—
143C4—22no—
144C4—41no—
145C4—5961no—
146C4—1492no—
147C4—1494no—
148C2—81no—
149C2—5961no—
150C2—11921no—
151C2D149⋊#10011yescharacteristic
152C2#2375061512yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750174C2
cosocleC4×Dic149C23
hypercenter#124#10597010
hypocenterC149#1543
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #23750643C2semidirect
2. #23750485C2semidirect
3. #23750483C2semidirect
76. C149#1543semidirect

Maximal subgroups

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

subgroupindex
#237506432
#237504852
#237504832
#237501742
#1543149