Finite Group Databasebeta

← #34060145

Subgroups — #34060145

Order 19072.

270 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C4×#14558745C212yesmaximal, complemented
2#23750481C212yesmaximal, complemented
3#23750480C212yesmaximal, complemented
4#23750171C211yesmaximal, characteristic
5C2×#14558745—22no—
6#18011966C2214yes—
7C4×#11924753—22no—
8C2×#14558736C411yescharacteristic
9#18011909C411yescharacteristic
10#18011907C411yescharacteristic
11#18011900C2211yescharacteristic
12#18011898C2211yescharacteristic
13#18011883—22no—
14C4×C22⋊D149—22no—
15C2×C4×Dic149C2211yescharacteristic
16C2×#41×C149C411yescharacteristic
17#14558745—28no—
18C2×#11924753—24no—
19#14558736—42no—
20C2×Dic298C2×C411yescharacteristic
21C2×D596C2×C411yescharacteristic
22C2×C22⋊D149—22no—
23C2×C22⋊D149—21no—
24C22×Dic149D412yes—
25C2×C4×D149—21no—
26#14558715—22no—
27C22⋊Dic149—22no—
28#14558713—22no—
29C4×Dic149C2×C411yescharacteristic
30C4×Dic149D412yes—
31C4×Dic149C2311yescharacteristic
32#41×C149—42no—
33C2×Q8×C149C2×C411yescharacteristic
34C2×D4×C149—21no—
35C2×D4×C149C2×C411yescharacteristic
36C22×C4×C149—21no—
37C22×C4×C149C2×C411yescharacteristic
38#11924753—28no—
39C22×D149—21no—
40Dic298—41no—
41D596—41no—
42C22⋊D149—42no—
43C22⋊D149—44no—
44C2×Dic149—24no—
45C2×Dic149—21no—
46C2×Dic149C22⋊C412yes—
47C2×Dic149C2×D412yes—
48C4×D149—42no—
49C23×C149—21no—
50C23×C149C22⋊C411yescharacteristic
51Q8×C149—41no—
52D4×C149—41no—
53D4×C149—42no—
54C2×C4×C149—22no—
55C2×C4×C149—21no—
56C2×C4×C149—42no—
57C2×C4×C149C22⋊C411yescharacteristic
58C2×C4×C149C22×C411yescharacteristic
59C22×C149—21no—
60C22×C149—22no—
61C22×C149—41no—
62C22×C149—42no—
63C22×C149C2×C22⋊C411yescharacteristic
64C2×D149—41no—
65C2×D149—42no—
66C4×C149—21no—
67C4×C149—41no—
68C4×C149#10012yes—
69Dic149—22no—
70Dic149—41no—
71Dic149#10414yes—
72C2×C149—41no—
73C2×C149—81no—
74C2×C149C2×#10011yescharacteristic
75C2×C149C2×#10412yes—
76D149—81no—
77C149#152511yescharacteristic, complemented, Sylow
78#1525—1491nomaximal, Sylow
79#532—1491no—
80C4×M16—1492no—
81#329—1492no—
82#329—1492no—
83C2×#41—1491no—
84C2×#41#1059701011yescharacteristic
85C2×M16—2982no—
86C4⋊Q8—1491no—
87#127—1491no—
88#124—1491no—
89#124—1491no—
90#121—2982no—
91C4×D4—2982no—
92C2×C42—1491no—
93#97—1494no—
94C4×C8—2982no—
95#41—42no—
96#41—5962no—
97C2×Q8—1491no—
98C2×Q8C2×#1059701011yescharacteristic
99C2×D4—21no—
100C2×D4—2981no—
101C2×D4—2982no—
102C2×D4—1491no—
103C2×D4C2×#1059701011yescharacteristic
104C22×C4—21no—
105C22×C4—2981no—
106C22×C4—1492no—
107C22×C4C2×#1059701011yescharacteristic
108M16—2988no—
109C2×C8—2984no—
110C4⋊C4—2982no—
111C22⋊C4—2982no—
112C22⋊C4—2982no—
113C42—1492no—
114C42—1491no—
115C42—1491no—
116C23—21no—
117C23—2981no—
118C23C22⋊#1059701011yescharacteristic
119Q8—41no—
120Q8—5961no—
121D4—41no—
122D4—42no—
123D4—5961no—
124D4—5962no—
125D4—5964no—
126C2×C4—22no—
127C2×C4—21no—
128C2×C4—42no—
129C2×C4—2984no—
130C2×C4—2981no—
131C2×C4—5962no—
132C2×C4—1492no—
133C2×C4—1492no—
134C2×C4C22⋊#1059701011yescharacteristic
135C2×C4C22×#1059701011yescharacteristic
136C8—2988no—
137C22—21no—
138C22—22no—
139C22—41no—
140C22—42no—
141C22—5961no—
142C22—5962no—
143C22C2×C22⋊#1059701011yescharacteristic
144C4—21no—
145C4—41no—
146C4—2982no—
147C4—5961no—
148C4—1494no—
149C4#1801197112yes—
150C2—41no—
151C2—81no—
152C2—11921no—
153C2C2×#1801197111yescharacteristic
154C2D149⋊#10412yes—
subgroupG/H
centerC2×C4C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×#41×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750171C2
cosocleC4×Dic149C23
hypercenterC2×#41#10597010
hypocenterC149#1525
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C4×#14558745C2semidirect
2. #23750481C2semidirect
3. #23750480C2semidirect
77. C149#1525semidirect

Maximal subgroups

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

subgroupindex
C4×#145587452
#237504812
#237504802
#237501712
#1525149