Finite Group Databasebeta

← #34060229

Subgroups — #34060229

Order 19072.

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

normal subgroups only

This group has 254 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#23750630C212yesmaximal, complemented
2#23750485C212yesmaximal, complemented
3#23750483C212yesmaximal, complemented
4#23750174C211yesmaximal, characteristic
5C2×#14558746—22no—
6#18011978—22no—
7#18011978C2214yes—
8C2×#14558737C411yescharacteristic
9C2×#14558735C411yescharacteristic
10#18011909C2211yescharacteristic
11#18011907C2211yescharacteristic
12#18011899C411yescharacteristic
13#18011884—22no—
14#18011871—22no—
15C42×D149C2211yescharacteristic
16#124×C149C411yescharacteristic
17#14558746—44no—
18C2×#11924753—24no—
19#14558737—42no—
20#14558735—42no—
21C2×Dic298C2×C411yescharacteristic
22C2×D596—21no—
23C2×D596C2×C411yescharacteristic
24C2×C22⋊D149—21no—
25C2×C22⋊D149—22no—
26C22×Dic149—21no—
27C2×C4×D149—21no—
28C2×C4×D149C2×C411yescharacteristic
29C2×C4×D149D412yes—
30#14558715—22no—
31#14558713—22no—
32C4×Dic149D412yes—
33C4×Dic149C2311yescharacteristic
34C2×Q8×C149C2×C411yescharacteristic
35C2×D4×C149C2×C411yescharacteristic
36C22⋊C4×C149—22no—
37C42×C149C2×C411yescharacteristic
38#11924753—44no—
39C22×D149—21no—
40C22×D149C22⋊C411yescharacteristic
41Dic298—41no—
42D596—41no—
43D596—42no—
44C22⋊D149—42no—
45C22⋊D149—42no—
46C22⋊D149—42no—
47C2×Dic149—21no—
48C2×Dic149—42no—
49C2×Dic149C22⋊C411yescharacteristic
50C2×Dic149C2×D412yes—
51C4×D149—22no—
52C4×D149—22no—
53C4×D149—22no—
54C4×D149—42no—
55C23×C149—21no—
56Q8×C149—41no—
57D4×C149—41no—
58C2×C4×C149—21no—
59C2×C4×C149C22⋊C412yes—
60C2×C4×C149C22×C411yescharacteristic
61C22×C149—41no—
62C22×C149—42no—
63C22×C149C2×C22⋊C411yescharacteristic
64C2×D149—21no—
65C2×D149—22no—
66C2×D149—41no—
67C2×D149—42no—
68C4×C149—21no—
69C4×C149—22no—
70C4×C149—41no—
71Dic149—41no—
72Dic149#10012yes—
73Dic149AGL(1,ℤ/8)12yes—
74Dic149#13712yes—
75C2×C149—81no—
76C2×C149C2×#10011yescharacteristic
77C2×C149#41712yes—
78D149—41no—
79D149—81no—
80C149#156011yescharacteristic, complemented, Sylow
81#1560—1491nomaximal, Sylow
82#532—1491no—
83#423—1492no—
84#333—1492no—
85#331—1492no—
86C2×#41—1491no—
87C2×#41—1491no—
88C2×M16—2982no—
89C4⋊Q8—1491no—
90#127—1491no—
91#124—1491no—
92#124#1059701011yescharacteristic
93#121—2982no—
94C4×D4—2982no—
95C2×C42—1491no—
96C4⋊C8—2982no—
97C4⋊C8—1494no—
98#41—5962no—
99#41—5962no—
100C2×Q8—1491no—
101C2×Q8C2×#1059701011yescharacteristic
102C2×D4—2981no—
103C2×D4—2981no—
104C2×D4—2982no—
105C2×D4—1491no—
106C2×D4C2×#1059701011yescharacteristic
107C22×C4—2981no—
108C22×C4—2981no—
109C22×C4—1492no—
110C22×C4—1491no—
111M16—5964no—
112C2×C8—2984no—
113C4⋊C4—2982no—
114C22⋊C4—22no—
115C22⋊C4—2982no—
116C42—1492no—
117C42—1491no—
118C42C2×#1059701011yescharacteristic
119C23—21no—
120C23—2981no—
121C23—1491no—
122Q8—41no—
123Q8—5961no—
124D4—41no—
125D4—5961no—
126D4—5962no—
127D4—5962no—
128D4—5962no—
129D4—5962no—
130C2×C4—21no—
131C2×C4—2982no—
132C2×C4—2982no—
133C2×C4—2982no—
134C2×C4—2981no—
135C2×C4—5962no—
136C2×C4—5962no—
137C2×C4—1491no—
138C2×C4—1492no—
139C2×C4C22⋊#1059701012yes—
140C2×C4C22×#1059701011yescharacteristic
141C8—5964no—
142C22—41no—
143C22—42no—
144C22—2981no—
145C22—2982no—
146C22—5961no—
147C22—5962no—
148C22C2×C22⋊#1059701011yescharacteristic
149C4—21no—
150C4—22no—
151C4—41no—
152C4—5961no—
153C4—1492no—
154C4—1492no—
155C4—1492no—
156C2—81no—
157C2—5961no—
158C2—11921no—
159C2D149⋊#10011yescharacteristic
160C2#2375061612yes—
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#1560
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. #23750630C2semidirect
2. #23750485C2semidirect
3. #23750483C2semidirect
80. C149#1560semidirect

Maximal subgroups

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

subgroupindex
#237506302
#237504852
#237504832
#237501742
#1560149