Finite Group Databasebeta

← #34055466

Subgroups — #34055466

Order 19072.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#18011890C212yesmaximal
2#23749961C214yesmaximal, complemented
3#23749866C214yesmaximal, complemented
4#23749783C214yesmaximal, complemented
5C2×C22⋊C8×C149C211yesmaximal, characteristic
6C22×Dic298C2212yes—
7C2×Dic596C2214yescomplemented
8#18011890—22no—
9#18011890—22no—
10#18011890C2214yes—
11#18011890C2214yes—
12C2×C4⋊Dic149C2212yes—
13C2×#14558715—22no—
14C2×C22⋊Dic149—22no—
15#18011845C2214yescomplemented
16#18011836C2218yescomplemented
17C23×C4×C149C2211yescharacteristic
18C22×C8×C149C2212yes—
19C22⋊C8×C149C2214yes—
20C2×Dic298—22no—
21C2×Dic298—44no—
22C2×Dic298C2314yes—
23C22×Dic149—22no—
24C22×Dic149—22no—
25Dic596—44no—
26C4⋊Dic149—22no—
27C4⋊Dic149C2314yes—
28#14558715—24no—
29#14558715—24no—
30C22⋊Dic149—24no—
31C22⋊Dic149—24no—
32C24×C149D411yescharacteristic
33C22×C4×C149—42no—
34C22×C4×C149D412yes—
35C22×C4×C149D411yescharacteristic
36C22×C4×C149C2312yes—
37C22×C4×C149C2311yescharacteristic
38C2×C8×C149—42no—
39C2×C8×C149C2314yes—
40Dic298—28no—
41Dic298—44no—
42C2×Dic149—24no—
43C2×Dic149—24no—
44C2×Dic149—44no—
45C2×Dic149—44no—
46C23×C149—41no—
47C23×C149—41no—
48C23×C149Q1614yescomplemented
49C23×C149C2×D412yes—
50C23×C149C2×D411yescharacteristic
51C2×C4×C149—24no—
52C2×C4×C149—22no—
53C2×C4×C149—42no—
54C2×C4×C149—41no—
55C2×C4×C149C2×D412yes—
56C2×C4×C149C2×D411yescharacteristic
57C2×C4×C149C2411yescharacteristic
58C8×C149—24no—
59C22×C149—21no—
60C22×C149—22no—
61C22×C149—21no—
62C22×C149—22no—
63C22×C149—44no—
64C22×C149C2×Q1614yes—
65C22×C149C2×Q1612yes—
66C22×C149C22×D411yescharacteristic
67C4×C149—21no—
68C4×C149—22no—
69C4×C149H(5,𝔽2)12yes—
70Dic149—44no—
71Dic149—44no—
72C2×C149—22no—
73C2×C149—24no—
74C2×C149#53411yescharacteristic
75C2×C149C22×Q1611yescharacteristic
76C2×C149#57511yescharacteristic
77C149#318911yescharacteristic, complemented, Sylow
78#3189—1491nomaximal, Sylow
79C2×C22⋊Q8—1492no—
80#484—1494no—
81#467—1494no—
82#451—1494no—
83C2×C22⋊C8D14911yescharacteristic
84C22×Q8—1492no—
85C23×C4C2×D14911yescharacteristic
86C2×Q16—1494no—
87C22×C8C2×D14912yes—
88C22⋊Q8—2982no—
89C22⋊Q8—2982no—
90C22⋊Q8—1494no—
91C22⋊Q8—1494no—
92C2×C4⋊C4—2982no—
93C2×C4⋊C4—1492no—
94C2×C22⋊C4—2982no—
95#107—1494no—
96#103—1498no—
97C22⋊C8C2×D14914yes—
98C24D59611yescharacteristic
99C2×Q8—2982no—
100C2×Q8—5964no—
101C2×Q8—1494no—
102C22×C4—42no—
103C22×C4—2982no—
104C22×C4—2982no—
105C22×C4D59612yes—
106C22×C4D59611yescharacteristic
107C22×C4C22×D14912yes—
108C22×C4C22×D14911yescharacteristic
109Q16—5964no—
110C2×C8—42no—
111C2×C8C22×D14914yes—
112C4⋊C4—2984no—
113C4⋊C4—2984no—
114C4⋊C4—2982no—
115C4⋊C4—1494no—
116C22⋊C4—2984no—
117C22⋊C4—2984no—
118C23—41no—
119C23—41no—
120C23Dic59614yescomplemented
121C23C2×D59611yescharacteristic
122C23C2×D59612yes—
123Q8—2988no—
124Q8—5964no—
125C2×C4—22no—
126C2×C4—24no—
127C2×C4—41no—
128C2×C4—42no—
129C2×C4—2984no—
130C2×C4—2984no—
131C2×C4—5964no—
132C2×C4—5964no—
133C2×C4C2×D59611yescharacteristic
134C2×C4C2×D59612yes—
135C2×C4C23×D14911yescharacteristic
136C8—24no—
137C22—22no—
138C22—21no—
139C22—22no—
140C22—21no—
141C22—44no—
142C22C2×Dic59612yes—
143C22C2×Dic59614yes—
144C22C22×D59611yescharacteristic
145C4—22no—
146C4—21no—
147C4—5964no—
148C4—5964no—
149C4#1801195612yes—
150C2—24no—
151C2—22no—
152C2#2375018711yescharacteristic
153C2C22×Dic59611yescharacteristic
154C2#2375042511yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×C22⋊C8×C149C2
socleC22×C149C22×D4
prime radicalC24×C149D4
hypercenterC2×C22⋊C8D149
hypocenterC149#3189
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #23749961C2semidirect
3. #23749866C2semidirect
4. #23749783C2semidirect
7. C2×Dic596C22semidirect
15. #18011845C22semidirect
16. #18011836C22semidirect
48. C23×C149Q16semidirect
77. C149#3189semidirect
120. C23Dic596semidirect

Maximal subgroups

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

subgroupindex
C2×#180118902
#237499612
#237498662
#237497832
C2×C22⋊C8×C1492
#3189149