Finite Group Databasebeta

← #34043643

Subgroups — #34043643

Order 19072.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#23749763C212yesmaximal, complemented
2#23749537C211yesmaximal, characteristic, complemented
3#23749359C212yesmaximal, complemented
4#23749349C211yesmaximal, characteristic, complemented
5#534×C149C211yesmaximal, characteristic
6C22×Dic298C2211yescharacteristic, complemented
7C2×#14558724—22no—
8C2×C22⋊Dic149—21no—
9#18011834—22no—
10C22⋊#11924746C2212yescomplemented
11#18011818—21no—
12#18011818C2211yescharacteristic, complemented
13C22×D4×C149—21no—
14#123×C149—22no—
15#121×C149—21no—
16#121×C149C2212yes—
17#120×C149—22no—
18C2×C22⋊C4×C149C2211yescharacteristic
19C2×Dic298—22no—
20C2×Dic298—42no—
21C22×Dic149—21no—
22C22×Dic149—21no—
23#14558724—44no—
24C2×#11924746—22no—
25C22⋊Dic149—42no—
26C24×C149—21no—
27C24×C149D411yescharacteristic
28C2×D4×C149—22no—
29C2×D4×C149—22no—
30C2×D4×C149—21no—
31C2×D4×C149—42no—
32C2×D4×C149—42no—
33C2×D4×C149D412yes—
34C22×C4×C149—21no—
35C22×C4×C149D411yescharacteristic
36C22×C4×C149C2311yescharacteristic
37C4⋊C4×C149—21no—
38C4⋊C4×C149D412yes—
39C22⋊C4×C149—22no—
40C22⋊C4×C149—22no—
41C22⋊C4×C149—22no—
42Dic298—24no—
43Dic298—42no—
44C2×Dic149—22no—
45C2×Dic149—41no—
46C2×Dic149—41no—
47C2×Dic149—41no—
48C2×Dic149—41no—
49C2×Dic149—41no—
50#11924746—42no—
51C23×C149—21no—
52C23×C149—21no—
53C23×C149—22no—
54C23×C149—41no—
55C23×C149—41no—
56C23×C149—42no—
57C23×C149—81no—
58C23×C149—81no—
59C23×C149SD1612yescomplemented
60C23×C149C2×D411yescharacteristic
61D4×C149—42no—
62D4×C149—44no—
63D4×C149—42no—
64D4×C149—42no—
65D4×C149—81no—
66C2×C4×C149—21no—
67C2×C4×C149—22no—
68C2×C4×C149—41no—
69C2×C4×C149—42no—
70C2×C4×C149—41no—
71C2×C4×C149C2×D412yes—
72C22×C149—21no—
73C22×C149—21no—
74C22×C149—22no—
75C22×C149—42no—
76C22×C149—41no—
77C22×C149—41no—
78C22×C149—42no—
79C22×C149—42no—
80C22×C149—42no—
81C22×C149—81no—
82C22×C149—84no—
83C22×C149#12011yescharacteristic
84C22×C149C2×SD1611yescharacteristic
85C22×C149AGL(1,ℤ/8)11yescharacteristic
86C4×C149—22no—
87C4×C149—42no—
88C4×C149—41no—
89Dic149—42no—
90Dic149—81no—
91C2×C149—21no—
92C2×C149—21no—
93C2×C149—42no—
94C2×C149—82no—
95C2×C149#45011yescharacteristic
96C2×C149#45511yescharacteristic
97C2×C149B(4,𝔽2)11yescharacteristic
98C149#160111yescharacteristic, complemented, Sylow
99#1601—1491nomaximal, Sylow
100#534D14911yescharacteristic
101#448—1492no—
102#393—1491no—
103#327—1492no—
104#323—1491no—
105C22×Q8—1491no—
106C22×D4—21no—
107C2×SD16—2982no—
108#123—22no—
109#121—21no—
110#121C2×D14912yes—
111#120—22no—
112C2×C22⋊C4—2981no—
113C2×C22⋊C4C2×D14911yescharacteristic
114#103—2982no—
115C22⋊C8—1492no—
116#95—2981no—
117#95—1491no—
118C24—21no—
119C24C22⋊D14911yescharacteristic
120C2×Q8—2982no—
121C2×Q8—5962no—
122C2×D4—22no—
123C2×D4—22no—
124C2×D4—21no—
125C2×D4—42no—
126C2×D4—42no—
127C2×D4C22⋊D14912yes—
128C22×C4—21no—
129C22×C4—2981no—
130C22×C4—2981no—
131C22×C4C22⋊D14911yescharacteristic
132C22×C4C22×D14911yescharacteristic
133SD16—5964no—
134C2×C8—2982no—
135C4⋊C4—21no—
136C4⋊C4C22⋊D14912yes—
137C22⋊C4—22no—
138C22⋊C4—22no—
139C22⋊C4—22no—
140C22⋊C4—5962no—
141C23—21no—
142C23—21no—
143C23—22no—
144C23—41no—
145C23—41no—
146C23—42no—
147C23—81no—
148C23—81no—
149C23#1455872412yescomplemented
150C23C2×C22⋊D14911yescharacteristic
151Q8—2984no—
152Q8—5962no—
153D4—42no—
154D4—44no—
155D4—42no—
156D4—42no—
157D4—81no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—2982no—
164C2×C4—5961no—
165C2×C4—5961no—
166C2×C4—5961no—
167C2×C4—5961no—
168C2×C4—5961no—
169C2×C4C2×C22⋊D14912yes—
170C8—5962no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—81no—
181C22—84no—
182C22#1801188011yescharacteristic
183C22C2×#1455872411yescharacteristic
184C22#1801193711yescharacteristic
185C4—22no—
186C4—42no—
187C4—41no—
188C4—5962no—
189C4—11921no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—82no—
194C2#2374977611yescharacteristic
195C2#2374980311yescharacteristic
196C2#2374981211yescharacteristic
subgroupG/H
centerC22#18011880
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting, prime radical#534×C149C2
socleC22×C149#120
hypercenter#534D149
hypocenterC149#1601
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #23749763C2semidirect
2. #23749537C2semidirect
3. #23749359C2semidirect
4. #23749349C2semidirect
6. C22×Dic298C22semidirect
10. C22⋊#11924746C22semidirect
12. #18011818C22semidirect
59. C23×C149SD16semidirect
98. C149#1601semidirect
149. C23#14558724semidirect

Maximal subgroups

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

subgroupindex
#237497632
#237495372
#237493592
#237493492
#534×C1492
#1601149