Finite Group Databasebeta

← #34045134

Subgroups — #34045134

Order 19072.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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#23750136C211yesmaximal, characteristic
2C2×#18011839C212yesmaximal, complemented
3#23749589C211yesmaximal, characteristic, complemented
4#23749385C212yesmaximal, complemented
5C22×C42×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2211yescharacteristic
7C2×#14558720C2212yes—
8#18011894—21no—
9#18011890C412yescomplemented
10#18011885C412yescomplemented
11#18011880—21no—
12C4×C22⋊D149—22no—
13#18011870C2211yescharacteristic
14#18011839—24no—
15C22⋊#11924746—22no—
16C23×C4×C149—21no—
17C23×C4×C149C2211yescharacteristic
18C2×C42×C149—21no—
19C2×C42×C149—24no—
20C2×C42×C149C2212yes—
21#14558736—22no—
22#14558736—22no—
23C2×Dic298C2×C411yescharacteristic, complemented
24C2×D596C2×C411yescharacteristic, complemented
25C2×C22⋊D149—22no—
26C2×C22⋊D149—21no—
27C2×C4×D149—21no—
28#14558720—22no—
29#14558720—22no—
30C2×#11924746—22no—
31C4⋊Dic149C2×C412yescomplemented
32#14558715—22no—
33C22⋊Dic149—22no—
34C22⋊Dic149—21no—
35#14558713—22no—
36C4×Dic149—21no—
37C24×C149D411yescharacteristic
38C22×C4×C149—24no—
39C22×C4×C149—28no—
40C22×C4×C149—22no—
41C22×C4×C149—22no—
42C22×C4×C149—22no—
43C22×C4×C149C2×C412yes—
44C22×C4×C149D411yescharacteristic
45C22×C4×C149D412yes—
46C22×C4×C149C2311yescharacteristic
47C42×C149—24no—
48C42×C149—22no—
49C42×C149D414yescomplemented
50C22×D149—21no—
51Dic298—22no—
52D596—22no—
53C22⋊D149—44no—
54C22⋊D149—41no—
55C22⋊D149—41no—
56C2×Dic149—21no—
57C2×Dic149—22no—
58C4×D149—42no—
59#11924746—42no—
60C23×C149—24no—
61C23×C149—21no—
62C23×C149—21no—
63C23×C149C22⋊C412yes—
64C23×C149C2×D411yescharacteristic
65C2×C4×C149—216no—
66C2×C4×C149—28no—
67C2×C4×C149—21no—
68C2×C4×C149—24no—
69C2×C4×C149—21no—
70C2×C4×C149—24no—
71C2×C4×C149—24no—
72C2×C4×C149C22⋊C412yes—
73C2×C4×C149C22×C411yescharacteristic
74C2×C4×C149C2×D412yes—
75C2×C4×C149C2×D411yescharacteristic
76C2×C4×C149#4112yes—
77C22×C149—24no—
78C22×C149—24no—
79C22×C149—22no—
80C22×C149—22no—
81C22×C149—22no—
82C22×C149#10414yescomplemented
83C22×C149C2×C22⋊C411yescharacteristic
84C22×C149#12011yescharacteristic
85C22×C149#12311yescharacteristic
86C2×D149—41no—
87C2×D149—42no—
88C4×C149—28no—
89C4×C149—22no—
90C4×C149C4×D412yes—
91C4×C149#12112yes—
92Dic149—41no—
93Dic149—42no—
94C2×C149—21no—
95C2×C149—24no—
96C2×C149—21no—
97C2×C149#38611yescharacteristic
98C2×C149C2×#10412yes—
99D149—81no—
100C149#189611yescharacteristic, complemented, Sylow
101#1896—1491nomaximal, Sylow
102#525—1491no—
103C22×C42D14911yescharacteristic, complemented
104C2×#104—1492no—
105#407—1491no—
106#339—1492no—
107C2×#41—1491no—
108C23×C4—21no—
109C23×C4C2×D14911yescharacteristic
110C2×M16—1492no—
111#123—2981no—
112C22⋊Q8—1492no—
113#121—1492no—
114#120—2981no—
115C4×D4—2982no—
116#117—1491no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D14912yes—
120#104—2984no—
121C22⋊C8—2982no—
122C24C22⋊D14911yescharacteristic
123#41—2982no—
124#41—2982no—
125C2×Q8—1491no—
126C2×D4—2981no—
127C2×D4—2982no—
128C2×D4—1491no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—2981no—
135C22×C4C4×D14912yes—
136C22×C4C22⋊D14911yescharacteristic
137C22×C4D59612yes—
138C22×C4C22×D14911yescharacteristic
139M16—2982no—
140M16—2982no—
141C2×C8—2982no—
142C4⋊C4—2982no—
143C4⋊C4—1492no—
144C22⋊C4—2981no—
145C22⋊C4—2982no—
146C22⋊C4—2982no—
147C42—24no—
148C42—22no—
149C42—2981no—
150C42C22⋊D14914yescomplemented
151C23—24no—
152C23—21no—
153C23—21no—
154C23—2981no—
155C23#1455871312yes—
156C23C2×C22⋊D14911yescharacteristic
157Q8—2982no—
158D4—2982no—
159D4—5964no—
160D4—5961no—
161D4—5961no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—2982no—
170C2×C4—2981no—
171C2×C4—5962no—
172C2×C4#1455871312yes—
173C2×C4C2×C4×D14911yescharacteristic
174C2×C4C2×C22⋊D14912yes—
175C2×C4C2×D59611yescharacteristic
176C2×C4#1455873612yes—
177C8—5962no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—5962no—
184C22—5961no—
185C22#1801183914yescomplemented
186C22C2×#1455871311yescharacteristic
187C22#1801188011yescharacteristic
188C22#1801189411yescharacteristic
189C4—28no—
190C4—22no—
191C4—5962no—
192C4—5961no—
193C4C4×C22⋊D14912yes—
194C4#1801188512yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—11921no—
199C2#2374950411yescharacteristic
200C2C2×#1801183912yes—
subgroupG/H
centerC2×C4C2×D596
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC22×C42×C149C2
socleC22×C149C2×C22⋊C4
prime radical#23750136C2
cosocleC22×C4×C149C23
hypercenterC22×C42D149
hypocenterC149#1896
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#18011839C2semidirect
3. #23749589C2semidirect
4. #23749385C2semidirect
5. C22×C42×C149C2semidirect
9. #18011890C4semidirect
10. #18011885C4semidirect
23. C2×Dic298C2×C4semidirect
24. C2×D596C2×C4semidirect
31. C4⋊Dic149C2×C4semidirect
49. C42×C149D4semidirect
82. C22×C149#104semidirect
100. C149#1896semidirect
103. C22×C42D149semidirect
150. C42C22⋊D149semidirect
185. C22#18011839semidirect

Maximal subgroups

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

subgroupindex
#237501362
C2×#180118392
#237495892
#237493852
C22×C42×C1492
#1896149