Finite Group Databasebeta

← #34060881

Subgroups — #34060881

Order 19072.

324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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#23750567C211yesmaximal, characteristic
2C4×C22⋊#10597010C211yesmaximal, characteristic
3#23750503C214yesmaximal
4C2×#18011891C211yesmaximal, characteristic
5C2×C4⋊#10597010—21no—
6C2×C22⋊#10597010C2212yes—
7C2×C22⋊#10597010C2212yes—
8C2×C4×#10597010—21no—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4—21no—
11C22×Dic298C411yescharacteristic, complemented
12C22×C4×D149C2211yescharacteristic
13#18011891—21no—
14#18011891—21no—
15#18011891—21no—
16#18011891—21no—
17C2×C4⋊Dic149C412yescomplemented
18C2×#14558713C2212yes—
19C2×C4⋊C4×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21C22×#10597010—22no—
22C4⋊#10597010—42no—
23C22⋊#10597010—22no—
24C22⋊#10597010—24no—
25C22⋊#10597010Q814yescomplemented
26C4×#10597010—42no—
27C23×D149C2311yescharacteristic
28C2×Dic298—21no—
29C2×Dic298—21no—
30C2×Dic298—42no—
31C22×Dic149C2×C412yes—
32C22×Dic149C2×C411yescharacteristic
33C2×C4×D149—42no—
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149D411yescharacteristic
37C2×C4×D149D411yescharacteristic
38C4⋊Dic149—22no—
39C4⋊Dic149—22no—
40#14558713—22no—
41#14558713—22no—
42C22×C4×C149C2×C411yescharacteristic
43C22×C4×C149C2×C412yes—
44C4⋊C4×C149—21no—
45C4⋊C4×C149—21no—
46C2×#10597010—24no—
47C2×#10597010—42no—
48C2×#10597010—42no—
49C2×#10597010—42no—
50C2×#10597010—42no—
51C2×#10597010—42no—
52C22×D149—41no—
53C22×D149—41no—
54C22×D149C2×D411yescharacteristic
55C22×D149C2×D411yescharacteristic
56C22×D149C2×Q812yes—
57C22×D149#4112yes—
58Dic298—42no—
59Dic298—42no—
60C2×Dic149—22no—
61C2×Dic149—41no—
62C2×Dic149—42no—
63C2×Dic149C22⋊C411yescharacteristic
64C2×Dic149C22⋊C411yescharacteristic
65C4×D149—22no—
66C4×D149—22no—
67C4×D149—41no—
68C4×D149—41no—
69C23×C149C22×C411yescharacteristic
70C2×C4×C149—22no—
71C2×C4×C149—22no—
72C2×C4×C149—42no—
73C2×C4×C149C22⋊C411yescharacteristic
74C2×C4×C149C22⋊C411yescharacteristic
75C22×C149—21no—
76C22×C149—21no—
77C22×C149C2×C22⋊C411yescharacteristic
78C22×C149C4×Q812yes—
79C2×D149—21no—
80C2×D149—21no—
81C2×D149—21no—
82C2×D149—21no—
83C2×D149—42no—
84C2×D149—42no—
85C2×D149C22⋊Q812yes—
86C2×D149#12411yescharacteristic
87C2×D149C4⋊Q811yescharacteristic
88#10597010—44no—
89#10597010—82no—
90C4×C149—21no—
91C4×C149—42no—
92C4×C149#9912yes—
93Dic149—21no—
94Dic149—21no—
95Dic149—42no—
96C2×C149—22no—
97C2×C149#39111yescharacteristic
98C2×C149C2×#9911yescharacteristic
99C2×C149#41011yescharacteristic
100D149—22no—
101D149—21no—
102D149—21no—
103C149#199611yescharacteristic, complemented, Sylow
104#1996—1491nomaximal, Sylow
105C2×C22⋊Q8—1491no—
106#380—1491no—
107C4×C22⋊C4—1491no—
108#342—1494no—
109C22×Q8—1491no—
110C23×C4—1491no—
111C22⋊Q8—2981no—
112C22⋊Q8—2981no—
113C22⋊Q8—2981no—
114C22⋊Q8—2981no—
115C2×C4⋊C4—2981no—
116C2×C4⋊C4—1492no—
117C2×C4⋊C4#1059701011yescharacteristic, complemented
118C2×C22⋊C4—1492no—
119C2×C22⋊C4—1492no—
120C2×C22⋊C4—1492no—
121C2×C42—2981no—
122#95—2981no—
123#95—2981no—
124C24—1491no—
125C2×Q8—2981no—
126C2×Q8—2981no—
127C2×Q8—5962no—
128C22×C4—2982no—
129C22×C4—2982no—
130C22×C4—5962no—
131C22×C4—1491no—
132C22×C4—1491no—
133C22×C4—1492no—
134C22×C4—1491no—
135C22×C4—1491no—
136C22×C4—1491no—
137C22×C4C2×#1059701012yes—
138C22×C4C2×#1059701011yescharacteristic
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—2982no—
142C4⋊C4—2982no—
143C4⋊C4—5962no—
144C22⋊C4—2982no—
145C22⋊C4—2982no—
146C22⋊C4—2982no—
147C22⋊C4—2984no—
148C22⋊C4—1494no—
149C42—5962no—
150C23—5961no—
151C23—5961no—
152C23—1491no—
153C23—1491no—
154C23—1492no—
155C23—1492no—
156C23C22×#1059701011yescharacteristic
157Q8—5962no—
158Q8—5962no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—2982no—
163C2×C4—2982no—
164C2×C4—2984no—
165C2×C4—2982no—
166C2×C4—5961no—
167C2×C4—5961no—
168C2×C4—5961no—
169C2×C4—5962no—
170C2×C4—5962no—
171C2×C4—5962no—
172C2×C4—5962no—
173C2×C4—5962no—
174C2×C4—5962no—
175C2×C4—1491no—
176C2×C4—1491no—
177C2×C4C22⋊#1059701011yescharacteristic
178C2×C4C22⋊#1059701011yescharacteristic
179C22—21no—
180C22—21no—
181C22—2981no—
182C22—2981no—
183C22—2981no—
184C22—2981no—
185C22—5962no—
186C22—5962no—
187C22—1492no—
188C22—1491no—
189C22—1491no—
190C22C2×C22⋊#1059701011yescharacteristic
191C22Q8×#1059701012yes—
192C4—21no—
193C4—42no—
194C4—2981no—
195C4—2981no—
196C4—5964no—
197C4—5962no—
198C4—11922no—
199C4#1801197012yes—
200C2—22no—
201C2—2982no—
202C2—2981no—
203C2—2981no—
204C2(C2×#10597010)⋊Q811yescharacteristic
205C2C2×#1801197011yescharacteristic
206C2#2375060511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radical, cosocleC23×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1996
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
11. C22×Dic298C4semidirect
17. C2×C4⋊Dic149C4semidirect
19. C2×C4⋊C4×C149C4semidirect
25. C22⋊#10597010Q8semidirect
103. C149#1996semidirect
117. C2×C4⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505672
C4×C22⋊#105970102
#237505032
C2×#180118912
#1996149