Finite Group Databasebeta

← C2×#23750478 #34060059

Subgroups — C2×#23750478 #34060059

Order 19072.

336 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 82 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×#18011968C211yesmaximal, characteristic
2C2×(C2×#10597010)⋊C4C211yesmaximal, characteristic
3#23750478C214yesmaximal, direct product factor
4C2×#18011891C211yesmaximal, characteristic
5C23×#10597010—21no—
6C22×#11924753—21no—
7#18011968—21no—
8#18011968C2212yes—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4C2212yes—
11C22×Dic298C411yescharacteristic, complemented
12C22×C4×D149C2211yescharacteristic
13#18011891—21no—
14#18011891—21no—
15#18011891C412yescomplemented
16#18011891C2212yes—
17C2×C4⋊Dic149—21no—
18C2×#14558713—21no—
19C2×C4⋊C4×C149C411yescharacteristic, complemented
20C22×#10597010—24no—
21C22×#10597010—22no—
22C22×#10597010—42no—
23C22×#10597010—42no—
24C2×#11924753—22no—
25C2×#11924753—42no—
26C23×D149D411yescharacteristic
27C2×Dic298—21no—
28C2×Dic298—42no—
29C2×Dic298C2×C412yescomplemented
30C22×Dic149—21no—
31C22×Dic149D411yescharacteristic
32C2×C4×D149—42no—
33C2×C4×D149C2×C411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149C2311yescharacteristic
37C4⋊Dic149—22no—
38C4⋊Dic149—22no—
39#14558713—22no—
40#14558713—22no—
41C22×C4×C149—21no—
42C22×C4×C149C2×C411yescharacteristic
43C4⋊C4×C149—21no—
44C4⋊C4×C149C2×C412yescomplemented
45C2×#10597010—24no—
46C2×#10597010—48no—
47C2×#10597010—42no—
48C2×#10597010—42no—
49#11924753—42no—
50C22×D149—22no—
51C22×D149—22no—
52C22×D149C22⋊C411yescharacteristic
53C22×D149SD1612yes—
54C22×D149Q1612yes—
55C22×D149C2×D411yescharacteristic
56Dic298—42no—
57Dic298—42no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—42no—
61C2×Dic149C22⋊C411yescharacteristic
62C2×Dic149C2×D411yescharacteristic
63C4×D149—41no—
64C4×D149—41no—
65C4×D149—41no—
66C4×D149—41no—
67C23×C149C22⋊C411yescharacteristic
68C2×C4×C149—22no—
69C2×C4×C149—22no—
70C2×C4×C149—42no—
71C2×C4×C149C22⋊C411yescharacteristic
72C2×C4×C149C22×C411yescharacteristic
73C22×C149#9912yes—
74C22×C149#10312yes—
75C22×C149#10412yes—
76C22×C149C2×C22⋊C411yescharacteristic
77C2×D149—24no—
78C2×D149—24no—
79C2×D149—21no—
80C2×D149—21no—
81C2×D149—21no—
82C2×D149—21no—
83C2×D149#10312yes—
84C2×D149C2×SD1611yescharacteristic
85C2×D149C2×Q1611yescharacteristic
86#10597010—44no—
87C4×C149—21no—
88C4×C149—21no—
89C4×C149—42no—
90Dic149—21no—
91Dic149—21no—
92Dic149—42no—
93C2×C149#32814yescomplemented
94C2×C149C2×#9911yescharacteristic
95C2×C149C2×#10311yescharacteristic
96C2×C149C2×#10411yescharacteristic
97D149—21no—
98D149—22no—
99D149—21no—
100C149C2×#32811yescharacteristic, complemented, Sylow
101C2×#328—1491nomaximal, Sylow
102C2×C22⋊Q8—1491no—
103C2×C22⋊C8—1491no—
104C2×#95—1491no—
105#328—1494no—
106C22×Q8—1491no—
107C23×C4—2981no—
108C23×C4—1491no—
109C22×C8—2981no—
110C22⋊Q8—2981no—
111C22⋊Q8—2981no—
112C22⋊Q8—1492no—
113C22⋊Q8—1492no—
114C2×C4⋊C4—2981no—
115C2×C4⋊C4#1059701011yescharacteristic, complemented
116C2×C22⋊C4—2981no—
117C22⋊C8—2981no—
118C22⋊C8—1492no—
119#95—2981no—
120#95—1492no—
121C24—1491no—
122C2×Q8—2981no—
123C2×Q8—5962no—
124C2×Q8—1492no—
125C22×C4—21no—
126C22×C4—2984no—
127C22×C4—2982no—
128C22×C4—2981no—
129C22×C4—5962no—
130C22×C4—5962no—
131C22×C4—5962no—
132C22×C4—1491no—
133C22×C4—1491no—
134C22×C4—1491no—
135C22×C4—1491no—
136C22×C4—1491no—
137C22×C4C2×#1059701011yescharacteristic
138C2×C8—2982no—
139C2×C8—5962no—
140C4⋊C4—21no—
141C4⋊C4—2982no—
142C4⋊C4—2982no—
143C4⋊C4C2×#1059701012yescomplemented
144C22⋊C4—2982no—
145C22⋊C4—2982no—
146C23—2982no—
147C23—2982no—
148C23—1492no—
149C23—1492no—
150C23—1491no—
151C23—1491no—
152C23C22⋊#1059701011yescharacteristic
153Q8—5962no—
154Q8—5962no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—42no—
158C2×C4—2982no—
159C2×C4—2984no—
160C2×C4—2982no—
161C2×C4—5961no—
162C2×C4—5961no—
163C2×C4—5961no—
164C2×C4—5961no—
165C2×C4—5968no—
166C2×C4—5962no—
167C2×C4—5962no—
168C2×C4—5962no—
169C2×C4—1491no—
170C2×C4—1491no—
171C2×C4C22⋊#1059701011yescharacteristic
172C2×C4C22×#1059701011yescharacteristic
173C8—5962no—
174C22—2984no—
175C22—2984no—
176C22—2981no—
177C22—2981no—
178C22—2981no—
179C22—2981no—
180C22—1491no—
181C22—1492no—
182C22—1491no—
183C22#1801197012yes—
184C22#1801197412yes—
185C22#1801197512yes—
186C22C2×C22⋊#1059701011yescharacteristic
187C4—21no—
188C4—21no—
189C4—42no—
190C4—2981no—
191C4—2981no—
192C4—5964no—
193C4—5962no—
194C2—2981no—
195C2—2982no—
196C2—2981no—
197C2#2375047814yesdirect product factor
198C2C2×#1801197011yescharacteristic
199C2C2×#1801197411yescharacteristic
200C2C2×#1801197511yescharacteristic
subgroupG/H
centerC23C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC23×C149C22⋊C4
prime radicalC23×D149D4
cosocleC2×C4×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149C2×#328
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #23750478C2direct (N × H)
11. C22×Dic298C4semidirect
15. #18011891C4semidirect
19. C2×C4⋊C4×C149C4semidirect
29. C2×Dic298C2×C4semidirect
44. C4⋊C4×C149C2×C4semidirect
93. C2×C149#328semidirect
100. C149C2×#328semidirect
115. C2×C4⋊C4#10597010semidirect
143. C4⋊C4C2×#10597010semidirect
197. C2#23750478direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180119682
C2×(C2×#10597010)⋊C42
#237504782
C2×#180118912
C2×#328149