Finite Group Databasebeta

← #34060027

Subgroups — #34060027

Order 19072.

266 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 70 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#23750629C211yesmaximal, characteristic, complemented
2C4×#14558746C211yesmaximal, characteristic, complemented
3#23750475C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5C4×#14558735C211yesmaximal, characteristic
6C2×#14558746—21no—
7C2×#14558746—21no—
8C4⋊#11924753—21no—
9C4⋊#11924753C2212yes—
10#18011966—21no—
11C4×#11924753C2212yes—
12C2×#14558735C411yescharacteristic
13C4×Dic298C411yescharacteristic
14#18011876C2211yescharacteristic
15D4×Dic149C2211yescharacteristic
16C4×C22⋊D149—21no—
17#18011871—21no—
18#18011869C411yescharacteristic
19#18011867—21no—
20C2×C4×Dic149—21no—
21C42×D149C2211yescharacteristic
22C4×D4×C149C411yescharacteristic
23#14558746—24no—
24#14558746—42no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27#14558735—22no—
28#14558735—22no—
29C2×Dic298C2×C411yescharacteristic
30C2×C22⋊D149—21no—
31C22×Dic149—21no—
32C22×Dic149—21no—
33C2×C4×D149C2×C411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C4⋊Dic149C2×C411yescharacteristic
37#14558715—21no—
38#14558715—21no—
39C22⋊Dic149—21no—
40#14558713—21no—
41C4×Dic149—21no—
42C4×Dic149—21no—
43C4×Dic149—21no—
44C4×Dic149D411yescharacteristic
45C4×Dic149D411yescharacteristic
46C4×Dic149C2311yescharacteristic
47C2×D4×C149C2×C411yescharacteristic
48C22×C4×C149—21no—
49C4⋊C4×C149C2×C411yescharacteristic
50C22⋊C4×C149—21no—
51C42×C149C2×C411yescharacteristic
52#11924753—24no—
53#11924753—42no—
54C22×D149C22⋊C411yescharacteristic
55Dic298—21no—
56Dic298M1612yescomplemented
57C22⋊D149—24no—
58C2×Dic149—24no—
59C2×Dic149—21no—
60C2×Dic149—21no—
61C2×Dic149—41no—
62C2×Dic149—41no—
63C2×Dic149C22⋊C411yescharacteristic
64C2×Dic149C2×D411yescharacteristic
65C2×Dic149C2×D411yescharacteristic
66C4×D149—22no—
67C4×D149—21no—
68C4×D149—21no—
69C4×D149—21no—
70C4×D149—21no—
71C23×C149—21no—
72D4×C149—21no—
73D4×C149M1612yescomplemented
74C2×C4×C149—21no—
75C2×C4×C149—42no—
76C2×C4×C149C22⋊C411yescharacteristic
77C2×C4×C149C22⋊C411yescharacteristic
78C2×C4×C149C22×C411yescharacteristic
79C22×C149—22no—
80C22×C149—41no—
81C22×C149—41no—
82C22×C149C2×C22⋊C411yescharacteristic
83C2×D149—21no—
84C2×D149—21no—
85C2×D149—21no—
86C4×C149—21no—
87C4×C149—41no—
88C4×C149#10412yes—
89C4×C149C2×M1611yescharacteristic
90C4×C149C2×M1611yescharacteristic
91Dic149—21no—
92Dic149—22no—
93Dic149—21no—
94Dic149—41no—
95Dic149AGL(1,ℤ/8)11yescharacteristic
96Dic149#13711yescharacteristic
97C2×C149—42no—
98C2×C149#40711yescharacteristic
99C2×C149#41711yescharacteristic
100C2×C149C2×#10411yescharacteristic
101D149—41no—
102C149#148911yescharacteristic, complemented, Sylow
103#1489—1491nomaximal, Sylow
104C4×#41—1491no—
105#423—1491no—
106C4×M16—1491no—
107Q8⋊C8—1492no—
108D4⋊C8—1492no—
109C2×#41—1491no—
110C2×M16—2981no—
111C2×M16—2981no—
112C4×Q8—1491no—
113C4×Q8—1491no—
114C4×D4—2981no—
115C4×D4—2981no—
116C4×D4—1491no—
117C4×D4#1059701011yescharacteristic
118#117—2981no—
119#117—1491no—
120C2×C42—2981no—
121C2×C42—1491no—
122C4⋊C8—2981no—
123C4⋊C8—1492no—
124#97—2981no—
125C4×C8—1492no—
126#41—2982no—
127#41—2982no—
128C2×Q8—1491no—
129C2×D4—2981no—
130C2×D4C2×#1059701011yescharacteristic
131C22×C4—21no—
132C22×C4—2981no—
133C22×C4—2981no—
134C22×C4—1491no—
135C22×C4—1491no—
136C22×C4—1491no—
137M16—2984no—
138M16—5962no—
139C2×C8—2982no—
140C2×C8—2982no—
141C4⋊C4—2981no—
142C4⋊C4—2981no—
143C4⋊C4—1491no—
144C4⋊C4C2×#1059701011yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—2981no—
147C22⋊C4—2981no—
148C42—2981no—
149C42—2981no—
150C42—2981no—
151C42—1491no—
152C42—1491no—
153C42—1491no—
154C42C2×#1059701011yescharacteristic
155C23—21no—
156C23—1491no—
157Q8—2981no—
158Q8—1492no—
159D4—21no—
160D4—2984no—
161D4#1455874612yescomplemented
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—2981no—
165C2×C4—2981no—
166C2×C4—2984no—
167C2×C4—2981no—
168C2×C4—2982no—
169C2×C4—2981no—
170C2×C4—2981no—
171C2×C4—2981no—
172C2×C4—5961no—
173C2×C4—5961no—
174C2×C4—1491no—
175C2×C4—1491no—
176C2×C4—1491no—
177C2×C4C22⋊#1059701011yescharacteristic
178C2×C4C22⋊#1059701011yescharacteristic
179C2×C4C22×#1059701011yescharacteristic
180C8—2984no—
181C8—5962no—
182C22—22no—
183C22—41no—
184C22—41no—
185C22—2981no—
186C22—2981no—
187C22—2981no—
188C22C2×C22⋊#1059701011yescharacteristic
189C4—21no—
190C4—41no—
191C4—2981no—
192C4—2982no—
193C4—2981no—
194C4—5961no—
195C4—1491no—
196C4—1491no—
197C4#1801197512yes—
198C4D149⋊M1611yescharacteristic
199C4C2×#1455874611yescharacteristic
200C2—42no—
201C2—5961no—
202C2#2375059611yescharacteristic
203C2#2375061611yescharacteristic
204C2C2×#1801197511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#14558735C4
cosocleC4×Dic149C23
hypercenterC4×D4#10597010
hypocenterC149#1489
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #23750629C2semidirect
2. C4×#14558746C2semidirect
3. #23750475C2semidirect
4. D4⋊#11924753C2semidirect
56. Dic298M16semidirect
73. D4×C149M16semidirect
102. C149#1489semidirect
161. D4#14558746semidirect

Maximal subgroups

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

subgroupindex
#237506292
C4×#145587462
#237504752
D4⋊#119247532
C4×#145587352
#1489149