Finite Group Databasebeta

← #34060031

Subgroups — #34060031

Order 19072.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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#23750647C211yesmaximal, characteristic, complemented
2C4×#14558746C211yesmaximal, characteristic, complemented
3#23750473C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5C4×D4×D149C211yesmaximal, characteristic
6C2×#14558746—21no—
7C4⋊#11924753C2212yescomplemented
8#18011968—21no—
9#18011966—21no—
10#18011966—21no—
11C4×#11924753C2212yescomplemented
12C2×D4×D149C411yescharacteristic
13C22×C4×D149—21no—
14C4×D596C411yescharacteristic
15D4×Dic149C2211yescharacteristic
16#18011873C2211yescharacteristic
17C4×C22⋊D149—21no—
18#18011871—21no—
19C4⋊C4×D149C411yescharacteristic
20C22⋊C4×D149—21no—
21C42×D149C2211yescharacteristic
22C4×D4×C149C411yescharacteristic
23#14558746—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C23×D149—21no—
27C2×D596C2×C411yescharacteristic
28C2×C22⋊D149—21no—
29D4×D149—22no—
30D4×D149—22no—
31C22×Dic149—21no—
32C2×C4×D149—21no—
33C2×C4×D149—21no—
34C2×C4×D149—21no—
35C2×C4×D149—44no—
36C2×C4×D149C2×C411yescharacteristic
37C2×C4×D149D411yescharacteristic
38C2×C4×D149D411yescharacteristic
39C4⋊Dic149C2×C411yescharacteristic
40#14558715—21no—
41C22⋊Dic149—21no—
42#14558713—21no—
43#14558713—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×D149—24no—
55C22×D149—21no—
56C22×D149—42no—
57C22×D149—42no—
58C22×D149C22⋊C411yescharacteristic
59D596—21no—
60D596M1612yescomplemented
61C22⋊D149—24no—
62C2×Dic149—21no—
63C2×Dic149—42no—
64C2×Dic149C22⋊C411yescharacteristic
65C2×Dic149C2×D411yescharacteristic
66C2×Dic149C2×D411yescharacteristic
67C4×D149—22no—
68C4×D149—21no—
69C4×D149—21no—
70C4×D149—22no—
71C4×D149—42no—
72C4×D149—42no—
73C4×D149—42no—
74C23×C149—21no—
75D4×C149—21no—
76D4×C149M1612yescomplemented
77C2×C4×C149—21no—
78C2×C4×C149—42no—
79C2×C4×C149C22⋊C411yescharacteristic
80C2×C4×C149C22⋊C411yescharacteristic
81C2×C4×C149C22×C411yescharacteristic
82C22×C149—22no—
83C22×C149—41no—
84C22×C149—41no—
85C22×C149C2×C22⋊C411yescharacteristic
86C2×D149—21no—
87C2×D149—21no—
88C2×D149—22no—
89C2×D149—48no—
90C2×D149—41no—
91C2×D149—41no—
92C2×D149#10412yes—
93C4×C149—21no—
94C4×C149—21no—
95C4×C149—41no—
96C4×C149C2×M1611yescharacteristic
97C4×C149C2×M1611yescharacteristic
98Dic149—21no—
99Dic149—21no—
100Dic149—41no—
101Dic149AGL(1,ℤ/8)12yes—
102C2×C149—42no—
103C2×C149#40711yescharacteristic
104C2×C149#41811yescharacteristic
105C2×C149C2×#10411yescharacteristic
106D149—22no—
107D149—42no—
108C149#149011yescharacteristic, complemented, Sylow
109#1490—1491nomaximal, Sylow
110C2×C4×D4—1491no—
111#432—1491no—
112C4×M16—1491no—
113D4⋊C8—1492no—
114D4⋊C8—1492no—
115C22×D4—1491no—
116C23×C4—2981no—
117C2×M16—2981no—
118C4×D4—2981no—
119C4×D4—2981no—
120C4×D4—1491no—
121C4×D4—1491no—
122C4×D4—1491no—
123C4×D4#1059701011yescharacteristic
124C2×C4⋊C4—1491no—
125C2×C22⋊C4—2981no—
126C2×C42—1491no—
127C4⋊C8—1492no—
128C22⋊C8—2981no—
129#97—2981no—
130#97—2981no—
131C4×C8—1492no—
132C24—2981no—
133C2×D4—2982no—
134C2×D4—2982no—
135C2×D4—2981no—
136C2×D4—1491no—
137C2×D4C2×#1059701011yescharacteristic
138C22×C4—21no—
139C22×C4—2981no—
140C22×C4—2981no—
141C22×C4—2981no—
142C22×C4—2981no—
143C22×C4—5964no—
144C22×C4—1491no—
145C22×C4—1491no—
146C22×C4—1491no—
147M16—2984no—
148C2×C8—2982no—
149C2×C8—2982no—
150C4⋊C4—2981no—
151C4⋊C4—1491no—
152C4⋊C4C2×#1059701011yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2981no—
155C22⋊C4—2981no—
156C22⋊C4—2981no—
157C42—1491no—
158C42—1491no—
159C42—1491no—
160C42C2×#1059701011yescharacteristic
161C23—21no—
162C23—2984no—
163C23—2981no—
164C23—5962no—
165C23—5962no—
166C23—1491no—
167D4—21no—
168D4—2984no—
169D4—2981no—
170D4—1492no—
171D4#1455874612yescomplemented
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—2981no—
177C2×C4—2981no—
178C2×C4—2981no—
179C2×C4—5962no—
180C2×C4—5962no—
181C2×C4—5962no—
182C2×C4—5962no—
183C2×C4—1491no—
184C2×C4—1491no—
185C2×C4—1491no—
186C2×C4C22⋊#1059701011yescharacteristic
187C2×C4C22⋊#1059701011yescharacteristic
188C2×C4C22×#1059701011yescharacteristic
189C8—2984no—
190C8—5962no—
191C22—22no—
192C22—41no—
193C22—41no—
194C22—2981no—
195C22—2981no—
196C22—2982no—
197C22—5968no—
198C22—5961no—
199C22—5961no—
200C22—1492no—
201C22C2×C22⋊#1059701011yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—2981no—
206C4—2981no—
207C4—5961no—
208C4—1492no—
209C4D149⋊M1611yescharacteristic
210C4C2×#1455874611yescharacteristic
211C2—42no—
212C2—2982no—
213C2—5962no—
214C2#2375059611yescharacteristic
215C2#2375061711yescharacteristic
216C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×D4×D149C4
cosocleC4×Dic149C23
hypercenterC4×D4#10597010
hypocenterC149#1490
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. #23750647C2semidirect
2. C4×#14558746C2semidirect
3. #23750473C2semidirect
4. D4⋊#11924753C2semidirect
7. C4⋊#11924753C22semidirect
11. C4×#11924753C22semidirect
60. D596M16semidirect
76. D4×C149M16semidirect
108. C149#1490semidirect
171. D4#14558746semidirect

Maximal subgroups

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

subgroupindex
#237506472
C4×#145587462
#237504732
D4⋊#119247532
C4×D4×D1492
#1490149