Finite Group Databasebeta

← #34060088

Subgroups — #34060088

Order 19072.

346 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 64 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#23750596C211yesmaximal, characteristic, complemented
2C4×C22⋊#10597010C211yesmaximal, characteristic, complemented
3#23750477C214yesmaximal, complemented
4C2×#18011886C211yesmaximal, characteristic
5C2×#14558746—21no—
6C2×C22⋊#10597010—21no—
7C2×C4×#10597010—21no—
8#18011968C2212yescomplemented
9C22⋊#11924753—21no—
10(C2×#10597010)⋊C4C2212yescomplemented
11C22×D596—21no—
12C22×D596C411yescharacteristic, complemented
13C22×C4×D149C2211yescharacteristic
14#18011886—21no—
15#18011886—21no—
16#18011886C412yescomplemented
17#18011886C2212yes—
18C2×#14558713—21no—
19C2×C4⋊C4×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21#14558746—42no—
22C2×#11924753—22no—
23C22⋊#10597010—24no—
24C4×#10597010—42no—
25C23×D149—21no—
26C23×D149D411yescharacteristic
27C2×D596—22no—
28C2×D596—22no—
29C2×D596—21no—
30C2×D596—42no—
31C2×D596—44no—
32C2×D596C2×C412yes—
33C22×Dic149D411yescharacteristic
34C2×C4×D149—42no—
35C2×C4×D149C2×C411yescharacteristic
36C2×C4×D149D411yescharacteristic
37C2×C4×D149D411yescharacteristic
38C2×C4×D149C2311yescharacteristic
39#14558713—22no—
40#14558713—22no—
41C22×C4×C149—21no—
42C22×C4×C149C2×C411yescharacteristic
43C4⋊C4×C149—21no—
44C4⋊C4×C149C2×C412yes—
45C2×#10597010—24no—
46C2×#10597010—42no—
47C2×#10597010—42no—
48#11924753—42no—
49C22×D149—22no—
50C22×D149—22no—
51C22×D149—22no—
52C22×D149—41no—
53C22×D149—42no—
54C22×D149—42no—
55C22×D149—42no—
56C22×D149C22⋊C411yescharacteristic
57C22×D149C2×D411yescharacteristic
58D596—42no—
59D596—44no—
60D596—44no—
61D596—42no—
62C2×Dic149—41no—
63C2×Dic149C22⋊C411yescharacteristic
64C2×Dic149C2×D411yescharacteristic
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×C149#10412yes—
78C22×C149C2×C22⋊C411yescharacteristic
79C2×D149—21no—
80C2×D149—21no—
81C2×D149—21no—
82C2×D149—21no—
83C2×D149—21no—
84C2×D149—44no—
85C2×D149—42no—
86C2×D149—42no—
87C2×D149—42no—
88C2×D149—84no—
89C2×D149AGL(1,ℤ/8)12yes—
90#10597010—44no—
91C4×C149—21no—
92C4×C149—42no—
93C4×C149#9912yes—
94Dic149—21no—
95Dic149—21no—
96C2×C149—22no—
97C2×C149C2×#9911yescharacteristic
98C2×C149#41811yescharacteristic
99C2×C149C2×#10411yescharacteristic
100D149—22no—
101D149—41no—
102D149—82no—
103C149#150711yescharacteristic, complemented, Sylow
104#1507—1491nomaximal, Sylow
105C2×#121—1491no—
106#407—1491no—
107C4×C22⋊C4—1491no—
108#327—1494no—
109C22×D4—2981no—
110C22×D4—1491no—
111C23×C4—1491no—
112C2×M16—2981no—
113#121—2981no—
114#121—2981no—
115#121—1492no—
116#121—1492no—
117C2×C4⋊C4#1059701011yescharacteristic, complemented
118C2×C22⋊C4—2981no—
119C2×C22⋊C4—2981no—
120C2×C42—2981no—
121C22⋊C8—2981no—
122C22⋊C8—1492no—
123#95—1492no—
124C24—2981no—
125C24—1491no—
126C2×D4—2982no—
127C2×D4—2982no—
128C2×D4—2981no—
129C2×D4—5962no—
130C2×D4—5964no—
131C2×D4—1492no—
132C22×C4—21no—
133C22×C4—2982no—
134C22×C4—5962no—
135C22×C4—1491no—
136C22×C4—1491no—
137C22×C4—1491no—
138C22×C4—1491no—
139C22×C4—1491no—
140C22×C4C2×#1059701011yescharacteristic
141M16—5962no—
142C2×C8—2982no—
143C4⋊C4—21no—
144C4⋊C4C2×#1059701012yes—
145C22⋊C4—2982no—
146C22⋊C4—2982no—
147C22⋊C4—2984no—
148C42—5962no—
149C23—2982no—
150C23—2982no—
151C23—2982no—
152C23—5961no—
153C23—5962no—
154C23—5962no—
155C23—5962no—
156C23—1491no—
157C23—1491no—
158C23C22⋊#1059701011yescharacteristic
159D4—5962no—
160D4—5964no—
161D4—5964no—
162D4—5962no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—42no—
166C2×C4—2982no—
167C2×C4—2982no—
168C2×C4—2984no—
169C2×C4—5961no—
170C2×C4—5961no—
171C2×C4—5961no—
172C2×C4—5962no—
173C2×C4—5962no—
174C2×C4—1491no—
175C2×C4—1491no—
176C2×C4C22⋊#1059701011yescharacteristic
177C2×C4C22×#1059701011yescharacteristic
178C8—5962no—
179C22—21no—
180C22—21no—
181C22—2981no—
182C22—2981no—
183C22—2981no—
184C22—2981no—
185C22—2981no—
186C22—5964no—
187C22—5962no—
188C22—5962no—
189C22—5962no—
190C22—1492no—
191C22—11924no—
192C22#1801197612yes—
193C22C2×C22⋊#1059701011yescharacteristic
194C4—21no—
195C4—42no—
196C4—2981no—
197C4—2981no—
198C4—5964no—
199C4#1801197012yes—
200C2—22no—
201C2—2982no—
202C2—5961no—
203C2—11922no—
204C2C2×#1801197011yescharacteristic
205C2#2375061711yescharacteristic
206C2C2×#1801197611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#18011886C2
cosocleC2×C4×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1507
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #23750596C2semidirect
2. C4×C22⋊#10597010C2semidirect
3. #23750477C2semidirect
8. #18011968C22semidirect
10. (C2×#10597010)⋊C4C22semidirect
12. C22×D596C4semidirect
16. #18011886C4semidirect
19. C2×C4⋊C4×C149C4semidirect
103. C149#1507semidirect
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
#237505962
C4×C22⋊#105970102
#237504772
C2×#180118862
#1507149