Finite Group Databasebeta

← #34059960

Subgroups — #34059960

Order 19072.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750645C211yesmaximal, characteristic, complemented
2#23750641C211yesmaximal, characteristic, complemented
3#23750469C212yesmaximal, complemented
4#23750468C212yesmaximal, complemented
5C2×#18011897C211yesmaximal, characteristic
6#18011978—21no—
7C4⋊#11924753—21no—
8C22⋊#11924753C2212yes—
9C22⋊#11924753C2212yes—
10#18011966—21no—
11C4×#11924753—21no—
12C22×Dic298C411yescharacteristic
13C22×C22⋊D149C411yescharacteristic
14#18011897—21no—
15#18011897—21no—
16#18011897—21no—
17#18011897—21no—
18C2×C22⋊Dic149C2211yescharacteristic
19C2×#14558713C411yescharacteristic
20C2×#14558713C2211yescharacteristic
21C2×C4×Dic149C2211yescharacteristic
22C2×C22⋊C4×C149C411yescharacteristic
23C2×#11924753—22no—
24C2×#11924753—22no—
25C23×D149C2×C411yescharacteristic
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×Dic298—42no—
29C2×C22⋊D149—21no—
30C2×C22⋊D149—21no—
31C2×C22⋊D149—42no—
32C22×Dic149C2×C411yescharacteristic
33C22×Dic149C2×C411yescharacteristic
34C22×Dic149C2311yescharacteristic
35C22⋊Dic149—21no—
36C22⋊Dic149—21no—
37#14558713—21no—
38#14558713—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C24×C149C2×C411yescharacteristic
46C22×C4×C149C2×C411yescharacteristic
47C22×C4×C149C2×C411yescharacteristic
48C22⋊C4×C149—21no—
49C22⋊C4×C149—21no—
50#11924753—42no—
51#11924753—42no—
52C22×D149—21no—
53C22×D149—22no—
54C22×D149—41no—
55C22×D149—41no—
56Dic298—42no—
57Dic298—42no—
58C22⋊D149—42no—
59C22⋊D149—42no—
60C2×Dic149—22no—
61C2×Dic149—21no—
62C2×Dic149—41no—
63C2×Dic149—41no—
64C2×Dic149C22⋊C411yescharacteristic
65C2×Dic149C22⋊C411yescharacteristic
66C2×Dic149C2×D411yescharacteristic
67C2×Dic149C2×D411yescharacteristic
68C23×C149—21no—
69C23×C149—22no—
70C23×C149—41no—
71C23×C149—41no—
72C23×C149C22×C411yescharacteristic
73C2×C4×C149—22no—
74C2×C4×C149—21no—
75C2×C4×C149—41no—
76C2×C4×C149C22⋊C411yescharacteristic
77C2×C4×C149C22⋊C411yescharacteristic
78C22×C149—21no—
79C22×C149—21no—
80C22×C149—41no—
81C22×C149—41no—
82C22×C149—41no—
83C22×C149—82no—
84C22×C149C2×C22⋊C411yescharacteristic
85C22×C149#13112yes—
86C2×D149—41no—
87C2×D149—41no—
88C2×D149—41no—
89C2×D149—82no—
90C4×C149—21no—
91C4×C149—21no—
92C4×C149—41no—
93Dic149—21no—
94Dic149—21no—
95Dic149—21no—
96Dic149—41no—
97Dic149#10012yes—
98C2×C149—22no—
99C2×C149—81no—
100C2×C149#40811yescharacteristic
101C2×C149#41011yescharacteristic
102C2×C149C2×#10011yescharacteristic
103D149—81no—
104C149#146911yescharacteristic, complemented, Sylow
105#1469—1491nomaximal, Sylow
106C2×#124—1491no—
107#432—1491no—
108#431—1491no—
109#323—1492no—
110#323—1492no—
111C22×Q8—1491no—
112C22×D4—1491no—
113#124—2981no—
114#124—2981no—
115#124—2981no—
116#124—2981no—
117C2×C22⋊C4—1491no—
118C2×C22⋊C4—1491no—
119C2×C22⋊C4—1491no—
120C2×C22⋊C4#1059701011yescharacteristic
121C2×C42—1491no—
122C4⋊C8—2981no—
123C4⋊C8—2981no—
124C22⋊C8—1492no—
125C22⋊C8—1492no—
126#97—2981no—
127C4×C8—2981no—
128C24—1491no—
129C24C2×#1059701011yescharacteristic
130C2×Q8—2981no—
131C2×Q8—2981no—
132C2×Q8—5962no—
133C2×D4—2981no—
134C2×D4—2981no—
135C2×D4—5962no—
136C22×C4—1491no—
137C22×C4—1491no—
138C22×C4—1491no—
139C22×C4C2×#1059701011yescharacteristic
140C22×C4C2×#1059701011yescharacteristic
141C2×C8—2982no—
142C2×C8—2982no—
143C22⋊C4—21no—
144C22⋊C4—21no—
145C22⋊C4—2981no—
146C22⋊C4—2981no—
147C22⋊C4—2981no—
148C22⋊C4—2981no—
149C22⋊C4—2981no—
150C22⋊C4—2981no—
151C42—1491no—
152C42—1491no—
153C42—1491no—
154C42—1491no—
155C23—21no—
156C23—22no—
157C23—41no—
158C23—41no—
159C23—2981no—
160C23—2982no—
161C23—5961no—
162C23—5961no—
163C23C22×#1059701011yescharacteristic
164Q8—5962no—
165Q8—5962no—
166D4—5962no—
167D4—5962no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—2982no—
172C2×C4—2981no—
173C2×C4—5961no—
174C2×C4—5961no—
175C2×C4—1491no—
176C2×C4—1491no—
177C2×C4—1491no—
178C2×C4—1491no—
179C2×C4C22⋊#1059701011yescharacteristic
180C2×C4C22⋊#1059701011yescharacteristic
181C8—5962no—
182C8—5962no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—82no—
189C22—5961no—
190C22—5961no—
191C22—5961no—
192C22—11922no—
193C22C2×C22⋊#1059701011yescharacteristic
194C22#1801199812yes—
195C4—21no—
196C4—21no—
197C4—41no—
198C4—2981no—
199C4—2981no—
200C4—2981no—
201C4—5961no—
202C4—1492no—
203C2—22no—
204C2—81no—
205C2—11921no—
206C2#2375059811yescharacteristic
207C2#2375060411yescharacteristic
208C2D149⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×C22⋊D149C4
cosocleC22×Dic149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1469
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #23750645C2semidirect
2. #23750641C2semidirect
3. #23750469C2semidirect
4. #23750468C2semidirect
104. C149#1469semidirect

Maximal subgroups

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

subgroupindex
#237506452
#237506412
#237504692
#237504682
C2×#180118972
#1469149