Finite Group Databasebeta

← #34059959

Subgroups — #34059959

Order 19072.

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

normal subgroups only

This group has 280 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#23750596C211yesmaximal, characteristic, complemented
2D149⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#23750471C212yesmaximal, complemented
4#23750469C212yesmaximal, complemented
5C2×#18011896C211yesmaximal, characteristic
6C2×#14558746—21no—
7C2×D149⋊C8—21no—
8#18011968—21no—
9#18011968—21no—
10C22⋊#11924753C2212yes—
11C22⋊#11924753C2212yes—
12C22×D596C411yescharacteristic
13C22×C4×D149C2211yescharacteristic
14#18011896—21no—
15#18011896—21no—
16#18011896—21no—
17#18011896—21no—
18C2×#14558715C2211yescharacteristic
19C2×#14558713C411yescharacteristic
20C2×#14558713C411yescharacteristic
21C2×#14558713C2211yescharacteristic
22C2×C4⋊C4×C149C411yescharacteristic
23#14558746—42no—
24D149⋊C8—42no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27C23×D149C2×C411yescharacteristic
28C23×D149C2×C411yescharacteristic
29C2×D596—21no—
30C2×D596—21no—
31C2×D596—42no—
32C22×Dic149C2×C411yescharacteristic
33C22×Dic149C2311yescharacteristic
34C2×C4×D149—42no—
35C2×C4×D149D411yescharacteristic
36C2×C4×D149D411yescharacteristic
37C2×C4×D149D411yescharacteristic
38C2×C4×D149D411yescharacteristic
39#14558715—21no—
40#14558715—21no—
41#14558713—21no—
42#14558713—21no—
43#14558713—21no—
44#14558713—21no—
45#14558713—21no—
46#14558713—21no—
47C22×C4×C149C2×C411yescharacteristic
48C22×C4×C149C2×C411yescharacteristic
49C22×C4×C149C2×C411yescharacteristic
50C4⋊C4×C149—21no—
51C4⋊C4×C149—21no—
52#11924753—42no—
53#11924753—42no—
54C22×D149—22no—
55C22×D149—22no—
56C22×D149—21no—
57C22×D149—22no—
58C22×D149—41no—
59C22×D149—41no—
60C22×D149—41no—
61C22×D149C22⋊C411yescharacteristic
62C22×D149C22⋊C411yescharacteristic
63D596—42no—
64D596—42no—
65C2×Dic149—21no—
66C2×Dic149—22no—
67C2×Dic149—41no—
68C2×Dic149C2×D411yescharacteristic
69C2×Dic149C2×D411yescharacteristic
70C4×D149—22no—
71C4×D149—22no—
72C4×D149—41no—
73C4×D149—41no—
74C23×C149C22×C411yescharacteristic
75C2×C4×C149—21no—
76C2×C4×C149—21no—
77C2×C4×C149—41no—
78C2×C4×C149—41no—
79C2×C4×C149—41no—
80C2×C4×C149C22⋊C411yescharacteristic
81C2×C4×C149C22⋊C411yescharacteristic
82C22×C149—21no—
83C22×C149—21no—
84C22×C149C2×C22⋊C411yescharacteristic
85C22×C149#13112yes—
86C2×D149—21no—
87C2×D149—21no—
88C2×D149—21no—
89C2×D149—21no—
90C2×D149—21no—
91C2×D149—44no—
92C2×D149—41no—
93C2×D149—41no—
94C2×D149—41no—
95C2×D149—82no—
96C2×D149#9912yes—
97C4×C149—21no—
98C4×C149—21no—
99C4×C149—41no—
100C4×C149—41no—
101Dic149—21no—
102Dic149—21no—
103Dic149—41no—
104C2×C149—22no—
105C2×C149#40811yescharacteristic
106C2×C149C2×#9911yescharacteristic
107C2×C149#41311yescharacteristic
108D149—22no—
109D149—41no—
110D149—81no—
111C149#146811yescharacteristic, complemented, Sylow
112#1468—1491nomaximal, Sylow
113C2×#123—1491no—
114#407—1491no—
115C2×C22⋊C8—1491no—
116#324—1492no—
117#323—1492no—
118C22×D4—1491no—
119C23×C4—1491no—
120C2×M16—2981no—
121C22×C8—2981no—
122#123—2981no—
123#123—2981no—
124#123—2981no—
125#123—2981no—
126C2×C4⋊C4—1491no—
127C2×C4⋊C4#1059701011yescharacteristic
128C2×C22⋊C4—1491no—
129C2×C22⋊C4—1491no—
130C2×C22⋊C4—1491no—
131C22⋊C8—2981no—
132C22⋊C8—2981no—
133C22⋊C8—1492no—
134C22⋊C8—1492no—
135C24—1491no—
136C24—1491no—
137C2×D4—2981no—
138C2×D4—2981no—
139C2×D4—5962no—
140C22×C4—5962no—
141C22×C4—1491no—
142C22×C4—1491no—
143C22×C4—1491no—
144C22×C4—1491no—
145C22×C4—1491no—
146C22×C4—1491no—
147C22×C4C2×#1059701011yescharacteristic
148C22×C4C2×#1059701011yescharacteristic
149C22×C4C2×#1059701011yescharacteristic
150M16—5962no—
151C2×C8—2982no—
152C2×C8—2982no—
153C2×C8—5962no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C22⋊C4—2981no—
159C22⋊C4—2981no—
160C22⋊C4—2981no—
161C22⋊C4—2981no—
162C22⋊C4—2981no—
163C22⋊C4—2981no—
164C23—2982no—
165C23—2982no—
166C23—2981no—
167C23—2982no—
168C23—5961no—
169C23—5961no—
170C23—5961no—
171C23—1491no—
172C23—1491no—
173C23C22×#1059701011yescharacteristic
174D4—5962no—
175D4—5962no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4—2981no—
184C2×C4—2982no—
185C2×C4—5961no—
186C2×C4—5961no—
187C2×C4—5961no—
188C2×C4—1491no—
189C2×C4—1491no—
190C2×C4C22⋊#1059701011yescharacteristic
191C2×C4C22⋊#1059701011yescharacteristic
192C8—5962no—
193C8—5962no—
194C22—21no—
195C22—21no—
196C22—2981no—
197C22—2981no—
198C22—2981no—
199C22—2981no—
200C22—2981no—
201C22—5964no—
202C22—5961no—
203C22—5961no—
204C22—5961no—
205C22—1492no—
206C22—11922no—
207C22C2×C22⋊#1059701011yescharacteristic
208C22#1801199912yes—
209C4—21no—
210C4—21no—
211C4—41no—
212C4—41no—
213C4—2981no—
214C4—2981no—
215C4—5961no—
216C2—22no—
217C2—2982no—
218C2—5961no—
219C2—11921no—
220C2#2375060011yescharacteristic
221C2D149⋊#9911yescharacteristic
222C2#2375061111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D596C4
cosocleC22×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1468
LCSG ▷ C23×C149 ▷ C2×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. D149⋊(C22⋊C8)C2semidirect
3. #23750471C2semidirect
4. #23750469C2semidirect
111. C149#1468semidirect

Maximal subgroups

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

subgroupindex
#237505962
D149⋊(C22⋊C8)2
#237504712
#237504692
C2×#180118962
#1468149