Finite Group Databasebeta

← #34080061

Subgroups — #34080061

Order 19328.

394 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752767C211yesmaximal, characteristic, complemented
2#23752760C211yesmaximal, characteristic
3#23752591C211yesmaximal, characteristic, complemented
4#23752563C211yesmaximal, characteristic, complemented
5#23752558C211yesmaximal, characteristic, complemented
6#23752432C214yesmaximal, complemented
7#23752371C214yesmaximal, complemented
8#23752263C211yesmaximal, characteristic, complemented
9#492×C151C211yesmaximal, characteristic, complemented
10C2×#14559003C2212yes—
11C2×#14558994C2214yes—
12#18012739C2211yescharacteristic
13#18012739C2211yescharacteristic
14#18012730—21no—
15#18012726C2212yes—
16#18012719—21no—
17#18012715C2212yes—
18#18012710—21no—
19#18012710—21no—
20Q8×Dic151C2212yes—
21#18012704—21no—
22D4×Dic151—21no—
23D4×Dic151—21no—
24#18012697—21no—
25C42×D151C2211yescharacteristic
26Dic151⋊C8C2212yes—
27#18012664C2214yes—
28#18012660C2214yes—
29(C2×D151)⋊C8C2212yes—
30C4×C151⋊C8C2211yescharacteristic
31C2×SD16×C151C2214yes—
32C4⋊Q8×C151C2211yescharacteristic
33#127×C151C2211yescharacteristic
34C4×C8×C151C2211yescharacteristic
35#14559003—44no—
36C2×Dic302—21no—
37C2×Dic302C2312yes—
38C2×C22⋊D151—22no—
39C22×Dic151—22no—
40C2×C4×D151D411yescharacteristic
41C2×C4×D151D411yescharacteristic
42C2×C4×D151C2311yescharacteristic
43#14558994—44no—
44C2×C151⋊C8C2312yes—
45C4⋊Dic151—22no—
46C4⋊Dic151—21no—
47C4⋊Dic151—21no—
48C4⋊Dic151—21no—
49C4⋊Dic151C2312yes—
50Dic151⋊C4—22no—
51C22⋊Dic151—22no—
52C22⋊Dic151—22no—
53(C2×D151)⋊C4—22no—
54C4×Dic151—22no—
55C4×Dic151D411yescharacteristic
56C4×Dic151D411yescharacteristic
57C4×Dic151C2311yescharacteristic
58C2×Q8×C151C2312yes—
59C2×D4×C151—21no—
60C2×D4×C151—21no—
61C2×D4×C151C2312yes—
62SD16×C151—44no—
63C2×C8×C151C2312yes—
64C4⋊C4×C151—21no—
65C4⋊C4×C151—21no—
66C42×C151C2311yescharacteristic
67C22×D151C2×D411yescharacteristic
68Dic302—24no—
69Dic302—42no—
70C22⋊D151—44no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—44no—
74C2×Dic151C2×D411yescharacteristic
75C2×Dic151C2×D411yescharacteristic
76C2×Dic151C2×D411yescharacteristic
77C4×D151—22no—
78C4×D151—22no—
79C4×D151—22no—
80C151⋊C8—22no—
81C23×C151—22no—
82Q8×C151—24no—
83D4×C151—24no—
84D4×C151—42no—
85D4×C151—42no—
86C2×C4×C151—22no—
87C2×C4×C151C2×D411yescharacteristic
88C2×C4×C151C2×D411yescharacteristic
89C2×C4×C151C2411yescharacteristic
90C8×C151—22no—
91C22×C151—42no—
92C22×C151—42no—
93C22×C151—42no—
94C22×C151C22×D411yescharacteristic
95C2×D151—21no—
96C2×D151—21no—
97C2×D151—21no—
98C4×C151—42no—
99C4×C151#13512yes—
100C4×C151#13712yes—
101C4×C151H(5,𝔽2)12yes—
102Dic151—21no—
103Dic151—21no—
104Dic151—21no—
105Dic151—42no—
106Dic151—42no—
107C2×C151—82no—
108C2×C151#53511yescharacteristic
109C2×C151C2×#13511yescharacteristic
110C2×C151C2×#13711yescharacteristic
111D151—41no—
112C151#321011yescharacteristic, complemented, Sylow
113#3210—1511nomaximal, Sylow
114#533—1511no—
115#532—1511no—
116#494—1511no—
117#492D15111yescharacteristic, complemented
118#487—1511no—
119#486—1511no—
120#464—1514no—
121#452—1514no—
122#431—1511no—
123C2×#41—1512no—
124C2×Q16—1514no—
125C2×SD16C2×D15114yes—
126C4⋊Q8—1511no—
127C4⋊Q8—1511no—
128C4⋊Q8C2×D15111yescharacteristic
129#127C2×D15111yescharacteristic
130#125—3021no—
131#124—1512no—
132C22⋊Q8—3021no—
133C22⋊Q8—1512no—
134#121—3021no—
135#121—3021no—
136C4×Q8—3021no—
137C4×Q8—1512no—
138C4×D4—3021no—
139C4×D4—3021no—
140#117—3021no—
141C2×C42—1511no—
142C4⋊C8—1512no—
143#103—1514no—
144#102—1514no—
145C22⋊C8—1512no—
146C4×C8—1511no—
147C4×C8C2×D15111yescharacteristic
148#41—6044no—
149C2×Q8—3021no—
150C2×Q8—1512no—
151C2×Q8C22×D15112yes—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—3022no—
155C2×D4C22×D15112yes—
156C22×C4—3022no—
157C22×C4—1511no—
158C22×C4—1511no—
159C22×C4—1511no—
160Q16—6044no—
161SD16—44no—
162C2×C8—1512no—
163C2×C8C22×D15112yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—3022no—
167C4⋊C4—3022no—
168C4⋊C4—3021no—
169C4⋊C4—3021no—
170C4⋊C4—3021no—
171C4⋊C4—1512no—
172C22⋊C4—3022no—
173C22⋊C4—3022no—
174C22⋊C4—3022no—
175C42—3022no—
176C42—1511no—
177C42—1511no—
178C42—1511no—
179C42C22×D15111yescharacteristic
180C23—22no—
181C23—1511no—
182Q8—24no—
183Q8—3024no—
184Q8—6042no—
185D4—24no—
186D4—42no—
187D4—42no—
188D4—6044no—
189C2×C4—22no—
190C2×C4—3022no—
191C2×C4—3022no—
192C2×C4—3022no—
193C2×C4—3022no—
194C2×C4—3022no—
195C2×C4—6044no—
196C2×C4—1511no—
197C2×C4—1511no—
198C2×C4—1511no—
199C2×C4D4×D15111yescharacteristic
200C2×C4D4×D15111yescharacteristic
201C2×C4C23×D15111yescharacteristic
202C8—22no—
203C8—3022no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—3021no—
208C22—3021no—
209C22—3021no—
210C22C2×D4×D15111yescharacteristic
211C4—42no—
212C4—3021no—
213C4—3021no—
214C4—3021no—
215C4—6042no—
216C4—6042no—
217C4#1801276012yes—
218C4#1801276812yes—
219C4#1801278412yes—
220C2—82no—
221C2—6041no—
222C2#2375277511yescharacteristic
223C2C2×#1801276011yescharacteristic
224C2C2×#1801276811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#492×C151C2
socleC22×C151C22×D4
prime radical#23752760C2
hypercenter#492D151
hypocenterC151#3210
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #23752767C2semidirect
3. #23752591C2semidirect
4. #23752563C2semidirect
5. #23752558C2semidirect
6. #23752432C2semidirect
7. #23752371C2semidirect
8. #23752263C2semidirect
9. #492×C151C2semidirect
112. C151#3210semidirect
117. #492D151semidirect

Maximal subgroups

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

subgroupindex
#237527672
#237527602
#237525912
#237525632
#237525582
#237524322
#237523712
#237522632
#492×C1512
#3210151