Finite Group Databasebeta

← #34080123

Subgroups — #34080123

Order 19328.

390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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#23752769C211yesmaximal, characteristic, complemented
2#23752762C211yesmaximal, characteristic
3#23752606C212yesmaximal, complemented
4#23752572C212yesmaximal, complemented
5#23752423C212yesmaximal, complemented
6#23752413C212yesmaximal, complemented
7#23752376C214yesmaximal, complemented
8#432×C151C211yesmaximal, characteristic, complemented
9C2×#14559004C2212yes—
10C2×Dic604C2214yes—
11C2×#14558993C2214yes—
12#18012739C2211yescharacteristic
13#18012739C2211yescharacteristic
14#18012739C2211yescharacteristic
15#18012736C2211yescharacteristic
16#18012731—21no—
17#18012727C2212yes—
18#18012718—21no—
19#18012718C2212yes—
20#18012713—21no—
21#18012713—21no—
22C4×Dic302—21no—
23C4×Dic302C2212yes—
24C4×D604—21no—
25C4×D604—21no—
26#18012698—21no—
27#18012664C2214yes—
28#18012661C2214yes—
29C2×C42×C151C2211yescharacteristic
30C4⋊C8×C151C2212yes—
31C22⋊C8×C151C2212yes—
32#97×C151C2212yes—
33#14559004—44no—
34C2×Dic302—21no—
35C2×Dic302C2312yes—
36C2×Dic302C2312yes—
37C2×D604—21no—
38C2×D604—21no—
39C2×D604C2312yes—
40C2×C22⋊D151—22no—
41C2×C4×D151—22no—
42Dic604—44no—
43#14558993—44no—
44C4⋊Dic151—21no—
45C4⋊Dic151—21no—
46C4⋊Dic151—21no—
47C4⋊Dic151—21no—
48C4⋊Dic151—21no—
49C4⋊Dic151C2312yes—
50Dic151⋊C4—22no—
51Dic151⋊C4—22no—
52C22⋊Dic151—22no—
53(C2×D151)⋊C4—22no—
54(C2×D151)⋊C4—22no—
55C4×Dic151—22no—
56C22×C4×C151D411yescharacteristic
57C22×C4×C151D411yescharacteristic
58C22×C4×C151C2311yescharacteristic
59C2×C8×C151C2314yes—
60C42×C151D411yescharacteristic
61C42×C151D411yescharacteristic
62C42×C151C2311yescharacteristic
63C42×C151C2311yescharacteristic
64C22×D151—22no—
65Dic302—22no—
66Dic302—22no—
67Dic302—24no—
68Dic302—42no—
69D604—24no—
70D604—42no—
71D604—42no—
72C22⋊D151—44no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C4×D151—44no—
77C23×C151C2×D411yescharacteristic
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151—41no—
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D411yescharacteristic
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2×D411yescharacteristic
86C2×C4×C151C2411yescharacteristic
87C8×C151—24no—
88C22×C151—21no—
89C22×C151—21no—
90C22×C151—21no—
91C22×C151C22×D411yescharacteristic
92C2×D151—42no—
93C2×D151—42no—
94C2×D151—42no—
95C4×C151—21no—
96C4×C151—21no—
97C4×C151—21no—
98C4×C151—21no—
99C4×C151#13712yes—
100C4×C151H(5,𝔽2)12yes—
101Dic151—42no—
102Dic151—42no—
103Dic151—42no—
104C2×C151—41no—
105C2×C151#53511yescharacteristic
106C2×C151C2×#13711yescharacteristic
107C2×C151#57511yescharacteristic
108D151—82no—
109C151#321611yescharacteristic, complemented, Sylow
110#3216—1511nomaximal, Sylow
111#533—1511no—
112#532—1511no—
113#497—1512no—
114#489—1512no—
115#462—1512no—
116#460—1512no—
117#452—1514no—
118#432D15111yescharacteristic, complemented
119C2×#41—1512no—
120C2×Q16—1514no—
121C2×SD16—1514no—
122C4⋊Q8—1511no—
123C4⋊Q8—1511no—
124C4⋊Q8—1511no—
125#127—1511no—
126#125—3021no—
127#124—1512no—
128C22⋊Q8—3021no—
129C22⋊Q8—1512no—
130#121—3021no—
131#121—3021no—
132C4×Q8—3021no—
133C4×Q8—1512no—
134C4×D4—3021no—
135C4×D4—3021no—
136#117—3021no—
137C2×C42C2×D15111yescharacteristic
138C4⋊C8C2×D15112yes—
139#103—1514no—
140#102—1514no—
141C22⋊C8C2×D15112yes—
142#97C2×D15112yes—
143#41—6044no—
144C2×Q8—3021no—
145C2×Q8—1512no—
146C2×Q8—1512no—
147C2×D4—3022no—
148C2×D4—3021no—
149C2×D4—3021no—
150C2×D4—1512no—
151C22×C4—3022no—
152C22×C4D60411yescharacteristic
153C22×C4D60411yescharacteristic
154C22×C4C22×D15111yescharacteristic
155Q16—6044no—
156SD16—6044no—
157C2×C8C22×D15114yes—
158C4⋊C4—3022no—
159C4⋊C4—3022no—
160C4⋊C4—3021no—
161C4⋊C4—3021no—
162C4⋊C4—3021no—
163C4⋊C4—3021no—
164C4⋊C4—3021no—
165C4⋊C4—1512no—
166C22⋊C4—3022no—
167C22⋊C4—3022no—
168C22⋊C4—3022no—
169C42—3022no—
170C42D60411yescharacteristic
171C42D60411yescharacteristic
172C42C22×D15111yescharacteristic
173C42C22×D15111yescharacteristic
174C23—3022no—
175C23C2×D60411yescharacteristic
176Q8—3022no—
177Q8—3022no—
178Q8—3024no—
179Q8—6042no—
180D4—3024no—
181D4—6042no—
182D4—6044no—
183D4—6042no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—3022no—
188C2×C4—3022no—
189C2×C4—3022no—
190C2×C4—6044no—
191C2×C4C2×D60411yescharacteristic
192C2×C4C2×D60411yescharacteristic
193C2×C4C2×D60411yescharacteristic
194C2×C4C2×D60411yescharacteristic
195C2×C4C2×D60411yescharacteristic
196C2×C4C23×D15111yescharacteristic
197C8—24no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—6042no—
202C22—6042no—
203C22—6042no—
204C22C22×D60411yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—6042no—
210C4—6042no—
211C4—6042no—
212C4#1801277212yes—
213C4#1801278512yes—
214C2—41no—
215C2—12082no—
216C2#2375278111yescharacteristic
217C2C2×#1801277211yescharacteristic
218C2#2375301211yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#432×C151C2
socleC22×C151C22×D4
prime radical#23752762C2
hypercenter#432D151
hypocenterC151#3216
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #23752769C2semidirect
3. #23752606C2semidirect
4. #23752572C2semidirect
5. #23752423C2semidirect
6. #23752413C2semidirect
7. #23752376C2semidirect
8. #432×C151C2semidirect
109. C151#3216semidirect
118. #432D151semidirect

Maximal subgroups

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

subgroupindex
#237527692
#237527622
#237526062
#237525722
#237524232
#237524132
#237523762
#432×C1512
#3216151