Finite Group Databasebeta

← #34082196

Subgroups — #34082196

Order 19328.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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#23752945C212yesmaximal, complemented
2#23752600C212yesmaximal, complemented
3#23752596C211yesmaximal, characteristic, complemented
4#23752433C212yesmaximal, complemented
5#23752427C212yesmaximal, complemented
6#23752406C212yesmaximal, complemented
7#23752342C211yesmaximal, characteristic, complemented
8#23752311C212yesmaximal, complemented
9C4×D8×C151C211yesmaximal, characteristic, complemented
10C2×Dic604C2211yescharacteristic
11C2×#14558993C2212yes—
12C2×#14558992C2212yes—
13C2×D1208C2211yescharacteristic
14C2×#14558989C2212yes—
15#18012735C2212yes—
16#18012727C2212yes—
17#18012726C2212yes—
18#18012725—22no—
19#18012722—22no—
20#18012721—22no—
21C4×Dic302C2211yescharacteristic
22#18012704C2212yes—
23#18012701C2212yes—
24C4×C22⋊D151—22no—
25C4⋊(C151⋊C8)C2211yescharacteristic
26Dic151⋊C8C2212yes—
27#18012662C2212yes—
28#18012659C2212yes—
29#18012649C2212yes—
30C2×D8×C151C2211yescharacteristic
31C4×D4×C151C2212yes—
32#107×C151C2211yescharacteristic
33#102×C151C2212yes—
34C4×C8×C151C2211yescharacteristic
35C2×Dic302D411yescharacteristic
36C2×Dic302C2312yes—
37C2×D604C2312yes—
38C2×C22⋊D151—22no—
39C2×C22⋊D151—22no—
40C2×C4×D151—22no—
41Dic604—41no—
42#14558993—24no—
43#14558992—42no—
44D1208—41no—
45#14558989—42no—
46C2×C151⋊C8C2312yes—
47C4⋊Dic151D411yescharacteristic
48Dic151⋊C4—22no—
49Dic151⋊C4D412yes—
50C22⋊Dic151—22no—
51C22⋊Dic151—22no—
52(C2×D151)⋊C4—22no—
53(C2×D151)⋊C4—22no—
54(C2×D151)⋊C4—22no—
55C4×Dic151—22no—
56C4×Dic151C2312yes—
57C2×D4×C151C2312yes—
58C22×C4×C151—22no—
59D8×C151—22no—
60C2×C8×C151C2311yescharacteristic
61C2×C8×C151C2311yescharacteristic
62C4⋊C4×C151C2312yes—
63C22⋊C4×C151—22no—
64C42×C151C2311yescharacteristic
65C22×D151—22no—
66Dic302—22no—
67Dic302—22no—
68Dic302—41no—
69D604—22no—
70D604—22no—
71C22⋊D151—44no—
72C22⋊D151—82no—
73C2×Dic151—22no—
74C2×Dic151C2×D412yes—
75C2×Dic151C2×D412yes—
76C4×D151—82no—
77C151⋊C8—22no—
78C23×C151—22no—
79D4×C151—22no—
80D4×C151—22no—
81C2×C4×C151—22no—
82C2×C4×C151—82no—
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2411yescharacteristic
86C8×C151—21no—
87C8×C151#4112yes—
88C22×C151—42no—
89C22×C151—42no—
90C22×C151—42no—
91C22×C151C22×D411yescharacteristic
92C2×D151—42no—
93C2×D151—42no—
94C2×D151—42no—
95C4×C151—21no—
96C4×C151—21no—
97C4×C151—42no—
98C4×C151C2×#4111yescharacteristic
99C4×C151H(5,𝔽2)11yescharacteristic
100Dic151—22no—
101Dic151—22no—
102Dic151—42no—
103C2×C151—82no—
104C2×C151#55011yescharacteristic
105C2×C151#57511yescharacteristic
106C2×C151#57611yescharacteristic
107D151—82no—
108C151#340311yescharacteristic, complemented, Sylow
109#3403—1511nomaximal, Sylow
110#559—1512no—
111#496—1512no—
112#495—1511no—
113#464—1512no—
114#463—1512no—
115#459—1512no—
116#446—1511no—
117#440—1512no—
118C4×D8D15111yescharacteristic, complemented
119C2×Q16—1511no—
120C2×SD16—1512no—
121C2×SD16—1512no—
122C2×D8—1512no—
123C2×D8—1511no—
124C2×D8C2×D15111yescharacteristic
125#127—1512no—
126#124—3022no—
127#124—1512no—
128#124—1512no—
129#123—3022no—
130#123—3022no—
131C4×Q8—1512no—
132C4×Q8—1511no—
133C4×D4—3022no—
134C4×D4—1512no—
135C4×D4C2×D15112yes—
136#107C2×D15111yescharacteristic
137C4⋊C8—1512no—
138C4⋊C8—1511no—
139#103—1512no—
140#102—1512no—
141#102C2×D15112yes—
142#97—1512no—
143C4×C8C2×D15111yescharacteristic
144C2×Q8—1512no—
145C2×Q8—1511no—
146C2×D4—3022no—
147C2×D4—3022no—
148C2×D4—1512no—
149C2×D4C22×D15112yes—
150C22×C4—22no—
151C22×C4—3022no—
152Q16—6041no—
153SD16—3024no—
154SD16—6042no—
155D8—22no—
156D8—6041no—
157D8—6042no—
158C2×C8—1512no—
159C2×C8C22×D15111yescharacteristic
160C2×C8C22×D15111yescharacteristic
161C4⋊C4—3022no—
162C4⋊C4—1512no—
163C4⋊C4—1511no—
164C4⋊C4C22×D15112yes—
165C22⋊C4—22no—
166C22⋊C4—3022no—
167C22⋊C4—3022no—
168C22⋊C4—3022no—
169C22⋊C4—3022no—
170C22⋊C4—3022no—
171C42—3022no—
172C42—1512no—
173C42C22×D15111yescharacteristic
174C23—22no—
175C23—3022no—
176Q8—3022no—
177Q8—3022no—
178Q8—6041no—
179D4—22no—
180D4—22no—
181D4—3022no—
182D4—3022no—
183D4—6044no—
184D4—12082no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—3022no—
188C2×C4—1512no—
189C2×C4—1512no—
190C2×C4—12082no—
191C2×C4D4×D15111yescharacteristic
192C2×C4D4×D15111yescharacteristic
193C2×C4C23×D15111yescharacteristic
194C8—21no—
195C8—3022no—
196C8#1455900412yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—6042no—
201C22—6042no—
202C22—6042no—
203C22C2×D4×D15111yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—3022no—
208C4—3022no—
209C4—6042no—
210C4C2×#1455900411yescharacteristic
211C4#1801278511yescharacteristic
212C2—82no—
213C2—12082no—
214C2#2375288311yescharacteristic
215C2#2375300911yescharacteristic
216C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC4×D8×C151C2
socleC22×C151C22×D4
hypercenterC4×D8D151
hypocenterC151#3403
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23752945C2semidirect
2. #23752600C2semidirect
3. #23752596C2semidirect
4. #23752433C2semidirect
5. #23752427C2semidirect
6. #23752406C2semidirect
7. #23752342C2semidirect
8. #23752311C2semidirect
9. C4×D8×C151C2semidirect
108. C151#3403semidirect
118. C4×D8D151semidirect

Maximal subgroups

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

subgroupindex
#237529452
#237526002
#237525962
#237524332
#237524272
#237524062
#237523422
#237523112
C4×D8×C1512
#3403151