Finite Group Databasebeta

← #34080165

Subgroups — #34080165

Order 19328.

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

normal subgroups only

This group has 388 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#23752788C211yesmaximal, characteristic, complemented
2#23752599C211yesmaximal, characteristic, complemented
3#23752584C211yesmaximal, characteristic, complemented
4#23752582C211yesmaximal, characteristic, complemented
5#23752569C211yesmaximal, characteristic, complemented
6#23752427C212yesmaximal, complemented
7#23752417C212yesmaximal, complemented
8#23752355C212yesmaximal, complemented
9#23752350C212yesmaximal, complemented
10#23752273C211yesmaximal, characteristic, complemented
11#540×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×Dic302C2211yescharacteristic
14C2×#14558992C2212yes—
15C2×#14558992C2212yes—
16C2×#14558992C2212yes—
17C2×#14558989C2212yes—
18#18012739C2211yescharacteristic
19#18012739C2211yescharacteristic
20#18012727C2211yescharacteristic
21#18012727C2211yescharacteristic
22#18012723—22no—
23#18012719—22no—
24C4⋊(C151⋊C8)C2212yes—
25#18012662C2212yes—
26#18012662C2212yes—
27#18012662C2212yes—
28#18012659C2212yes—
29C22⋊(C151⋊C8)C2212yes—
30#18012650C2211yescharacteristic
31C4×C151⋊C8C2211yescharacteristic
32#127×C151C2211yescharacteristic
33#125×C151C2211yescharacteristic
34#123×C151—22no—
35#121×C151—22no—
36#121×C151C2212yes—
37C4×D4×C151C2212yes—
38#117×C151C2211yescharacteristic
39#14559004—42no—
40C2×Dic302—21no—
41C2×Dic302—42no—
42C2×Dic302C2311yescharacteristic
43C2×Dic302C2311yescharacteristic
44C2×Dic302C2311yescharacteristic
45C2×D604C2311yescharacteristic
46C2×C22⋊D151—21no—
47C22×Dic151—21no—
48C2×C4×D151—21no—
49#14558992—42no—
50#14558992—42no—
51#14558992—42no—
52#14558989—42no—
53C2×C151⋊C8C2312yes—
54C2×C151⋊C8C2312yes—
55C4⋊Dic151—22no—
56C4⋊Dic151—22no—
57(C2×D151)⋊C4—22no—
58(C2×D151)⋊C4—22no—
59C2×D4×C151—22no—
60C2×D4×C151—22no—
61C2×D4×C151C2312yes—
62C22×C4×C151—22no—
63C22×C4×C151C2311yescharacteristic
64C4⋊C4×C151—22no—
65C4⋊C4×C151D412yes—
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C22⋊C4×C151—22no—
69C22⋊C4×C151D412yes—
70C42×C151C2311yescharacteristic
71C42×C151C2311yescharacteristic
72C22×D151—21no—
73Dic302—22no—
74Dic302—22no—
75Dic302—22no—
76Dic302—42no—
77D604—22no—
78C22⋊D151—42no—
79C2×Dic151—21no—
80C2×Dic151—21no—
81C2×Dic151—21no—
82C2×Dic151—42no—
83C4×D151—42no—
84C151⋊C8—22no—
85C151⋊C8—22no—
86C23×C151—22no—
87C23×C151C2×D411yescharacteristic
88D4×C151—22no—
89D4×C151—22no—
90D4×C151—82no—
91D4×C151—82no—
92C2×C4×C151—22no—
93C2×C4×C151—22no—
94C2×C4×C151—82no—
95C2×C4×C151C2×D412yes—
96C2×C4×C151C2×D412yes—
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2411yescharacteristic
99C22×C151—21no—
100C22×C151—22no—
101C22×C151—42no—
102C22×C151—42no—
103C22×C151—42no—
104C22×C151C22×D411yescharacteristic
105C2×D151—41no—
106C2×D151—42no—
107C4×C151—21no—
108C4×C151—22no—
109C4×C151—22no—
110C4×C151—42no—
111C4×C151H(5,𝔽2)12yes—
112Dic151—41no—
113Dic151—41no—
114Dic151—41no—
115C2×C151—41no—
116C2×C151—82no—
117C2×C151#53511yescharacteristic
118C2×C151#57712yes—
119D151—81no—
120C151#322111yescharacteristic, complemented, Sylow
121#3221—1511nomaximal, Sylow
122#540D15111yescharacteristic, complemented
123#536—1511no—
124#496—1511no—
125#492—1511no—
126#491—1511no—
127#488—1511no—
128#463—1512no—
129#461—1512no—
130#449—1512no—
131#448—1512no—
132#433—1511no—
133C2×#41—1511no—
134C22×Q8—1511no—
135C2×SD16—1512no—
136C2×SD16—1512no—
137C2×SD16—1512no—
138C2×D8—1512no—
139C4⋊Q8—1511no—
140C4⋊Q8—1511no—
141#127C2×D15111yescharacteristic
142#125C2×D15111yescharacteristic
143#124—1511no—
144#124—1511no—
145#123—22no—
146#123—3022no—
147C22⋊Q8—3022no—
148#121—22no—
149#121C2×D15112yes—
150C4×D4C2×D15112yes—
151#117C2×D15111yescharacteristic
152C4⋊C8—1512no—
153#103—1512no—
154#103—1512no—
155#103—1512no—
156#102—1512no—
157C22⋊C8—1512no—
158#97—1511no—
159C4×C8—1511no—
160#41—6042no—
161C2×Q8—3021no—
162C2×Q8—6042no—
163C2×Q8—1511no—
164C2×Q8—1511no—
165C2×Q8—1511no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—3021no—
169C2×D4—1511no—
170C2×D4C22×D15112yes—
171C22×C4—22no—
172C22×C4—3021no—
173C22×C4—3021no—
174C22×C4C22×D15111yescharacteristic
175SD16—6042no—
176SD16—6042no—
177SD16—6042no—
178D8—6042no—
179C2×C8—1512no—
180C2×C8—1512no—
181C4⋊C4—22no—
182C4⋊C4—3022no—
183C4⋊C4—3022no—
184C4⋊C4C22⋊D15112yes—
185C4⋊C4C22×D15112yes—
186C22⋊C4—22no—
187C22⋊C4—22no—
188C22⋊C4—3022no—
189C22⋊C4—3022no—
190C22⋊C4C22⋊D15112yes—
191C42C22×D15111yescharacteristic
192C42C22×D15111yescharacteristic
193C23—22no—
194C23—3021no—
195C23C2×C22⋊D15111yescharacteristic
196Q8—3022no—
197Q8—3022no—
198Q8—3022no—
199Q8—6042no—
200D4—22no—
201D4—22no—
202D4—82no—
203D4—82no—
204D4—3022no—
205D4—6042no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—82no—
209C2×C4—3021no—
210C2×C4—3021no—
211C2×C4—3021no—
212C2×C4—6042no—
213C2×C4—6042no—
214C2×C4C2×C22⋊D15112yes—
215C2×C4C2×C22⋊D15112yes—
216C2×C4C2×C22⋊D15111yescharacteristic
217C2×C4C23×D15111yescharacteristic
218C8—3022no—
219C8—3022no—
220C22—22no—
221C22—21no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—6042no—
226C22—6041no—
227C22C22×C22⋊D15111yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—42no—
232C4—6041no—
233C4—6041no—
234C4—6041no—
235C4#1801278512yes—
236C2—41no—
237C2—82no—
238C2—12081no—
239C2#2375277611yescharacteristic
240C2#2375302312yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#540×C151C2
socleC22×C151C22×D4
hypercenter#540D151
hypocenterC151#3221
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23752788C2semidirect
2. #23752599C2semidirect
3. #23752584C2semidirect
4. #23752582C2semidirect
5. #23752569C2semidirect
6. #23752427C2semidirect
7. #23752417C2semidirect
8. #23752355C2semidirect
9. #23752350C2semidirect
10. #23752273C2semidirect
11. #540×C151C2semidirect
120. C151#3221semidirect
122. #540D151semidirect

Maximal subgroups

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

subgroupindex
#237527882
#237525992
#237525842
#237525822
#237525692
#237524272
#237524172
#237523552
#237523502
#237522732
#540×C1512
#3221151