Finite Group Databasebeta

← #34071054

Subgroups — #34071054

Order 19328.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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#23753009C211yesmaximal, characteristic, complemented
2#23752648C211yesmaximal, characteristic, complemented
3#23752462C211yesmaximal, characteristic, complemented
4#23752023C211yesmaximal, characteristic, complemented
5#23752022C211yesmaximal, characteristic, complemented
6#23751993C211yesmaximal, characteristic, complemented
7#509×C151C211yesmaximal, characteristic, complemented
8#41×D151—21no—
9#18012771—21no—
10#18012768—21no—
11#18012766—21no—
12#18012763—21no—
13#18012761C2211yescharacteristic
14#18012759—21no—
15C2×#14558987C2211yescharacteristic
16#18012710—21no—
17#18012683—21no—
18#18012680—21no—
19#18012679C2211yescharacteristic, complemented
20#18012671C2211yescharacteristic, complemented
21#18012660—21no—
22#135×C151C2211yescharacteristic
23C2×D8×C151C2211yescharacteristic, complemented
24SD32×C151—21no—
25D16×C151—21no—
26M32×C151C2211yescharacteristic, complemented
27#14559005—21no—
28#14559004—21no—
29#14559004—41no—
30#14559003—21no—
31#14559003—41no—
32Q8×D151—21no—
33C2×C22⋊D151—41no—
34D4×D151—21no—
35D4×D151—41no—
36C2×C4×D151—41no—
37C2×C4×D151D411yescharacteristic
38Dic604D411yescharacteristic, complemented
39#14558994—21no—
40#14558993—21no—
41#14558992—21no—
42#14558991—21no—
43D1208D411yescharacteristic, complemented
44#14558989—21no—
45#14558987—21no—
46#14558987—21no—
47C2×C151⋊C8D411yescharacteristic
48C4⋊Dic151—21no—
49C22⋊Dic151—41no—
50C151⋊C16—21no—
51#41×C151—21no—
52C2×D4×C151—21no—
53Q16×C151D411yescharacteristic, complemented
54SD16×C151—21no—
55D8×C151—21no—
56D8×C151—21no—
57D8×C151D411yescharacteristic, complemented
58C2×C8×C151C2311yescharacteristic
59C16×C151—21no—
60C22×D151—41no—
61C22×D151D811yescharacteristic
62Dic302—21no—
63Dic302—41no—
64D604—21no—
65D604—41no—
66C22⋊D151—41no—
67C22⋊D151—41no—
68C22⋊D151—41no—
69C22⋊D151—82no—
70C2×Dic151—41no—
71C2×Dic151—41no—
72C2×Dic151D811yescharacteristic
73C4×D151—21no—
74C4×D151—21no—
75C4×D151—41no—
76C4×D151—41no—
77C4×D151—41no—
78C151⋊C8—21no—
79C23×C151—41no—
80Q8×C151—21no—
81D4×C151—21no—
82D4×C151—41no—
83D4×C151—41no—
84D4×C151—41no—
85C2×C4×C151—41no—
86C2×C4×C151C2×D411yescharacteristic
87C8×C151C2×D411yescharacteristic
88C8×C151C2×D411yescharacteristic
89C22×C151—41no—
90C22×C151—81no—
91C22×C151—81no—
92C22×C151—81no—
93C22×C151C2×D811yescharacteristic
94C2×D151—21no—
95C2×D151—41no—
96C2×D151—41no—
97C2×D151—82no—
98C4×C151—41no—
99C4×C151#12011yescharacteristic
100C4×C151AGL(1,ℤ/8)11yescharacteristic
101Dic151—21no—
102Dic151—41no—
103Dic151—81no—
104C2×C151—21no—
105C2×C151—81no—
106C2×C151—161no—
107C2×C151#44711yescharacteristic
108D151—41no—
109D151—81no—
110C151#219011yescharacteristic, complemented, Sylow
111#2190—1511nomaximal, Sylow
112#575—1511no—
113#509—1511no—
114#509D15111yescharacteristic, complemented
115#469—1511no—
116#360—1511no—
117#360—1511no—
118#349—1511no—
119C2×#41—3021no—
120#137—3021no—
121#137—3021no—
122AGL(1,ℤ/8)—3021no—
123AGL(1,ℤ/8)—3021no—
124#135—3021no—
125#135—1511no—
126#135C2×D15111yescharacteristic
127C2×D8C2×D15111yescharacteristic, complemented
128C2×M16—1511no—
129#121—3021no—
130SD32—21no—
131SD32—3021no—
132D16—21no—
133D16—3021no—
134M32—1511no—
135M32C2×D15111yescharacteristic, complemented
136#106—1511no—
137#102—3021no—
138#41—21no—
139#41—3021no—
140#41—3021no—
141#41—3021no—
142#41—6041no—
143#41—6041no—
144C2×Q8—3021no—
145C2×D4—21no—
146C2×D4—3021no—
147C2×D4—6041no—
148C2×D4—6041no—
149C22×C4—6041no—
150C22×C4—1511no—
151Q16—3021no—
152Q16—1511no—
153Q16C22⋊D15111yescharacteristic, complemented
154SD16—21no—
155SD16—3021no—
156SD16—3021no—
157SD16—3021no—
158D8—21no—
159D8—21no—
160D8—3021no—
161D8—1511no—
162D8C22⋊D15111yescharacteristic, complemented
163M16—3021no—
164M16—3021no—
165C2×C8—1511no—
166C2×C8C22×D15111yescharacteristic
167C4⋊C4—3021no—
168C22⋊C4—6041no—
169C16—21no—
170C16—3021no—
171C23—41no—
172C23—6041no—
173C23—1511no—
174Q8—21no—
175Q8—3021no—
176Q8—6041no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—3021no—
182D4—6041no—
183D4—6041no—
184D4—6041no—
185D4—6041no—
186D4—12082no—
187C2×C4—41no—
188C2×C4—3021no—
189C2×C4—3021no—
190C2×C4—6041no—
191C2×C4—6041no—
192C2×C4—6041no—
193C2×C4—6041no—
194C2×C4—6041no—
195C2×C4—1511no—
196C2×C4D4×D15111yescharacteristic
197C8—3021no—
198C8D4×D15111yescharacteristic
199C8C2×C22⋊D15111yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—3021no—
205C22—6041no—
206C22—6041no—
207C22—12082no—
208C22D8×D15111yescharacteristic
209C4—41no—
210C4—3021no—
211C4—6041no—
212C4—12081no—
213C4#1801270711yescharacteristic
214C4#1801276311yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—6041no—
219C2—12081no—
220C2#2375234411yescharacteristic
subgroupG/H
centerC2#23752344
commutator, cosocleC2×C8×C151C23
FrattiniC2×C8C22×D151
Fitting#509×C151C2
socleC2×C151#447
hypercenter#509D151
hypocenterC151#2190
LCSG ▷ C2×C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #23753009C2semidirect
2. #23752648C2semidirect
3. #23752462C2semidirect
4. #23752023C2semidirect
5. #23752022C2semidirect
6. #23751993C2semidirect
7. #509×C151C2semidirect
19. #18012679C22semidirect
20. #18012671C22semidirect
23. C2×D8×C151C22semidirect
26. M32×C151C22semidirect
38. Dic604D4semidirect
43. D1208D4semidirect
53. Q16×C151D4semidirect
57. D8×C151D4semidirect
110. C151#2190semidirect
114. #509D151semidirect
127. C2×D8C2×D151semidirect
135. M32C2×D151semidirect
153. Q16C22⋊D151semidirect
162. D8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237530092
#237526482
#237524622
#237520232
#237520222
#237519932
#509×C1512
#2190151