Finite Group Databasebeta

← #34102080

Subgroups — #34102080

Order 20096.

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#23758070C211yesmaximal, characteristic, complemented
2#23757709C211yesmaximal, characteristic, complemented
3#23757523C211yesmaximal, characteristic, complemented
4#23757084C211yesmaximal, characteristic, complemented
5#23757083C211yesmaximal, characteristic, complemented
6#23757054C211yesmaximal, characteristic, complemented
7#509×C157C211yesmaximal, characteristic, complemented
8#41×D157—21no—
9#19097803—21no—
10#19097800—21no—
11#19097798—21no—
12#19097795—21no—
13#19097793C2211yescharacteristic
14#19097791—21no—
15C2×#14578937C2211yescharacteristic
16#19097742—21no—
17#19097715—21no—
18#19097712—21no—
19#19097711C2211yescharacteristic, complemented
20#19097703C2211yescharacteristic, complemented
21#19097692—21no—
22#135×C157C2211yescharacteristic
23C2×D8×C157C2211yescharacteristic, complemented
24SD32×C157—21no—
25D16×C157—21no—
26M32×C157C2211yescharacteristic, complemented
27#14578955—21no—
28#14578954—21no—
29#14578954—41no—
30#14578953—21no—
31#14578953—41no—
32Q8×D157—21no—
33C2×C22⋊D157—41no—
34D4×D157—21no—
35D4×D157—41no—
36C2×C4×D157—41no—
37C2×C4×D157D411yescharacteristic
38Dic628D411yescharacteristic, complemented
39#14578944—21no—
40#14578943—21no—
41#14578942—21no—
42#14578941—21no—
43D1256D411yescharacteristic, complemented
44#14578939—21no—
45#14578937—21no—
46#14578937—21no—
47C2×#11929434D411yescharacteristic
48C4⋊Dic157—21no—
49C22⋊Dic157—41no—
50#14578929—21no—
51#41×C157—21no—
52C2×D4×C157—21no—
53Q16×C157D411yescharacteristic, complemented
54SD16×C157—21no—
55D8×C157—21no—
56D8×C157—21no—
57D8×C157D411yescharacteristic, complemented
58C2×C8×C157C2311yescharacteristic
59C16×C157—21no—
60C22×D157—41no—
61C22×D157D811yescharacteristic
62Dic314—21no—
63Dic314—41no—
64D628—21no—
65D628—41no—
66C22⋊D157—41no—
67C22⋊D157—41no—
68C22⋊D157—41no—
69C22⋊D157—82no—
70C2×Dic157—41no—
71C2×Dic157—41no—
72C2×Dic157D811yescharacteristic
73C4×D157—21no—
74C4×D157—21no—
75C4×D157—41no—
76C4×D157—41no—
77C4×D157—41no—
78#11929434—21no—
79C23×C157—41no—
80Q8×C157—21no—
81D4×C157—21no—
82D4×C157—41no—
83D4×C157—41no—
84D4×C157—41no—
85C2×C4×C157—41no—
86C2×C4×C157C2×D411yescharacteristic
87C8×C157C2×D411yescharacteristic
88C8×C157C2×D411yescharacteristic
89C22×C157—41no—
90C22×C157—81no—
91C22×C157—81no—
92C22×C157—81no—
93C22×C157C2×D811yescharacteristic
94C2×D157—21no—
95C2×D157—41no—
96C2×D157—41no—
97C2×D157—82no—
98C4×C157—41no—
99C4×C157#12011yescharacteristic
100C4×C157AGL(1,ℤ/8)11yescharacteristic
101Dic157—21no—
102Dic157—41no—
103Dic157—81no—
104C2×C157—21no—
105C2×C157—81no—
106C2×C157—161no—
107C2×C157#44711yescharacteristic
108D157—41no—
109D157—81no—
110C157#219011yescharacteristic, complemented, Sylow
111#2190—1571nomaximal, Sylow
112#575—1571no—
113#509—1571no—
114#509D15711yescharacteristic, complemented
115#469—1571no—
116#360—1571no—
117#360—1571no—
118#349—1571no—
119C2×#41—3141no—
120#137—3141no—
121#137—3141no—
122AGL(1,ℤ/8)—3141no—
123AGL(1,ℤ/8)—3141no—
124#135—3141no—
125#135—1571no—
126#135C2×D15711yescharacteristic
127C2×D8C2×D15711yescharacteristic, complemented
128C2×M16—1571no—
129#121—3141no—
130SD32—21no—
131SD32—3141no—
132D16—21no—
133D16—3141no—
134M32—1571no—
135M32C2×D15711yescharacteristic, complemented
136#106—1571no—
137#102—3141no—
138#41—21no—
139#41—3141no—
140#41—3141no—
141#41—3141no—
142#41—6281no—
143#41—6281no—
144C2×Q8—3141no—
145C2×D4—21no—
146C2×D4—3141no—
147C2×D4—6281no—
148C2×D4—6281no—
149C22×C4—6281no—
150C22×C4—1571no—
151Q16—3141no—
152Q16—1571no—
153Q16C22⋊D15711yescharacteristic, complemented
154SD16—21no—
155SD16—3141no—
156SD16—3141no—
157SD16—3141no—
158D8—21no—
159D8—21no—
160D8—3141no—
161D8—1571no—
162D8C22⋊D15711yescharacteristic, complemented
163M16—3141no—
164M16—3141no—
165C2×C8—1571no—
166C2×C8C22×D15711yescharacteristic
167C4⋊C4—3141no—
168C22⋊C4—6281no—
169C16—21no—
170C16—3141no—
171C23—41no—
172C23—6281no—
173C23—1571no—
174Q8—21no—
175Q8—3141no—
176Q8—6281no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—3141no—
182D4—6281no—
183D4—6281no—
184D4—6281no—
185D4—6281no—
186D4—12562no—
187C2×C4—41no—
188C2×C4—3141no—
189C2×C4—3141no—
190C2×C4—6281no—
191C2×C4—6281no—
192C2×C4—6281no—
193C2×C4—6281no—
194C2×C4—6281no—
195C2×C4—1571no—
196C2×C4D4×D15711yescharacteristic
197C8—3141no—
198C8D4×D15711yescharacteristic
199C8C2×C22⋊D15711yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—3141no—
205C22—6281no—
206C22—6281no—
207C22—12562no—
208C22D8×D15711yescharacteristic
209C4—41no—
210C4—3141no—
211C4—6281no—
212C4—12561no—
213C4#1909773911yescharacteristic
214C4#1909779511yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—6281no—
219C2—12561no—
220C2#2375740511yescharacteristic
subgroupG/H
centerC2#23757405
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#509×C157C2
socleC2×C157#447
hypercenter#509D157
hypocenterC157#2190
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #23758070C2semidirect
2. #23757709C2semidirect
3. #23757523C2semidirect
4. #23757084C2semidirect
5. #23757083C2semidirect
6. #23757054C2semidirect
7. #509×C157C2semidirect
19. #19097711C22semidirect
20. #19097703C22semidirect
23. C2×D8×C157C22semidirect
26. M32×C157C22semidirect
38. Dic628D4semidirect
43. D1256D4semidirect
53. Q16×C157D4semidirect
57. D8×C157D4semidirect
110. C157#2190semidirect
114. #509D157semidirect
127. C2×D8C2×D157semidirect
135. M32C2×D157semidirect
153. Q16C22⋊D157semidirect
162. D8C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
#237580702
#237577092
#237575232
#237570842
#237570832
#237570542
#509×C1572
#2190157