Finite Group Databasebeta

← #34102088

Subgroups — #34102088

Order 20096.

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

normal subgroups only

This group has 216 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
2#23757716C211yesmaximal, characteristic, complemented
3#23757713C211yesmaximal, characteristic, complemented
4#23757532C211yesmaximal, characteristic, complemented
5#23757082C211yesmaximal, characteristic, complemented
6#23757054C211yesmaximal, characteristic, complemented
7#360×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×Dic628C2211yescharacteristic, complemented
16C2×#14578937C2211yescharacteristic
17#19097751—21no—
18Dic1256—21no—
19#19097717—21no—
20#19097716—21no—
21#19097715—21no—
22#19097711C2211yescharacteristic, complemented
23#19097694—21no—
24#135×C157C2211yescharacteristic
25M32×C157C2211yescharacteristic, complemented
26#106×C157C2211yescharacteristic, complemented
27#14578955—21no—
28#14578954—21no—
29#14578954—41no—
30#14578953—21no—
31#14578953—41no—
32C2×Dic314—21no—
33Q8×D157—21no—
34D4×D157—21no—
35D4×D157—41no—
36C2×C4×D157—41no—
37C2×C4×D157D411yescharacteristic
38Dic628—21no—
39Dic628—21no—
40Dic628D411yescharacteristic
41#14578944—21no—
42#14578943—21no—
43#14578942—21no—
44#14578941—21no—
45D1256D411yescharacteristic
46#14578939—21no—
47#14578937—21no—
48#14578937—21no—
49C2×#11929434D411yescharacteristic
50C4⋊Dic157—41no—
51#14578931—41no—
52#14578929—21no—
53#41×C157—21no—
54Q16×C157D411yescharacteristic
55SD16×C157—21no—
56D8×C157D411yescharacteristic
57C2×C8×C157C2311yescharacteristic
58C4⋊C4×C157—21no—
59C16×C157—21no—
60C22×D157—41no—
61C22×D157D811yescharacteristic
62Dic314—21no—
63Dic314—41no—
64Dic314—41no—
65Dic314—41no—
66D628—21no—
67D628—41no—
68C22⋊D157—41no—
69C22⋊D157—41no—
70C22⋊D157—41no—
71C2×Dic157—41no—
72C2×Dic157—41no—
73C2×Dic157D811yescharacteristic
74C4×D157—21no—
75C4×D157—21no—
76C4×D157—41no—
77C4×D157—41no—
78C4×D157—41no—
79#11929434—21no—
80Q8×C157—21no—
81D4×C157—21no—
82D4×C157—41no—
83C2×C4×C157—41no—
84C2×C4×C157—41no—
85C2×C4×C157C2×D411yescharacteristic
86C8×C157C2×D411yescharacteristic
87C8×C157C2×D411yescharacteristic
88C22×C157—41no—
89C22×C157C2×D811yescharacteristic
90C2×D157—21no—
91C2×D157—41no—
92C2×D157—41no—
93C2×D157—82no—
94C4×C157—41no—
95C4×C157—81no—
96C4×C157#12011yescharacteristic
97C4×C157AGL(1,ℤ/8)11yescharacteristic
98Dic157—21no—
99Dic157—41no—
100Dic157—81no—
101C2×C157—21no—
102C2×C157—81no—
103C2×C157#44711yescharacteristic
104D157—41no—
105D157—81no—
106C157#219111yescharacteristic, complemented, Sylow
107#2191—1571nomaximal, Sylow
108#575—1571no—
109#510—1571no—
110#510—1571no—
111#470—1571no—
112#360—1571no—
113#360D15711yescharacteristic, complemented
114#349—1571no—
115C2×#41—3141no—
116#137—3141no—
117#137—3141no—
118AGL(1,ℤ/8)—3141no—
119AGL(1,ℤ/8)—3141no—
120#135—3141no—
121#135—1571no—
122#135C2×D15711yescharacteristic
123C2×Q16—1571no—
124C2×M16—1571no—
125C22⋊Q8—3141no—
126Q32—3141no—
127Q32—3141no—
128SD32—3141no—
129SD32—3141no—
130M32—1571no—
131M32C2×D15711yescharacteristic, complemented
132#106C2×D15711yescharacteristic, complemented
133#103—3141no—
134#41—21no—
135#41—3141no—
136#41—3141no—
137#41—3141no—
138#41—6281no—
139#41—6281no—
140C2×Q8—3141no—
141C2×Q8—3141no—
142C2×D4—3141no—
143C2×D4—6281no—
144C22×C4—6281no—
145C22×C4—1571no—
146Q16—3141no—
147Q16—3141no—
148Q16—3141no—
149Q16—1571no—
150Q16D62811yescharacteristic
151SD16—21no—
152SD16—3141no—
153SD16—3141no—
154SD16—3141no—
155D8—3141no—
156D8—1571no—
157D8D62811yescharacteristic
158M16—3141no—
159M16—3141no—
160C2×C8—1571no—
161C2×C8C22×D15711yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—6281no—
164C22⋊C4—6281no—
165C16—21no—
166C16—3141no—
167C23—6281no—
168C23—1571no—
169Q8—21no—
170Q8—3141no—
171Q8—6281no—
172Q8—6281no—
173Q8—6281no—
174D4—21no—
175D4—41no—
176D4—3141no—
177D4—6281no—
178D4—6281no—
179D4—6281no—
180D4—6281no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—3141no—
184C2×C4—3141no—
185C2×C4—6281no—
186C2×C4—6281no—
187C2×C4—6281no—
188C2×C4—6281no—
189C2×C4—6281no—
190C2×C4—1571no—
191C2×C4D4×D15711yescharacteristic
192C8—3141no—
193C8D4×D15711yescharacteristic
194C8C2×D62811yescharacteristic
195C22—41no—
196C22—3141no—
197C22—6281no—
198C22—6281no—
199C22—12562no—
200C22D8×D15711yescharacteristic
201C4—41no—
202C4—81no—
203C4—3141no—
204C4—6281no—
205C4—12561no—
206C4#1909774111yescharacteristic
207C4#1909779811yescharacteristic
208C2—21no—
209C2—81no—
210C2—6281no—
211C2—12561no—
212C2#2375740811yescharacteristic
subgroupG/H
centerC2#23757408
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#360×C157C2
socleC2×C157#447
prime radical#23758070C2
hypercenter#360D157
hypocenterC157#2191
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #23757716C2semidirect
3. #23757713C2semidirect
4. #23757532C2semidirect
5. #23757082C2semidirect
6. #23757054C2semidirect
7. #360×C157C2semidirect
15. C2×Dic628C22semidirect
22. #19097711C22semidirect
25. M32×C157C22semidirect
26. #106×C157C22semidirect
106. C157#2191semidirect
113. #360D157semidirect
131. M32C2×D157semidirect
132. #106C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237580702
#237577162
#237577132
#237575322
#237570822
#237570542
#360×C1572
#2191157