Finite Group Databasebeta

← #34099159

Subgroups — #34099159

Order 20096.

236 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 51 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#23757898C211yesmaximal, characteristic
2#23757608C211yesmaximal, characteristic, complemented
3#23757208C211yesmaximal, characteristic
4#23757011C211yesmaximal, characteristic, complemented
5#23757010C211yesmaximal, characteristic, complemented
6#23756996C211yesmaximal, characteristic
7#484×C157C211yesmaximal, characteristic, complemented
8#19097751—21no—
9#19097750C2211yescharacteristic
10#19097749—21no—
11#19097749—21no—
12#19097748—21no—
13#19097747—21no—
14C2×#14578933—21no—
15C2×#14578931—21no—
16C2×#14578931C2211yescharacteristic
17C22⋊C4×D157—21no—
18#19097704—21no—
19#19097694—21no—
20C22⋊#11929434C2211yescharacteristic
21#19097678C2211yescharacteristic
22C22⋊Q8×C157C2211yescharacteristic
23C2×C4⋊C4×C157C2211yescharacteristic
24#107×C157—21no—
25#103×C157—21no—
26C22⋊C8×C157C2211yescharacteristic
27C23×D157D411yescharacteristic
28C2×Dic314—21no—
29C2×Dic314D411yescharacteristic
30C22×Dic157—21no—
31C22×Dic157D411yescharacteristic
32C2×C4×D157—21no—
33C2×C4×D157—21no—
34C2×#11929434—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157D411yescharacteristic
37#14578933—21no—
38#14578933—21no—
39#14578933—21no—
40#14578933—42no—
41C22⋊Dic157—21no—
42#14578931—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46#14578931—42no—
47C2×Q8×C157D411yescharacteristic
48C22×C4×C157—21no—
49C22×C4×C157C2311yescharacteristic
50C2×C8×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157—21no—
54C4⋊C4×C157D411yescharacteristic
55C22⋊C4×C157—21no—
56C22×D157—21no—
57C22×D157—21no—
58C22×D157—41no—
59C22×D157—41no—
60C22×D157Q1612yes—
61Dic314—41no—
62Dic314—81no—
63C2×Dic157—22no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157—21no—
67C2×Dic157—41no—
68C2×Dic157—41no—
69C2×Dic157—41no—
70C4×D157—81no—
71C4×D157—81no—
72#11929434—41no—
73C23×C157C2×D411yescharacteristic
74Q8×C157—41no—
75C2×C4×C157—21no—
76C2×C4×C157—21no—
77C2×C4×C157—41no—
78C2×C4×C157—41no—
79C2×C4×C157—41no—
80C2×C4×C157—41no—
81C2×C4×C157C2×D411yescharacteristic
82C2×C4×C157C2×D411yescharacteristic
83C8×C157—41no—
84C22×C157—21no—
85C22×C157—21no—
86C22×C157#12011yescharacteristic
87C22×C157C2×Q1611yescharacteristic
88C22×C157#13711yescharacteristic
89C2×D157—22no—
90C2×D157—41no—
91C2×D157—41no—
92C2×D157—42no—
93C2×D157—81no—
94C4×C157—21no—
95C4×C157—21no—
96C4×C157—41no—
97C4×C157—41no—
98C4×C157—81no—
99Dic157—42no—
100Dic157—41no—
101Dic157—41no—
102Dic157—41no—
103C2×C157—21no—
104C2×C157—21no—
105C2×C157#45111yescharacteristic
106C2×C157#45311yescharacteristic
107C2×C157#45811yescharacteristic
108D157—42no—
109C157#161411yescharacteristic, complemented, Sylow
110#1614—1571nomaximal, Sylow
111#543—1571no—
112#484—1571no—
113#484D15711yescharacteristic, complemented
114#399—1571no—
115#328—1571no—
116#328—1571no—
117#323—1571no—
118C22⋊Q8—3141no—
119C22⋊Q8—3141no—
120C22⋊Q8—3141no—
121C22⋊Q8—3141no—
122C22⋊Q8—3141no—
123C22⋊Q8—1571no—
124C22⋊Q8C2×D15711yescharacteristic
125C2×C4⋊C4—3141no—
126C2×C4⋊C4C2×D15711yescharacteristic
127C2×C22⋊C4—3141no—
128C2×C22⋊C4—3141no—
129C2×C22⋊C4—1571no—
130#107—21no—
131#107—3141no—
132#103—21no—
133#103—3141no—
134C22⋊C8—1571no—
135C22⋊C8C2×D15711yescharacteristic
136#95—1571no—
137C24—1571no—
138C2×Q8—3141no—
139C2×Q8—1571no—
140C2×Q8C22⋊D15711yescharacteristic
141C22×C4—21no—
142C22×C4—3141no—
143C22×C4—3141no—
144C22×C4—3141no—
145C22×C4—1571no—
146C22×C4C22×D15711yescharacteristic
147C2×C8—21no—
148C2×C8—3141no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—3141no—
153C4⋊C4—3141no—
154C4⋊C4—3141no—
155C4⋊C4—3141no—
156C4⋊C4—6282no—
157C4⋊C4—1571no—
158C4⋊C4C22⋊D15711yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—3141no—
161C22⋊C4—3141no—
162C22⋊C4—3141no—
163C22⋊C4—3141no—
164C22⋊C4—3141no—
165C22⋊C4—6282no—
166C23—3141no—
167C23—3141no—
168C23—6281no—
169C23—6281no—
170C23—1572no—
171C23D4×D15711yescharacteristic
172Q8—41no—
173Q8—6281no—
174Q8—12561no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—3142no—
182C2×C4—3141no—
183C2×C4—3141no—
184C2×C4—3141no—
185C2×C4—6281no—
186C2×C4—6281no—
187C2×C4—6281no—
188C2×C4—12561no—
189C2×C4—12561no—
190C2×C4D4×D15711yescharacteristic
191C2×C4C2×C22⋊D15711yescharacteristic
192C8—41no—
193C8—6281no—
194C22—21no—
195C22—21no—
196C22—3142no—
197C22—6282no—
198C22—6281no—
199C22—6281no—
200C22—12561no—
201C22#1909773911yescharacteristic
202C22Q16×D15711yescharacteristic
203C22#1909780311yescharacteristic
204C4—21no—
205C4—21no—
206C4—41no—
207C4—41no—
208C4—81no—
209C4—6282no—
210C4—6281no—
211C4—6281no—
212C4—6281no—
213C2—21no—
214C2—21no—
215C2—6282no—
216C2#2375742711yescharacteristic
217C2#2375743911yescharacteristic
218C2#2375746211yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#484×C157C2
socleC22×C157#120
prime radicalC23×D157D4
hypercenter#484D157
hypocenterC157#1614
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #23757608C2semidirect
4. #23757011C2semidirect
5. #23757010C2semidirect
7. #484×C157C2semidirect
109. C157#1614semidirect
113. #484D157semidirect

Maximal subgroups

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

subgroupindex
#237578982
#237576082
#237572082
#237570112
#237570102
#237569962
#484×C1572
#1614157