Finite Group Databasebeta

← #34099097

Subgroups — #34099097

Order 20096.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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#23757870C211yesmaximal, characteristic
2#23757429C211yesmaximal, characteristic, complemented
3#23757412C211yesmaximal, characteristic
4#23757009C211yesmaximal, characteristic, complemented
5#23757006C211yesmaximal, characteristic
6#23756999C211yesmaximal, characteristic, complemented
7#395×C157C211yesmaximal, characteristic, complemented
8C2×#14578944—21no—
9C2×#14578941—21no—
10#19097766—21no—
11#19097761—21no—
12#19097756—21no—
13#19097754—21no—
14#19097750C2211yescharacteristic
15#19097749—21no—
16#19097745C2211yescharacteristic
17C4×C22⋊D157—21no—
18#19097695—21no—
19#19097695—21no—
20C22⋊#11929434C2211yescharacteristic
21C22⋊#11929434C2211yescharacteristic
22C22×Q8×C157C2211yescharacteristic
23C2×C4⋊C4×C157—21no—
24C2×C4⋊C4×C157C2211yescharacteristic
25#95×C157—21no—
26#95×C157C2211yescharacteristic
27C2×Dic314D411yescharacteristic
28C2×D628D411yescharacteristic
29C2×C22⋊D157—21no—
30C2×C4×D157—21no—
31#14578944—42no—
32#14578941—42no—
33C2×#11929434—21no—
34C2×#11929434—21no—
35C4⋊Dic157D411yescharacteristic
36C4⋊Dic157D411yescharacteristic
37#14578933—21no—
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41C22⋊Dic157—21no—
42#14578931—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46C4×Dic157—21no—
47C2×Q8×C157—21no—
48C2×Q8×C157—21no—
49C2×Q8×C157—42no—
50C22×C4×C157—21no—
51C22×C4×C157—21no—
52C22×C4×C157D411yescharacteristic
53C22×C4×C157D411yescharacteristic
54C22×C4×C157C2311yescharacteristic
55C4⋊C4×C157—21no—
56C4⋊C4×C157—21no—
57C4⋊C4×C157—42no—
58C22×D157—21no—
59Dic314—41no—
60D628—41no—
61C22⋊D157—41no—
62C22⋊D157—41no—
63C2×Dic157—21no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C4×D157—81no—
67#11929434—41no—
68#11929434—41no—
69C23×C157C2×D411yescharacteristic
70Q8×C157—22no—
71Q8×C157—22no—
72Q8×C157—41no—
73Q8×C157—41no—
74C2×C4×C157—22no—
75C2×C4×C157—22no—
76C2×C4×C157—21no—
77C2×C4×C157—21no—
78C2×C4×C157—21no—
79C2×C4×C157—21no—
80C2×C4×C157—41no—
81C2×C4×C157—41no—
82C2×C4×C157—41no—
83C2×C4×C157—41no—
84C2×C4×C157—41no—
85C2×C4×C157—41no—
86C2×C4×C157C2×D411yescharacteristic
87C2×C4×C157C2×D411yescharacteristic
88C22×C157—21no—
89C22×C157—21no—
90C22×C157#12011yescharacteristic
91C22×C157#13511yescharacteristic
92C22×C157#13711yescharacteristic
93C2×D157—41no—
94C2×D157—41no—
95C2×D157—41no—
96C4×C157—21no—
97C4×C157—21no—
98C4×C157—42no—
99C4×C157—41no—
100C4×C157—42no—
101C4×C157—41no—
102Dic157—41no—
103Dic157—41no—
104Dic157—41no—
105C2×C157—21no—
106C2×C157—21no—
107C2×C157#45211yescharacteristic
108C2×C157#45611yescharacteristic
109C2×C157B(4,𝔽2)11yescharacteristic
110D157—81no—
111C157#160311yescharacteristic, complemented, Sylow
112#1603—1571nomaximal, Sylow
113#539—1571no—
114#451—1571no—
115#448—1571no—
116#395D15711yescharacteristic, complemented
117#328—1571no—
118#327—1571no—
119#324—1571no—
120C22×Q8C2×D15711yescharacteristic
121C2×Q16—3141no—
122C2×SD16—3141no—
123#126—3141no—
124#125—3141no—
125#123—3141no—
126#123—3141no—
127C22⋊Q8—3141no—
128C22⋊Q8—1571no—
129#121—1571no—
130C4×D4—3141no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4C2×D15711yescharacteristic
133#103—3141no—
134#103—3141no—
135C22⋊C8—1571no—
136C22⋊C8—1571no—
137#95—21no—
138#95C2×D15711yescharacteristic
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8—1571no—
143C2×D4—3141no—
144C2×D4—1571no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—3141no—
148C22×C4C22⋊D15711yescharacteristic
149C22×C4C22⋊D15711yescharacteristic
150C22×C4C22×D15711yescharacteristic
151Q16—6282no—
152SD16—6282no—
153C2×C8—3141no—
154C2×C8—3141no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—42no—
158C4⋊C4—3141no—
159C4⋊C4—3141no—
160C4⋊C4—3141no—
161C4⋊C4—3141no—
162C4⋊C4—1571no—
163C4⋊C4—1571no—
164C22⋊C4—3141no—
165C22⋊C4—3141no—
166C22⋊C4—3141no—
167C22⋊C4—3141no—
168C22⋊C4—3141no—
169C42—3141no—
170C23—3141no—
171C23C2×C22⋊D15711yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—6281no—
177D4—6281no—
178D4—6281no—
179D4—6281no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—3141no—
193C2×C4—3141no—
194C2×C4—3141no—
195C2×C4—12561no—
196C2×C4D4×D15711yescharacteristic
197C2×C4D4×D15711yescharacteristic
198C8—6281no—
199C8—6281no—
200C22—21no—
201C22—21no—
202C22—6281no—
203C22—6281no—
204C22—6281no—
205C22#1909773911yescharacteristic
206C22#1909779111yescharacteristic
207C22#1909780211yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—42no—
213C4—41no—
214C4—6281no—
215C4—6281no—
216C4—6281no—
217C2—21no—
218C2—21no—
219C2—12561no—
220C2#2375743311yescharacteristic
221C2#2375745511yescharacteristic
222C2#2375745911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#395×C157C2
socleC22×C157#120
prime radical#19097745C22
hypercenter#395D157
hypocenterC157#1603
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #23757429C2semidirect
4. #23757009C2semidirect
6. #23756999C2semidirect
7. #395×C157C2semidirect
111. C157#1603semidirect
116. #395D157semidirect

Maximal subgroups

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

subgroupindex
#237578702
#237574292
#237574122
#237570092
#237570062
#237569992
#395×C1572
#1603157