Finite Group Databasebeta

← #34101177

Subgroups — #34101177

Order 20096.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#19097797C212yesmaximal, complemented
2#23757854C211yesmaximal, characteristic, complemented
3C2×#19097699C212yesmaximal, complemented
4#23757042C211yesmaximal, characteristic, complemented
5#390×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C2212yes—
7#19097797—24no—
8#19097797—24no—
9C2×#14578942—22no—
10C2×#14578939—22no—
11C2×#14578938C2212yes—
12#19097751—22no—
13#19097746—22no—
14#19097745—22no—
15#19097699—24no—
16C22×D4×C157C2211yescharacteristic
17C2×C4⋊C4×C157C2211yescharacteristic
18C2×C22⋊C4×C157—22no—
19C2×C42×C157C2211yescharacteristic
20#14578954—22no—
21#14578954—22no—
22#14578954—22no—
23#14578954—22no—
24C2×Dic314D412yes—
25C2×D628—22no—
26C2×D628D412yes—
27C2×C22⋊D157—22no—
28C2×C4×D157—22no—
29#14578942—28no—
30#14578939—28no—
31#14578938—22no—
32#14578938D414yescomplemented
33C2×#11929434—22no—
34C4⋊Dic157—22no—
35#14578931—24no—
36C24×C157—21no—
37C2×D4×C157—22no—
38C2×D4×C157—22no—
39C2×D4×C157—21no—
40C2×D4×C157D412yescomplemented
41C22×C4×C157—21no—
42C22×C4×C157D412yes—
43C22×C4×C157C2311yescharacteristic
44C4⋊C4×C157—22no—
45C22⋊C4×C157—44no—
46C42×C157—22no—
47C22×D157—22no—
48Dic314—22no—
49Dic314—22no—
50D628—22no—
51D628—22no—
52D628—82no—
53C22⋊D157—42no—
54C22⋊D157—42no—
55C2×Dic157—22no—
56C4×D157—42no—
57C4×D157—42no—
58#11929434—24no—
59C23×C157—22no—
60C23×C157—42no—
61C23×C157—42no—
62C23×C157—41no—
63C23×C157—41no—
64C23×C157C2×D411yescharacteristic
65D4×C157—24no—
66D4×C157—42no—
67C2×C4×C157—22no—
68C2×C4×C157—22no—
69C2×C4×C157—41no—
70C2×C4×C157—41no—
71C2×C4×C157—42no—
72C2×C4×C157C2×D412yes—
73C2×C4×C157C2×D412yes—
74C2×C4×C157C2×D411yescharacteristic
75C2×C4×C157#4111yescharacteristic
76C22×C157—21no—
77C22×C157—21no—
78C22×C157—44no—
79C22×C157—42no—
80C22×C157—82no—
81C22×C157—81no—
82C22×C157—81no—
83C22×C157#12011yescharacteristic
84C22×C157#12111yescharacteristic
85C22×C157#12711yescharacteristic
86C2×D157—42no—
87C2×D157—42no—
88C2×D157—42no—
89C4×C157—42no—
90C4×C157—42no—
91C4×C157#12012yes—
92C4×C157#12112yes—
93Dic157—42no—
94C2×C157—21no—
95C2×C157—21no—
96C2×C157—82no—
97C2×C157#39211yescharacteristic
98C2×C157#45311yescharacteristic
99C2×C157#45411yescharacteristic
100D157—82no—
101C157#200611yescharacteristic, complemented, Sylow
102#2006—1571nomaximal, Sylow
103C2×AGL(1,ℤ/8)—1572no—
104#537—1571no—
105C2×#104—1572no—
106#390D15711yescharacteristic, complemented
107#343—1571no—
108C2×#41—1572no—
109C22×D4C2×D15711yescharacteristic
110AGL(1,ℤ/8)—3144no—
111AGL(1,ℤ/8)—3144no—
112C2×SD16—3142no—
113C2×D8—3142no—
114C2×M16—1572no—
115C22⋊Q8—3142no—
116#121—3142no—
117#121—3142no—
118C2×C4⋊C4C2×D15711yescharacteristic
119C2×C22⋊C4—22no—
120C2×C42C2×D15711yescharacteristic
121#104—3144no—
122C24—21no—
123#41—3142no—
124#41—3142no—
125#41—3142no—
126#41—3142no—
127C2×Q8—1572no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—21no—
131C2×D4—3142no—
132C2×D4—3142no—
133C2×D4—1572no—
134C2×D4D62812yescomplemented
135C22×C4—21no—
136C22×C4—3142no—
137C22×C4C22⋊D15712yes—
138C22×C4C22×D15711yescharacteristic
139SD16—3148no—
140D8—3148no—
141M16—3142no—
142M16—1574no—
143C2×C8—3142no—
144C4⋊C4—22no—
145C4⋊C4—3142no—
146C22⋊C4—44no—
147C22⋊C4—3144no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—3142no—
155C23C2×C22⋊D15711yescharacteristic
156Q8—3142no—
157Q8—3142no—
158D4—24no—
159D4—42no—
160D4—3142no—
161D4—3142no—
162D4—6282no—
163D4—6282no—
164D4—12562no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—3142no—
171C2×C4—6282no—
172C2×C4—6282no—
173C2×C4D4×D15712yes—
174C2×C4D4×D15712yes—
175C2×C4C2×D62811yescharacteristic
176C2×C4#1457895411yescharacteristic
177C8—3144no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—6282no—
186C22—6282no—
187C22—6282no—
188C22#1909773911yescharacteristic
189C22#1909774511yescharacteristic
190C22#1909776711yescharacteristic
191C4—42no—
192C4—42no—
193C4—6282no—
194C4#1909774112yes—
195C4#1909774412yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—12562no—
200C2#2375718211yescharacteristic
201C2#2375744011yescharacteristic
202C2#2375744511yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#390×C157C2
socleC22×C157#120
hypercenter#390D157
hypocenterC157#2006
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#19097797C2semidirect
2. #23757854C2semidirect
3. C2×#19097699C2semidirect
4. #23757042C2semidirect
5. #390×C157C2semidirect
32. #14578938D4semidirect
40. C2×D4×C157D4semidirect
101. C157#2006semidirect
106. #390D157semidirect
134. C2×D4D628semidirect

Maximal subgroups

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

subgroupindex
C2×#190977972
#237578542
C2×#190976992
#237570422
#390×C1572
#2006157