Finite Group Databasebeta

← #34101178

Subgroups — #34101178

Order 20096.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#19097796C212yesmaximal, complemented
2C2×#19097698C212yesmaximal, complemented
3#23757174C211yesmaximal, characteristic, complemented
4#23757042C211yesmaximal, characteristic, complemented
5#537×C157C211yesmaximal, characteristic, complemented
6C22×D628C2211yescharacteristic
7#19097796—24no—
8#19097796—24no—
9C2×#14578941—22no—
10C2×#14578939—22no—
11C2×#14578938C2212yes—
12C2×#14578931—22no—
13C2×C4×Dic157C2211yescharacteristic
14#19097698—24no—
15C2×#41×C157C2212yes—
16C22⋊Q8×C157—22no—
17#121×C157—22no—
18#121×C157—22no—
19C2×C4⋊C4×C157C2211yescharacteristic
20C23×D157—21no—
21C2×D628—22no—
22C2×D628—22no—
23C2×D628—21no—
24C2×D628D412yescomplemented
25C22×Dic157—21no—
26#14578941—28no—
27#14578939—28no—
28#14578938—22no—
29#14578938D414yescomplemented
30C2×#11929434—22no—
31#14578931—44no—
32C4×Dic157—22no—
33#41×C157—22no—
34#41×C157—22no—
35#41×C157—22no—
36#41×C157—22no—
37C2×Q8×C157D412yes—
38C2×D4×C157—22no—
39C2×D4×C157—22no—
40C2×D4×C157D412yes—
41C22×C4×C157—22no—
42C22×C4×C157D412yes—
43C22×C4×C157C2311yescharacteristic
44C4⋊C4×C157—22no—
45C4⋊C4×C157—22no—
46C22⋊C4×C157—24no—
47C22×D157—22no—
48C22×D157—42no—
49C22×D157—42no—
50C22×D157—41no—
51C22×D157—41no—
52D628—24no—
53D628—42no—
54C2×Dic157—22no—
55C2×Dic157—41no—
56C2×Dic157—41no—
57#11929434—24no—
58C23×C157—22no—
59C23×C157C2×D411yescharacteristic
60Q8×C157—22no—
61Q8×C157—22no—
62D4×C157—22no—
63D4×C157—22no—
64D4×C157—42no—
65D4×C157—42no—
66D4×C157—82no—
67C2×C4×C157—22no—
68C2×C4×C157—22no—
69C2×C4×C157—42no—
70C2×C4×C157—42no—
71C2×C4×C157—42no—
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D412yes—
74C2×C4×C157C2×D412yes—
75C2×C4×C157#4111yescharacteristic
76C22×C157—21no—
77C22×C157—21no—
78C22×C157—42no—
79C22×C157—42no—
80C22×C157—42no—
81C22×C157#12011yescharacteristic
82C22×C157#12111yescharacteristic
83C22×C157#12711yescharacteristic
84C2×D157—44no—
85C2×D157—42no—
86C2×D157—82no—
87C2×D157—81no—
88C2×D157—81no—
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#537D15711yescharacteristic, complemented
105C2×#104—1572no—
106#390—1571no—
107#343—1571no—
108C2×#41C2×D15712yes—
109C22×D4—1571no—
110AGL(1,ℤ/8)—3144no—
111AGL(1,ℤ/8)—3144no—
112C2×SD16—3142no—
113C2×D8—3142no—
114C2×M16—1572no—
115C22⋊Q8—22no—
116#121—22no—
117#121—22no—
118C2×C4⋊C4C2×D15711yescharacteristic
119C2×C22⋊C4—3142no—
120C2×C42—1571no—
121#104—3144no—
122C24—3141no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D15712yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—3142no—
131C2×D4—3142no—
132C2×D4—3141no—
133C2×D4—1572no—
134C2×D4C22⋊D15712yes—
135C22×C4—22no—
136C22×C4—3141no—
137C22×C4C22⋊D15712yes—
138C22×C4C22×D15711yescharacteristic
139SD16—3148no—
140D8—3148no—
141M16—3142no—
142M16—1574no—
143C2×C8—3142no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—6284no—
148C42—3142no—
149C23—22no—
150C23—3142no—
151C23—6282no—
152C23—6282no—
153C23—6281no—
154C23—6281no—
155C23C2×C22⋊D15711yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—3144no—
164D4—6282no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—3142no—
171C2×C4—6281no—
172C2×C4—6281no—
173C2×C4D4×D15711yescharacteristic
174C2×C4D4×D15712yes—
175C2×C4C2×C22⋊D15712yes—
176C2×C4#1457895311yescharacteristic
177C8—3144no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—6284no—
184C22—6282no—
185C22—12562no—
186C22—12561no—
187C22—12561no—
188C22#1909774011yescharacteristic
189C22#1909774211yescharacteristic
190C22#1909776711yescharacteristic
191C4—42no—
192C4—42no—
193C4—6282no—
194C4#1909773912yes—
195C4#1909774312yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—12562no—
200C2#2375718111yescharacteristic
201C2#2375744111yescharacteristic
202C2#2375744611yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#537×C157C2
socleC22×C157#120
hypercenter#537D157
hypocenterC157#2006
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#19097796C2semidirect
2. C2×#19097698C2semidirect
3. #23757174C2semidirect
4. #23757042C2semidirect
5. #537×C157C2semidirect
24. C2×D628D4semidirect
29. #14578938D4semidirect
101. C157#2006semidirect
104. #537D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977962
C2×#190976982
#237571742
#237570422
#537×C1572
#2006157