Finite Group Databasebeta

← #34101479

Subgroups — #34101479

Order 20096.

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

normal subgroups only

This group has 246 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
1#23757901C211yesmaximal, characteristic
2#23757313C211yesmaximal, characteristic
3#23757142C211yesmaximal, characteristic
4#23757041C211yesmaximal, characteristic
5#23757034C211yesmaximal, characteristic
6#23757032C211yesmaximal, characteristic
7#428×C157C211yesmaximal, characteristic
8C2×#14578938C2211yescharacteristic
9#19097771—21no—
10#19097770—21no—
11#19097763—21no—
12#19097762—21no—
13#19097748—22no—
14#19097730C2211yescharacteristic
15C2×C4⋊Dic157C2211yescharacteristic
16C2×#14578933—22no—
17C2×C4×Dic157C2211yescharacteristic
18#19097704—21no—
19#19097702—21no—
20C2×M16×C157C2211yescharacteristic
21#117×C157C2211yescharacteristic
22C2×C4⋊C4×C157C2211yescharacteristic
23#107×C157—21no—
24#106×C157—21no—
25C2×Dic314—22no—
26C22×Dic157—21no—
27C22×Dic157D412yes—
28#14578938—21no—
29#14578938Q812yescomplemented
30C2×#11929434—21no—
31C4⋊Dic157—22no—
32C4⋊Dic157—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157D411yescharacteristic
35C4⋊Dic157D411yescharacteristic
36#14578933—22no—
37#14578933—22no—
38#14578933—44no—
39C22⋊Dic157—21no—
40C4×Dic157—21no—
41C4×Dic157—21no—
42C4×Dic157Q812yescomplemented
43C22×C4×C157—21no—
44C22×C4×C157C2311yescharacteristic
45M16×C157—21no—
46M16×C157Q812yescomplemented
47C2×C8×C157—21no—
48C4⋊C4×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157D411yescharacteristic
51C4⋊C4×C157D411yescharacteristic
52C22⋊C4×C157—21no—
53C42×C157—21no—
54Dic314—82no—
55C2×Dic157—22no—
56C2×Dic157—22no—
57C2×Dic157—22no—
58C2×Dic157—22no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—42no—
62#11929434—22no—
63C23×C157C2×D411yescharacteristic
64C2×C4×C157—21no—
65C2×C4×C157—21no—
66C2×C4×C157—42no—
67C2×C4×C157—41no—
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×D411yescharacteristic
70C2×C4×C157C2×Q811yescharacteristic
71C2×C4×C157C2×Q811yescharacteristic
72C2×C4×C157C2×Q811yescharacteristic
73C2×C4×C157#4111yescharacteristic
74C8×C157—22no—
75C22×C157—21no—
76C22×C157—21no—
77C22×C157#12011yescharacteristic
78C22×C157C22⋊Q811yescharacteristic
79C22×C157C4⋊Q811yescharacteristic
80C4×C157—41no—
81C4×C157—41no—
82C4×C157—81no—
83C4×C157C22⋊Q811yescharacteristic
84C4×C157C22⋊Q811yescharacteristic
85C4×C157C4⋊Q811yescharacteristic
86C4×C157C4⋊Q811yescharacteristic
87Dic157—24no—
88Dic157—42no—
89Dic157—41no—
90Dic157—41no—
91C2×C157—21no—
92C2×C157—21no—
93C2×C157#39511yescharacteristic
94C2×C157#45311yescharacteristic
95C2×C157#45611yescharacteristic
96C157#206011yescharacteristic, complemented, Sylow
97#2060—1571nomaximal, Sylow
98#544—1571no—
99#428—1571no—
100#428D15711yescharacteristic
101#384—1571no—
102#343—1571no—
103#339—1571no—
104#339—1571no—
105C2×M16—1571no—
106C2×M16C2×D15711yescharacteristic
107C4⋊Q8—3141no—
108C4⋊Q8—3141no—
109#125—3141no—
110#125—3141no—
111C22⋊Q8—3142no—
112#117—1571no—
113#117C2×D15711yescharacteristic
114C2×C4⋊C4—3142no—
115C2×C4⋊C4—1571no—
116C2×C4⋊C4C2×D15711yescharacteristic
117C2×C42—1571no—
118#107—21no—
119#107—3141no—
120#106—21no—
121#106—3141no—
122C2×Q8—3142no—
123C22×C4—21no—
124C22×C4—3141no—
125C22×C4—1572no—
126C22×C4C22×D15711yescharacteristic
127M16—21no—
128M16—3141no—
129M16—1572no—
130M16Dic31412yescomplemented
131C2×C8—21no—
132C2×C8—3141no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—3142no—
136C4⋊C4—3142no—
137C4⋊C4—3142no—
138C4⋊C4—3141no—
139C4⋊C4—3141no—
140C4⋊C4—6284no—
141C4⋊C4—1571no—
142C4⋊C4—1571no—
143C4⋊C4C22⋊D15711yescharacteristic
144C4⋊C4C22⋊D15711yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—3141no—
147C42—21no—
148C42—3141no—
149C42—3141no—
150C42—1572no—
151C23D4×D15711yescharacteristic
152Q8—12562no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—3142no—
158C2×C4—3142no—
159C2×C4—3142no—
160C2×C4—3141no—
161C2×C4—3141no—
162C2×C4—3142no—
163C2×C4—6282no—
164C2×C4D4×D15711yescharacteristic
165C2×C4C2×C22⋊D15711yescharacteristic
166C2×C4Q8×D15711yescharacteristic
167C2×C4Q8×D15711yescharacteristic
168C2×C4C2×Dic31411yescharacteristic
169C2×C4#1457895411yescharacteristic
170C8—22no—
171C8—3142no—
172C22—21no—
173C22—21no—
174C22#1909773911yescharacteristic
175C22#1909774911yescharacteristic
176C22#1909777011yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—3144no—
181C4—6282no—
182C4—6281no—
183C4—6281no—
184C4#1909774911yescharacteristic
185C4#1909775011yescharacteristic
186C4#1909776911yescharacteristic
187C4#1909777011yescharacteristic
188C2—21no—
189C2—21no—
190C2#2375719311yescharacteristic
191C2#2375743911yescharacteristic
192C2#2375745411yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#428×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#428D157
hypocenterC157#2060
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
29. #14578938Q8semidirect
42. C4×Dic157Q8semidirect
46. M16×C157Q8semidirect
96. C157#2060semidirect
130. M16Dic314semidirect

Maximal subgroups

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

subgroupindex
#237579012
#237573132
#237571422
#237570412
#237570342
#237570322
#428×C1572
#2060157