Finite Group Databasebeta

← #34101301

Subgroups — #34101301

Order 20096.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#23757899C211yesmaximal, characteristic, complemented
2#23757128C212yesmaximal
3#23757128C211yesmaximal, characteristic
4#23757039C212yesmaximal, complemented
5#342×C157C211yesmaximal, characteristic, complemented
6C24×D157C2211yescharacteristic
7#19097750—22no—
8#19097748—24no—
9C2×C22⋊Dic157C2211yescharacteristic
10C2×C22⋊Dic157C2212yes—
11C2×#14578931—22no—
12C2×#14578931—24no—
13C2×C22⋊C4×C157C2212yes—
14C2×C22⋊C4×C157C2211yescharacteristic
15C23×D157—22no—
16C23×D157—21no—
17C23×D157—21no—
18C23×D157—22no—
19C23×D157—44no—
20C23×D157Q812yescomplemented
21C2×Dic314—22no—
22C22×Dic157—21no—
23C22×Dic157D414yes—
24C4⋊Dic157—22no—
25#14578933—24no—
26C22⋊Dic157—22no—
27C22⋊Dic157—22no—
28C22⋊Dic157—22no—
29#14578931—44no—
30#14578931—48no—
31C24×C157C2311yescharacteristic
32C22×C4×C157—22no—
33C22×C4×C157D412yes—
34C22⋊C4×C157—22no—
35C22⋊C4×C157—22no—
36C22⋊C4×C157—22no—
37C22×D157—28no—
38C22×D157—24no—
39C22×D157—24no—
40C22×D157—22no—
41C22×D157—44no—
42C22×D157—44no—
43C22×D157—48no—
44C22×D157—44no—
45C22×D157—42no—
46C22×D157—41no—
47C22×D157—42no—
48C22×D157—41no—
49Dic314—82no—
50C2×Dic157—24no—
51C2×Dic157—44no—
52C2×Dic157—42no—
53C2×Dic157—41no—
54C23×C157—42no—
55C23×C157C2×D412yes—
56C23×C157C2×D411yescharacteristic
57C23×C157C2×Q811yescharacteristic
58C23×C157#4111yescharacteristic
59C23×C157#4112yes—
60C2×C4×C157—22no—
61C2×C4×C157—42no—
62C2×C4×C157—44no—
63C2×C4×C157—42no—
64C22×C157—24no—
65C22×C157—22no—
66C22×C157—41no—
67C22×C157—41no—
68C22×C157—42no—
69C22×C157#12011yescharacteristic
70C22×C157C22⋊Q812yes—
71C22×C157C22⋊Q811yescharacteristic
72C22×C157#12412yes—
73C22×C157#12411yescharacteristic
74C2×D157—28no—
75C2×D157—24no—
76C2×D157—44no—
77C2×D157—48no—
78C2×D157—44no—
79C2×D157—42no—
80C2×D157—42no—
81C2×D157—44no—
82C4×C157—42no—
83C4×C157—82no—
84Dic157—44no—
85Dic157—81no—
86C2×C157—21no—
87C2×C157—22no—
88C2×C157—22no—
89C2×C157—21no—
90C2×C157#39311yescharacteristic
91C2×C157B(4,𝔽2)12yes—
92D157—44no—
93C157#202911yescharacteristic, complemented, Sylow
94#2029—1571nomaximal, Sylow
95#543—1571no—
96#379—1572no—
97#379—1571no—
98#342—1572no—
99#342D15711yescharacteristic, complemented
100C25—1571no—
101C22⋊Q8—3144no—
102C22⋊Q8—3142no—
103C2×C22⋊C4—3144no—
104C2×C22⋊C4—3142no—
105C2×C22⋊C4—1571no—
106C2×C22⋊C4—1572no—
107C2×C22⋊C4C2×D15712yes—
108C2×C22⋊C4C2×D15711yescharacteristic
109C24—3142no—
110C24—3141no—
111C24—3141no—
112C24—3142no—
113C24—6284no—
114C24—1572no—
115C24C22×D15711yescharacteristic
116C2×Q8—3142no—
117C22×C4—22no—
118C22×C4—3141no—
119C22×C4—1574no—
120C22×C4D62812yes—
121C4⋊C4—3144no—
122C4⋊C4—3142no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—3142no—
127C22⋊C4—3142no—
128C22⋊C4—3142no—
129C22⋊C4—6284no—
130C22⋊C4—6288no—
131C23—42no—
132C23—3148no—
133C23—3144no—
134C23—3144no—
135C23—3142no—
136C23—6284no—
137C23—6282no—
138C23—6284no—
139C23—6284no—
140C23—6288no—
141C23—6281no—
142C23—6282no—
143C23—6281no—
144C23D4×D15712yes—
145C23C2×D62811yescharacteristic
146C23Q8×D15711yescharacteristic
147C23#1457895311yescharacteristic
148C23#1457895412yes—
149Q8—12562no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—3144no—
155C2×C4—6284no—
156C2×C4—6282no—
157C2×C4—6281no—
158C22—24no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22—42no—
163C22—3148no—
164C22—3144no—
165C22—6288no—
166C22—6284no—
167C22—6284no—
168C22—6282no—
169C22—6282no—
170C22—6284no—
171C22#1909774111yescharacteristic
172C22#1909774912yes—
173C22#1909775111yescharacteristic
174C22#1909775712yes—
175C22#1909775911yescharacteristic
176C4—42no—
177C4—82no—
178C4—6284no—
179C4—12561no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—6284no—
185C2#2375718611yescharacteristic
186C2#2375746112yes—
subgroupG/H
centerC22#19097741
commutator, cosocleC24×C157C23
FrattiniC24C22×D157
Fitting#342×C157C2
socleC22×C157#120
prime radicalC24×D157C22
hypercenter#342D157
hypocenterC157#2029
LCSG ▷ C24×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #23757899C2semidirect
4. #23757039C2semidirect
5. #342×C157C2semidirect
20. C23×D157Q8semidirect
93. C157#2029semidirect
99. #342D157semidirect

Maximal subgroups

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

subgroupindex
#237578992
#237571282
#237570392
#342×C1572
#2029157