Finite Group Databasebeta

← #34101286

Subgroups — #34101286

Order 20096.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19097762C211yesmaximal, characteristic
2C2×#19097696C211yesmaximal, characteristic
3C2×#19097694C211yesmaximal, characteristic
4#23757178C211yesmaximal, characteristic
5#23757035C211yesmaximal, characteristic
6#23757027C211yesmaximal, characteristic
7#340×C157C211yesmaximal, characteristic
8C22×Dic314C2211yescharacteristic
9C22×#11929434C2211yescharacteristic
10#19097762—22no—
11#19097762—22no—
12C2×C4⋊Dic157—21no—
13C2×C4⋊Dic157C2211yescharacteristic
14C2×#14578933—21no—
15C2×C4×Dic157C2211yescharacteristic
16#19097696—22no—
17#19097694—22no—
18#19097678—21no—
19#19097678—21no—
20C22×C8×C157C2211yescharacteristic
21C2×C4⋊C4×C157C2211yescharacteristic
22C2×C4⋊C4×C157C2211yescharacteristic
23C2×Dic314—21no—
24C2×Dic314—21no—
25C2×Dic314—21no—
26C2×Dic314—21no—
27C2×Dic314—21no—
28C2×Dic314Q812yes—
29C22×Dic157—21no—
30C22×Dic157—21no—
31C22×Dic157D411yescharacteristic
32C22×Dic157D411yescharacteristic
33C2×#11929434—21no—
34C2×#11929434—21no—
35C2×#11929434—21no—
36C4⋊Dic157—24no—
37C4⋊Dic157—21no—
38C4⋊Dic157D412yes—
39#14578933—24no—
40C4×Dic157—21no—
41C4×Dic157—21no—
42C22×C4×C157—21no—
43C22×C4×C157—21no—
44C22×C4×C157C2311yescharacteristic
45C2×C8×C157—21no—
46C2×C8×C157—21no—
47C2×C8×C157—21no—
48C4⋊C4×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157D412yes—
52Dic314—22no—
53Dic314—22no—
54Dic314—41no—
55Dic314—41no—
56C2×Dic157—22no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157—22no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—21no—
63C2×Dic157—21no—
64C2×Dic157—41no—
65C2×Dic157—41no—
66C2×Dic157—41no—
67C2×Dic157—41no—
68#11929434—41no—
69C23×C157C2×D411yescharacteristic
70C2×C4×C157—22no—
71C2×C4×C157—41no—
72C2×C4×C157—41no—
73C2×C4×C157—41no—
74C2×C4×C157—41no—
75C2×C4×C157—41no—
76C2×C4×C157C2×D411yescharacteristic
77C2×C4×C157C2×D411yescharacteristic
78C2×C4×C157C2×Q811yescharacteristic
79C2×C4×C157#4111yescharacteristic
80C2×C4×C157#4111yescharacteristic
81C2×C4×C157#4111yescharacteristic
82C8×C157—41no—
83C22×C157#12011yescharacteristic
84C22×C157C22⋊Q811yescharacteristic
85C22×C157#12411yescharacteristic
86C22×C157#13511yescharacteristic
87C22×C157#13511yescharacteristic
88C22×C157#13711yescharacteristic
89C22×C157#13711yescharacteristic
90C4×C157—42no—
91C4×C157—81no—
92C4×C157C22⋊Q811yescharacteristic
93C4×C157C22⋊Q811yescharacteristic
94C4×C157#12411yescharacteristic
95C4×C157#12411yescharacteristic
96Dic157—42no—
97Dic157—41no—
98Dic157—41no—
99Dic157—42no—
100C2×C157#39311yescharacteristic
101C2×C157#45211yescharacteristic
102C2×C157#45211yescharacteristic
103C2×C157#47911yescharacteristic
104C2×C157#47911yescharacteristic
105C2×C157#48811yescharacteristic
106C2×C157#49111yescharacteristic
107C157#202611yescharacteristic, complemented, Sylow
108#2026—1571nomaximal, Sylow
109C2×#125—1571no—
110C2×#103—1571no—
111C2×#103—1571no—
112#391—1571no—
113#340—1571no—
114#340D15711yescharacteristic
115#336—1571no—
116C22×Q8—1571no—
117C22×C8—1571no—
118C22×C8C2×D15711yescharacteristic
119#125—3142no—
120#125—3142no—
121C2×C4⋊C4—3141no—
122C2×C4⋊C4—3141no—
123C2×C4⋊C4—1571no—
124C2×C4⋊C4C2×D15711yescharacteristic
125C2×C4⋊C4C2×D15711yescharacteristic
126C2×C42—1571no—
127#103—3142no—
128#103—3142no—
129#95—3141no—
130#95—3141no—
131C2×Q8—3141no—
132C2×Q8—3141no—
133C2×Q8—3141no—
134C2×Q8—3141no—
135C2×Q8—3141no—
136C2×Q8—1572no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—3141no—
140C22×C4—3141no—
141C22×C4—1571no—
142C22×C4—1571no—
143C22×C4C22×D15711yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—3141no—
148C2×C8—3141no—
149C2×C8—3141no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—3144no—
154C4⋊C4—3144no—
155C4⋊C4—3141no—
156C4⋊C4—1572no—
157C4⋊C4D62812yes—
158C42—3141no—
159C42—3141no—
160C23D4×D15711yescharacteristic
161Q8—3142no—
162Q8—3142no—
163Q8—6281no—
164Q8—6281no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—3141no—
172C2×C4—3141no—
173C2×C4—3142no—
174C2×C4—3142no—
175C2×C4—3141no—
176C2×C4—3141no—
177C2×C4—3141no—
178C2×C4—3141no—
179C2×C4—6281no—
180C2×C4—6281no—
181C2×C4—6281no—
182C2×C4—6281no—
183C2×C4D4×D15711yescharacteristic
184C2×C4C2×D62811yescharacteristic
185C2×C4Q8×D15711yescharacteristic
186C2×C4#1457895311yescharacteristic
187C2×C4#1457895411yescharacteristic
188C2×C4#1457895411yescharacteristic
189C8—41no—
190C8—6281no—
191C22#1909774111yescharacteristic
192C22#1909774911yescharacteristic
193C22#1909775711yescharacteristic
194C22#1909779011yescharacteristic
195C22#1909779211yescharacteristic
196C22#1909780011yescharacteristic
197C22#1909780311yescharacteristic
198C4—42no—
199C4—81no—
200C4—6281no—
201C4—6281no—
202C4—6282no—
203C4—6282no—
204C4#1909774911yescharacteristic
205C4#1909775111yescharacteristic
206C4#1909775711yescharacteristic
207C4#1909775911yescharacteristic
208C2#2375718611yescharacteristic
209C2#2375743611yescharacteristic
210C2#2375743811yescharacteristic
211C2#2375757911yescharacteristic
212C2#2375758311yescharacteristic
213C2#2375762611yescharacteristic
214C2#2375764011yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#340×C157C2
socle, prime radicalC23×C157C2×D4
hypercenter#340D157
hypocenterC157#2026
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
107. C157#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#190977622
C2×#190976962
C2×#190976942
#237571782
#237570352
#237570272
#340×C1572
#2026157