Finite Group Databasebeta

← #34101512

Subgroups — #34101512

Order 20096.

248 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19097700C211yesmaximal, characteristic
2C2×#19097696C211yesmaximal, characteristic
3C2×#19097694C211yesmaximal, characteristic
4#23757178C211yesmaximal, characteristic
5#23757172C211yesmaximal, characteristic
6#23757035C211yesmaximal, characteristic
7C2×#106×C157C211yesmaximal, characteristic
8C22×Dic314C2211yescharacteristic
9C22×#11929434C2211yescharacteristic
10C2×C4⋊Dic157—21no—
11C2×C4⋊Dic157C2211yescharacteristic
12C2×C4×Dic157C2211yescharacteristic
13#19097700—22no—
14#19097696—22no—
15#19097694—22no—
16#19097678—21no—
17#19097678—21no—
18#19097678—21no—
19C22×C8×C157C2211yescharacteristic
20C2×C4⋊C4×C157C2211yescharacteristic
21C2×C4⋊C4×C157C2211yescharacteristic
22#106×C157—22no—
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—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157—42no—
39C4×Dic157—21no—
40C4×Dic157—21no—
41C22×C4×C157—21no—
42C22×C4×C157—21no—
43C22×C4×C157C2311yescharacteristic
44C2×C8×C157—21no—
45C2×C8×C157—21no—
46C2×C8×C157D412yes—
47C4⋊C4×C157—21no—
48C4⋊C4×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157D412yes—
51Dic314—22no—
52Dic314—22no—
53Dic314—41no—
54Dic314—41no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—22no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—41no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64C2×Dic157—41no—
65C2×Dic157—41no—
66C2×Dic157SD1612yes—
67#11929434—41no—
68C23×C157C2×D411yescharacteristic
69C2×C4×C157—22no—
70C2×C4×C157—41no—
71C2×C4×C157—41no—
72C2×C4×C157—41no—
73C2×C4×C157—41no—
74C2×C4×C157—41no—
75C2×C4×C157C2×D411yescharacteristic
76C2×C4×C157C2×D411yescharacteristic
77C2×C4×C157C2×Q811yescharacteristic
78C2×C4×C157#4111yescharacteristic
79C2×C4×C157#4111yescharacteristic
80C2×C4×C157#4111yescharacteristic
81C8×C157—22no—
82C22×C157#12111yescharacteristic
83C22×C157#12111yescharacteristic
84C22×C157C22⋊Q811yescharacteristic
85C22×C157C2×SD1611yescharacteristic
86C22×C157#13511yescharacteristic
87C22×C157#13711yescharacteristic
88C22×C157#13711yescharacteristic
89C4×C157—42no—
90C4×C157—81no—
91C4×C157#12111yescharacteristic
92C4×C157C22⋊Q811yescharacteristic
93C4×C157C22⋊Q811yescharacteristic
94C4×C157#12611yescharacteristic
95Dic157—22no—
96Dic157—42no—
97Dic157—41no—
98Dic157—81no—
99C2×C157#39611yescharacteristic
100C2×C157#46111yescharacteristic
101C2×C157#46411yescharacteristic
102C2×C157#46511yescharacteristic
103C2×C157#47011yescharacteristic
104C2×C157#47511yescharacteristic
105C2×C157#47911yescharacteristic
106C157#206611yescharacteristic, complemented, Sylow
107#2066—1571nomaximal, Sylow
108C2×#106D15711yescharacteristic
109C2×C4⋊C8—1571no—
110C2×#103—1571no—
111C2×#103—1571no—
112#391—1571no—
113#389—1571no—
114#340—1571no—
115C22×Q8—1571no—
116C22×C8—1571no—
117C22×C8C2×D15711yescharacteristic
118C2×C4⋊C4—3141no—
119C2×C4⋊C4—1571no—
120C2×C4⋊C4C2×D15711yescharacteristic
121C2×C4⋊C4C2×D15711yescharacteristic
122C2×C42—1571no—
123#106—22no—
124C4⋊C8—3142no—
125#103—3142no—
126#103—3142no—
127#95—3141no—
128#95—3141no—
129#95—3141no—
130C2×Q8—3141no—
131C2×Q8—3141no—
132C2×Q8—3141no—
133C2×Q8—3141no—
134C2×Q8—3141no—
135C2×Q8—1572no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—3141no—
139C22×C4—3141no—
140C22×C4—1571no—
141C22×C4—1571no—
142C22×C4C22×D15711yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—3141no—
146C2×C8—3141no—
147C2×C8—3141no—
148C2×C8D62812yes—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—3141no—
153C4⋊C4—3141no—
154C4⋊C4—6282no—
155C4⋊C4C22⋊D15712yes—
156C42—3141no—
157C42—3141no—
158C23D4×D15711yescharacteristic
159Q8—3142no—
160Q8—3142no—
161Q8—6281no—
162Q8—6281no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3141no—
170C2×C4—3141no—
171C2×C4—3141no—
172C2×C4—3142no—
173C2×C4—3141no—
174C2×C4—3141no—
175C2×C4—6281no—
176C2×C4—6281no—
177C2×C4—6281no—
178C2×C4—6281no—
179C2×C4—6281no—
180C2×C4—1572no—
181C2×C4C2×C22⋊D15711yescharacteristic
182C2×C4C2×D62811yescharacteristic
183C2×C4Q8×D15711yescharacteristic
184C2×C4#1457895311yescharacteristic
185C2×C4#1457895411yescharacteristic
186C2×C4#1457895511yescharacteristic
187C8—22no—
188C8—6281no—
189C22#1909774311yescharacteristic
190C22#1909774611yescharacteristic
191C22#1909774911yescharacteristic
192C22SD16×D15711yescharacteristic
193C22#1909779211yescharacteristic
194C22#1909780011yescharacteristic
195C22#1909780011yescharacteristic
196C4—42no—
197C4—81no—
198C4—3142no—
199C4—6282no—
200C4—6281no—
201C4—12561no—
202C4#1909774511yescharacteristic
203C4#1909774711yescharacteristic
204C4#1909775111yescharacteristic
205C4#1909776611yescharacteristic
206C2#2375719511yescharacteristic
207C2#2375747611yescharacteristic
208C2#2375749311yescharacteristic
209C2#2375750311yescharacteristic
210C2#2375753211yescharacteristic
211C2#2375755711yescharacteristic
212C2#2375758311yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#106×C157C2
socle, prime radicalC23×C157C2×D4
hypercenterC2×#106D157
hypocenterC157#2066
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
106. C157#2066semidirect

Maximal subgroups

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

subgroupindex
C2×#190977002
C2×#190976962
C2×#190976942
#237571782
#237571722
#237570352
C2×#106×C1572
#2066157