Finite Group Databasebeta

← #34100401

Subgroups — #34100401

Order 20096.

298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19097736C211yesmaximal, characteristic
2C2×#19097696C211yesmaximal, characteristic
3C2×#19097694C211yesmaximal, characteristic
4#23757169C211yesmaximal, characteristic
5#23757035C211yesmaximal, characteristic
6#23757027C211yesmaximal, characteristic
7C2×#106×C157C211yesmaximal, characteristic
8C22×Dic314C2211yescharacteristic
9C22×#11929434C2211yescharacteristic
10#19097736—22no—
11#19097736—22no—
12C2×C4⋊Dic157C2211yescharacteristic
13C2×#14578933—21no—
14C2×#14578933—21no—
15C2×C4×Dic157—21no—
16C2×C4×Dic157C2211yescharacteristic
17#19097696C414yescomplemented
18#19097694—22no—
19#19097678—21no—
20C22×C8×C157C2211yescharacteristic
21C2×C4⋊C4×C157C2211yescharacteristic
22C2×C4⋊C4×C157C2211yescharacteristic
23#106×C157—22no—
24C2×Dic314—21no—
25C2×Dic314—21no—
26C2×Dic314—21no—
27C2×Dic314C2×C412yes—
28C2×Dic314D412yes—
29C2×Dic314Q812yes—
30C22×Dic157—21no—
31C22×Dic157—21no—
32C22×Dic157D411yescharacteristic
33C22×Dic157D411yescharacteristic
34C2×#11929434—21no—
35C2×#11929434—21no—
36C2×#11929434—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157C2×C412yes—
39#14578933—24no—
40#14578933—42no—
41C4×Dic157—24no—
42C4×Dic157—21no—
43C4×Dic157—21no—
44C22×C4×C157—21no—
45C22×C4×C157—21no—
46C22×C4×C157C2311yescharacteristic
47C2×C8×C157—21no—
48C2×C8×C157—21no—
49C2×C8×C157C2×C412yes—
50C4⋊C4×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157D412yes—
54Dic314—22no—
55Dic314—22no—
56Dic314—22no—
57Dic314C4⋊C414yescomplemented
58C2×Dic157—22no—
59C2×Dic157—22no—
60C2×Dic157—21no—
61C2×Dic157—22no—
62C2×Dic157—21no—
63C2×Dic157—22no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157—21no—
67C2×Dic157—41no—
68C2×Dic157—41no—
69C2×Dic157SD1612yes—
70#11929434—41no—
71C23×C157C2×D411yescharacteristic
72C2×C4×C157—22no—
73C2×C4×C157—41no—
74C2×C4×C157—41no—
75C2×C4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157—41no—
78C2×C4×C157C22×C411yescharacteristic
79C2×C4×C157C2×D411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C2×C4×C157C2×Q811yescharacteristic
82C2×C4×C157#4111yescharacteristic
83C2×C4×C157#4111yescharacteristic
84C8×C157—22no—
85C22×C157C4×D411yescharacteristic
86C22×C157#12011yescharacteristic
87C22×C157C22⋊Q811yescharacteristic
88C22×C157C2×SD1611yescharacteristic
89C22×C157#13511yescharacteristic
90C22×C157#13711yescharacteristic
91C22×C157#13711yescharacteristic
92C4×C157—42no—
93C4×C157—81no—
94C4×C157C2×C4⋊C411yescharacteristic
95C4×C157C4×D411yescharacteristic
96C4×C157C22⋊Q811yescharacteristic
97C4×C157#12311yescharacteristic
98Dic157—24no—
99Dic157—22no—
100Dic157—42no—
101Dic157—41no—
102C2×C157#38511yescharacteristic
103C2×C157C4×SD1611yescharacteristic
104C2×C157#44111yescharacteristic
105C2×C157#44811yescharacteristic
106C2×C157#45211yescharacteristic
107C2×C157#47511yescharacteristic
108C2×C157#47911yescharacteristic
109C157#186511yescharacteristic, complemented, Sylow
110#1865—1571nomaximal, Sylow
111C2×C4×Q8—1571no—
112C2×#106D15711yescharacteristic
113C2×#103—1571no—
114C2×#103—1571no—
115#389—1571no—
116#340—1571no—
117#336—1571no—
118C22×Q8—1571no—
119C22×C8—1571no—
120C22×C8C2×D15711yescharacteristic
121C4×Q8—3142no—
122C4×Q8—3142no—
123C2×C4⋊C4—3141no—
124C2×C4⋊C4—3141no—
125C2×C4⋊C4—1571no—
126C2×C4⋊C4C2×D15711yescharacteristic
127C2×C4⋊C4C2×D15711yescharacteristic
128C2×C42—3141no—
129C2×C42—1571no—
130#106—22no—
131#103—3142no—
132#103—1574no—
133#95—3141no—
134C2×Q8—3141no—
135C2×Q8—3141no—
136C2×Q8—3141no—
137C2×Q8—1572no—
138C2×Q8—1572no—
139C2×Q8—1572no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—3141no—
143C22×C4—3141no—
144C22×C4—1571no—
145C22×C4—1571no—
146C22×C4C22×D15711yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—3141no—
150C2×C8—3141no—
151C2×C8—3141no—
152C2×C8C4×D15712yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—3144no—
157C4⋊C4—3141no—
158C4⋊C4—6282no—
159C4⋊C4—1572no—
160C4⋊C4C22⋊D15712yes—
161C42—3144no—
162C42—3141no—
163C42—3141no—
164C23D4×D15711yescharacteristic
165Q8—3142no—
166Q8—3142no—
167Q8—3142no—
168Q8—1574no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—3142no—
176C2×C4—3141no—
177C2×C4—3142no—
178C2×C4—3142no—
179C2×C4—3141no—
180C2×C4—3142no—
181C2×C4—3141no—
182C2×C4—3141no—
183C2×C4—3141no—
184C2×C4—6281no—
185C2×C4—6281no—
186C2×C4—1572no—
187C2×C4C2×C4×D15711yescharacteristic
188C2×C4D4×D15711yescharacteristic
189C2×C4C2×C22⋊D15711yescharacteristic
190C2×C4Q8×D15711yescharacteristic
191C2×C4#1457895411yescharacteristic
192C2×C4#1457895511yescharacteristic
193C8—22no—
194C8—6281no—
195C22#1909773311yescharacteristic
196C22#1909773911yescharacteristic
197C22#1909774911yescharacteristic
198C22SD16×D15711yescharacteristic
199C22#1909779211yescharacteristic
200C22#1909780011yescharacteristic
201C22#1909780011yescharacteristic
202C4—42no—
203C4—81no—
204C4—3144no—
205C4—3142no—
206C4—6282no—
207C4—6281no—
208C4C4⋊C4×D15711yescharacteristic
209C4C4×C22⋊D15711yescharacteristic
210C4#1909774711yescharacteristic
211C4#1909775611yescharacteristic
212C2#2375714411yescharacteristic
213C2#2375736011yescharacteristic
214C2#2375737911yescharacteristic
215C2#2375741011yescharacteristic
216C2#2375743211yescharacteristic
217C2#2375755711yescharacteristic
218C2#2375758311yescharacteristic
subgroupG/H
centerC23D4×D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×#106×C157C2
socle, prime radicalC23×C157C2×D4
cosocleC22×C4×C157C23
hypercenterC2×#106D157
hypocenterC157#1865
LCSG ▷ C2×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
17. #19097696C4semidirect
57. Dic314C4⋊C4semidirect
109. C157#1865semidirect

Maximal subgroups

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

subgroupindex
C2×#190977362
C2×#190976962
C2×#190976942
#237571692
#237570352
#237570272
C2×#106×C1572
#1865157