Finite Group Databasebeta

← #34100478

Subgroups — #34100478

Order 20096.

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

normal subgroups only

This group has 338 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
1C22×Dic628C211yesmaximal, characteristic
2C2×#19097736C211yesmaximal, characteristic
3C2×#19097694C211yesmaximal, characteristic
4C2×#19097694C211yesmaximal, characteristic
5#23757178C211yesmaximal, characteristic
6#23757027C211yesmaximal, characteristic
7#340×C157C211yesmaximal, characteristic
8C22×Dic314C2211yescharacteristic
9C22×Dic314C2211yescharacteristic
10C2×Dic628—22no—
11C2×Dic628—22no—
12C2×Dic628C414yescomplemented
13C22×#11929434C2211yescharacteristic
14#19097736—22no—
15#19097736—22no—
16C2×#14578933—21no—
17C2×C4×Dic157—21no—
18C2×C4×Dic157C2211yescharacteristic
19#19097694—22no—
20#19097694—22no—
21#19097678—21no—
22#19097678—21no—
23C22×C8×C157C2211yescharacteristic
24C2×C4⋊C4×C157C2211yescharacteristic
25C2×C4⋊C4×C157C2211yescharacteristic
26C2×Dic314—21no—
27C2×Dic314—21no—
28C2×Dic314—21no—
29C2×Dic314—21no—
30C2×Dic314—21no—
31C2×Dic314—21no—
32C2×Dic314—21no—
33C2×Dic314—21no—
34C2×Dic314C2×C412yes—
35C2×Dic314C2×C412yes—
36C2×Dic314D412yes—
37C2×Dic314D412yes—
38C22×Dic157—21no—
39C22×Dic157—21no—
40C22×Dic157D411yescharacteristic
41C22×Dic157D411yescharacteristic
42Dic628—28no—
43C2×#11929434—21no—
44C2×#11929434—21no—
45C2×#11929434—21no—
46#14578933—24no—
47C4×Dic157—24no—
48C4×Dic157—21no—
49C4×Dic157—21no—
50C22×C4×C157—21no—
51C22×C4×C157—21no—
52C22×C4×C157C2311yescharacteristic
53C2×C8×C157—21no—
54C2×C8×C157—21no—
55C2×C8×C157C2×C412yes—
56C4⋊C4×C157—21no—
57C4⋊C4×C157—21no—
58C4⋊C4×C157—21no—
59C4⋊C4×C157D412yes—
60Dic314—22no—
61Dic314—22no—
62Dic314—22no—
63Dic314—22no—
64Dic314—22no—
65Dic314—41no—
66Dic314—41no—
67Dic314C22⋊C414yes—
68C2×Dic157—22no—
69C2×Dic157—22no—
70C2×Dic157—21no—
71C2×Dic157—22no—
72C2×Dic157—21no—
73C2×Dic157—22no—
74C2×Dic157—21no—
75C2×Dic157—21no—
76C2×Dic157—21no—
77C2×Dic157—41no—
78C2×Dic157—41no—
79C2×Dic157Q1612yescomplemented
80#11929434—41no—
81C23×C157C2×D411yescharacteristic
82C2×C4×C157—22no—
83C2×C4×C157—41no—
84C2×C4×C157—41no—
85C2×C4×C157—41no—
86C2×C4×C157—41no—
87C2×C4×C157—41no—
88C2×C4×C157C22×C411yescharacteristic
89C2×C4×C157C2×D411yescharacteristic
90C2×C4×C157C2×D411yescharacteristic
91C2×C4×C157C2×D411yescharacteristic
92C2×C4×C157#4111yescharacteristic
93C2×C4×C157#4111yescharacteristic
94C8×C157—22no—
95C22×C157C4×D411yescharacteristic
96C22×C157#12011yescharacteristic
97C22×C157#12111yescharacteristic
98C22×C157C2×Q1611yescharacteristic
99C22×C157#13511yescharacteristic
100C22×C157#13711yescharacteristic
101C22×C157#13711yescharacteristic
102C4×C157—42no—
103C4×C157—81no—
104C4×C157C2×C22⋊C411yescharacteristic
105C4×C157C4×D411yescharacteristic
106C4×C157#12111yescharacteristic
107C4×C157#12311yescharacteristic
108Dic157—24no—
109Dic157—22no—
110Dic157—42no—
111Dic157—41no—
112C2×C157#38611yescharacteristic
113C2×C157C4×Q1611yescharacteristic
114C2×C157#44111yescharacteristic
115C2×C157#45111yescharacteristic
116C2×C157#45211yescharacteristic
117C2×C157#46211yescharacteristic
118C2×C157#46411yescharacteristic
119C157#187811yescharacteristic, complemented, Sylow
120#1878—1571nomaximal, Sylow
121C22×Q16—1571no—
122C2×C4×Q8—1571no—
123C2×#103—1571no—
124C2×#103—1571no—
125#391—1571no—
126#340D15711yescharacteristic
127#336—1571no—
128C22×Q8—1571no—
129C22×Q8—1571no—
130C2×Q16—3142no—
131C2×Q16—3142no—
132C2×Q16—1574no—
133C22×C8—1571no—
134C22×C8C2×D15711yescharacteristic
135C4×Q8—3142no—
136C4×Q8—3142no—
137C2×C4⋊C4—3141no—
138C2×C4⋊C4C2×D15711yescharacteristic
139C2×C4⋊C4C2×D15711yescharacteristic
140C2×C42—3141no—
141C2×C42—1571no—
142#103—3142no—
143#103—3142no—
144#95—3141no—
145#95—3141no—
146C2×Q8—3141no—
147C2×Q8—3141no—
148C2×Q8—3141no—
149C2×Q8—3141no—
150C2×Q8—3141no—
151C2×Q8—3141no—
152C2×Q8—3141no—
153C2×Q8—3141no—
154C2×Q8—1572no—
155C2×Q8—1572no—
156C2×Q8—1572no—
157C2×Q8—1572no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—3141no—
161C22×C4—3141no—
162C22×C4—1571no—
163C22×C4—1571no—
164C22×C4C22×D15711yescharacteristic
165Q16—3148no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—3141no—
169C2×C8—3141no—
170C2×C8—3141no—
171C2×C8C4×D15712yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—3144no—
176C4⋊C4D62812yes—
177C42—3144no—
178C42—3141no—
179C42—3141no—
180C23D4×D15711yescharacteristic
181Q8—3142no—
182Q8—3142no—
183Q8—3142no—
184Q8—3142no—
185Q8—3142no—
186Q8—6281no—
187Q8—6281no—
188Q8—1574no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—3142no—
196C2×C4—3141no—
197C2×C4—3142no—
198C2×C4—3142no—
199C2×C4—3141no—
200C2×C4—3142no—
201C2×C4—3141no—
202C2×C4—3141no—
203C2×C4—3141no—
204C2×C4—6281no—
205C2×C4—6281no—
206C2×C4—1572no—
207C2×C4C2×C4×D15711yescharacteristic
208C2×C4D4×D15711yescharacteristic
209C2×C4D4×D15711yescharacteristic
210C2×C4C2×D62811yescharacteristic
211C2×C4#1457895411yescharacteristic
212C2×C4#1457895511yescharacteristic
213C8—22no—
214C8—6281no—
215C22#1909773311yescharacteristic
216C22#1909774111yescharacteristic
217C22#1909774411yescharacteristic
218C22Q16×D15711yescharacteristic
219C22#1909779011yescharacteristic
220C22#1909780011yescharacteristic
221C22#1909780011yescharacteristic
222C4—42no—
223C4—81no—
224C4—3144no—
225C4—3142no—
226C4—6282no—
227C4—6281no—
228C4C22⋊C4×D15711yescharacteristic
229C4C4×D62811yescharacteristic
230C4#1909774611yescharacteristic
231C4#1909775611yescharacteristic
232C2#2375715111yescharacteristic
233C2#2375736711yescharacteristic
234C2#2375737911yescharacteristic
235C2#2375743011yescharacteristic
236C2#2375743611yescharacteristic
237C2#2375748211yescharacteristic
238C2#2375749411yescharacteristic
subgroupG/H
centerC23D4×D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#340×C157C2
socle, prime radicalC23×C157C2×D4
cosocleC22×C4×C157C23
hypercenter#340D157
hypocenterC157#1878
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
12. C2×Dic628C4semidirect
79. C2×Dic157Q16semidirect
119. C157#1878semidirect

Maximal subgroups

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

subgroupindex
C22×Dic6282
C2×#190977362
C2×#190976942
#237571782
#237570272
#340×C1572
#1878157