Finite Group Databasebeta

← #34101237

Subgroups — #34101237

Order 20096.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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
2C22×#14578944C211yesmaximal, characteristic
3C2×#19097769C211yesmaximal, characteristic
4C2×#19097694C211yesmaximal, characteristic
5#23757178C211yesmaximal, characteristic
6#23757027C211yesmaximal, characteristic
7C2×#103×C157C211yesmaximal, characteristic
8C22×Dic314C2211yescharacteristic
9C22×Dic314C2211yescharacteristic
10C2×Dic628—22no—
11C2×Dic628—22no—
12C2×Dic628—22no—
13C2×#14578944—22no—
14C2×#14578944—22no—
15C2×#14578944—22no—
16C22×#11929434C2211yescharacteristic
17#19097769—22no—
18#19097769—22no—
19C2×#14578933—22no—
20C2×C4×Dic157C2211yescharacteristic
21#19097694—22no—
22#19097678—22no—
23C22×Q8×C157C2211yescharacteristic
24C22×C8×C157C2211yescharacteristic
25C2×C4⋊C4×C157C2211yescharacteristic
26#103×C157—22no—
27C2×Dic314—21no—
28C2×Dic314—21no—
29C2×Dic314—21no—
30C2×Dic314—21no—
31C2×Dic314—21no—
32C2×Dic314—21no—
33C2×Dic314—21no—
34C2×Dic314—21no—
35C2×Dic314—21no—
36C2×Dic314—21no—
37C2×Dic314D412yes—
38C2×Dic314D412yes—
39C22×Dic157—21no—
40C22×Dic157—21no—
41C22×Dic157D412yes—
42Dic628—28no—
43#14578944—28no—
44C2×#11929434—21no—
45C2×#11929434—21no—
46C2×#11929434D412yes—
47#14578933—28no—
48C4×Dic157—21no—
49C4×Dic157—21no—
50C2×Q8×C157—21no—
51C2×Q8×C157—21no—
52C2×Q8×C157—21no—
53C2×Q8×C157—21no—
54C2×Q8×C157—21no—
55C2×Q8×C157D412yes—
56C22×C4×C157—21no—
57C22×C4×C157—21no—
58C22×C4×C157C2311yescharacteristic
59C2×C8×C157—21no—
60C2×C8×C157—21no—
61C2×C8×C157D412yes—
62C4⋊C4×C157—21no—
63C4⋊C4×C157—21no—
64Dic314—22no—
65Dic314—22no—
66Dic314—22no—
67Dic314—22no—
68Dic314—41no—
69Dic314—41no—
70Dic314—41no—
71Dic314—41no—
72C2×Dic157—22no—
73C2×Dic157—22no—
74C2×Dic157—22no—
75C2×Dic157—22no—
76C2×Dic157—41no—
77C2×Dic157—41no—
78C2×Dic157—41no—
79C2×Dic157—41no—
80C2×Dic157Q1614yescomplemented
81#11929434—22no—
82C23×C157C2×D411yescharacteristic
83Q8×C157—22no—
84Q8×C157—22no—
85Q8×C157—41no—
86Q8×C157—41no—
87C2×C4×C157—22no—
88C2×C4×C157—41no—
89C2×C4×C157—41no—
90C2×C4×C157—41no—
91C2×C4×C157—42no—
92C2×C4×C157C2×D411yescharacteristic
93C2×C4×C157C2×D411yescharacteristic
94C2×C4×C157C2×D411yescharacteristic
95C2×C4×C157C2×D411yescharacteristic
96C2×C4×C157C2×D411yescharacteristic
97C2×C4×C157#4111yescharacteristic
98C8×C157—22no—
99C22×C157#12011yescharacteristic
100C22×C157#12111yescharacteristic
101C22×C157#12711yescharacteristic
102C22×C157C2×Q1612yes—
103C22×C157#13712yes—
104C4×C157—42no—
105C4×C157—81no—
106C4×C157#12011yescharacteristic
107C4×C157#12011yescharacteristic
108C4×C157#12111yescharacteristic
109C4×C157#12111yescharacteristic
110Dic157—24no—
111Dic157—42no—
112Dic157—42no—
113C2×C157#39211yescharacteristic
114C2×C157#45112yes—
115C2×C157#46212yes—
116C2×C157#49411yescharacteristic
117C2×C157#49711yescharacteristic
118C157#201611yescharacteristic, complemented, Sylow
119#2016—1571nomaximal, Sylow
120C22×Q16—1571no—
121C22×Q16—1571no—
122C2×C4⋊Q8—1571no—
123C2×#103—1571no—
124C2×#103D15711yescharacteristic
125#391—1571no—
126#336—1571no—
127C22×Q8—1571no—
128C22×Q8—1571no—
129C22×Q8C2×D15711yescharacteristic
130C2×Q16—3142no—
131C2×Q16—3142no—
132C2×Q16—3142no—
133C2×Q16—3142no—
134C2×Q16—3142no—
135C2×Q16—3142no—
136C22×C8—1571no—
137C22×C8C2×D15711yescharacteristic
138C4⋊Q8—3142no—
139C4⋊Q8—3142no—
140C2×C4⋊C4—3142no—
141C2×C4⋊C4C2×D15711yescharacteristic
142C2×C42—1571no—
143#103—22no—
144#103—3142no—
145#95—3142no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—3141no—
152C2×Q8—3141no—
153C2×Q8—3141no—
154C2×Q8—3141no—
155C2×Q8—3141no—
156C2×Q8—3141no—
157C2×Q8—3141no—
158C2×Q8—3141no—
159C2×Q8—3141no—
160C2×Q8—3141no—
161C2×Q8—1572no—
162C2×Q8—1572no—
163C2×Q8D62812yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—3141no—
167C22×C4—3141no—
168C22×C4—1572no—
169C22×C4C22×D15711yescharacteristic
170Q16—3148no—
171Q16—3148no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—3141no—
175C2×C8—3141no—
176C2×C8—1572no—
177C2×C8C22⋊D15712yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—3148no—
181C42—3141no—
182C42—3141no—
183C23D4×D15711yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8—3142no—
189Q8—3142no—
190Q8—3142no—
191Q8—3142no—
192Q8—6281no—
193Q8—6281no—
194Q8—6281no—
195Q8—6281no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—3142no—
202C2×C4—3142no—
203C2×C4—3142no—
204C2×C4—3142no—
205C2×C4—6281no—
206C2×C4—6281no—
207C2×C4—6281no—
208C2×C4—6281no—
209C2×C4—1574no—
210C2×C4D4×D15711yescharacteristic
211C2×C4D4×D15711yescharacteristic
212C2×C4D4×D15711yescharacteristic
213C2×C4C2×C22⋊D15711yescharacteristic
214C2×C4C2×D62811yescharacteristic
215C2×C4#1457895411yescharacteristic
216C8—22no—
217C8—3142no—
218C22#1909774111yescharacteristic
219C22#1909774411yescharacteristic
220C22#1909776711yescharacteristic
221C22Q16×D15712yes—
222C22#1909780012yes—
223C4—42no—
224C4—81no—
225C4—3144no—
226C4—6282no—
227C4—6282no—
228C4#1909773911yescharacteristic
229C4#1909774111yescharacteristic
230C4#1909774411yescharacteristic
231C4#1909774511yescharacteristic
232C2#2375718211yescharacteristic
233C2#2375743012yes—
234C2#2375748212yes—
235C2#2375765111yescharacteristic
236C2#2375766411yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#103×C157C2
socle, prime radicalC23×C157C2×D4
hypercenterC2×#103D157
hypocenterC157#2016
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
80. C2×Dic157Q16semidirect
118. C157#2016semidirect

Maximal subgroups

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

subgroupindex
C22×Dic6282
C22×#145789442
C2×#190977692
C2×#190976942
#237571782
#237570272
C2×#103×C1572
#2016157