Finite Group Databasebeta

← #34101275

Subgroups — #34101275

Order 20096.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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×#19097770C211yesmaximal, characteristic
2C2×#19097695C211yesmaximal, characteristic
3#23757180C211yesmaximal, characteristic
4#23757036C211yesmaximal, characteristic
5#23757035C211yesmaximal, characteristic
6#23757027C211yesmaximal, characteristic
7C2×#103×C157C211yesmaximal, characteristic
8C22×Dic314—21no—
9C22×#11929434C2211yescharacteristic
10#19097770—22no—
11#19097770—22no—
12C2×C4⋊Dic157C2211yescharacteristic
13C2×C4⋊Dic157C2211yescharacteristic
14C2×#14578933—21no—
15C2×C4×Dic157C2211yescharacteristic
16#19097695—22no—
17#19097678—21no—
18#19097678—21no—
19C22×Q8×C157C2211yescharacteristic
20C22×C8×C157C2211yescharacteristic
21C2×C4⋊C4×C157C2211yescharacteristic
22#103×C157—22no—
23C2×Dic314—24no—
24C2×Dic314—42no—
25C2×Dic314—42no—
26C22×Dic157—21no—
27C22×Dic157—21no—
28C22×Dic157D411yescharacteristic
29C22×Dic157D411yescharacteristic
30C2×#11929434—21no—
31C2×#11929434—21no—
32C2×#11929434—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157D412yes—
37#14578933—24no—
38C4×Dic157—21no—
39C4×Dic157—21no—
40C2×Q8×C157—21no—
41C2×Q8×C157—21no—
42C2×Q8×C157—21no—
43C2×Q8×C157—21no—
44C2×Q8×C157—21no—
45C2×Q8×C157Q812yescomplemented
46C22×C4×C157—21no—
47C22×C4×C157—21no—
48C22×C4×C157C2311yescharacteristic
49C2×C8×C157—21no—
50C2×C8×C157—21no—
51C2×C8×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157D412yes—
54Dic314—48no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157—22no—
60C2×Dic157—41no—
61C2×Dic157—41no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64C2×Dic157—41no—
65C2×Dic157SD1612yes—
66C2×Dic157Q1612yes—
67#11929434—41no—
68C23×C157C2×D411yescharacteristic
69Q8×C157—22no—
70Q8×C157—22no—
71Q8×C157—41no—
72Q8×C157—41no—
73C2×C4×C157—22no—
74C2×C4×C157—22no—
75C2×C4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157—41no—
78C2×C4×C157—41no—
79C2×C4×C157C2×D411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C2×C4×C157C2×Q811yescharacteristic
82C2×C4×C157#4111yescharacteristic
83C2×C4×C157#4111yescharacteristic
84C2×C4×C157#4111yescharacteristic
85C8×C157—41no—
86C22×C157#12011yescharacteristic
87C22×C157C22⋊Q811yescharacteristic
88C22×C157#12411yescharacteristic
89C22×C157C2×SD1611yescharacteristic
90C22×C157C2×Q1611yescharacteristic
91C22×C157AGL(1,ℤ/8)11yescharacteristic
92C22×C157#13711yescharacteristic
93C4×C157—42no—
94C4×C157—42no—
95C4×C157C22⋊Q811yescharacteristic
96C4×C157C22⋊Q811yescharacteristic
97C4×C157#12411yescharacteristic
98C4×C157#12411yescharacteristic
99Dic157—22no—
100Dic157—22no—
101Dic157—42no—
102Dic157—81no—
103C2×C157#39311yescharacteristic
104C2×C157#45011yescharacteristic
105C2×C157#45111yescharacteristic
106C2×C157#47511yescharacteristic
107C2×C157#47711yescharacteristic
108C2×C157#48711yescharacteristic
109C2×C157#48911yescharacteristic
110C157#202411yescharacteristic, complemented, Sylow
111#2024—1571nomaximal, Sylow
112C2×C4⋊Q8—1571no—
113C2×#103—1571no—
114C2×#103D15711yescharacteristic
115#391—1571no—
116#340—1571no—
117#340—1571no—
118#336—1571no—
119C22×Q8—3141no—
120C22×Q8C2×D15711yescharacteristic
121C22×C8—1571no—
122C22×C8C2×D15711yescharacteristic
123C4⋊Q8—3142no—
124C4⋊Q8—3142no—
125C2×C4⋊C4—3141no—
126C2×C4⋊C4—1571no—
127C2×C4⋊C4—1571no—
128C2×C4⋊C4C2×D15711yescharacteristic
129C2×C42—1571no—
130#103—22no—
131#103—3142no—
132#95—3141no—
133#95—3141no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—3144no—
140C2×Q8—6282no—
141C2×Q8—6282no—
142C2×Q8Dic31412yescomplemented
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—3141no—
146C22×C4—3141no—
147C22×C4—1571no—
148C22×C4—1571no—
149C22×C4C22×D15711yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—3141no—
154C2×C8—3141no—
155C2×C8—3141no—
156C4⋊C4—21no—
157C4⋊C4—3144no—
158C4⋊C4—3141no—
159C4⋊C4—3141no—
160C4⋊C4—3141no—
161C4⋊C4—1572no—
162C4⋊C4C22⋊D15712yes—
163C42—3141no—
164C42—3141no—
165C23D4×D15711yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—6288no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—3141no—
178C2×C4—3141no—
179C2×C4—3141no—
180C2×C4—3141no—
181C2×C4—3142no—
182C2×C4—6281no—
183C2×C4—6281no—
184C2×C4—6281no—
185C2×C4—6281no—
186C2×C4—6281no—
187C2×C4—1572no—
188C2×C4—1572no—
189C2×C4D4×D15711yescharacteristic
190C2×C4C2×C22⋊D15711yescharacteristic
191C2×C4C2×Dic31411yescharacteristic
192C2×C4#1457895311yescharacteristic
193C2×C4#1457895311yescharacteristic
194C2×C4#1457895411yescharacteristic
195C8—41no—
196C8—6281no—
197C22#1909773911yescharacteristic
198C22#1909774811yescharacteristic
199C22#1909775711yescharacteristic
200C22SD16×D15711yescharacteristic
201C22Q16×D15711yescharacteristic
202C22#1909779811yescharacteristic
203C22#1909780311yescharacteristic
204C4—42no—
205C4—42no—
206C4—3142no—
207C4—3142no—
208C4—6282no—
209C4—12561no—
210C4#1909774811yescharacteristic
211C4#1909775011yescharacteristic
212C4#1909775711yescharacteristic
213C4#1909775811yescharacteristic
214C2#2375718511yescharacteristic
215C2#2375742211yescharacteristic
216C2#2375742711yescharacteristic
217C2#2375755611yescharacteristic
218C2#2375756611yescharacteristic
219C2#2375762211yescharacteristic
220C2#2375763411yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#103×C157C2
socle, prime radicalC23×C157C2×D4
hypercenterC2×#103D157
hypocenterC157#2024
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
45. C2×Q8×C157Q8semidirect
110. C157#2024semidirect
142. C2×Q8Dic314semidirect

Maximal subgroups

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

subgroupindex
C2×#190977702
C2×#190976952
#237571802
#237570362
#237570352
#237570272
C2×#103×C1572
#2024157