Finite Group Databasebeta

← #34113169

Subgroups — #34113169

Order 20096.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#23758002C211yesmaximal, characteristic, complemented
2#23757996C211yesmaximal, characteristic
3#23757667C212yesmaximal
4#23757653C211yesmaximal, characteristic, complemented
5#23757496C212yesmaximal
6#23757484C211yesmaximal, characteristic, complemented
7#23757484C212yesmaximal, complemented
8#23757479C211yesmaximal, characteristic
9#23757381C212yesmaximal, complemented
10C4×#14578943C211yesmaximal, characteristic
11#446×C157C211yesmaximal, characteristic, complemented
12C2×Dic628C2212yes—
13C2×Dic628C2212yes—
14C2×Dic628C2212yes—
15C2×#14578943C2211yescharacteristic
16C2×#14578943C2212yes—
17#19097771C2211yescharacteristic
18#19097771C2211yescharacteristic
19#19097771C2212yes—
20#19097766—22no—
21#19097762—21no—
22#19097762—22no—
23#19097759C2212yes—
24#19097747—21no—
25Q8×Dic157—21no—
26C4×Dic314C2211yescharacteristic
27C4×Dic314C2212yes—
28C4×Dic314C2212yes—
29C4×D628C2211yescharacteristic
30#19097729—21no—
31#19097703C2211yescharacteristic
32#19097696C2211yescharacteristic
33#19097696C2212yes—
34#19097696C2212yes—
35#19097693C2211yescharacteristic
36C4×Q8×C157C2211yescharacteristic
37C4⋊C8×C157C2211yescharacteristic
38C4⋊C8×C157C2212yes—
39#97×C157C2212yes—
40C4×C8×C157C2211yescharacteristic
41C2×Dic314C2312yes—
42C2×Dic314C2312yes—
43C2×Dic314C2311yescharacteristic
44C2×D628C2311yescharacteristic
45C2×C4×D157—21no—
46Dic628—24no—
47Dic628—42no—
48Dic628—42no—
49#14578943—22no—
50#14578943—42no—
51C4⋊Dic157—21no—
52C4⋊Dic157—22no—
53C4⋊Dic157—21no—
54C4⋊Dic157—22no—
55C4⋊Dic157—21no—
56C4⋊Dic157—21no—
57C4⋊Dic157C2311yescharacteristic
58C4⋊Dic157C2311yescharacteristic
59#14578933—22no—
60#14578933—22no—
61#14578933—21no—
62#14578931—22no—
63#14578931—21no—
64#14578931—22no—
65C4×Dic157—22no—
66C4×Dic157—22no—
67C4×Dic157—21no—
68C2×Q8×C157D411yescharacteristic
69C2×C8×C157C2311yescharacteristic
70C2×C8×C157C2312yes—
71C2×C8×C157C2311yescharacteristic
72C4⋊C4×C157D411yescharacteristic
73C4⋊C4×C157D412yes—
74C42×C157C2311yescharacteristic
75C42×C157C2312yes—
76C22×D157—21no—
77Dic314—22no—
78Dic314—22no—
79Dic314—21no—
80Dic314—22no—
81Dic314—21no—
82Dic314—22no—
83D628—21no—
84D628—21no—
85C2×Dic157—21no—
86C2×Dic157—22no—
87C2×Dic157—22no—
88C2×Dic157—21no—
89C2×Dic157—21no—
90C4×D157—42no—
91Q8×C157—22no—
92C2×C4×C157C2×D412yes—
93C2×C4×C157C2×D411yescharacteristic
94C2×C4×C157C2×D412yes—
95C2×C4×C157C2×D411yescharacteristic
96C2×C4×C157C2411yescharacteristic
97C8×C157—21no—
98C8×C157—22no—
99C8×C157#4112yes—
100C22×C157C22×D411yescharacteristic
101C2×D157—41no—
102C2×D157—41no—
103C2×D157—41no—
104C4×C157—22no—
105C4×C157—22no—
106C4×C157—21no—
107C4×C157#13712yes—
108C4×C157C2×#4111yescharacteristic
109C4×C157H(5,𝔽2)11yescharacteristic
110Dic157—42no—
111Dic157—42no—
112Dic157—41no—
113Dic157—41no—
114Dic157—41no—
115C2×C157#55011yescharacteristic
116C2×C157C2×#13711yescharacteristic
117C2×C157#57811yescharacteristic
118D157—81no—
119C157#339811yescharacteristic, complemented, Sylow
120#3398—1571nomaximal, Sylow
121#557—1571no—
122#556—1571no—
123#497—1572no—
124#494—1571no—
125#464—1572no—
126#462—1572no—
127#462—1571no—
128#461—1571no—
129#446D15711yescharacteristic, complemented
130#441—1572no—
131C4×SD16—1571no—
132C2×Q16—1572no—
133C2×Q16—1572no—
134C2×Q16—1572no—
135C2×SD16—1571no—
136C2×SD16—1572no—
137C4⋊Q8—1571no—
138C4⋊Q8—1571no—
139C4⋊Q8—1572no—
140#126—3142no—
141#125—3141no—
142#125—3142no—
143#124—1572no—
144C22⋊Q8—3141no—
145C4×Q8—3141no—
146C4×Q8—1572no—
147C4×Q8—1571no—
148C4×Q8—1572no—
149C4×Q8C2×D15711yescharacteristic
150C4×D4—1571no—
151#117—3141no—
152#106—1571no—
153C4⋊C8C2×D15711yescharacteristic
154C4⋊C8C2×D15712yes—
155#103—1571no—
156#103—1572no—
157#103—1572no—
158#102—1571no—
159#97C2×D15712yes—
160C4×C8C2×D15711yescharacteristic
161C2×Q8—1572no—
162C2×Q8—1571no—
163C2×Q8—1572no—
164C2×Q8D62811yescharacteristic
165C2×D4—1571no—
166C22×C4—3141no—
167Q16—3144no—
168Q16—6282no—
169Q16—6282no—
170SD16—3142no—
171SD16—6282no—
172C2×C8C22×D15711yescharacteristic
173C2×C8C22×D15712yes—
174C2×C8C22×D15711yescharacteristic
175C4⋊C4—3141no—
176C4⋊C4—3142no—
177C4⋊C4—3141no—
178C4⋊C4—3142no—
179C4⋊C4—3142no—
180C4⋊C4—3141no—
181C4⋊C4—3142no—
182C4⋊C4—3141no—
183C4⋊C4—3141no—
184C4⋊C4—1571no—
185C4⋊C4—1571no—
186C4⋊C4D62811yescharacteristic
187C4⋊C4D62812yes—
188C22⋊C4—3142no—
189C22⋊C4—3141no—
190C22⋊C4—3142no—
191C42—3142no—
192C42—3142no—
193C42—3141no—
194C42C22×D15711yescharacteristic
195C42C22×D15712yes—
196C23—3141no—
197Q8—22no—
198Q8—3141no—
199Q8—3142no—
200Q8—3142no—
201Q8—3142no—
202Q8—3142no—
203Q8—3141no—
204D4—3141no—
205D4—3141no—
206C2×C4—3141no—
207C2×C4—3141no—
208C2×C4—3142no—
209C2×C4—3141no—
210C2×C4—3142no—
211C2×C4—6282no—
212C2×C4C2×D62812yes—
213C2×C4C2×D62812yes—
214C2×C4C2×D62811yescharacteristic
215C2×C4C2×D62811yescharacteristic
216C2×C4C23×D15711yescharacteristic
217C8—22no—
218C8—21no—
219C8#1457895512yes—
220C22—6281no—
221C22—6281no—
222C22—6281no—
223C22C22×D62811yescharacteristic
224C4—22no—
225C4—21no—
226C4—22no—
227C4—6281no—
228C4—6282no—
229C4—6281no—
230C4—6282no—
231C4—6281no—
232C4#1909780412yes—
233C4C2×#1457895511yescharacteristic
234C4#1909781711yescharacteristic
235C2—12561no—
236C2#2375794511yescharacteristic
237C2C2×#1909780411yescharacteristic
238C2#2375809011yescharacteristic
subgroupG/H
centerC22C22×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#446×C157C2
socleC22×C157C22×D4
prime radicalC2×D628C23
hypercenter#446D157
hypocenterC157#3398
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #23758002C2semidirect
4. #23757653C2semidirect
6. #23757484C2semidirect
7. #23757484C2semidirect
9. #23757381C2semidirect
11. #446×C157C2semidirect
119. C157#3398semidirect
129. #446D157semidirect

Maximal subgroups

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

subgroupindex
#237580022
#237579962
#237576672
#237576532
#237574962
#237574842
#237574792
#237573812
C4×#145789432
#446×C1572
#3398157