Finite Group Databasebeta

← #34101040

Subgroups — #34101040

Order 20096.

296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14578941C211yesmaximal, characteristic
2C2×#19097706C211yesmaximal, characteristic, complemented
3#23757282C211yesmaximal, characteristic, complemented
4#23757279C211yesmaximal, characteristic
5C2×#19097687C211yesmaximal, characteristic
6#23757231C211yesmaximal, characteristic, complemented
7C2×#101×C157C211yesmaximal, characteristic, complemented
8C22×D628C2211yescharacteristic
9C2×#14578941—21no—
10C2×#14578941—21no—
11C2×#14578941—22no—
12C2×#14578941C414yescomplemented
13C2×#14578938C2211yescharacteristic
14C22×#11929434C2211yescharacteristic
15#19097730C2211yescharacteristic
16#19097706—22no—
17#19097695—22no—
18#19097693—22no—
19#19097687—22no—
20#19097681—21no—
21C8×Dic157—21no—
22C22×Q8×C157C2211yescharacteristic
23C2×M16×C157C2211yescharacteristic
24C2×M16×C157C2211yescharacteristic
25#101×C157—22no—
26C23×D157—21no—
27C2×D628—21no—
28C2×D628—21no—
29C2×D628—21no—
30C2×D628—21no—
31C2×D628—21no—
32C2×D628C2×C412yes—
33#14578941—24no—
34#14578941—24no—
35#14578938—21no—
36#14578938—21no—
37C2×#11929434—21no—
38C2×#11929434C2×C412yes—
39C2×#11929434D411yescharacteristic
40C2×#11929434D411yescharacteristic
41C2×#11929434D412yes—
42C4⋊Dic157D412yes—
43C22⋊Dic157—21no—
44C4×Dic157—21no—
45C2×Q8×C157—21no—
46C2×Q8×C157—21no—
47C2×Q8×C157—21no—
48C2×Q8×C157—21no—
49C2×Q8×C157—21no—
50C2×Q8×C157C2×C412yes—
51C22×C4×C157—21no—
52C22×C4×C157C2311yescharacteristic
53M16×C157—21no—
54M16×C157—21no—
55M16×C157—21no—
56M16×C157D412yes—
57C2×C8×C157—21no—
58C2×C8×C157—21no—
59C22×D157—22no—
60C22×D157—41no—
61C22×D157—41no—
62C22×D157—82no—
63D628—22no—
64D628—22no—
65D628—41no—
66D628—41no—
67C2×Dic157—22no—
68#11929434—41no—
69#11929434C22⋊C412yes—
70#11929434C22⋊C412yes—
71C23×C157#4111yescharacteristic
72Q8×C157—22no—
73Q8×C157—22no—
74Q8×C157—41no—
75Q8×C157—41no—
76C2×C4×C157—22no—
77C2×C4×C157—41no—
78C2×C4×C157—41no—
79C2×C4×C157C22×C411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C2×C4×C157C2×D411yescharacteristic
82C2×C4×C157C2×D411yescharacteristic
83C2×C4×C157C2×D411yescharacteristic
84C2×C4×C157#4111yescharacteristic
85C8×C157—22no—
86C8×C157—41no—
87C22×C157—22no—
88C22×C157C4×D411yescharacteristic
89C22×C157#12111yescharacteristic
90C22×C157#12411yescharacteristic
91C2×D157—42no—
92C2×D157—82no—
93C2×D157—82no—
94C2×D157—82no—
95C4×C157—42no—
96C4×C157C2×C22⋊C411yescharacteristic
97C4×C157C4×D411yescharacteristic
98C4×C157#12111yescharacteristic
99C4×C157#12711yescharacteristic
100Dic157—42no—
101C2×C157—21no—
102C2×C157—21no—
103C2×C157#39011yescharacteristic
104C2×C157#47112yes—
105D157—82no—
106C157#197711yescharacteristic, complemented, Sylow
107#1977—1571nomaximal, Sylow
108C22×SD16—1571no—
109C2×#108—1571no—
110#419—1571no—
111#418—1571no—
112C2×#101D15711yescharacteristic, complemented
113C2×#100—1571no—
114#405—1571no—
115C22×Q8C2×D15711yescharacteristic
116C22×D4—1571no—
117C2×SD16—3141no—
118C2×SD16—3141no—
119C2×SD16—3142no—
120C2×SD16—1574no—
121C2×M16—1571no—
122C2×M16C2×D15711yescharacteristic
123C2×M16C2×D15711yescharacteristic
124C22×C8—1571no—
125#117—1571no—
126#108—3142no—
127#103—3142no—
128#102—3142no—
129#101—22no—
130#100—3142no—
131#97—3141no—
132C4×C8—3141no—
133C24—3141no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8C4×D15712yes—
140C2×D4—3141no—
141C2×D4—3141no—
142C2×D4—3141no—
143C2×D4—3141no—
144C2×D4—3141no—
145C2×D4—1572no—
146C22×C4—21no—
147C22×C4C22×D15711yescharacteristic
148SD16—3144no—
149SD16—3144no—
150M16—21no—
151M16—21no—
152M16—21no—
153M16—3141no—
154M16—3141no—
155M16C22⋊D15712yes—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—3141no—
159C2×C8—1572no—
160C2×C8—1571no—
161C2×C8—1571no—
162C2×C8—1572no—
163C4⋊C4—1572no—
164C22⋊C4—3141no—
165C42—3141no—
166C23—3142no—
167C23—6281no—
168C23—6281no—
169C23—12562no—
170C23#1457895411yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—41no—
174Q8—41no—
175D4—3142no—
176D4—3142no—
177D4—6281no—
178D4—6281no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—3142no—
183C2×C4C2×C4×D15711yescharacteristic
184C2×C4D4×D15711yescharacteristic
185C2×C4D4×D15711yescharacteristic
186C2×C4D4×D15711yescharacteristic
187C2×C4C2×C22⋊D15711yescharacteristic
188C2×C4#1457895311yescharacteristic
189C8—22no—
190C8—41no—
191C8—6281no—
192C8—1572no—
193C8—1572no—
194C22—22no—
195C22—6282no—
196C22—12562no—
197C22—12562no—
198C22—12562no—
199C22C4×C22⋊D15711yescharacteristic
200C22#1909774411yescharacteristic
201C22#1909775711yescharacteristic
202C4—42no—
203C4—6282no—
204C4C22⋊C4×D15711yescharacteristic
205C4#1909773111yescharacteristic
206C4#1909774311yescharacteristic
207C4#1909776711yescharacteristic
208C2—21no—
209C2—21no—
210C2—12562no—
211C2#2375717311yescharacteristic
212C2#2375753912yes—
subgroupG/H
centerC22#19097744
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×#101×C157C2
socleC22×C157#121
prime radicalC22×D628C22
cosocleC22×C4×C157C23
hypercenterC2×#101D157
hypocenterC157#1977
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#19097706C2semidirect
3. #23757282C2semidirect
6. #23757231C2semidirect
7. C2×#101×C157C2semidirect
12. C2×#14578941C4semidirect
106. C157#1977semidirect
112. C2×#101D157semidirect

Maximal subgroups

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

subgroupindex
C22×#145789412
C2×#190977062
#237572822
#237572792
C2×#190976872
#237572312
C2×#101×C1572
#1977157