Finite Group Databasebeta

← #34100460

Subgroups — #34100460

Order 20096.

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

normal subgroups only

This group has 324 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
1C2×#19097791C211yesmaximal, characteristic
2C2×#19097779C211yesmaximal, characteristic, complemented
3C2×#19097699C211yesmaximal, characteristic, complemented
4#23757240C211yesmaximal, characteristic, complemented
5#23757037C211yesmaximal, characteristic, complemented
6#23757028C211yesmaximal, characteristic, complemented
7C2×#104×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9#19097791—22no—
10#19097791—22no—
11C2×#14578944C411yescharacteristic, complemented
12C2×#14578942C411yescharacteristic, complemented
13C2×#14578941C411yescharacteristic, complemented
14C2×#14578939C411yescharacteristic, complemented
15#19097779—22no—
16#19097779—22no—
17C2×#14578938C2211yescharacteristic
18C2×#14578937—21no—
19C22×#11929434C2211yescharacteristic
20C22×#11929434C2211yescharacteristic
21C2×C8×D157—21no—
22#19097699—22no—
23C22⋊#11929434—21no—
24C22⋊#11929434—21no—
25C2×#41×C157C2211yescharacteristic
26C2×M16×C157C2211yescharacteristic
27C2×C42×C157C2211yescharacteristic
28#104×C157—22no—
29#14578954—21no—
30#14578954—21no—
31#14578954D412yes—
32#14578954D412yes—
33C2×Dic314C2×C411yescharacteristic
34C2×D628C2×C411yescharacteristic
35C2×C22⋊D157—21no—
36C2×C4×D157—21no—
37#14578944—22no—
38#14578942—22no—
39#14578941—22no—
40#14578939—22no—
41#14578938—21no—
42#14578938—21no—
43#14578937—24no—
44C2×#11929434—21no—
45C2×#11929434—21no—
46C2×#11929434—21no—
47C2×#11929434—21no—
48C2×#11929434—21no—
49C2×#11929434C2×C411yescharacteristic
50C2×#11929434C2×C411yescharacteristic
51C2×#11929434D411yescharacteristic
52C2×#11929434D411yescharacteristic
53C8×D157—24no—
54#41×C157—21no—
55#41×C157—21no—
56#41×C157—21no—
57#41×C157—21no—
58C2×Q8×C157C2×C411yescharacteristic
59C2×D4×C157—21no—
60C2×D4×C157C2×C411yescharacteristic
61C22×C4×C157—21no—
62C22×C4×C157—21no—
63C22×C4×C157C2311yescharacteristic
64M16×C157—21no—
65M16×C157D412yes—
66C2×C8×C157—21no—
67C42×C157—21no—
68C42×C157—21no—
69C22×D157—21no—
70Dic314—21no—
71Dic314C22⋊C412yes—
72D628—21no—
73D628C22⋊C412yes—
74C22⋊D157—22no—
75C22⋊D157—22no—
76C2×Dic157—21no—
77C4×D157—22no—
78C4×D157—22no—
79#11929434—21no—
80#11929434—21no—
81#11929434—21no—
82#11929434—21no—
83#11929434—41no—
84C23×C157—21no—
85C23×C157#4111yescharacteristic
86Q8×C157—21no—
87Q8×C157—21no—
88D4×C157—21no—
89D4×C157—21no—
90D4×C157—41no—
91D4×C157—41no—
92C2×C4×C157—22no—
93C2×C4×C157—21no—
94C2×C4×C157—41no—
95C2×C4×C157—41no—
96C2×C4×C157—41no—
97C2×C4×C157—41no—
98C2×C4×C157C22×C411yescharacteristic
99C2×C4×C157C2×D411yescharacteristic
100C2×C4×C157C2×D411yescharacteristic
101C2×C4×C157C2×D411yescharacteristic
102C2×C4×C157C2×D411yescharacteristic
103C2×C4×C157#4111yescharacteristic
104C8×C157—22no—
105C22×C157—21no—
106C22×C157—21no—
107C22×C157—41no—
108C22×C157—41no—
109C22×C157—41no—
110C22×C157C4×D411yescharacteristic
111C22×C157#12111yescharacteristic
112C22×C157#12311yescharacteristic
113C2×D157—22no—
114C2×D157—41no—
115C2×D157—41no—
116C4×C157—42no—
117C4×C157—41no—
118C4×C157C2×C22⋊C411yescharacteristic
119C4×C157C4×D411yescharacteristic
120C4×C157#12011yescharacteristic
121C4×C157#12111yescharacteristic
122Dic157—22no—
123C2×C157—21no—
124C2×C157—21no—
125C2×C157—81no—
126C2×C157#38611yescharacteristic
127C2×C157#44311yescharacteristic
128C2×C157#44411yescharacteristic
129D157—42no—
130C157#187611yescharacteristic, complemented, Sylow
131#1876—1571nomaximal, Sylow
132C2×#135—1571no—
133C2×#131—1571no—
134C2×#104—1571no—
135C2×#104D15711yescharacteristic, complemented
136#408—1571no—
137#341—1571no—
138#336—1571no—
139C2×#41—1571no—
140C2×#41C2×D15711yescharacteristic
141#135—3142no—
142#135—3142no—
143C2×Q16—1571no—
144C2×SD16—1571no—
145C2×SD16—1571no—
146C2×D8—1571no—
147#131—3142no—
148#131—3142no—
149C2×M16—3141no—
150C2×M16—1571no—
151C2×M16C2×D15711yescharacteristic
152C22×C8—3141no—
153C22×C8—1571no—
154C22×C8—1571no—
155C2×C42C2×D15711yescharacteristic
156#104—22no—
157#104—3142no—
158C22⋊C8—3141no—
159C22⋊C8—3141no—
160#41—21no—
161#41—21no—
162#41—21no—
163#41—21no—
164#41—3141no—
165#41—3141no—
166#41—1572no—
167#41—1572no—
168C2×Q8—1571no—
169C2×Q8C4×D15711yescharacteristic
170C2×D4—21no—
171C2×D4—3141no—
172C2×D4—1571no—
173C2×D4C4×D15711yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—3141no—
177C22×C4C22×D15711yescharacteristic
178Q16—3142no—
179SD16—3142no—
180SD16—3142no—
181D8—3142no—
182M16—21no—
183M16—3144no—
184M16—3141no—
185M16—3141no—
186M16C22⋊D15712yes—
187C2×C8—21no—
188C2×C8—3144no—
189C2×C8—3141no—
190C2×C8—3141no—
191C2×C8—3141no—
192C2×C8—3141no—
193C2×C8—3141no—
194C2×C8—1571no—
195C2×C8—1571no—
196C2×C8—1571no—
197C2×C8—1571no—
198C42—21no—
199C42—21no—
200C23—21no—
201C23—3141no—
202C23#1457895311yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—3141no—
206Q8—1572no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211D4—3142no—
212D4—3142no—
213D4—3141no—
214D4—1572no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—3141no—
222C2×C4—3142no—
223C2×C4—3142no—
224C2×C4C2×C4×D15711yescharacteristic
225C2×C4D4×D15711yescharacteristic
226C2×C4D4×D15711yescharacteristic
227C2×C4D4×D15711yescharacteristic
228C2×C4C2×C22⋊D15711yescharacteristic
229C2×C4#1457895411yescharacteristic
230C8—22no—
231C8—3141no—
232C8—3141no—
233C8—3141no—
234C8—3141no—
235C8—6281no—
236C22—21no—
237C22—21no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—3142no—
242C22—6281no—
243C22—6281no—
244C22#1909773111yescharacteristic
245C22#1909774211yescharacteristic
246C22#1909775311yescharacteristic
247C4—42no—
248C4—41no—
249C4—3142no—
250C4C22⋊C4×D15711yescharacteristic
251C4C4×C22⋊D15711yescharacteristic
252C4#1909773911yescharacteristic
253C4#1909774411yescharacteristic
254C2—21no—
255C2—21no—
256C2—81no—
257C2—6282no—
258C2#2375714911yescharacteristic
259C2#2375738711yescharacteristic
260C2#2375739211yescharacteristic
subgroupG/H
centerC2×C4D4×D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×#104×C157C2
socleC22×C157C4×D4
prime radicalC2×#19097791C2
cosocleC22×C4×C157C23
hypercenterC2×#104D157
hypocenterC157#1876
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#19097779C2semidirect
3. C2×#19097699C2semidirect
4. #23757240C2semidirect
5. #23757037C2semidirect
6. #23757028C2semidirect
7. C2×#104×C157C2semidirect
11. C2×#14578944C4semidirect
12. C2×#14578942C4semidirect
13. C2×#14578941C4semidirect
14. C2×#14578939C4semidirect
130. C157#1876semidirect
135. C2×#104D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977912
C2×#190977792
C2×#190976992
#237572402
#237570372
#237570282
C2×#104×C1572
#1876157