Finite Group Databasebeta

← #34100601

Subgroups — #34100601

Order 20096.

338 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D157C211yesmaximal, characteristic
2C2×#19097747C211yesmaximal, characteristic
3C2×#19097690C211yesmaximal, characteristic, complemented
4#23757236C211yesmaximal, characteristic
5#23757041C211yesmaximal, characteristic, complemented
6#23757041C211yesmaximal, characteristic, complemented
7C2×#101×C157C211yesmaximal, characteristic, complemented
8C22×C4×D157C2211yescharacteristic
9C2×#14578938C2211yescharacteristic
10C2×#14578938C2211yescharacteristic
11C2×#14578937—21no—
12M16×D157—22no—
13M16×D157—22no—
14C2×C8×D157—21no—
15#19097747—21no—
16#19097747—21no—
17#19097747—21no—
18#19097747—21no—
19C2×C4⋊Dic157C2211yescharacteristic
20C2×#14578933C412yes—
21C2×#14578931C412yes—
22#19097690—22no—
23#19097683—21no—
24#19097683—21no—
25C22×Q8×C157C2211yescharacteristic
26C2×M16×C157C2211yescharacteristic
27C2×M16×C157C2211yescharacteristic
28#101×C157—22no—
29C23×D157C2×C411yescharacteristic
30C22×Dic157C2×C411yescharacteristic
31C22×Dic157C2×C412yes—
32C2×C4×D157—21no—
33C2×C4×D157—21no—
34C2×C4×D157—21no—
35C2×C4×D157—21no—
36C2×C4×D157D411yescharacteristic
37C2×C4×D157D411yescharacteristic
38C2×C4×D157D411yescharacteristic
39C2×C4×D157D411yescharacteristic
40#14578938—21no—
41#14578938—21no—
42#14578938—21no—
43#14578938D412yes—
44#14578937—24no—
45C2×#11929434—21no—
46C2×#11929434—21no—
47C8×D157—24no—
48C4⋊Dic157—21no—
49C4⋊Dic157—21no—
50#14578933—22no—
51#14578933—22no—
52#14578931—22no—
53#14578931—22no—
54C2×Q8×C157—21no—
55C2×Q8×C157—21no—
56C2×Q8×C157—21no—
57C2×Q8×C157—21no—
58C2×Q8×C157—21no—
59C2×Q8×C157—21no—
60C22×C4×C157C2×C412yes—
61C22×C4×C157C2311yescharacteristic
62M16×C157—21no—
63M16×C157—21no—
64M16×C157—21no—
65M16×C157D412yes—
66C2×C8×C157—21no—
67C2×C8×C157—21no—
68C22×D157—21no—
69C22×D157—21no—
70C22×D157—22no—
71C22×D157—41no—
72C22×D157C22⋊C411yescharacteristic
73C22×D157C22⋊C411yescharacteristic
74C2×Dic157—21no—
75C2×Dic157—21no—
76C2×Dic157—22no—
77C2×Dic157—42no—
78C2×Dic157C22⋊C411yescharacteristic
79C2×Dic157C22⋊C411yescharacteristic
80C4×D157—21no—
81C4×D157—21no—
82C4×D157—21no—
83C4×D157—21no—
84C4×D157—21no—
85C4×D157—21no—
86C4×D157—21no—
87C4×D157—21no—
88#11929434—22no—
89#11929434—41no—
90C23×C157C22×C411yescharacteristic
91Q8×C157—41no—
92Q8×C157—41no—
93Q8×C157—41no—
94Q8×C157—41no—
95C2×C4×C157—22no—
96C2×C4×C157—22no—
97C2×C4×C157—22no—
98C2×C4×C157C2×D411yescharacteristic
99C2×C4×C157C2×D411yescharacteristic
100C2×C4×C157C2×D411yescharacteristic
101C2×C4×C157C2×D411yescharacteristic
102C2×C4×C157#4111yescharacteristic
103C2×C4×C157#4111yescharacteristic
104C8×C157—22no—
105C8×C157—41no—
106C22×C157—21no—
107C22×C157—21no—
108C22×C157C2×C22⋊C411yescharacteristic
109C22×C157C4×D411yescharacteristic
110C22×C157C4×D411yescharacteristic
111C2×D157—21no—
112C2×D157—21no—
113C2×D157—21no—
114C2×D157—21no—
115C2×D157—21no—
116C2×D157—42no—
117C2×D157—42no—
118C2×D157#10112yescomplemented
119C4×C157—42no—
120C4×C157#12011yescharacteristic
121C4×C157#12111yescharacteristic
122C4×C157#12111yescharacteristic
123C4×C157#12311yescharacteristic
124Dic157—21no—
125Dic157—21no—
126Dic157—42no—
127C2×C157—21no—
128C2×C157—21no—
129C2×C157#38611yescharacteristic
130C2×C157C2×#10111yescharacteristic
131C2×C157#41311yescharacteristic
132D157—22no—
133D157—41no—
134C157#190111yescharacteristic, complemented, Sylow
135#1901—1571nomaximal, Sylow
136C22×M16—1571no—
137C2×C22⋊Q8—1571no—
138C2×#101—1571no—
139C2×#101D15711yescharacteristic, complemented
140#407—1571no—
141#343—1571no—
142#343—1571no—
143C22×Q8C2×D15711yescharacteristic
144C23×C4—1571no—
145C2×M16—3141no—
146C2×M16—3142no—
147C2×M16—3142no—
148C2×M16—1571no—
149C2×M16—1571no—
150C2×M16C2×D15711yescharacteristic
151C2×M16C2×D15711yescharacteristic
152C22×C8—3141no—
153C22⋊Q8—3141no—
154C22⋊Q8—3141no—
155C22⋊Q8—3141no—
156C22⋊Q8—3141no—
157C2×C4⋊C4—1572no—
158C2×C4⋊C4—1571no—
159C2×C22⋊C4—1572no—
160#101—22no—
161#101—3142no—
162C22⋊C8—3141no—
163C22⋊C8—3141no—
164C24—1571no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C22×C4—3141no—
172C22×C4—3141no—
173C22×C4—3141no—
174C22×C4—3141no—
175C22×C4—1571no—
176C22×C4—1571no—
177C22×C4—1571no—
178C22×C4—1571no—
179C22×C4—1571no—
180C22×C4—1572no—
181C22×C4C4×D15712yes—
182C22×C4C22×D15711yescharacteristic
183M16—21no—
184M16—21no—
185M16—21no—
186M16—3144no—
187M16—3141no—
188M16—3141no—
189M16—3141no—
190M16—1572no—
191M16C22⋊D15712yes—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—3144no—
195C2×C8—3141no—
196C2×C8—3141no—
197C4⋊C4—3142no—
198C4⋊C4—3142no—
199C4⋊C4—3141no—
200C4⋊C4—3141no—
201C22⋊C4—3142no—
202C22⋊C4—3142no—
203C23—3142no—
204C23—3141no—
205C23—3141no—
206C23—6281no—
207C23—1571no—
208C23—1571no—
209C23C2×C4×D15711yescharacteristic
210Q8—41no—
211Q8—41no—
212Q8—41no—
213Q8—41no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—3141no—
218C2×C4—3141no—
219C2×C4—3141no—
220C2×C4—3141no—
221C2×C4—3141no—
222C2×C4—3141no—
223C2×C4—3141no—
224C2×C4—3141no—
225C2×C4—3141no—
226C2×C4—3141no—
227C2×C4—3142no—
228C2×C4—6282no—
229C2×C4—1571no—
230C2×C4—1571no—
231C2×C4D4×D15711yescharacteristic
232C2×C4D4×D15711yescharacteristic
233C2×C4D4×D15711yescharacteristic
234C2×C4C2×C22⋊D15711yescharacteristic
235C2×C4#1457895311yescharacteristic
236C2×C4#1457895411yescharacteristic
237C8—22no—
238C8—41no—
239C8—3142no—
240C8—6281no—
241C22—21no—
242C22—21no—
243C22—3141no—
244C22—3141no—
245C22—3141no—
246C22—3141no—
247C22—3141no—
248C22—6282no—
249C22—6282no—
250C22—1572no—
251C22C22⋊C4×D15711yescharacteristic
252C22#1909773111yescharacteristic
253C22C4×C22⋊D15711yescharacteristic
254C4—42no—
255C4—3141no—
256C4—3141no—
257C4—6282no—
258C4#1909773911yescharacteristic
259C4#1909774211yescharacteristic
260C4#1909774411yescharacteristic
261C4#1909775311yescharacteristic
262C2—21no—
263C2—21no—
264C2—3142no—
265C2—6281no—
266C2#2375714911yescharacteristic
267C2#101×D15711yescharacteristic
268C2#2375725611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC23×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×#101×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC23×D157C2×C4
cosocleC22×C4×C157C23
hypercenterC2×#101D157
hypocenterC157#1901
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. C2×#19097690C2semidirect
5. #23757041C2semidirect
6. #23757041C2semidirect
7. C2×#101×C157C2semidirect
118. C2×D157#101semidirect
134. C157#1901semidirect
139. C2×#101D157semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D1572
C2×#190977472
C2×#190976902
#237572362
#237570412
C2×#101×C1572
#1901157