Finite Group Databasebeta

← #34109939

Subgroups — #34109939

Order 20096.

376 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757829C211yesmaximal, characteristic
2C4×Q8×D157C211yesmaximal, characteristic
3#23757581C211yesmaximal, characteristic, complemented
4#23757580C211yesmaximal, characteristic, complemented
5#23757577C211yesmaximal, characteristic, complemented
6#23757567C211yesmaximal, characteristic, complemented
7#23757566C211yesmaximal, characteristic, complemented
8#23757557C211yesmaximal, characteristic, complemented
9#23757556C211yesmaximal, characteristic, complemented
10#23757314C211yesmaximal, characteristic
11#23757312C211yesmaximal, characteristic
12#23757295C211yesmaximal, characteristic
13#23757280C211yesmaximal, characteristic
14#23757280C211yesmaximal, characteristic
15#479×C157C211yesmaximal, characteristic, complemented
16C2×Q8×D157C2211yescharacteristic
17C2×#14578937C2211yescharacteristic
18C2×#14578937C2211yescharacteristic
19#19097770C2211yescharacteristic
20#19097770C2211yescharacteristic
21#19097763C2211yescharacteristic
22#19097749—21no—
23#19097749—21no—
24Q8×Dic157C2211yescharacteristic
25C4×Dic314—21no—
26C4×Dic314C2211yescharacteristic
27#19097736—21no—
28#19097736—21no—
29#19097736—21no—
30#19097736C2211yescharacteristic
31#19097729C2211yescharacteristic
32#19097729C2211yescharacteristic
33C4⋊C4×D157—21no—
34C4⋊C4×D157C2211yescharacteristic
35C42×D157—21no—
36C42×D157C2211yescharacteristic
37#19097705C2211yescharacteristic
38#19097704C2211yescharacteristic
39#19097704C2211yescharacteristic
40#19097703C2211yescharacteristic
41#19097702C2211yescharacteristic
42#19097702C2211yescharacteristic
43C4⋊#11929434C2211yescharacteristic
44#19097700C2211yescharacteristic
45#19097700C2211yescharacteristic
46#19097696C2211yescharacteristic
47#19097696C2211yescharacteristic
48#19097695C2211yescharacteristic
49#19097695C2211yescharacteristic
50#19097694C2211yescharacteristic
51#19097694C2211yescharacteristic
52#125×C157C2211yescharacteristic
53C4×Q8×C157C2211yescharacteristic
54#107×C157C2211yescharacteristic
55#106×C157C2211yescharacteristic
56C4⋊C8×C157C2211yescharacteristic
57#103×C157C2211yescharacteristic
58#103×C157C2211yescharacteristic
59C2×Dic314—21no—
60C2×Dic314—21no—
61C2×Dic314—21no—
62C2×Dic314C2311yescharacteristic
63Q8×D157—22no—
64Q8×D157Q814yescomplemented
65C2×C4×D157—21no—
66C2×C4×D157—21no—
67C2×C4×D157D411yescharacteristic
68C2×C4×D157D411yescharacteristic
69C2×C4×D157C2311yescharacteristic
70#14578937—22no—
71#14578937—22no—
72C2×#11929434C2311yescharacteristic
73C2×#11929434C2311yescharacteristic
74C4⋊Dic157—21no—
75C4⋊Dic157C2311yescharacteristic
76C4⋊Dic157C2311yescharacteristic
77C4⋊Dic157C2311yescharacteristic
78#14578933—21no—
79#14578933—21no—
80#14578933—21no—
81#14578933—21no—
82#14578933—21no—
83#14578933—21no—
84#14578933—21no—
85#14578931—21no—
86#14578931—21no—
87C4×Dic157—21no—
88C4×Dic157—21no—
89C4×Dic157—21no—
90C4×Dic157—21no—
91C4×Dic157—21no—
92C4×Dic157D411yescharacteristic
93C4×Dic157D411yescharacteristic
94C4×Dic157C2311yescharacteristic
95C2×Q8×C157C2311yescharacteristic
96C2×C8×C157C2311yescharacteristic
97C2×C8×C157C2311yescharacteristic
98C4⋊C4×C157—21no—
99C4⋊C4×C157—21no—
100C4⋊C4×C157—21no—
101C4⋊C4×C157C2311yescharacteristic
102C4⋊C4×C157C2311yescharacteristic
103C4⋊C4×C157C2311yescharacteristic
104C42×C157—21no—
105C42×C157C2311yescharacteristic
106C22×D157C2×D411yescharacteristic
107Dic314—21no—
108Dic314—24no—
109Dic314—42no—
110Dic314—42no—
111Dic314C2×Q812yes—
112C2×Dic157—21no—
113C2×Dic157—21no—
114C2×Dic157—21no—
115C2×Dic157—21no—
116C2×Dic157C2×D411yescharacteristic
117C2×Dic157C2×D411yescharacteristic
118C2×Dic157C2×D411yescharacteristic
119C4×D157—24no—
120C4×D157—22no—
121C4×D157—41no—
122C4×D157—42no—
123C4×D157C2×Q812yes—
124C4×D157#4112yes—
125#11929434—21no—
126#11929434—21no—
127Q8×C157—21no—
128Q8×C157C2×Q812yes—
129C2×C4×C157—21no—
130C2×C4×C157—21no—
131C2×C4×C157—21no—
132C2×C4×C157—21no—
133C2×C4×C157C2×D411yescharacteristic
134C2×C4×C157C2×D411yescharacteristic
135C2×C4×C157C2411yescharacteristic
136C8×C157—21no—
137C8×C157—21no—
138C22×C157C22×D411yescharacteristic
139C2×D157—21no—
140C2×D157—21no—
141C2×D157C22⋊Q812yes—
142C4×C157—22no—
143C4×C157—21no—
144C4×C157—21no—
145C4×C157—41no—
146C4×C157—41no—
147C4×C157—41no—
148C4×C157C22×Q811yescharacteristic
149C4×C157C2×#4111yescharacteristic
150Dic157—22no—
151Dic157—21no—
152Dic157—41no—
153Dic157—41no—
154Dic157—41no—
155Dic157C22⋊Q812yes—
156Dic157#13712yes—
157C2×C157C2×C22⋊Q811yescharacteristic
158C2×C157C2×#13711yescharacteristic
159C2×C157#57511yescharacteristic
160D157—22no—
161C157#307811yescharacteristic, complemented, Sylow
162#3078—1571nomaximal, Sylow
163#533—1571no—
164C2×C4×Q8—1571no—
165#479—1571no—
166#479—1571no—
167#479—1571no—
168#479D15711yescharacteristic, complemented
169#477—1571no—
170#477—1571no—
171#475—1571no—
172#475—1571no—
173#428—1571no—
174#428—1571no—
175#423—1571no—
176#419—1571no—
177#419—1571no—
178C22×Q8—1571no—
179C2×M16—1571no—
180C2×M16—1571no—
181C4⋊Q8—1571no—
182C4⋊Q8—1571no—
183#125—1571no—
184#125C2×D15711yescharacteristic
185C22⋊Q8—3141no—
186C22⋊Q8—3141no—
187C4×Q8—3141no—
188C4×Q8—3141no—
189C4×Q8—3141no—
190C4×Q8—3141no—
191C4×Q8—1571no—
192C4×Q8—1571no—
193C4×Q8—1571no—
194C4×Q8C2×D15711yescharacteristic
195#117—1571no—
196#117—1571no—
197C2×C4⋊C4—3141no—
198C2×C4⋊C4—1571no—
199C2×C42—3141no—
200C2×C42—1571no—
201#107—1571no—
202#107—1571no—
203#107—1571no—
204#107C2×D15711yescharacteristic
205#106—1571no—
206#106—1571no—
207#106—1571no—
208#106C2×D15711yescharacteristic
209C4⋊C8—1571no—
210C4⋊C8—1571no—
211C4⋊C8—1571no—
212C4⋊C8C2×D15711yescharacteristic
213#103—1571no—
214#103—1571no—
215#103—1571no—
216#103—1571no—
217#103—1571no—
218#103—1571no—
219#103C2×D15711yescharacteristic
220#103C2×D15711yescharacteristic
221C2×Q8—3141no—
222C2×Q8—3141no—
223C2×Q8—3141no—
224C2×Q8—3142no—
225C2×Q8—1574no—
226C2×Q8—1571no—
227C2×Q8C22×D15711yescharacteristic
228C22×C4—3141no—
229C22×C4—3141no—
230C22×C4—1571no—
231C22×C4—1571no—
232C22×C4—1571no—
233M16—3142no—
234M16—3142no—
235C2×C8—1571no—
236C2×C8—1571no—
237C2×C8C22×D15711yescharacteristic
238C2×C8C22×D15711yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—3141no—
243C4⋊C4—3141no—
244C4⋊C4—3141no—
245C4⋊C4—3141no—
246C4⋊C4—3141no—
247C4⋊C4—3141no—
248C4⋊C4—3141no—
249C4⋊C4—3141no—
250C4⋊C4—1571no—
251C4⋊C4—1571no—
252C4⋊C4—1571no—
253C4⋊C4C22×D15711yescharacteristic
254C4⋊C4C22×D15711yescharacteristic
255C4⋊C4C22×D15711yescharacteristic
256C22⋊C4—3141no—
257C22⋊C4—3141no—
258C42—21no—
259C42—3141no—
260C42—3141no—
261C42—3141no—
262C42—3141no—
263C42—3141no—
264C42—1571no—
265C42—1571no—
266C42—1571no—
267C42C22×D15711yescharacteristic
268C23—1571no—
269Q8—21no—
270Q8—3144no—
271Q8—3141no—
272Q8—6282no—
273Q8—6282no—
274Q8—1572no—
275Q8Q8×D15712yes—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—3144no—
281C2×C4—3142no—
282C2×C4—3141no—
283C2×C4—3141no—
284C2×C4—3141no—
285C2×C4—3141no—
286C2×C4—6281no—
287C2×C4—6282no—
288C2×C4—1571no—
289C2×C4—1571no—
290C2×C4—1571no—
291C2×C4—1572no—
292C2×C4—1572no—
293C2×C4D4×D15711yescharacteristic
294C2×C4D4×D15711yescharacteristic
295C2×C4C23×D15711yescharacteristic
296C8—21no—
297C8—21no—
298C8—3141no—
299C8—3141no—
300C22—3141no—
301C22—3141no—
302C22—1572no—
303C22C2×D4×D15711yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—3142no—
311C4—3141no—
312C4—6281no—
313C4—6281no—
314C4—6281no—
315C4—1572no—
316C4—1572no—
317C4C2×Q8×D15711yescharacteristic
318C4#41×D15711yescharacteristic
319C2—3142no—
320C2C22⋊Q8×D15711yescharacteristic
321C2#137×D15711yescharacteristic
322C2#2375807011yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#479×C157C2
socleC22×C157C22×D4
prime radicalC22×D157C2×D4
hypercenter#479D157
hypocenterC157#3078
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #23757581C2semidirect
4. #23757580C2semidirect
5. #23757577C2semidirect
6. #23757567C2semidirect
7. #23757566C2semidirect
8. #23757557C2semidirect
9. #23757556C2semidirect
15. #479×C157C2semidirect
64. Q8×D157Q8semidirect
161. C157#3078semidirect
168. #479D157semidirect

Maximal subgroups

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

subgroupindex
#237578292
C4×Q8×D1572
#237575812
#237575802
#237575772
#237575672
#237575662
#237575572
#237575562
#237573142
#237573122
#237572952
#237572802
#479×C1572
#3078157