Finite Group Databasebeta

← #34110692

Subgroups — #34110692

Order 20096.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757827C211yesmaximal, characteristic, complemented
2#23757820C211yesmaximal, characteristic
3#23757670C211yesmaximal, characteristic, complemented
4#23757644C211yesmaximal, characteristic, complemented
5#23757622C211yesmaximal, characteristic, complemented
6#23757618C211yesmaximal, characteristic, complemented
7#23757505C211yesmaximal, characteristic, complemented
8#23757503C211yesmaximal, characteristic, complemented
9#23757501C211yesmaximal, characteristic, complemented
10#23757499C211yesmaximal, characteristic, complemented
11C4×#14578943C211yesmaximal, characteristic, complemented
12C4×#14578941C211yesmaximal, characteristic, complemented
13C4×#14578942C211yesmaximal, characteristic, complemented
14C4×C8×D157C211yesmaximal, characteristic, complemented
15C4×SD16×C157C211yesmaximal, characteristic, complemented
16C2×#14578954—21no—
17C2×#14578943C2211yescharacteristic
18C2×#14578942C2211yescharacteristic
19C2×#14578941C2211yescharacteristic
20C2×C8×D157C2211yescharacteristic
21C2×C8×D157C2211yescharacteristic
22#19097770C2211yescharacteristic
23#19097770C2211yescharacteristic
24#19097769C2211yescharacteristic
25#19097767C2211yescharacteristic
26#19097761—21no—
27#19097757—21no—
28#19097751C2211yescharacteristic
29#19097749—21no—
30#19097747C2211yescharacteristic
31#19097746C2211yescharacteristic
32#19097744—21no—
33#19097742C2211yescharacteristic
34C4×Dic314—21no—
35C4×Dic314C2211yescharacteristic
36C4×D628C2211yescharacteristic
37C4×C22⋊D157—21no—
38#19097728—21no—
39C42×D157C2211yescharacteristic
40#19097703C2211yescharacteristic
41#19097702C2211yescharacteristic
42#19097702C2211yescharacteristic
43#19097696C2211yescharacteristic
44#19097695C2211yescharacteristic
45#19097694C2211yescharacteristic
46#19097693C2211yescharacteristic
47#19097692C2211yescharacteristic
48#19097691C2211yescharacteristic
49C4×#11929434C2211yescharacteristic
50C8×Dic157C2211yescharacteristic
51C8×Dic157C2211yescharacteristic
52C2×SD16×C157C2211yescharacteristic
53C4×Q8×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic
55#106×C157C2211yescharacteristic
56#103×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58C4×C8×C157C2211yescharacteristic
59#14578954—44no—
60C2×Dic314—21no—
61C2×Dic314—21no—
62C2×Dic314C2311yescharacteristic
63C2×D628—21no—
64C2×D628C2311yescharacteristic
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C4×D157—21no—
69C2×C4×D157D411yescharacteristic
70C2×C4×D157D411yescharacteristic
71C2×C4×D157C2311yescharacteristic
72#14578943—22no—
73#14578942—22no—
74#14578941—22no—
75C2×#11929434C2311yescharacteristic
76C2×#11929434C2311yescharacteristic
77C8×D157—22no—
78C8×D157—22no—
79C4⋊Dic157—21no—
80C4⋊Dic157C2311yescharacteristic
81C4⋊Dic157C2311yescharacteristic
82#14578933—21no—
83#14578933—21no—
84#14578933—21no—
85#14578933—21no—
86#14578933—21no—
87#14578933—21no—
88C22⋊Dic157—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93C4×Dic157—21no—
94C4×Dic157D411yescharacteristic
95C4×Dic157D411yescharacteristic
96C4×Dic157C2311yescharacteristic
97C2×Q8×C157C2311yescharacteristic
98C2×D4×C157C2311yescharacteristic
99C22×C4×C157—21no—
100SD16×C157—22no—
101C2×C8×C157C2311yescharacteristic
102C2×C8×C157C2311yescharacteristic
103C4⋊C4×C157—21no—
104C4⋊C4×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C22⋊C4×C157—21no—
107C42×C157—21no—
108C42×C157C2311yescharacteristic
109C22×D157—21no—
110C22×D157C2×D411yescharacteristic
111Dic314—21no—
112Dic314—21no—
113Dic314—42no—
114Dic314—42no—
115D628—21no—
116D628—21no—
117D628—42no—
118C22⋊D157—42no—
119C22⋊D157—42no—
120C22⋊D157—42no—
121C2×Dic157—21no—
122C2×Dic157—21no—
123C2×Dic157—21no—
124C2×Dic157C2×D411yescharacteristic
125C2×Dic157C2×D411yescharacteristic
126C2×Dic157C2×D411yescharacteristic
127C4×D157—21no—
128C4×D157—21no—
129C4×D157—22no—
130C4×D157—42no—
131C4×D157SD1614yescomplemented
132#11929434—21no—
133#11929434#4112yescomplemented
134C23×C157—21no—
135Q8×C157—21no—
136Q8×C157—21no—
137D4×C157—21no—
138D4×C157—21no—
139C2×C4×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157—21no—
142C2×C4×C157—42no—
143C2×C4×C157C2×D411yescharacteristic
144C2×C4×C157C2×D411yescharacteristic
145C2×C4×C157C2411yescharacteristic
146C8×C157—21no—
147C8×C157#4112yescomplemented
148C22×C157—41no—
149C22×C157—41no—
150C22×C157—41no—
151C22×C157C22×D411yescharacteristic
152C2×D157—21no—
153C2×D157—21no—
154C2×D157—41no—
155C2×D157—41no—
156C2×D157—41no—
157C2×D157C2×SD1612yes—
158C4×C157—21no—
159C4×C157—41no—
160C4×C157—41no—
161C4×C157—41no—
162C4×C157C2×SD1612yes—
163C4×C157C2×#4111yescharacteristic
164C4×C157C2×#4111yescharacteristic
165Dic157—21no—
166Dic157—41no—
167Dic157—41no—
168Dic157—41no—
169Dic157C2×SD1612yes—
170Dic157#13512yes—
171C2×C157—81no—
172C2×C157#53211yescharacteristic
173C2×C157C22×SD1611yescharacteristic
174C2×C157C2×#13511yescharacteristic
175D157—22no—
176D157—81no—
177C157#316711yescharacteristic, complemented, Sylow
178#3167—1571nomaximal, Sylow
179#533—1571no—
180#532—1571no—
181#498—1571no—
182#492—1571no—
183#487—1571no—
184#486—1571no—
185#465—1571no—
186#465—1571no—
187#465—1571no—
188#465—1571no—
189C4×SD16—1571no—
190C4×SD16—1571no—
191C4×SD16—1571no—
192C4×SD16D15711yescharacteristic, complemented
193C2×C4×C8—1571no—
194C2×#41—3141no—
195C2×SD16—1571no—
196C2×SD16—1571no—
197C2×SD16—1571no—
198C2×SD16C2×D15711yescharacteristic
199C22×C8—1571no—
200C22×C8—1571no—
201C4⋊Q8—1571no—
202C4⋊Q8—1571no—
203C4⋊Q8—1571no—
204#127—1571no—
205#125—3141no—
206#124—3141no—
207C22⋊Q8—3141no—
208C22⋊Q8—1571no—
209C22⋊Q8—1571no—
210#121—3141no—
211#121—1571no—
212#121—1571no—
213C4×Q8—3141no—
214C4×Q8—1571no—
215C4×Q8C2×D15711yescharacteristic
216C4×D4—3141no—
217C4×D4—1571no—
218C4×D4C2×D15711yescharacteristic
219#117—3141no—
220C2×C42—1571no—
221#106—1571no—
222#106—1571no—
223#106—1571no—
224#106C2×D15711yescharacteristic
225#103—1571no—
226#103—1571no—
227#103—1571no—
228#103C2×D15711yescharacteristic
229#102—1571no—
230#102—1571no—
231#102—1571no—
232#102C2×D15711yescharacteristic
233C4×C8—1571no—
234C4×C8—1571no—
235C4×C8—1571no—
236C4×C8C2×D15711yescharacteristic
237#41—6284no—
238C2×Q8—3141no—
239C2×Q8—3141no—
240C2×Q8—1571no—
241C2×Q8C22×D15711yescharacteristic
242C2×D4—3141no—
243C2×D4—3141no—
244C2×D4—3141no—
245C2×D4—3141no—
246C2×D4—1571no—
247C2×D4C22×D15711yescharacteristic
248C22×C4—21no—
249C22×C4—3141no—
250C22×C4—1571no—
251C22×C4—1571no—
252C22×C4—1571no—
253SD16—22no—
254SD16—3142no—
255SD16—3142no—
256SD16—3142no—
257C2×C8—3142no—
258C2×C8—3142no—
259C2×C8—1571no—
260C2×C8—1571no—
261C2×C8C22×D15711yescharacteristic
262C2×C8C22×D15711yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—3141no—
265C4⋊C4—3141no—
266C4⋊C4—3141no—
267C4⋊C4—3141no—
268C4⋊C4—3141no—
269C4⋊C4—3141no—
270C4⋊C4—3141no—
271C4⋊C4—1571no—
272C4⋊C4—1571no—
273C4⋊C4C22×D15711yescharacteristic
274C4⋊C4C22×D15711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—3141no—
277C22⋊C4—3141no—
278C22⋊C4—3141no—
279C22⋊C4—3141no—
280C22⋊C4—3141no—
281C42—21no—
282C42—3141no—
283C42—1571no—
284C42—1571no—
285C42—1571no—
286C42C22×D15711yescharacteristic
287C23—21no—
288C23—3141no—
289C23—1571no—
290Q8—21no—
291Q8—21no—
292Q8—3141no—
293Q8—3141no—
294Q8—6282no—
295Q8—6282no—
296D4—21no—
297D4—21no—
298D4—3141no—
299D4—3141no—
300D4—6282no—
301D4—6282no—
302D4—6282no—
303D4—6282no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—3142no—
309C2×C4—3141no—
310C2×C4—3141no—
311C2×C4—3141no—
312C2×C4—3141no—
313C2×C4—3141no—
314C2×C4—6282no—
315C2×C4—1571no—
316C2×C4—1571no—
317C2×C4—1571no—
318C2×C4—1574no—
319C2×C4D4×D15711yescharacteristic
320C2×C4D4×D15711yescharacteristic
321C2×C4C23×D15711yescharacteristic
322C8—21no—
323C8—3141no—
324C8—1572no—
325C8#1457895412yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—3141no—
330C22—3141no—
331C22—6281no—
332C22—6281no—
333C22—6281no—
334C22—1572no—
335C22C2×D4×D15711yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—3141no—
341C4—6281no—
342C4—6281no—
343C4—6281no—
344C4—1572no—
345C4—1572no—
346C4SD16×D15712yes—
347C4#41×D15711yescharacteristic
348C4C2×#1457895411yescharacteristic
349C2—81no—
350C2—3142no—
351C2—12561no—
352C2#2375782011yescharacteristic
353C2C2×SD16×D15711yescharacteristic
354C2#135×D15711yescharacteristic
subgroupG/H
centerC2×C4D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC4×SD16×C157C2
socleC22×C157C22×D4
prime radical#23757820C2
hypercenterC4×SD16D157
hypocenterC157#3167
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #23757827C2semidirect
3. #23757670C2semidirect
4. #23757644C2semidirect
5. #23757622C2semidirect
6. #23757618C2semidirect
7. #23757505C2semidirect
8. #23757503C2semidirect
9. #23757501C2semidirect
10. #23757499C2semidirect
11. C4×#14578943C2semidirect
12. C4×#14578941C2semidirect
13. C4×#14578942C2semidirect
14. C4×C8×D157C2semidirect
15. C4×SD16×C157C2semidirect
131. C4×D157SD16semidirect
133. #11929434#41semidirect
147. C8×C157#41semidirect
177. C157#3167semidirect
192. C4×SD16D157semidirect
325. C8#14578954semidirect

Maximal subgroups

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

subgroupindex
#237578272
#237578202
#237576702
#237576442
#237576222
#237576182
#237575052
#237575032
#237575012
#237574992
C4×#145789432
C4×#145789412
C4×#145789422
C4×C8×D1572
C4×SD16×C1572
#3167157