Finite Group Databasebeta

← #34109672

Subgroups — #34109672

Order 20096.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097798C211yesmaximal, characteristic, complemented
2C2×#19097792C211yesmaximal, characteristic, complemented
3#23757836C211yesmaximal, characteristic, complemented
4#23757755C211yesmaximal, characteristic, complemented
5#23757495C211yesmaximal, characteristic, complemented
6#23757493C211yesmaximal, characteristic, complemented
7#23757489C211yesmaximal, characteristic, complemented
8#23757487C211yesmaximal, characteristic, complemented
9#23757471C211yesmaximal, characteristic, complemented
10#23757467C211yesmaximal, characteristic, complemented
11#23757465C211yesmaximal, characteristic, complemented
12#23757298C211yesmaximal, characteristic, complemented
13#23757271C211yesmaximal, characteristic, complemented
14#102×D157C211yesmaximal, characteristic, complemented
15#460×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578953C2211yescharacteristic
18C2×D4×D157C2211yescharacteristic
19#19097798—24no—
20#19097792—24no—
21C2×#14578944C2211yescharacteristic, complemented
22C2×#14578943C2211yescharacteristic, complemented
23C2×#14578941C2211yescharacteristic
24C2×D1256C2211yescharacteristic
25C2×#14578939C2211yescharacteristic
26C2×#14578939C2211yescharacteristic, complemented
27C2×#14578937C2211yescharacteristic
28C2×C8×D157C2211yescharacteristic
29#19097767C2211yescharacteristic
30#19097759C2211yescharacteristic
31#19097758C2211yescharacteristic
32#19097743—21no—
33#19097743—21no—
34#19097739—21no—
35#19097739—21no—
36Q8×Dic157C2211yescharacteristic, complemented
37C4×D628—21no—
38C4×D628C2211yescharacteristic, complemented
39#19097733—21no—
40#19097733C2211yescharacteristic, complemented
41#19097728—21no—
42#19097728C2211yescharacteristic
43C4⋊C4×D157—21no—
44C4⋊C4×D157C2211yescharacteristic
45C4⋊#11929434C2211yescharacteristic, complemented
46#19097700C2211yescharacteristic, complemented
47#19097700C2211yescharacteristic, complemented
48#19097696C2211yescharacteristic, complemented
49#19097694C2211yescharacteristic, complemented
50#19097693C2211yescharacteristic
51#19097692C2211yescharacteristic
52#19097692C2211yescharacteristic, complemented
53#19097691C2211yescharacteristic
54C2×SD16×C157C2211yescharacteristic
55C2×SD16×C157C2211yescharacteristic, complemented
56#127×C157C2211yescharacteristic
57C4×Q8×C157C2211yescharacteristic, complemented
58C4⋊C8×C157C2211yescharacteristic, complemented
59#102×C157C2211yescharacteristic
60#102×C157C2211yescharacteristic, complemented
61C23×D157—21no—
62#14578955—22no—
63#14578955D414yescomplemented
64#14578953—22no—
65#14578953—22no—
66C2×Dic314C2311yescharacteristic
67C2×D628—21no—
68C2×D628C2311yescharacteristic
69C2×D628C2311yescharacteristic
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72C2×C22⋊D157—21no—
73C2×C22⋊D157—21no—
74D4×D157—22no—
75D4×D157—22no—
76C22×Dic157—21no—
77C2×C4×D157—21no—
78C2×C4×D157—21no—
79C2×C4×D157—21no—
80C2×C4×D157—21no—
81C2×C4×D157C2311yescharacteristic
82#14578944—22no—
83#14578943—22no—
84#14578941—22no—
85D1256—22no—
86#14578939—22no—
87#14578939—22no—
88#14578937—22no—
89C2×#11929434C2311yescharacteristic
90C2×#11929434C2311yescharacteristic
91C8×D157—22no—
92C4⋊Dic157—21no—
93C4⋊Dic157C2311yescharacteristic
94#14578933—21no—
95#14578933D411yescharacteristic
96#14578933D411yescharacteristic
97C22⋊Dic157—21no—
98C22⋊Dic157—21no—
99#14578931—21no—
100#14578931—21no—
101#14578931—21no—
102#14578931—21no—
103#14578931D411yescharacteristic
104#14578931D411yescharacteristic
105C4×Dic157—21no—
106C4×Dic157C2311yescharacteristic
107C2×Q8×C157C2311yescharacteristic
108C2×D4×C157—21no—
109C2×D4×C157—21no—
110C2×D4×C157C2311yescharacteristic
111C2×D4×C157C2311yescharacteristic
112SD16×C157—22no—
113SD16×C157—22no—
114C2×C8×C157C2311yescharacteristic
115C2×C8×C157C2311yescharacteristic
116C4⋊C4×C157—21no—
117C4⋊C4×C157C2311yescharacteristic
118C42×C157—21no—
119C42×C157C2311yescharacteristic
120C22×D157—21no—
121C22×D157—21no—
122C22×D157—42no—
123C22×D157—81no—
124C22×D157—81no—
125C22×D157C2×D411yescharacteristic
126Dic314—21no—
127Dic314—21no—
128D628—24no—
129D628—21no—
130D628—21no—
131D628—21no—
132D628C2×D412yes—
133C22⋊D157—42no—
134C22⋊D157—42no—
135C22⋊D157—81no—
136C22⋊D157—81no—
137C2×Dic157—21no—
138C2×Dic157—21no—
139C2×Dic157—42no—
140C2×Dic157C2×D411yescharacteristic
141C2×Dic157C2×D411yescharacteristic
142C2×Dic157C2×D411yescharacteristic
143C4×D157—24no—
144C4×D157—81no—
145C4×D157—81no—
146C4×D157—81no—
147C4×D157C2×D412yes—
148C4×D157#4112yes—
149#11929434—21no—
150#11929434—21no—
151C23×C157—21no—
152C23×C157—21no—
153Q8×C157—21no—
154Q8×C157C2×D412yes—
155D4×C157—21no—
156D4×C157—21no—
157D4×C157—21no—
158D4×C157—21no—
159D4×C157—81no—
160D4×C157—81no—
161C2×C4×C157—21no—
162C2×C4×C157—21no—
163C2×C4×C157C2×D411yescharacteristic
164C2×C4×C157C2×D411yescharacteristic
165C2×C4×C157C2411yescharacteristic
166C8×C157—21no—
167C8×C157—21no—
168C22×C157—41no—
169C22×C157—41no—
170C22×C157—41no—
171C22×C157—41no—
172C22×C157—41no—
173C22×C157—41no—
174C22×C157C22×D411yescharacteristic
175C2×D157—21no—
176C2×D157—21no—
177C2×D157—22no—
178C2×D157—41no—
179C2×D157—41no—
180C2×D157—41no—
181C2×D157—41no—
182C2×D157—41no—
183C2×D157—84no—
184C2×D157#12112yes—
185C4×C157—22no—
186C4×C157—21no—
187C4×C157—21no—
188C4×C157—41no—
189C4×C157C22×D411yescharacteristic
190C4×C157C2×#4111yescharacteristic
191Dic157—21no—
192Dic157—21no—
193Dic157—41no—
194Dic157—41no—
195Dic157#12112yes—
196C2×C157—81no—
197C2×C157—81no—
198C2×C157C2×#12111yescharacteristic
199C2×C157#57611yescharacteristic
200C2×C157#57711yescharacteristic
201D157—22no—
202D157—42no—
203D157—81no—
204C157#304511yescharacteristic, complemented, Sylow
205#3045—1571nomaximal, Sylow
206C2×AGL(1,ℤ/8)—1571no—
207C2×#135—1571no—
208#535—1571no—
209#520—1571no—
210#464—1571no—
211#464—1571no—
212#463—1571no—
213#463—1571no—
214#460—1571no—
215#460D15711yescharacteristic, complemented
216#459—1571no—
217#459—1571no—
218#424—1571no—
219#417—1571no—
220C2×#102—1571no—
221C2×#41—1571no—
222C2×#41—1571no—
223C22×D4—1571no—
224AGL(1,ℤ/8)—3144no—
225#135—3144no—
226C2×Q16—1571no—
227C2×SD16—1571no—
228C2×SD16—1571no—
229C2×SD16C2×D15711yescharacteristic
230C2×SD16C2×D15711yescharacteristic, complemented
231C2×D8—1571no—
232C2×D8—1571no—
233C2×D8—1571no—
234C2×M16—1571no—
235C22×C8—1571no—
236#127—1571no—
237#127C2×D15711yescharacteristic
238#124—1571no—
239#124—1571no—
240#121—3141no—
241#121—3141no—
242#120—3141no—
243#120—3141no—
244C4×Q8—1571no—
245C4×Q8C2×D15711yescharacteristic, complemented
246C4×D4—3141no—
247C4×D4—3141no—
248C4×D4—1571no—
249C4×D4—1571no—
250#117—3141no—
251#117—1571no—
252C2×C4⋊C4—3141no—
253C2×C4⋊C4—1571no—
254C4⋊C8—1571no—
255C4⋊C8—1571no—
256C4⋊C8—1571no—
257C4⋊C8C2×D15711yescharacteristic, complemented
258#103—1571no—
259#103—1571no—
260#102—1571no—
261#102—1571no—
262#102—1571no—
263#102—1571no—
264#102C2×D15711yescharacteristic
265#102C2×D15711yescharacteristic, complemented
266C24—3141no—
267#41—3142no—
268#41—3142no—
269#41—3142no—
270#41—1574no—
271C2×Q8—1571no—
272C2×Q8C22×D15711yescharacteristic
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—3141no—
276C2×D4—3141no—
277C2×D4—3142no—
278C2×D4—3142no—
279C2×D4—3141no—
280C2×D4—3141no—
281C2×D4—3141no—
282C2×D4—1571no—
283C2×D4—1571no—
284C2×D4C22×D15711yescharacteristic
285C2×D4C22×D15711yescharacteristic
286C22×C4—3141no—
287C22×C4—3141no—
288C22×C4—3141no—
289C22×C4—3141no—
290C22×C4—3141no—
291C22×C4—1571no—
292Q16—3142no—
293SD16—22no—
294SD16—22no—
295SD16—3142no—
296SD16—3142no—
297D8—3142no—
298D8—3142no—
299D8—3142no—
300M16—3142no—
301C2×C8—3142no—
302C2×C8—1571no—
303C2×C8—1571no—
304C2×C8C22×D15711yescharacteristic
305C2×C8C22×D15711yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—3141no—
308C4⋊C4—3141no—
309C4⋊C4—1571no—
310C4⋊C4—1571no—
311C4⋊C4—1571no—
312C4⋊C4C22×D15711yescharacteristic
313C22⋊C4—3141no—
314C22⋊C4—3141no—
315C22⋊C4—3141no—
316C22⋊C4—3141no—
317C22⋊C4—3141no—
318C22⋊C4—3141no—
319C22⋊C4—1571no—
320C22⋊C4—1571no—
321C42—21no—
322C42—3141no—
323C42—1571no—
324C42C22×D15711yescharacteristic
325C23—21no—
326C23—21no—
327C23—3141no—
328C23—3141no—
329C23—6282no—
330C23—1571no—
331C23—12561no—
332C23—12561no—
333Q8—21no—
334Q8—3141no—
335Q8—3141no—
336Q8D4×D15712yes—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—81no—
343D4—3144no—
344D4—3141no—
345D4—3141no—
346D4—3141no—
347D4—6282no—
348D4—6282no—
349D4—1572no—
350D4—12561no—
351D4—12561no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—3144no—
355C2×C4—3141no—
356C2×C4—3141no—
357C2×C4—6282no—
358C2×C4—1571no—
359C2×C4—1571no—
360C2×C4—1571no—
361C2×C4—1572no—
362C2×C4—1572no—
363C2×C4—12561no—
364C2×C4—12561no—
365C2×C4—12561no—
366C2×C4D4×D15711yescharacteristic
367C2×C4D4×D15711yescharacteristic
368C2×C4C23×D15711yescharacteristic
369C8—21no—
370C8—21no—
371C8—3141no—
372C8—3141no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—3141no—
380C22—3141no—
381C22—3142no—
382C22—6281no—
383C22—6281no—
384C22—6281no—
385C22—6281no—
386C22—6281no—
387C22—1572no—
388C22—12564no—
389C22C2×D4×D15711yescharacteristic
390C4—22no—
391C4—21no—
392C4—21no—
393C4—41no—
394C4—3141no—
395C4—3141no—
396C4—6281no—
397C4—6281no—
398C4—1572no—
399C4C2×D4×D15711yescharacteristic
400C4#41×D15711yescharacteristic
401C2—81no—
402C2—81no—
403C2—3142no—
404C2—6282no—
405C2—12561no—
406C2#121×D15711yescharacteristic
407C2#2375807711yescharacteristic
408C2#2375807911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#460×C157C2
socleC22×C157C22×D4
hypercenter#460D157
hypocenterC157#3045
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#19097798C2semidirect
2. C2×#19097792C2semidirect
3. #23757836C2semidirect
4. #23757755C2semidirect
5. #23757495C2semidirect
6. #23757493C2semidirect
7. #23757489C2semidirect
8. #23757487C2semidirect
9. #23757471C2semidirect
10. #23757467C2semidirect
11. #23757465C2semidirect
12. #23757298C2semidirect
13. #23757271C2semidirect
14. #102×D157C2semidirect
15. #460×C157C2semidirect
21. C2×#14578944C22semidirect
22. C2×#14578943C22semidirect
26. C2×#14578939C22semidirect
36. Q8×Dic157C22semidirect
38. C4×D628C22semidirect
40. #19097733C22semidirect
45. C4⋊#11929434C22semidirect
46. #19097700C22semidirect
47. #19097700C22semidirect
48. #19097696C22semidirect
49. #19097694C22semidirect
52. #19097692C22semidirect
55. C2×SD16×C157C22semidirect
57. C4×Q8×C157C22semidirect
58. C4⋊C8×C157C22semidirect
60. #102×C157C22semidirect
63. #14578955D4semidirect
204. C157#3045semidirect
215. #460D157semidirect
230. C2×SD16C2×D157semidirect
245. C4×Q8C2×D157semidirect
257. C4⋊C8C2×D157semidirect
265. #102C2×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977982
C2×#190977922
#237578362
#237577552
#237574952
#237574932
#237574892
#237574872
#237574712
#237574672
#237574652
#237572982
#237572712
#102×D1572
#460×C1572
#3045157