Finite Group Databasebeta

← #453×D157 #34109457

Subgroups — #453×D157 #34109457

Order 20096.

844 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 135 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
1H(5,𝔽2)×D157C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×D157C212yesmaximal, complemented
3#127×D157C211yesmaximal, characteristic, complemented
4#23757443C211yesmaximal, characteristic, complemented
5#23757442C212yesmaximal, complemented
6#23757441C211yesmaximal, characteristic, complemented
7#23757440C211yesmaximal, characteristic, complemented
8#23757439C212yesmaximal, complemented
9#104×D157C212yesmaximal, complemented
10#100×D157C211yesmaximal, characteristic, complemented
11#453×C157C211yesmaximal, characteristic, complemented
12#19097817—22no—
13#19097817C2212yescomplemented
14#19097816—22no—
15#19097816—22no—
16#19097816C2211yescharacteristic, complemented
17#41×D157—22no—
18#41×D157C2212yes—
19C2×D4×D157—22no—
20C2×D4×D157—22no—
21C2×D4×D157—22no—
22C2×D4×D157C2211yescharacteristic
23C2×D4×D157C2211yescharacteristic, complemented
24#19097799C2212yescomplemented
25#19097798—22no—
26#19097797C2212yescomplemented
27#19097796C2212yescomplemented
28#19097795—22no—
29SD16×D157—22no—
30D8×D157—22no—
31M16×D157C2212yescomplemented
32#19097768C2211yescharacteristic, complemented
33#19097767—22no—
34#19097767C2211yescharacteristic, complemented
35#19097767C2211yescharacteristic, complemented
36C42×D157C2211yescharacteristic, complemented
37#19097699C2212yescomplemented
38#19097698C2212yescomplemented
39#19097697C2212yescomplemented
40#19097688C2211yescharacteristic, complemented
41#19097687C2212yescomplemented
42H(5,𝔽2)×C157C2211yescharacteristic, complemented
43AGL(1,ℤ/8)×C157C2212yescomplemented
44#127×C157C2211yescharacteristic, complemented
45#104×C157C2212yescomplemented
46#100×C157C2211yescharacteristic, complemented
47C23×D157—22no—
48C23×D157—21no—
49C23×D157D412yes—
50#14578955—22no—
51#14578955D412yescomplemented
52#14578954—24no—
53#14578954—22no—
54#14578954—22no—
55#14578954C2312yes—
56#14578953—24no—
57#14578953—22no—
58#14578953—22no—
59#14578953D412yescomplemented
60Q8×D157D412yescomplemented
61C2×D628—22no—
62C2×D628—22no—
63C2×D628—22no—
64C2×D628C2311yescharacteristic
65C2×D628C2311yescharacteristic, complemented
66C2×C22⋊D157—22no—
67C2×C22⋊D157—24no—
68C2×C22⋊D157—22no—
69C2×C22⋊D157—21no—
70C2×C22⋊D157—22no—
71C2×C22⋊D157—22no—
72C2×C22⋊D157D412yes—
73D4×D157—24no—
74D4×D157—24no—
75D4×D157—24no—
76D4×D157—22no—
77D4×D157—24no—
78D4×D157—22no—
79D4×D157—22no—
80D4×D157—22no—
81D4×D157—22no—
82D4×D157—22no—
83D4×D157—22no—
84D4×D157—48no—
85D4×D157D412yescomplemented
86C2×C4×D157—22no—
87C2×C4×D157—21no—
88C2×C4×D157—22no—
89C2×C4×D157C2311yescharacteristic
90#14578943—22no—
91#14578942—22no—
92#14578941—22no—
93D1256—22no—
94#14578939—22no—
95#14578939—22no—
96#14578938C2312yescomplemented
97#14578937—22no—
98C8×D157—22no—
99C4×Dic157—21no—
100C4×Dic157C2311yescharacteristic, complemented
101#41×C157—22no—
102#41×C157C2312yes—
103C2×D4×C157—22no—
104C2×D4×C157—22no—
105C2×D4×C157—22no—
106C2×D4×C157C2311yescharacteristic
107C2×D4×C157C2311yescharacteristic, complemented
108SD16×C157—22no—
109D8×C157—22no—
110M16×C157C2312yescomplemented
111C42×C157C2311yescharacteristic, complemented
112C22×D157—24no—
113C22×D157—22no—
114C22×D157—22no—
115C22×D157—22no—
116C22×D157—22no—
117C22×D157—21no—
118C22×D157—44no—
119C22×D157—44no—
120C22×D157—41no—
121C22×D157—41no—
122C22×D157—84no—
123C22×D157C2×D411yescharacteristic
124C22×D157C2×D412yes—
125Dic314—22no—
126Dic314C2×D412yescomplemented
127D628—24no—
128D628—22no—
129D628—22no—
130D628—22no—
131D628—44no—
132D628C2×D412yescomplemented
133C22⋊D157—24no—
134C22⋊D157—24no—
135C22⋊D157—22no—
136C22⋊D157—22no—
137C22⋊D157—24no—
138C22⋊D157—22no—
139C22⋊D157—44no—
140C22⋊D157—44no—
141C22⋊D157—42no—
142C2×Dic157—22no—
143C2×Dic157—21no—
144C2×Dic157—22no—
145C2×Dic157C2×D411yescharacteristic
146C4×D157—24no—
147C4×D157—24no—
148C4×D157—22no—
149C4×D157—22no—
150C4×D157—22no—
151C4×D157C2×D412yes—
152C4×D157C2×D412yes—
153#11929434—22no—
154C23×C157—22no—
155C23×C157—21no—
156C23×C157C2×D412yes—
157Q8×C157C2×D412yescomplemented
158D4×C157—24no—
159D4×C157—22no—
160D4×C157—22no—
161D4×C157—22no—
162D4×C157—44no—
163D4×C157C2×D412yescomplemented
164C2×C4×C157—22no—
165C2×C4×C157—21no—
166C2×C4×C157—22no—
167C2×C4×C157C2411yescharacteristic
168C8×C157—22no—
169C22×C157—22no—
170C22×C157—22no—
171C22×C157—42no—
172C22×C157—42no—
173C22×C157—41no—
174C22×C157—82no—
175C22×C157C22×D411yescharacteristic
176C2×D157—22no—
177C2×D157—22no—
178C2×D157—22no—
179C2×D157—44no—
180C2×D157—44no—
181C2×D157—42no—
182C2×D157—42no—
183C2×D157—41no—
184C2×D157—82no—
185C2×D157—82no—
186C2×D157—84no—
187C2×D157—82no—
188C2×D157—82no—
189C2×D157#12011yescharacteristic
190C2×D157#12011yescharacteristic
191C4×C157—22no—
192C4×C157—22no—
193C4×C157C22×D412yes—
194Dic157—22no—
195Dic157—22no—
196Dic157#12012yes—
197C2×C157—21no—
198C2×C157—42no—
199C2×C157—42no—
200C2×C157—81no—
201C2×C157C2×#12011yescharacteristic
202D157—21no—
203D157—42no—
204D157—42no—
205D157—81no—
206D157#45312yesdirect product factor
207C157C2×#45311yescharacteristic, complemented, Sylow
208C2×#453—1571nomaximal, Sylow
209C2×H(5,𝔽2)—1571no—
210C2×AGL(1,ℤ/8)—1572no—
211C2×#127—1571no—
212#453—1571no—
213#453—1572no—
214#453—1571no—
215#453—1572no—
216#453—1571no—
217#453D15711yescharacteristic, direct product factor
218C2×#104—1572no—
219C2×#100—1571no—
220H(5,𝔽2)—3142no—
221H(5,𝔽2)—3142no—
222H(5,𝔽2)—3142no—
223H(5,𝔽2)—1572no—
224H(5,𝔽2)—1571no—
225H(5,𝔽2)C2×D15711yescharacteristic, complemented
226C2×#41—3142no—
227C2×#41—1572no—
228C22×D4—3142no—
229C22×D4—3142no—
230C22×D4—3142no—
231C22×D4—1571no—
232C22×D4—1571no—
233AGL(1,ℤ/8)—3142no—
234AGL(1,ℤ/8)—3142no—
235AGL(1,ℤ/8)—1572no—
236AGL(1,ℤ/8)—1572no—
237AGL(1,ℤ/8)—1572no—
238AGL(1,ℤ/8)C2×D15712yescomplemented
239C2×SD16—3142no—
240C2×D8—3142no—
241C2×M16—1572no—
242#127—3142no—
243#127—1571no—
244#127—1571no—
245#127—1571no—
246#127C2×D15711yescharacteristic, complemented
247C2×C42—1571no—
248#104—1572no—
249#104—1572no—
250#104—1572no—
251#104C2×D15712yescomplemented
252#100—1571no—
253#100—1572no—
254#100C2×D15711yescharacteristic, complemented
255C24—3142no—
256C24—3141no—
257C24—1572no—
258#41—22no—
259#41—3144no—
260#41—3142no—
261#41—3142no—
262#41—3144no—
263#41—3142no—
264#41—3142no—
265#41—3142no—
266#41—1572no—
267#41—1572no—
268#41—1572no—
269#41C22×D15712yes—
270C2×Q8—1572no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—3142no—
275C2×D4—3142no—
276C2×D4—3142no—
277C2×D4—3144no—
278C2×D4—3144no—
279C2×D4—3144no—
280C2×D4—3142no—
281C2×D4—3144no—
282C2×D4—3142no—
283C2×D4—3142no—
284C2×D4—3144no—
285C2×D4—3142no—
286C2×D4—3142no—
287C2×D4—3142no—
288C2×D4—3142no—
289C2×D4—3142no—
290C2×D4—3142no—
291C2×D4—3142no—
292C2×D4—3142no—
293C2×D4—3141no—
294C2×D4—6288no—
295C2×D4—1572no—
296C2×D4—1572no—
297C2×D4—1571no—
298C2×D4—1571no—
299C2×D4C22×D15711yescharacteristic
300C2×D4C22×D15711yescharacteristic, complemented
301C22×C4—3142no—
302C22×C4—3141no—
303C22×C4—3142no—
304C22×C4—1571no—
305SD16—22no—
306SD16—3142no—
307SD16—3142no—
308SD16—3142no—
309D8—22no—
310D8—3142no—
311D8—3142no—
312D8—3142no—
313M16—3142no—
314M16—1572no—
315M16C22×D15712yescomplemented
316C2×C8—3142no—
317C42—3141no—
318C42—1571no—
319C42C22×D15711yescharacteristic, complemented
320C23—22no—
321C23—21no—
322C23—3142no—
323C23—3144no—
324C23—3142no—
325C23—3142no—
326C23—3142no—
327C23—3141no—
328C23—6284no—
329C23—6284no—
330C23—6281no—
331C23—6281no—
332C23—1571no—
333C23—1572no—
334C23—12564no—
335C23D4×D15712yes—
336Q8—3142no—
337Q8—1572no—
338Q8D4×D15712yescomplemented
339D4—24no—
340D4—22no—
341D4—22no—
342D4—22no—
343D4—44no—
344D4—3144no—
345D4—3142no—
346D4—3144no—
347D4—3144no—
348D4—3142no—
349D4—3142no—
350D4—3144no—
351D4—3142no—
352D4—3142no—
353D4—3142no—
354D4—6284no—
355D4—6284no—
356D4—6284no—
357D4—6282no—
358D4—1572no—
359D4D4×D15712yescomplemented
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—3144no—
364C2×C4—3144no—
365C2×C4—3142no—
366C2×C4—3142no—
367C2×C4—3142no—
368C2×C4—3141no—
369C2×C4—3142no—
370C2×C4—3142no—
371C2×C4—1571no—
372C2×C4—1572no—
373C2×C4—1572no—
374C2×C4C23×D15711yescharacteristic
375C8—22no—
376C8—3142no—
377C22—22no—
378C22—22no—
379C22—42no—
380C22—42no—
381C22—41no—
382C22—82no—
383C22—3142no—
384C22—3142no—
385C22—3142no—
386C22—6282no—
387C22—6282no—
388C22—6284no—
389C22—6284no—
390C22—6281no—
391C22—1571no—
392C22—1571no—
393C22—12562no—
394C22—12562no—
395C22—12564no—
396C22—12562no—
397C22—12562no—
398C22C2×D4×D15711yescharacteristic
399C4—22no—
400C4—22no—
401C4—3142no—
402C4—3142no—
403C4—1572no—
404C4C2×D4×D15712yes—
405C2—21no—
406C2—42no—
407C2—42no—
408C2—81no—
409C2—3141no—
410C2—6282no—
411C2—6282no—
412C2—1572no—
413C2—12561no—
414C2#120×D15711yescharacteristic
subgroupG/H
centerC2#120×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#453×C157C2
socleC2×C157C2×#120
hypercenter#453D157
hypocenterC157C2×#453
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. H(5,𝔽2)×D157C2semidirect
2. AGL(1,ℤ/8)×D157C2semidirect
3. #127×D157C2semidirect
4. #23757443C2semidirect
5. #23757442C2semidirect
6. #23757441C2semidirect
7. #23757440C2semidirect
8. #23757439C2semidirect
9. #104×D157C2semidirect
10. #100×D157C2semidirect
11. #453×C157C2semidirect
13. #19097817C22semidirect
16. #19097816C22semidirect
23. C2×D4×D157C22semidirect
24. #19097799C22semidirect
26. #19097797C22semidirect
27. #19097796C22semidirect
31. M16×D157C22semidirect
32. #19097768C22semidirect
34. #19097767C22semidirect
35. #19097767C22semidirect
36. C42×D157C22semidirect
37. #19097699C22semidirect
38. #19097698C22semidirect
39. #19097697C22semidirect
40. #19097688C22semidirect
41. #19097687C22semidirect
42. H(5,𝔽2)×C157C22semidirect
43. AGL(1,ℤ/8)×C157C22semidirect
44. #127×C157C22semidirect
45. #104×C157C22semidirect
46. #100×C157C22semidirect
51. #14578955D4semidirect
59. #14578953D4semidirect
60. Q8×D157D4semidirect
65. C2×D628C23semidirect
85. D4×D157D4semidirect
96. #14578938C23semidirect
100. C4×Dic157C23semidirect
107. C2×D4×C157C23semidirect
110. M16×C157C23semidirect
111. C42×C157C23semidirect
126. Dic314C2×D4semidirect
132. D628C2×D4semidirect
157. Q8×C157C2×D4semidirect
163. D4×C157C2×D4semidirect
206. D157#453direct (N × H)
207. C157C2×#453semidirect
217. #453D157direct (N × H)
225. H(5,𝔽2)C2×D157semidirect
238. AGL(1,ℤ/8)C2×D157semidirect
246. #127C2×D157semidirect
251. #104C2×D157semidirect
254. #100C2×D157semidirect
300. C2×D4C22×D157semidirect
315. M16C22×D157semidirect
319. C42C22×D157semidirect
338. Q8D4×D157semidirect
359. D4D4×D157semidirect

Maximal subgroups

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

subgroupindex
H(5,𝔽2)×D1572
AGL(1,ℤ/8)×D1572
#127×D1572
#237574432
#237574422
#237574412
#237574402
#237574392
#104×D1572
#100×D1572
#453×C1572
C2×#453157