Finite Group Databasebeta

← C101×#19142 #38801293

Subgroups — C101×#19142 #38801293

Order 25856.

684 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3131C211yesmaximal, characteristic, complemented
2C101×#3101C211yesmaximal, characteristic, complemented
3C101×#3100C211yesmaximal, characteristic
4C2×#436×C101C211yesmaximal, characteristic, complemented
5C101×#1703C212yesmaximal, complemented
6C101×#1701C212yesmaximal, complemented
7C101×#1699C212yesmaximal, complemented
8C101×#1697C212yesmaximal, complemented
9C101×#1564C211yesmaximal, characteristic, complemented
10C101×#1542C211yesmaximal, characteristic, complemented
11C101×#1540C211yesmaximal, characteristic, complemented
12C22×M16×C101—21no—
13#533×C101C2211yescharacteristic
14#532×C101C2211yescharacteristic
15C2×C4×D4×C101C2211yescharacteristic
16#488×C101—21no—
17#488×C101—21no—
18#487×C101C2211yescharacteristic, complemented
19#487×C101C2211yescharacteristic, complemented
20#486×C101C2211yescharacteristic, complemented
21#486×C101C2211yescharacteristic, complemented
22#483×C101—21no—
23#480×C101—21no—
24#476×C101C2212yes—
25#474×C101C2212yes—
26#461×C101C2212yes—
27#459×C101C2212yes—
28#450×C101—21no—
29#447×C101—21no—
30C4×SD16×C101—22no—
31C4×D8×C101—22no—
32#436×C101—21no—
33#436×C101—21no—
34#436×C101C2212yes—
35#436×C101C2212yes—
36#431×C101C2211yescharacteristic
37#431×C101C2211yescharacteristic
38C2×C4⋊C8×C101C2211yescharacteristic
39#416×C101—21no—
40#416×C101—21no—
41C2×C22⋊C8×C101—21no—
42C2×C4×C8×C101C2211yescharacteristic
43#335×C101C2212yescomplemented
44#334×C101C2212yescomplemented
45#333×C101C2212yescomplemented
46#332×C101C2212yescomplemented
47#332×C101C2212yescomplemented
48#331×C101C2212yescomplemented
49C2×#41×C101—21no—
50C22×D4×C101D411yescharacteristic
51C23×C4×C101—21no—
52C2×SD16×C101—22no—
53C2×D8×C101—22no—
54C2×M16×C101—22no—
55C2×M16×C101—22no—
56C2×M16×C101—44no—
57C22×C8×C101—21no—
58C22×C8×C101D411yescharacteristic
59C22×C8×C101D411yescharacteristic
60C4⋊Q8×C101C2311yescharacteristic
61C4⋊Q8×C101C2311yescharacteristic
62C4⋊Q8×C101C2311yescharacteristic
63#127×C101C2311yescharacteristic
64#125×C101—21no—
65#124×C101—21no—
66C22⋊Q8×C101—21no—
67C22⋊Q8×C101—21no—
68#121×C101—21no—
69#121×C101—21no—
70C4×Q8×C101—21no—
71C4×Q8×C101—21no—
72C4×D4×C101—21no—
73C4×D4×C101—21no—
74C4×D4×C101—21no—
75C4×D4×C101—21no—
76C4×D4×C101D412yes—
77C4×D4×C101C2312yes—
78#117×C101—21no—
79C2×C4⋊C4×C101D411yescharacteristic
80C2×C22⋊C4×C101—21no—
81C2×C42×C101C2311yescharacteristic
82#107×C101—22no—
83#106×C101—22no—
84C4⋊C8×C101—21no—
85C4⋊C8×C101C2312yes—
86C4⋊C8×C101C2312yes—
87C4⋊C8×C101C2312yes—
88#103×C101—21no—
89#103×C101—21no—
90#103×C101—21no—
91#103×C101—21no—
92#103×C101—22no—
93#102×C101—22no—
94#102×C101—22no—
95#102×C101—21no—
96#102×C101—21no—
97#102×C101—21no—
98#102×C101—21no—
99#102×C101—22no—
100C22⋊C8×C101—21no—
101C22⋊C8×C101—21no—
102C22⋊C8×C101—22no—
103C22⋊C8×C101—22no—
104C4×C8×C101—21no—
105C4×C8×C101—21no—
106C4×C8×C101D411yescharacteristic
107C4×C8×C101D411yescharacteristic
108C4×C8×C101C2311yescharacteristic
109C4×C8×C101C2311yescharacteristic
110C24×C101—21no—
111#41×C101—42no—
112#41×C101—42no—
113C2×Q8×C101—21no—
114C2×Q8×C101—21no—
115C2×Q8×C101—21no—
116C2×D4×C101—21no—
117C2×D4×C101—21no—
118C2×D4×C101—21no—
119C2×D4×C101—21no—
120C2×D4×C101—42no—
121C2×D4×C101—41no—
122C2×D4×C101C2×D412yes—
123C22×C4×C101—21no—
124C22×C4×C101—22no—
125C22×C4×C101—22no—
126C22×C4×C101—42no—
127C22×C4×C101—42no—
128C22×C4×C101—41no—
129C22×C4×C101C2×D411yescharacteristic
130C22×C4×C101C2×D411yescharacteristic
131C22×C4×C101#4111yescharacteristic
132SD16×C101—44no—
133D8×C101—44no—
134M16×C101—44no—
135M16×C101—44no—
136C2×C8×C101—22no—
137C2×C8×C101—22no—
138C2×C8×C101—22no—
139C2×C8×C101—22no—
140C2×C8×C101—22no—
141C2×C8×C101—42no—
142C2×C8×C101C2×D411yescharacteristic
143C2×C8×C101C2×D411yescharacteristic
144C2×C8×C101C2×D411yescharacteristic
145C2×C8×C101C2×D411yescharacteristic
146C4⋊C4×C101—21no—
147C4⋊C4×C101—21no—
148C4⋊C4×C101—21no—
149C4⋊C4×C101—21no—
150C4⋊C4×C101—21no—
151C4⋊C4×C101—21no—
152C4⋊C4×C101—21no—
153C4⋊C4×C101—41no—
154C4⋊C4×C101—41no—
155C4⋊C4×C101C2×D412yes—
156C22⋊C4×C101—22no—
157C22⋊C4×C101—22no—
158C22⋊C4×C101—41no—
159C22⋊C4×C101—41no—
160C22⋊C4×C101—41no—
161C42×C101—41no—
162C42×C101C2×D411yescharacteristic
163C42×C101C2×D411yescharacteristic
164C42×C101#4111yescharacteristic
165C42×C101C2411yescharacteristic
166C23×C101—22no—
167C23×C101—42no—
168C23×C101—42no—
169C23×C101—42no—
170C23×C101—41no—
171C23×C101#12111yescharacteristic
172Q8×C101—41no—
173Q8×C101—41no—
174Q8×C101—42no—
175Q8×C101—81no—
176D4×C101—22no—
177D4×C101—22no—
178D4×C101—42no—
179D4×C101—41no—
180D4×C101—41no—
181D4×C101—42no—
182D4×C101—81no—
183D4×C101—82no—
184C2×C4×C101—22no—
185C2×C4×C101—22no—
186C2×C4×C101—41no—
187C2×C4×C101—42no—
188C2×C4×C101—42no—
189C2×C4×C101—42no—
190C2×C4×C101—44no—
191C2×C4×C101—41no—
192C2×C4×C101—41no—
193C2×C4×C101—41no—
194C2×C4×C101—82no—
195C2×C4×C101#12111yescharacteristic
196C2×C4×C101#12111yescharacteristic
197C2×C4×C101#12111yescharacteristic
198C2×C4×C101#13512yes—
199C2×C4×C101AGL(1,ℤ/8)12yes—
200C2×C4×C101C22×D411yescharacteristic
201C2×C4×C101C22×D411yescharacteristic
202C2×C4×C101C2×#4111yescharacteristic
203C8×C101—21no—
204C8×C101—21no—
205C8×C101—21no—
206C8×C101—21no—
207C8×C101—42no—
208C8×C101—42no—
209C8×C101—42no—
210C22×C101—21no—
211C22×C101—21no—
212C22×C101—42no—
213C22×C101—42no—
214C22×C101—42no—
215C22×C101—84no—
216C22×C101—81no—
217C22×C101—81no—
218C22×C101—81no—
219C22×C101#46312yes—
220C22×C101C2×#12111yescharacteristic
221C4×C101—21no—
222C4×C101—21no—
223C4×C101—21no—
224C4×C101—42no—
225C4×C101—81no—
226C4×C101—81no—
227C4×C101—81no—
228C4×C101#46312yes—
229C4×C101C2×#13511yescharacteristic
230C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
231C4×C101#57512yes—
232#19142C10111yesmaximal, characteristic, direct product factor, Sylow
233C2×C101—22no—
234C2×C101—82no—
235C2×C101—161no—
236C2×C101C2×#46311yescharacteristic
237C2×C101#305411yescharacteristic
238C2×C101#306711yescharacteristic
239#3131C2×C10111yescharacteristic, complemented
240#3101C2×C10111yescharacteristic, complemented
241#3100C2×C10111yescharacteristic
242C2×#436C2×C10111yescharacteristic, complemented
243#1703C2×C10112yescomplemented
244#1701C2×C10112yescomplemented
245#1699C2×C10112yescomplemented
246#1697C2×C10112yescomplemented
247#1564C2×C10111yescharacteristic, complemented
248#1542C2×C10111yescharacteristic, complemented
249#1540C2×C10111yescharacteristic, complemented
250C101#1914211yescharacteristic, direct product factor, Sylow
251C22×M16—21no—
252#533C22×C10111yescharacteristic
253#532C22×C10111yescharacteristic
254C2×C4×D4C22×C10111yescharacteristic
255#488—21no—
256#488—21no—
257#487C22×C10111yescharacteristic, complemented
258#487C22×C10111yescharacteristic, complemented
259#486C22×C10111yescharacteristic, complemented
260#486C22×C10111yescharacteristic, complemented
261#483—21no—
262#480—21no—
263#476C22×C10112yes—
264#474C22×C10112yes—
265#461C22×C10112yes—
266#459C22×C10112yes—
267#450—21no—
268#447—21no—
269C4×SD16—22no—
270C4×D8—22no—
271#436—21no—
272#436—21no—
273#436C22×C10112yes—
274#436C22×C10112yes—
275#431C22×C10111yescharacteristic
276#431C22×C10111yescharacteristic
277C2×C4⋊C8C22×C10111yescharacteristic
278#416—21no—
279#416—21no—
280C2×C22⋊C8—21no—
281C2×C4×C8C22×C10111yescharacteristic
282#335C22×C10112yescomplemented
283#334C22×C10112yescomplemented
284#333C22×C10112yescomplemented
285#332C22×C10112yescomplemented
286#332C22×C10112yescomplemented
287#331C22×C10112yescomplemented
288C2×#41—21no—
289C22×D4D4×C10111yescharacteristic
290C23×C4—21no—
291C2×SD16—22no—
292C2×D8—22no—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—44no—
296C22×C8—21no—
297C22×C8D4×C10111yescharacteristic
298C22×C8D4×C10111yescharacteristic
299C4⋊Q8C23×C10111yescharacteristic
300C4⋊Q8C23×C10111yescharacteristic
301C4⋊Q8C23×C10111yescharacteristic
302#127C23×C10111yescharacteristic
303#125—21no—
304#124—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307#121—21no—
308#121—21no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4D4×C10112yes—
316C4×D4C23×C10112yes—
317#117—21no—
318C2×C4⋊C4D4×C10111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C42C23×C10111yescharacteristic
321#107—22no—
322#106—22no—
323C4⋊C8—21no—
324C4⋊C8C23×C10112yes—
325C4⋊C8C23×C10112yes—
326C4⋊C8C23×C10112yes—
327#103—21no—
328#103—21no—
329#103—21no—
330#103—21no—
331#103—22no—
332#102—22no—
333#102—22no—
334#102—21no—
335#102—21no—
336#102—21no—
337#102—21no—
338#102—22no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—22no—
342C22⋊C8—22no—
343C4×C8—21no—
344C4×C8—21no—
345C4×C8D4×C10111yescharacteristic
346C4×C8D4×C10111yescharacteristic
347C4×C8C23×C10111yescharacteristic
348C4×C8C23×C10111yescharacteristic
349C24—21no—
350#41—42no—
351#41—42no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—42no—
360C2×D4—41no—
361C2×D4C2×D4×C10112yes—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—41no—
368C22×C4C2×D4×C10111yescharacteristic
369C22×C4C2×D4×C10111yescharacteristic
370C22×C4#41×C10111yescharacteristic
371SD16—44no—
372D8—44no—
373M16—44no—
374M16—44no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—42no—
381C2×C8C2×D4×C10111yescharacteristic
382C2×C8C2×D4×C10111yescharacteristic
383C2×C8C2×D4×C10111yescharacteristic
384C2×C8C2×D4×C10111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4C2×D4×C10112yes—
395C22⋊C4—22no—
396C22⋊C4—22no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C42—41no—
401C42C2×D4×C10111yescharacteristic
402C42C2×D4×C10111yescharacteristic
403C42#41×C10111yescharacteristic
404C42C24×C10111yescharacteristic
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23#121×C10111yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—42no—
414Q8—81no—
415D4—22no—
416D4—22no—
417D4—42no—
418D4—41no—
419D4—41no—
420D4—42no—
421D4—81no—
422D4—82no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—82no—
434C2×C4#121×C10111yescharacteristic
435C2×C4#121×C10111yescharacteristic
436C2×C4#121×C10111yescharacteristic
437C2×C4#135×C10112yes—
438C2×C4AGL(1,ℤ/8)×C10112yes—
439C2×C4C22×D4×C10111yescharacteristic
440C2×C4C22×D4×C10111yescharacteristic
441C2×C4C2×#41×C10111yescharacteristic
442C8—21no—
443C8—21no—
444C8—21no—
445C8—21no—
446C8—42no—
447C8—42no—
448C8—42no—
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22#463×C10112yes—
459C22C2×#121×C10111yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4#463×C10112yes—
468C4C2×#135×C10111yescharacteristic
469C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
470C4#575×C10112yes—
471C2—22no—
472C2—82no—
473C2—161no—
474C2C2×#463×C10111yescharacteristic
475C2C101×#305411yescharacteristic
476C2C101×#306711yescharacteristic
subgroupG/H
centerC2×C4×C101#121
commutator, Frattini, cosocleC42C24×C101
socleC22×C101C2×#121
prime radicalC101×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3131C2semidirect
2. C101×#3101C2semidirect
4. C2×#436×C101C2semidirect
5. C101×#1703C2semidirect
6. C101×#1701C2semidirect
7. C101×#1699C2semidirect
8. C101×#1697C2semidirect
9. C101×#1564C2semidirect
10. C101×#1542C2semidirect
11. C101×#1540C2semidirect
18. #487×C101C22semidirect
19. #487×C101C22semidirect
20. #486×C101C22semidirect
21. #486×C101C22semidirect
43. #335×C101C22semidirect
44. #334×C101C22semidirect
45. #333×C101C22semidirect
46. #332×C101C22semidirect
47. #332×C101C22semidirect
48. #331×C101C22semidirect
232. #19142C101direct (N × H)
239. #3131C2×C101semidirect
240. #3101C2×C101semidirect
242. C2×#436C2×C101semidirect
243. #1703C2×C101semidirect
244. #1701C2×C101semidirect
245. #1699C2×C101semidirect
246. #1697C2×C101semidirect
247. #1564C2×C101semidirect
248. #1542C2×C101semidirect
249. #1540C2×C101semidirect
250. C101#19142direct (N × H)
257. #487C22×C101semidirect
258. #487C22×C101semidirect
259. #486C22×C101semidirect
260. #486C22×C101semidirect
282. #335C22×C101semidirect
283. #334C22×C101semidirect
284. #333C22×C101semidirect
285. #332C22×C101semidirect
286. #332C22×C101semidirect
287. #331C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31312
C101×#31012
C101×#31002
C2×#436×C1012
C101×#17032
C101×#17012
C101×#16992
C101×#16972
C101×#15642
C101×#15422
C101×#15402
#19142101