Finite Group Databasebeta

← C101×#19279 #38801430

Subgroups — C101×#19279 #38801430

Order 25856.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3167C211yesmaximal, characteristic, complemented
2C101×#3077C211yesmaximal, characteristic, complemented
3C101×#3036C211yesmaximal, characteristic
4C2×#436×C101C211yesmaximal, characteristic, complemented
5C101×#1699C212yesmaximal, complemented
6C101×#1697C212yesmaximal, complemented
7C101×#1691C212yesmaximal, complemented
8C101×#1685C212yesmaximal, complemented
9C101×#1567C211yesmaximal, characteristic, complemented
10C101×#1550C211yesmaximal, characteristic, complemented
11C101×#1547C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C101—21no—
13C22×M16×C101—21no—
14#533×C101C2211yescharacteristic
15#532×C101C2211yescharacteristic
16C2×C4×D4×C101C2211yescharacteristic
17#498×C101C2211yescharacteristic, complemented
18#492×C101C2211yescharacteristic, complemented
19#487×C101C2211yescharacteristic, complemented
20#486×C101C2211yescharacteristic, complemented
21#478×C101—22no—
22#476×C101C2212yes—
23#474×C101C2212yes—
24#465×C101—21no—
25#465×C101—21no—
26#463×C101—22no—
27#461×C101C2212yes—
28#459×C101C2212yes—
29C4×SD16×C101—21no—
30C4×SD16×C101—21no—
31#436×C101—21no—
32#436×C101—21no—
33#436×C101C2212yes—
34#436×C101C2212yes—
35#428×C101—21no—
36#423×C101C2211yescharacteristic
37#423×C101C2211yescharacteristic
38C2×C4⋊C8×C101C2211yescharacteristic
39#418×C101—21no—
40#417×C101—21no—
41C2×C22⋊C8×C101—21no—
42C2×C4×C8×C101C2211yescharacteristic
43#335×C101C2212yescomplemented
44#335×C101C2212yescomplemented
45#333×C101C2212yescomplemented
46#332×C101C2212yescomplemented
47#332×C101C2212yescomplemented
48#331×C101C2212yescomplemented
49C2×#41×C101—21no—
50C22×D4×C101D411yescharacteristic
51C23×C4×C101—21no—
52AGL(1,ℤ/8)×C101—44no—
53C2×SD16×C101—22no—
54C2×SD16×C101—21no—
55C2×SD16×C101—21no—
56C2×D8×C101—22no—
57C2×M16×C101—21no—
58C2×M16×C101—21no—
59C2×M16×C101—22no—
60C2×M16×C101—22no—
61C2×M16×C101—44no—
62C22×C8×C101—21no—
63C22×C8×C101D411yescharacteristic
64C22×C8×C101D411yescharacteristic
65C4⋊Q8×C101C2311yescharacteristic
66C4⋊Q8×C101C2311yescharacteristic
67C4⋊Q8×C101C2311yescharacteristic
68#127×C101C2311yescharacteristic
69#125×C101—21no—
70#124×C101—21no—
71C22⋊Q8×C101—21no—
72C22⋊Q8×C101—21no—
73#121×C101—21no—
74#121×C101—21no—
75C4×Q8×C101—21no—
76C4×Q8×C101—21no—
77C4×D4×C101—21no—
78C4×D4×C101—21no—
79C4×D4×C101—21no—
80C4×D4×C101—21no—
81C4×D4×C101D412yes—
82C4×D4×C101C2312yes—
83#117×C101—21no—
84C2×C4⋊C4×C101D411yescharacteristic
85C2×C22⋊C4×C101—21no—
86C2×C42×C101C2311yescharacteristic
87#107×C101—22no—
88#106×C101—21no—
89#106×C101—21no—
90#106×C101—22no—
91C4⋊C8×C101—21no—
92C4⋊C8×C101—21no—
93C4⋊C8×C101—21no—
94C4⋊C8×C101C2312yes—
95C4⋊C8×C101C2312yes—
96C4⋊C8×C101C2312yes—
97#103×C101—21no—
98#103×C101—21no—
99#103×C101—22no—
100#102×C101—22no—
101#102×C101—22no—
102#102×C101—21no—
103#102×C101—21no—
104#102×C101—22no—
105C22⋊C8×C101—22no—
106C22⋊C8×C101—22no—
107C4×C8×C101D411yescharacteristic
108C4×C8×C101D411yescharacteristic
109C4×C8×C101C2311yescharacteristic
110C4×C8×C101C2311yescharacteristic
111C24×C101—21no—
112#41×C101—42no—
113#41×C101—42no—
114C2×Q8×C101—21no—
115C2×Q8×C101—21no—
116C2×Q8×C101—21no—
117C2×D4×C101—21no—
118C2×D4×C101—22no—
119C2×D4×C101—22no—
120C2×D4×C101—21no—
121C2×D4×C101—21no—
122C2×D4×C101—21no—
123C2×D4×C101—41no—
124C2×D4×C101C2×D412yes—
125C22×C4×C101—21no—
126C22×C4×C101—22no—
127C22×C4×C101—22no—
128C22×C4×C101—42no—
129C22×C4×C101—42no—
130C22×C4×C101—41no—
131C22×C4×C101C2×D411yescharacteristic
132C22×C4×C101C2×D411yescharacteristic
133C22×C4×C101#4111yescharacteristic
134SD16×C101—42no—
135SD16×C101—44no—
136SD16×C101—42no—
137D8×C101—44no—
138M16×C101—44no—
139M16×C101—42no—
140M16×C101—42no—
141M16×C101—44no—
142C2×C8×C101—22no—
143C2×C8×C101—22no—
144C2×C8×C101—22no—
145C2×C8×C101—22no—
146C2×C8×C101—41no—
147C2×C8×C101—42no—
148C2×C8×C101C2×D411yescharacteristic
149C2×C8×C101C2×D411yescharacteristic
150C2×C8×C101C2×D411yescharacteristic
151C2×C8×C101C2×D411yescharacteristic
152C4⋊C4×C101—21no—
153C4⋊C4×C101—21no—
154C4⋊C4×C101—21no—
155C4⋊C4×C101—21no—
156C4⋊C4×C101—21no—
157C4⋊C4×C101—21no—
158C4⋊C4×C101—21no—
159C4⋊C4×C101—41no—
160C4⋊C4×C101—41no—
161C4⋊C4×C101C2×D412yes—
162C22⋊C4×C101—22no—
163C22⋊C4×C101—22no—
164C22⋊C4×C101—41no—
165C22⋊C4×C101—41no—
166C22⋊C4×C101—41no—
167C42×C101—41no—
168C42×C101C2×D411yescharacteristic
169C42×C101C2×D411yescharacteristic
170C42×C101#4111yescharacteristic
171C42×C101C2411yescharacteristic
172C23×C101—22no—
173C23×C101—42no—
174C23×C101—42no—
175C23×C101—42no—
176C23×C101—41no—
177C23×C101#12111yescharacteristic
178Q8×C101—41no—
179Q8×C101—41no—
180Q8×C101—41no—
181Q8×C101—41no—
182Q8×C101—81no—
183D4×C101—22no—
184D4×C101—22no—
185D4×C101—41no—
186D4×C101—41no—
187D4×C101—41no—
188D4×C101—41no—
189D4×C101—42no—
190D4×C101—81no—
191D4×C101—82no—
192C2×C4×C101—21no—
193C2×C4×C101—21no—
194C2×C4×C101—22no—
195C2×C4×C101—41no—
196C2×C4×C101—44no—
197C2×C4×C101—42no—
198C2×C4×C101—42no—
199C2×C4×C101—42no—
200C2×C4×C101—41no—
201C2×C4×C101—41no—
202C2×C4×C101—41no—
203C2×C4×C101—82no—
204C2×C4×C101#12111yescharacteristic
205C2×C4×C101#12111yescharacteristic
206C2×C4×C101#12111yescharacteristic
207C2×C4×C101AGL(1,ℤ/8)12yes—
208C2×C4×C101#13712yes—
209C2×C4×C101C22×D411yescharacteristic
210C2×C4×C101C22×D411yescharacteristic
211C2×C4×C101C2×#4111yescharacteristic
212C8×C101—21no—
213C8×C101—21no—
214C8×C101—21no—
215C8×C101—42no—
216C8×C101—42no—
217C8×C101—42no—
218C8×C101AGL(1,ℤ/8)12yescomplemented
219C22×C101—21no—
220C22×C101—21no—
221C22×C101—42no—
222C22×C101—42no—
223C22×C101—42no—
224C22×C101—84no—
225C22×C101—81no—
226C22×C101—81no—
227C22×C101—81no—
228C22×C101#46812yes—
229C22×C101C2×#12111yescharacteristic
230C4×C101—21no—
231C4×C101—21no—
232C4×C101—21no—
233C4×C101—42no—
234C4×C101—81no—
235C4×C101—81no—
236C4×C101—81no—
237C4×C101#46812yes—
238C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
240C4×C101C2×#13711yescharacteristic
241C4×C101#57511yescharacteristic
242#19279C10111yesmaximal, characteristic, direct product factor, Sylow
243C2×C101—22no—
244C2×C101—82no—
245C2×C101—161no—
246C2×C101#303611yescharacteristic
247C2×C101C2×#46811yescharacteristic
248C2×C101#306711yescharacteristic
249#3167C2×C10111yescharacteristic, complemented
250#3077C2×C10111yescharacteristic, complemented
251#3036C2×C10111yescharacteristic
252C2×#436C2×C10111yescharacteristic, complemented
253#1699C2×C10112yescomplemented
254#1697C2×C10112yescomplemented
255#1691C2×C10112yescomplemented
256#1685C2×C10112yescomplemented
257#1567C2×C10111yescharacteristic, complemented
258#1550C2×C10111yescharacteristic, complemented
259#1547C2×C10111yescharacteristic, complemented
260C101#1927911yescharacteristic, direct product factor, Sylow
261C2×AGL(1,ℤ/8)—21no—
262C22×M16—21no—
263#533C22×C10111yescharacteristic
264#532C22×C10111yescharacteristic
265C2×C4×D4C22×C10111yescharacteristic
266#498C22×C10111yescharacteristic, complemented
267#492C22×C10111yescharacteristic, complemented
268#487C22×C10111yescharacteristic, complemented
269#486C22×C10111yescharacteristic, complemented
270#478—22no—
271#476C22×C10112yes—
272#474C22×C10112yes—
273#465—21no—
274#465—21no—
275#463—22no—
276#461C22×C10112yes—
277#459C22×C10112yes—
278C4×SD16—21no—
279C4×SD16—21no—
280#436—21no—
281#436—21no—
282#436C22×C10112yes—
283#436C22×C10112yes—
284#428—21no—
285#423C22×C10111yescharacteristic
286#423C22×C10111yescharacteristic
287C2×C4⋊C8C22×C10111yescharacteristic
288#418—21no—
289#417—21no—
290C2×C22⋊C8—21no—
291C2×C4×C8C22×C10111yescharacteristic
292#335C22×C10112yescomplemented
293#335C22×C10112yescomplemented
294#333C22×C10112yescomplemented
295#332C22×C10112yescomplemented
296#332C22×C10112yescomplemented
297#331C22×C10112yescomplemented
298C2×#41—21no—
299C22×D4D4×C10111yescharacteristic
300C23×C4—21no—
301AGL(1,ℤ/8)—44no—
302C2×SD16—22no—
303C2×SD16—21no—
304C2×SD16—21no—
305C2×D8—22no—
306C2×M16—21no—
307C2×M16—21no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—44no—
311C22×C8—21no—
312C22×C8D4×C10111yescharacteristic
313C22×C8D4×C10111yescharacteristic
314C4⋊Q8C23×C10111yescharacteristic
315C4⋊Q8C23×C10111yescharacteristic
316C4⋊Q8C23×C10111yescharacteristic
317#127C23×C10111yescharacteristic
318#125—21no—
319#124—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322#121—21no—
323#121—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4D4×C10112yes—
331C4×D4C23×C10112yes—
332#117—21no—
333C2×C4⋊C4D4×C10111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C42C23×C10111yescharacteristic
336#107—22no—
337#106—21no—
338#106—21no—
339#106—22no—
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8C23×C10112yes—
344C4⋊C8C23×C10112yes—
345C4⋊C8C23×C10112yes—
346#103—21no—
347#103—21no—
348#103—22no—
349#102—22no—
350#102—22no—
351#102—21no—
352#102—21no—
353#102—22no—
354C22⋊C8—22no—
355C22⋊C8—22no—
356C4×C8D4×C10111yescharacteristic
357C4×C8D4×C10111yescharacteristic
358C4×C8C23×C10111yescharacteristic
359C4×C8C23×C10111yescharacteristic
360C24—21no—
361#41—42no—
362#41—42no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4C2×D4×C10112yes—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—41no—
380C22×C4C2×D4×C10111yescharacteristic
381C22×C4C2×D4×C10111yescharacteristic
382C22×C4#41×C10111yescharacteristic
383SD16—42no—
384SD16—44no—
385SD16—42no—
386D8—44no—
387M16—44no—
388M16—42no—
389M16—42no—
390M16—44no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—41no—
396C2×C8—42no—
397C2×C8C2×D4×C10111yescharacteristic
398C2×C8C2×D4×C10111yescharacteristic
399C2×C8C2×D4×C10111yescharacteristic
400C2×C8C2×D4×C10111yescharacteristic
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4C2×D4×C10112yes—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C42—41no—
417C42C2×D4×C10111yescharacteristic
418C42C2×D4×C10111yescharacteristic
419C42#41×C10111yescharacteristic
420C42C24×C10111yescharacteristic
421C23—22no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—41no—
426C23#121×C10111yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431Q8—81no—
432D4—22no—
433D4—22no—
434D4—42no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—81no—
440D4—82no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—82no—
453C2×C4#121×C10111yescharacteristic
454C2×C4#121×C10111yescharacteristic
455C2×C4#121×C10111yescharacteristic
456C2×C4AGL(1,ℤ/8)×C10112yes—
457C2×C4#137×C10112yes—
458C2×C4C22×D4×C10111yescharacteristic
459C2×C4C22×D4×C10111yescharacteristic
460C2×C4C2×#41×C10111yescharacteristic
461C8—21no—
462C8—21no—
463C8—21no—
464C8—42no—
465C8—42no—
466C8—42no—
467C8AGL(1,ℤ/8)×C10112yescomplemented
468C22—21no—
469C22—21no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—84no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22#468×C10112yes—
478C22C2×#121×C10111yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4#468×C10112yes—
487C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
488C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
489C4C2×#137×C10111yescharacteristic
490C4#575×C10111yescharacteristic
491C2—22no—
492C2—82no—
493C2—161no—
494C2C101×#303611yescharacteristic
495C2C2×#468×C10111yescharacteristic
496C2C101×#306711yescharacteristic
subgroupG/H
center, socleC22×C101C2×#121
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3036C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3167C2semidirect
2. C101×#3077C2semidirect
4. C2×#436×C101C2semidirect
5. C101×#1699C2semidirect
6. C101×#1697C2semidirect
7. C101×#1691C2semidirect
8. C101×#1685C2semidirect
9. C101×#1567C2semidirect
10. C101×#1550C2semidirect
11. C101×#1547C2semidirect
17. #498×C101C22semidirect
18. #492×C101C22semidirect
19. #487×C101C22semidirect
20. #486×C101C22semidirect
43. #335×C101C22semidirect
44. #335×C101C22semidirect
45. #333×C101C22semidirect
46. #332×C101C22semidirect
47. #332×C101C22semidirect
48. #331×C101C22semidirect
218. C8×C101AGL(1,ℤ/8)semidirect
242. #19279C101direct (N × H)
249. #3167C2×C101semidirect
250. #3077C2×C101semidirect
252. C2×#436C2×C101semidirect
253. #1699C2×C101semidirect
254. #1697C2×C101semidirect
255. #1691C2×C101semidirect
256. #1685C2×C101semidirect
257. #1567C2×C101semidirect
258. #1550C2×C101semidirect
259. #1547C2×C101semidirect
260. C101#19279direct (N × H)
266. #498C22×C101semidirect
267. #492C22×C101semidirect
268. #487C22×C101semidirect
269. #486C22×C101semidirect
292. #335C22×C101semidirect
293. #335C22×C101semidirect
294. #333C22×C101semidirect
295. #332C22×C101semidirect
296. #332C22×C101semidirect
297. #331C22×C101semidirect
467. C8AGL(1,ℤ/8)×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31672
C101×#30772
C101×#30362
C2×#436×C1012
C101×#16992
C101×#16972
C101×#16912
C101×#16852
C101×#15672
C101×#15502
C101×#15472
#19279101