Finite Group Databasebeta

← C101×#19169 #38801320

Subgroups — C101×#19169 #38801320

Order 25856.

728 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3141C211yesmaximal, characteristic, complemented
2C101×#3100C211yesmaximal, characteristic
3C2×#461×C101C211yesmaximal, characteristic, complemented
4D4×M16×C101C211yesmaximal, characteristic, complemented
5C101×#1701C212yesmaximal, complemented
6C101×#1699C212yesmaximal, complemented
7C101×#1681C212yesmaximal, complemented
8C101×#1679C212yesmaximal, complemented
9C101×#1565C211yesmaximal, characteristic, complemented
10C101×#1549C211yesmaximal, characteristic, complemented
11C101×#1547C211yesmaximal, characteristic, complemented
12C22×SD16×C101—21no—
13C22×M16×C101—21no—
14#532×C101C2211yescharacteristic
15C2×C4⋊Q8×C101C2211yescharacteristic
16C2×C4×D4×C101C2211yescharacteristic
17#489×C101—22no—
18#487×C101C2212yescomplemented
19#486×C101C2212yescomplemented
20#480×C101—21no—
21#474×C101C2211yescharacteristic
22#474×C101C2211yescharacteristic
23#461×C101—21no—
24#461×C101—21no—
25#461×C101C2212yes—
26#461×C101C2212yes—
27#459×C101C2211yescharacteristic
28#459×C101C2211yescharacteristic
29#447×C101—21no—
30C4×D8×C101—21no—
31C4×D8×C101—21no—
32#436×C101C2212yes—
33#435×C101—22no—
34C8×D4×C101C2212yes—
35#431×C101C2211yescharacteristic
36#423×C101C2211yescharacteristic
37C2×C4⋊C8×C101C2211yescharacteristic
38#417×C101—21no—
39#417×C101—21no—
40C2×#103×C101—21no—
41#407×C101—21no—
42C4×M16×C101C2211yescharacteristic
43#335×C101C2212yescomplemented
44#334×C101C2212yescomplemented
45#332×C101C2212yescomplemented
46#332×C101C2212yescomplemented
47#332×C101C2212yescomplemented
48#331×C101C2212yescomplemented
49C2×#41×C101—21no—
50C22×Q8×C101—21no—
51C22×D4×C101D411yescharacteristic
52C23×C4×C101—21no—
53C2×SD16×C101—22no—
54C2×SD16×C101—22no—
55C2×SD16×C101—44no—
56C2×D8×C101—21no—
57C2×D8×C101—21no—
58C2×M16×C101—21no—
59C2×M16×C101—22no—
60C2×M16×C101—44no—
61C2×M16×C101D411yescharacteristic
62C2×M16×C101D411yescharacteristic
63C22×C8×C101—21no—
64C22×C8×C101—22no—
65C4⋊Q8×C101—21no—
66C4⋊Q8×C101—21no—
67C4⋊Q8×C101—21no—
68C4⋊Q8×C101C2312yes—
69C4⋊Q8×C101C2311yescharacteristic
70#127×C101C2311yescharacteristic
71#124×C101—21no—
72#121×C101—21no—
73#121×C101—21no—
74C4×D4×C101—21no—
75C4×D4×C101—21no—
76C4×D4×C101—21no—
77C4×D4×C101—21no—
78C4×D4×C101D411yescharacteristic
79C4×D4×C101D411yescharacteristic
80C4×D4×C101C2311yescharacteristic
81C4×D4×C101C2311yescharacteristic
82C2×C4⋊C4×C101—21no—
83C2×C4⋊C4×C101—21no—
84C2×C4⋊C4×C101D411yescharacteristic
85C2×C22⋊C4×C101—21no—
86C2×C42×C101C2311yescharacteristic
87#107×C101—21no—
88#107×C101—21no—
89C4⋊C8×C101—21no—
90C4⋊C8×C101—21no—
91C4⋊C8×C101C2312yes—
92C4⋊C8×C101C2312yes—
93C4⋊C8×C101C2311yescharacteristic
94C4⋊C8×C101C2311yescharacteristic
95#103×C101—22no—
96#103×C101—22no—
97#103×C101—22no—
98#103×C101—22no—
99#102×C101—21no—
100#102×C101—21no—
101#102×C101—22no—
102#102×C101—22no—
103#102×C101—21no—
104#102×C101—21no—
105C22⋊C8×C101—21no—
106C22⋊C8×C101—22no—
107C22⋊C8×C101—22no—
108#97×C101D412yes—
109C4×C8×C101—21no—
110C4×C8×C101C2312yes—
111C24×C101—21no—
112#41×C101—42no—
113#41×C101—42no—
114C2×Q8×C101—21no—
115C2×Q8×C101—22no—
116C2×Q8×C101—42no—
117C2×Q8×C101—42no—
118C2×Q8×C101—41no—
119C2×D4×C101—22no—
120C2×D4×C101—21no—
121C2×D4×C101—21no—
122C2×D4×C101—21no—
123C2×D4×C101—21no—
124C2×D4×C101—41no—
125C2×D4×C101—41no—
126C2×D4×C101C2×D411yescharacteristic
127C2×D4×C101C2×D411yescharacteristic
128C22×C4×C101—21no—
129C22×C4×C101—21no—
130C22×C4×C101—21no—
131C22×C4×C101—21no—
132C22×C4×C101—21no—
133C22×C4×C101—42no—
134C22×C4×C101—42no—
135C22×C4×C101—41no—
136C22×C4×C101—41no—
137C22×C4×C101C2×D411yescharacteristic
138C22×C4×C101C2×D411yescharacteristic
139C22×C4×C101#4111yescharacteristic
140SD16×C101—44no—
141SD16×C101—44no—
142D8×C101—42no—
143D8×C101—42no—
144M16×C101—22no—
145M16×C101—22no—
146M16×C101—44no—
147M16×C101—42no—
148C2×C8×C101—21no—
149C2×C8×C101—21no—
150C2×C8×C101—22no—
151C2×C8×C101—22no—
152C2×C8×C101—44no—
153C2×C8×C101—42no—
154C2×C8×C101C2×D412yes—
155C2×C8×C101C2×D412yes—
156C4⋊C4×C101—21no—
157C4⋊C4×C101—22no—
158C4⋊C4×C101—21no—
159C4⋊C4×C101—22no—
160C4⋊C4×C101—21no—
161C4⋊C4×C101—41no—
162C4⋊C4×C101—41no—
163C4⋊C4×C101C2×D411yescharacteristic
164C4⋊C4×C101C2×D411yescharacteristic
165C22⋊C4×C101—21no—
166C22⋊C4×C101—21no—
167C22⋊C4×C101—21no—
168C22⋊C4×C101—21no—
169C22⋊C4×C101—41no—
170C22⋊C4×C101—41no—
171C42×C101C2×D411yescharacteristic
172C42×C101C2×D411yescharacteristic
173C42×C101#4111yescharacteristic
174C42×C101C2411yescharacteristic
175C23×C101—21no—
176C23×C101—21no—
177C23×C101—42no—
178C23×C101—42no—
179C23×C101—41no—
180C23×C101—81no—
181C23×C101#12111yescharacteristic
182Q8×C101—41no—
183Q8×C101—42no—
184Q8×C101—41no—
185Q8×C101—42no—
186Q8×C101—82no—
187D4×C101—21no—
188D4×C101—21no—
189D4×C101—21no—
190D4×C101—42no—
191D4×C101—41no—
192D4×C101—41no—
193D4×C101—41no—
194D4×C101—41no—
195D4×C101—81no—
196D4×C101—82no—
197D4×C101AGL(1,ℤ/8)12yes—
198C2×C4×C101—21no—
199C2×C4×C101—21no—
200C2×C4×C101—21no—
201C2×C4×C101—21no—
202C2×C4×C101—41no—
203C2×C4×C101—42no—
204C2×C4×C101—41no—
205C2×C4×C101—41no—
206C2×C4×C101—41no—
207C2×C4×C101—41no—
208C2×C4×C101—42no—
209C2×C4×C101—42no—
210C2×C4×C101—41no—
211C2×C4×C101—42no—
212C2×C4×C101—82no—
213C2×C4×C101—82no—
214C2×C4×C101#12111yescharacteristic
215C2×C4×C101#12111yescharacteristic
216C2×C4×C101#12111yescharacteristic
217C2×C4×C101#13512yes—
218C2×C4×C101AGL(1,ℤ/8)12yes—
219C2×C4×C101C22×D411yescharacteristic
220C2×C4×C101C22×D411yescharacteristic
221C2×C4×C101C2×#4111yescharacteristic
222C8×C101—22no—
223C8×C101—22no—
224C8×C101—42no—
225C8×C101—42no—
226C8×C101—41no—
227C8×C101—41no—
228C22×C101—21no—
229C22×C101—21no—
230C22×C101—22no—
231C22×C101—41no—
232C22×C101—41no—
233C22×C101—41no—
234C22×C101—41no—
235C22×C101—41no—
236C22×C101—84no—
237C22×C101—81no—
238C22×C101—81no—
239C22×C101—81no—
240C22×C101#46312yes—
241C22×C101C2×#12111yescharacteristic
242C4×C101—21no—
243C4×C101—21no—
244C4×C101—21no—
245C4×C101—41no—
246C4×C101—41no—
247C4×C101—81no—
248C4×C101—82no—
249C4×C101#46312yes—
250C4×C101C2×#13511yescharacteristic
251C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
252C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
253C4×C101#57511yescharacteristic
254#19169C10111yesmaximal, characteristic, direct product factor, Sylow
255C2×C101—22no—
256C2×C101—42no—
257C2×C101—81no—
258C2×C101—161no—
259C2×C101C2×#46311yescharacteristic
260C2×C101#305511yescharacteristic
261C2×C101#306911yescharacteristic
262#3141C2×C10111yescharacteristic, complemented
263#3100C2×C10111yescharacteristic
264C2×#461C2×C10111yescharacteristic, complemented
265D4×M16C2×C10111yescharacteristic, complemented
266#1701C2×C10112yescomplemented
267#1699C2×C10112yescomplemented
268#1681C2×C10112yescomplemented
269#1679C2×C10112yescomplemented
270#1565C2×C10111yescharacteristic, complemented
271#1549C2×C10111yescharacteristic, complemented
272#1547C2×C10111yescharacteristic, complemented
273C101#1916911yescharacteristic, direct product factor, Sylow
274C22×SD16—21no—
275C22×M16—21no—
276#532C22×C10111yescharacteristic
277C2×C4⋊Q8C22×C10111yescharacteristic
278C2×C4×D4C22×C10111yescharacteristic
279#489—22no—
280#487C22×C10112yescomplemented
281#486C22×C10112yescomplemented
282#480—21no—
283#474C22×C10111yescharacteristic
284#474C22×C10111yescharacteristic
285#461—21no—
286#461—21no—
287#461C22×C10112yes—
288#461C22×C10112yes—
289#459C22×C10111yescharacteristic
290#459C22×C10111yescharacteristic
291#447—21no—
292C4×D8—21no—
293C4×D8—21no—
294#436C22×C10112yes—
295#435—22no—
296C8×D4C22×C10112yes—
297#431C22×C10111yescharacteristic
298#423C22×C10111yescharacteristic
299C2×C4⋊C8C22×C10111yescharacteristic
300#417—21no—
301#417—21no—
302C2×#103—21no—
303#407—21no—
304C4×M16C22×C10111yescharacteristic
305#335C22×C10112yescomplemented
306#334C22×C10112yescomplemented
307#332C22×C10112yescomplemented
308#332C22×C10112yescomplemented
309#332C22×C10112yescomplemented
310#331C22×C10112yescomplemented
311C2×#41—21no—
312C22×Q8—21no—
313C22×D4D4×C10111yescharacteristic
314C23×C4—21no—
315C2×SD16—22no—
316C2×SD16—22no—
317C2×SD16—44no—
318C2×D8—21no—
319C2×D8—21no—
320C2×M16—21no—
321C2×M16—22no—
322C2×M16—44no—
323C2×M16D4×C10111yescharacteristic
324C2×M16D4×C10111yescharacteristic
325C22×C8—21no—
326C22×C8—22no—
327C4⋊Q8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8C23×C10112yes—
331C4⋊Q8C23×C10111yescharacteristic
332#127C23×C10111yescharacteristic
333#124—21no—
334#121—21no—
335#121—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4D4×C10111yescharacteristic
341C4×D4D4×C10111yescharacteristic
342C4×D4C23×C10111yescharacteristic
343C4×D4C23×C10111yescharacteristic
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4D4×C10111yescharacteristic
347C2×C22⋊C4—21no—
348C2×C42C23×C10111yescharacteristic
349#107—21no—
350#107—21no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8C23×C10112yes—
354C4⋊C8C23×C10112yes—
355C4⋊C8C23×C10111yescharacteristic
356C4⋊C8C23×C10111yescharacteristic
357#103—22no—
358#103—22no—
359#103—22no—
360#103—22no—
361#102—21no—
362#102—21no—
363#102—22no—
364#102—22no—
365#102—21no—
366#102—21no—
367C22⋊C8—21no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370#97D4×C10112yes—
371C4×C8—21no—
372C4×C8C23×C10112yes—
373C24—21no—
374#41—42no—
375#41—42no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8—41no—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4C2×D4×C10111yescharacteristic
389C2×D4C2×D4×C10111yescharacteristic
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4C2×D4×C10111yescharacteristic
400C22×C4C2×D4×C10111yescharacteristic
401C22×C4#41×C10111yescharacteristic
402SD16—44no—
403SD16—44no—
404D8—42no—
405D8—42no—
406M16—22no—
407M16—22no—
408M16—44no—
409M16—42no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—44no—
415C2×C8—42no—
416C2×C8C2×D4×C10112yes—
417C2×C8C2×D4×C10112yes—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4C2×D4×C10111yescharacteristic
426C4⋊C4C2×D4×C10111yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C42C2×D4×C10111yescharacteristic
434C42C2×D4×C10111yescharacteristic
435C42#41×C10111yescharacteristic
436C42C24×C10111yescharacteristic
437C23—21no—
438C23—21no—
439C23—42no—
440C23—42no—
441C23—41no—
442C23—81no—
443C23#121×C10111yescharacteristic
444Q8—41no—
445Q8—42no—
446Q8—41no—
447Q8—42no—
448Q8—82no—
449D4—21no—
450D4—21no—
451D4—21no—
452D4—42no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—81no—
458D4—82no—
459D4AGL(1,ℤ/8)×C10112yes—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4#121×C10111yescharacteristic
477C2×C4#121×C10111yescharacteristic
478C2×C4#121×C10111yescharacteristic
479C2×C4#135×C10112yes—
480C2×C4AGL(1,ℤ/8)×C10112yes—
481C2×C4C22×D4×C10111yescharacteristic
482C2×C4C22×D4×C10111yescharacteristic
483C2×C4C2×#41×C10111yescharacteristic
484C8—22no—
485C8—22no—
486C8—42no—
487C8—42no—
488C8—41no—
489C8—41no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—84no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22#463×C10112yes—
503C22C2×#121×C10111yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—41no—
508C4—41no—
509C4—81no—
510C4—82no—
511C4#463×C10112yes—
512C4C2×#135×C10111yescharacteristic
513C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
514C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
515C4#575×C10111yescharacteristic
516C2—22no—
517C2—42no—
518C2—81no—
519C2—161no—
520C2C2×#463×C10111yescharacteristic
521C2C101×#305511yescharacteristic
522C2C101×#306911yescharacteristic
subgroupG/H
center, socleC22×C101C2×#121
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3100C2
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×#3141C2semidirect
3. C2×#461×C101C2semidirect
4. D4×M16×C101C2semidirect
5. C101×#1701C2semidirect
6. C101×#1699C2semidirect
7. C101×#1681C2semidirect
8. C101×#1679C2semidirect
9. C101×#1565C2semidirect
10. C101×#1549C2semidirect
11. C101×#1547C2semidirect
18. #487×C101C22semidirect
19. #486×C101C22semidirect
43. #335×C101C22semidirect
44. #334×C101C22semidirect
45. #332×C101C22semidirect
46. #332×C101C22semidirect
47. #332×C101C22semidirect
48. #331×C101C22semidirect
254. #19169C101direct (N × H)
262. #3141C2×C101semidirect
264. C2×#461C2×C101semidirect
265. D4×M16C2×C101semidirect
266. #1701C2×C101semidirect
267. #1699C2×C101semidirect
268. #1681C2×C101semidirect
269. #1679C2×C101semidirect
270. #1565C2×C101semidirect
271. #1549C2×C101semidirect
272. #1547C2×C101semidirect
273. C101#19169direct (N × H)
280. #487C22×C101semidirect
281. #486C22×C101semidirect
305. #335C22×C101semidirect
306. #334C22×C101semidirect
307. #332C22×C101semidirect
308. #332C22×C101semidirect
309. #332C22×C101semidirect
310. #331C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31412
C101×#31002
C2×#461×C1012
D4×M16×C1012
C101×#17012
C101×#16992
C101×#16812
C101×#16792
C101×#15652
C101×#15492
C101×#15472
#19169101