Finite Group Databasebeta

← C101×#19163 #38801314

Subgroups — C101×#19163 #38801314

Order 25856.

760 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3152C211yesmaximal, characteristic, complemented
2C101×#3100C211yesmaximal, characteristic
3C2×#474×C101C211yesmaximal, characteristic, complemented
4D4×M16×C101C211yesmaximal, characteristic, complemented
5C101×#1689C212yesmaximal, complemented
6C101×#1685C212yesmaximal, complemented
7C101×#1669C212yesmaximal, complemented
8C101×#1665C212yesmaximal, complemented
9C101×#1565C211yesmaximal, characteristic, complemented
10C101×#1547C211yesmaximal, characteristic, complemented
11C101×#1546C211yesmaximal, characteristic, complemented
12C2×#137×C101—21no—
13C2×#137×C101—21no—
14C22×M16×C101—21no—
15#532×C101C2211yescharacteristic
16C2×C4⋊Q8×C101C2211yescharacteristic
17C2×C4×D4×C101C2211yescharacteristic
18#497×C101—22no—
19#494×C101C2212yescomplemented
20#492×C101C2212yescomplemented
21#480×C101—21no—
22#474×C101—21no—
23#474×C101—21no—
24#474×C101C2212yes—
25#474×C101C2211yescharacteristic
26#474×C101C2212yes—
27#474×C101C2211yescharacteristic
28#459×C101C2211yescharacteristic
29#459×C101C2211yescharacteristic
30#447×C101—21no—
31C4×D8×C101—21no—
32C4×D8×C101—21no—
33#436×C101C2212yes—
34#435×C101—22no—
35C8×D4×C101C2212yes—
36#431×C101C2211yescharacteristic
37C2×#107×C101—21no—
38#423×C101C2211yescharacteristic
39C2×C4⋊C8×C101C2211yescharacteristic
40C2×#102×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—
53#137×C101—44no—
54#137×C101—44no—
55C2×Q16×C101—22no—
56C2×Q16×C101—22no—
57C2×SD16×C101—22no—
58C2×SD16×C101—22no—
59C2×D8×C101—21no—
60C2×D8×C101—21no—
61C2×M16×C101—21no—
62C2×M16×C101—22no—
63C2×M16×C101—44no—
64C2×M16×C101D411yescharacteristic
65C2×M16×C101D411yescharacteristic
66C22×C8×C101—21no—
67C22×C8×C101—22no—
68C4⋊Q8×C101—21no—
69C4⋊Q8×C101—21no—
70C4⋊Q8×C101—21no—
71C4⋊Q8×C101C2312yes—
72C4⋊Q8×C101C2311yescharacteristic
73#127×C101C2311yescharacteristic
74#124×C101—21no—
75#121×C101—21no—
76#121×C101—21no—
77C4×D4×C101—21no—
78C4×D4×C101—21no—
79C4×D4×C101—21no—
80C4×D4×C101—21no—
81C4×D4×C101D411yescharacteristic
82C4×D4×C101D411yescharacteristic
83C4×D4×C101C2311yescharacteristic
84C4×D4×C101C2311yescharacteristic
85C2×C4⋊C4×C101—21no—
86C2×C4⋊C4×C101—21no—
87C2×C4⋊C4×C101D411yescharacteristic
88C2×C22⋊C4×C101—21no—
89C2×C42×C101C2311yescharacteristic
90#107×C101—22no—
91#107×C101—22no—
92#107×C101—21no—
93#107×C101—21no—
94C4⋊C8×C101—21no—
95C4⋊C8×C101—21no—
96C4⋊C8×C101C2312yes—
97C4⋊C8×C101C2312yes—
98C4⋊C8×C101C2311yescharacteristic
99C4⋊C8×C101C2311yescharacteristic
100#102×C101—22no—
101#102×C101—22no—
102#102×C101—21no—
103#102×C101—21no—
104#102×C101—21no—
105#102×C101—21no—
106C22⋊C8×C101—21no—
107C22⋊C8×C101—22no—
108C22⋊C8×C101—22no—
109#97×C101D412yes—
110C4×C8×C101—21no—
111C4×C8×C101C2312yes—
112C24×C101—21no—
113#41×C101—42no—
114#41×C101—42no—
115C2×Q8×C101—21no—
116C2×Q8×C101—22no—
117C2×Q8×C101—41no—
118C2×Q8×C101—42no—
119C2×Q8×C101—42no—
120C2×D4×C101—22no—
121C2×D4×C101—21no—
122C2×D4×C101—21no—
123C2×D4×C101—21no—
124C2×D4×C101—21no—
125C2×D4×C101—41no—
126C2×D4×C101—41no—
127C2×D4×C101C2×D411yescharacteristic
128C2×D4×C101C2×D411yescharacteristic
129C22×C4×C101—21no—
130C22×C4×C101—21no—
131C22×C4×C101—21no—
132C22×C4×C101—21no—
133C22×C4×C101—21no—
134C22×C4×C101—42no—
135C22×C4×C101—42no—
136C22×C4×C101—41no—
137C22×C4×C101—41no—
138C22×C4×C101C2×D411yescharacteristic
139C22×C4×C101C2×D411yescharacteristic
140C22×C4×C101#4111yescharacteristic
141Q16×C101—44no—
142Q16×C101—44no—
143SD16×C101—44no—
144SD16×C101—44no—
145D8×C101—42no—
146D8×C101—42no—
147M16×C101—22no—
148M16×C101—42no—
149M16×C101—44no—
150M16×C101D814yescomplemented
151C2×C8×C101—21no—
152C2×C8×C101—21no—
153C2×C8×C101—22no—
154C2×C8×C101—22no—
155C2×C8×C101—42no—
156C2×C8×C101—44no—
157C2×C8×C101C2×D412yes—
158C2×C8×C101C2×D412yes—
159C4⋊C4×C101—21no—
160C4⋊C4×C101—22no—
161C4⋊C4×C101—21no—
162C4⋊C4×C101—22no—
163C4⋊C4×C101—21no—
164C4⋊C4×C101—41no—
165C4⋊C4×C101—41no—
166C4⋊C4×C101C2×D411yescharacteristic
167C4⋊C4×C101C2×D411yescharacteristic
168C22⋊C4×C101—21no—
169C22⋊C4×C101—21no—
170C22⋊C4×C101—21no—
171C22⋊C4×C101—21no—
172C22⋊C4×C101—41no—
173C22⋊C4×C101—41no—
174C42×C101C2×D411yescharacteristic
175C42×C101C2×D411yescharacteristic
176C42×C101#4111yescharacteristic
177C42×C101C2411yescharacteristic
178C23×C101—21no—
179C23×C101—21no—
180C23×C101—42no—
181C23×C101—42no—
182C23×C101—41no—
183C23×C101—81no—
184C23×C101#12111yescharacteristic
185Q8×C101—42no—
186Q8×C101—41no—
187Q8×C101—42no—
188Q8×C101—41no—
189Q8×C101—82no—
190D4×C101—21no—
191D4×C101—21no—
192D4×C101—21no—
193D4×C101—42no—
194D4×C101—41no—
195D4×C101—41no—
196D4×C101—41no—
197D4×C101—41no—
198D4×C101—81no—
199D4×C101—82no—
200D4×C101#13712yescomplemented
201C2×C4×C101—21no—
202C2×C4×C101—21no—
203C2×C4×C101—21no—
204C2×C4×C101—21no—
205C2×C4×C101—41no—
206C2×C4×C101—42no—
207C2×C4×C101—41no—
208C2×C4×C101—41no—
209C2×C4×C101—41no—
210C2×C4×C101—41no—
211C2×C4×C101—42no—
212C2×C4×C101—42no—
213C2×C4×C101—41no—
214C2×C4×C101—42no—
215C2×C4×C101—82no—
216C2×C4×C101—82no—
217C2×C4×C101#12111yescharacteristic
218C2×C4×C101#12111yescharacteristic
219C2×C4×C101#12111yescharacteristic
220C2×C4×C101C2×D812yes—
221C2×C4×C101AGL(1,ℤ/8)12yes—
222C2×C4×C101C22×D411yescharacteristic
223C2×C4×C101C22×D411yescharacteristic
224C2×C4×C101C2×#4111yescharacteristic
225C8×C101—22no—
226C8×C101—42no—
227C8×C101—41no—
228C8×C101—42no—
229C8×C101—41no—
230C8×C101C2×D814yes—
231C22×C101—21no—
232C22×C101—21no—
233C22×C101—22no—
234C22×C101—41no—
235C22×C101—41no—
236C22×C101—41no—
237C22×C101—41no—
238C22×C101—41no—
239C22×C101—84no—
240C22×C101—81no—
241C22×C101—81no—
242C22×C101—81no—
243C22×C101#45912yes—
244C22×C101C2×#12111yescharacteristic
245C4×C101—21no—
246C4×C101—21no—
247C4×C101—21no—
248C4×C101—41no—
249C4×C101—41no—
250C4×C101—81no—
251C4×C101—82no—
252C4×C101#45912yes—
253C4×C101C22×D811yescharacteristic
254C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
255C4×C101C2×#13711yescharacteristic
256C4×C101#57511yescharacteristic
257#19163C10111yesmaximal, characteristic, direct product factor, Sylow
258C2×C101—22no—
259C2×C101—42no—
260C2×C101—81no—
261C2×C101—161no—
262C2×C101C2×#45911yescharacteristic
263C2×C101#305611yescharacteristic
264C2×C101#306911yescharacteristic
265#3152C2×C10111yescharacteristic, complemented
266#3100C2×C10111yescharacteristic
267C2×#474C2×C10111yescharacteristic, complemented
268D4×M16C2×C10111yescharacteristic, complemented
269#1689C2×C10112yescomplemented
270#1685C2×C10112yescomplemented
271#1669C2×C10112yescomplemented
272#1665C2×C10112yescomplemented
273#1565C2×C10111yescharacteristic, complemented
274#1547C2×C10111yescharacteristic, complemented
275#1546C2×C10111yescharacteristic, complemented
276C101#1916311yescharacteristic, direct product factor, Sylow
277C2×#137—21no—
278C2×#137—21no—
279C22×M16—21no—
280#532C22×C10111yescharacteristic
281C2×C4⋊Q8C22×C10111yescharacteristic
282C2×C4×D4C22×C10111yescharacteristic
283#497—22no—
284#494C22×C10112yescomplemented
285#492C22×C10112yescomplemented
286#480—21no—
287#474—21no—
288#474—21no—
289#474C22×C10111yescharacteristic
290#474C22×C10111yescharacteristic
291#474C22×C10112yes—
292#474C22×C10112yes—
293#459C22×C10111yescharacteristic
294#459C22×C10111yescharacteristic
295#447—21no—
296C4×D8—21no—
297C4×D8—21no—
298#436C22×C10112yes—
299#435—22no—
300C8×D4C22×C10112yes—
301#431C22×C10111yescharacteristic
302C2×#107—21no—
303#423C22×C10111yescharacteristic
304C2×C4⋊C8C22×C10111yescharacteristic
305C2×#102—21no—
306#407—21no—
307C4×M16C22×C10111yescharacteristic
308#335C22×C10112yescomplemented
309#334C22×C10112yescomplemented
310#332C22×C10112yescomplemented
311#332C22×C10112yescomplemented
312#332C22×C10112yescomplemented
313#331C22×C10112yescomplemented
314C2×#41—21no—
315C22×Q8—21no—
316C22×D4D4×C10111yescharacteristic
317C23×C4—21no—
318#137—44no—
319#137—44no—
320C2×Q16—22no—
321C2×Q16—22no—
322C2×SD16—22no—
323C2×SD16—22no—
324C2×D8—21no—
325C2×D8—21no—
326C2×M16—21no—
327C2×M16—22no—
328C2×M16—44no—
329C2×M16D4×C10111yescharacteristic
330C2×M16D4×C10111yescharacteristic
331C22×C8—21no—
332C22×C8—22no—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8C23×C10112yes—
337C4⋊Q8C23×C10111yescharacteristic
338#127C23×C10111yescharacteristic
339#124—21no—
340#121—21no—
341#121—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4D4×C10111yescharacteristic
347C4×D4D4×C10111yescharacteristic
348C4×D4C23×C10111yescharacteristic
349C4×D4C23×C10111yescharacteristic
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4D4×C10111yescharacteristic
353C2×C22⋊C4—21no—
354C2×C42C23×C10111yescharacteristic
355#107—22no—
356#107—22no—
357#107—21no—
358#107—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8C23×C10112yes—
362C4⋊C8C23×C10112yes—
363C4⋊C8C23×C10111yescharacteristic
364C4⋊C8C23×C10111yescharacteristic
365#102—22no—
366#102—22no—
367#102—21no—
368#102—21no—
369#102—21no—
370#102—21no—
371C22⋊C8—21no—
372C22⋊C8—22no—
373C22⋊C8—22no—
374#97D4×C10112yes—
375C4×C8—21no—
376C4×C8C23×C10112yes—
377C24—21no—
378#41—42no—
379#41—42no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—41no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4C2×D4×C10111yescharacteristic
393C2×D4C2×D4×C10111yescharacteristic
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4C2×D4×C10111yescharacteristic
404C22×C4C2×D4×C10111yescharacteristic
405C22×C4#41×C10111yescharacteristic
406Q16—44no—
407Q16—44no—
408SD16—44no—
409SD16—44no—
410D8—42no—
411D8—42no—
412M16—22no—
413M16—42no—
414M16—44no—
415M16D8×C10114yescomplemented
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—42no—
421C2×C8—44no—
422C2×C8C2×D4×C10112yes—
423C2×C8C2×D4×C10112yes—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4C2×D4×C10111yescharacteristic
432C4⋊C4C2×D4×C10111yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C42C2×D4×C10111yescharacteristic
440C42C2×D4×C10111yescharacteristic
441C42#41×C10111yescharacteristic
442C42C24×C10111yescharacteristic
443C23—21no—
444C23—21no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—81no—
449C23#121×C10111yescharacteristic
450Q8—42no—
451Q8—41no—
452Q8—42no—
453Q8—41no—
454Q8—82no—
455D4—21no—
456D4—21no—
457D4—21no—
458D4—42no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—81no—
464D4—82no—
465D4#137×C10112yescomplemented
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4#121×C10111yescharacteristic
483C2×C4#121×C10111yescharacteristic
484C2×C4#121×C10111yescharacteristic
485C2×C4C2×D8×C10112yes—
486C2×C4AGL(1,ℤ/8)×C10112yes—
487C2×C4C22×D4×C10111yescharacteristic
488C2×C4C22×D4×C10111yescharacteristic
489C2×C4C2×#41×C10111yescharacteristic
490C8—22no—
491C8—42no—
492C8—41no—
493C8—42no—
494C8—41no—
495C8C2×D8×C10114yes—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—84no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22#459×C10112yes—
509C22C2×#121×C10111yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—81no—
516C4—82no—
517C4#459×C10112yes—
518C4C22×D8×C10111yescharacteristic
519C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
520C4C2×#137×C10111yescharacteristic
521C4#575×C10111yescharacteristic
522C2—22no—
523C2—42no—
524C2—81no—
525C2—161no—
526C2C2×#459×C10111yescharacteristic
527C2C101×#305611yescharacteristic
528C2C101×#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×#3152C2semidirect
3. C2×#474×C101C2semidirect
4. D4×M16×C101C2semidirect
5. C101×#1689C2semidirect
6. C101×#1685C2semidirect
7. C101×#1669C2semidirect
8. C101×#1665C2semidirect
9. C101×#1565C2semidirect
10. C101×#1547C2semidirect
11. C101×#1546C2semidirect
19. #494×C101C22semidirect
20. #492×C101C22semidirect
43. #335×C101C22semidirect
44. #334×C101C22semidirect
45. #332×C101C22semidirect
46. #332×C101C22semidirect
47. #332×C101C22semidirect
48. #331×C101C22semidirect
150. M16×C101D8semidirect
200. D4×C101#137semidirect
257. #19163C101direct (N × H)
265. #3152C2×C101semidirect
267. C2×#474C2×C101semidirect
268. D4×M16C2×C101semidirect
269. #1689C2×C101semidirect
270. #1685C2×C101semidirect
271. #1669C2×C101semidirect
272. #1665C2×C101semidirect
273. #1565C2×C101semidirect
274. #1547C2×C101semidirect
275. #1546C2×C101semidirect
276. C101#19163direct (N × H)
284. #494C22×C101semidirect
285. #492C22×C101semidirect
308. #335C22×C101semidirect
309. #334C22×C101semidirect
310. #332C22×C101semidirect
311. #332C22×C101semidirect
312. #332C22×C101semidirect
313. #331C22×C101semidirect
415. M16D8×C101semidirect
465. D4#137×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31522
C101×#31002
C2×#474×C1012
D4×M16×C1012
C101×#16892
C101×#16852
C101×#16692
C101×#16652
C101×#15652
C101×#15472
C101×#15462
#19163101