Finite Group Databasebeta

← C107×#19947 #41045911

Subgroups — C107×#19947 #41045911

Order 27392.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3399C211yesmaximal, characteristic, complemented
2C107×#3394C211yesmaximal, characteristic, complemented
3C107×#3353C211yesmaximal, characteristic, complemented
4C107×#3284C211yesmaximal, characteristic, complemented
5C107×#1706C211yesmaximal, characteristic, complemented
6C107×#1694C211yesmaximal, characteristic, complemented
7C107×#1687C211yesmaximal, characteristic, complemented
8C107×#1666C211yesmaximal, characteristic, complemented
9C107×#1665C211yesmaximal, characteristic, complemented
10C107×#1641C211yesmaximal, characteristic, complemented
11C107×#1640C211yesmaximal, characteristic, complemented
12C107×#1628C211yesmaximal, characteristic, complemented
13C107×#1625C211yesmaximal, characteristic, complemented
14C107×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C107C211yesmaximal, characteristic, complemented
16C2×#135×C107—21no—
17#559×C107C2211yescharacteristic
18#556×C107C2211yescharacteristic
19#550×C107C2211yescharacteristic
20#547×C107C2211yescharacteristic
21#500×C107C2211yescharacteristic
22#496×C107—21no—
23#495×C107—21no—
24#493×C107C2211yescharacteristic
25#492×C107C2211yescharacteristic
26#492×C107C2211yescharacteristic
27#486×C107C2211yescharacteristic
28#486×C107C2211yescharacteristic
29#484×C107—21no—
30#482×C107—21no—
31#475×C107C2211yescharacteristic
32#474×C107C2211yescharacteristic
33#468×C107—21no—
34#465×C107—21no—
35#464×C107—21no—
36#463×C107—21no—
37#463×C107—21no—
38#462×C107C2211yescharacteristic
39#462×C107C2211yescharacteristic
40#460×C107C2211yescharacteristic
41#459×C107—21no—
42#459×C107C2211yescharacteristic
43#459×C107C2211yescharacteristic
44#459×C107C2211yescharacteristic
45#452×C107—21no—
46#449×C107—21no—
47#446×C107C2211yescharacteristic
48C8×Q8×C107C2211yescharacteristic
49#442×C107—21no—
50C4×SD16×C107—21no—
51C4×SD16×C107C2211yescharacteristic
52C4×SD16×C107C2211yescharacteristic
53#436×C107C2211yescharacteristic
54C8×D4×C107C2211yescharacteristic
55#428×C107—21no—
56#334×C107C2211yescharacteristic
57#334×C107C2211yescharacteristic
58#332×C107C2211yescharacteristic
59#332×C107C2211yescharacteristic
60#331×C107C2211yescharacteristic
61#331×C107C2211yescharacteristic
62Q8⋊C8×C107C2211yescharacteristic
63Q8⋊C8×C107C2211yescharacteristic
64D4⋊C8×C107C2211yescharacteristic
65D4⋊C8×C107C2211yescharacteristic
66C82×C107C2211yescharacteristic
67C2×#41×C107—21no—
68C2×#41×C107—21no—
69#135×C107—44no—
70C2×Q16×C107—21no—
71C2×Q16×C107—21no—
72C2×SD16×C107—21no—
73C2×SD16×C107—21no—
74C2×SD16×C107—21no—
75C2×SD16×C107—21no—
76C2×SD16×C107—21no—
77C2×SD16×C107D411yescharacteristic
78C2×SD16×C107D411yescharacteristic
79C2×D8×C107—21no—
80C2×D8×C107—21no—
81C2×D8×C107—21no—
82C2×D8×C107—21no—
83C2×D8×C107—21no—
84C2×M16×C107—21no—
85C22×C8×C107—21no—
86C4⋊Q8×C107C2311yescharacteristic
87C4⋊Q8×C107C2311yescharacteristic
88#127×C107—21no—
89#127×C107C2311yescharacteristic
90#127×C107C2311yescharacteristic
91#126×C107—41no—
92#124×C107—21no—
93#124×C107—21no—
94#124×C107—21no—
95#123×C107—41no—
96#123×C107—41no—
97C22⋊Q8×C107—21no—
98C22⋊Q8×C107—21no—
99#121×C107—21no—
100#121×C107—21no—
101#121×C107—41no—
102C4×Q8×C107—21no—
103C4×Q8×C107C2311yescharacteristic
104C4×Q8×C107C2311yescharacteristic
105C4×D4×C107—21no—
106C4×D4×C107—21no—
107C4×D4×C107—21no—
108C4×D4×C107C2311yescharacteristic
109C4×D4×C107C2311yescharacteristic
110#117×C107—21no—
111C2×C4⋊C4×C107—21no—
112#107×C107—21no—
113#107×C107—21no—
114#107×C107—21no—
115#106×C107—21no—
116#106×C107D411yescharacteristic
117#106×C107D411yescharacteristic
118C4⋊C8×C107—21no—
119C4⋊C8×C107—21no—
120C4⋊C8×C107C2311yescharacteristic
121C4⋊C8×C107C2311yescharacteristic
122C4⋊C8×C107C2311yescharacteristic
123C4⋊C8×C107C2311yescharacteristic
124#103×C107—21no—
125#103×C107—21no—
126#103×C107—21no—
127#103×C107D411yescharacteristic
128#103×C107D411yescharacteristic
129#102×C107—21no—
130#102×C107—21no—
131#102×C107—21no—
132#102×C107—21no—
133#102×C107—21no—
134#102×C107—41no—
135#102×C107—41no—
136#102×C107D411yescharacteristic
137#102×C107D411yescharacteristic
138C22⋊C8×C107—21no—
139C22⋊C8×C107—21no—
140#97×C107—21no—
141C4×C8×C107—21no—
142C4×C8×C107C2311yescharacteristic
143C4×C8×C107C2311yescharacteristic
144C4×C8×C107C2311yescharacteristic
145#41×C107—42no—
146#41×C107—42no—
147#41×C107—81no—
148#41×C107—81no—
149C2×Q8×C107—21no—
150C2×Q8×C107—21no—
151C2×Q8×C107C2×D411yescharacteristic
152C2×Q8×C107C2×D411yescharacteristic
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107—21no—
156C2×D4×C107—21no—
157C2×D4×C107—21no—
158C2×D4×C107—21no—
159C2×D4×C107—41no—
160C2×D4×C107—41no—
161C2×D4×C107—41no—
162C2×D4×C107C2×D411yescharacteristic
163C2×D4×C107C2×D411yescharacteristic
164C22×C4×C107—21no—
165C22×C4×C107—21no—
166C22×C4×C107—41no—
167C22×C4×C107—41no—
168C22×C4×C107—41no—
169Q16×C107—42no—
170Q16×C107—81no—
171SD16×C107—22no—
172SD16×C107—22no—
173SD16×C107—42no—
174SD16×C107—42no—
175SD16×C107—81no—
176SD16×C107—81no—
177SD16×C107—81no—
178D8×C107—42no—
179D8×C107—42no—
180D8×C107—81no—
181D8×C107—81no—
182D8×C107—81no—
183M16×C107—42no—
184C2×C8×C107—21no—
185C2×C8×C107—21no—
186C2×C8×C107—21no—
187C2×C8×C107—21no—
188C2×C8×C107—21no—
189C2×C8×C107—42no—
190C2×C8×C107C2×D411yescharacteristic
191C2×C8×C107C2×D411yescharacteristic
192C2×C8×C107C2×D411yescharacteristic
193C2×C8×C107C2×D411yescharacteristic
194C4⋊C4×C107—21no—
195C4⋊C4×C107—21no—
196C4⋊C4×C107—21no—
197C4⋊C4×C107—21no—
198C4⋊C4×C107—21no—
199C4⋊C4×C107—21no—
200C4⋊C4×C107—41no—
201C4⋊C4×C107—41no—
202C4⋊C4×C107C2×D411yescharacteristic
203C4⋊C4×C107C2×D411yescharacteristic
204C4⋊C4×C107C2×D411yescharacteristic
205C4⋊C4×C107C2×D411yescharacteristic
206C22⋊C4×C107—21no—
207C22⋊C4×C107—21no—
208C22⋊C4×C107—41no—
209C22⋊C4×C107—41no—
210C22⋊C4×C107—41no—
211C22⋊C4×C107—41no—
212C22⋊C4×C107—41no—
213C22⋊C4×C107—41no—
214C22⋊C4×C107—41no—
215C42×C107—21no—
216C42×C107—21no—
217C42×C107—41no—
218C42×C107C2411yescharacteristic
219C23×C107—21no—
220C23×C107—21no—
221C23×C107—41no—
222C23×C107—41no—
223Q8×C107—21no—
224Q8×C107—21no—
225Q8×C107—21no—
226Q8×C107—21no—
227Q8×C107—41no—
228Q8×C107—41no—
229Q8×C107—41no—
230Q8×C107—41no—
231D4×C107—21no—
232D4×C107—21no—
233D4×C107—21no—
234D4×C107—21no—
235D4×C107—41no—
236D4×C107—41no—
237D4×C107—41no—
238D4×C107—41no—
239D4×C107—41no—
240D4×C107—41no—
241D4×C107—41no—
242D4×C107—41no—
243D4×C107—81no—
244D4×C107—81no—
245D4×C107—82no—
246D4×C107—82no—
247D4×C107—161no—
248C2×C4×C107—21no—
249C2×C4×C107—21no—
250C2×C4×C107—21no—
251C2×C4×C107—21no—
252C2×C4×C107—21no—
253C2×C4×C107—21no—
254C2×C4×C107—41no—
255C2×C4×C107—41no—
256C2×C4×C107—41no—
257C2×C4×C107—41no—
258C2×C4×C107—41no—
259C2×C4×C107—41no—
260C2×C4×C107—82no—
261C2×C4×C107—82no—
262C2×C4×C107—161no—
263C2×C4×C107C22×D411yescharacteristic
264C2×C4×C107C22×D411yescharacteristic
265C2×C4×C107H(5,𝔽2)11yescharacteristic
266C8×C107—21no—
267C8×C107—21no—
268C8×C107—41no—
269C8×C107—41no—
270C8×C107—41no—
271C8×C107—41no—
272C8×C107—41no—
273C8×C107#13512yescomplemented
274C8×C107AGL(1,ℤ/8)12yes—
275C22×C107—41no—
276C22×C107—41no—
277C22×C107—41no—
278C22×C107—41no—
279C22×C107—41no—
280C22×C107—41no—
281C22×C107—81no—
282C22×C107—81no—
283C22×C107—81no—
284C22×C107—81no—
285C22×C107—81no—
286C22×C107—81no—
287C22×C107D4211yescharacteristic
288C4×C107—21no—
289C4×C107—41no—
290C4×C107—41no—
291C4×C107—41no—
292C4×C107—41no—
293C4×C107—41no—
294C4×C107—41no—
295C4×C107—81no—
296C4×C107—81no—
297C4×C107C2×#13511yescharacteristic
298C4×C107C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C107#57611yescharacteristic
300C4×C107#57711yescharacteristic
301#19947C10711yesmaximal, characteristic, direct product factor, Sylow
302C2×C107—81no—
303C2×C107—81no—
304C2×C107—161no—
305C2×C107—161no—
306C2×C107#327411yescharacteristic
307C2×C107#328411yescharacteristic
308C2×C107#329011yescharacteristic
309#3399C2×C10711yescharacteristic, complemented
310#3394C2×C10711yescharacteristic, complemented
311#3353C2×C10711yescharacteristic, complemented
312#3284C2×C10711yescharacteristic, complemented
313#1706C2×C10711yescharacteristic, complemented
314#1694C2×C10711yescharacteristic, complemented
315#1687C2×C10711yescharacteristic, complemented
316#1666C2×C10711yescharacteristic, complemented
317#1665C2×C10711yescharacteristic, complemented
318#1641C2×C10711yescharacteristic, complemented
319#1640C2×C10711yescharacteristic, complemented
320#1628C2×C10711yescharacteristic, complemented
321#1625C2×C10711yescharacteristic, complemented
322#1590C2×C10711yescharacteristic, complemented
323C8×SD16C2×C10711yescharacteristic, complemented
324C107#1994711yescharacteristic, direct product factor, Sylow
325C2×#135—21no—
326#559C22×C10711yescharacteristic
327#556C22×C10711yescharacteristic
328#550C22×C10711yescharacteristic
329#547C22×C10711yescharacteristic
330#500C22×C10711yescharacteristic
331#496—21no—
332#495—21no—
333#493C22×C10711yescharacteristic
334#492C22×C10711yescharacteristic
335#492C22×C10711yescharacteristic
336#486C22×C10711yescharacteristic
337#486C22×C10711yescharacteristic
338#484—21no—
339#482—21no—
340#475C22×C10711yescharacteristic
341#474C22×C10711yescharacteristic
342#468—21no—
343#465—21no—
344#464—21no—
345#463—21no—
346#463—21no—
347#462C22×C10711yescharacteristic
348#462C22×C10711yescharacteristic
349#460C22×C10711yescharacteristic
350#459—21no—
351#459C22×C10711yescharacteristic
352#459C22×C10711yescharacteristic
353#459C22×C10711yescharacteristic
354#452—21no—
355#449—21no—
356#446C22×C10711yescharacteristic
357C8×Q8C22×C10711yescharacteristic
358#442—21no—
359C4×SD16—21no—
360C4×SD16C22×C10711yescharacteristic
361C4×SD16C22×C10711yescharacteristic
362#436C22×C10711yescharacteristic
363C8×D4C22×C10711yescharacteristic
364#428—21no—
365#334C22×C10711yescharacteristic
366#334C22×C10711yescharacteristic
367#332C22×C10711yescharacteristic
368#332C22×C10711yescharacteristic
369#331C22×C10711yescharacteristic
370#331C22×C10711yescharacteristic
371Q8⋊C8C22×C10711yescharacteristic
372Q8⋊C8C22×C10711yescharacteristic
373D4⋊C8C22×C10711yescharacteristic
374D4⋊C8C22×C10711yescharacteristic
375C82C22×C10711yescharacteristic
376C2×#41—21no—
377C2×#41—21no—
378#135—44no—
379C2×Q16—21no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16D4×C10711yescharacteristic
387C2×SD16D4×C10711yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×M16—21no—
394C22×C8—21no—
395C4⋊Q8C23×C10711yescharacteristic
396C4⋊Q8C23×C10711yescharacteristic
397#127—21no—
398#127C23×C10711yescharacteristic
399#127C23×C10711yescharacteristic
400#126—41no—
401#124—21no—
402#124—21no—
403#124—21no—
404#123—41no—
405#123—41no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408#121—21no—
409#121—21no—
410#121—41no—
411C4×Q8—21no—
412C4×Q8C23×C10711yescharacteristic
413C4×Q8C23×C10711yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C10711yescharacteristic
418C4×D4C23×C10711yescharacteristic
419#117—21no—
420C2×C4⋊C4—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#106—21no—
425#106D4×C10711yescharacteristic
426#106D4×C10711yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8C23×C10711yescharacteristic
430C4⋊C8C23×C10711yescharacteristic
431C4⋊C8C23×C10711yescharacteristic
432C4⋊C8C23×C10711yescharacteristic
433#103—21no—
434#103—21no—
435#103—21no—
436#103D4×C10711yescharacteristic
437#103D4×C10711yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—41no—
444#102—41no—
445#102D4×C10711yescharacteristic
446#102D4×C10711yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97—21no—
450C4×C8—21no—
451C4×C8C23×C10711yescharacteristic
452C4×C8C23×C10711yescharacteristic
453C4×C8C23×C10711yescharacteristic
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C10711yescharacteristic
461C2×Q8C2×D4×C10711yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4C2×D4×C10711yescharacteristic
472C2×D4C2×D4×C10711yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478Q16—42no—
479Q16—81no—
480SD16—22no—
481SD16—22no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487D8—42no—
488D8—42no—
489D8—81no—
490D8—81no—
491D8—81no—
492M16—42no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8C2×D4×C10711yescharacteristic
500C2×C8C2×D4×C10711yescharacteristic
501C2×C8C2×D4×C10711yescharacteristic
502C2×C8C2×D4×C10711yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C10711yescharacteristic
512C4⋊C4C2×D4×C10711yescharacteristic
513C4⋊C4C2×D4×C10711yescharacteristic
514C4⋊C4C2×D4×C10711yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C42—21no—
525C42—21no—
526C42—41no—
527C42C24×C10711yescharacteristic
528C23—21no—
529C23—21no—
530C23—41no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556D4—161no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4C22×D4×C10711yescharacteristic
573C2×C4C22×D4×C10711yescharacteristic
574C2×C4H(5,𝔽2)×C10711yescharacteristic
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8#135×C10712yescomplemented
583C8AGL(1,ℤ/8)×C10712yes—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C10711yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×#135×C10711yescharacteristic
607C4C2×AGL(1,ℤ/8)×C10711yescharacteristic
608C4#576×C10711yescharacteristic
609C4#577×C10711yescharacteristic
610C2—81no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2C107×#327411yescharacteristic
615C2C107×#328411yescharacteristic
616C2C107×#329011yescharacteristic
subgroupG/H
center, socleC22×C107D42
commutator, Frattini, cosocleC42C24×C107
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3399C2semidirect
2. C107×#3394C2semidirect
3. C107×#3353C2semidirect
4. C107×#3284C2semidirect
5. C107×#1706C2semidirect
6. C107×#1694C2semidirect
7. C107×#1687C2semidirect
8. C107×#1666C2semidirect
9. C107×#1665C2semidirect
10. C107×#1641C2semidirect
11. C107×#1640C2semidirect
12. C107×#1628C2semidirect
13. C107×#1625C2semidirect
14. C107×#1590C2semidirect
15. C8×SD16×C107C2semidirect
273. C8×C107#135semidirect
301. #19947C107direct (N × H)
309. #3399C2×C107semidirect
310. #3394C2×C107semidirect
311. #3353C2×C107semidirect
312. #3284C2×C107semidirect
313. #1706C2×C107semidirect
314. #1694C2×C107semidirect
315. #1687C2×C107semidirect
316. #1666C2×C107semidirect
317. #1665C2×C107semidirect
318. #1641C2×C107semidirect
319. #1640C2×C107semidirect
320. #1628C2×C107semidirect
321. #1625C2×C107semidirect
322. #1590C2×C107semidirect
323. C8×SD16C2×C107semidirect
324. C107#19947direct (N × H)
582. C8#135×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#33992
C107×#33942
C107×#33532
C107×#32842
C107×#17062
C107×#16942
C107×#16872
C107×#16662
C107×#16652
C107×#16412
C107×#16402
C107×#16282
C107×#16252
C107×#15902
C8×SD16×C1072
#19947107