Finite Group Databasebeta

← C107×#19871 #41045835

Subgroups — C107×#19871 #41045835

Order 27392.

632 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3399C211yesmaximal, characteristic, complemented
2C107×#3396C211yesmaximal, characteristic, complemented
3C107×#3394C211yesmaximal, characteristic, complemented
4C107×#3304C211yesmaximal, characteristic, complemented
5C107×#1721C211yesmaximal, characteristic, complemented
6C107×#1686C211yesmaximal, characteristic, complemented
7C107×#1682C211yesmaximal, characteristic, complemented
8C107×#1668C211yesmaximal, characteristic, complemented
9C107×#1667C211yesmaximal, characteristic, complemented
10C107×#1640C211yesmaximal, characteristic, complemented
11C107×#1628C211yesmaximal, characteristic, complemented
12C107×#1621C211yesmaximal, characteristic, complemented
13C107×#1620C211yesmaximal, characteristic, complemented
14C107×#1584C211yesmaximal, characteristic, complemented
15C107×SD16⋊C8C211yesmaximal, characteristic, complemented
16#559×C107C2211yescharacteristic
17#559×C107C2211yescharacteristic
18#556×C107C2211yescharacteristic
19#550×C107C2211yescharacteristic
20#496×C107—21no—
21#495×C107—21no—
22#495×C107—21no—
23#493×C107C2211yescharacteristic
24#493×C107C2211yescharacteristic
25#493×C107C2211yescharacteristic
26#492×C107C2211yescharacteristic
27#486×C107C2211yescharacteristic
28#486×C107C2211yescharacteristic
29#482×C107—21no—
30#475×C107C2211yescharacteristic
31#465×C107—21no—
32#464×C107—21no—
33#463×C107—21no—
34#463×C107—21no—
35#463×C107—21no—
36#463×C107—21no—
37#462×C107C2211yescharacteristic
38#460×C107C2211yescharacteristic
39#460×C107C2211yescharacteristic
40#460×C107C2211yescharacteristic
41#460×C107C2211yescharacteristic
42#459×C107—21no—
43#459×C107C2211yescharacteristic
44#459×C107C2211yescharacteristic
45#452×C107—21no—
46#446×C107C2211yescharacteristic
47C8×Q8×C107C2211yescharacteristic
48C8×Q8×C107C2211yescharacteristic
49#442×C107—21no—
50C4×Q16×C107C2211yescharacteristic
51C4×SD16×C107—21no—
52C4×SD16×C107C2211yescharacteristic
53C4×D8×C107—21no—
54C8×D4×C107C2211yescharacteristic
55#416×C107—21no—
56#335×C107C2211yescharacteristic
57#335×C107C2211yescharacteristic
58#332×C107C2211yescharacteristic
59#331×C107C2211yescharacteristic
60#331×C107C2211yescharacteristic
61#331×C107C2211yescharacteristic
62Q8⋊C8×C107C2211yescharacteristic
63Q8⋊C8×C107C2211yescharacteristic
64Q8⋊C8×C107C2211yescharacteristic
65D4⋊C8×C107C2211yescharacteristic
66#322×C107C2211yescharacteristic
67C2×#41×C107—21no—
68C2×Q16×C107—21no—
69C2×Q16×C107D411yescharacteristic
70C2×SD16×C107—21no—
71C2×SD16×C107—21no—
72C2×SD16×C107—21no—
73C2×SD16×C107—21no—
74C2×SD16×C107—21no—
75C2×SD16×C107—21no—
76C2×SD16×C107D411yescharacteristic
77C2×D8×C107—21no—
78C2×D8×C107—21no—
79C2×D8×C107—21no—
80C2×D8×C107—21no—
81C2×D8×C107—21no—
82C2×D8×C107—21no—
83C2×D8×C107—41no—
84C22×C8×C107—21no—
85C4⋊Q8×C107C2311yescharacteristic
86#127×C107—21no—
87#127×C107C2311yescharacteristic
88#127×C107C2311yescharacteristic
89#127×C107C2311yescharacteristic
90#126×C107—41no—
91#124×C107—21no—
92#124×C107—21no—
93#124×C107—21no—
94#124×C107—21no—
95#124×C107—21no—
96#123×C107—41no—
97#123×C107—41no—
98C22⋊Q8×C107—21no—
99#121×C107—21no—
100#121×C107—41no—
101C4×Q8×C107—21no—
102C4×Q8×C107C2311yescharacteristic
103C4×Q8×C107C2311yescharacteristic
104C4×Q8×C107C2311yescharacteristic
105C4×D4×C107—21no—
106C4×D4×C107—21no—
107C4×D4×C107—21no—
108C4×D4×C107—21no—
109C4×D4×C107—21no—
110C4×D4×C107C2311yescharacteristic
111#117×C107—21no—
112#107×C107D411yescharacteristic
113#106×C107—21no—
114#106×C107D411yescharacteristic
115C4⋊C8×C107—21no—
116C4⋊C8×C107—21no—
117C4⋊C8×C107—21no—
118C4⋊C8×C107C2311yescharacteristic
119C4⋊C8×C107C2311yescharacteristic
120C4⋊C8×C107C2311yescharacteristic
121C4⋊C8×C107C2311yescharacteristic
122#103×C107—21no—
123#103×C107—21no—
124#103×C107D411yescharacteristic
125#103×C107D411yescharacteristic
126#103×C107D411yescharacteristic
127#102×C107—21no—
128#102×C107—21no—
129#102×C107—21no—
130#102×C107—21no—
131#102×C107—21no—
132#102×C107—21no—
133#102×C107—21no—
134#102×C107—21no—
135#102×C107—41no—
136#102×C107D411yescharacteristic
137C22⋊C8×C107—21no—
138#97×C107—21no—
139C4×C8×C107—21no—
140C4×C8×C107—21no—
141C4×C8×C107C2311yescharacteristic
142C4×C8×C107C2311yescharacteristic
143C4×C8×C107C2311yescharacteristic
144#41×C107—42no—
145#41×C107—81no—
146C2×Q8×C107—21no—
147C2×Q8×C107C2×D411yescharacteristic
148C2×Q8×C107C2×D411yescharacteristic
149C2×Q8×C107C2×D411yescharacteristic
150C2×D4×C107—21no—
151C2×D4×C107—21no—
152C2×D4×C107—21no—
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×C107C2×D411yescharacteristic
162C22×C4×C107—21no—
163C22×C4×C107—41no—
164C22×C4×C107—41no—
165C22×C4×C107—41no—
166Q16×C107—41no—
167Q16×C107—81no—
168SD16×C107—22no—
169SD16×C107—42no—
170SD16×C107—81no—
171SD16×C107—81no—
172SD16×C107—81no—
173SD16×C107—81no—
174SD16×C107—81no—
175D8×C107—42no—
176D8×C107—42no—
177D8×C107—81no—
178D8×C107—81no—
179D8×C107—81no—
180D8×C107—81no—
181D8×C107—82no—
182C2×C8×C107—21no—
183C2×C8×C107—21no—
184C2×C8×C107—21no—
185C2×C8×C107—21no—
186C2×C8×C107—21no—
187C2×C8×C107—81no—
188C2×C8×C107C2×D411yescharacteristic
189C2×C8×C107C2×D411yescharacteristic
190C2×C8×C107C2×D411yescharacteristic
191C2×C8×C107C2×D411yescharacteristic
192C4⋊C4×C107—21no—
193C4⋊C4×C107—21no—
194C4⋊C4×C107—21no—
195C4⋊C4×C107—21no—
196C4⋊C4×C107—21no—
197C4⋊C4×C107—41no—
198C4⋊C4×C107C2×D411yescharacteristic
199C4⋊C4×C107C2×D411yescharacteristic
200C4⋊C4×C107C2×D411yescharacteristic
201C4⋊C4×C107C2×D411yescharacteristic
202C22⋊C4×C107—21no—
203C22⋊C4×C107—41no—
204C22⋊C4×C107—41no—
205C22⋊C4×C107—41no—
206C22⋊C4×C107—41no—
207C22⋊C4×C107—41no—
208C22⋊C4×C107—41no—
209C22⋊C4×C107—41no—
210C22⋊C4×C107—41no—
211C22⋊C4×C107—41no—
212C42×C107—21no—
213C42×C107—21no—
214C42×C107—21no—
215C42×C107—41no—
216C42×C107C2411yescharacteristic
217C23×C107—21no—
218C23×C107—41no—
219C23×C107—41no—
220C23×C107—41no—
221Q8×C107—21no—
222Q8×C107—21no—
223Q8×C107—21no—
224Q8×C107—21no—
225Q8×C107—21no—
226Q8×C107—21no—
227Q8×C107—41no—
228Q8×C107—41no—
229D4×C107—21no—
230D4×C107—21no—
231D4×C107—41no—
232D4×C107—41no—
233D4×C107—41no—
234D4×C107—41no—
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—81no—
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—21no—
255C2×C4×C107—41no—
256C2×C4×C107—41no—
257C2×C4×C107—41no—
258C2×C4×C107—82no—
259C2×C4×C107—161no—
260C2×C4×C107—161no—
261C2×C4×C107C22×D411yescharacteristic
262C2×C4×C107C22×D411yescharacteristic
263C2×C4×C107H(5,𝔽2)11yescharacteristic
264C8×C107—21no—
265C8×C107—21no—
266C8×C107—21no—
267C8×C107—41no—
268C8×C107—41no—
269C8×C107—41no—
270C8×C107—41no—
271C8×C107—41no—
272C8×C107#13512yes—
273C22×C107—41no—
274C22×C107—41no—
275C22×C107—41no—
276C22×C107—81no—
277C22×C107—81no—
278C22×C107—81no—
279C22×C107—81no—
280C22×C107—81no—
281C22×C107—81no—
282C22×C107—81no—
283C22×C107—81no—
284C22×C107—81no—
285C22×C107D4211yescharacteristic
286C4×C107—21no—
287C4×C107—41no—
288C4×C107—41no—
289C4×C107—41no—
290C4×C107—41no—
291C4×C107—41no—
292C4×C107—41no—
293C4×C107—41no—
294C4×C107—81no—
295C4×C107C2×#13511yescharacteristic
296C4×C107#57511yescharacteristic
297C4×C107#57611yescharacteristic
298C4×C107#57611yescharacteristic
299#19871C10711yesmaximal, characteristic, direct product factor, Sylow
300C2×C107—81no—
301C2×C107—161no—
302C2×C107—161no—
303C2×C107—161no—
304C2×C107#326811yescharacteristic
305C2×C107#328711yescharacteristic
306C2×C107#328811yescharacteristic
307#3399C2×C10711yescharacteristic, complemented
308#3396C2×C10711yescharacteristic, complemented
309#3394C2×C10711yescharacteristic, complemented
310#3304C2×C10711yescharacteristic, complemented
311#1721C2×C10711yescharacteristic, complemented
312#1686C2×C10711yescharacteristic, complemented
313#1682C2×C10711yescharacteristic, complemented
314#1668C2×C10711yescharacteristic, complemented
315#1667C2×C10711yescharacteristic, complemented
316#1640C2×C10711yescharacteristic, complemented
317#1628C2×C10711yescharacteristic, complemented
318#1621C2×C10711yescharacteristic, complemented
319#1620C2×C10711yescharacteristic, complemented
320#1584C2×C10711yescharacteristic, complemented
321SD16⋊C8C2×C10711yescharacteristic, complemented
322C107#1987111yescharacteristic, direct product factor, Sylow
323#559C22×C10711yescharacteristic
324#559C22×C10711yescharacteristic
325#556C22×C10711yescharacteristic
326#550C22×C10711yescharacteristic
327#496—21no—
328#495—21no—
329#495—21no—
330#493C22×C10711yescharacteristic
331#493C22×C10711yescharacteristic
332#493C22×C10711yescharacteristic
333#492C22×C10711yescharacteristic
334#486C22×C10711yescharacteristic
335#486C22×C10711yescharacteristic
336#482—21no—
337#475C22×C10711yescharacteristic
338#465—21no—
339#464—21no—
340#463—21no—
341#463—21no—
342#463—21no—
343#463—21no—
344#462C22×C10711yescharacteristic
345#460C22×C10711yescharacteristic
346#460C22×C10711yescharacteristic
347#460C22×C10711yescharacteristic
348#460C22×C10711yescharacteristic
349#459—21no—
350#459C22×C10711yescharacteristic
351#459C22×C10711yescharacteristic
352#452—21no—
353#446C22×C10711yescharacteristic
354C8×Q8C22×C10711yescharacteristic
355C8×Q8C22×C10711yescharacteristic
356#442—21no—
357C4×Q16C22×C10711yescharacteristic
358C4×SD16—21no—
359C4×SD16C22×C10711yescharacteristic
360C4×D8—21no—
361C8×D4C22×C10711yescharacteristic
362#416—21no—
363#335C22×C10711yescharacteristic
364#335C22×C10711yescharacteristic
365#332C22×C10711yescharacteristic
366#331C22×C10711yescharacteristic
367#331C22×C10711yescharacteristic
368#331C22×C10711yescharacteristic
369Q8⋊C8C22×C10711yescharacteristic
370Q8⋊C8C22×C10711yescharacteristic
371Q8⋊C8C22×C10711yescharacteristic
372D4⋊C8C22×C10711yescharacteristic
373#322C22×C10711yescharacteristic
374C2×#41—21no—
375C2×Q16—21no—
376C2×Q16D4×C10711yescharacteristic
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16D4×C10711yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—41no—
391C22×C8—21no—
392C4⋊Q8C23×C10711yescharacteristic
393#127—21no—
394#127C23×C10711yescharacteristic
395#127C23×C10711yescharacteristic
396#127C23×C10711yescharacteristic
397#126—41no—
398#124—21no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#123—41no—
404#123—41no—
405C22⋊Q8—21no—
406#121—21no—
407#121—41no—
408C4×Q8—21no—
409C4×Q8C23×C10711yescharacteristic
410C4×Q8C23×C10711yescharacteristic
411C4×Q8C23×C10711yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C10711yescharacteristic
418#117—21no—
419#107D4×C10711yescharacteristic
420#106—21no—
421#106D4×C10711yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8C23×C10711yescharacteristic
426C4⋊C8C23×C10711yescharacteristic
427C4⋊C8C23×C10711yescharacteristic
428C4⋊C8C23×C10711yescharacteristic
429#103—21no—
430#103—21no—
431#103D4×C10711yescharacteristic
432#103D4×C10711yescharacteristic
433#103D4×C10711yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C10711yescharacteristic
444C22⋊C8—21no—
445#97—21no—
446C4×C8—21no—
447C4×C8—21no—
448C4×C8C23×C10711yescharacteristic
449C4×C8C23×C10711yescharacteristic
450C4×C8C23×C10711yescharacteristic
451#41—42no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8C2×D4×C10711yescharacteristic
455C2×Q8C2×D4×C10711yescharacteristic
456C2×Q8C2×D4×C10711yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C10711yescharacteristic
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—41no—
474Q16—81no—
475SD16—22no—
476SD16—42no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482D8—42no—
483D8—42no—
484D8—81no—
485D8—81no—
486D8—81no—
487D8—81no—
488D8—82no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—81no—
495C2×C8C2×D4×C10711yescharacteristic
496C2×C8C2×D4×C10711yescharacteristic
497C2×C8C2×D4×C10711yescharacteristic
498C2×C8C2×D4×C10711yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C10711yescharacteristic
506C4⋊C4C2×D4×C10711yescharacteristic
507C4⋊C4C2×D4×C10711yescharacteristic
508C4⋊C4C2×D4×C10711yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42C24×C10711yescharacteristic
524C23—21no—
525C23—41no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—82no—
554D4—161no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4C22×D4×C10711yescharacteristic
569C2×C4C22×D4×C10711yescharacteristic
570C2×C4H(5,𝔽2)×C10711yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8#135×C10712yes—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C10711yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4C2×#135×C10711yescharacteristic
603C4#575×C10711yescharacteristic
604C4#576×C10711yescharacteristic
605C4#576×C10711yescharacteristic
606C2—81no—
607C2—161no—
608C2—161no—
609C2—161no—
610C2C107×#326811yescharacteristic
611C2C107×#328711yescharacteristic
612C2C107×#328811yescharacteristic
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×#3396C2semidirect
3. C107×#3394C2semidirect
4. C107×#3304C2semidirect
5. C107×#1721C2semidirect
6. C107×#1686C2semidirect
7. C107×#1682C2semidirect
8. C107×#1668C2semidirect
9. C107×#1667C2semidirect
10. C107×#1640C2semidirect
11. C107×#1628C2semidirect
12. C107×#1621C2semidirect
13. C107×#1620C2semidirect
14. C107×#1584C2semidirect
15. C107×SD16⋊C8C2semidirect
299. #19871C107direct (N × H)
307. #3399C2×C107semidirect
308. #3396C2×C107semidirect
309. #3394C2×C107semidirect
310. #3304C2×C107semidirect
311. #1721C2×C107semidirect
312. #1686C2×C107semidirect
313. #1682C2×C107semidirect
314. #1668C2×C107semidirect
315. #1667C2×C107semidirect
316. #1640C2×C107semidirect
317. #1628C2×C107semidirect
318. #1621C2×C107semidirect
319. #1620C2×C107semidirect
320. #1584C2×C107semidirect
321. SD16⋊C8C2×C107semidirect
322. C107#19871direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#33992
C107×#33962
C107×#33942
C107×#33042
C107×#17212
C107×#16862
C107×#16822
C107×#16682
C107×#16672
C107×#16402
C107×#16282
C107×#16212
C107×#16202
C107×#15842
C107×SD16⋊C82
#19871107