Finite Group Databasebeta

← C107×#19911 #41045875

Subgroups — C107×#19911 #41045875

Order 27392.

666 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3366C211yesmaximal, characteristic, complemented
2C107×#3325C211yesmaximal, characteristic, complemented
3C107×#3305C211yesmaximal, characteristic, complemented
4C107×#3295C211yesmaximal, characteristic, complemented
5C107×#1709C211yesmaximal, characteristic, complemented
6C107×#1698C211yesmaximal, characteristic, complemented
7C107×#1697C211yesmaximal, characteristic, complemented
8C107×#1677C211yesmaximal, characteristic, complemented
9C107×#1677C211yesmaximal, characteristic, complemented
10C107×#1634C211yesmaximal, characteristic, complemented
11C107×#1632C211yesmaximal, characteristic, complemented
12C107×#1621C211yesmaximal, characteristic, complemented
13C107×#1619C211yesmaximal, characteristic, complemented
14C107×#1590C211yesmaximal, characteristic, complemented
15C8×D8×C107C211yesmaximal, characteristic, complemented
16#555×C107C2211yescharacteristic
17#554×C107C2211yescharacteristic
18#550×C107C2211yescharacteristic, complemented
19D42×C107C2211yescharacteristic
20#494×C107C2211yescharacteristic, complemented
21#493×C107C2211yescharacteristic
22#490×C107—21no—
23#486×C107C2211yescharacteristic
24#486×C107C2211yescharacteristic
25#486×C107C2211yescharacteristic, complemented
26#486×C107C2211yescharacteristic, complemented
27#482×C107—21no—
28#482×C107—21no—
29#481×C107—21no—
30#478×C107—21no—
31#477×C107C2211yescharacteristic, complemented
32#476×C107C2211yescharacteristic
33#476×C107C2211yescharacteristic
34#476×C107C2211yescharacteristic, complemented
35#469×C107—21no—
36#466×C107—21no—
37#465×C107—21no—
38#460×C107C2211yescharacteristic
39#459×C107—21no—
40#459×C107C2211yescharacteristic
41#459×C107C2211yescharacteristic
42#459×C107C2211yescharacteristic
43#450×C107—21no—
44#449×C107—21no—
45#447×C107—21no—
46#446×C107C2211yescharacteristic, complemented
47#442×C107—21no—
48C4×SD16×C107C2211yescharacteristic
49C4×D8×C107C2211yescharacteristic
50#436×C107C2211yescharacteristic
51C8×D4×C107C2211yescharacteristic
52C8×D4×C107C2211yescharacteristic, complemented
53#418×C107—21no—
54#416×C107—21no—
55C2×#102×C107—21no—
56#335×C107C2211yescharacteristic, complemented
57#334×C107C2211yescharacteristic, complemented
58#333×C107C2211yescharacteristic, complemented
59#333×C107C2211yescharacteristic, complemented
60#331×C107C2211yescharacteristic
61#331×C107C2211yescharacteristic, complemented
62Q8⋊C8×C107C2211yescharacteristic, complemented
63D4⋊C8×C107C2211yescharacteristic
64D4⋊C8×C107C2211yescharacteristic
65D4⋊C8×C107C2211yescharacteristic, complemented
66C82×C107C2211yescharacteristic, complemented
67C2×#41×C107—21no—
68C22×D4×C107—21no—
69C22×D4×C107—21no—
70C2×Q16×C107—41no—
71C2×SD16×C107—21no—
72C2×SD16×C107D411yescharacteristic
73C2×D8×C107—21no—
74C2×D8×C107—21no—
75C2×D8×C107—21no—
76C2×D8×C107—41no—
77C2×D8×C107D411yescharacteristic
78C2×M16×C107—21no—
79C22×C8×C107—21no—
80C22×C8×C107—21no—
81C4⋊Q8×C107C2311yescharacteristic
82C4⋊Q8×C107C2311yescharacteristic
83#127×C107—21no—
84#127×C107C2311yescharacteristic
85#127×C107C2311yescharacteristic
86#125×C107—21no—
87#124×C107—41no—
88C22⋊Q8×C107—21no—
89C22⋊Q8×C107—41no—
90#121×C107—21no—
91#121×C107—21no—
92#121×C107—21no—
93#121×C107—21no—
94#121×C107—21no—
95#121×C107—41no—
96#120×C107—41no—
97C4×Q8×C107C2311yescharacteristic
98C4×D4×C107—21no—
99C4×D4×C107—21no—
100C4×D4×C107C2311yescharacteristic
101C4×D4×C107C2311yescharacteristic
102C4×D4×C107C2311yescharacteristic
103#117×C107—21no—
104#117×C107—21no—
105C2×C4⋊C4×C107—21no—
106#107×C107—21no—
107#107×C107D411yescharacteristic
108#106×C107—21no—
109#106×C107—21no—
110#106×C107—21no—
111#106×C107D411yescharacteristic
112C4⋊C8×C107—21no—
113C4⋊C8×C107C2311yescharacteristic
114C4⋊C8×C107C2311yescharacteristic
115C4⋊C8×C107C2311yescharacteristic
116C4⋊C8×C107C2311yescharacteristic
117#103×C107—21no—
118#103×C107D411yescharacteristic
119#102×C107—21no—
120#102×C107—21no—
121#102×C107—21no—
122#102×C107—21no—
123#102×C107—21no—
124#102×C107—21no—
125#102×C107—21no—
126#102×C107—21no—
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×C107D411yescharacteristic
135#102×C107D411yescharacteristic
136#102×C107D411yescharacteristic
137C22⋊C8×C107—21no—
138C22⋊C8×C107—21no—
139C22⋊C8×C107—21no—
140#97×C107—21no—
141C4×C8×C107C2311yescharacteristic
142C4×C8×C107C2311yescharacteristic
143C4×C8×C107C2311yescharacteristic
144C24×C107—41no—
145#41×C107—42no—
146#41×C107—81no—
147C2×Q8×C107—21no—
148C2×Q8×C107—21no—
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—41no—
157C2×D4×C107—41no—
158C2×D4×C107—41no—
159C2×D4×C107—41no—
160C2×D4×C107—42no—
161C2×D4×C107—42no—
162C2×D4×C107—41no—
163C2×D4×C107—81no—
164C2×D4×C107—81no—
165C2×D4×C107C2×D411yescharacteristic
166C2×D4×C107C2×D411yescharacteristic
167C2×D4×C107C2×D411yescharacteristic
168C22×C4×C107—21no—
169C22×C4×C107—21no—
170C22×C4×C107—21no—
171C22×C4×C107—41no—
172C22×C4×C107—41no—
173Q16×C107—82no—
174SD16×C107—41no—
175SD16×C107—81no—
176D8×C107—22no—
177D8×C107—42no—
178D8×C107—82no—
179D8×C107—81no—
180D8×C107—81no—
181M16×C107—81no—
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×C107—81no—
189C2×C8×C107C2×D411yescharacteristic
190C2×C8×C107C2×D411yescharacteristic
191C2×C8×C107C2×D411yescharacteristic
192C2×C8×C107C2×D411yescharacteristic
193C4⋊C4×C107—21no—
194C4⋊C4×C107—21no—
195C4⋊C4×C107—21no—
196C4⋊C4×C107—21no—
197C4⋊C4×C107—21no—
198C4⋊C4×C107—41no—
199C4⋊C4×C107—41no—
200C4⋊C4×C107C2×D411yescharacteristic
201C4⋊C4×C107C2×D411yescharacteristic
202C4⋊C4×C107C2×D411yescharacteristic
203C4⋊C4×C107C2×D411yescharacteristic
204C22⋊C4×C107—21no—
205C22⋊C4×C107—21no—
206C22⋊C4×C107—21no—
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—41no—
214C42×C107C2411yescharacteristic
215C23×C107—21no—
216C23×C107—21no—
217C23×C107—21no—
218C23×C107—41no—
219C23×C107—41no—
220C23×C107—82no—
221C23×C107—82no—
222C23×C107—161no—
223Q8×C107—21no—
224Q8×C107—21no—
225Q8×C107—81no—
226Q8×C107—81no—
227D4×C107—21no—
228D4×C107—21no—
229D4×C107—21no—
230D4×C107—21no—
231D4×C107—21no—
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—81no—
241D4×C107—81no—
242D4×C107—82no—
243D4×C107—82no—
244D4×C107—82no—
245D4×C107—161no—
246D4×C107—161no—
247D4×C107#13512yes—
248C2×C4×C107—21no—
249C2×C4×C107—21no—
250C2×C4×C107—21no—
251C2×C4×C107—21no—
252C2×C4×C107—21no—
253C2×C4×C107—41no—
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—41no—
261C2×C4×C107—82no—
262C2×C4×C107—161no—
263C2×C4×C107C22×D411yescharacteristic
264C2×C4×C107C22×D411yescharacteristic
265C2×C4×C107H(5,𝔽2)11yescharacteristic
266C8×C107—22no—
267C8×C107—21no—
268C8×C107—21no—
269C8×C107—21no—
270C8×C107—21no—
271C8×C107—41no—
272C8×C107—41no—
273C8×C107—41no—
274C8×C107—41no—
275C22×C107—22no—
276C22×C107—41no—
277C22×C107—41no—
278C22×C107—41no—
279C22×C107—41no—
280C22×C107—41no—
281C22×C107—41no—
282C22×C107—41no—
283C22×C107—41no—
284C22×C107—81no—
285C22×C107—81no—
286C22×C107—81no—
287C22×C107—81no—
288C22×C107—81no—
289C22×C107—81no—
290C22×C107—164no—
291C22×C107D4211yescharacteristic
292C4×C107—21no—
293C4×C107—41no—
294C4×C107—41no—
295C4×C107—41no—
296C4×C107—41no—
297C4×C107—41no—
298C4×C107—81no—
299C4×C107—81no—
300C4×C107C2×#13511yescharacteristic
301C4×C107#57511yescharacteristic
302C4×C107#57611yescharacteristic
303C4×C107#57711yescharacteristic
304#19911C10711yesmaximal, characteristic, direct product factor, Sylow
305C2×C107—42no—
306C2×C107—81no—
307C2×C107—81no—
308C2×C107—161no—
309C2×C107—161no—
310C2×C107#327311yescharacteristic
311C2×C107#328211yescharacteristic
312C2×C107#329211yescharacteristic
313#3366C2×C10711yescharacteristic, complemented
314#3325C2×C10711yescharacteristic, complemented
315#3305C2×C10711yescharacteristic, complemented
316#3295C2×C10711yescharacteristic, complemented
317#1709C2×C10711yescharacteristic, complemented
318#1698C2×C10711yescharacteristic, complemented
319#1697C2×C10711yescharacteristic, complemented
320#1677C2×C10711yescharacteristic, complemented
321#1677C2×C10711yescharacteristic, complemented
322#1634C2×C10711yescharacteristic, complemented
323#1632C2×C10711yescharacteristic, complemented
324#1621C2×C10711yescharacteristic, complemented
325#1619C2×C10711yescharacteristic, complemented
326#1590C2×C10711yescharacteristic, complemented
327C8×D8C2×C10711yescharacteristic, complemented
328C107#1991111yescharacteristic, direct product factor, Sylow
329#555C22×C10711yescharacteristic
330#554C22×C10711yescharacteristic
331#550C22×C10711yescharacteristic, complemented
332D42C22×C10711yescharacteristic
333#494C22×C10711yescharacteristic, complemented
334#493C22×C10711yescharacteristic
335#490—21no—
336#486C22×C10711yescharacteristic
337#486C22×C10711yescharacteristic
338#486C22×C10711yescharacteristic, complemented
339#486C22×C10711yescharacteristic, complemented
340#482—21no—
341#482—21no—
342#481—21no—
343#478—21no—
344#477C22×C10711yescharacteristic, complemented
345#476C22×C10711yescharacteristic
346#476C22×C10711yescharacteristic
347#476C22×C10711yescharacteristic, complemented
348#469—21no—
349#466—21no—
350#465—21no—
351#460C22×C10711yescharacteristic
352#459—21no—
353#459C22×C10711yescharacteristic
354#459C22×C10711yescharacteristic
355#459C22×C10711yescharacteristic
356#450—21no—
357#449—21no—
358#447—21no—
359#446C22×C10711yescharacteristic, complemented
360#442—21no—
361C4×SD16C22×C10711yescharacteristic
362C4×D8C22×C10711yescharacteristic
363#436C22×C10711yescharacteristic
364C8×D4C22×C10711yescharacteristic
365C8×D4C22×C10711yescharacteristic, complemented
366#418—21no—
367#416—21no—
368C2×#102—21no—
369#335C22×C10711yescharacteristic, complemented
370#334C22×C10711yescharacteristic, complemented
371#333C22×C10711yescharacteristic, complemented
372#333C22×C10711yescharacteristic, complemented
373#331C22×C10711yescharacteristic
374#331C22×C10711yescharacteristic, complemented
375Q8⋊C8C22×C10711yescharacteristic, complemented
376D4⋊C8C22×C10711yescharacteristic
377D4⋊C8C22×C10711yescharacteristic
378D4⋊C8C22×C10711yescharacteristic, complemented
379C82C22×C10711yescharacteristic, complemented
380C2×#41—21no—
381C22×D4—21no—
382C22×D4—21no—
383C2×Q16—41no—
384C2×SD16—21no—
385C2×SD16D4×C10711yescharacteristic
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—41no—
390C2×D8D4×C10711yescharacteristic
391C2×M16—21no—
392C22×C8—21no—
393C22×C8—21no—
394C4⋊Q8C23×C10711yescharacteristic
395C4⋊Q8C23×C10711yescharacteristic
396#127—21no—
397#127C23×C10711yescharacteristic
398#127C23×C10711yescharacteristic
399#125—21no—
400#124—41no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—41no—
409#120—41no—
410C4×Q8C23×C10711yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C23×C10711yescharacteristic
414C4×D4C23×C10711yescharacteristic
415C4×D4C23×C10711yescharacteristic
416#117—21no—
417#117—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107D4×C10711yescharacteristic
421#106—21no—
422#106—21no—
423#106—21no—
424#106D4×C10711yescharacteristic
425C4⋊C8—21no—
426C4⋊C8C23×C10711yescharacteristic
427C4⋊C8C23×C10711yescharacteristic
428C4⋊C8C23×C10711yescharacteristic
429C4⋊C8C23×C10711yescharacteristic
430#103—21no—
431#103D4×C10711yescharacteristic
432#102—21no—
433#102—21no—
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—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102D4×C10711yescharacteristic
448#102D4×C10711yescharacteristic
449#102D4×C10711yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453#97—21no—
454C4×C8C23×C10711yescharacteristic
455C4×C8C23×C10711yescharacteristic
456C4×C8C23×C10711yescharacteristic
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C10711yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C10711yescharacteristic
479C2×D4C2×D4×C10711yescharacteristic
480C2×D4C2×D4×C10711yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486Q16—82no—
487SD16—41no—
488SD16—81no—
489D8—22no—
490D8—42no—
491D8—82no—
492D8—81no—
493D8—81no—
494M16—81no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—81no—
501C2×C8—81no—
502C2×C8C2×D4×C10711yescharacteristic
503C2×C8C2×D4×C10711yescharacteristic
504C2×C8C2×D4×C10711yescharacteristic
505C2×C8C2×D4×C10711yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C10711yescharacteristic
514C4⋊C4C2×D4×C10711yescharacteristic
515C4⋊C4C2×D4×C10711yescharacteristic
516C4⋊C4C2×D4×C10711yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C42—21no—
526C42—41no—
527C42C24×C10711yescharacteristic
528C23—21no—
529C23—21no—
530C23—21no—
531C23—41no—
532C23—41no—
533C23—82no—
534C23—82no—
535C23—161no—
536Q8—21no—
537Q8—21no—
538Q8—81no—
539Q8—81no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—81no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—161no—
559D4—161no—
560D4#135×C10712yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—82no—
575C2×C4—161no—
576C2×C4C22×D4×C10711yescharacteristic
577C2×C4C22×D4×C10711yescharacteristic
578C2×C4H(5,𝔽2)×C10711yescharacteristic
579C8—22no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—164no—
604C22D42×C10711yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4C2×#135×C10711yescharacteristic
614C4#575×C10711yescharacteristic
615C4#576×C10711yescharacteristic
616C4#577×C10711yescharacteristic
617C2—42no—
618C2—81no—
619C2—81no—
620C2—161no—
621C2—161no—
622C2C107×#327311yescharacteristic
623C2C107×#328211yescharacteristic
624C2C107×#329211yescharacteristic
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×#3366C2semidirect
2. C107×#3325C2semidirect
3. C107×#3305C2semidirect
4. C107×#3295C2semidirect
5. C107×#1709C2semidirect
6. C107×#1698C2semidirect
7. C107×#1697C2semidirect
8. C107×#1677C2semidirect
9. C107×#1677C2semidirect
10. C107×#1634C2semidirect
11. C107×#1632C2semidirect
12. C107×#1621C2semidirect
13. C107×#1619C2semidirect
14. C107×#1590C2semidirect
15. C8×D8×C107C2semidirect
18. #550×C107C22semidirect
20. #494×C107C22semidirect
25. #486×C107C22semidirect
26. #486×C107C22semidirect
31. #477×C107C22semidirect
34. #476×C107C22semidirect
46. #446×C107C22semidirect
52. C8×D4×C107C22semidirect
56. #335×C107C22semidirect
57. #334×C107C22semidirect
58. #333×C107C22semidirect
59. #333×C107C22semidirect
61. #331×C107C22semidirect
62. Q8⋊C8×C107C22semidirect
65. D4⋊C8×C107C22semidirect
66. C82×C107C22semidirect
304. #19911C107direct (N × H)
313. #3366C2×C107semidirect
314. #3325C2×C107semidirect
315. #3305C2×C107semidirect
316. #3295C2×C107semidirect
317. #1709C2×C107semidirect
318. #1698C2×C107semidirect
319. #1697C2×C107semidirect
320. #1677C2×C107semidirect
321. #1677C2×C107semidirect
322. #1634C2×C107semidirect
323. #1632C2×C107semidirect
324. #1621C2×C107semidirect
325. #1619C2×C107semidirect
326. #1590C2×C107semidirect
327. C8×D8C2×C107semidirect
328. C107#19911direct (N × H)
331. #550C22×C107semidirect
333. #494C22×C107semidirect
338. #486C22×C107semidirect
339. #486C22×C107semidirect
344. #477C22×C107semidirect
347. #476C22×C107semidirect
359. #446C22×C107semidirect
365. C8×D4C22×C107semidirect
369. #335C22×C107semidirect
370. #334C22×C107semidirect
371. #333C22×C107semidirect
372. #333C22×C107semidirect
374. #331C22×C107semidirect
375. Q8⋊C8C22×C107semidirect
378. D4⋊C8C22×C107semidirect
379. C82C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#33662
C107×#33252
C107×#33052
C107×#32952
C107×#17092
C107×#16982
C107×#16972
C107×#16772
C107×#16342
C107×#16322
C107×#16212
C107×#16192
C107×#15902
C8×D8×C1072
#19911107