Finite Group Databasebeta

← C107×#19899 #41045863

Subgroups — C107×#19899 #41045863

Order 27392.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3330C211yesmaximal, characteristic, complemented
2C107×#3325C211yesmaximal, characteristic, complemented
3C107×#3303C211yesmaximal, characteristic, complemented
4C107×#3294C211yesmaximal, characteristic, complemented
5C107×#1711C211yesmaximal, characteristic, complemented
6C107×#1699C211yesmaximal, characteristic, complemented
7C107×#1697C211yesmaximal, characteristic, complemented
8C107×#1683C211yesmaximal, characteristic, complemented
9C107×#1681C211yesmaximal, characteristic, complemented
10C107×#1646C211yesmaximal, characteristic, complemented
11C107×#1639C211yesmaximal, characteristic, complemented
12C107×#1635C211yesmaximal, characteristic, complemented
13C107×#1625C211yesmaximal, characteristic, complemented
14C107×#1589C211yesmaximal, characteristic, complemented
15C8×D8×C107C211yesmaximal, characteristic, complemented
16#555×C107C2211yescharacteristic
17#547×C107C2211yescharacteristic
18#547×C107C2211yescharacteristic, complemented
19D42×C107C2211yescharacteristic
20#487×C107C2211yescharacteristic, complemented
21#487×C107C2211yescharacteristic, complemented
22#487×C107C2211yescharacteristic, complemented
23#486×C107C2211yescharacteristic
24#486×C107C2211yescharacteristic
25#486×C107C2211yescharacteristic
26#485×C107—21no—
27#484×C107—21no—
28#482×C107—21no—
29#480×C107—21no—
30#476×C107C2211yescharacteristic
31#476×C107C2211yescharacteristic, complemented
32#474×C107C2211yescharacteristic
33#474×C107C2211yescharacteristic
34#469×C107—21no—
35#468×C107—21no—
36#466×C107—21no—
37#465×C107—21no—
38#461×C107C2211yescharacteristic
39#461×C107C2211yescharacteristic, complemented
40#459×C107C2211yescharacteristic
41#459×C107C2211yescharacteristic
42#449×C107—21no—
43#449×C107—21no—
44#447×C107—21no—
45#447×C107—21no—
46C4×D8×C107C2211yescharacteristic
47C4×D8×C107C2211yescharacteristic
48#436×C107C2211yescharacteristic
49#436×C107C2211yescharacteristic, complemented
50C8×D4×C107C2211yescharacteristic
51C8×D4×C107C2211yescharacteristic, complemented
52#418×C107—21no—
53#417×C107—21no—
54#416×C107—21no—
55C2×#102×C107—21no—
56#335×C107C2211yescharacteristic, complemented
57#335×C107C2211yescharacteristic, complemented
58#333×C107C2211yescharacteristic, complemented
59#332×C107C2211yescharacteristic, complemented
60#332×C107C2211yescharacteristic, complemented
61#331×C107C2211yescharacteristic
62D4⋊C8×C107C2211yescharacteristic
63D4⋊C8×C107C2211yescharacteristic
64D4⋊C8×C107C2211yescharacteristic, complemented
65D4⋊C8×C107C2211yescharacteristic, complemented
66C82×C107C2211yescharacteristic, complemented
67C2×#41×C107—21no—
68C2×#41×C107—21no—
69C22×D4×C107—21no—
70C22×D4×C107—21no—
71C2×SD16×C107—21no—
72C2×SD16×C107—21no—
73C2×D8×C107—21no—
74C2×D8×C107—21no—
75C2×D8×C107D411yescharacteristic
76C2×D8×C107D411yescharacteristic
77C2×M16×C107—21no—
78C2×M16×C107—21no—
79C22×C8×C107—21no—
80C22×C8×C107—21no—
81C4⋊Q8×C107C2311yescharacteristic
82C4⋊Q8×C107C2311yescharacteristic
83C4⋊Q8×C107C2311yescharacteristic
84#127×C107C2311yescharacteristic
85#124×C107—41no—
86#123×C107—41no—
87#123×C107—41no—
88C22⋊Q8×C107—21no—
89C22⋊Q8×C107—21no—
90#121×C107—21no—
91#121×C107—21no—
92#121×C107—21no—
93#121×C107—21no—
94#121×C107—21no—
95#121×C107—21no—
96#120×C107—41no—
97C4×D4×C107C2311yescharacteristic
98C4×D4×C107C2311yescharacteristic
99C4×D4×C107C2311yescharacteristic
100C4×D4×C107C2311yescharacteristic
101#117×C107—21no—
102#117×C107—21no—
103C2×C4⋊C4×C107—21no—
104C2×C4⋊C4×C107—21no—
105#107×C107—21no—
106#107×C107—21no—
107#107×C107D411yescharacteristic
108#107×C107D411yescharacteristic
109#106×C107—21no—
110#106×C107—21no—
111C4⋊C8×C107C2311yescharacteristic
112C4⋊C8×C107C2311yescharacteristic
113C4⋊C8×C107C2311yescharacteristic
114C4⋊C8×C107C2311yescharacteristic
115#103×C107—21no—
116#103×C107—21no—
117#103×C107—21no—
118#103×C107—21no—
119#103×C107—21no—
120#103×C107—21no—
121#103×C107—41no—
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—41no—
133#102×C107D411yescharacteristic
134#102×C107D411yescharacteristic
135#102×C107D411yescharacteristic
136#102×C107D411yescharacteristic
137C22⋊C8×C107—21no—
138C22⋊C8×C107—21no—
139C22⋊C8×C107—21no—
140C22⋊C8×C107—21no—
141C4×C8×C107C2311yescharacteristic
142C4×C8×C107C2311yescharacteristic
143C4×C8×C107C2311yescharacteristic
144C24×C107—41no—
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×C107—21no—
152C2×D4×C107—21no—
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107—41no—
156C2×D4×C107—41no—
157C2×D4×C107—42no—
158C2×D4×C107—42no—
159C2×D4×C107—41no—
160C2×D4×C107—41no—
161C2×D4×C107—41no—
162C2×D4×C107—81no—
163C2×D4×C107—81no—
164C2×D4×C107C2×D411yescharacteristic
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—21no—
172C22×C4×C107—41no—
173C22×C4×C107—41no—
174SD16×C107—81no—
175SD16×C107—81no—
176D8×C107—22no—
177D8×C107—41no—
178D8×C107—81no—
179D8×C107—81no—
180M16×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—21no—
199C4⋊C4×C107—41no—
200C4⋊C4×C107—41no—
201C4⋊C4×C107C2×D411yescharacteristic
202C4⋊C4×C107C2×D411yescharacteristic
203C4⋊C4×C107C2×D411yescharacteristic
204C4⋊C4×C107C2×D411yescharacteristic
205C22⋊C4×C107—21no—
206C22⋊C4×C107—21no—
207C22⋊C4×C107—21no—
208C22⋊C4×C107—21no—
209C22⋊C4×C107—41no—
210C22⋊C4×C107—41no—
211C22⋊C4×C107—41no—
212C22⋊C4×C107—41no—
213C22⋊C4×C107—41no—
214C42×C107—41no—
215C42×C107C2411yescharacteristic
216C23×C107—21no—
217C23×C107—21no—
218C23×C107—21no—
219C23×C107—21no—
220C23×C107—41no—
221C23×C107—82no—
222C23×C107—82no—
223C23×C107—161no—
224Q8×C107—41no—
225Q8×C107—41no—
226Q8×C107—41no—
227Q8×C107—41no—
228Q8×C107—81no—
229D4×C107—21no—
230D4×C107—21no—
231D4×C107—21no—
232D4×C107—21no—
233D4×C107—21no—
234D4×C107—21no—
235D4×C107—21no—
236D4×C107—41no—
237D4×C107—41no—
238D4×C107—41no—
239D4×C107—41no—
240D4×C107—81no—
241D4×C107—82no—
242D4×C107—82no—
243D4×C107—82no—
244D4×C107—82no—
245D4×C107—161no—
246D4×C107#13512yes—
247C2×C4×C107—21no—
248C2×C4×C107—21no—
249C2×C4×C107—21no—
250C2×C4×C107—21no—
251C2×C4×C107—41no—
252C2×C4×C107—41no—
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—41no—
262C2×C4×C107—82no—
263C2×C4×C107—82no—
264C2×C4×C107C22×D411yescharacteristic
265C2×C4×C107C22×D411yescharacteristic
266C2×C4×C107H(5,𝔽2)11yescharacteristic
267C8×C107—21no—
268C8×C107—21no—
269C8×C107—21no—
270C8×C107—21no—
271C8×C107—41no—
272C8×C107—41no—
273C8×C107—41no—
274C8×C107—41no—
275C8×C107—41no—
276C22×C107—22no—
277C22×C107—41no—
278C22×C107—41no—
279C22×C107—41no—
280C22×C107—41no—
281C22×C107—41no—
282C22×C107—41no—
283C22×C107—41no—
284C22×C107—41no—
285C22×C107—41no—
286C22×C107—41no—
287C22×C107—41no—
288C22×C107—81no—
289C22×C107—81no—
290C22×C107—81no—
291C22×C107—164no—
292C22×C107D4211yescharacteristic
293C4×C107—21no—
294C4×C107—41no—
295C4×C107—41no—
296C4×C107—41no—
297C4×C107—41no—
298C4×C107—81no—
299C4×C107—81no—
300C4×C107—81no—
301C4×C107C2×#13511yescharacteristic
302C4×C107#57511yescharacteristic
303C4×C107#57611yescharacteristic
304C4×C107#57611yescharacteristic
305#19899C10711yesmaximal, characteristic, direct product factor, Sylow
306C2×C107—42no—
307C2×C107—81no—
308C2×C107—81no—
309C2×C107—81no—
310C2×C107—161no—
311C2×C107#327311yescharacteristic
312C2×C107#328011yescharacteristic
313C2×C107#329011yescharacteristic
314#3330C2×C10711yescharacteristic, complemented
315#3325C2×C10711yescharacteristic, complemented
316#3303C2×C10711yescharacteristic, complemented
317#3294C2×C10711yescharacteristic, complemented
318#1711C2×C10711yescharacteristic, complemented
319#1699C2×C10711yescharacteristic, complemented
320#1697C2×C10711yescharacteristic, complemented
321#1683C2×C10711yescharacteristic, complemented
322#1681C2×C10711yescharacteristic, complemented
323#1646C2×C10711yescharacteristic, complemented
324#1639C2×C10711yescharacteristic, complemented
325#1635C2×C10711yescharacteristic, complemented
326#1625C2×C10711yescharacteristic, complemented
327#1589C2×C10711yescharacteristic, complemented
328C8×D8C2×C10711yescharacteristic, complemented
329C107#1989911yescharacteristic, direct product factor, Sylow
330#555C22×C10711yescharacteristic
331#547C22×C10711yescharacteristic
332#547C22×C10711yescharacteristic, complemented
333D42C22×C10711yescharacteristic
334#487C22×C10711yescharacteristic, complemented
335#487C22×C10711yescharacteristic, complemented
336#487C22×C10711yescharacteristic, complemented
337#486C22×C10711yescharacteristic
338#486C22×C10711yescharacteristic
339#486C22×C10711yescharacteristic
340#485—21no—
341#484—21no—
342#482—21no—
343#480—21no—
344#476C22×C10711yescharacteristic
345#476C22×C10711yescharacteristic, complemented
346#474C22×C10711yescharacteristic
347#474C22×C10711yescharacteristic
348#469—21no—
349#468—21no—
350#466—21no—
351#465—21no—
352#461C22×C10711yescharacteristic
353#461C22×C10711yescharacteristic, complemented
354#459C22×C10711yescharacteristic
355#459C22×C10711yescharacteristic
356#449—21no—
357#449—21no—
358#447—21no—
359#447—21no—
360C4×D8C22×C10711yescharacteristic
361C4×D8C22×C10711yescharacteristic
362#436C22×C10711yescharacteristic
363#436C22×C10711yescharacteristic, complemented
364C8×D4C22×C10711yescharacteristic
365C8×D4C22×C10711yescharacteristic, complemented
366#418—21no—
367#417—21no—
368#416—21no—
369C2×#102—21no—
370#335C22×C10711yescharacteristic, complemented
371#335C22×C10711yescharacteristic, complemented
372#333C22×C10711yescharacteristic, complemented
373#332C22×C10711yescharacteristic, complemented
374#332C22×C10711yescharacteristic, complemented
375#331C22×C10711yescharacteristic
376D4⋊C8C22×C10711yescharacteristic
377D4⋊C8C22×C10711yescharacteristic
378D4⋊C8C22×C10711yescharacteristic, complemented
379D4⋊C8C22×C10711yescharacteristic, complemented
380C82C22×C10711yescharacteristic, complemented
381C2×#41—21no—
382C2×#41—21no—
383C22×D4—21no—
384C22×D4—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8D4×C10711yescharacteristic
390C2×D8D4×C10711yescharacteristic
391C2×M16—21no—
392C2×M16—21no—
393C22×C8—21no—
394C22×C8—21no—
395C4⋊Q8C23×C10711yescharacteristic
396C4⋊Q8C23×C10711yescharacteristic
397C4⋊Q8C23×C10711yescharacteristic
398#127C23×C10711yescharacteristic
399#124—41no—
400#123—41no—
401#123—41no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#120—41no—
411C4×D4C23×C10711yescharacteristic
412C4×D4C23×C10711yescharacteristic
413C4×D4C23×C10711yescharacteristic
414C4×D4C23×C10711yescharacteristic
415#117—21no—
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107—21no—
421#107D4×C10711yescharacteristic
422#107D4×C10711yescharacteristic
423#106—21no—
424#106—21no—
425C4⋊C8C23×C10711yescharacteristic
426C4⋊C8C23×C10711yescharacteristic
427C4⋊C8C23×C10711yescharacteristic
428C4⋊C8C23×C10711yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—41no—
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—41no—
447#102D4×C10711yescharacteristic
448#102D4×C10711yescharacteristic
449#102D4×C10711yescharacteristic
450#102D4×C10711yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C4×C8C23×C10711yescharacteristic
456C4×C8C23×C10711yescharacteristic
457C4×C8C23×C10711yescharacteristic
458C24—41no—
459#41—42no—
460#41—42no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C10711yescharacteristic
479C2×D4C2×D4×C10711yescharacteristic
480C2×D4C2×D4×C10711yescharacteristic
481C2×D4C2×D4×C10711yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488SD16—81no—
489SD16—81no—
490D8—22no—
491D8—41no—
492D8—81no—
493D8—81no—
494M16—81no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—81no—
502C2×C8—81no—
503C2×C8C2×D4×C10711yescharacteristic
504C2×C8C2×D4×C10711yescharacteristic
505C2×C8C2×D4×C10711yescharacteristic
506C2×C8C2×D4×C10711yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C10711yescharacteristic
516C4⋊C4C2×D4×C10711yescharacteristic
517C4⋊C4C2×D4×C10711yescharacteristic
518C4⋊C4C2×D4×C10711yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—41no—
529C42C24×C10711yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—81no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—82no—
559D4—161no—
560D4#135×C10712yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
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—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C22×D4×C10711yescharacteristic
579C2×C4C22×D4×C10711yescharacteristic
580C2×C4H(5,𝔽2)×C10711yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—164no—
606C22D42×C10711yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4C2×#135×C10711yescharacteristic
616C4#575×C10711yescharacteristic
617C4#576×C10711yescharacteristic
618C4#576×C10711yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—81no—
623C2—161no—
624C2C107×#327311yescharacteristic
625C2C107×#328011yescharacteristic
626C2C107×#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×#3330C2semidirect
2. C107×#3325C2semidirect
3. C107×#3303C2semidirect
4. C107×#3294C2semidirect
5. C107×#1711C2semidirect
6. C107×#1699C2semidirect
7. C107×#1697C2semidirect
8. C107×#1683C2semidirect
9. C107×#1681C2semidirect
10. C107×#1646C2semidirect
11. C107×#1639C2semidirect
12. C107×#1635C2semidirect
13. C107×#1625C2semidirect
14. C107×#1589C2semidirect
15. C8×D8×C107C2semidirect
18. #547×C107C22semidirect
20. #487×C107C22semidirect
21. #487×C107C22semidirect
22. #487×C107C22semidirect
31. #476×C107C22semidirect
39. #461×C107C22semidirect
49. #436×C107C22semidirect
51. C8×D4×C107C22semidirect
56. #335×C107C22semidirect
57. #335×C107C22semidirect
58. #333×C107C22semidirect
59. #332×C107C22semidirect
60. #332×C107C22semidirect
64. D4⋊C8×C107C22semidirect
65. D4⋊C8×C107C22semidirect
66. C82×C107C22semidirect
305. #19899C107direct (N × H)
314. #3330C2×C107semidirect
315. #3325C2×C107semidirect
316. #3303C2×C107semidirect
317. #3294C2×C107semidirect
318. #1711C2×C107semidirect
319. #1699C2×C107semidirect
320. #1697C2×C107semidirect
321. #1683C2×C107semidirect
322. #1681C2×C107semidirect
323. #1646C2×C107semidirect
324. #1639C2×C107semidirect
325. #1635C2×C107semidirect
326. #1625C2×C107semidirect
327. #1589C2×C107semidirect
328. C8×D8C2×C107semidirect
329. C107#19899direct (N × H)
332. #547C22×C107semidirect
334. #487C22×C107semidirect
335. #487C22×C107semidirect
336. #487C22×C107semidirect
345. #476C22×C107semidirect
353. #461C22×C107semidirect
363. #436C22×C107semidirect
365. C8×D4C22×C107semidirect
370. #335C22×C107semidirect
371. #335C22×C107semidirect
372. #333C22×C107semidirect
373. #332C22×C107semidirect
374. #332C22×C107semidirect
378. D4⋊C8C22×C107semidirect
379. D4⋊C8C22×C107semidirect
380. C82C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#33302
C107×#33252
C107×#33032
C107×#32942
C107×#17112
C107×#16992
C107×#16972
C107×#16832
C107×#16812
C107×#16462
C107×#16392
C107×#16352
C107×#16252
C107×#15892
C8×D8×C1072
#19899107