Finite Group Databasebeta

← C107×#19825 #41045789

Subgroups — C107×#19825 #41045789

Order 27392.

642 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3394C211yesmaximal, characteristic, complemented
2C107×#3361C211yesmaximal, characteristic, complemented
3C107×#3324C211yesmaximal, characteristic, complemented
4C107×#3295C211yesmaximal, characteristic, complemented
5C107×#1717C211yesmaximal, characteristic, complemented
6C107×#1697C211yesmaximal, characteristic, complemented
7C107×#1682C211yesmaximal, characteristic, complemented
8C107×#1678C211yesmaximal, characteristic, complemented
9C107×#1665C211yesmaximal, characteristic, complemented
10C107×#1644C211yesmaximal, characteristic, complemented
11C107×#1638C211yesmaximal, characteristic, complemented
12C107×#1620C211yesmaximal, characteristic, complemented
13C107×#1619C211yesmaximal, characteristic
14C107×#1583C211yesmaximal, characteristic, complemented
15C107×SD16⋊C8C211yesmaximal, characteristic, complemented
16#559×C107C2211yescharacteristic, complemented
17#556×C107C2211yescharacteristic
18#554×C107C2211yescharacteristic
19D42×C107C2211yescharacteristic
20#495×C107—21no—
21#493×C107C2211yescharacteristic
22#492×C107C2211yescharacteristic, complemented
23#488×C107—21no—
24#487×C107C2211yescharacteristic, complemented
25#486×C107C2211yescharacteristic
26#486×C107C2211yescharacteristic
27#486×C107C2211yescharacteristic, complemented
28#482×C107—21no—
29#481×C107—21no—
30#478×C107—21no—
31#477×C107C2211yescharacteristic, complemented
32#476×C107C2211yescharacteristic
33#474×C107C2211yescharacteristic
34#468×C107—21no—
35#465×C107—21no—
36#464×C107—21no—
37#463×C107—21no—
38#463×C107—21no—
39#462×C107C2211yescharacteristic, complemented
40#460×C107C2211yescharacteristic
41#460×C107C2211yescharacteristic
42#459×C107C2211yescharacteristic
43#459×C107C2211yescharacteristic
44#450×C107—21no—
45#450×C107—21no—
46C8×Q8×C107C2211yescharacteristic, complemented
47C8×Q8×C107C2211yescharacteristic, complemented
48C4×SD16×C107—21no—
49C4×SD16×C107C2211yescharacteristic
50C4×SD16×C107C2211yescharacteristic
51C4×D8×C107—21no—
52#436×C107C2211yescharacteristic
53C8×D4×C107C2211yescharacteristic
54#418×C107—21no—
55C2×#102×C107—21no—
56#335×C107C2211yescharacteristic, complemented
57#334×C107C2211yescharacteristic, complemented
58#333×C107C2211yescharacteristic, complemented
59#332×C107C2211yescharacteristic, complemented
60#331×C107C2211yescharacteristic
61#331×C107C2211yescharacteristic, complemented
62Q8⋊C8×C107C2211yescharacteristic, complemented
63Q8⋊C8×C107C2211yescharacteristic, complemented
64D4⋊C8×C107C2211yescharacteristic
65D4⋊C8×C107C2211yescharacteristic
66#322×C107C2211yescharacteristic, complemented
67C22×D4×C107—21no—
68C22×D4×C107—21no—
69C2×Q16×C107—21no—
70C2×SD16×C107—21no—
71C2×SD16×C107—21no—
72C2×SD16×C107—21no—
73C2×SD16×C107—21no—
74C2×SD16×C107D411yescharacteristic
75C2×SD16×C107D411yescharacteristic
76C2×D8×C107—21no—
77C2×D8×C107—21no—
78C2×D8×C107—41no—
79C2×M16×C107—21no—
80C22×C8×C107—21no—
81C4⋊Q8×C107C2311yescharacteristic
82C4⋊Q8×C107C2311yescharacteristic
83#127×C107C2311yescharacteristic
84#127×C107C2311yescharacteristic
85#126×C107—41no—
86#125×C107—21no—
87#124×C107—21no—
88#124×C107—21no—
89#124×C107—21no—
90#123×C107—41no—
91C22⋊Q8×C107—21no—
92C22⋊Q8×C107—21no—
93C22⋊Q8×C107—41no—
94#121×C107—21no—
95#121×C107—21no—
96#120×C107—41no—
97C4×Q8×C107—21no—
98C4×Q8×C107C2311yescharacteristic
99C4×Q8×C107C2311yescharacteristic
100C4×D4×C107—21no—
101C4×D4×C107—21no—
102C4×D4×C107—21no—
103C4×D4×C107C2311yescharacteristic
104C4×D4×C107C2311yescharacteristic
105#117×C107—21no—
106C2×C4⋊C4×C107—21no—
107#107×C107—21no—
108#107×C107—21no—
109#106×C107—21no—
110#106×C107D411yescharacteristic
111#106×C107D411yescharacteristic
112C4⋊C8×C107—21no—
113C4⋊C8×C107—21no—
114C4⋊C8×C107C2311yescharacteristic
115C4⋊C8×C107C2311yescharacteristic
116C4⋊C8×C107C2311yescharacteristic
117C4⋊C8×C107C2311yescharacteristic
118#103×C107—21no—
119#103×C107—21no—
120#103×C107—41no—
121#103×C107D411yescharacteristic
122#103×C107D411yescharacteristic
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×C107—21no—
135#102×C107D411yescharacteristic
136#102×C107D411yescharacteristic
137C22⋊C8×C107—21no—
138C22⋊C8×C107—21no—
139C4×C8×C107—21no—
140C4×C8×C107—21no—
141C4×C8×C107C2311yescharacteristic
142C4×C8×C107C2311yescharacteristic
143C4×C8×C107C2311yescharacteristic
144C24×C107—41no—
145C2×Q8×C107—21no—
146C2×Q8×C107—21no—
147C2×Q8×C107C2×D411yescharacteristic
148C2×Q8×C107C2×D411yescharacteristic
149C2×D4×C107—21no—
150C2×D4×C107—21no—
151C2×D4×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—81no—
160C2×D4×C107—81no—
161C2×D4×C107C2×D411yescharacteristic
162C2×D4×C107C2×D411yescharacteristic
163C22×C4×C107—21no—
164C22×C4×C107—21no—
165C22×C4×C107—41no—
166C22×C4×C107—41no—
167Q16×C107—81no—
168SD16×C107—22no—
169SD16×C107—41no—
170SD16×C107—42no—
171SD16×C107—81no—
172SD16×C107—81no—
173SD16×C107—81no—
174D8×C107—42no—
175D8×C107—81no—
176D8×C107—82no—
177M16×C107—81no—
178C2×C8×C107—21no—
179C2×C8×C107—21no—
180C2×C8×C107—21no—
181C2×C8×C107—21no—
182C2×C8×C107—21no—
183C2×C8×C107—81no—
184C2×C8×C107C2×D411yescharacteristic
185C2×C8×C107C2×D411yescharacteristic
186C2×C8×C107C2×D411yescharacteristic
187C2×C8×C107C2×D411yescharacteristic
188C4⋊C4×C107—21no—
189C4⋊C4×C107—21no—
190C4⋊C4×C107—21no—
191C4⋊C4×C107—21no—
192C4⋊C4×C107—21no—
193C4⋊C4×C107—21no—
194C4⋊C4×C107—41no—
195C4⋊C4×C107—41no—
196C4⋊C4×C107—41no—
197C4⋊C4×C107C2×D411yescharacteristic
198C4⋊C4×C107C2×D411yescharacteristic
199C4⋊C4×C107C2×D411yescharacteristic
200C4⋊C4×C107C2×D411yescharacteristic
201C22⋊C4×C107—21no—
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—
210C42×C107—21no—
211C42×C107—21no—
212C42×C107—41no—
213C42×C107C2411yescharacteristic
214C23×C107—21no—
215C23×C107—21no—
216C23×C107—41no—
217C23×C107—41no—
218C23×C107—82no—
219C23×C107—82no—
220C23×C107—161no—
221Q8×C107—21no—
222Q8×C107—21no—
223Q8×C107—21no—
224Q8×C107—21no—
225Q8×C107—41no—
226Q8×C107—41no—
227Q8×C107—81no—
228D4×C107—21no—
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—81no—
240D4×C107—81no—
241D4×C107—82no—
242D4×C107—82no—
243D4×C107#13512yes—
244C2×C4×C107—21no—
245C2×C4×C107—21no—
246C2×C4×C107—21no—
247C2×C4×C107—21no—
248C2×C4×C107—21no—
249C2×C4×C107—21no—
250C2×C4×C107—41no—
251C2×C4×C107—41no—
252C2×C4×C107—41no—
253C2×C4×C107—41no—
254C2×C4×C107—41no—
255C2×C4×C107—41no—
256C2×C4×C107—161no—
257C2×C4×C107—161no—
258C2×C4×C107C22×D411yescharacteristic
259C2×C4×C107C22×D411yescharacteristic
260C2×C4×C107H(5,𝔽2)11yescharacteristic
261C8×C107—21no—
262C8×C107—21no—
263C8×C107—21no—
264C8×C107—21no—
265C8×C107—41no—
266C8×C107—41no—
267C8×C107—41no—
268C8×C107—41no—
269C8×C107—41no—
270C22×C107—22no—
271C22×C107—41no—
272C22×C107—41no—
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—164no—
283C22×C107D4211yescharacteristic
284C4×C107—21no—
285C4×C107—41no—
286C4×C107—41no—
287C4×C107—41no—
288C4×C107—41no—
289C4×C107—41no—
290C4×C107—41no—
291C4×C107—81no—
292C4×C107—81no—
293C4×C107C2×#13511yescharacteristic
294C4×C107#57511yescharacteristic
295C4×C107#57611yescharacteristic
296C4×C107#57711yescharacteristic
297#19825C10711yesmaximal, characteristic, direct product factor, Sylow
298C2×C107—42no—
299C2×C107—81no—
300C2×C107—161no—
301C2×C107—161no—
302C2×C107#326811yescharacteristic
303C2×C107#328211yescharacteristic
304C2×C107#328811yescharacteristic
305#3394C2×C10711yescharacteristic, complemented
306#3361C2×C10711yescharacteristic, complemented
307#3324C2×C10711yescharacteristic, complemented
308#3295C2×C10711yescharacteristic, complemented
309#1717C2×C10711yescharacteristic, complemented
310#1697C2×C10711yescharacteristic, complemented
311#1682C2×C10711yescharacteristic, complemented
312#1678C2×C10711yescharacteristic, complemented
313#1665C2×C10711yescharacteristic, complemented
314#1644C2×C10711yescharacteristic, complemented
315#1638C2×C10711yescharacteristic, complemented
316#1620C2×C10711yescharacteristic, complemented
317#1619C2×C10711yescharacteristic
318#1583C2×C10711yescharacteristic, complemented
319SD16⋊C8C2×C10711yescharacteristic, complemented
320C107#1982511yescharacteristic, direct product factor, Sylow
321#559C22×C10711yescharacteristic, complemented
322#556C22×C10711yescharacteristic
323#554C22×C10711yescharacteristic
324D42C22×C10711yescharacteristic
325#495—21no—
326#493C22×C10711yescharacteristic
327#492C22×C10711yescharacteristic, complemented
328#488—21no—
329#487C22×C10711yescharacteristic, complemented
330#486C22×C10711yescharacteristic
331#486C22×C10711yescharacteristic
332#486C22×C10711yescharacteristic, complemented
333#482—21no—
334#481—21no—
335#478—21no—
336#477C22×C10711yescharacteristic, complemented
337#476C22×C10711yescharacteristic
338#474C22×C10711yescharacteristic
339#468—21no—
340#465—21no—
341#464—21no—
342#463—21no—
343#463—21no—
344#462C22×C10711yescharacteristic, complemented
345#460C22×C10711yescharacteristic
346#460C22×C10711yescharacteristic
347#459C22×C10711yescharacteristic
348#459C22×C10711yescharacteristic
349#450—21no—
350#450—21no—
351C8×Q8C22×C10711yescharacteristic, complemented
352C8×Q8C22×C10711yescharacteristic, complemented
353C4×SD16—21no—
354C4×SD16C22×C10711yescharacteristic
355C4×SD16C22×C10711yescharacteristic
356C4×D8—21no—
357#436C22×C10711yescharacteristic
358C8×D4C22×C10711yescharacteristic
359#418—21no—
360C2×#102—21no—
361#335C22×C10711yescharacteristic, complemented
362#334C22×C10711yescharacteristic, complemented
363#333C22×C10711yescharacteristic, complemented
364#332C22×C10711yescharacteristic, complemented
365#331C22×C10711yescharacteristic
366#331C22×C10711yescharacteristic, complemented
367Q8⋊C8C22×C10711yescharacteristic, complemented
368Q8⋊C8C22×C10711yescharacteristic, complemented
369D4⋊C8C22×C10711yescharacteristic
370D4⋊C8C22×C10711yescharacteristic
371#322C22×C10711yescharacteristic, complemented
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16D4×C10711yescharacteristic
380C2×SD16D4×C10711yescharacteristic
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—41no—
384C2×M16—21no—
385C22×C8—21no—
386C4⋊Q8C23×C10711yescharacteristic
387C4⋊Q8C23×C10711yescharacteristic
388#127C23×C10711yescharacteristic
389#127C23×C10711yescharacteristic
390#126—41no—
391#125—21no—
392#124—21no—
393#124—21no—
394#124—21no—
395#123—41no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401#120—41no—
402C4×Q8—21no—
403C4×Q8C23×C10711yescharacteristic
404C4×Q8C23×C10711yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C23×C10711yescharacteristic
409C4×D4C23×C10711yescharacteristic
410#117—21no—
411C2×C4⋊C4—21no—
412#107—21no—
413#107—21no—
414#106—21no—
415#106D4×C10711yescharacteristic
416#106D4×C10711yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C23×C10711yescharacteristic
420C4⋊C8C23×C10711yescharacteristic
421C4⋊C8C23×C10711yescharacteristic
422C4⋊C8C23×C10711yescharacteristic
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C10711yescharacteristic
427#103D4×C10711yescharacteristic
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
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#102D4×C10711yescharacteristic
441#102D4×C10711yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C10711yescharacteristic
447C4×C8C23×C10711yescharacteristic
448C4×C8C23×C10711yescharacteristic
449C24—41no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8C2×D4×C10711yescharacteristic
453C2×Q8C2×D4×C10711yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×D4×C10711yescharacteristic
467C2×D4C2×D4×C10711yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472Q16—81no—
473SD16—22no—
474SD16—41no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—42no—
480D8—81no—
481D8—82no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—81no—
489C2×C8C2×D4×C10711yescharacteristic
490C2×C8C2×D4×C10711yescharacteristic
491C2×C8C2×D4×C10711yescharacteristic
492C2×C8C2×D4×C10711yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C10711yescharacteristic
503C4⋊C4C2×D4×C10711yescharacteristic
504C4⋊C4C2×D4×C10711yescharacteristic
505C4⋊C4C2×D4×C10711yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—21no—
516C42—21no—
517C42—41no—
518C42C24×C10711yescharacteristic
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23—82no—
525C23—161no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4#135×C10712yes—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—161no—
562C2×C4—161no—
563C2×C4C22×D4×C10711yescharacteristic
564C2×C4C22×D4×C10711yescharacteristic
565C2×C4H(5,𝔽2)×C10711yescharacteristic
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—164no—
588C22D42×C10711yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4C2×#135×C10711yescharacteristic
599C4#575×C10711yescharacteristic
600C4#576×C10711yescharacteristic
601C4#577×C10711yescharacteristic
602C2—42no—
603C2—81no—
604C2—161no—
605C2—161no—
606C2C107×#326811yescharacteristic
607C2C107×#328211yescharacteristic
608C2C107×#328811yescharacteristic
subgroupG/H
center, socleC22×C107D42
commutator, Frattini, cosocleC42C24×C107
prime radicalC107×#1619C2
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×#3394C2semidirect
2. C107×#3361C2semidirect
3. C107×#3324C2semidirect
4. C107×#3295C2semidirect
5. C107×#1717C2semidirect
6. C107×#1697C2semidirect
7. C107×#1682C2semidirect
8. C107×#1678C2semidirect
9. C107×#1665C2semidirect
10. C107×#1644C2semidirect
11. C107×#1638C2semidirect
12. C107×#1620C2semidirect
14. C107×#1583C2semidirect
15. C107×SD16⋊C8C2semidirect
16. #559×C107C22semidirect
22. #492×C107C22semidirect
24. #487×C107C22semidirect
27. #486×C107C22semidirect
31. #477×C107C22semidirect
39. #462×C107C22semidirect
46. C8×Q8×C107C22semidirect
47. C8×Q8×C107C22semidirect
56. #335×C107C22semidirect
57. #334×C107C22semidirect
58. #333×C107C22semidirect
59. #332×C107C22semidirect
61. #331×C107C22semidirect
62. Q8⋊C8×C107C22semidirect
63. Q8⋊C8×C107C22semidirect
66. #322×C107C22semidirect
297. #19825C107direct (N × H)
305. #3394C2×C107semidirect
306. #3361C2×C107semidirect
307. #3324C2×C107semidirect
308. #3295C2×C107semidirect
309. #1717C2×C107semidirect
310. #1697C2×C107semidirect
311. #1682C2×C107semidirect
312. #1678C2×C107semidirect
313. #1665C2×C107semidirect
314. #1644C2×C107semidirect
315. #1638C2×C107semidirect
316. #1620C2×C107semidirect
318. #1583C2×C107semidirect
319. SD16⋊C8C2×C107semidirect
320. C107#19825direct (N × H)
321. #559C22×C107semidirect
327. #492C22×C107semidirect
329. #487C22×C107semidirect
332. #486C22×C107semidirect
336. #477C22×C107semidirect
344. #462C22×C107semidirect
351. C8×Q8C22×C107semidirect
352. C8×Q8C22×C107semidirect
361. #335C22×C107semidirect
362. #334C22×C107semidirect
363. #333C22×C107semidirect
364. #332C22×C107semidirect
366. #331C22×C107semidirect
367. Q8⋊C8C22×C107semidirect
368. Q8⋊C8C22×C107semidirect
371. #322C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#33942
C107×#33612
C107×#33242
C107×#32952
C107×#17172
C107×#16972
C107×#16822
C107×#16782
C107×#16652
C107×#16442
C107×#16382
C107×#16202
C107×#16192
C107×#15832
C107×SD16⋊C82
#19825107