Finite Group Databasebeta

← C107×#19847 #41045811

Subgroups — C107×#19847 #41045811

Order 27392.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3395C211yesmaximal, characteristic, complemented
2C107×#3368C211yesmaximal, characteristic
3C107×#3364C211yesmaximal, characteristic, complemented
4C107×#3304C211yesmaximal, characteristic
5C107×#1720C211yesmaximal, characteristic, complemented
6C107×#1700C211yesmaximal, characteristic, complemented
7C107×#1682C211yesmaximal, characteristic, complemented
8C107×#1682C211yesmaximal, characteristic, complemented
9C107×#1669C211yesmaximal, characteristic, complemented
10C107×#1653C211yesmaximal, characteristic, complemented
11C107×#1652C211yesmaximal, characteristic, complemented
12C107×#1641C211yesmaximal, characteristic
13C107×#1626C211yesmaximal, characteristic, complemented
14C107×#1584C211yesmaximal, characteristic, complemented
15C107×SD16⋊C8C211yesmaximal, characteristic, complemented
16#557×C107C2211yescharacteristic
17#557×C107C2211yescharacteristic
18#556×C107C2211yescharacteristic
19#550×C107C2211yescharacteristic
20#498×C107C2211yescharacteristic
21#494×C107—21no—
22#494×C107C2211yescharacteristic
23#490×C107—21no—
24#488×C107—21no—
25#487×C107C2211yescharacteristic
26#486×C107C2211yescharacteristic
27#486×C107C2211yescharacteristic
28#486×C107C2211yescharacteristic
29#482×C107—21no—
30#479×C107—21no—
31#478×C107—21no—
32#475×C107C2211yescharacteristic
33#474×C107C2211yescharacteristic
34#474×C107C2211yescharacteristic
35#465×C107—21no—
36#464×C107—21no—
37#462×C107—21no—
38#462×C107—21no—
39#462×C107C2211yescharacteristic
40#462×C107C2211yescharacteristic
41#462×C107C2211yescharacteristic
42#460×C107—21no—
43#460×C107C2211yescharacteristic
44#460×C107C2211yescharacteristic
45#452×C107—21no—
46#446×C107C2211yescharacteristic
47C8×Q8×C107C2211yescharacteristic
48C8×Q8×C107C2211yescharacteristic
49#440×C107—21no—
50C4×Q16×C107—21no—
51C4×Q16×C107—21no—
52C4×Q16×C107C2211yescharacteristic
53C4×SD16×C107C2211yescharacteristic
54C8×D4×C107C2211yescharacteristic
55#416×C107—21no—
56#335×C107C2211yescharacteristic
57#335×C107C2211yescharacteristic
58#332×C107C2211yescharacteristic
59#332×C107C2211yescharacteristic
60#332×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×C107—21no—
70C2×Q16×C107—21no—
71C2×Q16×C107—21no—
72C2×Q16×C107—21no—
73C2×Q16×C107D411yescharacteristic
74C2×SD16×C107—21no—
75C2×SD16×C107—21no—
76C2×SD16×C107D411yescharacteristic
77C22×C8×C107—21no—
78C4⋊Q8×C107—21no—
79C4⋊Q8×C107—21no—
80C4⋊Q8×C107C2311yescharacteristic
81C4⋊Q8×C107C2311yescharacteristic
82C4⋊Q8×C107C2311yescharacteristic
83#127×C107—21no—
84#127×C107C2311yescharacteristic
85#126×C107—41no—
86#125×C107—21no—
87#125×C107—21no—
88#125×C107—41no—
89#125×C107—41no—
90#124×C107—21no—
91C22⋊Q8×C107—21no—
92#121×C107—21no—
93#121×C107—41no—
94C4×Q8×C107—21no—
95C4×Q8×C107—21no—
96C4×Q8×C107—21no—
97C4×Q8×C107—21no—
98C4×Q8×C107—21no—
99C4×Q8×C107C2311yescharacteristic
100C4×Q8×C107C2311yescharacteristic
101C4×Q8×C107C2311yescharacteristic
102C4×D4×C107—21no—
103C4×D4×C107C2311yescharacteristic
104#117×C107—21no—
105#107×C107—21no—
106#107×C107—21no—
107#107×C107D411yescharacteristic
108#106×C107—21no—
109#106×C107—41no—
110#106×C107D411yescharacteristic
111C4⋊C8×C107—21no—
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—21no—
121#103×C107—21no—
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×C107—21no—
148C2×Q8×C107—21no—
149C2×Q8×C107C2×D411yescharacteristic
150C2×Q8×C107C2×D411yescharacteristic
151C2×Q8×C107C2×D411yescharacteristic
152C2×D4×C107—21no—
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107—41no—
156C2×D4×C107—41no—
157C2×D4×C107C2×D411yescharacteristic
158C22×C4×C107—21no—
159C22×C4×C107—41no—
160Q16×C107—41no—
161Q16×C107—42no—
162Q16×C107—42no—
163Q16×C107—81no—
164Q16×C107—81no—
165Q16×C107—81no—
166SD16×C107—22no—
167SD16×C107—42no—
168SD16×C107—81no—
169C2×C8×C107—21no—
170C2×C8×C107—21no—
171C2×C8×C107—21no—
172C2×C8×C107—21no—
173C2×C8×C107—21no—
174C2×C8×C107—81no—
175C2×C8×C107C2×D411yescharacteristic
176C2×C8×C107C2×D411yescharacteristic
177C2×C8×C107C2×D411yescharacteristic
178C2×C8×C107C2×D411yescharacteristic
179C4⋊C4×C107—21no—
180C4⋊C4×C107—21no—
181C4⋊C4×C107—21no—
182C4⋊C4×C107—21no—
183C4⋊C4×C107—21no—
184C4⋊C4×C107—21no—
185C4⋊C4×C107—21no—
186C4⋊C4×C107—21no—
187C4⋊C4×C107—21no—
188C4⋊C4×C107—41no—
189C4⋊C4×C107—41no—
190C4⋊C4×C107—41no—
191C4⋊C4×C107—41no—
192C4⋊C4×C107—41no—
193C4⋊C4×C107—41no—
194C4⋊C4×C107—41no—
195C4⋊C4×C107C2×D411yescharacteristic
196C4⋊C4×C107C2×D411yescharacteristic
197C4⋊C4×C107C2×D411yescharacteristic
198C4⋊C4×C107C2×D411yescharacteristic
199C22⋊C4×C107—21no—
200C22⋊C4×C107—41no—
201C22⋊C4×C107—41no—
202C22⋊C4×C107—41no—
203C42×C107—21no—
204C42×C107—21no—
205C42×C107—21no—
206C42×C107—41no—
207C42×C107—41no—
208C42×C107—41no—
209C42×C107C2411yescharacteristic
210C23×C107—21no—
211C23×C107—41no—
212Q8×C107—21no—
213Q8×C107—21no—
214Q8×C107—21no—
215Q8×C107—21no—
216Q8×C107—21no—
217Q8×C107—41no—
218Q8×C107—41no—
219Q8×C107—41no—
220Q8×C107—41no—
221Q8×C107—41no—
222Q8×C107—41no—
223Q8×C107#13512yes—
224D4×C107—21no—
225D4×C107—21no—
226D4×C107—41no—
227D4×C107—41no—
228D4×C107—41no—
229D4×C107—41no—
230D4×C107—81no—
231D4×C107—82no—
232D4×C107—161no—
233C2×C4×C107—21no—
234C2×C4×C107—21no—
235C2×C4×C107—21no—
236C2×C4×C107—21no—
237C2×C4×C107—21no—
238C2×C4×C107—21no—
239C2×C4×C107—21no—
240C2×C4×C107—41no—
241C2×C4×C107—41no—
242C2×C4×C107—41no—
243C2×C4×C107—41no—
244C2×C4×C107—41no—
245C2×C4×C107—82no—
246C2×C4×C107C22×D411yescharacteristic
247C2×C4×C107C22×D411yescharacteristic
248C2×C4×C107H(5,𝔽2)11yescharacteristic
249C8×C107—21no—
250C8×C107—21no—
251C8×C107—21no—
252C8×C107—21no—
253C8×C107—41no—
254C8×C107—41no—
255C8×C107—41no—
256C8×C107—41no—
257C8×C107—41no—
258C22×C107—41no—
259C22×C107—41no—
260C22×C107—41no—
261C22×C107—81no—
262C22×C107—81no—
263C22×C107—81no—
264C22×C107D4211yescharacteristic
265C4×C107—22no—
266C4×C107—21no—
267C4×C107—41no—
268C4×C107—41no—
269C4×C107—41no—
270C4×C107—41no—
271C4×C107—41no—
272C4×C107—41no—
273C4×C107—81no—
274C4×C107—81no—
275C4×C107—81no—
276C4×C107C2×#13511yescharacteristic
277C4×C107#57511yescharacteristic
278C4×C107#57611yescharacteristic
279C4×C107#57811yescharacteristic
280#19847C10711yesmaximal, characteristic, direct product factor, Sylow
281C2×C107—81no—
282C2×C107—161no—
283C2×C107#326811yescharacteristic
284C2×C107#328511yescharacteristic
285C2×C107#328911yescharacteristic
286#3395C2×C10711yescharacteristic, complemented
287#3368C2×C10711yescharacteristic
288#3364C2×C10711yescharacteristic, complemented
289#3304C2×C10711yescharacteristic
290#1720C2×C10711yescharacteristic, complemented
291#1700C2×C10711yescharacteristic, complemented
292#1682C2×C10711yescharacteristic, complemented
293#1682C2×C10711yescharacteristic, complemented
294#1669C2×C10711yescharacteristic, complemented
295#1653C2×C10711yescharacteristic, complemented
296#1652C2×C10711yescharacteristic, complemented
297#1641C2×C10711yescharacteristic
298#1626C2×C10711yescharacteristic, complemented
299#1584C2×C10711yescharacteristic, complemented
300SD16⋊C8C2×C10711yescharacteristic, complemented
301C107#1984711yescharacteristic, direct product factor, Sylow
302#557C22×C10711yescharacteristic
303#557C22×C10711yescharacteristic
304#556C22×C10711yescharacteristic
305#550C22×C10711yescharacteristic
306#498C22×C10711yescharacteristic
307#494—21no—
308#494C22×C10711yescharacteristic
309#490—21no—
310#488—21no—
311#487C22×C10711yescharacteristic
312#486C22×C10711yescharacteristic
313#486C22×C10711yescharacteristic
314#486C22×C10711yescharacteristic
315#482—21no—
316#479—21no—
317#478—21no—
318#475C22×C10711yescharacteristic
319#474C22×C10711yescharacteristic
320#474C22×C10711yescharacteristic
321#465—21no—
322#464—21no—
323#462—21no—
324#462—21no—
325#462C22×C10711yescharacteristic
326#462C22×C10711yescharacteristic
327#462C22×C10711yescharacteristic
328#460—21no—
329#460C22×C10711yescharacteristic
330#460C22×C10711yescharacteristic
331#452—21no—
332#446C22×C10711yescharacteristic
333C8×Q8C22×C10711yescharacteristic
334C8×Q8C22×C10711yescharacteristic
335#440—21no—
336C4×Q16—21no—
337C4×Q16—21no—
338C4×Q16C22×C10711yescharacteristic
339C4×SD16C22×C10711yescharacteristic
340C8×D4C22×C10711yescharacteristic
341#416—21no—
342#335C22×C10711yescharacteristic
343#335C22×C10711yescharacteristic
344#332C22×C10711yescharacteristic
345#332C22×C10711yescharacteristic
346#332C22×C10711yescharacteristic
347#331C22×C10711yescharacteristic
348Q8⋊C8C22×C10711yescharacteristic
349Q8⋊C8C22×C10711yescharacteristic
350Q8⋊C8C22×C10711yescharacteristic
351D4⋊C8C22×C10711yescharacteristic
352#322C22×C10711yescharacteristic
353C2×#41—21no—
354C2×Q16—21no—
355C2×Q16—21no—
356C2×Q16—21no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16D4×C10711yescharacteristic
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16D4×C10711yescharacteristic
363C22×C8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8C23×C10711yescharacteristic
367C4⋊Q8C23×C10711yescharacteristic
368C4⋊Q8C23×C10711yescharacteristic
369#127—21no—
370#127C23×C10711yescharacteristic
371#126—41no—
372#125—21no—
373#125—21no—
374#125—41no—
375#125—41no—
376#124—21no—
377C22⋊Q8—21no—
378#121—21no—
379#121—41no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C10711yescharacteristic
386C4×Q8C23×C10711yescharacteristic
387C4×Q8C23×C10711yescharacteristic
388C4×D4—21no—
389C4×D4C23×C10711yescharacteristic
390#117—21no—
391#107—21no—
392#107—21no—
393#107D4×C10711yescharacteristic
394#106—21no—
395#106—41no—
396#106D4×C10711yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C23×C10711yescharacteristic
401C4⋊C8C23×C10711yescharacteristic
402C4⋊C8C23×C10711yescharacteristic
403C4⋊C8C23×C10711yescharacteristic
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103D4×C10711yescharacteristic
411#103D4×C10711yescharacteristic
412#103D4×C10711yescharacteristic
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—41no—
422#102D4×C10711yescharacteristic
423C22⋊C8—21no—
424#97—21no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8C23×C10711yescharacteristic
428C4×C8C23×C10711yescharacteristic
429C4×C8C23×C10711yescharacteristic
430#41—42no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×D4×C10711yescharacteristic
436C2×Q8C2×D4×C10711yescharacteristic
437C2×Q8C2×D4×C10711yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4C2×D4×C10711yescharacteristic
444C22×C4—21no—
445C22×C4—41no—
446Q16—41no—
447Q16—42no—
448Q16—42no—
449Q16—81no—
450Q16—81no—
451Q16—81no—
452SD16—22no—
453SD16—42no—
454SD16—81no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—81no—
461C2×C8C2×D4×C10711yescharacteristic
462C2×C8C2×D4×C10711yescharacteristic
463C2×C8C2×D4×C10711yescharacteristic
464C2×C8C2×D4×C10711yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C10711yescharacteristic
482C4⋊C4C2×D4×C10711yescharacteristic
483C4⋊C4C2×D4×C10711yescharacteristic
484C4⋊C4C2×D4×C10711yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42—41no—
494C42—41no—
495C42C24×C10711yescharacteristic
496C23—21no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8#135×C10712yes—
510D4—21no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4—161no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4C22×D4×C10711yescharacteristic
533C2×C4C22×D4×C10711yescharacteristic
534C2×C4H(5,𝔽2)×C10711yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22D42×C10711yescharacteristic
551C4—22no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4C2×#135×C10711yescharacteristic
563C4#575×C10711yescharacteristic
564C4#576×C10711yescharacteristic
565C4#578×C10711yescharacteristic
566C2—81no—
567C2—161no—
568C2C107×#326811yescharacteristic
569C2C107×#328511yescharacteristic
570C2C107×#328911yescharacteristic
subgroupG/H
center, socleC22×C107D42
commutator, Frattini, cosocleC42C24×C107
prime radical#550×C107C22
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×#3395C2semidirect
3. C107×#3364C2semidirect
5. C107×#1720C2semidirect
6. C107×#1700C2semidirect
7. C107×#1682C2semidirect
8. C107×#1682C2semidirect
9. C107×#1669C2semidirect
10. C107×#1653C2semidirect
11. C107×#1652C2semidirect
13. C107×#1626C2semidirect
14. C107×#1584C2semidirect
15. C107×SD16⋊C8C2semidirect
280. #19847C107direct (N × H)
286. #3395C2×C107semidirect
288. #3364C2×C107semidirect
290. #1720C2×C107semidirect
291. #1700C2×C107semidirect
292. #1682C2×C107semidirect
293. #1682C2×C107semidirect
294. #1669C2×C107semidirect
295. #1653C2×C107semidirect
296. #1652C2×C107semidirect
298. #1626C2×C107semidirect
299. #1584C2×C107semidirect
300. SD16⋊C8C2×C107semidirect
301. C107#19847direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#33952
C107×#33682
C107×#33642
C107×#33042
C107×#17202
C107×#17002
C107×#16822
C107×#16692
C107×#16532
C107×#16522
C107×#16412
C107×#16262
C107×#15842
C107×SD16⋊C82
#19847107