Finite Group Databasebeta

← C107×#19880 #41045844

Subgroups — C107×#19880 #41045844

Order 27392.

588 conjugacy classes of subgroups.

The subgroup lattice has 574 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×#3357C211yesmaximal, characteristic, complemented
4C107×#3340C211yesmaximal, characteristic, complemented
5C107×#1714C211yesmaximal, characteristic, complemented
6C107×#1685C211yesmaximal, characteristic, complemented
7C107×#1677C211yesmaximal, characteristic, complemented
8C107×#1676C211yesmaximal, characteristic, complemented
9C107×#1672C211yesmaximal, characteristic, complemented
10C107×#1644C211yesmaximal, characteristic, complemented
11C107×#1638C211yesmaximal, characteristic, complemented
12C107×#1630C211yesmaximal, characteristic, complemented
13C107×#1624C211yesmaximal, characteristic
14C107×#1583C211yesmaximal, characteristic, complemented
15C107×SD16⋊C8C211yesmaximal, characteristic, complemented
16#559×C107C2211yescharacteristic
17#556×C107C2211yescharacteristic
18#555×C107C2211yescharacteristic
19#554×C107C2211yescharacteristic
20#500×C107C2211yescharacteristic
21#498×C107C2211yescharacteristic
22#495×C107—21no—
23#492×C107C2211yescharacteristic
24#492×C107C2211yescharacteristic
25#488×C107—21no—
26#487×C107C2211yescharacteristic
27#486×C107C2211yescharacteristic
28#485×C107—21no—
29#485×C107—21no—
30#482×C107—21no—
31#480×C107—21no—
32#478×C107—21no—
33#477×C107C2211yescharacteristic
34#477×C107C2211yescharacteristic
35#477×C107C2211yescharacteristic
36#476×C107C2211yescharacteristic
37#474×C107C2211yescharacteristic
38#468×C107—21no—
39#465×C107—21no—
40#464×C107—21no—
41#463×C107—21no—
42#463×C107—21no—
43#462×C107C2211yescharacteristic
44#459×C107C2211yescharacteristic
45#459×C107C2211yescharacteristic
46C8×Q8×C107C2211yescharacteristic
47C8×Q8×C107C2211yescharacteristic
48C4×SD16×C107—21no—
49C4×SD16×C107C2211yescharacteristic
50C4×SD16×C107C2211yescharacteristic
51C4×D8×C107—21no—
52#436×C107C2211yescharacteristic
53C8×D4×C107C2211yescharacteristic
54#428×C107—21no—
55#427×C107—21no—
56#335×C107C2211yescharacteristic
57#334×C107C2211yescharacteristic
58#333×C107C2211yescharacteristic
59#333×C107C2211yescharacteristic
60#332×C107C2211yescharacteristic
61#331×C107C2211yescharacteristic
62Q8⋊C8×C107C2211yescharacteristic
63Q8⋊C8×C107C2211yescharacteristic
64D4⋊C8×C107C2211yescharacteristic
65D4⋊C8×C107C2211yescharacteristic
66#322×C107C2211yescharacteristic
67C2×Q16×C107—21no—
68C2×SD16×C107—21no—
69C2×SD16×C107—21no—
70C2×SD16×C107—41no—
71C2×SD16×C107D411yescharacteristic
72C2×SD16×C107D411yescharacteristic
73C2×D8×C107—21no—
74C2×D8×C107—21no—
75C2×M16×C107—21no—
76C22×C8×C107—21no—
77C4⋊Q8×C107C2311yescharacteristic
78C4⋊Q8×C107C2311yescharacteristic
79C4⋊Q8×C107C2311yescharacteristic
80#127×C107C2311yescharacteristic
81#126×C107—41no—
82#125×C107—21no—
83#124×C107—21no—
84#124×C107—21no—
85#124×C107—21no—
86#124×C107—41no—
87#123×C107—41no—
88C22⋊Q8×C107—21no—
89C22⋊Q8×C107—21no—
90C22⋊Q8×C107—41no—
91#121×C107—21no—
92#121×C107—21no—
93C4×Q8×C107—21no—
94C4×Q8×C107C2311yescharacteristic
95C4×Q8×C107C2311yescharacteristic
96C4×D4×C107—21no—
97C4×D4×C107—21no—
98C4×D4×C107—21no—
99C4×D4×C107C2311yescharacteristic
100C4×D4×C107C2311yescharacteristic
101#117×C107—21no—
102#117×C107—21no—
103#117×C107—21no—
104C2×C4⋊C4×C107—21no—
105#107×C107—21no—
106#107×C107—21no—
107#107×C107—21no—
108#107×C107—21no—
109#107×C107—21no—
110#107×C107—21no—
111#106×C107—21no—
112#106×C107—21no—
113#106×C107—21no—
114#106×C107D411yescharacteristic
115#106×C107D411yescharacteristic
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×C107—21no—
125#103×C107—21no—
126#103×C107—41no—
127#103×C107D411yescharacteristic
128#103×C107D411yescharacteristic
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
144C2×Q8×C107—21no—
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—41no—
153C2×D4×C107C2×D411yescharacteristic
154C2×D4×C107C2×D411yescharacteristic
155C22×C4×C107—21no—
156C22×C4×C107—21no—
157C22×C4×C107—41no—
158C22×C4×C107—41no—
159Q16×C107—81no—
160SD16×C107—22no—
161SD16×C107—41no—
162SD16×C107—42no—
163SD16×C107—81no—
164SD16×C107—82no—
165D8×C107—42no—
166D8×C107—81no—
167M16×C107—42no—
168C2×C8×C107—21no—
169C2×C8×C107—21no—
170C2×C8×C107—21no—
171C2×C8×C107—21no—
172C2×C8×C107—21no—
173C2×C8×C107—42no—
174C2×C8×C107C2×D411yescharacteristic
175C2×C8×C107C2×D411yescharacteristic
176C2×C8×C107C2×D411yescharacteristic
177C2×C8×C107C2×D411yescharacteristic
178C4⋊C4×C107—21no—
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—41no—
187C4⋊C4×C107—41no—
188C4⋊C4×C107—41no—
189C4⋊C4×C107C2×D411yescharacteristic
190C4⋊C4×C107C2×D411yescharacteristic
191C4⋊C4×C107C2×D411yescharacteristic
192C4⋊C4×C107C2×D411yescharacteristic
193C22⋊C4×C107—21no—
194C22⋊C4×C107—21no—
195C22⋊C4×C107—41no—
196C22⋊C4×C107—41no—
197C22⋊C4×C107—41no—
198C22⋊C4×C107—41no—
199C22⋊C4×C107—41no—
200C22⋊C4×C107—41no—
201C22⋊C4×C107—41no—
202C22⋊C4×C107—41no—
203C42×C107—21no—
204C42×C107—21no—
205C42×C107—41no—
206C42×C107—41no—
207C42×C107C2411yescharacteristic
208C23×C107—21no—
209C23×C107—21no—
210C23×C107—41no—
211Q8×C107—21no—
212Q8×C107—21no—
213Q8×C107—21no—
214Q8×C107—21no—
215Q8×C107—41no—
216Q8×C107—41no—
217Q8×C107—81no—
218Q8×C107—81no—
219D4×C107—21no—
220D4×C107—21no—
221D4×C107—21no—
222D4×C107—21no—
223D4×C107—41no—
224D4×C107—41no—
225D4×C107—41no—
226D4×C107—41no—
227D4×C107—81no—
228D4×C107—161no—
229C2×C4×C107—21no—
230C2×C4×C107—21no—
231C2×C4×C107—21no—
232C2×C4×C107—21no—
233C2×C4×C107—21no—
234C2×C4×C107—21no—
235C2×C4×C107—41no—
236C2×C4×C107—41no—
237C2×C4×C107—41no—
238C2×C4×C107—41no—
239C2×C4×C107—41no—
240C2×C4×C107—41no—
241C2×C4×C107—41no—
242C2×C4×C107—161no—
243C2×C4×C107—161no—
244C2×C4×C107C22×D411yescharacteristic
245C2×C4×C107C22×D411yescharacteristic
246C2×C4×C107H(5,𝔽2)11yescharacteristic
247C8×C107—21no—
248C8×C107—21no—
249C8×C107—21no—
250C8×C107—41no—
251C8×C107—41no—
252C8×C107—41no—
253C8×C107—41no—
254C8×C107—41no—
255C8×C107#13512yes—
256C22×C107—41no—
257C22×C107—41no—
258C22×C107—41no—
259C22×C107—41no—
260C22×C107—41no—
261C22×C107—41no—
262C22×C107—81no—
263C22×C107—81no—
264C22×C107—81no—
265C22×C107D4211yescharacteristic
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#57711yescharacteristic
279C4×C107#57811yescharacteristic
280#19880C10711yesmaximal, characteristic, direct product factor, Sylow
281C2×C107—81no—
282C2×C107—81no—
283C2×C107—161no—
284C2×C107#326911yescharacteristic
285C2×C107#328411yescharacteristic
286C2×C107#328811yescharacteristic
287#3394C2×C10711yescharacteristic, complemented
288#3361C2×C10711yescharacteristic, complemented
289#3357C2×C10711yescharacteristic, complemented
290#3340C2×C10711yescharacteristic, complemented
291#1714C2×C10711yescharacteristic, complemented
292#1685C2×C10711yescharacteristic, complemented
293#1677C2×C10711yescharacteristic, complemented
294#1676C2×C10711yescharacteristic, complemented
295#1672C2×C10711yescharacteristic, complemented
296#1644C2×C10711yescharacteristic, complemented
297#1638C2×C10711yescharacteristic, complemented
298#1630C2×C10711yescharacteristic, complemented
299#1624C2×C10711yescharacteristic
300#1583C2×C10711yescharacteristic, complemented
301SD16⋊C8C2×C10711yescharacteristic, complemented
302C107#1988011yescharacteristic, direct product factor, Sylow
303#559C22×C10711yescharacteristic
304#556C22×C10711yescharacteristic
305#555C22×C10711yescharacteristic
306#554C22×C10711yescharacteristic
307#500C22×C10711yescharacteristic
308#498C22×C10711yescharacteristic
309#495—21no—
310#492C22×C10711yescharacteristic
311#492C22×C10711yescharacteristic
312#488—21no—
313#487C22×C10711yescharacteristic
314#486C22×C10711yescharacteristic
315#485—21no—
316#485—21no—
317#482—21no—
318#480—21no—
319#478—21no—
320#477C22×C10711yescharacteristic
321#477C22×C10711yescharacteristic
322#477C22×C10711yescharacteristic
323#476C22×C10711yescharacteristic
324#474C22×C10711yescharacteristic
325#468—21no—
326#465—21no—
327#464—21no—
328#463—21no—
329#463—21no—
330#462C22×C10711yescharacteristic
331#459C22×C10711yescharacteristic
332#459C22×C10711yescharacteristic
333C8×Q8C22×C10711yescharacteristic
334C8×Q8C22×C10711yescharacteristic
335C4×SD16—21no—
336C4×SD16C22×C10711yescharacteristic
337C4×SD16C22×C10711yescharacteristic
338C4×D8—21no—
339#436C22×C10711yescharacteristic
340C8×D4C22×C10711yescharacteristic
341#428—21no—
342#427—21no—
343#335C22×C10711yescharacteristic
344#334C22×C10711yescharacteristic
345#333C22×C10711yescharacteristic
346#333C22×C10711yescharacteristic
347#332C22×C10711yescharacteristic
348#331C22×C10711yescharacteristic
349Q8⋊C8C22×C10711yescharacteristic
350Q8⋊C8C22×C10711yescharacteristic
351D4⋊C8C22×C10711yescharacteristic
352D4⋊C8C22×C10711yescharacteristic
353#322C22×C10711yescharacteristic
354C2×Q16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—41no—
358C2×SD16D4×C10711yescharacteristic
359C2×SD16D4×C10711yescharacteristic
360C2×D8—21no—
361C2×D8—21no—
362C2×M16—21no—
363C22×C8—21no—
364C4⋊Q8C23×C10711yescharacteristic
365C4⋊Q8C23×C10711yescharacteristic
366C4⋊Q8C23×C10711yescharacteristic
367#127C23×C10711yescharacteristic
368#126—41no—
369#125—21no—
370#124—21no—
371#124—21no—
372#124—21no—
373#124—41no—
374#123—41no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—41no—
378#121—21no—
379#121—21no—
380C4×Q8—21no—
381C4×Q8C23×C10711yescharacteristic
382C4×Q8C23×C10711yescharacteristic
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C23×C10711yescharacteristic
387C4×D4C23×C10711yescharacteristic
388#117—21no—
389#117—21no—
390#117—21no—
391C2×C4⋊C4—21no—
392#107—21no—
393#107—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106D4×C10711yescharacteristic
402#106D4×C10711yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C23×C10711yescharacteristic
406C4⋊C8C23×C10711yescharacteristic
407C4⋊C8C23×C10711yescharacteristic
408C4⋊C8C23×C10711yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—41no—
414#103D4×C10711yescharacteristic
415#103D4×C10711yescharacteristic
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102D4×C10711yescharacteristic
423#102D4×C10711yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—21no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8C23×C10711yescharacteristic
429C4×C8C23×C10711yescharacteristic
430C4×C8C23×C10711yescharacteristic
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C2×D4×C10711yescharacteristic
435C2×Q8C2×D4×C10711yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4C2×D4×C10711yescharacteristic
441C2×D4C2×D4×C10711yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—41no—
446Q16—81no—
447SD16—22no—
448SD16—41no—
449SD16—42no—
450SD16—81no—
451SD16—82no—
452D8—42no—
453D8—81no—
454M16—42no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
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—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4C2×D4×C10711yescharacteristic
477C4⋊C4C2×D4×C10711yescharacteristic
478C4⋊C4C2×D4×C10711yescharacteristic
479C4⋊C4C2×D4×C10711yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42—41no—
494C42C24×C10711yescharacteristic
495C23—21no—
496C23—21no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—81no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—161no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—161no—
530C2×C4—161no—
531C2×C4C22×D4×C10711yescharacteristic
532C2×C4C22×D4×C10711yescharacteristic
533C2×C4H(5,𝔽2)×C10711yescharacteristic
534C8—21no—
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8#135×C10712yes—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22D42×C10711yescharacteristic
553C4—21no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4C2×#135×C10711yescharacteristic
564C4#575×C10711yescharacteristic
565C4#577×C10711yescharacteristic
566C4#578×C10711yescharacteristic
567C2—81no—
568C2—81no—
569C2—161no—
570C2C107×#326911yescharacteristic
571C2C107×#328411yescharacteristic
572C2C107×#328811yescharacteristic
subgroupG/H
center, socleC22×C107D42
commutator, Frattini, cosocleC42C24×C107
prime radicalC107×#1624C2
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×#3357C2semidirect
4. C107×#3340C2semidirect
5. C107×#1714C2semidirect
6. C107×#1685C2semidirect
7. C107×#1677C2semidirect
8. C107×#1676C2semidirect
9. C107×#1672C2semidirect
10. C107×#1644C2semidirect
11. C107×#1638C2semidirect
12. C107×#1630C2semidirect
14. C107×#1583C2semidirect
15. C107×SD16⋊C8C2semidirect
280. #19880C107direct (N × H)
287. #3394C2×C107semidirect
288. #3361C2×C107semidirect
289. #3357C2×C107semidirect
290. #3340C2×C107semidirect
291. #1714C2×C107semidirect
292. #1685C2×C107semidirect
293. #1677C2×C107semidirect
294. #1676C2×C107semidirect
295. #1672C2×C107semidirect
296. #1644C2×C107semidirect
297. #1638C2×C107semidirect
298. #1630C2×C107semidirect
300. #1583C2×C107semidirect
301. SD16⋊C8C2×C107semidirect
302. C107#19880direct (N × H)

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×#33572
C107×#33402
C107×#17142
C107×#16852
C107×#16772
C107×#16762
C107×#16722
C107×#16442
C107×#16382
C107×#16302
C107×#16242
C107×#15832
C107×SD16⋊C82
#19880107