Finite Group Databasebeta

← C107×#19619 #41045583

Subgroups — C107×#19619 #41045583

Order 27392.

820 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3169C211yesmaximal, characteristic, complemented
2C107×#3169C211yesmaximal, characteristic, complemented
3C107×#3167C211yesmaximal, characteristic, complemented
4C107×#3167C211yesmaximal, characteristic, complemented
5C107×#3147C211yesmaximal, characteristic, complemented
6C107×#3131C211yesmaximal, characteristic, complemented
7C107×#1723C211yesmaximal, characteristic, complemented
8C107×#1721C211yesmaximal, characteristic, complemented
9C107×#1720C211yesmaximal, characteristic, complemented
10C107×#1719C211yesmaximal, characteristic, complemented
11C107×#1717C211yesmaximal, characteristic, complemented
12C107×#1717C211yesmaximal, characteristic, complemented
13C107×#1715C211yesmaximal, characteristic, complemented
14C107×#1714C211yesmaximal, characteristic, complemented
15C2×#322×C107C211yesmaximal, characteristic, complemented
16C2×#135×C107—22no—
17#533×C107C2211yescharacteristic
18#532×C107C2211yescharacteristic
19#532×C107C2211yescharacteristic
20#532×C107C2211yescharacteristic
21#500×C107C2211yescharacteristic
22#500×C107C2211yescharacteristic
23#498×C107C2211yescharacteristic
24#498×C107C2211yescharacteristic
25#495×C107—22no—
26#494×C107C2211yescharacteristic
27#493×C107C2211yescharacteristic
28#493×C107C2211yescharacteristic
29#493×C107C2211yescharacteristic
30#492×C107C2211yescharacteristic
31#492×C107C2211yescharacteristic
32#492×C107C2211yescharacteristic
33#492×C107C2211yescharacteristic
34#488×C107—22no—
35#487×C107C2211yescharacteristic
36#487×C107C2211yescharacteristic
37#487×C107C2211yescharacteristic
38#487×C107C2211yescharacteristic
39#486×C107C2211yescharacteristic
40#486×C107C2211yescharacteristic
41#486×C107C2211yescharacteristic
42#486×C107C2211yescharacteristic
43#486×C107C2211yescharacteristic
44#486×C107C2211yescharacteristic
45#486×C107C2211yescharacteristic
46#486×C107C2211yescharacteristic
47#466×C107—22no—
48#466×C107—22no—
49#465×C107—22no—
50#465×C107—22no—
51C4×SD16×C107—22no—
52C4×SD16×C107—22no—
53C4×D8×C107—22no—
54C4×D8×C107—22no—
55#416×C107—22no—
56C2×C4×C8×C107C2211yescharacteristic
57C2×C4×C8×C107C2211yescharacteristic
58C2×C4×C8×C107C2211yescharacteristic
59#322×C107C2211yescharacteristic
60#322×C107C2211yescharacteristic
61#322×C107C2211yescharacteristic
62#322×C107C2211yescharacteristic
63C2×#41×C107—21no—
64C2×#41×C107—21no—
65C2×#41×C107—21no—
66#135×C107—48no—
67C2×Q16×C107—22no—
68C2×SD16×C107—22no—
69C2×SD16×C107—22no—
70C2×SD16×C107—22no—
71C2×SD16×C107—22no—
72C2×D8×C107—22no—
73C2×D8×C107—22no—
74C2×D8×C107—22no—
75C22×C8×C107D412yes—
76C22×C8×C107D412yes—
77C22×C8×C107D412yes—
78C4⋊Q8×C107C2311yescharacteristic
79C4⋊Q8×C107C2311yescharacteristic
80C4⋊Q8×C107C2311yescharacteristic
81C4⋊Q8×C107C2311yescharacteristic
82C4⋊Q8×C107C2311yescharacteristic
83#127×C107C2311yescharacteristic
84#127×C107C2311yescharacteristic
85#127×C107C2311yescharacteristic
86#125×C107—21no—
87#124×C107—21no—
88#124×C107—21no—
89#124×C107—21no—
90C22⋊Q8×C107—21no—
91C22⋊Q8×C107—21no—
92#121×C107—21no—
93#121×C107—21no—
94#121×C107—21no—
95#121×C107—21no—
96#121×C107—21no—
97#121×C107—21no—
98C4×Q8×C107—21no—
99C4×Q8×C107—21no—
100C4×D4×C107—21no—
101C4×D4×C107—21no—
102C4×D4×C107—21no—
103C4×D4×C107—21no—
104C4×D4×C107—21no—
105C4×D4×C107—21no—
106#117×C107—21no—
107C2×C42×C107C2311yescharacteristic
108#107×C107—22no—
109#107×C107—22no—
110#106×C107—22no—
111#106×C107—22no—
112#103×C107—22no—
113#103×C107—22no—
114#103×C107—22no—
115#103×C107—22no—
116#102×C107—22no—
117#102×C107—22no—
118#102×C107—22no—
119#102×C107—22no—
120#102×C107—22no—
121#102×C107—22no—
122#102×C107—22no—
123#102×C107—22no—
124C4×C8×C107D412yes—
125C4×C8×C107D412yes—
126C4×C8×C107D412yes—
127C4×C8×C107C2311yescharacteristic
128C4×C8×C107C2311yescharacteristic
129C4×C8×C107C2311yescharacteristic
130C4×C8×C107C2311yescharacteristic
131C4×C8×C107C2311yescharacteristic
132C4×C8×C107C2311yescharacteristic
133#41×C107—44no—
134#41×C107—44no—
135#41×C107—44no—
136C2×Q8×C107—21no—
137C2×Q8×C107—21no—
138C2×Q8×C107—21no—
139C2×Q8×C107—21no—
140C2×Q8×C107—21no—
141C2×D4×C107—21no—
142C2×D4×C107—21no—
143C2×D4×C107—21no—
144C2×D4×C107—21no—
145C2×D4×C107—21no—
146C2×D4×C107—21no—
147C2×D4×C107—21no—
148C2×D4×C107—21no—
149C2×D4×C107—21no—
150C2×D4×C107—41no—
151C2×D4×C107—41no—
152C2×D4×C107—41no—
153C22×C4×C107—41no—
154C22×C4×C107—41no—
155C22×C4×C107—41no—
156C22×C4×C107C2×D411yescharacteristic
157C22×C4×C107C2×D411yescharacteristic
158C22×C4×C107C2×D411yescharacteristic
159Q16×C107—44no—
160SD16×C107—44no—
161SD16×C107—44no—
162SD16×C107—44no—
163SD16×C107—44no—
164D8×C107—44no—
165D8×C107—44no—
166D8×C107—44no—
167C2×C8×C107—24no—
168C2×C8×C107—24no—
169C2×C8×C107—42no—
170C2×C8×C107C2×D412yes—
171C2×C8×C107C2×D412yes—
172C2×C8×C107C2×D412yes—
173C2×C8×C107C2×D412yes—
174C2×C8×C107C2×D412yes—
175C2×C8×C107C2×D412yes—
176C4⋊C4×C107—21no—
177C4⋊C4×C107—21no—
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—
188C22⋊C4×C107—41no—
189C22⋊C4×C107—41no—
190C22⋊C4×C107—41no—
191C22⋊C4×C107—41no—
192C22⋊C4×C107—41no—
193C22⋊C4×C107—41no—
194C22⋊C4×C107—41no—
195C42×C107—41no—
196C42×C107C2×D411yescharacteristic
197C42×C107C2×D411yescharacteristic
198C42×C107C2×D411yescharacteristic
199C42×C107C2411yescharacteristic
200C23×C107—41no—
201C23×C107—41no—
202C23×C107—41no—
203C23×C107#12711yescharacteristic
204Q8×C107—42no—
205Q8×C107—42no—
206Q8×C107—42no—
207Q8×C107—42no—
208Q8×C107—42no—
209D4×C107—42no—
210D4×C107—42no—
211D4×C107—42no—
212D4×C107—42no—
213D4×C107—42no—
214D4×C107—42no—
215D4×C107—42no—
216D4×C107—42no—
217D4×C107—42no—
218D4×C107—82no—
219D4×C107—82no—
220D4×C107—82no—
221C2×C4×C107—22no—
222C2×C4×C107—22no—
223C2×C4×C107—41no—
224C2×C4×C107—41no—
225C2×C4×C107—41no—
226C2×C4×C107—41no—
227C2×C4×C107—41no—
228C2×C4×C107—82no—
229C2×C4×C107—82no—
230C2×C4×C107—82no—
231C2×C4×C107#12711yescharacteristic
232C2×C4×C107#12711yescharacteristic
233C2×C4×C107#12711yescharacteristic
234C2×C4×C107AGL(1,ℤ/8)14yes—
235C2×C4×C107C22×D411yescharacteristic
236C2×C4×C107C22×D411yescharacteristic
237C2×C4×C107C22×D411yescharacteristic
238C8×C107—22no—
239C8×C107—22no—
240C8×C107—22no—
241C8×C107—22no—
242C8×C107—22no—
243C8×C107#13514yescomplemented
244C22×C107—21no—
245C22×C107—21no—
246C22×C107—81no—
247C22×C107—81no—
248C22×C107—81no—
249C22×C107—81no—
250C22×C107—81no—
251C22×C107—81no—
252C22×C107—81no—
253C22×C107—81no—
254C22×C107—81no—
255C22×C107#49612yes—
256C22×C107C2×#12711yescharacteristic
257C4×C107—21no—
258C4×C107—21no—
259C4×C107—81no—
260C4×C107—81no—
261C4×C107—81no—
262C4×C107—81no—
263C4×C107—81no—
264C4×C107#49612yes—
265C4×C107C2×#13512yes—
266C4×C107C2×AGL(1,ℤ/8)12yes—
267C4×C107#57512yes—
268#19619C10711yesmaximal, characteristic, direct product factor, Sylow
269C2×C107—22no—
270C2×C107—161no—
271C2×C107—161no—
272C2×C107—161no—
273C2×C107#314711yescharacteristic
274C2×C107C2×#49611yescharacteristic
275C2×C107#315011yescharacteristic
276#3169C2×C10711yescharacteristic, complemented
277#3169C2×C10711yescharacteristic, complemented
278#3167C2×C10711yescharacteristic, complemented
279#3167C2×C10711yescharacteristic, complemented
280#3147C2×C10711yescharacteristic, complemented
281#3131C2×C10711yescharacteristic, complemented
282#1723C2×C10711yescharacteristic, complemented
283#1721C2×C10711yescharacteristic, complemented
284#1720C2×C10711yescharacteristic, complemented
285#1719C2×C10711yescharacteristic, complemented
286#1717C2×C10711yescharacteristic, complemented
287#1717C2×C10711yescharacteristic, complemented
288#1715C2×C10711yescharacteristic, complemented
289#1714C2×C10711yescharacteristic, complemented
290C2×#322C2×C10711yescharacteristic, complemented
291C107#1961911yescharacteristic, direct product factor, Sylow
292C2×#135—22no—
293#533C22×C10711yescharacteristic
294#532C22×C10711yescharacteristic
295#532C22×C10711yescharacteristic
296#532C22×C10711yescharacteristic
297#500C22×C10711yescharacteristic
298#500C22×C10711yescharacteristic
299#498C22×C10711yescharacteristic
300#498C22×C10711yescharacteristic
301#495—22no—
302#494C22×C10711yescharacteristic
303#493C22×C10711yescharacteristic
304#493C22×C10711yescharacteristic
305#493C22×C10711yescharacteristic
306#492C22×C10711yescharacteristic
307#492C22×C10711yescharacteristic
308#492C22×C10711yescharacteristic
309#492C22×C10711yescharacteristic
310#488—22no—
311#487C22×C10711yescharacteristic
312#487C22×C10711yescharacteristic
313#487C22×C10711yescharacteristic
314#487C22×C10711yescharacteristic
315#486C22×C10711yescharacteristic
316#486C22×C10711yescharacteristic
317#486C22×C10711yescharacteristic
318#486C22×C10711yescharacteristic
319#486C22×C10711yescharacteristic
320#486C22×C10711yescharacteristic
321#486C22×C10711yescharacteristic
322#486C22×C10711yescharacteristic
323#466—22no—
324#466—22no—
325#465—22no—
326#465—22no—
327C4×SD16—22no—
328C4×SD16—22no—
329C4×D8—22no—
330C4×D8—22no—
331#416—22no—
332C2×C4×C8C22×C10711yescharacteristic
333C2×C4×C8C22×C10711yescharacteristic
334C2×C4×C8C22×C10711yescharacteristic
335#322C22×C10711yescharacteristic
336#322C22×C10711yescharacteristic
337#322C22×C10711yescharacteristic
338#322C22×C10711yescharacteristic
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342#135—48no—
343C2×Q16—22no—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—22no—
347C2×SD16—22no—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8—22no—
351C22×C8D4×C10712yes—
352C22×C8D4×C10712yes—
353C22×C8D4×C10712yes—
354C4⋊Q8C23×C10711yescharacteristic
355C4⋊Q8C23×C10711yescharacteristic
356C4⋊Q8C23×C10711yescharacteristic
357C4⋊Q8C23×C10711yescharacteristic
358C4⋊Q8C23×C10711yescharacteristic
359#127C23×C10711yescharacteristic
360#127C23×C10711yescharacteristic
361#127C23×C10711yescharacteristic
362#125—21no—
363#124—21no—
364#124—21no—
365#124—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—21no—
373#121—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382#117—21no—
383C2×C42C23×C10711yescharacteristic
384#107—22no—
385#107—22no—
386#106—22no—
387#106—22no—
388#103—22no—
389#103—22no—
390#103—22no—
391#103—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398#102—22no—
399#102—22no—
400C4×C8D4×C10712yes—
401C4×C8D4×C10712yes—
402C4×C8D4×C10712yes—
403C4×C8C23×C10711yescharacteristic
404C4×C8C23×C10711yescharacteristic
405C4×C8C23×C10711yescharacteristic
406C4×C8C23×C10711yescharacteristic
407C4×C8C23×C10711yescharacteristic
408C4×C8C23×C10711yescharacteristic
409#41—44no—
410#41—44no—
411#41—44no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4C2×D4×C10711yescharacteristic
433C22×C4C2×D4×C10711yescharacteristic
434C22×C4C2×D4×C10711yescharacteristic
435Q16—44no—
436SD16—44no—
437SD16—44no—
438SD16—44no—
439SD16—44no—
440D8—44no—
441D8—44no—
442D8—44no—
443C2×C8—24no—
444C2×C8—24no—
445C2×C8—42no—
446C2×C8C2×D4×C10712yes—
447C2×C8C2×D4×C10712yes—
448C2×C8C2×D4×C10712yes—
449C2×C8C2×D4×C10712yes—
450C2×C8C2×D4×C10712yes—
451C2×C8C2×D4×C10712yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C42—41no—
472C42C2×D4×C10711yescharacteristic
473C42C2×D4×C10711yescharacteristic
474C42C2×D4×C10711yescharacteristic
475C42C24×C10711yescharacteristic
476C23—41no—
477C23—41no—
478C23—41no—
479C23#127×C10711yescharacteristic
480Q8—42no—
481Q8—42no—
482Q8—42no—
483Q8—42no—
484Q8—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—82no—
495D4—82no—
496D4—82no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4#127×C10711yescharacteristic
508C2×C4#127×C10711yescharacteristic
509C2×C4#127×C10711yescharacteristic
510C2×C4AGL(1,ℤ/8)×C10714yes—
511C2×C4C22×D4×C10711yescharacteristic
512C2×C4C22×D4×C10711yescharacteristic
513C2×C4C22×D4×C10711yescharacteristic
514C8—22no—
515C8—22no—
516C8—22no—
517C8—22no—
518C8—22no—
519C8#135×C10714yescomplemented
520C22—21no—
521C22—21no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22#496×C10712yes—
532C22C2×#127×C10711yescharacteristic
533C4—21no—
534C4—21no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4#496×C10712yes—
541C4C2×#135×C10712yes—
542C4C2×AGL(1,ℤ/8)×C10712yes—
543C4#575×C10712yes—
544C2—22no—
545C2—161no—
546C2—161no—
547C2—161no—
548C2C107×#314711yescharacteristic
549C2C2×#496×C10711yescharacteristic
550C2C107×#315011yescharacteristic
subgroupG/H
centerC2×C4×C107#127
commutator, Frattini, cosocleC42C24×C107
socleC22×C107C2×#127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C2×C42×C107 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C107×#3169C2semidirect
2. C107×#3169C2semidirect
3. C107×#3167C2semidirect
4. C107×#3167C2semidirect
5. C107×#3147C2semidirect
6. C107×#3131C2semidirect
7. C107×#1723C2semidirect
8. C107×#1721C2semidirect
9. C107×#1720C2semidirect
10. C107×#1719C2semidirect
11. C107×#1717C2semidirect
12. C107×#1717C2semidirect
13. C107×#1715C2semidirect
14. C107×#1714C2semidirect
15. C2×#322×C107C2semidirect
243. C8×C107#135semidirect
268. #19619C107direct (N × H)
276. #3169C2×C107semidirect
277. #3169C2×C107semidirect
278. #3167C2×C107semidirect
279. #3167C2×C107semidirect
280. #3147C2×C107semidirect
281. #3131C2×C107semidirect
282. #1723C2×C107semidirect
283. #1721C2×C107semidirect
284. #1720C2×C107semidirect
285. #1719C2×C107semidirect
286. #1717C2×C107semidirect
287. #1717C2×C107semidirect
288. #1715C2×C107semidirect
289. #1714C2×C107semidirect
290. C2×#322C2×C107semidirect
291. C107#19619direct (N × H)
519. C8#135×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#31692
C107×#31672
C107×#31472
C107×#31312
C107×#17232
C107×#17212
C107×#17202
C107×#17192
C107×#17172
C107×#17152
C107×#17142
C2×#322×C1072
#19619107