Finite Group Databasebeta

← C107×#33855 #41059819

Subgroups — C107×#33855 #41059819

Order 27392.

640 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3417C211yesmaximal, characteristic, complemented
2C107×#3416C211yesmaximal, characteristic, complemented
3C107×#3293C211yesmaximal, characteristic, complemented
4C107×#3290C211yesmaximal, characteristic, complemented
5C107×#2251C211yesmaximal, characteristic, complemented
6C107×#2223C211yesmaximal, characteristic, complemented
7C107×#2222C211yesmaximal, characteristic, complemented
8C107×#2214C211yesmaximal, characteristic, complemented
9C107×#2212C211yesmaximal, characteristic, complemented
10C107×#2195C211yesmaximal, characteristic, complemented
11C107×#2195C211yesmaximal, characteristic, complemented
12C107×#2194C211yesmaximal, characteristic, complemented
13C107×#2193C211yesmaximal, characteristic, complemented
14C107×#2179C211yesmaximal, characteristic, complemented
15C107×#2171C211yesmaximal, characteristic, complemented
16#578×C107—21no—
17#578×C107C2211yescharacteristic
18#578×C107C2211yescharacteristic
19#578×C107C2211yescharacteristic, complemented
20#577×C107—21no—
21#576×C107C2211yescharacteristic
22#510×C107—21no—
23#510×C107—21no—
24#510×C107—21no—
25#510×C107C2211yescharacteristic
26#510×C107C2211yescharacteristic
27#510×C107C2211yescharacteristic, complemented
28#509×C107—21no—
29#509×C107C2211yescharacteristic
30#508×C107—21no—
31#508×C107—21no—
32#508×C107C2211yescharacteristic
33C2×Q32×C107—21no—
34C2×Q32×C107C2211yescharacteristic, complemented
35C2×Q32×C107C2211yescharacteristic, complemented
36C2×SD32×C107—21no—
37C2×SD32×C107C2211yescharacteristic
38C2×SD32×C107C2211yescharacteristic
39#504×C107C2211yescharacteristic
40#504×C107C2211yescharacteristic, complemented
41#495×C107C2211yescharacteristic
42#494×C107C2211yescharacteristic, complemented
43#473×C107—21no—
44#473×C107C2211yescharacteristic
45#473×C107C2211yescharacteristic
46#473×C107C2211yescharacteristic, complemented
47#472×C107C2211yescharacteristic
48#471×C107—21no—
49#456×C107—21no—
50#456×C107—21no—
51#455×C107—21no—
52#454×C107—21no—
53#443×C107C2211yescharacteristic
54#443×C107C2211yescharacteristic
55#443×C107C2211yescharacteristic, complemented
56#368×C107C2211yescharacteristic, complemented
57#364×C107C2211yescharacteristic, complemented
58#362×C107C2211yescharacteristic, complemented
59#362×C107C2211yescharacteristic, complemented
60#362×C107C2211yescharacteristic, complemented
61#361×C107C2211yescharacteristic
62#359×C107C2211yescharacteristic
63#359×C107C2211yescharacteristic, complemented
64#350×C107C2211yescharacteristic
65#350×C107C2211yescharacteristic, complemented
66#346×C107C2211yescharacteristic, complemented
672−1+4×C107—21no—
682−1+4×C107—21no—
692−1+4×C107—21no—
70H(5,𝔽2)×C107—21no—
71#137×C107—21no—
72#137×C107—21no—
73#137×C107—21no—
74#137×C107—21no—
75#137×C107—21no—
76#137×C107—21no—
77#137×C107—41no—
78#137×C107—41no—
79#137×C107—41no—
80#137×C107—41no—
81#137×C107—41no—
82#137×C107—41no—
83AGL(1,ℤ/8)×C107—21no—
84AGL(1,ℤ/8)×C107—21no—
85AGL(1,ℤ/8)×C107—41no—
86AGL(1,ℤ/8)×C107—41no—
87#135×C107—21no—
88#135×C107—21no—
89#135×C107—21no—
90#135×C107—21no—
91#135×C107—41no—
92#135×C107—41no—
93#135×C107D411yescharacteristic
94#135×C107C2311yescharacteristic
95#135×C107C2311yescharacteristic
96C2×Q16×C107—21no—
97C2×Q16×C107—21no—
98C2×Q16×C107—21no—
99C2×Q16×C107—21no—
100C2×Q16×C107—41no—
101C2×Q16×C107C2311yescharacteristic
102C2×Q16×C107C2311yescharacteristic
103C2×Q16×C107C2311yescharacteristic
104C2×SD16×C107—21no—
105C2×SD16×C107—41no—
106C2×D8×C107—21no—
107C2×D8×C107C2311yescharacteristic
108#131×C107—21no—
109#131×C107—21no—
110#131×C107C2311yescharacteristic
111#131×C107C2311yescharacteristic
112C4⋊Q8×C107—21no—
113#124×C107—21no—
114Q32×C107—21no—
115Q32×C107—21no—
116Q32×C107—21no—
117Q32×C107—21no—
118Q32×C107—21no—
119Q32×C107—41no—
120Q32×C107D411yescharacteristic
121SD32×C107—21no—
122SD32×C107—21no—
123SD32×C107—21no—
124SD32×C107—21no—
125SD32×C107—21no—
126SD32×C107—21no—
127SD32×C107—41no—
128SD32×C107D411yescharacteristic
129SD32×C107D411yescharacteristic
130D16×C107—21no—
131D16×C107D411yescharacteristic
132M32×C107—21no—
133M32×C107—21no—
134M32×C107C2311yescharacteristic
135M32×C107C2311yescharacteristic
136C2×C16×C107—21no—
137C2×C16×C107—21no—
138C2×C16×C107C2311yescharacteristic
139C2×C16×C107C2311yescharacteristic
140#108×C107D411yescharacteristic
141#108×C107C2311yescharacteristic
142#108×C107C2311yescharacteristic
143#104×C107—21no—
144#104×C107—21no—
145#104×C107D411yescharacteristic
146#104×C107D411yescharacteristic
147#101×C107—21no—
148#101×C107—21no—
149#101×C107—21no—
150#100×C107—21no—
151C4×C8×C107C2311yescharacteristic
152#41×C107—21no—
153#41×C107—21no—
154#41×C107—41no—
155#41×C107—41no—
156#41×C107—41no—
157#41×C107—41no—
158#41×C107—41no—
159#41×C107—41no—
160#41×C107—41no—
161#41×C107—41no—
162#41×C107—81no—
163#41×C107—81no—
164#41×C107—81no—
165#41×C107C2×D411yescharacteristic
166#41×C107C2×D411yescharacteristic
167C2×Q8×C107—21no—
168C2×Q8×C107—21no—
169C2×Q8×C107—21no—
170C2×Q8×C107—41no—
171C2×Q8×C107—41no—
172C2×Q8×C107—41no—
173C2×Q8×C107—41no—
174C2×Q8×C107—41no—
175C2×Q8×C107—41no—
176C2×D4×C107—21no—
177C2×D4×C107—41no—
178C2×D4×C107—41no—
179C2×D4×C107—81no—
180Q16×C107—21no—
181Q16×C107—21no—
182Q16×C107—21no—
183Q16×C107—21no—
184Q16×C107—21no—
185Q16×C107—21no—
186Q16×C107—41no—
187Q16×C107—41no—
188Q16×C107—41no—
189Q16×C107—41no—
190Q16×C107—41no—
191Q16×C107—41no—
192Q16×C107—41no—
193Q16×C107—41no—
194Q16×C107D811yescharacteristic
195Q16×C107C2×D411yescharacteristic
196Q16×C107C2×D411yescharacteristic
197SD16×C107—21no—
198SD16×C107—21no—
199SD16×C107—41no—
200SD16×C107—41no—
201SD16×C107—41no—
202SD16×C107—41no—
203SD16×C107—41no—
204SD16×C107—41no—
205SD16×C107—41no—
206SD16×C107—41no—
207SD16×C107—41no—
208SD16×C107—41no—
209SD16×C107D811yescharacteristic
210SD16×C107D811yescharacteristic
211D8×C107—21no—
212D8×C107—21no—
213D8×C107—41no—
214D8×C107—41no—
215D8×C107D811yescharacteristic
216D8×C107C2×D411yescharacteristic
217D8×C107C2×D411yescharacteristic
218M16×C107—21no—
219M16×C107—21no—
220M16×C107—21no—
221M16×C107—21no—
222M16×C107—41no—
223M16×C107—41no—
224M16×C107C2×D411yescharacteristic
225M16×C107C2×D411yescharacteristic
226C2×C8×C107—21no—
227C2×C8×C107—21no—
228C2×C8×C107—41no—
229C2×C8×C107—41no—
230C2×C8×C107C2×D411yescharacteristic
231C2×C8×C107C2411yescharacteristic
232C4⋊C4×C107—81no—
233C22⋊C4×C107—81no—
234C42×C107C2×D411yescharacteristic
235C16×C107—21no—
236C16×C107—21no—
237C16×C107—21no—
238C16×C107C2×D411yescharacteristic
239C16×C107C2×D411yescharacteristic
240C23×C107—41no—
241C23×C107—81no—
242Q8×C107—21no—
243Q8×C107—21no—
244Q8×C107—41no—
245Q8×C107—41no—
246Q8×C107—41no—
247Q8×C107—41no—
248Q8×C107—41no—
249Q8×C107—41no—
250Q8×C107—81no—
251Q8×C107—81no—
252Q8×C107—81no—
253Q8×C107C2×D811yescharacteristic
254Q8×C107C2×D811yescharacteristic
255D4×C107—21no—
256D4×C107—21no—
257D4×C107—21no—
258D4×C107—21no—
259D4×C107—41no—
260D4×C107—41no—
261D4×C107—41no—
262D4×C107—41no—
263D4×C107—81no—
264D4×C107—81no—
265D4×C107—81no—
266D4×C107—81no—
267D4×C107—81no—
268D4×C107C2×D811yescharacteristic
269D4×C107C2×D811yescharacteristic
270C2×C4×C107—21no—
271C2×C4×C107—21no—
272C2×C4×C107—21no—
273C2×C4×C107—41no—
274C2×C4×C107—41no—
275C2×C4×C107—41no—
276C2×C4×C107—41no—
277C2×C4×C107—41no—
278C2×C4×C107—81no—
279C2×C4×C107—81no—
280C2×C4×C107—81no—
281C2×C4×C107—81no—
282C2×C4×C107—81no—
283C2×C4×C107—81no—
284C2×C4×C107—81no—
285C2×C4×C107C22×D411yescharacteristic
286C8×C107—21no—
287C8×C107—21no—
288C8×C107—41no—
289C8×C107—41no—
290C8×C107C2×D811yescharacteristic
291C8×C107C2×D811yescharacteristic
292C8×C107C22×D411yescharacteristic
293C8×C107H(5,𝔽2)11yescharacteristic
294C22×C107—21no—
295C22×C107—21no—
296C22×C107—41no—
297C22×C107—41no—
298C22×C107—81no—
299C22×C107—161no—
300C22×C107—321no—
301C22×C107#57611yescharacteristic
302C4×C107—21no—
303C4×C107—21no—
304C4×C107—41no—
305C4×C107—41no—
306C4×C107—41no—
307C4×C107—81no—
308C4×C107—81no—
309C4×C107—81no—
310C4×C107D4211yescharacteristic
311C4×C107C22×D811yescharacteristic
312#33855C10711yesmaximal, characteristic, direct product factor, Sylow
313C2×C107—21no—
314C2×C107—41no—
315C2×C107—41no—
316C2×C107—81no—
317C2×C107—81no—
318C2×C107—161no—
319C2×C107D4×D811yescharacteristic
320#3417C2×C10711yescharacteristic, complemented
321#3416C2×C10711yescharacteristic, complemented
322#3293C2×C10711yescharacteristic, complemented
323#3290C2×C10711yescharacteristic, complemented
324#2251C2×C10711yescharacteristic, complemented
325#2223C2×C10711yescharacteristic, complemented
326#2222C2×C10711yescharacteristic, complemented
327#2214C2×C10711yescharacteristic, complemented
328#2212C2×C10711yescharacteristic, complemented
329#2195C2×C10711yescharacteristic, complemented
330#2195C2×C10711yescharacteristic, complemented
331#2194C2×C10711yescharacteristic, complemented
332#2193C2×C10711yescharacteristic, complemented
333#2179C2×C10711yescharacteristic, complemented
334#2171C2×C10711yescharacteristic, complemented
335C107#3385511yescharacteristic, direct product factor, Sylow
336#578—21no—
337#578C22×C10711yescharacteristic
338#578C22×C10711yescharacteristic
339#578C22×C10711yescharacteristic, complemented
340#577—21no—
341#576C22×C10711yescharacteristic
342#510—21no—
343#510—21no—
344#510—21no—
345#510C22×C10711yescharacteristic
346#510C22×C10711yescharacteristic
347#510C22×C10711yescharacteristic, complemented
348#509—21no—
349#509C22×C10711yescharacteristic
350#508—21no—
351#508—21no—
352#508C22×C10711yescharacteristic
353C2×Q32—21no—
354C2×Q32C22×C10711yescharacteristic, complemented
355C2×Q32C22×C10711yescharacteristic, complemented
356C2×SD32—21no—
357C2×SD32C22×C10711yescharacteristic
358C2×SD32C22×C10711yescharacteristic
359#504C22×C10711yescharacteristic
360#504C22×C10711yescharacteristic, complemented
361#495C22×C10711yescharacteristic
362#494C22×C10711yescharacteristic, complemented
363#473—21no—
364#473C22×C10711yescharacteristic
365#473C22×C10711yescharacteristic
366#473C22×C10711yescharacteristic, complemented
367#472C22×C10711yescharacteristic
368#471—21no—
369#456—21no—
370#456—21no—
371#455—21no—
372#454—21no—
373#443C22×C10711yescharacteristic
374#443C22×C10711yescharacteristic
375#443C22×C10711yescharacteristic, complemented
376#368C22×C10711yescharacteristic, complemented
377#364C22×C10711yescharacteristic, complemented
378#362C22×C10711yescharacteristic, complemented
379#362C22×C10711yescharacteristic, complemented
380#362C22×C10711yescharacteristic, complemented
381#361C22×C10711yescharacteristic
382#359C22×C10711yescharacteristic
383#359C22×C10711yescharacteristic, complemented
384#350C22×C10711yescharacteristic
385#350C22×C10711yescharacteristic, complemented
386#346C22×C10711yescharacteristic, complemented
3872−1+4—21no—
3882−1+4—21no—
3892−1+4—21no—
390H(5,𝔽2)—21no—
391#137—21no—
392#137—21no—
393#137—21no—
394#137—21no—
395#137—21no—
396#137—21no—
397#137—41no—
398#137—41no—
399#137—41no—
400#137—41no—
401#137—41no—
402#137—41no—
403AGL(1,ℤ/8)—21no—
404AGL(1,ℤ/8)—21no—
405AGL(1,ℤ/8)—41no—
406AGL(1,ℤ/8)—41no—
407#135—21no—
408#135—21no—
409#135—21no—
410#135—21no—
411#135—41no—
412#135—41no—
413#135D4×C10711yescharacteristic
414#135C23×C10711yescharacteristic
415#135C23×C10711yescharacteristic
416C2×Q16—21no—
417C2×Q16—21no—
418C2×Q16—21no—
419C2×Q16—21no—
420C2×Q16—41no—
421C2×Q16C23×C10711yescharacteristic
422C2×Q16C23×C10711yescharacteristic
423C2×Q16C23×C10711yescharacteristic
424C2×SD16—21no—
425C2×SD16—41no—
426C2×D8—21no—
427C2×D8C23×C10711yescharacteristic
428#131—21no—
429#131—21no—
430#131C23×C10711yescharacteristic
431#131C23×C10711yescharacteristic
432C4⋊Q8—21no—
433#124—21no—
434Q32—21no—
435Q32—21no—
436Q32—21no—
437Q32—21no—
438Q32—21no—
439Q32—41no—
440Q32D4×C10711yescharacteristic
441SD32—21no—
442SD32—21no—
443SD32—21no—
444SD32—21no—
445SD32—21no—
446SD32—21no—
447SD32—41no—
448SD32D4×C10711yescharacteristic
449SD32D4×C10711yescharacteristic
450D16—21no—
451D16D4×C10711yescharacteristic
452M32—21no—
453M32—21no—
454M32C23×C10711yescharacteristic
455M32C23×C10711yescharacteristic
456C2×C16—21no—
457C2×C16—21no—
458C2×C16C23×C10711yescharacteristic
459C2×C16C23×C10711yescharacteristic
460#108D4×C10711yescharacteristic
461#108C23×C10711yescharacteristic
462#108C23×C10711yescharacteristic
463#104—21no—
464#104—21no—
465#104D4×C10711yescharacteristic
466#104D4×C10711yescharacteristic
467#101—21no—
468#101—21no—
469#101—21no—
470#100—21no—
471C4×C8C23×C10711yescharacteristic
472#41—21no—
473#41—21no—
474#41—41no—
475#41—41no—
476#41—41no—
477#41—41no—
478#41—41no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—81no—
483#41—81no—
484#41—81no—
485#41C2×D4×C10711yescharacteristic
486#41C2×D4×C10711yescharacteristic
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×D4—21no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—81no—
500Q16—21no—
501Q16—21no—
502Q16—21no—
503Q16—21no—
504Q16—21no—
505Q16—21no—
506Q16—41no—
507Q16—41no—
508Q16—41no—
509Q16—41no—
510Q16—41no—
511Q16—41no—
512Q16—41no—
513Q16—41no—
514Q16D8×C10711yescharacteristic
515Q16C2×D4×C10711yescharacteristic
516Q16C2×D4×C10711yescharacteristic
517SD16—21no—
518SD16—21no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—41no—
523SD16—41no—
524SD16—41no—
525SD16—41no—
526SD16—41no—
527SD16—41no—
528SD16—41no—
529SD16D8×C10711yescharacteristic
530SD16D8×C10711yescharacteristic
531D8—21no—
532D8—21no—
533D8—41no—
534D8—41no—
535D8D8×C10711yescharacteristic
536D8C2×D4×C10711yescharacteristic
537D8C2×D4×C10711yescharacteristic
538M16—21no—
539M16—21no—
540M16—21no—
541M16—21no—
542M16—41no—
543M16—41no—
544M16C2×D4×C10711yescharacteristic
545M16C2×D4×C10711yescharacteristic
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8C2×D4×C10711yescharacteristic
551C2×C8C24×C10711yescharacteristic
552C4⋊C4—81no—
553C22⋊C4—81no—
554C42C2×D4×C10711yescharacteristic
555C16—21no—
556C16—21no—
557C16—21no—
558C16C2×D4×C10711yescharacteristic
559C16C2×D4×C10711yescharacteristic
560C23—41no—
561C23—81no—
562Q8—21no—
563Q8—21no—
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570Q8—81no—
571Q8—81no—
572Q8—81no—
573Q8C2×D8×C10711yescharacteristic
574Q8C2×D8×C10711yescharacteristic
575D4—21no—
576D4—21no—
577D4—21no—
578D4—21no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—81no—
584D4—81no—
585D4—81no—
586D4—81no—
587D4—81no—
588D4C2×D8×C10711yescharacteristic
589D4C2×D8×C10711yescharacteristic
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—81no—
604C2×C4—81no—
605C2×C4C22×D4×C10711yescharacteristic
606C8—21no—
607C8—21no—
608C8—41no—
609C8—41no—
610C8C2×D8×C10711yescharacteristic
611C8C2×D8×C10711yescharacteristic
612C8C22×D4×C10711yescharacteristic
613C8H(5,𝔽2)×C10711yescharacteristic
614C22—21no—
615C22—21no—
616C22—41no—
617C22—41no—
618C22—81no—
619C22—161no—
620C22—321no—
621C22#576×C10711yescharacteristic
622C4—21no—
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4D42×C10711yescharacteristic
631C4C22×D8×C10711yescharacteristic
632C2—21no—
633C2—41no—
634C2—41no—
635C2—81no—
636C2—81no—
637C2—161no—
638C2D4×D8×C10711yescharacteristic
subgroupG/H
center, socleC2×C107D4×D8
commutator, Frattini, cosocleC2×C8C24×C107
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C2×C4×C107 ◁ #443×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3417C2semidirect
2. C107×#3416C2semidirect
3. C107×#3293C2semidirect
4. C107×#3290C2semidirect
5. C107×#2251C2semidirect
6. C107×#2223C2semidirect
7. C107×#2222C2semidirect
8. C107×#2214C2semidirect
9. C107×#2212C2semidirect
10. C107×#2195C2semidirect
11. C107×#2195C2semidirect
12. C107×#2194C2semidirect
13. C107×#2193C2semidirect
14. C107×#2179C2semidirect
15. C107×#2171C2semidirect
19. #578×C107C22semidirect
27. #510×C107C22semidirect
34. C2×Q32×C107C22semidirect
35. C2×Q32×C107C22semidirect
40. #504×C107C22semidirect
42. #494×C107C22semidirect
46. #473×C107C22semidirect
55. #443×C107C22semidirect
56. #368×C107C22semidirect
57. #364×C107C22semidirect
58. #362×C107C22semidirect
59. #362×C107C22semidirect
60. #362×C107C22semidirect
63. #359×C107C22semidirect
65. #350×C107C22semidirect
66. #346×C107C22semidirect
312. #33855C107direct (N × H)
320. #3417C2×C107semidirect
321. #3416C2×C107semidirect
322. #3293C2×C107semidirect
323. #3290C2×C107semidirect
324. #2251C2×C107semidirect
325. #2223C2×C107semidirect
326. #2222C2×C107semidirect
327. #2214C2×C107semidirect
328. #2212C2×C107semidirect
329. #2195C2×C107semidirect
330. #2195C2×C107semidirect
331. #2194C2×C107semidirect
332. #2193C2×C107semidirect
333. #2179C2×C107semidirect
334. #2171C2×C107semidirect
335. C107#33855direct (N × H)
339. #578C22×C107semidirect
347. #510C22×C107semidirect
354. C2×Q32C22×C107semidirect
355. C2×Q32C22×C107semidirect
360. #504C22×C107semidirect
362. #494C22×C107semidirect
366. #473C22×C107semidirect
375. #443C22×C107semidirect
376. #368C22×C107semidirect
377. #364C22×C107semidirect
378. #362C22×C107semidirect
379. #362C22×C107semidirect
380. #362C22×C107semidirect
383. #359C22×C107semidirect
385. #350C22×C107semidirect
386. #346C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34172
C107×#34162
C107×#32932
C107×#32902
C107×#22512
C107×#22232
C107×#22222
C107×#22142
C107×#22122
C107×#21952
C107×#21942
C107×#21932
C107×#21792
C107×#21712
#33855107