Finite Group Databasebeta

← C107×#24808 #41050772

Subgroups — C107×#24808 #41050772

Order 27392.

820 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3069C211yesmaximal, characteristic, complemented
2C107×#3068C211yesmaximal, characteristic
3C2×#471×C107C211yesmaximal, characteristic, complemented
4C2×#471×C107C211yesmaximal, characteristic, complemented
5C107×#2955C211yesmaximal, characteristic, complemented
6C107×#2916C211yesmaximal, characteristic, complemented
7C107×#2070C211yesmaximal, characteristic, complemented
8C107×#2069C211yesmaximal, characteristic, complemented
9C107×#2049C211yesmaximal, characteristic, complemented
10C107×#2048C211yesmaximal, characteristic, complemented
11C107×#1977C211yesmaximal, characteristic, complemented
12C107×#1953C211yesmaximal, characteristic, complemented
13C107×#1903C211yesmaximal, characteristic, complemented
14C107×#1902C211yesmaximal, characteristic, complemented
15C107×#1813C211yesmaximal, characteristic, complemented
16#575×C107C2211yescharacteristic
17C2×#137×C107C2211yescharacteristic
18C2×#137×C107C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
21C22×SD16×C107C2211yescharacteristic
22#568×C107C2211yescharacteristic
23#568×C107C2211yescharacteristic
24C2×#131×C107C2211yescharacteristic
25C2×#131×C107C2211yescharacteristic
26#473×C107—22no—
27#472×C107—22no—
28#471×C107—22no—
29#471×C107—22no—
30#471×C107—22no—
31#471×C107—22no—
32#471×C107—22no—
33#471×C107—22no—
34#444×C107—22no—
35#443×C107—22no—
36#430×C107—22no—
37#430×C107C2211yescharacteristic
38#430×C107C2211yescharacteristic
39#430×C107C2211yescharacteristic
40#430×C107C2211yescharacteristic
41#430×C107C2211yescharacteristic
42C2×#108×C107—22no—
43C2×#108×C107C2211yescharacteristic
44C2×#108×C107C2211yescharacteristic
45C2×#108×C107C2211yescharacteristic
46#421×C107C2211yescharacteristic
47#421×C107C2211yescharacteristic
48#419×C107C2211yescharacteristic
49#418×C107C2211yescharacteristic
50#413×C107C2211yescharacteristic
51#413×C107C2211yescharacteristic
52C2×#101×C107C2211yescharacteristic
53C2×#101×C107C2211yescharacteristic
54C2×#101×C107C2211yescharacteristic
55C2×#100×C107C2211yescharacteristic
56C2×#100×C107C2211yescharacteristic
57C2×#100×C107C2211yescharacteristic
58#405×C107C2211yescharacteristic
59#344×C107C2211yescharacteristic
60#344×C107C2211yescharacteristic
61#338×C107C2211yescharacteristic
62#338×C107C2211yescharacteristic
63C2×#41×C107C2311yescharacteristic
64C2×#41×C107C2311yescharacteristic
65C22×Q8×C107C2311yescharacteristic
66C22×D4×C107C2311yescharacteristic
67#137×C107—21no—
68#137×C107—22no—
69#137×C107—22no—
70#137×C107—22no—
71#137×C107—41no—
72#137×C107D412yes—
73AGL(1,ℤ/8)×C107—21no—
74AGL(1,ℤ/8)×C107—22no—
75AGL(1,ℤ/8)×C107—22no—
76AGL(1,ℤ/8)×C107—22no—
77AGL(1,ℤ/8)×C107—41no—
78AGL(1,ℤ/8)×C107D412yes—
79#135×C107—22no—
80C2×Q16×C107—21no—
81C2×Q16×C107—21no—
82C2×SD16×C107—21no—
83C2×SD16×C107—21no—
84C2×SD16×C107—21no—
85C2×SD16×C107—21no—
86C2×SD16×C107—21no—
87C2×SD16×C107—21no—
88C2×SD16×C107—21no—
89C2×SD16×C107—21no—
90C2×SD16×C107—21no—
91C2×SD16×C107—21no—
92C2×D8×C107—21no—
93C2×D8×C107—21no—
94#131×C107—21no—
95#131×C107—21no—
96#131×C107—22no—
97#131×C107—22no—
98#131×C107—21no—
99#131×C107—21no—
100#131×C107—21no—
101#131×C107—21no—
102#131×C107—41no—
103#131×C107—41no—
104#131×C107D412yes—
105#131×C107D412yes—
106C2×M16×C107—21no—
107C2×M16×C107—21no—
108C2×M16×C107—22no—
109C2×M16×C107—22no—
110C2×M16×C107C2311yescharacteristic
111C2×M16×C107C2311yescharacteristic
112C2×M16×C107C2311yescharacteristic
113C2×M16×C107C2311yescharacteristic
114C2×M16×C107C2311yescharacteristic
115C2×M16×C107C2311yescharacteristic
116C2×M16×C107C2311yescharacteristic
117C2×M16×C107C2311yescharacteristic
118C2×M16×C107C2311yescharacteristic
119C22×C8×C107—21no—
120C22×C8×C107—21no—
121C22×C8×C107C2311yescharacteristic
122#117×C107C2311yescharacteristic
123#108×C107—22no—
124#108×C107—22no—
125#108×C107—22no—
126#108×C107—22no—
127#108×C107—22no—
128#108×C107—21no—
129#108×C107—21no—
130#108×C107—21no—
131#108×C107—21no—
132#108×C107D412yes—
133#108×C107D412yes—
134#104×C107—22no—
135#104×C107—22no—
136#103×C107—41no—
137#102×C107—41no—
138#101×C107—21no—
139#101×C107—21no—
140#101×C107—22no—
141#101×C107—22no—
142#101×C107—22no—
143#100×C107—21no—
144#100×C107—21no—
145#100×C107—22no—
146#100×C107—22no—
147#100×C107—22no—
148#97×C107—21no—
149C4×C8×C107—21no—
150C24×C107—21no—
151#41×C107—21no—
152#41×C107—21no—
153#41×C107—21no—
154#41×C107—21no—
155#41×C107—21no—
156#41×C107—21no—
157#41×C107C2×D412yes—
158#41×C107C2×D412yes—
159C2×Q8×C107—21no—
160C2×Q8×C107—21no—
161C2×Q8×C107—21no—
162C2×Q8×C107—21no—
163C2×Q8×C107—21no—
164C2×Q8×C107—21no—
165C2×Q8×C107C2×D411yescharacteristic
166C2×Q8×C107#4111yescharacteristic
167C2×D4×C107—21no—
168C2×D4×C107—21no—
169C2×D4×C107—21no—
170C2×D4×C107—21no—
171C2×D4×C107—21no—
172C2×D4×C107—21no—
173C2×D4×C107—21no—
174C2×D4×C107—21no—
175C2×D4×C107C2×D411yescharacteristic
176C2×D4×C107#4111yescharacteristic
177C22×C4×C107—21no—
178C22×C4×C107—21no—
179C22×C4×C107—21no—
180C22×C4×C107C2411yescharacteristic
181Q16×C107—22no—
182Q16×C107—42no—
183Q16×C107—42no—
184SD16×C107—22no—
185SD16×C107—22no—
186SD16×C107—42no—
187SD16×C107—42no—
188SD16×C107—42no—
189SD16×C107—42no—
190SD16×C107—41no—
191SD16×C107—41no—
192SD16×C107—41no—
193SD16×C107—41no—
194D8×C107—22no—
195D8×C107—42no—
196D8×C107—42no—
197M16×C107—21no—
198M16×C107—21no—
199M16×C107—21no—
200M16×C107—21no—
201M16×C107—22no—
202M16×C107—22no—
203M16×C107—21no—
204M16×C107—21no—
205M16×C107—21no—
206M16×C107—21no—
207M16×C107—21no—
208M16×C107—21no—
209M16×C107—21no—
210M16×C107—21no—
211M16×C107—21no—
212M16×C107—21no—
213M16×C107—42no—
214M16×C107—42no—
215M16×C107—41no—
216M16×C107—41no—
217M16×C107C2×D412yes—
218M16×C107C2×D412yes—
219M16×C107C2×D412yes—
220M16×C107C2×D412yes—
221C2×C8×C107—21no—
222C2×C8×C107—21no—
223C2×C8×C107—21no—
224C2×C8×C107—21no—
225C2×C8×C107—22no—
226C2×C8×C107—22no—
227C2×C8×C107—21no—
228C2×C8×C107—21no—
229C2×C8×C107—21no—
230C2×C8×C107—21no—
231C2×C8×C107—21no—
232C2×C8×C107—42no—
233C2×C8×C107—42no—
234C2×C8×C107—41no—
235C2×C8×C107—41no—
236C2×C8×C107C2×D411yescharacteristic
237C2×C8×C107C2×D411yescharacteristic
238C2×C8×C107C2×D411yescharacteristic
239C2×C8×C107C2×D411yescharacteristic
240C2×C8×C107#4111yescharacteristic
241C2×C8×C107#4111yescharacteristic
242C4⋊C4×C107—21no—
243C22⋊C4×C107—21no—
244C42×C107—21no—
245C23×C107—21no—
246C23×C107—21no—
247C23×C107—41no—
248C23×C107—41no—
249C23×C107—41no—
250C23×C107—161no—
251C23×C1072−1+411yescharacteristic
252Q8×C107—21no—
253Q8×C107—21no—
254Q8×C107—21no—
255Q8×C107—41no—
256Q8×C107—41no—
257Q8×C107—41no—
258Q8×C107—41no—
259Q8×C107#12112yes—
260D4×C107—22no—
261D4×C107—22no—
262D4×C107—21no—
263D4×C107—21no—
264D4×C107—21no—
265D4×C107—41no—
266D4×C107—41no—
267D4×C107—41no—
268D4×C107—41no—
269D4×C107—41no—
270D4×C107—41no—
271D4×C107#12112yes—
272C2×C4×C107—21no—
273C2×C4×C107—22no—
274C2×C4×C107—22no—
275C2×C4×C107—21no—
276C2×C4×C107—41no—
277C2×C4×C107—41no—
278C2×C4×C107—41no—
279C2×C4×C107—41no—
280C2×C4×C107—41no—
281C2×C4×C107—41no—
282C2×C4×C107C22×D411yescharacteristic
283C2×C4×C107C22×D411yescharacteristic
284C2×C4×C107C22×D411yescharacteristic
285C2×C4×C107C2×#4111yescharacteristic
286C2×C4×C107C2×#4111yescharacteristic
287C2×C4×C107H(5,𝔽2)11yescharacteristic
288C8×C107—22no—
289C8×C107—22no—
290C8×C107—22no—
291C8×C107—22no—
292C8×C107—41no—
293C8×C107—41no—
294C8×C107—41no—
295C8×C107—41no—
296C8×C107—41no—
297C8×C107#12111yescharacteristic
298C8×C107#12111yescharacteristic
299C8×C107#12111yescharacteristic
300C8×C107#12111yescharacteristic
301C22×C107—22no—
302C22×C107—41no—
303C22×C107—41no—
304C22×C107—81no—
305C22×C107—81no—
306C22×C107—81no—
307C22×C107—161no—
308C22×C107—161no—
309C22×C107—161no—
310C22×C107#53711yescharacteristic
311C22×C107#54711yescharacteristic
312C22×C107#54811yescharacteristic
313C4×C107—22no—
314C4×C107—41no—
315C4×C107—81no—
316C4×C107—81no—
317C4×C107C2×#12111yescharacteristic
318C4×C107C2×#12111yescharacteristic
319C4×C107D4211yescharacteristic
320C4×C107#55311yescharacteristic
321#24808C10711yesmaximal, characteristic, direct product factor, Sylow
322C2×C107—21no—
323C2×C107—21no—
324C2×C107—21no—
325C2×C107—42no—
326C2×C107—81no—
327C2×C107—161no—
328C2×C107#241611yescharacteristic
329#3069C2×C10711yescharacteristic, complemented
330#3068C2×C10711yescharacteristic
331C2×#471C2×C10711yescharacteristic, complemented
332C2×#471C2×C10711yescharacteristic, complemented
333#2955C2×C10711yescharacteristic, complemented
334#2916C2×C10711yescharacteristic, complemented
335#2070C2×C10711yescharacteristic, complemented
336#2069C2×C10711yescharacteristic, complemented
337#2049C2×C10711yescharacteristic, complemented
338#2048C2×C10711yescharacteristic, complemented
339#1977C2×C10711yescharacteristic, complemented
340#1953C2×C10711yescharacteristic, complemented
341#1903C2×C10711yescharacteristic, complemented
342#1902C2×C10711yescharacteristic, complemented
343#1813C2×C10711yescharacteristic, complemented
344C107#2480811yescharacteristic, direct product factor, Sylow
345#575C22×C10711yescharacteristic
346C2×#137C22×C10711yescharacteristic
347C2×#137C22×C10711yescharacteristic
348C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
349C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
350C22×SD16C22×C10711yescharacteristic
351#568C22×C10711yescharacteristic
352#568C22×C10711yescharacteristic
353C2×#131C22×C10711yescharacteristic
354C2×#131C22×C10711yescharacteristic
355#473—22no—
356#472—22no—
357#471—22no—
358#471—22no—
359#471—22no—
360#471—22no—
361#471—22no—
362#471—22no—
363#444—22no—
364#443—22no—
365#430—22no—
366#430C22×C10711yescharacteristic
367#430C22×C10711yescharacteristic
368#430C22×C10711yescharacteristic
369#430C22×C10711yescharacteristic
370#430C22×C10711yescharacteristic
371C2×#108—22no—
372C2×#108C22×C10711yescharacteristic
373C2×#108C22×C10711yescharacteristic
374C2×#108C22×C10711yescharacteristic
375#421C22×C10711yescharacteristic
376#421C22×C10711yescharacteristic
377#419C22×C10711yescharacteristic
378#418C22×C10711yescharacteristic
379#413C22×C10711yescharacteristic
380#413C22×C10711yescharacteristic
381C2×#101C22×C10711yescharacteristic
382C2×#101C22×C10711yescharacteristic
383C2×#101C22×C10711yescharacteristic
384C2×#100C22×C10711yescharacteristic
385C2×#100C22×C10711yescharacteristic
386C2×#100C22×C10711yescharacteristic
387#405C22×C10711yescharacteristic
388#344C22×C10711yescharacteristic
389#344C22×C10711yescharacteristic
390#338C22×C10711yescharacteristic
391#338C22×C10711yescharacteristic
392C2×#41C23×C10711yescharacteristic
393C2×#41C23×C10711yescharacteristic
394C22×Q8C23×C10711yescharacteristic
395C22×D4C23×C10711yescharacteristic
396#137—21no—
397#137—22no—
398#137—22no—
399#137—22no—
400#137—41no—
401#137D4×C10712yes—
402AGL(1,ℤ/8)—21no—
403AGL(1,ℤ/8)—22no—
404AGL(1,ℤ/8)—22no—
405AGL(1,ℤ/8)—22no—
406AGL(1,ℤ/8)—41no—
407AGL(1,ℤ/8)D4×C10712yes—
408#135—22no—
409C2×Q16—21no—
410C2×Q16—21no—
411C2×SD16—21no—
412C2×SD16—21no—
413C2×SD16—21no—
414C2×SD16—21no—
415C2×SD16—21no—
416C2×SD16—21no—
417C2×SD16—21no—
418C2×SD16—21no—
419C2×SD16—21no—
420C2×SD16—21no—
421C2×D8—21no—
422C2×D8—21no—
423#131—21no—
424#131—21no—
425#131—22no—
426#131—22no—
427#131—21no—
428#131—21no—
429#131—21no—
430#131—21no—
431#131—41no—
432#131—41no—
433#131D4×C10712yes—
434#131D4×C10712yes—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—22no—
438C2×M16—22no—
439C2×M16C23×C10711yescharacteristic
440C2×M16C23×C10711yescharacteristic
441C2×M16C23×C10711yescharacteristic
442C2×M16C23×C10711yescharacteristic
443C2×M16C23×C10711yescharacteristic
444C2×M16C23×C10711yescharacteristic
445C2×M16C23×C10711yescharacteristic
446C2×M16C23×C10711yescharacteristic
447C2×M16C23×C10711yescharacteristic
448C22×C8—21no—
449C22×C8—21no—
450C22×C8C23×C10711yescharacteristic
451#117C23×C10711yescharacteristic
452#108—22no—
453#108—22no—
454#108—22no—
455#108—22no—
456#108—22no—
457#108—21no—
458#108—21no—
459#108—21no—
460#108—21no—
461#108D4×C10712yes—
462#108D4×C10712yes—
463#104—22no—
464#104—22no—
465#103—41no—
466#102—41no—
467#101—21no—
468#101—21no—
469#101—22no—
470#101—22no—
471#101—22no—
472#100—21no—
473#100—21no—
474#100—22no—
475#100—22no—
476#100—22no—
477#97—21no—
478C4×C8—21no—
479C24—21no—
480#41—21no—
481#41—21no—
482#41—21no—
483#41—21no—
484#41—21no—
485#41—21no—
486#41C2×D4×C10712yes—
487#41C2×D4×C10712yes—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×D4×C10711yescharacteristic
495C2×Q8#41×C10711yescharacteristic
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C10711yescharacteristic
505C2×D4#41×C10711yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4C24×C10711yescharacteristic
510Q16—22no—
511Q16—42no—
512Q16—42no—
513SD16—22no—
514SD16—22no—
515SD16—42no—
516SD16—42no—
517SD16—42no—
518SD16—42no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—41no—
523D8—22no—
524D8—42no—
525D8—42no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—22no—
531M16—22no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—21no—
539M16—21no—
540M16—21no—
541M16—21no—
542M16—42no—
543M16—42no—
544M16—41no—
545M16—41no—
546M16C2×D4×C10712yes—
547M16C2×D4×C10712yes—
548M16C2×D4×C10712yes—
549M16C2×D4×C10712yes—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8C2×D4×C10711yescharacteristic
566C2×C8C2×D4×C10711yescharacteristic
567C2×C8C2×D4×C10711yescharacteristic
568C2×C8C2×D4×C10711yescharacteristic
569C2×C8#41×C10711yescharacteristic
570C2×C8#41×C10711yescharacteristic
571C4⋊C4—21no—
572C22⋊C4—21no—
573C42—21no—
574C23—21no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—161no—
580C232−1+4×C10711yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8#121×C10712yes—
589D4—22no—
590D4—22no—
591D4—21no—
592D4—21no—
593D4—21no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4#121×C10712yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4C22×D4×C10711yescharacteristic
612C2×C4C22×D4×C10711yescharacteristic
613C2×C4C22×D4×C10711yescharacteristic
614C2×C4C2×#41×C10711yescharacteristic
615C2×C4C2×#41×C10711yescharacteristic
616C2×C4H(5,𝔽2)×C10711yescharacteristic
617C8—22no—
618C8—22no—
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8#121×C10711yescharacteristic
627C8#121×C10711yescharacteristic
628C8#121×C10711yescharacteristic
629C8#121×C10711yescharacteristic
630C22—22no—
631C22—41no—
632C22—41no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—161no—
637C22—161no—
638C22—161no—
639C22#537×C10711yescharacteristic
640C22#547×C10711yescharacteristic
641C22#548×C10711yescharacteristic
642C4—22no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4C2×#121×C10711yescharacteristic
647C4C2×#121×C10711yescharacteristic
648C4D42×C10711yescharacteristic
649C4#553×C10711yescharacteristic
650C2—21no—
651C2—21no—
652C2—21no—
653C2—42no—
654C2—81no—
655C2—161no—
656C2C107×#241611yescharacteristic
subgroupG/H
center, socleC2×C107#2416
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3068C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3069C2semidirect
3. C2×#471×C107C2semidirect
4. C2×#471×C107C2semidirect
5. C107×#2955C2semidirect
6. C107×#2916C2semidirect
7. C107×#2070C2semidirect
8. C107×#2069C2semidirect
9. C107×#2049C2semidirect
10. C107×#2048C2semidirect
11. C107×#1977C2semidirect
12. C107×#1953C2semidirect
13. C107×#1903C2semidirect
14. C107×#1902C2semidirect
15. C107×#1813C2semidirect
321. #24808C107direct (N × H)
329. #3069C2×C107semidirect
331. C2×#471C2×C107semidirect
332. C2×#471C2×C107semidirect
333. #2955C2×C107semidirect
334. #2916C2×C107semidirect
335. #2070C2×C107semidirect
336. #2069C2×C107semidirect
337. #2049C2×C107semidirect
338. #2048C2×C107semidirect
339. #1977C2×C107semidirect
340. #1953C2×C107semidirect
341. #1903C2×C107semidirect
342. #1902C2×C107semidirect
343. #1813C2×C107semidirect
344. C107#24808direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#30692
C107×#30682
C2×#471×C1072
C107×#29552
C107×#29162
C107×#20702
C107×#20692
C107×#20492
C107×#20482
C107×#19772
C107×#19532
C107×#19032
C107×#19022
C107×#18132
#24808107