Finite Group Databasebeta

← C107×#24524 #41050488

Subgroups — C107×#24524 #41050488

Order 27392.

884 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3094C211yesmaximal, characteristic, complemented
2C2×#449×C107C211yesmaximal, characteristic
3C107×#2924C211yesmaximal, characteristic, complemented
4C107×#2896C211yesmaximal, characteristic, complemented
5C107×#2064C211yesmaximal, characteristic, complemented
6C107×#2063C211yesmaximal, characteristic, complemented
7C107×#2046C211yesmaximal, characteristic, complemented
8C107×#2045C211yesmaximal, characteristic, complemented
9C107×#1978C211yesmaximal, characteristic, complemented
10C107×#1977C211yesmaximal, characteristic, complemented
11C107×#1931C211yesmaximal, characteristic, complemented
12C107×#1930C211yesmaximal, characteristic, complemented
13C107×#1900C211yesmaximal, characteristic, complemented
14C107×#1855C211yesmaximal, characteristic, complemented
15C107×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×D8×C107C2211yescharacteristic
19C22×M16×C107C2211yescharacteristic
20C2×#121×C107C2211yescharacteristic
21C2×#117×C107C2211yescharacteristic
22#482×C107—21no—
23#482×C107—21no—
24#481×C107—21no—
25#480×C107—21no—
26#449×C107—21no—
27#449×C107—21no—
28#449×C107—21no—
29#449×C107—21no—
30#433×C107—21no—
31#433×C107—21no—
32#432×C107—21no—
33#431×C107—21no—
34C2×#108×C107C2211yescharacteristic
35C2×#108×C107C2211yescharacteristic
36#428×C107C2211yescharacteristic
37#428×C107C2211yescharacteristic
38#424×C107C2211yescharacteristic
39#424×C107C2211yescharacteristic
40#419×C107C2211yescharacteristic
41#419×C107C2211yescharacteristic
42#418×C107C2211yescharacteristic
43#418×C107C2211yescharacteristic
44#418×C107C2211yescharacteristic
45#418×C107C2211yescharacteristic
46#417×C107—21no—
47#417×C107—21no—
48#416×C107—21no—
49#416×C107—21no—
50C2×#103×C107C2211yescharacteristic
51C2×#102×C107C2211yescharacteristic
52C2×#101×C107C2211yescharacteristic
53C2×#101×C107C2211yescharacteristic
54C2×#100×C107C2211yescharacteristic
55C2×#100×C107C2211yescharacteristic
56C2×#100×C107C2211yescharacteristic
57C2×#100×C107C2211yescharacteristic
58#407×C107C2211yescharacteristic
59#407×C107C2211yescharacteristic
60C2×C22⋊C8×C107C2211yescharacteristic
61#405×C107C2211yescharacteristic
62#405×C107C2211yescharacteristic
63#343×C107C2211yescharacteristic
64#343×C107C2211yescharacteristic
65#341×C107C2211yescharacteristic
66#341×C107C2211yescharacteristic
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—21no—
70C2×#41×C107—21no—
71C2×#41×C107—21no—
72C2×#41×C107—21no—
73C2×#41×C107—41no—
74C2×#41×C107—41no—
75C22×Q8×C107C2311yescharacteristic
76C22×D4×C107—21no—
77C22×D4×C107—21no—
78C22×D4×C107C2311yescharacteristic
79C22×D4×C107C2311yescharacteristic
80C23×C4×C107—21no—
81C23×C4×C107C2311yescharacteristic
82C2×SD16×C107—22no—
83C2×SD16×C107—21no—
84C2×SD16×C107—21no—
85C2×SD16×C107—41no—
86C2×D8×C107—22no—
87C2×D8×C107—21no—
88C2×D8×C107—21no—
89C2×D8×C107—41no—
90C2×M16×C107—21no—
91C2×M16×C107—41no—
92C2×M16×C107—41no—
93C2×M16×C107C2311yescharacteristic
94C2×M16×C107C2311yescharacteristic
95C2×M16×C107C2311yescharacteristic
96C2×M16×C107C2311yescharacteristic
97C2×M16×C107C2311yescharacteristic
98C2×M16×C107C2311yescharacteristic
99C22×C8×C107—21no—
100C22×C8×C107C2311yescharacteristic
101C22×C8×C107C2311yescharacteristic
102#121×C107—21no—
103#121×C107—21no—
104#121×C107—21no—
105#121×C107—21no—
106#117×C107—21no—
107#117×C107—21no—
108#117×C107D411yescharacteristic
109#117×C107D411yescharacteristic
110#117×C107C2311yescharacteristic
111#117×C107C2311yescharacteristic
112C2×C4⋊C4×C107D411yescharacteristic
113C2×C4⋊C4×C107D411yescharacteristic
114C2×C4⋊C4×C107C2311yescharacteristic
115C2×C22⋊C4×C107—21no—
116C2×C22⋊C4×C107—21no—
117C2×C42×C107—21no—
118#108×C107—41no—
119#108×C107—41no—
120#107×C107—21no—
121#107×C107—21no—
122#106×C107—21no—
123#106×C107—21no—
124C4⋊C8×C107—21no—
125C4⋊C8×C107—21no—
126C4⋊C8×C107—21no—
127C4⋊C8×C107—21no—
128#103×C107—21no—
129#103×C107—21no—
130#103×C107—21no—
131#103×C107—21no—
132#103×C107—21no—
133#103×C107—21no—
134#102×C107—21no—
135#102×C107—21no—
136#102×C107—21no—
137#102×C107—21no—
138#102×C107—21no—
139#102×C107—21no—
140#102×C107—21no—
141#102×C107—21no—
142#102×C107—21no—
143#102×C107—21no—
144#101×C107—22no—
145#101×C107—41no—
146#100×C107—22no—
147#100×C107—41no—
148#100×C107—41no—
149#100×C107—41no—
150C22⋊C8×C107—21no—
151C22⋊C8×C107—21no—
152C22⋊C8×C107—21no—
153C22⋊C8×C107—21no—
154C22⋊C8×C107D411yescharacteristic
155C22⋊C8×C107D411yescharacteristic
156C22⋊C8×C107D411yescharacteristic
157C22⋊C8×C107D411yescharacteristic
158#97×C107—21no—
159#97×C107—21no—
160C4×C8×C107—21no—
161C4×C8×C107—21no—
162C24×C107—21no—
163C24×C107—21no—
164C24×C107#4111yescharacteristic
165#41×C107—24no—
166#41×C107—24no—
167#41×C107—42no—
168#41×C107—42no—
169#41×C107—42no—
170#41×C107—42no—
171#41×C107—42no—
172#41×C107—42no—
173C2×Q8×C107—21no—
174C2×Q8×C107—21no—
175C2×Q8×C107—21no—
176C2×Q8×C107—21no—
177C2×Q8×C107—21no—
178C2×Q8×C107#4112yes—
179C2×D4×C107—21no—
180C2×D4×C107—21no—
181C2×D4×C107—21no—
182C2×D4×C107—21no—
183C2×D4×C107—21no—
184C2×D4×C107—21no—
185C2×D4×C107—21no—
186C2×D4×C107—21no—
187C2×D4×C107—21no—
188C2×D4×C107—21no—
189C2×D4×C107—21no—
190C2×D4×C107—42no—
191C2×D4×C107—42no—
192C2×D4×C107—41no—
193C2×D4×C107—41no—
194C2×D4×C107—41no—
195C2×D4×C107—41no—
196C2×D4×C107—82no—
197C2×D4×C107#4112yes—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—21no—
205C22×C4×C107—21no—
206C22×C4×C107—42no—
207C22×C4×C107—42no—
208C22×C4×C107—41no—
209C22×C4×C107—41no—
210C22×C4×C107C2×D411yescharacteristic
211C22×C4×C107C2×D411yescharacteristic
212C22×C4×C107C2×D411yescharacteristic
213C22×C4×C107C2×D411yescharacteristic
214C22×C4×C107#4111yescharacteristic
215C22×C4×C107C2411yescharacteristic
216SD16×C107—42no—
217SD16×C107—42no—
218D8×C107—42no—
219D8×C107—42no—
220M16×C107—21no—
221M16×C107—21no—
222M16×C107—21no—
223M16×C107—21no—
224M16×C107—21no—
225M16×C107—21no—
226M16×C107—21no—
227M16×C107—21no—
228M16×C107—21no—
229M16×C107—21no—
230M16×C107—21no—
231M16×C107—21no—
232M16×C107—42no—
233C2×C8×C107—21no—
234C2×C8×C107—21no—
235C2×C8×C107—21no—
236C2×C8×C107—21no—
237C2×C8×C107—21no—
238C2×C8×C107—21no—
239C2×C8×C107—21no—
240C2×C8×C107—21no—
241C2×C8×C107—21no—
242C2×C8×C107—21no—
243C2×C8×C107—42no—
244C2×C8×C107C2×D411yescharacteristic
245C2×C8×C107C2×D411yescharacteristic
246C2×C8×C107C2×D411yescharacteristic
247C2×C8×C107C2×D411yescharacteristic
248C4⋊C4×C107—21no—
249C4⋊C4×C107—21no—
250C4⋊C4×C107—21no—
251C4⋊C4×C107—21no—
252C4⋊C4×C107C2×D411yescharacteristic
253C4⋊C4×C107C2×D411yescharacteristic
254C4⋊C4×C107C2×D411yescharacteristic
255C4⋊C4×C107C2×D411yescharacteristic
256C22⋊C4×C107—21no—
257C22⋊C4×C107—21no—
258C22⋊C4×C107—21no—
259C22⋊C4×C107—21no—
260C22⋊C4×C107—41no—
261C22⋊C4×C107—41no—
262C42×C107—21no—
263C42×C107—21no—
264C42×C107—21no—
265C42×C107—21no—
266C23×C107—21no—
267C23×C107—21no—
268C23×C107—22no—
269C23×C107—41no—
270C23×C107—41no—
271C23×C107—41no—
272C23×C107—41no—
273C23×C107—41no—
274C23×C107—41no—
275C23×C107—41no—
276C23×C107—81no—
277C23×C107—81no—
278C23×C107—81no—
279C23×C107—81no—
280C23×C107#12111yescharacteristic
281C23×C107#12111yescharacteristic
282C23×C107C2×#4111yescharacteristic
283Q8×C107—22no—
284Q8×C107—22no—
285Q8×C107—41no—
286Q8×C107—41no—
287D4×C107—22no—
288D4×C107—22no—
289D4×C107—44no—
290D4×C107—44no—
291D4×C107—41no—
292D4×C107—41no—
293D4×C107—41no—
294D4×C107—41no—
295D4×C107—41no—
296D4×C107—41no—
297D4×C107—82no—
298D4×C107—82no—
299C2×C4×C107—21no—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
312C2×C4×C107—21no—
313C2×C4×C107—22no—
314C2×C4×C107—44no—
315C2×C4×C107—44no—
316C2×C4×C107—42no—
317C2×C4×C107—41no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—81no—
321C2×C4×C107—81no—
322C2×C4×C107#12111yescharacteristic
323C2×C4×C107#12111yescharacteristic
324C2×C4×C107C22×D411yescharacteristic
325C2×C4×C107C22×D411yescharacteristic
326C2×C4×C107C2×#4111yescharacteristic
327C2×C4×C107C2×#4111yescharacteristic
328C2×C4×C107H(5,𝔽2)11yescharacteristic
329C2×C4×C107H(5,𝔽2)11yescharacteristic
330C8×C107—21no—
331C8×C107—21no—
332C8×C107—21no—
333C8×C107—21no—
334C8×C107—41no—
335C8×C107—41no—
336C8×C107—41no—
337C8×C107—41no—
338C8×C107—41no—
339C8×C107—41no—
340C22×C107—21no—
341C22×C107—21no—
342C22×C107—21no—
343C22×C107—21no—
344C22×C107—21no—
345C22×C107—21no—
346C22×C107—21no—
347C22×C107—21no—
348C22×C107—42no—
349C22×C107—81no—
350C22×C107—81no—
351C22×C107—82no—
352C22×C107—82no—
353C22×C107—81no—
354C22×C107—81no—
355C22×C107—81no—
356C22×C107—81no—
357C22×C107—81no—
358C22×C107—161no—
359C22×C107—161no—
360C22×C107C2×#12111yescharacteristic
361C22×C107#55111yescharacteristic
362C22×C107#55111yescharacteristic
363C4×C107—21no—
364C4×C107—21no—
365C4×C107—42no—
366C4×C107—41no—
367C4×C107—41no—
368C4×C107—41no—
369C4×C107—41no—
370C4×C107—81no—
371C4×C107#52511yescharacteristic
372C4×C107#53511yescharacteristic
373C4×C107#54611yescharacteristic
374C4×C107#54611yescharacteristic
375#24524C10711yesmaximal, characteristic, direct product factor, Sylow
376C2×C107—21no—
377C2×C107—21no—
378C2×C107—41no—
379C2×C107—41no—
380C2×C107—82no—
381C2×C107—161no—
382C2×C107#241111yescharacteristic
383C2×C107#306711yescharacteristic
384C2×C107#306811yescharacteristic
385#3094C2×C10711yescharacteristic, complemented
386C2×#449C2×C10711yescharacteristic
387#2924C2×C10711yescharacteristic, complemented
388#2896C2×C10711yescharacteristic, complemented
389#2064C2×C10711yescharacteristic, complemented
390#2063C2×C10711yescharacteristic, complemented
391#2046C2×C10711yescharacteristic, complemented
392#2045C2×C10711yescharacteristic, complemented
393#1978C2×C10711yescharacteristic, complemented
394#1977C2×C10711yescharacteristic, complemented
395#1931C2×C10711yescharacteristic, complemented
396#1930C2×C10711yescharacteristic, complemented
397#1900C2×C10711yescharacteristic, complemented
398#1855C2×C10711yescharacteristic, complemented
399#1785C2×C10711yescharacteristic, complemented
400C107#2452411yescharacteristic, direct product factor, Sylow
401C22×#41C22×C10711yescharacteristic
402C22×SD16C22×C10711yescharacteristic
403C22×D8C22×C10711yescharacteristic
404C22×M16C22×C10711yescharacteristic
405C2×#121C22×C10711yescharacteristic
406C2×#117C22×C10711yescharacteristic
407#482—21no—
408#482—21no—
409#481—21no—
410#480—21no—
411#449—21no—
412#449—21no—
413#449—21no—
414#449—21no—
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108C22×C10711yescharacteristic
420C2×#108C22×C10711yescharacteristic
421#428C22×C10711yescharacteristic
422#428C22×C10711yescharacteristic
423#424C22×C10711yescharacteristic
424#424C22×C10711yescharacteristic
425#419C22×C10711yescharacteristic
426#419C22×C10711yescharacteristic
427#418C22×C10711yescharacteristic
428#418C22×C10711yescharacteristic
429#418C22×C10711yescharacteristic
430#418C22×C10711yescharacteristic
431#417—21no—
432#417—21no—
433#416—21no—
434#416—21no—
435C2×#103C22×C10711yescharacteristic
436C2×#102C22×C10711yescharacteristic
437C2×#101C22×C10711yescharacteristic
438C2×#101C22×C10711yescharacteristic
439C2×#100C22×C10711yescharacteristic
440C2×#100C22×C10711yescharacteristic
441C2×#100C22×C10711yescharacteristic
442C2×#100C22×C10711yescharacteristic
443#407C22×C10711yescharacteristic
444#407C22×C10711yescharacteristic
445C2×C22⋊C8C22×C10711yescharacteristic
446#405C22×C10711yescharacteristic
447#405C22×C10711yescharacteristic
448#343C22×C10711yescharacteristic
449#343C22×C10711yescharacteristic
450#341C22×C10711yescharacteristic
451#341C22×C10711yescharacteristic
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—41no—
459C2×#41—41no—
460C22×Q8C23×C10711yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C23×C10711yescharacteristic
464C22×D4C23×C10711yescharacteristic
465C23×C4—21no—
466C23×C4C23×C10711yescharacteristic
467C2×SD16—22no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—41no—
471C2×D8—22no—
472C2×D8—21no—
473C2×D8—21no—
474C2×D8—41no—
475C2×M16—21no—
476C2×M16—41no—
477C2×M16—41no—
478C2×M16C23×C10711yescharacteristic
479C2×M16C23×C10711yescharacteristic
480C2×M16C23×C10711yescharacteristic
481C2×M16C23×C10711yescharacteristic
482C2×M16C23×C10711yescharacteristic
483C2×M16C23×C10711yescharacteristic
484C22×C8—21no—
485C22×C8C23×C10711yescharacteristic
486C22×C8C23×C10711yescharacteristic
487#121—21no—
488#121—21no—
489#121—21no—
490#121—21no—
491#117—21no—
492#117—21no—
493#117D4×C10711yescharacteristic
494#117D4×C10711yescharacteristic
495#117C23×C10711yescharacteristic
496#117C23×C10711yescharacteristic
497C2×C4⋊C4D4×C10711yescharacteristic
498C2×C4⋊C4D4×C10711yescharacteristic
499C2×C4⋊C4C23×C10711yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503#108—41no—
504#108—41no—
505#107—21no—
506#107—21no—
507#106—21no—
508#106—21no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513#103—21no—
514#103—21no—
515#103—21no—
516#103—21no—
517#103—21no—
518#103—21no—
519#102—21no—
520#102—21no—
521#102—21no—
522#102—21no—
523#102—21no—
524#102—21no—
525#102—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529#101—22no—
530#101—41no—
531#100—22no—
532#100—41no—
533#100—41no—
534#100—41no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8D4×C10711yescharacteristic
540C22⋊C8D4×C10711yescharacteristic
541C22⋊C8D4×C10711yescharacteristic
542C22⋊C8D4×C10711yescharacteristic
543#97—21no—
544#97—21no—
545C4×C8—21no—
546C4×C8—21no—
547C24—21no—
548C24—21no—
549C24#41×C10711yescharacteristic
550#41—24no—
551#41—24no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—42no—
557#41—42no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8#41×C10712yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—82no—
582C2×D4#41×C10712yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4C2×D4×C10711yescharacteristic
596C22×C4C2×D4×C10711yescharacteristic
597C22×C4C2×D4×C10711yescharacteristic
598C22×C4C2×D4×C10711yescharacteristic
599C22×C4#41×C10711yescharacteristic
600C22×C4C24×C10711yescharacteristic
601SD16—42no—
602SD16—42no—
603D8—42no—
604D8—42no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—42no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—42no—
629C2×C8C2×D4×C10711yescharacteristic
630C2×C8C2×D4×C10711yescharacteristic
631C2×C8C2×D4×C10711yescharacteristic
632C2×C8C2×D4×C10711yescharacteristic
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4C2×D4×C10711yescharacteristic
638C4⋊C4C2×D4×C10711yescharacteristic
639C4⋊C4C2×D4×C10711yescharacteristic
640C4⋊C4C2×D4×C10711yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—81no—
662C23—81no—
663C23—81no—
664C23—81no—
665C23#121×C10711yescharacteristic
666C23#121×C10711yescharacteristic
667C23C2×#41×C10711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—44no—
675D4—44no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—82no—
683D4—82no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4#121×C10711yescharacteristic
708C2×C4#121×C10711yescharacteristic
709C2×C4C22×D4×C10711yescharacteristic
710C2×C4C22×D4×C10711yescharacteristic
711C2×C4C2×#41×C10711yescharacteristic
712C2×C4C2×#41×C10711yescharacteristic
713C2×C4H(5,𝔽2)×C10711yescharacteristic
714C2×C4H(5,𝔽2)×C10711yescharacteristic
715C8—21no—
716C8—21no—
717C8—21no—
718C8—21no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—82no—
737C22—82no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—161no—
744C22—161no—
745C22C2×#121×C10711yescharacteristic
746C22#551×C10711yescharacteristic
747C22#551×C10711yescharacteristic
748C4—21no—
749C4—21no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—81no—
756C4#525×C10711yescharacteristic
757C4#535×C10711yescharacteristic
758C4#546×C10711yescharacteristic
759C4#546×C10711yescharacteristic
760C2—21no—
761C2—21no—
762C2—41no—
763C2—41no—
764C2—82no—
765C2—161no—
766C2C107×#241111yescharacteristic
767C2C107×#306711yescharacteristic
768C2C107×#306811yescharacteristic
subgroupG/H
center, socleC22×C107C2×#121
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#449×C107C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3094C2semidirect
3. C107×#2924C2semidirect
4. C107×#2896C2semidirect
5. C107×#2064C2semidirect
6. C107×#2063C2semidirect
7. C107×#2046C2semidirect
8. C107×#2045C2semidirect
9. C107×#1978C2semidirect
10. C107×#1977C2semidirect
11. C107×#1931C2semidirect
12. C107×#1930C2semidirect
13. C107×#1900C2semidirect
14. C107×#1855C2semidirect
15. C107×#1785C2semidirect
375. #24524C107direct (N × H)
385. #3094C2×C107semidirect
387. #2924C2×C107semidirect
388. #2896C2×C107semidirect
389. #2064C2×C107semidirect
390. #2063C2×C107semidirect
391. #2046C2×C107semidirect
392. #2045C2×C107semidirect
393. #1978C2×C107semidirect
394. #1977C2×C107semidirect
395. #1931C2×C107semidirect
396. #1930C2×C107semidirect
397. #1900C2×C107semidirect
398. #1855C2×C107semidirect
399. #1785C2×C107semidirect
400. C107#24524direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#30942
C2×#449×C1072
C107×#29242
C107×#28962
C107×#20642
C107×#20632
C107×#20462
C107×#20452
C107×#19782
C107×#19772
C107×#19312
C107×#19302
C107×#19002
C107×#18552
C107×#17852
#24524107