Finite Group Databasebeta

← C107×#25196 #41051160

Subgroups — C107×#25196 #41051160

Order 27392.

1032 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3068C211yesmaximal, characteristic, complemented
2C107×#3068C211yesmaximal, characteristic, complemented
3C107×#3019C211yesmaximal, characteristic, complemented
4C2×#453×C107C211yesmaximal, characteristic, complemented
5C107×#2956C211yesmaximal, characteristic, complemented
6C107×#2888C211yesmaximal, characteristic, complemented
7C107×#2069C211yesmaximal, characteristic, complemented
8C107×#2050C211yesmaximal, characteristic, complemented
9C107×#2048C211yesmaximal, characteristic, complemented
10C107×#2002C211yesmaximal, characteristic, complemented
11C107×#1965C211yesmaximal, characteristic, complemented
12C107×#1932C211yesmaximal, characteristic, complemented
13C107×#1914C211yesmaximal, characteristic, complemented
14C107×#1903C211yesmaximal, characteristic, complemented
15C107×#1861C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C107C2211yescharacteristic
17#575×C107C2211yescharacteristic
18#575×C107C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C107C2211yescharacteristic, complemented
22#568×C107C2211yescharacteristic
23#568×C107C2211yescharacteristic
24#568×C107C2211yescharacteristic, complemented
25#535×C107C2211yescharacteristic
26C2×#127×C107C2211yescharacteristic
27#472×C107—22no—
28#472×C107—22no—
29#471×C107—22no—
30#471×C107—22no—
31#455×C107—22no—
32#453×C107—22no—
33#453×C107—22no—
34#453×C107—22no—
35#444×C107—22no—
36#443×C107—22no—
37#430×C107C2211yescharacteristic, complemented
38#430×C107C2211yescharacteristic, complemented
39#430×C107C2211yescharacteristic, complemented
40#423×C107C2211yescharacteristic, complemented
41#421×C107C2211yescharacteristic
42#421×C107C2211yescharacteristic
43C2×#104×C107C2211yescharacteristic
44C2×#104×C107C2211yescharacteristic
45C2×#104×C107C2211yescharacteristic, complemented
46#418×C107C2211yescharacteristic, complemented
47#413×C107—22no—
48#413×C107C2211yescharacteristic
49#413×C107C2211yescharacteristic
50#413×C107C2211yescharacteristic, complemented
51C2×#100×C107—22no—
52C2×#100×C107C2211yescharacteristic
53C2×#100×C107C2211yescharacteristic
54C2×#100×C107C2211yescharacteristic
55C2×#100×C107C2211yescharacteristic
56C2×#100×C107C2211yescharacteristic, complemented
57C2×#100×C107C2211yescharacteristic, complemented
58C4×M16×C107C2211yescharacteristic, complemented
59#344×C107C2211yescharacteristic, complemented
60#344×C107C2211yescharacteristic, complemented
61#339×C107C2211yescharacteristic, complemented
62#338×C107C2211yescharacteristic, complemented
63H(5,𝔽2)×C107—22no—
64H(5,𝔽2)×C107—22no—
65H(5,𝔽2)×C107—41no—
66H(5,𝔽2)×C107—41no—
67C2×#41×C107—21no—
68C2×#41×C107—21no—
69C2×#41×C107C2311yescharacteristic
70C2×#41×C107C2311yescharacteristic
71C2×#41×C107C2311yescharacteristic
72C22×D4×C107—22no—
73C22×D4×C107—21no—
74C22×D4×C107—21no—
75C22×D4×C107—22no—
76C22×D4×C107C2311yescharacteristic
77C22×D4×C107C2311yescharacteristic
78#137×C107—21no—
79#137×C107—21no—
80#137×C107—21no—
81#137×C107D412yescomplemented
82AGL(1,ℤ/8)×C107—21no—
83AGL(1,ℤ/8)×C107—22no—
84AGL(1,ℤ/8)×C107—22no—
85AGL(1,ℤ/8)×C107—21no—
86AGL(1,ℤ/8)×C107—21no—
87AGL(1,ℤ/8)×C107—22no—
88AGL(1,ℤ/8)×C107—22no—
89AGL(1,ℤ/8)×C107—41no—
90AGL(1,ℤ/8)×C107—41no—
91AGL(1,ℤ/8)×C107D412yescomplemented
92#135×C107—22no—
93#135×C107—41no—
94C2×SD16×C107—21no—
95C2×SD16×C107—21no—
96C2×SD16×C107—21no—
97C2×D8×C107—21no—
98C2×D8×C107—21no—
99C2×D8×C107—21no—
100#131×C107—22no—
101#131×C107—22no—
102#131×C107—22no—
103#131×C107—22no—
104#131×C107—41no—
105#131×C107—41no—
106C2×M16×C107—22no—
107C2×M16×C107—22no—
108C2×M16×C107—41no—
109C2×M16×C107C2311yescharacteristic
110C2×M16×C107C2311yescharacteristic
111C2×M16×C107C2311yescharacteristic
112C2×M16×C107C2311yescharacteristic
113C2×M16×C107C2311yescharacteristic
114C2×M16×C107C2311yescharacteristic
115C2×M16×C107C2311yescharacteristic
116C2×M16×C107C2311yescharacteristic
117#127×C107—21no—
118#127×C107—21no—
119#127×C107—21no—
120#127×C107—41no—
121#124×C107—21no—
122#121×C107—41no—
123#120×C107—22no—
124#117×C107C2311yescharacteristic
125C2×C42×C107C2311yescharacteristic
126#108×C107—22no—
127#108×C107—22no—
128#108×C107—22no—
129C4⋊C8×C107—41no—
130#104×C107—22no—
131#104×C107—22no—
132#104×C107—21no—
133#104×C107—21no—
134#104×C107—21no—
135#104×C107—21no—
136#104×C107D412yescomplemented
137#104×C107D412yescomplemented
138#102×C107—41no—
139#101×C107—21no—
140#101×C107—21no—
141#101×C107D412yescomplemented
142#100×C107—21no—
143#100×C107—21no—
144#100×C107—22no—
145#100×C107—22no—
146#100×C107—22no—
147#100×C107—22no—
148#100×C107—22no—
149#100×C107—22no—
150#100×C107D412yescomplemented
151#97×C107—21no—
152C4×C8×C107—21no—
153C24×C107—22no—
154C24×C107—21no—
155C24×C107#4112yes—
156#41×C107—21no—
157#41×C107—21no—
158#41×C107—21no—
159#41×C107—21no—
160#41×C107—21no—
161#41×C107—21no—
162#41×C107—21no—
163#41×C107—21no—
164#41×C107—21no—
165#41×C107—21no—
166#41×C107—42no—
167#41×C107—42no—
168#41×C107—42no—
169#41×C107—42no—
170#41×C107C2×D412yes—
171#41×C107C2×D412yes—
172C2×Q8×C107C2×D411yescharacteristic
173C2×Q8×C107C2×D411yescharacteristic
174C2×Q8×C107#4111yescharacteristic
175C2×D4×C107—21no—
176C2×D4×C107—22no—
177C2×D4×C107—22no—
178C2×D4×C107—21no—
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—21no—
191C2×D4×C107—21no—
192C2×D4×C107—42no—
193C2×D4×C107—42no—
194C2×D4×C107—42no—
195C2×D4×C107—42no—
196C2×D4×C107—44no—
197C2×D4×C107—44no—
198C2×D4×C107—42no—
199C2×D4×C107—42no—
200C2×D4×C107—42no—
201C2×D4×C107—84no—
202C2×D4×C107C2×D411yescharacteristic
203C2×D4×C107C2×D411yescharacteristic
204C2×D4×C107#4111yescharacteristic
205C22×C4×C107—21no—
206C22×C4×C107—22no—
207C22×C4×C107—21no—
208C22×C4×C107—21no—
209C22×C4×C107—21no—
210C22×C4×C107C2411yescharacteristic
211Q16×C107—22no—
212Q16×C107—41no—
213SD16×C107—22no—
214SD16×C107—22no—
215SD16×C107—42no—
216SD16×C107—42no—
217SD16×C107—41no—
218SD16×C107—41no—
219SD16×C107—42no—
220D8×C107—22no—
221D8×C107—42no—
222D8×C107—42no—
223D8×C107—41no—
224D8×C107—42no—
225M16×C107—21no—
226M16×C107—21no—
227M16×C107—21no—
228M16×C107—21no—
229M16×C107—21no—
230M16×C107—21no—
231M16×C107—21no—
232M16×C107—21no—
233M16×C107—21no—
234M16×C107—21no—
235M16×C107—21no—
236M16×C107—21no—
237M16×C107—42no—
238M16×C107—42no—
239M16×C107—42no—
240M16×C107C2×D412yes—
241M16×C107C2×D412yes—
242M16×C107C2×D412yes—
243M16×C107C2×D412yes—
244C2×C8×C107—21no—
245C2×C8×C107—21no—
246C2×C8×C107—21no—
247C2×C8×C107—21no—
248C2×C8×C107—21no—
249C2×C8×C107—21no—
250C2×C8×C107—21no—
251C2×C8×C107—21no—
252C2×C8×C107—42no—
253C2×C8×C107—42no—
254C2×C8×C107—42no—
255C4⋊C4×C107—21no—
256C22⋊C4×C107—21no—
257C22⋊C4×C107—42no—
258C42×C107—21no—
259C42×C107—21no—
260C42×C107C2×D411yescharacteristic
261C42×C107C2×D411yescharacteristic
262C23×C107—21no—
263C23×C107—22no—
264C23×C107—21no—
265C23×C107—22no—
266C23×C107—21no—
267C23×C107—22no—
268C23×C107—44no—
269C23×C107—41no—
270C23×C107—41no—
271C23×C107—41no—
272C23×C107—82no—
273C23×C107—82no—
274C23×C107—162no—
275C23×C107C2×#4111yescharacteristic
276Q8×C107—21no—
277Q8×C107—21no—
278Q8×C107—21no—
279Q8×C107—21no—
280Q8×C107—21no—
281Q8×C107#12112yes—
282D4×C107—22no—
283D4×C107—22no—
284D4×C107—21no—
285D4×C107—21no—
286D4×C107—21no—
287D4×C107—21no—
288D4×C107—21no—
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—41no—
298D4×C107—41no—
299D4×C107—41no—
300D4×C107—41no—
301D4×C107—41no—
302D4×C107—41no—
303D4×C107—84no—
304D4×C107—84no—
305D4×C107—162no—
306D4×C107#12112yes—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—22no—
310C2×C4×C107—22no—
311C2×C4×C107—21no—
312C2×C4×C107—21no—
313C2×C4×C107—21no—
314C2×C4×C107—44no—
315C2×C4×C107—42no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—41no—
321C2×C4×C107C22×D411yescharacteristic
322C2×C4×C107C22×D411yescharacteristic
323C2×C4×C107C22×D411yescharacteristic
324C2×C4×C107C2×#4111yescharacteristic
325C2×C4×C107H(5,𝔽2)11yescharacteristic
326C2×C4×C107H(5,𝔽2)11yescharacteristic
327C8×C107—22no—
328C8×C107—22no—
329C8×C107—22no—
330C8×C107—22no—
331C8×C107—41no—
332C8×C107—41no—
333C8×C107—41no—
334C8×C107—41no—
335C22×C107—22no—
336C22×C107—41no—
337C22×C107—41no—
338C22×C107—41no—
339C22×C107—42no—
340C22×C107—81no—
341C22×C107—82no—
342C22×C107—81no—
343C22×C107—82no—
344C22×C107—82no—
345C22×C107—81no—
346C22×C107—82no—
347C22×C107—81no—
348C22×C107—161no—
349C22×C107—161no—
350C22×C107—164no—
351C22×C107#52511yescharacteristic
352C22×C107#54611yescharacteristic
353C22×C107#54611yescharacteristic
354C4×C107—22no—
355C4×C107—22no—
356C4×C107—41no—
357C4×C107—41no—
358C4×C107—41no—
359C4×C107—81no—
360C4×C107C2×#12111yescharacteristic
361C4×C107#53811yescharacteristic
362C4×C107D4211yescharacteristic
363C4×C107D4211yescharacteristic
364#25196C10711yesmaximal, characteristic, direct product factor, Sylow
365C2×C107—21no—
366C2×C107—21no—
367C2×C107—21no—
368C2×C107—42no—
369C2×C107—81no—
370C2×C107—82no—
371C2×C107—81no—
372C2×C107—161no—
373C2×C107#242411yescharacteristic
374#3068C2×C10711yescharacteristic, complemented
375#3068C2×C10711yescharacteristic, complemented
376#3019C2×C10711yescharacteristic, complemented
377C2×#453C2×C10711yescharacteristic, complemented
378#2956C2×C10711yescharacteristic, complemented
379#2888C2×C10711yescharacteristic, complemented
380#2069C2×C10711yescharacteristic, complemented
381#2050C2×C10711yescharacteristic, complemented
382#2048C2×C10711yescharacteristic, complemented
383#2002C2×C10711yescharacteristic, complemented
384#1965C2×C10711yescharacteristic, complemented
385#1932C2×C10711yescharacteristic, complemented
386#1914C2×C10711yescharacteristic, complemented
387#1903C2×C10711yescharacteristic, complemented
388#1861C2×C10711yescharacteristic, complemented
389C107#2519611yescharacteristic, direct product factor, Sylow
390C2×H(5,𝔽2)C22×C10711yescharacteristic
391#575C22×C10711yescharacteristic
392#575C22×C10711yescharacteristic
393C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
394C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
395C2×AGL(1,ℤ/8)C22×C10711yescharacteristic, complemented
396#568C22×C10711yescharacteristic
397#568C22×C10711yescharacteristic
398#568C22×C10711yescharacteristic, complemented
399#535C22×C10711yescharacteristic
400C2×#127C22×C10711yescharacteristic
401#472—22no—
402#472—22no—
403#471—22no—
404#471—22no—
405#455—22no—
406#453—22no—
407#453—22no—
408#453—22no—
409#444—22no—
410#443—22no—
411#430C22×C10711yescharacteristic, complemented
412#430C22×C10711yescharacteristic, complemented
413#430C22×C10711yescharacteristic, complemented
414#423C22×C10711yescharacteristic, complemented
415#421C22×C10711yescharacteristic
416#421C22×C10711yescharacteristic
417C2×#104C22×C10711yescharacteristic
418C2×#104C22×C10711yescharacteristic
419C2×#104C22×C10711yescharacteristic, complemented
420#418C22×C10711yescharacteristic, complemented
421#413—22no—
422#413C22×C10711yescharacteristic
423#413C22×C10711yescharacteristic
424#413C22×C10711yescharacteristic, complemented
425C2×#100—22no—
426C2×#100C22×C10711yescharacteristic
427C2×#100C22×C10711yescharacteristic
428C2×#100C22×C10711yescharacteristic
429C2×#100C22×C10711yescharacteristic
430C2×#100C22×C10711yescharacteristic, complemented
431C2×#100C22×C10711yescharacteristic, complemented
432C4×M16C22×C10711yescharacteristic, complemented
433#344C22×C10711yescharacteristic, complemented
434#344C22×C10711yescharacteristic, complemented
435#339C22×C10711yescharacteristic, complemented
436#338C22×C10711yescharacteristic, complemented
437H(5,𝔽2)—22no—
438H(5,𝔽2)—22no—
439H(5,𝔽2)—41no—
440H(5,𝔽2)—41no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41C23×C10711yescharacteristic
444C2×#41C23×C10711yescharacteristic
445C2×#41C23×C10711yescharacteristic
446C22×D4—22no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—22no—
450C22×D4C23×C10711yescharacteristic
451C22×D4C23×C10711yescharacteristic
452#137—21no—
453#137—21no—
454#137—21no—
455#137D4×C10712yescomplemented
456AGL(1,ℤ/8)—21no—
457AGL(1,ℤ/8)—22no—
458AGL(1,ℤ/8)—22no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—22no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—41no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)D4×C10712yescomplemented
466#135—22no—
467#135—41no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×D8—21no—
472C2×D8—21no—
473C2×D8—21no—
474#131—22no—
475#131—22no—
476#131—22no—
477#131—22no—
478#131—41no—
479#131—41no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16—41no—
483C2×M16C23×C10711yescharacteristic
484C2×M16C23×C10711yescharacteristic
485C2×M16C23×C10711yescharacteristic
486C2×M16C23×C10711yescharacteristic
487C2×M16C23×C10711yescharacteristic
488C2×M16C23×C10711yescharacteristic
489C2×M16C23×C10711yescharacteristic
490C2×M16C23×C10711yescharacteristic
491#127—21no—
492#127—21no—
493#127—21no—
494#127—41no—
495#124—21no—
496#121—41no—
497#120—22no—
498#117C23×C10711yescharacteristic
499C2×C42C23×C10711yescharacteristic
500#108—22no—
501#108—22no—
502#108—22no—
503C4⋊C8—41no—
504#104—22no—
505#104—22no—
506#104—21no—
507#104—21no—
508#104—21no—
509#104—21no—
510#104D4×C10712yescomplemented
511#104D4×C10712yescomplemented
512#102—41no—
513#101—21no—
514#101—21no—
515#101D4×C10712yescomplemented
516#100—21no—
517#100—21no—
518#100—22no—
519#100—22no—
520#100—22no—
521#100—22no—
522#100—22no—
523#100—22no—
524#100D4×C10712yescomplemented
525#97—21no—
526C4×C8—21no—
527C24—22no—
528C24—21no—
529C24#41×C10712yes—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41C2×D4×C10712yes—
545#41C2×D4×C10712yes—
546C2×Q8C2×D4×C10711yescharacteristic
547C2×Q8C2×D4×C10711yescharacteristic
548C2×Q8#41×C10711yescharacteristic
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—84no—
576C2×D4C2×D4×C10711yescharacteristic
577C2×D4C2×D4×C10711yescharacteristic
578C2×D4#41×C10711yescharacteristic
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C10711yescharacteristic
585Q16—22no—
586Q16—41no—
587SD16—22no—
588SD16—22no—
589SD16—42no—
590SD16—42no—
591SD16—41no—
592SD16—41no—
593SD16—42no—
594D8—22no—
595D8—42no—
596D8—42no—
597D8—41no—
598D8—42no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—42no—
612M16—42no—
613M16—42no—
614M16C2×D4×C10712yes—
615M16C2×D4×C10712yes—
616M16C2×D4×C10712yes—
617M16C2×D4×C10712yes—
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—42no—
627C2×C8—42no—
628C2×C8—42no—
629C4⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—42no—
632C42—21no—
633C42—21no—
634C42C2×D4×C10711yescharacteristic
635C42C2×D4×C10711yescharacteristic
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—44no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—82no—
647C23—82no—
648C23—162no—
649C23C2×#41×C10711yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8#121×C10712yes—
656D4—22no—
657D4—22no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—44no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—162no—
680D4#121×C10712yes—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4C22×D4×C10711yescharacteristic
696C2×C4C22×D4×C10711yescharacteristic
697C2×C4C22×D4×C10711yescharacteristic
698C2×C4C2×#41×C10711yescharacteristic
699C2×C4H(5,𝔽2)×C10711yescharacteristic
700C2×C4H(5,𝔽2)×C10711yescharacteristic
701C8—22no—
702C8—22no—
703C8—22no—
704C8—22no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—81no—
715C22—82no—
716C22—81no—
717C22—82no—
718C22—82no—
719C22—81no—
720C22—82no—
721C22—81no—
722C22—161no—
723C22—161no—
724C22—164no—
725C22#525×C10711yescharacteristic
726C22#546×C10711yescharacteristic
727C22#546×C10711yescharacteristic
728C4—22no—
729C4—22no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4C2×#121×C10711yescharacteristic
735C4#538×C10711yescharacteristic
736C4D42×C10711yescharacteristic
737C4D42×C10711yescharacteristic
738C2—21no—
739C2—21no—
740C2—21no—
741C2—42no—
742C2—82no—
743C2—81no—
744C2—81no—
745C2—161no—
746C2C107×#242411yescharacteristic
subgroupG/H
center, socleC2×C107#2424
commutator, Frattini, cosocleC22×C4C24×C107
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×#3068C2semidirect
2. C107×#3068C2semidirect
3. C107×#3019C2semidirect
4. C2×#453×C107C2semidirect
5. C107×#2956C2semidirect
6. C107×#2888C2semidirect
7. C107×#2069C2semidirect
8. C107×#2050C2semidirect
9. C107×#2048C2semidirect
10. C107×#2002C2semidirect
11. C107×#1965C2semidirect
12. C107×#1932C2semidirect
13. C107×#1914C2semidirect
14. C107×#1903C2semidirect
15. C107×#1861C2semidirect
21. C2×AGL(1,ℤ/8)×C107C22semidirect
24. #568×C107C22semidirect
37. #430×C107C22semidirect
38. #430×C107C22semidirect
39. #430×C107C22semidirect
40. #423×C107C22semidirect
45. C2×#104×C107C22semidirect
46. #418×C107C22semidirect
50. #413×C107C22semidirect
56. C2×#100×C107C22semidirect
57. C2×#100×C107C22semidirect
58. C4×M16×C107C22semidirect
59. #344×C107C22semidirect
60. #344×C107C22semidirect
61. #339×C107C22semidirect
62. #338×C107C22semidirect
81. #137×C107D4semidirect
91. AGL(1,ℤ/8)×C107D4semidirect
136. #104×C107D4semidirect
137. #104×C107D4semidirect
141. #101×C107D4semidirect
150. #100×C107D4semidirect
364. #25196C107direct (N × H)
374. #3068C2×C107semidirect
375. #3068C2×C107semidirect
376. #3019C2×C107semidirect
377. C2×#453C2×C107semidirect
378. #2956C2×C107semidirect
379. #2888C2×C107semidirect
380. #2069C2×C107semidirect
381. #2050C2×C107semidirect
382. #2048C2×C107semidirect
383. #2002C2×C107semidirect
384. #1965C2×C107semidirect
385. #1932C2×C107semidirect
386. #1914C2×C107semidirect
387. #1903C2×C107semidirect
388. #1861C2×C107semidirect
389. C107#25196direct (N × H)
395. C2×AGL(1,ℤ/8)C22×C107semidirect
398. #568C22×C107semidirect
411. #430C22×C107semidirect
412. #430C22×C107semidirect
413. #430C22×C107semidirect
414. #423C22×C107semidirect
419. C2×#104C22×C107semidirect
420. #418C22×C107semidirect
424. #413C22×C107semidirect
430. C2×#100C22×C107semidirect
431. C2×#100C22×C107semidirect
432. C4×M16C22×C107semidirect
433. #344C22×C107semidirect
434. #344C22×C107semidirect
435. #339C22×C107semidirect
436. #338C22×C107semidirect
455. #137D4×C107semidirect
465. AGL(1,ℤ/8)D4×C107semidirect
510. #104D4×C107semidirect
511. #104D4×C107semidirect
515. #101D4×C107semidirect
524. #100D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#30682
C107×#30192
C2×#453×C1072
C107×#29562
C107×#28882
C107×#20692
C107×#20502
C107×#20482
C107×#20022
C107×#19652
C107×#19322
C107×#19142
C107×#19032
C107×#18612
#25196107