Finite Group Databasebeta

← C107×#25446 #41051410

Subgroups — C107×#25446 #41051410

Order 27392.

876 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3154C211yesmaximal, characteristic, complemented
2C107×#3069C211yesmaximal, characteristic, complemented
3C107×#3068C211yesmaximal, characteristic, complemented
4C107×#3067C211yesmaximal, characteristic, complemented
5C2×#471×C107C211yesmaximal, characteristic, complemented
6C107×#2957C211yesmaximal, characteristic, complemented
7C107×#2049C211yesmaximal, characteristic, complemented
8C107×#2048C211yesmaximal, characteristic, complemented
9C107×#2009C211yesmaximal, characteristic, complemented
10C107×#2008C211yesmaximal, characteristic, complemented
11C107×#1977C211yesmaximal, characteristic, complemented
12C107×#1953C211yesmaximal, characteristic, complemented
13C107×#1915C211yesmaximal, characteristic, complemented
14C107×#1914C211yesmaximal, characteristic, complemented
15C107×#1757C211yesmaximal, characteristic, complemented
16#575×C107C2211yescharacteristic
17#575×C107C2211yescharacteristic
18C2×#137×C107C2211yescharacteristic
19C2×#137×C107C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
22C2×#135×C107C2211yescharacteristic
23C22×SD16×C107C2211yescharacteristic
24#568×C107C2211yescharacteristic
25#568×C107C2211yescharacteristic
26C2×#131×C107C2211yescharacteristic
27#536×C107C2211yescharacteristic
28#535×C107C2211yescharacteristic
29#497×C107—21no—
30#496×C107—21no—
31#495×C107—21no—
32#492×C107—21no—
33#473×C107—21no—
34#473×C107—22no—
35#472×C107—21no—
36#472×C107—22no—
37#471×C107—21no—
38#471×C107—21no—
39#471×C107—22no—
40#471×C107—22no—
41#471×C107—22no—
42#471×C107—22no—
43#444×C107—22no—
44#443×C107—22no—
45#430×C107C2211yescharacteristic
46#430×C107C2211yescharacteristic
47C2×#108×C107C2211yescharacteristic
48C2×#108×C107C2211yescharacteristic
49#421×C107C2211yescharacteristic
50#421×C107C2211yescharacteristic
51#419×C107C2211yescharacteristic
52#418×C107C2211yescharacteristic
53#413×C107C2211yescharacteristic
54#413×C107C2211yescharacteristic
55#413×C107C2211yescharacteristic
56C2×#101×C107C2211yescharacteristic
57C2×#101×C107C2211yescharacteristic
58C2×#100×C107C2211yescharacteristic
59C2×#100×C107C2211yescharacteristic
60#410×C107C2211yescharacteristic
61#405×C107C2211yescharacteristic
62#405×C107C2211yescharacteristic
63#344×C107C2211yescharacteristic
64#344×C107C2211yescharacteristic
65#344×C107C2211yescharacteristic
66#344×C107C2211yescharacteristic
67C2×#41×C107C2311yescharacteristic
68C2×#41×C107C2311yescharacteristic
69C2×#41×C107C2311yescharacteristic
70C22×Q8×C107C2311yescharacteristic
71C22×D4×C107C2311yescharacteristic
72#137×C107—21no—
73#137×C107—21no—
74#137×C107—21no—
75#137×C107—21no—
76#137×C107—22no—
77#137×C107—22no—
78#137×C107—41no—
79#137×C107—41no—
80AGL(1,ℤ/8)×C107—21no—
81AGL(1,ℤ/8)×C107—21no—
82AGL(1,ℤ/8)×C107—21no—
83AGL(1,ℤ/8)×C107—21no—
84AGL(1,ℤ/8)×C107—22no—
85AGL(1,ℤ/8)×C107—22no—
86AGL(1,ℤ/8)×C107—41no—
87AGL(1,ℤ/8)×C107—41no—
88#135×C107—21no—
89#135×C107—21no—
90#135×C107—21no—
91#135×C107—21no—
92#135×C107—41no—
93#135×C107—41no—
94C2×Q16×C107—21no—
95C2×Q16×C107—21no—
96C2×Q16×C107D411yescharacteristic
97C2×SD16×C107—21no—
98C2×SD16×C107—21no—
99C2×SD16×C107—21no—
100C2×SD16×C107—21no—
101C2×SD16×C107—21no—
102C2×SD16×C107—21no—
103C2×SD16×C107—21no—
104C2×SD16×C107—21no—
105C2×SD16×C107—21no—
106C2×SD16×C107—21no—
107C2×SD16×C107D411yescharacteristic
108C2×SD16×C107D411yescharacteristic
109C2×D8×C107—21no—
110C2×D8×C107—21no—
111C2×D8×C107D411yescharacteristic
112#131×C107—22no—
113#131×C107—22no—
114#131×C107—22no—
115#131×C107—22no—
116#131×C107—21no—
117#131×C107—21no—
118#131×C107—21no—
119#131×C107—21no—
120C2×M16×C107—21no—
121C2×M16×C107—41no—
122C2×M16×C107—41no—
123C2×M16×C107C2311yescharacteristic
124C2×M16×C107C2311yescharacteristic
125C2×M16×C107C2311yescharacteristic
126C2×M16×C107C2311yescharacteristic
127C2×M16×C107C2311yescharacteristic
128C2×M16×C107C2311yescharacteristic
129C2×M16×C107C2311yescharacteristic
130C22×C8×C107—21no—
131C22×C8×C107C2311yescharacteristic
132C4⋊Q8×C107—21no—
133#127×C107—21no—
134#124×C107—21no—
135#124×C107—21no—
136#123×C107—22no—
137C22⋊Q8×C107—41no—
138#121×C107—41no—
139#120×C107—22no—
140#117×C107C2311yescharacteristic
141#117×C107C2311yescharacteristic
142#108×C107—22no—
143#108×C107—22no—
144#108×C107—21no—
145#108×C107—21no—
146#108×C107D412yescomplemented
147#108×C107D412yescomplemented
148#104×C107—22no—
149#104×C107—22no—
150#103×C107—41no—
151#102×C107—41no—
152#101×C107—21no—
153#101×C107—21no—
154#101×C107—22no—
155#101×C107—22no—
156#101×C107D412yescomplemented
157#100×C107—21no—
158#100×C107—21no—
159#100×C107—22no—
160#100×C107—22no—
161#100×C107D412yescomplemented
162#99×C107—22no—
163#97×C107—21no—
164#97×C107—21no—
165C4×C8×C107—21no—
166C4×C8×C107—21no—
167C24×C107—21no—
168#41×C107—21no—
169#41×C107—21no—
170#41×C107—21no—
171#41×C107—21no—
172#41×C107—21no—
173#41×C107—21no—
174#41×C107—21no—
175#41×C107—21no—
176#41×C107—21no—
177#41×C107—21no—
178#41×C107—21no—
179#41×C107—21no—
180C2×Q8×C107—21no—
181C2×Q8×C107—21no—
182C2×Q8×C107—21no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107C2×D411yescharacteristic
187C2×Q8×C107C2×D411yescharacteristic
188C2×Q8×C107C2×D411yescharacteristic
189C2×D4×C107—21no—
190C2×D4×C107—21no—
191C2×D4×C107—21no—
192C2×D4×C107—21no—
193C2×D4×C107—21no—
194C2×D4×C107—21no—
195C2×D4×C107—21no—
196C2×D4×C107—21no—
197C2×D4×C107—21no—
198C2×D4×C107—42no—
199C2×D4×C107C2×D411yescharacteristic
200C2×D4×C107C2×D411yescharacteristic
201C2×D4×C107C2×D411yescharacteristic
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—21no—
205C22×C4×C107—21no—
206C22×C4×C107C2411yescharacteristic
207Q16×C107—21no—
208Q16×C107—21no—
209Q16×C107—42no—
210Q16×C107—42no—
211Q16×C107—41no—
212Q16×C107—41no—
213SD16×C107—21no—
214SD16×C107—21no—
215SD16×C107—21no—
216SD16×C107—21no—
217SD16×C107—42no—
218SD16×C107—42no—
219SD16×C107—42no—
220SD16×C107—42no—
221SD16×C107—41no—
222SD16×C107—41no—
223SD16×C107—41no—
224SD16×C107—41no—
225SD16×C107—41no—
226SD16×C107—41no—
227SD16×C107—41no—
228SD16×C107—41no—
229D8×C107—21no—
230D8×C107—21no—
231D8×C107—42no—
232D8×C107—42no—
233D8×C107—41no—
234D8×C107—41no—
235M16×C107—21no—
236M16×C107—21no—
237M16×C107—21no—
238M16×C107—21no—
239M16×C107—21no—
240M16×C107—21no—
241M16×C107—21no—
242M16×C107—21no—
243M16×C107—21no—
244M16×C107—21no—
245M16×C107—42no—
246M16×C107—42no—
247M16×C107—41no—
248M16×C107—41no—
249M16×C107C2×D412yes—
250M16×C107C2×D412yes—
251M16×C107C2×D412yes—
252M16×C107C2×D412yes—
253C2×C8×C107—21no—
254C2×C8×C107—21no—
255C2×C8×C107—21no—
256C2×C8×C107—21no—
257C2×C8×C107—21no—
258C2×C8×C107—21no—
259C2×C8×C107—21no—
260C2×C8×C107—42no—
261C2×C8×C107—42no—
262C2×C8×C107—41no—
263C2×C8×C107—41no—
264C2×C8×C107C2×D411yescharacteristic
265C2×C8×C107C2×D411yescharacteristic
266C2×C8×C107C2×D411yescharacteristic
267C2×C8×C107C2×D411yescharacteristic
268C2×C8×C107#4111yescharacteristic
269C2×C8×C107#4111yescharacteristic
270C4⋊C4×C107—21no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107—42no—
273C22⋊C4×C107—21no—
274C22⋊C4×C107—42no—
275C22⋊C4×C107—42no—
276C22⋊C4×C107#4112yes—
277C42×C107—21no—
278C42×C107—21no—
279C23×C107—21no—
280C23×C107—21no—
281C23×C107—21no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—41no—
285C23×C107—161no—
286C23×C107C2×#4111yescharacteristic
287Q8×C107—21no—
288Q8×C107—21no—
289Q8×C107—21no—
290Q8×C107—21no—
291Q8×C107—21no—
292Q8×C107—21no—
293Q8×C107—41no—
294Q8×C107—41no—
295Q8×C107—41no—
296Q8×C107—41no—
297D4×C107—21no—
298D4×C107—21no—
299D4×C107—21no—
300D4×C107—21no—
301D4×C107—21no—
302D4×C107—21no—
303D4×C107—41no—
304D4×C107—41no—
305D4×C107—41no—
306D4×C107—41no—
307D4×C107—41no—
308D4×C107—41no—
309D4×C107—41no—
310D4×C107—41no—
311D4×C107—41no—
312D4×C107—41no—
313D4×C107—162no—
314C2×C4×C107—21no—
315C2×C4×C107—22no—
316C2×C4×C107—21no—
317C2×C4×C107—21no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—41no—
321C2×C4×C107—41no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107C22×D411yescharacteristic
329C2×C4×C107C22×D411yescharacteristic
330C2×C4×C107C22×D411yescharacteristic
331C2×C4×C107C2×#4111yescharacteristic
332C2×C4×C107H(5,𝔽2)11yescharacteristic
333C2×C4×C107H(5,𝔽2)11yescharacteristic
334C8×C107—22no—
335C8×C107—22no—
336C8×C107—22no—
337C8×C107—22no—
338C8×C107—41no—
339C8×C107—41no—
340C8×C107—41no—
341C8×C107#12111yescharacteristic
342C8×C107#12111yescharacteristic
343C8×C107#12111yescharacteristic
344C8×C107#12111yescharacteristic
345C22×C107—41no—
346C22×C107—41no—
347C22×C107—41no—
348C22×C107—41no—
349C22×C107—81no—
350C22×C107—81no—
351C22×C107—81no—
352C22×C107—82no—
353C22×C107—81no—
354C22×C107—161no—
355C22×C107—161no—
356C22×C107#53211yescharacteristic
357C22×C107#54611yescharacteristic
358C22×C107#55011yescharacteristic
359C4×C107—42no—
360C4×C107—41no—
361C4×C107—41no—
362C4×C107—41no—
363C4×C107—81no—
364C4×C107—81no—
365C4×C107C2×#12111yescharacteristic
366C4×C107#54011yescharacteristic
367C4×C107D4211yescharacteristic
368C4×C107D4211yescharacteristic
369#25446C10711yesmaximal, characteristic, direct product factor, Sylow
370C2×C107—21no—
371C2×C107—21no—
372C2×C107—21no—
373C2×C107—81no—
374C2×C107—81no—
375C2×C107—81no—
376C2×C107—161no—
377C2×C107#242811yescharacteristic
378#3154C2×C10711yescharacteristic, complemented
379#3069C2×C10711yescharacteristic, complemented
380#3068C2×C10711yescharacteristic, complemented
381#3067C2×C10711yescharacteristic, complemented
382C2×#471C2×C10711yescharacteristic, complemented
383#2957C2×C10711yescharacteristic, complemented
384#2049C2×C10711yescharacteristic, complemented
385#2048C2×C10711yescharacteristic, complemented
386#2009C2×C10711yescharacteristic, complemented
387#2008C2×C10711yescharacteristic, complemented
388#1977C2×C10711yescharacteristic, complemented
389#1953C2×C10711yescharacteristic, complemented
390#1915C2×C10711yescharacteristic, complemented
391#1914C2×C10711yescharacteristic, complemented
392#1757C2×C10711yescharacteristic, complemented
393C107#2544611yescharacteristic, direct product factor, Sylow
394#575C22×C10711yescharacteristic
395#575C22×C10711yescharacteristic
396C2×#137C22×C10711yescharacteristic
397C2×#137C22×C10711yescharacteristic
398C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
399C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
400C2×#135C22×C10711yescharacteristic
401C22×SD16C22×C10711yescharacteristic
402#568C22×C10711yescharacteristic
403#568C22×C10711yescharacteristic
404C2×#131C22×C10711yescharacteristic
405#536C22×C10711yescharacteristic
406#535C22×C10711yescharacteristic
407#497—21no—
408#496—21no—
409#495—21no—
410#492—21no—
411#473—21no—
412#473—22no—
413#472—21no—
414#472—22no—
415#471—21no—
416#471—21no—
417#471—22no—
418#471—22no—
419#471—22no—
420#471—22no—
421#444—22no—
422#443—22no—
423#430C22×C10711yescharacteristic
424#430C22×C10711yescharacteristic
425C2×#108C22×C10711yescharacteristic
426C2×#108C22×C10711yescharacteristic
427#421C22×C10711yescharacteristic
428#421C22×C10711yescharacteristic
429#419C22×C10711yescharacteristic
430#418C22×C10711yescharacteristic
431#413C22×C10711yescharacteristic
432#413C22×C10711yescharacteristic
433#413C22×C10711yescharacteristic
434C2×#101C22×C10711yescharacteristic
435C2×#101C22×C10711yescharacteristic
436C2×#100C22×C10711yescharacteristic
437C2×#100C22×C10711yescharacteristic
438#410C22×C10711yescharacteristic
439#405C22×C10711yescharacteristic
440#405C22×C10711yescharacteristic
441#344C22×C10711yescharacteristic
442#344C22×C10711yescharacteristic
443#344C22×C10711yescharacteristic
444#344C22×C10711yescharacteristic
445C2×#41C23×C10711yescharacteristic
446C2×#41C23×C10711yescharacteristic
447C2×#41C23×C10711yescharacteristic
448C22×Q8C23×C10711yescharacteristic
449C22×D4C23×C10711yescharacteristic
450#137—21no—
451#137—21no—
452#137—21no—
453#137—21no—
454#137—22no—
455#137—22no—
456#137—41no—
457#137—41no—
458AGL(1,ℤ/8)—21no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—21no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—22no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)—41no—
466#135—21no—
467#135—21no—
468#135—21no—
469#135—21no—
470#135—41no—
471#135—41no—
472C2×Q16—21no—
473C2×Q16—21no—
474C2×Q16D4×C10711yescharacteristic
475C2×SD16—21no—
476C2×SD16—21no—
477C2×SD16—21no—
478C2×SD16—21no—
479C2×SD16—21no—
480C2×SD16—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16D4×C10711yescharacteristic
486C2×SD16D4×C10711yescharacteristic
487C2×D8—21no—
488C2×D8—21no—
489C2×D8D4×C10711yescharacteristic
490#131—22no—
491#131—22no—
492#131—22no—
493#131—22no—
494#131—21no—
495#131—21no—
496#131—21no—
497#131—21no—
498C2×M16—21no—
499C2×M16—41no—
500C2×M16—41no—
501C2×M16C23×C10711yescharacteristic
502C2×M16C23×C10711yescharacteristic
503C2×M16C23×C10711yescharacteristic
504C2×M16C23×C10711yescharacteristic
505C2×M16C23×C10711yescharacteristic
506C2×M16C23×C10711yescharacteristic
507C2×M16C23×C10711yescharacteristic
508C22×C8—21no—
509C22×C8C23×C10711yescharacteristic
510C4⋊Q8—21no—
511#127—21no—
512#124—21no—
513#124—21no—
514#123—22no—
515C22⋊Q8—41no—
516#121—41no—
517#120—22no—
518#117C23×C10711yescharacteristic
519#117C23×C10711yescharacteristic
520#108—22no—
521#108—22no—
522#108—21no—
523#108—21no—
524#108D4×C10712yescomplemented
525#108D4×C10712yescomplemented
526#104—22no—
527#104—22no—
528#103—41no—
529#102—41no—
530#101—21no—
531#101—21no—
532#101—22no—
533#101—22no—
534#101D4×C10712yescomplemented
535#100—21no—
536#100—21no—
537#100—22no—
538#100—22no—
539#100D4×C10712yescomplemented
540#99—22no—
541#97—21no—
542#97—21no—
543C4×C8—21no—
544C4×C8—21no—
545C24—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8C2×D4×C10711yescharacteristic
565C2×Q8C2×D4×C10711yescharacteristic
566C2×Q8C2×D4×C10711yescharacteristic
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—21no—
576C2×D4—42no—
577C2×D4C2×D4×C10711yescharacteristic
578C2×D4C2×D4×C10711yescharacteristic
579C2×D4C2×D4×C10711yescharacteristic
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C10711yescharacteristic
585Q16—21no—
586Q16—21no—
587Q16—42no—
588Q16—42no—
589Q16—41no—
590Q16—41no—
591SD16—21no—
592SD16—21no—
593SD16—21no—
594SD16—21no—
595SD16—42no—
596SD16—42no—
597SD16—42no—
598SD16—42no—
599SD16—41no—
600SD16—41no—
601SD16—41no—
602SD16—41no—
603SD16—41no—
604SD16—41no—
605SD16—41no—
606SD16—41no—
607D8—21no—
608D8—21no—
609D8—42no—
610D8—42no—
611D8—41no—
612D8—41no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—21no—
621M16—21no—
622M16—21no—
623M16—42no—
624M16—42no—
625M16—41no—
626M16—41no—
627M16C2×D4×C10712yes—
628M16C2×D4×C10712yes—
629M16C2×D4×C10712yes—
630M16C2×D4×C10712yes—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8C2×D4×C10711yescharacteristic
643C2×C8C2×D4×C10711yescharacteristic
644C2×C8C2×D4×C10711yescharacteristic
645C2×C8C2×D4×C10711yescharacteristic
646C2×C8#41×C10711yescharacteristic
647C2×C8#41×C10711yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C22⋊C4—21no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4#41×C10712yes—
655C42—21no—
656C42—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—161no—
664C23C2×#41×C10711yescharacteristic
665Q8—21no—
666Q8—21no—
667Q8—21no—
668Q8—21no—
669Q8—21no—
670Q8—21no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675D4—21no—
676D4—21no—
677D4—21no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—162no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4C22×D4×C10711yescharacteristic
707C2×C4C22×D4×C10711yescharacteristic
708C2×C4C22×D4×C10711yescharacteristic
709C2×C4C2×#41×C10711yescharacteristic
710C2×C4H(5,𝔽2)×C10711yescharacteristic
711C2×C4H(5,𝔽2)×C10711yescharacteristic
712C8—22no—
713C8—22no—
714C8—22no—
715C8—22no—
716C8—41no—
717C8—41no—
718C8—41no—
719C8#121×C10711yescharacteristic
720C8#121×C10711yescharacteristic
721C8#121×C10711yescharacteristic
722C8#121×C10711yescharacteristic
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—82no—
731C22—81no—
732C22—161no—
733C22—161no—
734C22#532×C10711yescharacteristic
735C22#546×C10711yescharacteristic
736C22#550×C10711yescharacteristic
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—81no—
742C4—81no—
743C4C2×#121×C10711yescharacteristic
744C4#540×C10711yescharacteristic
745C4D42×C10711yescharacteristic
746C4D42×C10711yescharacteristic
747C2—21no—
748C2—21no—
749C2—21no—
750C2—81no—
751C2—81no—
752C2—81no—
753C2—161no—
754C2C107×#242811yescharacteristic
subgroupG/H
center, socleC2×C107#2428
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×#3154C2semidirect
2. C107×#3069C2semidirect
3. C107×#3068C2semidirect
4. C107×#3067C2semidirect
5. C2×#471×C107C2semidirect
6. C107×#2957C2semidirect
7. C107×#2049C2semidirect
8. C107×#2048C2semidirect
9. C107×#2009C2semidirect
10. C107×#2008C2semidirect
11. C107×#1977C2semidirect
12. C107×#1953C2semidirect
13. C107×#1915C2semidirect
14. C107×#1914C2semidirect
15. C107×#1757C2semidirect
146. #108×C107D4semidirect
147. #108×C107D4semidirect
156. #101×C107D4semidirect
161. #100×C107D4semidirect
369. #25446C107direct (N × H)
378. #3154C2×C107semidirect
379. #3069C2×C107semidirect
380. #3068C2×C107semidirect
381. #3067C2×C107semidirect
382. C2×#471C2×C107semidirect
383. #2957C2×C107semidirect
384. #2049C2×C107semidirect
385. #2048C2×C107semidirect
386. #2009C2×C107semidirect
387. #2008C2×C107semidirect
388. #1977C2×C107semidirect
389. #1953C2×C107semidirect
390. #1915C2×C107semidirect
391. #1914C2×C107semidirect
392. #1757C2×C107semidirect
393. C107#25446direct (N × H)
524. #108D4×C107semidirect
525. #108D4×C107semidirect
534. #101D4×C107semidirect
539. #100D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#31542
C107×#30692
C107×#30682
C107×#30672
C2×#471×C1072
C107×#29572
C107×#20492
C107×#20482
C107×#20092
C107×#20082
C107×#19772
C107×#19532
C107×#19152
C107×#19142
C107×#17572
#25446107