Finite Group Databasebeta

← C107×#25443 #41051407

Subgroups — C107×#25443 #41051407

Order 27392.

910 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3154C211yesmaximal, characteristic, complemented
2C2×#471×C107C211yesmaximal, characteristic, complemented
3C107×#3063C211yesmaximal, characteristic, complemented
4C107×#3062C211yesmaximal, characteristic, complemented
5C107×#3061C211yesmaximal, characteristic, complemented
6C2×#444×C107C211yesmaximal, characteristic, complemented
7C107×#2038C211yesmaximal, characteristic, complemented
8C107×#2037C211yesmaximal, characteristic, complemented
9C107×#2007C211yesmaximal, characteristic, complemented
10C107×#2006C211yesmaximal, characteristic, complemented
11C107×#1973C211yesmaximal, characteristic, complemented
12C107×#1952C211yesmaximal, characteristic, complemented
13C107×#1908C211yesmaximal, characteristic, complemented
14C107×#1907C211yesmaximal, characteristic, complemented
15C107×#1765C211yesmaximal, characteristic, complemented
16C2×#137×C107C2211yescharacteristic
17C2×#137×C107C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
20C2×#135×C107C2211yescharacteristic
21C22×SD16×C107C2211yescharacteristic
22C2×#131×C107C2211yescharacteristic
23C2×#131×C107C2211yescharacteristic
24C2×#131×C107C2211yescharacteristic
25#537×C107C2211yescharacteristic
26#537×C107C2211yescharacteristic
27#536×C107C2211yescharacteristic
28#535×C107C2211yescharacteristic
29#497×C107—21no—
30#496×C107—21no—
31#495×C107—21no—
32#492×C107—21no—
33#471×C107—24no—
34#470×C107—21no—
35#469×C107—21no—
36#468×C107—21no—
37#468×C107—21no—
38#468×C107—21no—
39#468×C107—21no—
40#467×C107—21no—
41#467×C107—21no—
42#466×C107—21no—
43#466×C107—21no—
44#465×C107—21no—
45#465×C107—21no—
46#444×C107—24no—
47C2×#108×C107C2211yescharacteristic
48#428×C107C2211yescharacteristic
49#428×C107C2211yescharacteristic
50C2×#107×C107C2211yescharacteristic
51C2×#104×C107C2211yescharacteristic
52C2×#104×C107C2211yescharacteristic
53C2×#104×C107C2211yescharacteristic
54#417×C107C2211yescharacteristic
55#417×C107C2211yescharacteristic
56#416×C107C2211yescharacteristic
57C2×#103×C107C2211yescharacteristic
58C2×#102×C107C2211yescharacteristic
59C2×#101×C107C2211yescharacteristic
60C2×#100×C107C2211yescharacteristic
61#405×C107C2211yescharacteristic
62C2×#97×C107C2211yescharacteristic
63#391×C107C2211yescharacteristic
64#390×C107C2211yescharacteristic
65#343×C107C2211yescharacteristic
66#343×C107C2211yescharacteristic
67#341×C107C2211yescharacteristic
68#339×C107C2211yescharacteristic
69C2×#41×C107C2311yescharacteristic
70C2×#41×C107C2311yescharacteristic
71C2×#41×C107C2311yescharacteristic
72C22×Q8×C107C2311yescharacteristic
73C22×D4×C107C2311yescharacteristic
74#137×C107—22no—
75#137×C107—22no—
76#137×C107—41no—
77#137×C107—41no—
78AGL(1,ℤ/8)×C107—22no—
79AGL(1,ℤ/8)×C107—22no—
80AGL(1,ℤ/8)×C107—41no—
81AGL(1,ℤ/8)×C107—41no—
82#135×C107—22no—
83#135×C107—22no—
84C2×Q16×C107—21no—
85C2×Q16×C107—21no—
86C2×Q16×C107D411yescharacteristic
87C2×SD16×C107—21no—
88C2×SD16×C107—21no—
89C2×SD16×C107—21no—
90C2×SD16×C107—21no—
91C2×SD16×C107—22no—
92C2×SD16×C107—21no—
93C2×SD16×C107—21no—
94C2×SD16×C107—22no—
95C2×SD16×C107D411yescharacteristic
96C2×SD16×C107D411yescharacteristic
97C2×D8×C107—21no—
98C2×D8×C107—21no—
99C2×D8×C107D411yescharacteristic
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—21no—
107C2×M16×C107—21no—
108C2×M16×C107—21no—
109C2×M16×C107C2311yescharacteristic
110C2×M16×C107C2311yescharacteristic
111C2×M16×C107C2311yescharacteristic
112C2×M16×C107C2311yescharacteristic
113C22×C8×C107—21no—
114C22×C8×C107—21no—
115C22×C8×C107—21no—
116C22×C8×C107C2311yescharacteristic
117C22×C8×C107C2311yescharacteristic
118C4⋊Q8×C107—21no—
119#127×C107—21no—
120#124×C107—21no—
121#124×C107—21no—
122#123×C107—41no—
123C22⋊Q8×C107—21no—
124C22⋊Q8×C107—21no—
125C22⋊Q8×C107—21no—
126C22⋊Q8×C107—21no—
127C22⋊Q8×C107—21no—
128C22⋊Q8×C107—21no—
129#121×C107—21no—
130#121×C107—21no—
131#121×C107—21no—
132#121×C107—21no—
133#121×C107—21no—
134#121×C107—21no—
135#121×C107—41no—
136#121×C107—41no—
137#120×C107—41no—
138#117×C107C2311yescharacteristic
139C2×C4⋊C4×C107C2311yescharacteristic
140C2×C4⋊C4×C107C2311yescharacteristic
141C2×C22⋊C4×C107—41no—
142C2×C42×C107C2311yescharacteristic
143#108×C107D414yescomplemented
144#107×C107—21no—
145#107×C107—21no—
146#107×C107—21no—
147#107×C107—21no—
148#106×C107—21no—
149#106×C107—21no—
150#104×C107—22no—
151#104×C107—22no—
152#104×C107—22no—
153#103×C107—21no—
154#103×C107—21no—
155#103×C107—21no—
156#103×C107—21no—
157#103×C107D411yescharacteristic
158#103×C107D411yescharacteristic
159#102×C107—21no—
160#102×C107—21no—
161#102×C107—21no—
162#102×C107—21no—
163#102×C107D411yescharacteristic
164#102×C107D411yescharacteristic
165#101×C107—22no—
166#100×C107—22no—
167#97×C107—22no—
168#97×C107—21no—
169C4×C8×C107—21no—
170#95×C107—41no—
171C24×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—
180#41×C107—21no—
181#41×C107—21no—
182#41×C107—21no—
183#41×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107—21no—
188C2×Q8×C107—21no—
189C2×Q8×C107—21no—
190C2×Q8×C107C2×D411yescharacteristic
191C2×Q8×C107C2×D411yescharacteristic
192C2×Q8×C107C2×D411yescharacteristic
193C2×D4×C107—21no—
194C2×D4×C107—21no—
195C2×D4×C107—21no—
196C2×D4×C107—21no—
197C2×D4×C107—21no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—41no—
203C2×D4×C107—41no—
204C2×D4×C107—41no—
205C2×D4×C107—41no—
206C2×D4×C107C2×D411yescharacteristic
207C2×D4×C107C2×D411yescharacteristic
208C2×D4×C107C2×D411yescharacteristic
209C22×C4×C107—21no—
210C22×C4×C107—21no—
211C22×C4×C107—21no—
212C22×C4×C107—21no—
213C22×C4×C107—21no—
214C22×C4×C107—21no—
215C22×C4×C107—21no—
216C22×C4×C107C2411yescharacteristic
217Q16×C107—22no—
218Q16×C107—42no—
219Q16×C107—42no—
220SD16×C107—22no—
221SD16×C107—22no—
222SD16×C107—42no—
223SD16×C107—42no—
224SD16×C107—42no—
225SD16×C107—42no—
226SD16×C107—42no—
227SD16×C107—42no—
228D8×C107—22no—
229D8×C107—42no—
230D8×C107—42no—
231M16×C107—21no—
232M16×C107—21no—
233M16×C107—21no—
234M16×C107—21no—
235M16×C107—21no—
236M16×C107—42no—
237M16×C107—42no—
238M16×C107—42no—
239M16×C107C2×D412yes—
240M16×C107C2×D412yes—
241M16×C107#4112yes—
242C2×C8×C107—21no—
243C2×C8×C107—21no—
244C2×C8×C107—21no—
245C2×C8×C107—21no—
246C2×C8×C107—21no—
247C2×C8×C107—21no—
248C2×C8×C107—42no—
249C2×C8×C107—42no—
250C2×C8×C107—42no—
251C2×C8×C107C2×D411yescharacteristic
252C2×C8×C107C2×D411yescharacteristic
253C2×C8×C107C2×D411yescharacteristic
254C2×C8×C107C2×D411yescharacteristic
255C2×C8×C107C2×D412yes—
256C2×C8×C107#4112yes—
257C4⋊C4×C107—21no—
258C4⋊C4×C107—21no—
259C4⋊C4×C107—21no—
260C4⋊C4×C107—21no—
261C4⋊C4×C107—41no—
262C4⋊C4×C107—41no—
263C4⋊C4×C107—41no—
264C4⋊C4×C107—41no—
265C4⋊C4×C107C2×D411yescharacteristic
266C4⋊C4×C107C2×D411yescharacteristic
267C22⋊C4×C107—21no—
268C22⋊C4×C107—41no—
269C22⋊C4×C107—41no—
270C22⋊C4×C107—41no—
271C22⋊C4×C107—41no—
272C22⋊C4×C107—41no—
273C22⋊C4×C107—41no—
274C22⋊C4×C107—41no—
275C22⋊C4×C107—41no—
276C22⋊C4×C107—82no—
277C42×C107—21no—
278C42×C107—21no—
279C42×C107—21no—
280C23×C107—21no—
281C23×C107—21no—
282C23×C107—21no—
283C23×C107—41no—
284C23×C107—41no—
285C23×C107—41no—
286C23×C107—81no—
287C23×C107—81no—
288C23×C107H(5,𝔽2)11yescharacteristic
289Q8×C107—21no—
290Q8×C107—21no—
291Q8×C107—21no—
292Q8×C107—21no—
293Q8×C107—21no—
294Q8×C107—21no—
295Q8×C107—41no—
296Q8×C107—41no—
297Q8×C107—41no—
298Q8×C107—41no—
299D4×C107—21no—
300D4×C107—21no—
301D4×C107—21no—
302D4×C107—21no—
303D4×C107—21no—
304D4×C107—21no—
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—41no—
314D4×C107—41no—
315D4×C107—161no—
316D4×C107—161no—
317D4×C107—161no—
318D4×C107—161no—
319C2×C4×C107—21no—
320C2×C4×C107—21no—
321C2×C4×C107—21no—
322C2×C4×C107—21no—
323C2×C4×C107—21no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107—41no—
329C2×C4×C107—41no—
330C2×C4×C107—41no—
331C2×C4×C107—41no—
332C2×C4×C107—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
335C2×C4×C107—41no—
336C2×C4×C107—41no—
337C2×C4×C107—41no—
338C2×C4×C107—81no—
339C2×C4×C107—81no—
340C2×C4×C107C22×D411yescharacteristic
341C2×C4×C107C22×D411yescharacteristic
342C2×C4×C107C22×D411yescharacteristic
343C2×C4×C107C2×#4111yescharacteristic
344C2×C4×C107C2×#4111yescharacteristic
345C2×C4×C107H(5,𝔽2)11yescharacteristic
346C8×C107—21no—
347C8×C107—21no—
348C8×C107—22no—
349C8×C107—22no—
350C8×C107—22no—
351C8×C107—41no—
352C8×C107#12112yes—
353C8×C107#12112yes—
354C22×C107—21no—
355C22×C107—21no—
356C22×C107—41no—
357C22×C107—41no—
358C22×C107—41no—
359C22×C107—41no—
360C22×C107—41no—
361C22×C107—41no—
362C22×C107—41no—
363C22×C107—41no—
364C22×C107—41no—
365C22×C107—82no—
366C22×C107—81no—
367C22×C107—81no—
368C22×C107—81no—
369C22×C107—161no—
370C22×C107#54011yescharacteristic
371C22×C107D4211yescharacteristic
372C22×C107#55011yescharacteristic
373C4×C107—41no—
374C4×C107—41no—
375C4×C107—41no—
376C4×C107—41no—
377C4×C107—41no—
378C4×C107—81no—
379C4×C107—81no—
380C4×C107—81no—
381C4×C107—81no—
382C4×C107C2×#12111yescharacteristic
383C4×C107#53211yescharacteristic
384C4×C107D4211yescharacteristic
385C4×C107#54611yescharacteristic
386#25443C10711yesmaximal, characteristic, direct product factor, Sylow
387C2×C107—21no—
388C2×C107—21no—
389C2×C107—81no—
390C2×C107—81no—
391C2×C107—81no—
392C2×C107—161no—
393C2×C107#242811yescharacteristic
394C2×C107#328811yescharacteristic
395C2×C107#328911yescharacteristic
396#3154C2×C10711yescharacteristic, complemented
397C2×#471C2×C10711yescharacteristic, complemented
398#3063C2×C10711yescharacteristic, complemented
399#3062C2×C10711yescharacteristic, complemented
400#3061C2×C10711yescharacteristic, complemented
401C2×#444C2×C10711yescharacteristic, complemented
402#2038C2×C10711yescharacteristic, complemented
403#2037C2×C10711yescharacteristic, complemented
404#2007C2×C10711yescharacteristic, complemented
405#2006C2×C10711yescharacteristic, complemented
406#1973C2×C10711yescharacteristic, complemented
407#1952C2×C10711yescharacteristic, complemented
408#1908C2×C10711yescharacteristic, complemented
409#1907C2×C10711yescharacteristic, complemented
410#1765C2×C10711yescharacteristic, complemented
411C107#2544311yescharacteristic, direct product factor, Sylow
412C2×#137C22×C10711yescharacteristic
413C2×#137C22×C10711yescharacteristic
414C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
415C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
416C2×#135C22×C10711yescharacteristic
417C22×SD16C22×C10711yescharacteristic
418C2×#131C22×C10711yescharacteristic
419C2×#131C22×C10711yescharacteristic
420C2×#131C22×C10711yescharacteristic
421#537C22×C10711yescharacteristic
422#537C22×C10711yescharacteristic
423#536C22×C10711yescharacteristic
424#535C22×C10711yescharacteristic
425#497—21no—
426#496—21no—
427#495—21no—
428#492—21no—
429#471—24no—
430#470—21no—
431#469—21no—
432#468—21no—
433#468—21no—
434#468—21no—
435#468—21no—
436#467—21no—
437#467—21no—
438#466—21no—
439#466—21no—
440#465—21no—
441#465—21no—
442#444—24no—
443C2×#108C22×C10711yescharacteristic
444#428C22×C10711yescharacteristic
445#428C22×C10711yescharacteristic
446C2×#107C22×C10711yescharacteristic
447C2×#104C22×C10711yescharacteristic
448C2×#104C22×C10711yescharacteristic
449C2×#104C22×C10711yescharacteristic
450#417C22×C10711yescharacteristic
451#417C22×C10711yescharacteristic
452#416C22×C10711yescharacteristic
453C2×#103C22×C10711yescharacteristic
454C2×#102C22×C10711yescharacteristic
455C2×#101C22×C10711yescharacteristic
456C2×#100C22×C10711yescharacteristic
457#405C22×C10711yescharacteristic
458C2×#97C22×C10711yescharacteristic
459#391C22×C10711yescharacteristic
460#390C22×C10711yescharacteristic
461#343C22×C10711yescharacteristic
462#343C22×C10711yescharacteristic
463#341C22×C10711yescharacteristic
464#339C22×C10711yescharacteristic
465C2×#41C23×C10711yescharacteristic
466C2×#41C23×C10711yescharacteristic
467C2×#41C23×C10711yescharacteristic
468C22×Q8C23×C10711yescharacteristic
469C22×D4C23×C10711yescharacteristic
470#137—22no—
471#137—22no—
472#137—41no—
473#137—41no—
474AGL(1,ℤ/8)—22no—
475AGL(1,ℤ/8)—22no—
476AGL(1,ℤ/8)—41no—
477AGL(1,ℤ/8)—41no—
478#135—22no—
479#135—22no—
480C2×Q16—21no—
481C2×Q16—21no—
482C2×Q16D4×C10711yescharacteristic
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×SD16—22no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—22no—
491C2×SD16D4×C10711yescharacteristic
492C2×SD16D4×C10711yescharacteristic
493C2×D8—21no—
494C2×D8—21no—
495C2×D8D4×C10711yescharacteristic
496#131—22no—
497#131—22no—
498#131—22no—
499#131—22no—
500#131—41no—
501#131—41no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16C23×C10711yescharacteristic
506C2×M16C23×C10711yescharacteristic
507C2×M16C23×C10711yescharacteristic
508C2×M16C23×C10711yescharacteristic
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8C23×C10711yescharacteristic
513C22×C8C23×C10711yescharacteristic
514C4⋊Q8—21no—
515#127—21no—
516#124—21no—
517#124—21no—
518#123—41no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121—41no—
532#121—41no—
533#120—41no—
534#117C23×C10711yescharacteristic
535C2×C4⋊C4C23×C10711yescharacteristic
536C2×C4⋊C4C23×C10711yescharacteristic
537C2×C22⋊C4—41no—
538C2×C42C23×C10711yescharacteristic
539#108D4×C10714yescomplemented
540#107—21no—
541#107—21no—
542#107—21no—
543#107—21no—
544#106—21no—
545#106—21no—
546#104—22no—
547#104—22no—
548#104—22no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103D4×C10711yescharacteristic
554#103D4×C10711yescharacteristic
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102D4×C10711yescharacteristic
560#102D4×C10711yescharacteristic
561#101—22no—
562#100—22no—
563#97—22no—
564#97—21no—
565C4×C8—21no—
566#95—41no—
567C24—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C10711yescharacteristic
587C2×Q8C2×D4×C10711yescharacteristic
588C2×Q8C2×D4×C10711yescharacteristic
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4C2×D4×C10711yescharacteristic
603C2×D4C2×D4×C10711yescharacteristic
604C2×D4C2×D4×C10711yescharacteristic
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4C24×C10711yescharacteristic
613Q16—22no—
614Q16—42no—
615Q16—42no—
616SD16—22no—
617SD16—22no—
618SD16—42no—
619SD16—42no—
620SD16—42no—
621SD16—42no—
622SD16—42no—
623SD16—42no—
624D8—22no—
625D8—42no—
626D8—42no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16C2×D4×C10712yes—
636M16C2×D4×C10712yes—
637M16#41×C10712yes—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—42no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8C2×D4×C10711yescharacteristic
648C2×C8C2×D4×C10711yescharacteristic
649C2×C8C2×D4×C10711yescharacteristic
650C2×C8C2×D4×C10711yescharacteristic
651C2×C8C2×D4×C10712yes—
652C2×C8#41×C10712yes—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4C2×D4×C10711yescharacteristic
662C4⋊C4C2×D4×C10711yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C22⋊C4—82no—
673C42—21no—
674C42—21no—
675C42—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—81no—
683C23—81no—
684C23H(5,𝔽2)×C10711yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—161no—
712D4—161no—
713D4—161no—
714D4—161no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4C22×D4×C10711yescharacteristic
737C2×C4C22×D4×C10711yescharacteristic
738C2×C4C22×D4×C10711yescharacteristic
739C2×C4C2×#41×C10711yescharacteristic
740C2×C4C2×#41×C10711yescharacteristic
741C2×C4H(5,𝔽2)×C10711yescharacteristic
742C8—21no—
743C8—21no—
744C8—22no—
745C8—22no—
746C8—22no—
747C8—41no—
748C8#121×C10712yes—
749C8#121×C10712yes—
750C22—21no—
751C22—21no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—82no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—161no—
766C22#540×C10711yescharacteristic
767C22D42×C10711yescharacteristic
768C22#550×C10711yescharacteristic
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4C2×#121×C10711yescharacteristic
779C4#532×C10711yescharacteristic
780C4D42×C10711yescharacteristic
781C4#546×C10711yescharacteristic
782C2—21no—
783C2—21no—
784C2—81no—
785C2—81no—
786C2—81no—
787C2—161no—
788C2C107×#242811yescharacteristic
789C2C107×#328811yescharacteristic
790C2C107×#328911yescharacteristic
subgroupG/H
center, socleC22×C107D42
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3154C2semidirect
2. C2×#471×C107C2semidirect
3. C107×#3063C2semidirect
4. C107×#3062C2semidirect
5. C107×#3061C2semidirect
6. C2×#444×C107C2semidirect
7. C107×#2038C2semidirect
8. C107×#2037C2semidirect
9. C107×#2007C2semidirect
10. C107×#2006C2semidirect
11. C107×#1973C2semidirect
12. C107×#1952C2semidirect
13. C107×#1908C2semidirect
14. C107×#1907C2semidirect
15. C107×#1765C2semidirect
143. #108×C107D4semidirect
386. #25443C107direct (N × H)
396. #3154C2×C107semidirect
397. C2×#471C2×C107semidirect
398. #3063C2×C107semidirect
399. #3062C2×C107semidirect
400. #3061C2×C107semidirect
401. C2×#444C2×C107semidirect
402. #2038C2×C107semidirect
403. #2037C2×C107semidirect
404. #2007C2×C107semidirect
405. #2006C2×C107semidirect
406. #1973C2×C107semidirect
407. #1952C2×C107semidirect
408. #1908C2×C107semidirect
409. #1907C2×C107semidirect
410. #1765C2×C107semidirect
411. C107#25443direct (N × H)
539. #108D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#31542
C2×#471×C1072
C107×#30632
C107×#30622
C107×#30612
C2×#444×C1072
C107×#20382
C107×#20372
C107×#20072
C107×#20062
C107×#19732
C107×#19522
C107×#19082
C107×#19072
C107×#17652
#25443107