Finite Group Databasebeta

← C107×#25192 #41051156

Subgroups — C107×#25192 #41051156

Order 27392.

1054 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3062C211yesmaximal, characteristic, complemented
2C107×#3045C211yesmaximal, characteristic, complemented
3C2×#453×C107C211yesmaximal, characteristic, complemented
4C107×#3012C211yesmaximal, characteristic, complemented
5C2×#444×C107C211yesmaximal, characteristic, complemented
6C107×#2897C211yesmaximal, characteristic, complemented
7C107×#2063C211yesmaximal, characteristic, complemented
8C107×#2051C211yesmaximal, characteristic, complemented
9C107×#2040C211yesmaximal, characteristic, complemented
10C107×#2002C211yesmaximal, characteristic, complemented
11C107×#1961C211yesmaximal, characteristic, complemented
12C107×#1938C211yesmaximal, characteristic, complemented
13C107×#1907C211yesmaximal, characteristic, complemented
14C107×#1907C211yesmaximal, characteristic, complemented
15C107×#1860C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C107C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
20C2×#135×C107C2211yescharacteristic
21C2×#131×C107C2211yescharacteristic
22C2×#131×C107C2211yescharacteristic, complemented
23#537×C107C2211yescharacteristic
24#535×C107C2211yescharacteristic, complemented
25C2×#127×C107C2211yescharacteristic
26#520×C107C2211yescharacteristic
27#469×C107—21no—
28#468×C107—21no—
29#466×C107—21no—
30#465×C107—21no—
31#464×C107—21no—
32#463×C107—21no—
33#460×C107—21no—
34#459×C107—21no—
35#453×C107—24no—
36#452×C107—21no—
37#450×C107—21no—
38#449×C107—21no—
39#447×C107—21no—
40#444×C107—24no—
41C2×#108×C107C2211yescharacteristic, complemented
42#428×C107C2211yescharacteristic, complemented
43#424×C107C2211yescharacteristic, complemented
44C2×#104×C107C2211yescharacteristic
45C2×#104×C107C2211yescharacteristic
46C2×#104×C107C2211yescharacteristic, complemented
47#418×C107—21no—
48#418×C107C2211yescharacteristic
49#417×C107—21no—
50#417×C107C2211yescharacteristic
51#417×C107C2211yescharacteristic
52#417×C107C2211yescharacteristic, complemented
53#416×C107—21no—
54#416×C107C2211yescharacteristic
55C2×#102×C107—21no—
56C2×#102×C107C2211yescharacteristic
57C2×#102×C107C2211yescharacteristic
58C2×#102×C107C2211yescharacteristic, complemented
59C2×#102×C107C2211yescharacteristic, complemented
60C2×#100×C107C2211yescharacteristic
61C2×#100×C107C2211yescharacteristic, complemented
62#408×C107C2211yescharacteristic
63C2×#97×C107C2211yescharacteristic, complemented
64#382×C107C2211yescharacteristic, complemented
65#343×C107C2211yescharacteristic, complemented
66#343×C107C2211yescharacteristic, complemented
67#341×C107C2211yescharacteristic, complemented
68#339×C107C2211yescharacteristic, complemented
69H(5,𝔽2)×C107—22no—
70H(5,𝔽2)×C107—22no—
71H(5,𝔽2)×C107—22no—
72H(5,𝔽2)×C107—41no—
73C2×#41×C107—21no—
74C2×#41×C107—21no—
75C2×#41×C107C2311yescharacteristic
76C2×#41×C107C2311yescharacteristic
77C2×#41×C107C2311yescharacteristic
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107—41no—
81C22×D4×C107—41no—
82C22×D4×C107C2311yescharacteristic
83C22×D4×C107C2311yescharacteristic
84AGL(1,ℤ/8)×C107—22no—
85AGL(1,ℤ/8)×C107—22no—
86AGL(1,ℤ/8)×C107—22no—
87AGL(1,ℤ/8)×C107—22no—
88AGL(1,ℤ/8)×C107—41no—
89AGL(1,ℤ/8)×C107—41no—
90#135×C107—22no—
91#135×C107—22no—
92C2×Q16×C107D411yescharacteristic, complemented
93C2×SD16×C107—21no—
94C2×SD16×C107—21no—
95C2×SD16×C107—21no—
96C2×SD16×C107D411yescharacteristic, complemented
97C2×SD16×C107D411yescharacteristic, complemented
98C2×D8×C107—21no—
99C2×D8×C107—21no—
100C2×D8×C107—21no—
101C2×D8×C107D411yescharacteristic, complemented
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×C107C2311yescharacteristic
109C2×M16×C107C2311yescharacteristic
110C2×M16×C107C2311yescharacteristic
111C2×M16×C107C2311yescharacteristic
112C22×C8×C107—21no—
113C22×C8×C107—21no—
114C22×C8×C107C2311yescharacteristic
115C22×C8×C107C2311yescharacteristic
116#127×C107—21no—
117#127×C107—22no—
118#127×C107—22no—
119#124×C107—21no—
120C22⋊Q8×C107—21no—
121C22⋊Q8×C107—21no—
122#121×C107—21no—
123#121×C107—21no—
124#121×C107—21no—
125#121×C107—21no—
126#121×C107—41no—
127#120×C107—41no—
128C4×Q8×C107—21no—
129C4×D4×C107—21no—
130C4×D4×C107—41no—
131#117×C107—21no—
132#117×C107C2311yescharacteristic
133C2×C4⋊C4×C107—21no—
134C2×C4⋊C4×C107C2311yescharacteristic
135C2×C4⋊C4×C107C2311yescharacteristic
136C2×C42×C107C2311yescharacteristic
137#108×C107—22no—
138#107×C107—21no—
139#106×C107—21no—
140C4⋊C8×C107—21no—
141C4⋊C8×C107—21no—
142#104×C107—22no—
143#104×C107—22no—
144#104×C107D414yescomplemented
145#103×C107—21no—
146#103×C107—21no—
147#103×C107—21no—
148#103×C107D411yescharacteristic, complemented
149#103×C107D411yescharacteristic, complemented
150#102×C107—21no—
151#102×C107—21no—
152#102×C107—21no—
153#102×C107—21no—
154#102×C107—21no—
155#102×C107—21no—
156#102×C107—21no—
157#102×C107—21no—
158#102×C107—21no—
159#102×C107—21no—
160#102×C107—21no—
161#102×C107—21no—
162#102×C107—21no—
163#102×C107D411yescharacteristic, complemented
164#102×C107D411yescharacteristic, complemented
165#100×C107—22no—
166#100×C107—41no—
167C22⋊C8×C107—21no—
168C22⋊C8×C107—21no—
169#97×C107—22no—
170#95×C107—41no—
171C24×C107—21no—
172C24×C107—21no—
173C24×C107—41no—
174#41×C107—21no—
175#41×C107—21no—
176#41×C107—24no—
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—
184#41×C107—21no—
185#41×C107—42no—
186#41×C107—42no—
187#41×C107—42no—
188#41×C107C2×D412yes—
189#41×C107#4112yes—
190C2×Q8×C107C2×D411yescharacteristic
191C2×Q8×C107C2×D411yescharacteristic
192C2×Q8×C107C2×D411yescharacteristic
193C2×D4×C107—21no—
194C2×D4×C107—24no—
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—21no—
203C2×D4×C107—21no—
204C2×D4×C107—21no—
205C2×D4×C107—21no—
206C2×D4×C107—21no—
207C2×D4×C107—21no—
208C2×D4×C107—42no—
209C2×D4×C107—41no—
210C2×D4×C107—41no—
211C2×D4×C107—44no—
212C2×D4×C107—41no—
213C2×D4×C107—41no—
214C2×D4×C107—42no—
215C2×D4×C107—44no—
216C2×D4×C107—44no—
217C2×D4×C107—42no—
218C2×D4×C107—41no—
219C2×D4×C107—82no—
220C2×D4×C107—82no—
221C2×D4×C107C2×D411yescharacteristic
222C2×D4×C107C2×D411yescharacteristic
223C2×D4×C107C2×D411yescharacteristic
224C2×D4×C107#4112yes—
225C22×C4×C107—21no—
226C22×C4×C107—21no—
227C22×C4×C107—21no—
228C22×C4×C107—21no—
229C22×C4×C107—21no—
230C22×C4×C107—21no—
231C22×C4×C107—41no—
232C22×C4×C107—41no—
233C22×C4×C107C2411yescharacteristic
234Q16×C107—22no—
235SD16×C107—22no—
236SD16×C107—22no—
237SD16×C107—42no—
238SD16×C107—42no—
239SD16×C107—42no—
240D8×C107—22no—
241D8×C107—42no—
242D8×C107—42no—
243D8×C107—42no—
244M16×C107—21no—
245M16×C107—21no—
246M16×C107—21no—
247M16×C107—21no—
248M16×C107—21no—
249M16×C107—21no—
250M16×C107—21no—
251M16×C107—42no—
252M16×C107—42no—
253M16×C107C2×D412yes—
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—21no—
261C2×C8×C107—21no—
262C2×C8×C107—42no—
263C2×C8×C107—42no—
264C2×C8×C107C2×D411yescharacteristic
265C2×C8×C107C2×D411yescharacteristic
266C2×C8×C107C2×D411yescharacteristic
267C2×C8×C107C2×D411yescharacteristic
268C4⋊C4×C107—21no—
269C4⋊C4×C107—21no—
270C4⋊C4×C107—21no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107—41no—
273C4⋊C4×C107—41no—
274C4⋊C4×C107C2×D411yescharacteristic
275C4⋊C4×C107C2×D411yescharacteristic
276C22⋊C4×C107—21no—
277C22⋊C4×C107—41no—
278C22⋊C4×C107—41no—
279C22⋊C4×C107—41no—
280C22⋊C4×C107—41no—
281C22⋊C4×C107—41no—
282C42×C107—21no—
283C42×C107—21no—
284C42×C107—41no—
285C42×C107C2×D412yes—
286C23×C107—21no—
287C23×C107—21no—
288C23×C107—21no—
289C23×C107—22no—
290C23×C107—44no—
291C23×C107—41no—
292C23×C107—41no—
293C23×C107—41no—
294C23×C107—41no—
295C23×C107—41no—
296C23×C107—81no—
297C23×C107—81no—
298C23×C107—81no—
299C23×C107—81no—
300C23×C107—161no—
301C23×C107—161no—
302C23×C107H(5,𝔽2)11yescharacteristic
303Q8×C107—21no—
304Q8×C107—21no—
305Q8×C107—21no—
306Q8×C107—21no—
307Q8×C107—21no—
308Q8×C107#12112yes—
309D4×C107—22no—
310D4×C107—22no—
311D4×C107—21no—
312D4×C107—21no—
313D4×C107—22no—
314D4×C107—21no—
315D4×C107—21no—
316D4×C107—21no—
317D4×C107—22no—
318D4×C107—44no—
319D4×C107—44no—
320D4×C107—41no—
321D4×C107—41no—
322D4×C107—41no—
323D4×C107—41no—
324D4×C107—41no—
325D4×C107—41no—
326D4×C107—41no—
327D4×C107—41no—
328D4×C107—41no—
329D4×C107—41no—
330D4×C107—88no—
331D4×C107—161no—
332D4×C107—161no—
333D4×C107—161no—
334D4×C107#12112yes—
335C2×C4×C107—21no—
336C2×C4×C107—22no—
337C2×C4×C107—22no—
338C2×C4×C107—21no—
339C2×C4×C107—21no—
340C2×C4×C107—21no—
341C2×C4×C107—21no—
342C2×C4×C107—22no—
343C2×C4×C107—44no—
344C2×C4×C107—41no—
345C2×C4×C107—41no—
346C2×C4×C107—41no—
347C2×C4×C107—41no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—41no—
351C2×C4×C107—41no—
352C2×C4×C107—81no—
353C2×C4×C107—81no—
354C2×C4×C107—161no—
355C2×C4×C107C22×D411yescharacteristic
356C2×C4×C107C22×D411yescharacteristic
357C2×C4×C107C22×D411yescharacteristic
358C2×C4×C107C2×#4111yescharacteristic
359C2×C4×C107C2×#4111yescharacteristic
360C2×C4×C107H(5,𝔽2)11yescharacteristic
361C8×C107—21no—
362C8×C107—21no—
363C8×C107—21no—
364C8×C107—21no—
365C8×C107—22no—
366C8×C107—41no—
367C8×C107—41no—
368C8×C107—41no—
369C22×C107—21no—
370C22×C107—21no—
371C22×C107—22no—
372C22×C107—41no—
373C22×C107—41no—
374C22×C107—41no—
375C22×C107—42no—
376C22×C107—41no—
377C22×C107—41no—
378C22×C107—41no—
379C22×C107—41no—
380C22×C107—41no—
381C22×C107—82no—
382C22×C107—82no—
383C22×C107—81no—
384C22×C107—81no—
385C22×C107—81no—
386C22×C107—81no—
387C22×C107—81no—
388C22×C107—161no—
389C22×C107—161no—
390C22×C107—164no—
391C22×C107#53811yescharacteristic
392C22×C107D4211yescharacteristic
393C22×C107#54611yescharacteristic
394C4×C107—22no—
395C4×C107—42no—
396C4×C107—41no—
397C4×C107—41no—
398C4×C107—41no—
399C4×C107—41no—
400C4×C107—81no—
401C4×C107—81no—
402C4×C107C2×#12111yescharacteristic
403C4×C107#52511yescharacteristic
404C4×C107D4211yescharacteristic
405C4×C107#54611yescharacteristic
406#25192C10711yesmaximal, characteristic, direct product factor, Sylow
407C2×C107—21no—
408C2×C107—21no—
409C2×C107—42no—
410C2×C107—81no—
411C2×C107—81no—
412C2×C107—82no—
413C2×C107—161no—
414C2×C107#242411yescharacteristic
415C2×C107#328811yescharacteristic
416C2×C107#328811yescharacteristic
417#3062C2×C10711yescharacteristic, complemented
418#3045C2×C10711yescharacteristic, complemented
419C2×#453C2×C10711yescharacteristic, complemented
420#3012C2×C10711yescharacteristic, complemented
421C2×#444C2×C10711yescharacteristic, complemented
422#2897C2×C10711yescharacteristic, complemented
423#2063C2×C10711yescharacteristic, complemented
424#2051C2×C10711yescharacteristic, complemented
425#2040C2×C10711yescharacteristic, complemented
426#2002C2×C10711yescharacteristic, complemented
427#1961C2×C10711yescharacteristic, complemented
428#1938C2×C10711yescharacteristic, complemented
429#1907C2×C10711yescharacteristic, complemented
430#1907C2×C10711yescharacteristic, complemented
431#1860C2×C10711yescharacteristic, complemented
432C107#2519211yescharacteristic, direct product factor, Sylow
433C2×H(5,𝔽2)C22×C10711yescharacteristic
434C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
435C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
436C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
437C2×#135C22×C10711yescharacteristic
438C2×#131C22×C10711yescharacteristic
439C2×#131C22×C10711yescharacteristic, complemented
440#537C22×C10711yescharacteristic
441#535C22×C10711yescharacteristic, complemented
442C2×#127C22×C10711yescharacteristic
443#520C22×C10711yescharacteristic
444#469—21no—
445#468—21no—
446#466—21no—
447#465—21no—
448#464—21no—
449#463—21no—
450#460—21no—
451#459—21no—
452#453—24no—
453#452—21no—
454#450—21no—
455#449—21no—
456#447—21no—
457#444—24no—
458C2×#108C22×C10711yescharacteristic, complemented
459#428C22×C10711yescharacteristic, complemented
460#424C22×C10711yescharacteristic, complemented
461C2×#104C22×C10711yescharacteristic
462C2×#104C22×C10711yescharacteristic
463C2×#104C22×C10711yescharacteristic, complemented
464#418—21no—
465#418C22×C10711yescharacteristic
466#417—21no—
467#417C22×C10711yescharacteristic
468#417C22×C10711yescharacteristic
469#417C22×C10711yescharacteristic, complemented
470#416—21no—
471#416C22×C10711yescharacteristic
472C2×#102—21no—
473C2×#102C22×C10711yescharacteristic
474C2×#102C22×C10711yescharacteristic
475C2×#102C22×C10711yescharacteristic, complemented
476C2×#102C22×C10711yescharacteristic, complemented
477C2×#100C22×C10711yescharacteristic
478C2×#100C22×C10711yescharacteristic, complemented
479#408C22×C10711yescharacteristic
480C2×#97C22×C10711yescharacteristic, complemented
481#382C22×C10711yescharacteristic, complemented
482#343C22×C10711yescharacteristic, complemented
483#343C22×C10711yescharacteristic, complemented
484#341C22×C10711yescharacteristic, complemented
485#339C22×C10711yescharacteristic, complemented
486H(5,𝔽2)—22no—
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—41no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41C23×C10711yescharacteristic
493C2×#41C23×C10711yescharacteristic
494C2×#41C23×C10711yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C10711yescharacteristic
500C22×D4C23×C10711yescharacteristic
501AGL(1,ℤ/8)—22no—
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—41no—
506AGL(1,ℤ/8)—41no—
507#135—22no—
508#135—22no—
509C2×Q16D4×C10711yescharacteristic, complemented
510C2×SD16—21no—
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16D4×C10711yescharacteristic, complemented
514C2×SD16D4×C10711yescharacteristic, complemented
515C2×D8—21no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8D4×C10711yescharacteristic, complemented
519#131—22no—
520#131—22no—
521#131—41no—
522#131—41no—
523C2×M16—21no—
524C2×M16—21no—
525C2×M16C23×C10711yescharacteristic
526C2×M16C23×C10711yescharacteristic
527C2×M16C23×C10711yescharacteristic
528C2×M16C23×C10711yescharacteristic
529C22×C8—21no—
530C22×C8—21no—
531C22×C8C23×C10711yescharacteristic
532C22×C8C23×C10711yescharacteristic
533#127—21no—
534#127—22no—
535#127—22no—
536#124—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—41no—
544#120—41no—
545C4×Q8—21no—
546C4×D4—21no—
547C4×D4—41no—
548#117—21no—
549#117C23×C10711yescharacteristic
550C2×C4⋊C4—21no—
551C2×C4⋊C4C23×C10711yescharacteristic
552C2×C4⋊C4C23×C10711yescharacteristic
553C2×C42C23×C10711yescharacteristic
554#108—22no—
555#107—21no—
556#106—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559#104—22no—
560#104—22no—
561#104D4×C10714yescomplemented
562#103—21no—
563#103—21no—
564#103—21no—
565#103D4×C10711yescharacteristic, complemented
566#103D4×C10711yescharacteristic, complemented
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102D4×C10711yescharacteristic, complemented
581#102D4×C10711yescharacteristic, complemented
582#100—22no—
583#100—41no—
584C22⋊C8—21no—
585C22⋊C8—21no—
586#97—22no—
587#95—41no—
588C24—21no—
589C24—21no—
590C24—41no—
591#41—21no—
592#41—21no—
593#41—24no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41C2×D4×C10712yes—
606#41#41×C10712yes—
607C2×Q8C2×D4×C10711yescharacteristic
608C2×Q8C2×D4×C10711yescharacteristic
609C2×Q8C2×D4×C10711yescharacteristic
610C2×D4—21no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—42no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—44no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—41no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C10711yescharacteristic
639C2×D4C2×D4×C10711yescharacteristic
640C2×D4C2×D4×C10711yescharacteristic
641C2×D4#41×C10712yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C10711yescharacteristic
651Q16—22no—
652SD16—22no—
653SD16—22no—
654SD16—42no—
655SD16—42no—
656SD16—42no—
657D8—22no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16—42no—
670M16C2×D4×C10712yes—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—42no—
680C2×C8—42no—
681C2×C8C2×D4×C10711yescharacteristic
682C2×C8C2×D4×C10711yescharacteristic
683C2×C8C2×D4×C10711yescharacteristic
684C2×C8C2×D4×C10711yescharacteristic
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—41no—
690C4⋊C4—41no—
691C4⋊C4C2×D4×C10711yescharacteristic
692C4⋊C4C2×D4×C10711yescharacteristic
693C22⋊C4—21no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C42—21no—
700C42—21no—
701C42—41no—
702C42C2×D4×C10712yes—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—161no—
718C23—161no—
719C23H(5,𝔽2)×C10711yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8#121×C10712yes—
726D4—22no—
727D4—22no—
728D4—21no—
729D4—21no—
730D4—22no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—22no—
735D4—44no—
736D4—44no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—88no—
748D4—161no—
749D4—161no—
750D4—161no—
751D4#121×C10712yes—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—161no—
772C2×C4C22×D4×C10711yescharacteristic
773C2×C4C22×D4×C10711yescharacteristic
774C2×C4C22×D4×C10711yescharacteristic
775C2×C4C2×#41×C10711yescharacteristic
776C2×C4C2×#41×C10711yescharacteristic
777C2×C4H(5,𝔽2)×C10711yescharacteristic
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—82no—
799C22—82no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—161no—
806C22—161no—
807C22—164no—
808C22#538×C10711yescharacteristic
809C22D42×C10711yescharacteristic
810C22#546×C10711yescharacteristic
811C4—22no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4C2×#121×C10711yescharacteristic
820C4#525×C10711yescharacteristic
821C4D42×C10711yescharacteristic
822C4#546×C10711yescharacteristic
823C2—21no—
824C2—21no—
825C2—42no—
826C2—81no—
827C2—81no—
828C2—82no—
829C2—161no—
830C2C107×#242411yescharacteristic
831C2C107×#328811yescharacteristic
832C2C107×#328811yescharacteristic
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×#3062C2semidirect
2. C107×#3045C2semidirect
3. C2×#453×C107C2semidirect
4. C107×#3012C2semidirect
5. C2×#444×C107C2semidirect
6. C107×#2897C2semidirect
7. C107×#2063C2semidirect
8. C107×#2051C2semidirect
9. C107×#2040C2semidirect
10. C107×#2002C2semidirect
11. C107×#1961C2semidirect
12. C107×#1938C2semidirect
13. C107×#1907C2semidirect
14. C107×#1907C2semidirect
15. C107×#1860C2semidirect
22. C2×#131×C107C22semidirect
24. #535×C107C22semidirect
41. C2×#108×C107C22semidirect
42. #428×C107C22semidirect
43. #424×C107C22semidirect
46. C2×#104×C107C22semidirect
52. #417×C107C22semidirect
58. C2×#102×C107C22semidirect
59. C2×#102×C107C22semidirect
61. C2×#100×C107C22semidirect
63. C2×#97×C107C22semidirect
64. #382×C107C22semidirect
65. #343×C107C22semidirect
66. #343×C107C22semidirect
67. #341×C107C22semidirect
68. #339×C107C22semidirect
92. C2×Q16×C107D4semidirect
96. C2×SD16×C107D4semidirect
97. C2×SD16×C107D4semidirect
101. C2×D8×C107D4semidirect
144. #104×C107D4semidirect
148. #103×C107D4semidirect
149. #103×C107D4semidirect
163. #102×C107D4semidirect
164. #102×C107D4semidirect
406. #25192C107direct (N × H)
417. #3062C2×C107semidirect
418. #3045C2×C107semidirect
419. C2×#453C2×C107semidirect
420. #3012C2×C107semidirect
421. C2×#444C2×C107semidirect
422. #2897C2×C107semidirect
423. #2063C2×C107semidirect
424. #2051C2×C107semidirect
425. #2040C2×C107semidirect
426. #2002C2×C107semidirect
427. #1961C2×C107semidirect
428. #1938C2×C107semidirect
429. #1907C2×C107semidirect
430. #1907C2×C107semidirect
431. #1860C2×C107semidirect
432. C107#25192direct (N × H)
439. C2×#131C22×C107semidirect
441. #535C22×C107semidirect
458. C2×#108C22×C107semidirect
459. #428C22×C107semidirect
460. #424C22×C107semidirect
463. C2×#104C22×C107semidirect
469. #417C22×C107semidirect
475. C2×#102C22×C107semidirect
476. C2×#102C22×C107semidirect
478. C2×#100C22×C107semidirect
480. C2×#97C22×C107semidirect
481. #382C22×C107semidirect
482. #343C22×C107semidirect
483. #343C22×C107semidirect
484. #341C22×C107semidirect
485. #339C22×C107semidirect
509. C2×Q16D4×C107semidirect
513. C2×SD16D4×C107semidirect
514. C2×SD16D4×C107semidirect
518. C2×D8D4×C107semidirect
561. #104D4×C107semidirect
565. #103D4×C107semidirect
566. #103D4×C107semidirect
580. #102D4×C107semidirect
581. #102D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#30622
C107×#30452
C2×#453×C1072
C107×#30122
C2×#444×C1072
C107×#28972
C107×#20632
C107×#20512
C107×#20402
C107×#20022
C107×#19612
C107×#19382
C107×#19072
C107×#18602
#25192107