Finite Group Databasebeta

← C107×#25188 #41051152

Subgroups — C107×#25188 #41051152

Order 27392.

1066 conjugacy classes of subgroups.

The subgroup lattice has 836 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×#443×C107C211yesmaximal, characteristic, complemented
6C107×#2897C211yesmaximal, characteristic, complemented
7C107×#2063C211yesmaximal, characteristic, complemented
8C107×#2051C211yesmaximal, characteristic, complemented
9C107×#2039C211yesmaximal, characteristic, complemented
10C107×#2002C211yesmaximal, characteristic, complemented
11C107×#1957C211yesmaximal, characteristic, complemented
12C107×#1937C211yesmaximal, characteristic, complemented
13C107×#1907C211yesmaximal, characteristic, complemented
14C107×#1907C211yesmaximal, characteristic, complemented
15C107×#1859C211yesmaximal, 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#443×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×C4×C8×C107C2211yescharacteristic, complemented
64#384×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×C107—41no—
135C2×C4⋊C4×C107C2311yescharacteristic
136C2×C4⋊C4×C107C2311yescharacteristic
137C2×C42×C107C2311yescharacteristic
138#108×C107—22no—
139#107×C107—21no—
140#106×C107—21no—
141C4⋊C8×C107—21no—
142C4⋊C8×C107—21no—
143#104×C107—22no—
144#104×C107—22no—
145#104×C107D414yescomplemented
146#103×C107—21no—
147#103×C107—21no—
148#103×C107—21no—
149#103×C107D411yescharacteristic, complemented
150#103×C107D411yescharacteristic, complemented
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×C107—21no—
164#102×C107D411yescharacteristic, complemented
165#102×C107D411yescharacteristic, complemented
166#100×C107—22no—
167#100×C107—41no—
168C22⋊C8×C107—21no—
169C22⋊C8×C107—21no—
170C4×C8×C107—22no—
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×C107—82no—
275C4⋊C4×C107C2×D411yescharacteristic
276C4⋊C4×C107C2×D411yescharacteristic
277C22⋊C4×C107—21no—
278C22⋊C4×C107—41no—
279C22⋊C4×C107—41no—
280C22⋊C4×C107—41no—
281C22⋊C4×C107—41no—
282C22⋊C4×C107—41no—
283C42×C107—21no—
284C42×C107—21no—
285C42×C107—41no—
286C42×C107C2×D412yes—
287C23×C107—21no—
288C23×C107—21no—
289C23×C107—21no—
290C23×C107—22no—
291C23×C107—44no—
292C23×C107—41no—
293C23×C107—41no—
294C23×C107—41no—
295C23×C107—41no—
296C23×C107—41no—
297C23×C107—81no—
298C23×C107—81no—
299C23×C107—81no—
300C23×C107—81no—
301C23×C107—161no—
302C23×C107—161no—
303C23×C107H(5,𝔽2)11yescharacteristic
304Q8×C107—21no—
305Q8×C107—21no—
306Q8×C107—21no—
307Q8×C107—21no—
308Q8×C107—21no—
309Q8×C107#12112yes—
310D4×C107—22no—
311D4×C107—22no—
312D4×C107—21no—
313D4×C107—21no—
314D4×C107—22no—
315D4×C107—21no—
316D4×C107—21no—
317D4×C107—21no—
318D4×C107—22no—
319D4×C107—44no—
320D4×C107—44no—
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—41no—
331D4×C107—88no—
332D4×C107—161no—
333D4×C107—161no—
334D4×C107—161no—
335D4×C107#12112yes—
336C2×C4×C107—22no—
337C2×C4×C107—22no—
338C2×C4×C107—21no—
339C2×C4×C107—22no—
340C2×C4×C107—22no—
341C2×C4×C107—22no—
342C2×C4×C107—21no—
343C2×C4×C107—21no—
344C2×C4×C107—21no—
345C2×C4×C107—21no—
346C2×C4×C107—44no—
347C2×C4×C107—41no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—41no—
351C2×C4×C107—41no—
352C2×C4×C107—41no—
353C2×C4×C107—81no—
354C2×C4×C107—81no—
355C2×C4×C107—161no—
356C2×C4×C107C22×D411yescharacteristic
357C2×C4×C107C22×D411yescharacteristic
358C2×C4×C107C22×D411yescharacteristic
359C2×C4×C107C2×#4111yescharacteristic
360C2×C4×C107C2×#4111yescharacteristic
361C2×C4×C107H(5,𝔽2)11yescharacteristic
362C8×C107—21no—
363C8×C107—21no—
364C8×C107—21no—
365C8×C107—21no—
366C8×C107—22no—
367C8×C107—41no—
368C8×C107—41no—
369C8×C107—41no—
370C22×C107—21no—
371C22×C107—21no—
372C22×C107—22no—
373C22×C107—41no—
374C22×C107—41no—
375C22×C107—41no—
376C22×C107—42no—
377C22×C107—41no—
378C22×C107—41no—
379C22×C107—41no—
380C22×C107—41no—
381C22×C107—41no—
382C22×C107—82no—
383C22×C107—82no—
384C22×C107—81no—
385C22×C107—81no—
386C22×C107—81no—
387C22×C107—81no—
388C22×C107—81no—
389C22×C107—161no—
390C22×C107—161no—
391C22×C107—164no—
392C22×C107#53811yescharacteristic
393C22×C107D4211yescharacteristic
394C22×C107#54611yescharacteristic
395C4×C107—24no—
396C4×C107—22no—
397C4×C107—41no—
398C4×C107—41no—
399C4×C107—41no—
400C4×C107—41no—
401C4×C107—81no—
402C4×C107—81no—
403C4×C107C2×#12111yescharacteristic
404C4×C107#52511yescharacteristic
405C4×C107D4211yescharacteristic
406C4×C107#54611yescharacteristic
407#25188C10711yesmaximal, characteristic, direct product factor, Sylow
408C2×C107—21no—
409C2×C107—21no—
410C2×C107—42no—
411C2×C107—81no—
412C2×C107—81no—
413C2×C107—82no—
414C2×C107—161no—
415C2×C107#242411yescharacteristic
416C2×C107#329111yescharacteristic
417C2×C107#329211yescharacteristic
418#3062C2×C10711yescharacteristic, complemented
419#3045C2×C10711yescharacteristic, complemented
420C2×#453C2×C10711yescharacteristic, complemented
421#3012C2×C10711yescharacteristic, complemented
422C2×#443C2×C10711yescharacteristic, complemented
423#2897C2×C10711yescharacteristic, complemented
424#2063C2×C10711yescharacteristic, complemented
425#2051C2×C10711yescharacteristic, complemented
426#2039C2×C10711yescharacteristic, complemented
427#2002C2×C10711yescharacteristic, complemented
428#1957C2×C10711yescharacteristic, complemented
429#1937C2×C10711yescharacteristic, complemented
430#1907C2×C10711yescharacteristic, complemented
431#1907C2×C10711yescharacteristic, complemented
432#1859C2×C10711yescharacteristic, complemented
433C107#2518811yescharacteristic, direct product factor, Sylow
434C2×H(5,𝔽2)C22×C10711yescharacteristic
435C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
436C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
437C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
438C2×#135C22×C10711yescharacteristic
439C2×#131C22×C10711yescharacteristic
440C2×#131C22×C10711yescharacteristic, complemented
441#537C22×C10711yescharacteristic
442#535C22×C10711yescharacteristic, complemented
443C2×#127C22×C10711yescharacteristic
444#520C22×C10711yescharacteristic
445#469—21no—
446#468—21no—
447#466—21no—
448#465—21no—
449#464—21no—
450#463—21no—
451#460—21no—
452#459—21no—
453#453—24no—
454#452—21no—
455#450—21no—
456#449—21no—
457#447—21no—
458#443—24no—
459C2×#108C22×C10711yescharacteristic, complemented
460#428C22×C10711yescharacteristic, complemented
461#424C22×C10711yescharacteristic, complemented
462C2×#104C22×C10711yescharacteristic
463C2×#104C22×C10711yescharacteristic
464C2×#104C22×C10711yescharacteristic, complemented
465#418—21no—
466#418C22×C10711yescharacteristic
467#417—21no—
468#417C22×C10711yescharacteristic
469#417C22×C10711yescharacteristic
470#417C22×C10711yescharacteristic, complemented
471#416—21no—
472#416C22×C10711yescharacteristic
473C2×#102—21no—
474C2×#102C22×C10711yescharacteristic
475C2×#102C22×C10711yescharacteristic
476C2×#102C22×C10711yescharacteristic, complemented
477C2×#102C22×C10711yescharacteristic, complemented
478C2×#100C22×C10711yescharacteristic
479C2×#100C22×C10711yescharacteristic, complemented
480#408C22×C10711yescharacteristic
481C2×C4×C8C22×C10711yescharacteristic, complemented
482#384C22×C10711yescharacteristic, complemented
483#343C22×C10711yescharacteristic, complemented
484#343C22×C10711yescharacteristic, complemented
485#341C22×C10711yescharacteristic, complemented
486#339C22×C10711yescharacteristic, complemented
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C10711yescharacteristic
494C2×#41C23×C10711yescharacteristic
495C2×#41C23×C10711yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C23×C10711yescharacteristic
501C22×D4C23×C10711yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)—41no—
508#135—22no—
509#135—22no—
510C2×Q16D4×C10711yescharacteristic, complemented
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16D4×C10711yescharacteristic, complemented
515C2×SD16D4×C10711yescharacteristic, complemented
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8D4×C10711yescharacteristic, complemented
520#131—22no—
521#131—22no—
522#131—41no—
523#131—41no—
524C2×M16—21no—
525C2×M16—21no—
526C2×M16C23×C10711yescharacteristic
527C2×M16C23×C10711yescharacteristic
528C2×M16C23×C10711yescharacteristic
529C2×M16C23×C10711yescharacteristic
530C22×C8—21no—
531C22×C8—21no—
532C22×C8C23×C10711yescharacteristic
533C22×C8C23×C10711yescharacteristic
534#127—21no—
535#127—22no—
536#127—22no—
537#124—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—41no—
545#120—41no—
546C4×Q8—21no—
547C4×D4—21no—
548C4×D4—41no—
549#117—21no—
550#117C23×C10711yescharacteristic
551C2×C4⋊C4—21no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4C23×C10711yescharacteristic
554C2×C4⋊C4C23×C10711yescharacteristic
555C2×C42C23×C10711yescharacteristic
556#108—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8—21no—
561#104—22no—
562#104—22no—
563#104D4×C10714yescomplemented
564#103—21no—
565#103—21no—
566#103—21no—
567#103D4×C10711yescharacteristic, complemented
568#103D4×C10711yescharacteristic, complemented
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#102—21no—
581#102—21no—
582#102D4×C10711yescharacteristic, complemented
583#102D4×C10711yescharacteristic, complemented
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C4×C8—22no—
589C24—21no—
590C24—21no—
591C24—41no—
592#41—21no—
593#41—21no—
594#41—24no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41C2×D4×C10712yes—
607#41#41×C10712yes—
608C2×Q8C2×D4×C10711yescharacteristic
609C2×Q8C2×D4×C10711yescharacteristic
610C2×Q8C2×D4×C10711yescharacteristic
611C2×D4—21no—
612C2×D4—24no—
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—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—42no—
636C2×D4—41no—
637C2×D4—82no—
638C2×D4—82no—
639C2×D4C2×D4×C10711yescharacteristic
640C2×D4C2×D4×C10711yescharacteristic
641C2×D4C2×D4×C10711yescharacteristic
642C2×D4#41×C10712yes—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4C24×C10711yescharacteristic
652Q16—22no—
653SD16—22no—
654SD16—22no—
655SD16—42no—
656SD16—42no—
657SD16—42no—
658D8—22no—
659D8—42no—
660D8—42no—
661D8—42no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—42no—
670M16—42no—
671M16C2×D4×C10712yes—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—42no—
681C2×C8—42no—
682C2×C8C2×D4×C10711yescharacteristic
683C2×C8C2×D4×C10711yescharacteristic
684C2×C8C2×D4×C10711yescharacteristic
685C2×C8C2×D4×C10711yescharacteristic
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—82no—
693C4⋊C4C2×D4×C10711yescharacteristic
694C4⋊C4C2×D4×C10711yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C42—21no—
702C42—21no—
703C42—41no—
704C42C2×D4×C10712yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—44no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—161no—
720C23—161no—
721C23H(5,𝔽2)×C10711yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C10712yes—
728D4—22no—
729D4—22no—
730D4—21no—
731D4—21no—
732D4—22no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4—161no—
753D4#121×C10712yes—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—44no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—161no—
774C2×C4C22×D4×C10711yescharacteristic
775C2×C4C22×D4×C10711yescharacteristic
776C2×C4C22×D4×C10711yescharacteristic
777C2×C4C2×#41×C10711yescharacteristic
778C2×C4C2×#41×C10711yescharacteristic
779C2×C4H(5,𝔽2)×C10711yescharacteristic
780C8—21no—
781C8—21no—
782C8—21no—
783C8—21no—
784C8—22no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—21no—
789C22—21no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—82no—
801C22—82no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22#538×C10711yescharacteristic
811C22D42×C10711yescharacteristic
812C22#546×C10711yescharacteristic
813C4—24no—
814C4—22no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—81no—
820C4—81no—
821C4C2×#121×C10711yescharacteristic
822C4#525×C10711yescharacteristic
823C4D42×C10711yescharacteristic
824C4#546×C10711yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—81no—
830C2—82no—
831C2—161no—
832C2C107×#242411yescharacteristic
833C2C107×#329111yescharacteristic
834C2C107×#329211yescharacteristic
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×#443×C107C2semidirect
6. C107×#2897C2semidirect
7. C107×#2063C2semidirect
8. C107×#2051C2semidirect
9. C107×#2039C2semidirect
10. C107×#2002C2semidirect
11. C107×#1957C2semidirect
12. C107×#1937C2semidirect
13. C107×#1907C2semidirect
14. C107×#1907C2semidirect
15. C107×#1859C2semidirect
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×C4×C8×C107C22semidirect
64. #384×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
145. #104×C107D4semidirect
149. #103×C107D4semidirect
150. #103×C107D4semidirect
164. #102×C107D4semidirect
165. #102×C107D4semidirect
407. #25188C107direct (N × H)
418. #3062C2×C107semidirect
419. #3045C2×C107semidirect
420. C2×#453C2×C107semidirect
421. #3012C2×C107semidirect
422. C2×#443C2×C107semidirect
423. #2897C2×C107semidirect
424. #2063C2×C107semidirect
425. #2051C2×C107semidirect
426. #2039C2×C107semidirect
427. #2002C2×C107semidirect
428. #1957C2×C107semidirect
429. #1937C2×C107semidirect
430. #1907C2×C107semidirect
431. #1907C2×C107semidirect
432. #1859C2×C107semidirect
433. C107#25188direct (N × H)
440. C2×#131C22×C107semidirect
442. #535C22×C107semidirect
459. C2×#108C22×C107semidirect
460. #428C22×C107semidirect
461. #424C22×C107semidirect
464. C2×#104C22×C107semidirect
470. #417C22×C107semidirect
476. C2×#102C22×C107semidirect
477. C2×#102C22×C107semidirect
479. C2×#100C22×C107semidirect
481. C2×C4×C8C22×C107semidirect
482. #384C22×C107semidirect
483. #343C22×C107semidirect
484. #343C22×C107semidirect
485. #341C22×C107semidirect
486. #339C22×C107semidirect
510. C2×Q16D4×C107semidirect
514. C2×SD16D4×C107semidirect
515. C2×SD16D4×C107semidirect
519. C2×D8D4×C107semidirect
563. #104D4×C107semidirect
567. #103D4×C107semidirect
568. #103D4×C107semidirect
582. #102D4×C107semidirect
583. #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×#443×C1072
C107×#28972
C107×#20632
C107×#20512
C107×#20392
C107×#20022
C107×#19572
C107×#19372
C107×#19072
C107×#18592
#25188107