Finite Group Databasebeta

← C107×#13041 #41039005

Subgroups — C107×#13041 #41039005

Order 27392.

964 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×B(4,𝔽2)×C107C211yesmaximal, characteristic
2C107×#2358C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C107C211yesmaximal, characteristic, complemented
4C107×#1792C211yesmaximal, characteristic, complemented
5C107×#1790C211yesmaximal, characteristic, complemented
6C107×#1393C211yesmaximal, characteristic, complemented
7C107×#1390C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C107C2211yescharacteristic
9C2×#120×C107—21no—
10C2×#120×C107C2211yescharacteristic
11C2×C4×D4×C107—21no—
12C22×C22⋊C4×C107—21no—
13B(4,𝔽2)×C107—22no—
14B(4,𝔽2)×C107C414yescomplemented
15C2×#104×C107—21no—
16#417×C107—21no—
17C2×#100×C107C2211yescharacteristic
18C2×#99×C107—21no—
19C2×#99×C107—21no—
20C2×#99×C107C2211yescharacteristic
21C2×#99×C107C2211yescharacteristic
22#390×C107C2211yescharacteristic
23#388×C107—21no—
24#386×C107—21no—
25#386×C107—21no—
26#386×C107C2211yescharacteristic
27#385×C107—21no—
28C4×C22⋊C4×C107—21no—
29AΣL(1,𝔽16)×C107—22no—
30C25×C107D411yescharacteristic
31H(5,𝔽2)×C107—21no—
32H(5,𝔽2)×C107—21no—
33H(5,𝔽2)×C107—21no—
34H(5,𝔽2)×C107—42no—
35H(5,𝔽2)×C107C2×C412yescomplemented
36C2×#41×C107—21no—
37C2×#41×C107—41no—
38C22×D4×C107—21no—
39C22×D4×C107—21no—
40C22×D4×C107—21no—
41C22×D4×C107—41no—
42C22×D4×C107—41no—
43C22×D4×C107C2311yescharacteristic
44C23×C4×C107—21no—
45C23×C4×C107—21no—
46C23×C4×C107D411yescharacteristic, complemented
47C2×M16×C107—21no—
48#120×C107—21no—
49#120×C107—21no—
50#120×C107—24no—
51#120×C107—42no—
52#120×C107C2×C412yes—
53#120×C107D412yes—
54C4×D4×C107—44no—
55C2×C4⋊C4×C107—21no—
56C2×C4⋊C4×C107D411yescharacteristic, complemented
57C2×C22⋊C4×C107—21no—
58C2×C22⋊C4×C107—21no—
59C2×C22⋊C4×C107—21no—
60C2×C22⋊C4×C107—21no—
61C2×C22⋊C4×C107—21no—
62C2×C22⋊C4×C107—21no—
63C2×C22⋊C4×C107—21no—
64C2×C22⋊C4×C107—21no—
65C2×C22⋊C4×C107—44no—
66C2×C22⋊C4×C107—41no—
67C2×C22⋊C4×C107—41no—
68C2×C22⋊C4×C107D411yescharacteristic
69C2×C22⋊C4×C107D411yescharacteristic, complemented
70C2×C42×C107—21no—
71C2×C42×C107D411yescharacteristic, complemented
72#104×C107—42no—
73#103×C107—41no—
74#102×C107—41no—
75#100×C107—21no—
76#100×C107—21no—
77#99×C107—21no—
78#99×C107—24no—
79#99×C107—21no—
80#99×C107—21no—
81#99×C107—42no—
82#99×C107C2×C412yescomplemented
83#95×C107—21no—
84#95×C107—21no—
85#95×C107—21no—
86#95×C107—41no—
87C24×C107—21no—
88C24×C107—21no—
89C24×C107—21no—
90C24×C107—21no—
91C24×C107—42no—
92C24×C107—41no—
93C24×C107—42no—
94C24×C107—41no—
95C24×C107C22⋊C412yescomplemented
96C24×C107C2×D411yescharacteristic
97C24×C107C2×D411yescharacteristic
98#41×C107—22no—
99#41×C107—22no—
100#41×C107—42no—
101#41×C107—41no—
102#41×C107—42no—
103#41×C107—42no—
104#41×C107—42no—
105#41×C107—41no—
106C2×Q8×C107—21no—
107C2×D4×C107—21no—
108C2×D4×C107—22no—
109C2×D4×C107—22no—
110C2×D4×C107—22no—
111C2×D4×C107—22no—
112C2×D4×C107—22no—
113C2×D4×C107—22no—
114C2×D4×C107—41no—
115C2×D4×C107—41no—
116C2×D4×C107—42no—
117C2×D4×C107—42no—
118C2×D4×C107—42no—
119C2×D4×C107—42no—
120C2×D4×C107—41no—
121C2×D4×C107—41no—
122C2×D4×C107—41no—
123C2×D4×C107—41no—
124C2×D4×C107—42no—
125C2×D4×C107—42no—
126C2×D4×C107—41no—
127C2×D4×C107—41no—
128C2×D4×C107—41no—
129C2×D4×C107—44no—
130C2×D4×C107—82no—
131C2×D4×C107—82no—
132C2×D4×C107C22×C411yescharacteristic
133C2×D4×C107C2×D411yescharacteristic
134C2×D4×C107#4111yescharacteristic
135C2×D4×C107#4111yescharacteristic
136C22×C4×C107—21no—
137C22×C4×C107—21no—
138C22×C4×C107—21no—
139C22×C4×C107—21no—
140C22×C4×C107—21no—
141C22×C4×C107—21no—
142C22×C4×C107—21no—
143C22×C4×C107—41no—
144C22×C4×C107—42no—
145C22×C4×C107—42no—
146C22×C4×C107—42no—
147C22×C4×C107—41no—
148C22×C4×C107—41no—
149C22×C4×C107—42no—
150C22×C4×C107—42no—
151C22×C4×C107—41no—
152C22×C4×C107—81no—
153C22×C4×C107—81no—
154C22×C4×C107C2×D411yescharacteristic
155M16×C107—41no—
156M16×C107—41no—
157C2×C8×C107—41no—
158C4⋊C4×C107—41no—
159C4⋊C4×C107—42no—
160C22⋊C4×C107—24no—
161C22⋊C4×C107—21no—
162C22⋊C4×C107—22no—
163C22⋊C4×C107—22no—
164C22⋊C4×C107—22no—
165C22⋊C4×C107—42no—
166C22⋊C4×C107—42no—
167C22⋊C4×C107—42no—
168C22⋊C4×C107—44no—
169C22⋊C4×C107—42no—
170C22⋊C4×C107—41no—
171C22⋊C4×C107—41no—
172C22⋊C4×C107—41no—
173C22⋊C4×C107—41no—
174C22⋊C4×C107—82no—
175C22⋊C4×C107C22⋊C412yescomplemented
176C42×C107—41no—
177C42×C107—42no—
178C23×C107—22no—
179C23×C107—22no—
180C23×C107—22no—
181C23×C107—21no—
182C23×C107—21no—
183C23×C107—21no—
184C23×C107—21no—
185C23×C107—22no—
186C23×C107—22no—
187C23×C107—41no—
188C23×C107—41no—
189C23×C107—41no—
190C23×C107—41no—
191C23×C107—42no—
192C23×C107—41no—
193C23×C107—44no—
194C23×C107—41no—
195C23×C107—44no—
196C23×C107—41no—
197C23×C107—41no—
198C23×C107—41no—
199C23×C107—41no—
200C23×C107—42no—
201C23×C107—42no—
202C23×C107—41no—
203C23×C107—81no—
204C23×C107—84no—
205C23×C107—81no—
206C23×C107—81no—
207C23×C107—81no—
208C23×C107—81no—
209C23×C107—81no—
210C23×C107—81no—
211C23×C107C2×C22⋊C411yescharacteristic
212C23×C107C4×D411yescharacteristic
213C23×C107#12011yescharacteristic
214C23×C107#12111yescharacteristic
215C23×C107#12311yescharacteristic
216Q8×C107—22no—
217Q8×C107—41no—
218D4×C107—22no—
219D4×C107—41no—
220D4×C107—41no—
221D4×C107—41no—
222D4×C107—41no—
223D4×C107—41no—
224D4×C107—44no—
225D4×C107—44no—
226D4×C107—42no—
227D4×C107—42no—
228D4×C107—42no—
229D4×C107—42no—
230D4×C107—42no—
231D4×C107—42no—
232D4×C107—88no—
233C2×C4×C107—21no—
234C2×C4×C107—21no—
235C2×C4×C107—22no—
236C2×C4×C107—22no—
237C2×C4×C107—22no—
238C2×C4×C107—22no—
239C2×C4×C107—22no—
240C2×C4×C107—42no—
241C2×C4×C107—42no—
242C2×C4×C107—41no—
243C2×C4×C107—41no—
244C2×C4×C107—41no—
245C2×C4×C107—41no—
246C2×C4×C107—41no—
247C2×C4×C107—41no—
248C2×C4×C107—41no—
249C2×C4×C107—41no—
250C2×C4×C107—41no—
251C2×C4×C107—42no—
252C2×C4×C107—42no—
253C2×C4×C107—41no—
254C2×C4×C107—41no—
255C2×C4×C107—41no—
256C2×C4×C107—41no—
257C2×C4×C107—41no—
258C2×C4×C107—41no—
259C2×C4×C107—81no—
260C2×C4×C107—84no—
261C2×C4×C107—84no—
262C2×C4×C107—81no—
263C2×C4×C107—81no—
264C2×C4×C107—81no—
265C2×C4×C107—81no—
266C2×C4×C107—81no—
267C2×C4×C107C4×D411yescharacteristic
268C2×C4×C107#12111yescharacteristic
269C8×C107—81no—
270C22×C107—21no—
271C22×C107—21no—
272C22×C107—24no—
273C22×C107—21no—
274C22×C107—21no—
275C22×C107—21no—
276C22×C107—21no—
277C22×C107—41no—
278C22×C107—41no—
279C22×C107—41no—
280C22×C107—41no—
281C22×C107—42no—
282C22×C107—42no—
283C22×C107—42no—
284C22×C107—44no—
285C22×C107—42no—
286C22×C107—41no—
287C22×C107—42no—
288C22×C107—41no—
289C22×C107—41no—
290C22×C107—41no—
291C22×C107—42no—
292C22×C107—42no—
293C22×C107—81no—
294C22×C107—81no—
295C22×C107—82no—
296C22×C107—82no—
297C22×C107—82no—
298C22×C107—82no—
299C22×C107—82no—
300C22×C107—81no—
301C22×C107—81no—
302C22×C107—161no—
303C22×C107—161no—
304C22×C107#38611yescharacteristic
305C22×C107B(4,𝔽2)11yescharacteristic
306C22×C107B(4,𝔽2)11yescharacteristic
307C4×C107—21no—
308C4×C107—21no—
309C4×C107—42no—
310C4×C107—42no—
311C4×C107—42no—
312C4×C107—42no—
313C4×C107—81no—
314C4×C107—82no—
315C4×C107—81no—
316C4×C107—161no—
317#13041C10711yesmaximal, characteristic, direct product factor, Sylow
318C2×C107—21no—
319C2×C107—21no—
320C2×C107—41no—
321C2×C107—41no—
322C2×C107—44no—
323C2×C107—41no—
324C2×C107—41no—
325C2×C107—82no—
326C2×C107#188911yescharacteristic
327C2×C107#219611yescharacteristic
328C2×C107#219711yescharacteristic
329C2×B(4,𝔽2)C2×C10711yescharacteristic
330#2358C2×C10711yescharacteristic, complemented
331C2×AΣL(1,𝔽16)C2×C10711yescharacteristic, complemented
332#1792C2×C10711yescharacteristic, complemented
333#1790C2×C10711yescharacteristic, complemented
334#1393C2×C10711yescharacteristic, complemented
335#1390C2×C10711yescharacteristic, complemented
336C107#1304111yescharacteristic, direct product factor, Sylow
337C2×H(5,𝔽2)C22×C10711yescharacteristic
338C2×#120—21no—
339C2×#120C22×C10711yescharacteristic
340C2×C4×D4—21no—
341C22×C22⋊C4—21no—
342B(4,𝔽2)—22no—
343B(4,𝔽2)C4×C10714yescomplemented
344C2×#104—21no—
345#417—21no—
346C2×#100C22×C10711yescharacteristic
347C2×#99—21no—
348C2×#99—21no—
349C2×#99C22×C10711yescharacteristic
350C2×#99C22×C10711yescharacteristic
351#390C22×C10711yescharacteristic
352#388—21no—
353#386—21no—
354#386—21no—
355#386C22×C10711yescharacteristic
356#385—21no—
357C4×C22⋊C4—21no—
358AΣL(1,𝔽16)—22no—
359C25D4×C10711yescharacteristic
360H(5,𝔽2)—21no—
361H(5,𝔽2)—21no—
362H(5,𝔽2)—21no—
363H(5,𝔽2)—42no—
364H(5,𝔽2)C2×C4×C10712yescomplemented
365C2×#41—21no—
366C2×#41—41no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—41no—
371C22×D4—41no—
372C22×D4C23×C10711yescharacteristic
373C23×C4—21no—
374C23×C4—21no—
375C23×C4D4×C10711yescharacteristic, complemented
376C2×M16—21no—
377#120—21no—
378#120—21no—
379#120—24no—
380#120—42no—
381#120C2×C4×C10712yes—
382#120D4×C10712yes—
383C4×D4—44no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4D4×C10711yescharacteristic, complemented
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4D4×C10711yescharacteristic
398C2×C22⋊C4D4×C10711yescharacteristic, complemented
399C2×C42—21no—
400C2×C42D4×C10711yescharacteristic, complemented
401#104—42no—
402#103—41no—
403#102—41no—
404#100—21no—
405#100—21no—
406#99—21no—
407#99—24no—
408#99—21no—
409#99—21no—
410#99—42no—
411#99C2×C4×C10712yescomplemented
412#95—21no—
413#95—21no—
414#95—21no—
415#95—41no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—42no—
421C24—41no—
422C24—42no—
423C24—41no—
424C24C22⋊C4×C10712yescomplemented
425C24C2×D4×C10711yescharacteristic
426C24C2×D4×C10711yescharacteristic
427#41—22no—
428#41—22no—
429#41—42no—
430#41—41no—
431#41—42no—
432#41—42no—
433#41—42no—
434#41—41no—
435C2×Q8—21no—
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—44no—
459C2×D4—82no—
460C2×D4—82no—
461C2×D4C22×C4×C10711yescharacteristic
462C2×D4C2×D4×C10711yescharacteristic
463C2×D4#41×C10711yescharacteristic
464C2×D4#41×C10711yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—41no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4C2×D4×C10711yescharacteristic
484M16—41no—
485M16—41no—
486C2×C8—41no—
487C4⋊C4—41no—
488C4⋊C4—42no—
489C22⋊C4—24no—
490C22⋊C4—21no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—44no—
498C22⋊C4—42no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—82no—
504C22⋊C4C22⋊C4×C10712yescomplemented
505C42—41no—
506C42—42no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—22no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—41no—
522C23—44no—
523C23—41no—
524C23—44no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—41no—
532C23—81no—
533C23—84no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23C2×C22⋊C4×C10711yescharacteristic
541C23C4×D4×C10711yescharacteristic
542C23#120×C10711yescharacteristic
543C23#121×C10711yescharacteristic
544C23#123×C10711yescharacteristic
545Q8—22no—
546Q8—41no—
547D4—22no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—42no—
557D4—44no—
558D4—44no—
559D4—42no—
560D4—42no—
561D4—88no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—81no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—81no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4C4×D4×C10711yescharacteristic
597C2×C4#121×C10711yescharacteristic
598C8—81no—
599C22—21no—
600C22—21no—
601C22—24no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—42no—
615C22—41no—
616C22—42no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—42no—
622C22—81no—
623C22—81no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—81no—
630C22—81no—
631C22—161no—
632C22—161no—
633C22#386×C10711yescharacteristic
634C22B(4,𝔽2)×C10711yescharacteristic
635C22B(4,𝔽2)×C10711yescharacteristic
636C4—21no—
637C4—21no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—81no—
643C4—82no—
644C4—81no—
645C4—161no—
646C2—21no—
647C2—21no—
648C2—41no—
649C2—41no—
650C2—44no—
651C2—41no—
652C2—41no—
653C2—82no—
654C2C107×#188911yescharacteristic
655C2C107×#219611yescharacteristic
656C2C107×#219711yescharacteristic
subgroupG/H
center, socleC22×C107B(4,𝔽2)
commutatorC2×D4C22×C4×C107
Frattini, cosocleC22×D4C23×C107
prime radicalC2×B(4,𝔽2)×C107C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C107 ◁ C22×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2358C2semidirect
3. C2×AΣL(1,𝔽16)×C107C2semidirect
4. C107×#1792C2semidirect
5. C107×#1790C2semidirect
6. C107×#1393C2semidirect
7. C107×#1390C2semidirect
14. B(4,𝔽2)×C107C4semidirect
35. H(5,𝔽2)×C107C2×C4semidirect
46. C23×C4×C107D4semidirect
56. C2×C4⋊C4×C107D4semidirect
69. C2×C22⋊C4×C107D4semidirect
71. C2×C42×C107D4semidirect
82. #99×C107C2×C4semidirect
95. C24×C107C22⋊C4semidirect
175. C22⋊C4×C107C22⋊C4semidirect
317. #13041C107direct (N × H)
330. #2358C2×C107semidirect
331. C2×AΣL(1,𝔽16)C2×C107semidirect
332. #1792C2×C107semidirect
333. #1790C2×C107semidirect
334. #1393C2×C107semidirect
335. #1390C2×C107semidirect
336. C107#13041direct (N × H)
343. B(4,𝔽2)C4×C107semidirect
364. H(5,𝔽2)C2×C4×C107semidirect
375. C23×C4D4×C107semidirect
385. C2×C4⋊C4D4×C107semidirect
398. C2×C22⋊C4D4×C107semidirect
400. C2×C42D4×C107semidirect
411. #99C2×C4×C107semidirect
424. C24C22⋊C4×C107semidirect
504. C22⋊C4C22⋊C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×B(4,𝔽2)×C1072
C107×#23582
C2×AΣL(1,𝔽16)×C1072
C107×#17922
C107×#17902
C107×#13932
C107×#13902
#13041107