Finite Group Databasebeta

← C107×#9042 #41035006

Subgroups — C107×#9042 #41035006

Order 27392.

966 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C107C211yesmaximal, characteristic
2C107×#2329C211yesmaximal, characteristic, complemented
3C107×#1786C211yesmaximal, characteristic
4C2×#328×C107C211yesmaximal, characteristic, complemented
5C107×#1438C211yesmaximal, characteristic
6C107×#1294C211yesmaximal, characteristic, complemented
7C107×#1280C211yesmaximal, characteristic, complemented
8C23×D4×C107C2211yescharacteristic
9C22×SD16×C107—21no—
10C2×C22⋊Q8×C107C2211yescharacteristic
11C22×C22⋊C4×C107—21no—
12C22×C22⋊C4×C107—21no—
13#450×C107—22no—
14#450×C107C414yescomplemented
15C2×#102×C107—21no—
16C2×#102×C107—21no—
17C2×#102×C107—21no—
18C2×C22⋊C8×C107C2211yescharacteristic
19C2×C22⋊C8×C107C2211yescharacteristic
20#391×C107—21no—
21#389×C107—21no—
22#387×C107—21no—
23#387×C107—21no—
24#385×C107—21no—
25#380×C107C2211yescharacteristic
26C4×C22⋊C4×C107—21no—
27C2×#95×C107C2211yescharacteristic
28C2×#95×C107C2211yescharacteristic
29#328×C107—22no—
30C25×C107—21no—
31C22×Q8×C107D411yescharacteristic
32C22×D4×C107—21no—
33C22×D4×C107—21no—
34C22×D4×C107—21no—
35C22×D4×C107—21no—
36C22×D4×C107—21no—
37C22×D4×C107—42no—
38C22×D4×C107—42no—
39C22×D4×C107C2×C412yes—
40C23×C4×C107—21no—
41C23×C4×C107D411yescharacteristic
42C23×C4×C107D411yescharacteristic
43C23×C4×C107C2311yescharacteristic
44C2×SD16×C107—24no—
45C2×SD16×C107—42no—
46C2×SD16×C107—42no—
47C22×C8×C107—21no—
48C22×C8×C107—21no—
49C22⋊Q8×C107—21no—
50C22⋊Q8×C107—21no—
51C22⋊Q8×C107C2×C412yes—
52C22⋊Q8×C107D412yes—
53C2×C4⋊C4×C107—21no—
54C2×C4⋊C4×C107—21no—
55C2×C4⋊C4×C107—21no—
56C2×C4⋊C4×C107D411yescharacteristic
57C2×C4⋊C4×C107D411yescharacteristic
58C2×C4⋊C4×C107D411yescharacteristic
59C2×C22⋊C4×C107—21no—
60C2×C22⋊C4×C107—21no—
61C2×C22⋊C4×C107—42no—
62C2×C22⋊C4×C107—42no—
63C2×C22⋊C4×C107—42no—
64C2×C22⋊C4×C107—42no—
65C2×C22⋊C4×C107—42no—
66C2×C22⋊C4×C107—42no—
67C2×C42×C107—21no—
68C2×C42×C107—21no—
69#102×C107—24no—
70#102×C107—42no—
71#102×C107—42no—
72C22⋊C8×C107—21no—
73C22⋊C8×C107—21no—
74C22⋊C8×C107—21no—
75C22⋊C8×C107C2×C412yes—
76#95×C107—21no—
77#95×C107—21no—
78#95×C107—21no—
79#95×C107—21no—
80#95×C107—21no—
81#95×C107—21no—
82#95×C107—21no—
83#95×C107—21no—
84#95×C107—21no—
85C24×C107—22no—
86C24×C107—22no—
87C24×C107—22no—
88C24×C107—41no—
89C24×C107—41no—
90C24×C107—41no—
91C24×C107—41no—
92C24×C107—41no—
93C24×C107—41no—
94C24×C107—41no—
95C24×C107—41no—
96C24×C107—41no—
97C24×C107—41no—
98C24×C107—41no—
99C24×C107—41no—
100C24×C107C2×D411yescharacteristic
101C2×Q8×C107—21no—
102C2×Q8×C107—41no—
103C2×Q8×C107—41no—
104C2×Q8×C107C22⋊C412yescomplemented
105C2×D4×C107—22no—
106C2×D4×C107—22no—
107C2×D4×C107—22no—
108C2×D4×C107—22no—
109C2×D4×C107—22no—
110C2×D4×C107—22no—
111C2×D4×C107—41no—
112C2×D4×C107—41no—
113C2×D4×C107—41no—
114C2×D4×C107—41no—
115C2×D4×C107—44no—
116C2×D4×C107—44no—
117C2×D4×C107—44no—
118C2×D4×C107—44no—
119C2×D4×C107—41no—
120C2×D4×C107—41no—
121C22×C4×C107—21no—
122C22×C4×C107—21no—
123C22×C4×C107—21no—
124C22×C4×C107—21no—
125C22×C4×C107—22no—
126C22×C4×C107—21no—
127C22×C4×C107—21no—
128C22×C4×C107—21no—
129C22×C4×C107—21no—
130C22×C4×C107—21no—
131C22×C4×C107—41no—
132C22×C4×C107—41no—
133C22×C4×C107—41no—
134C22×C4×C107—41no—
135C22×C4×C107—41no—
136C22×C4×C107—41no—
137C22×C4×C107—41no—
138C22×C4×C107—41no—
139C22×C4×C107—41no—
140C22×C4×C107—41no—
141C22×C4×C107—41no—
142C22×C4×C107—41no—
143C22×C4×C107SD1612yescomplemented
144C22×C4×C107C22×C411yescharacteristic
145C22×C4×C107C2×D411yescharacteristic
146C22×C4×C107C2×D411yescharacteristic
147C22×C4×C107C2×D411yescharacteristic
148C22×C4×C107#4111yescharacteristic
149C22×C4×C107#4111yescharacteristic
150SD16×C107—48no—
151C2×C8×C107—22no—
152C2×C8×C107—41no—
153C2×C8×C107—41no—
154C2×C8×C107—41no—
155C2×C8×C107—41no—
156C2×C8×C107—41no—
157C4⋊C4×C107—22no—
158C4⋊C4×C107—22no—
159C4⋊C4×C107—21no—
160C4⋊C4×C107—41no—
161C4⋊C4×C107—41no—
162C4⋊C4×C107—81no—
163C4⋊C4×C107—81no—
164C4⋊C4×C107C22⋊C412yescomplemented
165C22⋊C4×C107—22no—
166C22⋊C4×C107—22no—
167C22⋊C4×C107—48no—
168C22⋊C4×C107—48no—
169C22⋊C4×C107—41no—
170C22⋊C4×C107—41no—
171C42×C107—81no—
172C42×C107—81no—
173C23×C107—21no—
174C23×C107—21no—
175C23×C107—21no—
176C23×C107—21no—
177C23×C107—24no—
178C23×C107—42no—
179C23×C107—42no—
180C23×C107—42no—
181C23×C107—42no—
182C23×C107—42no—
183C23×C107—42no—
184C23×C107—42no—
185C23×C107—42no—
186C23×C107—42no—
187C23×C107—42no—
188C23×C107—42no—
189C23×C107—42no—
190C23×C107—42no—
191C23×C107—42no—
192C23×C107—42no—
193C23×C107—42no—
194C23×C107—42no—
195C23×C107—42no—
196C23×C107—81no—
197C23×C107—81no—
198C23×C107—81no—
199C23×C107—81no—
200C23×C107—81no—
201C23×C107—81no—
202C23×C107—81no—
203C23×C107—81no—
204C23×C107—81no—
205C23×C107—81no—
206C23×C107—81no—
207C23×C107—81no—
208C23×C107—81no—
209C23×C107—81no—
210C23×C107—81no—
211C23×C107—81no—
212C23×C107C4×D411yescharacteristic
213C23×C107#12011yescharacteristic
214C23×C107#12111yescharacteristic
215C23×C107C2×SD1611yescharacteristic
216C23×C107#13511yescharacteristic
217C23×C107AGL(1,ℤ/8)11yescharacteristic
218C23×C107#13711yescharacteristic
219Q8×C107—42no—
220Q8×C107—81no—
221D4×C107—24no—
222D4×C107—24no—
223D4×C107—42no—
224D4×C107—42no—
225D4×C107—42no—
226D4×C107—42no—
227D4×C107—42no—
228D4×C107—42no—
229C2×C4×C107—21no—
230C2×C4×C107—21no—
231C2×C4×C107—21no—
232C2×C4×C107—21no—
233C2×C4×C107—22no—
234C2×C4×C107—22no—
235C2×C4×C107—22no—
236C2×C4×C107—41no—
237C2×C4×C107—41no—
238C2×C4×C107—41no—
239C2×C4×C107—41no—
240C2×C4×C107—41no—
241C2×C4×C107—41no—
242C2×C4×C107—41no—
243C2×C4×C107—41no—
244C2×C4×C107—41no—
245C2×C4×C107—41no—
246C2×C4×C107—42no—
247C2×C4×C107—42no—
248C2×C4×C107—42no—
249C2×C4×C107—42no—
250C2×C4×C107—42no—
251C2×C4×C107—41no—
252C2×C4×C107—41no—
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—41no—
260C2×C4×C107—81no—
261C2×C4×C107—81no—
262C2×C4×C107—81no—
263C2×C4×C107—81no—
264C2×C4×C107—81no—
265C2×C4×C107—81no—
266C2×C4×C107C2×C22⋊C411yescharacteristic
267C2×C4×C107C4×D411yescharacteristic
268C2×C4×C107#12111yescharacteristic
269C2×C4×C107#12311yescharacteristic
270C8×C107—42no—
271C8×C107—81no—
272C22×C107—21no—
273C22×C107—21no—
274C22×C107—21no—
275C22×C107—21no—
276C22×C107—21no—
277C22×C107—21no—
278C22×C107—21no—
279C22×C107—21no—
280C22×C107—21no—
281C22×C107—21no—
282C22×C107—21no—
283C22×C107—21no—
284C22×C107—44no—
285C22×C107—44no—
286C22×C107—44no—
287C22×C107—82no—
288C22×C107—82no—
289C22×C107—82no—
290C22×C107—82no—
291C22×C107—82no—
292C22×C107—82no—
293C22×C107—82no—
294C22×C107—82no—
295C22×C107—82no—
296C22×C107—82no—
297C22×C107—82no—
298C22×C107—82no—
299C22×C107#38611yescharacteristic
300C22×C107C4×SD1611yescharacteristic
301C22×C107#44011yescharacteristic
302C22×C107#44811yescharacteristic
303C22×C107#44911yescharacteristic
304C22×C107#45311yescharacteristic
305C22×C107#45411yescharacteristic
306C22×C107B(4,𝔽2)11yescharacteristic
307C22×C107B(4,𝔽2)11yescharacteristic
308C22×C107#46011yescharacteristic
309C22×C107#46411yescharacteristic
310C4×C107—21no—
311C4×C107—21no—
312C4×C107—21no—
313C4×C107—21no—
314C4×C107—42no—
315C4×C107—42no—
316C4×C107—42no—
317C4×C107—82no—
318C4×C107—81no—
319C4×C107—81no—
320C4×C107—81no—
321#9042C10711yesmaximal, characteristic, direct product factor, Sylow
322C2×C107—21no—
323C2×C107—21no—
324C2×C107—21no—
325C2×C107—21no—
326C2×C107—84no—
327C2×C107#159611yescharacteristic
328C2×C107#159711yescharacteristic
329C2×C107#159911yescharacteristic
330C2×C107#160011yescharacteristic
331C2×C107#188011yescharacteristic
332C2×C107#188311yescharacteristic
333C2×C107#188911yescharacteristic
334C2×#450C2×C10711yescharacteristic
335#2329C2×C10711yescharacteristic, complemented
336#1786C2×C10711yescharacteristic
337C2×#328C2×C10711yescharacteristic, complemented
338#1438C2×C10711yescharacteristic
339#1294C2×C10711yescharacteristic, complemented
340#1280C2×C10711yescharacteristic, complemented
341C107#904211yescharacteristic, direct product factor, Sylow
342C23×D4C22×C10711yescharacteristic
343C22×SD16—21no—
344C2×C22⋊Q8C22×C10711yescharacteristic
345C22×C22⋊C4—21no—
346C22×C22⋊C4—21no—
347#450—22no—
348#450C4×C10714yescomplemented
349C2×#102—21no—
350C2×#102—21no—
351C2×#102—21no—
352C2×C22⋊C8C22×C10711yescharacteristic
353C2×C22⋊C8C22×C10711yescharacteristic
354#391—21no—
355#389—21no—
356#387—21no—
357#387—21no—
358#385—21no—
359#380C22×C10711yescharacteristic
360C4×C22⋊C4—21no—
361C2×#95C22×C10711yescharacteristic
362C2×#95C22×C10711yescharacteristic
363#328—22no—
364C25—21no—
365C22×Q8D4×C10711yescharacteristic
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4C2×C4×C10712yes—
374C23×C4—21no—
375C23×C4D4×C10711yescharacteristic
376C23×C4D4×C10711yescharacteristic
377C23×C4C23×C10711yescharacteristic
378C2×SD16—24no—
379C2×SD16—42no—
380C2×SD16—42no—
381C22×C8—21no—
382C22×C8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8C2×C4×C10712yes—
386C22⋊Q8D4×C10712yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4D4×C10711yescharacteristic
391C2×C4⋊C4D4×C10711yescharacteristic
392C2×C4⋊C4D4×C10711yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C42—21no—
402C2×C42—21no—
403#102—24no—
404#102—42no—
405#102—42no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8C2×C4×C10712yes—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24C2×D4×C10711yescharacteristic
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8C22⋊C4×C10712yescomplemented
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—41no—
454C2×D4—41no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4SD16×C10712yescomplemented
478C22×C4C22×C4×C10711yescharacteristic
479C22×C4C2×D4×C10711yescharacteristic
480C22×C4C2×D4×C10711yescharacteristic
481C22×C4C2×D4×C10711yescharacteristic
482C22×C4#41×C10711yescharacteristic
483C22×C4#41×C10711yescharacteristic
484SD16—48no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—81no—
497C4⋊C4—81no—
498C4⋊C4C22⋊C4×C10712yescomplemented
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—48no—
502C22⋊C4—48no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—81no—
506C42—81no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23—81no—
541C23—81no—
542C23—81no—
543C23—81no—
544C23—81no—
545C23—81no—
546C23C4×D4×C10711yescharacteristic
547C23#120×C10711yescharacteristic
548C23#121×C10711yescharacteristic
549C23C2×SD16×C10711yescharacteristic
550C23#135×C10711yescharacteristic
551C23AGL(1,ℤ/8)×C10711yescharacteristic
552C23#137×C10711yescharacteristic
553Q8—42no—
554Q8—81no—
555D4—24no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
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—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4C2×C22⋊C4×C10711yescharacteristic
601C2×C4C4×D4×C10711yescharacteristic
602C2×C4#121×C10711yescharacteristic
603C2×C4#123×C10711yescharacteristic
604C8—42no—
605C8—81no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22#386×C10711yescharacteristic
634C22C4×SD16×C10711yescharacteristic
635C22#440×C10711yescharacteristic
636C22#448×C10711yescharacteristic
637C22#449×C10711yescharacteristic
638C22#453×C10711yescharacteristic
639C22#454×C10711yescharacteristic
640C22B(4,𝔽2)×C10711yescharacteristic
641C22B(4,𝔽2)×C10711yescharacteristic
642C22#460×C10711yescharacteristic
643C22#464×C10711yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—82no—
652C4—81no—
653C4—81no—
654C4—81no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—84no—
660C2C107×#159611yescharacteristic
661C2C107×#159711yescharacteristic
662C2C107×#159911yescharacteristic
663C2C107×#160011yescharacteristic
664C2C107×#188011yescharacteristic
665C2C107×#188311yescharacteristic
666C2C107×#188911yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutatorC22×C4C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC23×D4×C107C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2329C2semidirect
4. C2×#328×C107C2semidirect
6. C107×#1294C2semidirect
7. C107×#1280C2semidirect
14. #450×C107C4semidirect
104. C2×Q8×C107C22⋊C4semidirect
143. C22×C4×C107SD16semidirect
164. C4⋊C4×C107C22⋊C4semidirect
321. #9042C107direct (N × H)
335. #2329C2×C107semidirect
337. C2×#328C2×C107semidirect
339. #1294C2×C107semidirect
340. #1280C2×C107semidirect
341. C107#9042direct (N × H)
348. #450C4×C107semidirect
438. C2×Q8C22⋊C4×C107semidirect
477. C22×C4SD16×C107semidirect
498. C4⋊C4C22⋊C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1072
C107×#23292
C107×#17862
C2×#328×C1072
C107×#14382
C107×#12942
C107×#12802
#9042107