Finite Group Databasebeta

← C107×#9914 #41035878

Subgroups — C107×#9914 #41035878

Order 27392.

1356 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C107C211yesmaximal, characteristic, complemented
2C107×#2617C211yesmaximal, characteristic, complemented
3C2×#392×C107C211yesmaximal, characteristic, complemented
4C107×#1786C211yesmaximal, characteristic, complemented
5C2×#327×C107C211yesmaximal, characteristic, complemented
6C2×#323×C107C211yesmaximal, characteristic, complemented
7C107×#1294C211yesmaximal, characteristic, complemented
8C23×D4×C107—21no—
9C23×D4×C107C2211yescharacteristic
10C22×D8×C107—21no—
11C2×#121×C107C2211yescharacteristic
12C2×#120×C107—21no—
13C22×C22⋊C4×C107—21no—
14C22×C22⋊C4×C107C2211yescharacteristic
15#447×C107—22no—
16#447×C107—22no—
17C2×#102×C107—21no—
18C2×#102×C107—22no—
19C2×C22⋊C8×C107C2211yescharacteristic
20C2×C22⋊C8×C107C2211yescharacteristic
21#397×C107—21no—
22#394×C107—22no—
23#392×C107—22no—
24#392×C107—21no—
25#392×C107—22no—
26#386×C107—21no—
27#380×C107C2211yescharacteristic
28C2×#95×C107C2211yescharacteristic
29#327×C107—22no—
30#323×C107—22no—
31C25×C107—21no—
32C25×C107D411yescharacteristic
33C22×D4×C107—24no—
34C22×D4×C107—21no—
35C22×D4×C107—22no—
36C22×D4×C107—21no—
37C22×D4×C107—21no—
38C22×D4×C107—21no—
39C22×D4×C107—21no—
40C22×D4×C107—21no—
41C22×D4×C107—44no—
42C22×D4×C107—44no—
43C22×D4×C107—44no—
44C22×D4×C107—42no—
45C22×D4×C107—42no—
46C22×D4×C107D412yescomplemented
47C22×D4×C107D411yescharacteristic, complemented
48C23×C4×C107—21no—
49C23×C4×C107D411yescharacteristic
50C23×C4×C107C2311yescharacteristic
51C2×D8×C107—24no—
52C2×D8×C107—44no—
53C22×C8×C107—21no—
54C22×C8×C107—21no—
55#121×C107—21no—
56#121×C107—21no—
57#121×C107—21no—
58#121×C107—21no—
59#120×C107—42no—
60#120×C107—42no—
61C2×C4⋊C4×C107D411yescharacteristic, complemented
62C2×C4⋊C4×C107D412yescomplemented
63C2×C22⋊C4×C107—24no—
64C2×C22⋊C4×C107—22no—
65C2×C22⋊C4×C107—21no—
66C2×C22⋊C4×C107—21no—
67C2×C22⋊C4×C107—21no—
68C2×C22⋊C4×C107—21no—
69C2×C22⋊C4×C107—21no—
70C2×C22⋊C4×C107—21no—
71C2×C22⋊C4×C107—21no—
72C2×C22⋊C4×C107—21no—
73C2×C22⋊C4×C107—22no—
74C2×C22⋊C4×C107—44no—
75#102×C107—24no—
76#102×C107—44no—
77C22⋊C8×C107—21no—
78C22⋊C8×C107—21no—
79C22⋊C8×C107—21no—
80C22⋊C8×C107D412yescomplemented
81#95×C107—22no—
82#95×C107—21no—
83#95×C107—21no—
84#95×C107D412yescomplemented
85C24×C107—24no—
86C24×C107—21no—
87C24×C107—22no—
88C24×C107—21no—
89C24×C107—21no—
90C24×C107—21no—
91C24×C107—21no—
92C24×C107—21no—
93C24×C107—21no—
94C24×C107—42no—
95C24×C107—42no—
96C24×C107—42no—
97C24×C107—42no—
98C24×C107—42no—
99C24×C107—41no—
100C24×C107—41no—
101C24×C107—41no—
102C24×C107—41no—
103C24×C107—41no—
104C24×C107—41no—
105C24×C107D812yescomplemented
106C24×C107C2×D411yescharacteristic
107C2×D4×C107—24no—
108C2×D4×C107—24no—
109C2×D4×C107—22no—
110C2×D4×C107—21no—
111C2×D4×C107—22no—
112C2×D4×C107—21no—
113C2×D4×C107—42no—
114C2×D4×C107—42no—
115C2×D4×C107—48no—
116C2×D4×C107—42no—
117C2×D4×C107—44no—
118C2×D4×C107—44no—
119C2×D4×C107—44no—
120C2×D4×C107—44no—
121C2×D4×C107—48no—
122C2×D4×C107—48no—
123C2×D4×C107—416no—
124C2×D4×C107—416no—
125C2×D4×C107—44no—
126C2×D4×C107—41no—
127C2×D4×C107—41no—
128C2×D4×C107—41no—
129C2×D4×C107—41no—
130C2×D4×C107—41no—
131C2×D4×C107—41no—
132C2×D4×C107—41no—
133C2×D4×C107—41no—
134C2×D4×C107—82no—
135C2×D4×C107—82no—
136C22×C4×C107—24no—
137C22×C4×C107—22no—
138C22×C4×C107—21no—
139C22×C4×C107—21no—
140C22×C4×C107—21no—
141C22×C4×C107—22no—
142C22×C4×C107—21no—
143C22×C4×C107—42no—
144C22×C4×C107—42no—
145C22×C4×C107—41no—
146C22×C4×C107—41no—
147C22×C4×C107—42no—
148C22×C4×C107C2×D411yescharacteristic
149C22×C4×C107C2×D411yescharacteristic
150C22×C4×C107C2×D411yescharacteristic
151C22×C4×C107C2×D411yescharacteristic
152C22×C4×C107C2×D411yescharacteristic
153C22×C4×C107#4111yescharacteristic
154D8×C107—48no—
155C2×C8×C107—22no—
156C2×C8×C107—42no—
157C2×C8×C107—42no—
158C2×C8×C107—41no—
159C4⋊C4×C107—21no—
160C4⋊C4×C107—21no—
161C4⋊C4×C107—42no—
162C22⋊C4×C107—48no—
163C22⋊C4×C107—44no—
164C22⋊C4×C107—41no—
165C22⋊C4×C107—41no—
166C22⋊C4×C107—41no—
167C22⋊C4×C107—41no—
168C22⋊C4×C107—41no—
169C22⋊C4×C107—41no—
170C22⋊C4×C107—41no—
171C22⋊C4×C107—41no—
172C22⋊C4×C107—82no—
173C23×C107—22no—
174C23×C107—22no—
175C23×C107—24no—
176C23×C107—22no—
177C23×C107—22no—
178C23×C107—22no—
179C23×C107—44no—
180C23×C107—42no—
181C23×C107—44no—
182C23×C107—44no—
183C23×C107—44no—
184C23×C107—42no—
185C23×C107—42no—
186C23×C107—42no—
187C23×C107—42no—
188C23×C107—44no—
189C23×C107—44no—
190C23×C107—44no—
191C23×C107—41no—
192C23×C107—42no—
193C23×C107—42no—
194C23×C107—41no—
195C23×C107—41no—
196C23×C107—42no—
197C23×C107—42no—
198C23×C107—44no—
199C23×C107—42no—
200C23×C107—41no—
201C23×C107—41no—
202C23×C107—41no—
203C23×C107—41no—
204C23×C107—42no—
205C23×C107—42no—
206C23×C107—82no—
207C23×C107—82no—
208C23×C107—81no—
209C23×C107—81no—
210C23×C107—82no—
211C23×C107—82no—
212C23×C107—82no—
213C23×C107—82no—
214C23×C107—82no—
215C23×C107—81no—
216C23×C107—81no—
217C23×C107—82no—
218C23×C107—81no—
219C23×C107—81no—
220C23×C107#12011yescharacteristic
221C23×C107#12011yescharacteristic
222C23×C107#12111yescharacteristic
223C23×C107C2×D811yescharacteristic
224C23×C107#13511yescharacteristic
225C23×C107AGL(1,ℤ/8)11yescharacteristic
226C23×C107AGL(1,ℤ/8)11yescharacteristic
227D4×C107—24no—
228D4×C107—24no—
229D4×C107—42no—
230D4×C107—44no—
231D4×C107—42no—
232D4×C107—44no—
233D4×C107—42no—
234D4×C107—432no—
235D4×C107—81no—
236D4×C107—88no—
237D4×C107—81no—
238D4×C107—81no—
239D4×C107—81no—
240D4×C107—81no—
241C2×C4×C107—22no—
242C2×C4×C107—22no—
243C2×C4×C107—24no—
244C2×C4×C107—41no—
245C2×C4×C107—41no—
246C2×C4×C107—41no—
247C2×C4×C107—41no—
248C2×C4×C107—44no—
249C2×C4×C107—44no—
250C2×C4×C107—42no—
251C2×C4×C107—42no—
252C2×C4×C107—42no—
253C2×C4×C107—41no—
254C2×C4×C107—41no—
255C2×C4×C107—42no—
256C2×C4×C107—41no—
257C2×C4×C107—41no—
258C2×C4×C107—42no—
259C2×C4×C107—42no—
260C2×C4×C107—42no—
261C2×C4×C107—81no—
262C2×C4×C107#12011yescharacteristic
263C2×C4×C107#12111yescharacteristic
264C2×C4×C107#12111yescharacteristic
265C2×C4×C107#12711yescharacteristic
266C8×C107—42no—
267C8×C107—81no—
268C22×C107—22no—
269C22×C107—22no—
270C22×C107—22no—
271C22×C107—22no—
272C22×C107—21no—
273C22×C107—21no—
274C22×C107—21no—
275C22×C107—21no—
276C22×C107—44no—
277C22×C107—44no—
278C22×C107—44no—
279C22×C107—44no—
280C22×C107—42no—
281C22×C107—44no—
282C22×C107—82no—
283C22×C107—82no—
284C22×C107—82no—
285C22×C107—82no—
286C22×C107—84no—
287C22×C107—82no—
288C22×C107—84no—
289C22×C107—84no—
290C22×C107—82no—
291C22×C107—84no—
292C22×C107—82no—
293C22×C107—81no—
294C22×C107—82no—
295C22×C107—81no—
296C22×C107—82no—
297C22×C107—82no—
298C22×C107—81no—
299C22×C107—81no—
300C22×C107—81no—
301C22×C107#39211yescharacteristic
302C22×C107#44711yescharacteristic
303C22×C107#44711yescharacteristic
304C22×C107#44911yescharacteristic
305C22×C107#44911yescharacteristic
306C22×C107#45312yes—
307C22×C107B(4,𝔽2)12yes—
308C22×C107#46611yescharacteristic
309C22×C107#46911yescharacteristic
310C4×C107—21no—
311C4×C107—21no—
312C4×C107—21no—
313C4×C107—21no—
314C4×C107—44no—
315C4×C107—82no—
316C4×C107—81no—
317C4×C107—81no—
318#9914C10711yesmaximal, characteristic, direct product factor, Sylow
319C2×C107—21no—
320C2×C107—21no—
321C2×C107—21no—
322C2×C107—21no—
323C2×C107—82no—
324C2×C107—84no—
325C2×C107—161no—
326C2×C107#159512yes—
327C2×C107#160012yes—
328C2×C107#199911yescharacteristic
329C2×C107#200211yescharacteristic
330C2×C107#202111yescharacteristic
331C2×#447C2×C10711yescharacteristic, complemented
332#2617C2×C10711yescharacteristic, complemented
333C2×#392C2×C10711yescharacteristic, complemented
334#1786C2×C10711yescharacteristic, complemented
335C2×#327C2×C10711yescharacteristic, complemented
336C2×#323C2×C10711yescharacteristic, complemented
337#1294C2×C10711yescharacteristic, complemented
338C107#991411yescharacteristic, direct product factor, Sylow
339C23×D4—21no—
340C23×D4C22×C10711yescharacteristic
341C22×D8—21no—
342C2×#121C22×C10711yescharacteristic
343C2×#120—21no—
344C22×C22⋊C4—21no—
345C22×C22⋊C4C22×C10711yescharacteristic
346#447—22no—
347#447—22no—
348C2×#102—21no—
349C2×#102—22no—
350C2×C22⋊C8C22×C10711yescharacteristic
351C2×C22⋊C8C22×C10711yescharacteristic
352#397—21no—
353#394—22no—
354#392—21no—
355#392—22no—
356#392—22no—
357#386—21no—
358#380C22×C10711yescharacteristic
359C2×#95C22×C10711yescharacteristic
360#327—22no—
361#323—22no—
362C25—21no—
363C25D4×C10711yescharacteristic
364C22×D4—24no—
365C22×D4—21no—
366C22×D4—22no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—44no—
373C22×D4—44no—
374C22×D4—44no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4D4×C10711yescharacteristic, complemented
378C22×D4D4×C10712yescomplemented
379C23×C4—21no—
380C23×C4D4×C10711yescharacteristic
381C23×C4C23×C10711yescharacteristic
382C2×D8—24no—
383C2×D8—44no—
384C22×C8—21no—
385C22×C8—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#120—42no—
391#120—42no—
392C2×C4⋊C4D4×C10711yescharacteristic, complemented
393C2×C4⋊C4D4×C10712yescomplemented
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—44no—
406#102—24no—
407#102—44no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8D4×C10712yescomplemented
412#95—22no—
413#95—21no—
414#95—21no—
415#95D4×C10712yescomplemented
416C24—24no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24D8×C10712yescomplemented
437C24C2×D4×C10711yescharacteristic
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—48no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—416no—
455C2×D4—416no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—82no—
466C2×D4—82no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4C2×D4×C10711yescharacteristic
480C22×C4C2×D4×C10711yescharacteristic
481C22×C4C2×D4×C10711yescharacteristic
482C22×C4C2×D4×C10711yescharacteristic
483C22×C4C2×D4×C10711yescharacteristic
484C22×C4#41×C10711yescharacteristic
485D8—48no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—41no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C22⋊C4—48no—
494C22⋊C4—44no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—82no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—44no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—44no—
517C23—44no—
518C23—44no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—44no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—82no—
538C23—81no—
539C23—81no—
540C23—82no—
541C23—82no—
542C23—82no—
543C23—82no—
544C23—82no—
545C23—82no—
546C23—81no—
547C23—81no—
548C23—82no—
549C23—81no—
550C23—81no—
551C23#120×C10711yescharacteristic
552C23#120×C10711yescharacteristic
553C23#121×C10711yescharacteristic
554C23C2×D8×C10711yescharacteristic
555C23#135×C10711yescharacteristic
556C23AGL(1,ℤ/8)×C10711yescharacteristic
557C23AGL(1,ℤ/8)×C10711yescharacteristic
558D4—24no—
559D4—24no—
560D4—42no—
561D4—44no—
562D4—42no—
563D4—44no—
564D4—42no—
565D4—432no—
566D4—81no—
567D4—88no—
568D4—81no—
569D4—81no—
570D4—81no—
571D4—81no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—81no—
593C2×C4#120×C10711yescharacteristic
594C2×C4#121×C10711yescharacteristic
595C2×C4#121×C10711yescharacteristic
596C2×C4#127×C10711yescharacteristic
597C8—42no—
598C8—81no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—42no—
611C22—44no—
612C22—44no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—84no—
618C22—82no—
619C22—84no—
620C22—82no—
621C22—81no—
622C22—82no—
623C22—81no—
624C22—84no—
625C22—82no—
626C22—84no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—82no—
631C22—82no—
632C22#392×C10711yescharacteristic
633C22#447×C10711yescharacteristic
634C22#447×C10711yescharacteristic
635C22#449×C10711yescharacteristic
636C22#449×C10711yescharacteristic
637C22#453×C10712yes—
638C22B(4,𝔽2)×C10712yes—
639C22#466×C10711yescharacteristic
640C22#469×C10711yescharacteristic
641C4—21no—
642C4—21no—
643C4—21no—
644C4—21no—
645C4—44no—
646C4—81no—
647C4—81no—
648C4—82no—
649C2—21no—
650C2—21no—
651C2—21no—
652C2—21no—
653C2—82no—
654C2—84no—
655C2—161no—
656C2C107×#159512yes—
657C2C107×#160012yes—
658C2C107×#199911yescharacteristic
659C2C107×#200211yescharacteristic
660C2C107×#202111yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutator, Frattini, cosocleC23×C4C23×C107
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#447×C107C2semidirect
2. C107×#2617C2semidirect
3. C2×#392×C107C2semidirect
4. C107×#1786C2semidirect
5. C2×#327×C107C2semidirect
6. C2×#323×C107C2semidirect
7. C107×#1294C2semidirect
46. C22×D4×C107D4semidirect
47. C22×D4×C107D4semidirect
61. C2×C4⋊C4×C107D4semidirect
62. C2×C4⋊C4×C107D4semidirect
80. C22⋊C8×C107D4semidirect
84. #95×C107D4semidirect
105. C24×C107D8semidirect
318. #9914C107direct (N × H)
331. C2×#447C2×C107semidirect
332. #2617C2×C107semidirect
333. C2×#392C2×C107semidirect
334. #1786C2×C107semidirect
335. C2×#327C2×C107semidirect
336. C2×#323C2×C107semidirect
337. #1294C2×C107semidirect
338. C107#9914direct (N × H)
377. C22×D4D4×C107semidirect
378. C22×D4D4×C107semidirect
392. C2×C4⋊C4D4×C107semidirect
393. C2×C4⋊C4D4×C107semidirect
411. C22⋊C8D4×C107semidirect
415. #95D4×C107semidirect
436. C24D8×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1072
C107×#26172
C2×#392×C1072
C107×#17862
C2×#327×C1072
C2×#323×C1072
C107×#12942
#9914107