Finite Group Databasebeta

← C107×#9922 #41035886

Subgroups — C107×#9922 #41035886

Order 27392.

1278 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C107C211yesmaximal, characteristic, complemented
2C107×#2626C211yesmaximal, characteristic, complemented
3C2×#392×C107C211yesmaximal, characteristic
4C107×#1786C211yesmaximal, characteristic, complemented
5C2×#328×C107C211yesmaximal, characteristic, complemented
6C2×#323×C107C211yesmaximal, characteristic, complemented
7C107×#1294C211yesmaximal, characteristic, complemented
8C23×D4×C107—21no—
9C23×D4×C107C2211yescharacteristic
10C22×SD16×C107—21no—
11C2×C22⋊Q8×C107C2211yescharacteristic
12C22×C22⋊C4×C107—21no—
13C22×C22⋊C4×C107C2211yescharacteristic
14#450×C107—22no—
15#450×C107—22no—
16C2×#102×C107—21no—
17C2×#102×C107—22no—
18C2×C22⋊C8×C107C2211yescharacteristic
19C2×C22⋊C8×C107C2211yescharacteristic
20#399×C107—21no—
21#396×C107—22no—
22#393×C107—21no—
23#392×C107—22no—
24#392×C107—22no—
25#385×C107—21no—
26#380×C107C2211yescharacteristic
27#379×C107—21no—
28C2×#95×C107C2211yescharacteristic
29#328×C107—22no—
30#323×C107—22no—
31C25×C107—21no—
32C25×C107D411yescharacteristic
33C22×Q8×C107D411yescharacteristic, complemented
34C22×D4×C107—24no—
35C22×D4×C107—21no—
36C22×D4×C107—21no—
37C22×D4×C107—21no—
38C22×D4×C107—21no—
39C22×D4×C107—21no—
40C22×D4×C107—44no—
41C22×D4×C107—44no—
42C22×D4×C107—44no—
43C22×D4×C107—42no—
44C22×D4×C107—42no—
45C22×D4×C107D412yes—
46C23×C4×C107—21no—
47C23×C4×C107D411yescharacteristic
48C23×C4×C107C2311yescharacteristic
49C2×SD16×C107—24no—
50C2×SD16×C107—44no—
51C22×C8×C107—21no—
52C22×C8×C107—21no—
53C22⋊Q8×C107—21no—
54C22⋊Q8×C107—21no—
55C22⋊Q8×C107—21no—
56C22⋊Q8×C107—21no—
57C2×C4⋊C4×C107—21no—
58C2×C4⋊C4×C107—22no—
59C2×C4⋊C4×C107D411yescharacteristic, complemented
60C2×C4⋊C4×C107D412yescomplemented
61C2×C22⋊C4×C107—24no—
62C2×C22⋊C4×C107—21no—
63C2×C22⋊C4×C107—21no—
64C2×C22⋊C4×C107—21no—
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—22no—
71C2×C22⋊C4×C107—22no—
72C2×C22⋊C4×C107—44no—
73#102×C107—24no—
74#102×C107—44no—
75C22⋊C8×C107—21no—
76C22⋊C8×C107—21no—
77C22⋊C8×C107—21no—
78C22⋊C8×C107D412yescomplemented
79#95×C107—22no—
80#95×C107—21no—
81#95×C107—21no—
82#95×C107D412yes—
83C24×C107—24no—
84C24×C107—21no—
85C24×C107—22no—
86C24×C107—21no—
87C24×C107—21no—
88C24×C107—21no—
89C24×C107—21no—
90C24×C107—21no—
91C24×C107—42no—
92C24×C107—42no—
93C24×C107—42no—
94C24×C107—42no—
95C24×C107—42no—
96C24×C107—41no—
97C24×C107—41no—
98C24×C107—41no—
99C24×C107—41no—
100C24×C107—41no—
101C24×C107—41no—
102C24×C107SD1612yescomplemented
103C24×C107C2×D411yescharacteristic
104C2×Q8×C107—21no—
105C2×Q8×C107—21no—
106C2×Q8×C107—42no—
107C2×D4×C107—24no—
108C2×D4×C107—24no—
109C2×D4×C107—22no—
110C2×D4×C107—22no—
111C2×D4×C107—42no—
112C2×D4×C107—42no—
113C2×D4×C107—48no—
114C2×D4×C107—44no—
115C2×D4×C107—44no—
116C2×D4×C107—44no—
117C2×D4×C107—44no—
118C2×D4×C107—48no—
119C2×D4×C107—48no—
120C2×D4×C107—416no—
121C2×D4×C107—416no—
122C2×D4×C107—41no—
123C2×D4×C107—41no—
124C22×C4×C107—24no—
125C22×C4×C107—22no—
126C22×C4×C107—21no—
127C22×C4×C107—22no—
128C22×C4×C107—21no—
129C22×C4×C107—21no—
130C22×C4×C107—21no—
131C22×C4×C107—21no—
132C22×C4×C107—42no—
133C22×C4×C107—42no—
134C22×C4×C107—41no—
135C22×C4×C107—41no—
136C22×C4×C107—42no—
137C22×C4×C107C2×D411yescharacteristic
138C22×C4×C107C2×D411yescharacteristic
139C22×C4×C107C2×D411yescharacteristic
140C22×C4×C107C2×D411yescharacteristic
141C22×C4×C107C2×D411yescharacteristic
142C22×C4×C107#4111yescharacteristic
143SD16×C107—48no—
144C2×C8×C107—22no—
145C2×C8×C107—42no—
146C2×C8×C107—42no—
147C2×C8×C107—41no—
148C4⋊C4×C107—21no—
149C4⋊C4×C107—21no—
150C4⋊C4×C107—42no—
151C4⋊C4×C107—41no—
152C4⋊C4×C107—41no—
153C4⋊C4×C107—82no—
154C22⋊C4×C107—48no—
155C22⋊C4×C107—41no—
156C22⋊C4×C107—41no—
157C22⋊C4×C107—41no—
158C22⋊C4×C107—41no—
159C22⋊C4×C107—41no—
160C22⋊C4×C107—41no—
161C22⋊C4×C107—41no—
162C22⋊C4×C107—41no—
163C22⋊C4×C107—82no—
164C22⋊C4×C107—82no—
165C23×C107—22no—
166C23×C107—22no—
167C23×C107—24no—
168C23×C107—22no—
169C23×C107—22no—
170C23×C107—22no—
171C23×C107—44no—
172C23×C107—42no—
173C23×C107—44no—
174C23×C107—44no—
175C23×C107—44no—
176C23×C107—42no—
177C23×C107—42no—
178C23×C107—42no—
179C23×C107—42no—
180C23×C107—44no—
181C23×C107—44no—
182C23×C107—44no—
183C23×C107—41no—
184C23×C107—42no—
185C23×C107—41no—
186C23×C107—42no—
187C23×C107—41no—
188C23×C107—42no—
189C23×C107—42no—
190C23×C107—42no—
191C23×C107—44no—
192C23×C107—41no—
193C23×C107—82no—
194C23×C107—82no—
195C23×C107—81no—
196C23×C107—81no—
197C23×C107—82no—
198C23×C107—82no—
199C23×C107—82no—
200C23×C107—82no—
201C23×C107—82no—
202C23×C107—81no—
203C23×C107—81no—
204C23×C107—82no—
205C23×C107—81no—
206C23×C107—81no—
207C23×C107#12011yescharacteristic
208C23×C107#12011yescharacteristic
209C23×C107#12111yescharacteristic
210C23×C107C2×SD1611yescharacteristic
211C23×C107#13511yescharacteristic
212C23×C107AGL(1,ℤ/8)11yescharacteristic
213C23×C107#13711yescharacteristic
214Q8×C107—42no—
215Q8×C107—81no—
216D4×C107—24no—
217D4×C107—24no—
218D4×C107—42no—
219D4×C107—44no—
220D4×C107—42no—
221D4×C107—44no—
222D4×C107—432no—
223C2×C4×C107—22no—
224C2×C4×C107—22no—
225C2×C4×C107—24no—
226C2×C4×C107—41no—
227C2×C4×C107—41no—
228C2×C4×C107—41no—
229C2×C4×C107—41no—
230C2×C4×C107—44no—
231C2×C4×C107—44no—
232C2×C4×C107—42no—
233C2×C4×C107—42no—
234C2×C4×C107—42no—
235C2×C4×C107—41no—
236C2×C4×C107—41no—
237C2×C4×C107—41no—
238C2×C4×C107—42no—
239C2×C4×C107—42no—
240C2×C4×C107—42no—
241C2×C4×C107—42no—
242C2×C4×C107—42no—
243C2×C4×C107—42no—
244C2×C4×C107—81no—
245C2×C4×C107#12011yescharacteristic
246C2×C4×C107#12111yescharacteristic
247C2×C4×C107#12111yescharacteristic
248C2×C4×C107#12711yescharacteristic
249C8×C107—42no—
250C8×C107—81no—
251C22×C107—22no—
252C22×C107—22no—
253C22×C107—22no—
254C22×C107—22no—
255C22×C107—21no—
256C22×C107—21no—
257C22×C107—21no—
258C22×C107—21no—
259C22×C107—44no—
260C22×C107—44no—
261C22×C107—44no—
262C22×C107—44no—
263C22×C107—42no—
264C22×C107—44no—
265C22×C107—82no—
266C22×C107—82no—
267C22×C107—82no—
268C22×C107—82no—
269C22×C107—84no—
270C22×C107—82no—
271C22×C107—84no—
272C22×C107—84no—
273C22×C107—82no—
274C22×C107—84no—
275C22×C107—82no—
276C22×C107—81no—
277C22×C107—82no—
278C22×C107—81no—
279C22×C107#39211yescharacteristic
280C22×C107#44811yescharacteristic
281C22×C107#44911yescharacteristic
282C22×C107#45011yescharacteristic
283C22×C107#45211yescharacteristic
284C22×C107#45312yes—
285C22×C107B(4,𝔽2)12yes—
286C22×C107#46511yescharacteristic
287C22×C107#46811yescharacteristic
288C4×C107—21no—
289C4×C107—21no—
290C4×C107—21no—
291C4×C107—21no—
292C4×C107—44no—
293C4×C107—82no—
294C4×C107—81no—
295C4×C107—81no—
296C4×C107—81no—
297#9922C10711yesmaximal, characteristic, direct product factor, Sylow
298C2×C107—21no—
299C2×C107—21no—
300C2×C107—21no—
301C2×C107—21no—
302C2×C107—82no—
303C2×C107—84no—
304C2×C107#159612yes—
305C2×C107#160012yes—
306C2×C107#200011yescharacteristic
307C2×C107#200211yescharacteristic
308C2×C107#202111yescharacteristic
309C2×#450C2×C10711yescharacteristic, complemented
310#2626C2×C10711yescharacteristic, complemented
311C2×#392C2×C10711yescharacteristic
312#1786C2×C10711yescharacteristic, complemented
313C2×#328C2×C10711yescharacteristic, complemented
314C2×#323C2×C10711yescharacteristic, complemented
315#1294C2×C10711yescharacteristic, complemented
316C107#992211yescharacteristic, direct product factor, Sylow
317C23×D4—21no—
318C23×D4C22×C10711yescharacteristic
319C22×SD16—21no—
320C2×C22⋊Q8C22×C10711yescharacteristic
321C22×C22⋊C4—21no—
322C22×C22⋊C4C22×C10711yescharacteristic
323#450—22no—
324#450—22no—
325C2×#102—21no—
326C2×#102—22no—
327C2×C22⋊C8C22×C10711yescharacteristic
328C2×C22⋊C8C22×C10711yescharacteristic
329#399—21no—
330#396—22no—
331#393—21no—
332#392—22no—
333#392—22no—
334#385—21no—
335#380C22×C10711yescharacteristic
336#379—21no—
337C2×#95C22×C10711yescharacteristic
338#328—22no—
339#323—22no—
340C25—21no—
341C25D4×C10711yescharacteristic
342C22×Q8D4×C10711yescharacteristic, complemented
343C22×D4—24no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4—44no—
350C22×D4—44no—
351C22×D4—44no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4D4×C10712yes—
355C23×C4—21no—
356C23×C4D4×C10711yescharacteristic
357C23×C4C23×C10711yescharacteristic
358C2×SD16—24no—
359C2×SD16—44no—
360C22×C8—21no—
361C22×C8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4D4×C10711yescharacteristic, complemented
369C2×C4⋊C4D4×C10712yescomplemented
370C2×C22⋊C4—24no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—44no—
382#102—24no—
383#102—44no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—21no—
387C22⋊C8D4×C10712yescomplemented
388#95—22no—
389#95—21no—
390#95—21no—
391#95D4×C10712yes—
392C24—24no—
393C24—21no—
394C24—21no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24SD16×C10712yescomplemented
412C24C2×D4×C10711yescharacteristic
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—42no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—48no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—416no—
430C2×D4—416no—
431C2×D4—41no—
432C2×D4—41no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—42no—
446C22×C4C2×D4×C10711yescharacteristic
447C22×C4C2×D4×C10711yescharacteristic
448C22×C4C2×D4×C10711yescharacteristic
449C22×C4C2×D4×C10711yescharacteristic
450C22×C4C2×D4×C10711yescharacteristic
451C22×C4#41×C10711yescharacteristic
452SD16—48no—
453C2×C8—22no—
454C2×C8—42no—
455C2×C8—42no—
456C2×C8—41no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—42no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—82no—
463C22⋊C4—48no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—82no—
473C22⋊C4—82no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—44no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—44no—
487C23—44no—
488C23—44no—
489C23—44no—
490C23—44no—
491C23—44no—
492C23—41no—
493C23—42no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—44no—
501C23—41no—
502C23—82no—
503C23—81no—
504C23—81no—
505C23—82no—
506C23—82no—
507C23—82no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—81no—
512C23—81no—
513C23—82no—
514C23—81no—
515C23—81no—
516C23#120×C10711yescharacteristic
517C23#120×C10711yescharacteristic
518C23#121×C10711yescharacteristic
519C23C2×SD16×C10711yescharacteristic
520C23#135×C10711yescharacteristic
521C23AGL(1,ℤ/8)×C10711yescharacteristic
522C23#137×C10711yescharacteristic
523Q8—42no—
524Q8—81no—
525D4—24no—
526D4—24no—
527D4—42no—
528D4—44no—
529D4—42no—
530D4—44no—
531D4—432no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—81no—
554C2×C4#120×C10711yescharacteristic
555C2×C4#121×C10711yescharacteristic
556C2×C4#121×C10711yescharacteristic
557C2×C4#127×C10711yescharacteristic
558C8—42no—
559C8—81no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—44no—
569C22—44no—
570C22—44no—
571C22—42no—
572C22—44no—
573C22—44no—
574C22—82no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22—84no—
579C22—82no—
580C22—84no—
581C22—82no—
582C22—81no—
583C22—82no—
584C22—81no—
585C22—84no—
586C22—82no—
587C22—84no—
588C22#392×C10711yescharacteristic
589C22#448×C10711yescharacteristic
590C22#449×C10711yescharacteristic
591C22#450×C10711yescharacteristic
592C22#452×C10711yescharacteristic
593C22#453×C10712yes—
594C22B(4,𝔽2)×C10712yes—
595C22#465×C10711yescharacteristic
596C22#468×C10711yescharacteristic
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—44no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4—82no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—82no—
611C2—84no—
612C2C107×#159612yes—
613C2C107×#160012yes—
614C2C107×#200011yescharacteristic
615C2C107×#200211yescharacteristic
616C2C107×#202111yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutator, Frattini, cosocleC23×C4C23×C107
prime radicalC2×#392×C107C2
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×#450×C107C2semidirect
2. C107×#2626C2semidirect
4. C107×#1786C2semidirect
5. C2×#328×C107C2semidirect
6. C2×#323×C107C2semidirect
7. C107×#1294C2semidirect
33. C22×Q8×C107D4semidirect
59. C2×C4⋊C4×C107D4semidirect
60. C2×C4⋊C4×C107D4semidirect
78. C22⋊C8×C107D4semidirect
102. C24×C107SD16semidirect
297. #9922C107direct (N × H)
309. C2×#450C2×C107semidirect
310. #2626C2×C107semidirect
312. #1786C2×C107semidirect
313. C2×#328C2×C107semidirect
314. C2×#323C2×C107semidirect
315. #1294C2×C107semidirect
316. C107#9922direct (N × H)
342. C22×Q8D4×C107semidirect
368. C2×C4⋊C4D4×C107semidirect
369. C2×C4⋊C4D4×C107semidirect
387. C22⋊C8D4×C107semidirect
411. C24SD16×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×#26262
C2×#392×C1072
C107×#17862
C2×#328×C1072
C2×#323×C1072
C107×#12942
#9922107