Finite Group Databasebeta

← C107×#18264 #41044228

Subgroups — C107×#18264 #41044228

Order 27392.

1068 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3537C211yesmaximal, characteristic
2C107×#3092C211yesmaximal, characteristic, complemented
3C2×#480×C107C211yesmaximal, characteristic, complemented
4C107×#2504C211yesmaximal, characteristic, complemented
5C107×#1612C214yesmaximal, complemented
6C107×#1607C214yesmaximal, complemented
7C107×#1507C211yesmaximal, characteristic, complemented
8C107×#1501C211yesmaximal, characteristic, complemented
9C107×#1471C211yesmaximal, characteristic, complemented
10#560×C107—22no—
11#553×C107—21no—
12#553×C107—21no—
13D42×C107—22no—
14D42×C107—21no—
15D42×C107—21no—
16#540×C107—21no—
17#538×C107—21no—
18#538×C107C2212yes—
19#535×C107—21no—
20#534×C107—21no—
21#534×C107C2212yes—
22#525×C107C2211yescharacteristic
23C2×#121×C107C2211yescharacteristic
24C2×#121×C107C2211yescharacteristic
25C22×C4⋊C4×C107C2211yescharacteristic, complemented
26#484×C107—21no—
27#483×C107C2212yescomplemented
28#481×C107—21no—
29#480×C107—22no—
30#480×C107C2212yescomplemented
31#480×C107C2214yescomplemented
32#428×C107—21no—
33C2×#107×C107—21no—
34#417×C107—21no—
35C2×#102×C107—21no—
36#407×C107C2211yescharacteristic, complemented
37C2×C22⋊C8×C107C2211yescharacteristic, complemented
38#397×C107C2214yescomplemented
39#390×C107—21no—
40#386×C107—22no—
41#382×C107—21no—
42C4×C22⋊C4×C107C2211yescharacteristic, complemented
43#328×C107C2212yescomplemented
44#327×C107C2212yescomplemented
45#327×C107C2214yescomplemented
46#323×C107C2214yescomplemented
47C2×#41×C107D411yescharacteristic
48C22×D4×C107—22no—
49C22×D4×C107—21no—
50C22×D4×C107—21no—
51C22×D4×C107—22no—
52C22×D4×C107D412yes—
53C22×D4×C107D411yescharacteristic
54C22×D4×C107D411yescharacteristic
55C23×C4×C107—21no—
56C23×C4×C107C2311yescharacteristic
57C2×M16×C107—21no—
58C22×C8×C107—21no—
59#127×C107—22no—
60#127×C107—21no—
61#126×C107—22no—
62#126×C107—22no—
63#125×C107—21no—
64#124×C107—22no—
65#123×C107—22no—
66#123×C107—21no—
67#123×C107—22no—
68#123×C107—22no—
69#123×C107—22no—
70C22⋊Q8×C107D411yescharacteristic
71C22⋊Q8×C107C2311yescharacteristic
72#121×C107—22no—
73#121×C107—21no—
74#121×C107—21no—
75#121×C107—22no—
76#121×C107—22no—
77#121×C107—22no—
78#121×C107—22no—
79#121×C107—21no—
80#121×C107—21no—
81#121×C107—21no—
82#121×C107—21no—
83#121×C107—21no—
84#121×C107—21no—
85#121×C107—22no—
86#121×C107D412yes—
87#121×C107D411yescharacteristic
88#121×C107C2312yes—
89#121×C107C2311yescharacteristic
90#120×C107—22no—
91#120×C107—22no—
92#120×C107—22no—
93#120×C107—21no—
94#120×C107—22no—
95#120×C107—22no—
96#120×C107—22no—
97C4×D4×C107—22no—
98C4×D4×C107—21no—
99C4×D4×C107—21no—
100C4×D4×C107—21no—
101C4×D4×C107—21no—
102C4×D4×C107—22no—
103#117×C107—21no—
104#117×C107D411yescharacteristic
105C2×C4⋊C4×C107—21no—
106C2×C4⋊C4×C107—21no—
107C2×C4⋊C4×C107—21no—
108C2×C4⋊C4×C107—21no—
109C2×C4⋊C4×C107—21no—
110C2×C4⋊C4×C107D411yescharacteristic
111C2×C4⋊C4×C107D411yescharacteristic
112C2×C4⋊C4×C107C2312yes—
113C2×C22⋊C4×C107—21no—
114C2×C22⋊C4×C107—21no—
115C2×C22⋊C4×C107—24no—
116C2×C22⋊C4×C107C2312yes—
117C2×C42×C107—21no—
118#107×C107—24no—
119#107×C107—22no—
120#106×C107—22no—
121#103×C107—22no—
122#102×C107—24no—
123#102×C107—22no—
124C22⋊C8×C107—21no—
125C22⋊C8×C107—21no—
126C22⋊C8×C107C2312yes—
127C22⋊C8×C107C2312yes—
128#95×C107—24no—
129#95×C107C2312yes—
130C24×C107—22no—
131C24×C107—21no—
132C24×C107C2×D411yescharacteristic
133C24×C107C2×D412yes—
134#41×C107—42no—
135C2×Q8×C107C2×D411yescharacteristic
136C2×D4×C107—22no—
137C2×D4×C107—21no—
138C2×D4×C107—21no—
139C2×D4×C107—22no—
140C2×D4×C107—22no—
141C2×D4×C107—22no—
142C2×D4×C107—22no—
143C2×D4×C107—22no—
144C2×D4×C107—22no—
145C2×D4×C107—21no—
146C2×D4×C107—22no—
147C2×D4×C107—22no—
148C2×D4×C107—21no—
149C2×D4×C107—21no—
150C2×D4×C107—21no—
151C2×D4×C107—42no—
152C2×D4×C107—42no—
153C2×D4×C107—44no—
154C2×D4×C107—82no—
155C2×D4×C107—82no—
156C2×D4×C107—84no—
157C2×D4×C107—84no—
158C2×D4×C107C2×D411yescharacteristic
159C2×D4×C107C2×D412yes—
160C22×C4×C107—22no—
161C22×C4×C107—22no—
162C22×C4×C107—21no—
163C22×C4×C107—21no—
164C22×C4×C107—22no—
165C22×C4×C107—22no—
166C22×C4×C107—42no—
167C22×C4×C107—41no—
168C22×C4×C107—41no—
169C22×C4×C107—82no—
170C22×C4×C107C2×D411yescharacteristic
171C22×C4×C107C2×D411yescharacteristic
172C22×C4×C107C2×D411yescharacteristic
173C22×C4×C107C2×D412yes—
174C22×C4×C107C2×D411yescharacteristic
175C22×C4×C107C2×D411yescharacteristic
176C22×C4×C107C2411yescharacteristic
177M16×C107—42no—
178C2×C8×C107—22no—
179C2×C8×C107—22no—
180C2×C8×C107—42no—
181C4⋊C4×C107—22no—
182C4⋊C4×C107—22no—
183C4⋊C4×C107—21no—
184C4⋊C4×C107—21no—
185C4⋊C4×C107—21no—
186C4⋊C4×C107—21no—
187C4⋊C4×C107—21no—
188C4⋊C4×C107—22no—
189C4⋊C4×C107—22no—
190C4⋊C4×C107—41no—
191C4⋊C4×C107—41no—
192C4⋊C4×C107C2×D411yescharacteristic
193C4⋊C4×C107C2×D412yes—
194C4⋊C4×C107C2×D411yescharacteristic
195C22⋊C4×C107—22no—
196C22⋊C4×C107—22no—
197C22⋊C4×C107—22no—
198C22⋊C4×C107—22no—
199C22⋊C4×C107—22no—
200C22⋊C4×C107—21no—
201C22⋊C4×C107—21no—
202C22⋊C4×C107—21no—
203C22⋊C4×C107—22no—
204C22⋊C4×C107—21no—
205C22⋊C4×C107—22no—
206C22⋊C4×C107—22no—
207C22⋊C4×C107—22no—
208C22⋊C4×C107—21no—
209C22⋊C4×C107—42no—
210C22⋊C4×C107—84no—
211C42×C107—22no—
212C42×C107—21no—
213C42×C107—42no—
214C23×C107—22no—
215C23×C107—22no—
216C23×C107—22no—
217C23×C107—22no—
218C23×C107—21no—
219C23×C107—24no—
220C23×C107—41no—
221C23×C107—42no—
222C23×C107—42no—
223C23×C107—42no—
224C23×C107—81no—
225C23×C107—81no—
226C23×C107—82no—
227C23×C107—82no—
228C23×C107—82no—
229C23×C107#12011yescharacteristic
230C23×C107#12011yescharacteristic
231C23×C107C22×D411yescharacteristic
232Q8×C107—41no—
233D4×C107—42no—
234D4×C107—41no—
235D4×C107—44no—
236D4×C107—42no—
237D4×C107—44no—
238D4×C107—42no—
239D4×C107—42no—
240D4×C107—42no—
241D4×C107—81no—
242D4×C107—82no—
243D4×C107—82no—
244D4×C107—81no—
245D4×C107—82no—
246D4×C107—82no—
247D4×C107—82no—
248D4×C107—82no—
249D4×C107—82no—
250C2×C4×C107—22no—
251C2×C4×C107—22no—
252C2×C4×C107—22no—
253C2×C4×C107—21no—
254C2×C4×C107—22no—
255C2×C4×C107—22no—
256C2×C4×C107—21no—
257C2×C4×C107—21no—
258C2×C4×C107—41no—
259C2×C4×C107—41no—
260C2×C4×C107—41no—
261C2×C4×C107—42no—
262C2×C4×C107—42no—
263C2×C4×C107—42no—
264C2×C4×C107—42no—
265C2×C4×C107—42no—
266C2×C4×C107—42no—
267C2×C4×C107—44no—
268C2×C4×C107—81no—
269C2×C4×C107—82no—
270C2×C4×C107—82no—
271C2×C4×C107—82no—
272C2×C4×C107—82no—
273C2×C4×C107#12011yescharacteristic
274C2×C4×C107#12011yescharacteristic
275C2×C4×C107C22×D411yescharacteristic
276C2×C4×C107C22×D411yescharacteristic
277C8×C107—42no—
278C8×C107—42no—
279C22×C107—21no—
280C22×C107—21no—
281C22×C107—21no—
282C22×C107—21no—
283C22×C107—21no—
284C22×C107—21no—
285C22×C107—21no—
286C22×C107—44no—
287C22×C107—42no—
288C22×C107—42no—
289C22×C107—41no—
290C22×C107—42no—
291C22×C107—42no—
292C22×C107—41no—
293C22×C107—41no—
294C22×C107—42no—
295C22×C107—42no—
296C22×C107—84no—
297C22×C107—162no—
298C22×C107—164no—
299C22×C107#45512yes—
300C22×C107C2×#12011yescharacteristic
301C22×C107#57612yes—
302C4×C107—21no—
303C4×C107—21no—
304C4×C107—21no—
305C4×C107—42no—
306C4×C107—41no—
307C4×C107—42no—
308C4×C107—41no—
309C4×C107—41no—
310C4×C107—82no—
311C4×C107—82no—
312C4×C107#45812yes—
313#18264C10711yesmaximal, characteristic, direct product factor, Sylow
314C2×C107—22no—
315C2×C107—22no—
316C2×C107—41no—
317C2×C107—82no—
318C2×C107—82no—
319C2×C107—81no—
320C2×C107#300811yescharacteristic
321C2×C107C2×#45511yescharacteristic
322C2×C107C2×#45811yescharacteristic
323#3537C2×C10711yescharacteristic
324#3092C2×C10711yescharacteristic, complemented
325C2×#480C2×C10711yescharacteristic, complemented
326#2504C2×C10711yescharacteristic, complemented
327#1612C2×C10714yescomplemented
328#1607C2×C10714yescomplemented
329#1507C2×C10711yescharacteristic, complemented
330#1501C2×C10711yescharacteristic, complemented
331#1471C2×C10711yescharacteristic, complemented
332C107#1826411yescharacteristic, direct product factor, Sylow
333#560—22no—
334#553—21no—
335#553—21no—
336D42—22no—
337D42—21no—
338D42—21no—
339#540—21no—
340#538—21no—
341#538C22×C10712yes—
342#535—21no—
343#534—21no—
344#534C22×C10712yes—
345#525C22×C10711yescharacteristic
346C2×#121C22×C10711yescharacteristic
347C2×#121C22×C10711yescharacteristic
348C22×C4⋊C4C22×C10711yescharacteristic, complemented
349#484—21no—
350#483C22×C10712yescomplemented
351#481—21no—
352#480—22no—
353#480C22×C10714yescomplemented
354#480C22×C10712yescomplemented
355#428—21no—
356C2×#107—21no—
357#417—21no—
358C2×#102—21no—
359#407C22×C10711yescharacteristic, complemented
360C2×C22⋊C8C22×C10711yescharacteristic, complemented
361#397C22×C10714yescomplemented
362#390—21no—
363#386—22no—
364#382—21no—
365C4×C22⋊C4C22×C10711yescharacteristic, complemented
366#328C22×C10712yescomplemented
367#327C22×C10712yescomplemented
368#327C22×C10714yescomplemented
369#323C22×C10714yescomplemented
370C2×#41D4×C10711yescharacteristic
371C22×D4—22no—
372C22×D4—21no—
373C22×D4—21no—
374C22×D4—22no—
375C22×D4D4×C10712yes—
376C22×D4D4×C10711yescharacteristic
377C22×D4D4×C10711yescharacteristic
378C23×C4—21no—
379C23×C4C23×C10711yescharacteristic
380C2×M16—21no—
381C22×C8—21no—
382#127—22no—
383#127—21no—
384#126—22no—
385#126—22no—
386#125—21no—
387#124—22no—
388#123—22no—
389#123—21no—
390#123—22no—
391#123—22no—
392#123—22no—
393C22⋊Q8D4×C10711yescharacteristic
394C22⋊Q8C23×C10711yescharacteristic
395#121—22no—
396#121—21no—
397#121—21no—
398#121—22no—
399#121—22no—
400#121—22no—
401#121—22no—
402#121—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—22no—
409#121D4×C10712yes—
410#121D4×C10711yescharacteristic
411#121C23×C10712yes—
412#121C23×C10711yescharacteristic
413#120—22no—
414#120—22no—
415#120—22no—
416#120—21no—
417#120—22no—
418#120—22no—
419#120—22no—
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—22no—
426#117—21no—
427#117D4×C10711yescharacteristic
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C10711yescharacteristic
434C2×C4⋊C4D4×C10711yescharacteristic
435C2×C4⋊C4C23×C10712yes—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4C23×C10712yes—
440C2×C42—21no—
441#107—24no—
442#107—22no—
443#106—22no—
444#103—22no—
445#102—24no—
446#102—22no—
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8C23×C10712yes—
450C22⋊C8C23×C10712yes—
451#95—24no—
452#95C23×C10712yes—
453C24—22no—
454C24—21no—
455C24C2×D4×C10711yescharacteristic
456C24C2×D4×C10712yes—
457#41—42no—
458C2×Q8C2×D4×C10711yescharacteristic
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—44no—
477C2×D4—82no—
478C2×D4—82no—
479C2×D4—84no—
480C2×D4—84no—
481C2×D4C2×D4×C10711yescharacteristic
482C2×D4C2×D4×C10712yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—42no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—82no—
493C22×C4C2×D4×C10711yescharacteristic
494C22×C4C2×D4×C10711yescharacteristic
495C22×C4C2×D4×C10711yescharacteristic
496C22×C4C2×D4×C10712yes—
497C22×C4C2×D4×C10711yescharacteristic
498C22×C4C2×D4×C10711yescharacteristic
499C22×C4C24×C10711yescharacteristic
500M16—42no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—42no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C10711yescharacteristic
516C4⋊C4C2×D4×C10712yes—
517C4⋊C4C2×D4×C10711yescharacteristic
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—42no—
533C22⋊C4—84no—
534C42—22no—
535C42—21no—
536C42—42no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—21no—
542C23—24no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—81no—
548C23—81no—
549C23—82no—
550C23—82no—
551C23—82no—
552C23#120×C10711yescharacteristic
553C23#120×C10711yescharacteristic
554C23C22×D4×C10711yescharacteristic
555Q8—41no—
556D4—42no—
557D4—41no—
558D4—44no—
559D4—42no—
560D4—44no—
561D4—42no—
562D4—42no—
563D4—42no—
564D4—81no—
565D4—82no—
566D4—82no—
567D4—81no—
568D4—82no—
569D4—82no—
570D4—82no—
571D4—82no—
572D4—82no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—44no—
591C2×C4—81no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4#120×C10711yescharacteristic
597C2×C4#120×C10711yescharacteristic
598C2×C4C22×D4×C10711yescharacteristic
599C2×C4C22×D4×C10711yescharacteristic
600C8—42no—
601C8—42no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22—42no—
614C22—42no—
615C22—41no—
616C22—41no—
617C22—42no—
618C22—42no—
619C22—84no—
620C22—162no—
621C22—164no—
622C22#455×C10712yes—
623C22C2×#120×C10711yescharacteristic
624C22#576×C10712yes—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—41no—
633C4—82no—
634C4—82no—
635C4#458×C10712yes—
636C2—22no—
637C2—22no—
638C2—41no—
639C2—82no—
640C2—82no—
641C2—81no—
642C2C107×#300811yescharacteristic
643C2C2×#455×C10711yescharacteristic
644C2C2×#458×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3537C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#3092C2semidirect
3. C2×#480×C107C2semidirect
4. C107×#2504C2semidirect
5. C107×#1612C2semidirect
6. C107×#1607C2semidirect
7. C107×#1507C2semidirect
8. C107×#1501C2semidirect
9. C107×#1471C2semidirect
25. C22×C4⋊C4×C107C22semidirect
27. #483×C107C22semidirect
30. #480×C107C22semidirect
31. #480×C107C22semidirect
36. #407×C107C22semidirect
37. C2×C22⋊C8×C107C22semidirect
38. #397×C107C22semidirect
42. C4×C22⋊C4×C107C22semidirect
43. #328×C107C22semidirect
44. #327×C107C22semidirect
45. #327×C107C22semidirect
46. #323×C107C22semidirect
313. #18264C107direct (N × H)
324. #3092C2×C107semidirect
325. C2×#480C2×C107semidirect
326. #2504C2×C107semidirect
327. #1612C2×C107semidirect
328. #1607C2×C107semidirect
329. #1507C2×C107semidirect
330. #1501C2×C107semidirect
331. #1471C2×C107semidirect
332. C107#18264direct (N × H)
348. C22×C4⋊C4C22×C107semidirect
350. #483C22×C107semidirect
353. #480C22×C107semidirect
354. #480C22×C107semidirect
359. #407C22×C107semidirect
360. C2×C22⋊C8C22×C107semidirect
361. #397C22×C107semidirect
365. C4×C22⋊C4C22×C107semidirect
366. #328C22×C107semidirect
367. #327C22×C107semidirect
368. #327C22×C107semidirect
369. #323C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35372
C107×#30922
C2×#480×C1072
C107×#25042
C107×#16122
C107×#16072
C107×#15072
C107×#15012
C107×#14712
#18264107