Finite Group Databasebeta

← C107×#23901 #41049865

Subgroups — C107×#23901 #41049865

Order 27392.

2056 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3484C211yesmaximal, characteristic
2C22×#123×C107C211yesmaximal, characteristic, complemented
3C2×#458×C107C212yesmaximal, complemented
4C107×#2849C212yesmaximal, complemented
5C107×#2022C214yesmaximal, complemented
6C107×#1898C212yesmaximal, complemented
7C107×#1890C212yesmaximal, complemented
8C107×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C107C2211yescharacteristic
10C23×D4×C107C2211yescharacteristic
11C24×C4×C107C2211yescharacteristic, complemented
12#546×C107—24no—
13D42×C107—24no—
14#535×C107—21no—
15#534×C107—21no—
16#534×C107C2212yes—
17#525×C107—21no—
18C2×#123×C107—21no—
19C2×#123×C107—21no—
20C2×#123×C107—28no—
21C2×#123×C107C2212yes—
22C2×#123×C107C2212yescomplemented
23C2×#123×C107C2214yescomplemented
24C2×#120×C107—21no—
25C2×#120×C107C2212yes—
26#518×C107C2211yescharacteristic
27C22×C4⋊C4×C107—21no—
28C22×C22⋊C4×C107—21no—
29C22×C22⋊C4×C107C2211yescharacteristic, complemented
30#458×C107—28no—
31C2×#99×C107C2212yes—
32C2×#99×C107C2214yescomplemented
33C2×#99×C107C2212yescomplemented
34#386×C107—24no—
35#385×C107—24no—
36#381×C107C2214yescomplemented
37#379×C107C2212yescomplemented
38#342×C107C2214yescomplemented
39C25×C107D411yescharacteristic
40C25×C107C2311yescharacteristic
41H(5,𝔽2)×C107—24no—
42H(5,𝔽2)×C107—42no—
43C2×#41×C107—21no—
44C2×#41×C107—22no—
45C22×D4×C107—21no—
46C22×D4×C107—22no—
47C22×D4×C107—24no—
48C22×D4×C107—22no—
49C22×D4×C107—24no—
50C22×D4×C107—42no—
51C22×D4×C107D411yescharacteristic
52C22×D4×C107D411yescharacteristic
53C22×D4×C107D414yes—
54C22×D4×C107C2312yes—
55C22×D4×C107C2311yescharacteristic
56C22×D4×C107C2311yescharacteristic
57C23×C4×C107—21no—
58C23×C4×C107—21no—
59C23×C4×C107—21no—
60C23×C4×C107—24no—
61C23×C4×C107—24no—
62C23×C4×C107—42no—
63C23×C4×C107D411yescharacteristic
64C23×C4×C107C2312yes—
65#127×C107—22no—
66#124×C107—22no—
67#123×C107—28no—
68#123×C107—28no—
69#123×C107—22no—
70#123×C107—24no—
71#123×C107—22no—
72#123×C107—22no—
73#123×C107—24no—
74#123×C107—24no—
75#123×C107—28no—
76#123×C107—44no—
77#123×C107D418yescomplemented
78C22⋊Q8×C107—22no—
79#121×C107—22no—
80#121×C107—24no—
81#121×C107—24no—
82#121×C107—24no—
83#120×C107—24no—
84#120×C107—22no—
85#120×C107—22no—
86#120×C107—22no—
87#120×C107—22no—
88#120×C107—24no—
89#120×C107—22no—
90C4×D4×C107—24no—
91C4×D4×C107—24no—
92#117×C107—21no—
93C2×C4⋊C4×C107—28no—
94C2×C4⋊C4×C107—22no—
95C2×C4⋊C4×C107—22no—
96C2×C4⋊C4×C107—24no—
97C2×C22⋊C4×C107—28no—
98C2×C22⋊C4×C107—22no—
99C2×C22⋊C4×C107—22no—
100C2×C22⋊C4×C107—22no—
101C2×C22⋊C4×C107—21no—
102C2×C22⋊C4×C107—21no—
103C2×C22⋊C4×C107—24no—
104C2×C22⋊C4×C107—24no—
105C2×C22⋊C4×C107—24no—
106C2×C22⋊C4×C107D414yes—
107C2×C22⋊C4×C107C2314yes—
108C2×C22⋊C4×C107C2312yes—
109C2×C22⋊C4×C107C2312yes—
110#99×C107—24no—
111#99×C107—28no—
112#99×C107—42no—
113#95×C107—28no—
114C24×C107—22no—
115C24×C107—22no—
116C24×C107—21no—
117C24×C107—22no—
118C24×C107—22no—
119C24×C107—44no—
120C24×C107—41no—
121C24×C107—44no—
122C24×C107C2×D411yescharacteristic
123C24×C107C2×D414yes—
124C24×C107C2×D411yescharacteristic
125C24×C107C2×D412yes—
126C24×C107C2×D411yescharacteristic
127C24×C107C2×D411yescharacteristic
128C24×C107C2411yescharacteristic
129#41×C107—48no—
130#41×C107—42no—
131#41×C107—42no—
132C2×Q8×C107—21no—
133C2×D4×C107—22no—
134C2×D4×C107—22no—
135C2×D4×C107—22no—
136C2×D4×C107—21no—
137C2×D4×C107—24no—
138C2×D4×C107—22no—
139C2×D4×C107—22no—
140C2×D4×C107—22no—
141C2×D4×C107—24no—
142C2×D4×C107—22no—
143C2×D4×C107—22no—
144C2×D4×C107—22no—
145C2×D4×C107—22no—
146C2×D4×C107—22no—
147C2×D4×C107—24no—
148C2×D4×C107—24no—
149C2×D4×C107—24no—
150C2×D4×C107—22no—
151C2×D4×C107—41no—
152C2×D4×C107—41no—
153C2×D4×C107—416no—
154C2×D4×C107—48no—
155C2×D4×C107—42no—
156C2×D4×C107—42no—
157C2×D4×C107—48no—
158C2×D4×C107—84no—
159C2×D4×C107C2×D414yes—
160C22×C4×C107—24no—
161C22×C4×C107—24no—
162C22×C4×C107—21no—
163C22×C4×C107—22no—
164C22×C4×C107—24no—
165C22×C4×C107—22no—
166C22×C4×C107—24no—
167C22×C4×C107—22no—
168C22×C4×C107—22no—
169C22×C4×C107—22no—
170C22×C4×C107—24no—
171C22×C4×C107—22no—
172C22×C4×C107—22no—
173C22×C4×C107—24no—
174C22×C4×C107—41no—
175C22×C4×C107—416no—
176C22×C4×C107—44no—
177C22×C4×C107—42no—
178C22×C4×C107—42no—
179C22×C4×C107—42no—
180C22×C4×C107—42no—
181C22×C4×C107C2×D412yes—
182C22×C4×C107C2×D411yescharacteristic
183C22×C4×C107C2×D411yescharacteristic
184C22×C4×C107C2×D414yes—
185C22×C4×C107C2×D414yescomplemented
186C4⋊C4×C107—28no—
187C4⋊C4×C107—22no—
188C4⋊C4×C107—24no—
189C4⋊C4×C107—28no—
190C4⋊C4×C107—48no—
191C22⋊C4×C107—24no—
192C22⋊C4×C107—28no—
193C22⋊C4×C107—22no—
194C22⋊C4×C107—24no—
195C22⋊C4×C107—24no—
196C22⋊C4×C107—28no—
197C22⋊C4×C107—24no—
198C22⋊C4×C107—24no—
199C22⋊C4×C107—22no—
200C22⋊C4×C107—22no—
201C22⋊C4×C107—22no—
202C22⋊C4×C107—24no—
203C22⋊C4×C107—24no—
204C22⋊C4×C107—48no—
205C22⋊C4×C107—48no—
206C22⋊C4×C107C2×D414yescomplemented
207C42×C107—22no—
208C23×C107—21no—
209C23×C107—21no—
210C23×C107—24no—
211C23×C107—21no—
212C23×C107—21no—
213C23×C107—21no—
214C23×C107—28no—
215C23×C107—28no—
216C23×C107—21no—
217C23×C107—21no—
218C23×C107—21no—
219C23×C107—22no—
220C23×C107—21no—
221C23×C107—24no—
222C23×C107—44no—
223C23×C107—42no—
224C23×C107—42no—
225C23×C107—44no—
226C23×C107—48no—
227C23×C107—48no—
228C23×C107—42no—
229C23×C107—42no—
230C23×C107—48no—
231C23×C107—42no—
232C23×C107—44no—
233C23×C107—44no—
234C23×C107—82no—
235C23×C107—84no—
236C23×C107—82no—
237C23×C107#12012yes—
238C23×C107#12012yes—
239C23×C107#12012yes—
240C23×C107C22×D411yescharacteristic
241C23×C107C22×D412yes—
242C23×C107C22×D412yes—
243C23×C107H(5,𝔽2)12yes—
244Q8×C107—42no—
245D4×C107—28no—
246D4×C107—44no—
247D4×C107—42no—
248D4×C107—44no—
249D4×C107—44no—
250D4×C107—42no—
251D4×C107—42no—
252D4×C107—44no—
253D4×C107—44no—
254D4×C107—48no—
255D4×C107—84no—
256D4×C107—84no—
257C2×C4×C107—21no—
258C2×C4×C107—21no—
259C2×C4×C107—24no—
260C2×C4×C107—24no—
261C2×C4×C107—21no—
262C2×C4×C107—24no—
263C2×C4×C107—22no—
264C2×C4×C107—21no—
265C2×C4×C107—21no—
266C2×C4×C107—28no—
267C2×C4×C107—24no—
268C2×C4×C107—44no—
269C2×C4×C107—44no—
270C2×C4×C107—48no—
271C2×C4×C107—44no—
272C2×C4×C107—48no—
273C2×C4×C107—48no—
274C2×C4×C107—42no—
275C2×C4×C107—42no—
276C2×C4×C107—42no—
277C2×C4×C107—44no—
278C2×C4×C107—44no—
279C2×C4×C107—48no—
280C2×C4×C107—44no—
281C2×C4×C107—82no—
282C2×C4×C107#12012yes—
283C22×C107—24no—
284C22×C107—24no—
285C22×C107—22no—
286C22×C107—24no—
287C22×C107—22no—
288C22×C107—22no—
289C22×C107—22no—
290C22×C107—22no—
291C22×C107—24no—
292C22×C107—42no—
293C22×C107—42no—
294C22×C107—416no—
295C22×C107—42no—
296C22×C107—42no—
297C22×C107—42no—
298C22×C107—42no—
299C22×C107—42no—
300C22×C107—42no—
301C22×C107—41no—
302C22×C107—44no—
303C22×C107—42no—
304C22×C107—81no—
305C22×C107—88no—
306C22×C107—84no—
307C22×C107—81no—
308C22×C107—162no—
309C22×C107#45814yescomplemented
310C22×C107C2×#12011yescharacteristic
311C22×C107C2×#12011yescharacteristic
312C22×C107#53411yescharacteristic
313C22×C107D4214yes—
314C4×C107—22no—
315C4×C107—44no—
316C4×C107—44no—
317C4×C107—41no—
318C4×C107—42no—
319C4×C107—44no—
320C4×C107—84no—
321#23901C10711yesmaximal, characteristic, direct product factor, Sylow
322C2×C107—21no—
323C2×C107—24no—
324C2×C107—21no—
325C2×C107—24no—
326C2×C107—42no—
327C2×C107—42no—
328C2×C107—81no—
329C2×C107—82no—
330C2×C107#240311yescharacteristic
331C2×C107C2×#45812yes—
332#3484C2×C10711yescharacteristic
333C22×#123C2×C10711yescharacteristic, complemented
334C2×#458C2×C10712yescomplemented
335#2849C2×C10712yescomplemented
336#2022C2×C10714yescomplemented
337#1898C2×C10712yescomplemented
338#1890C2×C10712yescomplemented
339#1781C2×C10711yescharacteristic, complemented
340C107#2390111yescharacteristic, direct product factor, Sylow
341C2×H(5,𝔽2)C22×C10711yescharacteristic
342C23×D4C22×C10711yescharacteristic
343C24×C4C22×C10711yescharacteristic, complemented
344#546—24no—
345D42—24no—
346#535—21no—
347#534—21no—
348#534C22×C10712yes—
349#525—21no—
350C2×#123—21no—
351C2×#123—21no—
352C2×#123—28no—
353C2×#123C22×C10712yes—
354C2×#123C22×C10712yescomplemented
355C2×#123C22×C10714yescomplemented
356C2×#120—21no—
357C2×#120C22×C10712yes—
358#518C22×C10711yescharacteristic
359C22×C4⋊C4—21no—
360C22×C22⋊C4—21no—
361C22×C22⋊C4C22×C10711yescharacteristic, complemented
362#458—28no—
363C2×#99C22×C10712yes—
364C2×#99C22×C10714yescomplemented
365C2×#99C22×C10712yescomplemented
366#386—24no—
367#385—24no—
368#381C22×C10714yescomplemented
369#379C22×C10712yescomplemented
370#342C22×C10714yescomplemented
371C25D4×C10711yescharacteristic
372C25C23×C10711yescharacteristic
373H(5,𝔽2)—24no—
374H(5,𝔽2)—42no—
375C2×#41—21no—
376C2×#41—22no—
377C22×D4—21no—
378C22×D4—22no—
379C22×D4—24no—
380C22×D4—22no—
381C22×D4—24no—
382C22×D4—42no—
383C22×D4D4×C10711yescharacteristic
384C22×D4D4×C10711yescharacteristic
385C22×D4D4×C10714yes—
386C22×D4C23×C10712yes—
387C22×D4C23×C10711yescharacteristic
388C22×D4C23×C10711yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—42no—
395C23×C4D4×C10711yescharacteristic
396C23×C4C23×C10712yes—
397#127—22no—
398#124—22no—
399#123—28no—
400#123—28no—
401#123—22no—
402#123—24no—
403#123—22no—
404#123—22no—
405#123—24no—
406#123—24no—
407#123—28no—
408#123—44no—
409#123D4×C10718yescomplemented
410C22⋊Q8—22no—
411#121—22no—
412#121—24no—
413#121—24no—
414#121—24no—
415#120—24no—
416#120—22no—
417#120—22no—
418#120—22no—
419#120—22no—
420#120—24no—
421#120—22no—
422C4×D4—24no—
423C4×D4—24no—
424#117—21no—
425C2×C4⋊C4—28no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4D4×C10714yes—
439C2×C22⋊C4C23×C10714yes—
440C2×C22⋊C4C23×C10712yes—
441C2×C22⋊C4C23×C10712yes—
442#99—24no—
443#99—28no—
444#99—42no—
445#95—28no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—44no—
452C24—41no—
453C24—44no—
454C24C2×D4×C10711yescharacteristic
455C24C2×D4×C10714yes—
456C24C2×D4×C10711yescharacteristic
457C24C2×D4×C10712yes—
458C24C2×D4×C10711yescharacteristic
459C24C2×D4×C10711yescharacteristic
460C24C24×C10711yescharacteristic
461#41—48no—
462#41—42no—
463#41—42no—
464C2×Q8—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—416no—
486C2×D4—48no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—48no—
490C2×D4—84no—
491C2×D4C2×D4×C10714yes—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—41no—
507C22×C4—416no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—44no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4C2×D4×C10712yes—
514C22×C4C2×D4×C10711yescharacteristic
515C22×C4C2×D4×C10711yescharacteristic
516C22×C4C2×D4×C10714yes—
517C22×C4C2×D4×C10714yescomplemented
518C4⋊C4—28no—
519C4⋊C4—22no—
520C4⋊C4—24no—
521C4⋊C4—28no—
522C4⋊C4—48no—
523C22⋊C4—24no—
524C22⋊C4—28no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—28no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4C2×D4×C10714yescomplemented
539C42—22no—
540C23—24no—
541C23—21no—
542C23—21no—
543C23—28no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—28no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—21no—
553C23—24no—
554C23—44no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—48no—
559C23—48no—
560C23—42no—
561C23—42no—
562C23—48no—
563C23—42no—
564C23—44no—
565C23—44no—
566C23—82no—
567C23—84no—
568C23—82no—
569C23#120×C10712yes—
570C23#120×C10712yes—
571C23#120×C10712yes—
572C23C22×D4×C10711yescharacteristic
573C23C22×D4×C10712yes—
574C23C22×D4×C10712yes—
575C23H(5,𝔽2)×C10712yes—
576Q8—42no—
577D4—28no—
578D4—44no—
579D4—42no—
580D4—44no—
581D4—44no—
582D4—48no—
583D4—42no—
584D4—42no—
585D4—44no—
586D4—44no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—28no—
599C2×C4—24no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—48no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—44no—
613C2×C4—82no—
614C2×C4#120×C10712yes—
615C22—24no—
616C22—24no—
617C22—22no—
618C22—24no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—24no—
624C22—42no—
625C22—42no—
626C22—416no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—41no—
634C22—44no—
635C22—42no—
636C22—81no—
637C22—88no—
638C22—81no—
639C22—84no—
640C22—162no—
641C22#458×C10714yescomplemented
642C22C2×#120×C10711yescharacteristic
643C22C2×#120×C10711yescharacteristic
644C22#534×C10711yescharacteristic
645C22D42×C10714yes—
646C4—22no—
647C4—44no—
648C4—44no—
649C4—41no—
650C4—42no—
651C4—44no—
652C4—84no—
653C2—21no—
654C2—24no—
655C2—24no—
656C2—21no—
657C2—42no—
658C2—42no—
659C2—81no—
660C2—82no—
661C2C107×#240311yescharacteristic
662C2C2×#458×C10712yes—
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC24C24×C107
prime radicalC107×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C25×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#123×C107C2semidirect
3. C2×#458×C107C2semidirect
4. C107×#2849C2semidirect
5. C107×#2022C2semidirect
6. C107×#1898C2semidirect
7. C107×#1890C2semidirect
8. C107×#1781C2semidirect
11. C24×C4×C107C22semidirect
22. C2×#123×C107C22semidirect
23. C2×#123×C107C22semidirect
29. C22×C22⋊C4×C107C22semidirect
32. C2×#99×C107C22semidirect
33. C2×#99×C107C22semidirect
36. #381×C107C22semidirect
37. #379×C107C22semidirect
38. #342×C107C22semidirect
77. #123×C107D4semidirect
185. C22×C4×C107C2×D4semidirect
206. C22⋊C4×C107C2×D4semidirect
309. C22×C107#458semidirect
321. #23901C107direct (N × H)
333. C22×#123C2×C107semidirect
334. C2×#458C2×C107semidirect
335. #2849C2×C107semidirect
336. #2022C2×C107semidirect
337. #1898C2×C107semidirect
338. #1890C2×C107semidirect
339. #1781C2×C107semidirect
340. C107#23901direct (N × H)
343. C24×C4C22×C107semidirect
354. C2×#123C22×C107semidirect
355. C2×#123C22×C107semidirect
361. C22×C22⋊C4C22×C107semidirect
364. C2×#99C22×C107semidirect
365. C2×#99C22×C107semidirect
368. #381C22×C107semidirect
369. #379C22×C107semidirect
370. #342C22×C107semidirect
409. #123D4×C107semidirect
517. C22×C4C2×D4×C107semidirect
538. C22⋊C4C2×D4×C107semidirect
641. C22#458×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34842
C22×#123×C1072
C2×#458×C1072
C107×#28492
C107×#20222
C107×#18982
C107×#18902
C107×#17812
#23901107