Finite Group Databasebeta

← C113×#23901 #43291921

Subgroups — C113×#23901 #43291921

Order 28928.

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
1C113×#3484C211yesmaximal, characteristic
2C22×#123×C113C211yesmaximal, characteristic, complemented
3C2×#458×C113C212yesmaximal, complemented
4C113×#2849C212yesmaximal, complemented
5C113×#2022C214yesmaximal, complemented
6C113×#1898C212yesmaximal, complemented
7C113×#1890C212yesmaximal, complemented
8C113×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C113C2211yescharacteristic
10C23×D4×C113C2211yescharacteristic
11C24×C4×C113C2211yescharacteristic, complemented
12#546×C113—24no—
13D42×C113—24no—
14#535×C113—21no—
15#534×C113—21no—
16#534×C113C2212yes—
17#525×C113—21no—
18C2×#123×C113—21no—
19C2×#123×C113—21no—
20C2×#123×C113—28no—
21C2×#123×C113C2212yes—
22C2×#123×C113C2212yescomplemented
23C2×#123×C113C2214yescomplemented
24C2×#120×C113—21no—
25C2×#120×C113C2212yes—
26#518×C113C2211yescharacteristic
27C22×C4⋊C4×C113—21no—
28C22×C22⋊C4×C113—21no—
29C22×C22⋊C4×C113C2211yescharacteristic, complemented
30#458×C113—28no—
31C2×#99×C113C2212yes—
32C2×#99×C113C2214yescomplemented
33C2×#99×C113C2212yescomplemented
34#386×C113—24no—
35#385×C113—24no—
36#381×C113C2214yescomplemented
37#379×C113C2212yescomplemented
38#342×C113C2214yescomplemented
39C25×C113D411yescharacteristic
40C25×C113C2311yescharacteristic
41H(5,𝔽2)×C113—24no—
42H(5,𝔽2)×C113—42no—
43C2×#41×C113—21no—
44C2×#41×C113—22no—
45C22×D4×C113—21no—
46C22×D4×C113—22no—
47C22×D4×C113—24no—
48C22×D4×C113—22no—
49C22×D4×C113—24no—
50C22×D4×C113—42no—
51C22×D4×C113D411yescharacteristic
52C22×D4×C113D411yescharacteristic
53C22×D4×C113D414yes—
54C22×D4×C113C2312yes—
55C22×D4×C113C2311yescharacteristic
56C22×D4×C113C2311yescharacteristic
57C23×C4×C113—21no—
58C23×C4×C113—21no—
59C23×C4×C113—21no—
60C23×C4×C113—24no—
61C23×C4×C113—24no—
62C23×C4×C113—42no—
63C23×C4×C113D411yescharacteristic
64C23×C4×C113C2312yes—
65#127×C113—22no—
66#124×C113—22no—
67#123×C113—28no—
68#123×C113—28no—
69#123×C113—22no—
70#123×C113—24no—
71#123×C113—22no—
72#123×C113—22no—
73#123×C113—24no—
74#123×C113—24no—
75#123×C113—28no—
76#123×C113—44no—
77#123×C113D418yescomplemented
78C22⋊Q8×C113—22no—
79#121×C113—22no—
80#121×C113—24no—
81#121×C113—24no—
82#121×C113—24no—
83#120×C113—24no—
84#120×C113—22no—
85#120×C113—22no—
86#120×C113—22no—
87#120×C113—22no—
88#120×C113—24no—
89#120×C113—22no—
90C4×D4×C113—24no—
91C4×D4×C113—24no—
92#117×C113—21no—
93C2×C4⋊C4×C113—28no—
94C2×C4⋊C4×C113—22no—
95C2×C4⋊C4×C113—22no—
96C2×C4⋊C4×C113—24no—
97C2×C22⋊C4×C113—28no—
98C2×C22⋊C4×C113—22no—
99C2×C22⋊C4×C113—22no—
100C2×C22⋊C4×C113—22no—
101C2×C22⋊C4×C113—21no—
102C2×C22⋊C4×C113—21no—
103C2×C22⋊C4×C113—24no—
104C2×C22⋊C4×C113—24no—
105C2×C22⋊C4×C113—24no—
106C2×C22⋊C4×C113D414yes—
107C2×C22⋊C4×C113C2314yes—
108C2×C22⋊C4×C113C2312yes—
109C2×C22⋊C4×C113C2312yes—
110#99×C113—24no—
111#99×C113—28no—
112#99×C113—42no—
113#95×C113—28no—
114C24×C113—22no—
115C24×C113—22no—
116C24×C113—21no—
117C24×C113—22no—
118C24×C113—22no—
119C24×C113—44no—
120C24×C113—41no—
121C24×C113—44no—
122C24×C113C2×D411yescharacteristic
123C24×C113C2×D414yes—
124C24×C113C2×D411yescharacteristic
125C24×C113C2×D412yes—
126C24×C113C2×D411yescharacteristic
127C24×C113C2×D411yescharacteristic
128C24×C113C2411yescharacteristic
129#41×C113—48no—
130#41×C113—42no—
131#41×C113—42no—
132C2×Q8×C113—21no—
133C2×D4×C113—22no—
134C2×D4×C113—22no—
135C2×D4×C113—22no—
136C2×D4×C113—21no—
137C2×D4×C113—24no—
138C2×D4×C113—22no—
139C2×D4×C113—22no—
140C2×D4×C113—22no—
141C2×D4×C113—24no—
142C2×D4×C113—22no—
143C2×D4×C113—22no—
144C2×D4×C113—22no—
145C2×D4×C113—22no—
146C2×D4×C113—22no—
147C2×D4×C113—24no—
148C2×D4×C113—24no—
149C2×D4×C113—24no—
150C2×D4×C113—22no—
151C2×D4×C113—41no—
152C2×D4×C113—41no—
153C2×D4×C113—416no—
154C2×D4×C113—48no—
155C2×D4×C113—42no—
156C2×D4×C113—42no—
157C2×D4×C113—48no—
158C2×D4×C113—84no—
159C2×D4×C113C2×D414yes—
160C22×C4×C113—24no—
161C22×C4×C113—24no—
162C22×C4×C113—21no—
163C22×C4×C113—22no—
164C22×C4×C113—24no—
165C22×C4×C113—22no—
166C22×C4×C113—24no—
167C22×C4×C113—22no—
168C22×C4×C113—22no—
169C22×C4×C113—22no—
170C22×C4×C113—24no—
171C22×C4×C113—22no—
172C22×C4×C113—22no—
173C22×C4×C113—24no—
174C22×C4×C113—41no—
175C22×C4×C113—416no—
176C22×C4×C113—44no—
177C22×C4×C113—42no—
178C22×C4×C113—42no—
179C22×C4×C113—42no—
180C22×C4×C113—42no—
181C22×C4×C113C2×D412yes—
182C22×C4×C113C2×D411yescharacteristic
183C22×C4×C113C2×D411yescharacteristic
184C22×C4×C113C2×D414yes—
185C22×C4×C113C2×D414yescomplemented
186C4⋊C4×C113—28no—
187C4⋊C4×C113—22no—
188C4⋊C4×C113—24no—
189C4⋊C4×C113—28no—
190C4⋊C4×C113—48no—
191C22⋊C4×C113—24no—
192C22⋊C4×C113—28no—
193C22⋊C4×C113—22no—
194C22⋊C4×C113—24no—
195C22⋊C4×C113—24no—
196C22⋊C4×C113—28no—
197C22⋊C4×C113—24no—
198C22⋊C4×C113—24no—
199C22⋊C4×C113—22no—
200C22⋊C4×C113—22no—
201C22⋊C4×C113—22no—
202C22⋊C4×C113—24no—
203C22⋊C4×C113—24no—
204C22⋊C4×C113—48no—
205C22⋊C4×C113—48no—
206C22⋊C4×C113C2×D414yescomplemented
207C42×C113—22no—
208C23×C113—21no—
209C23×C113—21no—
210C23×C113—24no—
211C23×C113—21no—
212C23×C113—21no—
213C23×C113—21no—
214C23×C113—28no—
215C23×C113—28no—
216C23×C113—21no—
217C23×C113—21no—
218C23×C113—21no—
219C23×C113—22no—
220C23×C113—21no—
221C23×C113—24no—
222C23×C113—44no—
223C23×C113—42no—
224C23×C113—42no—
225C23×C113—44no—
226C23×C113—48no—
227C23×C113—48no—
228C23×C113—42no—
229C23×C113—42no—
230C23×C113—48no—
231C23×C113—42no—
232C23×C113—44no—
233C23×C113—44no—
234C23×C113—82no—
235C23×C113—84no—
236C23×C113—82no—
237C23×C113#12012yes—
238C23×C113#12012yes—
239C23×C113#12012yes—
240C23×C113C22×D411yescharacteristic
241C23×C113C22×D412yes—
242C23×C113C22×D412yes—
243C23×C113H(5,𝔽2)12yes—
244Q8×C113—42no—
245D4×C113—28no—
246D4×C113—44no—
247D4×C113—42no—
248D4×C113—44no—
249D4×C113—44no—
250D4×C113—42no—
251D4×C113—42no—
252D4×C113—44no—
253D4×C113—44no—
254D4×C113—48no—
255D4×C113—84no—
256D4×C113—84no—
257C2×C4×C113—21no—
258C2×C4×C113—21no—
259C2×C4×C113—24no—
260C2×C4×C113—24no—
261C2×C4×C113—21no—
262C2×C4×C113—24no—
263C2×C4×C113—22no—
264C2×C4×C113—21no—
265C2×C4×C113—21no—
266C2×C4×C113—28no—
267C2×C4×C113—24no—
268C2×C4×C113—44no—
269C2×C4×C113—44no—
270C2×C4×C113—48no—
271C2×C4×C113—44no—
272C2×C4×C113—48no—
273C2×C4×C113—48no—
274C2×C4×C113—42no—
275C2×C4×C113—42no—
276C2×C4×C113—42no—
277C2×C4×C113—44no—
278C2×C4×C113—44no—
279C2×C4×C113—48no—
280C2×C4×C113—44no—
281C2×C4×C113—82no—
282C2×C4×C113#12012yes—
283C22×C113—24no—
284C22×C113—24no—
285C22×C113—22no—
286C22×C113—24no—
287C22×C113—22no—
288C22×C113—22no—
289C22×C113—22no—
290C22×C113—22no—
291C22×C113—24no—
292C22×C113—42no—
293C22×C113—42no—
294C22×C113—416no—
295C22×C113—42no—
296C22×C113—42no—
297C22×C113—42no—
298C22×C113—42no—
299C22×C113—42no—
300C22×C113—42no—
301C22×C113—41no—
302C22×C113—44no—
303C22×C113—42no—
304C22×C113—81no—
305C22×C113—88no—
306C22×C113—84no—
307C22×C113—81no—
308C22×C113—162no—
309C22×C113#45814yescomplemented
310C22×C113C2×#12011yescharacteristic
311C22×C113C2×#12011yescharacteristic
312C22×C113#53411yescharacteristic
313C22×C113D4214yes—
314C4×C113—22no—
315C4×C113—44no—
316C4×C113—44no—
317C4×C113—41no—
318C4×C113—42no—
319C4×C113—44no—
320C4×C113—84no—
321#23901C11311yesmaximal, characteristic, direct product factor, Sylow
322C2×C113—21no—
323C2×C113—24no—
324C2×C113—21no—
325C2×C113—24no—
326C2×C113—42no—
327C2×C113—42no—
328C2×C113—81no—
329C2×C113—82no—
330C2×C113#240311yescharacteristic
331C2×C113C2×#45812yes—
332#3484C2×C11311yescharacteristic
333C22×#123C2×C11311yescharacteristic, complemented
334C2×#458C2×C11312yescomplemented
335#2849C2×C11312yescomplemented
336#2022C2×C11314yescomplemented
337#1898C2×C11312yescomplemented
338#1890C2×C11312yescomplemented
339#1781C2×C11311yescharacteristic, complemented
340C113#2390111yescharacteristic, direct product factor, Sylow
341C2×H(5,𝔽2)C22×C11311yescharacteristic
342C23×D4C22×C11311yescharacteristic
343C24×C4C22×C11311yescharacteristic, complemented
344#546—24no—
345D42—24no—
346#535—21no—
347#534—21no—
348#534C22×C11312yes—
349#525—21no—
350C2×#123—21no—
351C2×#123—21no—
352C2×#123—28no—
353C2×#123C22×C11312yes—
354C2×#123C22×C11312yescomplemented
355C2×#123C22×C11314yescomplemented
356C2×#120—21no—
357C2×#120C22×C11312yes—
358#518C22×C11311yescharacteristic
359C22×C4⋊C4—21no—
360C22×C22⋊C4—21no—
361C22×C22⋊C4C22×C11311yescharacteristic, complemented
362#458—28no—
363C2×#99C22×C11312yes—
364C2×#99C22×C11314yescomplemented
365C2×#99C22×C11312yescomplemented
366#386—24no—
367#385—24no—
368#381C22×C11314yescomplemented
369#379C22×C11312yescomplemented
370#342C22×C11314yescomplemented
371C25D4×C11311yescharacteristic
372C25C23×C11311yescharacteristic
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×C11311yescharacteristic
384C22×D4D4×C11311yescharacteristic
385C22×D4D4×C11314yes—
386C22×D4C23×C11312yes—
387C22×D4C23×C11311yescharacteristic
388C22×D4C23×C11311yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—42no—
395C23×C4D4×C11311yescharacteristic
396C23×C4C23×C11312yes—
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×C11318yescomplemented
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×C11314yes—
439C2×C22⋊C4C23×C11314yes—
440C2×C22⋊C4C23×C11312yes—
441C2×C22⋊C4C23×C11312yes—
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×C11311yescharacteristic
455C24C2×D4×C11314yes—
456C24C2×D4×C11311yescharacteristic
457C24C2×D4×C11312yes—
458C24C2×D4×C11311yescharacteristic
459C24C2×D4×C11311yescharacteristic
460C24C24×C11311yescharacteristic
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×C11314yes—
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×C11312yes—
514C22×C4C2×D4×C11311yescharacteristic
515C22×C4C2×D4×C11311yescharacteristic
516C22×C4C2×D4×C11314yes—
517C22×C4C2×D4×C11314yescomplemented
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×C11314yescomplemented
539C42—22no—
540C23—21no—
541C23—21no—
542C23—24no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—28no—
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×C11312yes—
570C23#120×C11312yes—
571C23#120×C11312yes—
572C23C22×D4×C11311yescharacteristic
573C23C22×D4×C11312yes—
574C23C22×D4×C11312yes—
575C23H(5,𝔽2)×C11312yes—
576Q8—42no—
577D4—28no—
578D4—44no—
579D4—42no—
580D4—44no—
581D4—44no—
582D4—42no—
583D4—42no—
584D4—44no—
585D4—44no—
586D4—48no—
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×C11312yes—
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×C11314yescomplemented
642C22C2×#120×C11311yescharacteristic
643C22C2×#120×C11311yescharacteristic
644C22#534×C11311yescharacteristic
645C22D42×C11314yes—
646C4—22no—
647C4—44no—
648C4—44no—
649C4—41no—
650C4—42no—
651C4—44no—
652C4—84no—
653C2—21no—
654C2—24no—
655C2—21no—
656C2—24no—
657C2—42no—
658C2—42no—
659C2—81no—
660C2—82no—
661C2C113×#240311yescharacteristic
662C2C2×#458×C11312yes—
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC24C24×C113
prime radicalC113×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C25×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#123×C113C2semidirect
3. C2×#458×C113C2semidirect
4. C113×#2849C2semidirect
5. C113×#2022C2semidirect
6. C113×#1898C2semidirect
7. C113×#1890C2semidirect
8. C113×#1781C2semidirect
11. C24×C4×C113C22semidirect
22. C2×#123×C113C22semidirect
23. C2×#123×C113C22semidirect
29. C22×C22⋊C4×C113C22semidirect
32. C2×#99×C113C22semidirect
33. C2×#99×C113C22semidirect
36. #381×C113C22semidirect
37. #379×C113C22semidirect
38. #342×C113C22semidirect
77. #123×C113D4semidirect
185. C22×C4×C113C2×D4semidirect
206. C22⋊C4×C113C2×D4semidirect
309. C22×C113#458semidirect
321. #23901C113direct (N × H)
333. C22×#123C2×C113semidirect
334. C2×#458C2×C113semidirect
335. #2849C2×C113semidirect
336. #2022C2×C113semidirect
337. #1898C2×C113semidirect
338. #1890C2×C113semidirect
339. #1781C2×C113semidirect
340. C113#23901direct (N × H)
343. C24×C4C22×C113semidirect
354. C2×#123C22×C113semidirect
355. C2×#123C22×C113semidirect
361. C22×C22⋊C4C22×C113semidirect
364. C2×#99C22×C113semidirect
365. C2×#99C22×C113semidirect
368. #381C22×C113semidirect
369. #379C22×C113semidirect
370. #342C22×C113semidirect
409. #123D4×C113semidirect
517. C22×C4C2×D4×C113semidirect
538. C22⋊C4C2×D4×C113semidirect
641. C22#458×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34842
C22×#123×C1132
C2×#458×C1132
C113×#28492
C113×#20222
C113×#18982
C113×#18902
C113×#17812
#23901113