Finite Group Databasebeta

← C113×#18241 #43286261

Subgroups — C113×#18241 #43286261

Order 28928.

992 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×#3558C211yesmaximal, characteristic
2C113×#3117C211yesmaximal, characteristic, complemented
3C113×#3103C211yesmaximal, characteristic, complemented
4C113×#2632C211yesmaximal, characteristic, complemented
5C113×#1618C212yesmaximal, complemented
6C113×#1613C212yesmaximal, complemented
7C113×#1606C212yesmaximal, complemented
8C113×#1601C212yesmaximal, complemented
9C113×#1521C211yesmaximal, characteristic, complemented
10C113×#1514C211yesmaximal, characteristic, complemented
11C113×#1469C211yesmaximal, characteristic, complemented
12#562×C113—21no—
13H(3,𝔽4)×C113—21no—
14#559×C113—21no—
15#548×C113—21no—
16#546×C113—21no—
17#546×C113—22no—
18D42×C113—21no—
19#542×C113—21no—
20#538×C113—22no—
21#538×C113C2212yes—
22#535×C113—21no—
23#534×C113C2212yes—
24#532×C113C2211yescharacteristic
25#529×C113C2211yescharacteristic
26C2×#124×C113C2211yescharacteristic
27C2×C4×Q8×C113C2211yescharacteristic, complemented
28#484×C113C2211yescharacteristic, complemented
29#481×C113C2211yescharacteristic
30#481×C113C2212yescomplemented
31#479×C113—21no—
32#475×C113—21no—
33#464×C113—21no—
34#460×C113—21no—
35#451×C113C2211yescharacteristic, complemented
36#448×C113C2211yescharacteristic
37#448×C113C2212yescomplemented
38#441×C113—21no—
39#440×C113—21no—
40C4×SD16×C113—22no—
41#432×C113C2211yescharacteristic, complemented
42#431×C113C2211yescharacteristic, complemented
43#399×C113C2212yescomplemented
44#395×C113—21no—
45#394×C113—21no—
46#393×C113C2212yescomplemented
47#388×C113—22no—
48#383×C113C2211yescharacteristic, complemented
49#328×C113C2212yescomplemented
50#327×C113C2212yes—
51#327×C113C2212yescomplemented
52#327×C113C2212yescomplemented
53#323×C113C2212yescomplemented
54#323×C113C2212yescomplemented
55C2×#41×C113—21no—
56C2×#41×C113—21no—
57C22×Q8×C113D411yescharacteristic
58C22×Q8×C113C2311yescharacteristic
59C22×D4×C113—21no—
60C22×D4×C113—22no—
61C22×D4×C113D411yescharacteristic
62C2×Q16×C113—21no—
63C2×SD16×C113—22no—
64C2×SD16×C113—21no—
65C4⋊Q8×C113D411yescharacteristic
66#127×C113—21no—
67#127×C113D411yescharacteristic
68#126×C113—22no—
69#126×C113—21no—
70#125×C113D411yescharacteristic
71#124×C113—21no—
72#124×C113—22no—
73#124×C113—22no—
74#124×C113—22no—
75#124×C113—21no—
76#124×C113—21no—
77#124×C113—21no—
78#124×C113—21no—
79#124×C113—21no—
80#124×C113D411yescharacteristic
81#123×C113—22no—
82#123×C113—21no—
83#123×C113—22no—
84#123×C113—22no—
85#123×C113—22no—
86C22⋊Q8×C113—22no—
87C22⋊Q8×C113—21no—
88C22⋊Q8×C113—22no—
89C22⋊Q8×C113C2311yescharacteristic
90#121×C113—22no—
91#121×C113—22no—
92#121×C113—22no—
93#121×C113—21no—
94#121×C113—22no—
95#121×C113—21no—
96#121×C113—22no—
97#121×C113C2311yescharacteristic
98#121×C113C2312yes—
99#120×C113—22no—
100#120×C113—22no—
101#120×C113—22no—
102#120×C113—22no—
103#120×C113—22no—
104C4×Q8×C113—21no—
105C4×Q8×C113—21no—
106C4×Q8×C113—21no—
107C4×Q8×C113—21no—
108C4×Q8×C113—21no—
109C4×Q8×C113D411yescharacteristic
110C4×D4×C113—22no—
111C4×D4×C113—21no—
112C4×D4×C113—21no—
113C4×D4×C113—22no—
114C4×D4×C113—21no—
115C4×D4×C113D411yescharacteristic
116C4×D4×C113D412yes—
117#117×C113—21no—
118C2×C4⋊C4×C113—21no—
119C2×C4⋊C4×C113—22no—
120C2×C4⋊C4×C113C2311yescharacteristic
121C2×C22⋊C4×C113—22no—
122C2×C22⋊C4×C113—22no—
123C2×C22⋊C4×C113—22no—
124C2×C22⋊C4×C113D412yes—
125C2×C22⋊C4×C113C2312yes—
126C2×C42×C113—21no—
127C2×C42×C113C2311yescharacteristic
128#107×C113—21no—
129#106×C113—22no—
130#106×C113—21no—
131C4⋊C8×C113—21no—
132C4⋊C8×C113—21no—
133#103×C113—21no—
134#103×C113—22no—
135#103×C113—21no—
136#103×C113—21no—
137#102×C113—22no—
138#102×C113—21no—
139C22⋊C8×C113C2312yes—
140C22⋊C8×C113C2311yescharacteristic
141C22⋊C8×C113C2311yescharacteristic
142#97×C113—21no—
143C4×C8×C113—21no—
144#95×C113—21no—
145#95×C113—21no—
146#95×C113—22no—
147#95×C113C2312yes—
148C24×C113—22no—
149C24×C113C2×D412yes—
150#41×C113—82no—
151#41×C113—82no—
152C2×Q8×C113—21no—
153C2×Q8×C113—21no—
154C2×Q8×C113—21no—
155C2×Q8×C113—21no—
156C2×Q8×C113—21no—
157C2×Q8×C113—42no—
158C2×Q8×C113—81no—
159C2×Q8×C113C2×D411yescharacteristic
160C2×D4×C113—22no—
161C2×D4×C113—21no—
162C2×D4×C113—22no—
163C2×D4×C113—22no—
164C2×D4×C113—22no—
165C2×D4×C113—22no—
166C2×D4×C113—22no—
167C2×D4×C113—21no—
168C2×D4×C113—21no—
169C2×D4×C113—21no—
170C2×D4×C113—21no—
171C2×D4×C113—82no—
172C2×D4×C113—81no—
173C2×D4×C113—84no—
174C2×D4×C113C2×D411yescharacteristic
175C2×D4×C113C2×D412yes—
176C22×C4×C113—21no—
177C22×C4×C113—22no—
178C22×C4×C113—22no—
179C22×C4×C113—21no—
180C22×C4×C113—22no—
181C22×C4×C113—22no—
182C22×C4×C113—21no—
183C22×C4×C113C2×D411yescharacteristic
184C22×C4×C113C2×D412yes—
185C22×C4×C113C2×D411yescharacteristic
186C22×C4×C113C2411yescharacteristic
187Q16×C113—42no—
188SD16×C113—44no—
189SD16×C113—42no—
190C2×C8×C113—22no—
191C2×C8×C113—21no—
192C2×C8×C113—21no—
193C4⋊C4×C113—22no—
194C4⋊C4×C113—22no—
195C4⋊C4×C113—21no—
196C4⋊C4×C113—21no—
197C4⋊C4×C113—21no—
198C4⋊C4×C113—21no—
199C4⋊C4×C113—21no—
200C4⋊C4×C113—21no—
201C4⋊C4×C113—21no—
202C4⋊C4×C113—41no—
203C4⋊C4×C113—41no—
204C4⋊C4×C113—82no—
205C4⋊C4×C113C2×D412yes—
206C4⋊C4×C113C2×D411yescharacteristic
207C4⋊C4×C113C2×D411yescharacteristic
208C22⋊C4×C113—22no—
209C22⋊C4×C113—22no—
210C22⋊C4×C113—22no—
211C22⋊C4×C113—22no—
212C22⋊C4×C113—22no—
213C22⋊C4×C113—21no—
214C22⋊C4×C113—21no—
215C22⋊C4×C113—22no—
216C22⋊C4×C113—22no—
217C22⋊C4×C113—21no—
218C22⋊C4×C113—21no—
219C22⋊C4×C113—22no—
220C22⋊C4×C113—22no—
221C22⋊C4×C113—22no—
222C22⋊C4×C113—21no—
223C22⋊C4×C113—22no—
224C22⋊C4×C113—44no—
225C22⋊C4×C113—82no—
226C42×C113—22no—
227C42×C113—21no—
228C42×C113—41no—
229C42×C113—41no—
230C42×C113C2×D411yescharacteristic
231C42×C113C2×D411yescharacteristic
232C42×C113C2×D411yescharacteristic
233C42×C113C2×D411yescharacteristic
234C23×C113—22no—
235C23×C113—21no—
236C23×C113—22no—
237C23×C113—24no—
238C23×C113—42no—
239C23×C113—42no—
240C23×C113—82no—
241C23×C113—82no—
242C23×C113—82no—
243C23×C113C22×D411yescharacteristic
244Q8×C113—22no—
245Q8×C113—22no—
246Q8×C113—41no—
247Q8×C113—41no—
248Q8×C113—41no—
249Q8×C113—42no—
250Q8×C113—81no—
251Q8×C113—81no—
252D4×C113—42no—
253D4×C113—41no—
254D4×C113—42no—
255D4×C113—42no—
256D4×C113—42no—
257D4×C113—44no—
258D4×C113—81no—
259D4×C113—81no—
260D4×C113—82no—
261D4×C113—82no—
262D4×C113—82no—
263D4×C113—82no—
264D4×C113—82no—
265C2×C4×C113—22no—
266C2×C4×C113—22no—
267C2×C4×C113—21no—
268C2×C4×C113—22no—
269C2×C4×C113—22no—
270C2×C4×C113—21no—
271C2×C4×C113—21no—
272C2×C4×C113—41no—
273C2×C4×C113—41no—
274C2×C4×C113—42no—
275C2×C4×C113—41no—
276C2×C4×C113—41no—
277C2×C4×C113—42no—
278C2×C4×C113—42no—
279C2×C4×C113—42no—
280C2×C4×C113—42no—
281C2×C4×C113—41no—
282C2×C4×C113—42no—
283C2×C4×C113—82no—
284C2×C4×C113—82no—
285C2×C4×C113—82no—
286C2×C4×C113#12011yescharacteristic
287C2×C4×C113#12011yescharacteristic
288C2×C4×C113#12011yescharacteristic
289C2×C4×C113#12011yescharacteristic
290C2×C4×C113C22×D411yescharacteristic
291C2×C4×C113C22×D411yescharacteristic
292C8×C113—42no—
293C8×C113—41no—
294C8×C113—41no—
295C22×C113—21no—
296C22×C113—21no—
297C22×C113—42no—
298C22×C113—42no—
299C22×C113—41no—
300C22×C113—41no—
301C22×C113—42no—
302C22×C113—42no—
303C22×C113—42no—
304C22×C113—41no—
305C22×C113—42no—
306C22×C113—84no—
307C22×C113—164no—
308C22×C113C2×#12011yescharacteristic
309C22×C113#57712yes—
310C4×C113—21no—
311C4×C113—21no—
312C4×C113—21no—
313C4×C113—21no—
314C4×C113—21no—
315C4×C113—21no—
316C4×C113—41no—
317C4×C113—42no—
318C4×C113—41no—
319C4×C113—42no—
320C4×C113—42no—
321C4×C113—41no—
322C4×C113—82no—
323C4×C113—81no—
324#18241C11311yesmaximal, characteristic, direct product factor, Sylow
325C2×C113—22no—
326C2×C113—82no—
327C2×C113—82no—
328C2×C113—81no—
329C2×C113#300911yescharacteristic
330C2×C113#301911yescharacteristic
331C2×C113#302511yescharacteristic
332#3558C2×C11311yescharacteristic
333#3117C2×C11311yescharacteristic, complemented
334#3103C2×C11311yescharacteristic, complemented
335#2632C2×C11311yescharacteristic, complemented
336#1618C2×C11312yescomplemented
337#1613C2×C11312yescomplemented
338#1606C2×C11312yescomplemented
339#1601C2×C11312yescomplemented
340#1521C2×C11311yescharacteristic, complemented
341#1514C2×C11311yescharacteristic, complemented
342#1469C2×C11311yescharacteristic, complemented
343C113#1824111yescharacteristic, direct product factor, Sylow
344#562—21no—
345H(3,𝔽4)—21no—
346#559—21no—
347#548—21no—
348#546—21no—
349#546—22no—
350D42—21no—
351#542—21no—
352#538—22no—
353#538C22×C11312yes—
354#535—21no—
355#534C22×C11312yes—
356#532C22×C11311yescharacteristic
357#529C22×C11311yescharacteristic
358C2×#124C22×C11311yescharacteristic
359C2×C4×Q8C22×C11311yescharacteristic, complemented
360#484C22×C11311yescharacteristic, complemented
361#481C22×C11311yescharacteristic
362#481C22×C11312yescomplemented
363#479—21no—
364#475—21no—
365#464—21no—
366#460—21no—
367#451C22×C11311yescharacteristic, complemented
368#448C22×C11311yescharacteristic
369#448C22×C11312yescomplemented
370#441—21no—
371#440—21no—
372C4×SD16—22no—
373#432C22×C11311yescharacteristic, complemented
374#431C22×C11311yescharacteristic, complemented
375#399C22×C11312yescomplemented
376#395—21no—
377#394—21no—
378#393C22×C11312yescomplemented
379#388—22no—
380#383C22×C11311yescharacteristic, complemented
381#328C22×C11312yescomplemented
382#327C22×C11312yes—
383#327C22×C11312yescomplemented
384#327C22×C11312yescomplemented
385#323C22×C11312yescomplemented
386#323C22×C11312yescomplemented
387C2×#41—21no—
388C2×#41—21no—
389C22×Q8D4×C11311yescharacteristic
390C22×Q8C23×C11311yescharacteristic
391C22×D4—21no—
392C22×D4—22no—
393C22×D4D4×C11311yescharacteristic
394C2×Q16—21no—
395C2×SD16—22no—
396C2×SD16—21no—
397C4⋊Q8D4×C11311yescharacteristic
398#127—21no—
399#127D4×C11311yescharacteristic
400#126—22no—
401#126—21no—
402#125D4×C11311yescharacteristic
403#124—21no—
404#124—22no—
405#124—22no—
406#124—22no—
407#124—21no—
408#124—21no—
409#124—21no—
410#124—21no—
411#124—21no—
412#124D4×C11311yescharacteristic
413#123—22no—
414#123—21no—
415#123—22no—
416#123—22no—
417#123—22no—
418C22⋊Q8—22no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8C23×C11311yescharacteristic
422#121—22no—
423#121—22no—
424#121—22no—
425#121—21no—
426#121—22no—
427#121—21no—
428#121—22no—
429#121C23×C11311yescharacteristic
430#121C23×C11312yes—
431#120—22no—
432#120—22no—
433#120—22no—
434#120—22no—
435#120—22no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8—21no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8D4×C11311yescharacteristic
442C4×D4—22no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—22no—
446C4×D4—21no—
447C4×D4D4×C11311yescharacteristic
448C4×D4D4×C11312yes—
449#117—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4C23×C11311yescharacteristic
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4D4×C11312yes—
457C2×C22⋊C4C23×C11312yes—
458C2×C42—21no—
459C2×C42C23×C11311yescharacteristic
460#107—21no—
461#106—22no—
462#106—21no—
463C4⋊C8—21no—
464C4⋊C8—21no—
465#103—21no—
466#103—22no—
467#103—21no—
468#103—21no—
469#102—22no—
470#102—21no—
471C22⋊C8C23×C11312yes—
472C22⋊C8C23×C11311yescharacteristic
473C22⋊C8C23×C11311yescharacteristic
474#97—21no—
475C4×C8—21no—
476#95—21no—
477#95—21no—
478#95—22no—
479#95C23×C11312yes—
480C24—22no—
481C24C2×D4×C11312yes—
482#41—82no—
483#41—82no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—42no—
490C2×Q8—81no—
491C2×Q8C2×D4×C11311yescharacteristic
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—82no—
504C2×D4—81no—
505C2×D4—84no—
506C2×D4C2×D4×C11311yescharacteristic
507C2×D4C2×D4×C11312yes—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4C2×D4×C11311yescharacteristic
516C22×C4C2×D4×C11312yes—
517C22×C4C2×D4×C11311yescharacteristic
518C22×C4C24×C11311yescharacteristic
519Q16—42no—
520SD16—44no—
521SD16—42no—
522C2×C8—22no—
523C2×C8—21no—
524C2×C8—21no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—82no—
537C4⋊C4C2×D4×C11312yes—
538C4⋊C4C2×D4×C11311yescharacteristic
539C4⋊C4C2×D4×C11311yescharacteristic
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—21no—
555C22⋊C4—22no—
556C22⋊C4—44no—
557C22⋊C4—82no—
558C42—22no—
559C42—21no—
560C42—41no—
561C42—41no—
562C42C2×D4×C11311yescharacteristic
563C42C2×D4×C11311yescharacteristic
564C42C2×D4×C11311yescharacteristic
565C42C2×D4×C11311yescharacteristic
566C23—22no—
567C23—21no—
568C23—22no—
569C23—24no—
570C23—42no—
571C23—42no—
572C23—82no—
573C23—82no—
574C23—82no—
575C23C22×D4×C11311yescharacteristic
576Q8—22no—
577Q8—22no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—42no—
582Q8—81no—
583Q8—81no—
584D4—42no—
585D4—41no—
586D4—42no—
587D4—42no—
588D4—42no—
589D4—44no—
590D4—81no—
591D4—81no—
592D4—82no—
593D4—82no—
594D4—82no—
595D4—82no—
596D4—82no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—82no—
616C2×C4—82no—
617C2×C4—82no—
618C2×C4#120×C11311yescharacteristic
619C2×C4#120×C11311yescharacteristic
620C2×C4#120×C11311yescharacteristic
621C2×C4#120×C11311yescharacteristic
622C2×C4C22×D4×C11311yescharacteristic
623C2×C4C22×D4×C11311yescharacteristic
624C8—42no—
625C8—41no—
626C8—41no—
627C22—21no—
628C22—21no—
629C22—42no—
630C22—42no—
631C22—41no—
632C22—41no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—41no—
637C22—42no—
638C22—84no—
639C22—164no—
640C22C2×#120×C11311yescharacteristic
641C22#577×C11312yes—
642C4—21no—
643C4—21no—
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—41no—
649C4—42no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—41no—
654C4—82no—
655C4—81no—
656C2—22no—
657C2—82no—
658C2—81no—
659C2—82no—
660C2C113×#300911yescharacteristic
661C2C113×#301911yescharacteristic
662C2C113×#302511yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3558C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#3117C2semidirect
3. C113×#3103C2semidirect
4. C113×#2632C2semidirect
5. C113×#1618C2semidirect
6. C113×#1613C2semidirect
7. C113×#1606C2semidirect
8. C113×#1601C2semidirect
9. C113×#1521C2semidirect
10. C113×#1514C2semidirect
11. C113×#1469C2semidirect
27. C2×C4×Q8×C113C22semidirect
28. #484×C113C22semidirect
30. #481×C113C22semidirect
35. #451×C113C22semidirect
37. #448×C113C22semidirect
41. #432×C113C22semidirect
42. #431×C113C22semidirect
43. #399×C113C22semidirect
46. #393×C113C22semidirect
48. #383×C113C22semidirect
49. #328×C113C22semidirect
51. #327×C113C22semidirect
52. #327×C113C22semidirect
53. #323×C113C22semidirect
54. #323×C113C22semidirect
324. #18241C113direct (N × H)
333. #3117C2×C113semidirect
334. #3103C2×C113semidirect
335. #2632C2×C113semidirect
336. #1618C2×C113semidirect
337. #1613C2×C113semidirect
338. #1606C2×C113semidirect
339. #1601C2×C113semidirect
340. #1521C2×C113semidirect
341. #1514C2×C113semidirect
342. #1469C2×C113semidirect
343. C113#18241direct (N × H)
359. C2×C4×Q8C22×C113semidirect
360. #484C22×C113semidirect
362. #481C22×C113semidirect
367. #451C22×C113semidirect
369. #448C22×C113semidirect
373. #432C22×C113semidirect
374. #431C22×C113semidirect
375. #399C22×C113semidirect
378. #393C22×C113semidirect
380. #383C22×C113semidirect
381. #328C22×C113semidirect
383. #327C22×C113semidirect
384. #327C22×C113semidirect
385. #323C22×C113semidirect
386. #323C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35582
C113×#31172
C113×#31032
C113×#26322
C113×#16182
C113×#16132
C113×#16062
C113×#16012
C113×#15212
C113×#15142
C113×#14692
#18241113