Finite Group Databasebeta

← C113×#18883 #43286903

Subgroups — C113×#18883 #43286903

Order 28928.

1096 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3499C211yesmaximal, characteristic
2C113×#3246C211yesmaximal, characteristic, complemented
3C113×#3229C211yesmaximal, characteristic, complemented
4C113×#3076C211yesmaximal, characteristic, complemented
5C113×#1654C212yesmaximal, complemented
6C113×#1651C212yesmaximal, complemented
7C113×#1637C212yesmaximal, complemented
8C113×#1635C212yesmaximal, complemented
9C2×#332×C113C211yesmaximal, characteristic, complemented
10C113×#1480C211yesmaximal, characteristic, complemented
11C113×#1477C211yesmaximal, characteristic, complemented
12C2×2−1+4×C113—21no—
13D4×Q8×C113—21no—
14D4×Q8×C113C2212yes—
15#547×C113—22no—
16#547×C113—21no—
17#547×C113—22no—
18#547×C113C2212yes—
19#536×C113—22no—
20#536×C113—21no—
21#533×C113C2211yescharacteristic
22#532×C113—21no—
23#532×C113C2211yescharacteristic
24C2×C4⋊Q8×C113—21no—
25C2×C4⋊Q8×C113C2211yescharacteristic
26C4×#41×C113C2211yescharacteristic
27#498×C113C2212yes—
28#487×C113C2212yes—
29#483×C113—22no—
30#479×C113—21no—
31#478×C113—21no—
32#477×C113C2211yescharacteristic
33#476×C113C2211yescharacteristic
34#476×C113C2212yes—
35#475×C113—22no—
36#475×C113—21no—
37#475×C113C2211yescharacteristic
38#474×C113C2211yescharacteristic
39#465×C113—22no—
40#461×C113C2212yes—
41#460×C113—21no—
42#431×C113C2211yescharacteristic
43#427×C113—21no—
44C2×C4⋊C8×C113C2211yescharacteristic
45C2×C4⋊C8×C113C2211yescharacteristic
46#416×C113—21no—
47#332×C113C2212yes—
48#332×C113C2212yes—
49Q8⋊C8×C113C2212yes—
50D4⋊C8×C113C2212yes—
51D4⋊C8×C113C2212yes—
52D4⋊C8×C113C2212yes—
532−1+4×C113—44no—
542−1+4×C113—44no—
55C2×#41×C113—22no—
56C2×#41×C113—24no—
57C2×#41×C113—22no—
58C2×#41×C113—21no—
59C2×#41×C113D411yescharacteristic
60C22×Q8×C113—22no—
61C22×Q8×C113—22no—
62C22×Q8×C113—21no—
63C2×SD16×C113—22no—
64C22×C8×C113—21no—
65C22×C8×C113—21no—
66C4⋊Q8×C113—22no—
67C4⋊Q8×C113—22no—
68C4⋊Q8×C113—22no—
69C4⋊Q8×C113—21no—
70C4⋊Q8×C113—21no—
71C4⋊Q8×C113D411yescharacteristic
72C4⋊Q8×C113D412yes—
73C4⋊Q8×C113C2311yescharacteristic
74C4⋊Q8×C113C2311yescharacteristic
75C4⋊Q8×C113C2312yes—
76#127×C113D411yescharacteristic
77#125×C113—21no—
78#124×C113—22no—
79#124×C113—21no—
80#123×C113—24no—
81#123×C113—24no—
82#123×C113—24no—
83C22⋊Q8×C113—24no—
84C22⋊Q8×C113—22no—
85C22⋊Q8×C113—24no—
86C22⋊Q8×C113—22no—
87C22⋊Q8×C113—21no—
88C22⋊Q8×C113—21no—
89#121×C113—22no—
90#121×C113—22no—
91#121×C113—21no—
92#121×C113D412yes—
93C4×Q8×C113—21no—
94C4×Q8×C113—21no—
95C4×Q8×C113D411yescharacteristic
96C4×Q8×C113C2311yescharacteristic
97C4×D4×C113—22no—
98C4×D4×C113—22no—
99C4×D4×C113—21no—
100C4×D4×C113—21no—
101C4×D4×C113—21no—
102C4×D4×C113D411yescharacteristic
103C4×D4×C113C2311yescharacteristic
104C4×D4×C113C2312yes—
105#117×C113—21no—
106#117×C113—21no—
107#117×C113D411yescharacteristic
108C2×C4⋊C4×C113—22no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113—22no—
111C2×C4⋊C4×C113D412yes—
112C2×C42×C113—21no—
113C2×C42×C113C2311yescharacteristic
114#107×C113—21no—
115#107×C113—21no—
116#106×C113—21no—
117#106×C113—21no—
118#106×C113—22no—
119#106×C113—24no—
120C4⋊C8×C113—21no—
121C4⋊C8×C113—21no—
122C4⋊C8×C113—21no—
123C4⋊C8×C113C2311yescharacteristic
124C4⋊C8×C113C2311yescharacteristic
125C4⋊C8×C113C2312yes—
126#103×C113—21no—
127#103×C113—21no—
128#103×C113—22no—
129#103×C113—24no—
130#102×C113—21no—
131#102×C113—21no—
132#102×C113—22no—
133C22⋊C8×C113—21no—
134C4×C8×C113C2312yes—
135#41×C113—22no—
136#41×C113—48no—
137#41×C113—416no—
138#41×C113—44no—
139#41×C113—44no—
140#41×C113—42no—
141#41×C113—42no—
142#41×C113SD1614yescomplemented
143C2×Q8×C113—24no—
144C2×Q8×C113—22no—
145C2×Q8×C113—21no—
146C2×Q8×C113—22no—
147C2×Q8×C113—21no—
148C2×Q8×C113—21no—
149C2×Q8×C113—48no—
150C2×Q8×C113—44no—
151C2×Q8×C113—44no—
152C2×Q8×C113—42no—
153C2×Q8×C113—42no—
154C2×Q8×C113C2×D411yescharacteristic
155C2×D4×C113—21no—
156C2×D4×C113—24no—
157C2×D4×C113—22no—
158C2×D4×C113—21no—
159C2×D4×C113—21no—
160C2×D4×C113C2×D412yes—
161C2×D4×C113C2×D411yescharacteristic
162C22×C4×C113—21no—
163C22×C4×C113—24no—
164C22×C4×C113—24no—
165C22×C4×C113—22no—
166C22×C4×C113—21no—
167C22×C4×C113—21no—
168C22×C4×C113—22no—
169C22×C4×C113C2×D411yescharacteristic
170C22×C4×C113C2×D411yescharacteristic
171C22×C4×C113C2×D411yescharacteristic
172SD16×C113—82no—
173C2×C8×C113—22no—
174C2×C8×C113—21no—
175C2×C8×C113—22no—
176C2×C8×C113—21no—
177C2×C8×C113—42no—
178C2×C8×C113—81no—
179C4⋊C4×C113—24no—
180C4⋊C4×C113—24no—
181C4⋊C4×C113—21no—
182C4⋊C4×C113—22no—
183C4⋊C4×C113—22no—
184C4⋊C4×C113—21no—
185C4⋊C4×C113—22no—
186C4⋊C4×C113—21no—
187C4⋊C4×C113—21no—
188C4⋊C4×C113—21no—
189C4⋊C4×C113—21no—
190C4⋊C4×C113—21no—
191C4⋊C4×C113—41no—
192C4⋊C4×C113—41no—
193C4⋊C4×C113C2×D412yes—
194C4⋊C4×C113C2×D414yes—
195C4⋊C4×C113C2×D411yescharacteristic
196C4⋊C4×C113C2×D411yescharacteristic
197C22⋊C4×C113—24no—
198C22⋊C4×C113—24no—
199C22⋊C4×C113—21no—
200C22⋊C4×C113—21no—
201C22⋊C4×C113—22no—
202C22⋊C4×C113—21no—
203C22⋊C4×C113—22no—
204C22⋊C4×C113—41no—
205C42×C113—21no—
206C42×C113—21no—
207C42×C113—21no—
208C42×C113—41no—
209C42×C113C2×D411yescharacteristic
210C42×C113C2×D411yescharacteristic
211C42×C113C2×D411yescharacteristic
212C42×C113C2411yescharacteristic
213C23×C113—21no—
214C23×C113—22no—
215C23×C113#12011yescharacteristic
216Q8×C113—21no—
217Q8×C113—48no—
218Q8×C113—42no—
219Q8×C113—42no—
220Q8×C113—42no—
221Q8×C113—42no—
222Q8×C113—44no—
223Q8×C113—41no—
224Q8×C113—41no—
225Q8×C113C2×SD1612yes—
226D4×C113—24no—
227D4×C113—21no—
228D4×C113—22no—
229D4×C113—22no—
230D4×C113—42no—
231D4×C113—48no—
232D4×C113—44no—
233D4×C113—42no—
234D4×C113C2×SD1612yes—
235C2×C4×C113—21no—
236C2×C4×C113—21no—
237C2×C4×C113—21no—
238C2×C4×C113—24no—
239C2×C4×C113—21no—
240C2×C4×C113—21no—
241C2×C4×C113—24no—
242C2×C4×C113—22no—
243C2×C4×C113—41no—
244C2×C4×C113—42no—
245C2×C4×C113—48no—
246C2×C4×C113—48no—
247C2×C4×C113—44no—
248C2×C4×C113—42no—
249C2×C4×C113—42no—
250C2×C4×C113—41no—
251C2×C4×C113—41no—
252C2×C4×C113—41no—
253C2×C4×C113—41no—
254C2×C4×C113#12011yescharacteristic
255C2×C4×C113#12011yescharacteristic
256C2×C4×C113#12011yescharacteristic
257C2×C4×C113C2×SD1612yes—
258C2×C4×C113AGL(1,ℤ/8)12yes—
259C2×C4×C113C22×D411yescharacteristic
260C2×C4×C113C22×D411yescharacteristic
261C2×C4×C113C22×D411yescharacteristic
262C8×C113—42no—
263C8×C113—41no—
264C8×C113—41no—
265C8×C113—42no—
266C22×C113—21no—
267C22×C113—21no—
268C22×C113—22no—
269C22×C113—41no—
270C22×C113—41no—
271C22×C113—42no—
272C22×C113—42no—
273C22×C113—42no—
274C22×C113#45012yes—
275C22×C113C2×#12011yescharacteristic
276C4×C113—22no—
277C4×C113—21no—
278C4×C113—21no—
279C4×C113—21no—
280C4×C113—44no—
281C4×C113—42no—
282C4×C113—41no—
283C4×C113—41no—
284C4×C113—81no—
285C4×C113—81no—
286C4×C113#45012yes—
287C4×C113C22×SD1611yescharacteristic
288C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C113#57711yescharacteristic
290C4×C113#57811yescharacteristic
291#18883C11311yesmaximal, characteristic, direct product factor, Sylow
292C2×C113—22no—
293C2×C113—42no—
294C2×C113—82no—
295C2×C113C2×#45011yescharacteristic
296C2×C113#301311yescharacteristic
297C2×C113#302011yescharacteristic
298#3499C2×C11311yescharacteristic
299#3246C2×C11311yescharacteristic, complemented
300#3229C2×C11311yescharacteristic, complemented
301#3076C2×C11311yescharacteristic, complemented
302#1654C2×C11312yescomplemented
303#1651C2×C11312yescomplemented
304#1637C2×C11312yescomplemented
305#1635C2×C11312yescomplemented
306C2×#332C2×C11311yescharacteristic, complemented
307#1480C2×C11311yescharacteristic, complemented
308#1477C2×C11311yescharacteristic, complemented
309C113#1888311yescharacteristic, direct product factor, Sylow
310C2×2−1+4—21no—
311D4×Q8—21no—
312D4×Q8C22×C11312yes—
313#547—22no—
314#547—21no—
315#547—22no—
316#547C22×C11312yes—
317#536—22no—
318#536—21no—
319#533C22×C11311yescharacteristic
320#532—21no—
321#532C22×C11311yescharacteristic
322C2×C4⋊Q8—21no—
323C2×C4⋊Q8C22×C11311yescharacteristic
324C4×#41C22×C11311yescharacteristic
325#498C22×C11312yes—
326#487C22×C11312yes—
327#483—22no—
328#479—21no—
329#478—21no—
330#477C22×C11311yescharacteristic
331#476C22×C11311yescharacteristic
332#476C22×C11312yes—
333#475—22no—
334#475—21no—
335#475C22×C11311yescharacteristic
336#474C22×C11311yescharacteristic
337#465—22no—
338#461C22×C11312yes—
339#460—21no—
340#431C22×C11311yescharacteristic
341#427—21no—
342C2×C4⋊C8C22×C11311yescharacteristic
343C2×C4⋊C8C22×C11311yescharacteristic
344#416—21no—
345#332C22×C11312yes—
346#332C22×C11312yes—
347Q8⋊C8C22×C11312yes—
348D4⋊C8C22×C11312yes—
349D4⋊C8C22×C11312yes—
350D4⋊C8C22×C11312yes—
3512−1+4—44no—
3522−1+4—44no—
353C2×#41—22no—
354C2×#41—24no—
355C2×#41—22no—
356C2×#41—21no—
357C2×#41D4×C11311yescharacteristic
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—21no—
361C2×SD16—22no—
362C22×C8—21no—
363C22×C8—21no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8D4×C11311yescharacteristic
370C4⋊Q8D4×C11312yes—
371C4⋊Q8C23×C11311yescharacteristic
372C4⋊Q8C23×C11311yescharacteristic
373C4⋊Q8C23×C11312yes—
374#127D4×C11311yescharacteristic
375#125—21no—
376#124—22no—
377#124—21no—
378#123—24no—
379#123—24no—
380#123—24no—
381C22⋊Q8—24no—
382C22⋊Q8—22no—
383C22⋊Q8—24no—
384C22⋊Q8—22no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387#121—22no—
388#121—22no—
389#121—21no—
390#121D4×C11312yes—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8D4×C11311yescharacteristic
394C4×Q8C23×C11311yescharacteristic
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4D4×C11311yescharacteristic
401C4×D4C23×C11311yescharacteristic
402C4×D4C23×C11312yes—
403#117—21no—
404#117—21no—
405#117D4×C11311yescharacteristic
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4D4×C11312yes—
410C2×C42—21no—
411C2×C42C23×C11311yescharacteristic
412#107—21no—
413#107—21no—
414#106—21no—
415#106—21no—
416#106—22no—
417#106—24no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8C23×C11311yescharacteristic
422C4⋊C8C23×C11311yescharacteristic
423C4⋊C8C23×C11312yes—
424#103—21no—
425#103—21no—
426#103—22no—
427#103—24no—
428#102—21no—
429#102—21no—
430#102—22no—
431C22⋊C8—21no—
432C4×C8C23×C11312yes—
433#41—22no—
434#41—48no—
435#41—416no—
436#41—44no—
437#41—44no—
438#41—42no—
439#41—42no—
440#41SD16×C11314yescomplemented
441C2×Q8—24no—
442C2×Q8—22no—
443C2×Q8—21no—
444C2×Q8—22no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—48no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—42no—
451C2×Q8—42no—
452C2×Q8C2×D4×C11311yescharacteristic
453C2×D4—21no—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4C2×D4×C11312yes—
459C2×D4C2×D4×C11311yescharacteristic
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4C2×D4×C11311yescharacteristic
468C22×C4C2×D4×C11311yescharacteristic
469C22×C4C2×D4×C11311yescharacteristic
470SD16—82no—
471C2×C8—22no—
472C2×C8—21no—
473C2×C8—22no—
474C2×C8—21no—
475C2×C8—42no—
476C2×C8—81no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C11312yes—
492C4⋊C4C2×D4×C11314yes—
493C4⋊C4C2×D4×C11311yescharacteristic
494C4⋊C4C2×D4×C11311yescharacteristic
495C22⋊C4—24no—
496C22⋊C4—24no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—22no—
500C22⋊C4—21no—
501C22⋊C4—22no—
502C22⋊C4—41no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42C2×D4×C11311yescharacteristic
508C42C2×D4×C11311yescharacteristic
509C42C2×D4×C11311yescharacteristic
510C42C24×C11311yescharacteristic
511C23—21no—
512C23—22no—
513C23#120×C11311yescharacteristic
514Q8—21no—
515Q8—48no—
516Q8—42no—
517Q8—42no—
518Q8—42no—
519Q8—42no—
520Q8—44no—
521Q8—41no—
522Q8—41no—
523Q8C2×SD16×C11312yes—
524D4—24no—
525D4—21no—
526D4—22no—
527D4—22no—
528D4—42no—
529D4—48no—
530D4—44no—
531D4—42no—
532D4C2×SD16×C11312yes—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—24no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—48no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4#120×C11311yescharacteristic
553C2×C4#120×C11311yescharacteristic
554C2×C4#120×C11311yescharacteristic
555C2×C4C2×SD16×C11312yes—
556C2×C4AGL(1,ℤ/8)×C11312yes—
557C2×C4C22×D4×C11311yescharacteristic
558C2×C4C22×D4×C11311yescharacteristic
559C2×C4C22×D4×C11311yescharacteristic
560C8—42no—
561C8—41no—
562C8—41no—
563C8—42no—
564C22—21no—
565C22—21no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22#450×C11312yes—
573C22C2×#120×C11311yescharacteristic
574C4—22no—
575C4—21no—
576C4—21no—
577C4—21no—
578C4—44no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4#450×C11312yes—
585C4C22×SD16×C11311yescharacteristic
586C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
587C4#577×C11311yescharacteristic
588C4#578×C11311yescharacteristic
589C2—22no—
590C2—42no—
591C2—82no—
592C2C2×#450×C11311yescharacteristic
593C2C113×#301311yescharacteristic
594C2C113×#302011yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3499C2
LCSG ▷ C42 ▷ 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×#3246C2semidirect
3. C113×#3229C2semidirect
4. C113×#3076C2semidirect
5. C113×#1654C2semidirect
6. C113×#1651C2semidirect
7. C113×#1637C2semidirect
8. C113×#1635C2semidirect
9. C2×#332×C113C2semidirect
10. C113×#1480C2semidirect
11. C113×#1477C2semidirect
142. #41×C113SD16semidirect
291. #18883C113direct (N × H)
299. #3246C2×C113semidirect
300. #3229C2×C113semidirect
301. #3076C2×C113semidirect
302. #1654C2×C113semidirect
303. #1651C2×C113semidirect
304. #1637C2×C113semidirect
305. #1635C2×C113semidirect
306. C2×#332C2×C113semidirect
307. #1480C2×C113semidirect
308. #1477C2×C113semidirect
309. C113#18883direct (N × H)
440. #41SD16×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34992
C113×#32462
C113×#32292
C113×#30762
C113×#16542
C113×#16512
C113×#16372
C113×#16352
C2×#332×C1132
C113×#14802
C113×#14772
#18883113