Finite Group Databasebeta

← C113×#23990 #43292010

Subgroups — C113×#23990 #43292010

Order 28928.

1260 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3508C211yesmaximal, characteristic, complemented
2C113×#3027C211yesmaximal, characteristic, complemented
3C113×#3021C211yesmaximal, characteristic, complemented
4C113×#2901C211yesmaximal, characteristic, complemented
5C113×#2031C212yesmaximal, complemented
6C113×#2002C212yesmaximal, complemented
7C113×#1914C211yesmaximal, characteristic, complemented
8C113×#1911C212yesmaximal, complemented
9C113×#1910C211yesmaximal, characteristic, complemented
10C113×#1904C212yesmaximal, complemented
11C113×#1827C211yesmaximal, characteristic, complemented
12#585×C113C2211yescharacteristic
13C2×AGL(1,ℤ/8)×C113C2212yes—
14#568×C113C2211yescharacteristic
15#559×C113—22no—
16#550×C113—22no—
17#546×C113—24no—
18#540×C113—22no—
19#535×C113C2211yescharacteristic
20#535×C113C2212yes—
21#535×C113C2211yescharacteristic
22#533×C113C2211yescharacteristic, complemented
23#532×C113—22no—
24C2×#127×C113C2211yescharacteristic, complemented
25#518×C113C2211yescharacteristic, complemented
26#518×C113C2211yescharacteristic, complemented
27C4×#41×C113C2211yescharacteristic
28B(4,𝔽2)×C113—24no—
29#454×C113—22no—
30#453×C113—22no—
31#421×C113—22no—
32#421×C113C2212yes—
33#421×C113C2212yes—
34C2×#104×C113—22no—
35C2×#104×C113C2212yes—
36#418×C113C2212yescomplemented
37#413×C113C2211yescharacteristic
38C2×#100×C113C2212yescomplemented
39#410×C113C2212yes—
40#410×C113C2211yescharacteristic
41#344×C113C2212yescomplemented
42#339×C113C2212yescomplemented
43H(3,ℤ/4)×C113C2212yescomplemented
44H(3,ℤ/4)×C113C2212yescomplemented
452−1+4×C113—22no—
462−1+4×C113—21no—
47H(5,𝔽2)×C113—22no—
48H(5,𝔽2)×C113—22no—
49H(5,𝔽2)×C113—21no—
50C2×#41×C113—24no—
51C2×#41×C113—22no—
52C2×#41×C113—42no—
53C2×#41×C113C2312yes—
54C2×#41×C113C2311yescharacteristic
55C22×D4×C113—22no—
56C22×D4×C113C2311yescharacteristic
57C22×D4×C113C2311yescharacteristic
58AGL(1,ℤ/8)×C113—24no—
59AGL(1,ℤ/8)×C113—42no—
60C2×SD16×C113—22no—
61C2×D8×C113—22no—
62#131×C113—42no—
63C2×M16×C113—22no—
64C2×M16×C113C2312yes—
65C2×M16×C113C2312yes—
66C4⋊Q8×C113—21no—
67#127×C113—22no—
68#127×C113—21no—
69#127×C113—22no—
70#127×C113—21no—
71#127×C113—21no—
72#127×C113D412yescomplemented
73#125×C113—21no—
74#124×C113—24no—
75#124×C113—21no—
76#124×C113—22no—
77#124×C113D412yescomplemented
78#123×C113—24no—
79#123×C113—24no—
80C22⋊Q8×C113—22no—
81#121×C113—24no—
82#121×C113—24no—
83#121×C113—24no—
84#121×C113—22no—
85#121×C113—22no—
86#121×C113—42no—
87#120×C113—22no—
88#120×C113—24no—
89#120×C113D414yes—
90C4×Q8×C113—21no—
91C4×Q8×C113—22no—
92C4×D4×C113—24no—
93C4×D4×C113—22no—
94C4×D4×C113—21no—
95C4×D4×C113—22no—
96C4×D4×C113—22no—
97C4×D4×C113—22no—
98C4×D4×C113—22no—
99#117×C113D412yescomplemented
100#117×C113C2312yes—
101#117×C113C2311yescharacteristic
102#117×C113C2311yescharacteristic
103#117×C113C2311yescharacteristic
104C2×C22⋊C4×C113—22no—
105C2×C22⋊C4×C113—22no—
106C2×C42×C113D412yescomplemented
107C2×C42×C113C2311yescharacteristic
108#104×C113—22no—
109#104×C113—24no—
110#104×C113—22no—
111#104×C113—24no—
112#102×C113—42no—
113#101×C113—21no—
114#100×C113—21no—
115#100×C113—42no—
116#99×C113—22no—
117#99×C113—24no—
118C24×C113—21no—
119C24×C113C2×D412yes—
120#41×C113—22no—
121#41×C113—22no—
122#41×C113—24no—
123#41×C113—22no—
124#41×C113—22no—
125#41×C113—22no—
126#41×C113—22no—
127#41×C113—44no—
128#41×C113—42no—
129#41×C113—42no—
130#41×C113—42no—
131#41×C113—42no—
132#41×C113—88no—
133C2×Q8×C113—22no—
134C2×Q8×C113—22no—
135C2×Q8×C113—42no—
136C2×Q8×C113C2×D411yescharacteristic
137C2×Q8×C113#4112yescomplemented
138C2×D4×C113—22no—
139C2×D4×C113—24no—
140C2×D4×C113—22no—
141C2×D4×C113—24no—
142C2×D4×C113—24no—
143C2×D4×C113—24no—
144C2×D4×C113—21no—
145C2×D4×C113—21no—
146C2×D4×C113—21no—
147C2×D4×C113—22no—
148C2×D4×C113—22no—
149C2×D4×C113—22no—
150C2×D4×C113—22no—
151C2×D4×C113—42no—
152C2×D4×C113—44no—
153C2×D4×C113—42no—
154C2×D4×C113—44no—
155C2×D4×C113—84no—
156C2×D4×C113C2×D412yes—
157C2×D4×C113C2×D412yes—
158C2×D4×C113C2×D411yescharacteristic
159C2×D4×C113#4112yescomplemented
160C22×C4×C113—22no—
161C22×C4×C113—21no—
162C22×C4×C113—24no—
163C22×C4×C113—24no—
164C22×C4×C113—22no—
165C22×C4×C113—42no—
166C22×C4×C113C2×D412yes—
167C22×C4×C113C2411yescharacteristic
168SD16×C113—44no—
169D8×C113—44no—
170M16×C113—22no—
171M16×C113—22no—
172M16×C113—22no—
173M16×C113—22no—
174M16×C113—42no—
175C2×C8×C113—22no—
176C2×C8×C113—22no—
177C2×C8×C113—42no—
178C4⋊C4×C113—22no—
179C4⋊C4×C113—22no—
180C4⋊C4×C113—22no—
181C4⋊C4×C113—22no—
182C4⋊C4×C113—21no—
183C4⋊C4×C113—21no—
184C4⋊C4×C113—21no—
185C4⋊C4×C113—22no—
186C22⋊C4×C113—24no—
187C22⋊C4×C113—24no—
188C22⋊C4×C113—22no—
189C22⋊C4×C113—21no—
190C22⋊C4×C113—21no—
191C22⋊C4×C113—24no—
192C22⋊C4×C113—24no—
193C22⋊C4×C113—22no—
194C22⋊C4×C113—44no—
195C22⋊C4×C113C2×D412yes—
196C42×C113—22no—
197C42×C113—21no—
198C42×C113—21no—
199C42×C113—22no—
200C42×C113C2×D411yescharacteristic
201C42×C113C2×D412yes—
202C42×C113C2×D411yescharacteristic
203C42×C113C2×D412yes—
204C23×C113—22no—
205C23×C113—22no—
206C23×C113—24no—
207C23×C113—22no—
208C23×C113—42no—
209C23×C113—42no—
210C23×C113—82no—
211C23×C113—82no—
212C23×C113#12012yes—
213C23×C113C22×D411yescharacteristic
214Q8×C113—22no—
215Q8×C113—22no—
216Q8×C113—22no—
217Q8×C113—42no—
218Q8×C113—44no—
219D4×C113—24no—
220D4×C113—22no—
221D4×C113—22no—
222D4×C113—22no—
223D4×C113—24no—
224D4×C113—42no—
225D4×C113—48no—
226D4×C113—44no—
227D4×C113—42no—
228D4×C113—42no—
229D4×C113—41no—
230D4×C113—41no—
231D4×C113—41no—
232D4×C113—41no—
233D4×C113—42no—
234D4×C113—84no—
235D4×C113—84no—
236D4×C113—84no—
237D4×C113—164no—
238C2×C4×C113—21no—
239C2×C4×C113—22no—
240C2×C4×C113—22no—
241C2×C4×C113—22no—
242C2×C4×C113—21no—
243C2×C4×C113—22no—
244C2×C4×C113—22no—
245C2×C4×C113—22no—
246C2×C4×C113—42no—
247C2×C4×C113—44no—
248C2×C4×C113—44no—
249C2×C4×C113—42no—
250C2×C4×C113—42no—
251C2×C4×C113—42no—
252C2×C4×C113—42no—
253C2×C4×C113—84no—
254C2×C4×C113—84no—
255C2×C4×C113#12012yes—
256C2×C4×C113C22×D411yescharacteristic
257C2×C4×C113C22×D411yescharacteristic
258C2×C4×C113C2×#4112yes—
259C2×C4×C113H(5,𝔽2)12yes—
260C8×C113—42no—
261C8×C113—42no—
262C22×C113—22no—
263C22×C113—41no—
264C22×C113—42no—
265C22×C113—44no—
266C22×C113—44no—
267C22×C113—42no—
268C22×C113—42no—
269C22×C113—42no—
270C22×C113—82no—
271C22×C113—84no—
272C22×C113—162no—
273C22×C113—162no—
274C22×C113C2×#12011yescharacteristic
275C22×C113#54612yes—
276C4×C113—22no—
277C4×C113—22no—
278C4×C113—42no—
279C4×C113—41no—
280C4×C113—42no—
281C4×C113—42no—
282C4×C113—42no—
283C4×C113—82no—
284C4×C113#52511yescharacteristic
285C4×C113#53511yescharacteristic
286C4×C113#54612yes—
287#23990C11311yesmaximal, characteristic, direct product factor, Sylow
288C2×C113—21no—
289C2×C113—22no—
290C2×C113—42no—
291C2×C113—82no—
292C2×C113—82no—
293C2×C113—82no—
294C2×C113#240411yescharacteristic
295#3508C2×C11311yescharacteristic, complemented
296#3027C2×C11311yescharacteristic, complemented
297#3021C2×C11311yescharacteristic, complemented
298#2901C2×C11311yescharacteristic, complemented
299#2031C2×C11312yescomplemented
300#2002C2×C11312yescomplemented
301#1914C2×C11311yescharacteristic, complemented
302#1911C2×C11312yescomplemented
303#1910C2×C11311yescharacteristic, complemented
304#1904C2×C11312yescomplemented
305#1827C2×C11311yescharacteristic, complemented
306C113#2399011yescharacteristic, direct product factor, Sylow
307#585C22×C11311yescharacteristic
308C2×AGL(1,ℤ/8)C22×C11312yes—
309#568C22×C11311yescharacteristic
310#559—22no—
311#550—22no—
312#546—24no—
313#540—22no—
314#535C22×C11311yescharacteristic
315#535C22×C11312yes—
316#535C22×C11311yescharacteristic
317#533C22×C11311yescharacteristic, complemented
318#532—22no—
319C2×#127C22×C11311yescharacteristic, complemented
320#518C22×C11311yescharacteristic, complemented
321#518C22×C11311yescharacteristic, complemented
322C4×#41C22×C11311yescharacteristic
323B(4,𝔽2)—24no—
324#454—22no—
325#453—22no—
326#421—22no—
327#421C22×C11312yes—
328#421C22×C11312yes—
329C2×#104—22no—
330C2×#104C22×C11312yes—
331#418C22×C11312yescomplemented
332#413C22×C11311yescharacteristic
333C2×#100C22×C11312yescomplemented
334#410C22×C11311yescharacteristic
335#410C22×C11312yes—
336#344C22×C11312yescomplemented
337#339C22×C11312yescomplemented
338H(3,ℤ/4)C22×C11312yescomplemented
339H(3,ℤ/4)C22×C11312yescomplemented
3402−1+4—22no—
3412−1+4—21no—
342H(5,𝔽2)—22no—
343H(5,𝔽2)—22no—
344H(5,𝔽2)—21no—
345C2×#41—24no—
346C2×#41—22no—
347C2×#41—42no—
348C2×#41C23×C11312yes—
349C2×#41C23×C11311yescharacteristic
350C22×D4—22no—
351C22×D4C23×C11311yescharacteristic
352C22×D4C23×C11311yescharacteristic
353AGL(1,ℤ/8)—24no—
354AGL(1,ℤ/8)—42no—
355C2×SD16—22no—
356C2×D8—22no—
357#131—42no—
358C2×M16—22no—
359C2×M16C23×C11312yes—
360C2×M16C23×C11312yes—
361C4⋊Q8—21no—
362#127—22no—
363#127—21no—
364#127—22no—
365#127—21no—
366#127—21no—
367#127D4×C11312yescomplemented
368#125—21no—
369#124—24no—
370#124—21no—
371#124—22no—
372#124D4×C11312yescomplemented
373#123—24no—
374#123—24no—
375C22⋊Q8—22no—
376#121—24no—
377#121—24no—
378#121—24no—
379#121—22no—
380#121—22no—
381#121—42no—
382#120—22no—
383#120—24no—
384#120D4×C11314yes—
385C4×Q8—21no—
386C4×Q8—22no—
387C4×D4—24no—
388C4×D4—22no—
389C4×D4—21no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394#117D4×C11312yescomplemented
395#117C23×C11312yes—
396#117C23×C11311yescharacteristic
397#117C23×C11311yescharacteristic
398#117C23×C11311yescharacteristic
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C42D4×C11312yescomplemented
402C2×C42C23×C11311yescharacteristic
403#104—22no—
404#104—24no—
405#104—22no—
406#104—24no—
407#102—42no—
408#101—21no—
409#100—21no—
410#100—42no—
411#99—22no—
412#99—24no—
413C24—21no—
414C24C2×D4×C11312yes—
415#41—22no—
416#41—22no—
417#41—24no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—44no—
423#41—42no—
424#41—42no—
425#41—42no—
426#41—42no—
427#41—88no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—42no—
431C2×Q8C2×D4×C11311yescharacteristic
432C2×Q8#41×C11312yescomplemented
433C2×D4—22no—
434C2×D4—24no—
435C2×D4—22no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—42no—
447C2×D4—44no—
448C2×D4—42no—
449C2×D4—44no—
450C2×D4—84no—
451C2×D4C2×D4×C11312yes—
452C2×D4C2×D4×C11312yes—
453C2×D4C2×D4×C11311yescharacteristic
454C2×D4#41×C11312yescomplemented
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—42no—
461C22×C4C2×D4×C11312yes—
462C22×C4C24×C11311yescharacteristic
463SD16—44no—
464D8—44no—
465M16—22no—
466M16—22no—
467M16—22no—
468M16—22no—
469M16—42no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—42no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—22no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—22no—
489C22⋊C4—44no—
490C22⋊C4C2×D4×C11312yes—
491C42—22no—
492C42—21no—
493C42—21no—
494C42—22no—
495C42C2×D4×C11311yescharacteristic
496C42C2×D4×C11312yes—
497C42C2×D4×C11311yescharacteristic
498C42C2×D4×C11312yes—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—22no—
503C23—42no—
504C23—42no—
505C23—82no—
506C23—82no—
507C23#120×C11312yes—
508C23C22×D4×C11311yescharacteristic
509Q8—22no—
510Q8—22no—
511Q8—22no—
512Q8—42no—
513Q8—44no—
514D4—24no—
515D4—22no—
516D4—22no—
517D4—22no—
518D4—24no—
519D4—42no—
520D4—48no—
521D4—44no—
522D4—42no—
523D4—42no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—42no—
529D4—84no—
530D4—84no—
531D4—84no—
532D4—164no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—42no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—84no—
549C2×C4—84no—
550C2×C4#120×C11312yes—
551C2×C4C22×D4×C11311yescharacteristic
552C2×C4C22×D4×C11311yescharacteristic
553C2×C4C2×#41×C11312yes—
554C2×C4H(5,𝔽2)×C11312yes—
555C8—42no—
556C8—42no—
557C22—22no—
558C22—41no—
559C22—42no—
560C22—44no—
561C22—44no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—82no—
566C22—84no—
567C22—162no—
568C22—162no—
569C22C2×#120×C11311yescharacteristic
570C22#546×C11312yes—
571C4—22no—
572C4—22no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4#525×C11311yescharacteristic
580C4#535×C11311yescharacteristic
581C4#546×C11312yes—
582C2—21no—
583C2—22no—
584C2—42no—
585C2—82no—
586C2—82no—
587C2—82no—
588C2C113×#240411yescharacteristic
subgroupG/H
center, socleC2×C113#2404
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C113 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3508C2semidirect
2. C113×#3027C2semidirect
3. C113×#3021C2semidirect
4. C113×#2901C2semidirect
5. C113×#2031C2semidirect
6. C113×#2002C2semidirect
7. C113×#1914C2semidirect
8. C113×#1911C2semidirect
9. C113×#1910C2semidirect
10. C113×#1904C2semidirect
11. C113×#1827C2semidirect
22. #533×C113C22semidirect
24. C2×#127×C113C22semidirect
25. #518×C113C22semidirect
26. #518×C113C22semidirect
36. #418×C113C22semidirect
38. C2×#100×C113C22semidirect
41. #344×C113C22semidirect
42. #339×C113C22semidirect
43. H(3,ℤ/4)×C113C22semidirect
44. H(3,ℤ/4)×C113C22semidirect
72. #127×C113D4semidirect
77. #124×C113D4semidirect
99. #117×C113D4semidirect
106. C2×C42×C113D4semidirect
137. C2×Q8×C113#41semidirect
159. C2×D4×C113#41semidirect
287. #23990C113direct (N × H)
295. #3508C2×C113semidirect
296. #3027C2×C113semidirect
297. #3021C2×C113semidirect
298. #2901C2×C113semidirect
299. #2031C2×C113semidirect
300. #2002C2×C113semidirect
301. #1914C2×C113semidirect
302. #1911C2×C113semidirect
303. #1910C2×C113semidirect
304. #1904C2×C113semidirect
305. #1827C2×C113semidirect
306. C113#23990direct (N × H)
317. #533C22×C113semidirect
319. C2×#127C22×C113semidirect
320. #518C22×C113semidirect
321. #518C22×C113semidirect
331. #418C22×C113semidirect
333. C2×#100C22×C113semidirect
336. #344C22×C113semidirect
337. #339C22×C113semidirect
338. H(3,ℤ/4)C22×C113semidirect
339. H(3,ℤ/4)C22×C113semidirect
367. #127D4×C113semidirect
372. #124D4×C113semidirect
394. #117D4×C113semidirect
401. C2×C42D4×C113semidirect
432. C2×Q8#41×C113semidirect
454. C2×D4#41×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35082
C113×#30272
C113×#30212
C113×#29012
C113×#20312
C113×#20022
C113×#19142
C113×#19112
C113×#19102
C113×#19042
C113×#18272
#23990113