Finite Group Databasebeta

← C113×#24000 #43292020

Subgroups — C113×#24000 #43292020

Order 28928.

1170 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3510C211yesmaximal, characteristic, complemented
2C113×#3019C211yesmaximal, characteristic
3C2×#455×C113C211yesmaximal, characteristic, complemented
4C113×#2883C211yesmaximal, characteristic, complemented
5C113×#2031C212yesmaximal, complemented
6C113×#2009C212yesmaximal, complemented
7C113×#1911C211yesmaximal, characteristic, complemented
8C113×#1906C212yesmaximal, complemented
9C113×#1905C212yesmaximal, complemented
10C113×#1885C211yesmaximal, characteristic, complemented
11C113×#1829C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C113C2211yescharacteristic
13#575×C113C2212yes—
14C2×#137×C113C2212yes—
15#559×C113—22no—
16#556×C113—22no—
17#551×C113—24no—
18#542×C113—22no—
19#536×C113C2211yescharacteristic, complemented
20#535×C113C2211yescharacteristic
21#533×C113C2211yescharacteristic, complemented
22#529×C113—22no—
23C2×#124×C113C2211yescharacteristic
24#519×C113C2211yescharacteristic, complemented
25#518×C113C2211yescharacteristic
26#518×C113C2211yescharacteristic
27C4×#41×C113C2211yescharacteristic, complemented
28#455×C113—22no—
29#455×C113—22no—
30#455×C113—22no—
31#453×C113—22no—
32#421×C113C2212yes—
33#421×C113C2212yescomplemented
34C2×#104×C113C2212yes—
35#419×C113C2212yescomplemented
36C2×#100×C113C2211yescharacteristic
37C2×#100×C113C2211yescharacteristic
38#410×C113C2212yes—
39#410×C113C2212yes—
40C2×#99×C113—24no—
41#344×C113C2212yescomplemented
42#344×C113C2212yescomplemented
43#339×C113C2212yescomplemented
44H(3,ℤ/4)×C113C2212yescomplemented
45H(5,𝔽2)×C113—22no—
46H(5,𝔽2)×C113—22no—
47H(5,𝔽2)×C113—42no—
48C2×#41×C113—22no—
49C2×#41×C113C2311yescharacteristic
50C2×#41×C113C2312yes—
51C22×Q8×C113C2311yescharacteristic
52C22×D4×C113—22no—
53C22×D4×C113—22no—
54C22×D4×C113C2311yescharacteristic
55#137×C113—24no—
56#137×C113—22no—
57#137×C113—22no—
58#137×C113—42no—
59AGL(1,ℤ/8)×C113—22no—
60AGL(1,ℤ/8)×C113—22no—
61#135×C113—42no—
62C2×Q16×C113—22no—
63C2×SD16×C113—22no—
64C2×M16×C113C2312yes—
65C2×M16×C113C2312yes—
66C4⋊Q8×C113—21no—
67C4⋊Q8×C113—21no—
68#127×C113D412yes—
69#126×C113—24no—
70#126×C113—24no—
71#125×C113—21no—
72#124×C113—24no—
73#124×C113—22no—
74#124×C113—21no—
75#124×C113D412yes—
76#124×C113D412yes—
77#124×C113D412yes—
78#123×C113—24no—
79#123×C113—24no—
80#123×C113—22no—
81C22⋊Q8×C113—24no—
82C22⋊Q8×C113—22no—
83C22⋊Q8×C113—22no—
84#121×C113—22no—
85#120×C113—22no—
86C4×Q8×C113—21no—
87C4×Q8×C113—22no—
88C4×Q8×C113—22no—
89C4×Q8×C113—22no—
90C4×D4×C113—24no—
91C4×D4×C113—21no—
92C4×D4×C113—22no—
93C4×D4×C113—22no—
94C4×D4×C113—22no—
95C4×D4×C113—42no—
96#117×C113—24no—
97#117×C113—22no—
98#117×C113—21no—
99#117×C113C2312yes—
100#117×C113C2311yescharacteristic
101#117×C113C2311yescharacteristic
102#117×C113C2311yescharacteristic
103C2×C22⋊C4×C113—22no—
104C2×C22⋊C4×C113—22no—
105C2×C22⋊C4×C113D414yes—
106C2×C42×C113—21no—
107C2×C42×C113C2311yescharacteristic
108#104×C113—22no—
109#104×C113—22no—
110#104×C113—24no—
111#104×C113—42no—
112#103×C113—42no—
113#100×C113—22no—
114#100×C113—22no—
115#99×C113—24no—
116#99×C113—24no—
117C24×C113—22no—
118C24×C113C2×D412yes—
119#41×C113—22no—
120#41×C113—22no—
121#41×C113—22no—
122#41×C113—22no—
123#41×C113—22no—
124#41×C113—22no—
125#41×C113—44no—
126#41×C113—44no—
127C2×Q8×C113—22no—
128C2×Q8×C113—21no—
129C2×Q8×C113—22no—
130C2×Q8×C113—22no—
131C2×Q8×C113C2×D412yes—
132C2×Q8×C113C2×D411yescharacteristic
133C2×Q8×C113#4112yes—
134C2×D4×C113—24no—
135C2×D4×C113—22no—
136C2×D4×C113—21no—
137C2×D4×C113—24no—
138C2×D4×C113—22no—
139C2×D4×C113—22no—
140C2×D4×C113—44no—
141C2×D4×C113—44no—
142C2×D4×C113—44no—
143C2×D4×C113—44no—
144C2×D4×C113C2×D411yescharacteristic
145C2×D4×C113C2×D412yes—
146C2×D4×C113C2×D412yes—
147C2×D4×C113#4112yes—
148C22×C4×C113—22no—
149C22×C4×C113—21no—
150C22×C4×C113—22no—
151C22×C4×C113—24no—
152C22×C4×C113—21no—
153C22×C4×C113—21no—
154C22×C4×C113—22no—
155C22×C4×C113—42no—
156C22×C4×C113C2411yescharacteristic
157Q16×C113—44no—
158Q16×C113—42no—
159SD16×C113—44no—
160SD16×C113—42no—
161SD16×C113—42no—
162D8×C113—42no—
163M16×C113—22no—
164M16×C113—22no—
165M16×C113—22no—
166M16×C113—22no—
167C2×C8×C113—22no—
168C2×C8×C113—22no—
169C4⋊C4×C113—22no—
170C4⋊C4×C113—22no—
171C4⋊C4×C113—24no—
172C4⋊C4×C113—24no—
173C4⋊C4×C113—22no—
174C4⋊C4×C113—22no—
175C4⋊C4×C113—21no—
176C4⋊C4×C113—21no—
177C4⋊C4×C113—21no—
178C4⋊C4×C113—22no—
179C22⋊C4×C113—22no—
180C22⋊C4×C113—24no—
181C22⋊C4×C113—24no—
182C22⋊C4×C113—24no—
183C22⋊C4×C113—24no—
184C22⋊C4×C113—24no—
185C22⋊C4×C113—21no—
186C22⋊C4×C113—22no—
187C22⋊C4×C113—42no—
188C22⋊C4×C113C2×D412yes—
189C22⋊C4×C113C2×D412yes—
190C42×C113—22no—
191C42×C113—24no—
192C42×C113—21no—
193C42×C113—21no—
194C42×C113—21no—
195C42×C113—22no—
196C42×C113C2×D411yescharacteristic
197C42×C113C2×D411yescharacteristic
198C42×C113C2×D412yes—
199C23×C113—22no—
200C23×C113—22no—
201C23×C113—21no—
202C23×C113—22no—
203C23×C113—44no—
204C23×C113—82no—
205C23×C113—162no—
206C23×C113#12014yes—
207C23×C113C22×D411yescharacteristic
208Q8×C113—24no—
209Q8×C113—22no—
210Q8×C113—22no—
211Q8×C113—22no—
212Q8×C113—42no—
213Q8×C113—82no—
214D4×C113—24no—
215D4×C113—24no—
216D4×C113—22no—
217D4×C113—22no—
218D4×C113—22no—
219D4×C113—48no—
220D4×C113—42no—
221D4×C113—41no—
222D4×C113—42no—
223D4×C113—41no—
224D4×C113—84no—
225C2×C4×C113—22no—
226C2×C4×C113—21no—
227C2×C4×C113—22no—
228C2×C4×C113—22no—
229C2×C4×C113—21no—
230C2×C4×C113—21no—
231C2×C4×C113—22no—
232C2×C4×C113—22no—
233C2×C4×C113—44no—
234C2×C4×C113—41no—
235C2×C4×C113—41no—
236C2×C4×C113—42no—
237C2×C4×C113—42no—
238C2×C4×C113—42no—
239C2×C4×C113—42no—
240C2×C4×C113—82no—
241C2×C4×C113—84no—
242C2×C4×C113—81no—
243C2×C4×C113—162no—
244C2×C4×C113C22×D411yescharacteristic
245C2×C4×C113C22×D411yescharacteristic
246C2×C4×C113C2×#4112yes—
247C2×C4×C113H(5,𝔽2)12yes—
248C8×C113—42no—
249C8×C113—42no—
250C22×C113—24no—
251C22×C113—41no—
252C22×C113—44no—
253C22×C113—42no—
254C22×C113—42no—
255C22×C113—41no—
256C22×C113—82no—
257C22×C113—82no—
258C22×C113—82no—
259C22×C113—164no—
260C22×C113C2×#12011yescharacteristic
261C22×C113#52511yescharacteristic
262C22×C113#53511yescharacteristic
263C4×C113—42no—
264C4×C113—41no—
265C4×C113—42no—
266C4×C113—41no—
267C4×C113—42no—
268C4×C113—42no—
269C4×C113—41no—
270C4×C113—42no—
271C4×C113—82no—
272C4×C113#54612yes—
273C4×C113#54612yes—
274#24000C11311yesmaximal, characteristic, direct product factor, Sylow
275C2×C113—21no—
276C2×C113—21no—
277C2×C113—21no—
278C2×C113—44no—
279C2×C113—81no—
280C2×C113—82no—
281C2×C113#240411yescharacteristic
282#3510C2×C11311yescharacteristic, complemented
283#3019C2×C11311yescharacteristic
284C2×#455C2×C11311yescharacteristic, complemented
285#2883C2×C11311yescharacteristic, complemented
286#2031C2×C11312yescomplemented
287#2009C2×C11312yescomplemented
288#1911C2×C11311yescharacteristic, complemented
289#1906C2×C11312yescomplemented
290#1905C2×C11312yescomplemented
291#1885C2×C11311yescharacteristic, complemented
292#1829C2×C11311yescharacteristic, complemented
293C113#2400011yescharacteristic, direct product factor, Sylow
294C2×H(5,𝔽2)C22×C11311yescharacteristic
295#575C22×C11312yes—
296C2×#137C22×C11312yes—
297#559—22no—
298#556—22no—
299#551—24no—
300#542—22no—
301#536C22×C11311yescharacteristic, complemented
302#535C22×C11311yescharacteristic
303#533C22×C11311yescharacteristic, complemented
304#529—22no—
305C2×#124C22×C11311yescharacteristic
306#519C22×C11311yescharacteristic, complemented
307#518C22×C11311yescharacteristic
308#518C22×C11311yescharacteristic
309C4×#41C22×C11311yescharacteristic, complemented
310#455—22no—
311#455—22no—
312#455—22no—
313#453—22no—
314#421C22×C11312yes—
315#421C22×C11312yescomplemented
316C2×#104C22×C11312yes—
317#419C22×C11312yescomplemented
318C2×#100C22×C11311yescharacteristic
319C2×#100C22×C11311yescharacteristic
320#410C22×C11312yes—
321#410C22×C11312yes—
322C2×#99—24no—
323#344C22×C11312yescomplemented
324#344C22×C11312yescomplemented
325#339C22×C11312yescomplemented
326H(3,ℤ/4)C22×C11312yescomplemented
327H(5,𝔽2)—22no—
328H(5,𝔽2)—22no—
329H(5,𝔽2)—42no—
330C2×#41—22no—
331C2×#41C23×C11311yescharacteristic
332C2×#41C23×C11312yes—
333C22×Q8C23×C11311yescharacteristic
334C22×D4—22no—
335C22×D4—22no—
336C22×D4C23×C11311yescharacteristic
337#137—24no—
338#137—22no—
339#137—22no—
340#137—42no—
341AGL(1,ℤ/8)—22no—
342AGL(1,ℤ/8)—22no—
343#135—42no—
344C2×Q16—22no—
345C2×SD16—22no—
346C2×M16C23×C11312yes—
347C2×M16C23×C11312yes—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350#127D4×C11312yes—
351#126—24no—
352#126—24no—
353#125—21no—
354#124—24no—
355#124—22no—
356#124—21no—
357#124D4×C11312yes—
358#124D4×C11312yes—
359#124D4×C11312yes—
360#123—24no—
361#123—24no—
362#123—22no—
363C22⋊Q8—24no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366#121—22no—
367#120—22no—
368C4×Q8—21no—
369C4×Q8—22no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×D4—24no—
373C4×D4—21no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—42no—
378#117—24no—
379#117—22no—
380#117—21no—
381#117C23×C11312yes—
382#117C23×C11311yescharacteristic
383#117C23×C11311yescharacteristic
384#117C23×C11311yescharacteristic
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4D4×C11314yes—
388C2×C42—21no—
389C2×C42C23×C11311yescharacteristic
390#104—22no—
391#104—22no—
392#104—24no—
393#104—42no—
394#103—42no—
395#100—22no—
396#100—22no—
397#99—24no—
398#99—24no—
399C24—22no—
400C24C2×D4×C11312yes—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—44no—
408#41—44no—
409C2×Q8—22no—
410C2×Q8—21no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8C2×D4×C11312yes—
414C2×Q8C2×D4×C11311yescharacteristic
415C2×Q8#41×C11312yes—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4C2×D4×C11311yescharacteristic
427C2×D4C2×D4×C11312yes—
428C2×D4C2×D4×C11312yes—
429C2×D4#41×C11312yes—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—42no—
438C22×C4C24×C11311yescharacteristic
439Q16—44no—
440Q16—42no—
441SD16—44no—
442SD16—42no—
443SD16—42no—
444D8—42no—
445M16—22no—
446M16—22no—
447M16—22no—
448M16—22no—
449C2×C8—22no—
450C2×C8—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—21no—
468C22⋊C4—22no—
469C22⋊C4—42no—
470C22⋊C4C2×D4×C11312yes—
471C22⋊C4C2×D4×C11312yes—
472C42—22no—
473C42—24no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—22no—
478C42C2×D4×C11311yescharacteristic
479C42C2×D4×C11311yescharacteristic
480C42C2×D4×C11312yes—
481C23—22no—
482C23—22no—
483C23—21no—
484C23—22no—
485C23—44no—
486C23—82no—
487C23—162no—
488C23#120×C11314yes—
489C23C22×D4×C11311yescharacteristic
490Q8—24no—
491Q8—22no—
492Q8—22no—
493Q8—22no—
494Q8—42no—
495Q8—82no—
496D4—24no—
497D4—24no—
498D4—22no—
499D4—22no—
500D4—22no—
501D4—48no—
502D4—42no—
503D4—41no—
504D4—42no—
505D4—41no—
506D4—84no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—44no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—82no—
523C2×C4—84no—
524C2×C4—81no—
525C2×C4—162no—
526C2×C4C22×D4×C11311yescharacteristic
527C2×C4C22×D4×C11311yescharacteristic
528C2×C4C2×#41×C11312yes—
529C2×C4H(5,𝔽2)×C11312yes—
530C8—42no—
531C8—42no—
532C22—24no—
533C22—41no—
534C22—44no—
535C22—42no—
536C22—42no—
537C22—41no—
538C22—82no—
539C22—82no—
540C22—82no—
541C22—164no—
542C22C2×#120×C11311yescharacteristic
543C22#525×C11311yescharacteristic
544C22#535×C11311yescharacteristic
545C4—42no—
546C4—41no—
547C4—42no—
548C4—41no—
549C4—42no—
550C4—42no—
551C4—41no—
552C4—42no—
553C4—82no—
554C4#546×C11312yes—
555C4#546×C11312yes—
556C2—21no—
557C2—21no—
558C2—21no—
559C2—44no—
560C2—81no—
561C2—82no—
562C2C113×#240411yescharacteristic
subgroupG/H
center, socleC2×C113#2404
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3019C2
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×#3510C2semidirect
3. C2×#455×C113C2semidirect
4. C113×#2883C2semidirect
5. C113×#2031C2semidirect
6. C113×#2009C2semidirect
7. C113×#1911C2semidirect
8. C113×#1906C2semidirect
9. C113×#1905C2semidirect
10. C113×#1885C2semidirect
11. C113×#1829C2semidirect
19. #536×C113C22semidirect
21. #533×C113C22semidirect
24. #519×C113C22semidirect
27. C4×#41×C113C22semidirect
33. #421×C113C22semidirect
35. #419×C113C22semidirect
41. #344×C113C22semidirect
42. #344×C113C22semidirect
43. #339×C113C22semidirect
44. H(3,ℤ/4)×C113C22semidirect
274. #24000C113direct (N × H)
282. #3510C2×C113semidirect
284. C2×#455C2×C113semidirect
285. #2883C2×C113semidirect
286. #2031C2×C113semidirect
287. #2009C2×C113semidirect
288. #1911C2×C113semidirect
289. #1906C2×C113semidirect
290. #1905C2×C113semidirect
291. #1885C2×C113semidirect
292. #1829C2×C113semidirect
293. C113#24000direct (N × H)
301. #536C22×C113semidirect
303. #533C22×C113semidirect
306. #519C22×C113semidirect
309. C4×#41C22×C113semidirect
315. #421C22×C113semidirect
317. #419C22×C113semidirect
323. #344C22×C113semidirect
324. #344C22×C113semidirect
325. #339C22×C113semidirect
326. H(3,ℤ/4)C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35102
C113×#30192
C2×#455×C1132
C113×#28832
C113×#20312
C113×#20092
C113×#19112
C113×#19062
C113×#19052
C113×#18852
C113×#18292
#24000113