Finite Group Databasebeta

← C113×#18892 #43286912

Subgroups — C113×#18892 #43286912

Order 28928.

1302 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3496C211yesmaximal, characteristic, complemented
2C113×#3205C211yesmaximal, characteristic, complemented
3C113×#3205C211yesmaximal, characteristic, complemented
4C2×#459×C113C211yesmaximal, characteristic, complemented
5C113×#1625C214yesmaximal, complemented
6C113×#1619C214yesmaximal, complemented
7C113×#1540C211yesmaximal, characteristic, complemented
8C113×#1480C211yesmaximal, characteristic, complemented
9C113×#1478C211yesmaximal, characteristic, complemented
10C2×H(5,𝔽2)×C113—21no—
11C22×D8×C113—21no—
12#547×C113—21no—
13#547×C113C2212yescomplemented
14#546×C113—22no—
15#546×C113—22no—
16D42×C113—21no—
17D42×C113C2212yescomplemented
18#537×C113—21no—
19#534×C113—22no—
20#532×C113C2211yescharacteristic
21#532×C113C2211yescharacteristic
22C2×#127×C113C2211yescharacteristic, complemented
23C2×#121×C113—22no—
24C2×C4×D4×C113C2211yescharacteristic
25#493×C113—21no—
26#493×C113C2212yescomplemented
27#486×C113—21no—
28#486×C113C2212yescomplemented
29#459×C113—22no—
30#459×C113—22no—
31#459×C113C2214yescomplemented
32#459×C113C2214yescomplemented
33#447×C113—22no—
34#447×C113—22no—
35#431×C113C2211yescharacteristic, complemented
36#431×C113C2211yescharacteristic, complemented
37C2×C4⋊C8×C113C2211yescharacteristic, complemented
38C2×#102×C113—21no—
39#332×C113C2212yescomplemented
40#331×C113C2212yescomplemented
41D4⋊C8×C113C2214yescomplemented
42D4⋊C8×C113C2214yescomplemented
43H(5,𝔽2)×C113—44no—
44H(5,𝔽2)×C113—44no—
45C2×#41×C113—22no—
46C2×#41×C113—22no—
47C2×#41×C113—21no—
48C2×#41×C113—21no—
49C22×D4×C113—24no—
50C22×D4×C113—22no—
51C22×D4×C113—22no—
52C22×D4×C113—22no—
53C22×D4×C113—21no—
54C22×D4×C113—21no—
55C22×D4×C113—21no—
56C22×D4×C113D411yescharacteristic
57C23×C4×C113—21no—
58C2×D8×C113—24no—
59C2×D8×C113—24no—
60C2×D8×C113—24no—
61C2×D8×C113—44no—
62C22×C8×C113—21no—
63C4⋊Q8×C113D411yescharacteristic
64C4⋊Q8×C113C2311yescharacteristic
65#127×C113—21no—
66#127×C113—21no—
67#127×C113—21no—
68#127×C113D411yescharacteristic
69#127×C113C2312yes—
70#127×C113C2311yescharacteristic
71#124×C113—21no—
72#124×C113—21no—
73#123×C113—24no—
74#123×C113—24no—
75C22⋊Q8×C113—22no—
76C22⋊Q8×C113—22no—
77#121×C113—24no—
78#121×C113—24no—
79#121×C113—22no—
80#121×C113—22no—
81#121×C113—21no—
82#121×C113—21no—
83#121×C113—22no—
84#121×C113—22no—
85#121×C113D412yes—
86#121×C113D412yes—
87#120×C113—24no—
88#120×C113—24no—
89C4×D4×C113—21no—
90C4×D4×C113—21no—
91C4×D4×C113—21no—
92C4×D4×C113—21no—
93C4×D4×C113D412yes—
94C4×D4×C113D412yes—
95C4×D4×C113C2312yes—
96C4×D4×C113C2312yes—
97C2×C4⋊C4×C113—22no—
98C2×C4⋊C4×C113D411yescharacteristic
99C2×C22⋊C4×C113—24no—
100C2×C22⋊C4×C113—21no—
101C2×C42×C113C2311yescharacteristic
102C4⋊C8×C113—21no—
103C4⋊C8×C113—21no—
104C4⋊C8×C113C2312yes—
105C4⋊C8×C113C2312yes—
106#102×C113—24no—
107#102×C113—24no—
108#102×C113—24no—
109C22⋊C8×C113—21no—
110C22⋊C8×C113—21no—
111C4×C8×C113—21no—
112C4×C8×C113C2312yes—
113C24×C113—21no—
114C24×C113—24no—
115C24×C113—41no—
116#41×C113—44no—
117#41×C113—48no—
118#41×C113—44no—
119#41×C113—42no—
120#41×C113—42no—
121#41×C113—42no—
122#41×C113—42no—
123C2×Q8×C113—21no—
124C2×Q8×C113—21no—
125C2×D4×C113—24no—
126C2×D4×C113—24no—
127C2×D4×C113—22no—
128C2×D4×C113—22no—
129C2×D4×C113—24no—
130C2×D4×C113—21no—
131C2×D4×C113—21no—
132C2×D4×C113—21no—
133C2×D4×C113—22no—
134C2×D4×C113—21no—
135C2×D4×C113—21no—
136C2×D4×C113—22no—
137C2×D4×C113—22no—
138C2×D4×C113—22no—
139C2×D4×C113—44no—
140C2×D4×C113—48no—
141C2×D4×C113—416no—
142C2×D4×C113—44no—
143C2×D4×C113—41no—
144C2×D4×C113—41no—
145C2×D4×C113—41no—
146C2×D4×C113—42no—
147C2×D4×C113—42no—
148C2×D4×C113—82no—
149C2×D4×C113—84no—
150C2×D4×C113—82no—
151C2×D4×C113D814yescomplemented
152C2×D4×C113C2×D412yes—
153C2×D4×C113C2×D412yes—
154C2×D4×C113C2×D412yes—
155C22×C4×C113—24no—
156C22×C4×C113—21no—
157C22×C4×C113—22no—
158C22×C4×C113—22no—
159C22×C4×C113—22no—
160C22×C4×C113—22no—
161C22×C4×C113—82no—
162C22×C4×C113C2×D411yescharacteristic
163C22×C4×C113C2×D411yescharacteristic
164C22×C4×C113C2×D411yescharacteristic
165D8×C113—48no—
166D8×C113—84no—
167D8×C113—84no—
168C2×C8×C113—22no—
169C2×C8×C113—22no—
170C2×C8×C113—22no—
171C2×C8×C113—42no—
172C4⋊C4×C113—24no—
173C4⋊C4×C113—21no—
174C4⋊C4×C113—21no—
175C4⋊C4×C113—21no—
176C4⋊C4×C113C2×D412yes—
177C4⋊C4×C113C2×D412yes—
178C4⋊C4×C113C2×D412yes—
179C22⋊C4×C113—24no—
180C22⋊C4×C113—24no—
181C22⋊C4×C113—22no—
182C22⋊C4×C113—22no—
183C22⋊C4×C113—22no—
184C22⋊C4×C113—22no—
185C22⋊C4×C113—22no—
186C22⋊C4×C113—22no—
187C42×C113C2×D411yescharacteristic
188C42×C113C2×D411yescharacteristic
189C42×C113C2×D411yescharacteristic
190C42×C113C2411yescharacteristic
191C23×C113—22no—
192C23×C113—24no—
193C23×C113—22no—
194C23×C113—22no—
195C23×C113—48no—
196C23×C113—42no—
197C23×C113—81no—
198C23×C113—81no—
199C23×C113—82no—
200C23×C113—82no—
201C23×C113—84no—
202C23×C113—84no—
203C23×C113—82no—
204C23×C113#12011yescharacteristic
205Q8×C113—41no—
206Q8×C113—41no—
207Q8×C113—42no—
208D4×C113—22no—
209D4×C113—24no—
210D4×C113—24no—
211D4×C113—42no—
212D4×C113—44no—
213D4×C113—48no—
214D4×C113—48no—
215D4×C113—44no—
216D4×C113—44no—
217D4×C113—41no—
218D4×C113—42no—
219D4×C113—41no—
220D4×C113—42no—
221D4×C113—42no—
222D4×C113—44no—
223D4×C113—42no—
224D4×C113—81no—
225D4×C113—82no—
226D4×C113—82no—
227D4×C113—84no—
228D4×C113—82no—
229D4×C113C2×D814yes—
230C2×C4×C113—22no—
231C2×C4×C113—22no—
232C2×C4×C113—22no—
233C2×C4×C113—22no—
234C2×C4×C113—41no—
235C2×C4×C113—48no—
236C2×C4×C113—42no—
237C2×C4×C113—42no—
238C2×C4×C113—44no—
239C2×C4×C113—44no—
240C2×C4×C113—82no—
241C2×C4×C113—81no—
242C2×C4×C113#12011yescharacteristic
243C2×C4×C113#12011yescharacteristic
244C2×C4×C113#12011yescharacteristic
245C2×C4×C113C2×D812yes—
246C2×C4×C113AGL(1,ℤ/8)12yes—
247C2×C4×C113C22×D411yescharacteristic
248C2×C4×C113C22×D411yescharacteristic
249C2×C4×C113C22×D411yescharacteristic
250C8×C113—42no—
251C8×C113—42no—
252C8×C113—42no—
253C22×C113—21no—
254C22×C113—21no—
255C22×C113—24no—
256C22×C113—42no—
257C22×C113—42no—
258C22×C113—42no—
259C22×C113—42no—
260C22×C113—42no—
261C22×C113—42no—
262C22×C113—42no—
263C22×C113—42no—
264C22×C113—84no—
265C22×C113—82no—
266C22×C113—82no—
267C22×C113—82no—
268C22×C113—164no—
269C22×C113—168no—
270C22×C113#44712yes—
271C22×C113C2×#12011yescharacteristic
272C4×C113—21no—
273C4×C113—21no—
274C4×C113—21no—
275C4×C113—42no—
276C4×C113—42no—
277C4×C113—42no—
278C4×C113#44712yes—
279C4×C113C22×D811yescharacteristic
280C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C113#57612yes—
282#18892C11311yesmaximal, characteristic, direct product factor, Sylow
283C2×C113—22no—
284C2×C113—44no—
285C2×C113—82no—
286C2×C113—82no—
287C2×C113—162no—
288C2×C113C2×#44711yescharacteristic
289C2×C113#300811yescharacteristic
290C2×C113#302111yescharacteristic
291#3496C2×C11311yescharacteristic, complemented
292#3205C2×C11311yescharacteristic, complemented
293#3205C2×C11311yescharacteristic, complemented
294C2×#459C2×C11311yescharacteristic, complemented
295#1625C2×C11314yescomplemented
296#1619C2×C11314yescomplemented
297#1540C2×C11311yescharacteristic, complemented
298#1480C2×C11311yescharacteristic, complemented
299#1478C2×C11311yescharacteristic, complemented
300C113#1889211yescharacteristic, direct product factor, Sylow
301C2×H(5,𝔽2)—21no—
302C22×D8—21no—
303#547—21no—
304#547C22×C11312yescomplemented
305#546—22no—
306#546—22no—
307D42—21no—
308D42C22×C11312yescomplemented
309#537—21no—
310#534—22no—
311#532C22×C11311yescharacteristic
312#532C22×C11311yescharacteristic
313C2×#127C22×C11311yescharacteristic, complemented
314C2×#121—22no—
315C2×C4×D4C22×C11311yescharacteristic
316#493—21no—
317#493C22×C11312yescomplemented
318#486—21no—
319#486C22×C11312yescomplemented
320#459—22no—
321#459—22no—
322#459C22×C11314yescomplemented
323#459C22×C11314yescomplemented
324#447—22no—
325#447—22no—
326#431C22×C11311yescharacteristic, complemented
327#431C22×C11311yescharacteristic, complemented
328C2×C4⋊C8C22×C11311yescharacteristic, complemented
329C2×#102—21no—
330#332C22×C11312yescomplemented
331#331C22×C11312yescomplemented
332D4⋊C8C22×C11314yescomplemented
333D4⋊C8C22×C11314yescomplemented
334H(5,𝔽2)—44no—
335H(5,𝔽2)—44no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—21no—
339C2×#41—21no—
340C22×D4—24no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4D4×C11311yescharacteristic
348C23×C4—21no—
349C2×D8—24no—
350C2×D8—24no—
351C2×D8—24no—
352C2×D8—44no—
353C22×C8—21no—
354C4⋊Q8D4×C11311yescharacteristic
355C4⋊Q8C23×C11311yescharacteristic
356#127—21no—
357#127—21no—
358#127—21no—
359#127D4×C11311yescharacteristic
360#127C23×C11312yes—
361#127C23×C11311yescharacteristic
362#124—21no—
363#124—21no—
364#123—24no—
365#123—24no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368#121—24no—
369#121—24no—
370#121—22no—
371#121—22no—
372#121—21no—
373#121—21no—
374#121—22no—
375#121—22no—
376#121D4×C11312yes—
377#121D4×C11312yes—
378#120—24no—
379#120—24no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4D4×C11312yes—
385C4×D4D4×C11312yes—
386C4×D4C23×C11312yes—
387C4×D4C23×C11312yes—
388C2×C4⋊C4—22no—
389C2×C4⋊C4D4×C11311yescharacteristic
390C2×C22⋊C4—24no—
391C2×C22⋊C4—21no—
392C2×C42C23×C11311yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C11312yes—
396C4⋊C8C23×C11312yes—
397#102—24no—
398#102—24no—
399#102—24no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C4×C8—21no—
403C4×C8C23×C11312yes—
404C24—21no—
405C24—24no—
406C24—41no—
407#41—44no—
408#41—48no—
409#41—44no—
410#41—42no—
411#41—42no—
412#41—42no—
413#41—42no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—44no—
431C2×D4—48no—
432C2×D4—416no—
433C2×D4—44no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—82no—
440C2×D4—84no—
441C2×D4—82no—
442C2×D4D8×C11314yescomplemented
443C2×D4C2×D4×C11312yes—
444C2×D4C2×D4×C11312yes—
445C2×D4C2×D4×C11312yes—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—82no—
453C22×C4C2×D4×C11311yescharacteristic
454C22×C4C2×D4×C11311yescharacteristic
455C22×C4C2×D4×C11311yescharacteristic
456D8—48no—
457D8—84no—
458D8—84no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—42no—
463C4⋊C4—24no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4C2×D4×C11312yes—
468C4⋊C4C2×D4×C11312yes—
469C4⋊C4C2×D4×C11312yes—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C42C2×D4×C11311yescharacteristic
479C42C2×D4×C11311yescharacteristic
480C42C2×D4×C11311yescharacteristic
481C42C24×C11311yescharacteristic
482C23—22no—
483C23—24no—
484C23—22no—
485C23—22no—
486C23—48no—
487C23—42no—
488C23—81no—
489C23—81no—
490C23—82no—
491C23—82no—
492C23—84no—
493C23—84no—
494C23—82no—
495C23#120×C11311yescharacteristic
496Q8—41no—
497Q8—41no—
498Q8—42no—
499D4—22no—
500D4—24no—
501D4—24no—
502D4—42no—
503D4—44no—
504D4—48no—
505D4—48no—
506D4—44no—
507D4—44no—
508D4—41no—
509D4—42no—
510D4—41no—
511D4—42no—
512D4—42no—
513D4—44no—
514D4—42no—
515D4—81no—
516D4—82no—
517D4—82no—
518D4—84no—
519D4—82no—
520D4C2×D8×C11314yes—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—48no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—44no—
531C2×C4—82no—
532C2×C4—81no—
533C2×C4#120×C11311yescharacteristic
534C2×C4#120×C11311yescharacteristic
535C2×C4#120×C11311yescharacteristic
536C2×C4C2×D8×C11312yes—
537C2×C4AGL(1,ℤ/8)×C11312yes—
538C2×C4C22×D4×C11311yescharacteristic
539C2×C4C22×D4×C11311yescharacteristic
540C2×C4C22×D4×C11311yescharacteristic
541C8—42no—
542C8—42no—
543C8—42no—
544C22—21no—
545C22—21no—
546C22—24no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—84no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—164no—
560C22—168no—
561C22#447×C11312yes—
562C22C2×#120×C11311yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4#447×C11312yes—
570C4C22×D8×C11311yescharacteristic
571C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
572C4#576×C11312yes—
573C2—22no—
574C2—44no—
575C2—82no—
576C2—82no—
577C2—162no—
578C2C2×#447×C11311yescharacteristic
579C2C113×#300811yescharacteristic
580C2C113×#302111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
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
1. C113×#3496C2semidirect
2. C113×#3205C2semidirect
3. C113×#3205C2semidirect
4. C2×#459×C113C2semidirect
5. C113×#1625C2semidirect
6. C113×#1619C2semidirect
7. C113×#1540C2semidirect
8. C113×#1480C2semidirect
9. C113×#1478C2semidirect
13. #547×C113C22semidirect
17. D42×C113C22semidirect
22. C2×#127×C113C22semidirect
26. #493×C113C22semidirect
28. #486×C113C22semidirect
31. #459×C113C22semidirect
32. #459×C113C22semidirect
35. #431×C113C22semidirect
36. #431×C113C22semidirect
37. C2×C4⋊C8×C113C22semidirect
39. #332×C113C22semidirect
40. #331×C113C22semidirect
41. D4⋊C8×C113C22semidirect
42. D4⋊C8×C113C22semidirect
151. C2×D4×C113D8semidirect
282. #18892C113direct (N × H)
291. #3496C2×C113semidirect
292. #3205C2×C113semidirect
293. #3205C2×C113semidirect
294. C2×#459C2×C113semidirect
295. #1625C2×C113semidirect
296. #1619C2×C113semidirect
297. #1540C2×C113semidirect
298. #1480C2×C113semidirect
299. #1478C2×C113semidirect
300. C113#18892direct (N × H)
304. #547C22×C113semidirect
308. D42C22×C113semidirect
313. C2×#127C22×C113semidirect
317. #493C22×C113semidirect
319. #486C22×C113semidirect
322. #459C22×C113semidirect
323. #459C22×C113semidirect
326. #431C22×C113semidirect
327. #431C22×C113semidirect
328. C2×C4⋊C8C22×C113semidirect
330. #332C22×C113semidirect
331. #331C22×C113semidirect
332. D4⋊C8C22×C113semidirect
333. D4⋊C8C22×C113semidirect
442. C2×D4D8×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34962
C113×#32052
C2×#459×C1132
C113×#16252
C113×#16192
C113×#15402
C113×#14802
C113×#14782
#18892113