Finite Group Databasebeta

← C113×#18916 #43286936

Subgroups — C113×#18916 #43286936

Order 28928.

1042 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3506C211yesmaximal, characteristic, complemented
2C113×#3208C211yesmaximal, characteristic, complemented
3C113×#3205C211yesmaximal, characteristic, complemented
4C2×#459×C113C211yesmaximal, characteristic, complemented
5C113×#1628C214yesmaximal, complemented
6C113×#1621C214yesmaximal, complemented
7C113×#1540C211yesmaximal, characteristic, complemented
8C113×#1481C211yesmaximal, characteristic, complemented
9C113×#1478C211yesmaximal, characteristic, complemented
10C22×D8×C113—21no—
11#559×C113—22no—
12#556×C113C2212yescomplemented
13#555×C113—21no—
14#553×C113—22no—
15#550×C113C2212yescomplemented
16#547×C113—21no—
17#538×C113—22no—
18#535×C113—21no—
19#533×C113C2211yescharacteristic
20#532×C113C2211yescharacteristic
21C2×#127×C113C2211yescharacteristic
22#525×C113—22no—
23#520×C113—21no—
24C2×C4×D4×C113C2211yescharacteristic
25#493×C113C2212yescomplemented
26#492×C113—21no—
27#486×C113—21no—
28#486×C113C2212yescomplemented
29#460×C113C2214yescomplemented
30#459×C113—22no—
31#459×C113—22no—
32#459×C113C2214yes—
33#450×C113—22no—
34#447×C113—22no—
35#431×C113C2211yescharacteristic
36#431×C113C2211yescharacteristic
37C2×C4⋊C8×C113C2211yescharacteristic
38C2×#102×C113—21no—
39#332×C113C2212yescomplemented
40#331×C113C2212yescomplemented
41Q8⋊C8×C113C2214yescomplemented
42D4⋊C8×C113C2214yescomplemented
43C2×#41×C113—22no—
44C2×#41×C113—21no—
45C22×D4×C113—21no—
46C22×D4×C113—21no—
47C22×D4×C113—21no—
48C22×D4×C113D411yescharacteristic
49C23×C4×C113—21no—
50C2×SD16×C113—24no—
51C2×D8×C113—24no—
52C2×D8×C113—24no—
53C2×D8×C113—44no—
54C22×C8×C113—21no—
55C4⋊Q8×C113D411yescharacteristic
56C4⋊Q8×C113D411yescharacteristic
57C4⋊Q8×C113C2311yescharacteristic
58#127×C113—22no—
59#127×C113—21no—
60#127×C113—21no—
61#127×C113—21no—
62#127×C113C2312yes—
63#127×C113C2311yescharacteristic
64#126×C113—24no—
65#125×C113—21no—
66#124×C113—24no—
67#124×C113—22no—
68#124×C113—21no—
69#123×C113—24no—
70#123×C113—24no—
71C22⋊Q8×C113—22no—
72C22⋊Q8×C113—21no—
73C22⋊Q8×C113D412yes—
74#121×C113—22no—
75#121×C113—22no—
76#121×C113—24no—
77#121×C113—21no—
78#121×C113—22no—
79#121×C113D412yes—
80#120×C113—24no—
81C4×Q8×C113—22no—
82C4×Q8×C113—21no—
83C4×Q8×C113C2312yes—
84C4×D4×C113—24no—
85C4×D4×C113—24no—
86C4×D4×C113—22no—
87C4×D4×C113—21no—
88C4×D4×C113—21no—
89C4×D4×C113—21no—
90C4×D4×C113D412yes—
91C4×D4×C113D412yes—
92C4×D4×C113C2312yes—
93#117×C113—22no—
94#117×C113—21no—
95#117×C113—22no—
96C2×C4⋊C4×C113—22no—
97C2×C4⋊C4×C113D411yescharacteristic
98C2×C22⋊C4×C113—21no—
99C2×C42×C113C2311yescharacteristic
100C4⋊C8×C113—21no—
101C4⋊C8×C113—21no—
102C4⋊C8×C113C2312yes—
103C4⋊C8×C113C2312yes—
104#102×C113—24no—
105#102×C113—24no—
106#102×C113—24no—
107C22⋊C8×C113—21no—
108C22⋊C8×C113—21no—
109C4×C8×C113—21no—
110C4×C8×C113C2312yes—
111C24×C113—21no—
112C24×C113—41no—
113#41×C113—42no—
114#41×C113—42no—
115#41×C113—84no—
116C2×Q8×C113—21no—
117C2×Q8×C113—21no—
118C2×Q8×C113C2×D412yes—
119C2×D4×C113—22no—
120C2×D4×C113—24no—
121C2×D4×C113—24no—
122C2×D4×C113—21no—
123C2×D4×C113—22no—
124C2×D4×C113—22no—
125C2×D4×C113—21no—
126C2×D4×C113—21no—
127C2×D4×C113—22no—
128C2×D4×C113—22no—
129C2×D4×C113—22no—
130C2×D4×C113—41no—
131C2×D4×C113—41no—
132C2×D4×C113—41no—
133C2×D4×C113—42no—
134C2×D4×C113—42no—
135C2×D4×C113—82no—
136C2×D4×C113—82no—
137C2×D4×C113C2×D412yes—
138C2×D4×C113C2×D412yes—
139C22×C4×C113—24no—
140C22×C4×C113—21no—
141C22×C4×C113—22no—
142C22×C4×C113—22no—
143C22×C4×C113—22no—
144C22×C4×C113—82no—
145C22×C4×C113C2×D411yescharacteristic
146C22×C4×C113C2×D411yescharacteristic
147C22×C4×C113C2×D411yescharacteristic
148SD16×C113—84no—
149D8×C113—48no—
150D8×C113—84no—
151C2×C8×C113—22no—
152C2×C8×C113—22no—
153C2×C8×C113—22no—
154C2×C8×C113—42no—
155C4⋊C4×C113—24no—
156C4⋊C4×C113—21no—
157C4⋊C4×C113—21no—
158C4⋊C4×C113—21no—
159C4⋊C4×C113—22no—
160C4⋊C4×C113—21no—
161C4⋊C4×C113—21no—
162C4⋊C4×C113—22no—
163C4⋊C4×C113C2×D412yes—
164C4⋊C4×C113C2×D412yes—
165C4⋊C4×C113C2×D412yes—
166C22⋊C4×C113—24no—
167C22⋊C4×C113—24no—
168C22⋊C4×C113—24no—
169C22⋊C4×C113—22no—
170C22⋊C4×C113—22no—
171C22⋊C4×C113—22no—
172C22⋊C4×C113—22no—
173C22⋊C4×C113—22no—
174C42×C113—24no—
175C42×C113—22no—
176C42×C113C2×D411yescharacteristic
177C42×C113C2×D411yescharacteristic
178C42×C113C2×D411yescharacteristic
179C42×C113C2411yescharacteristic
180C23×C113—22no—
181C23×C113—22no—
182C23×C113—42no—
183C23×C113—42no—
184C23×C113—81no—
185C23×C113—81no—
186C23×C113—82no—
187C23×C113—82no—
188C23×C113—82no—
189C23×C113#12011yescharacteristic
190Q8×C113—24no—
191Q8×C113—41no—
192Q8×C113—41no—
193Q8×C113—81no—
194D4×C113—22no—
195D4×C113—22no—
196D4×C113—42no—
197D4×C113—44no—
198D4×C113—44no—
199D4×C113—41no—
200D4×C113—42no—
201D4×C113—41no—
202D4×C113—42no—
203D4×C113—42no—
204D4×C113—44no—
205D4×C113—42no—
206D4×C113—82no—
207D4×C113—82no—
208D4×C113—84no—
209D4×C113—84no—
210D4×C113—82no—
211C2×C4×C113—22no—
212C2×C4×C113—22no—
213C2×C4×C113—22no—
214C2×C4×C113—22no—
215C2×C4×C113—22no—
216C2×C4×C113—41no—
217C2×C4×C113—44no—
218C2×C4×C113—44no—
219C2×C4×C113—82no—
220C2×C4×C113—81no—
221C2×C4×C113—84no—
222C2×C4×C113#12011yescharacteristic
223C2×C4×C113#12011yescharacteristic
224C2×C4×C113#12011yescharacteristic
225C2×C4×C113#13512yes—
226C2×C4×C113AGL(1,ℤ/8)12yes—
227C2×C4×C113C22×D411yescharacteristic
228C2×C4×C113C22×D411yescharacteristic
229C2×C4×C113C22×D411yescharacteristic
230C8×C113—42no—
231C8×C113—42no—
232C8×C113—42no—
233C22×C113—21no—
234C22×C113—21no—
235C22×C113—42no—
236C22×C113—42no—
237C22×C113—42no—
238C22×C113—42no—
239C22×C113—42no—
240C22×C113—42no—
241C22×C113—84no—
242C22×C113—82no—
243C22×C113—82no—
244C22×C113—82no—
245C22×C113—164no—
246C22×C113#44912yes—
247C22×C113C2×#12011yescharacteristic
248C4×C113—21no—
249C4×C113—21no—
250C4×C113—21no—
251C4×C113—42no—
252C4×C113—42no—
253C4×C113—42no—
254C4×C113—42no—
255C4×C113#44912yes—
256C4×C113C2×#13511yescharacteristic
257C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
258C4×C113#57612yes—
259#18916C11311yesmaximal, characteristic, direct product factor, Sylow
260C2×C113—22no—
261C2×C113—82no—
262C2×C113—82no—
263C2×C113—162no—
264C2×C113C2×#44911yescharacteristic
265C2×C113#300811yescharacteristic
266C2×C113#302111yescharacteristic
267#3506C2×C11311yescharacteristic, complemented
268#3208C2×C11311yescharacteristic, complemented
269#3205C2×C11311yescharacteristic, complemented
270C2×#459C2×C11311yescharacteristic, complemented
271#1628C2×C11314yescomplemented
272#1621C2×C11314yescomplemented
273#1540C2×C11311yescharacteristic, complemented
274#1481C2×C11311yescharacteristic, complemented
275#1478C2×C11311yescharacteristic, complemented
276C113#1891611yescharacteristic, direct product factor, Sylow
277C22×D8—21no—
278#559—22no—
279#556C22×C11312yescomplemented
280#555—21no—
281#553—22no—
282#550C22×C11312yescomplemented
283#547—21no—
284#538—22no—
285#535—21no—
286#533C22×C11311yescharacteristic
287#532C22×C11311yescharacteristic
288C2×#127C22×C11311yescharacteristic
289#525—22no—
290#520—21no—
291C2×C4×D4C22×C11311yescharacteristic
292#493C22×C11312yescomplemented
293#492—21no—
294#486—21no—
295#486C22×C11312yescomplemented
296#460C22×C11314yescomplemented
297#459—22no—
298#459—22no—
299#459C22×C11314yes—
300#450—22no—
301#447—22no—
302#431C22×C11311yescharacteristic
303#431C22×C11311yescharacteristic
304C2×C4⋊C8C22×C11311yescharacteristic
305C2×#102—21no—
306#332C22×C11312yescomplemented
307#331C22×C11312yescomplemented
308Q8⋊C8C22×C11314yescomplemented
309D4⋊C8C22×C11314yescomplemented
310C2×#41—22no—
311C2×#41—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4D4×C11311yescharacteristic
316C23×C4—21no—
317C2×SD16—24no—
318C2×D8—24no—
319C2×D8—24no—
320C2×D8—44no—
321C22×C8—21no—
322C4⋊Q8D4×C11311yescharacteristic
323C4⋊Q8D4×C11311yescharacteristic
324C4⋊Q8C23×C11311yescharacteristic
325#127—22no—
326#127—21no—
327#127—21no—
328#127—21no—
329#127C23×C11312yes—
330#127C23×C11311yescharacteristic
331#126—24no—
332#125—21no—
333#124—24no—
334#124—22no—
335#124—21no—
336#123—24no—
337#123—24no—
338C22⋊Q8—22no—
339C22⋊Q8—21no—
340C22⋊Q8D4×C11312yes—
341#121—22no—
342#121—22no—
343#121—24no—
344#121—21no—
345#121—22no—
346#121D4×C11312yes—
347#120—24no—
348C4×Q8—22no—
349C4×Q8—21no—
350C4×Q8C23×C11312yes—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4—22no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4D4×C11312yes—
358C4×D4D4×C11312yes—
359C4×D4C23×C11312yes—
360#117—22no—
361#117—21no—
362#117—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4D4×C11311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C42C23×C11311yescharacteristic
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8C23×C11312yes—
370C4⋊C8C23×C11312yes—
371#102—24no—
372#102—24no—
373#102—24no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C4×C8—21no—
377C4×C8C23×C11312yes—
378C24—21no—
379C24—41no—
380#41—42no—
381#41—42no—
382#41—84no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8C2×D4×C11312yes—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—82no—
403C2×D4—82no—
404C2×D4C2×D4×C11312yes—
405C2×D4C2×D4×C11312yes—
406C22×C4—24no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—82no—
412C22×C4C2×D4×C11311yescharacteristic
413C22×C4C2×D4×C11311yescharacteristic
414C22×C4C2×D4×C11311yescharacteristic
415SD16—84no—
416D8—48no—
417D8—84no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—42no—
422C4⋊C4—24no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4C2×D4×C11312yes—
431C4⋊C4C2×D4×C11312yes—
432C4⋊C4C2×D4×C11312yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C42—24no—
442C42—22no—
443C42C2×D4×C11311yescharacteristic
444C42C2×D4×C11311yescharacteristic
445C42C2×D4×C11311yescharacteristic
446C42C24×C11311yescharacteristic
447C23—22no—
448C23—22no—
449C23—42no—
450C23—42no—
451C23—81no—
452C23—81no—
453C23—82no—
454C23—82no—
455C23—82no—
456C23#120×C11311yescharacteristic
457Q8—24no—
458Q8—41no—
459Q8—41no—
460Q8—81no—
461D4—22no—
462D4—22no—
463D4—42no—
464D4—44no—
465D4—44no—
466D4—41no—
467D4—42no—
468D4—41no—
469D4—42no—
470D4—42no—
471D4—44no—
472D4—42no—
473D4—82no—
474D4—82no—
475D4—84no—
476D4—84no—
477D4—82no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—41no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—82no—
487C2×C4—81no—
488C2×C4—84no—
489C2×C4#120×C11311yescharacteristic
490C2×C4#120×C11311yescharacteristic
491C2×C4#120×C11311yescharacteristic
492C2×C4#135×C11312yes—
493C2×C4AGL(1,ℤ/8)×C11312yes—
494C2×C4C22×D4×C11311yescharacteristic
495C2×C4C22×D4×C11311yescharacteristic
496C2×C4C22×D4×C11311yescharacteristic
497C8—42no—
498C8—42no—
499C8—42no—
500C22—21no—
501C22—21no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—84no—
509C22—82no—
510C22—82no—
511C22—82no—
512C22—164no—
513C22#449×C11312yes—
514C22C2×#120×C11311yescharacteristic
515C4—21no—
516C4—21no—
517C4—21no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4#449×C11312yes—
523C4C2×#135×C11311yescharacteristic
524C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
525C4#576×C11312yes—
526C2—22no—
527C2—82no—
528C2—82no—
529C2—162no—
530C2C2×#449×C11311yescharacteristic
531C2C113×#300811yescharacteristic
532C2C113×#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×#3506C2semidirect
2. C113×#3208C2semidirect
3. C113×#3205C2semidirect
4. C2×#459×C113C2semidirect
5. C113×#1628C2semidirect
6. C113×#1621C2semidirect
7. C113×#1540C2semidirect
8. C113×#1481C2semidirect
9. C113×#1478C2semidirect
12. #556×C113C22semidirect
15. #550×C113C22semidirect
25. #493×C113C22semidirect
28. #486×C113C22semidirect
29. #460×C113C22semidirect
39. #332×C113C22semidirect
40. #331×C113C22semidirect
41. Q8⋊C8×C113C22semidirect
42. D4⋊C8×C113C22semidirect
259. #18916C113direct (N × H)
267. #3506C2×C113semidirect
268. #3208C2×C113semidirect
269. #3205C2×C113semidirect
270. C2×#459C2×C113semidirect
271. #1628C2×C113semidirect
272. #1621C2×C113semidirect
273. #1540C2×C113semidirect
274. #1481C2×C113semidirect
275. #1478C2×C113semidirect
276. C113#18916direct (N × H)
279. #556C22×C113semidirect
282. #550C22×C113semidirect
292. #493C22×C113semidirect
295. #486C22×C113semidirect
296. #460C22×C113semidirect
306. #332C22×C113semidirect
307. #331C22×C113semidirect
308. Q8⋊C8C22×C113semidirect
309. D4⋊C8C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35062
C113×#32082
C113×#32052
C2×#459×C1132
C113×#16282
C113×#16212
C113×#15402
C113×#14812
C113×#14782
#18916113