Finite Group Databasebeta

← C113×#18624 #43286644

Subgroups — C113×#18624 #43286644

Order 28928.

1152 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3508C211yesmaximal, characteristic, complemented
2C113×#3208C211yesmaximal, characteristic, complemented
3C2×#493×C113C211yesmaximal, characteristic, complemented
4C113×#3038C211yesmaximal, characteristic, complemented
5C113×#1621C214yesmaximal, complemented
6C113×#1620C214yesmaximal, complemented
7C113×#1545C211yesmaximal, characteristic, complemented
8C113×#1493C211yesmaximal, characteristic, complemented
9C113×#1476C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C113—21no—
11C22×D8×C113—22no—
12#559×C113—21no—
13#559×C113C2212yescomplemented
14#550×C113—21no—
15#550×C113C2212yescomplemented
16#546×C113—22no—
17#546×C113—22no—
18#540×C113—22no—
19#535×C113—21no—
20#533×C113C2211yescharacteristic
21#532×C113—21no—
22#532×C113—21no—
23C2×#127×C113C2211yescharacteristic
24C2×#127×C113C2211yescharacteristic
25#518×C113—21no—
26C4×#41×C113C2211yescharacteristic
27#493×C113—22no—
28#493×C113C2214yes—
29#492×C113—21no—
30#486×C113—21no—
31#460×C113—21no—
32#460×C113C2212yescomplemented
33#460×C113C2214yescomplemented
34#459×C113—21no—
35#459×C113C2212yescomplemented
36#450×C113—22no—
37#431×C113C2211yescharacteristic
38#423×C113C2211yescharacteristic
39#418×C113—21no—
40C2×C4×C8×C113C2211yescharacteristic
41#331×C113C2214yescomplemented
42Q8⋊C8×C113C2212yescomplemented
43Q8⋊C8×C113C2214yescomplemented
44D4⋊C8×C113C2212yescomplemented
45C2×#41×C113—22no—
46C2×#41×C113—22no—
47C2×#41×C113D411yescharacteristic
48C22×D4×C113—21no—
49C22×D4×C113—21no—
50C22×D4×C113—21no—
51C22×D4×C113—21no—
52C22×D4×C113—21no—
53C22×D4×C113D412yes—
54AGL(1,ℤ/8)×C113—44no—
55C2×SD16×C113—22no—
56C2×SD16×C113—24no—
57C2×D8×C113—28no—
58C2×D8×C113—22no—
59C2×D8×C113—48no—
60C2×M16×C113—21no—
61C22×C8×C113—21no—
62C4⋊Q8×C113D411yescharacteristic
63C4⋊Q8×C113D411yescharacteristic
64#127×C113—22no—
65#127×C113—21no—
66#127×C113—21no—
67#127×C113—21no—
68#127×C113—21no—
69#127×C113—21no—
70#127×C113D412yes—
71#127×C113C2312yes—
72#127×C113C2312yes—
73#125×C113—21no—
74#124×C113—22no—
75#124×C113—22no—
76#124×C113—22no—
77#123×C113—24no—
78#123×C113—24no—
79C22⋊Q8×C113—21no—
80C22⋊Q8×C113D412yes—
81#121×C113—22no—
82#121×C113—22no—
83#121×C113—22no—
84#121×C113—24no—
85#121×C113—24no—
86#121×C113—22no—
87#120×C113—24no—
88C4×Q8×C113—21no—
89C4×Q8×C113D411yescharacteristic
90C4×Q8×C113C2311yescharacteristic
91C4×Q8×C113C2312yes—
92C4×D4×C113—22no—
93C4×D4×C113—22no—
94C4×D4×C113—22no—
95C4×D4×C113—21no—
96C4×D4×C113—21no—
97C4×D4×C113—22no—
98C4×D4×C113—22no—
99C4×D4×C113—22no—
100C4×D4×C113D411yescharacteristic
101C4×D4×C113C2311yescharacteristic
102#117×C113—21no—
103#117×C113—21no—
104#117×C113D411yescharacteristic
105C2×C22⋊C4×C113—24no—
106C2×C42×C113—21no—
107C2×C42×C113C2311yescharacteristic
108C4⋊C8×C113—21no—
109C4⋊C8×C113C2312yes—
110C4⋊C8×C113C2312yes—
111#102×C113—22no—
112#102×C113—22no—
113#102×C113—24no—
114C22⋊C8×C113—21no—
115C4×C8×C113—21no—
116C4×C8×C113—21no—
117C4×C8×C113C2312yes—
118C24×C113—22no—
119C24×C113—41no—
120#41×C113—22no—
121#41×C113—22no—
122#41×C113—84no—
123#41×C113—84no—
124C2×Q8×C113—21no—
125C2×Q8×C113C2×D411yescharacteristic
126C2×Q8×C113C2×D412yes—
127C2×D4×C113—21no—
128C2×D4×C113—24no—
129C2×D4×C113—24no—
130C2×D4×C113—22no—
131C2×D4×C113—22no—
132C2×D4×C113—22no—
133C2×D4×C113—22no—
134C2×D4×C113—22no—
135C2×D4×C113—22no—
136C2×D4×C113—22no—
137C2×D4×C113—22no—
138C2×D4×C113—44no—
139C2×D4×C113—44no—
140C2×D4×C113—41no—
141C2×D4×C113—41no—
142C2×D4×C113—41no—
143C2×D4×C113—42no—
144C2×D4×C113—42no—
145C2×D4×C113—42no—
146C2×D4×C113—42no—
147C2×D4×C113—82no—
148C2×D4×C113—82no—
149C2×D4×C113C2×D411yescharacteristic
150C2×D4×C113C2×D414yes—
151C22×C4×C113—24no—
152C22×C4×C113—24no—
153C22×C4×C113—21no—
154C22×C4×C113—21no—
155C22×C4×C113—21no—
156C22×C4×C113C2×D411yescharacteristic
157C22×C4×C113C2×D411yescharacteristic
158C22×C4×C113C2×D411yescharacteristic
159SD16×C113—44no—
160SD16×C113—84no—
161D8×C113—416no—
162D8×C113—44no—
163M16×C113—42no—
164C2×C8×C113—24no—
165C2×C8×C113—22no—
166C2×C8×C113—22no—
167C2×C8×C113—22no—
168C4⋊C4×C113—21no—
169C4⋊C4×C113—21no—
170C4⋊C4×C113—21no—
171C4⋊C4×C113—21no—
172C4⋊C4×C113—22no—
173C4⋊C4×C113—21no—
174C4⋊C4×C113—22no—
175C4⋊C4×C113C2×D411yescharacteristic
176C4⋊C4×C113C2×D411yescharacteristic
177C4⋊C4×C113C2×D412yes—
178C22⋊C4×C113—24no—
179C22⋊C4×C113—24no—
180C22⋊C4×C113—24no—
181C22⋊C4×C113—24no—
182C22⋊C4×C113—21no—
183C22⋊C4×C113—22no—
184C22⋊C4×C113—21no—
185C22⋊C4×C113—21no—
186C42×C113—21no—
187C42×C113—21no—
188C42×C113—21no—
189C42×C113—22no—
190C42×C113C2×D411yescharacteristic
191C42×C113C2×D411yescharacteristic
192C42×C113C2×D411yescharacteristic
193C42×C113C2411yescharacteristic
194C23×C113—24no—
195C23×C113—21no—
196C23×C113—44no—
197C23×C113—42no—
198C23×C113—82no—
199C23×C113—82no—
200C23×C113—82no—
201C23×C113—82no—
202C23×C113—82no—
203C23×C113#12011yescharacteristic
204Q8×C113—21no—
205Q8×C113—21no—
206Q8×C113—24no—
207Q8×C113—42no—
208D4×C113—21no—
209D4×C113—21no—
210D4×C113—44no—
211D4×C113—44no—
212D4×C113—42no—
213D4×C113—42no—
214D4×C113—42no—
215D4×C113—42no—
216D4×C113—42no—
217D4×C113—44no—
218D4×C113—44no—
219D4×C113—44no—
220D4×C113—44no—
221D4×C113—82no—
222D4×C113—82no—
223D4×C113—84no—
224D4×C113—84no—
225D4×C113—82no—
226D4×C113—82no—
227C2×C4×C113—22no—
228C2×C4×C113—22no—
229C2×C4×C113—21no—
230C2×C4×C113—21no—
231C2×C4×C113—21no—
232C2×C4×C113—22no—
233C2×C4×C113—22no—
234C2×C4×C113—42no—
235C2×C4×C113—42no—
236C2×C4×C113—42no—
237C2×C4×C113—84no—
238C2×C4×C113—84no—
239C2×C4×C113#12011yescharacteristic
240C2×C4×C113#12011yescharacteristic
241C2×C4×C113#12011yescharacteristic
242C2×C4×C113#13512yes—
243C2×C4×C113AGL(1,ℤ/8)12yes—
244C2×C4×C113C22×D411yescharacteristic
245C2×C4×C113C22×D411yescharacteristic
246C2×C4×C113C22×D411yescharacteristic
247C8×C113—24no—
248C8×C113—42no—
249C8×C113—42no—
250C22×C113—21no—
251C22×C113—21no—
252C22×C113—41no—
253C22×C113—44no—
254C22×C113—41no—
255C22×C113—44no—
256C22×C113—41no—
257C22×C113—44no—
258C22×C113—82no—
259C22×C113—82no—
260C22×C113—82no—
261C22×C113—164no—
262C22×C113—164no—
263C22×C113#44912yes—
264C22×C113C2×#12011yescharacteristic
265C4×C113—21no—
266C4×C113—21no—
267C4×C113—41no—
268C4×C113—41no—
269C4×C113—42no—
270C4×C113—41no—
271C4×C113—42no—
272C4×C113#44912yes—
273C4×C113#45312yes—
274C4×C113C2×#13511yescharacteristic
275C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
276C4×C113#57612yes—
277#18624C11311yesmaximal, characteristic, direct product factor, Sylow
278C2×C113—22no—
279C2×C113—81no—
280C2×C113—84no—
281C2×C113—162no—
282C2×C113C2×#44911yescharacteristic
283C2×C113#300811yescharacteristic
284C2×C113C2×#45311yescharacteristic
285#3508C2×C11311yescharacteristic, complemented
286#3208C2×C11311yescharacteristic, complemented
287C2×#493C2×C11311yescharacteristic, complemented
288#3038C2×C11311yescharacteristic, complemented
289#1621C2×C11314yescomplemented
290#1620C2×C11314yescomplemented
291#1545C2×C11311yescharacteristic, complemented
292#1493C2×C11311yescharacteristic, complemented
293#1476C2×C11311yescharacteristic, complemented
294C113#1862411yescharacteristic, direct product factor, Sylow
295C2×AGL(1,ℤ/8)—21no—
296C22×D8—22no—
297#559—21no—
298#559C22×C11312yescomplemented
299#550—21no—
300#550C22×C11312yescomplemented
301#546—22no—
302#546—22no—
303#540—22no—
304#535—21no—
305#533C22×C11311yescharacteristic
306#532—21no—
307#532—21no—
308C2×#127C22×C11311yescharacteristic
309C2×#127C22×C11311yescharacteristic
310#518—21no—
311C4×#41C22×C11311yescharacteristic
312#493—22no—
313#493C22×C11314yes—
314#492—21no—
315#486—21no—
316#460—21no—
317#460C22×C11312yescomplemented
318#460C22×C11314yescomplemented
319#459—21no—
320#459C22×C11312yescomplemented
321#450—22no—
322#431C22×C11311yescharacteristic
323#423C22×C11311yescharacteristic
324#418—21no—
325C2×C4×C8C22×C11311yescharacteristic
326#331C22×C11314yescomplemented
327Q8⋊C8C22×C11312yescomplemented
328Q8⋊C8C22×C11314yescomplemented
329D4⋊C8C22×C11312yescomplemented
330C2×#41—22no—
331C2×#41—22no—
332C2×#41D4×C11311yescharacteristic
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4D4×C11312yes—
339AGL(1,ℤ/8)—44no—
340C2×SD16—22no—
341C2×SD16—24no—
342C2×D8—28no—
343C2×D8—22no—
344C2×D8—48no—
345C2×M16—21no—
346C22×C8—21no—
347C4⋊Q8D4×C11311yescharacteristic
348C4⋊Q8D4×C11311yescharacteristic
349#127—22no—
350#127—21no—
351#127—21no—
352#127—21no—
353#127—21no—
354#127—21no—
355#127D4×C11312yes—
356#127C23×C11312yes—
357#127C23×C11312yes—
358#125—21no—
359#124—22no—
360#124—22no—
361#124—22no—
362#123—24no—
363#123—24no—
364C22⋊Q8—21no—
365C22⋊Q8D4×C11312yes—
366#121—22no—
367#121—22no—
368#121—22no—
369#121—24no—
370#121—24no—
371#121—22no—
372#120—24no—
373C4×Q8—21no—
374C4×Q8D4×C11311yescharacteristic
375C4×Q8C23×C11311yescharacteristic
376C4×Q8C23×C11312yes—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4D4×C11311yescharacteristic
386C4×D4C23×C11311yescharacteristic
387#117—21no—
388#117—21no—
389#117D4×C11311yescharacteristic
390C2×C22⋊C4—24no—
391C2×C42—21no—
392C2×C42C23×C11311yescharacteristic
393C4⋊C8—21no—
394C4⋊C8C23×C11312yes—
395C4⋊C8C23×C11312yes—
396#102—22no—
397#102—22no—
398#102—24no—
399C22⋊C8—21no—
400C4×C8—21no—
401C4×C8—21no—
402C4×C8C23×C11312yes—
403C24—22no—
404C24—41no—
405#41—22no—
406#41—22no—
407#41—84no—
408#41—84no—
409C2×Q8—21no—
410C2×Q8C2×D4×C11311yescharacteristic
411C2×Q8C2×D4×C11312yes—
412C2×D4—21no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—82no—
433C2×D4—82no—
434C2×D4C2×D4×C11311yescharacteristic
435C2×D4C2×D4×C11314yes—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4C2×D4×C11311yescharacteristic
442C22×C4C2×D4×C11311yescharacteristic
443C22×C4C2×D4×C11311yescharacteristic
444SD16—44no—
445SD16—84no—
446D8—416no—
447D8—44no—
448M16—42no—
449C2×C8—24no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4C2×D4×C11311yescharacteristic
461C4⋊C4C2×D4×C11311yescharacteristic
462C4⋊C4C2×D4×C11312yes—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—21no—
468C22⋊C4—22no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—22no—
475C42C2×D4×C11311yescharacteristic
476C42C2×D4×C11311yescharacteristic
477C42C2×D4×C11311yescharacteristic
478C42C24×C11311yescharacteristic
479C23—24no—
480C23—21no—
481C23—44no—
482C23—42no—
483C23—82no—
484C23—82no—
485C23—82no—
486C23—82no—
487C23—82no—
488C23#120×C11311yescharacteristic
489Q8—21no—
490Q8—21no—
491Q8—24no—
492Q8—42no—
493D4—21no—
494D4—21no—
495D4—44no—
496D4—44no—
497D4—42no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—44no—
505D4—44no—
506D4—82no—
507D4—82no—
508D4—84no—
509D4—84no—
510D4—82no—
511D4—82no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—84no—
523C2×C4—84no—
524C2×C4#120×C11311yescharacteristic
525C2×C4#120×C11311yescharacteristic
526C2×C4#120×C11311yescharacteristic
527C2×C4#135×C11312yes—
528C2×C4AGL(1,ℤ/8)×C11312yes—
529C2×C4C22×D4×C11311yescharacteristic
530C2×C4C22×D4×C11311yescharacteristic
531C2×C4C22×D4×C11311yescharacteristic
532C8—24no—
533C8—42no—
534C8—42no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—44no—
539C22—41no—
540C22—44no—
541C22—41no—
542C22—44no—
543C22—82no—
544C22—82no—
545C22—82no—
546C22—164no—
547C22—164no—
548C22#449×C11312yes—
549C22C2×#120×C11311yescharacteristic
550C4—21no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—42no—
557C4#449×C11312yes—
558C4#453×C11312yes—
559C4C2×#135×C11311yescharacteristic
560C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
561C4#576×C11312yes—
562C2—22no—
563C2—84no—
564C2—81no—
565C2—162no—
566C2C2×#449×C11311yescharacteristic
567C2C113×#300811yescharacteristic
568C2C2×#453×C11311yescharacteristic
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×#3508C2semidirect
2. C113×#3208C2semidirect
3. C2×#493×C113C2semidirect
4. C113×#3038C2semidirect
5. C113×#1621C2semidirect
6. C113×#1620C2semidirect
7. C113×#1545C2semidirect
8. C113×#1493C2semidirect
9. C113×#1476C2semidirect
13. #559×C113C22semidirect
15. #550×C113C22semidirect
32. #460×C113C22semidirect
33. #460×C113C22semidirect
35. #459×C113C22semidirect
41. #331×C113C22semidirect
42. Q8⋊C8×C113C22semidirect
43. Q8⋊C8×C113C22semidirect
44. D4⋊C8×C113C22semidirect
277. #18624C113direct (N × H)
285. #3508C2×C113semidirect
286. #3208C2×C113semidirect
287. C2×#493C2×C113semidirect
288. #3038C2×C113semidirect
289. #1621C2×C113semidirect
290. #1620C2×C113semidirect
291. #1545C2×C113semidirect
292. #1493C2×C113semidirect
293. #1476C2×C113semidirect
294. C113#18624direct (N × H)
298. #559C22×C113semidirect
300. #550C22×C113semidirect
317. #460C22×C113semidirect
318. #460C22×C113semidirect
320. #459C22×C113semidirect
326. #331C22×C113semidirect
327. Q8⋊C8C22×C113semidirect
328. Q8⋊C8C22×C113semidirect
329. D4⋊C8C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35082
C113×#32082
C2×#493×C1132
C113×#30382
C113×#16212
C113×#16202
C113×#15452
C113×#14932
C113×#14762
#18624113