Finite Group Databasebeta

← C113×#18902 #43286922

Subgroups — C113×#18902 #43286922

Order 28928.

1226 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3496C211yesmaximal, characteristic
2C113×#3226C211yesmaximal, characteristic, complemented
3C113×#3226C211yesmaximal, characteristic, complemented
4C2×#461×C113C211yesmaximal, characteristic, complemented
5C113×#1647C214yesmaximal, complemented
6C113×#1639C214yesmaximal, complemented
7C113×#1540C211yesmaximal, characteristic, complemented
8C113×#1480C211yesmaximal, characteristic, complemented
9C113×#1478C211yesmaximal, characteristic, complemented
10C2×H(5,𝔽2)×C113—21no—
11C22×SD16×C113—21no—
12#547×C113—21no—
13#547×C113C2212yes—
14#546×C113—22no—
15#546×C113—22no—
16D42×C113—21no—
17D42×C113C2212yes—
18#537×C113—21no—
19#534×C113—22no—
20#532×C113C2211yescharacteristic
21#532×C113C2211yescharacteristic
22C2×C4⋊Q8×C113C2211yescharacteristic, complemented
23C2×#121×C113—22no—
24C2×C4×D4×C113C2211yescharacteristic
25#500×C113—21no—
26#500×C113C2212yescomplemented
27#486×C113—21no—
28#486×C113C2212yescomplemented
29#480×C113—22no—
30#480×C113—22no—
31#474×C113—22no—
32#474×C113C2214yescomplemented
33#461×C113—22no—
34#461×C113C2214yescomplemented
35#431×C113C2211yescharacteristic, complemented
36#431×C113C2211yescharacteristic, complemented
37C2×C4⋊C8×C113C2211yescharacteristic, complemented
38C2×#103×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×Q8×C113—21no—
50C22×D4×C113—24no—
51C22×D4×C113—22no—
52C22×D4×C113—22no—
53C22×D4×C113—22no—
54C22×D4×C113D411yescharacteristic
55C23×C4×C113—21no—
56C2×SD16×C113—24no—
57C2×SD16×C113—44no—
58C22×C8×C113—21no—
59C4⋊Q8×C113—21no—
60C4⋊Q8×C113—21no—
61C4⋊Q8×C113—21no—
62C4⋊Q8×C113D411yescharacteristic
63C4⋊Q8×C113C2312yes—
64C4⋊Q8×C113C2311yescharacteristic
65#127×C113D411yescharacteristic
66#127×C113C2311yescharacteristic
67#124×C113—21no—
68#124×C113—21no—
69#123×C113—24no—
70#123×C113—24no—
71C22⋊Q8×C113—22no—
72C22⋊Q8×C113—22no—
73#121×C113—24no—
74#121×C113—24no—
75#121×C113—22no—
76#121×C113—22no—
77#121×C113—21no—
78#121×C113—21no—
79#121×C113—22no—
80#121×C113—22no—
81#121×C113D412yes—
82#121×C113D412yes—
83#120×C113—24no—
84#120×C113—24no—
85C4×D4×C113—21no—
86C4×D4×C113—21no—
87C4×D4×C113—21no—
88C4×D4×C113—21no—
89C4×D4×C113D412yes—
90C4×D4×C113D412yes—
91C4×D4×C113C2312yes—
92C4×D4×C113C2312yes—
93C2×C4⋊C4×C113—22no—
94C2×C4⋊C4×C113—21no—
95C2×C4⋊C4×C113—21no—
96C2×C4⋊C4×C113D411yescharacteristic
97C2×C22⋊C4×C113—24no—
98C2×C22⋊C4×C113—21no—
99C2×C42×C113C2311yescharacteristic
100#107×C113—24no—
101#107×C113—24no—
102C4⋊C8×C113—21no—
103C4⋊C8×C113—21no—
104C4⋊C8×C113C2312yes—
105C4⋊C8×C113C2312yes—
106#103×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—
115#41×C113—44no—
116#41×C113—48no—
117#41×C113—44no—
118#41×C113—42no—
119#41×C113—42no—
120#41×C113—42no—
121#41×C113—42no—
122C2×Q8×C113—21no—
123C2×Q8×C113—21no—
124C2×Q8×C113—22no—
125C2×Q8×C113—41no—
126C2×Q8×C113—42no—
127C2×Q8×C113—42no—
128C2×D4×C113—24no—
129C2×D4×C113—24no—
130C2×D4×C113—22no—
131C2×D4×C113—22no—
132C2×D4×C113—24no—
133C2×D4×C113—21no—
134C2×D4×C113—21no—
135C2×D4×C113—21no—
136C2×D4×C113—22no—
137C2×D4×C113—21no—
138C2×D4×C113—21no—
139C2×D4×C113—44no—
140C2×D4×C113—48no—
141C2×D4×C113—416no—
142C2×D4×C113—44no—
143C2×D4×C113—84no—
144C2×D4×C113D814yes—
145C2×D4×C113C2×D412yes—
146C2×D4×C113C2×D412yes—
147C2×D4×C113C2×D412yes—
148C22×C4×C113—24no—
149C22×C4×C113—21no—
150C22×C4×C113—22no—
151C22×C4×C113—22no—
152C22×C4×C113—22no—
153C22×C4×C113—22no—
154C22×C4×C113—41no—
155C22×C4×C113—82no—
156C22×C4×C113C2×D411yescharacteristic
157C22×C4×C113C2×D411yescharacteristic
158C22×C4×C113C2×D411yescharacteristic
159SD16×C113—48no—
160C2×C8×C113—22no—
161C2×C8×C113—22no—
162C2×C8×C113—22no—
163C2×C8×C113—42no—
164C4⋊C4×C113—24no—
165C4⋊C4×C113—21no—
166C4⋊C4×C113—21no—
167C4⋊C4×C113—21no—
168C4⋊C4×C113—22no—
169C4⋊C4×C113—22no—
170C4⋊C4×C113—41no—
171C4⋊C4×C113—41no—
172C4⋊C4×C113C2×D412yes—
173C4⋊C4×C113C2×D412yes—
174C4⋊C4×C113C2×D412yes—
175C22⋊C4×C113—24no—
176C22⋊C4×C113—24no—
177C22⋊C4×C113—22no—
178C22⋊C4×C113—22no—
179C22⋊C4×C113—22no—
180C22⋊C4×C113—22no—
181C22⋊C4×C113—22no—
182C22⋊C4×C113—22no—
183C42×C113C2×D411yescharacteristic
184C42×C113C2×D411yescharacteristic
185C42×C113C2×D411yescharacteristic
186C42×C113C2411yescharacteristic
187C23×C113—22no—
188C23×C113—24no—
189C23×C113—22no—
190C23×C113—22no—
191C23×C113—48no—
192C23×C113—81no—
193C23×C113—81no—
194C23×C113—84no—
195C23×C113—84no—
196C23×C113#12011yescharacteristic
197Q8×C113—41no—
198Q8×C113—41no—
199Q8×C113—42no—
200Q8×C113—42no—
201Q8×C113—42no—
202Q8×C113—82no—
203D4×C113—22no—
204D4×C113—24no—
205D4×C113—24no—
206D4×C113—42no—
207D4×C113—48no—
208D4×C113—48no—
209D4×C113—44no—
210D4×C113—44no—
211D4×C113—41no—
212D4×C113—41no—
213D4×C113—42no—
214D4×C113—42no—
215D4×C113—81no—
216D4×C113—84no—
217D4×C113C2×D814yes—
218C2×C4×C113—22no—
219C2×C4×C113—22no—
220C2×C4×C113—22no—
221C2×C4×C113—22no—
222C2×C4×C113—41no—
223C2×C4×C113—48no—
224C2×C4×C113—42no—
225C2×C4×C113—42no—
226C2×C4×C113—44no—
227C2×C4×C113—44no—
228C2×C4×C113—42no—
229C2×C4×C113—82no—
230C2×C4×C113—81no—
231C2×C4×C113—82no—
232C2×C4×C113#12011yescharacteristic
233C2×C4×C113#12011yescharacteristic
234C2×C4×C113#12011yescharacteristic
235C2×C4×C113C2×D812yes—
236C2×C4×C113AGL(1,ℤ/8)12yes—
237C2×C4×C113C22×D411yescharacteristic
238C2×C4×C113C22×D411yescharacteristic
239C2×C4×C113C22×D411yescharacteristic
240C8×C113—42no—
241C8×C113—42no—
242C8×C113—42no—
243C22×C113—21no—
244C22×C113—21no—
245C22×C113—24no—
246C22×C113—42no—
247C22×C113—42no—
248C22×C113—42no—
249C22×C113—42no—
250C22×C113—42no—
251C22×C113—42no—
252C22×C113—42no—
253C22×C113—42no—
254C22×C113—84no—
255C22×C113—168no—
256C22×C113#44712yes—
257C22×C113C2×#12011yescharacteristic
258C4×C113—21no—
259C4×C113—21no—
260C4×C113—21no—
261C4×C113—42no—
262C4×C113—42no—
263C4×C113—42no—
264C4×C113—82no—
265C4×C113#44712yes—
266C4×C113C22×D811yescharacteristic
267C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
268C4×C113#57712yes—
269#18902C11311yesmaximal, characteristic, direct product factor, Sylow
270C2×C113—22no—
271C2×C113—44no—
272C2×C113—82no—
273C2×C113—82no—
274C2×C113C2×#44711yescharacteristic
275C2×C113#300911yescharacteristic
276C2×C113#302211yescharacteristic
277#3496C2×C11311yescharacteristic
278#3226C2×C11311yescharacteristic, complemented
279#3226C2×C11311yescharacteristic, complemented
280C2×#461C2×C11311yescharacteristic, complemented
281#1647C2×C11314yescomplemented
282#1639C2×C11314yescomplemented
283#1540C2×C11311yescharacteristic, complemented
284#1480C2×C11311yescharacteristic, complemented
285#1478C2×C11311yescharacteristic, complemented
286C113#1890211yescharacteristic, direct product factor, Sylow
287C2×H(5,𝔽2)—21no—
288C22×SD16—21no—
289#547—21no—
290#547C22×C11312yes—
291#546—22no—
292#546—22no—
293D42—21no—
294D42C22×C11312yes—
295#537—21no—
296#534—22no—
297#532C22×C11311yescharacteristic
298#532C22×C11311yescharacteristic
299C2×C4⋊Q8C22×C11311yescharacteristic, complemented
300C2×#121—22no—
301C2×C4×D4C22×C11311yescharacteristic
302#500—21no—
303#500C22×C11312yescomplemented
304#486—21no—
305#486C22×C11312yescomplemented
306#480—22no—
307#480—22no—
308#474—22no—
309#474C22×C11314yescomplemented
310#461—22no—
311#461C22×C11314yescomplemented
312#431C22×C11311yescharacteristic, complemented
313#431C22×C11311yescharacteristic, complemented
314C2×C4⋊C8C22×C11311yescharacteristic, complemented
315C2×#103—21no—
316#332C22×C11312yescomplemented
317#331C22×C11312yescomplemented
318D4⋊C8C22×C11314yescomplemented
319D4⋊C8C22×C11314yescomplemented
320H(5,𝔽2)—44no—
321H(5,𝔽2)—44no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—21no—
325C2×#41—21no—
326C22×Q8—21no—
327C22×D4—24no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4D4×C11311yescharacteristic
332C23×C4—21no—
333C2×SD16—24no—
334C2×SD16—44no—
335C22×C8—21no—
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8D4×C11311yescharacteristic
340C4⋊Q8C23×C11312yes—
341C4⋊Q8C23×C11311yescharacteristic
342#127D4×C11311yescharacteristic
343#127C23×C11311yescharacteristic
344#124—21no—
345#124—21no—
346#123—24no—
347#123—24no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350#121—24no—
351#121—24no—
352#121—22no—
353#121—22no—
354#121—21no—
355#121—21no—
356#121—22no—
357#121—22no—
358#121D4×C11312yes—
359#121D4×C11312yes—
360#120—24no—
361#120—24no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4D4×C11312yes—
367C4×D4D4×C11312yes—
368C4×D4C23×C11312yes—
369C4×D4C23×C11312yes—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4D4×C11311yescharacteristic
374C2×C22⋊C4—24no—
375C2×C22⋊C4—21no—
376C2×C42C23×C11311yescharacteristic
377#107—24no—
378#107—24no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8C23×C11312yes—
382C4⋊C8C23×C11312yes—
383#103—24no—
384#102—24no—
385#102—24no—
386C22⋊C8—21no—
387C22⋊C8—21no—
388C4×C8—21no—
389C4×C8C23×C11312yes—
390C24—21no—
391C24—24no—
392#41—44no—
393#41—48no—
394#41—44no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8—41no—
403C2×Q8—42no—
404C2×Q8—42no—
405C2×D4—24no—
406C2×D4—24no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—24no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—44no—
417C2×D4—48no—
418C2×D4—416no—
419C2×D4—44no—
420C2×D4—84no—
421C2×D4D8×C11314yes—
422C2×D4C2×D4×C11312yes—
423C2×D4C2×D4×C11312yes—
424C2×D4C2×D4×C11312yes—
425C22×C4—24no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—41no—
432C22×C4—82no—
433C22×C4C2×D4×C11311yescharacteristic
434C22×C4C2×D4×C11311yescharacteristic
435C22×C4C2×D4×C11311yescharacteristic
436SD16—48no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—42no—
441C4⋊C4—24no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4C2×D4×C11312yes—
450C4⋊C4C2×D4×C11312yes—
451C4⋊C4C2×D4×C11312yes—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C42C2×D4×C11311yescharacteristic
461C42C2×D4×C11311yescharacteristic
462C42C2×D4×C11311yescharacteristic
463C42C24×C11311yescharacteristic
464C23—22no—
465C23—24no—
466C23—22no—
467C23—22no—
468C23—48no—
469C23—81no—
470C23—81no—
471C23—84no—
472C23—84no—
473C23#120×C11311yescharacteristic
474Q8—41no—
475Q8—41no—
476Q8—42no—
477Q8—42no—
478Q8—42no—
479Q8—82no—
480D4—22no—
481D4—24no—
482D4—24no—
483D4—42no—
484D4—48no—
485D4—48no—
486D4—44no—
487D4—44no—
488D4—41no—
489D4—41no—
490D4—42no—
491D4—42no—
492D4—81no—
493D4—84no—
494D4C2×D8×C11314yes—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—48no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—82no—
507C2×C4—81no—
508C2×C4—82no—
509C2×C4#120×C11311yescharacteristic
510C2×C4#120×C11311yescharacteristic
511C2×C4#120×C11311yescharacteristic
512C2×C4C2×D8×C11312yes—
513C2×C4AGL(1,ℤ/8)×C11312yes—
514C2×C4C22×D4×C11311yescharacteristic
515C2×C4C22×D4×C11311yescharacteristic
516C2×C4C22×D4×C11311yescharacteristic
517C8—42no—
518C8—42no—
519C8—42no—
520C22—21no—
521C22—21no—
522C22—24no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—84no—
532C22—168no—
533C22#447×C11312yes—
534C22C2×#120×C11311yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—42no—
539C4—42no—
540C4—42no—
541C4—82no—
542C4#447×C11312yes—
543C4C22×D8×C11311yescharacteristic
544C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
545C4#577×C11312yes—
546C2—22no—
547C2—44no—
548C2—82no—
549C2—82no—
550C2C2×#447×C11311yescharacteristic
551C2C113×#300911yescharacteristic
552C2C113×#302211yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3496C2
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
2. C113×#3226C2semidirect
3. C113×#3226C2semidirect
4. C2×#461×C113C2semidirect
5. C113×#1647C2semidirect
6. C113×#1639C2semidirect
7. C113×#1540C2semidirect
8. C113×#1480C2semidirect
9. C113×#1478C2semidirect
22. C2×C4⋊Q8×C113C22semidirect
26. #500×C113C22semidirect
28. #486×C113C22semidirect
32. #474×C113C22semidirect
34. #461×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
269. #18902C113direct (N × H)
278. #3226C2×C113semidirect
279. #3226C2×C113semidirect
280. C2×#461C2×C113semidirect
281. #1647C2×C113semidirect
282. #1639C2×C113semidirect
283. #1540C2×C113semidirect
284. #1480C2×C113semidirect
285. #1478C2×C113semidirect
286. C113#18902direct (N × H)
299. C2×C4⋊Q8C22×C113semidirect
303. #500C22×C113semidirect
305. #486C22×C113semidirect
309. #474C22×C113semidirect
311. #461C22×C113semidirect
312. #431C22×C113semidirect
313. #431C22×C113semidirect
314. C2×C4⋊C8C22×C113semidirect
316. #332C22×C113semidirect
317. #331C22×C113semidirect
318. D4⋊C8C22×C113semidirect
319. D4⋊C8C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34962
C113×#32262
C2×#461×C1132
C113×#16472
C113×#16392
C113×#15402
C113×#14802
C113×#14782
#18902113