Finite Group Databasebeta

← C113×#18356 #43286376

Subgroups — C113×#18356 #43286376

Order 28928.

1054 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×#3491C211yesmaximal, characteristic, complemented
2C113×#3217C212yesmaximal, complemented
3C113×#2619C211yesmaximal, characteristic, complemented
4C113×#1597C214yesmaximal, complemented
5C113×#1596C212yesmaximal, complemented
6C113×#1595C212yesmaximal, complemented
7C113×#1512C212yesmaximal, complemented
8C113×#1464C211yesmaximal, characteristic, complemented
9#552×C113—22no—
10#552×C113—22no—
11#551×C113—22no—
12#551×C113—22no—
13#543×C113C2211yescharacteristic
14#539×C113—21no—
15#539×C113C2212yes—
16#534×C113C2211yescharacteristic
17C2×#127×C113C2211yescharacteristic, complemented
18#529×C113—21no—
19#529×C113C2212yes—
20C2×#123×C113—21no—
21C2×#121×C113—21no—
22#518×C113—21no—
23C2×#117×C113C2211yescharacteristic
24#496×C113—22no—
25#490×C113—22no—
26#460×C113—22no—
27#459×C113—22no—
28#450×C113C2214yescomplemented
29#447×C113C2214yes—
30#432×C113C2212yescomplemented
31#394×C113—21no—
32#394×C113C2212yescomplemented
33#392×C113—21no—
34#392×C113C2212yes—
35#390×C113—21no—
36#382×C113C2211yescharacteristic, complemented
37#328×C113C2214yescomplemented
38#327×C113C2214yes—
39#324×C113C2212yescomplemented
40#323×C113C2212yes—
41C22×D4×C113—21no—
42C22×D4×C113—22no—
43C22×D4×C113—21no—
44C22×D4×C113—21no—
45C22×D4×C113C2312yes—
46C23×C4×C113D411yescharacteristic
47C2×SD16×C113—24no—
48C2×D8×C113—24no—
49#127×C113—22no—
50#127×C113—22no—
51#126×C113—22no—
52#126×C113—22no—
53#126×C113—22no—
54#126×C113—22no—
55#125×C113—21no—
56#125×C113—22no—
57#125×C113—22no—
58#125×C113D412yescomplemented
59#124×C113—21no—
60#124×C113D412yescomplemented
61#123×C113—22no—
62#123×C113—22no—
63#123×C113—22no—
64#123×C113—22no—
65#123×C113—22no—
66#123×C113—22no—
67#123×C113—22no—
68C22⋊Q8×C113—22no—
69C22⋊Q8×C113—22no—
70C22⋊Q8×C113—22no—
71C22⋊Q8×C113—21no—
72C22⋊Q8×C113—22no—
73C22⋊Q8×C113C2312yes—
74#121×C113—21no—
75#121×C113—44no—
76#121×C113C2312yes—
77#120×C113—22no—
78C4×Q8×C113—21no—
79C4×Q8×C113D412yescomplemented
80C4×D4×C113—22no—
81C4×D4×C113—22no—
82C4×D4×C113—21no—
83C4×D4×C113—22no—
84C4×D4×C113—22no—
85C4×D4×C113D412yescomplemented
86#117×C113—22no—
87#117×C113—22no—
88#117×C113—22no—
89#117×C113—22no—
90#117×C113—22no—
91C2×C4⋊C4×C113—21no—
92C2×C4⋊C4×C113—21no—
93C2×C4⋊C4×C113—21no—
94C2×C4⋊C4×C113D411yescharacteristic
95C2×C4⋊C4×C113C2311yescharacteristic
96C2×C22⋊C4×C113—22no—
97C2×C22⋊C4×C113—21no—
98C2×C22⋊C4×C113—21no—
99C2×C22⋊C4×C113—21no—
100C2×C22⋊C4×C113—22no—
101C2×C22⋊C4×C113—22no—
102C2×C22⋊C4×C113—22no—
103C2×C22⋊C4×C113D411yescharacteristic
104C2×C22⋊C4×C113C2311yescharacteristic
105C2×C42×C113D411yescharacteristic
106C2×C42×C113C2311yescharacteristic
107C4⋊C8×C113—22no—
108#102×C113—24no—
109#102×C113—24no—
110C22⋊C8×C113C2314yes—
111#97×C113—22no—
112#95×C113—21no—
113#95×C113C2312yes—
114C24×C113—21no—
115C24×C113—22no—
116C24×C113C2×D411yescharacteristic
117C2×Q8×C113—21no—
118C2×Q8×C113C2×D412yes—
119C2×D4×C113—22no—
120C2×D4×C113—22no—
121C2×D4×C113—21no—
122C2×D4×C113—24no—
123C2×D4×C113—42no—
124C2×D4×C113—42no—
125C2×D4×C113—42no—
126C2×D4×C113—42no—
127C2×D4×C113—44no—
128C2×D4×C113—41no—
129C2×D4×C113—41no—
130C2×D4×C113—42no—
131C2×D4×C113—82no—
132C2×D4×C113—82no—
133C2×D4×C113—82no—
134C2×D4×C113—82no—
135C2×D4×C113C2×D412yes—
136C22×C4×C113—21no—
137C22×C4×C113—22no—
138C22×C4×C113—21no—
139C22×C4×C113—21no—
140C22×C4×C113—22no—
141C22×C4×C113—21no—
142C22×C4×C113—21no—
143C22×C4×C113—22no—
144C22×C4×C113—22no—
145C22×C4×C113—41no—
146C22×C4×C113C2×D411yescharacteristic
147C22×C4×C113C2×D411yescharacteristic
148C22×C4×C113C2×D411yescharacteristic
149C22×C4×C113C2×D411yescharacteristic
150C22×C4×C113C2×D411yescharacteristic
151C22×C4×C113C2411yescharacteristic
152SD16×C113—84no—
153D8×C113—84no—
154C2×C8×C113—24no—
155C4⋊C4×C113—22no—
156C4⋊C4×C113—22no—
157C4⋊C4×C113—22no—
158C4⋊C4×C113—22no—
159C4⋊C4×C113—21no—
160C4⋊C4×C113—21no—
161C4⋊C4×C113—22no—
162C4⋊C4×C113—22no—
163C4⋊C4×C113—22no—
164C4⋊C4×C113—22no—
165C4⋊C4×C113—22no—
166C4⋊C4×C113—22no—
167C4⋊C4×C113—42no—
168C4⋊C4×C113C2×D412yes—
169C4⋊C4×C113C2×D412yes—
170C22⋊C4×C113—22no—
171C22⋊C4×C113—22no—
172C22⋊C4×C113—22no—
173C22⋊C4×C113—22no—
174C22⋊C4×C113—22no—
175C22⋊C4×C113—22no—
176C22⋊C4×C113—22no—
177C22⋊C4×C113—22no—
178C22⋊C4×C113—22no—
179C22⋊C4×C113—22no—
180C22⋊C4×C113—22no—
181C22⋊C4×C113—22no—
182C22⋊C4×C113—44no—
183C22⋊C4×C113—82no—
184C22⋊C4×C113—82no—
185C42×C113—22no—
186C42×C113—21no—
187C42×C113—21no—
188C42×C113—22no—
189C42×C113C2×D412yes—
190C42×C113C2×D412yes—
191C23×C113—21no—
192C23×C113—21no—
193C23×C113—22no—
194C23×C113—41no—
195C23×C113—41no—
196C23×C113—42no—
197C23×C113—42no—
198C23×C113—42no—
199C23×C113—42no—
200C23×C113—42no—
201C23×C113—42no—
202C23×C113—42no—
203C23×C113—42no—
204C23×C113—81no—
205C23×C113—81no—
206C23×C113AGL(1,ℤ/8)12yes—
207C23×C113C22×D411yescharacteristic
208Q8×C113—42no—
209Q8×C113—81no—
210D4×C113—42no—
211D4×C113—44no—
212D4×C113—44no—
213D4×C113—44no—
214D4×C113—42no—
215D4×C113—42no—
216D4×C113—82no—
217D4×C113—82no—
218D4×C113—84no—
219D4×C113—81no—
220D4×C113—88no—
221C2×C4×C113—21no—
222C2×C4×C113—21no—
223C2×C4×C113—21no—
224C2×C4×C113—21no—
225C2×C4×C113—22no—
226C2×C4×C113—22no—
227C2×C4×C113—22no—
228C2×C4×C113—21no—
229C2×C4×C113—21no—
230C2×C4×C113—21no—
231C2×C4×C113—41no—
232C2×C4×C113—41no—
233C2×C4×C113—42no—
234C2×C4×C113—42no—
235C2×C4×C113—42no—
236C2×C4×C113—41no—
237C2×C4×C113—41no—
238C2×C4×C113—42no—
239C2×C4×C113—42no—
240C2×C4×C113—42no—
241C2×C4×C113—82no—
242C2×C4×C113—81no—
243C2×C4×C113—82no—
244C2×C4×C113—81no—
245C2×C4×C113#12011yescharacteristic
246C2×C4×C113#12011yescharacteristic
247C2×C4×C113#12012yes—
248C2×C4×C113C22×D412yes—
249C8×C113—44no—
250C22×C113—21no—
251C22×C113—21no—
252C22×C113—22no—
253C22×C113—42no—
254C22×C113—41no—
255C22×C113—41no—
256C22×C113—42no—
257C22×C113—42no—
258C22×C113—42no—
259C22×C113—81no—
260C22×C113—82no—
261C22×C113—82no—
262C22×C113—82no—
263C22×C113—82no—
264C22×C113—82no—
265C22×C113—82no—
266C22×C113—82no—
267C22×C113—162no—
268C22×C113C2×#12011yescharacteristic
269C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C113#57511yescharacteristic
271C4×C113—21no—
272C4×C113—21no—
273C4×C113—22no—
274C4×C113—22no—
275C4×C113—41no—
276C4×C113—42no—
277C4×C113—41no—
278C4×C113—42no—
279C4×C113—41no—
280C4×C113—42no—
281C4×C113—82no—
282#18356C11311yesmaximal, characteristic, direct product factor, Sylow
283C2×C113—21no—
284C2×C113—21no—
285C2×C113—42no—
286C2×C113—82no—
287C2×C113—162no—
288C2×C113#300611yescharacteristic
289C2×C113#302111yescharacteristic
290C2×C113#302711yescharacteristic
291#3491C2×C11311yescharacteristic, complemented
292#3217C2×C11312yescomplemented
293#2619C2×C11311yescharacteristic, complemented
294#1597C2×C11314yescomplemented
295#1596C2×C11312yescomplemented
296#1595C2×C11312yescomplemented
297#1512C2×C11312yescomplemented
298#1464C2×C11311yescharacteristic, complemented
299C113#1835611yescharacteristic, direct product factor, Sylow
300#552—22no—
301#552—22no—
302#551—22no—
303#551—22no—
304#543C22×C11311yescharacteristic
305#539—21no—
306#539C22×C11312yes—
307#534C22×C11311yescharacteristic
308C2×#127C22×C11311yescharacteristic, complemented
309#529—21no—
310#529C22×C11312yes—
311C2×#123—21no—
312C2×#121—21no—
313#518—21no—
314C2×#117C22×C11311yescharacteristic
315#496—22no—
316#490—22no—
317#460—22no—
318#459—22no—
319#450C22×C11314yescomplemented
320#447C22×C11314yes—
321#432C22×C11312yescomplemented
322#394—21no—
323#394C22×C11312yescomplemented
324#392—21no—
325#392C22×C11312yes—
326#390—21no—
327#382C22×C11311yescharacteristic, complemented
328#328C22×C11314yescomplemented
329#327C22×C11314yes—
330#324C22×C11312yescomplemented
331#323C22×C11312yes—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4C23×C11312yes—
337C23×C4D4×C11311yescharacteristic
338C2×SD16—24no—
339C2×D8—24no—
340#127—22no—
341#127—22no—
342#126—22no—
343#126—22no—
344#126—22no—
345#126—22no—
346#125—21no—
347#125—22no—
348#125—22no—
349#125D4×C11312yescomplemented
350#124—21no—
351#124D4×C11312yescomplemented
352#123—22no—
353#123—22no—
354#123—22no—
355#123—22no—
356#123—22no—
357#123—22no—
358#123—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—21no—
363C22⋊Q8—22no—
364C22⋊Q8C23×C11312yes—
365#121—21no—
366#121—44no—
367#121C23×C11312yes—
368#120—22no—
369C4×Q8—21no—
370C4×Q8D4×C11312yescomplemented
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—21no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4D4×C11312yescomplemented
377#117—22no—
378#117—22no—
379#117—22no—
380#117—22no—
381#117—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4D4×C11311yescharacteristic
386C2×C4⋊C4C23×C11311yescharacteristic
387C2×C22⋊C4—22no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4D4×C11311yescharacteristic
395C2×C22⋊C4C23×C11311yescharacteristic
396C2×C42D4×C11311yescharacteristic
397C2×C42C23×C11311yescharacteristic
398C4⋊C8—22no—
399#102—24no—
400#102—24no—
401C22⋊C8C23×C11314yes—
402#97—22no—
403#95—21no—
404#95C23×C11312yes—
405C24—21no—
406C24—22no—
407C24C2×D4×C11311yescharacteristic
408C2×Q8—21no—
409C2×Q8C2×D4×C11312yes—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—24no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—42no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4—82no—
425C2×D4—82no—
426C2×D4C2×D4×C11312yes—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—41no—
437C22×C4C2×D4×C11311yescharacteristic
438C22×C4C2×D4×C11311yescharacteristic
439C22×C4C2×D4×C11311yescharacteristic
440C22×C4C2×D4×C11311yescharacteristic
441C22×C4C2×D4×C11311yescharacteristic
442C22×C4C24×C11311yescharacteristic
443SD16—84no—
444D8—84no—
445C2×C8—24no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—42no—
459C4⋊C4C2×D4×C11312yes—
460C4⋊C4C2×D4×C11312yes—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—44no—
474C22⋊C4—82no—
475C22⋊C4—82no—
476C42—22no—
477C42—21no—
478C42—21no—
479C42—22no—
480C42C2×D4×C11312yes—
481C42C2×D4×C11312yes—
482C23—21no—
483C23—21no—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23AGL(1,ℤ/8)×C11312yes—
498C23C22×D4×C11311yescharacteristic
499Q8—42no—
500Q8—81no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—44no—
505D4—42no—
506D4—42no—
507D4—82no—
508D4—82no—
509D4—84no—
510D4—81no—
511D4—88no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4—81no—
534C2×C4—82no—
535C2×C4—81no—
536C2×C4#120×C11311yescharacteristic
537C2×C4#120×C11311yescharacteristic
538C2×C4#120×C11312yes—
539C2×C4C22×D4×C11312yes—
540C8—44no—
541C22—21no—
542C22—21no—
543C22—22no—
544C22—42no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—81no—
551C22—82no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—162no—
559C22C2×#120×C11311yescharacteristic
560C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
561C22#575×C11311yescharacteristic
562C4—21no—
563C4—21no—
564C4—22no—
565C4—22no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—41no—
571C4—42no—
572C4—82no—
573C2—21no—
574C2—21no—
575C2—42no—
576C2—82no—
577C2—162no—
578C2C113×#300611yescharacteristic
579C2C113×#302111yescharacteristic
580C2C113×#302711yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ 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×#3491C2semidirect
2. C113×#3217C2semidirect
3. C113×#2619C2semidirect
4. C113×#1597C2semidirect
5. C113×#1596C2semidirect
6. C113×#1595C2semidirect
7. C113×#1512C2semidirect
8. C113×#1464C2semidirect
17. C2×#127×C113C22semidirect
28. #450×C113C22semidirect
30. #432×C113C22semidirect
32. #394×C113C22semidirect
36. #382×C113C22semidirect
37. #328×C113C22semidirect
39. #324×C113C22semidirect
58. #125×C113D4semidirect
60. #124×C113D4semidirect
79. C4×Q8×C113D4semidirect
85. C4×D4×C113D4semidirect
282. #18356C113direct (N × H)
291. #3491C2×C113semidirect
292. #3217C2×C113semidirect
293. #2619C2×C113semidirect
294. #1597C2×C113semidirect
295. #1596C2×C113semidirect
296. #1595C2×C113semidirect
297. #1512C2×C113semidirect
298. #1464C2×C113semidirect
299. C113#18356direct (N × H)
308. C2×#127C22×C113semidirect
319. #450C22×C113semidirect
321. #432C22×C113semidirect
323. #394C22×C113semidirect
327. #382C22×C113semidirect
328. #328C22×C113semidirect
330. #324C22×C113semidirect
349. #125D4×C113semidirect
351. #124D4×C113semidirect
370. C4×Q8D4×C113semidirect
376. C4×D4D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34912
C113×#32172
C113×#26192
C113×#15972
C113×#15962
C113×#15952
C113×#15122
C113×#14642
#18356113