Finite Group Databasebeta

← C113×#18889 #43286909

Subgroups — C113×#18889 #43286909

Order 28928.

910 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3511C211yesmaximal, characteristic
2C113×#3246C211yesmaximal, characteristic, complemented
3C113×#3230C211yesmaximal, characteristic, complemented
4C113×#3076C211yesmaximal, characteristic, complemented
5C113×#1650C212yesmaximal, complemented
6C113×#1647C212yesmaximal, complemented
7C113×#1638C212yesmaximal, complemented
8C113×#1635C212yesmaximal, complemented
9C2×#332×C113C211yesmaximal, characteristic, complemented
10C113×#1480C211yesmaximal, characteristic, complemented
11C113×#1477C211yesmaximal, characteristic, complemented
12#556×C113C2212yes—
13#555×C113—21no—
14#554×C113—21no—
15#553×C113—22no—
16#548×C113—22no—
17#547×C113C2212yes—
18#542×C113—22no—
19#537×C113—21no—
20#533×C113—21no—
21#533×C113C2211yescharacteristic
22#532×C113—21no—
23#532×C113C2211yescharacteristic
24C2×C4⋊Q8×C113C2211yescharacteristic
25#520×C113—21no—
26C4×#41×C113C2211yescharacteristic
27#500×C113C2212yes—
28#487×C113C2212yes—
29#484×C113—22no—
30#479×C113—21no—
31#478×C113—21no—
32#477×C113—22no—
33#477×C113C2211yescharacteristic
34#476×C113C2211yescharacteristic
35#476×C113C2212yes—
36#475×C113—21no—
37#475×C113C2211yescharacteristic
38#474×C113C2211yescharacteristic
39#465×C113—22no—
40#461×C113C2212yes—
41#460×C113—21no—
42#431×C113C2211yescharacteristic
43#427×C113—21no—
44C2×C4⋊C8×C113C2211yescharacteristic
45C2×C4⋊C8×C113C2211yescharacteristic
46#416×C113—21no—
47#332×C113C2212yes—
48#332×C113C2212yes—
49Q8⋊C8×C113C2212yes—
50D4⋊C8×C113C2212yes—
51D4⋊C8×C113C2212yes—
52D4⋊C8×C113C2212yes—
53C2×#41×C113—22no—
54C2×#41×C113—21no—
55C2×#41×C113D411yescharacteristic
56C22×Q8×C113—21no—
57C2×SD16×C113—22no—
58C22×C8×C113—21no—
59C22×C8×C113—21no—
60C4⋊Q8×C113—21no—
61C4⋊Q8×C113—21no—
62C4⋊Q8×C113D412yes—
63C4⋊Q8×C113D411yescharacteristic
64C4⋊Q8×C113C2311yescharacteristic
65C4⋊Q8×C113C2311yescharacteristic
66C4⋊Q8×C113C2312yes—
67#127×C113D411yescharacteristic
68#126×C113—24no—
69#125×C113—22no—
70#125×C113—21no—
71#124×C113—24no—
72#124×C113—22no—
73#124×C113—21no—
74#123×C113—24no—
75C22⋊Q8×C113—22no—
76C22⋊Q8×C113—24no—
77C22⋊Q8×C113—22no—
78C22⋊Q8×C113—22no—
79C22⋊Q8×C113—21no—
80C22⋊Q8×C113—21no—
81#121×C113—22no—
82#121×C113—22no—
83#121×C113—24no—
84#121×C113—22no—
85#121×C113—21no—
86#121×C113D412yes—
87C4×Q8×C113—22no—
88C4×Q8×C113—22no—
89C4×Q8×C113—21no—
90C4×Q8×C113—21no—
91C4×Q8×C113D411yescharacteristic
92C4×Q8×C113C2311yescharacteristic
93C4×D4×C113—22no—
94C4×D4×C113—24no—
95C4×D4×C113—22no—
96C4×D4×C113—21no—
97C4×D4×C113—21no—
98C4×D4×C113—21no—
99C4×D4×C113D411yescharacteristic
100C4×D4×C113C2311yescharacteristic
101C4×D4×C113C2312yes—
102#117×C113—22no—
103#117×C113—22no—
104#117×C113—21no—
105#117×C113—21no—
106#117×C113D411yescharacteristic
107C2×C4⋊C4×C113—21no—
108C2×C4⋊C4×C113—22no—
109C2×C4⋊C4×C113D412yes—
110C2×C42×C113—21no—
111C2×C42×C113C2311yescharacteristic
112#107×C113—21no—
113#107×C113—21no—
114#107×C113—24no—
115#106×C113—21no—
116#106×C113—21no—
117#106×C113—22no—
118C4⋊C8×C113—21no—
119C4⋊C8×C113—21no—
120C4⋊C8×C113—21no—
121C4⋊C8×C113C2311yescharacteristic
122C4⋊C8×C113C2311yescharacteristic
123C4⋊C8×C113C2312yes—
124#103×C113—21no—
125#103×C113—21no—
126#103×C113—22no—
127#103×C113—24no—
128#102×C113—21no—
129#102×C113—21no—
130#102×C113—22no—
131C22⋊C8×C113—21no—
132C4×C8×C113C2312yes—
133#41×C113—22no—
134#41×C113—22no—
135#41×C113—42no—
136#41×C113—42no—
137#41×C113—82no—
138#41×C113—82no—
139C2×Q8×C113—21no—
140C2×Q8×C113—22no—
141C2×Q8×C113—22no—
142C2×Q8×C113—21no—
143C2×Q8×C113—21no—
144C2×Q8×C113—81no—
145C2×Q8×C113—81no—
146C2×Q8×C113C2×D411yescharacteristic
147C2×D4×C113—21no—
148C2×D4×C113—22no—
149C2×D4×C113—24no—
150C2×D4×C113—21no—
151C2×D4×C113—21no—
152C2×D4×C113C2×D411yescharacteristic
153C2×D4×C113C2×D412yes—
154C22×C4×C113—24no—
155C22×C4×C113—22no—
156C22×C4×C113—21no—
157C22×C4×C113—21no—
158C22×C4×C113—21no—
159C22×C4×C113—22no—
160C22×C4×C113C2×D411yescharacteristic
161C22×C4×C113C2×D411yescharacteristic
162C22×C4×C113C2×D411yescharacteristic
163SD16×C113—82no—
164C2×C8×C113—22no—
165C2×C8×C113—21no—
166C2×C8×C113—22no—
167C2×C8×C113—21no—
168C2×C8×C113—42no—
169C2×C8×C113—81no—
170C4⋊C4×C113—24no—
171C4⋊C4×C113—24no—
172C4⋊C4×C113—22no—
173C4⋊C4×C113—22no—
174C4⋊C4×C113—21no—
175C4⋊C4×C113—21no—
176C4⋊C4×C113—22no—
177C4⋊C4×C113—21no—
178C4⋊C4×C113—21no—
179C4⋊C4×C113—21no—
180C4⋊C4×C113—21no—
181C4⋊C4×C113—21no—
182C4⋊C4×C113—41no—
183C4⋊C4×C113—41no—
184C4⋊C4×C113C2×D412yes—
185C4⋊C4×C113C2×D414yes—
186C4⋊C4×C113C2×D411yescharacteristic
187C4⋊C4×C113C2×D411yescharacteristic
188C22⋊C4×C113—24no—
189C22⋊C4×C113—24no—
190C22⋊C4×C113—24no—
191C22⋊C4×C113—21no—
192C22⋊C4×C113—21no—
193C22⋊C4×C113—22no—
194C22⋊C4×C113—21no—
195C22⋊C4×C113—22no—
196C22⋊C4×C113—41no—
197C42×C113—24no—
198C42×C113—21no—
199C42×C113—21no—
200C42×C113—21no—
201C42×C113—41no—
202C42×C113C2×D411yescharacteristic
203C42×C113C2×D411yescharacteristic
204C42×C113C2×D411yescharacteristic
205C42×C113C2411yescharacteristic
206C23×C113—21no—
207C23×C113—22no—
208C23×C113#12011yescharacteristic
209Q8×C113—21no—
210Q8×C113—21no—
211Q8×C113—42no—
212Q8×C113—42no—
213Q8×C113—42no—
214Q8×C113—42no—
215Q8×C113—41no—
216Q8×C113—41no—
217Q8×C113—82no—
218D4×C113—21no—
219D4×C113—21no—
220D4×C113—22no—
221D4×C113—22no—
222D4×C113—42no—
223D4×C113—42no—
224D4×C113—44no—
225D4×C113—42no—
226D4×C113—84no—
227C2×C4×C113—21no—
228C2×C4×C113—21no—
229C2×C4×C113—21no—
230C2×C4×C113—21no—
231C2×C4×C113—22no—
232C2×C4×C113—21no—
233C2×C4×C113—24no—
234C2×C4×C113—41no—
235C2×C4×C113—42no—
236C2×C4×C113—42no—
237C2×C4×C113—42no—
238C2×C4×C113—41no—
239C2×C4×C113—41no—
240C2×C4×C113—42no—
241C2×C4×C113—41no—
242C2×C4×C113—41no—
243C2×C4×C113—82no—
244C2×C4×C113—84no—
245C2×C4×C113#12011yescharacteristic
246C2×C4×C113#12011yescharacteristic
247C2×C4×C113#12011yescharacteristic
248C2×C4×C113#13512yes—
249C2×C4×C113#13712yes—
250C2×C4×C113C22×D411yescharacteristic
251C2×C4×C113C22×D411yescharacteristic
252C2×C4×C113C22×D411yescharacteristic
253C8×C113—42no—
254C8×C113—41no—
255C8×C113—41no—
256C8×C113—42no—
257C22×C113—21no—
258C22×C113—21no—
259C22×C113—41no—
260C22×C113—42no—
261C22×C113—41no—
262C22×C113—42no—
263C22×C113—41no—
264C22×C113—42no—
265C22×C113#45212yes—
266C22×C113C2×#12011yescharacteristic
267C4×C113—21no—
268C4×C113—21no—
269C4×C113—21no—
270C4×C113—41no—
271C4×C113—42no—
272C4×C113—41no—
273C4×C113—44no—
274C4×C113—41no—
275C4×C113—81no—
276C4×C113—81no—
277C4×C113#45212yes—
278C4×C113C2×#13511yescharacteristic
279C4×C113C2×#13711yescharacteristic
280C4×C113#57611yescharacteristic
281C4×C113#57711yescharacteristic
282#18889C11311yesmaximal, characteristic, direct product factor, Sylow
283C2×C113—22no—
284C2×C113—81no—
285C2×C113—82no—
286C2×C113C2×#45211yescharacteristic
287C2×C113#301211yescharacteristic
288C2×C113#302011yescharacteristic
289#3511C2×C11311yescharacteristic
290#3246C2×C11311yescharacteristic, complemented
291#3230C2×C11311yescharacteristic, complemented
292#3076C2×C11311yescharacteristic, complemented
293#1650C2×C11312yescomplemented
294#1647C2×C11312yescomplemented
295#1638C2×C11312yescomplemented
296#1635C2×C11312yescomplemented
297C2×#332C2×C11311yescharacteristic, complemented
298#1480C2×C11311yescharacteristic, complemented
299#1477C2×C11311yescharacteristic, complemented
300C113#1888911yescharacteristic, direct product factor, Sylow
301#556C22×C11312yes—
302#555—21no—
303#554—21no—
304#553—22no—
305#548—22no—
306#547C22×C11312yes—
307#542—22no—
308#537—21no—
309#533—21no—
310#533C22×C11311yescharacteristic
311#532—21no—
312#532C22×C11311yescharacteristic
313C2×C4⋊Q8C22×C11311yescharacteristic
314#520—21no—
315C4×#41C22×C11311yescharacteristic
316#500C22×C11312yes—
317#487C22×C11312yes—
318#484—22no—
319#479—21no—
320#478—21no—
321#477—22no—
322#477C22×C11311yescharacteristic
323#476C22×C11311yescharacteristic
324#476C22×C11312yes—
325#475—21no—
326#475C22×C11311yescharacteristic
327#474C22×C11311yescharacteristic
328#465—22no—
329#461C22×C11312yes—
330#460—21no—
331#431C22×C11311yescharacteristic
332#427—21no—
333C2×C4⋊C8C22×C11311yescharacteristic
334C2×C4⋊C8C22×C11311yescharacteristic
335#416—21no—
336#332C22×C11312yes—
337#332C22×C11312yes—
338Q8⋊C8C22×C11312yes—
339D4⋊C8C22×C11312yes—
340D4⋊C8C22×C11312yes—
341D4⋊C8C22×C11312yes—
342C2×#41—22no—
343C2×#41—21no—
344C2×#41D4×C11311yescharacteristic
345C22×Q8—21no—
346C2×SD16—22no—
347C22×C8—21no—
348C22×C8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8D4×C11312yes—
352C4⋊Q8D4×C11311yescharacteristic
353C4⋊Q8C23×C11311yescharacteristic
354C4⋊Q8C23×C11311yescharacteristic
355C4⋊Q8C23×C11312yes—
356#127D4×C11311yescharacteristic
357#126—24no—
358#125—22no—
359#125—21no—
360#124—24no—
361#124—22no—
362#124—21no—
363#123—24no—
364C22⋊Q8—22no—
365C22⋊Q8—24no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370#121—22no—
371#121—22no—
372#121—24no—
373#121—22no—
374#121—21no—
375#121D4×C11312yes—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8D4×C11311yescharacteristic
381C4×Q8C23×C11311yescharacteristic
382C4×D4—22no—
383C4×D4—24no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4D4×C11311yescharacteristic
389C4×D4C23×C11311yescharacteristic
390C4×D4C23×C11312yes—
391#117—22no—
392#117—22no—
393#117—21no—
394#117—21no—
395#117D4×C11311yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4D4×C11312yes—
399C2×C42—21no—
400C2×C42C23×C11311yescharacteristic
401#107—21no—
402#107—21no—
403#107—24no—
404#106—21no—
405#106—21no—
406#106—22no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C11311yescharacteristic
411C4⋊C8C23×C11311yescharacteristic
412C4⋊C8C23×C11312yes—
413#103—21no—
414#103—21no—
415#103—22no—
416#103—24no—
417#102—21no—
418#102—21no—
419#102—22no—
420C22⋊C8—21no—
421C4×C8C23×C11312yes—
422#41—22no—
423#41—22no—
424#41—42no—
425#41—42no—
426#41—82no—
427#41—82no—
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—81no—
434C2×Q8—81no—
435C2×Q8C2×D4×C11311yescharacteristic
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—24no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×D4×C11311yescharacteristic
442C2×D4C2×D4×C11312yes—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4C2×D4×C11311yescharacteristic
450C22×C4C2×D4×C11311yescharacteristic
451C22×C4C2×D4×C11311yescharacteristic
452SD16—82no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—22no—
456C2×C8—21no—
457C2×C8—42no—
458C2×C8—81no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C11312yes—
474C4⋊C4C2×D4×C11314yes—
475C4⋊C4C2×D4×C11311yescharacteristic
476C4⋊C4C2×D4×C11311yescharacteristic
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—22no—
485C22⋊C4—41no—
486C42—24no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—41no—
491C42C2×D4×C11311yescharacteristic
492C42C2×D4×C11311yescharacteristic
493C42C2×D4×C11311yescharacteristic
494C42C24×C11311yescharacteristic
495C23—21no—
496C23—22no—
497C23#120×C11311yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—42no—
501Q8—42no—
502Q8—42no—
503Q8—42no—
504Q8—41no—
505Q8—41no—
506Q8—82no—
507D4—21no—
508D4—21no—
509D4—22no—
510D4—22no—
511D4—42no—
512D4—42no—
513D4—44no—
514D4—42no—
515D4—84no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—24no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4—84no—
534C2×C4#120×C11311yescharacteristic
535C2×C4#120×C11311yescharacteristic
536C2×C4#120×C11311yescharacteristic
537C2×C4#135×C11312yes—
538C2×C4#137×C11312yes—
539C2×C4C22×D4×C11311yescharacteristic
540C2×C4C22×D4×C11311yescharacteristic
541C2×C4C22×D4×C11311yescharacteristic
542C8—42no—
543C8—41no—
544C8—41no—
545C8—42no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—42no—
550C22—41no—
551C22—42no—
552C22—41no—
553C22—42no—
554C22#452×C11312yes—
555C22C2×#120×C11311yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—42no—
561C4—41no—
562C4—44no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4#452×C11312yes—
567C4C2×#135×C11311yescharacteristic
568C4C2×#137×C11311yescharacteristic
569C4#576×C11311yescharacteristic
570C4#577×C11311yescharacteristic
571C2—22no—
572C2—81no—
573C2—82no—
574C2C2×#452×C11311yescharacteristic
575C2C113×#301211yescharacteristic
576C2C113×#302011yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3511C2
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×#3246C2semidirect
3. C113×#3230C2semidirect
4. C113×#3076C2semidirect
5. C113×#1650C2semidirect
6. C113×#1647C2semidirect
7. C113×#1638C2semidirect
8. C113×#1635C2semidirect
9. C2×#332×C113C2semidirect
10. C113×#1480C2semidirect
11. C113×#1477C2semidirect
282. #18889C113direct (N × H)
290. #3246C2×C113semidirect
291. #3230C2×C113semidirect
292. #3076C2×C113semidirect
293. #1650C2×C113semidirect
294. #1647C2×C113semidirect
295. #1638C2×C113semidirect
296. #1635C2×C113semidirect
297. C2×#332C2×C113semidirect
298. #1480C2×C113semidirect
299. #1477C2×C113semidirect
300. C113#18889direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35112
C113×#32462
C113×#32302
C113×#30762
C113×#16502
C113×#16472
C113×#16382
C113×#16352
C2×#332×C1132
C113×#14802
C113×#14772
#18889113