Finite Group Databasebeta

← C113×#25625 #43293645

Subgroups — C113×#25625 #43293645

Order 28928.

1172 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3506C211yesmaximal, characteristic, complemented
2C113×#3153C211yesmaximal, characteristic, complemented
3C113×#3140C211yesmaximal, characteristic, complemented
4C113×#2544C211yesmaximal, characteristic, complemented
5C113×#2004C212yesmaximal, complemented
6C113×#2002C212yesmaximal, complemented
7C113×#1986C211yesmaximal, characteristic, complemented
8C113×#1980C211yesmaximal, characteristic, complemented
9C113×#1883C212yesmaximal, complemented
10C113×#1882C212yesmaximal, complemented
11C4×#100×C113C211yesmaximal, characteristic, complemented
12C2×#137×C113C2212yes—
13C2×AGL(1,ℤ/8)×C113C2212yes—
14#559×C113—22no—
15#556×C113—21no—
16#555×C113—21no—
17#553×C113—22no—
18#550×C113—21no—
19#547×C113—21no—
20#538×C113—22no—
21#535×C113C2212yes—
22#533×C113C2211yescharacteristic
23#532×C113C2211yescharacteristic
24C2×#127×C113C2211yescharacteristic
25C2×#124×C113C2211yescharacteristic
26C2×#124×C113C2211yescharacteristic
27#525×C113—22no—
28#520×C113C2212yes—
29C2×C4×D4×C113C2211yescharacteristic
30#497×C113—21no—
31#496×C113—21no—
32#495×C113—22no—
33#489×C113—21no—
34#489×C113—21no—
35#488×C113—22no—
36C2×#104×C113C2212yes—
37C2×#104×C113C2212yes—
38#419×C113C2212yes—
39#418×C113C2212yes—
40C2×#100×C113C2212yes—
41C4×M16×C113C2211yescharacteristic
42C4×M16×C113C2211yescharacteristic
43#394×C113—22no—
44#391×C113C2211yescharacteristic
45#390×C113C2211yescharacteristic
46#386×C113—22no—
47C4×C4⋊C4×C113C2211yescharacteristic
48#343×C113C2212yes—
49#339×C113C2212yes—
50#339×C113C2212yes—
51C2×#41×C113—22no—
52C2×#41×C113C2312yes—
53C22×Q8×C113C2311yescharacteristic
54C22×D4×C113—22no—
55C22×D4×C113C2311yescharacteristic
56C22×D4×C113C2311yescharacteristic
57C23×C4×C113D412yes—
58#137×C113—24no—
59#137×C113—42no—
60AGL(1,ℤ/8)×C113—24no—
61AGL(1,ℤ/8)×C113—42no—
62C2×Q16×C113—22no—
63C2×SD16×C113—22no—
64C2×SD16×C113—22no—
65C2×D8×C113—22no—
66C2×M16×C113C2312yes—
67C2×M16×C113C2312yes—
68C4⋊Q8×C113D411yescharacteristic, complemented
69C4⋊Q8×C113D411yescharacteristic, complemented
70C4⋊Q8×C113D411yescharacteristic, complemented
71#127×C113—22no—
72#127×C113—42no—
73#127×C113D411yescharacteristic, complemented
74#126×C113—24no—
75#125×C113D412yescomplemented
76#124×C113—24no—
77#124×C113—22no—
78#124×C113—21no—
79#124×C113—21no—
80#124×C113—21no—
81#124×C113—21no—
82#124×C113—42no—
83#124×C113D412yescomplemented
84#123×C113—24no—
85#123×C113—24no—
86C22⋊Q8×C113—22no—
87C22⋊Q8×C113—21no—
88C22⋊Q8×C113—21no—
89#121×C113—22no—
90#121×C113—24no—
91#121×C113—21no—
92#121×C113—21no—
93#121×C113—22no—
94#121×C113—22no—
95#120×C113—24no—
96C4×Q8×C113—22no—
97C4×Q8×C113—21no—
98C4×Q8×C113—21no—
99C4×D4×C113—24no—
100C4×D4×C113—22no—
101C4×D4×C113—24no—
102C4×D4×C113—21no—
103C4×D4×C113—21no—
104C4×D4×C113—21no—
105C4×D4×C113—21no—
106C4×D4×C113—21no—
107C4×D4×C113—21no—
108#117×C113—22no—
109#117×C113—22no—
110#117×C113C2312yes—
111C2×C4⋊C4×C113—22no—
112C2×C4⋊C4×C113—21no—
113C2×C4⋊C4×C113C2311yescharacteristic
114C2×C22⋊C4×C113—22no—
115C2×C22⋊C4×C113—21no—
116C2×C22⋊C4×C113—21no—
117C2×C22⋊C4×C113—22no—
118C2×C22⋊C4×C113D412yes—
119C2×C42×C113C2311yescharacteristic
120C2×C42×C113C2311yescharacteristic
121C2×C42×C113C2311yescharacteristic
122#104×C113—42no—
123#104×C113—42no—
124#103×C113—22no—
125#103×C113—22no—
126#102×C113—22no—
127#102×C113—22no—
128#100×C113—24no—
129#97×C113—21no—
130#97×C113—21no—
131C4×C8×C113—21no—
132C4×C8×C113—21no—
133#95×C113—21no—
134#95×C113—22no—
135C24×C113—21no—
136C24×C113C2×D412yes—
137#41×C113—22no—
138#41×C113—22no—
139#41×C113—22no—
140#41×C113—22no—
141#41×C113—84no—
142C2×Q8×C113—21no—
143C2×Q8×C113—21no—
144C2×Q8×C113—21no—
145C2×Q8×C113—21no—
146C2×Q8×C113—22no—
147C2×Q8×C113—22no—
148C2×Q8×C113C2×D412yes—
149C2×D4×C113—22no—
150C2×D4×C113—24no—
151C2×D4×C113—24no—
152C2×D4×C113—21no—
153C2×D4×C113—21no—
154C2×D4×C113—21no—
155C2×D4×C113—21no—
156C2×D4×C113—21no—
157C2×D4×C113—21no—
158C2×D4×C113—22no—
159C2×D4×C113—22no—
160C2×D4×C113—22no—
161C2×D4×C113—22no—
162C2×D4×C113—44no—
163C2×D4×C113—44no—
164C2×D4×C113—82no—
165C2×D4×C113C2×D412yes—
166C22×C4×C113—21no—
167C22×C4×C113—24no—
168C22×C4×C113—22no—
169C22×C4×C113—22no—
170C22×C4×C113—22no—
171C22×C4×C113—21no—
172C22×C4×C113—21no—
173C22×C4×C113—82no—
174C22×C4×C113C2×D412yes—
175C22×C4×C113C2×D411yescharacteristic
176C22×C4×C113C2×D411yescharacteristic
177C22×C4×C113C2411yescharacteristic
178Q16×C113—44no—
179SD16×C113—44no—
180SD16×C113—44no—
181D8×C113—44no—
182M16×C113—22no—
183M16×C113—22no—
184M16×C113—22no—
185M16×C113#4114yescomplemented
186C2×C8×C113—22no—
187C2×C8×C113—22no—
188C4⋊C4×C113—24no—
189C4⋊C4×C113—21no—
190C4⋊C4×C113—21no—
191C4⋊C4×C113—22no—
192C4⋊C4×C113—21no—
193C4⋊C4×C113—22no—
194C4⋊C4×C113—21no—
195C4⋊C4×C113—21no—
196C4⋊C4×C113—21no—
197C4⋊C4×C113—42no—
198C4⋊C4×C113C2×D412yes—
199C4⋊C4×C113C2×D412yes—
200C22⋊C4×C113—24no—
201C22⋊C4×C113—24no—
202C22⋊C4×C113—24no—
203C22⋊C4×C113—22no—
204C22⋊C4×C113—22no—
205C22⋊C4×C113—22no—
206C22⋊C4×C113—22no—
207C22⋊C4×C113—22no—
208C22⋊C4×C113—44no—
209C22⋊C4×C113—41no—
210C22⋊C4×C113—41no—
211C22⋊C4×C113—41no—
212C22⋊C4×C113—41no—
213C22⋊C4×C113—82no—
214C42×C113—24no—
215C42×C113—22no—
216C42×C113—22no—
217C42×C113—22no—
218C42×C113C2×D411yescharacteristic
219C42×C113C2×D411yescharacteristic
220C42×C113C2×D411yescharacteristic
221C42×C113C2×D411yescharacteristic
222C23×C113—22no—
223C23×C113—22no—
224C23×C113—22no—
225C23×C113—22no—
226C23×C113—42no—
227C23×C113—42no—
228C23×C113—42no—
229C23×C113—42no—
230C23×C113—41no—
231C23×C113—41no—
232C23×C113—41no—
233C23×C113C22×D411yescharacteristic
234Q8×C113—22no—
235Q8×C113—22no—
236Q8×C113—42no—
237Q8×C113—42no—
238Q8×C113—42no—
239Q8×C113—81no—
240D4×C113—22no—
241D4×C113—22no—
242D4×C113—42no—
243D4×C113—42no—
244D4×C113—42no—
245D4×C113—42no—
246D4×C113—42no—
247D4×C113—42no—
248D4×C113—42no—
249D4×C113—81no—
250D4×C113—84no—
251D4×C113—84no—
252D4×C113—88no—
253C2×C4×C113—22no—
254C2×C4×C113—22no—
255C2×C4×C113—22no—
256C2×C4×C113—22no—
257C2×C4×C113—22no—
258C2×C4×C113—41no—
259C2×C4×C113—41no—
260C2×C4×C113—44no—
261C2×C4×C113—41no—
262C2×C4×C113—41no—
263C2×C4×C113—42no—
264C2×C4×C113—42no—
265C2×C4×C113—42no—
266C2×C4×C113—41no—
267C2×C4×C113—41no—
268C2×C4×C113—41no—
269C2×C4×C113—41no—
270C2×C4×C113—41no—
271C2×C4×C113—41no—
272C2×C4×C113—82no—
273C2×C4×C113—84no—
274C2×C4×C113#12011yescharacteristic
275C2×C4×C113#12011yescharacteristic
276C2×C4×C113#12011yescharacteristic
277C2×C4×C113#12011yescharacteristic
278C2×C4×C113C22×D411yescharacteristic
279C2×C4×C113C22×D411yescharacteristic
280C2×C4×C113C2×#4112yes—
281C2×C4×C113H(5,𝔽2)12yes—
282C8×C113—24no—
283C8×C113—42no—
284C22×C113—21no—
285C22×C113—21no—
286C22×C113—44no—
287C22×C113—42no—
288C22×C113—42no—
289C22×C113—42no—
290C22×C113—42no—
291C22×C113—42no—
292C22×C113—42no—
293C22×C113—82no—
294C22×C113—82no—
295C22×C113—82no—
296C22×C113—81no—
297C22×C113—81no—
298C22×C113—81no—
299C22×C113C2×#12011yescharacteristic
300C22×C113#53211yescharacteristic
301C22×C113#53511yescharacteristic
302C4×C113—21no—
303C4×C113—21no—
304C4×C113—21no—
305C4×C113—21no—
306C4×C113—42no—
307C4×C113—42no—
308C4×C113—42no—
309C4×C113—42no—
310C4×C113—42no—
311C4×C113—81no—
312C4×C113—81no—
313C4×C113#54612yes—
314C4×C113#55012yes—
315#25625C11311yesmaximal, characteristic, direct product factor, Sylow
316C2×C113—21no—
317C2×C113—21no—
318C2×C113—82no—
319C2×C113—82no—
320C2×C113—161no—
321C2×C113#243111yescharacteristic
322C2×C113#301811yescharacteristic
323C2×C113#301911yescharacteristic
324#3506C2×C11311yescharacteristic, complemented
325#3153C2×C11311yescharacteristic, complemented
326#3140C2×C11311yescharacteristic, complemented
327#2544C2×C11311yescharacteristic, complemented
328#2004C2×C11312yescomplemented
329#2002C2×C11312yescomplemented
330#1986C2×C11311yescharacteristic, complemented
331#1980C2×C11311yescharacteristic, complemented
332#1883C2×C11312yescomplemented
333#1882C2×C11312yescomplemented
334C4×#100C2×C11311yescharacteristic, complemented
335C113#2562511yescharacteristic, direct product factor, Sylow
336C2×#137C22×C11312yes—
337C2×AGL(1,ℤ/8)C22×C11312yes—
338#559—22no—
339#556—21no—
340#555—21no—
341#553—22no—
342#550—21no—
343#547—21no—
344#538—22no—
345#535C22×C11312yes—
346#533C22×C11311yescharacteristic
347#532C22×C11311yescharacteristic
348C2×#127C22×C11311yescharacteristic
349C2×#124C22×C11311yescharacteristic
350C2×#124C22×C11311yescharacteristic
351#525—22no—
352#520C22×C11312yes—
353C2×C4×D4C22×C11311yescharacteristic
354#497—21no—
355#496—21no—
356#495—22no—
357#489—21no—
358#489—21no—
359#488—22no—
360C2×#104C22×C11312yes—
361C2×#104C22×C11312yes—
362#419C22×C11312yes—
363#418C22×C11312yes—
364C2×#100C22×C11312yes—
365C4×M16C22×C11311yescharacteristic
366C4×M16C22×C11311yescharacteristic
367#394—22no—
368#391C22×C11311yescharacteristic
369#390C22×C11311yescharacteristic
370#386—22no—
371C4×C4⋊C4C22×C11311yescharacteristic
372#343C22×C11312yes—
373#339C22×C11312yes—
374#339C22×C11312yes—
375C2×#41—22no—
376C2×#41C23×C11312yes—
377C22×Q8C23×C11311yescharacteristic
378C22×D4—22no—
379C22×D4C23×C11311yescharacteristic
380C22×D4C23×C11311yescharacteristic
381C23×C4D4×C11312yes—
382#137—24no—
383#137—42no—
384AGL(1,ℤ/8)—24no—
385AGL(1,ℤ/8)—42no—
386C2×Q16—22no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×D8—22no—
390C2×M16C23×C11312yes—
391C2×M16C23×C11312yes—
392C4⋊Q8D4×C11311yescharacteristic, complemented
393C4⋊Q8D4×C11311yescharacteristic, complemented
394C4⋊Q8D4×C11311yescharacteristic, complemented
395#127—22no—
396#127—42no—
397#127D4×C11311yescharacteristic, complemented
398#126—24no—
399#125D4×C11312yescomplemented
400#124—24no—
401#124—22no—
402#124—21no—
403#124—21no—
404#124—21no—
405#124—21no—
406#124—42no—
407#124D4×C11312yescomplemented
408#123—24no—
409#123—24no—
410C22⋊Q8—22no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413#121—22no—
414#121—24no—
415#121—21no—
416#121—21no—
417#121—22no—
418#121—22no—
419#120—24no—
420C4×Q8—22no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×D4—24no—
424C4×D4—22no—
425C4×D4—24no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432#117—22no—
433#117—22no—
434#117C23×C11312yes—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4C23×C11311yescharacteristic
438C2×C22⋊C4—22no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4D4×C11312yes—
443C2×C42C23×C11311yescharacteristic
444C2×C42C23×C11311yescharacteristic
445C2×C42C23×C11311yescharacteristic
446#104—42no—
447#104—42no—
448#103—22no—
449#103—22no—
450#102—22no—
451#102—22no—
452#100—24no—
453#97—21no—
454#97—21no—
455C4×C8—21no—
456C4×C8—21no—
457#95—21no—
458#95—22no—
459C24—21no—
460C24C2×D4×C11312yes—
461#41—22no—
462#41—22no—
463#41—22no—
464#41—22no—
465#41—84no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8C2×D4×C11312yes—
473C2×D4—22no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—82no—
489C2×D4C2×D4×C11312yes—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—82no—
498C22×C4C2×D4×C11312yes—
499C22×C4C2×D4×C11311yescharacteristic
500C22×C4C2×D4×C11311yescharacteristic
501C22×C4C24×C11311yescharacteristic
502Q16—44no—
503SD16—44no—
504SD16—44no—
505D8—44no—
506M16—22no—
507M16—22no—
508M16—22no—
509M16#41×C11314yescomplemented
510C2×C8—22no—
511C2×C8—22no—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4C2×D4×C11312yes—
523C4⋊C4C2×D4×C11312yes—
524C22⋊C4—24no—
525C22⋊C4—24no—
526C22⋊C4—24no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—44no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—82no—
538C42—24no—
539C42—22no—
540C42—22no—
541C42—22no—
542C42C2×D4×C11311yescharacteristic
543C42C2×D4×C11311yescharacteristic
544C42C2×D4×C11311yescharacteristic
545C42C2×D4×C11311yescharacteristic
546C23—22no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C22×D4×C11311yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—42no—
561Q8—42no—
562Q8—42no—
563Q8—81no—
564D4—22no—
565D4—22no—
566D4—42no—
567D4—42no—
568D4—42no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—42no—
573D4—81no—
574D4—84no—
575D4—84no—
576D4—88no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—44no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—82no—
597C2×C4—84no—
598C2×C4#120×C11311yescharacteristic
599C2×C4#120×C11311yescharacteristic
600C2×C4#120×C11311yescharacteristic
601C2×C4#120×C11311yescharacteristic
602C2×C4C22×D4×C11311yescharacteristic
603C2×C4C22×D4×C11311yescharacteristic
604C2×C4C2×#41×C11312yes—
605C2×C4H(5,𝔽2)×C11312yes—
606C8—24no—
607C8—42no—
608C22—21no—
609C22—21no—
610C22—44no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—82no—
618C22—82no—
619C22—82no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22C2×#120×C11311yescharacteristic
624C22#532×C11311yescharacteristic
625C22#535×C11311yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—42no—
631C4—42no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4#546×C11312yes—
638C4#550×C11312yes—
639C2—21no—
640C2—21no—
641C2—82no—
642C2—82no—
643C2—161no—
644C2C113×#243111yescharacteristic
645C2C113×#301811yescharacteristic
646C2C113×#301911yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ 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×#3153C2semidirect
3. C113×#3140C2semidirect
4. C113×#2544C2semidirect
5. C113×#2004C2semidirect
6. C113×#2002C2semidirect
7. C113×#1986C2semidirect
8. C113×#1980C2semidirect
9. C113×#1883C2semidirect
10. C113×#1882C2semidirect
11. C4×#100×C113C2semidirect
68. C4⋊Q8×C113D4semidirect
69. C4⋊Q8×C113D4semidirect
70. C4⋊Q8×C113D4semidirect
73. #127×C113D4semidirect
75. #125×C113D4semidirect
83. #124×C113D4semidirect
185. M16×C113#41semidirect
315. #25625C113direct (N × H)
324. #3506C2×C113semidirect
325. #3153C2×C113semidirect
326. #3140C2×C113semidirect
327. #2544C2×C113semidirect
328. #2004C2×C113semidirect
329. #2002C2×C113semidirect
330. #1986C2×C113semidirect
331. #1980C2×C113semidirect
332. #1883C2×C113semidirect
333. #1882C2×C113semidirect
334. C4×#100C2×C113semidirect
335. C113#25625direct (N × H)
392. C4⋊Q8D4×C113semidirect
393. C4⋊Q8D4×C113semidirect
394. C4⋊Q8D4×C113semidirect
397. #127D4×C113semidirect
399. #125D4×C113semidirect
407. #124D4×C113semidirect
509. M16#41×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35062
C113×#31532
C113×#31402
C113×#25442
C113×#20042
C113×#20022
C113×#19862
C113×#19802
C113×#18832
C113×#18822
C4×#100×C1132
#25625113