Finite Group Databasebeta

← C113×#24117 #43292137

Subgroups — C113×#24117 #43292137

Order 28928.

1238 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C113C211yesmaximal, characteristic, complemented
2C2×#476×C113C211yesmaximal, characteristic, complemented
3C2×C4×D8×C113C211yesmaximal, characteristic, complemented
4C113×#2537C211yesmaximal, characteristic, complemented
5C113×#2034C212yesmaximal, complemented
6C113×#1999C212yesmaximal, complemented
7C113×#1990C211yesmaximal, characteristic, complemented
8C113×#1954C211yesmaximal, characteristic, complemented
9C113×#1875C212yesmaximal, complemented
10C113×#1854C212yesmaximal, complemented
11C113×#1802C211yesmaximal, characteristic, complemented
12C22×D8×C113C2211yescharacteristic
13#555×C113—24no—
14#555×C113—24no—
15C2×C4⋊Q8×C113C2211yescharacteristic
16C2×#124×C113—22no—
17C2×#121×C113—21no—
18C2×#121×C113—21no—
19C2×#121×C113C2212yes—
20C2×#121×C113C2212yes—
21C2×C4×D4×C113C2211yescharacteristic
22C2×C4×D4×C113C2211yescharacteristic
23C2×C4×D4×C113C2211yescharacteristic
24C2×#117×C113—21no—
25C2×#117×C113C2212yes—
26#476×C113—24no—
27C4×D8×C113—24no—
28C2×#107×C113C2211yescharacteristic
29C2×#106×C113C2212yes—
30C2×C4⋊C8×C113C2211yescharacteristic
31C2×#102×C113C2211yescharacteristic
32C2×#102×C113C2212yes—
33C2×#102×C113C2211yescharacteristic
34C2×#102×C113C2212yes—
35C2×C22⋊C8×C113C2212yes—
36C2×C22⋊C8×C113C2212yes—
37C2×C4×C8×C113C2211yescharacteristic
38#394×C113—22no—
39#384×C113C2211yescharacteristic
40#380×C113—21no—
41#380×C113C2212yes—
42#340×C113C2212yes—
43#340×C113C2212yes—
44#340×C113C2212yes—
45C22×Q8×C113—21no—
46C22×D4×C113—22no—
47C22×D4×C113—22no—
48C22×D4×C113D411yescharacteristic
49C22×D4×C113C2311yescharacteristic
50C22×D4×C113C2311yescharacteristic
51C23×C4×C113—21no—
52C23×C4×C113—21no—
53C23×C4×C113C2312yes—
54C2×D8×C113—22no—
55C2×D8×C113—22no—
56C2×D8×C113—22no—
57C22×C8×C113C2311yescharacteristic
58C22×C8×C113C2312yes—
59C22×C8×C113C2311yescharacteristic
60C4⋊Q8×C113—22no—
61C4⋊Q8×C113D414yescomplemented
62#124×C113—216no—
63#121×C113—28no—
64#121×C113—24no—
65#121×C113—24no—
66#121×C113—24no—
67#121×C113—42no—
68#121×C113—44no—
69C4×D4×C113—22no—
70C4×D4×C113—22no—
71C4×D4×C113—22no—
72C4×D4×C113—22no—
73C4×D4×C113—22no—
74C4×D4×C113D414yescomplemented
75#117×C113—28no—
76#117×C113—24no—
77#117×C113—24no—
78C2×C4⋊C4×C113—21no—
79C2×C4⋊C4×C113—21no—
80C2×C4⋊C4×C113—21no—
81C2×C4⋊C4×C113D411yescharacteristic
82C2×C4⋊C4×C113C2311yescharacteristic
83C2×C4⋊C4×C113C2312yes—
84C2×C4⋊C4×C113C2311yescharacteristic
85C2×C4⋊C4×C113C2312yes—
86C2×C22⋊C4×C113—22no—
87C2×C22⋊C4×C113—22no—
88C2×C22⋊C4×C113—21no—
89C2×C22⋊C4×C113—22no—
90C2×C22⋊C4×C113—21no—
91C2×C22⋊C4×C113—22no—
92C2×C22⋊C4×C113D412yes—
93C2×C42×C113—22no—
94C2×C42×C113C2311yescharacteristic
95#107×C113—22no—
96#106×C113—24no—
97C4⋊C8×C113—22no—
98#102×C113—22no—
99#102×C113—22no—
100#102×C113—24no—
101#102×C113—42no—
102C22⋊C8×C113—24no—
103C22⋊C8×C113—42no—
104C4×C8×C113—22no—
105#95×C113—22no—
106C24×C113—21no—
107C24×C113—21no—
108C24×C113C2×D412yes—
109C2×Q8×C113—24no—
110C2×Q8×C113—81no—
111C2×Q8×C113—81no—
112C2×D4×C113—28no—
113C2×D4×C113—22no—
114C2×D4×C113—22no—
115C2×D4×C113—22no—
116C2×D4×C113—21no—
117C2×D4×C113—21no—
118C2×D4×C113—21no—
119C2×D4×C113—21no—
120C2×D4×C113—21no—
121C2×D4×C113—21no—
122C2×D4×C113—21no—
123C2×D4×C113—21no—
124C2×D4×C113—21no—
125C2×D4×C113—21no—
126C2×D4×C113—44no—
127C2×D4×C113—44no—
128C2×D4×C113—82no—
129C2×D4×C113—82no—
130C2×D4×C113—82no—
131C2×D4×C113C2×D412yes—
132C2×D4×C113#4112yes—
133C22×C4×C113—21no—
134C22×C4×C113—22no—
135C22×C4×C113—24no—
136C22×C4×C113—22no—
137C22×C4×C113—22no—
138C22×C4×C113—22no—
139C22×C4×C113—22no—
140C22×C4×C113—22no—
141C22×C4×C113—22no—
142C22×C4×C113—21no—
143C22×C4×C113—22no—
144C22×C4×C113—42no—
145C22×C4×C113—42no—
146C22×C4×C113—42no—
147C22×C4×C113—42no—
148C22×C4×C113—42no—
149C22×C4×C113C2×D412yes—
150C22×C4×C113C2×D411yescharacteristic
151C22×C4×C113C2×D411yescharacteristic
152C22×C4×C113C2411yescharacteristic
153D8×C113—28no—
154C2×C8×C113—21no—
155C2×C8×C113—21no—
156C2×C8×C113—21no—
157C2×C8×C113—22no—
158C2×C8×C113—22no—
159C2×C8×C113—21no—
160C2×C8×C113—22no—
161C2×C8×C113—21no—
162C2×C8×C113#4112yes—
163C4⋊C4×C113—24no—
164C4⋊C4×C113—22no—
165C4⋊C4×C113—21no—
166C4⋊C4×C113—22no—
167C4⋊C4×C113—21no—
168C4⋊C4×C113—21no—
169C4⋊C4×C113—22no—
170C4⋊C4×C113—22no—
171C4⋊C4×C113—42no—
172C4⋊C4×C113—81no—
173C4⋊C4×C113C2×D414yes—
174C4⋊C4×C113C2×D412yes—
175C22⋊C4×C113—28no—
176C22⋊C4×C113—28no—
177C22⋊C4×C113—24no—
178C22⋊C4×C113—24no—
179C22⋊C4×C113—44no—
180C22⋊C4×C113—44no—
181C22⋊C4×C113—42no—
182C42×C113—28no—
183C42×C113C2×D412yes—
184C42×C113C2×D412yes—
185C23×C113—22no—
186C23×C113—22no—
187C23×C113—22no—
188C23×C113—22no—
189C23×C113—22no—
190C23×C113—22no—
191C23×C113—22no—
192C23×C113—22no—
193C23×C113—22no—
194C23×C113—41no—
195C23×C113—41no—
196C23×C113—41no—
197C23×C113—41no—
198C23×C113—41no—
199C23×C113—41no—
200C23×C113—41no—
201C23×C113—41no—
202C23×C113—41no—
203C23×C113—41no—
204C23×C113—41no—
205C23×C113—41no—
206C23×C113C22×D411yescharacteristic
207Q8×C113—84no—
208D4×C113—22no—
209D4×C113—22no—
210D4×C113—22no—
211D4×C113—22no—
212D4×C113—41no—
213D4×C113—41no—
214D4×C113—41no—
215D4×C113—41no—
216D4×C113—44no—
217D4×C113—88no—
218D4×C113—88no—
219C2×C4×C113—21no—
220C2×C4×C113—21no—
221C2×C4×C113—22no—
222C2×C4×C113—22no—
223C2×C4×C113—24no—
224C2×C4×C113—22no—
225C2×C4×C113—22no—
226C2×C4×C113—41no—
227C2×C4×C113—41no—
228C2×C4×C113—42no—
229C2×C4×C113—42no—
230C2×C4×C113—42no—
231C2×C4×C113—42no—
232C2×C4×C113—42no—
233C2×C4×C113—42no—
234C2×C4×C113—48no—
235C2×C4×C113—41no—
236C2×C4×C113—42no—
237C2×C4×C113—41no—
238C2×C4×C113—41no—
239C2×C4×C113—42no—
240C2×C4×C113—42no—
241C2×C4×C113—84no—
242C2×C4×C113#12012yes—
243C2×C4×C113#12012yes—
244C2×C4×C113#13512yes—
245C2×C4×C113AGL(1,ℤ/8)12yes—
246C2×C4×C113C22×D411yescharacteristic
247C2×C4×C113C22×D411yescharacteristic
248C2×C4×C113C2×#4111yescharacteristic
249C2×C4×C113C2×#4111yescharacteristic
250C2×C4×C113H(5,𝔽2)11yescharacteristic
251C2×C4×C1132−1+411yescharacteristic
252C8×C113—22no—
253C8×C113—41no—
254C8×C113—42no—
255C22×C113—42no—
256C22×C113—42no—
257C22×C113—42no—
258C22×C113—42no—
259C22×C113—42no—
260C22×C113—42no—
261C22×C113—42no—
262C22×C113—42no—
263C22×C113—42no—
264C22×C113—42no—
265C22×C113—42no—
266C22×C113—42no—
267C22×C113—42no—
268C22×C113—81no—
269C22×C113—81no—
270C22×C113—81no—
271C22×C113—81no—
272C22×C113—81no—
273C22×C113—81no—
274C22×C113—81no—
275C22×C113—81no—
276C22×C113C2×#12011yescharacteristic
277C22×C113#54611yescharacteristic
278C22×C113#54711yescharacteristic
279C22×C113C2×#13511yescharacteristic
280C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C113#57611yescharacteristic
282C22×C113#57711yescharacteristic
283C4×C113—22no—
284C4×C113—42no—
285C4×C113—42no—
286C4×C113—44no—
287C4×C113—81no—
288C4×C113—82no—
289C4×C113#44914yes—
290C4×C113#52511yescharacteristic
291C4×C113#53711yescharacteristic
292C4×C113#54811yescharacteristic
293C4×C113#55011yescharacteristic
294#24117C11311yesmaximal, characteristic, direct product factor, Sylow
295C2×C113—82no—
296C2×C113—82no—
297C2×C113—82no—
298C2×C113#240711yescharacteristic
299C2×C113C2×#44911yescharacteristic
300C2×C113#301211yescharacteristic
301C2×C113#330311yescharacteristic
302C2×C113#332511yescharacteristic
303C2×C113#334111yescharacteristic
304C2×C113#335411yescharacteristic
305C2×#555C2×C11311yescharacteristic, complemented
306C2×#476C2×C11311yescharacteristic, complemented
307C2×C4×D8C2×C11311yescharacteristic, complemented
308#2537C2×C11311yescharacteristic, complemented
309#2034C2×C11312yescomplemented
310#1999C2×C11312yescomplemented
311#1990C2×C11311yescharacteristic, complemented
312#1954C2×C11311yescharacteristic, complemented
313#1875C2×C11312yescomplemented
314#1854C2×C11312yescomplemented
315#1802C2×C11311yescharacteristic, complemented
316C113#2411711yescharacteristic, direct product factor, Sylow
317C22×D8C22×C11311yescharacteristic
318#555—24no—
319#555—24no—
320C2×C4⋊Q8C22×C11311yescharacteristic
321C2×#124—22no—
322C2×#121—21no—
323C2×#121—21no—
324C2×#121C22×C11312yes—
325C2×#121C22×C11312yes—
326C2×C4×D4C22×C11311yescharacteristic
327C2×C4×D4C22×C11311yescharacteristic
328C2×C4×D4C22×C11311yescharacteristic
329C2×#117—21no—
330C2×#117C22×C11312yes—
331#476—24no—
332C4×D8—24no—
333C2×#107C22×C11311yescharacteristic
334C2×#106C22×C11312yes—
335C2×C4⋊C8C22×C11311yescharacteristic
336C2×#102C22×C11311yescharacteristic
337C2×#102C22×C11312yes—
338C2×#102C22×C11311yescharacteristic
339C2×#102C22×C11312yes—
340C2×C22⋊C8C22×C11312yes—
341C2×C22⋊C8C22×C11312yes—
342C2×C4×C8C22×C11311yescharacteristic
343#394—22no—
344#384C22×C11311yescharacteristic
345#380—21no—
346#380C22×C11312yes—
347#340C22×C11312yes—
348#340C22×C11312yes—
349#340C22×C11312yes—
350C22×Q8—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4D4×C11311yescharacteristic
354C22×D4C23×C11311yescharacteristic
355C22×D4C23×C11311yescharacteristic
356C23×C4—21no—
357C23×C4—21no—
358C23×C4C23×C11312yes—
359C2×D8—22no—
360C2×D8—22no—
361C2×D8—22no—
362C22×C8C23×C11311yescharacteristic
363C22×C8C23×C11312yes—
364C22×C8C23×C11311yescharacteristic
365C4⋊Q8—22no—
366C4⋊Q8D4×C11314yescomplemented
367#124—216no—
368#121—28no—
369#121—24no—
370#121—24no—
371#121—24no—
372#121—42no—
373#121—44no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4D4×C11314yescomplemented
380#117—28no—
381#117—24no—
382#117—24no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4D4×C11311yescharacteristic
387C2×C4⋊C4C23×C11311yescharacteristic
388C2×C4⋊C4C23×C11312yes—
389C2×C4⋊C4C23×C11311yescharacteristic
390C2×C4⋊C4C23×C11312yes—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4D4×C11312yes—
398C2×C42—22no—
399C2×C42C23×C11311yescharacteristic
400#107—22no—
401#106—24no—
402C4⋊C8—22no—
403#102—22no—
404#102—22no—
405#102—24no—
406#102—42no—
407C22⋊C8—24no—
408C22⋊C8—42no—
409C4×C8—22no—
410#95—22no—
411C24—21no—
412C24—21no—
413C24C2×D4×C11312yes—
414C2×Q8—24no—
415C2×Q8—81no—
416C2×Q8—81no—
417C2×D4—28no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—82no—
434C2×D4—82no—
435C2×D4—82no—
436C2×D4C2×D4×C11312yes—
437C2×D4#41×C11312yes—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4C2×D4×C11312yes—
455C22×C4C2×D4×C11311yescharacteristic
456C22×C4C2×D4×C11311yescharacteristic
457C22×C4C24×C11311yescharacteristic
458D8—28no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—21no—
465C2×C8—22no—
466C2×C8—21no—
467C2×C8#41×C11312yes—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—42no—
477C4⋊C4—81no—
478C4⋊C4C2×D4×C11314yes—
479C4⋊C4C2×D4×C11312yes—
480C22⋊C4—28no—
481C22⋊C4—28no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—44no—
485C22⋊C4—44no—
486C22⋊C4—42no—
487C42—28no—
488C42C2×D4×C11312yes—
489C42C2×D4×C11312yes—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×D4×C11311yescharacteristic
512Q8—84no—
513D4—22no—
514D4—22no—
515D4—22no—
516D4—22no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—44no—
522D4—88no—
523D4—88no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—48no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—84no—
547C2×C4#120×C11312yes—
548C2×C4#120×C11312yes—
549C2×C4#135×C11312yes—
550C2×C4AGL(1,ℤ/8)×C11312yes—
551C2×C4C22×D4×C11311yescharacteristic
552C2×C4C22×D4×C11311yescharacteristic
553C2×C4C2×#41×C11311yescharacteristic
554C2×C4C2×#41×C11311yescharacteristic
555C2×C4H(5,𝔽2)×C11311yescharacteristic
556C2×C42−1+4×C11311yescharacteristic
557C8—22no—
558C8—41no—
559C8—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22C2×#120×C11311yescharacteristic
582C22#546×C11311yescharacteristic
583C22#547×C11311yescharacteristic
584C22C2×#135×C11311yescharacteristic
585C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
586C22#576×C11311yescharacteristic
587C22#577×C11311yescharacteristic
588C4—22no—
589C4—42no—
590C4—42no—
591C4—44no—
592C4—82no—
593C4—81no—
594C4#449×C11314yes—
595C4#525×C11311yescharacteristic
596C4#537×C11311yescharacteristic
597C4#548×C11311yescharacteristic
598C4#550×C11311yescharacteristic
599C2—82no—
600C2—82no—
601C2—82no—
602C2C113×#240711yescharacteristic
603C2C2×#449×C11311yescharacteristic
604C2C113×#301211yescharacteristic
605C2C113×#330311yescharacteristic
606C2C113×#332511yescharacteristic
607C2C113×#334111yescharacteristic
608C2C113×#335411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#555×C113C2semidirect
2. C2×#476×C113C2semidirect
3. C2×C4×D8×C113C2semidirect
4. C113×#2537C2semidirect
5. C113×#2034C2semidirect
6. C113×#1999C2semidirect
7. C113×#1990C2semidirect
8. C113×#1954C2semidirect
9. C113×#1875C2semidirect
10. C113×#1854C2semidirect
11. C113×#1802C2semidirect
61. C4⋊Q8×C113D4semidirect
74. C4×D4×C113D4semidirect
294. #24117C113direct (N × H)
305. C2×#555C2×C113semidirect
306. C2×#476C2×C113semidirect
307. C2×C4×D8C2×C113semidirect
308. #2537C2×C113semidirect
309. #2034C2×C113semidirect
310. #1999C2×C113semidirect
311. #1990C2×C113semidirect
312. #1954C2×C113semidirect
313. #1875C2×C113semidirect
314. #1854C2×C113semidirect
315. #1802C2×C113semidirect
316. C113#24117direct (N × H)
366. C4⋊Q8D4×C113semidirect
379. C4×D4D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C1132
C2×#476×C1132
C2×C4×D8×C1132
C113×#25372
C113×#20342
C113×#19992
C113×#19902
C113×#19542
C113×#18752
C113×#18542
C113×#18022
#24117113