Finite Group Databasebeta

← C113×#27083 #43295103

Subgroups — C113×#27083 #43295103

Order 28928.

756 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2512C211yesmaximal, characteristic
2C113×#2365C211yesmaximal, characteristic, complemented
3C113×#2095C211yesmaximal, characteristic, complemented
4C113×#2055C211yesmaximal, characteristic
5C113×#2043C211yesmaximal, characteristic, complemented
6C113×#2013C211yesmaximal, characteristic
7C113×#1973C211yesmaximal, characteristic
8C113×#1928C211yesmaximal, characteristic, complemented
9C113×#1925C211yesmaximal, characteristic
10C113×#1918C211yesmaximal, characteristic, complemented
11C113×#1917C211yesmaximal, characteristic, complemented
12C113×#1880C211yesmaximal, characteristic
13C113×#1880C211yesmaximal, characteristic
14C113×#1803C211yesmaximal, characteristic, complemented
15C113×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C2×C4⋊Q8×C113C2211yescharacteristic
19C2×#126×C113—21no—
20C2×C4×Q8×C113C2211yescharacteristic
21C2×C4×Q8×C113C2211yescharacteristic
22C2×#107×C113C2211yescharacteristic
23C2×#107×C113C2211yescharacteristic
24C2×C4⋊C8×C113C2211yescharacteristic
25C2×#103×C113C2211yescharacteristic
26C2×#103×C113C2211yescharacteristic
27C2×#103×C113C2211yescharacteristic
28C2×#103×C113C2211yescharacteristic
29C2×#103×C113C2211yescharacteristic
30C2×#103×C113C2211yescharacteristic
31C2×#102×C113C2211yescharacteristic
32C2×#102×C113C2211yescharacteristic
33C2×#97×C113C2211yescharacteristic
34#397×C113—21no—
35#396×C113—21no—
36#391×C113C2211yescharacteristic
37#391×C113C2211yescharacteristic
38#390×C113C2211yescharacteristic
39#390×C113C2211yescharacteristic
40#390×C113C2211yescharacteristic
41#389×C113—21no—
42#389×C113C2211yescharacteristic
43#388×C113—21no—
44#387×C113—21no—
45#387×C113—21no—
46#384×C113C2211yescharacteristic
47C4×C4⋊C4×C113—21no—
48C4×C4⋊C4×C113C2211yescharacteristic
49C4×C4⋊C4×C113C2211yescharacteristic
50C4×C4⋊C4×C113C2211yescharacteristic
51#340×C113C2211yescharacteristic
52#340×C113C2211yescharacteristic
53#340×C113C2211yescharacteristic
54#340×C113C2211yescharacteristic
55#336×C113C2211yescharacteristic
56#336×C113C2211yescharacteristic
57#336×C113C2211yescharacteristic
58#336×C113C2211yescharacteristic
59C22×Q8×C113C2311yescharacteristic
60C22×Q8×C113C2311yescharacteristic
61C22×D4×C113C2311yescharacteristic
62C2×SD16×C113—22no—
63C2×SD16×C113—22no—
64C2×SD16×C113—22no—
65C2×SD16×C113—41no—
66C2×SD16×C113—41no—
67C2×SD16×C113—41no—
68C22×C8×C113C2311yescharacteristic
69C22×C8×C113C2311yescharacteristic
70C22×C8×C113C2311yescharacteristic
71C22×C8×C113C2311yescharacteristic
72C4⋊Q8×C113—22no—
73C4⋊Q8×C113—22no—
74#126×C113—44no—
75C4×Q8×C113—22no—
76C4×Q8×C113—22no—
77C4×Q8×C113—41no—
78C4×Q8×C113—41no—
79C2×C4⋊C4×C113—21no—
80C2×C4⋊C4×C113—21no—
81C2×C4⋊C4×C113—21no—
82C2×C4⋊C4×C113—21no—
83C2×C4⋊C4×C113—21no—
84C2×C4⋊C4×C113—21no—
85C2×C4⋊C4×C113—21no—
86C2×C4⋊C4×C113D411yescharacteristic
87C2×C4⋊C4×C113D411yescharacteristic
88C2×C4⋊C4×C113C2311yescharacteristic
89C2×C4⋊C4×C113C2311yescharacteristic
90C2×C4⋊C4×C113C2311yescharacteristic
91C2×C4⋊C4×C113C2311yescharacteristic
92C2×C4⋊C4×C113C2311yescharacteristic
93C2×C22⋊C4×C113—21no—
94C2×C22⋊C4×C113—21no—
95C2×C22⋊C4×C113—21no—
96C2×C22⋊C4×C113—21no—
97C2×C22⋊C4×C113—21no—
98C2×C22⋊C4×C113—21no—
99C2×C42×C113—21no—
100C2×C42×C113—21no—
101C2×C42×C113—21no—
102C2×C42×C113—21no—
103C2×C42×C113C2311yescharacteristic
104C2×C42×C113C2311yescharacteristic
105C2×C42×C113C2311yescharacteristic
106#107×C113—22no—
107#107×C113—41no—
108C4⋊C8×C113—41no—
109#103×C113—22no—
110#103×C113—22no—
111#103×C113—22no—
112#103×C113—41no—
113#103×C113—41no—
114#103×C113—41no—
115#102×C113—22no—
116#102×C113—41no—
117#97×C113—41no—
118#95×C113—21no—
119#95×C113—21no—
120#95×C113—21no—
121#95×C113—21no—
122#95×C113—21no—
123#95×C113—21no—
124#95×C113—21no—
125#95×C113D411yescharacteristic
126#95×C113D411yescharacteristic
127C24×C113—21no—
128C2×Q8×C113—21no—
129C2×Q8×C113—21no—
130C2×Q8×C113—21no—
131C2×Q8×C113—21no—
132C2×Q8×C113—21no—
133C2×Q8×C113—21no—
134C2×Q8×C113—21no—
135C2×Q8×C113—21no—
136C2×Q8×C113—21no—
137C2×Q8×C113—21no—
138C2×Q8×C113#4112yes—
139C2×Q8×C113#4112yes—
140C2×D4×C113—21no—
141C2×D4×C113—21no—
142C2×D4×C113—21no—
143C2×D4×C113—21no—
144C2×D4×C113—21no—
145C2×D4×C113—21no—
146C22×C4×C113—21no—
147C22×C4×C113—21no—
148C22×C4×C113—21no—
149C22×C4×C113—21no—
150C22×C4×C113—21no—
151C22×C4×C113—21no—
152C22×C4×C113—21no—
153C22×C4×C113C2×D411yescharacteristic
154C22×C4×C113C2×D411yescharacteristic
155C22×C4×C113C2×D411yescharacteristic
156C22×C4×C113C2×D411yescharacteristic
157C22×C4×C113C2×D411yescharacteristic
158C22×C4×C113C2×D411yescharacteristic
159C22×C4×C113C2411yescharacteristic
160SD16×C113—44no—
161SD16×C113—44no—
162C2×C8×C113—21no—
163C2×C8×C113—21no—
164C2×C8×C113—21no—
165C2×C8×C113—21no—
166C2×C8×C113—21no—
167C2×C8×C113—21no—
168C2×C8×C113—21no—
169C2×C8×C113—21no—
170C2×C8×C113—21no—
171C2×C8×C113—21no—
172C2×C8×C113—21no—
173C2×C8×C113#4112yes—
174C4⋊C4×C113—24no—
175C4⋊C4×C113—24no—
176C4⋊C4×C113—22no—
177C4⋊C4×C113—22no—
178C4⋊C4×C113—21no—
179C4⋊C4×C113—21no—
180C4⋊C4×C113—21no—
181C4⋊C4×C113—21no—
182C4⋊C4×C113—21no—
183C4⋊C4×C113—21no—
184C4⋊C4×C113—21no—
185C4⋊C4×C113—21no—
186C4⋊C4×C113—21no—
187C4⋊C4×C113—42no—
188C4⋊C4×C113—42no—
189C4⋊C4×C113—42no—
190C4⋊C4×C113—42no—
191C4⋊C4×C113—81no—
192C4⋊C4×C113#4112yes—
193C22⋊C4×C113—42no—
194C22⋊C4×C113—42no—
195C22⋊C4×C113—42no—
196C22⋊C4×C113—42no—
197C22⋊C4×C113—81no—
198C22⋊C4×C113—81no—
199C42×C113—21no—
200C42×C113—21no—
201C42×C113—21no—
202C42×C113—21no—
203C42×C113—21no—
204C42×C113—21no—
205C42×C113—42no—
206C42×C113—42no—
207C42×C113—42no—
208C42×C113—42no—
209C23×C113—41no—
210C23×C113—41no—
211C23×C113—41no—
212C23×C113—41no—
213C23×C113—41no—
214C23×C113—41no—
215C23×C113—41no—
216C23×C113C22×D411yescharacteristic
217Q8×C113—22no—
218Q8×C113—22no—
219Q8×C113—22no—
220Q8×C113—22no—
221Q8×C113—41no—
222Q8×C113—41no—
223Q8×C113—41no—
224Q8×C113—41no—
225D4×C113—41no—
226D4×C113—41no—
227D4×C113—41no—
228D4×C113—41no—
229C2×C4×C113—21no—
230C2×C4×C113—21no—
231C2×C4×C113—21no—
232C2×C4×C113—21no—
233C2×C4×C113—21no—
234C2×C4×C113—22no—
235C2×C4×C113—22no—
236C2×C4×C113—21no—
237C2×C4×C113—21no—
238C2×C4×C113—21no—
239C2×C4×C113—22no—
240C2×C4×C113—21no—
241C2×C4×C113—21no—
242C2×C4×C113—21no—
243C2×C4×C113—21no—
244C2×C4×C113—21no—
245C2×C4×C113—21no—
246C2×C4×C113—21no—
247C2×C4×C113—21no—
248C2×C4×C113—41no—
249C2×C4×C113—41no—
250C2×C4×C113—41no—
251C2×C4×C113—41no—
252C2×C4×C113—41no—
253C2×C4×C113—41no—
254C2×C4×C113—41no—
255C2×C4×C113—41no—
256C2×C4×C113—41no—
257C2×C4×C113—41no—
258C2×C4×C113—41no—
259C2×C4×C113—41no—
260C2×C4×C113—41no—
261C2×C4×C113—41no—
262C2×C4×C113—41no—
263C2×C4×C113—41no—
264C2×C4×C113—41no—
265C2×C4×C113—41no—
266C2×C4×C113AGL(1,ℤ/8)12yes—
267C2×C4×C113#13712yes—
268C2×C4×C113C2×#4111yescharacteristic
269C2×C4×C113C2×#4111yescharacteristic
270C2×C4×C113C2×#4111yescharacteristic
271C2×C4×C113C2×#4111yescharacteristic
272C2×C4×C113H(5,𝔽2)11yescharacteristic
273C2×C4×C113H(5,𝔽2)11yescharacteristic
274C8×C113—22no—
275C8×C113—41no—
276C8×C113—41no—
277C8×C113—41no—
278C22×C113—81no—
279C22×C113—81no—
280C22×C113—81no—
281C22×C113—81no—
282C22×C113—81no—
283C22×C113—81no—
284C22×C113—81no—
285C22×C113#52511yescharacteristic
286C22×C113#54611yescharacteristic
287C22×C113#55011yescharacteristic
288C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C113C2×#13711yescharacteristic
290C22×C113#57711yescharacteristic
291C22×C113#57811yescharacteristic
292C4×C113—22no—
293C4×C113—22no—
294C4×C113—41no—
295C4×C113—41no—
296C4×C113—42no—
297C4×C113—41no—
298C4×C113—42no—
299C4×C113—42no—
300C4×C113—41no—
301C4×C113—81no—
302C4×C113—81no—
303C4×C113—81no—
304C4×C113—81no—
305C4×C113#52911yescharacteristic
306C4×C113#53811yescharacteristic
307C4×C113#55111yescharacteristic
308C4×C113#55311yescharacteristic
309#27083C11311yesmaximal, characteristic, direct product factor, Sylow
310C2×C113—161no—
311C2×C113#246711yescharacteristic
312C2×C113#311211yescharacteristic
313C2×C113#312111yescharacteristic
314C2×C113#332011yescharacteristic
315C2×C113#333011yescharacteristic
316C2×C113#339711yescharacteristic
317C2×C113#339811yescharacteristic
318#2512C2×C11311yescharacteristic
319#2365C2×C11311yescharacteristic, complemented
320#2095C2×C11311yescharacteristic, complemented
321#2055C2×C11311yescharacteristic
322#2043C2×C11311yescharacteristic, complemented
323#2013C2×C11311yescharacteristic
324#1973C2×C11311yescharacteristic
325#1928C2×C11311yescharacteristic, complemented
326#1925C2×C11311yescharacteristic
327#1918C2×C11311yescharacteristic, complemented
328#1917C2×C11311yescharacteristic, complemented
329#1880C2×C11311yescharacteristic
330#1880C2×C11311yescharacteristic
331#1803C2×C11311yescharacteristic, complemented
332#1763C2×C11311yescharacteristic, complemented
333C113#2708311yescharacteristic, direct product factor, Sylow
334C22×SD16C22×C11311yescharacteristic
335C22×SD16C22×C11311yescharacteristic
336C2×C4⋊Q8C22×C11311yescharacteristic
337C2×#126—21no—
338C2×C4×Q8C22×C11311yescharacteristic
339C2×C4×Q8C22×C11311yescharacteristic
340C2×#107C22×C11311yescharacteristic
341C2×#107C22×C11311yescharacteristic
342C2×C4⋊C8C22×C11311yescharacteristic
343C2×#103C22×C11311yescharacteristic
344C2×#103C22×C11311yescharacteristic
345C2×#103C22×C11311yescharacteristic
346C2×#103C22×C11311yescharacteristic
347C2×#103C22×C11311yescharacteristic
348C2×#103C22×C11311yescharacteristic
349C2×#102C22×C11311yescharacteristic
350C2×#102C22×C11311yescharacteristic
351C2×#97C22×C11311yescharacteristic
352#397—21no—
353#396—21no—
354#391C22×C11311yescharacteristic
355#391C22×C11311yescharacteristic
356#390C22×C11311yescharacteristic
357#390C22×C11311yescharacteristic
358#390C22×C11311yescharacteristic
359#389—21no—
360#389C22×C11311yescharacteristic
361#388—21no—
362#387—21no—
363#387—21no—
364#384C22×C11311yescharacteristic
365C4×C4⋊C4—21no—
366C4×C4⋊C4C22×C11311yescharacteristic
367C4×C4⋊C4C22×C11311yescharacteristic
368C4×C4⋊C4C22×C11311yescharacteristic
369#340C22×C11311yescharacteristic
370#340C22×C11311yescharacteristic
371#340C22×C11311yescharacteristic
372#340C22×C11311yescharacteristic
373#336C22×C11311yescharacteristic
374#336C22×C11311yescharacteristic
375#336C22×C11311yescharacteristic
376#336C22×C11311yescharacteristic
377C22×Q8C23×C11311yescharacteristic
378C22×Q8C23×C11311yescharacteristic
379C22×D4C23×C11311yescharacteristic
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—41no—
384C2×SD16—41no—
385C2×SD16—41no—
386C22×C8C23×C11311yescharacteristic
387C22×C8C23×C11311yescharacteristic
388C22×C8C23×C11311yescharacteristic
389C22×C8C23×C11311yescharacteristic
390C4⋊Q8—22no—
391C4⋊Q8—22no—
392#126—44no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—41no—
396C4×Q8—41no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4D4×C11311yescharacteristic
405C2×C4⋊C4D4×C11311yescharacteristic
406C2×C4⋊C4C23×C11311yescharacteristic
407C2×C4⋊C4C23×C11311yescharacteristic
408C2×C4⋊C4C23×C11311yescharacteristic
409C2×C4⋊C4C23×C11311yescharacteristic
410C2×C4⋊C4C23×C11311yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42C23×C11311yescharacteristic
422C2×C42C23×C11311yescharacteristic
423C2×C42C23×C11311yescharacteristic
424#107—22no—
425#107—41no—
426C4⋊C8—41no—
427#103—22no—
428#103—22no—
429#103—22no—
430#103—41no—
431#103—41no—
432#103—41no—
433#102—22no—
434#102—41no—
435#97—41no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95D4×C11311yescharacteristic
444#95D4×C11311yescharacteristic
445C24—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8#41×C11312yes—
457C2×Q8#41×C11312yes—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4C2×D4×C11311yescharacteristic
472C22×C4C2×D4×C11311yescharacteristic
473C22×C4C2×D4×C11311yescharacteristic
474C22×C4C2×D4×C11311yescharacteristic
475C22×C4C2×D4×C11311yescharacteristic
476C22×C4C2×D4×C11311yescharacteristic
477C22×C4C24×C11311yescharacteristic
478SD16—44no—
479SD16—44no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8#41×C11312yes—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—81no—
510C4⋊C4#41×C11312yes—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—81no—
516C22⋊C4—81no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—42no—
525C42—42no—
526C42—42no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C22×D4×C11311yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4AGL(1,ℤ/8)×C11312yes—
585C2×C4#137×C11312yes—
586C2×C4C2×#41×C11311yescharacteristic
587C2×C4C2×#41×C11311yescharacteristic
588C2×C4C2×#41×C11311yescharacteristic
589C2×C4C2×#41×C11311yescharacteristic
590C2×C4H(5,𝔽2)×C11311yescharacteristic
591C2×C4H(5,𝔽2)×C11311yescharacteristic
592C8—22no—
593C8—41no—
594C8—41no—
595C8—41no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22#525×C11311yescharacteristic
604C22#546×C11311yescharacteristic
605C22#550×C11311yescharacteristic
606C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
607C22C2×#137×C11311yescharacteristic
608C22#577×C11311yescharacteristic
609C22#578×C11311yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—41no—
617C4—42no—
618C4—42no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4#529×C11311yescharacteristic
624C4#538×C11311yescharacteristic
625C4#551×C11311yescharacteristic
626C4#553×C11311yescharacteristic
627C2—161no—
628C2C113×#246711yescharacteristic
629C2C113×#311211yescharacteristic
630C2C113×#312111yescharacteristic
631C2C113×#332011yescharacteristic
632C2C113×#333011yescharacteristic
633C2C113×#339711yescharacteristic
634C2C113×#339811yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC22×D4×C113C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C4×C4⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2365C2semidirect
3. C113×#2095C2semidirect
5. C113×#2043C2semidirect
8. C113×#1928C2semidirect
10. C113×#1918C2semidirect
11. C113×#1917C2semidirect
14. C113×#1803C2semidirect
15. C113×#1763C2semidirect
309. #27083C113direct (N × H)
319. #2365C2×C113semidirect
320. #2095C2×C113semidirect
322. #2043C2×C113semidirect
325. #1928C2×C113semidirect
327. #1918C2×C113semidirect
328. #1917C2×C113semidirect
331. #1803C2×C113semidirect
332. #1763C2×C113semidirect
333. C113#27083direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#25122
C113×#23652
C113×#20952
C113×#20552
C113×#20432
C113×#20132
C113×#19732
C113×#19282
C113×#19252
C113×#19182
C113×#19172
C113×#18802
C113×#18032
C113×#17632
#27083113