Finite Group Databasebeta

← C113×#24464 #43292484

Subgroups — C113×#24464 #43292484

Order 28928.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3488C211yesmaximal, characteristic, complemented
2C113×#3055C211yesmaximal, characteristic, complemented
3C2×#453×C113C211yesmaximal, characteristic, complemented
4C113×#3006C211yesmaximal, characteristic, complemented
5C22×#104×C113C211yesmaximal, characteristic, complemented
6C113×#2856C211yesmaximal, characteristic, complemented
7C113×#2039C211yesmaximal, characteristic, complemented
8C113×#2037C211yesmaximal, characteristic, complemented
9C113×#2006C211yesmaximal, characteristic, complemented
10C113×#2002C211yesmaximal, characteristic, complemented
11C113×#1900C211yesmaximal, characteristic, complemented
12C113×#1896C211yesmaximal, characteristic, complemented
13C113×#1883C211yesmaximal, characteristic, complemented
14C113×#1859C211yesmaximal, characteristic, complemented
15C113×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
21C22×M16×C113C2211yescharacteristic, complemented
22#550×C113—21no—
23#548×C113—21no—
24#546×C113—21no—
25#546×C113—22no—
26D42×C113—22no—
27D42×C113—21no—
28#537×C113—21no—
29#537×C113C2211yescharacteristic
30#535×C113—21no—
31#535×C113C2211yescharacteristic
32C2×#127×C113C2211yescharacteristic, complemented
33#525×C113—21no—
34#525×C113C2211yescharacteristic
35C2×#121×C113—21no—
36C2×#121×C113—22no—
37C2×#121×C113C2211yescharacteristic
38C2×#121×C113C2211yescharacteristic, complemented
39#520×C113C2211yescharacteristic
40C22×C42×C113C2211yescharacteristic, complemented
41#469×C113—21no—
42#468×C113—21no—
43#466×C113—21no—
44#465×C113—21no—
45#453×C113—24no—
46#449×C113—21no—
47#449×C113—21no—
48#448×C113—21no—
49#447×C113—21no—
50#428×C113C2211yescharacteristic, complemented
51C2×#104×C113—24no—
52C2×#104×C113C2211yescharacteristic
53C2×#104×C113C2211yescharacteristic
54C2×#104×C113C2211yescharacteristic, complemented
55C2×#104×C113C2211yescharacteristic, complemented
56C2×#104×C113C2211yescharacteristic, complemented
57C2×#104×C113C2211yescharacteristic, complemented
58#418×C113C2211yescharacteristic, complemented
59#417×C113C2211yescharacteristic
60#417×C113C2211yescharacteristic, complemented
61#417×C113C2211yescharacteristic, complemented
62C2×#100×C113C2211yescharacteristic, complemented
63C2×#100×C113C2211yescharacteristic, complemented
64#407×C113C2211yescharacteristic, complemented
65#390×C113—22no—
66#390×C113C2211yescharacteristic, complemented
67#390×C113C2211yescharacteristic, complemented
68#384×C113C2211yescharacteristic, complemented
69#343×C113C2211yescharacteristic, complemented
70#343×C113C2211yescharacteristic, complemented
71#339×C113C2211yescharacteristic, complemented
72#339×C113C2211yescharacteristic, complemented
73H(5,𝔽2)×C113—22no—
74H(5,𝔽2)×C113—22no—
75H(5,𝔽2)×C113—41no—
76H(5,𝔽2)×C113—41no—
77C2×#41×C113—21no—
78C2×#41×C113—21no—
79C2×#41×C113—21no—
80C2×#41×C113—21no—
81C2×#41×C113—22no—
82C2×#41×C113—22no—
83C2×#41×C113—41no—
84C2×#41×C113—41no—
85C2×#41×C113D411yescharacteristic, complemented
86C2×#41×C113D411yescharacteristic, complemented
87C2×#41×C113C2311yescharacteristic
88C2×#41×C113C2311yescharacteristic
89C2×#41×C113C2311yescharacteristic
90C22×Q8×C113D411yescharacteristic, complemented
91C22×D4×C113—21no—
92C22×D4×C113—22no—
93C22×D4×C113—22no—
94C22×D4×C113—21no—
95C22×D4×C113—21no—
96C22×D4×C113—21no—
97C22×D4×C113—22no—
98C22×D4×C113D412yes—
99C22×D4×C113D411yescharacteristic, complemented
100C22×D4×C113C2311yescharacteristic
101C22×D4×C113C2311yescharacteristic
102C23×C4×C113—21no—
103C23×C4×C113—21no—
104C23×C4×C113C2311yescharacteristic
105AGL(1,ℤ/8)×C113—22no—
106AGL(1,ℤ/8)×C113—22no—
107AGL(1,ℤ/8)×C113—22no—
108AGL(1,ℤ/8)×C113—41no—
109AGL(1,ℤ/8)×C113—41no—
110AGL(1,ℤ/8)×C113—41no—
111C2×SD16×C113—21no—
112C2×SD16×C113—21no—
113C2×SD16×C113—21no—
114C2×D8×C113—21no—
115C2×D8×C113—21no—
116C2×D8×C113—21no—
117C2×M16×C113—21no—
118C2×M16×C113—22no—
119C2×M16×C113—41no—
120C2×M16×C113C2311yescharacteristic
121C2×M16×C113C2311yescharacteristic
122C2×M16×C113C2311yescharacteristic
123C2×M16×C113C2311yescharacteristic
124C22×C8×C113—21no—
125#127×C113—22no—
126#127×C113—21no—
127#127×C113—22no—
128#127×C113—41no—
129#124×C113—22no—
130#124×C113—21no—
131#123×C113—22no—
132#123×C113—21no—
133C22⋊Q8×C113—22no—
134C22⋊Q8×C113—21no—
135C22⋊Q8×C113—21no—
136C22⋊Q8×C113D411yescharacteristic, complemented
137C22⋊Q8×C113D411yescharacteristic, complemented
138#121×C113—22no—
139#121×C113—22no—
140#121×C113—22no—
141#121×C113—22no—
142#121×C113—22no—
143#121×C113—21no—
144#121×C113—21no—
145#121×C113—21no—
146#121×C113—21no—
147#121×C113—21no—
148#121×C113—21no—
149#121×C113—22no—
150#121×C113—21no—
151#121×C113—21no—
152#121×C113—21no—
153#121×C113—21no—
154#121×C113—21no—
155#121×C113—21no—
156#121×C113—48no—
157#121×C113D411yescharacteristic, complemented
158#121×C113D411yescharacteristic, complemented
159#120×C113—22no—
160#120×C113—22no—
161#120×C113—22no—
162#120×C113—21no—
163#120×C113—22no—
164C4×Q8×C113—21no—
165C4×D4×C113—22no—
166C4×D4×C113—22no—
167C4×D4×C113—21no—
168C4×D4×C113—22no—
169C4×D4×C113—21no—
170C4×D4×C113—21no—
171#117×C113—21no—
172#117×C113C2311yescharacteristic
173C2×C4⋊C4×C113—21no—
174C2×C4⋊C4×C113—22no—
175C2×C4⋊C4×C113C2311yescharacteristic
176C2×C4⋊C4×C113C2311yescharacteristic
177C2×C22⋊C4×C113—22no—
178C2×C22⋊C4×C113—22no—
179C2×C22⋊C4×C113—22no—
180C2×C22⋊C4×C113—21no—
181C2×C22⋊C4×C113D412yes—
182C2×C42×C113—22no—
183C2×C42×C113—21no—
184C2×C42×C113—41no—
185C2×C42×C113C2311yescharacteristic
186C2×C42×C113C2311yescharacteristic
187#107×C113—21no—
188#106×C113—21no—
189#104×C113—22no—
190#104×C113—22no—
191#104×C113—22no—
192#104×C113—22no—
193#104×C113—41no—
194#104×C113D414yescomplemented
195#103×C113—21no—
196#103×C113—21no—
197#103×C113—21no—
198#102×C113—21no—
199#102×C113—21no—
200#102×C113—21no—
201#102×C113—21no—
202#102×C113—21no—
203#100×C113—22no—
204#100×C113—41no—
205C22⋊C8×C113—21no—
206C22⋊C8×C113—21no—
207C24×C113—22no—
208C24×C113—21no—
209C24×C113—21no—
210C24×C113C2×D411yescharacteristic
211C24×C113C2×D412yes—
212#41×C113—21no—
213#41×C113—21no—
214#41×C113—22no—
215#41×C113—22no—
216#41×C113—21no—
217#41×C113—21no—
218#41×C113—21no—
219#41×C113—21no—
220#41×C113—21no—
221#41×C113—21no—
222#41×C113—21no—
223#41×C113—21no—
224#41×C113—42no—
225#41×C113—42no—
226#41×C113—41no—
227#41×C113—41no—
228#41×C113—42no—
229#41×C113—42no—
230#41×C113—42no—
231#41×C113—42no—
232#41×C113—42no—
233#41×C113—42no—
234#41×C113C2×D412yes—
235#41×C113#4112yes—
236C2×Q8×C113—21no—
237C2×Q8×C113—22no—
238C2×Q8×C113—41no—
239C2×Q8×C113C2×D411yescharacteristic
240C2×Q8×C113C2×D411yescharacteristic
241C2×Q8×C113C2×D411yescharacteristic
242C2×D4×C113—21no—
243C2×D4×C113—22no—
244C2×D4×C113—22no—
245C2×D4×C113—22no—
246C2×D4×C113—22no—
247C2×D4×C113—21no—
248C2×D4×C113—21no—
249C2×D4×C113—21no—
250C2×D4×C113—21no—
251C2×D4×C113—21no—
252C2×D4×C113—22no—
253C2×D4×C113—22no—
254C2×D4×C113—22no—
255C2×D4×C113—21no—
256C2×D4×C113—22no—
257C2×D4×C113—21no—
258C2×D4×C113—21no—
259C2×D4×C113—21no—
260C2×D4×C113—21no—
261C2×D4×C113—21no—
262C2×D4×C113—21no—
263C2×D4×C113—21no—
264C2×D4×C113—21no—
265C2×D4×C113—21no—
266C2×D4×C113—21no—
267C2×D4×C113—21no—
268C2×D4×C113—21no—
269C2×D4×C113—21no—
270C2×D4×C113—41no—
271C2×D4×C113—42no—
272C2×D4×C113—42no—
273C2×D4×C113—44no—
274C2×D4×C113—44no—
275C2×D4×C113—44no—
276C2×D4×C113—42no—
277C2×D4×C113—42no—
278C2×D4×C113—44no—
279C2×D4×C113—44no—
280C2×D4×C113—42no—
281C2×D4×C113—42no—
282C2×D4×C113—44no—
283C2×D4×C113—44no—
284C2×D4×C113—41no—
285C2×D4×C113—41no—
286C2×D4×C113—84no—
287C2×D4×C113C2×D411yescharacteristic
288C2×D4×C113C2×D411yescharacteristic
289C2×D4×C113C2×D411yescharacteristic
290C22×C4×C113—21no—
291C22×C4×C113—21no—
292C22×C4×C113—21no—
293C22×C4×C113—21no—
294C22×C4×C113—21no—
295C22×C4×C113—21no—
296C22×C4×C113—22no—
297C22×C4×C113—24no—
298C22×C4×C113—21no—
299C22×C4×C113—21no—
300C22×C4×C113—22no—
301C22×C4×C113—21no—
302C22×C4×C113—21no—
303C22×C4×C113—21no—
304C22×C4×C113—21no—
305C22×C4×C113—21no—
306C22×C4×C113—42no—
307C22×C4×C113—42no—
308C22×C4×C113—42no—
309C22×C4×C113—42no—
310C22×C4×C113C2×D411yescharacteristic
311C22×C4×C113C2×D411yescharacteristic
312C22×C4×C113C2×D411yescharacteristic
313C22×C4×C113C2×D411yescharacteristic
314C22×C4×C113C2×D411yescharacteristic
315C22×C4×C113C2×D412yes—
316C22×C4×C113C2411yescharacteristic
317SD16×C113—42no—
318SD16×C113—42no—
319SD16×C113—42no—
320D8×C113—42no—
321D8×C113—42no—
322D8×C113—42no—
323M16×C113—21no—
324M16×C113—21no—
325M16×C113—21no—
326M16×C113—21no—
327M16×C113—21no—
328M16×C113—21no—
329M16×C113—21no—
330M16×C113—42no—
331M16×C113C2×D412yescomplemented
332C2×C8×C113—21no—
333C2×C8×C113—21no—
334C2×C8×C113—21no—
335C2×C8×C113—21no—
336C2×C8×C113—42no—
337C4⋊C4×C113—22no—
338C4⋊C4×C113—22no—
339C4⋊C4×C113—21no—
340C4⋊C4×C113—21no—
341C4⋊C4×C113—21no—
342C4⋊C4×C113—21no—
343C4⋊C4×C113—21no—
344C4⋊C4×C113—21no—
345C4⋊C4×C113—44no—
346C4⋊C4×C113C2×D411yescharacteristic
347C4⋊C4×C113C2×D411yescharacteristic
348C22⋊C4×C113—22no—
349C22⋊C4×C113—22no—
350C22⋊C4×C113—22no—
351C22⋊C4×C113—22no—
352C22⋊C4×C113—22no—
353C22⋊C4×C113—21no—
354C22⋊C4×C113—21no—
355C22⋊C4×C113—21no—
356C22⋊C4×C113—21no—
357C22⋊C4×C113—22no—
358C22⋊C4×C113—22no—
359C22⋊C4×C113—21no—
360C22⋊C4×C113—44no—
361C22⋊C4×C113—44no—
362C22⋊C4×C113—41no—
363C22⋊C4×C113—41no—
364C42×C113—22no—
365C42×C113—21no—
366C42×C113—21no—
367C42×C113—21no—
368C42×C113—21no—
369C42×C113—42no—
370C42×C113C2×D412yescomplemented
371C23×C113—21no—
372C23×C113—21no—
373C23×C113—21no—
374C23×C113—22no—
375C23×C113—22no—
376C23×C113—21no—
377C23×C113—21no—
378C23×C113—22no—
379C23×C113—22no—
380C23×C113—41no—
381C23×C113—42no—
382C23×C113—44no—
383C23×C113—42no—
384C23×C113—42no—
385C23×C113—42no—
386C23×C113—42no—
387C23×C113—42no—
388C23×C113—41no—
389C23×C113—41no—
390C23×C113—41no—
391C23×C113—81no—
392C23×C113—82no—
393C23×C113—82no—
394C23×C113#12011yescharacteristic
395C23×C113#12011yescharacteristic
396C23×C113C22×D411yescharacteristic
397Q8×C113—21no—
398Q8×C113—21no—
399Q8×C113—21no—
400Q8×C113—21no—
401Q8×C113—21no—
402Q8×C113—42no—
403Q8×C113#12112yescomplemented
404D4×C113—22no—
405D4×C113—22no—
406D4×C113—21no—
407D4×C113—21no—
408D4×C113—21no—
409D4×C113—21no—
410D4×C113—21no—
411D4×C113—42no—
412D4×C113—42no—
413D4×C113—44no—
414D4×C113—42no—
415D4×C113—44no—
416D4×C113—41no—
417D4×C113—41no—
418D4×C113—41no—
419D4×C113—41no—
420D4×C113—44no—
421D4×C113—42no—
422D4×C113—41no—
423D4×C113—41no—
424D4×C113—41no—
425D4×C113—41no—
426D4×C113—41no—
427D4×C113—41no—
428D4×C113—41no—
429D4×C113—41no—
430D4×C113—88no—
431D4×C113—81no—
432D4×C113—82no—
433D4×C113—82no—
434D4×C113—82no—
435D4×C113—82no—
436D4×C113—82no—
437D4×C113—82no—
438D4×C113#12112yescomplemented
439C2×C4×C113—22no—
440C2×C4×C113—22no—
441C2×C4×C113—21no—
442C2×C4×C113—22no—
443C2×C4×C113—21no—
444C2×C4×C113—21no—
445C2×C4×C113—21no—
446C2×C4×C113—21no—
447C2×C4×C113—21no—
448C2×C4×C113—21no—
449C2×C4×C113—21no—
450C2×C4×C113—21no—
451C2×C4×C113—22no—
452C2×C4×C113—21no—
453C2×C4×C113—21no—
454C2×C4×C113—22no—
455C2×C4×C113—22no—
456C2×C4×C113—21no—
457C2×C4×C113—22no—
458C2×C4×C113—21no—
459C2×C4×C113—21no—
460C2×C4×C113—21no—
461C2×C4×C113—42no—
462C2×C4×C113—42no—
463C2×C4×C113—42no—
464C2×C4×C113—48no—
465C2×C4×C113—44no—
466C2×C4×C113—41no—
467C2×C4×C113—41no—
468C2×C4×C113—41no—
469C2×C4×C113—41no—
470C2×C4×C113—41no—
471C2×C4×C113—41no—
472C2×C4×C113—42no—
473C2×C4×C113—42no—
474C2×C4×C113—41no—
475C2×C4×C113—82no—
476C2×C4×C113#12011yescharacteristic
477C2×C4×C113#12011yescharacteristic
478C2×C4×C113C22×D411yescharacteristic
479C2×C4×C113C22×D411yescharacteristic
480C2×C4×C113C22×D411yescharacteristic
481C2×C4×C113C2×#4111yescharacteristic
482C2×C4×C113H(5,𝔽2)11yescharacteristic
483C2×C4×C113H(5,𝔽2)11yescharacteristic
484C8×C113—22no—
485C8×C113—41no—
486C8×C113—41no—
487C8×C113—41no—
488C22×C113—21no—
489C22×C113—21no—
490C22×C113—21no—
491C22×C113—21no—
492C22×C113—21no—
493C22×C113—22no—
494C22×C113—21no—
495C22×C113—21no—
496C22×C113—42no—
497C22×C113—42no—
498C22×C113—41no—
499C22×C113—41no—
500C22×C113—41no—
501C22×C113—41no—
502C22×C113—42no—
503C22×C113—42no—
504C22×C113—41no—
505C22×C113—41no—
506C22×C113—41no—
507C22×C113—42no—
508C22×C113—41no—
509C22×C113—84no—
510C22×C113—82no—
511C22×C113—82no—
512C22×C113—82no—
513C22×C113—82no—
514C22×C113—81no—
515C22×C113—81no—
516C22×C113—81no—
517C22×C113—164no—
518C22×C113#45312yescomplemented
519C22×C113C2×#12011yescharacteristic
520C22×C113D4211yescharacteristic
521C22×C113#54611yescharacteristic
522C4×C113—24no—
523C4×C113—21no—
524C4×C113—21no—
525C4×C113—22no—
526C4×C113—42no—
527C4×C113—41no—
528C4×C113—41no—
529C4×C113—42no—
530C4×C113—41no—
531C4×C113—41no—
532C4×C113—81no—
533C4×C113C2×#12111yescharacteristic
534C4×C113#53411yescharacteristic
535C4×C113D4211yescharacteristic
536C4×C113#54611yescharacteristic
537#24464C11311yesmaximal, characteristic, direct product factor, Sylow
538C2×C113—21no—
539C2×C113—21no—
540C2×C113—22no—
541C2×C113—41no—
542C2×C113—42no—
543C2×C113—81no—
544C2×C113—82no—
545C2×C113—81no—
546C2×C113—161no—
547C2×C113#241011yescharacteristic
548C2×C113C2×#45311yescharacteristic
549C2×C113#301811yescharacteristic
550#3488C2×C11311yescharacteristic, complemented
551#3055C2×C11311yescharacteristic, complemented
552C2×#453C2×C11311yescharacteristic, complemented
553#3006C2×C11311yescharacteristic, complemented
554C22×#104C2×C11311yescharacteristic, complemented
555#2856C2×C11311yescharacteristic, complemented
556#2039C2×C11311yescharacteristic, complemented
557#2037C2×C11311yescharacteristic, complemented
558#2006C2×C11311yescharacteristic, complemented
559#2002C2×C11311yescharacteristic, complemented
560#1900C2×C11311yescharacteristic, complemented
561#1896C2×C11311yescharacteristic, complemented
562#1883C2×C11311yescharacteristic, complemented
563#1859C2×C11311yescharacteristic, complemented
564#1792C2×C11311yescharacteristic, complemented
565C113#2446411yescharacteristic, direct product factor, Sylow
566C2×H(5,𝔽2)C22×C11311yescharacteristic
567C22×#41C22×C11311yescharacteristic
568C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
569C2×AGL(1,ℤ/8)C22×C11311yescharacteristic, complemented
570C2×AGL(1,ℤ/8)C22×C11311yescharacteristic, complemented
571C22×M16C22×C11311yescharacteristic, complemented
572#550—21no—
573#548—21no—
574#546—21no—
575#546—22no—
576D42—22no—
577D42—21no—
578#537—21no—
579#537C22×C11311yescharacteristic
580#535—21no—
581#535C22×C11311yescharacteristic
582C2×#127C22×C11311yescharacteristic, complemented
583#525—21no—
584#525C22×C11311yescharacteristic
585C2×#121—21no—
586C2×#121—22no—
587C2×#121C22×C11311yescharacteristic
588C2×#121C22×C11311yescharacteristic, complemented
589#520C22×C11311yescharacteristic
590C22×C42C22×C11311yescharacteristic, complemented
591#469—21no—
592#468—21no—
593#466—21no—
594#465—21no—
595#453—24no—
596#449—21no—
597#449—21no—
598#448—21no—
599#447—21no—
600#428C22×C11311yescharacteristic, complemented
601C2×#104—24no—
602C2×#104C22×C11311yescharacteristic
603C2×#104C22×C11311yescharacteristic
604C2×#104C22×C11311yescharacteristic, complemented
605C2×#104C22×C11311yescharacteristic, complemented
606C2×#104C22×C11311yescharacteristic, complemented
607C2×#104C22×C11311yescharacteristic, complemented
608#418C22×C11311yescharacteristic, complemented
609#417C22×C11311yescharacteristic
610#417C22×C11311yescharacteristic, complemented
611#417C22×C11311yescharacteristic, complemented
612C2×#100C22×C11311yescharacteristic, complemented
613C2×#100C22×C11311yescharacteristic, complemented
614#407C22×C11311yescharacteristic, complemented
615#390—22no—
616#390C22×C11311yescharacteristic, complemented
617#390C22×C11311yescharacteristic, complemented
618#384C22×C11311yescharacteristic, complemented
619#343C22×C11311yescharacteristic, complemented
620#343C22×C11311yescharacteristic, complemented
621#339C22×C11311yescharacteristic, complemented
622#339C22×C11311yescharacteristic, complemented
623H(5,𝔽2)—22no—
624H(5,𝔽2)—22no—
625H(5,𝔽2)—41no—
626H(5,𝔽2)—41no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—22no—
632C2×#41—22no—
633C2×#41—41no—
634C2×#41—41no—
635C2×#41D4×C11311yescharacteristic, complemented
636C2×#41D4×C11311yescharacteristic, complemented
637C2×#41C23×C11311yescharacteristic
638C2×#41C23×C11311yescharacteristic
639C2×#41C23×C11311yescharacteristic
640C22×Q8D4×C11311yescharacteristic, complemented
641C22×D4—21no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—21no—
647C22×D4—22no—
648C22×D4D4×C11312yes—
649C22×D4D4×C11311yescharacteristic, complemented
650C22×D4C23×C11311yescharacteristic
651C22×D4C23×C11311yescharacteristic
652C23×C4—21no—
653C23×C4—21no—
654C23×C4C23×C11311yescharacteristic
655AGL(1,ℤ/8)—22no—
656AGL(1,ℤ/8)—22no—
657AGL(1,ℤ/8)—22no—
658AGL(1,ℤ/8)—41no—
659AGL(1,ℤ/8)—41no—
660AGL(1,ℤ/8)—41no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×D8—21no—
665C2×D8—21no—
666C2×D8—21no—
667C2×M16—21no—
668C2×M16—22no—
669C2×M16—41no—
670C2×M16C23×C11311yescharacteristic
671C2×M16C23×C11311yescharacteristic
672C2×M16C23×C11311yescharacteristic
673C2×M16C23×C11311yescharacteristic
674C22×C8—21no—
675#127—22no—
676#127—21no—
677#127—22no—
678#127—41no—
679#124—22no—
680#124—21no—
681#123—22no—
682#123—21no—
683C22⋊Q8—22no—
684C22⋊Q8—21no—
685C22⋊Q8—21no—
686C22⋊Q8D4×C11311yescharacteristic, complemented
687C22⋊Q8D4×C11311yescharacteristic, complemented
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—22no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—21no—
706#121—48no—
707#121D4×C11311yescharacteristic, complemented
708#121D4×C11311yescharacteristic, complemented
709#120—22no—
710#120—22no—
711#120—22no—
712#120—21no—
713#120—22no—
714C4×Q8—21no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—22no—
719C4×D4—21no—
720C4×D4—21no—
721#117—21no—
722#117C23×C11311yescharacteristic
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4C23×C11311yescharacteristic
726C2×C4⋊C4C23×C11311yescharacteristic
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4D4×C11312yes—
732C2×C42—22no—
733C2×C42—21no—
734C2×C42—41no—
735C2×C42C23×C11311yescharacteristic
736C2×C42C23×C11311yescharacteristic
737#107—21no—
738#106—21no—
739#104—22no—
740#104—22no—
741#104—22no—
742#104—22no—
743#104—41no—
744#104D4×C11314yescomplemented
745#103—21no—
746#103—21no—
747#103—21no—
748#102—21no—
749#102—21no—
750#102—21no—
751#102—21no—
752#102—21no—
753#100—22no—
754#100—41no—
755C22⋊C8—21no—
756C22⋊C8—21no—
757C24—22no—
758C24—21no—
759C24—21no—
760C24C2×D4×C11311yescharacteristic
761C24C2×D4×C11312yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41C2×D4×C11312yes—
785#41#41×C11312yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×D4×C11311yescharacteristic
790C2×Q8C2×D4×C11311yescharacteristic
791C2×Q8C2×D4×C11311yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—84no—
837C2×D4C2×D4×C11311yescharacteristic
838C2×D4C2×D4×C11311yescharacteristic
839C2×D4C2×D4×C11311yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4C2×D4×C11311yescharacteristic
861C22×C4C2×D4×C11311yescharacteristic
862C22×C4C2×D4×C11311yescharacteristic
863C22×C4C2×D4×C11311yescharacteristic
864C22×C4C2×D4×C11311yescharacteristic
865C22×C4C2×D4×C11312yes—
866C22×C4C24×C11311yescharacteristic
867SD16—42no—
868SD16—42no—
869SD16—42no—
870D8—42no—
871D8—42no—
872D8—42no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—21no—
880M16—42no—
881M16C2×D4×C11312yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—44no—
896C4⋊C4C2×D4×C11311yescharacteristic
897C4⋊C4C2×D4×C11311yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42C2×D4×C11312yescomplemented
921C23—21no—
922C23—21no—
923C23—21no—
924C23—22no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23#120×C11311yescharacteristic
945C23#120×C11311yescharacteristic
946C23C22×D4×C11311yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8#121×C11312yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—44no—
971D4—42no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—82no—
982D4—81no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4#121×C11312yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4#120×C11311yescharacteristic
1027C2×C4#120×C11311yescharacteristic
1028C2×C4C22×D4×C11311yescharacteristic
1029C2×C4C22×D4×C11311yescharacteristic
1030C2×C4C22×D4×C11311yescharacteristic
1031C2×C4C2×#41×C11311yescharacteristic
1032C2×C4H(5,𝔽2)×C11311yescharacteristic
1033C2×C4H(5,𝔽2)×C11311yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—21no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—41no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22#453×C11312yescomplemented
1069C22C2×#120×C11311yescharacteristic
1070C22D42×C11311yescharacteristic
1071C22#546×C11311yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—42no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×#121×C11311yescharacteristic
1084C4#534×C11311yescharacteristic
1085C4D42×C11311yescharacteristic
1086C4#546×C11311yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2C113×#241011yescharacteristic
1097C2C2×#453×C11311yescharacteristic
1098C2C113×#301811yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3488C2semidirect
2. C113×#3055C2semidirect
3. C2×#453×C113C2semidirect
4. C113×#3006C2semidirect
5. C22×#104×C113C2semidirect
6. C113×#2856C2semidirect
7. C113×#2039C2semidirect
8. C113×#2037C2semidirect
9. C113×#2006C2semidirect
10. C113×#2002C2semidirect
11. C113×#1900C2semidirect
12. C113×#1896C2semidirect
13. C113×#1883C2semidirect
14. C113×#1859C2semidirect
15. C113×#1792C2semidirect
19. C2×AGL(1,ℤ/8)×C113C22semidirect
20. C2×AGL(1,ℤ/8)×C113C22semidirect
21. C22×M16×C113C22semidirect
32. C2×#127×C113C22semidirect
38. C2×#121×C113C22semidirect
40. C22×C42×C113C22semidirect
50. #428×C113C22semidirect
54. C2×#104×C113C22semidirect
55. C2×#104×C113C22semidirect
56. C2×#104×C113C22semidirect
57. C2×#104×C113C22semidirect
58. #418×C113C22semidirect
60. #417×C113C22semidirect
61. #417×C113C22semidirect
62. C2×#100×C113C22semidirect
63. C2×#100×C113C22semidirect
64. #407×C113C22semidirect
66. #390×C113C22semidirect
67. #390×C113C22semidirect
68. #384×C113C22semidirect
69. #343×C113C22semidirect
70. #343×C113C22semidirect
71. #339×C113C22semidirect
72. #339×C113C22semidirect
85. C2×#41×C113D4semidirect
86. C2×#41×C113D4semidirect
90. C22×Q8×C113D4semidirect
99. C22×D4×C113D4semidirect
136. C22⋊Q8×C113D4semidirect
137. C22⋊Q8×C113D4semidirect
157. #121×C113D4semidirect
158. #121×C113D4semidirect
194. #104×C113D4semidirect
331. M16×C113C2×D4semidirect
370. C42×C113C2×D4semidirect
403. Q8×C113#121semidirect
438. D4×C113#121semidirect
518. C22×C113#453semidirect
537. #24464C113direct (N × H)
550. #3488C2×C113semidirect
551. #3055C2×C113semidirect
552. C2×#453C2×C113semidirect
553. #3006C2×C113semidirect
554. C22×#104C2×C113semidirect
555. #2856C2×C113semidirect
556. #2039C2×C113semidirect
557. #2037C2×C113semidirect
558. #2006C2×C113semidirect
559. #2002C2×C113semidirect
560. #1900C2×C113semidirect
561. #1896C2×C113semidirect
562. #1883C2×C113semidirect
563. #1859C2×C113semidirect
564. #1792C2×C113semidirect
565. C113#24464direct (N × H)
569. C2×AGL(1,ℤ/8)C22×C113semidirect
570. C2×AGL(1,ℤ/8)C22×C113semidirect
571. C22×M16C22×C113semidirect
582. C2×#127C22×C113semidirect
588. C2×#121C22×C113semidirect
590. C22×C42C22×C113semidirect
600. #428C22×C113semidirect
604. C2×#104C22×C113semidirect
605. C2×#104C22×C113semidirect
606. C2×#104C22×C113semidirect
607. C2×#104C22×C113semidirect
608. #418C22×C113semidirect
610. #417C22×C113semidirect
611. #417C22×C113semidirect
612. C2×#100C22×C113semidirect
613. C2×#100C22×C113semidirect
614. #407C22×C113semidirect
616. #390C22×C113semidirect
617. #390C22×C113semidirect
618. #384C22×C113semidirect
619. #343C22×C113semidirect
620. #343C22×C113semidirect
621. #339C22×C113semidirect
622. #339C22×C113semidirect
635. C2×#41D4×C113semidirect
636. C2×#41D4×C113semidirect
640. C22×Q8D4×C113semidirect
649. C22×D4D4×C113semidirect
686. C22⋊Q8D4×C113semidirect
687. C22⋊Q8D4×C113semidirect
707. #121D4×C113semidirect
708. #121D4×C113semidirect
744. #104D4×C113semidirect
881. M16C2×D4×C113semidirect
920. C42C2×D4×C113semidirect
953. Q8#121×C113semidirect
988. D4#121×C113semidirect
1068. C22#453×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34882
C113×#30552
C2×#453×C1132
C113×#30062
C22×#104×C1132
C113×#28562
C113×#20392
C113×#20372
C113×#20062
C113×#20022
C113×#19002
C113×#18962
C113×#18832
C113×#18592
C113×#17922
#24464113