Finite Group Databasebeta

← C131×#33551 #45719435

Subgroups — C131×#33551 #45719435

Order 33536.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3532×C131C211yesmaximal, characteristic, complemented
2#3026×C131C211yesmaximal, characteristic, complemented
3C2×B(4,𝔽2)×C131C211yesmaximal, characteristic, complemented
4#3019×C131C211yesmaximal, characteristic, complemented
5#2200×C131C212yesmaximal, complemented
6#2199×C131C212yesmaximal, complemented
7#2197×C131C212yesmaximal, complemented
8#2196×C131C212yesmaximal, complemented
9#2127×C131C211yesmaximal, characteristic, complemented
10#2121×C131C211yesmaximal, characteristic, complemented
11C2×AΣL(1,𝔽16)×C131C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C131C2211yescharacteristic, complemented
13#575×C131—21no—
14H(3,𝔽4)×C131C2211yescharacteristic, complemented
15#560×C131—21no—
16#560×C131C2211yescharacteristic, complemented
17#551×C131—21no—
18#551×C131C2211yescharacteristic, complemented
19#546×C131—21no—
20#546×C131—21no—
21#546×C131—21no—
22D42×C131—21no—
23D42×C131C2211yescharacteristic, complemented
24#538×C131—21no—
25#538×C131—21no—
26#538×C131—21no—
27#535×C131—21no—
28#535×C131C2211yescharacteristic
29#534×C131—21no—
30#534×C131—21no—
31#534×C131C2211yescharacteristic
32C2×#120×C131—21no—
33C2×#120×C131—21no—
34C2×#120×C131C2211yescharacteristic
35#458×C131—21no—
36#458×C131C2212yescomplemented
37B(4,𝔽2)×C131—21no—
38B(4,𝔽2)×C131—21no—
39B(4,𝔽2)×C131—21no—
40B(4,𝔽2)×C131C2212yes—
41B(4,𝔽2)×C131C2212yescomplemented
42B(4,𝔽2)×C131C2212yescomplemented
43#455×C131—21no—
44#455×C131C2212yescomplemented
45#453×C131—21no—
46#453×C131C2212yescomplemented
47#421×C131—21no—
48C2×#100×C131C2211yescharacteristic, complemented
49C2×#99×C131—21no—
50C2×#99×C131—21no—
51C2×#99×C131C2211yescharacteristic, complemented
52C2×#99×C131C2211yescharacteristic, complemented
53#354×C131C2212yescomplemented
54#353×C131C2212yescomplemented
55#352×C131C2212yescomplemented
56AΣL(1,𝔽16)×C131C2212yescomplemented
57AΣL(1,𝔽16)×C131C2212yescomplemented
58AΣL(1,𝔽16)×C131C2212yescomplemented
59C25×C131D411yescharacteristic, complemented
60H(5,𝔽2)×C131—21no—
61H(5,𝔽2)×C131—21no—
62H(5,𝔽2)×C131—21no—
63H(5,𝔽2)×C131—42no—
64H(5,𝔽2)×C131C2312yes—
65C2×#41×C131—21no—
66C2×#41×C131—21no—
67C2×#41×C131—41no—
68C2×#41×C131D411yescharacteristic, complemented
69C22×D4×C131—21no—
70C22×D4×C131—21no—
71C22×D4×C131—21no—
72C22×D4×C131—21no—
73C22×D4×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131—21no—
76C22×D4×C131—41no—
77C22×D4×C131—41no—
78C22×D4×C131D411yescharacteristic, complemented
79C22×D4×C131C2311yescharacteristic
80#137×C131—22no—
81#137×C131—41no—
82AGL(1,ℤ/8)×C131—22no—
83AGL(1,ℤ/8)×C131—41no—
84#135×C131—42no—
85C2×M16×C131—21no—
86#127×C131—21no—
87#127×C131D411yescharacteristic, complemented
88#127×C131C2311yescharacteristic
89#126×C131—21no—
90#126×C131—21no—
91#126×C131—21no—
92#126×C131—21no—
93#124×C131—21no—
94#124×C131—21no—
95#124×C131—21no—
96#124×C131—21no—
97#124×C131—21no—
98#124×C131D411yescharacteristic, complemented
99#124×C131C2311yescharacteristic
100#123×C131—21no—
101#123×C131—21no—
102#123×C131—21no—
103#123×C131—21no—
104#123×C131—21no—
105#123×C131—21no—
106#123×C131—21no—
107#123×C131—21no—
108#123×C131—22no—
109#123×C131—41no—
110#123×C131D411yescharacteristic, complemented
111#123×C131C2311yescharacteristic
112C22⋊Q8×C131—21no—
113C22⋊Q8×C131—21no—
114C22⋊Q8×C131—21no—
115#121×C131—21no—
116#121×C131—21no—
117#121×C131—21no—
118#121×C131—21no—
119#121×C131—21no—
120#121×C131—21no—
121#121×C131—21no—
122#121×C131—21no—
123#121×C131—21no—
124#121×C131—21no—
125#121×C131—21no—
126#121×C131—21no—
127#121×C131—21no—
128#121×C131—21no—
129#121×C131—21no—
130#121×C131—42no—
131#120×C131—21no—
132#120×C131—21no—
133#120×C131—21no—
134#120×C131—21no—
135#120×C131—21no—
136#120×C131—21no—
137#120×C131—21no—
138#120×C131—21no—
139#120×C131—21no—
140#120×C131—21no—
141#120×C131—21no—
142#120×C131—21no—
143#120×C131—21no—
144#120×C131—21no—
145#120×C131—22no—
146#120×C131—22no—
147#120×C131—22no—
148#120×C131—42no—
149#120×C131—41no—
150#120×C131D411yescharacteristic, complemented
151#120×C131D411yescharacteristic, complemented
152#120×C131D411yescharacteristic, complemented
153#120×C131C2311yescharacteristic
154#120×C131C2311yescharacteristic
155#120×C131C2311yescharacteristic
156C4×D4×C131—21no—
157C4×D4×C131—21no—
158C4×D4×C131—21no—
159C4×D4×C131—21no—
160C4×D4×C131—21no—
161C4×D4×C131—21no—
162#117×C131—21no—
163#117×C131D411yescharacteristic, complemented
164C2×C22⋊C4×C131—21no—
165C2×C22⋊C4×C131—21no—
166C2×C22⋊C4×C131—21no—
167C2×C22⋊C4×C131—21no—
168C2×C22⋊C4×C131—21no—
169C2×C22⋊C4×C131—21no—
170C2×C22⋊C4×C131—21no—
171C2×C22⋊C4×C131—41no—
172C2×C22⋊C4×C131D411yescharacteristic, complemented
173C2×C22⋊C4×C131D411yescharacteristic, complemented
174#104×C131—22no—
175#104×C131—22no—
176#100×C131—21no—
177#100×C131C2312yes—
178#99×C131—21no—
179#99×C131—21no—
180#99×C131—22no—
181#99×C131—22no—
182#99×C131—22no—
183#99×C131—22no—
184#99×C131C2312yes—
185#99×C131C2312yes—
186C24×C131—21no—
187C24×C131—21no—
188C24×C131—21no—
189C24×C131—21no—
190C24×C131—21no—
191C24×C131—41no—
192C24×C131—41no—
193C24×C131—82no—
194C24×C131C2×D411yescharacteristic
195C24×C131C2×D411yescharacteristic
196C24×C131C2×D411yescharacteristic
197C24×C131C2×D411yescharacteristic
198C24×C131C2×D411yescharacteristic, complemented
199#41×C131—22no—
200#41×C131—22no—
201#41×C131—42no—
202#41×C131—41no—
203#41×C131—42no—
204#41×C131—42no—
205#41×C131—41no—
206#41×C131—41no—
207#41×C131—42no—
208#41×C131—41no—
209#41×C131—82no—
210C2×Q8×C131—21no—
211C2×Q8×C131—21no—
212C2×Q8×C131C2×D411yescharacteristic, complemented
213C2×D4×C131—21no—
214C2×D4×C131—21no—
215C2×D4×C131—21no—
216C2×D4×C131—22no—
217C2×D4×C131—22no—
218C2×D4×C131—21no—
219C2×D4×C131—21no—
220C2×D4×C131—21no—
221C2×D4×C131—22no—
222C2×D4×C131—22no—
223C2×D4×C131—21no—
224C2×D4×C131—21no—
225C2×D4×C131—21no—
226C2×D4×C131—21no—
227C2×D4×C131—21no—
228C2×D4×C131—21no—
229C2×D4×C131—21no—
230C2×D4×C131—21no—
231C2×D4×C131—21no—
232C2×D4×C131—21no—
233C2×D4×C131—21no—
234C2×D4×C131—21no—
235C2×D4×C131—21no—
236C2×D4×C131—21no—
237C2×D4×C131—21no—
238C2×D4×C131—41no—
239C2×D4×C131—41no—
240C2×D4×C131—42no—
241C2×D4×C131—42no—
242C2×D4×C131—41no—
243C2×D4×C131—41no—
244C2×D4×C131—41no—
245C2×D4×C131—41no—
246C2×D4×C131—42no—
247C2×D4×C131—42no—
248C2×D4×C131—41no—
249C2×D4×C131—41no—
250C2×D4×C131—41no—
251C2×D4×C131—41no—
252C2×D4×C131—41no—
253C2×D4×C131—42no—
254C2×D4×C131—42no—
255C2×D4×C131—42no—
256C2×D4×C131—82no—
257C2×D4×C131—82no—
258C2×D4×C131—82no—
259C2×D4×C131—82no—
260C2×D4×C131—81no—
261C2×D4×C131—81no—
262C2×D4×C131—84no—
263C2×D4×C131C2×D411yescharacteristic
264C2×D4×C131C2×D411yescharacteristic
265C2×D4×C131C2×D411yescharacteristic
266C2×D4×C131C2×D411yescharacteristic, complemented
267C2×D4×C131C2411yescharacteristic
268C22×C4×C131—21no—
269C22×C4×C131—21no—
270C22×C4×C131—21no—
271C22×C4×C131—21no—
272C22×C4×C131—21no—
273C22×C4×C131—21no—
274C22×C4×C131—21no—
275C22×C4×C131—21no—
276C22×C4×C131—21no—
277C22×C4×C131—21no—
278C22×C4×C131—41no—
279C22×C4×C131—41no—
280C22×C4×C131—41no—
281C22×C4×C131C2×D411yescharacteristic
282C22×C4×C131C2×D411yescharacteristic, complemented
283Q16×C131—42no—
284SD16×C131—42no—
285SD16×C131—42no—
286D8×C131—42no—
287M16×C131—22no—
288M16×C131—41no—
289C2×C8×C131—41no—
290C4⋊C4×C131—21no—
291C4⋊C4×C131—21no—
292C4⋊C4×C131—21no—
293C4⋊C4×C131—21no—
294C4⋊C4×C131—21no—
295C4⋊C4×C131—21no—
296C4⋊C4×C131—21no—
297C4⋊C4×C131—21no—
298C4⋊C4×C131—21no—
299C4⋊C4×C131—42no—
300C22⋊C4×C131—21no—
301C22⋊C4×C131—21no—
302C22⋊C4×C131—21no—
303C22⋊C4×C131—21no—
304C22⋊C4×C131—21no—
305C22⋊C4×C131—21no—
306C22⋊C4×C131—21no—
307C22⋊C4×C131—21no—
308C22⋊C4×C131—21no—
309C22⋊C4×C131—21no—
310C22⋊C4×C131—21no—
311C22⋊C4×C131—21no—
312C22⋊C4×C131—21no—
313C22⋊C4×C131—21no—
314C22⋊C4×C131—21no—
315C22⋊C4×C131—21no—
316C22⋊C4×C131—21no—
317C22⋊C4×C131—21no—
318C22⋊C4×C131—21no—
319C22⋊C4×C131—21no—
320C22⋊C4×C131—21no—
321C22⋊C4×C131—21no—
322C22⋊C4×C131—21no—
323C22⋊C4×C131—21no—
324C22⋊C4×C131—21no—
325C22⋊C4×C131—22no—
326C22⋊C4×C131—22no—
327C22⋊C4×C131—42no—
328C22⋊C4×C131—42no—
329C22⋊C4×C131—42no—
330C22⋊C4×C131—41no—
331C22⋊C4×C131—41no—
332C22⋊C4×C131—42no—
333C22⋊C4×C131C2×D411yescharacteristic
334C22⋊C4×C131C2×D411yescharacteristic
335C22⋊C4×C131C2×D411yescharacteristic, complemented
336C22⋊C4×C131C2×D411yescharacteristic, complemented
337C42×C131—21no—
338C42×C131—21no—
339C42×C131C2×D411yescharacteristic, complemented
340C42×C131C2×D411yescharacteristic, complemented
341C23×C131—21no—
342C23×C131—21no—
343C23×C131—21no—
344C23×C131—21no—
345C23×C131—21no—
346C23×C131—22no—
347C23×C131—22no—
348C23×C131—21no—
349C23×C131—21no—
350C23×C131—21no—
351C23×C131—41no—
352C23×C131—41no—
353C23×C131—42no—
354C23×C131—42no—
355C23×C131—42no—
356C23×C131—41no—
357C23×C131—41no—
358C23×C131—42no—
359C23×C131—41no—
360C23×C131—44no—
361C23×C131—41no—
362C23×C131—41no—
363C23×C131—41no—
364C23×C131—81no—
365C23×C131—81no—
366C23×C131—81no—
367C23×C131—81no—
368C23×C131—81no—
369C23×C131—81no—
370C23×C131—81no—
371C23×C131—81no—
372C23×C131—81no—
373C23×C131—82no—
374C23×C131—82no—
375C23×C131—82no—
376C23×C131—82no—
377C23×C131—161no—
378C23×C131#12011yescharacteristic
379C23×C131#12011yescharacteristic
380C23×C131#12011yescharacteristic
381C23×C131C22×D411yescharacteristic
382C23×C131C22×D411yescharacteristic
383Q8×C131—22no—
384Q8×C131—41no—
385Q8×C131—41no—
386Q8×C131—81no—
387D4×C131—22no—
388D4×C131—41no—
389D4×C131—41no—
390D4×C131—41no—
391D4×C131—41no—
392D4×C131—41no—
393D4×C131—41no—
394D4×C131—42no—
395D4×C131—42no—
396D4×C131—42no—
397D4×C131—42no—
398D4×C131—42no—
399D4×C131—42no—
400D4×C131—42no—
401D4×C131—42no—
402D4×C131—42no—
403D4×C131—42no—
404D4×C131—41no—
405D4×C131—41no—
406D4×C131—41no—
407D4×C131—41no—
408D4×C131—81no—
409D4×C131—81no—
410D4×C131—81no—
411D4×C131—81no—
412D4×C131—81no—
413D4×C131—81no—
414D4×C131—81no—
415D4×C131—81no—
416D4×C131—81no—
417D4×C131—81no—
418D4×C131—81no—
419D4×C131—81no—
420D4×C131—81no—
421D4×C131—81no—
422D4×C131—84no—
423D4×C131—84no—
424D4×C131—162no—
425C2×C4×C131—21no—
426C2×C4×C131—21no—
427C2×C4×C131—22no—
428C2×C4×C131—22no—
429C2×C4×C131—21no—
430C2×C4×C131—21no—
431C2×C4×C131—21no—
432C2×C4×C131—21no—
433C2×C4×C131—21no—
434C2×C4×C131—21no—
435C2×C4×C131—21no—
436C2×C4×C131—21no—
437C2×C4×C131—42no—
438C2×C4×C131—42no—
439C2×C4×C131—41no—
440C2×C4×C131—41no—
441C2×C4×C131—42no—
442C2×C4×C131—41no—
443C2×C4×C131—41no—
444C2×C4×C131—42no—
445C2×C4×C131—42no—
446C2×C4×C131—81no—
447C2×C4×C131—81no—
448C2×C4×C131—81no—
449C2×C4×C131—81no—
450C2×C4×C131—81no—
451C2×C4×C131—81no—
452C2×C4×C131—81no—
453C2×C4×C131—82no—
454C2×C4×C131—161no—
455C2×C4×C131#12011yescharacteristic
456C2×C4×C131C22×D411yescharacteristic
457C8×C131—42no—
458C22×C131—22no—
459C22×C131—21no—
460C22×C131—21no—
461C22×C131—21no—
462C22×C131—21no—
463C22×C131—41no—
464C22×C131—41no—
465C22×C131—41no—
466C22×C131—41no—
467C22×C131—41no—
468C22×C131—41no—
469C22×C131—42no—
470C22×C131—41no—
471C22×C131—41no—
472C22×C131—41no—
473C22×C131—41no—
474C22×C131—41no—
475C22×C131—41no—
476C22×C131—42no—
477C22×C131—41no—
478C22×C131—42no—
479C22×C131—42no—
480C22×C131—41no—
481C22×C131—41no—
482C22×C131—41no—
483C22×C131—81no—
484C22×C131—81no—
485C22×C131—81no—
486C22×C131—82no—
487C22×C131—82no—
488C22×C131—82no—
489C22×C131—81no—
490C22×C131—84no—
491C22×C131—82no—
492C22×C131—82no—
493C22×C131—82no—
494C22×C131—81no—
495C22×C131—162no—
496C22×C131—161no—
497C22×C131—161no—
498C22×C131B(4,𝔽2)11yescharacteristic
499C22×C131B(4,𝔽2)11yescharacteristic
500C22×C131C2×#12011yescharacteristic
501C4×C131—21no—
502C4×C131—21no—
503C4×C131—41no—
504C4×C131—41no—
505C4×C131—41no—
506C4×C131—41no—
507C4×C131—41no—
508C4×C131—41no—
509C4×C131—42no—
510C4×C131—41no—
511C4×C131—41no—
512C4×C131—82no—
513C4×C131—82no—
514C2×C131—21no—
515C2×C131—21no—
516C2×C131—21no—
517C2×C131—41no—
518C2×C131—41no—
519C2×C131—42no—
520C2×C131—41no—
521C2×C131—41no—
522C2×C131—81no—
523C2×C131—81no—
524C2×C131—81no—
525C2×C131—82no—
526C2×C131C2×B(4,𝔽2)11yescharacteristic
527#33551C13111yesmaximal, characteristic, direct product factor, Sylow
528C131#3355111yescharacteristic, direct product factor, Sylow
529#3532C2×C13111yescharacteristic, complemented
530#3026C2×C13111yescharacteristic, complemented
531C2×B(4,𝔽2)C2×C13111yescharacteristic, complemented
532#3019C2×C13111yescharacteristic, complemented
533#2200C2×C13112yescomplemented
534#2199C2×C13112yescomplemented
535#2197C2×C13112yescomplemented
536#2196C2×C13112yescomplemented
537#2127C2×C13111yescharacteristic, complemented
538#2121C2×C13111yescharacteristic, complemented
539C2×AΣL(1,𝔽16)C2×C13111yescharacteristic, complemented
540C2×H(5,𝔽2)C22×C13111yescharacteristic, complemented
541#575—21no—
542H(3,𝔽4)C22×C13111yescharacteristic, complemented
543#560—21no—
544#560C22×C13111yescharacteristic, complemented
545#551—21no—
546#551C22×C13111yescharacteristic, complemented
547#546—21no—
548#546—21no—
549#546—21no—
550D42—21no—
551D42C22×C13111yescharacteristic, complemented
552#538—21no—
553#538—21no—
554#538—21no—
555#535—21no—
556#535C22×C13111yescharacteristic
557#534—21no—
558#534—21no—
559#534C22×C13111yescharacteristic
560C2×#120—21no—
561C2×#120—21no—
562C2×#120C22×C13111yescharacteristic
563#458—21no—
564#458C22×C13112yescomplemented
565B(4,𝔽2)—21no—
566B(4,𝔽2)—21no—
567B(4,𝔽2)—21no—
568B(4,𝔽2)C22×C13112yes—
569B(4,𝔽2)C22×C13112yescomplemented
570B(4,𝔽2)C22×C13112yescomplemented
571#455—21no—
572#455C22×C13112yescomplemented
573#453—21no—
574#453C22×C13112yescomplemented
575#421—21no—
576C2×#100C22×C13111yescharacteristic, complemented
577C2×#99—21no—
578C2×#99—21no—
579C2×#99C22×C13111yescharacteristic, complemented
580C2×#99C22×C13111yescharacteristic, complemented
581#354C22×C13112yescomplemented
582#353C22×C13112yescomplemented
583#352C22×C13112yescomplemented
584AΣL(1,𝔽16)C22×C13112yescomplemented
585AΣL(1,𝔽16)C22×C13112yescomplemented
586AΣL(1,𝔽16)C22×C13112yescomplemented
587C25D4×C13111yescharacteristic, complemented
588H(5,𝔽2)—21no—
589H(5,𝔽2)—21no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—42no—
592H(5,𝔽2)C23×C13112yes—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—41no—
596C2×#41D4×C13111yescharacteristic, complemented
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—21no—
602C22×D4—21no—
603C22×D4—21no—
604C22×D4—41no—
605C22×D4—41no—
606C22×D4D4×C13111yescharacteristic, complemented
607C22×D4C23×C13111yescharacteristic
608#137—22no—
609#137—41no—
610AGL(1,ℤ/8)—22no—
611AGL(1,ℤ/8)—41no—
612#135—42no—
613C2×M16—21no—
614#127—21no—
615#127D4×C13111yescharacteristic, complemented
616#127C23×C13111yescharacteristic
617#126—21no—
618#126—21no—
619#126—21no—
620#126—21no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—21no—
625#124—21no—
626#124D4×C13111yescharacteristic, complemented
627#124C23×C13111yescharacteristic
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—22no—
637#123—41no—
638#123D4×C13111yescharacteristic, complemented
639#123C23×C13111yescharacteristic
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—21no—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—21no—
658#121—42no—
659#120—21no—
660#120—21no—
661#120—21no—
662#120—21no—
663#120—21no—
664#120—21no—
665#120—21no—
666#120—21no—
667#120—21no—
668#120—21no—
669#120—21no—
670#120—21no—
671#120—21no—
672#120—21no—
673#120—22no—
674#120—22no—
675#120—22no—
676#120—42no—
677#120—41no—
678#120D4×C13111yescharacteristic, complemented
679#120D4×C13111yescharacteristic, complemented
680#120D4×C13111yescharacteristic, complemented
681#120C23×C13111yescharacteristic
682#120C23×C13111yescharacteristic
683#120C23×C13111yescharacteristic
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690#117—21no—
691#117D4×C13111yescharacteristic, complemented
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4D4×C13111yescharacteristic, complemented
701C2×C22⋊C4D4×C13111yescharacteristic, complemented
702#104—22no—
703#104—22no—
704#100—21no—
705#100C23×C13112yes—
706#99—21no—
707#99—21no—
708#99—22no—
709#99—22no—
710#99—22no—
711#99—22no—
712#99C23×C13112yes—
713#99C23×C13112yes—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—41no—
720C24—41no—
721C24—82no—
722C24C2×D4×C13111yescharacteristic
723C24C2×D4×C13111yescharacteristic
724C24C2×D4×C13111yescharacteristic
725C24C2×D4×C13111yescharacteristic
726C24C2×D4×C13111yescharacteristic, complemented
727#41—22no—
728#41—22no—
729#41—42no—
730#41—41no—
731#41—42no—
732#41—42no—
733#41—41no—
734#41—41no—
735#41—42no—
736#41—41no—
737#41—82no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8C2×D4×C13111yescharacteristic, complemented
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—82no—
787C2×D4—82no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—84no—
791C2×D4C2×D4×C13111yescharacteristic
792C2×D4C2×D4×C13111yescharacteristic
793C2×D4C2×D4×C13111yescharacteristic
794C2×D4C2×D4×C13111yescharacteristic, complemented
795C2×D4C24×C13111yescharacteristic
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4C2×D4×C13111yescharacteristic
810C22×C4C2×D4×C13111yescharacteristic, complemented
811Q16—42no—
812SD16—42no—
813SD16—42no—
814D8—42no—
815M16—22no—
816M16—41no—
817C2×C8—41no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—42no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—41no—
859C22⋊C4—41no—
860C22⋊C4—42no—
861C22⋊C4C2×D4×C13111yescharacteristic
862C22⋊C4C2×D4×C13111yescharacteristic
863C22⋊C4C2×D4×C13111yescharacteristic, complemented
864C22⋊C4C2×D4×C13111yescharacteristic, complemented
865C42—21no—
866C42—21no—
867C42C2×D4×C13111yescharacteristic, complemented
868C42C2×D4×C13111yescharacteristic, complemented
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—44no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—81no—
893C23—81no—
894C23—81no—
895C23—81no—
896C23—81no—
897C23—81no—
898C23—81no—
899C23—81no—
900C23—81no—
901C23—82no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—161no—
906C23#120×C13111yescharacteristic
907C23#120×C13111yescharacteristic
908C23#120×C13111yescharacteristic
909C23C22×D4×C13111yescharacteristic
910C23C22×D4×C13111yescharacteristic
911Q8—22no—
912Q8—41no—
913Q8—41no—
914Q8—81no—
915D4—22no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—42no—
936D4—81no—
937D4—81no—
938D4—81no—
939D4—81no—
940D4—81no—
941D4—81no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—84no—
951D4—84no—
952D4—162no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—82no—
982C2×C4—161no—
983C2×C4#120×C13111yescharacteristic
984C2×C4C22×D4×C13111yescharacteristic
985C8—42no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—42no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—41no—
1006C22—42no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—81no—
1012C22—81no—
1013C22—81no—
1014C22—82no—
1015C22—82no—
1016C22—82no—
1017C22—81no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—82no—
1022C22—81no—
1023C22—162no—
1024C22—161no—
1025C22—161no—
1026C22B(4,𝔽2)×C13111yescharacteristic
1027C22B(4,𝔽2)×C13111yescharacteristic
1028C22C2×#120×C13111yescharacteristic
1029C4—21no—
1030C4—21no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—41no—
1040C4—82no—
1041C4—82no—
1042C2—21no—
1043C2—21no—
1044C2—21no—
1045C2—41no—
1046C2—41no—
1047C2—42no—
1048C2—41no—
1049C2—41no—
1050C2—81no—
1051C2—81no—
1052C2—81no—
1053C2—82no—
1054C2C2×B(4,𝔽2)×C13111yescharacteristic
subgroupG/H
center, socleC2×C131C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C131
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C23×C131 ◁ C22×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3532×C131C2semidirect
2. #3026×C131C2semidirect
3. C2×B(4,𝔽2)×C131C2semidirect
4. #3019×C131C2semidirect
5. #2200×C131C2semidirect
6. #2199×C131C2semidirect
7. #2197×C131C2semidirect
8. #2196×C131C2semidirect
9. #2127×C131C2semidirect
10. #2121×C131C2semidirect
11. C2×AΣL(1,𝔽16)×C131C2semidirect
12. C2×H(5,𝔽2)×C131C22semidirect
14. H(3,𝔽4)×C131C22semidirect
16. #560×C131C22semidirect
18. #551×C131C22semidirect
23. D42×C131C22semidirect
36. #458×C131C22semidirect
41. B(4,𝔽2)×C131C22semidirect
42. B(4,𝔽2)×C131C22semidirect
44. #455×C131C22semidirect
46. #453×C131C22semidirect
48. C2×#100×C131C22semidirect
51. C2×#99×C131C22semidirect
52. C2×#99×C131C22semidirect
53. #354×C131C22semidirect
54. #353×C131C22semidirect
55. #352×C131C22semidirect
56. AΣL(1,𝔽16)×C131C22semidirect
57. AΣL(1,𝔽16)×C131C22semidirect
58. AΣL(1,𝔽16)×C131C22semidirect
59. C25×C131D4semidirect
68. C2×#41×C131D4semidirect
78. C22×D4×C131D4semidirect
87. #127×C131D4semidirect
98. #124×C131D4semidirect
110. #123×C131D4semidirect
150. #120×C131D4semidirect
151. #120×C131D4semidirect
152. #120×C131D4semidirect
163. #117×C131D4semidirect
172. C2×C22⋊C4×C131D4semidirect
173. C2×C22⋊C4×C131D4semidirect
198. C24×C131C2×D4semidirect
212. C2×Q8×C131C2×D4semidirect
266. C2×D4×C131C2×D4semidirect
282. C22×C4×C131C2×D4semidirect
335. C22⋊C4×C131C2×D4semidirect
336. C22⋊C4×C131C2×D4semidirect
339. C42×C131C2×D4semidirect
340. C42×C131C2×D4semidirect
527. #33551C131direct (N × H)
528. C131#33551direct (N × H)
529. #3532C2×C131semidirect
530. #3026C2×C131semidirect
531. C2×B(4,𝔽2)C2×C131semidirect
532. #3019C2×C131semidirect
533. #2200C2×C131semidirect
534. #2199C2×C131semidirect
535. #2197C2×C131semidirect
536. #2196C2×C131semidirect
537. #2127C2×C131semidirect
538. #2121C2×C131semidirect
539. C2×AΣL(1,𝔽16)C2×C131semidirect
540. C2×H(5,𝔽2)C22×C131semidirect
542. H(3,𝔽4)C22×C131semidirect
544. #560C22×C131semidirect
546. #551C22×C131semidirect
551. D42C22×C131semidirect
564. #458C22×C131semidirect
569. B(4,𝔽2)C22×C131semidirect
570. B(4,𝔽2)C22×C131semidirect
572. #455C22×C131semidirect
574. #453C22×C131semidirect
576. C2×#100C22×C131semidirect
579. C2×#99C22×C131semidirect
580. C2×#99C22×C131semidirect
581. #354C22×C131semidirect
582. #353C22×C131semidirect
583. #352C22×C131semidirect
584. AΣL(1,𝔽16)C22×C131semidirect
585. AΣL(1,𝔽16)C22×C131semidirect
586. AΣL(1,𝔽16)C22×C131semidirect
587. C25D4×C131semidirect
596. C2×#41D4×C131semidirect
606. C22×D4D4×C131semidirect
615. #127D4×C131semidirect
626. #124D4×C131semidirect
638. #123D4×C131semidirect
678. #120D4×C131semidirect
679. #120D4×C131semidirect
680. #120D4×C131semidirect
691. #117D4×C131semidirect
700. C2×C22⋊C4D4×C131semidirect
701. C2×C22⋊C4D4×C131semidirect
726. C24C2×D4×C131semidirect
740. C2×Q8C2×D4×C131semidirect
794. C2×D4C2×D4×C131semidirect
810. C22×C4C2×D4×C131semidirect
863. C22⋊C4C2×D4×C131semidirect
864. C22⋊C4C2×D4×C131semidirect
867. C42C2×D4×C131semidirect
868. C42C2×D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3532×C1312
#3026×C1312
C2×B(4,𝔽2)×C1312
#3019×C1312
#2200×C1312
#2199×C1312
#2197×C1312
#2196×C1312
#2127×C1312
#2121×C1312
C2×AΣL(1,𝔽16)×C1312
#33551131