Finite Group Databasebeta

← C131×#33552 #45719436

Subgroups — C131×#33552 #45719436

Order 33536.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3533×C131C211yesmaximal, characteristic, complemented
2#3026×C131C211yesmaximal, characteristic, complemented
3C2×#458×C131C211yesmaximal, characteristic, complemented
4#3019×C131C211yesmaximal, characteristic, complemented
5#2201×C131C212yesmaximal, complemented
6#2200×C131C212yesmaximal, complemented
7#2198×C131C212yesmaximal, complemented
8#2197×C131C212yesmaximal, complemented
9#2127×C131C211yesmaximal, characteristic, complemented
10#2121×C131C211yesmaximal, characteristic, complemented
11C2×#352×C131C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C131C2211yescharacteristic
13#575×C131—21no—
14#563×C131C2211yescharacteristic, complemented
15#562×C131—21no—
16#560×C131C2211yescharacteristic, complemented
17#559×C131C2211yescharacteristic, complemented
18#553×C131—21no—
19#552×C131—21no—
20#551×C131—21no—
21#551×C131C2211yescharacteristic, complemented
22#547×C131—21no—
23#546×C131—21no—
24#542×C131—21no—
25#540×C131—21no—
26#539×C131—21no—
27#538×C131—21no—
28#538×C131—21no—
29#535×C131C2211yescharacteristic
30#534×C131—21no—
31#534×C131C2211yescharacteristic
32#525×C131—21no—
33C2×#123×C131—21no—
34C2×#123×C131C2211yescharacteristic
35#458×C131—21no—
36#458×C131—21no—
37#458×C131—21no—
38#458×C131C2212yes—
39#458×C131C2212yes—
40#458×C131C2212yes—
41B(4,𝔽2)×C131—21no—
42B(4,𝔽2)×C131C2212yes—
43#455×C131—21no—
44#455×C131C2212yes—
45#453×C131—21no—
46#453×C131C2212yes—
47#421×C131—21no—
48C2×#100×C131C2211yescharacteristic
49C2×#99×C131—21no—
50C2×#99×C131—21no—
51C2×#99×C131C2211yescharacteristic
52C2×#99×C131C2211yescharacteristic
53#354×C131C2212yescomplemented
54#353×C131C2212yescomplemented
55#352×C131C2212yescomplemented
56#352×C131C2212yescomplemented
57#352×C131C2212yescomplemented
58AΣL(1,𝔽16)×C131C2212yescomplemented
59H(5,𝔽2)×C131—21no—
60H(5,𝔽2)×C131—21no—
61H(5,𝔽2)×C131—21no—
62H(5,𝔽2)×C131—42no—
63H(5,𝔽2)×C131C2312yes—
64C2×#41×C131—21no—
65C2×#41×C131—21no—
66C2×#41×C131—41no—
67C2×#41×C131D411yescharacteristic, complemented
68C22×D4×C131—21no—
69C22×D4×C131—21no—
70C22×D4×C131—41no—
71C22×D4×C131D411yescharacteristic
72C22×D4×C131C2311yescharacteristic
73C23×C4×C131D411yescharacteristic, complemented
74#137×C131—22no—
75#137×C131—41no—
76AGL(1,ℤ/8)×C131—22no—
77AGL(1,ℤ/8)×C131—41no—
78#135×C131—42no—
79C2×M16×C131—21no—
80C4⋊Q8×C131—21no—
81#127×C131D411yescharacteristic, complemented
82#127×C131C2311yescharacteristic
83#126×C131—21no—
84#126×C131—21no—
85#126×C131—21no—
86#126×C131—21no—
87#126×C131—21no—
88#126×C131—21no—
89#125×C131—21no—
90#125×C131—21no—
91#125×C131—21no—
92#124×C131—21no—
93#124×C131—21no—
94#124×C131—21no—
95#124×C131—21no—
96#124×C131D411yescharacteristic, complemented
97#124×C131C2311yescharacteristic
98#123×C131—21no—
99#123×C131—21no—
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—21no—
109#123×C131—21no—
110#123×C131—22no—
111#123×C131—22no—
112#123×C131—22no—
113#123×C131—41no—
114#123×C131—42no—
115#123×C131D411yescharacteristic
116#123×C131D411yescharacteristic, complemented
117#123×C131D411yescharacteristic, complemented
118#123×C131C2311yescharacteristic
119#123×C131C2311yescharacteristic
120#123×C131C2311yescharacteristic
121C22⋊Q8×C131—21no—
122C22⋊Q8×C131—21no—
123C22⋊Q8×C131—21no—
124C22⋊Q8×C131—21no—
125C22⋊Q8×C131—21no—
126C22⋊Q8×C131—21no—
127C22⋊Q8×C131—21no—
128C22⋊Q8×C131—21no—
129#121×C131—21no—
130#121×C131—21no—
131#121×C131—21no—
132#121×C131—21no—
133#121×C131—21no—
134#121×C131—21no—
135#121×C131—21no—
136#121×C131—21no—
137#121×C131—21no—
138#121×C131—21no—
139#121×C131—21no—
140#121×C131—21no—
141#121×C131—42no—
142#120×C131—21no—
143#120×C131—21no—
144#120×C131—21no—
145#120×C131—21no—
146#120×C131—22no—
147#120×C131—41no—
148#120×C131D411yescharacteristic
149#120×C131C2311yescharacteristic
150C4×Q8×C131—21no—
151C4×D4×C131—21no—
152C4×D4×C131—21no—
153C4×D4×C131—21no—
154C4×D4×C131—21no—
155C4×D4×C131—21no—
156C4×D4×C131—21no—
157C4×D4×C131—21no—
158C4×D4×C131—21no—
159C4×D4×C131—21no—
160#117×C131—21no—
161#117×C131—21no—
162#117×C131—21no—
163#117×C131D411yescharacteristic, complemented
164C2×C4⋊C4×C131—21no—
165C2×C4⋊C4×C131—21no—
166C2×C4⋊C4×C131—41no—
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
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×C131C2×D411yescharacteristic
189C24×C131C2×D411yescharacteristic
190C24×C131C2×D411yescharacteristic
191#41×C131—22no—
192#41×C131—22no—
193#41×C131—42no—
194#41×C131—41no—
195#41×C131—42no—
196#41×C131—42no—
197#41×C131—41no—
198#41×C131—41no—
199#41×C131—42no—
200#41×C131—41no—
201#41×C131—81no—
202#41×C131—81no—
203C2×Q8×C131—21no—
204C2×Q8×C131—21no—
205C2×Q8×C131—21no—
206C2×Q8×C131C2×D411yescharacteristic
207C2×D4×C131—21no—
208C2×D4×C131—22no—
209C2×D4×C131—22no—
210C2×D4×C131—21no—
211C2×D4×C131—21no—
212C2×D4×C131—22no—
213C2×D4×C131—22no—
214C2×D4×C131—21no—
215C2×D4×C131—21no—
216C2×D4×C131—21no—
217C2×D4×C131—21no—
218C2×D4×C131—21no—
219C2×D4×C131—21no—
220C2×D4×C131—21no—
221C2×D4×C131—21no—
222C2×D4×C131—21no—
223C2×D4×C131—41no—
224C2×D4×C131—41no—
225C2×D4×C131—42no—
226C2×D4×C131—42no—
227C2×D4×C131—41no—
228C2×D4×C131—41no—
229C2×D4×C131—41no—
230C2×D4×C131—41no—
231C2×D4×C131—42no—
232C2×D4×C131—42no—
233C2×D4×C131—41no—
234C2×D4×C131—41no—
235C2×D4×C131—41no—
236C2×D4×C131—41no—
237C2×D4×C131—41no—
238C2×D4×C131—42no—
239C2×D4×C131C2×D411yescharacteristic
240C2×D4×C131C2×D411yescharacteristic
241C2×D4×C131C2×D411yescharacteristic
242C2×D4×C131C2×D411yescharacteristic
243C2×D4×C131C2411yescharacteristic
244C22×C4×C131—21no—
245C22×C4×C131—21no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—21no—
249C22×C4×C131—21no—
250C22×C4×C131—21no—
251C22×C4×C131—21no—
252C22×C4×C131—21no—
253C22×C4×C131—21no—
254C22×C4×C131—21no—
255C22×C4×C131—41no—
256C22×C4×C131—41no—
257C22×C4×C131—41no—
258C22×C4×C131—41no—
259C22×C4×C131—41no—
260C22×C4×C131C2×D411yescharacteristic
261C22×C4×C131C2×D411yescharacteristic
262C22×C4×C131C2×D411yescharacteristic
263C22×C4×C131C2×D411yescharacteristic
264Q16×C131—42no—
265SD16×C131—42no—
266SD16×C131—42no—
267D8×C131—42no—
268M16×C131—22no—
269M16×C131—41no—
270C2×C8×C131—41no—
271C4⋊C4×C131—21no—
272C4⋊C4×C131—21no—
273C4⋊C4×C131—21no—
274C4⋊C4×C131—21no—
275C4⋊C4×C131—21no—
276C4⋊C4×C131—21no—
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—21no—
280C4⋊C4×C131—21no—
281C4⋊C4×C131—21no—
282C4⋊C4×C131—21no—
283C4⋊C4×C131—21no—
284C4⋊C4×C131—21no—
285C4⋊C4×C131—21no—
286C4⋊C4×C131—21no—
287C4⋊C4×C131—21no—
288C4⋊C4×C131—21no—
289C4⋊C4×C131—21no—
290C4⋊C4×C131—42no—
291C4⋊C4×C131—42no—
292C4⋊C4×C131—42no—
293C22⋊C4×C131—21no—
294C22⋊C4×C131—21no—
295C22⋊C4×C131—21no—
296C22⋊C4×C131—21no—
297C22⋊C4×C131—21no—
298C22⋊C4×C131—21no—
299C22⋊C4×C131—21no—
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—22no—
317C22⋊C4×C131—22no—
318C22⋊C4×C131—42no—
319C22⋊C4×C131—41no—
320C22⋊C4×C131—41no—
321C22⋊C4×C131—42no—
322C22⋊C4×C131—42no—
323C22⋊C4×C131—42no—
324C22⋊C4×C131C2×D411yescharacteristic
325C22⋊C4×C131C2×D411yescharacteristic
326C22⋊C4×C131C2×D411yescharacteristic
327C22⋊C4×C131C2×D411yescharacteristic
328C42×C131—21no—
329C42×C131—21no—
330C42×C131—21no—
331C42×C131—21no—
332C42×C131C2×D411yescharacteristic
333C42×C131C2×D411yescharacteristic
334C23×C131—21no—
335C23×C131—21no—
336C23×C131—21no—
337C23×C131—21no—
338C23×C131—22no—
339C23×C131—22no—
340C23×C131—21no—
341C23×C131—21no—
342C23×C131—41no—
343C23×C131—41no—
344C23×C131—41no—
345C23×C131—41no—
346C23×C131—81no—
347C23×C131—81no—
348C23×C131—81no—
349C23×C131—82no—
350C23×C131—161no—
351C23×C131#12011yescharacteristic
352C23×C131#12011yescharacteristic
353C23×C131#12011yescharacteristic
354C23×C131C22×D411yescharacteristic
355C23×C131C22×D411yescharacteristic
356Q8×C131—22no—
357Q8×C131—41no—
358Q8×C131—41no—
359Q8×C131—81no—
360Q8×C131—81no—
361D4×C131—22no—
362D4×C131—41no—
363D4×C131—41no—
364D4×C131—41no—
365D4×C131—41no—
366D4×C131—41no—
367D4×C131—41no—
368D4×C131—42no—
369D4×C131—42no—
370D4×C131—42no—
371D4×C131—42no—
372D4×C131—42no—
373D4×C131—42no—
374D4×C131—41no—
375D4×C131—41no—
376D4×C131—41no—
377D4×C131—41no—
378D4×C131—81no—
379D4×C131—81no—
380D4×C131—81no—
381D4×C131—81no—
382D4×C131—81no—
383D4×C131—81no—
384D4×C131—81no—
385D4×C131—81no—
386D4×C131—81no—
387D4×C131—162no—
388C2×C4×C131—21no—
389C2×C4×C131—21no—
390C2×C4×C131—22no—
391C2×C4×C131—22no—
392C2×C4×C131—21no—
393C2×C4×C131—21no—
394C2×C4×C131—21no—
395C2×C4×C131—21no—
396C2×C4×C131—21no—
397C2×C4×C131—21no—
398C2×C4×C131—21no—
399C2×C4×C131—21no—
400C2×C4×C131—21no—
401C2×C4×C131—21no—
402C2×C4×C131—42no—
403C2×C4×C131—42no—
404C2×C4×C131—41no—
405C2×C4×C131—41no—
406C2×C4×C131—41no—
407C2×C4×C131—41no—
408C2×C4×C131—41no—
409C2×C4×C131—41no—
410C2×C4×C131—41no—
411C2×C4×C131—41no—
412C2×C4×C131—42no—
413C2×C4×C131—42no—
414C2×C4×C131—81no—
415C2×C4×C131—81no—
416C2×C4×C131—81no—
417C2×C4×C131—81no—
418C2×C4×C131—81no—
419C2×C4×C131—81no—
420C2×C4×C131—81no—
421C2×C4×C131—81no—
422C2×C4×C131—82no—
423C2×C4×C131—161no—
424C2×C4×C131#12011yescharacteristic
425C2×C4×C131C22×D411yescharacteristic
426C8×C131—42no—
427C22×C131—21no—
428C22×C131—21no—
429C22×C131—21no—
430C22×C131—21no—
431C22×C131—41no—
432C22×C131—41no—
433C22×C131—41no—
434C22×C131—41no—
435C22×C131—41no—
436C22×C131—42no—
437C22×C131—41no—
438C22×C131—41no—
439C22×C131—41no—
440C22×C131—41no—
441C22×C131—42no—
442C22×C131—41no—
443C22×C131—41no—
444C22×C131—81no—
445C22×C131—81no—
446C22×C131—81no—
447C22×C131—82no—
448C22×C131—82no—
449C22×C131—82no—
450C22×C131—82no—
451C22×C131—161no—
452C22×C131—161no—
453C22×C131B(4,𝔽2)11yescharacteristic
454C22×C131B(4,𝔽2)11yescharacteristic
455C22×C131C2×#12011yescharacteristic
456C4×C131—21no—
457C4×C131—21no—
458C4×C131—41no—
459C4×C131—41no—
460C4×C131—41no—
461C4×C131—41no—
462C4×C131—41no—
463C4×C131—41no—
464C4×C131—42no—
465C4×C131—41no—
466C4×C131—41no—
467C4×C131—41no—
468C4×C131—41no—
469C4×C131—82no—
470C4×C131—82no—
471C2×C131—21no—
472C2×C131—21no—
473C2×C131—21no—
474C2×C131—41no—
475C2×C131—41no—
476C2×C131—41no—
477C2×C131—41no—
478C2×C131—81no—
479C2×C131—81no—
480C2×C131—82no—
481C2×C131C2×B(4,𝔽2)11yescharacteristic
482#33552C13111yesmaximal, characteristic, direct product factor, Sylow
483C131#3355211yescharacteristic, direct product factor, Sylow
484#3533C2×C13111yescharacteristic, complemented
485#3026C2×C13111yescharacteristic, complemented
486C2×#458C2×C13111yescharacteristic, complemented
487#3019C2×C13111yescharacteristic, complemented
488#2201C2×C13112yescomplemented
489#2200C2×C13112yescomplemented
490#2198C2×C13112yescomplemented
491#2197C2×C13112yescomplemented
492#2127C2×C13111yescharacteristic, complemented
493#2121C2×C13111yescharacteristic, complemented
494C2×#352C2×C13111yescharacteristic, complemented
495C2×H(5,𝔽2)C22×C13111yescharacteristic
496#575—21no—
497#563C22×C13111yescharacteristic, complemented
498#562—21no—
499#560C22×C13111yescharacteristic, complemented
500#559C22×C13111yescharacteristic, complemented
501#553—21no—
502#552—21no—
503#551—21no—
504#551C22×C13111yescharacteristic, complemented
505#547—21no—
506#546—21no—
507#542—21no—
508#540—21no—
509#539—21no—
510#538—21no—
511#538—21no—
512#535C22×C13111yescharacteristic
513#534—21no—
514#534C22×C13111yescharacteristic
515#525—21no—
516C2×#123—21no—
517C2×#123C22×C13111yescharacteristic
518#458—21no—
519#458—21no—
520#458—21no—
521#458C22×C13112yes—
522#458C22×C13112yes—
523#458C22×C13112yes—
524B(4,𝔽2)—21no—
525B(4,𝔽2)C22×C13112yes—
526#455—21no—
527#455C22×C13112yes—
528#453—21no—
529#453C22×C13112yes—
530#421—21no—
531C2×#100C22×C13111yescharacteristic
532C2×#99—21no—
533C2×#99—21no—
534C2×#99C22×C13111yescharacteristic
535C2×#99C22×C13111yescharacteristic
536#354C22×C13112yescomplemented
537#353C22×C13112yescomplemented
538#352C22×C13112yescomplemented
539#352C22×C13112yescomplemented
540#352C22×C13112yescomplemented
541AΣL(1,𝔽16)C22×C13112yescomplemented
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C13112yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C13111yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C13111yescharacteristic
555C22×D4C23×C13111yescharacteristic
556C23×C4D4×C13111yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C13111yescharacteristic, complemented
565#127C23×C13111yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C13111yescharacteristic, complemented
580#124C23×C13111yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C13111yescharacteristic
599#123D4×C13111yescharacteristic, complemented
600#123D4×C13111yescharacteristic, complemented
601#123C23×C13111yescharacteristic
602#123C23×C13111yescharacteristic
603#123C23×C13111yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C13111yescharacteristic
632#120C23×C13111yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C13111yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C13111yescharacteristic
656C2×C22⋊C4D4×C13111yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C13112yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C13112yes—
668#99C23×C13112yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C13111yescharacteristic
672C24C2×D4×C13111yescharacteristic
673C24C2×D4×C13111yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C13111yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C13111yescharacteristic
723C2×D4C2×D4×C13111yescharacteristic
724C2×D4C2×D4×C13111yescharacteristic
725C2×D4C2×D4×C13111yescharacteristic
726C2×D4C24×C13111yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C13111yescharacteristic
744C22×C4C2×D4×C13111yescharacteristic
745C22×C4C2×D4×C13111yescharacteristic
746C22×C4C2×D4×C13111yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C13111yescharacteristic
808C22⋊C4C2×D4×C13111yescharacteristic
809C22⋊C4C2×D4×C13111yescharacteristic
810C22⋊C4C2×D4×C13111yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C13111yescharacteristic
816C42C2×D4×C13111yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C13111yescharacteristic
835C23#120×C13111yescharacteristic
836C23#120×C13111yescharacteristic
837C23C22×D4×C13111yescharacteristic
838C23C22×D4×C13111yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—42no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C13111yescharacteristic
908C2×C4C22×D4×C13111yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22B(4,𝔽2)×C13111yescharacteristic
937C22B(4,𝔽2)×C13111yescharacteristic
938C22C2×#120×C13111yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×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. #3533×C131C2semidirect
2. #3026×C131C2semidirect
3. C2×#458×C131C2semidirect
4. #3019×C131C2semidirect
5. #2201×C131C2semidirect
6. #2200×C131C2semidirect
7. #2198×C131C2semidirect
8. #2197×C131C2semidirect
9. #2127×C131C2semidirect
10. #2121×C131C2semidirect
11. C2×#352×C131C2semidirect
14. #563×C131C22semidirect
16. #560×C131C22semidirect
17. #559×C131C22semidirect
21. #551×C131C22semidirect
53. #354×C131C22semidirect
54. #353×C131C22semidirect
55. #352×C131C22semidirect
56. #352×C131C22semidirect
57. #352×C131C22semidirect
58. AΣL(1,𝔽16)×C131C22semidirect
67. C2×#41×C131D4semidirect
73. C23×C4×C131D4semidirect
81. #127×C131D4semidirect
96. #124×C131D4semidirect
116. #123×C131D4semidirect
117. #123×C131D4semidirect
163. #117×C131D4semidirect
173. C2×C22⋊C4×C131D4semidirect
482. #33552C131direct (N × H)
483. C131#33552direct (N × H)
484. #3533C2×C131semidirect
485. #3026C2×C131semidirect
486. C2×#458C2×C131semidirect
487. #3019C2×C131semidirect
488. #2201C2×C131semidirect
489. #2200C2×C131semidirect
490. #2198C2×C131semidirect
491. #2197C2×C131semidirect
492. #2127C2×C131semidirect
493. #2121C2×C131semidirect
494. C2×#352C2×C131semidirect
497. #563C22×C131semidirect
499. #560C22×C131semidirect
500. #559C22×C131semidirect
504. #551C22×C131semidirect
536. #354C22×C131semidirect
537. #353C22×C131semidirect
538. #352C22×C131semidirect
539. #352C22×C131semidirect
540. #352C22×C131semidirect
541. AΣL(1,𝔽16)C22×C131semidirect
550. C2×#41D4×C131semidirect
556. C23×C4D4×C131semidirect
564. #127D4×C131semidirect
579. #124D4×C131semidirect
599. #123D4×C131semidirect
600. #123D4×C131semidirect
646. #117D4×C131semidirect
656. C2×C22⋊C4D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3533×C1312
#3026×C1312
C2×#458×C1312
#3019×C1312
#2201×C1312
#2200×C1312
#2198×C1312
#2197×C1312
#2127×C1312
#2121×C1312
C2×#352×C1312
#33552131