Finite Group Databasebeta

← #28293092

Subgroups — #28293092

Order 13568.

6624 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289412C213yesmaximal, complemented
2#20289411C213yesmaximal, complemented
3#20289409C211yesmaximal, characteristic, complemented
4#20289125C213yesmaximal, complemented
5#20289119C211yesmaximal, characteristic, complemented
6#20288986C216yesmaximal, complemented
7#20288980C216yesmaximal, complemented
8#20288728C216yesmaximal, complemented
9#20288725C216yesmaximal, complemented
10#20288668C216yesmaximal, complemented
11#20288665C216yesmaximal, complemented
12#20288605C216yesmaximal, complemented
13#20288603C216yesmaximal, complemented
14#20288009C213yesmaximal, complemented
15C53×#3568C211yesmaximal, characteristic, complemented
16#16811377C2213yescomplemented
17#16811377C2213yescomplemented
18#16811373C2213yescomplemented
19#16811366C2212yescomplemented
20#16811365C2213yescomplemented
21#16811365C2216yescomplemented
22#16811364C2212yescomplemented
23#16811361C2216yescomplemented
24#16811358C2216yescomplemented
25#16811357C2216yescomplemented
26#16811357C2216yescomplemented
27#16811356C2216yescomplemented
28#16811355C2216yescomplemented
29#16811353C2216yescomplemented
30#16811347C2216yescomplemented
31#16811345C2216yescomplemented
32#16811345C2216yescomplemented
33#16811344C2216yescomplemented
34#16811342C2216yescomplemented
35#16811342C2216yescomplemented
36#16811341C2216yescomplemented
37#16811340C2216yescomplemented
38#16811340C2216yescomplemented
39#16811340C2216yescomplemented
40#16811340C2216yescomplemented
41#16811340C2216yescomplemented
42#16811340C2216yescomplemented
43#16811337C2216yescomplemented
44#16811336C2216yescomplemented
45#16811335C2216yescomplemented
46#16811335C2216yescomplemented
47#16811335C2216yescomplemented
48#16811304C2216yescomplemented
49#16811302C2216yescomplemented
50#16811300C2216yescomplemented
51#16811300C2216yescomplemented
52#16811299C2216yescomplemented
53#16811298C2216yescomplemented
54#16811298C2216yescomplemented
55#16811298C2216yescomplemented
56#16811297C2216yescomplemented
57#16811297C2216yescomplemented
58#16811296C2216yescomplemented
59#16811286C2216yescomplemented
60#16811286C2216yescomplemented
61#16811283C2216yescomplemented
62#16811282C2216yescomplemented
63#16811281C2216yescomplemented
64#16811279C2216yescomplemented
65#16811265C2216yescomplemented
66#16811263C2216yescomplemented
67#16811262C2216yescomplemented
68#16811260C2216yescomplemented
69#16811255C2216yescomplemented
70#16811247C2216yescomplemented
71#16811246C2216yescomplemented
72#16811243C2216yescomplemented
73#16811243C2216yescomplemented
74#16811243C2216yescomplemented
75#16811243C2216yescomplemented
76#16811241C2216yescomplemented
77#16811241C2216yescomplemented
78#16811239C2216yescomplemented
79#16811239C2216yescomplemented
80#16811239C2216yescomplemented
81#16811239C2216yescomplemented
82#16811238C2216yescomplemented
83#16811237C2216yescomplemented
84#16811237C2216yescomplemented
85#16811213C2216yescomplemented
86#16811212C2216yescomplemented
87#16811209C2216yescomplemented
88#16811209C2216yescomplemented
89#16811208C2216yescomplemented
90#16811206C2216yescomplemented
91#16811205C2216yescomplemented
92#16811198C2216yescomplemented
93#16811195C2216yescomplemented
94#16811191C2216yes—
95#16811188C2216yes—
96#16811179C2213yescomplemented
97#16811177C2213yescomplemented
98#16811177C2216yescomplemented
99#16811175C2213yescomplemented
100#16811175C2216yescomplemented
101#16811172C2213yes—
102#16811170C2213yes—
103#16811168C2213yes—
104#16811158C2213yescomplemented
105#16811157C2213yescomplemented
106#16811156C2216yescomplemented
107#16811156C2216yescomplemented
108#16811156C2216yescomplemented
109#16811153C2216yescomplemented
110#16811152C2213yescomplemented
111#16811151C2216yescomplemented
112#16811151C2216yescomplemented
113#16811150C2216yescomplemented
114#16811150C2216yescomplemented
115C2×#13133203C2216yescomplemented
116#124×D53C2216yescomplemented
117#16811136C2213yescomplemented
118#16811133C2213yescomplemented
119#16811132C2216yescomplemented
120#16811131C2216yescomplemented
121#16811100C2216yescomplemented
122#16811099C2216yescomplemented
123#16811096C2216yescomplemented
124#16811095C2216yescomplemented
125C4×#11719949C2213yescomplemented
126#16811091C2216yescomplemented
127C4×#11719947C2213yescomplemented
128C4×#11719947C2216yescomplemented
129C2×C42×D53C2211yescharacteristic, complemented
130C53×#563C2213yescomplemented
131C53×H(3,𝔽4)C2211yescharacteristic, complemented
132C53×#556C2216yescomplemented
133C53×#551C2216yescomplemented
134C53×#542C2216yescomplemented
135C53×#538C2216yescomplemented
136C53×#529C2213yescomplemented
137C2×#11719949C2313yes—
138C2×#11719945C2316yes—
139C2×#11719947C2316yes—
140C2×#11719947C2313yes—
141C22×Dic106C2316yes—
142C2×Q8×D53C2316yes—
143C22×C22⋊D53C2316yes—
144C2×D4×D53C2316yes—
145C22×C4×D53C2313yes—
146#13133216C2313yes—
147#13133216C2313yes—
148#13133216C2316yes—
149#13133216C2316yes—
150#13133216C2316yes—
151#13133216C2316yes—
152#13133215C2316yes—
153#13133215C2316yes—
154#13133215C2313yes—
155#13133215C2316yes—
156#13133214C2312yes—
157#13133213C2316yes—
158#13133213C2313yes—
159#13133212C2316yes—
160#13133212C2316yes—
161#13133212C2316yes—
162#13133212C2316yes—
163#13133212C2316yes—
164#13133212C2316yes—
165#13133212C2316yes—
166#13133212C2316yes—
167#13133212C2316yes—
168#13133211C2316yes—
169#13133211C2316yes—
170#13133211C2312yes—
171#13133210C2316yes—
172#13133210C2316yes—
173#13133210C2316yes—
174#13133210C2316yes—
175#13133210C2316yes—
176#13133210C2316yes—
177#13133210C2316yes—
178#13133209C2313yes—
179#13133207C2316yes—
180#13133207C2316yes—
181#13133206C2316yes—
182#13133206C2316yes—
183#13133206C2316yes—
184#13133206C2316yes—
185#13133205C2316yes—
186#13133205C2316yes—
187#13133205C2316yes—
188#13133205C2313yes—
189#13133204C2316yes—
190#13133204C2316yes—
191#13133203C2316yes—
192#13133203C2316yes—
193#13133203C2316yes—
194#13133203C2316yes—
195#13133203C2316yes—
196#13133203C2316yes—
197#13133203C2316yes—
198#13133203C2316yes—
199#13133203C2316yes—
200#13133203C2316yes—
201#13133203C2316yes—
202#13133203C2316yes—
203#13133203C2316yes—
204#13133203C2316yes—
205#13133203C2316yes—
206#13133203C2316yes—
207#13133203C2316yes—
208#13133203C2316yes—
209#13133202C2316yes—
210#13133202C2316yes—
211#13133202C2316yes—
212#13133202C2316yes—
213#13133202C2316yes—
214#13133202C2316yes—
215#13133202C2316yes—
216#13133202C2316yes—
217#13133201C2316yes—
218#13133201C2316yes—
219#13133200C2316yes—
220#13133200C2316yes—
221#13133200C2316yes—
222#13133199C2316yes—
223#13133199C2316yes—
224#13133199C2316yes—
225#13133199C2316yes—
226#13133198C2316yes—
227#13133198C2316yes—
228#13133197C2316yes—
229#13133197C2316yes—
230#13133197C2316yes—
231#13133197C2313yes—
232#13133196C2316yes—
233#13133196C2313yes—
234#13133195C2316yes—
235#13133195C2316yes—
236#13133195C2316yes—
237#13133195C2316yes—
238#13133195C2316yes—
239#13133195C2316yes—
240#13133195C2316yes—
241#13133195C2316yes—
242#13133195C2316yes—
243#13133194C2316yes—
244#13133194C2316yes—
245#13133194C2316yes—
246#13133194C2316yes—
247#13133194C2316yes—
248#13133194C2316yes—
249#13133194C2316yes—
250#13133193C2316yes—
251#13133193C2313yes—
252#13133192C2316yes—
253#13133192C2313yes—
254#13133191C2316yes—
255#13133191C2313yes—
256#13133190C2316yes—
257#13133190C2316yes—
258#13133190C2316yes—
259#13133190C2316yes—
260#13133190C2316yes—
261#13133190C2316yes—
262#13133190C2316yes—
263#13133189C2316yes—
264#13133189C2316yes—
265#13133189C2316yes—
266#13133189C2316yes—
267#13133189C2316yes—
268#13133188C2316yes—
269#13133188C2313yes—
270#13133187C2316yes—
271#13133187C2316yes—
272#13133187C2316yes—
273#13133187C2316yes—
274#13133187C2316yes—
275#13133186C2312yes—
276#13133186C2312yes—
277#13133185C2316yes—
278#13133185C2316yes—
279#13133185C2316yes—
280Q8×Dic53C2313yes—
281Q8×Dic53C2316yes—
282C4×Dic106C2316yes—
283C4×Dic106C2316yes—
284C4×Dic106C2313yes—
285C4×Dic106C2316yes—
286C4×Dic106C2316yes—
287C4×Dic106C2316yes—
288C4×Dic106C2316yes—
289#13133182C2316yes—
290#13133182C2316yes—
291#13133182C2316yes—
292#13133182C2316yes—
293#13133182C2313yes—
294#13133182C2316yes—
295#13133182C2316yes—
296#13133182C2316yes—
297#13133182C2316yes—
298C4×D212C2316yes—
299C4×D212C2313yes—
300C4×D212C2316yes—
301D4×Dic53C2316yes—
302D4×Dic53C2316yes—
303D4×Dic53C2313yes—
304#13133179C2316yes—
305#13133179C2316yes—
306#13133179C2313yes—
307#13133179C2316yes—
308#13133179C2316yes—
309C4×C22⋊D53C2316yes—
310C4×C22⋊D53C2316yes—
311C4×C22⋊D53C2316yes—
312C4×C22⋊D53C2316yes—
313C4×C22⋊D53C2316yes—
314C4×C22⋊D53C2316yes—
315C4×C22⋊D53C2316yes—
316#13133177C2316yes—
317#13133177C2316yes—
318#13133177C2316yes—
319#13133177C2316yes—
320#13133177C2316yes—
321#13133177C2316yes—
322#13133177C2316yes—
323#13133177C2316yes—
324#13133177C2316yes—
325#13133177C2316yes—
326#13133177C2316yes—
327#13133176C2316yes—
328#13133175C2316yes—
329#13133175C2316yes—
330#13133175C2316yes—
331#13133175C2313yes—
332#13133175C2316yes—
333#13133175C2313yes—
334#13133174C2316yes—
335#13133174C2316yes—
336#13133174C2316yes—
337#13133174C2316yes—
338#13133174C2316yes—
339#13133174C2316yes—
340#13133173C2316yes—
341#13133173C2316yes—
342#13133173C2316yes—
343#13133173C2316yes—
344#13133173C2316yes—
345#13133173C2316yes—
346#13133173C2316yes—
347C2×C22⋊Dic53C2316yes—
348C2×#11719921C2316yes—
349C2×#11719921C2316yes—
350C22⋊C4×D53C2316yes—
351C22⋊C4×D53C2316yes—
352C22⋊C4×D53C2316yes—
353C22⋊C4×D53C2316yes—
354C2×C4×Dic53C2313yes—
355C2×C4×Dic53C2316yes—
356C42×D53C2313yes—
357C42×D53C2313yes—
358C42×D53C2311yescharacteristic
359C42×D53C2311yescharacteristic
360C42×D53C2316yes—
361C4⋊Q8×C53C2316yes—
362#126×C53C2316yes—
363#126×C53C2316yes—
364#126×C53C2316yes—
365#126×C53C2312yes—
366#126×C53C2316yes—
367#125×C53C2313yes—
368#124×C53C2316yes—
369#124×C53C2313yes—
370#124×C53C2316yes—
371#124×C53C2316yes—
372#123×C53C2316yes—
373#123×C53C2316yes—
374#123×C53C2316yes—
375C22⋊Q8×C53C2316yes—
376C22⋊Q8×C53C2316yes—
377C22⋊Q8×C53C2316yes—
378C22⋊Q8×C53C2313yes—
379#121×C53C2316yes—
380#121×C53C2313yes—
381#120×C53C2316yes—
382#120×C53C2312yes—
383C4×Q8×C53C2313yes—
384C4×Q8×C53C2316yes—
385C4×D4×C53C2316yes—
386C4×D4×C53C2313yes—
387C4×D4×C53C2316yes—
388#117×C53C2316yes—
389#117×C53C2316yes—
390C2×C22⋊C4×C53C2316yes—
391C2×C42×C53C2311yescharacteristic
392C24×C53C2412yes—
393C23×D53C2416yes—
394C23×D53C2411yescharacteristic
395C2×Q8×C53C2416yes—
396C2×Q8×C53C2413yes—
397C2×D4×C53C2413yes—
398C2×D4×C53C2416yes—
399C2×D4×C53C2416yes—
400C22×C4×C53C2413yes—
401C22×C4×C53C2416yes—
402C22×C4×C53C2416yes—
403C2×C22⋊D53—412no—
404C2×C22⋊D53C2416yes—
405C2×C22⋊D53C2416yes—
406C2×C22⋊D53C2416yes—
407C2×C22⋊D53C2416yes—
408C2×C22⋊D53C2416yes—
409C2×C22⋊D53C2416yes—
410C2×C22⋊D53C2416yes—
411C22×Dic53C2413yes—
412C22×Dic53C2416yes—
413C22×Dic53C2416yes—
414C22×Dic53C2416yes—
415#11719949—46no—
416Q8×D53—412no—
417#11719947—412no—
418#11719947—46no—
419D4×D53—412no—
420#11719945—412no—
421C2×D212C2416yes—
422C2×D212C2413yes—
423C2×D212C2416yes—
424C2×D212C2416yes—
425C2×C4×D53—46no—
426C2×C4×D53C2413yes—
427C2×C4×D53C2413yes—
428C2×C4×D53C2416yes—
429C2×C4×D53C2413yes—
430C2×C4×D53C2413yes—
431C2×C4×D53C2416yes—
432C2×C4×D53C2416yes—
433C2×C4×D53C2416yes—
434C2×C4×D53C2416yes—
435C2×Dic106—412no—
436C2×Dic106C2416yes—
437C2×Dic106C2416yes—
438C2×Dic106C2416yes—
439C2×Dic106C2416yes—
440C2×Dic106C2413yes—
441C2×Dic106C2416yes—
442C4⋊C4×C53C2416yes—
443C4⋊C4×C53C2416yes—
444C4⋊C4×C53C2416yes—
445C4⋊C4×C53C2416yes—
446C4⋊C4×C53C2413yes—
447C4⋊C4×C53C2416yes—
448C4⋊C4×C53C2413yes—
449C4⋊C4×C53C2416yes—
450C22⋊C4×C53C2416yes—
451C22⋊C4×C53C2416yes—
452C22⋊C4×C53C2416yes—
453C22⋊C4×C53C2416yes—
454C22⋊C4×C53C2416yes—
455C22⋊C4×C53C2416yes—
456C22⋊C4×C53C2416yes—
457C22⋊C4×C53C2416yes—
458C22⋊C4×C53C2416yes—
459C42×C53C2413yes—
460C42×C53C2411yescharacteristic
461C42×C53C2416yes—
462C42×C53C2416yes—
463C42×C53C2412yes—
464C22⋊Dic53C2416yes—
465C22⋊Dic53C2416yes—
466C22⋊Dic53C2416yes—
467C22⋊Dic53C2416yes—
468C22⋊Dic53C2416yes—
469C22⋊Dic53C2416yes—
470C22⋊Dic53C2416yes—
471#11719921C2416yes—
472#11719921C2416yes—
473#11719921C2416yes—
474#11719921C2416yes—
475#11719921C2416yes—
476#11719921C2416yes—
477#11719921C2416yes—
478#11719921C2416yes—
479#11719921C2416yes—
480#11719921C2416yes—
481#11719921C2416yes—
482#11719921C2416yes—
483#11719921C2416yes—
484#11719921C2416yes—
485#11719921C2416yes—
486#11719921C2416yes—
487#11719921C2416yes—
488#11719921C2416yes—
489C4⋊Dic53C2416yes—
490C4⋊Dic53C2416yes—
491C4⋊Dic53C2413yes—
492C4⋊Dic53C2413yes—
493C4⋊Dic53C2416yes—
494C4⋊Dic53C2416yes—
495#11719919C2416yes—
496#11719919C2416yes—
497#11719919C2416yes—
498#11719919C2416yes—
499#11719919C2416yes—
500#11719919C2416yes—
501#11719919C2416yes—
502#11719919C2416yes—
503#11719919C2416yes—
504#11719919C2416yes—
505#11719919C2416yes—
506#11719919C2416yes—
507#11719919C2416yes—
508#11719919C2416yes—
509C4×Dic53C2413yes—
510C4×Dic53C2413yes—
511C4×Dic53C2413yes—
512C4×Dic53C2413yes—
513C4×Dic53C2416yes—
514C4×Dic53C2416yes—
515C4×Dic53C2416yes—
516C4×Dic53C2416yes—
517C4×Dic53C2416yes—
518C4×Dic53C2416yes—
519C4×Dic53C2416yes—
520C4×Dic53C2416yes—
521C4×Dic53C2416yes—
522C23×C53—46no—
523C23×C53C2511yescharacteristic
524C23×C53C2516yes—
525C22×D53—43no—
526C22×D53—46no—
527C22×D53—46no—
528C22×D53—46no—
529C22×D53C2511yescharacteristic
530C22×D53C2511yescharacteristic
531C22×D53C2516yes—
532Q8×C53—46no—
533Q8×C53—43no—
534D4×C53—46no—
535D4×C53—46no—
536D4×C53—43no—
537C2×C4×C53—46no—
538C2×C4×C53—43no—
539C2×C4×C53—46no—
540C2×C4×C53C2516yes—
541C2×C4×C53C2516yes—
542C2×C4×C53C2513yes—
543C2×C4×C53C2516yes—
544C2×C4×C53C2513yes—
545C22⋊D53—212no—
546C22⋊D53—212no—
547C22⋊D53—46no—
548C22⋊D53—46no—
549C22⋊D53—46no—
550C22⋊D53—46no—
551C22⋊D53—46no—
552C2×Dic53—212no—
553C2×Dic53—26no—
554C2×Dic53—46no—
555C2×Dic53—46no—
556C2×Dic53C2516yes—
557C2×Dic53C2516yes—
558C2×Dic53C2516yes—
559C2×Dic53C2513yes—
560C2×Dic53C2513yes—
561D212—46no—
562D212—46no—
563D212—43no—
564D212—46no—
565C4×D53—26no—
566C4×D53—26no—
567C4×D53—212no—
568C4×D53—43no—
569C4×D53—43no—
570C4×D53—46no—
571C4×D53—46no—
572C4×D53—46no—
573C4×D53—46no—
574Dic106—212no—
575Dic106—212no—
576Dic106—46no—
577Dic106—46no—
578Dic106—43no—
579Dic106—46no—
580#62841—531nomaximal, Sylow
581C22×C53—26no—
582C22×C53—23no—
583C22×C53—26no—
584C22×C53—26no—
585C22×C53—162no—
586C22×C53C2611yescharacteristic
587C2×D53—26no—
588C2×D53—23no—
589C2×D53—23no—
590C2×D53—26no—
591C2×D53—26no—
592C2×D53—44no—
593C2×D53—166no—
594C4×C53—26no—
595C4×C53—26no—
596C4×C53—23no—
597C4×C53—26no—
598C4×C53—23no—
599Dic53—26no—
600Dic53—26no—
601Dic53—26no—
602Dic53—23no—
603Dic53#58516yes—
604#3568—533no—
605#3568—531no—
606#3568—533no—
607#3568D5311yescharacteristic, complemented
608#3550—533no—
609#3549—531no—
610#3540—536no—
611#3540—536no—
612#3518—536no—
613#3518—536no—
614#3514—536no—
615#3514—536no—
616#3510—536no—
617#3510—536no—
618#3444—533no—
619C2×C53—41no—
620C2×C53—46no—
621C2×C53C2×#58513yes—
622D53—41no—
623D53—41no—
624D53—46no—
625#563—533no—
626#563—533no—
627#563—533no—
628#563C2×D5313yescomplemented
629H(3,𝔽4)—536no—
630H(3,𝔽4)—533no—
631H(3,𝔽4)—532no—
632H(3,𝔽4)C2×D5311yescharacteristic, complemented
633#560—532no—
634#560—536no—
635#559—536no—
636#559—536no—
637#559—536no—
638#559—536no—
639#559—536no—
640Q82—536no—
641#556—536no—
642#556—536no—
643#556—536no—
644#556—536no—
645#556—536no—
646#556—536no—
647#556—536no—
648#556—536no—
649#556—536no—
650#556—536no—
651#556—536no—
652#556—536no—
653#556—536no—
654#556C2×D5316yescomplemented
655#555—536no—
656#555—536no—
657#555—536no—
658#555—536no—
659#555—536no—
660#551—536no—
661#551—536no—
662#551—536no—
663#551—536no—
664#551—536no—
665#551—536no—
666#551—536no—
667#551—536no—
668#551—536no—
669#551—536no—
670#551—536no—
671#551C2×D5316yescomplemented
672D4×Q8—536no—
673D4×Q8—536no—
674#548—536no—
675#548—536no—
676#548—536no—
677#548—536no—
678#546—536no—
679#546—536no—
680#546—536no—
681#546—536no—
682D42—536no—
683#542—536no—
684#542—536no—
685#542—536no—
686#542—536no—
687#542—536no—
688#542—536no—
689#542—536no—
690#542—536no—
691#542—536no—
692#542—536no—
693#542—536no—
694#542—536no—
695#542—536no—
696#542—536no—
697#542—536no—
698#542C2×D5316yescomplemented
699#538—536no—
700#538—536no—
701#538—536no—
702#538—536no—
703#538—536no—
704#538—536no—
705#538—536no—
706#538C2×D5316yescomplemented
707#536—536no—
708#536—536no—
709#535—536no—
710#535—536no—
711#533—533no—
712#533—533no—
713#533—536no—
714#533—533no—
715#533—536no—
716#532—533no—
717#532—533no—
718#532—533no—
719#529—536no—
720#529—536no—
721#529—536no—
722#529—533no—
723#529—533no—
724#529—536no—
725#529—536no—
726#529—536no—
727#529—536no—
728#529—536no—
729#529—533no—
730#529C2×D5313yescomplemented
731C2×#124—536no—
732C2×#124—536no—
733#525—536no—
734#525—533no—
735#525—533no—
736#525—536no—
737#519—536no—
738#519—536no—
739#518—536no—
740#518—536no—
741C4×#41—533no—
742C4×#41—533no—
743C4×#41—536no—
744C4×#41—536no—
745C22×C42—531no—
746C53#6284111yescharacteristic, complemented, Sylow
747C2×#41—533no—
748C2×#41—533no—
749C2×#41—536no—
750C2×#41—536no—
751C22×Q8—536no—
752C22×Q8—536no—
753C22×D4—536no—
754C22×D4—536no—
755C23×C4—533no—
756C4⋊Q8—533no—
757C4⋊Q8—536no—
758C4⋊Q8—536no—
759C4⋊Q8—536no—
760C4⋊Q8—533no—
761C4⋊Q8—533no—
762C4⋊Q8—536no—
763C4⋊Q8—536no—
764C4⋊Q8—536no—
765C4⋊Q8—536no—
766C4⋊Q8C22×D5316yes—
767#127—533no—
768#127—536no—
769#127—532no—
770#126—536no—
771#126—536no—
772#126—536no—
773#126—536no—
774#126—536no—
775#126—536no—
776#126—536no—
777#126—536no—
778#126—536no—
779#126—536no—
780#126—536no—
781#126—536no—
782#126—536no—
783#126—536no—
784#126—536no—
785#126—536no—
786#126—536no—
787#126—536no—
788#126—532no—
789#126C22×D5316yes—
790#126C22×D5316yes—
791#126C22×D5316yes—
792#126C22×D5316yes—
793#126C22×D5312yes—
794#125—536no—
795#125—536no—
796#125—533no—
797#125C22×D5313yes—
798#124—536no—
799#124—536no—
800#124—536no—
801#124—536no—
802#124—536no—
803#124—536no—
804#124—536no—
805#124—536no—
806#124—536no—
807#124—536no—
808#124—536no—
809#124—536no—
810#124—536no—
811#124—536no—
812#124—536no—
813#124—536no—
814#124—536no—
815#124—536no—
816#124—536no—
817#124—536no—
818#124—536no—
819#124—536no—
820#124—536no—
821#124—536no—
822#124—536no—
823#124—533no—
824#124—536no—
825#124—536no—
826#124C22×D5316yes—
827#124C22×D5313yes—
828#124C22×D5316yes—
829#124C22×D5316yes—
830#123—536no—
831#123—536no—
832#123—536no—
833#123—536no—
834#123—536no—
835#123—536no—
836#123—536no—
837#123—536no—
838#123—536no—
839#123—536no—
840#123—536no—
841#123—536no—
842#123—536no—
843#123—536no—
844#123—536no—
845#123—536no—
846#123—536no—
847#123—536no—
848#123—536no—
849#123C22×D5316yes—
850#123C22×D5316yes—
851#123C22×D5316yes—
852C22⋊Q8—533no—
853C22⋊Q8—536no—
854C22⋊Q8—533no—
855C22⋊Q8—536no—
856C22⋊Q8—536no—
857C22⋊Q8—536no—
858C22⋊Q8—533no—
859C22⋊Q8—536no—
860C22⋊Q8—536no—
861C22⋊Q8—536no—
862C22⋊Q8—536no—
863C22⋊Q8—536no—
864C22⋊Q8—536no—
865C22⋊Q8—536no—
866C22⋊Q8—536no—
867C22⋊Q8—536no—
868C22⋊Q8—536no—
869C22⋊Q8—536no—
870C22⋊Q8—536no—
871C22⋊Q8—536no—
872C22⋊Q8—536no—
873C22⋊Q8—536no—
874C22⋊Q8—536no—
875C22⋊Q8—536no—
876C22⋊Q8C22×D5313yes—
877C22⋊Q8C22×D5316yes—
878C22⋊Q8C22×D5316yes—
879C22⋊Q8C22×D5316yes—
880#121—533no—
881#121—536no—
882#121—536no—
883#121—536no—
884#121—536no—
885#121—536no—
886#121—536no—
887#121—533no—
888#121—536no—
889#121—533no—
890#121—536no—
891#121—536no—
892#121—536no—
893#121—536no—
894#121—536no—
895#121—536no—
896#121—536no—
897#121—536no—
898#121C22×D5313yes—
899#121C22×D5316yes—
900#120—532no—
901#120—532no—
902#120—536no—
903#120—536no—
904#120—536no—
905#120—536no—
906#120—536no—
907#120—536no—
908#120—536no—
909#120—536no—
910#120C22×D5316yes—
911#120C22×D5312yes—
912C4×Q8—533no—
913C4×Q8—536no—
914C4×Q8—536no—
915C4×Q8—536no—
916C4×Q8—536no—
917C4×Q8—533no—
918C4×Q8—536no—
919C4×Q8—536no—
920C4×Q8—536no—
921C4×Q8—536no—
922C4×Q8—536no—
923C4×Q8—536no—
924C4×Q8—533no—
925C4×Q8—536no—
926C4×Q8—536no—
927C4×Q8—536no—
928C4×Q8—536no—
929C4×Q8—536no—
930C4×Q8C22×D5313yes—
931C4×Q8C22×D5316yes—
932C4×D4—536no—
933C4×D4—533no—
934C4×D4—536no—
935C4×D4—536no—
936C4×D4—536no—
937C4×D4—536no—
938C4×D4—536no—
939C4×D4—536no—
940C4×D4—536no—
941C4×D4—536no—
942C4×D4—536no—
943C4×D4—536no—
944C4×D4—536no—
945C4×D4—533no—
946C4×D4—536no—
947C4×D4—536no—
948C4×D4—536no—
949C4×D4—536no—
950C4×D4—536no—
951C4×D4—536no—
952C4×D4—536no—
953C4×D4—536no—
954C4×D4—536no—
955C4×D4—536no—
956C4×D4—536no—
957C4×D4—536no—
958C4×D4—536no—
959C4×D4—533no—
960C4×D4—536no—
961C4×D4C22×D5316yes—
962C4×D4C22×D5313yes—
963C4×D4C22×D5316yes—
964#117—536no—
965#117—536no—
966#117—533no—
967#117—533no—
968#117—536no—
969#117—536no—
970#117—536no—
971#117—536no—
972#117—536no—
973#117—536no—
974#117—536no—
975#117—536no—
976#117—536no—
977#117—536no—
978#117—536no—
979#117—536no—
980#117—536no—
981#117—536no—
982#117—536no—
983#117—536no—
984#117C22×D5316yes—
985#117C22×D5316yes—
986C2×C22⋊C4—536no—
987C2×C22⋊C4—536no—
988C2×C22⋊C4—536no—
989C2×C22⋊C4—536no—
990C2×C22⋊C4—536no—
991C2×C22⋊C4—536no—
992C2×C22⋊C4—536no—
993C2×C22⋊C4C22×D5316yes—
994C2×C42—536no—
995C2×C42—533no—
996C2×C42—536no—
997C2×C42—533no—
998C2×C42—533no—
999C2×C42—531no—
1000C2×C42—531no—
1001C2×C42C22×D5311yescharacteristic
1002C24—536no—
1003C24—531no—
1004C24C23×D5312yes—
1005#41—21212no—
1006#41—2126no—
1007#41—2126no—
1008#41—21212no—
1009C2×Q8—536no—
1010C2×Q8—536no—
1011C2×Q8—536no—
1012C2×Q8—536no—
1013C2×Q8—536no—
1014C2×Q8—533no—
1015C2×Q8—21212no—
1016C2×Q8—21212no—
1017C2×Q8C23×D5316yes—
1018C2×Q8C23×D5313yes—
1019C2×D4—536no—
1020C2×D4—536no—
1021C2×D4—536no—
1022C2×D4—536no—
1023C2×D4—536no—
1024C2×D4—536no—
1025C2×D4—536no—
1026C2×D4—533no—
1027C2×D4—536no—
1028C2×D4—536no—
1029C2×D4—536no—
1030C2×D4—21212no—
1031C2×D4—21212no—
1032C2×D4C23×D5313yes—
1033C2×D4C23×D5316yes—
1034C2×D4C23×D5316yes—
1035C22×C4—533no—
1036C22×C4—536no—
1037C22×C4—536no—
1038C22×C4—536no—
1039C22×C4—533no—
1040C22×C4—533no—
1041C22×C4—536no—
1042C22×C4—533no—
1043C22×C4—533no—
1044C22×C4—536no—
1045C22×C4—536no—
1046C22×C4—536no—
1047C22×C4—536no—
1048C22×C4—2126no—
1049C22×C4C23×D5313yes—
1050C22×C4C23×D5316yes—
1051C22×C4C23×D5316yes—
1052C4⋊C4—536no—
1053C4⋊C4—536no—
1054C4⋊C4—536no—
1055C4⋊C4—536no—
1056C4⋊C4—536no—
1057C4⋊C4—536no—
1058C4⋊C4—536no—
1059C4⋊C4—536no—
1060C4⋊C4—536no—
1061C4⋊C4—536no—
1062C4⋊C4—533no—
1063C4⋊C4—533no—
1064C4⋊C4—536no—
1065C4⋊C4—536no—
1066C4⋊C4—536no—
1067C4⋊C4—536no—
1068C4⋊C4—536no—
1069C4⋊C4—536no—
1070C4⋊C4—536no—
1071C4⋊C4—536no—
1072C4⋊C4C23×D5316yes—
1073C4⋊C4C23×D5316yes—
1074C4⋊C4C23×D5313yes—
1075C4⋊C4C23×D5313yes—
1076C4⋊C4C23×D5316yes—
1077C4⋊C4C23×D5316yes—
1078C4⋊C4C23×D5316yes—
1079C4⋊C4C23×D5316yes—
1080C22⋊C4—536no—
1081C22⋊C4—536no—
1082C22⋊C4—536no—
1083C22⋊C4—536no—
1084C22⋊C4—536no—
1085C22⋊C4—536no—
1086C22⋊C4—536no—
1087C22⋊C4—536no—
1088C22⋊C4—536no—
1089C22⋊C4—536no—
1090C22⋊C4—536no—
1091C22⋊C4—536no—
1092C22⋊C4—536no—
1093C22⋊C4—536no—
1094C22⋊C4—536no—
1095C22⋊C4—536no—
1096C22⋊C4—536no—
1097C22⋊C4—536no—
1098C22⋊C4—536no—
1099C22⋊C4—536no—
1100C22⋊C4—536no—
1101C22⋊C4—536no—
1102C22⋊C4—536no—
1103C22⋊C4—536no—
1104C22⋊C4—536no—
1105C22⋊C4C23×D5316yes—
1106C22⋊C4C23×D5316yes—
1107C22⋊C4C23×D5316yes—
1108C22⋊C4C23×D5316yes—
1109C22⋊C4C23×D5316yes—
1110C22⋊C4C23×D5316yes—
1111C22⋊C4C23×D5316yes—
1112C22⋊C4C23×D5316yes—
1113C22⋊C4C23×D5316yes—
1114C42—533no—
1115C42—533no—
1116C42—533no—
1117C42—533no—
1118C42—536no—
1119C42—536no—
1120C42—536no—
1121C42—536no—
1122C42—536no—
1123C42—536no—
1124C42—536no—
1125C42—536no—
1126C42—536no—
1127C42C23×D5313yes—
1128C42C23×D5311yescharacteristic
1129C42C23×D5316yes—
1130C42C23×D5312yes—
1131C42C23×D5316yes—
1132C23—46no—
1133C23—536no—
1134C23—531no—
1135C23—531no—
1136C23—2126no—
1137C23—2126no—
1138C23—2126no—
1139C23—2123no—
1140C23C24×D5316yes—
1141C23C24×D5311yescharacteristic
1142Q8—46no—
1143Q8—43no—
1144Q8—10612no—
1145Q8—10612no—
1146Q8—2126no—
1147Q8—2126no—
1148Q8—2126no—
1149Q8—2123no—
1150D4—46no—
1151D4—43no—
1152D4—46no—
1153D4—10612no—
1154D4—10612no—
1155D4—2126no—
1156D4—2126no—
1157D4—2123no—
1158D4—2126no—
1159D4—2126no—
1160D4—2126no—
1161D4—2126no—
1162D4—2126no—
1163D4—2126no—
1164C2×C4—43no—
1165C2×C4—46no—
1166C2×C4—46no—
1167C2×C4—533no—
1168C2×C4—533no—
1169C2×C4—536no—
1170C2×C4—536no—
1171C2×C4—536no—
1172C2×C4—1066no—
1173C2×C4—1066no—
1174C2×C4—10612no—
1175C2×C4—1066no—
1176C2×C4—10612no—
1177C2×C4—2123no—
1178C2×C4—2123no—
1179C2×C4—2126no—
1180C2×C4—2126no—
1181C2×C4—2126no—
1182C2×C4—2126no—
1183C2×C4—2126no—
1184C2×C4—2126no—
1185C2×C4C24×D5313yes—
1186C2×C4C24×D5316yes—
1187C2×C4C24×D5316yes—
1188C2×C4C24×D5316yes—
1189C2×C4C24×D5313yes—
1190C22—26no—
1191C22—23no—
1192C22—26no—
1193C22—26no—
1194C22—162no—
1195C22—8486no—
1196C22—1066no—
1197C22—1063no—
1198C22—1063no—
1199C22—1066no—
1200C22—1066no—
1201C22—2124no—
1202C22C25×D5311yescharacteristic
1203C4—23no—
1204C4—26no—
1205C4—23no—
1206C4—26no—
1207C4—26no—
1208C4—536no—
1209C4—1063no—
1210C4—1066no—
1211C4—1066no—
1212C4—1066no—
1213C2—46no—
1214C2—41no—
1215C2—2126no—
1216C2—2121no—
1217C2—2121no—
1218C2#585×D5313yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3568C2
hypercenter#3568D53
hypocenterC53#62841
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3568

Complements

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

NH ≅ G/Ntype
1. #20289412C2semidirect
2. #20289411C2semidirect
3. #20289409C2semidirect
4. #20289125C2semidirect
5. #20289119C2semidirect
6. #20288986C2semidirect
7. #20288980C2semidirect
8. #20288728C2semidirect
9. #20288725C2semidirect
10. #20288668C2semidirect
11. #20288665C2semidirect
12. #20288605C2semidirect
13. #20288603C2semidirect
14. #20288009C2semidirect
15. C53×#3568C2semidirect
16. #16811377C22semidirect
17. #16811377C22semidirect
18. #16811373C22semidirect
19. #16811366C22semidirect
20. #16811365C22semidirect
21. #16811365C22semidirect
22. #16811364C22semidirect
23. #16811361C22semidirect
24. #16811358C22semidirect
25. #16811357C22semidirect
26. #16811357C22semidirect
27. #16811356C22semidirect
28. #16811355C22semidirect
29. #16811353C22semidirect
30. #16811347C22semidirect
31. #16811345C22semidirect
32. #16811345C22semidirect
33. #16811344C22semidirect
34. #16811342C22semidirect
35. #16811342C22semidirect
36. #16811341C22semidirect
37. #16811340C22semidirect
38. #16811340C22semidirect
39. #16811340C22semidirect
40. #16811340C22semidirect
41. #16811340C22semidirect
42. #16811340C22semidirect
43. #16811337C22semidirect
44. #16811336C22semidirect
45. #16811335C22semidirect
46. #16811335C22semidirect
47. #16811335C22semidirect
48. #16811304C22semidirect
49. #16811302C22semidirect
50. #16811300C22semidirect
51. #16811300C22semidirect
52. #16811299C22semidirect
53. #16811298C22semidirect
54. #16811298C22semidirect
55. #16811298C22semidirect
56. #16811297C22semidirect
57. #16811297C22semidirect
58. #16811296C22semidirect
59. #16811286C22semidirect
60. #16811286C22semidirect
61. #16811283C22semidirect
62. #16811282C22semidirect
63. #16811281C22semidirect
64. #16811279C22semidirect
65. #16811265C22semidirect
66. #16811263C22semidirect
67. #16811262C22semidirect
68. #16811260C22semidirect
69. #16811255C22semidirect
70. #16811247C22semidirect
71. #16811246C22semidirect
72. #16811243C22semidirect
73. #16811243C22semidirect
74. #16811243C22semidirect
75. #16811243C22semidirect
76. #16811241C22semidirect
77. #16811241C22semidirect
78. #16811239C22semidirect
79. #16811239C22semidirect
80. #16811239C22semidirect
81. #16811239C22semidirect
82. #16811238C22semidirect
83. #16811237C22semidirect
84. #16811237C22semidirect
85. #16811213C22semidirect
86. #16811212C22semidirect
87. #16811209C22semidirect
88. #16811209C22semidirect
89. #16811208C22semidirect
90. #16811206C22semidirect
91. #16811205C22semidirect
92. #16811198C22semidirect
93. #16811195C22semidirect
96. #16811179C22semidirect
97. #16811177C22semidirect
98. #16811177C22semidirect
99. #16811175C22semidirect
100. #16811175C22semidirect
104. #16811158C22semidirect
105. #16811157C22semidirect
106. #16811156C22semidirect
107. #16811156C22semidirect
108. #16811156C22semidirect
109. #16811153C22semidirect
110. #16811152C22semidirect
111. #16811151C22semidirect
112. #16811151C22semidirect
113. #16811150C22semidirect
114. #16811150C22semidirect
115. C2×#13133203C22semidirect
116. #124×D53C22semidirect
117. #16811136C22semidirect
118. #16811133C22semidirect
119. #16811132C22semidirect
120. #16811131C22semidirect
121. #16811100C22semidirect
122. #16811099C22semidirect
123. #16811096C22semidirect
124. #16811095C22semidirect
125. C4×#11719949C22semidirect
126. #16811091C22semidirect
127. C4×#11719947C22semidirect
128. C4×#11719947C22semidirect
129. C2×C42×D53C22semidirect
130. C53×#563C22semidirect
131. C53×H(3,𝔽4)C22semidirect
132. C53×#556C22semidirect
133. C53×#551C22semidirect
134. C53×#542C22semidirect
135. C53×#538C22semidirect
136. C53×#529C22semidirect
607. #3568D53semidirect
628. #563C2×D53semidirect
632. H(3,𝔽4)C2×D53semidirect
654. #556C2×D53semidirect
671. #551C2×D53semidirect
698. #542C2×D53semidirect
706. #538C2×D53semidirect
730. #529C2×D53semidirect
746. C53#62841semidirect

Maximal subgroups

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

subgroupindex
#202894122
#202894112
#202894092
#202891252
#202891192
#202889862
#202889802
#202887282
#202887252
#202886682
#202886652
#202886052
#202886032
#202880092
C53×#35682
#6284153