Finite Group Databasebeta

← #28293318

Subgroups — #28293318

Order 13568.

6854 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288811C212yesmaximal, complemented
2#20288805C212yesmaximal, complemented
3#20288785C216yesmaximal, complemented
4#20288783C216yesmaximal, complemented
5#20288710C212yesmaximal, complemented
6#20288708C212yesmaximal, complemented
7#20288693C216yesmaximal, complemented
8#20288683C216yesmaximal, complemented
9#20288632C213yesmaximal, complemented
10#20288596C213yesmaximal, complemented
11#20288537C211yesmaximal, characteristic, complemented
12#20288496C211yesmaximal, characteristic, complemented
13#20288468C213yesmaximal, complemented
14#20288457C213yesmaximal, complemented
15#20288396C211yesmaximal, characteristic, complemented
16#20288388C211yesmaximal, characteristic, complemented
17#20288148C213yesmaximal, complemented
18#20288142C213yesmaximal, complemented
19#20288100C213yesmaximal, complemented
20C2×#16811231C213yesmaximal, complemented
21C4×#13133264C211yesmaximal, characteristic, complemented
22#20287914C211yesmaximal, characteristic, complemented
23C4×2−1+4×C53C211yesmaximal, characteristic, complemented
24C2×#13133264C2211yescharacteristic
25C2×#41×D53C2211yescharacteristic
26#16811352C2212yescomplemented
27#16811351C2216yescomplemented
28#16811351C2216yescomplemented
29#16811349C2212yescomplemented
30#16811346C2216yes—
31#16811345C2216yescomplemented
32#16811345C2216yescomplemented
33#16811341C2216yes—
34#16811333C2216yescomplemented
35#16811332C2216yescomplemented
36#16811330C2216yescomplemented
37#16811328C2216yescomplemented
38#16811322C22112yescomplemented
39#16811321C2216yescomplemented
40#16811319C22112yescomplemented
41#16811317C2216yescomplemented
42#16811314C2216yes—
43#16811314C2216yescomplemented
44#16811313C22112yescomplemented
45#16811312C2216yescomplemented
46#16811312C2216yescomplemented
47#16811308C2216yes—
48#16811308C2216yescomplemented
49#16811306C22112yescomplemented
50#16811306C22112yescomplemented
51#16811306C22112yescomplemented
52#16811302C22112yes—
53#16811297C22112yes—
54Q8×D212C2212yes—
55Q8×C22⋊D53C2212yes—
56Q8×C22⋊D53C2212yescomplemented
57Q8×C22⋊D53C2212yescomplemented
58#16811285C2212yes—
59#16811284C2212yes—
60#16811277C2216yes—
61#16811272C2216yes—
62#16811272C2216yescomplemented
63#16811272C2216yescomplemented
64#16811268C2216yes—
65#16811261C2216yes—
66#16811254C2213yescomplemented
67#16811251C2213yescomplemented
68#16811245C2213yes—
69#16811245C2216yescomplemented
70#16811245C2213yescomplemented
71#16811244C2216yescomplemented
72#16811238C2213yes—
73#16811238C2213yescomplemented
74#16811235C2216yescomplemented
75#16811231C2216yes—
76#16811231C2216yes—
77#16811231C2213yes—
78#16811231C2216yes—
79#16811231C2216yescomplemented
80#16811231C2216yescomplemented
81#16811231C2216yescomplemented
82#16811231C2216yescomplemented
83#16811231C2216yescomplemented
84#16811231C2213yescomplemented
85#16811224C2211yescharacteristic
86#16811224C2213yescomplemented
87#16811220C22112yescomplemented
88#16811215C22112yescomplemented
89#16811215C2216yescomplemented
90#16811215C2216yescomplemented
91#16811206C2216yes—
92#16811206C2216yes—
93#16811204C2213yes—
94#16811201C2213yes—
95#16811199C2213yes—
96#16811197C2213yes—
97#16811197C2213yescomplemented
98#16811194C2213yescomplemented
99#16811180C2216yescomplemented
100#16811177C2216yescomplemented
101#16811177C2216yescomplemented
102#16811177C2216yescomplemented
103#16811176C2213yescomplemented
104#16811169C2213yescomplemented
105C2×#13133215C2213yescomplemented
106#16811160C2216yescomplemented
107#16811160C2216yescomplemented
108#16811157C2216yes—
109#16811157C2216yescomplemented
110#16811157C22112yescomplemented
111#16811157C2216yescomplemented
112#16811155C2216yescomplemented
113#16811153C22112yescomplemented
114#16811151C2216yes—
115#16811151C2216yescomplemented
116C2×#13133212C2216yes—
117C2×#13133211C2216yes—
118C2×#13133209C2216yescomplemented
119C2×#13133208C2213yescomplemented
120C2×#13133207C2216yescomplemented
121#16811135C2213yes—
122#16811130C2213yes—
123C2×#13133197C2213yes—
124C2×#13133193C2213yes—
125#16811106C2211yescharacteristic
126#16811105C2211yescharacteristic
127#16811105C2211yescharacteristic
128#16811103C2213yescomplemented
129#16811102C2213yes—
130#16811102C2213yes—
131#16811102C2216yescomplemented
132#16811100C2213yescomplemented
133#16811099C2211yescharacteristic
134#16811099C2211yescharacteristic
135#16811099C2212yescomplemented
136#16811095C2213yes—
137#16811095C2213yes—
138#41×Dic53C2211yescharacteristic
139C4×#11719945C2213yes—
140C4×#11719945C2213yescomplemented
141#16811091C2213yes—
142C4×#11719947C2216yescomplemented
143C2×C4×Dic106C2213yescomplemented
144C4×Q8×D53C2212yescomplemented
145C2×#13133174C2213yes—
146#117×D53C2213yes—
147C2×2−1+4×C53C2211yescharacteristic
148C53×#520C2211yescharacteristic
149C53×#520C2216yescomplemented
150C53×#520C2213yescomplemented
151C53×#519C2212yescomplemented
152C53×#519C2213yescomplemented
153C4×#41×C53C2211yescharacteristic
154C4×#41×C53C2216yescomplemented
155C4×#41×C53C2213yescomplemented
156C2×C4×Q8×C53C2212yescomplemented
157C2×C4×Q8×C53C2213yescomplemented
158#13133264—28no—
159C2×#11719949C2311yescharacteristic
160C2×#11719945C2313yes—
161C2×#11719945C2313yes—
162C2×#11719947C2316yes—
163C2×#11719947C2313yes—
164#41×D53—28no—
165C22×Dic106C2313yes—
166C2×Q8×D53C2312yes—
167C2×Q8×D53C2311yescharacteristic
168C2×D4×D53C2313yes—
169C22×C4×D53C2313yes—
170#13133217C2316yes—
171#13133217C2316yes—
172#13133216C2316yes—
173#13133216C2313yes—
174#13133216C2313yes—
175#13133215C2316yes—
176#13133215C2316yes—
177#13133215C2316yes—
178#13133215C2313yes—
179#13133215C2316yes—
180#13133213C2311yescharacteristic
181#13133212C23112yes—
182#13133212C2316yes—
183#13133212C23112yes—
184#13133212C23112yes—
185#13133212C2316yes—
186#13133212C23112yes—
187#13133211C23112yes—
188#13133211C2316yes—
189#13133211C2316yes—
190#13133211C23112yes—
191#13133211C2316yes—
192#13133211C23112yes—
193#13133211C2316yes—
194#13133210C2316yes—
195#13133210C23112yes—
196#13133210C2316yes—
197#13133209C2316yes—
198#13133209C23112yes—
199#13133209C23112yes—
200#13133209C2316yes—
201#13133209C2316yes—
202#13133209C23112yes—
203#13133208C2316yes—
204#13133208C2316yes—
205#13133208C2316yes—
206#13133208C2313yes—
207#13133208C2316yes—
208#13133208C2311yescharacteristic
209#13133207C23112yes—
210#13133207C2316yes—
211#13133207C23112yes—
212#13133207C23112yes—
213#13133207C23112yes—
214#13133207C2316yes—
215#13133207C23112yes—
216#13133206C2316yes—
217#13133206C2313yes—
218#13133205C2316yes—
219#13133205C2316yes—
220#13133205C2316yes—
221#13133204C2313yes—
222#13133203C2316yes—
223#13133203C2316yes—
224#13133202C2316yes—
225#13133202C23112yes—
226#13133202C2316yes—
227#13133201C23112yes—
228#13133201C2316yes—
229#13133200C23112yes—
230#13133200C23112yes—
231#13133200C2316yes—
232#13133200C2316yes—
233#13133200C2316yes—
234#13133200C2312yes—
235#13133199C23112yes—
236#13133199C2316yes—
237#13133199C2312yes—
238#13133198C2316yes—
239#13133198C23112yes—
240#13133197C2316yes—
241#13133197C2316yes—
242#13133197C2316yes—
243#13133197C2313yes—
244#13133197C2316yes—
245#13133197C2313yes—
246#13133196C2316yes—
247#13133196C2316yes—
248#13133196C2316yes—
249#13133196C23112yes—
250#13133196C2316yes—
251#13133196C2316yes—
252#13133195C23112yes—
253#13133195C23112yes—
254#13133195C2316yes—
255#13133195C2316yes—
256#13133194C23112yes—
257#13133194C2316yes—
258#13133194C2316yes—
259#13133193C2316yes—
260#13133193C2316yes—
261#13133193C2316yes—
262#13133193C2316yes—
263#13133193C2313yes—
264#13133193C2316yes—
265#13133193C2313yes—
266#13133192C2316yes—
267#13133192C2311yescharacteristic
268#13133192C2313yes—
269#13133191C23112yes—
270#13133191C2316yes—
271#13133191C2316yes—
272#13133191C2312yes—
273#13133190C2316yes—
274#13133190C2312yes—
275#13133189C23112yes—
276#13133189C2316yes—
277#13133189C2316yes—
278#13133188C2311yescharacteristic
279#13133188C2313yes—
280#13133187C2316yes—
281#13133185C2316yes—
282Q8×Dic53C2312yes—
283Q8×Dic53C2311yescharacteristic
284Q8×Dic53C2311yescharacteristic
285C4×Dic106C23112yes—
286C4×Dic106C23112yes—
287C4×Dic106C2316yes—
288C4×Dic106C2316yes—
289C4×Dic106C2316yes—
290C4×Dic106C2313yes—
291C4×Dic106C2316yes—
292C4×Dic106C2316yes—
293C4×Dic106C2313yes—
294C4×Dic106C2313yes—
295C4×Dic106C2313yes—
296#13133182C2316yes—
297#13133182C2313yes—
298#13133182C2313yes—
299#13133182C2316yes—
300C4×D212C2316yes—
301C4×D212C2316yes—
302C4×D212C23112yes—
303C4×D212C2313yes—
304C4×D212C2313yes—
305C4×D212C2311yescharacteristic
306C4×D212C2313yes—
307D4×Dic53C2316yes—
308D4×Dic53C2313yes—
309D4×Dic53C2313yes—
310#13133179C2313yes—
311#13133179C2313yes—
312C4×C22⋊D53C2316yes—
313C4×C22⋊D53C2316yes—
314C4×C22⋊D53C2316yes—
315C4×C22⋊D53C2316yes—
316C4×C22⋊D53C23112yes—
317C4×C22⋊D53C2316yes—
318C4×C22⋊D53C2316yes—
319C4×C22⋊D53C2316yes—
320C4×C22⋊D53C2316yes—
321#13133177C23112yes—
322#13133177C2316yes—
323#13133177C2316yes—
324#13133176C23112yes—
325#13133176C2313yes—
326#13133176C2313yes—
327#13133175C2313yes—
328#13133175C2316yes—
329#13133175C2313yes—
330#13133174C23112yes—
331#13133174C23112yes—
332#13133174C23112yes—
333#13133174C2313yes—
334#13133174C2311yescharacteristic
335#13133174C2313yes—
336#13133174C2313yes—
337#13133174C2313yes—
338#13133174C2313yes—
339#13133174C2313yes—
340#13133174C2313yes—
341#13133174C2316yes—
342#13133173C23112yes—
343#13133173C2316yes—
344C2×C4⋊Dic53C2316yes—
345C2×C4⋊Dic53C2316yes—
346C2×C4⋊Dic53C2313yes—
347C2×#11719919C2316yes—
348C2×#11719919C2316yes—
349C2×#11719919C2316yes—
350C2×#11719919C2316yes—
351C2×#11719919C2313yes—
352C2×#11719919C2313yes—
353C2×#11719919C2316yes—
354C4⋊C4×D53C2313yes—
355C4⋊C4×D53C2316yes—
356C4⋊C4×D53C2313yes—
357C2×#11719921C2316yes—
358C2×#11719921C2316yes—
359C2×#11719921C2313yes—
360C2×#11719921C2313yes—
361C22⋊C4×D53C2316yes—
362C2×C4×Dic53C2313yes—
363C2×C4×Dic53C2316yes—
364C42×D53C2316yes—
365C42×D53C2316yes—
3662−1+4×C53—28no—
367C2×#41×C53C2316yes—
368C2×#41×C53C2313yes—
369C2×#41×C53C2311yescharacteristic
370C22×Q8×C53C2312yes—
371C22×Q8×C53C2313yes—
372C4×Q8×C53C2312yes—
373C4×Q8×C53C2311yescharacteristic
374C4×Q8×C53C2316yes—
375C4×Q8×C53C2313yes—
376C4×Q8×C53C2316yes—
377C4×Q8×C53C2316yes—
378C4×Q8×C53C2316yes—
379C4×Q8×C53C2311yescharacteristic
380C4×Q8×C53C2316yes—
381C4×Q8×C53C2313yes—
382C4×D4×C53C2316yes—
383C4×D4×C53C2313yes—
384C4×D4×C53C2313yes—
385C4×D4×C53C2316yes—
386C4×D4×C53C2311yescharacteristic
387C4×D4×C53C23112yes—
388C4×D4×C53C2316yes—
389C4×D4×C53C2313yes—
390#117×C53C2313yes—
391#117×C53C23112yes—
392#117×C53C2313yes—
393#117×C53C2316yes—
394#117×C53C2316yes—
395C2×C4⋊C4×C53C2313yes—
396C2×C4⋊C4×C53C2316yes—
397C2×C4⋊C4×C53C2316yes—
398C2×C42×C53C2313yes—
399C2×C42×C53C2316yes—
400C2×C42×C53C2316yes—
401C23×D53C2413yes—
402#41×C53—224no—
403#41×C53—212no—
404#41×C53#4118yes—
405C2×Q8×C53—28no—
406C2×Q8×C53—212no—
407C2×Q8×C53C2416yes—
408C2×Q8×C53C2413yes—
409C2×Q8×C53C2411yescharacteristic
410C2×D4×C53C2416yes—
411C2×D4×C53C2411yescharacteristic
412C2×D4×C53C2413yes—
413C22×C4×C53C2416yes—
414C22×C4×C53C2416yes—
415C22×C4×C53C2413yes—
416C22×C4×C53C2412yes—
417C22×C4×C53C2413yes—
418C22×C4×C53C2416yes—
419C22×C4×C53C2416yes—
420C22×C4×C53C2413yes—
421C2×C22⋊D53C2416yes—
422C2×C22⋊D53C2416yes—
423C2×C22⋊D53C2412yes—
424C2×C22⋊D53C2416yes—
425C2×C22⋊D53C2412yes—
426C2×C22⋊D53C2412yes—
427C22×Dic53C2416yes—
428C22×Dic53C2413yes—
429C22×Dic53C2413yes—
430C22×Dic53C2413yes—
431C22×Dic53C2416yes—
432#11719949—24no—
433Q8×D53—24no—
434Q8×D53—28no—
435#11719947—212no—
436#11719947—224no—
437D4×D53—212no—
438#11719945—212no—
439#11719945—212no—
440C2×D212C2413yes—
441C2×D212C2411yescharacteristic
442C2×D212C2412yes—
443C2×D212C2416yes—
444C2×C4×D53—212no—
445C2×C4×D53C2413yes—
446C2×C4×D53C2416yes—
447C2×C4×D53C2413yes—
448C2×C4×D53C2411yescharacteristic
449C2×C4×D53C2413yes—
450C2×C4×D53C2412yes—
451C2×C4×D53C2416yes—
452C2×C4×D53C2416yes—
453C2×C4×D53C2416yes—
454C2×Dic106—212no—
455C2×Dic106C2416yes—
456C2×Dic106C2413yes—
457C2×Dic106C2413yes—
458C2×Dic106C2416yes—
459C2×Dic106C2416yes—
460C4⋊C4×C53C2413yes—
461C4⋊C4×C53C2413yes—
462C4⋊C4×C53C2416yes—
463C4⋊C4×C53C24112yes—
464C4⋊C4×C53C2416yes—
465C4⋊C4×C53C2413yes—
466C4⋊C4×C53C2411yescharacteristic
467C4⋊C4×C53C2416yes—
468C22⋊C4×C53C2416yes—
469C22⋊C4×C53C2416yes—
470C22⋊C4×C53C2416yes—
471C22⋊C4×C53C2412yes—
472C42×C53C2411yescharacteristic
473C42×C53C2413yes—
474C42×C53C2416yes—
475C42×C53C2413yes—
476C42×C53C2413yes—
477C42×C53C24112yes—
478C42×C53C2416yes—
479C42×C53C2416yes—
480C22⋊Dic53C2416yes—
481C22⋊Dic53C2416yes—
482C22⋊Dic53C2416yes—
483C22⋊Dic53C2416yes—
484C22⋊Dic53C2412yes—
485C22⋊Dic53C2416yes—
486#11719921C2413yes—
487#11719921C2413yes—
488#11719921C2411yescharacteristic
489#11719921C2411yescharacteristic
490#11719921C2416yes—
491#11719921C2416yes—
492#11719921C2413yes—
493#11719921C2413yes—
494#11719921C2413yes—
495#11719921C2413yes—
496#11719921C24112yes—
497#11719921C24112yes—
498#11719921C2412yes—
499#11719921C2416yes—
500#11719921C2416yes—
501#11719921C2416yes—
502#11719921C2416yes—
503#11719921C2416yes—
504#11719921C2416yes—
505#11719921C2412yes—
506C4⋊Dic53C2416yes—
507C4⋊Dic53C2413yes—
508C4⋊Dic53C2413yes—
509C4⋊Dic53C2413yes—
510C4⋊Dic53C2416yes—
511C4⋊Dic53C2416yes—
512C4⋊Dic53C24112yes—
513C4⋊Dic53C24112yes—
514C4⋊Dic53C2411yescharacteristic
515C4⋊Dic53C2416yes—
516C4⋊Dic53C2412yes—
517#11719919C2413yes—
518#11719919C2413yes—
519#11719919C24112yes—
520#11719919C2411yescharacteristic
521#11719919C2411yescharacteristic
522#11719919C2416yes—
523#11719919C2416yes—
524#11719919C2416yes—
525#11719919C2416yes—
526#11719919C2416yes—
527#11719919C2413yes—
528#11719919C2413yes—
529#11719919C2413yes—
530#11719919C2413yes—
531#11719919C24112yes—
532#11719919C24112yes—
533#11719919C24112yes—
534#11719919C24112yes—
535#11719919C2416yes—
536#11719919C2416yes—
537#11719919C2416yes—
538#11719919C2416yes—
539#11719919C2412yes—
540C4×Dic53C2413yes—
541C4×Dic53C2416yes—
542C4×Dic53C2416yes—
543C4×Dic53C2416yes—
544C4×Dic53C2416yes—
545C4×Dic53C2416yes—
546C4×Dic53C2411yescharacteristic
547C4×Dic53C24112yes—
548C4×Dic53C2413yes—
549C4×Dic53C2413yes—
550C23×C53C2512yes—
551C23×C53C2513yes—
552C22×D53—26no—
553C22×D53—43no—
554C22×D53—43no—
555C22×D53C2512yes—
556C22×D53C2513yes—
557C22×D53C2511yescharacteristic
558Q8×C53—212no—
559Q8×C53—26no—
560Q8×C53C2×#4114yes—
561D4×C53—212no—
562D4×C53—22no—
563D4×C53C2×#41112yes—
564C2×C4×C53—212no—
565C2×C4×C53—212no—
566C2×C4×C53—42no—
567C2×C4×C53—46no—
568C2×C4×C53—46no—
569C2×C4×C53—43no—
570C2×C4×C53—43no—
571C2×C4×C53C2×#41112yes—
572C2×C4×C53C2512yes—
573C2×C4×C53C2516yes—
574C2×C4×C53C2513yes—
575C2×C4×C53C2511yescharacteristic
576C2×C4×C53C2513yes—
577C2×C4×C53C2511yescharacteristic
578C2×C4×C53C2516yes—
579C2×C4×C53C2513yes—
580C2×C4×C53C2511yescharacteristic
581C22⋊D53—212no—
582C22⋊D53—212no—
583C22⋊D53—42no—
584C22⋊D53—46no—
585C22⋊D53—42no—
586C22⋊D53—42no—
587C2×Dic53—212no—
588C2×Dic53—26no—
589C2×Dic53—43no—
590C2×Dic53—43no—
591C2×Dic53—46no—
592C2×Dic53C2516yes—
593C2×Dic53C2512yes—
594C2×Dic53C2513yes—
595C2×Dic53C2513yes—
596C2×Dic53C2513yes—
597C2×Dic53C2516yes—
598C2×Dic53C2511yescharacteristic
599C2×Dic53C2511yescharacteristic
600C2×Dic53C2511yescharacteristic
601D212—22no—
602D212—26no—
603D212—42no—
604D212—46no—
605C4×D53—22no—
606C4×D53—26no—
607C4×D53—26no—
608C4×D53—26no—
609C4×D53—212no—
610C4×D53—42no—
611C4×D53—46no—
612C4×D53—46no—
613C4×D53—46no—
614Dic106—26no—
615Dic106—212no—
616Dic106—26no—
617Dic106—46no—
618Dic106—46no—
619#62861—531nomaximal, Sylow
620C22×C53—23no—
621C22×C53—23no—
622C22×C53—22no—
623C22×C53—22no—
624C22×C53—22no—
625C22×C53C22×#4116yes—
626C22×C53C2611yescharacteristic
627C2×D53—21no—
628C2×D53—22no—
629C2×D53—23no—
630C2×D53—22no—
631C2×D53—23no—
632C2×D53—23no—
633C2×D53—22no—
634C2×D53—21no—
635C2×D53—21no—
636C2×D53—86no—
637C4×C53—26no—
638C4×C53—22no—
639C4×C53—26no—
640C4×C53—23no—
641C4×C53—21no—
642C4×C53—23no—
643C4×C53—21no—
644C4×C53C22×#4116yes—
645C4×C53C22×#4112yes—
646Dic53—26no—
647Dic53—23no—
648Dic53—21no—
649Dic53—22no—
650Dic53—23no—
651Dic53—23no—
652Dic53—26no—
653Dic53—21no—
654Dic53—21no—
655#3523—532no—
656#3523—532no—
657#3521—536no—
658#3521—536no—
659#3516—532no—
660#3516—532no—
661#3515—536no—
662#3515—536no—
663#3512—533no—
664#3509—533no—
665#3504—531no—
666#3499—531no—
667#3495—533no—
668#3495—533no—
669#3489—531no—
670#3489—531no—
671#3461—533no—
672#3461—533no—
673#3455—533no—
674C2×#541—533no—
675C4×2−1+4—531no—
676C4×2−1+4D5311yescharacteristic, complemented
677#3428—531no—
678C2×C53—26no—
679C2×C53—42no—
680C2×C53C23×#4111yescharacteristic
681C2×C532−1+611yescharacteristic
682C2×C532−1+611yescharacteristic
683D53—42no—
684D53—43no—
685D53—41no—
686C2×2−1+4—531no—
687C2×2−1+4C2×D5311yescharacteristic
688C22×#41—531no—
689#557—532no—
690#557—536no—
691#557—536no—
692#557—532no—
693#556—536no—
694#556—536no—
695#556—536no—
696#556—536no—
697#554—536no—
698#554—536no—
699#554—536no—
700#554—536no—
701#553—5312no—
702#553—5312no—
703#553—536no—
704#553—536no—
705#552—536no—
706#552—536no—
707#552—5312no—
708#552—5312no—
709#552—5312no—
710#552—5312no—
711#552—536no—
712#552—536no—
713#552—536no—
714#552—536no—
715#551—5312no—
716#551—5312no—
717D4×Q8—532no—
718D4×Q8—532no—
719D4×Q8—532no—
720D4×Q8—532no—
721#548—532no—
722#548—532no—
723#547—536no—
724#547—536no—
725#547—536no—
726#547—536no—
727#546—536no—
728#546—536no—
729#544—533no—
730#544—533no—
731#542—533no—
732#542—533no—
733#542—536no—
734#542—533no—
735#542—533no—
736#542—536no—
737#541—533no—
738#541—536no—
739#541—536no—
740#541—536no—
741#541—536no—
742#541—536no—
743#541—536no—
744#541—536no—
745#541—533no—
746#541—536no—
747#541—536no—
748#540—531no—
749#540—533no—
750#539—536no—
751#539—536no—
752#539—5312no—
753#539—5312no—
754#538—536no—
755#538—536no—
756#537—533no—
757#537—533no—
758#536—533no—
759#536—533no—
760#536—533no—
761#536—533no—
762#533—536no—
763#533—536no—
764#533—536no—
765#533—533no—
766#533—536no—
767#532—533no—
768C2×C4⋊Q8—533no—
769#529—536no—
770#529—536no—
771#529—5312no—
772#529—536no—
773#529—536no—
774#529—536no—
775#529—536no—
776#529—536no—
777#529—5312no—
778#529—536no—
779C2×#126—536no—
780C2×#126—536no—
781C2×#125—536no—
782C2×#125—533no—
783C2×#125—536no—
784#525—533no—
785#525—533no—
786C2×C22⋊Q8—533no—
787C2×C22⋊Q8—533no—
788#520—531no—
789#520—531no—
790#520—531no—
791#520—533no—
792#520—533no—
793#520—536no—
794#520—533no—
795#520C2×D5311yescharacteristic
796#520C2×D5313yescomplemented
797#520C2×D5316yescomplemented
798#519—531no—
799#519—531no—
800#519—532no—
801#519—533no—
802#519C2×D5313yescomplemented
803#519C2×D5312yescomplemented
804#518—533no—
805#518—533no—
806C4×#41—531no—
807C4×#41—536no—
808C4×#41—533no—
809C4×#41—533no—
810C4×#41—533no—
811C4×#41C2×D5311yescharacteristic
812C4×#41C2×D5313yescomplemented
813C4×#41C2×D5316yescomplemented
814C2×C4×Q8—532no—
815C2×C4×Q8—533no—
816C2×C4×Q8C2×D5313yescomplemented
817C2×C4×Q8C2×D5312yescomplemented
818C2×#117—533no—
819C2×#117—533no—
820C53#6286111yescharacteristic, complemented, Sylow
8212−1+4—28no—
8222−1+4—1068no—
823C2×#41—531no—
824C2×#41—536no—
825C2×#41—533no—
826C2×#41—533no—
827C2×#41—533no—
828C2×#41—1068no—
829C2×#41C22×D5313yes—
830C2×#41C22×D5316yes—
831C2×#41C22×D5311yescharacteristic
832C22×Q8—532no—
833C22×Q8—531no—
834C22×Q8—533no—
835C22×Q8C22×D5313yes—
836C22×Q8C22×D5312yes—
837C22×D4—533no—
838C23×C4—533no—
839C4⋊Q8—533no—
840C4⋊Q8—536no—
841C4⋊Q8—536no—
842C4⋊Q8—536no—
843C4⋊Q8—536no—
844C4⋊Q8—533no—
845C4⋊Q8—533no—
846C4⋊Q8—536no—
847C4⋊Q8—536no—
848C4⋊Q8—536no—
849#127—531no—
850#126—536no—
851#126—5312no—
852#126—5312no—
853#126—5312no—
854#126—536no—
855#126—5312no—
856#126—536no—
857#126—5312no—
858#126—536no—
859#126—536no—
860#126—5312no—
861#126—5312no—
862#126—5312no—
863#126—536no—
864#126—536no—
865#126—536no—
866#125—536no—
867#125—533no—
868#125—536no—
869#125—5312no—
870#125—5312no—
871#125—5312no—
872#125—536no—
873#125—536no—
874#125—536no—
875#125—536no—
876#125—531no—
877#125—5312no—
878#125—5312no—
879#125—536no—
880#125—5312no—
881#125—5312no—
882#125—5312no—
883#125—536no—
884#125—536no—
885#124—533no—
886#124—536no—
887#124—533no—
888#124—536no—
889#124—536no—
890#124—536no—
891#124—536no—
892#124—536no—
893#123—536no—
894#123—5312no—
895#123—536no—
896#123—532no—
897#123—5312no—
898#123—5312no—
899#123—536no—
900#123—536no—
901#123—536no—
902#123—536no—
903#123—5312no—
904#123—536no—
905#123—532no—
906#123—5312no—
907#123—536no—
908#123—5312no—
909C22⋊Q8—533no—
910C22⋊Q8—536no—
911C22⋊Q8—536no—
912C22⋊Q8—536no—
913C22⋊Q8—533no—
914C22⋊Q8—536no—
915C22⋊Q8—536no—
916C22⋊Q8—536no—
917C22⋊Q8—536no—
918C22⋊Q8—536no—
919C22⋊Q8—5312no—
920C22⋊Q8—536no—
921C22⋊Q8—536no—
922C22⋊Q8—533no—
923C22⋊Q8—536no—
924C22⋊Q8—536no—
925C22⋊Q8—536no—
926C22⋊Q8—533no—
927C22⋊Q8—536no—
928C22⋊Q8—536no—
929C22⋊Q8—536no—
930C22⋊Q8—5312no—
931C22⋊Q8—5312no—
932C22⋊Q8—5312no—
933C22⋊Q8—536no—
934C22⋊Q8—536no—
935#121—531no—
936#121—533no—
937#121—5312no—
938#121—536no—
939#121—536no—
940#121—532no—
941#121—5312no—
942#121—536no—
943#121—536no—
944#121—531no—
945#121—533no—
946#121—536no—
947#121—532no—
948#121—536no—
949#120—536no—
950#120—536no—
951C4×Q8—532no—
952C4×Q8—531no—
953C4×Q8—531no—
954C4×Q8—536no—
955C4×Q8—536no—
956C4×Q8—533no—
957C4×Q8—533no—
958C4×Q8—536no—
959C4×Q8—533no—
960C4×Q8—536no—
961C4×Q8—536no—
962C4×Q8—533no—
963C4×Q8—533no—
964C4×Q8—533no—
965C4×Q8—536no—
966C4×Q8—536no—
967C4×Q8—5312no—
968C4×Q8—5312no—
969C4×Q8C22×D5311yescharacteristic
970C4×Q8C22×D5311yescharacteristic
971C4×Q8C22×D5313yes—
972C4×Q8C22×D5316yes—
973C4×Q8C22×D5312yes—
974C4×Q8C22×D5316yes—
975C4×Q8C22×D5316yes—
976C4×Q8C22×D5316yes—
977C4×Q8C22×D5313yes—
978C4×Q8C22×D5316yes—
979C4×D4—533no—
980C4×D4—533no—
981C4×D4—536no—
982C4×D4—536no—
983C4×D4—536no—
984C4×D4—536no—
985C4×D4—536no—
986C4×D4—536no—
987C4×D4—536no—
988C4×D4—5312no—
989C4×D4—536no—
990C4×D4—536no—
991C4×D4—533no—
992C4×D4—533no—
993C4×D4—536no—
994C4×D4—536no—
995C4×D4—5312no—
996C4×D4—531no—
997C4×D4—533no—
998C4×D4—533no—
999C4×D4—533no—
1000C4×D4—536no—
1001C4×D4—536no—
1002C4×D4—5312no—
1003C4×D4C22×D5313yes—
1004C4×D4C22×D5313yes—
1005C4×D4C22×D5316yes—
1006C4×D4C22×D5311yescharacteristic
1007C4×D4C22×D5316yes—
1008C4×D4C22×D5316yes—
1009C4×D4C22×D5313yes—
1010C4×D4C22×D53112yes—
1011#117—533no—
1012#117—533no—
1013#117—5312no—
1014#117—533no—
1015#117—533no—
1016#117—536no—
1017#117—536no—
1018#117—5312no—
1019#117—531no—
1020#117—533no—
1021#117—533no—
1022#117—533no—
1023#117—533no—
1024#117—533no—
1025#117—533no—
1026#117—533no—
1027#117—536no—
1028#117—5312no—
1029#117—5312no—
1030#117—5312no—
1031#117C22×D5313yes—
1032#117C22×D5313yes—
1033#117C22×D5316yes—
1034#117C22×D53112yes—
1035#117C22×D5316yes—
1036C2×C4⋊C4—533no—
1037C2×C4⋊C4—533no—
1038C2×C4⋊C4—533no—
1039C2×C4⋊C4—536no—
1040C2×C4⋊C4—536no—
1041C2×C4⋊C4—536no—
1042C2×C4⋊C4—536no—
1043C2×C4⋊C4—536no—
1044C2×C4⋊C4—536no—
1045C2×C4⋊C4—536no—
1046C2×C4⋊C4—533no—
1047C2×C4⋊C4—533no—
1048C2×C4⋊C4—536no—
1049C2×C4⋊C4C22×D5313yes—
1050C2×C4⋊C4C22×D5316yes—
1051C2×C4⋊C4C22×D5316yes—
1052C2×C22⋊C4—533no—
1053C2×C22⋊C4—533no—
1054C2×C22⋊C4—536no—
1055C2×C22⋊C4—536no—
1056C2×C22⋊C4—536no—
1057C2×C42—533no—
1058C2×C42—536no—
1059C2×C42—536no—
1060C2×C42—536no—
1061C2×C42C22×D5313yes—
1062C2×C42C22×D5316yes—
1063C2×C42C22×D5316yes—
1064C24—533no—
1065#41—224no—
1066#41—212no—
1067#41—1064no—
1068#41—10612no—
1069#41—10624no—
1070#41—10612no—
1071#41—10612no—
1072#41#1171994518yes—
1073C2×Q8—28no—
1074C2×Q8—212no—
1075C2×Q8—536no—
1076C2×Q8—533no—
1077C2×Q8—533no—
1078C2×Q8—536no—
1079C2×Q8—536no—
1080C2×Q8—1064no—
1081C2×Q8—1068no—
1082C2×Q8—10612no—
1083C2×Q8C23×D5313yes—
1084C2×Q8C23×D5316yes—
1085C2×Q8C23×D5311yescharacteristic
1086C2×D4—536no—
1087C2×D4—536no—
1088C2×D4—532no—
1089C2×D4—536no—
1090C2×D4—532no—
1091C2×D4—532no—
1092C2×D4—533no—
1093C2×D4—531no—
1094C2×D4—532no—
1095C2×D4—536no—
1096C2×D4—10612no—
1097C2×D4C23×D5316yes—
1098C2×D4C23×D5311yescharacteristic
1099C2×D4C23×D5313yes—
1100C22×C4—536no—
1101C22×C4—533no—
1102C22×C4—533no—
1103C22×C4—533no—
1104C22×C4—536no—
1105C22×C4—533no—
1106C22×C4—536no—
1107C22×C4—533no—
1108C22×C4—533no—
1109C22×C4—531no—
1110C22×C4—532no—
1111C22×C4—536no—
1112C22×C4—536no—
1113C22×C4—536no—
1114C22×C4—10612no—
1115C22×C4C23×D5316yes—
1116C22×C4C23×D5316yes—
1117C22×C4C23×D5313yes—
1118C22×C4C23×D5313yes—
1119C22×C4C23×D5312yes—
1120C22×C4C23×D5316yes—
1121C22×C4C23×D5316yes—
1122C22×C4C23×D5313yes—
1123C4⋊C4—533no—
1124C4⋊C4—533no—
1125C4⋊C4—531no—
1126C4⋊C4—531no—
1127C4⋊C4—533no—
1128C4⋊C4—536no—
1129C4⋊C4—5312no—
1130C4⋊C4—536no—
1131C4⋊C4—536no—
1132C4⋊C4—536no—
1133C4⋊C4—536no—
1134C4⋊C4—536no—
1135C4⋊C4—536no—
1136C4⋊C4—536no—
1137C4⋊C4—533no—
1138C4⋊C4—533no—
1139C4⋊C4—533no—
1140C4⋊C4—533no—
1141C4⋊C4—533no—
1142C4⋊C4—533no—
1143C4⋊C4—5312no—
1144C4⋊C4—5312no—
1145C4⋊C4—5312no—
1146C4⋊C4—5312no—
1147C4⋊C4—5312no—
1148C4⋊C4—5312no—
1149C4⋊C4—531no—
1150C4⋊C4—536no—
1151C4⋊C4—536no—
1152C4⋊C4—536no—
1153C4⋊C4—536no—
1154C4⋊C4—536no—
1155C4⋊C4—532no—
1156C4⋊C4—532no—
1157C4⋊C4C23×D5313yes—
1158C4⋊C4C23×D5313yes—
1159C4⋊C4C23×D5313yes—
1160C4⋊C4C23×D5316yes—
1161C4⋊C4C23×D5316yes—
1162C4⋊C4C23×D53112yes—
1163C4⋊C4C23×D5311yescharacteristic
1164C4⋊C4C23×D5316yes—
1165C22⋊C4—536no—
1166C22⋊C4—536no—
1167C22⋊C4—536no—
1168C22⋊C4—536no—
1169C22⋊C4—532no—
1170C22⋊C4—536no—
1171C22⋊C4—531no—
1172C22⋊C4—531no—
1173C22⋊C4—533no—
1174C22⋊C4—533no—
1175C22⋊C4—536no—
1176C22⋊C4—536no—
1177C22⋊C4—533no—
1178C22⋊C4—533no—
1179C22⋊C4—533no—
1180C22⋊C4—533no—
1181C22⋊C4—5312no—
1182C22⋊C4—5312no—
1183C22⋊C4—536no—
1184C22⋊C4—532no—
1185C22⋊C4—536no—
1186C22⋊C4—536no—
1187C22⋊C4—536no—
1188C22⋊C4—536no—
1189C22⋊C4—532no—
1190C22⋊C4—536no—
1191C22⋊C4C23×D5316yes—
1192C22⋊C4C23×D5316yes—
1193C22⋊C4C23×D5316yes—
1194C22⋊C4C23×D5312yes—
1195C42—533no—
1196C42—531no—
1197C42—536no—
1198C42—536no—
1199C42—536no—
1200C42—5312no—
1201C42—536no—
1202C42—533no—
1203C42—533no—
1204C42—536no—
1205C42C23×D5313yes—
1206C42C23×D5313yes—
1207C42C23×D5311yescharacteristic
1208C42C23×D5313yes—
1209C42C23×D5316yes—
1210C42C23×D53112yes—
1211C42C23×D5316yes—
1212C42C23×D5316yes—
1213C23—531no—
1214C23—533no—
1215C23—532no—
1216C23—1066no—
1217C23—2123no—
1218C23—2123no—
1219C23C24×D5312yes—
1220C23C24×D5313yes—
1221Q8—212no—
1222Q8—26no—
1223Q8—10612no—
1224Q8—1066no—
1225Q8—1066no—
1226Q8—2126no—
1227Q8—2126no—
1228Q8C2×#1171994514yes—
1229D4—212no—
1230D4—22no—
1231D4—10612no—
1232D4—10612no—
1233D4—1066no—
1234D4—1062no—
1235D4—2122no—
1236D4—2126no—
1237D4—2122no—
1238D4—2126no—
1239D4—2122no—
1240D4—2122no—
1241D4C2×#11719945112yes—
1242C2×C4—212no—
1243C2×C4—212no—
1244C2×C4—43no—
1245C2×C4—42no—
1246C2×C4—43no—
1247C2×C4—46no—
1248C2×C4—46no—
1249C2×C4—532no—
1250C2×C4—533no—
1251C2×C4—533no—
1252C2×C4—536no—
1253C2×C4—536no—
1254C2×C4—531no—
1255C2×C4—531no—
1256C2×C4—533no—
1257C2×C4—531no—
1258C2×C4—1066no—
1259C2×C4—10612no—
1260C2×C4—1062no—
1261C2×C4—1066no—
1262C2×C4—1066no—
1263C2×C4—1066no—
1264C2×C4—10612no—
1265C2×C4—2126no—
1266C2×C4—2126no—
1267C2×C4—2126no—
1268C2×C4—2122no—
1269C2×C4—2123no—
1270C2×C4—2126no—
1271C2×C4—2123no—
1272C2×C4C2×#11719945112yes—
1273C2×C4C24×D5311yescharacteristic
1274C2×C4C24×D5313yes—
1275C2×C4C24×D5313yes—
1276C2×C4C24×D5311yescharacteristic
1277C2×C4C24×D5312yes—
1278C2×C4C24×D5316yes—
1279C2×C4C24×D5316yes—
1280C2×C4C24×D5313yes—
1281C2×C4C24×D5311yescharacteristic
1282C22—23no—
1283C22—23no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—1061no—
1288C22—1062no—
1289C22—1063no—
1290C22—1062no—
1291C22—1063no—
1292C22—1061no—
1293C22—1063no—
1294C22—1062no—
1295C22—1061no—
1296C22—4246no—
1297C22C22×#1171994516yes—
1298C22C25×D5311yescharacteristic
1299C4—26no—
1300C4—21no—
1301C4—23no—
1302C4—22no—
1303C4—21no—
1304C4—23no—
1305C4—26no—
1306C4—1061no—
1307C4—1063no—
1308C4—1066no—
1309C4—1061no—
1310C4—1066no—
1311C4—1063no—
1312C4—1061no—
1313C4—1063no—
1314C4—1062no—
1315C4C22×#1171994516yes—
1316C4C22×#1171994512yes—
1317C2—26no—
1318C2—42no—
1319C2—2121no—
1320C2—2123no—
1321C2—2122no—
1322C2C23×#1171994511yescharacteristic
1323C2#2028952711yescharacteristic
1324C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC4×2−1+4×C53C2
hypercenterC4×2−1+4D53
hypocenterC53#62861
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20288811C2semidirect
2. #20288805C2semidirect
3. #20288785C2semidirect
4. #20288783C2semidirect
5. #20288710C2semidirect
6. #20288708C2semidirect
7. #20288693C2semidirect
8. #20288683C2semidirect
9. #20288632C2semidirect
10. #20288596C2semidirect
11. #20288537C2semidirect
12. #20288496C2semidirect
13. #20288468C2semidirect
14. #20288457C2semidirect
15. #20288396C2semidirect
16. #20288388C2semidirect
17. #20288148C2semidirect
18. #20288142C2semidirect
19. #20288100C2semidirect
20. C2×#16811231C2semidirect
21. C4×#13133264C2semidirect
22. #20287914C2semidirect
23. C4×2−1+4×C53C2semidirect
26. #16811352C22semidirect
27. #16811351C22semidirect
28. #16811351C22semidirect
29. #16811349C22semidirect
31. #16811345C22semidirect
32. #16811345C22semidirect
34. #16811333C22semidirect
35. #16811332C22semidirect
36. #16811330C22semidirect
37. #16811328C22semidirect
38. #16811322C22semidirect
39. #16811321C22semidirect
40. #16811319C22semidirect
41. #16811317C22semidirect
43. #16811314C22semidirect
44. #16811313C22semidirect
45. #16811312C22semidirect
46. #16811312C22semidirect
48. #16811308C22semidirect
49. #16811306C22semidirect
50. #16811306C22semidirect
51. #16811306C22semidirect
56. Q8×C22⋊D53C22semidirect
57. Q8×C22⋊D53C22semidirect
62. #16811272C22semidirect
63. #16811272C22semidirect
66. #16811254C22semidirect
67. #16811251C22semidirect
69. #16811245C22semidirect
70. #16811245C22semidirect
71. #16811244C22semidirect
73. #16811238C22semidirect
74. #16811235C22semidirect
79. #16811231C22semidirect
80. #16811231C22semidirect
81. #16811231C22semidirect
82. #16811231C22semidirect
83. #16811231C22semidirect
84. #16811231C22semidirect
86. #16811224C22semidirect
87. #16811220C22semidirect
88. #16811215C22semidirect
89. #16811215C22semidirect
90. #16811215C22semidirect
97. #16811197C22semidirect
98. #16811194C22semidirect
99. #16811180C22semidirect
100. #16811177C22semidirect
101. #16811177C22semidirect
102. #16811177C22semidirect
103. #16811176C22semidirect
104. #16811169C22semidirect
105. C2×#13133215C22semidirect
106. #16811160C22semidirect
107. #16811160C22semidirect
109. #16811157C22semidirect
110. #16811157C22semidirect
111. #16811157C22semidirect
112. #16811155C22semidirect
113. #16811153C22semidirect
115. #16811151C22semidirect
118. C2×#13133209C22semidirect
119. C2×#13133208C22semidirect
120. C2×#13133207C22semidirect
128. #16811103C22semidirect
131. #16811102C22semidirect
132. #16811100C22semidirect
135. #16811099C22semidirect
140. C4×#11719945C22semidirect
142. C4×#11719947C22semidirect
143. C2×C4×Dic106C22semidirect
144. C4×Q8×D53C22semidirect
149. C53×#520C22semidirect
150. C53×#520C22semidirect
151. C53×#519C22semidirect
152. C53×#519C22semidirect
154. C4×#41×C53C22semidirect
155. C4×#41×C53C22semidirect
156. C2×C4×Q8×C53C22semidirect
157. C2×C4×Q8×C53C22semidirect
676. C4×2−1+4D53semidirect
796. #520C2×D53semidirect
797. #520C2×D53semidirect
802. #519C2×D53semidirect
803. #519C2×D53semidirect
812. C4×#41C2×D53semidirect
813. C4×#41C2×D53semidirect
816. C2×C4×Q8C2×D53semidirect
817. C2×C4×Q8C2×D53semidirect
820. C53#62861semidirect

Maximal subgroups

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

subgroupindex
#202888112
#202888052
#202887852
#202887832
#202887102
#202887082
#202886932
#202886832
#202886322
#202885962
#202885372
#202884962
#202884682
#202884572
#202883962
#202883882
#202881482
#202881422
#202881002
C2×#168112312
C4×#131332642
#202879142
C4×2−1+4×C532
#6286153