Finite Group Databasebeta

← #28292784

Subgroups — #28292784

Order 13568.

7274 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289271C218yesmaximal, complemented
2#20289253C214yesmaximal, complemented
3#20289238C214yesmaximal, complemented
4#20289072C214yesmaximal, complemented
5#20289059C212yesmaximal, complemented
6#20289048C212yesmaximal, complemented
7#20288792C214yesmaximal, complemented
8#20288742C214yesmaximal, complemented
9#20288655C218yesmaximal, complemented
10#20288549C214yesmaximal, complemented
11#20288472C214yesmaximal, complemented
12#20288445C218yesmaximal, complemented
13#20288359C214yesmaximal, complemented
14C2×#16811157C212yesmaximal, complemented
15C2×C53×#532C211yesmaximal, characteristic, complemented
16C2×#13133262C2214yescomplemented
17#16811373C2214yescomplemented
18#16811372C2218yescomplemented
19#16811367C2218yescomplemented
20#16811365C2214yescomplemented
21#16811360C2218yescomplemented
22#16811359C2212yescomplemented
23#16811356C2218yescomplemented
24#16811353C2212yescomplemented
25#16811339C2212yescomplemented
26#16811335C2218yescomplemented
27#16811334C2214yescomplemented
28#16811332C2218yescomplemented
29#16811325C2218yescomplemented
30#16811323C2218yescomplemented
31#16811322C22116yescomplemented
32#16811316C22116yescomplemented
33#16811308C2218yescomplemented
34#16811303C2218yescomplemented
35#16811302C22116yescomplemented
36#16811299C22116yescomplemented
37#16811293C2214yescomplemented
38#16811279C2218yescomplemented
39#16811274C2218yescomplemented
40#16811273C2218yescomplemented
41#16811272C22116yescomplemented
42#16811272C22116yescomplemented
43#16811268C2218yescomplemented
44#16811267C2218yescomplemented
45#16811263C22116yescomplemented
46#16811262C22116yescomplemented
47#16811261C22116yescomplemented
48#16811261C22116yescomplemented
49#16811258C2212yescomplemented
50#16811257C2218yescomplemented
51D4×C22⋊D53C2218yescomplemented
52#16811250C2218yescomplemented
53#16811247C2218yescomplemented
54#16811238C2218yescomplemented
55#16811237C22116yescomplemented
56#16811227C2218yescomplemented
57#16811224C2218yescomplemented
58#16811218C2218yescomplemented
59#16811215C22116yescomplemented
60#16811210C2218yescomplemented
61#16811207C22116yescomplemented
62#16811206C22116yescomplemented
63#16811200C2218yescomplemented
64#16811197C2218yescomplemented
65#16811186C2218yescomplemented
66#16811182C2218yescomplemented
67#16811182C2218yescomplemented
68#16811181C2218yescomplemented
69#16811168C2218yescomplemented
70#16811157C2214yescomplemented
71#16811157C2214yescomplemented
72#16811157C2214yescomplemented
73#16811157C2214yescomplemented
74#16811157C2214yescomplemented
75#16811157C2214yescomplemented
76#16811157C2214yescomplemented
77#16811157C2214yescomplemented
78#16811154C2218yescomplemented
79C2×#13133211C2214yescomplemented
80C2×#13133209C2212yescomplemented
81C2×#13133205C2212yescomplemented
82#16811134C2218yescomplemented
83#16811133C2218yescomplemented
84C2×#13133200C2214yescomplemented
85C2×#13133200C2218yescomplemented
86C2×#13133196C2212yescomplemented
87C2×#13133191C2212yes—
88#121×D53C2218yescomplemented
89#16811102C2218yescomplemented
90#16811098C2214yescomplemented
91#16811095C2218yescomplemented
92C2×C4×Dic106C2212yescomplemented
93C2×C4×D212C2212yescomplemented
94C2×C4×C22⋊D53C2214yescomplemented
95C2×#13133174C2214yescomplemented
96C22×#41×C53C2212yescomplemented
97C53×#532C2214yescomplemented
98C53×#532C2214yescomplemented
99C53×#532C2214yescomplemented
100C53×#532C2214yescomplemented
101C2×C4⋊Q8×C53C2211yescharacteristic, complemented
102C2×#127×C53C2211yescharacteristic, complemented
103C2×#124×C53C2212yescomplemented
104C2×#121×C53C2214yescomplemented
105C2×C4×D4×C53C2214yescomplemented
106C22×C42×C53C2211yescharacteristic, complemented
107#13133262—416no—
108C2×#11719945C2318yes—
109C2×#11719947C2318yes—
110C2×#11719947C23116yes—
111C22×Dic106C2312yes—
112C22×D212C2312yes—
113C22×C22⋊D53C2314yes—
114C22×C22⋊D53C2318yes—
115C2×D4×D53C2318yes—
116C2×D4×D53C23116yes—
117C22×C4×D53C2314yes—
118#13133216C2318yes—
119#13133215C2318yes—
120#13133215C2318yes—
121#13133213C2318yes—
122#13133212C23116yes—
123#13133211C2318yes—
124#13133211C2318yes—
125#13133211C2318yes—
126#13133211C2318yes—
127#13133210C23116yes—
128#13133210C23116yes—
129#13133209C2314yes—
130#13133209C2314yes—
131#13133209C2314yes—
132#13133209C2314yes—
133#13133208C2318yes—
134#13133207C23116yes—
135#13133206C2318yes—
136#13133206C2318yes—
137#13133205C2314yes—
138#13133205C2314yes—
139#13133205C2314yes—
140#13133205C2314yes—
141#13133204C2318yes—
142#13133203C23116yes—
143#13133203C23116yes—
144#13133202C23116yes—
145#13133201C23116yes—
146#13133200C2318yes—
147#13133200C2318yes—
148#13133200C23116yes—
149#13133200C23116yes—
150#13133200C23116yes—
151#13133200C2318yes—
152#13133200C2318yes—
153#13133199C23116yes—
154#13133199C23116yes—
155#13133198C23116yes—
156#13133198C23116yes—
157#13133198C2318yes—
158#13133198C2318yes—
159#13133197C2318yes—
160#13133196C2314yes—
161#13133196C23116yes—
162#13133196C2314yes—
163#13133196C2314yes—
164#13133196C2314yes—
165#13133195C23116yes—
166#13133194C23116yes—
167#13133194C23116yes—
168#13133193C23116yes—
169#13133193C23116yes—
170#13133192C2318yes—
171#13133191C23116yes—
172#13133191C2314yes—
173#13133191C2314yes—
174#13133191C2314yes—
175#13133191C2314yes—
176#13133190C23116yes—
177#13133190C23116yes—
178#13133189C23116yes—
179#13133189C23116yes—
180#13133189C23116yes—
181#13133189C23116yes—
182#13133189C23116yes—
183#13133189C23116yes—
184#13133188C2318yes—
185#13133188C2318yes—
186#13133187C23116yes—
187#13133186C23116yes—
188#13133185C23116yes—
189#13133185C2318yes—
190#13133185C2318yes—
191#13133185C23116yes—
192C4×Dic106C2314yes—
193C4×Dic106C2314yes—
194C4×Dic106C2314yes—
195C4×Dic106C2314yes—
196#13133182C2318yes—
197C4×D212C2314yes—
198C4×D212C2314yes—
199C4×D212C2314yes—
200C4×D212C2314yes—
201D4×Dic53C2318yes—
202D4×Dic53C23116yes—
203D4×Dic53C23116yes—
204D4×Dic53C2318yes—
205#13133179C2318yes—
206C4×C22⋊D53C2318yes—
207C4×C22⋊D53C23116yes—
208C4×C22⋊D53C23116yes—
209C4×C22⋊D53C2318yes—
210C4×C22⋊D53C2318yes—
211C4×C22⋊D53C2318yes—
212#13133177C23116yes—
213#13133177C23116yes—
214#13133176C2318yes—
215#13133175C2318yes—
216#13133174C2318yes—
217#13133174C2318yes—
218#13133174C2318yes—
219#13133174C2318yes—
220#13133173C23116yes—
221C2×C4⋊Dic53C2312yes—
222C2×C4⋊Dic53C2312yes—
223C2×#11719919C2314yes—
224C2×#11719919C2314yes—
225C2×#11719919C23116yes—
226C2×#11719919C2314yes—
227C2×#11719919C2314yes—
228C4⋊C4×D53C2318yes—
229C2×C22⋊Dic53C2318yes—
230C2×C22⋊Dic53C2314yes—
231C2×#11719921C23116yes—
232C2×#11719921C2314yes—
233C2×#11719921C2314yes—
234C2×#11719921C2314yes—
235C2×#11719921C2314yes—
236C22⋊C4×D53C23116yes—
237C2×C4×Dic53C2314yes—
238C2×#41×C53—48no—
239C2×#41×C53C2318yes—
240C2×#41×C53C2318yes—
241C22×Q8×C53C2312yes—
242C22×D4×C53C2314yes—
243C22×D4×C53C2314yes—
244C22×D4×C53C2312yes—
245C23×C4×C53C2311yescharacteristic
246C23×C4×C53C2312yes—
247C23×C4×C53C2314yes—
248C4⋊Q8×C53C2312yes—
249C4⋊Q8×C53C2312yes—
250C4⋊Q8×C53C2314yes—
251#127×C53C2312yes—
252#127×C53C2312yes—
253#127×C53C2314yes—
254#124×C53C2314yes—
255#124×C53C2314yes—
256#124×C53C2318yes—
257#121×C53C2318yes—
258#121×C53C2318yes—
259#121×C53C2318yes—
260#121×C53C2318yes—
261C4×D4×C53C2318yes—
262C4×D4×C53C2318yes—
263C4×D4×C53C2318yes—
264C4×D4×C53C2318yes—
265C2×C4⋊C4×C53C2314yes—
266C2×C22⋊C4×C53C2318yes—
267C2×C42×C53C2312yes—
268C2×C42×C53C2311yescharacteristic
269C2×C42×C53C2311yescharacteristic
270C2×C42×C53C2312yes—
271C2×C42×C53C2312yes—
272C2×C42×C53C2312yes—
273C2×C42×C53C2312yes—
274C24×C53C2414yes—
275C24×C53C2411yescharacteristic
276C23×D53C2414yes—
277C23×D53C2418yes—
278#41×C53—416no—
279#41×C53—416no—
280C2×Q8×C53—44no—
281C2×Q8×C53C2414yes—
282C2×Q8×C53C2414yes—
283C2×D4×C53—216no—
284C2×D4×C53—48no—
285C2×D4×C53—44no—
286C2×D4×C53C2418yes—
287C2×D4×C53C24116yes—
288C2×D4×C53C2418yes—
289C2×D4×C53C2414yes—
290C2×D4×C53C2414yes—
291C22×C4×C53—24no—
292C22×C4×C53—44no—
293C22×C4×C53—48no—
294C22×C4×C53C2412yes—
295C22×C4×C53C2412yes—
296C22×C4×C53C2412yes—
297C22×C4×C53C2411yescharacteristic
298C22×C4×C53C2411yescharacteristic
299C22×C4×C53C2412yes—
300C22×C4×C53C2412yes—
301C22×C4×C53C2414yes—
302C22×C4×C53C2412yes—
303C22×C4×C53C2412yes—
304C22×C4×C53C2412yes—
305C22×C4×C53C24116yes—
306C2×C22⋊D53—216no—
307C2×C22⋊D53—416no—
308C2×C22⋊D53C2418yes—
309C2×C22⋊D53C2418yes—
310C2×C22⋊D53C24116yes—
311C2×C22⋊D53C24116yes—
312C2×C22⋊D53C24116yes—
313C22×Dic53C2414yes—
314C22×Dic53C2414yes—
315C22×Dic53C2414yes—
316C22×Dic53C24116yes—
317C22×Dic53C2418yes—
318#11719947—416no—
319#11719947—432no—
320D4×D53—416no—
321D4×D53—432no—
322#11719945—416no—
323C2×D212—44no—
324C2×D212C2414yes—
325C2×D212C2414yes—
326C2×D212C2418yes—
327C2×C4×D53—48no—
328C2×C4×D53C2418yes—
329C2×C4×D53C2418yes—
330C2×C4×D53C24116yes—
331C2×Dic106—44no—
332C2×Dic106C2414yes—
333C2×Dic106C2414yes—
334C2×Dic106C2418yes—
335C4⋊C4×C53C2418yes—
336C4⋊C4×C53C2418yes—
337C22⋊C4×C53C24116yes—
338C22⋊C4×C53C24116yes—
339C42×C53C2412yes—
340C42×C53C2412yes—
341C42×C53C2412yes—
342C42×C53C2412yes—
343C42×C53C2411yescharacteristic
344C42×C53C2412yes—
345C42×C53C2411yescharacteristic
346C42×C53C2412yes—
347C42×C53C2411yescharacteristic
348C42×C53C2411yescharacteristic
349C22⋊Dic53C24116yes—
350C22⋊Dic53C2418yes—
351C22⋊Dic53C2418yes—
352C22⋊Dic53C2418yes—
353C22⋊Dic53C2418yes—
354C22⋊Dic53C24116yes—
355#11719921C2418yes—
356#11719921C24116yes—
357#11719921C2418yes—
358#11719921C2418yes—
359#11719921C2418yes—
360#11719921C2418yes—
361#11719921C24116yes—
362#11719921C2418yes—
363#11719921C2418yes—
364#11719921C2418yes—
365C4⋊Dic53C2414yes—
366C4⋊Dic53C2414yes—
367C4⋊Dic53C2414yes—
368C4⋊Dic53C2414yes—
369C4⋊Dic53C24116yes—
370#11719919C24116yes—
371#11719919C2418yes—
372#11719919C2418yes—
373#11719919C2418yes—
374#11719919C2418yes—
375#11719919C2418yes—
376#11719919C24116yes—
377#11719919C2418yes—
378#11719919C2418yes—
379#11719919C2418yes—
380C4×Dic53C2418yes—
381C4×Dic53C2418yes—
382C4×Dic53C2418yes—
383C4×Dic53C2418yes—
384C23×C53—28no—
385C23×C53—42no—
386C23×C53—48no—
387C23×C53H(5,𝔽2)14yes—
388C23×C53C2518yes—
389C23×C53C2512yes—
390C23×C53C2511yescharacteristic
391C22×D53—28no—
392C22×D53—44no—
393C22×D53—44no—
394C22×D53—48no—
395C22×D53—416no—
396C22×D53C2518yes—
397Q8×C53—44no—
398Q8×C53—44no—
399D4×C53—232no—
400D4×C53—216no—
401D4×C53—48no—
402D4×C53—44no—
403D4×C53—44no—
404C2×C4×C53—28no—
405C2×C4×C53—22no—
406C2×C4×C53—22no—
407C2×C4×C53—24no—
408C2×C4×C53—24no—
409C2×C4×C53—24no—
410C2×C4×C53—24no—
411C2×C4×C53—24no—
412C2×C4×C53—42no—
413C2×C4×C53—42no—
414C2×C4×C53—42no—
415C2×C4×C53—416no—
416C2×C4×C53C2512yes—
417C2×C4×C53C2518yes—
418C2×C4×C53C2512yes—
419C2×C4×C53C2512yes—
420C2×C4×C53C2511yescharacteristic
421C2×C4×C53C2511yescharacteristic
422C2×C4×C53C2512yes—
423C2×C4×C53C2512yes—
424C22⋊D53—216no—
425C22⋊D53—216no—
426C22⋊D53—416no—
427C22⋊D53—416no—
428C22⋊D53—416no—
429C2×Dic53—28no—
430C2×Dic53—44no—
431C2×Dic53—44no—
432C2×Dic53—48no—
433C2×Dic53—416no—
434C2×Dic53C2518yes—
435C2×Dic53C2518yes—
436C2×Dic53C2518yes—
437D212—28no—
438D212—44no—
439D212—48no—
440C4×D53—216no—
441C4×D53—48no—
442C4×D53—416no—
443Dic106—28no—
444Dic106—44no—
445Dic106—48no—
446#62822—531nomaximal, Sylow
447C22×C53—22no—
448C22×C53—22no—
449C22×C53—22no—
450C22×C53—28no—
451C22×C53—216no—
452C22×C53—44no—
453C22×C53—88no—
454C22×C53C2×H(5,𝔽2)14yes—
455C22×C53C2×H(5,𝔽2)12yes—
456C22×C53C2611yescharacteristic
457C2×D53—28no—
458C2×D53—28no—
459C2×D53—28no—
460C2×D53—88no—
461C2×D53—168no—
462C4×C53—28no—
463C4×C53—22no—
464C4×C53—21no—
465C4×C53—21no—
466C4×C53—22no—
467C4×C53—22no—
468C4×C53—22no—
469C4×C53#58514yes—
470Dic53—28no—
471Dic53—28no—
472Dic53—28no—
473#3560—538no—
474#3559—534no—
475#3558—534no—
476#3545—534no—
477#3544—532no—
478#3543—532no—
479#3522—534no—
480#3519—534no—
481#3513—538no—
482#3505—534no—
483#3496—534no—
484#3494—538no—
485#3485—534no—
486C2×#532D5311yescharacteristic, complemented
487C2×#529—532no—
488C2×C53—24no—
489C2×C53—22no—
490C2×C53—48no—
491C2×C53C22×H(5,𝔽2)11yescharacteristic
492C2×C53C2×#58512yes—
493D53—48no—
494C2×H(5,𝔽2)—534no—
495C22×#41C2×D5312yescomplemented
496#563—538no—
497#563—534no—
498#562—538no—
499H(3,𝔽4)—534no—
500#560—538no—
501#559—532no—
502#559—538no—
503Q82—532no—
504#555—532no—
505#555—538no—
506#554—534no—
507#554—538no—
508#553—5316no—
509#553—538no—
510#553—5316no—
511#553—538no—
512#552—538no—
513#551—538no—
514#551—5316no—
515#551—5316no—
516#550—534no—
517#548—538no—
518#547—5316no—
519#547—5316no—
520#547—538no—
521#547—538no—
522#546—5316no—
523#546—5316no—
524#546—538no—
525#546—5316no—
526#546—538no—
527#546—5316no—
528D42—538no—
529D42—532no—
530D42—538no—
531#544—538no—
532#542—538no—
533#542—5316no—
534#542—538no—
535#540—538no—
536#540—538no—
537#539—538no—
538#539—5316no—
539#538—5316no—
540#538—538no—
541#538—5316no—
542#537—538no—
543#536—538no—
544#535—538no—
545#534—538no—
546#534—538no—
547#534—538no—
548#532—538no—
549#532C2×D5314yescomplemented
550#532C2×D5314yescomplemented
551#532C2×D5314yescomplemented
552#532C2×D5314yescomplemented
553C2×C4⋊Q8C2×D5311yescharacteristic, complemented
554C2×#127C2×D5311yescharacteristic, complemented
555#529—538no—
556#529—534no—
557#529—534no—
558#529—534no—
559#529—534no—
560#529—534no—
561#529—534no—
562#529—534no—
563#529—534no—
564C2×#126—534no—
565C2×#125—532no—
566C2×#124—532no—
567C2×#124C2×D5312yescomplemented
568#525—538no—
569#525—538no—
570C2×#123—534no—
571C2×#123—538no—
572C2×C22⋊Q8—532no—
573C2×#121—532no—
574C2×#121—538no—
575C2×#121C2×D5314yescomplemented
576#520—538no—
577#518—534no—
578#518—538no—
579C2×C4×Q8—532no—
580C2×C4×D4—534no—
581C2×C4×D4—532no—
582C2×C4×D4C2×D5314yescomplemented
583C2×#117—534no—
584C22×C42C2×D5311yescharacteristic, complemented
585C53#6282211yescharacteristic, complemented, Sylow
586H(5,𝔽2)—21216no—
587C2×#41—48no—
588C2×#41—538no—
589C2×#41—5316no—
590C2×#41—538no—
591C2×#41C22×D5318yes—
592C2×#41C22×D5318yes—
593C22×Q8—532no—
594C22×Q8C22×D5312yes—
595C22×D4—534no—
596C22×D4—538no—
597C22×D4—538no—
598C22×D4—5316no—
599C22×D4—532no—
600C22×D4C22×D5314yes—
601C22×D4C22×D5314yes—
602C22×D4C22×D5312yes—
603C23×C4—534no—
604C23×C4C22×D5311yescharacteristic
605C23×C4C22×D5312yes—
606C23×C4C22×D5314yes—
607C4⋊Q8—538no—
608C4⋊Q8—538no—
609C4⋊Q8—538no—
610C4⋊Q8C22×D5314yes—
611C4⋊Q8C22×D5312yes—
612C4⋊Q8C22×D5312yes—
613#127—538no—
614#127C22×D5314yes—
615#127C22×D5312yes—
616#127C22×D5312yes—
617#126—5316no—
618#126—5316no—
619#126—5316no—
620#126—538no—
621#126—538no—
622#126—538no—
623#126—538no—
624#125—538no—
625#125—5316no—
626#125—534no—
627#125—534no—
628#125—534no—
629#125—534no—
630#124—538no—
631#124—538no—
632#124—538no—
633#124—5316no—
634#124—5316no—
635#124—534no—
636#124—534no—
637#124—534no—
638#124—534no—
639#124C22×D5318yes—
640#124C22×D5314yes—
641#124C22×D5314yes—
642#123—5316no—
643#123—538no—
644#123—538no—
645#123—5316no—
646#123—538no—
647#123—538no—
648#123—538no—
649#123—538no—
650#123—5316no—
651#123—5316no—
652#123—5316no—
653#123—5316no—
654#123—5316no—
655#123—5316no—
656#123—5316no—
657C22⋊Q8—5316no—
658C22⋊Q8—5316no—
659C22⋊Q8—534no—
660C22⋊Q8—534no—
661C22⋊Q8—534no—
662C22⋊Q8—534no—
663C22⋊Q8—5316no—
664C22⋊Q8—538no—
665C22⋊Q8—5316no—
666C22⋊Q8—5316no—
667C22⋊Q8—5316no—
668#121—5316no—
669#121—538no—
670#121—538no—
671#121—5316no—
672#121—5316no—
673#121—5316no—
674#121—5316no—
675#121—5316no—
676#121—534no—
677#121—534no—
678#121—534no—
679#121—534no—
680#121—5316no—
681#121—538no—
682#121—5316no—
683#121—5316no—
684#121C22×D5318yes—
685#121C22×D5318yes—
686#121C22×D5318yes—
687#121C22×D5318yes—
688#120—5316no—
689#120—5316no—
690#120—538no—
691#120—5316no—
692#120—538no—
693#120—5316no—
694C4×Q8—538no—
695C4×Q8—534no—
696C4×Q8—534no—
697C4×Q8—534no—
698C4×Q8—534no—
699C4×D4—5316no—
700C4×D4—5316no—
701C4×D4—538no—
702C4×D4—538no—
703C4×D4—538no—
704C4×D4—538no—
705C4×D4—538no—
706C4×D4—538no—
707C4×D4—5316no—
708C4×D4—5316no—
709C4×D4—538no—
710C4×D4—5316no—
711C4×D4—5316no—
712C4×D4—534no—
713C4×D4—534no—
714C4×D4—534no—
715C4×D4—534no—
716C4×D4C22×D5318yes—
717C4×D4C22×D5318yes—
718C4×D4C22×D5318yes—
719C4×D4C22×D5318yes—
720#117—538no—
721#117—538no—
722#117—5316no—
723#117—538no—
724#117—538no—
725#117—538no—
726#117—538no—
727C2×C4⋊C4—534no—
728C2×C4⋊C4—534no—
729C2×C4⋊C4—532no—
730C2×C4⋊C4—534no—
731C2×C4⋊C4—532no—
732C2×C4⋊C4—534no—
733C2×C4⋊C4—5316no—
734C2×C4⋊C4—538no—
735C2×C4⋊C4C22×D5314yes—
736C2×C22⋊C4—534no—
737C2×C22⋊C4—538no—
738C2×C22⋊C4—534no—
739C2×C22⋊C4—534no—
740C2×C22⋊C4—534no—
741C2×C22⋊C4—534no—
742C2×C22⋊C4—5316no—
743C2×C22⋊C4—5316no—
744C2×C22⋊C4C22×D5318yes—
745C2×C42—534no—
746C2×C42C22×D5312yes—
747C2×C42C22×D5312yes—
748C2×C42C22×D5312yes—
749C2×C42C22×D5312yes—
750C2×C42C22×D5311yescharacteristic
751C2×C42C22×D5312yes—
752C2×C42C22×D5311yescharacteristic
753C24—534no—
754C24—538no—
755C24C23×D5314yes—
756C24C23×D5311yescharacteristic
757#41—416no—
758#41—416no—
759#41—21216no—
760#41—21232no—
761#41—21216no—
762C2×Q8—44no—
763C2×Q8—534no—
764C2×Q8—534no—
765C2×Q8—538no—
766C2×Q8—2124no—
767C2×Q8C23×D5314yes—
768C2×Q8C23×D5314yes—
769C2×D4—216no—
770C2×D4—48no—
771C2×D4—44no—
772C2×D4—538no—
773C2×D4—538no—
774C2×D4—5316no—
775C2×D4—5316no—
776C2×D4—5316no—
777C2×D4—534no—
778C2×D4—534no—
779C2×D4—538no—
780C2×D4—10616no—
781C2×D4—2124no—
782C2×D4—21216no—
783C2×D4—21232no—
784C2×D4—21216no—
785C2×D4C23×D5318yes—
786C2×D4C23×D53116yes—
787C2×D4C23×D5318yes—
788C2×D4C23×D5314yes—
789C2×D4C23×D5314yes—
790C22×C4—24no—
791C22×C4—44no—
792C22×C4—48no—
793C22×C4—534no—
794C22×C4—534no—
795C22×C4—534no—
796C22×C4—5316no—
797C22×C4—538no—
798C22×C4—538no—
799C22×C4—538no—
800C22×C4—5316no—
801C22×C4—2128no—
802C22×C4C23×D5312yes—
803C22×C4C23×D5312yes—
804C22×C4C23×D5312yes—
805C22×C4C23×D5312yes—
806C22×C4C23×D5312yes—
807C22×C4C23×D5311yescharacteristic
808C22×C4C23×D5311yescharacteristic
809C22×C4C23×D5314yes—
810C22×C4C23×D5312yes—
811C22×C4C23×D5312yes—
812C22×C4C23×D5312yes—
813C22×C4C23×D53116yes—
814C4⋊C4—538no—
815C4⋊C4—534no—
816C4⋊C4—538no—
817C4⋊C4—5316no—
818C4⋊C4—538no—
819C4⋊C4—534no—
820C4⋊C4—538no—
821C4⋊C4—538no—
822C4⋊C4—538no—
823C4⋊C4—538no—
824C4⋊C4—534no—
825C4⋊C4—5316no—
826C4⋊C4—534no—
827C4⋊C4—538no—
828C4⋊C4—5316no—
829C4⋊C4C23×D5318yes—
830C4⋊C4C23×D5318yes—
831C22⋊C4—538no—
832C22⋊C4—538no—
833C22⋊C4—5316no—
834C22⋊C4—538no—
835C22⋊C4—538no—
836C22⋊C4—5316no—
837C22⋊C4—538no—
838C22⋊C4—538no—
839C22⋊C4—538no—
840C22⋊C4—5316no—
841C22⋊C4—538no—
842C22⋊C4—538no—
843C22⋊C4—538no—
844C22⋊C4—538no—
845C22⋊C4—5316no—
846C22⋊C4—538no—
847C22⋊C4C23×D53116yes—
848C22⋊C4C23×D53116yes—
849C42—538no—
850C42—538no—
851C42—538no—
852C42—538no—
853C42C23×D5311yescharacteristic
854C42C23×D5312yes—
855C42C23×D5312yes—
856C42C23×D5312yes—
857C42C23×D5311yescharacteristic
858C42C23×D5312yes—
859C42C23×D5312yes—
860C42C23×D5312yes—
861C42C23×D5311yescharacteristic
862C42C23×D5311yescharacteristic
863C23—28no—
864C23—42no—
865C23—48no—
866C23—538no—
867C23—1068no—
868C23—2128no—
869C23—21216no—
870C23—2124no—
871C23—2124no—
872C23#1313326214yes—
873C23C24×D5318yes—
874C23C24×D5311yescharacteristic
875C23C24×D5312yes—
876Q8—44no—
877Q8—44no—
878Q8—1068no—
879Q8—2124no—
880Q8—2128no—
881D4—232no—
882D4—216no—
883D4—48no—
884D4—44no—
885D4—44no—
886D4—10616no—
887D4—10616no—
888D4—1068no—
889D4—2124no—
890D4—2128no—
891D4—21216no—
892D4—21216no—
893D4—21216no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—28no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—416no—
906C2×C4—538no—
907C2×C4—538no—
908C2×C4—538no—
909C2×C4—1068no—
910C2×C4—10616no—
911C2×C4—2128no—
912C2×C4—21216no—
913C2×C4—2124no—
914C2×C4—2128no—
915C2×C4—2124no—
916C2×C4—21216no—
917C2×C4C24×D5312yes—
918C2×C4C24×D5318yes—
919C2×C4C24×D5312yes—
920C2×C4C24×D5312yes—
921C2×C4C24×D5311yescharacteristic
922C2×C4C24×D5311yescharacteristic
923C2×C4C24×D5312yes—
924C2×C4C24×D5312yes—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—28no—
929C22—216no—
930C22—44no—
931C22—88no—
932C22—8488no—
933C22—1068no—
934C22—1068no—
935C22—1068no—
936C22—4248no—
937C22C2×#1313326212yes—
938C22C2×#1313326214yes—
939C22C25×D5311yescharacteristic
940C4—22no—
941C4—21no—
942C4—21no—
943C4—28no—
944C4—22no—
945C4—22no—
946C4—22no—
947C4—1068no—
948C4—1068no—
949C4—1068no—
950C4#1681145914yes—
951C2—22no—
952C2—24no—
953C2—48no—
954C2—2128no—
955C2C22×#1313326211yescharacteristic
956C2C2×#1681145912yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC2×C53×#532C2
hypercenterC2×#532D53
hypocenterC53#62822
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #20289271C2semidirect
2. #20289253C2semidirect
3. #20289238C2semidirect
4. #20289072C2semidirect
5. #20289059C2semidirect
6. #20289048C2semidirect
7. #20288792C2semidirect
8. #20288742C2semidirect
9. #20288655C2semidirect
10. #20288549C2semidirect
11. #20288472C2semidirect
12. #20288445C2semidirect
13. #20288359C2semidirect
14. C2×#16811157C2semidirect
15. C2×C53×#532C2semidirect
16. C2×#13133262C22semidirect
17. #16811373C22semidirect
18. #16811372C22semidirect
19. #16811367C22semidirect
20. #16811365C22semidirect
21. #16811360C22semidirect
22. #16811359C22semidirect
23. #16811356C22semidirect
24. #16811353C22semidirect
25. #16811339C22semidirect
26. #16811335C22semidirect
27. #16811334C22semidirect
28. #16811332C22semidirect
29. #16811325C22semidirect
30. #16811323C22semidirect
31. #16811322C22semidirect
32. #16811316C22semidirect
33. #16811308C22semidirect
34. #16811303C22semidirect
35. #16811302C22semidirect
36. #16811299C22semidirect
37. #16811293C22semidirect
38. #16811279C22semidirect
39. #16811274C22semidirect
40. #16811273C22semidirect
41. #16811272C22semidirect
42. #16811272C22semidirect
43. #16811268C22semidirect
44. #16811267C22semidirect
45. #16811263C22semidirect
46. #16811262C22semidirect
47. #16811261C22semidirect
48. #16811261C22semidirect
49. #16811258C22semidirect
50. #16811257C22semidirect
51. D4×C22⋊D53C22semidirect
52. #16811250C22semidirect
53. #16811247C22semidirect
54. #16811238C22semidirect
55. #16811237C22semidirect
56. #16811227C22semidirect
57. #16811224C22semidirect
58. #16811218C22semidirect
59. #16811215C22semidirect
60. #16811210C22semidirect
61. #16811207C22semidirect
62. #16811206C22semidirect
63. #16811200C22semidirect
64. #16811197C22semidirect
65. #16811186C22semidirect
66. #16811182C22semidirect
67. #16811182C22semidirect
68. #16811181C22semidirect
69. #16811168C22semidirect
70. #16811157C22semidirect
71. #16811157C22semidirect
72. #16811157C22semidirect
73. #16811157C22semidirect
74. #16811157C22semidirect
75. #16811157C22semidirect
76. #16811157C22semidirect
77. #16811157C22semidirect
78. #16811154C22semidirect
79. C2×#13133211C22semidirect
80. C2×#13133209C22semidirect
81. C2×#13133205C22semidirect
82. #16811134C22semidirect
83. #16811133C22semidirect
84. C2×#13133200C22semidirect
85. C2×#13133200C22semidirect
86. C2×#13133196C22semidirect
88. #121×D53C22semidirect
89. #16811102C22semidirect
90. #16811098C22semidirect
91. #16811095C22semidirect
92. C2×C4×Dic106C22semidirect
93. C2×C4×D212C22semidirect
94. C2×C4×C22⋊D53C22semidirect
95. C2×#13133174C22semidirect
96. C22×#41×C53C22semidirect
97. C53×#532C22semidirect
98. C53×#532C22semidirect
99. C53×#532C22semidirect
100. C53×#532C22semidirect
101. C2×C4⋊Q8×C53C22semidirect
102. C2×#127×C53C22semidirect
103. C2×#124×C53C22semidirect
104. C2×#121×C53C22semidirect
105. C2×C4×D4×C53C22semidirect
106. C22×C42×C53C22semidirect
486. C2×#532D53semidirect
495. C22×#41C2×D53semidirect
549. #532C2×D53semidirect
550. #532C2×D53semidirect
551. #532C2×D53semidirect
552. #532C2×D53semidirect
553. C2×C4⋊Q8C2×D53semidirect
554. C2×#127C2×D53semidirect
567. C2×#124C2×D53semidirect
575. C2×#121C2×D53semidirect
582. C2×C4×D4C2×D53semidirect
584. C22×C42C2×D53semidirect
585. C53#62822semidirect

Maximal subgroups

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

subgroupindex
#202892712
#202892532
#202892382
#202890722
#202890592
#202890482
#202887922
#202887422
#202886552
#202885492
#202884722
#202884452
#202883592
C2×#168111572
C2×C53×#5322
#6282253