Finite Group Databasebeta

← #28293178

Subgroups — #28293178

Order 13568.

6846 conjugacy classes of subgroups.

The subgroup lattice has 1470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288822C214yesmaximal, complemented
2#20288814C214yesmaximal, complemented
3#20288807C214yesmaximal, complemented
4#20288803C214yesmaximal, complemented
5#20288728C214yesmaximal, complemented
6#20288724C214yesmaximal, complemented
7#20288706C214yesmaximal, complemented
8#20288698C214yesmaximal, complemented
9#20288579C212yesmaximal, complemented
10#20288571C214yesmaximal, complemented
11#20288523C211yesmaximal, characteristic, complemented
12#20288484C211yesmaximal, characteristic, complemented
13#20288436C211yesmaximal, characteristic, complemented
14#20288434C211yesmaximal, characteristic, complemented
15#20288427C214yesmaximal, complemented
16#20288364C212yesmaximal, complemented
17#20288148C211yesmaximal, characteristic, complemented
18#20288145C214yesmaximal, complemented
19#20288101C214yesmaximal, complemented
20#20288100C212yesmaximal, complemented
21C4×#13133264C212yesmaximal, complemented
22C2×#16811099C211yesmaximal, characteristic, complemented
23C53×#3461C211yesmaximal, characteristic, complemented
24C2×#13133264C2212yes—
25C22×Q8×D53C2211yescharacteristic
26#16811356C2214yescomplemented
27#16811355C2214yescomplemented
28#16811355C2214yescomplemented
29#16811353C2214yescomplemented
30#16811350C2214yescomplemented
31#16811350C2214yescomplemented
32#16811350C2214yescomplemented
33#16811349C2214yescomplemented
34#16811348C2214yescomplemented
35#16811348C2214yescomplemented
36#16811347C2214yes—
37#16811347C2214yescomplemented
38#16811345C2218yes—
39#16811345C2214yescomplemented
40#16811344C2214yes—
41#16811344C2214yescomplemented
42#16811342C2214yescomplemented
43#16811342C2214yescomplemented
44#16811341C2218yescomplemented
45#16811340C2218yes—
46#16811340C2218yescomplemented
47#16811339C2214yes—
48#16811337C2214yes—
49#16811336C2218yes—
50#16811335C2218yes—
51#16811332C2214yescomplemented
52#16811331C2214yescomplemented
53#16811329C2214yescomplemented
54#16811326C2214yes—
55#16811325C2214yes—
56#16811324C2218yes—
57#16811322C2218yes—
58#16811315C2214yes—
59#16811315C2214yescomplemented
60#16811311C2214yes—
61#16811309C2218yescomplemented
62#16811307C2214yescomplemented
63#16811306C2218yes—
64#16811306C2218yescomplemented
65#16811305C2218yes—
66#16811291C2214yescomplemented
67#16811288C2214yes—
68#16811288C2214yes—
69#16811286C2214yes—
70#16811286C2214yes—
71#16811286C2214yescomplemented
72#16811283C2214yes—
73#16811283C2214yes—
74#16811283C2214yescomplemented
75#16811281C2214yes—
76#16811281C2214yes—
77#16811279C2214yescomplemented
78#16811254C2211yescharacteristic
79#16811252C2214yes—
80#16811245C2212yes—
81#16811245C2212yes—
82#16811245C2214yescomplemented
83#16811243C2218yes—
84#16811243C2218yescomplemented
85#16811241C2218yescomplemented
86#16811239C2218yes—
87#16811238C2212yes—
88#16811238C2212yes—
89#16811232C2218yes—
90#16811232C2218yescomplemented
91#16811231C2212yes—
92#16811231C2212yes—
93#16811231C2214yescomplemented
94#16811230C2218yescomplemented
95#16811225C2218yes—
96#16811224C2212yes—
97#16811224C2212yes—
98#16811220C2214yes—
99#16811217C2218yes—
100#16811215C2214yes—
101#16811215C2214yes—
102#16811213C2214yes—
103#16811210C2214yes—
104#16811206C2214yes—
105#16811206C2214yes—
106#16811204C2211yescharacteristic
107#16811200C2214yes—
108#16811197C2212yes—
109#16811195C2218yes—
110#16811179C2218yescomplemented
111#16811177C2214yescomplemented
112#16811176C2212yes—
113#16811175C2214yes—
114#16811175C2218yescomplemented
115#16811169C2212yes—
116#16811168C2214yes—
117#16811160C2214yescomplemented
118#16811159C2218yes—
119#16811159C2214yes—
120#16811158C2218yes—
121#16811157C2214yes—
122#16811157C2214yes—
123#16811157C2214yes—
124#16811156C2218yes—
125#16811156C2218yescomplemented
126#16811154C2214yes—
127#16811151C2214yes—
128#16811151C2214yes—
129#16811150C2218yes—
130#16811150C2218yes—
131#16811150C2218yescomplemented
132#16811135C2212yes—
133#16811131C2218yes—
134#16811130C2212yes—
135#16811106C2212yes—
136#16811103C2212yes—
137#16811103C2214yescomplemented
138#16811102C2218yes—
139#16811102C2214yescomplemented
140#16811100C2212yes—
141#16811100C2214yescomplemented
142#16811099C2214yes—
143#16811099C2214yes—
144#16811099C2214yes—
145#16811099C2214yes—
146#16811099C2214yescomplemented
147C4×#11719945C2212yes—
148C4×#11719945C2214yescomplemented
149C4×#11719947C2218yes—
150C4×#11719947C2214yescomplemented
151C2×Q8×Dic53C2211yescharacteristic
152C2×C4×Dic106C2212yes—
153C2×C4×Dic106C2211yescharacteristic
154C2×C4×Dic106C2214yescomplemented
155C2×#13133182C2211yescharacteristic
156C2×#13133182C2212yes—
157C4×Q8×D53C2214yescomplemented
158C2×#13133175C2212yes—
159C2×#13133175C2211yescharacteristic
160C2×#13133174C2211yescharacteristic
161C2×#13133174C2212yes—
162C53×#544C2211yescharacteristic
163C53×#542C2214yescomplemented
164C53×#541C2214yescomplemented
165C53×#539C2214yes—
166C53×#537C2211yescharacteristic
167C53×#536C2212yes—
168C53×#533C2214yescomplemented
169C53×#529C2214yes—
170C53×#529C2214yescomplemented
171C4×#41×C53C2212yes—
172C2×C4×Q8×C53C2211yescharacteristic
173#13133264—216no—
174C2×#11719945C2314yes—
175C2×#11719945C2312yes—
176C2×#11719947C2314yes—
177C2×#11719947C2318yes—
178C22×Dic106C2314yes—
179C22×Dic106C2312yes—
180C22×Dic106C2311yescharacteristic
181C2×Q8×D53—28no—
182C2×Q8×D53C2314yes—
183C2×Q8×D53C2314yes—
184C2×Q8×D53C2314yes—
185C22×C4×D53C2311yescharacteristic
186C22×C4×D53C2312yes—
187#13133216C2318yes—
188#13133216C2318yes—
189#13133216C2314yes—
190#13133216C2314yes—
191#13133216C2312yes—
192#13133216C2318yes—
193#13133216C2314yes—
194#13133216C2312yes—
195#13133215C2314yes—
196#13133215C2312yes—
197#13133215C2318yes—
198#13133215C2314yes—
199#13133213C2312yes—
200#13133213C2314yes—
201#13133212C2314yes—
202#13133212C2318yes—
203#13133212C2318yes—
204#13133212C2318yes—
205#13133212C2318yes—
206#13133212C2318yes—
207#13133212C2318yes—
208#13133212C2314yes—
209#13133211C2314yes—
210#13133211C2318yes—
211#13133211C2314yes—
212#13133211C2314yes—
213#13133211C2314yes—
214#13133210C2318yes—
215#13133210C2318yes—
216#13133210C2314yes—
217#13133210C2318yes—
218#13133210C2314yes—
219#13133209C2314yes—
220#13133209C2314yes—
221#13133209C2314yes—
222#13133208C2312yes—
223#13133208C2318yes—
224#13133208C2314yes—
225#13133208C2314yes—
226#13133208C2314yes—
227#13133208C2312yes—
228#13133207C2318yes—
229#13133207C2318yes—
230#13133207C2318yes—
231#13133207C2318yes—
232#13133207C2318yes—
233#13133207C2314yes—
234#13133207C2318yes—
235#13133207C2314yes—
236#13133206C2314yes—
237#13133206C2312yes—
238#13133206C2318yes—
239#13133206C2314yes—
240#13133205C2314yes—
241#13133205C2314yes—
242#13133205C2314yes—
243#13133204C2312yes—
244#13133204C2314yes—
245#13133203C2318yes—
246#13133203C2318yes—
247#13133203C2318yes—
248#13133203C2314yes—
249#13133203C2318yes—
250#13133203C2318yes—
251#13133203C2314yes—
252#13133202C2314yes—
253#13133202C2318yes—
254#13133202C2314yes—
255#13133202C2318yes—
256#13133201C2318yes—
257#13133201C2318yes—
258#13133201C2314yes—
259#13133200C2314yes—
260#13133200C2314yes—
261#13133200C2318yes—
262#13133200C2314yes—
263#13133200C2314yes—
264#13133199C2318yes—
265#13133199C2314yes—
266#13133199C2314yes—
267#13133198C2314yes—
268#13133197C2314yes—
269#13133197C2312yes—
270#13133197C2312yes—
271#13133197C2318yes—
272#13133196C2314yes—
273#13133196C2314yes—
274#13133196C2314yes—
275#13133195C2318yes—
276#13133195C2318yes—
277#13133195C2318yes—
278#13133195C2318yes—
279#13133195C2318yes—
280#13133195C2314yes—
281#13133195C2314yes—
282#13133195C2318yes—
283#13133194C2318yes—
284#13133194C2318yes—
285#13133194C2318yes—
286#13133194C2318yes—
287#13133194C2314yes—
288#13133194C2314yes—
289#13133193C2314yes—
290#13133193C2314yes—
291#13133193C2312yes—
292#13133193C2312yes—
293#13133192C2312yes—
294#13133192C2312yes—
295#13133192C2314yes—
296#13133192C2318yes—
297#13133191C2314yes—
298#13133191C2314yes—
299#13133191C2314yes—
300#13133190C2318yes—
301#13133190C2318yes—
302#13133190C2318yes—
303#13133190C2314yes—
304#13133190C2314yes—
305#13133189C2318yes—
306#13133189C2318yes—
307#13133189C2314yes—
308#13133189C2314yes—
309#13133188C2312yes—
310#13133188C2312yes—
311#13133187C2314yes—
312#13133185C2314yes—
313Q8×Dic53C2314yes—
314Q8×Dic53C2314yes—
315Q8×Dic53C2314yes—
316Q8×Dic53C2314yes—
317Q8×Dic53C2314yes—
318C4×Dic106C2314yes—
319C4×Dic106C2314yes—
320C4×Dic106C2318yes—
321C4×Dic106C2314yes—
322C4×Dic106C2314yes—
323C4×Dic106C2314yes—
324C4×Dic106C2314yes—
325C4×Dic106C2314yes—
326C4×Dic106C2314yes—
327C4×Dic106C2314yes—
328C4×Dic106C2318yes—
329C4×Dic106C2314yes—
330C4×Dic106C2314yes—
331C4×Dic106C2312yes—
332C4×Dic106C2312yes—
333C4×Dic106C2314yes—
334#13133182C2314yes—
335#13133182C2314yes—
336#13133182C2314yes—
337#13133182C2314yes—
338#13133182C2318yes—
339#13133182C2318yes—
340#13133182C2318yes—
341#13133182C2318yes—
342#13133182C2318yes—
343#13133182C2314yes—
344#13133182C2318yes—
345#13133182C2314yes—
346C4×D212C2314yes—
347C4×D212C2314yes—
348C4×D212C2314yes—
349C4×D212C2314yes—
350C4×D212C2312yes—
351C4×D212C2312yes—
352D4×Dic53C2314yes—
353D4×Dic53C2314yes—
354D4×Dic53C2314yes—
355D4×Dic53C2318yes—
356#13133179C2318yes—
357#13133179C2318yes—
358#13133179C2314yes—
359#13133179C2314yes—
360C4×C22⋊D53C2314yes—
361C4×C22⋊D53C2314yes—
362C4×C22⋊D53C2314yes—
363C4×C22⋊D53C2314yes—
364C4×C22⋊D53C2318yes—
365C4×C22⋊D53C2314yes—
366C4×C22⋊D53C2318yes—
367C4×C22⋊D53C2314yes—
368#13133177C2318yes—
369#13133177C2318yes—
370#13133177C2318yes—
371#13133177C2318yes—
372#13133177C2318yes—
373#13133177C2318yes—
374#13133177C2318yes—
375#13133176C2314yes—
376#13133176C2312yes—
377#13133175C2318yes—
378#13133175C2318yes—
379#13133175C2314yes—
380#13133175C2314yes—
381#13133175C2314yes—
382#13133175C2318yes—
383#13133175C2318yes—
384#13133175C2318yes—
385#13133174C2318yes—
386#13133174C2318yes—
387#13133174C2318yes—
388#13133174C2318yes—
389#13133174C2312yes—
390#13133174C2312yes—
391#13133174C2312yes—
392#13133174C2312yes—
393#13133174C2314yes—
394#13133173C2318yes—
395#13133173C2318yes—
396#13133173C2318yes—
397#13133173C2318yes—
398#13133173C2318yes—
399C2×C4⋊Dic53C2314yes—
400C2×C4⋊Dic53C2311yescharacteristic
401C2×C4⋊Dic53C2312yes—
402C2×#11719919C2318yes—
403C2×#11719919C2312yes—
404C2×#11719919C2311yescharacteristic
405C2×#11719919C2312yes—
406C2×#11719919C2311yescharacteristic
407C4⋊C4×D53C2318yes—
408C4⋊C4×D53C2314yes—
409C2×#11719921C2311yescharacteristic
410C2×#11719921C2311yescharacteristic
411C2×#11719921C2312yes—
412C2×C4×Dic53C2312yes—
413C2×C4×Dic53C2311yescharacteristic
414C2×C4×Dic53C2312yes—
415C2×C4×Dic53C2312yes—
416C2×C4×Dic53C2312yes—
417C2×C4×Dic53C2318yes—
418C42×D53C2318yes—
419C42×D53C2314yes—
420C2×#41×C53C2312yes—
421C22×Q8×C53C2311yescharacteristic
422C4⋊Q8×C53C2314yes—
423C4⋊Q8×C53C2314yes—
424#126×C53C2318yes—
425#126×C53C2318yes—
426#125×C53C2314yes—
427#125×C53C2314yes—
428#125×C53C2318yes—
429#124×C53C2314yes—
430#124×C53C2314yes—
431#123×C53C2318yes—
432#123×C53C2318yes—
433C22⋊Q8×C53C2314yes—
434C22⋊Q8×C53C2314yes—
435C22⋊Q8×C53C2314yes—
436C22⋊Q8×C53C2314yes—
437C22⋊Q8×C53C2318yes—
438#121×C53C2314yes—
439#121×C53C2314yes—
440C4×Q8×C53C2314yes—
441C4×Q8×C53C2314yes—
442C4×Q8×C53C2312yes—
443C4×Q8×C53C2312yes—
444C4×Q8×C53C2314yes—
445C4×D4×C53C2314yes—
446C4×D4×C53C2312yes—
447C4×D4×C53C2314yes—
448C4×D4×C53C2312yes—
449C4×D4×C53C2314yes—
450#117×C53C2312yes—
451#117×C53C2314yes—
452#117×C53C2318yes—
453C2×C4⋊C4×C53C2311yescharacteristic
454C2×C4⋊C4×C53C2312yes—
455C2×C42×C53C2311yescharacteristic
456C2×C42×C53C2312yes—
457C2×C42×C53C2314yes—
458C23×D53C2411yescharacteristic
459#41×C53—28no—
460C2×Q8×C53—24no—
461C2×Q8×C53C2414yes—
462C2×Q8×C53C2412yes—
463C2×Q8×C53C2414yes—
464C2×D4×C53C2414yes—
465C2×D4×C53C2412yes—
466C2×D4×C53C2414yes—
467C22×C4×C53C2412yes—
468C22×C4×C53C2414yes—
469C22×C4×C53C2411yescharacteristic
470C22×C4×C53C2411yescharacteristic
471C22×C4×C53C2412yes—
472C22×C4×C53C2414yes—
473C22×C4×C53C2414yes—
474C22×C4×C53C2411yescharacteristic
475C2×C22⋊D53C2414yes—
476C2×C22⋊D53C2418yes—
477C2×C22⋊D53C2414yes—
478C2×C22⋊D53C2414yes—
479C2×C22⋊D53C2414yes—
480C2×C22⋊D53C2414yes—
481C22×Dic53C2411yescharacteristic
482C22×Dic53C2418yes—
483C22×Dic53C2411yescharacteristic
484C22×Dic53C2412yes—
485C22×Dic53C2411yescharacteristic
486C22×Dic53C2418yes—
487C22×Dic53C2412yes—
488Q8×D53—216no—
489Q8×D53—216no—
490Q8×D53—216no—
491#11719947—232no—
492#11719947—216no—
493#11719945—28no—
494#11719945—216no—
495C2×D212C2412yes—
496C2×D212C2414yes—
497C2×D212C2414yes—
498C2×D212C2414yes—
499C2×C4×D53—24no—
500C2×C4×D53—28no—
501C2×C4×D53C2418yes—
502C2×C4×D53C2414yes—
503C2×C4×D53C2418yes—
504C2×C4×D53C2412yes—
505C2×C4×D53C2412yes—
506C2×C4×D53C2414yes—
507C2×C4×D53C2414yes—
508C2×C4×D53C2418yes—
509C2×Dic106—28no—
510C2×Dic106—216no—
511C2×Dic106#4118yes—
512C2×Dic106C2414yes—
513C2×Dic106C2414yes—
514C2×Dic106C2418yes—
515C2×Dic106C2412yes—
516C2×Dic106C2414yes—
517C2×Dic106C2414yes—
518C2×Dic106C2414yes—
519C2×Dic106C2414yes—
520C4⋊C4×C53C2414yes—
521C4⋊C4×C53C2418yes—
522C4⋊C4×C53C2412yes—
523C4⋊C4×C53C2414yes—
524C4⋊C4×C53C2412yes—
525C4⋊C4×C53C2414yes—
526C4⋊C4×C53C2418yes—
527C4⋊C4×C53C2418yes—
528C4⋊C4×C53C2414yes—
529C4⋊C4×C53C2414yes—
530C4⋊C4×C53C2418yes—
531C22⋊C4×C53C2414yes—
532C22⋊C4×C53C2414yes—
533C22⋊C4×C53C2414yes—
534C22⋊C4×C53C2418yes—
535C22⋊C4×C53C2418yes—
536C22⋊C4×C53C2418yes—
537C42×C53C2412yes—
538C42×C53C2412yes—
539C42×C53C2414yes—
540C42×C53C2414yes—
541C42×C53C2414yes—
542C42×C53C2414yes—
543C42×C53C2414yes—
544C22⋊Dic53C2414yes—
545C22⋊Dic53C2418yes—
546C22⋊Dic53C2414yes—
547C22⋊Dic53C2414yes—
548C22⋊Dic53C2414yes—
549C22⋊Dic53C2414yes—
550#11719921C2412yes—
551#11719921C2412yes—
552#11719921C2418yes—
553#11719921C2412yes—
554#11719921C2412yes—
555#11719921C2414yes—
556#11719921C2414yes—
557#11719921C2418yes—
558#11719921C2418yes—
559#11719921C2418yes—
560#11719921C2414yes—
561#11719921C2414yes—
562#11719921C2414yes—
563#11719921C2414yes—
564#11719921C2418yes—
565#11719921C2414yes—
566#11719921C2414yes—
567#11719921C2414yes—
568#11719921C2414yes—
569C4⋊Dic53C2414yes—
570C4⋊Dic53C2418yes—
571C4⋊Dic53C2412yes—
572C4⋊Dic53C2414yes—
573C4⋊Dic53C2414yes—
574C4⋊Dic53C2414yes—
575C4⋊Dic53C2414yes—
576C4⋊Dic53C2412yes—
577C4⋊Dic53C2414yes—
578C4⋊Dic53C2414yes—
579C4⋊Dic53C2414yes—
580C4⋊Dic53C2414yes—
581#11719919C2414yes—
582#11719919C2418yes—
583#11719919C2418yes—
584#11719919C2414yes—
585#11719919C2414yes—
586#11719919C2418yes—
587#11719919C2412yes—
588#11719919C2412yes—
589#11719919C2411yescharacteristic
590#11719919C2411yescharacteristic
591#11719919C2411yescharacteristic
592#11719919C2411yescharacteristic
593#11719919C2418yes—
594#11719919C2414yes—
595#11719919C2414yes—
596#11719919C2414yes—
597#11719919C2418yes—
598#11719919C2418yes—
599#11719919C2414yes—
600#11719919C2414yes—
601#11719919C2418yes—
602#11719919C2414yes—
603#11719919C2414yes—
604#11719919C2414yes—
605#11719919C2414yes—
606C4×Dic53C2418yes—
607C4×Dic53C2414yes—
608C4×Dic53C2414yes—
609C4×Dic53C2418yes—
610C4×Dic53C2418yes—
611C4×Dic53C2414yes—
612C4×Dic53C2418yes—
613C4×Dic53C2414yes—
614C4×Dic53C2418yes—
615C4×Dic53C2418yes—
616C4×Dic53C2412yes—
617C4×Dic53C2412yes—
618C4×Dic53C2414yes—
619C4×Dic53C2414yes—
620C4×Dic53C2414yes—
621C23×C53C2514yes—
622C23×C53C2511yescharacteristic
623C22×D53—22no—
624C22×D53—41no—
625C22×D53—41no—
626C22×D53C2514yes—
627C22×D53C2512yes—
628Q8×C53—28no—
629Q8×C53—24no—
630Q8×C53—44no—
631D4×C53—28no—
632D4×C53—24no—
633D4×C53—44no—
634C2×C4×C53—24no—
635C2×C4×C53—28no—
636C2×C4×C53—44no—
637C2×C4×C53—42no—
638C2×C4×C53—44no—
639C2×C4×C53—41no—
640C2×C4×C53—41no—
641C2×C4×C53C2×#4114yes—
642C2×C4×C53C2514yes—
643C2×C4×C53C2514yes—
644C2×C4×C53C2514yes—
645C2×C4×C53C2514yes—
646C2×C4×C53C2514yes—
647C2×C4×C53C2511yescharacteristic
648C2×C4×C53C2512yes—
649C2×C4×C53C2511yescharacteristic
650C2×C4×C53C2512yes—
651C22⋊D53—28no—
652C22⋊D53—216no—
653C22⋊D53—44no—
654C22⋊D53—44no—
655C22⋊D53—44no—
656C22⋊D53—44no—
657C2×Dic53—22no—
658C2×Dic53—216no—
659C2×Dic53—41no—
660C2×Dic53—41no—
661C2×Dic53—48no—
662C2×Dic53—42no—
663C2×Dic53C2×#4118yes—
664C2×Dic53C2511yescharacteristic
665C2×Dic53C2511yescharacteristic
666C2×Dic53C2511yescharacteristic
667C2×Dic53C2514yes—
668C2×Dic53C2514yes—
669C2×Dic53C2512yes—
670C2×Dic53C2514yes—
671C2×Dic53C2514yes—
672C2×Dic53C2511yescharacteristic
673C2×Dic53C2514yes—
674D212—24no—
675D212—44no—
676D212—44no—
677D212—44no—
678C4×D53—24no—
679C4×D53—24no—
680C4×D53—28no—
681C4×D53—216no—
682C4×D53—216no—
683C4×D53—44no—
684C4×D53—44no—
685C4×D53—48no—
686Dic106—24no—
687Dic106—216no—
688Dic106—28no—
689Dic106—28no—
690Dic106—44no—
691Dic106—44no—
692Dic106—44no—
693Dic106C2×#41116yes—
694#62850—531nomaximal, Sylow
695C22×C53—21no—
696C22×C53—21no—
697C22×C53—24no—
698C22×C53—24no—
699C22×C53—24no—
700C22×C53C22×#4112yes—
701C22×C53C2611yescharacteristic
702C2×D53—22no—
703C2×D53—24no—
704C2×D53—24no—
705C2×D53—24no—
706C2×D53—22no—
707C2×D53—22no—
708C2×D53—44no—
709C4×C53—24no—
710C4×C53—24no—
711C4×C53—24no—
712C4×C53—24no—
713C4×C53—24no—
714C4×C53—21no—
715C4×C53—22no—
716C4×C53—21no—
717C4×C53C22×#4114yes—
718Dic53—21no—
719Dic53—21no—
720Dic53—24no—
721Dic53—21no—
722Dic53—24no—
723Dic53—22no—
724Dic53—24no—
725Dic53—24no—
726Dic53—21no—
727Dic53C22×#4118yes—
728#3524—534no—
729#3524—534no—
730#3523—534no—
731#3523—534no—
732#3518—534no—
733#3518—534no—
734#3516—534no—
735#3516—534no—
736#3507—532no—
737#3507—534no—
738#3502—531no—
739#3497—531no—
740#3493—531no—
741#3493—531no—
742#3493—534no—
743#3486—532no—
744#3461—534no—
745#3461—531no—
746#3461D5311yescharacteristic, complemented
747#3455—534no—
748#3455—532no—
749C4×2−1+4—532no—
750C2×#519—531no—
751C2×C53—22no—
752C2×C53—44no—
753C2×C53C23×#4111yescharacteristic
754C2×C532−1+611yescharacteristic
755C2×C532−1+611yescharacteristic
756D53—44no—
757D53—42no—
758C2×2−1+4—532no—
759C23×Q8—531no—
760#559—534no—
761#559—534no—
762#559—534no—
763Q82—534no—
764#557—534no—
765#557—534no—
766#557—534no—
767#557—534no—
768#557—534no—
769#557—534no—
770#556—534no—
771#556—534no—
772#556—538no—
773#556—538no—
774#556—534no—
775#556—534no—
776#556—534no—
777#556—534no—
778#556—538no—
779#556—534no—
780#556—538no—
781#555—534no—
782#555—538no—
783#555—534no—
784#555—538no—
785#554—534no—
786#554—534no—
787#554—534no—
788#553—538no—
789#553—534no—
790#553—534no—
791#553—538no—
792#552—538no—
793#552—538no—
794#552—534no—
795#552—534no—
796#552—534no—
797#552—534no—
798#552—538no—
799#552—538no—
800#550—534no—
801D4×Q8—534no—
802D4×Q8—534no—
803D4×Q8—534no—
804D4×Q8—534no—
805D4×Q8—534no—
806#548—534no—
807#548—534no—
808#548—534no—
809#548—534no—
810#548—534no—
811#548—534no—
812#544—534no—
813#544—531no—
814#544C2×D5311yescharacteristic
815#542—538no—
816#542—538no—
817#542—538no—
818#542—538no—
819#542—532no—
820#542—532no—
821#542—534no—
822#542—532no—
823#542—532no—
824#542C2×D5314yescomplemented
825#541—538no—
826#541—538no—
827#541—538no—
828#541—532no—
829#541—532no—
830#541—534no—
831#541C2×D5314yescomplemented
832#540—538no—
833#540—532no—
834#540—532no—
835#539—538no—
836#539—534no—
837#539—534no—
838#539—534no—
839#539C2×D5314yes—
840#538—534no—
841#538—534no—
842#538—534no—
843#538—534no—
844#537—534no—
845#537—531no—
846#537C2×D5311yescharacteristic
847#536—532no—
848#536—538no—
849#536C2×D5312yes—
850#533—538no—
851#533—534no—
852#533—538no—
853#533—534no—
854#533—532no—
855#533C2×D5314yescomplemented
856#532—532no—
857#532—534no—
858#529—538no—
859#529—538no—
860#529—538no—
861#529—538no—
862#529—538no—
863#529—538no—
864#529—538no—
865#529—534no—
866#529—534no—
867#529—534no—
868#529—534no—
869#529—534no—
870#529—534no—
871#529—534no—
872#529—534no—
873#529C2×D5314yes—
874#529C2×D5314yescomplemented
875#525—532no—
876#525—538no—
877#525—532no—
878#520—532no—
879#520—538no—
880#520—534no—
881#520—532no—
882#520—534no—
883#519—534no—
884#519—534no—
885#519—534no—
886#519—534no—
887#519—534no—
888#519—532no—
889#519—534no—
890C4×#41—538no—
891C4×#41—534no—
892C4×#41—532no—
893C4×#41—534no—
894C4×#41C2×D5312yes—
895C2×C4×Q8—531no—
896C2×C4×Q8—534no—
897C2×C4×Q8—532no—
898C2×C4×Q8—531no—
899C2×C4×Q8—531no—
900C2×C4×Q8—532no—
901C2×C4×Q8—534no—
902C2×C4×Q8C2×D5311yescharacteristic
903C2×#117—532no—
904C2×#117—531no—
905C2×#117—531no—
906C2×#117—532no—
907C53#6285011yescharacteristic, complemented, Sylow
9082−1+4—10616no—
909C2×#41—538no—
910C2×#41—534no—
911C2×#41—532no—
912C2×#41—534no—
913C2×#41C22×D5312yes—
914C22×Q8—534no—
915C22×Q8—534no—
916C22×Q8—534no—
917C22×Q8—531no—
918C22×Q8—532no—
919C22×Q8—534no—
920C22×Q8—1068no—
921C22×Q8C22×D5311yescharacteristic
922C23×C4—532no—
923C23×C4—531no—
924C4⋊Q8—532no—
925C4⋊Q8—534no—
926C4⋊Q8—534no—
927C4⋊Q8—538no—
928C4⋊Q8—534no—
929C4⋊Q8—538no—
930C4⋊Q8—538no—
931C4⋊Q8—534no—
932C4⋊Q8—532no—
933C4⋊Q8—532no—
934C4⋊Q8—538no—
935C4⋊Q8—534no—
936C4⋊Q8C22×D5314yes—
937C4⋊Q8C22×D5314yes—
938#127—534no—
939#127—532no—
940#126—534no—
941#126—538no—
942#126—538no—
943#126—538no—
944#126—534no—
945#126—538no—
946#126—538no—
947#126—538no—
948#126—534no—
949#126—538no—
950#126—534no—
951#126—538no—
952#126—538no—
953#126—534no—
954#126—534no—
955#126—534no—
956#126—534no—
957#126—538no—
958#126C22×D5318yes—
959#126C22×D5318yes—
960#125—534no—
961#125—538no—
962#125—538no—
963#125—534no—
964#125—538no—
965#125—538no—
966#125—534no—
967#125—534no—
968#125—538no—
969#125—538no—
970#125—534no—
971#125—538no—
972#125—532no—
973#125—532no—
974#125—534no—
975#125—534no—
976#125—534no—
977#125C22×D5318yes—
978#125C22×D5314yes—
979#125C22×D5314yes—
980#124—534no—
981#124—538no—
982#124—534no—
983#124—532no—
984#124—534no—
985#124—532no—
986#124—534no—
987#124—538no—
988#124—538no—
989#124—538no—
990#124—534no—
991#124—538no—
992#124—538no—
993#124—534no—
994#124—534no—
995#124—534no—
996#124C22×D5314yes—
997#124C22×D5314yes—
998#123—534no—
999#123—538no—
1000#123—534no—
1001#123—534no—
1002#123—534no—
1003#123—534no—
1004#123—534no—
1005#123—538no—
1006#123—538no—
1007#123—534no—
1008#123—534no—
1009#123—534no—
1010#123—538no—
1011#123—538no—
1012#123—534no—
1013#123—538no—
1014#123C22×D5318yes—
1015#123C22×D5318yes—
1016C22⋊Q8—532no—
1017C22⋊Q8—532no—
1018C22⋊Q8—534no—
1019C22⋊Q8—534no—
1020C22⋊Q8—534no—
1021C22⋊Q8—534no—
1022C22⋊Q8—534no—
1023C22⋊Q8—538no—
1024C22⋊Q8—532no—
1025C22⋊Q8—538no—
1026C22⋊Q8—532no—
1027C22⋊Q8—534no—
1028C22⋊Q8—538no—
1029C22⋊Q8—538no—
1030C22⋊Q8—534no—
1031C22⋊Q8—538no—
1032C22⋊Q8—538no—
1033C22⋊Q8—538no—
1034C22⋊Q8—534no—
1035C22⋊Q8—534no—
1036C22⋊Q8—538no—
1037C22⋊Q8—538no—
1038C22⋊Q8—534no—
1039C22⋊Q8—538no—
1040C22⋊Q8—538no—
1041C22⋊Q8C22×D5314yes—
1042C22⋊Q8C22×D5318yes—
1043C22⋊Q8C22×D5314yes—
1044C22⋊Q8C22×D5314yes—
1045C22⋊Q8C22×D5314yes—
1046#121—532no—
1047#121—532no—
1048#121—534no—
1049#121—538no—
1050#121—538no—
1051#121—534no—
1052#121—534no—
1053#121—534no—
1054#121—534no—
1055#121—532no—
1056#121—532no—
1057#121—534no—
1058#121—538no—
1059#121—538no—
1060#121—538no—
1061#121—534no—
1062#121—538no—
1063#121—534no—
1064#121C22×D5314yes—
1065#121C22×D5314yes—
1066#120—534no—
1067#120—534no—
1068C4×Q8—534no—
1069C4×Q8—534no—
1070C4×Q8—534no—
1071C4×Q8—534no—
1072C4×Q8—534no—
1073C4×Q8—538no—
1074C4×Q8—538no—
1075C4×Q8—534no—
1076C4×Q8—534no—
1077C4×Q8—534no—
1078C4×Q8—538no—
1079C4×Q8—538no—
1080C4×Q8—534no—
1081C4×Q8—538no—
1082C4×Q8—534no—
1083C4×Q8—538no—
1084C4×Q8—534no—
1085C4×Q8—534no—
1086C4×Q8—534no—
1087C4×Q8—538no—
1088C4×Q8—532no—
1089C4×Q8—534no—
1090C4×Q8—534no—
1091C4×Q8—534no—
1092C4×Q8—534no—
1093C4×Q8—534no—
1094C4×Q8—534no—
1095C4×Q8—538no—
1096C4×Q8—532no—
1097C4×Q8—534no—
1098C4×Q8—534no—
1099C4×Q8—534no—
1100C4×Q8—534no—
1101C4×Q8C22×D5312yes—
1102C4×Q8C22×D5314yes—
1103C4×Q8C22×D5314yes—
1104C4×Q8C22×D5312yes—
1105C4×Q8C22×D5314yes—
1106C4×D4—538no—
1107C4×D4—534no—
1108C4×D4—534no—
1109C4×D4—534no—
1110C4×D4—534no—
1111C4×D4—538no—
1112C4×D4—534no—
1113C4×D4—538no—
1114C4×D4—534no—
1115C4×D4—534no—
1116C4×D4—534no—
1117C4×D4—534no—
1118C4×D4—538no—
1119C4×D4—538no—
1120C4×D4—534no—
1121C4×D4—534no—
1122C4×D4—538no—
1123C4×D4—538no—
1124C4×D4—538no—
1125C4×D4—538no—
1126C4×D4—538no—
1127C4×D4—538no—
1128C4×D4—538no—
1129C4×D4—532no—
1130C4×D4—532no—
1131C4×D4—534no—
1132C4×D4—534no—
1133C4×D4—534no—
1134C4×D4—534no—
1135C4×D4C22×D5314yes—
1136C4×D4C22×D5312yes—
1137C4×D4C22×D5314yes—
1138C4×D4C22×D5312yes—
1139C4×D4C22×D5314yes—
1140#117—532no—
1141#117—534no—
1142#117—538no—
1143#117—538no—
1144#117—534no—
1145#117—534no—
1146#117—538no—
1147#117—534no—
1148#117—538no—
1149#117—538no—
1150#117—538no—
1151#117—538no—
1152#117—538no—
1153#117—538no—
1154#117—538no—
1155#117—532no—
1156#117—532no—
1157#117—532no—
1158#117—532no—
1159#117—538no—
1160#117—538no—
1161#117—534no—
1162#117—538no—
1163#117—538no—
1164#117C22×D5312yes—
1165#117C22×D5314yes—
1166#117C22×D5318yes—
1167C2×C4⋊C4—532no—
1168C2×C4⋊C4—531no—
1169C2×C4⋊C4—532no—
1170C2×C4⋊C4—531no—
1171C2×C4⋊C4—531no—
1172C2×C4⋊C4—532no—
1173C2×C4⋊C4—538no—
1174C2×C4⋊C4—534no—
1175C2×C4⋊C4—538no—
1176C2×C4⋊C4—534no—
1177C2×C4⋊C4C22×D5311yescharacteristic
1178C2×C4⋊C4C22×D5312yes—
1179C2×C22⋊C4—531no—
1180C2×C22⋊C4—532no—
1181C2×C22⋊C4—531no—
1182C2×C42—532no—
1183C2×C42—532no—
1184C2×C42—532no—
1185C2×C42—532no—
1186C2×C42—531no—
1187C2×C42—538no—
1188C2×C42—538no—
1189C2×C42—534no—
1190C2×C42C22×D5311yescharacteristic
1191C2×C42C22×D5312yes—
1192C2×C42C22×D5314yes—
1193C24—531no—
1194#41—28no—
1195#41—10616no—
1196#41—10632no—
1197#41—10616no—
1198#41—1068no—
1199C2×Q8—24no—
1200C2×Q8—538no—
1201C2×Q8—534no—
1202C2×Q8—534no—
1203C2×Q8—534no—
1204C2×Q8—538no—
1205C2×Q8—532no—
1206C2×Q8—534no—
1207C2×Q8—534no—
1208C2×Q8—534no—
1209C2×Q8—1068no—
1210C2×Q8—10616no—
1211C2×Q8—10616no—
1212C2×Q8—10616no—
1213C2×Q8—10616no—
1214C2×Q8C23×D5314yes—
1215C2×Q8C23×D5312yes—
1216C2×Q8C23×D5314yes—
1217C2×D4—534no—
1218C2×D4—538no—
1219C2×D4—534no—
1220C2×D4—534no—
1221C2×D4—534no—
1222C2×D4—534no—
1223C2×D4—532no—
1224C2×D4—534no—
1225C2×D4—534no—
1226C2×D4—534no—
1227C2×D4C23×D5314yes—
1228C2×D4C23×D5312yes—
1229C2×D4C23×D5314yes—
1230C22×C4—532no—
1231C22×C4—531no—
1232C22×C4—538no—
1233C22×C4—532no—
1234C22×C4—531no—
1235C22×C4—531no—
1236C22×C4—538no—
1237C22×C4—538no—
1238C22×C4—534no—
1239C22×C4—538no—
1240C22×C4—532no—
1241C22×C4—532no—
1242C22×C4—534no—
1243C22×C4—538no—
1244C22×C4—534no—
1245C22×C4—1068no—
1246C22×C4—1064no—
1247C22×C4C23×D5312yes—
1248C22×C4C23×D5314yes—
1249C22×C4C23×D5311yescharacteristic
1250C22×C4C23×D5312yes—
1251C22×C4C23×D5314yes—
1252C22×C4C23×D5311yescharacteristic
1253C22×C4C23×D5314yes—
1254C22×C4C23×D5311yescharacteristic
1255C4⋊C4—534no—
1256C4⋊C4—534no—
1257C4⋊C4—534no—
1258C4⋊C4—538no—
1259C4⋊C4—532no—
1260C4⋊C4—538no—
1261C4⋊C4—534no—
1262C4⋊C4—538no—
1263C4⋊C4—538no—
1264C4⋊C4—531no—
1265C4⋊C4—531no—
1266C4⋊C4—534no—
1267C4⋊C4—532no—
1268C4⋊C4—532no—
1269C4⋊C4—531no—
1270C4⋊C4—531no—
1271C4⋊C4—534no—
1272C4⋊C4—538no—
1273C4⋊C4—532no—
1274C4⋊C4—534no—
1275C4⋊C4—534no—
1276C4⋊C4—538no—
1277C4⋊C4—534no—
1278C4⋊C4—538no—
1279C4⋊C4—534no—
1280C4⋊C4—534no—
1281C4⋊C4—534no—
1282C4⋊C4—534no—
1283C4⋊C4—534no—
1284C4⋊C4—534no—
1285C4⋊C4—534no—
1286C4⋊C4—534no—
1287C4⋊C4—538no—
1288C4⋊C4—534no—
1289C4⋊C4—534no—
1290C4⋊C4—534no—
1291C4⋊C4—534no—
1292C4⋊C4C23×D5312yes—
1293C4⋊C4C23×D5314yes—
1294C4⋊C4C23×D5314yes—
1295C4⋊C4C23×D5318yes—
1296C4⋊C4C23×D5312yes—
1297C4⋊C4C23×D5314yes—
1298C4⋊C4C23×D5318yes—
1299C4⋊C4C23×D5318yes—
1300C4⋊C4C23×D5314yes—
1301C4⋊C4C23×D5314yes—
1302C4⋊C4C23×D5318yes—
1303C22⋊C4—534no—
1304C22⋊C4—538no—
1305C22⋊C4—534no—
1306C22⋊C4—534no—
1307C22⋊C4—534no—
1308C22⋊C4—534no—
1309C22⋊C4—532no—
1310C22⋊C4—538no—
1311C22⋊C4—532no—
1312C22⋊C4—532no—
1313C22⋊C4—532no—
1314C22⋊C4—534no—
1315C22⋊C4—538no—
1316C22⋊C4—534no—
1317C22⋊C4—534no—
1318C22⋊C4—538no—
1319C22⋊C4—538no—
1320C22⋊C4—534no—
1321C22⋊C4—534no—
1322C22⋊C4—534no—
1323C22⋊C4—534no—
1324C22⋊C4—534no—
1325C22⋊C4—534no—
1326C22⋊C4—538no—
1327C22⋊C4—534no—
1328C22⋊C4C23×D5314yes—
1329C22⋊C4C23×D5314yes—
1330C22⋊C4C23×D5314yes—
1331C22⋊C4C23×D5318yes—
1332C22⋊C4C23×D5318yes—
1333C22⋊C4C23×D5318yes—
1334C42—538no—
1335C42—534no—
1336C42—538no—
1337C42—538no—
1338C42—534no—
1339C42—534no—
1340C42—538no—
1341C42—534no—
1342C42—538no—
1343C42—538no—
1344C42—534no—
1345C42—534no—
1346C42—532no—
1347C42—534no—
1348C42—532no—
1349C42C23×D5312yes—
1350C42C23×D5314yes—
1351C42C23×D5312yes—
1352C42C23×D5314yes—
1353C42C23×D5314yes—
1354C42C23×D5314yes—
1355C42C23×D5314yes—
1356C23—532no—
1357C23—534no—
1358C23—1062no—
1359C23—2121no—
1360C23—2121no—
1361C23C24×D5314yes—
1362C23C24×D5311yescharacteristic
1363Q8—28no—
1364Q8—24no—
1365Q8—44no—
1366Q8—5316no—
1367Q8—1068no—
1368Q8—1068no—
1369Q8—10616no—
1370Q8—1064no—
1371Q8—2124no—
1372Q8—2124no—
1373Q8—2124no—
1374D4—28no—
1375D4—24no—
1376D4—44no—
1377D4—10616no—
1378D4—1068no—
1379D4—1064no—
1380D4—2124no—
1381D4—2124no—
1382D4—2124no—
1383D4—2124no—
1384D4—2124no—
1385D4—2124no—
1386D4—2124no—
1387C2×C4—24no—
1388C2×C4—28no—
1389C2×C4—41no—
1390C2×C4—44no—
1391C2×C4—41no—
1392C2×C4—44no—
1393C2×C4—42no—
1394C2×C4—538no—
1395C2×C4—534no—
1396C2×C4—534no—
1397C2×C4—531no—
1398C2×C4—534no—
1399C2×C4—532no—
1400C2×C4—531no—
1401C2×C4—531no—
1402C2×C4—531no—
1403C2×C4—534no—
1404C2×C4—534no—
1405C2×C4—10616no—
1406C2×C4—10616no—
1407C2×C4—10616no—
1408C2×C4—1062no—
1409C2×C4—1064no—
1410C2×C4—1064no—
1411C2×C4—1068no—
1412C2×C4—2124no—
1413C2×C4—2128no—
1414C2×C4—2124no—
1415C2×C4—2122no—
1416C2×C4—2128no—
1417C2×C4—2121no—
1418C2×C4—2121no—
1419C2×C4#41×D5314yes—
1420C2×C4C24×D5312yes—
1421C2×C4C24×D5311yescharacteristic
1422C2×C4C24×D5314yes—
1423C2×C4C24×D5314yes—
1424C2×C4C24×D5314yes—
1425C2×C4C24×D5314yes—
1426C2×C4C24×D5314yes—
1427C2×C4C24×D5311yescharacteristic
1428C2×C4C24×D5312yes—
1429C22—21no—
1430C22—21no—
1431C22—24no—
1432C22—24no—
1433C22—24no—
1434C22—1062no—
1435C22—1064no—
1436C22—1064no—
1437C22—1062no—
1438C22—1064no—
1439C22—1062no—
1440C22—2124no—
1441C22C2×#41×D5312yes—
1442C22C25×D5311yescharacteristic
1443C4—24no—
1444C4—24no—
1445C4—21no—
1446C4—21no—
1447C4—24no—
1448C4—22no—
1449C4—24no—
1450C4—24no—
1451C4—538no—
1452C4—1064no—
1453C4—1061no—
1454C4—1061no—
1455C4—1064no—
1456C4—1064no—
1457C4—1061no—
1458C4—1061no—
1459C4—1062no—
1460C4—1064no—
1461C4C2×#41×D5314yes—
1462C2—22no—
1463C2—44no—
1464C2—2122no—
1465C2—2124no—
1466C2C22×#41×D5311yescharacteristic
1467C2#2028952711yescharacteristic
1468C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3461C2
hypercenter#3461D53
hypocenterC53#62850
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #20288822C2semidirect
2. #20288814C2semidirect
3. #20288807C2semidirect
4. #20288803C2semidirect
5. #20288728C2semidirect
6. #20288724C2semidirect
7. #20288706C2semidirect
8. #20288698C2semidirect
9. #20288579C2semidirect
10. #20288571C2semidirect
11. #20288523C2semidirect
12. #20288484C2semidirect
13. #20288436C2semidirect
14. #20288434C2semidirect
15. #20288427C2semidirect
16. #20288364C2semidirect
17. #20288148C2semidirect
18. #20288145C2semidirect
19. #20288101C2semidirect
20. #20288100C2semidirect
21. C4×#13133264C2semidirect
22. C2×#16811099C2semidirect
23. C53×#3461C2semidirect
26. #16811356C22semidirect
27. #16811355C22semidirect
28. #16811355C22semidirect
29. #16811353C22semidirect
30. #16811350C22semidirect
31. #16811350C22semidirect
32. #16811350C22semidirect
33. #16811349C22semidirect
34. #16811348C22semidirect
35. #16811348C22semidirect
37. #16811347C22semidirect
39. #16811345C22semidirect
41. #16811344C22semidirect
42. #16811342C22semidirect
43. #16811342C22semidirect
44. #16811341C22semidirect
46. #16811340C22semidirect
51. #16811332C22semidirect
52. #16811331C22semidirect
53. #16811329C22semidirect
59. #16811315C22semidirect
61. #16811309C22semidirect
62. #16811307C22semidirect
64. #16811306C22semidirect
66. #16811291C22semidirect
71. #16811286C22semidirect
74. #16811283C22semidirect
77. #16811279C22semidirect
82. #16811245C22semidirect
84. #16811243C22semidirect
85. #16811241C22semidirect
90. #16811232C22semidirect
93. #16811231C22semidirect
94. #16811230C22semidirect
110. #16811179C22semidirect
111. #16811177C22semidirect
114. #16811175C22semidirect
117. #16811160C22semidirect
125. #16811156C22semidirect
131. #16811150C22semidirect
137. #16811103C22semidirect
139. #16811102C22semidirect
141. #16811100C22semidirect
146. #16811099C22semidirect
148. C4×#11719945C22semidirect
150. C4×#11719947C22semidirect
154. C2×C4×Dic106C22semidirect
157. C4×Q8×D53C22semidirect
163. C53×#542C22semidirect
164. C53×#541C22semidirect
168. C53×#533C22semidirect
170. C53×#529C22semidirect
746. #3461D53semidirect
824. #542C2×D53semidirect
831. #541C2×D53semidirect
855. #533C2×D53semidirect
874. #529C2×D53semidirect
907. C53#62850semidirect

Maximal subgroups

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

subgroupindex
#202888222
#202888142
#202888072
#202888032
#202887282
#202887242
#202887062
#202886982
#202885792
#202885712
#202885232
#202884842
#202884362
#202884342
#202884272
#202883642
#202881482
#202881452
#202881012
#202881002
C4×#131332642
C2×#168110992
C53×#34612
#6285053