Finite Group Databasebeta

← #28293034

Subgroups — #28293034

Order 13568.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289307C218yesmaximal, complemented
2#20289180C214yesmaximal, complemented
3#20289081C214yesmaximal, complemented
4#20289035C218yesmaximal, complemented
5#20288713C214yesmaximal, complemented
6#20288671C214yesmaximal, complemented
7#20288655C218yesmaximal, complemented
8#20288616C214yesmaximal, complemented
9#20288609C212yesmaximal, complemented
10#20288599C211yesmaximal, characteristic, complemented
11#20288589C211yesmaximal, characteristic, complemented
12#20288584C214yesmaximal, complemented
13#20288505C212yesmaximal, complemented
14#20288498C211yesmaximal, characteristic, complemented
15#20288491C211yesmaximal, characteristic, complemented
16#20288373C212yesmaximal, complemented
17#20288359C212yesmaximal, complemented
18#20288011C211yesmaximal, characteristic, complemented
19#20288011C211yesmaximal, characteristic, complemented
20C2×C53×#532C211yesmaximal, characteristic, complemented
21C2×#13133265C2212yescomplemented
22C2×#13133262C2212yes—
23#16811368C22116yescomplemented
24#16811361C22116yescomplemented
25#16811359C2214yescomplemented
26#16811356C2218yescomplemented
27#16811355C2218yescomplemented
28#16811348C2214yescomplemented
29#16811347C2214yescomplemented
30#16811342C2218yescomplemented
31#16811337C2218yescomplemented
32#16811332C2218yescomplemented
33#16811323C2218yescomplemented
34#16811322C22116yescomplemented
35#16811320C2218yescomplemented
36#16811308C2218yescomplemented
37#16811302C22116yescomplemented
38#16811299C22116yescomplemented
39#16811293C2214yescomplemented
40#16811293C2214yescomplemented
41#16811292C2218yescomplemented
42#16811292C2218yescomplemented
43#16811291C2218yescomplemented
44#16811288C2214yescomplemented
45#16811281C2218yescomplemented
46#16811280C2218yescomplemented
47#16811280C2218yescomplemented
48#16811276C2214yescomplemented
49#16811274C2218yescomplemented
50#16811272C2218yescomplemented
51#16811272C2218yescomplemented
52#16811270C2218yescomplemented
53#16811268C2218yescomplemented
54#16811267C2218yescomplemented
55#16811266C2218yescomplemented
56#16811263C22116yescomplemented
57#16811261C2218yescomplemented
58#16811261C2218yescomplemented
59#16811258C2214yescomplemented
60D4×C22⋊D53C2218yes—
61#16811242C2218yescomplemented
62#16811240C2218yescomplemented
63#16811238C2218yescomplemented
64#16811234C2214yescomplemented
65#16811227C2214yescomplemented
66#16811226C2218yescomplemented
67#16811224C2218yescomplemented
68#16811223C22116yescomplemented
69#16811215C22116yescomplemented
70#16811206C22116yescomplemented
71#16811205C22116yescomplemented
72#16811202C2218yescomplemented
73#16811198C2214yescomplemented
74#16811197C2212yes—
75#16811197C2212yescomplemented
76#16811193C2214yescomplemented
77#16811191C2214yescomplemented
78#16811190C2212yes—
79#16811190C2218yescomplemented
80#16811190C2212yescomplemented
81#16811189C2218yescomplemented
82#16811186C2214yescomplemented
83#16811182C2218yescomplemented
84#16811180C2211yescharacteristic, complemented
85#16811180C2211yescharacteristic, complemented
86#16811180C2212yescomplemented
87#16811180C2212yescomplemented
88#16811178C2214yescomplemented
89#16811174C2212yescomplemented
90#16811173C2211yescharacteristic
91#16811173C2211yescharacteristic
92#16811173C2212yescomplemented
93#16811173C2212yescomplemented
94#16811172C2214yescomplemented
95#16811171C2214yescomplemented
96#16811171C2212yescomplemented
97C4⋊Q8×D53C2212yescomplemented
98#127×D53C2212yescomplemented
99#16811157C2214yescomplemented
100#16811157C2214yescomplemented
101#16811157C2214yescomplemented
102#16811157C2214yescomplemented
103#16811157C2214yescomplemented
104#16811157C2212yescomplemented
105#16811157C2212yescomplemented
106#16811152C2218yescomplemented
107#124×D53C2214yescomplemented
108#16811134C2211yescharacteristic
109#16811134C2214yescomplemented
110#16811134C2214yescomplemented
111#16811134C2212yescomplemented
112#16811134C2211yescharacteristic, complemented
113#16811134C2218yescomplemented
114C2×#13133200C2218yescomplemented
115#16811102C2218yescomplemented
116#16811101C2212yescomplemented
117#16811098C2212yescomplemented
118#16811095C2218yescomplemented
119C4×#11719945C2211yescharacteristic
120C4×#11719945C2214yescomplemented
121C4×#11719945C2211yescharacteristic, complemented
122C4×#11719945C2212yescomplemented
123C4×#11719945C2214yescomplemented
124C22×#41×C53C2212yescomplemented
125C53×#532C2214yescomplemented
126C53×#532C2214yescomplemented
127C53×#532C2214yescomplemented
128C53×#532C2214yescomplemented
129C2×C4⋊Q8×C53C2211yescharacteristic, complemented
130C2×#127×C53C2211yescharacteristic
131C2×#124×C53C2212yescomplemented
132C2×#121×C53C2214yescomplemented
133C2×C4×D4×C53C2214yescomplemented
134C22×C42×C53C2211yescharacteristic, complemented
135#13133265—48no—
136#13133262—48no—
137C2×#11719949C2314yes—
138C2×#11719949C2314yes—
139C2×#11719945C2311yescharacteristic
140C2×#11719945C2312yes—
141C2×#11719945C2311yescharacteristic
142C2×#11719945C2314yes—
143C2×#11719945C2318yes—
144C2×#11719945C2314yes—
145C2×#11719947C2318yes—
146C2×#11719947C2314yes—
147C2×#11719947C2314yes—
148C2×Q8×D53C2314yes—
149C2×Q8×D53C2314yes—
150C22×C22⋊D53C2318yes—
151C2×D4×D53C2314yes—
152C2×D4×D53C2318yes—
153C2×D4×D53C2314yes—
154#13133217C2311yescharacteristic
155#13133217C2312yes—
156#13133217C2311yescharacteristic
157#13133217C2312yes—
158#13133216C2318yes—
159#13133215C2314yes—
160#13133215C2314yes—
161#13133214C2311yescharacteristic
162#13133214C2311yescharacteristic
163#13133213C23116yes—
164#13133213C2318yes—
165#13133213C2314yes—
166#13133213C2314yes—
167#13133212C23116yes—
168#13133211C2314yes—
169#13133211C2314yes—
170#13133211C2318yes—
171#13133210C23116yes—
172#13133210C23116yes—
173#13133209C2314yes—
174#13133209C2312yes—
175#13133209C2314yes—
176#13133209C2312yes—
177#13133208C2318yes—
178#13133207C23116yes—
179#13133206C2314yes—
180#13133206C2314yes—
181#13133205C2314yes—
182#13133205C2311yescharacteristic
183#13133205C2311yescharacteristic
184#13133205C2312yes—
185#13133205C2314yes—
186#13133204C2318yes—
187#13133204C23116yes—
188#13133204C2314yes—
189#13133204C2314yes—
190#13133203C23116yes—
191#13133203C23116yes—
192#13133202C23116yes—
193#13133201C23116yes—
194#13133200C23116yes—
195#13133200C23116yes—
196#13133200C2318yes—
197#13133200C2318yes—
198#13133200C2318yes—
199#13133200C2312yes—
200#13133200C2314yes—
201#13133200C2312yes—
202#13133200C2314yes—
203#13133200C2314yes—
204#13133199C23116yes—
205#13133199C23116yes—
206#13133198C23116yes—
207#13133198C23116yes—
208#13133197C2318yes—
209#13133196C2314yes—
210#13133196C2312yes—
211#13133196C2314yes—
212#13133196C2312yes—
213#13133196C23116yes—
214#13133196C2314yes—
215#13133196C2314yes—
216#13133196C2314yes—
217#13133195C23116yes—
218#13133194C23116yes—
219#13133194C23116yes—
220#13133193C2318yes—
221#13133193C2318yes—
222#13133192C2318yes—
223#13133191C23116yes—
224#13133191C2314yes—
225#13133191C2312yes—
226#13133191C2314yes—
227#13133191C2314yes—
228#13133191C2312yes—
229#13133191C2314yes—
230#13133191C2314yes—
231#13133190C23116yes—
232#13133190C23116yes—
233#13133189C23116yes—
234#13133189C23116yes—
235#13133189C23116yes—
236#13133189C23116yes—
237#13133188C2318yes—
238#13133188C2318yes—
239#13133188C23116yes—
240#13133188C2318yes—
241#13133188C23116yes—
242#13133188C2318yes—
243#13133187C23116yes—
244#13133186C2318yes—
245#13133186C2318yes—
246#13133186C2312yes—
247#13133186C2314yes—
248#13133186C2312yes—
249#13133185C23116yes—
250#13133185C23116yes—
251Q8×Dic53C2318yes—
252Q8×Dic53C2318yes—
253C4×Dic106C2314yes—
254C4×Dic106C2312yes—
255C4×Dic106C2312yes—
256C4×Dic106C2314yes—
257C4×Dic106C2314yes—
258C4×Dic106C2314yes—
259C4×Dic106C2314yes—
260#13133182C2318yes—
261C4×D212C2314yes—
262C4×D212C2314yes—
263C4×D212C2314yes—
264C4×D212C2312yes—
265C4×D212C2314yes—
266C4×D212C2312yes—
267C4×D212C2314yes—
268D4×Dic53C2318yes—
269D4×Dic53C2318yes—
270D4×Dic53C2318yes—
271D4×Dic53C2318yes—
272#13133179C2318yes—
273C4×C22⋊D53C2314yes—
274C4×C22⋊D53C2314yes—
275C4×C22⋊D53C2314yes—
276C4×C22⋊D53C2318yes—
277C4×C22⋊D53C2314yes—
278C4×C22⋊D53C23116yes—
279C4×C22⋊D53C23116yes—
280C4×C22⋊D53C2314yes—
281C4×C22⋊D53C2318yes—
282C4×C22⋊D53C2314yes—
283C4×C22⋊D53C2318yes—
284#13133177C23116yes—
285#13133177C23116yes—
286#13133176C2318yes—
287#13133176C2314yes—
288#13133176C2311yescharacteristic
289#13133176C2311yescharacteristic
290#13133176C2312yes—
291#13133176C2314yes—
292#13133175C2318yes—
293#13133174C2318yes—
294#13133174C2312yes—
295#13133174C2314yes—
296#13133174C2314yes—
297#13133174C2314yes—
298#13133174C2312yes—
299#13133173C23116yes—
300C2×#11719919C23116yes—
301C4⋊C4×D53C2318yes—
302C2×C22⋊Dic53C2318yes—
303C2×#11719921C23116yes—
304C22⋊C4×D53C23116yes—
305C42×D53C2312yes—
306C42×D53C2314yes—
307C42×D53C2312yes—
308C2×#41×C53—48no—
309C2×#41×C53C2318yes—
310C2×#41×C53C2318yes—
311C22×Q8×C53C2312yes—
312C22×D4×C53C2312yes—
313C22×D4×C53C2314yes—
314C22×D4×C53C2314yes—
315C23×C4×C53C2311yescharacteristic
316C23×C4×C53C2312yes—
317C23×C4×C53C2314yes—
318C4⋊Q8×C53C2314yes—
319C4⋊Q8×C53C2312yes—
320C4⋊Q8×C53C2312yes—
321#127×C53C2314yes—
322#127×C53C2312yes—
323#127×C53C2312yes—
324#124×C53C2318yes—
325#124×C53C2314yes—
326#124×C53C2314yes—
327#121×C53C2318yes—
328#121×C53C2318yes—
329#121×C53C2318yes—
330#121×C53C2318yes—
331C4×D4×C53C2318yes—
332C4×D4×C53C2318yes—
333C4×D4×C53C2318yes—
334C4×D4×C53C2318yes—
335C2×C4⋊C4×C53C2314yes—
336C2×C22⋊C4×C53C2318yes—
337C2×C42×C53C2312yes—
338C2×C42×C53C2311yescharacteristic
339C2×C42×C53C2311yescharacteristic
340C2×C42×C53C2312yes—
341C2×C42×C53C2312yes—
342C2×C42×C53C2312yes—
343C2×C42×C53C2312yes—
344C24×C53C2414yes—
345C24×C53C2411yescharacteristic
346C23×D53C2418yes—
347#41×C53—416no—
348#41×C53—416no—
349C2×Q8×C53—28no—
350C2×Q8×C53C2414yes—
351C2×Q8×C53C2414yes—
352C2×D4×C53—28no—
353C2×D4×C53—48no—
354C2×D4×C53—48no—
355C2×D4×C53C2418yes—
356C2×D4×C53C2414yes—
357C2×D4×C53C2414yes—
358C2×D4×C53C2418yes—
359C2×D4×C53C24116yes—
360C22×C4×C53—24no—
361C22×C4×C53—44no—
362C22×C4×C53—48no—
363C22×C4×C53C2412yes—
364C22×C4×C53C2412yes—
365C22×C4×C53C2412yes—
366C22×C4×C53C2411yescharacteristic
367C22×C4×C53C2412yes—
368C22×C4×C53C2412yes—
369C22×C4×C53C2414yes—
370C22×C4×C53C2412yes—
371C22×C4×C53C2412yes—
372C22×C4×C53C2412yes—
373C22×C4×C53C24116yes—
374C22×C4×C53C2411yescharacteristic
375C2×C22⋊D53—416no—
376C2×C22⋊D53C2412yes—
377C2×C22⋊D53C2414yes—
378C2×C22⋊D53C2412yes—
379C2×C22⋊D53C24116yes—
380C2×C22⋊D53C24116yes—
381C2×C22⋊D53C2414yes—
382C2×C22⋊D53C2418yes—
383C2×C22⋊D53C2414yes—
384C2×C22⋊D53C2418yes—
385C2×C22⋊D53C2418yes—
386C22×Dic53C24116yes—
387C22×Dic53C2418yes—
388#11719949—48no—
389#11719949—48no—
390Q8×D53—48no—
391Q8×D53—48no—
392#11719947—416no—
393#11719947—48no—
394#11719947—48no—
395D4×D53—416no—
396D4×D53—48no—
397D4×D53—48no—
398#11719945—24no—
399#11719945—28no—
400#11719945—24no—
401#11719945—48no—
402#11719945—48no—
403#11719945—416no—
404C2×D212C2414yes—
405C2×D212C2411yescharacteristic
406C2×D212C2412yes—
407C2×D212C2411yescharacteristic
408C2×D212C2414yes—
409C2×D212C2418yes—
410C2×C4×D53C2414yes—
411C2×C4×D53C2414yes—
412C2×C4×D53C2412yes—
413C2×C4×D53C2414yes—
414C2×C4×D53C2412yes—
415C2×C4×D53C2418yes—
416C2×C4×D53C2418yes—
417C2×C4×D53C2418yes—
418C2×Dic106C2414yes—
419C2×Dic106C2411yescharacteristic
420C2×Dic106C2412yes—
421C2×Dic106C2411yescharacteristic
422C2×Dic106C2414yes—
423C2×Dic106C2418yes—
424C4⋊C4×C53C2418yes—
425C4⋊C4×C53C2418yes—
426C22⋊C4×C53C24116yes—
427C22⋊C4×C53C24116yes—
428C42×C53C2412yes—
429C42×C53C2412yes—
430C42×C53C2412yes—
431C42×C53C2412yes—
432C42×C53C2411yescharacteristic
433C42×C53C2411yescharacteristic
434C42×C53C2412yes—
435C42×C53C2411yescharacteristic
436C42×C53C2411yescharacteristic
437C42×C53C2412yes—
438C22⋊Dic53C24116yes—
439C22⋊Dic53C2412yes—
440C22⋊Dic53C2414yes—
441C22⋊Dic53C24116yes—
442C22⋊Dic53C24116yes—
443C22⋊Dic53C2412yes—
444C22⋊Dic53C2414yes—
445C22⋊Dic53C2418yes—
446C22⋊Dic53C2414yes—
447#11719921C2414yes—
448#11719921C24116yes—
449#11719921C2414yes—
450#11719921C2418yes—
451#11719921C24116yes—
452#11719921C2414yes—
453#11719921C2414yes—
454#11719921C2414yes—
455#11719921C2418yes—
456#11719921C2418yes—
457#11719921C2414yes—
458C4⋊Dic53C2414yes—
459C4⋊Dic53C2414yes—
460C4⋊Dic53C2412yes—
461C4⋊Dic53C2414yes—
462C4⋊Dic53C2412yes—
463C4⋊Dic53C2414yes—
464C4⋊Dic53C2414yes—
465C4⋊Dic53C24116yes—
466#11719919C24116yes—
467#11719919C2414yes—
468#11719919C2418yes—
469#11719919C24116yes—
470#11719919C2414yes—
471#11719919C2414yes—
472#11719919C2414yes—
473#11719919C2414yes—
474#11719919C2418yes—
475#11719919C2418yes—
476#11719919C2414yes—
477C4×Dic53C2418yes—
478C4×Dic53C2414yes—
479C4×Dic53C2412yes—
480C4×Dic53C2414yes—
481C4×Dic53C2414yes—
482C4×Dic53C2412yes—
483C4×Dic53C24116yes—
484C23×C53—22no—
485C23×C53—28no—
486C23×C53—42no—
487C23×C53—48no—
488C23×C53C2518yes—
489C23×C53C2512yes—
490C23×C53C2511yescharacteristic
491C22×D53—48no—
492C22×D53—416no—
493C22×D53C2512yes—
494C22×D53C2514yes—
495C22×D53C2512yes—
496Q8×C53—28no—
497Q8×C53—28no—
498D4×C53—28no—
499D4×C53—28no—
500D4×C53—216no—
501D4×C53—48no—
502D4×C53—416no—
503C2×C4×C53—28no—
504C2×C4×C53—22no—
505C2×C4×C53—24no—
506C2×C4×C53—24no—
507C2×C4×C53—24no—
508C2×C4×C53—24no—
509C2×C4×C53—24no—
510C2×C4×C53—42no—
511C2×C4×C53—42no—
512C2×C4×C53—42no—
513C2×C4×C53—416no—
514C2×C4×C53H(5,𝔽2)14yes—
515C2×C4×C53C2512yes—
516C2×C4×C53C2518yes—
517C2×C4×C53C2512yes—
518C2×C4×C53C2512yes—
519C2×C4×C53C2512yes—
520C2×C4×C53C2511yescharacteristic
521C2×C4×C53C2511yescharacteristic
522C2×C4×C53C2512yes—
523C22⋊D53—24no—
524C22⋊D53—28no—
525C22⋊D53—24no—
526C22⋊D53—48no—
527C22⋊D53—44no—
528C22⋊D53—44no—
529C22⋊D53—48no—
530C22⋊D53—48no—
531C22⋊D53—416no—
532C22⋊D53—416no—
533C2×Dic53—48no—
534C2×Dic53—416no—
535C2×Dic53C2512yes—
536C2×Dic53C2514yes—
537C2×Dic53C2512yes—
538C2×Dic53C2514yes—
539C2×Dic53C2518yes—
540C2×Dic53C2514yes—
541D212—22no—
542D212—24no—
543D212—22no—
544D212—28no—
545D212—44no—
546D212—48no—
547C4×D53—24no—
548C4×D53—28no—
549C4×D53—24no—
550C4×D53—28no—
551C4×D53—28no—
552C4×D53—48no—
553C4×D53—48no—
554C4×D53—48no—
555Dic106—22no—
556Dic106—24no—
557Dic106—22no—
558Dic106—28no—
559Dic106—44no—
560Dic106—48no—
561#62836—531nomaximal, Sylow
562C22×C53—22no—
563C22×C53—28no—
564C22×C53—22no—
565C22×C53—216no—
566C22×C53—22no—
567C22×C53—22no—
568C22×C53—44no—
569C22×C53—88no—
570C22×C53C2×H(5,𝔽2)12yes—
571C22×C53C2611yescharacteristic
572C2×D53—22no—
573C2×D53—24no—
574C2×D53—22no—
575C2×D53—24no—
576C2×D53—24no—
577C2×D53—28no—
578C2×D53—168no—
579C4×C53—28no—
580C4×C53—22no—
581C4×C53—22no—
582C4×C53—22no—
583C4×C53—22no—
584C4×C53C2×H(5,𝔽2)12yes—
585C4×C53C2×H(5,𝔽2)12yes—
586C4×C53#58514yes—
587Dic53—22no—
588Dic53—24no—
589Dic53—22no—
590Dic53—28no—
591Dic53—24no—
592Dic53—24no—
593#3562—538no—
594#3554—534no—
595#3546—534no—
596#3542—538no—
597#3517—534no—
598#3514—534no—
599#3513—538no—
600#3511—534no—
601#3510—532no—
602#3509—531no—
603#3508—534no—
604#3508—531no—
605#3500—532no—
606#3499—531no—
607#3498—531no—
608#3487—532no—
609#3485—532no—
610#3444—531no—
611#3444—531no—
612C2×#532D5311yescharacteristic, complemented
613C2×C53—22no—
614C2×C53—48no—
615C2×C53—42no—
616C2×C53C22×H(5,𝔽2)11yescharacteristic
617C2×C53C2×#58512yes—
618D53—42no—
619D53—44no—
620D53—42no—
621C2×2−1+4—532no—
622C2×H(5,𝔽2)—532no—
623C22×#41C2×D5312yescomplemented
624#562—5316no—
625#560—5316no—
626#559—534no—
627#559—538no—
628#559—538no—
629#557—534no—
630#556—534no—
631#556—538no—
632#555—538no—
633#554—538no—
634#553—538no—
635#553—5316no—
636#553—538no—
637#552—538no—
638#551—5316no—
639#551—5316no—
640#550—538no—
641#550—538no—
642#550—534no—
643#550—534no—
644#550—538no—
645D4×Q8—534no—
646#548—538no—
647#548—538no—
648#548—538no—
649#547—538no—
650#547—538no—
651#547—534no—
652#547—538no—
653#546—538no—
654#546—538no—
655#546—538no—
656#546—538no—
657#546—538no—
658#546—538no—
659#546—5316no—
660D42—538no—
661D42—534no—
662#542—538no—
663#542—538no—
664#542—538no—
665#541—534no—
666#540—534no—
667#540—538no—
668#540—5316no—
669#540—538no—
670#539—5316no—
671#538—5316no—
672#538—5316no—
673#537—538no—
674#536—532no—
675#536—532no—
676#536—534no—
677#536—534no—
678#535—532no—
679#535—532no—
680#535—538no—
681#535—534no—
682#535—534no—
683#535—538no—
684#534—538no—
685#533—534no—
686#533—531no—
687#533—531no—
688#533—532no—
689#533—532no—
690#532—532no—
691#532—532no—
692#532—534no—
693#532—534no—
694#532—531no—
695#532—531no—
696#532—532no—
697#532—532no—
698#532C2×D5314yescomplemented
699#532C2×D5314yescomplemented
700#532C2×D5314yescomplemented
701#532C2×D5314yescomplemented
702C2×C4⋊Q8—532no—
703C2×C4⋊Q8C2×D5311yescharacteristic, complemented
704C2×#127—532no—
705C2×#127C2×D5311yescharacteristic
706#529—538no—
707#529—534no—
708#529—534no—
709#529—532no—
710#529—532no—
711#529—534no—
712#529—534no—
713#529—534no—
714C2×#124—534no—
715C2×#124C2×D5312yescomplemented
716#525—531no—
717#525—532no—
718#525—531no—
719#525—534no—
720#525—534no—
721#525—538no—
722C2×#123—538no—
723C2×#121C2×D5314yescomplemented
724#520—538no—
725#519—532no—
726#518—532no—
727#518—538no—
728C4×#41—531no—
729C4×#41—531no—
730C4×#41—532no—
731C4×#41—534no—
732C4×#41—534no—
733C2×C4×D4C2×D5314yescomplemented
734C22×C42C2×D5311yescharacteristic, complemented
735C53#6283611yescharacteristic, complemented, Sylow
7362−1+4—2128no—
737H(5,𝔽2)—2128no—
738C2×#41—48no—
739C2×#41—534no—
740C2×#41—534no—
741C2×#41—538no—
742C2×#41—534no—
743C2×#41—534no—
744C2×#41—531no—
745C2×#41—532no—
746C2×#41—531no—
747C2×#41—534no—
748C2×#41—534no—
749C2×#41—538no—
750C2×#41C22×D5318yes—
751C2×#41C22×D5318yes—
752C22×Q8—534no—
753C22×Q8—534no—
754C22×Q8C22×D5312yes—
755C22×D4—538no—
756C22×D4—538no—
757C22×D4—534no—
758C22×D4—534no—
759C22×D4C22×D5312yes—
760C22×D4C22×D5314yes—
761C22×D4C22×D5314yes—
762C23×C4C22×D5311yescharacteristic
763C23×C4C22×D5314yes—
764C23×C4C22×D5312yes—
765C4⋊Q8—534no—
766C4⋊Q8—534no—
767C4⋊Q8—538no—
768C4⋊Q8—531no—
769C4⋊Q8—532no—
770C4⋊Q8—531no—
771C4⋊Q8—532no—
772C4⋊Q8C22×D5312yes—
773C4⋊Q8C22×D5312yes—
774C4⋊Q8C22×D5314yes—
775#127—534no—
776#127—538no—
777#127—534no—
778#127—5316no—
779#127—531no—
780#127—531no—
781#127C22×D5312yes—
782#127C22×D5312yes—
783#127C22×D5314yes—
784#126—5316no—
785#126—5316no—
786#126—5316no—
787#126—538no—
788#126—534no—
789#126—534no—
790#125—538no—
791#125—5316no—
792#125—532no—
793#125—534no—
794#125—532no—
795#125—534no—
796#124—534no—
797#124—534no—
798#124—534no—
799#124—534no—
800#124—538no—
801#124—5316no—
802#124—5316no—
803#124—5316no—
804#124—531no—
805#124—531no—
806#124—532no—
807#124—534no—
808#124—534no—
809#124C22×D5314yes—
810#124C22×D5314yes—
811#124C22×D5318yes—
812#123—5316no—
813#123—5316no—
814#123—532no—
815#123—534no—
816#123—538no—
817#123—538no—
818#123—5316no—
819#123—5316no—
820#123—532no—
821#123—534no—
822#123—534no—
823#123—538no—
824#123—5316no—
825#123—5316no—
826#123—5316no—
827#123—5316no—
828C22⋊Q8—538no—
829C22⋊Q8—538no—
830C22⋊Q8—534no—
831C22⋊Q8—534no—
832C22⋊Q8—532no—
833C22⋊Q8—534no—
834C22⋊Q8—532no—
835C22⋊Q8—534no—
836C22⋊Q8—534no—
837C22⋊Q8—5316no—
838C22⋊Q8—538no—
839C22⋊Q8—5316no—
840C22⋊Q8—5316no—
841C22⋊Q8—5316no—
842#121—538no—
843#121—538no—
844#121—538no—
845#121—538no—
846#121—5316no—
847#121—5316no—
848#121—5316no—
849#121—5316no—
850#121—5316no—
851#121—5316no—
852#121—534no—
853#121—534no—
854#121—532no—
855#121—534no—
856#121—534no—
857#121—532no—
858#121—534no—
859#121—5316no—
860#121—538no—
861#121—5316no—
862#121—5316no—
863#121C22×D5318yes—
864#121C22×D5318yes—
865#121C22×D5318yes—
866#121C22×D5318yes—
867#120—532no—
868#120—534no—
869#120—532no—
870#120—538no—
871#120—538no—
872#120—5316no—
873#120—5316no—
874#120—5316no—
875C4×Q8—538no—
876C4×Q8—538no—
877C4×Q8—538no—
878C4×Q8—534no—
879C4×Q8—534no—
880C4×Q8—532no—
881C4×Q8—532no—
882C4×Q8—534no—
883C4×Q8—534no—
884C4×Q8—534no—
885C4×D4—538no—
886C4×D4—538no—
887C4×D4—538no—
888C4×D4—538no—
889C4×D4—538no—
890C4×D4—534no—
891C4×D4—534no—
892C4×D4—534no—
893C4×D4—538no—
894C4×D4—534no—
895C4×D4—538no—
896C4×D4—534no—
897C4×D4—534no—
898C4×D4—5316no—
899C4×D4—5316no—
900C4×D4—538no—
901C4×D4—5316no—
902C4×D4—5316no—
903C4×D4—534no—
904C4×D4—532no—
905C4×D4—534no—
906C4×D4—534no—
907C4×D4—534no—
908C4×D4—534no—
909C4×D4—532no—
910C4×D4C22×D5318yes—
911C4×D4C22×D5318yes—
912C4×D4C22×D5318yes—
913C4×D4C22×D5318yes—
914#117—531no—
915#117—532no—
916#117—531no—
917#117—534no—
918#117—534no—
919#117—538no—
920#117—538no—
921#117—5316no—
922#117—534no—
923#117—534no—
924#117—532no—
925#117—534no—
926#117—532no—
927#117—538no—
928C2×C4⋊C4—5316no—
929C2×C4⋊C4—538no—
930C2×C4⋊C4C22×D5314yes—
931C2×C22⋊C4—538no—
932C2×C22⋊C4—5316no—
933C2×C22⋊C4—5316no—
934C2×C22⋊C4C22×D5318yes—
935C2×C42—534no—
936C2×C42—532no—
937C2×C42—532no—
938C2×C42C22×D5312yes—
939C2×C42C22×D5311yescharacteristic
940C2×C42C22×D5312yes—
941C2×C42C22×D5311yescharacteristic
942C2×C42C22×D5312yes—
943C2×C42C22×D5312yes—
944C2×C42C22×D5312yes—
945C24—538no—
946C24C23×D5314yes—
947C24C23×D5311yescharacteristic
948#41—416no—
949#41—416no—
950#41—1064no—
951#41—1068no—
952#41—1064no—
953#41—2128no—
954#41—21216no—
955#41—2128no—
956#41—21216no—
957#41—2128no—
958#41—2128no—
959#41—2128no—
960#41—2128no—
961C2×Q8—28no—
962C2×Q8—534no—
963C2×Q8—531no—
964C2×Q8—532no—
965C2×Q8—531no—
966C2×Q8—534no—
967C2×Q8—538no—
968C2×Q8—2128no—
969C2×Q8—2128no—
970C2×Q8C23×D5314yes—
971C2×Q8C23×D5314yes—
972C2×D4—28no—
973C2×D4—48no—
974C2×D4—48no—
975C2×D4—532no—
976C2×D4—534no—
977C2×D4—532no—
978C2×D4—534no—
979C2×D4—538no—
980C2×D4—5316no—
981C2×D4—5316no—
982C2×D4—534no—
983C2×D4—538no—
984C2×D4—538no—
985C2×D4—534no—
986C2×D4—531no—
987C2×D4—532no—
988C2×D4—531no—
989C2×D4—534no—
990C2×D4—538no—
991C2×D4—21216no—
992C2×D4—2128no—
993C2×D4—2128no—
994C2×D4—21216no—
995C2×D4C23×D5318yes—
996C2×D4C23×D5314yes—
997C2×D4C23×D5314yes—
998C2×D4C23×D5318yes—
999C2×D4C23×D53116yes—
1000C22×C4—24no—
1001C22×C4—44no—
1002C22×C4—48no—
1003C22×C4—5316no—
1004C22×C4—538no—
1005C22×C4—534no—
1006C22×C4—534no—
1007C22×C4—532no—
1008C22×C4—534no—
1009C22×C4—532no—
1010C22×C4—538no—
1011C22×C4—538no—
1012C22×C4—538no—
1013C22×C4C23×D5312yes—
1014C22×C4C23×D5312yes—
1015C22×C4C23×D5312yes—
1016C22×C4C23×D5312yes—
1017C22×C4C23×D5312yes—
1018C22×C4C23×D5311yescharacteristic
1019C22×C4C23×D5314yes—
1020C22×C4C23×D5312yes—
1021C22×C4C23×D5312yes—
1022C22×C4C23×D5312yes—
1023C22×C4C23×D53116yes—
1024C22×C4C23×D5311yescharacteristic
1025C4⋊C4—534no—
1026C4⋊C4—534no—
1027C4⋊C4—538no—
1028C4⋊C4—5316no—
1029C4⋊C4—5316no—
1030C4⋊C4—534no—
1031C4⋊C4—534no—
1032C4⋊C4—532no—
1033C4⋊C4—534no—
1034C4⋊C4—534no—
1035C4⋊C4—534no—
1036C4⋊C4—532no—
1037C4⋊C4—534no—
1038C4⋊C4—538no—
1039C4⋊C4—538no—
1040C4⋊C4—534no—
1041C4⋊C4—534no—
1042C4⋊C4—534no—
1043C4⋊C4—5316no—
1044C4⋊C4C23×D5318yes—
1045C4⋊C4C23×D5318yes—
1046C22⋊C4—532no—
1047C22⋊C4—534no—
1048C22⋊C4—5316no—
1049C22⋊C4—5316no—
1050C22⋊C4—532no—
1051C22⋊C4—5316no—
1052C22⋊C4—534no—
1053C22⋊C4—538no—
1054C22⋊C4—534no—
1055C22⋊C4—534no—
1056C22⋊C4—534no—
1057C22⋊C4—538no—
1058C22⋊C4—5316no—
1059C22⋊C4—5316no—
1060C22⋊C4—534no—
1061C22⋊C4—534no—
1062C22⋊C4—534no—
1063C22⋊C4—538no—
1064C22⋊C4—538no—
1065C22⋊C4—534no—
1066C22⋊C4C23×D53116yes—
1067C22⋊C4C23×D53116yes—
1068C42—538no—
1069C42—532no—
1070C42—534no—
1071C42—534no—
1072C42—534no—
1073C42—532no—
1074C42—5316no—
1075C42C23×D5311yescharacteristic
1076C42C23×D5311yescharacteristic
1077C42C23×D5312yes—
1078C42C23×D5312yes—
1079C42C23×D5311yescharacteristic
1080C42C23×D5311yescharacteristic
1081C42C23×D5312yes—
1082C42C23×D5312yes—
1083C42C23×D5312yes—
1084C42C23×D5312yes—
1085C23—22no—
1086C23—28no—
1087C23—42no—
1088C23—48no—
1089C23—532no—
1090C23—534no—
1091C23—532no—
1092C23—2128no—
1093C23—21216no—
1094C23C24×D5312yes—
1095C23C24×D5318yes—
1096C23C24×D5311yescharacteristic
1097Q8—28no—
1098Q8—28no—
1099Q8—1062no—
1100Q8—1064no—
1101Q8—1062no—
1102Q8—1068no—
1103Q8—2128no—
1104Q8—2124no—
1105D4—28no—
1106D4—28no—
1107D4—216no—
1108D4—48no—
1109D4—416no—
1110D4—1064no—
1111D4—1068no—
1112D4—1064no—
1113D4—1062no—
1114D4—1064no—
1115D4—1062no—
1116D4—1068no—
1117D4—2124no—
1118D4—2128no—
1119D4—21216no—
1120D4—2128no—
1121D4—2128no—
1122D4—2124no—
1123D4—2124no—
1124D4—2128no—
1125D4—21216no—
1126C2×C4—22no—
1127C2×C4—28no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—416no—
1137C2×C4—534no—
1138C2×C4—538no—
1139C2×C4—534no—
1140C2×C4—532no—
1141C2×C4—534no—
1142C2×C4—532no—
1143C2×C4—1064no—
1144C2×C4—1068no—
1145C2×C4—1064no—
1146C2×C4—1068no—
1147C2×C4—1068no—
1148C2×C4—2128no—
1149C2×C4—2128no—
1150C2×C4—2128no—
1151C2×C4—2128no—
1152C2×C4—21216no—
1153C2×C4#1313326214yes—
1154C2×C4C24×D5312yes—
1155C2×C4C24×D5318yes—
1156C2×C4C24×D5312yes—
1157C2×C4C24×D5312yes—
1158C2×C4C24×D5312yes—
1159C2×C4C24×D5311yescharacteristic
1160C2×C4C24×D5311yescharacteristic
1161C2×C4C24×D5312yes—
1162C22—22no—
1163C22—22no—
1164C22—28no—
1165C22—22no—
1166C22—22no—
1167C22—216no—
1168C22—44no—
1169C22—88no—
1170C22—8488no—
1171C22—1062no—
1172C22—1064no—
1173C22—1062no—
1174C22—1064no—
1175C22—1064no—
1176C22—1068no—
1177C22C2×#1313326212yes—
1178C22C25×D5311yescharacteristic
1179C4—22no—
1180C4—28no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—1062no—
1185C4—1064no—
1186C4—1062no—
1187C4—1064no—
1188C4—1064no—
1189C4—1068no—
1190C4C2×#1313326212yes—
1191C4C2×#1313326212yes—
1192C4#1681145914yes—
1193C2—22no—
1194C2—42no—
1195C2—48no—
1196C2—2122no—
1197C2—2124no—
1198C2—2122no—
1199C2C22×#1313326211yescharacteristic
1200C2C2×#1681145912yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC2×C53×#532C2
hypercenterC2×#532D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #20289307C2semidirect
2. #20289180C2semidirect
3. #20289081C2semidirect
4. #20289035C2semidirect
5. #20288713C2semidirect
6. #20288671C2semidirect
7. #20288655C2semidirect
8. #20288616C2semidirect
9. #20288609C2semidirect
10. #20288599C2semidirect
11. #20288589C2semidirect
12. #20288584C2semidirect
13. #20288505C2semidirect
14. #20288498C2semidirect
15. #20288491C2semidirect
16. #20288373C2semidirect
17. #20288359C2semidirect
18. #20288011C2semidirect
19. #20288011C2semidirect
20. C2×C53×#532C2semidirect
21. C2×#13133265C22semidirect
23. #16811368C22semidirect
24. #16811361C22semidirect
25. #16811359C22semidirect
26. #16811356C22semidirect
27. #16811355C22semidirect
28. #16811348C22semidirect
29. #16811347C22semidirect
30. #16811342C22semidirect
31. #16811337C22semidirect
32. #16811332C22semidirect
33. #16811323C22semidirect
34. #16811322C22semidirect
35. #16811320C22semidirect
36. #16811308C22semidirect
37. #16811302C22semidirect
38. #16811299C22semidirect
39. #16811293C22semidirect
40. #16811293C22semidirect
41. #16811292C22semidirect
42. #16811292C22semidirect
43. #16811291C22semidirect
44. #16811288C22semidirect
45. #16811281C22semidirect
46. #16811280C22semidirect
47. #16811280C22semidirect
48. #16811276C22semidirect
49. #16811274C22semidirect
50. #16811272C22semidirect
51. #16811272C22semidirect
52. #16811270C22semidirect
53. #16811268C22semidirect
54. #16811267C22semidirect
55. #16811266C22semidirect
56. #16811263C22semidirect
57. #16811261C22semidirect
58. #16811261C22semidirect
59. #16811258C22semidirect
61. #16811242C22semidirect
62. #16811240C22semidirect
63. #16811238C22semidirect
64. #16811234C22semidirect
65. #16811227C22semidirect
66. #16811226C22semidirect
67. #16811224C22semidirect
68. #16811223C22semidirect
69. #16811215C22semidirect
70. #16811206C22semidirect
71. #16811205C22semidirect
72. #16811202C22semidirect
73. #16811198C22semidirect
75. #16811197C22semidirect
76. #16811193C22semidirect
77. #16811191C22semidirect
79. #16811190C22semidirect
80. #16811190C22semidirect
81. #16811189C22semidirect
82. #16811186C22semidirect
83. #16811182C22semidirect
84. #16811180C22semidirect
85. #16811180C22semidirect
86. #16811180C22semidirect
87. #16811180C22semidirect
88. #16811178C22semidirect
89. #16811174C22semidirect
92. #16811173C22semidirect
93. #16811173C22semidirect
94. #16811172C22semidirect
95. #16811171C22semidirect
96. #16811171C22semidirect
97. C4⋊Q8×D53C22semidirect
98. #127×D53C22semidirect
99. #16811157C22semidirect
100. #16811157C22semidirect
101. #16811157C22semidirect
102. #16811157C22semidirect
103. #16811157C22semidirect
104. #16811157C22semidirect
105. #16811157C22semidirect
106. #16811152C22semidirect
107. #124×D53C22semidirect
109. #16811134C22semidirect
110. #16811134C22semidirect
111. #16811134C22semidirect
112. #16811134C22semidirect
113. #16811134C22semidirect
114. C2×#13133200C22semidirect
115. #16811102C22semidirect
116. #16811101C22semidirect
117. #16811098C22semidirect
118. #16811095C22semidirect
120. C4×#11719945C22semidirect
121. C4×#11719945C22semidirect
122. C4×#11719945C22semidirect
123. C4×#11719945C22semidirect
124. C22×#41×C53C22semidirect
125. C53×#532C22semidirect
126. C53×#532C22semidirect
127. C53×#532C22semidirect
128. C53×#532C22semidirect
129. C2×C4⋊Q8×C53C22semidirect
131. C2×#124×C53C22semidirect
132. C2×#121×C53C22semidirect
133. C2×C4×D4×C53C22semidirect
134. C22×C42×C53C22semidirect
612. C2×#532D53semidirect
623. C22×#41C2×D53semidirect
698. #532C2×D53semidirect
699. #532C2×D53semidirect
700. #532C2×D53semidirect
701. #532C2×D53semidirect
703. C2×C4⋊Q8C2×D53semidirect
715. C2×#124C2×D53semidirect
723. C2×#121C2×D53semidirect
733. C2×C4×D4C2×D53semidirect
734. C22×C42C2×D53semidirect
735. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202893072
#202891802
#202890812
#202890352
#202887132
#202886712
#202886552
#202886162
#202886092
#202885992
#202885892
#202885842
#202885052
#202884982
#202884912
#202883732
#202883592
#202880112
C2×C53×#5322
#6283653