Finite Group Databasebeta

← #28292983

Subgroups — #28292983

Order 13568.

7050 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289161C214yesmaximal, complemented
2#20289159C218yesmaximal, complemented
3#20289145C214yesmaximal, complemented
4#20289057C218yesmaximal, complemented
5#20288627C214yesmaximal, complemented
6#20288619C214yesmaximal, complemented
7#20288602C211yesmaximal, characteristic, complemented
8#20288596C212yesmaximal, complemented
9#20288532C214yesmaximal, complemented
10#20288527C214yesmaximal, complemented
11#20288500C211yesmaximal, characteristic, complemented
12#20288498C211yesmaximal, characteristic, complemented
13#20288497C212yesmaximal, complemented
14#20288415C218yesmaximal, complemented
15#20288367C212yesmaximal, complemented
16#20288364C212yesmaximal, complemented
17#20288012C211yesmaximal, characteristic, complemented
18#20288008C211yesmaximal, characteristic, complemented
19C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
20C53×#3509C211yesmaximal, characteristic, complemented
21C2×#13133265C2212yes—
22C2×#13133264C2212yes—
23C22×Q8×D53C2212yes—
24#16811377C22116yescomplemented
25#16811375C22116yescomplemented
26Q8×Dic106C2218yescomplemented
27#16811352C2214yescomplemented
28#16811351C2218yescomplemented
29#16811346C2214yescomplemented
30#16811345C2218yescomplemented
31#16811336C2218yescomplemented
32#16811333C2218yes—
33#16811331C2218yes—
34#16811331C2218yescomplemented
35#16811329C22116yes—
36#16811329C2218yescomplemented
37#16811326C2218yes—
38#16811324C22116yes—
39#16811317C2218yes—
40#16811315C2218yes—
41#16811306C22116yes—
42Q8×D212C2218yes—
43Q8×D212C2218yes—
44Q8×D212C2214yescomplemented
45#16811288C2218yes—
46#16811288C2214yescomplemented
47#16811286C2218yes—
48#16811286C2218yescomplemented
49#16811285C2218yes—
50#16811285C2218yes—
51#16811283C2218yes—
52#16811281C2218yes—
53#16811277C2218yes—
54#16811277C2214yescomplemented
55#16811276C2214yescomplemented
56#16811275C2218yescomplemented
57#16811274C2218yes—
58#16811271C22116yes—
59#16811253C2218yes—
60#16811253C2218yescomplemented
61#16811253C22116yescomplemented
62#16811251C2218yescomplemented
63#16811246C2218yescomplemented
64#16811245C2218yescomplemented
65#16811239C22116yescomplemented
66#16811236C2214yescomplemented
67#16811231C2218yescomplemented
68#16811221C22116yes—
69#16811214C22116yes—
70#16811203C2218yes—
71#16811199C2218yes—
72#16811199C2212yes—
73#16811199C2212yes—
74#16811199C2214yescomplemented
75#16811198C2214yescomplemented
76#16811198C2214yescomplemented
77#16811197C2212yes—
78#16811195C2218yes—
79#16811193C2214yescomplemented
80#16811178C2212yes—
81#16811178C2214yescomplemented
82#16811177C2212yes—
83#16811177C2218yescomplemented
84#16811176C2211yescharacteristic
85#16811174C2212yes—
86#16811174C2212yescomplemented
87#16811173C2211yescharacteristic
88#16811173C2212yescomplemented
89#16811172C2214yescomplemented
90#16811170C2212yes—
91#16811169C2211yescharacteristic
92C2×#13133217C2211yescharacteristic
93C2×#13133217C2212yescomplemented
94C2×#13133216C2214yes—
95C2×#13133215C2212yes—
96C4⋊Q8×D53C2214yes—
97C4⋊Q8×D53C2214yes—
98C4⋊Q8×D53C2214yes—
99C4⋊Q8×D53C2214yes—
100C4⋊Q8×D53C2212yescomplemented
101C4⋊Q8×D53C2214yescomplemented
102#16811160C2212yes—
103#16811160C2214yes—
104#16811159C2214yes—
105#16811158C2214yes—
106#16811155C2212yes—
107#16811153C2214yes—
108#16811151C2214yes—
109#16811136C2214yes—
110#16811135C2211yescharacteristic
111#16811135C2212yes—
112#16811135C2218yes—
113#16811132C2214yes—
114#16811131C2218yes—
115#16811130C2211yescharacteristic
116#16811105C2218yes—
117#16811103C2218yes—
118#16811100C2212yes—
119C4×#11719949C2214yes—
120C4×#11719945C2214yes—
121C4×#11719945C2211yescharacteristic
122#16811091C2212yes—
123C2×C4⋊C4×D53C2214yes—
124C2×C42×D53C2211yescharacteristic
125C53×#557C2214yescomplemented
126C53×#556C2214yescomplemented
127C53×#552C2218yes—
128C53×#541C2214yescomplemented
129C53×#536C2212yes—
130C53×#533C2211yescharacteristic
131C53×#533C2214yescomplemented
132C2×C4⋊Q8×C53C2211yescharacteristic
133C53×#519C2212yes—
134C4×#41×C53C2211yescharacteristic
135#13133265—48no—
136#13133264—48no—
137C2×#11719949C2314yes—
138C2×#11719949C2314yes—
139C2×#11719949C2314yes—
140C2×#11719945C2312yes—
141C2×#11719945C2314yes—
142C2×#11719945C2311yescharacteristic
143C2×#11719945C2318yes—
144C2×#11719945C2314yes—
145C2×#11719947C2318yes—
146C2×#11719947C2314yes—
147C22×Dic106C2312yes—
148C22×Dic106C2314yes—
149C22×Dic106C2314yes—
150C2×Q8×D53—48no—
151C2×Q8×D53C2318yes—
152C2×Q8×D53C2318yes—
153C2×Q8×D53C2314yes—
154C2×Q8×D53C2314yes—
155C2×Q8×D53C2314yes—
156C22×C4×D53C2312yes—
157C22×C4×D53C2311yescharacteristic
158C22×C4×D53C2314yes—
159#13133217C2318yes—
160#13133217C2314yes—
161#13133217C2314yes—
162#13133217C2314yes—
163#13133217C23116yes—
164#13133217C2312yes—
165#13133217C2312yes—
166#13133217C2311yescharacteristic
167#13133216C23116yes—
168#13133216C2318yes—
169#13133216C23116yes—
170#13133216C2318yes—
171#13133216C2318yes—
172#13133216C2318yes—
173#13133216C2318yes—
174#13133216C2312yes—
175#13133215C2318yes—
176#13133215C2314yes—
177#13133215C2314yes—
178#13133215C2314yes—
179#13133215C2311yescharacteristic
180#13133214C2311yescharacteristic
181#13133213C2311yescharacteristic
182#13133212C23116yes—
183#13133212C23116yes—
184#13133212C2318yes—
185#13133212C2314yes—
186#13133211C23116yes—
187#13133210C2314yes—
188#13133209C23116yes—
189#13133208C2318yes—
190#13133208C23116yes—
191#13133208C2312yes—
192#13133208C2314yes—
193#13133207C23116yes—
194#13133207C23116yes—
195#13133207C2314yes—
196#13133206C2314yes—
197#13133206C2314yes—
198#13133206C2311yescharacteristic
199#13133205C23116yes—
200#13133205C2314yes—
201#13133205C2314yes—
202#13133205C2312yes—
203#13133204C2311yescharacteristic
204#13133203C23116yes—
205#13133203C2314yes—
206#13133202C23116yes—
207#13133202C23116yes—
208#13133202C2314yes—
209#13133202C2318yes—
210#13133201C2318yes—
211#13133201C2318yes—
212#13133201C23116yes—
213#13133201C2312yes—
214#13133201C2314yes—
215#13133200C2318yes—
216#13133199C23116yes—
217#13133199C2314yes—
218#13133198C2312yes—
219#13133197C2318yes—
220#13133197C23116yes—
221#13133197C2318yes—
222#13133197C23116yes—
223#13133197C23116yes—
224#13133197C2314yes—
225#13133197C2312yes—
226#13133197C23116yes—
227#13133195C23116yes—
228#13133195C23116yes—
229#13133195C23116yes—
230#13133195C23116yes—
231#13133195C23116yes—
232#13133195C2314yes—
233#13133194C23116yes—
234#13133194C23116yes—
235#13133194C2314yes—
236#13133193C2318yes—
237#13133193C2312yes—
238#13133193C2318yes—
239#13133193C2314yes—
240#13133192C2318yes—
241#13133192C2314yes—
242#13133192C2312yes—
243#13133192C23116yes—
244#13133192C2314yes—
245#13133191C2314yes—
246#13133191C2318yes—
247#13133190C23116yes—
248#13133190C23116yes—
249#13133190C2314yes—
250#13133189C2314yes—
251#13133188C2312yes—
252#13133187C2314yes—
253#13133187C2312yes—
254#13133185C2312yes—
255Q8×Dic53C2318yes—
256Q8×Dic53C2314yes—
257C4×Dic106C2318yes—
258C4×Dic106C2312yes—
259C4×Dic106C23116yes—
260C4×Dic106C2314yes—
261C4×Dic106C2314yes—
262#13133182C2318yes—
263#13133182C2314yes—
264C4×D212C2312yes—
265C4×D212C2314yes—
266C4×D212C2318yes—
267C4×D212C2318yes—
268C4×D212C2314yes—
269C4×D212C23116yes—
270C4×D212C23116yes—
271C4×D212C2314yes—
272#13133179C2318yes—
273#13133179C2314yes—
274#13133179C23116yes—
275#13133179C2318yes—
276#13133179C2314yes—
277C4×C22⋊D53C2314yes—
278C4×C22⋊D53C2314yes—
279C4×C22⋊D53C2314yes—
280C4×C22⋊D53C2314yes—
281C4×C22⋊D53C2314yes—
282#13133177C2318yes—
283#13133177C23116yes—
284#13133177C23116yes—
285#13133176C2311yescharacteristic
286#13133176C2314yes—
287#13133175C2318yes—
288#13133175C2314yes—
289#13133175C2318yes—
290#13133174C23116yes—
291#13133174C2314yes—
292#13133174C2314yes—
293#13133174C2312yes—
294#13133174C2314yes—
295#13133173C2318yes—
296C2×C4⋊Dic53C2314yes—
297C2×C4⋊Dic53C2318yes—
298C2×#11719919C2318yes—
299C4⋊C4×D53C23116yes—
300C4⋊C4×D53C2318yes—
301C4⋊C4×D53C2318yes—
302C4⋊C4×D53C2318yes—
303C4⋊C4×D53C2318yes—
304C4⋊C4×D53C2318yes—
305C2×C4×Dic53C2311yescharacteristic
306C2×C4×Dic53C2312yes—
307C42×D53C2312yes—
308C42×D53C2312yes—
309C42×D53C2312yes—
310C42×D53C2312yes—
311C42×D53C2314yes—
312C42×D53C2312yes—
313C2×#41×C53C2311yescharacteristic
314C22×Q8×C53C2312yes—
315C4⋊Q8×C53C2314yes—
316C4⋊Q8×C53C2314yes—
317C4⋊Q8×C53C2312yes—
318C4⋊Q8×C53C2312yes—
319C4⋊Q8×C53C2312yes—
320#126×C53C23116yes—
321#125×C53C2312yes—
322#125×C53C2318yes—
323#125×C53C23116yes—
324#124×C53C2314yes—
325#123×C53C2318yes—
326C22⋊Q8×C53C2318yes—
327C22⋊Q8×C53C2314yes—
328C22⋊Q8×C53C2318yes—
329C4×Q8×C53C2318yes—
330C4×Q8×C53C2318yes—
331C4×Q8×C53C2312yes—
332C4×Q8×C53C2314yes—
333C4×Q8×C53C2318yes—
334C4×D4×C53C2314yes—
335C4×D4×C53C2312yes—
336#117×C53C2311yescharacteristic
337#117×C53C2312yes—
338#117×C53C2318yes—
339#117×C53C2312yes—
340#117×C53C2318yes—
341C2×C4⋊C4×C53C2314yes—
342C2×C42×C53C2311yescharacteristic
343C2×C42×C53C2312yes—
344C23×D53C2411yescharacteristic
345#41×C53—24no—
346C2×Q8×C53—28no—
347C2×Q8×C53C2414yes—
348C2×Q8×C53C2414yes—
349C2×Q8×C53C2414yes—
350C2×Q8×C53C2411yescharacteristic
351C2×D4×C53C2412yes—
352C2×D4×C53C2411yescharacteristic
353C22×C4×C53C2412yes—
354C22×C4×C53C2414yes—
355C22×C4×C53C2412yes—
356C22×C4×C53C2414yes—
357C22×C4×C53C2411yescharacteristic
358C2×C22⋊D53C2414yes—
359C2×C22⋊D53C2414yes—
360C2×C22⋊D53C2414yes—
361C2×C22⋊D53C2412yes—
362C2×C22⋊D53C2418yes—
363C22×Dic53C2412yes—
364C22×Dic53C2411yescharacteristic
365C22×Dic53C2414yes—
366C22×Dic53C2418yes—
367#11719949—216no—
368#11719949—48no—
369#11719949—48no—
370Q8×D53—416no—
371Q8×D53—416no—
372Q8×D53—48no—
373Q8×D53—48no—
374Q8×D53—48no—
375#11719947—48no—
376#11719947—416no—
377#11719945—28no—
378#11719945—24no—
379#11719945—216no—
380#11719945—48no—
381#11719945—416no—
382C2×D212C2418yes—
383C2×D212C2414yes—
384C2×D212C2412yes—
385C2×D212C2414yes—
386C2×D212C2411yescharacteristic
387C2×D212C2418yes—
388C2×C4×D53—24no—
389C2×C4×D53—28no—
390C2×C4×D53—48no—
391C2×C4×D53C2412yes—
392C2×C4×D53C2412yes—
393C2×C4×D53C2412yes—
394C2×C4×D53C2412yes—
395C2×C4×D53C2412yes—
396C2×C4×D53C2418yes—
397C2×C4×D53C2414yes—
398C2×C4×D53C2412yes—
399C2×C4×D53C2414yes—
400C2×C4×D53C24116yes—
401C2×C4×D53C2418yes—
402C2×C4×D53C2418yes—
403C2×C4×D53C2418yes—
404C2×C4×D53C2412yes—
405C2×Dic106—28no—
406C2×Dic106—48no—
407C2×Dic106—48no—
408C2×Dic106C2414yes—
409C2×Dic106C2412yes—
410C2×Dic106C2414yes—
411C2×Dic106C2411yescharacteristic
412C2×Dic106C2414yes—
413C2×Dic106C2418yes—
414C2×Dic106C24116yes—
415C2×Dic106C2418yes—
416C4⋊C4×C53C2418yes—
417C4⋊C4×C53C2418yes—
418C4⋊C4×C53C2414yes—
419C4⋊C4×C53C2412yes—
420C4⋊C4×C53C2414yes—
421C4⋊C4×C53C2414yes—
422C4⋊C4×C53C24116yes—
423C4⋊C4×C53C24116yes—
424C4⋊C4×C53C2418yes—
425C22⋊C4×C53C2412yes—
426C22⋊C4×C53C2414yes—
427C22⋊C4×C53C2414yes—
428C22⋊C4×C53C24116yes—
429C42×C53C2411yescharacteristic
430C42×C53C2412yes—
431C42×C53C2411yescharacteristic
432C42×C53C2414yes—
433C42×C53C2412yes—
434C42×C53C24116yes—
435C42×C53C2414yes—
436C22⋊Dic53C2412yes—
437C22⋊Dic53C2414yes—
438C22⋊Dic53C2414yes—
439#11719921C2418yes—
440#11719921C2414yes—
441#11719921C2414yes—
442#11719921C2414yes—
443#11719921C2414yes—
444#11719921C2414yes—
445#11719921C24116yes—
446#11719921C24116yes—
447#11719921C2418yes—
448#11719921C24116yes—
449#11719921C2418yes—
450#11719921C2418yes—
451C4⋊Dic53C2414yes—
452C4⋊Dic53C2418yes—
453C4⋊Dic53C2418yes—
454C4⋊Dic53C24116yes—
455C4⋊Dic53C24116yes—
456C4⋊Dic53C2418yes—
457C4⋊Dic53C2412yes—
458C4⋊Dic53C2414yes—
459C4⋊Dic53C2414yes—
460#11719919C2414yes—
461#11719919C24116yes—
462#11719919C24116yes—
463#11719919C24116yes—
464#11719919C24116yes—
465#11719919C2414yes—
466#11719919C2418yes—
467#11719919C2414yes—
468#11719919C2414yes—
469#11719919C2414yes—
470C4×Dic53C2411yescharacteristic
471C4×Dic53C2411yescharacteristic
472C4×Dic53C2412yes—
473C4×Dic53C2412yes—
474C4×Dic53C2412yes—
475C4×Dic53C2412yes—
476C4×Dic53C2412yes—
477C4×Dic53C2414yes—
478C4×Dic53C2412yes—
479C4×Dic53C2418yes—
480C4×Dic53C24116yes—
481C23×C53C2512yes—
482C23×C53C2511yescharacteristic
483C22×D53—22no—
484C22×D53—24no—
485C22×D53C2512yes—
486C22×D53C2514yes—
487C22×D53C2512yes—
488Q8×C53—22no—
489Q8×C53—28no—
490Q8×C53—28no—
491Q8×C53—28no—
492D4×C53—24no—
493D4×C53—22no—
494C2×C4×C53—28no—
495C2×C4×C53—24no—
496C2×C4×C53—24no—
497C2×C4×C53—28no—
498C2×C4×C53H(5,𝔽2)14yes—
499C2×C4×C53C2512yes—
500C2×C4×C53C2518yes—
501C2×C4×C53C2514yes—
502C2×C4×C53C2512yes—
503C2×C4×C53C2518yes—
504C2×C4×C53C2511yescharacteristic
505C2×C4×C53C2511yescharacteristic
506C2×C4×C53C2512yes—
507C22⋊D53—24no—
508C22⋊D53—28no—
509C22⋊D53—28no—
510C22⋊D53—28no—
511C22⋊D53—48no—
512C2×Dic53—28no—
513C2×Dic53—22no—
514C2×Dic53—24no—
515C2×Dic53—48no—
516C2×Dic53C2512yes—
517C2×Dic53C2512yes—
518C2×Dic53C2518yes—
519C2×Dic53C2514yes—
520C2×Dic53C2514yes—
521C2×Dic53C2512yes—
522C2×Dic53C2512yes—
523D212—28no—
524D212—216no—
525D212—24no—
526D212—22no—
527D212—28no—
528D212—48no—
529C4×D53—24no—
530C4×D53—24no—
531C4×D53—24no—
532C4×D53—28no—
533C4×D53—24no—
534C4×D53—24no—
535C4×D53—28no—
536C4×D53—24no—
537C4×D53—216no—
538C4×D53—416no—
539C4×D53—48no—
540C4×D53—48no—
541C4×D53—48no—
542C4×D532−1+418yescomplemented
543Dic106—28no—
544Dic106—28no—
545Dic106—24no—
546Dic106—22no—
547Dic106—28no—
548Dic106—48no—
549Dic106—416no—
550Dic106—48no—
551#62833—531nomaximal, Sylow
552C22×C53—22no—
553C22×C53—22no—
554C22×C53—24no—
555C22×C53C2×H(5,𝔽2)12yes—
556C22×C53C2611yescharacteristic
557C2×D53—28no—
558C2×D53—22no—
559C2×D53—22no—
560C2×D53—22no—
561C2×D53—24no—
562C2×D53—28no—
563C2×D53—24no—
564C2×D53C2×2−1+414yes—
565C4×C53—22no—
566C4×C53—28no—
567C4×C53—24no—
568C4×C53—22no—
569C4×C53—28no—
570C4×C53C2×H(5,𝔽2)12yes—
571C4×C53C2×H(5,𝔽2)12yes—
572C4×C53C2×2−1+414yes—
573Dic53—28no—
574Dic53—22no—
575Dic53—24no—
576Dic53—22no—
577Dic53—24no—
578Dic53—22no—
579Dic53C2×2−1+414yes—
580#3552—534no—
581#3552—534no—
582#3552—538no—
583#3544—538no—
584#3511—534no—
585#3511—534no—
586#3509—531no—
587#3509—532no—
588#3509D5311yescharacteristic, complemented
589#3503—534no—
590#3503—534no—
591#3499—532no—
592#3499—531no—
593#3499—531no—
594#3492—538no—
595#3486—532no—
596#3486—532no—
597#3444—531no—
598#3444—531no—
599C22×C4⋊Q8—531no—
600C2×C53—22no—
601C2×C53—42no—
602C2×C53C22×H(5,𝔽2)11yescharacteristic
603C2×C53C22×2−1+412yes—
604D53—24no—
605D53—42no—
606D53—44no—
607C2×2−1+4—532no—
608C2×2−1+4—532no—
609C23×Q8—532no—
610#563—5316no—
611#563—5316no—
612Q82—538no—
613#557—538no—
614#557—534no—
615#557C2×D5314yescomplemented
616#556—538no—
617#556—534no—
618#556C2×D5314yescomplemented
619#555—538no—
620#554—5316no—
621#554—538no—
622#554—538no—
623#554—538no—
624#554—538no—
625#553—5316no—
626#553—538no—
627#553—538no—
628#552—538no—
629#552—5316no—
630#552C2×D5318yes—
631D4×Q8—538no—
632D4×Q8—534no—
633D4×Q8—538no—
634D4×Q8—538no—
635D4×Q8—538no—
636D4×Q8—538no—
637D4×Q8—534no—
638#548—538no—
639#548—538no—
640#548—538no—
641#548—538no—
642#547—534no—
643#547—5316no—
644#547—538no—
645#547—538no—
646#547—534no—
647#547—538no—
648#544—538no—
649#544—5316no—
650#544—538no—
651#544—538no—
652#542—5316no—
653#542—538no—
654#542—538no—
655#541—534no—
656#541—538no—
657#541C2×D5314yescomplemented
658#539—5316no—
659#539—5316no—
660#537—538no—
661#536—532no—
662#536—534no—
663#536—534no—
664#536—534no—
665#536—538no—
666#536—532no—
667#536—532no—
668#536—538no—
669#536—534no—
670#536C2×D5312yes—
671#533—532no—
672#533—534no—
673#533—532no—
674#533—538no—
675#533—531no—
676#533C2×D5311yescharacteristic
677#533C2×D5314yescomplemented
678#532—531no—
679#532—532no—
680#532—532no—
681#532—534no—
682#532—532no—
683#532—531no—
684#532—532no—
685C2×C4⋊Q8—532no—
686C2×C4⋊Q8—534no—
687C2×C4⋊Q8—534no—
688C2×C4⋊Q8—534no—
689C2×C4⋊Q8—534no—
690C2×C4⋊Q8—534no—
691C2×C4⋊Q8—532no—
692C2×C4⋊Q8—534no—
693C2×C4⋊Q8—531no—
694C2×C4⋊Q8—532no—
695C2×C4⋊Q8C2×D5311yescharacteristic
696#529—534no—
697#529—534no—
698#529—534no—
699#529—532no—
700#529—534no—
701#529—532no—
702#529—534no—
703#525—531no—
704#525—538no—
705#525—534no—
706#525—534no—
707#525—532no—
708#525—531no—
709#525—538no—
710#520—538no—
711#520—538no—
712#519—532no—
713#519C2×D5312yes—
714C4×#41—534no—
715C4×#41—532no—
716C4×#41—531no—
717C4×#41—534no—
718C4×#41C2×D5311yescharacteristic
719C22×C4⋊C4—534no—
720C22×C42—531no—
721C53#6283311yescharacteristic, complemented, Sylow
7222−1+4—2128no—
7232−1+4—2128no—
724C2×#41—534no—
725C2×#41—534no—
726C2×#41—534no—
727C2×#41—538no—
728C2×#41—534no—
729C2×#41—534no—
730C2×#41—532no—
731C2×#41—531no—
732C2×#41—538no—
733C2×#41—534no—
734C2×#41C22×D5311yescharacteristic
735C22×Q8—538no—
736C22×Q8—538no—
737C22×Q8—534no—
738C22×Q8—534no—
739C22×Q8—534no—
740C22×Q8—532no—
741C22×Q8—534no—
742C22×Q8—534no—
743C22×Q8—2128no—
744C22×Q8C22×D5312yes—
745C23×C4—532no—
746C23×C4—531no—
747C23×C4—534no—
748C4⋊Q8—531no—
749C4⋊Q8—534no—
750C4⋊Q8—534no—
751C4⋊Q8—538no—
752C4⋊Q8—534no—
753C4⋊Q8—538no—
754C4⋊Q8—538no—
755C4⋊Q8—538no—
756C4⋊Q8—538no—
757C4⋊Q8—5316no—
758C4⋊Q8—538no—
759C4⋊Q8—532no—
760C4⋊Q8—5316no—
761C4⋊Q8—532no—
762C4⋊Q8—531no—
763C4⋊Q8—532no—
764C4⋊Q8—534no—
765C4⋊Q8—534no—
766C4⋊Q8—534no—
767C4⋊Q8—538no—
768C4⋊Q8—5316no—
769C4⋊Q8C22×D5312yes—
770C4⋊Q8C22×D5312yes—
771C4⋊Q8C22×D5314yes—
772C4⋊Q8C22×D5314yes—
773C4⋊Q8C22×D5312yes—
774#127—531no—
775#127—531no—
776#126—538no—
777#126—534no—
778#126—5316no—
779#126—5316no—
780#126—534no—
781#126—5316no—
782#126C22×D53116yes—
783#125—532no—
784#125—534no—
785#125—534no—
786#125—5316no—
787#125—538no—
788#125—5316no—
789#125—5316no—
790#125—5316no—
791#125C22×D5312yes—
792#125C22×D5318yes—
793#125C22×D53116yes—
794#124—531no—
795#124—534no—
796#124—534no—
797#124—531no—
798#124—534no—
799#124—5316no—
800#124—532no—
801#124—534no—
802#124—534no—
803#124—5316no—
804#124C22×D5314yes—
805#123—532no—
806#123—538no—
807#123—538no—
808#123—534no—
809#123—5316no—
810#123—5316no—
811#123—534no—
812#123—532no—
813#123—534no—
814#123—538no—
815#123—538no—
816#123—5316no—
817#123—5316no—
818#123C22×D5318yes—
819C22⋊Q8—532no—
820C22⋊Q8—534no—
821C22⋊Q8—538no—
822C22⋊Q8—538no—
823C22⋊Q8—534no—
824C22⋊Q8—532no—
825C22⋊Q8—534no—
826C22⋊Q8—5316no—
827C22⋊Q8—5316no—
828C22⋊Q8—538no—
829C22⋊Q8—538no—
830C22⋊Q8—5316no—
831C22⋊Q8—5316no—
832C22⋊Q8—5316no—
833C22⋊Q8—5316no—
834C22⋊Q8—5316no—
835C22⋊Q8—5316no—
836C22⋊Q8—5316no—
837C22⋊Q8—534no—
838C22⋊Q8—5316no—
839C22⋊Q8—5316no—
840C22⋊Q8C22×D5314yes—
841C22⋊Q8C22×D5318yes—
842C22⋊Q8C22×D5318yes—
843#121—534no—
844#121—532no—
845#121—534no—
846#121—538no—
847#121—534no—
848#121—532no—
849#121—534no—
850#121—5316no—
851#121—538no—
852#121—534no—
853#121—5316no—
854#121—5316no—
855#120—532no—
856#120—534no—
857#120—532no—
858C4×Q8—534no—
859C4×Q8—538no—
860C4×Q8—534no—
861C4×Q8—538no—
862C4×Q8—532no—
863C4×Q8—534no—
864C4×Q8—534no—
865C4×Q8—538no—
866C4×Q8—5316no—
867C4×Q8C22×D5314yes—
868C4×Q8C22×D5312yes—
869C4×Q8C22×D5318yes—
870C4×Q8C22×D5318yes—
871C4×Q8C22×D5318yes—
872C4×D4—534no—
873C4×D4—534no—
874C4×D4—534no—
875C4×D4—534no—
876C4×D4—534no—
877C4×D4—538no—
878C4×D4—534no—
879C4×D4—534no—
880C4×D4—5316no—
881C4×D4—538no—
882C4×D4—538no—
883C4×D4—5316no—
884C4×D4—5316no—
885C4×D4—538no—
886C4×D4—534no—
887C4×D4—534no—
888C4×D4—534no—
889C4×D4—532no—
890C4×D4—5316no—
891C4×D4—5316no—
892C4×D4—538no—
893C4×D4C22×D5314yes—
894C4×D4C22×D5312yes—
895#117—531no—
896#117—534no—
897#117—534no—
898#117—538no—
899#117—538no—
900#117—538no—
901#117—534no—
902#117—534no—
903#117—532no—
904#117—534no—
905#117—5316no—
906#117C22×D5312yes—
907#117C22×D5311yescharacteristic
908#117C22×D5312yes—
909#117C22×D5318yes—
910#117C22×D5318yes—
911C2×C4⋊C4—538no—
912C2×C4⋊C4—534no—
913C2×C4⋊C4—538no—
914C2×C4⋊C4—538no—
915C2×C4⋊C4—538no—
916C2×C4⋊C4—538no—
917C2×C4⋊C4—538no—
918C2×C4⋊C4—5316no—
919C2×C4⋊C4—538no—
920C2×C4⋊C4C22×D5314yes—
921C2×C42—531no—
922C2×C42—532no—
923C2×C42—534no—
924C2×C42—532no—
925C2×C42—532no—
926C2×C42—532no—
927C2×C42—532no—
928C2×C42—532no—
929C2×C42C22×D5312yes—
930C2×C42C22×D5311yescharacteristic
931C24—531no—
932#41—24no—
933#41—10616no—
934#41—10616no—
935#41—1068no—
936#41—1064no—
937#41—21216no—
938#41—2128no—
939#41—21216no—
940#41—2128no—
941#41—2128no—
942#41—2128no—
943C2×Q8—28no—
944C2×Q8—534no—
945C2×Q8—534no—
946C2×Q8—532no—
947C2×Q8—534no—
948C2×Q8—531no—
949C2×Q8—538no—
950C2×Q8—538no—
951C2×Q8—5316no—
952C2×Q8—1068no—
953C2×Q8—2128no—
954C2×Q8—2128no—
955C2×Q8—21216no—
956C2×Q8—21216no—
957C2×Q8—2128no—
958C2×Q8—2128no—
959C2×Q8—2128no—
960C2×Q8C23×D5314yes—
961C2×Q8C23×D5311yescharacteristic
962C2×Q8C23×D5314yes—
963C2×Q8C23×D5314yes—
964C2×D4—534no—
965C2×D4—534no—
966C2×D4—534no—
967C2×D4—532no—
968C2×D4—538no—
969C2×D4—538no—
970C2×D4—534no—
971C2×D4—534no—
972C2×D4—532no—
973C2×D4—531no—
974C2×D4—538no—
975C2×D4C23×D5312yes—
976C2×D4C23×D5311yescharacteristic
977C22×C4—532no—
978C22×C4—532no—
979C22×C4—531no—
980C22×C4—534no—
981C22×C4—538no—
982C22×C4—532no—
983C22×C4—532no—
984C22×C4—532no—
985C22×C4—532no—
986C22×C4—532no—
987C22×C4—538no—
988C22×C4—534no—
989C22×C4—532no—
990C22×C4—534no—
991C22×C4—5316no—
992C22×C4—538no—
993C22×C4—538no—
994C22×C4—538no—
995C22×C4—1068no—
996C22×C4—1064no—
997C22×C4—2128no—
998C22×C4C23×D5312yes—
999C22×C4C23×D5314yes—
1000C22×C4C23×D5312yes—
1001C22×C4C23×D5314yes—
1002C22×C4C23×D5311yescharacteristic
1003C4⋊C4—534no—
1004C4⋊C4—5316no—
1005C4⋊C4—538no—
1006C4⋊C4—534no—
1007C4⋊C4—5316no—
1008C4⋊C4—538no—
1009C4⋊C4—5316no—
1010C4⋊C4—5316no—
1011C4⋊C4—5316no—
1012C4⋊C4—534no—
1013C4⋊C4—532no—
1014C4⋊C4—534no—
1015C4⋊C4—538no—
1016C4⋊C4—534no—
1017C4⋊C4—538no—
1018C4⋊C4—534no—
1019C4⋊C4—534no—
1020C4⋊C4—534no—
1021C4⋊C4—5316no—
1022C4⋊C4C23×D5318yes—
1023C4⋊C4C23×D5318yes—
1024C4⋊C4C23×D53116yes—
1025C4⋊C4C23×D5314yes—
1026C4⋊C4C23×D5318yes—
1027C4⋊C4C23×D5314yes—
1028C4⋊C4C23×D5312yes—
1029C4⋊C4C23×D5314yes—
1030C4⋊C4C23×D53116yes—
1031C22⋊C4—532no—
1032C22⋊C4—534no—
1033C22⋊C4—534no—
1034C22⋊C4—534no—
1035C22⋊C4—538no—
1036C22⋊C4—534no—
1037C22⋊C4—5316no—
1038C22⋊C4—5316no—
1039C22⋊C4—5316no—
1040C22⋊C4—534no—
1041C22⋊C4—538no—
1042C22⋊C4—538no—
1043C22⋊C4—534no—
1044C22⋊C4—534no—
1045C22⋊C4—538no—
1046C22⋊C4C23×D5314yes—
1047C22⋊C4C23×D5312yes—
1048C22⋊C4C23×D53116yes—
1049C22⋊C4C23×D5314yes—
1050C42—531no—
1051C42—532no—
1052C42—531no—
1053C42—532no—
1054C42—532no—
1055C42—532no—
1056C42—532no—
1057C42—538no—
1058C42—534no—
1059C42—532no—
1060C42—5316no—
1061C42C23×D5311yescharacteristic
1062C42C23×D5311yescharacteristic
1063C42C23×D5312yes—
1064C42C23×D5314yes—
1065C42C23×D5314yes—
1066C42C23×D5312yes—
1067C42C23×D53116yes—
1068C23—532no—
1069C23—532no—
1070C23—534no—
1071C23—1064no—
1072C23—1062no—
1073C23C24×D5312yes—
1074C23C24×D5311yescharacteristic
1075Q8—28no—
1076Q8—28no—
1077Q8—22no—
1078Q8—28no—
1079Q8—1068no—
1080Q8—1068no—
1081Q8—1068no—
1082Q8—1064no—
1083Q8—1062no—
1084Q8—21216no—
1085Q8—2128no—
1086Q8—2128no—
1087D4—24no—
1088D4—22no—
1089D4—1068no—
1090D4—10616no—
1091D4—1068no—
1092D4—1068no—
1093D4—1064no—
1094D4—1068no—
1095D4—1064no—
1096D4—1062no—
1097D4—1068no—
1098D4—2128no—
1099D4—2128no—
1100C2×C4—28no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—28no—
1104C2×C4—532no—
1105C2×C4—538no—
1106C2×C4—534no—
1107C2×C4—532no—
1108C2×C4—532no—
1109C2×C4—532no—
1110C2×C4—534no—
1111C2×C4—538no—
1112C2×C4—1064no—
1113C2×C4—10616no—
1114C2×C4—1064no—
1115C2×C4—1064no—
1116C2×C4—1062no—
1117C2×C4—1068no—
1118C2×C4—1064no—
1119C2×C4—1064no—
1120C2×C4—1064no—
1121C2×C4—1068no—
1122C2×C4—1064no—
1123C2×C4—1068no—
1124C2×C4—21216no—
1125C2×C4—2128no—
1126C2×C4—2128no—
1127C2×C4—2128no—
1128C2×C4—2128no—
1129C2×C4#1313326314yes—
1130C2×C4C24×D5318yes—
1131C2×C4C24×D5312yes—
1132C2×C4C24×D5314yes—
1133C2×C4C24×D5312yes—
1134C2×C4C24×D5318yes—
1135C2×C4C24×D5311yescharacteristic
1136C2×C4C24×D5311yescharacteristic
1137C2×C4C24×D5312yes—
1138C22—22no—
1139C22—22no—
1140C22—24no—
1141C22—534no—
1142C22—1068no—
1143C22—1062no—
1144C22—1062no—
1145C22—1062no—
1146C22—1064no—
1147C22—1068no—
1148C22—1064no—
1149C22C2×#1313326312yes—
1150C22C25×D5311yescharacteristic
1151C4—22no—
1152C4—28no—
1153C4—22no—
1154C4—24no—
1155C4—28no—
1156C4—534no—
1157C4—1062no—
1158C4—1062no—
1159C4—1064no—
1160C4—1068no—
1161C4—1062no—
1162C4—1064no—
1163C4C2×#1313326312yes—
1164C4C2×#1313326312yes—
1165C42−1+4×D5314yes—
1166C2—22no—
1167C2—42no—
1168C2—1064no—
1169C2—2122no—
1170C2—2124no—
1171C2C22×#1313326311yescharacteristic
1172C2C2×2−1+4×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3509C2
hypercenter#3509D53
hypocenterC53#62833
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #20289161C2semidirect
2. #20289159C2semidirect
3. #20289145C2semidirect
4. #20289057C2semidirect
5. #20288627C2semidirect
6. #20288619C2semidirect
7. #20288602C2semidirect
8. #20288596C2semidirect
9. #20288532C2semidirect
10. #20288527C2semidirect
11. #20288500C2semidirect
12. #20288498C2semidirect
13. #20288497C2semidirect
14. #20288415C2semidirect
15. #20288367C2semidirect
16. #20288364C2semidirect
17. #20288012C2semidirect
18. #20288008C2semidirect
19. C2×C4⋊Q8×D53C2semidirect
20. C53×#3509C2semidirect
24. #16811377C22semidirect
25. #16811375C22semidirect
26. Q8×Dic106C22semidirect
27. #16811352C22semidirect
28. #16811351C22semidirect
29. #16811346C22semidirect
30. #16811345C22semidirect
31. #16811336C22semidirect
34. #16811331C22semidirect
36. #16811329C22semidirect
44. Q8×D212C22semidirect
46. #16811288C22semidirect
48. #16811286C22semidirect
54. #16811277C22semidirect
55. #16811276C22semidirect
56. #16811275C22semidirect
60. #16811253C22semidirect
61. #16811253C22semidirect
62. #16811251C22semidirect
63. #16811246C22semidirect
64. #16811245C22semidirect
65. #16811239C22semidirect
66. #16811236C22semidirect
67. #16811231C22semidirect
74. #16811199C22semidirect
75. #16811198C22semidirect
76. #16811198C22semidirect
79. #16811193C22semidirect
81. #16811178C22semidirect
83. #16811177C22semidirect
86. #16811174C22semidirect
88. #16811173C22semidirect
89. #16811172C22semidirect
93. C2×#13133217C22semidirect
100. C4⋊Q8×D53C22semidirect
101. C4⋊Q8×D53C22semidirect
125. C53×#557C22semidirect
126. C53×#556C22semidirect
128. C53×#541C22semidirect
131. C53×#533C22semidirect
542. C4×D532−1+4semidirect
588. #3509D53semidirect
615. #557C2×D53semidirect
618. #556C2×D53semidirect
657. #541C2×D53semidirect
677. #533C2×D53semidirect
721. C53#62833semidirect

Maximal subgroups

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

subgroupindex
#202891612
#202891592
#202891452
#202890572
#202886272
#202886192
#202886022
#202885962
#202885322
#202885272
#202885002
#202884982
#202884972
#202884152
#202883672
#202883642
#202880122
#202880082
C2×C4⋊Q8×D532
C53×#35092
#6283353