Finite Group Databasebeta

← #28293033

Subgroups — #28293033

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#20289309C218yesmaximal, complemented
2#20289189C214yesmaximal, complemented
3#20289090C214yesmaximal, complemented
4#20289025C218yesmaximal, complemented
5#20288722C214yesmaximal, complemented
6#20288679C214yesmaximal, complemented
7#20288660C218yesmaximal, complemented
8#20288627C214yesmaximal, complemented
9#20288612C212yesmaximal, complemented
10#20288592C211yesmaximal, characteristic, complemented
11#20288592C214yesmaximal, complemented
12#20288504C212yesmaximal, complemented
13#20288498C211yesmaximal, characteristic, complemented
14#20288493C211yesmaximal, characteristic, complemented
15#20288374C212yesmaximal, complemented
16#20288358C212yesmaximal, complemented
17#20288012C211yesmaximal, characteristic, complemented
18#20288008C211yesmaximal, characteristic, complemented
19C2×#16811174C211yesmaximal, characteristic, complemented
20C53×#3509C211yesmaximal, characteristic, complemented
21C2×#13133265C2212yescomplemented
22C2×#13133263C2212yes—
23C22×#11719949C2212yescomplemented
24#16811371C22116yescomplemented
25#16811364C22116yescomplemented
26#16811358C2218yescomplemented
27#16811358C2218yescomplemented
28#16811358C2214yescomplemented
29#16811345C2218yescomplemented
30#16811336C2218yescomplemented
31#16811329C2218yescomplemented
32#16811326C2218yescomplemented
33#16811326C22116yescomplemented
34#16811317C2218yescomplemented
35#16811298C22116yescomplemented
36#16811297C22116yescomplemented
37#16811295C2218yescomplemented
38#16811295C2218yescomplemented
39#16811295C2214yescomplemented
40#16811295C2218yescomplemented
41#16811295C2214yescomplemented
42#16811288C2214yescomplemented
43#16811285C2218yescomplemented
44#16811285C2218yescomplemented
45#16811283C2218yescomplemented
46#16811276C2214yescomplemented
47#16811276C2218yescomplemented
48#16811275C2218yescomplemented
49#16811274C2218yescomplemented
50#16811266C2218yescomplemented
51#16811265C22116yescomplemented
52#16811264C2218yescomplemented
53#16811264C2218yescomplemented
54#16811264C2218yescomplemented
55#16811264C2218yescomplemented
56#16811264C2218yescomplemented
57D4×D212C2218yes—
58D4×D212C2214yescomplemented
59#16811246C2218yescomplemented
60#16811245C2218yescomplemented
61#16811245C2218yescomplemented
62#16811229C22116yescomplemented
63#16811229C2218yescomplemented
64#16811229C2214yescomplemented
65#16811229C2218yescomplemented
66#16811221C22116yescomplemented
67#16811212C22116yescomplemented
68#16811212C22116yescomplemented
69#16811203C2218yescomplemented
70#16811198C2214yescomplemented
71#16811198C2214yescomplemented
72#16811197C2212yescomplemented
73#16811192C2212yes—
74#16811192C2218yescomplemented
75#16811192C2218yescomplemented
76#16811192C2214yescomplemented
77#16811192C2212yescomplemented
78#16811191C2214yescomplemented
79#16811184C2218yescomplemented
80#16811178C2212yescomplemented
81#16811177C2212yescomplemented
82#16811176C2211yescharacteristic, complemented
83#16811174C2212yescomplemented
84#16811174C2214yescomplemented
85#16811174C2214yescomplemented
86#16811174C2214yescomplemented
87#16811174C2212yescomplemented
88#16811174C2214yescomplemented
89#16811174C2214yescomplemented
90#16811174C2214yescomplemented
91#16811173C2211yescharacteristic
92#16811173C2212yescomplemented
93#16811170C2212yescomplemented
94#16811169C2211yescharacteristic
95C4⋊Q8×D53C2212yescomplemented
96C2×#13133214C2211yescharacteristic
97C2×#13133214C2212yescomplemented
98#16811160C2212yescomplemented
99#16811160C2214yescomplemented
100#16811160C2218yescomplemented
101#16811159C2214yescomplemented
102#16811158C2214yescomplemented
103#16811155C2212yescomplemented
104#16811153C2214yescomplemented
105#16811151C2214yescomplemented
106C2×#13133206C2212yescomplemented
107#124×D53C2214yescomplemented
108#16811136C2214yescomplemented
109#16811135C2211yescharacteristic, complemented
110#16811135C2212yescomplemented
111#16811135C2218yescomplemented
112#16811132C2214yescomplemented
113#16811130C2211yescharacteristic
114#123×D53C2218yescomplemented
115C2×#13133192C2214yescomplemented
116#16811105C2218yescomplemented
117#16811097C2212yescomplemented
118#16811097C2218yescomplemented
119C4×#11719949C2214yescomplemented
120C4×#11719945C2214yescomplemented
121C4×#11719945C2211yescharacteristic, complemented
122#16811091C2212yescomplemented
123C2×#13133179C2214yescomplemented
124C2×C42×D53C2211yescharacteristic, complemented
125C53×#557C2214yescomplemented
126C53×#556C2214yescomplemented
127C53×#552C2218yescomplemented
128C53×#541C2214yescomplemented
129C53×#536C2212yes—
130C53×#533C2211yescharacteristic, complemented
131C53×#533C2214yescomplemented
132C2×C4⋊Q8×C53C2211yescharacteristic, complemented
133C53×#519C2212yescomplemented
134C4×#41×C53C2211yescharacteristic
135#13133265—48no—
136#13133263—48no—
137C2×#11719949—48no—
138C2×#11719949C2314yes—
139C2×#11719949C2318yes—
140C2×#11719949C2314yes—
141C2×#11719949C2318yes—
142C2×#11719949C2318yes—
143C2×#11719949C2314yes—
144C2×#11719949C2314yes—
145C2×#11719945C2312yes—
146C2×#11719945C2311yescharacteristic
147C2×#11719945C2318yes—
148C2×#11719945C2314yes—
149C2×#11719945C2314yes—
150C2×Q8×D53C2314yes—
151C2×Q8×D53C2314yes—
152C22×D212C2312yes—
153C22×D212C2314yes—
154C22×D212C2314yes—
155C22×D212C2318yes—
156C22×D212C2314yes—
157C2×D4×D53C2318yes—
158C2×D4×D53C2314yes—
159C22×C4×D53C2311yescharacteristic
160C22×C4×D53C2312yes—
161C22×C4×D53C2314yes—
162#13133217C2311yescharacteristic
163#13133216C2318yes—
164#13133216C2312yes—
165#13133215C2314yes—
166#13133215C2311yescharacteristic
167#13133214C2314yes—
168#13133214C23116yes—
169#13133214C2314yes—
170#13133214C2314yes—
171#13133214C2318yes—
172#13133214C2312yes—
173#13133214C2312yes—
174#13133214C2311yescharacteristic
175#13133213C2311yescharacteristic
176#13133212C23116yes—
177#13133212C2314yes—
178#13133212C2318yes—
179#13133211C23116yes—
180#13133210C2314yes—
181#13133208C2314yes—
182#13133208C2312yes—
183#13133207C2314yes—
184#13133206C2314yes—
185#13133206C2314yes—
186#13133206C2318yes—
187#13133206C2318yes—
188#13133206C2314yes—
189#13133206C2314yes—
190#13133206C2311yescharacteristic
191#13133205C23116yes—
192#13133205C2314yes—
193#13133205C2314yes—
194#13133205C23116yes—
195#13133205C2312yes—
196#13133204C2311yescharacteristic
197#13133203C23116yes—
198#13133203C2314yes—
199#13133202C23116yes—
200#13133202C23116yes—
201#13133202C23116yes—
202#13133202C23116yes—
203#13133202C23116yes—
204#13133202C23116yes—
205#13133202C23116yes—
206#13133202C2318yes—
207#13133202C2314yes—
208#13133201C2314yes—
209#13133201C2312yes—
210#13133200C2318yes—
211#13133199C23116yes—
212#13133199C2314yes—
213#13133198C2312yes—
214#13133197C2314yes—
215#13133197C2312yes—
216#13133197C23116yes—
217#13133195C23116yes—
218#13133195C23116yes—
219#13133195C23116yes—
220#13133195C2314yes—
221#13133194C2314yes—
222#13133193C2318yes—
223#13133193C2312yes—
224#13133193C2314yes—
225#13133192C2314yes—
226#13133192C23116yes—
227#13133192C2318yes—
228#13133192C23116yes—
229#13133192C2318yes—
230#13133192C23116yes—
231#13133192C23116yes—
232#13133192C2318yes—
233#13133192C2318yes—
234#13133192C23116yes—
235#13133192C2318yes—
236#13133192C23116yes—
237#13133192C2312yes—
238#13133192C23116yes—
239#13133192C2318yes—
240#13133192C2318yes—
241#13133192C2318yes—
242#13133192C2314yes—
243#13133191C2314yes—
244#13133191C2318yes—
245#13133190C23116yes—
246#13133190C23116yes—
247#13133190C2314yes—
248#13133189C2314yes—
249#13133188C2312yes—
250#13133187C2318yes—
251#13133187C23116yes—
252#13133187C23116yes—
253#13133187C2318yes—
254#13133187C23116yes—
255#13133187C2312yes—
256#13133187C2314yes—
257#13133185C2312yes—
258Q8×Dic53C2314yes—
259C4×Dic106C2312yes—
260C4×Dic106C2314yes—
261C4×Dic106C2314yes—
262#13133182C2314yes—
263C4×D212C2318yes—
264C4×D212C2318yes—
265C4×D212C2312yes—
266C4×D212C2314yes—
267C4×D212C2314yes—
268C4×D212C23116yes—
269C4×D212C23116yes—
270C4×D212C2314yes—
271C4×D212C23116yes—
272C4×D212C2318yes—
273#13133179C2314yes—
274#13133179C2318yes—
275#13133179C2318yes—
276#13133179C2318yes—
277#13133179C2318yes—
278#13133179C23116yes—
279#13133179C2318yes—
280#13133179C2318yes—
281#13133179C2318yes—
282#13133179C2314yes—
283#13133179C2318yes—
284C4×C22⋊D53C2314yes—
285C4×C22⋊D53C2314yes—
286C4×C22⋊D53C2314yes—
287C4×C22⋊D53C2314yes—
288C4×C22⋊D53C2314yes—
289#13133177C2318yes—
290#13133176C2311yescharacteristic
291#13133176C2314yes—
292#13133175C2318yes—
293#13133175C2314yes—
294#13133174C23116yes—
295#13133174C2314yes—
296#13133174C2314yes—
297#13133174C2314yes—
298#13133174C2312yes—
299C4⋊C4×D53C2318yes—
300C4⋊C4×D53C23116yes—
301C2×#11719921C2318yes—
302C22⋊C4×D53C23116yes—
303C22⋊C4×D53C23116yes—
304C22⋊C4×D53C2318yes—
305C2×C4×Dic53C2312yes—
306C2×C4×Dic53C2311yescharacteristic
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×C53C2318yes—
333C4×Q8×C53C2314yes—
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×D53C2414yes—
345C23×D53C2411yescharacteristic
346C23×D53C2418yes—
347#41×C53—24no—
348C2×Q8×C53—28no—
349C2×Q8×C53C2414yes—
350C2×Q8×C53C2414yes—
351C2×Q8×C53C2414yes—
352C2×Q8×C53C2411yescharacteristic
353C2×D4×C53C2412yes—
354C2×D4×C53C2411yescharacteristic
355C22×C4×C53C2412yes—
356C22×C4×C53C2414yes—
357C22×C4×C53C2412yes—
358C22×C4×C53C2414yes—
359C22×C4×C53C2411yescharacteristic
360C2×C22⋊D53C2414yes—
361C2×C22⋊D53C2412yes—
362C2×C22⋊D53C2414yes—
363C2×C22⋊D53C2414yes—
364C2×C22⋊D53C2418yes—
365C22×Dic53C2411yescharacteristic
366C22×Dic53C2412yes—
367#11719949—416no—
368#11719949—416no—
369#11719949—48no—
370#11719949—416no—
371#11719949—48no—
372#11719949—48no—
373#11719949—48no—
374Q8×D53—48no—
375Q8×D53—48no—
376D4×D53—48no—
377D4×D53—416no—
378#11719945—28no—
379#11719945—24no—
380#11719945—48no—
381#11719945—48no—
382#11719945—416no—
383C2×D212—28no—
384C2×D212—48no—
385C2×D212—416no—
386C2×D212—48no—
387C2×D212—48no—
388C2×D212C2414yes—
389C2×D212C2418yes—
390C2×D212C2414yes—
391C2×D212C2412yes—
392C2×D212C2414yes—
393C2×D212C2411yescharacteristic
394C2×D212C2418yes—
395C2×D212C2418yes—
396C2×D212C24116yes—
397C2×D212C24116yes—
398C2×D212C2414yes—
399C2×D212C2418yes—
400C2×D212C24116yes—
401C2×D212C2418yes—
402C2×C4×D53—24no—
403C2×C4×D53—44no—
404C2×C4×D53—48no—
405C2×C4×D53C2412yes—
406C2×C4×D53C2412yes—
407C2×C4×D53C2412yes—
408C2×C4×D53C2412yes—
409C2×C4×D53C2414yes—
410C2×C4×D53C2412yes—
411C2×C4×D53C2414yes—
412C2×C4×D53C2412yes—
413C2×C4×D53C2412yes—
414C2×C4×D53C2418yes—
415C2×C4×D53C24116yes—
416C2×C4×D53C2418yes—
417C2×C4×D53C24116yes—
418C2×C4×D53C2418yes—
419C2×C4×D53C2418yes—
420C2×Dic106C2412yes—
421C2×Dic106C2411yescharacteristic
422C2×Dic106C2414yes—
423C2×Dic106C2418yes—
424C4⋊C4×C53C2418yes—
425C4⋊C4×C53C2418yes—
426C4⋊C4×C53C2414yes—
427C4⋊C4×C53C2412yes—
428C4⋊C4×C53C2414yes—
429C4⋊C4×C53C2414yes—
430C4⋊C4×C53C24116yes—
431C4⋊C4×C53C24116yes—
432C4⋊C4×C53C2418yes—
433C22⋊C4×C53C2412yes—
434C22⋊C4×C53C2414yes—
435C22⋊C4×C53C2414yes—
436C22⋊C4×C53C24116yes—
437C42×C53C2411yescharacteristic
438C42×C53C2412yes—
439C42×C53C2411yescharacteristic
440C42×C53C2414yes—
441C42×C53C2412yes—
442C42×C53C24116yes—
443C42×C53C2414yes—
444C22⋊Dic53C2412yes—
445C22⋊Dic53C2414yes—
446C22⋊Dic53C2414yes—
447#11719921C2418yes—
448#11719921C24116yes—
449#11719921C24116yes—
450#11719921C24116yes—
451#11719921C24116yes—
452#11719921C24116yes—
453#11719921C2418yes—
454#11719921C2414yes—
455#11719921C2414yes—
456#11719921C2414yes—
457#11719921C2414yes—
458#11719921C2414yes—
459#11719921C24116yes—
460#11719921C2418yes—
461#11719921C2418yes—
462C4⋊Dic53C2414yes—
463C4⋊Dic53C2418yes—
464C4⋊Dic53C2412yes—
465C4⋊Dic53C2414yes—
466C4⋊Dic53C2414yes—
467#11719919C2414yes—
468#11719919C24116yes—
469#11719919C2414yes—
470#11719919C2418yes—
471#11719919C2414yes—
472#11719919C2414yes—
473#11719919C2414yes—
474C4×Dic53C2411yescharacteristic
475C4×Dic53C2411yescharacteristic
476C4×Dic53C2412yes—
477C4×Dic53C2412yes—
478C4×Dic53C2412yes—
479C4×Dic53C2412yes—
480C4×Dic53C2412yes—
481C4×Dic53C2418yes—
482C4×Dic53C2412yes—
483C4×Dic53C2414yes—
484C23×C53C2512yes—
485C23×C53C2511yescharacteristic
486C22×D53—22no—
487C22×D53—28no—
488C22×D53—42no—
489C22×D53—48no—
490C22×D53—48no—
491C22×D53—416no—
492C22×D53C2512yes—
493C22×D53C2512yes—
494C22×D53C2514yes—
495C22×D53C2518yes—
496Q8×C53—28no—
497Q8×C53—28no—
498Q8×C53—22no—
499Q8×C53—28no—
500D4×C53—24no—
501D4×C53—22no—
502C2×C4×C53—28no—
503C2×C4×C53—24no—
504C2×C4×C53—24no—
505C2×C4×C53—28no—
506C2×C4×C53H(5,𝔽2)14yes—
507C2×C4×C53C2518yes—
508C2×C4×C53C2514yes—
509C2×C4×C53C2512yes—
510C2×C4×C53C2518yes—
511C2×C4×C53C2512yes—
512C2×C4×C53C2511yescharacteristic
513C2×C4×C53C2511yescharacteristic
514C2×C4×C53C2512yes—
515C22⋊D53—24no—
516C22⋊D53—28no—
517C22⋊D53—48no—
518C22⋊D53—44no—
519C22⋊D53—44no—
520C2×Dic53—22no—
521C2×Dic53—42no—
522C2×Dic53C2512yes—
523C2×Dic53C2514yes—
524C2×Dic53C2512yes—
525C2×Dic53C2514yes—
526C2×Dic53C2512yes—
527C2×Dic53C2512yes—
528D212—28no—
529D212—28no—
530D212—24no—
531D212—22no—
532D212—216no—
533D212—28no—
534D212—416no—
535D212—48no—
536D212—48no—
537D212—416no—
538D212—44no—
539D212—48no—
540D212—48no—
541D212—416no—
542C4×D53—24no—
543C4×D53—24no—
544C4×D53—28no—
545C4×D53—24no—
546C4×D53—24no—
547C4×D53—24no—
548C4×D53—28no—
549C4×D53—42no—
550C4×D53—42no—
551C4×D53—416no—
552C4×D53—48no—
553C4×D53—48no—
554C4×D53—48no—
555C4×D53—416no—
556C4×D53—48no—
557Dic106—24no—
558Dic106—22no—
559Dic106—44no—
560Dic106—48no—
561#62836—531nomaximal, Sylow
562C22×C53—22no—
563C22×C53—22no—
564C22×C53—24no—
565C22×C53C2×H(5,𝔽2)12yes—
566C22×C53C2611yescharacteristic
567C2×D53—22no—
568C2×D53—22no—
569C2×D53—24no—
570C2×D53—28no—
571C2×D53—22no—
572C2×D53—22no—
573C2×D53—24no—
574C2×D53—216no—
575C2×D53—28no—
576C2×D53—44no—
577C2×D53—88no—
578C2×D53—168no—
579C4×C53—28no—
580C4×C53—22no—
581C4×C53—24no—
582C4×C53—28no—
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—22no—
591Dic53—24no—
592Dic53—22no—
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#3509D5311yescharacteristic, complemented
603#3508—531no—
604#3508—534no—
605#3500—532no—
606#3499—531no—
607#3498—531no—
608#3487—532no—
609#3485—532no—
610#3444—531no—
611#3444—531no—
612C2×#532—531no—
613C2×C53—22no—
614C2×C53—42no—
615C2×C53C22×H(5,𝔽2)11yescharacteristic
616C2×C53C2×#58512yes—
617D53—42no—
618D53—42no—
619D53—48no—
620D53—44no—
621C2×2−1+4—532no—
622C2×H(5,𝔽2)—532no—
623C22×#41—532no—
624#562—5316no—
625#560—5316no—
626#559—538no—
627#559—538no—
628#559—534no—
629#557C2×D5314yescomplemented
630#556—538no—
631#556C2×D5314yescomplemented
632#555—538no—
633#554—538no—
634#553—538no—
635#553—5316no—
636#553—538no—
637#552C2×D5318yescomplemented
638#551—5316no—
639#551—5316no—
640#550—538no—
641#550—538no—
642#550—534no—
643#550—538no—
644#550—534no—
645D4×Q8—534no—
646#548—538no—
647#548—538no—
648#548—538no—
649#547—538no—
650#547—534no—
651#547—538no—
652#547—538no—
653#546—538no—
654#546—5316no—
655#546—538no—
656#546—538no—
657#546—538no—
658#546—538no—
659#546—538no—
660D42—538no—
661D42—534no—
662#542—538no—
663#542—538no—
664#542—538no—
665#541C2×D5314yescomplemented
666#540—538no—
667#540—538no—
668#540—534no—
669#540—5316no—
670#539—5316no—
671#538—5316no—
672#538—5316no—
673#537—538no—
674#536—532no—
675#536—534no—
676#536—534no—
677#536C2×D5312yes—
678#535—534no—
679#535—532no—
680#535—532no—
681#535—538no—
682#535—534no—
683#535—538no—
684#534—538no—
685#533—532no—
686#533—532no—
687#533—531no—
688#533C2×D5311yescharacteristic, complemented
689#533C2×D5314yescomplemented
690#532—531no—
691#532—534no—
692#532—534no—
693#532—534no—
694#532—534no—
695#532—532no—
696#532—532no—
697#532—534no—
698#532—534no—
699#532—532no—
700#532—531no—
701#532—532no—
702C2×C4⋊Q8—532no—
703C2×C4⋊Q8C2×D5311yescharacteristic, complemented
704C2×#127—531no—
705C2×#127—532no—
706#529—534no—
707#529—534no—
708#529—532no—
709#529—534no—
710#529—538no—
711#529—534no—
712#529—532no—
713#529—534no—
714C2×#124—532no—
715C2×#124—534no—
716#525—531no—
717#525—534no—
718#525—534no—
719#525—532no—
720#525—531no—
721#525—538no—
722C2×#123—538no—
723C2×#121—534no—
724#520—538no—
725#519C2×D5312yescomplemented
726#518—532no—
727#518—538no—
728C4×#41—534no—
729C4×#41—532no—
730C4×#41—531no—
731C4×#41—534no—
732C4×#41C2×D5311yescharacteristic
733C2×C4×D4—534no—
734C22×C42—531no—
735C53#6283611yescharacteristic, complemented, Sylow
7362−1+4—2128no—
737H(5,𝔽2)—2128no—
738C2×#41—534no—
739C2×#41—538no—
740C2×#41—538no—
741C2×#41—538no—
742C2×#41—534no—
743C2×#41—534no—
744C2×#41—534no—
745C2×#41—531no—
746C2×#41—532no—
747C2×#41—534no—
748C2×#41—538no—
749C2×#41—534no—
750C2×#41—2128no—
751C2×#41C22×D5311yescharacteristic
752C22×Q8—534no—
753C22×Q8—534no—
754C22×Q8C22×D5312yes—
755C22×D4—538no—
756C22×D4—534no—
757C22×D4—532no—
758C22×D4—534no—
759C22×D4—538no—
760C22×D4—534no—
761C22×D4—534no—
762C23×C4—531no—
763C23×C4—534no—
764C23×C4—532no—
765C4⋊Q8—534no—
766C4⋊Q8—531no—
767C4⋊Q8—538no—
768C4⋊Q8—532no—
769C4⋊Q8—531no—
770C4⋊Q8C22×D5312yes—
771C4⋊Q8C22×D5312yes—
772C4⋊Q8C22×D5314yes—
773C4⋊Q8C22×D5312yes—
774C4⋊Q8C22×D5314yes—
775#127—531no—
776#127—532no—
777#127—531no—
778#127—532no—
779#127—534no—
780#127—534no—
781#127—538no—
782#127—534no—
783#127—5316no—
784#126—538no—
785#126—534no—
786#126—5316no—
787#126—534no—
788#126—5316no—
789#126C22×D53116yes—
790#125—532no—
791#125—534no—
792#125—534no—
793#125C22×D5312yes—
794#125C22×D5318yes—
795#125C22×D53116yes—
796#124—534no—
797#124—534no—
798#124—538no—
799#124—531no—
800#124—534no—
801#124—534no—
802#124—538no—
803#124—531no—
804#124—5316no—
805#124—534no—
806#124—534no—
807#124—532no—
808#124—534no—
809#124—5316no—
810#124—5316no—
811#124C22×D5314yes—
812#123—532no—
813#123—538no—
814#123—5316no—
815#123—534no—
816#123—538no—
817#123—5316no—
818#123—5316no—
819#123—5316no—
820#123—5316no—
821#123—5316no—
822#123—5316no—
823#123—534no—
824#123—5316no—
825#123—532no—
826#123—534no—
827#123C22×D5318yes—
828C22⋊Q8—534no—
829C22⋊Q8—532no—
830C22⋊Q8—538no—
831C22⋊Q8—534no—
832C22⋊Q8—532no—
833C22⋊Q8—534no—
834C22⋊Q8—5316no—
835C22⋊Q8—5316no—
836C22⋊Q8—5316no—
837C22⋊Q8—5316no—
838C22⋊Q8—534no—
839C22⋊Q8C22×D5314yes—
840C22⋊Q8C22×D5318yes—
841C22⋊Q8C22×D5318yes—
842#121—532no—
843#121—534no—
844#121—534no—
845#121—538no—
846#121—538no—
847#121—538no—
848#121—538no—
849#121—538no—
850#121—534no—
851#121—534no—
852#121—532no—
853#121—5316no—
854#121—538no—
855#121—538no—
856#121—538no—
857#121—538no—
858#121—5316no—
859#121—5316no—
860#121—5316no—
861#121—5316no—
862#121—5316no—
863#121—5316no—
864#121—534no—
865#121—5316no—
866#121—5316no—
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—534no—
876C4×Q8—534no—
877C4×Q8—532no—
878C4×Q8—534no—
879C4×Q8—534no—
880C4×Q8C22×D5314yes—
881C4×Q8C22×D5312yes—
882C4×Q8C22×D5318yes—
883C4×Q8C22×D5318yes—
884C4×Q8C22×D5318yes—
885C4×D4—534no—
886C4×D4—534no—
887C4×D4—534no—
888C4×D4—534no—
889C4×D4—534no—
890C4×D4—538no—
891C4×D4—538no—
892C4×D4—538no—
893C4×D4—538no—
894C4×D4—534no—
895C4×D4—538no—
896C4×D4—534no—
897C4×D4—538no—
898C4×D4—538no—
899C4×D4—538no—
900C4×D4—5316no—
901C4×D4—538no—
902C4×D4—538no—
903C4×D4—534no—
904C4×D4—534no—
905C4×D4—534no—
906C4×D4—532no—
907C4×D4—5316no—
908C4×D4—5316no—
909C4×D4—538no—
910C4×D4—5316no—
911C4×D4—538no—
912C4×D4C22×D5314yes—
913C4×D4C22×D5312yes—
914#117—531no—
915#117—534no—
916#117—534no—
917#117—538no—
918#117—534no—
919#117—534no—
920#117—534no—
921#117—532no—
922#117—5316no—
923#117C22×D5312yes—
924#117C22×D5311yescharacteristic
925#117C22×D5312yes—
926#117C22×D5318yes—
927#117C22×D5318yes—
928C2×C4⋊C4—5316no—
929C2×C4⋊C4—538no—
930C2×C4⋊C4C22×D5314yes—
931C2×C22⋊C4—538no—
932C2×C22⋊C4—538no—
933C2×C22⋊C4—5316no—
934C2×C22⋊C4—5316no—
935C2×C42—532no—
936C2×C42—531no—
937C2×C42—534no—
938C2×C42—532no—
939C2×C42—532no—
940C2×C42—532no—
941C2×C42—532no—
942C2×C42—532no—
943C2×C42C22×D5312yes—
944C2×C42C22×D5311yescharacteristic
945C24—534no—
946C24—531no—
947C24—538no—
948#41—24no—
949#41—1068no—
950#41—1064no—
951#41—2128no—
952#41—21216no—
953#41—2128no—
954#41—2128no—
955#41—21216no—
956#41—21216no—
957#41—21216no—
958#41—2128no—
959#41—2128no—
960#41—2128no—
961C2×Q8—28no—
962C2×Q8—531no—
963C2×Q8—532no—
964C2×Q8—534no—
965C2×Q8—538no—
966C2×Q8—2128no—
967C2×Q8—2128no—
968C2×Q8C23×D5314yes—
969C2×Q8C23×D5314yes—
970C2×Q8C23×D5311yescharacteristic
971C2×Q8C23×D5314yes—
972C2×D4—532no—
973C2×D4—534no—
974C2×D4—534no—
975C2×D4—534no—
976C2×D4—538no—
977C2×D4—538no—
978C2×D4—534no—
979C2×D4—534no—
980C2×D4—532no—
981C2×D4—534no—
982C2×D4—531no—
983C2×D4—538no—
984C2×D4—5316no—
985C2×D4—538no—
986C2×D4—5316no—
987C2×D4—534no—
988C2×D4—538no—
989C2×D4—5316no—
990C2×D4—538no—
991C2×D4—1068no—
992C2×D4—2128no—
993C2×D4—21216no—
994C2×D4—2128no—
995C2×D4—2128no—
996C2×D4—2128no—
997C2×D4—21216no—
998C2×D4C23×D5312yes—
999C2×D4C23×D5311yescharacteristic
1000C22×C4—531no—
1001C22×C4—532no—
1002C22×C4—532no—
1003C22×C4—532no—
1004C22×C4—532no—
1005C22×C4—532no—
1006C22×C4—534no—
1007C22×C4—532no—
1008C22×C4—534no—
1009C22×C4—532no—
1010C22×C4—532no—
1011C22×C4—538no—
1012C22×C4—5316no—
1013C22×C4—538no—
1014C22×C4—5316no—
1015C22×C4—538no—
1016C22×C4—538no—
1017C22×C4—1064no—
1018C22×C4—2124no—
1019C22×C4—2128no—
1020C22×C4C23×D5312yes—
1021C22×C4C23×D5314yes—
1022C22×C4C23×D5312yes—
1023C22×C4C23×D5314yes—
1024C22×C4C23×D5311yescharacteristic
1025C4⋊C4—534no—
1026C4⋊C4—534no—
1027C4⋊C4—538no—
1028C4⋊C4—5316no—
1029C4⋊C4—534no—
1030C4⋊C4—532no—
1031C4⋊C4—534no—
1032C4⋊C4—534no—
1033C4⋊C4—538no—
1034C4⋊C4—534no—
1035C4⋊C4—534no—
1036C4⋊C4—534no—
1037C4⋊C4C23×D5318yes—
1038C4⋊C4C23×D53116yes—
1039C4⋊C4C23×D5318yes—
1040C4⋊C4C23×D5314yes—
1041C4⋊C4C23×D5318yes—
1042C4⋊C4C23×D5314yes—
1043C4⋊C4C23×D5312yes—
1044C4⋊C4C23×D5314yes—
1045C4⋊C4C23×D53116yes—
1046C22⋊C4—532no—
1047C22⋊C4—534no—
1048C22⋊C4—534no—
1049C22⋊C4—538no—
1050C22⋊C4—5316no—
1051C22⋊C4—5316no—
1052C22⋊C4—5316no—
1053C22⋊C4—5316no—
1054C22⋊C4—5316no—
1055C22⋊C4—534no—
1056C22⋊C4—534no—
1057C22⋊C4—5316no—
1058C22⋊C4—538no—
1059C22⋊C4—538no—
1060C22⋊C4—534no—
1061C22⋊C4—538no—
1062C22⋊C4—534no—
1063C22⋊C4—534no—
1064C22⋊C4C23×D5314yes—
1065C22⋊C4C23×D53116yes—
1066C22⋊C4C23×D5312yes—
1067C22⋊C4C23×D5314yes—
1068C42—531no—
1069C42—532no—
1070C42—532no—
1071C42—531no—
1072C42—532no—
1073C42—532no—
1074C42—532no—
1075C42—538no—
1076C42—532no—
1077C42—534no—
1078C42C23×D5311yescharacteristic
1079C42C23×D5311yescharacteristic
1080C42C23×D5312yes—
1081C42C23×D5314yes—
1082C42C23×D5314yes—
1083C42C23×D5312yes—
1084C42C23×D53116yes—
1085C23—534no—
1086C23—538no—
1087C23—532no—
1088C23—532no—
1089C23—1068no—
1090C23—1062no—
1091C23—2128no—
1092C23—21216no—
1093C23—2128no—
1094C23—2122no—
1095C23C24×D5312yes—
1096C23C24×D5311yescharacteristic
1097Q8—28no—
1098Q8—28no—
1099Q8—22no—
1100Q8—28no—
1101Q8—1062no—
1102Q8—1064no—
1103Q8—2128no—
1104Q8—2124no—
1105D4—24no—
1106D4—22no—
1107D4—1068no—
1108D4—1064no—
1109D4—1068no—
1110D4—1068no—
1111D4—1064no—
1112D4—1062no—
1113D4—1068no—
1114D4—10616no—
1115D4—2128no—
1116D4—21216no—
1117D4—2128no—
1118D4—21216no—
1119D4—2124no—
1120D4—2128no—
1121D4—21216no—
1122D4—2128no—
1123D4—2128no—
1124D4—2124no—
1125D4—2124no—
1126C2×C4—28no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—28no—
1130C2×C4—532no—
1131C2×C4—532no—
1132C2×C4—532no—
1133C2×C4—534no—
1134C2×C4—532no—
1135C2×C4—534no—
1136C2×C4—1062no—
1137C2×C4—1064no—
1138C2×C4—1064no—
1139C2×C4—1068no—
1140C2×C4—1064no—
1141C2×C4—1064no—
1142C2×C4—1064no—
1143C2×C4—1068no—
1144C2×C4—2122no—
1145C2×C4—2122no—
1146C2×C4—21216no—
1147C2×C4—2128no—
1148C2×C4—2128no—
1149C2×C4—2128no—
1150C2×C4—2128no—
1151C2×C4—21216no—
1152C2×C4—2122no—
1153C2×C4#1313326314yes—
1154C2×C4C24×D5312yes—
1155C2×C4C24×D5318yes—
1156C2×C4C24×D5314yes—
1157C2×C4C24×D5318yes—
1158C2×C4C24×D5312yes—
1159C2×C4C24×D5311yescharacteristic
1160C2×C4C24×D5311yescharacteristic
1161C2×C4C24×D5312yes—
1162C22—22no—
1163C22—22no—
1164C22—24no—
1165C22—8488no—
1166C22—1062no—
1167C22—1062no—
1168C22—1064no—
1169C22—1068no—
1170C22—1062no—
1171C22—1062no—
1172C22—1064no—
1173C22—1068no—
1174C22—10616no—
1175C22—4248no—
1176C22—2124no—
1177C22C2×#1313326312yes—
1178C22C25×D5311yescharacteristic
1179C4—22no—
1180C4—28no—
1181C4—22no—
1182C4—24no—
1183C4—28no—
1184C4—1062no—
1185C4—1064no—
1186C4—1062no—
1187C4—1062no—
1188C4—1064no—
1189C4—1062no—
1190C4C2×#1313326312yes—
1191C4C2×#1313326312yes—
1192C4#1681146014yes—
1193C2—22no—
1194C2—42no—
1195C2—2124no—
1196C2—2128no—
1197C2—2122no—
1198C2—2122no—
1199C2C22×#1313326311yescharacteristic
1200C2C2×#1681146012yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3509C2
hypercenter#3509D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #20289309C2semidirect
2. #20289189C2semidirect
3. #20289090C2semidirect
4. #20289025C2semidirect
5. #20288722C2semidirect
6. #20288679C2semidirect
7. #20288660C2semidirect
8. #20288627C2semidirect
9. #20288612C2semidirect
10. #20288592C2semidirect
11. #20288592C2semidirect
12. #20288504C2semidirect
13. #20288498C2semidirect
14. #20288493C2semidirect
15. #20288374C2semidirect
16. #20288358C2semidirect
17. #20288012C2semidirect
18. #20288008C2semidirect
19. C2×#16811174C2semidirect
20. C53×#3509C2semidirect
21. C2×#13133265C22semidirect
23. C22×#11719949C22semidirect
24. #16811371C22semidirect
25. #16811364C22semidirect
26. #16811358C22semidirect
27. #16811358C22semidirect
28. #16811358C22semidirect
29. #16811345C22semidirect
30. #16811336C22semidirect
31. #16811329C22semidirect
32. #16811326C22semidirect
33. #16811326C22semidirect
34. #16811317C22semidirect
35. #16811298C22semidirect
36. #16811297C22semidirect
37. #16811295C22semidirect
38. #16811295C22semidirect
39. #16811295C22semidirect
40. #16811295C22semidirect
41. #16811295C22semidirect
42. #16811288C22semidirect
43. #16811285C22semidirect
44. #16811285C22semidirect
45. #16811283C22semidirect
46. #16811276C22semidirect
47. #16811276C22semidirect
48. #16811275C22semidirect
49. #16811274C22semidirect
50. #16811266C22semidirect
51. #16811265C22semidirect
52. #16811264C22semidirect
53. #16811264C22semidirect
54. #16811264C22semidirect
55. #16811264C22semidirect
56. #16811264C22semidirect
58. D4×D212C22semidirect
59. #16811246C22semidirect
60. #16811245C22semidirect
61. #16811245C22semidirect
62. #16811229C22semidirect
63. #16811229C22semidirect
64. #16811229C22semidirect
65. #16811229C22semidirect
66. #16811221C22semidirect
67. #16811212C22semidirect
68. #16811212C22semidirect
69. #16811203C22semidirect
70. #16811198C22semidirect
71. #16811198C22semidirect
72. #16811197C22semidirect
74. #16811192C22semidirect
75. #16811192C22semidirect
76. #16811192C22semidirect
77. #16811192C22semidirect
78. #16811191C22semidirect
79. #16811184C22semidirect
80. #16811178C22semidirect
81. #16811177C22semidirect
82. #16811176C22semidirect
83. #16811174C22semidirect
84. #16811174C22semidirect
85. #16811174C22semidirect
86. #16811174C22semidirect
87. #16811174C22semidirect
88. #16811174C22semidirect
89. #16811174C22semidirect
90. #16811174C22semidirect
92. #16811173C22semidirect
93. #16811170C22semidirect
95. C4⋊Q8×D53C22semidirect
97. C2×#13133214C22semidirect
98. #16811160C22semidirect
99. #16811160C22semidirect
100. #16811160C22semidirect
101. #16811159C22semidirect
102. #16811158C22semidirect
103. #16811155C22semidirect
104. #16811153C22semidirect
105. #16811151C22semidirect
106. C2×#13133206C22semidirect
107. #124×D53C22semidirect
108. #16811136C22semidirect
109. #16811135C22semidirect
110. #16811135C22semidirect
111. #16811135C22semidirect
112. #16811132C22semidirect
114. #123×D53C22semidirect
115. C2×#13133192C22semidirect
116. #16811105C22semidirect
117. #16811097C22semidirect
118. #16811097C22semidirect
119. C4×#11719949C22semidirect
120. C4×#11719945C22semidirect
121. C4×#11719945C22semidirect
122. #16811091C22semidirect
123. C2×#13133179C22semidirect
124. C2×C42×D53C22semidirect
125. C53×#557C22semidirect
126. C53×#556C22semidirect
127. C53×#552C22semidirect
128. C53×#541C22semidirect
130. C53×#533C22semidirect
131. C53×#533C22semidirect
132. C2×C4⋊Q8×C53C22semidirect
133. C53×#519C22semidirect
602. #3509D53semidirect
629. #557C2×D53semidirect
631. #556C2×D53semidirect
637. #552C2×D53semidirect
665. #541C2×D53semidirect
688. #533C2×D53semidirect
689. #533C2×D53semidirect
703. C2×C4⋊Q8C2×D53semidirect
725. #519C2×D53semidirect
735. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202893092
#202891892
#202890902
#202890252
#202887222
#202886792
#202886602
#202886272
#202886122
#202885922
#202885042
#202884982
#202884932
#202883742
#202883582
#202880122
#202880082
C2×#168111742
C53×#35092
#6283653