Finite Group Databasebeta

← #28292326

Subgroups — #28292326

Order 13568.

7094 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288811C211yesmaximal, characteristic, complemented
2#20288809C213yesmaximal, complemented
3#20288792C213yesmaximal, complemented
4#20288702C216yesmaximal, complemented
5#20288700C212yesmaximal, complemented
6#20288578C213yesmaximal, complemented
7#20288572C213yesmaximal, complemented
8#20288524C211yesmaximal, characteristic, complemented
9#20288480C211yesmaximal, characteristic, complemented
10#20288417C216yesmaximal, complemented
11#20288361C212yesmaximal, complemented
12#20288331C212yesmaximal, complemented
13#20288327C216yesmaximal, complemented
14#20288314C211yesmaximal, characteristic, complemented
15#20288311C213yesmaximal, complemented
16Q8×#11719949C211yesmaximal, characteristic, complemented
17#20288294C213yesmaximal, complemented
18#20288141C216yesmaximal, complemented
19#20288010C213yesmaximal, complemented
20#20288009C213yesmaximal, complemented
21#20287926C212yesmaximal, complemented
22C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
23C53×#3522C211yesmaximal, characteristic, complemented
24C2×#13133264C2212yes—
25C22×Q8×D53C2211yescharacteristic
26#16811359C2213yescomplemented
27#16811356C2216yescomplemented
28#16811353C2213yescomplemented
29#16811352C2211yescharacteristic, complemented
30#16811352C2213yescomplemented
31#16811351C2213yescomplemented
32#16811351C2213yescomplemented
33#16811350C2216yescomplemented
34#16811349C2212yescomplemented
35#16811348C2216yescomplemented
36#16811346C2213yescomplemented
37#16811344C22112yescomplemented
38#16811343C2213yescomplemented
39#16811343C2216yescomplemented
40#16811342C2216yescomplemented
41#16811342C2216yescomplemented
42#16811334C2216yes—
43#16811334C2213yescomplemented
44#16811332C2216yescomplemented
45#16811328C2216yes—
46#16811327C22112yes—
47#16811323C2216yes—
48#16811320C2216yes—
49#16811318C22112yes—
50#16811313C2216yes—
51#16811310C22112yes—
52#16811310C22112yescomplemented
53#16811308C2216yes—
54#16811308C2216yescomplemented
55#16811307C2216yescomplemented
56#16811293C2213yescomplemented
57Q8×D212C2212yes—
58Q8×D212C2211yescharacteristic, complemented
59D4×Dic106C2216yes—
60D4×Dic106C2213yescomplemented
61Q8×C22⋊D53C2212yes—
62#16811286C2216yes—
63#16811281C2216yes—
64#16811280C2212yes—
65#16811280C2212yescomplemented
66#16811279C2216yes—
67#16811279C2216yescomplemented
68#16811273C2216yes—
69#16811272C22112yes—
70#16811250C2216yes—
71#16811238C2216yescomplemented
72#16811237C22112yescomplemented
73#16811235C2216yescomplemented
74#16811231C2216yescomplemented
75#16811230C22112yescomplemented
76#16811219C22112yes—
77#16811216C22112yes—
78#16811202C2216yes—
79#16811196C2216yes—
80#16811193C2216yes—
81#16811180C2213yes—
82#16811179C2213yes—
83#16811178C2213yes—
84#16811178C2213yes—
85#16811178C2216yescomplemented
86#16811177C2213yes—
87#16811175C2213yes—
88#16811175C22112yescomplemented
89#16811175C2216yescomplemented
90#16811172C2213yes—
91#16811171C2213yes—
92#16811171C2213yes—
93#16811170C2213yes—
94#16811168C2213yes—
95#16811158C2213yes—
96#16811157C2213yes—
97#16811156C2216yes—
98#16811156C2216yes—
99#16811155C2216yes—
100#16811155C2216yes—
101#16811154C2216yes—
102#16811154C2216yes—
103#16811154C2216yescomplemented
104#16811152C2213yes—
105#16811152C2216yes—
106#16811152C2216yes—
107#16811152C2216yescomplemented
108#16811151C2216yes—
109#16811150C2216yes—
110#16811150C22112yescomplemented
111#16811136C2211yescharacteristic
112#16811133C2213yes—
113#16811133C2216yes—
114#16811132C2216yes—
115#16811131C2216yes—
116#16811130C2216yes—
117#16811104C2216yes—
118#16811102C2216yes—
119#16811102C2216yescomplemented
120#16811100C2216yescomplemented
121#16811099C2212yes—
122#16811099C2212yescomplemented
123#41×Dic53C2216yes—
124#41×Dic53C2212yescomplemented
125C4×#11719949C2213yes—
126#16811091C2216yes—
127C4×#11719947C2213yes—
128C4×#11719947C2216yes—
129C4×#11719947C2216yes—
130C4×#11719947C2216yes—
131C4×#11719947C2216yescomplemented
132C2×Q8×Dic53C2211yescharacteristic
133C2×C4×Dic106C2213yes—
134C2×#13133182C2213yes—
135C2×#13133182C2216yescomplemented
136C4×Q8×D53C2211yescharacteristic
137C4×Q8×D53C2213yes—
138C4×Q8×D53C2211yescharacteristic
139C4×Q8×D53C2213yes—
140C4×Q8×D53C2213yes—
141C4×Q8×D53C2211yescharacteristic
142C4×Q8×D53C2211yescharacteristic
143C4×Q8×D53C2213yes—
144C4×Q8×D53C2212yescomplemented
145C2×C4⋊C4×D53C2213yes—
146C2×C42×D53C2213yes—
147C53×#559C2213yescomplemented
148Q82×C53C2211yescharacteristic, complemented
149C53×#554C2213yescomplemented
150C53×#550C2211yescharacteristic, complemented
151C53×#548C2212yes—
152C53×#547C2216yes—
153C53×#542C2216yescomplemented
154C53×#532C2213yes—
155C53×#529C2213yes—
156C53×#520C2212yescomplemented
157C2×C4×Q8×C53C2211yescharacteristic
158#13133264—216no—
159C2×#11719949C2311yescharacteristic
160C2×#11719945C2316yes—
161C2×#11719947C2316yes—
162C2×#11719947C2313yes—
163C2×#11719947C2316yes—
164C2×#11719947C2316yes—
165C22×Dic106C2313yes—
166C22×Dic106C2316yes—
167C2×Q8×D53—28no—
168C2×Q8×D53C2311yescharacteristic
169C2×Q8×D53C2312yes—
170C2×Q8×D53C2313yes—
171C2×Q8×D53C2313yes—
172C2×Q8×D53C2311yescharacteristic
173C22×C4×D53C2311yescharacteristic
174C22×C4×D53C2313yes—
175C22×C4×D53C2313yes—
176#13133217C2316yes—
177#13133217C2313yes—
178#13133217C2313yes—
179#13133216C2316yes—
180#13133216C23112yes—
181#13133216C2313yes—
182#13133216C2313yes—
183#13133215C23112yes—
184#13133215C2316yes—
185#13133215C2313yes—
186#13133213C2313yes—
187#13133212C23112yes—
188#13133212C2316yes—
189#13133211C2316yes—
190#13133210C23112yes—
191#13133210C23112yes—
192#13133210C23112yes—
193#13133210C2316yes—
194#13133210C23112yes—
195#13133210C23112yes—
196#13133209C2316yes—
197#13133209C2313yes—
198#13133209C2316yes—
199#13133208C2316yes—
200#13133208C2316yes—
201#13133208C23112yes—
202#13133208C2316yes—
203#13133207C23112yes—
204#13133207C23112yes—
205#13133207C23112yes—
206#13133207C23112yes—
207#13133207C2316yes—
208#13133207C2316yes—
209#13133205C2313yes—
210#13133204C2316yes—
211#13133204C2316yes—
212#13133204C2316yes—
213#13133203C23112yes—
214#13133203C2316yes—
215#13133203C2316yes—
216#13133202C2316yes—
217#13133202C2312yes—
218#13133200C2316yes—
219#13133200C23112yes—
220#13133199C23112yes—
221#13133199C2316yes—
222#13133199C2316yes—
223#13133199C23112yes—
224#13133198C23112yes—
225#13133198C23112yes—
226#13133197C2316yes—
227#13133197C2316yes—
228#13133197C2316yes—
229#13133197C2313yes—
230#13133196C23112yes—
231#13133196C2316yes—
232#13133196C2316yes—
233#13133196C2316yes—
234#13133196C2313yes—
235#13133195C2316yes—
236#13133195C2316yes—
237#13133195C2316yes—
238#13133194C23112yes—
239#13133194C23112yes—
240#13133194C23112yes—
241#13133194C23112yes—
242#13133194C2316yes—
243#13133193C23112yes—
244#13133193C2316yes—
245#13133193C2316yes—
246#13133193C2316yes—
247#13133193C2311yescharacteristic
248#13133192C2311yescharacteristic
249#13133191C2311yescharacteristic
250#13133190C2316yes—
251#13133190C2316yes—
252#13133190C2316yes—
253#13133189C2316yes—
254#13133189C23112yes—
255#13133188C2316yes—
256#13133188C2316yes—
257#13133188C2316yes—
258#13133188C2316yes—
259#13133188C2313yes—
260#13133187C2312yes—
261#13133185C2316yes—
262Q8×Dic53C2312yes—
263Q8×Dic53C2311yescharacteristic
264Q8×Dic53C2313yes—
265Q8×Dic53C2311yescharacteristic
266Q8×Dic53C2313yes—
267Q8×Dic53C2313yes—
268Q8×Dic53C2316yes—
269Q8×Dic53C2316yes—
270C4×Dic106C2316yes—
271C4×Dic106C2313yes—
272C4×Dic106C2316yes—
273C4×Dic106C2316yes—
274C4×Dic106C2313yes—
275C4×Dic106C2313yes—
276C4×Dic106C2316yes—
277C4×Dic106C2313yes—
278C4×Dic106C2316yes—
279C4×Dic106C2316yes—
280C4×Dic106C2313yes—
281C4×Dic106C2316yes—
282#13133182C2316yes—
283#13133182C2313yes—
284#13133182C2316yes—
285#13133182C2313yes—
286#13133182C23112yes—
287#13133182C2316yes—
288#13133182C2313yes—
289#13133182C2316yes—
290#13133182C2313yes—
291#13133182C2316yes—
292#13133182C2316yes—
293#13133182C2313yes—
294#13133182C2316yes—
295#13133182C2316yes—
296#13133182C2316yes—
297C4×D212C2316yes—
298C4×D212C2313yes—
299D4×Dic53C23112yes—
300D4×Dic53C2316yes—
301D4×Dic53C2316yes—
302D4×Dic53C2316yes—
303D4×Dic53C2313yes—
304D4×Dic53C2316yes—
305D4×Dic53C2316yes—
306D4×Dic53C2316yes—
307#13133179C2316yes—
308#13133179C2313yes—
309#13133179C2312yes—
310#13133179C2316yes—
311C4×C22⋊D53C23112yes—
312C4×C22⋊D53C2316yes—
313C4×C22⋊D53C2316yes—
314C4×C22⋊D53C2316yes—
315C4×C22⋊D53C23112yes—
316C4×C22⋊D53C23112yes—
317#13133177C23112yes—
318#13133177C2316yes—
319#13133177C2312yes—
320#13133177C2316yes—
321#13133177C2316yes—
322#13133177C2316yes—
323#13133177C2316yes—
324#13133177C2316yes—
325#13133176C2316yes—
326#13133176C2316yes—
327#13133176C23112yes—
328#13133175C2316yes—
329#13133175C2316yes—
330#13133175C2311yescharacteristic
331#13133175C2313yes—
332#13133175C2316yes—
333#13133175C2316yes—
334#13133174C2316yes—
335#13133174C2316yes—
336#13133173C2316yes—
337#13133173C23112yes—
338#13133173C2316yes—
339#13133173C23112yes—
340#13133173C2316yes—
341#13133173C23112yes—
342C2×C4⋊Dic53C2313yes—
343C2×#11719919C2316yes—
344C2×#11719919C23112yes—
345C4⋊C4×D53C2316yes—
346C4⋊C4×D53C2316yes—
347C4⋊C4×D53C2313yes—
348C4⋊C4×D53C2313yes—
349C4⋊C4×D53C2313yes—
350C4⋊C4×D53C2313yes—
351C4⋊C4×D53C2316yes—
352C2×C4×Dic53C2313yes—
353C2×C4×Dic53C2313yes—
354C2×C4×Dic53C2313yes—
355C2×C4×Dic53C23112yes—
356C2×C4×Dic53C2316yes—
357C42×D53C2313yes—
358C42×D53C2313yes—
359C42×D53C2313yes—
360C42×D53C2313yes—
361C42×D53C2313yes—
362C42×D53C2313yes—
363C42×D53C2313yes—
364C42×D53C2313yes—
365C42×D53C2316yes—
366C2×#41×C53C2312yes—
367C2×#41×C53C2316yes—
368C22×Q8×C53C2311yescharacteristic
369C4⋊Q8×C53C2313yes—
370C4⋊Q8×C53C2316yes—
371#127×C53C2313yes—
372#126×C53C2316yes—
373#125×C53C2313yes—
374#124×C53C2316yes—
375#124×C53C2313yes—
376#124×C53C2316yes—
377#123×C53C2316yes—
378#123×C53C23112yes—
379C22⋊Q8×C53C2316yes—
380C22⋊Q8×C53C2311yescharacteristic
381C22⋊Q8×C53C23112yes—
382#121×C53C2316yes—
383#121×C53C2316yes—
384#121×C53C2313yes—
385C4×Q8×C53C2312yes—
386C4×Q8×C53C2311yescharacteristic
387C4×Q8×C53C2311yescharacteristic
388C4×Q8×C53C2313yes—
389C4×Q8×C53C2313yes—
390C4×Q8×C53C2313yes—
391C4×D4×C53C2316yes—
392C4×D4×C53C2313yes—
393C4×D4×C53C2316yes—
394C4×D4×C53C2316yes—
395C4×D4×C53C2316yes—
396#117×C53C2316yes—
397C2×C4⋊C4×C53C2313yes—
398C2×C4⋊C4×C53C2316yes—
399C2×C42×C53C2313yes—
400C23×D53C2411yescharacteristic
401#41×C53—28no—
402#41×C53—412no—
403C2×Q8×C53—24no—
404C2×Q8×C53C2411yescharacteristic
405C2×Q8×C53C2413yes—
406C2×Q8×C53C2416yes—
407C2×Q8×C53C2411yescharacteristic
408C2×D4×C53C2413yes—
409C2×D4×C53C2416yes—
410C2×D4×C53C2416yes—
411C2×D4×C53C2416yes—
412C22×C4×C53C2411yescharacteristic
413C22×C4×C53C2413yes—
414C22×C4×C53C2413yes—
415C22×C4×C53C2416yes—
416C22×C4×C53C24112yes—
417C2×C22⋊D53C2416yes—
418C2×C22⋊D53C2416yes—
419C2×C22⋊D53C2416yes—
420C2×C22⋊D53C2412yes—
421C2×C22⋊D53C2416yes—
422C22×Dic53C2411yescharacteristic
423C22×Dic53C2416yes—
424C22×Dic53C2413yes—
425C22×Dic53C2413yes—
426C22×Dic53C24112yes—
427C22×Dic53C2416yes—
428#11719949—24no—
429Q8×D53—24no—
430Q8×D53—28no—
431Q8×D53—212no—
432Q8×D53—212no—
433Q8×D53#4118yescomplemented
434#11719947—224no—
435#11719947—212no—
436#11719947—224no—
437#11719947—412no—
438#11719945—224no—
439C2×D212C2412yes—
440C2×D212C2412yes—
441C2×D212C2411yescharacteristic
442C2×C4×D53—212no—
443C2×C4×D53—24no—
444C2×C4×D53—46no—
445C2×C4×D53C2411yescharacteristic
446C2×C4×D53C2411yescharacteristic
447C2×C4×D53C2411yescharacteristic
448C2×C4×D53C2412yes—
449C2×C4×D53C2413yes—
450C2×C4×D53C2413yes—
451C2×C4×D53C2413yes—
452C2×C4×D53C2416yes—
453C2×C4×D53C2413yes—
454C2×C4×D53C2413yes—
455C2×C4×D53C2413yes—
456C2×C4×D53C2413yes—
457C2×C4×D53C2416yes—
458C2×C4×D53C2413yes—
459C2×C4×D53C2411yescharacteristic
460C2×Dic106—212no—
461C2×Dic106—224no—
462C2×Dic106C2416yes—
463C2×Dic106C2413yes—
464C2×Dic106C2416yes—
465C2×Dic106C2413yes—
466C2×Dic106C2416yes—
467C2×Dic106C2416yes—
468C2×Dic106C2413yes—
469C4⋊C4×C53C2413yes—
470C4⋊C4×C53C2416yes—
471C4⋊C4×C53C2416yes—
472C4⋊C4×C53C2413yes—
473C4⋊C4×C53C2416yes—
474C4⋊C4×C53C2412yes—
475C4⋊C4×C53C2411yescharacteristic
476C4⋊C4×C53C2413yes—
477C4⋊C4×C53C2416yes—
478C4⋊C4×C53C2416yes—
479C22⋊C4×C53C2416yes—
480C22⋊C4×C53C2416yes—
481C22⋊C4×C53C2412yes—
482C22⋊C4×C53C2416yes—
483C22⋊C4×C53C24112yes—
484C22⋊C4×C53C2416yes—
485C42×C53C2413yes—
486C42×C53C2413yes—
487C42×C53C2413yes—
488C42×C53C2413yes—
489C42×C53C2416yes—
490C22⋊Dic53C24112yes—
491C22⋊Dic53C2416yes—
492C22⋊Dic53C2416yes—
493C22⋊Dic53C24112yes—
494C22⋊Dic53C2416yes—
495C22⋊Dic53C24112yes—
496#11719921C2412yes—
497#11719921C2412yes—
498#11719921C2416yes—
499#11719921C2416yes—
500#11719921C2412yes—
501#11719921C2412yes—
502#11719921C2416yes—
503#11719921C2416yes—
504#11719921C2416yes—
505#11719921C2416yes—
506C4⋊Dic53C2413yes—
507C4⋊Dic53C2413yes—
508C4⋊Dic53C2416yes—
509C4⋊Dic53C2416yes—
510C4⋊Dic53C2416yes—
511C4⋊Dic53C2411yescharacteristic
512C4⋊Dic53C2413yes—
513C4⋊Dic53C2416yes—
514C4⋊Dic53C2416yes—
515C4⋊Dic53C2416yes—
516C4⋊Dic53C24112yes—
517#11719919C2416yes—
518#11719919C2416yes—
519#11719919C2416yes—
520#11719919C2416yes—
521#11719919C24112yes—
522#11719919C2416yes—
523#11719919C2416yes—
524#11719919C2412yes—
525#11719919C2416yes—
526#11719919C2416yes—
527#11719919C2416yes—
528#11719919C24112yes—
529#11719919C2416yes—
530#11719919C2416yes—
531#11719919C24112yes—
532#11719919C2416yes—
533#11719919C2416yes—
534C4×Dic53C2413yes—
535C4×Dic53C2413yes—
536C4×Dic53C2413yes—
537C4×Dic53C2413yes—
538C4×Dic53C2413yes—
539C4×Dic53C2413yes—
540C4×Dic53C2413yes—
541C4×Dic53C2413yes—
542C4×Dic53C2413yes—
543C4×Dic53C2413yes—
544C4×Dic53C2413yes—
545C4×Dic53C2413yes—
546C4×Dic53C2416yes—
547C4×Dic53C2416yes—
548C4×Dic53C2412yes—
549C4×Dic53C2416yes—
550C4×Dic53C24112yes—
551C4×Dic53C24112yes—
552C4×Dic53C2416yes—
553C23×C53C2516yes—
554C23×C53C2511yescharacteristic
555C22×D53—22no—
556C22×D53—22no—
557C22×D53—22no—
558C22×D53C2512yes—
559C22×D53C2511yescharacteristic
560C22×D53C2511yescharacteristic
561Q8×C53—26no—
562Q8×C53—22no—
563Q8×C53—46no—
564Q8×C53C2×#4114yes—
565D4×C53—212no—
566D4×C53—212no—
567D4×C53—26no—
568D4×C53—46no—
569C2×C4×C53—26no—
570C2×C4×C53—26no—
571C2×C4×C53—212no—
572C2×C4×C53—22no—
573C2×C4×C53—412no—
574C2×C4×C53C2512yes—
575C2×C4×C53C2513yes—
576C2×C4×C53C2516yes—
577C2×C4×C53C2513yes—
578C2×C4×C53C2513yes—
579C2×C4×C53C2511yescharacteristic
580C2×C4×C53C2512yes—
581C2×C4×C53C2513yes—
582C2×C4×C53C2511yescharacteristic
583C22⋊D53—24no—
584C22⋊D53—212no—
585C22⋊D53—212no—
586C22⋊D53—212no—
587C22⋊D53—46no—
588C2×Dic53—26no—
589C2×Dic53—26no—
590C2×Dic53—224no—
591C2×Dic53—22no—
592C2×Dic53—212no—
593C2×Dic53—46no—
594C2×Dic53C2513yes—
595C2×Dic53C2516yes—
596C2×Dic53C2512yes—
597C2×Dic53C2513yes—
598C2×Dic53C2516yes—
599C2×Dic53C2513yes—
600C2×Dic53C2511yescharacteristic
601C2×Dic53C2513yes—
602C2×Dic53C2511yescharacteristic
603D212—24no—
604D212—24no—
605D212—22no—
606C4×D53—26no—
607C4×D53—22no—
608C4×D53—26no—
609C4×D53—212no—
610C4×D53—22no—
611C4×D53—26no—
612C4×D53—22no—
613C4×D53—24no—
614C4×D53—43no—
615C4×D53—43no—
616C4×D53—43no—
617C4×D53—43no—
618C4×D53—46no—
619C4×D53C2×#41112yes—
620C4×D532−1+414yescomplemented
621Dic106—212no—
622Dic106—26no—
623Dic106—26no—
624Dic106—212no—
625Dic106—212no—
626Dic106—46no—
627Dic106C2×#41112yes—
628#62788—531nomaximal, Sylow
629C22×C53—21no—
630C22×C53—21no—
631C22×C53—26no—
632C22×C53—26no—
633C22×C53—26no—
634C22×C53#58512yes—
635C22×C53C2611yescharacteristic
636C2×D53—28no—
637C2×D53—21no—
638C2×D53—21no—
639C2×D53—21no—
640C2×D53—21no—
641C2×D53—22no—
642C2×D53—22no—
643C2×D53—22no—
644C2×D53C22×#4112yes—
645C2×D53C2×2−1+412yes—
646C4×C53—22no—
647C4×C53—23no—
648C4×C53—21no—
649C4×C53—22no—
650C4×C53—26no—
651C4×C53—23no—
652C4×C53—23no—
653C4×C53C22×#4116yes—
654C4×C53C2×2−1+412yes—
655Dic53—23no—
656Dic53—26no—
657Dic53—26no—
658Dic53—21no—
659Dic53—22no—
660Dic53—23no—
661Dic53—23no—
662Dic53C22×#4116yes—
663Dic53C2×2−1+412yes—
664#3523—533no—
665#3523—531no—
666#3522—533no—
667#3522D5311yescharacteristic, complemented
668#3516—536no—
669#3516—532no—
670#3507—533no—
671#3507—533no—
672#3502—531no—
673#3497—531no—
674#3492—536no—
675#3486—532no—
676#3482—532no—
677#3482—536no—
678#3480—533no—
679#3480—531no—
680Q8×#41—531no—
681Q8×#41—533no—
682#3461—536no—
683#3444—533no—
684#3444—533no—
685C4×2−1+4—532no—
686C22×C4×Q8—531no—
687C2×C53—22no—
688C2×C53—46no—
689C2×C53C23×#4111yescharacteristic
690C2×C53C22×2−1+411yescharacteristic
691C2×C53C2×#58511yescharacteristic
692D53—22no—
693D53—22no—
694D53—42no—
695C2×2−1+4—532no—
696C23×Q8—531no—
697#559—533no—
698#559—536no—
699#559C2×D5313yescomplemented
700Q82—533no—
701Q82C2×D5311yescharacteristic, complemented
702#557—536no—
703#557—536no—
704#557—532no—
705#557—533no—
706#557—533no—
707#557—533no—
708#557—531no—
709#556—536no—
710#556—536no—
711#556—5312no—
712#556—533no—
713#556—533no—
714#556—536no—
715#554—536no—
716#554—533no—
717#554—5312no—
718#554—536no—
719#554—536no—
720#554C2×D5313yescomplemented
721#553—5312no—
722#553—536no—
723#553—536no—
724#552—5312no—
725#552—5312no—
726#552—536no—
727#552—536no—
728#552—536no—
729#552—536no—
730#550—533no—
731#550C2×D5311yescharacteristic, complemented
732D4×Q8—532no—
733D4×Q8—536no—
734D4×Q8—532no—
735D4×Q8—531no—
736D4×Q8—536no—
737D4×Q8—533no—
738#548—532no—
739#548—532no—
740#548—536no—
741#548—536no—
742#548—536no—
743#548C2×D5312yes—
744#547—5312no—
745#547—536no—
746#547C2×D5316yes—
747#544—536no—
748#542—5312no—
749#542—536no—
750#542C2×D5316yescomplemented
751#541—5312no—
752#541—536no—
753#541—536no—
754#539—5312no—
755#539—5312no—
756#537—536no—
757#536—536no—
758#536—536no—
759#533—533no—
760#533—533no—
761#533—536no—
762#533—533no—
763#533—533no—
764#533—536no—
765#533—5312no—
766#533—533no—
767#533—533no—
768#532—533no—
769#532—533no—
770#532—533no—
771#532—533no—
772#532—533no—
773#532C2×D5313yes—
774#529—536no—
775#529—536no—
776#529—533no—
777#529—536no—
778#529—533no—
779#529—536no—
780#529—536no—
781#529—536no—
782#529—5312no—
783#529—536no—
784#529—536no—
785#529—536no—
786#529—536no—
787#529—536no—
788#529—536no—
789#529—533no—
790#529C2×D5313yes—
791#525—536no—
792#525—536no—
793#525—531no—
794#525—533no—
795#525—536no—
796#525—536no—
797#520—536no—
798#520—536no—
799#520—536no—
800#520C2×D5312yescomplemented
801#519—532no—
802#519—532no—
803#519—536no—
804C4×#41—536no—
805C4×#41—532no—
806C4×#41—533no—
807C4×#41—536no—
808C4×#41—536no—
809C4×#41—533no—
810C4×#41—536no—
811C4×#41—536no—
812C4×#41—536no—
813C2×C4×Q8—531no—
814C2×C4×Q8—531no—
815C2×C4×Q8—533no—
816C2×C4×Q8—531no—
817C2×C4×Q8—533no—
818C2×C4×Q8—531no—
819C2×C4×Q8—533no—
820C2×C4×Q8—531no—
821C2×C4×Q8—533no—
822C2×C4×Q8—532no—
823C2×C4×Q8—533no—
824C2×C4×Q8—536no—
825C2×C4×Q8—533no—
826C2×C4×Q8C2×D5311yescharacteristic
827C22×C4⋊C4—533no—
828C22×C42—533no—
829C53#6278811yescharacteristic, complemented, Sylow
8302−1+4—10616no—
831C2×#41—531no—
832C2×#41—533no—
833C2×#41—536no—
834C2×#41—536no—
835C2×#41—536no—
836C2×#41—536no—
837C2×#41C22×D5312yes—
838C2×#41C22×D5316yes—
839C22×Q8—531no—
840C22×Q8—533no—
841C22×Q8—533no—
842C22×Q8—531no—
843C22×Q8—532no—
844C22×Q8—533no—
845C22×Q8—536no—
846C22×Q8—1068no—
847C22×Q8C22×D5311yescharacteristic
848C23×C4—533no—
849C23×C4—531no—
850C23×C4—533no—
851C4⋊Q8—533no—
852C4⋊Q8—536no—
853C4⋊Q8—5312no—
854C4⋊Q8—533no—
855C4⋊Q8—533no—
856C4⋊Q8—5312no—
857C4⋊Q8—536no—
858C4⋊Q8—533no—
859C4⋊Q8—533no—
860C4⋊Q8—536no—
861C4⋊Q8C22×D5313yes—
862C4⋊Q8C22×D5316yes—
863#127—533no—
864#127C22×D5313yes—
865#126—536no—
866#126—5312no—
867#126—5312no—
868#126—5312no—
869#126—536no—
870#126—5312no—
871#126—5312no—
872#126—5312no—
873#126—536no—
874#126C22×D5316yes—
875#125—536no—
876#125—536no—
877#125—536no—
878#125—536no—
879#125—5312no—
880#125—536no—
881#125—5312no—
882#125—5312no—
883#125—5312no—
884#125—5312no—
885#125—536no—
886#125—533no—
887#125—536no—
888#125C22×D5313yes—
889#124—536no—
890#124—536no—
891#124—536no—
892#124—536no—
893#124—536no—
894#124—5312no—
895#124—533no—
896#124C22×D5316yes—
897#124C22×D5313yes—
898#124C22×D5316yes—
899#123—5312no—
900#123—5312no—
901#123—536no—
902#123—5312no—
903#123—532no—
904#123—536no—
905#123—536no—
906#123—536no—
907#123—5312no—
908#123—5312no—
909#123C22×D5316yes—
910#123C22×D53112yes—
911C22⋊Q8—531no—
912C22⋊Q8—536no—
913C22⋊Q8—536no—
914C22⋊Q8—536no—
915C22⋊Q8—5312no—
916C22⋊Q8—533no—
917C22⋊Q8—536no—
918C22⋊Q8—536no—
919C22⋊Q8—536no—
920C22⋊Q8—5312no—
921C22⋊Q8—533no—
922C22⋊Q8—536no—
923C22⋊Q8—536no—
924C22⋊Q8—536no—
925C22⋊Q8—536no—
926C22⋊Q8—536no—
927C22⋊Q8—536no—
928C22⋊Q8—536no—
929C22⋊Q8—5312no—
930C22⋊Q8—5312no—
931C22⋊Q8—5312no—
932C22⋊Q8—5312no—
933C22⋊Q8C22×D5311yescharacteristic
934C22⋊Q8C22×D5316yes—
935C22⋊Q8C22×D53112yes—
936#121—533no—
937#121—536no—
938#121—536no—
939#121—536no—
940#121—536no—
941#121—536no—
942#121—5312no—
943#121—531no—
944#121—531no—
945#121—536no—
946#121—536no—
947#121—536no—
948#121C22×D5313yes—
949#121C22×D5316yes—
950#121C22×D5316yes—
951#120—536no—
952#120—532no—
953C4×Q8—531no—
954C4×Q8—533no—
955C4×Q8—531no—
956C4×Q8—533no—
957C4×Q8—532no—
958C4×Q8—536no—
959C4×Q8—533no—
960C4×Q8—536no—
961C4×Q8—533no—
962C4×Q8—536no—
963C4×Q8—533no—
964C4×Q8—533no—
965C4×Q8—536no—
966C4×Q8—533no—
967C4×Q8—536no—
968C4×Q8—536no—
969C4×Q8—536no—
970C4×Q8—5312no—
971C4×Q8—536no—
972C4×Q8—536no—
973C4×Q8—536no—
974C4×Q8—533no—
975C4×Q8—536no—
976C4×Q8—533no—
977C4×Q8—536no—
978C4×Q8—533no—
979C4×Q8—533no—
980C4×Q8—533no—
981C4×Q8—536no—
982C4×Q8—536no—
983C4×Q8—536no—
984C4×Q8—536no—
985C4×Q8—536no—
986C4×Q8—536no—
987C4×Q8—533no—
988C4×Q8C22×D5311yescharacteristic
989C4×Q8C22×D5313yes—
990C4×Q8C22×D5311yescharacteristic
991C4×Q8C22×D5313yes—
992C4×Q8C22×D5312yes—
993C4×Q8C22×D5313yes—
994C4×D4—536no—
995C4×D4—536no—
996C4×D4—536no—
997C4×D4—5312no—
998C4×D4—536no—
999C4×D4—536no—
1000C4×D4—536no—
1001C4×D4—533no—
1002C4×D4—5312no—
1003C4×D4—5312no—
1004C4×D4—536no—
1005C4×D4—536no—
1006C4×D4—5312no—
1007C4×D4—536no—
1008C4×D4—532no—
1009C4×D4—536no—
1010C4×D4—536no—
1011C4×D4—533no—
1012C4×D4—536no—
1013C4×D4—532no—
1014C4×D4—536no—
1015C4×D4—536no—
1016C4×D4—536no—
1017C4×D4—5312no—
1018C4×D4—536no—
1019C4×D4—536no—
1020C4×D4—536no—
1021C4×D4—533no—
1022C4×D4C22×D5316yes—
1023C4×D4C22×D5316yes—
1024C4×D4C22×D5316yes—
1025C4×D4C22×D5316yes—
1026C4×D4C22×D5313yes—
1027#117—536no—
1028#117—536no—
1029#117—5312no—
1030#117—533no—
1031#117—531no—
1032#117—536no—
1033#117—536no—
1034#117—536no—
1035#117—536no—
1036#117—5312no—
1037#117—5312no—
1038#117—536no—
1039#117—5312no—
1040#117—536no—
1041#117—536no—
1042#117—536no—
1043#117—536no—
1044#117C22×D5316yes—
1045C2×C4⋊C4—536no—
1046C2×C4⋊C4—533no—
1047C2×C4⋊C4—5312no—
1048C2×C4⋊C4—533no—
1049C2×C4⋊C4—533no—
1050C2×C4⋊C4—536no—
1051C2×C4⋊C4—536no—
1052C2×C4⋊C4—533no—
1053C2×C4⋊C4—533no—
1054C2×C4⋊C4—536no—
1055C2×C4⋊C4C22×D5313yes—
1056C2×C4⋊C4C22×D5316yes—
1057C2×C42—533no—
1058C2×C42—533no—
1059C2×C42—533no—
1060C2×C42—5312no—
1061C2×C42—536no—
1062C2×C42—533no—
1063C2×C42—533no—
1064C2×C42—533no—
1065C2×C42—533no—
1066C2×C42—533no—
1067C2×C42—533no—
1068C2×C42—533no—
1069C2×C42—533no—
1070C2×C42—536no—
1071C2×C42C22×D5313yes—
1072C24—531no—
1073#41—28no—
1074#41—412no—
1075#41—10624no—
1076#41—10612no—
1077#41—10624no—
1078#41—1064no—
1079#41—10624no—
1080#41—21212no—
1081C2×Q8—24no—
1082C2×Q8—538no—
1083C2×Q8—533no—
1084C2×Q8—533no—
1085C2×Q8—536no—
1086C2×Q8—533no—
1087C2×Q8—536no—
1088C2×Q8—536no—
1089C2×Q8—536no—
1090C2×Q8—10612no—
1091C2×Q8—10624no—
1092C2×Q8—10612no—
1093C2×Q8—10612no—
1094C2×Q8—1064no—
1095C2×Q8—1068no—
1096C2×Q8C23×D5311yescharacteristic
1097C2×Q8C23×D5313yes—
1098C2×Q8C23×D5316yes—
1099C2×Q8C23×D5311yescharacteristic
1100C2×D4—536no—
1101C2×D4—536no—
1102C2×D4—532no—
1103C2×D4—536no—
1104C2×D4—536no—
1105C2×D4—532no—
1106C2×D4—531no—
1107C2×D4—532no—
1108C2×D4C23×D5313yes—
1109C2×D4C23×D5316yes—
1110C2×D4C23×D5316yes—
1111C2×D4C23×D5316yes—
1112C22×C4—531no—
1113C22×C4—533no—
1114C22×C4—531no—
1115C22×C4—536no—
1116C22×C4—533no—
1117C22×C4—533no—
1118C22×C4—5312no—
1119C22×C4—536no—
1120C22×C4—531no—
1121C22×C4—531no—
1122C22×C4—531no—
1123C22×C4—532no—
1124C22×C4—533no—
1125C22×C4—533no—
1126C22×C4—533no—
1127C22×C4—536no—
1128C22×C4—533no—
1129C22×C4—533no—
1130C22×C4—533no—
1131C22×C4—533no—
1132C22×C4—536no—
1133C22×C4—1064no—
1134C22×C4—10612no—
1135C22×C4—2126no—
1136C22×C4C23×D5311yescharacteristic
1137C22×C4C23×D5313yes—
1138C22×C4C23×D5313yes—
1139C22×C4C23×D5316yes—
1140C22×C4C23×D53112yes—
1141C4⋊C4—536no—
1142C4⋊C4—533no—
1143C4⋊C4—536no—
1144C4⋊C4—533no—
1145C4⋊C4—536no—
1146C4⋊C4—536no—
1147C4⋊C4—536no—
1148C4⋊C4—536no—
1149C4⋊C4—5312no—
1150C4⋊C4—536no—
1151C4⋊C4—536no—
1152C4⋊C4—536no—
1153C4⋊C4—532no—
1154C4⋊C4—536no—
1155C4⋊C4—536no—
1156C4⋊C4—533no—
1157C4⋊C4—531no—
1158C4⋊C4—536no—
1159C4⋊C4—536no—
1160C4⋊C4—536no—
1161C4⋊C4—536no—
1162C4⋊C4—536no—
1163C4⋊C4—5312no—
1164C4⋊C4—536no—
1165C4⋊C4—5312no—
1166C4⋊C4—536no—
1167C4⋊C4—536no—
1168C4⋊C4—5312no—
1169C4⋊C4C23×D5313yes—
1170C4⋊C4C23×D5313yes—
1171C4⋊C4C23×D5316yes—
1172C4⋊C4C23×D5316yes—
1173C4⋊C4C23×D5316yes—
1174C4⋊C4C23×D5313yes—
1175C4⋊C4C23×D5316yes—
1176C4⋊C4C23×D5311yescharacteristic
1177C4⋊C4C23×D5316yes—
1178C4⋊C4C23×D5312yes—
1179C22⋊C4—536no—
1180C22⋊C4—5312no—
1181C22⋊C4—536no—
1182C22⋊C4—5312no—
1183C22⋊C4—536no—
1184C22⋊C4—5312no—
1185C22⋊C4—536no—
1186C22⋊C4—532no—
1187C22⋊C4—536no—
1188C22⋊C4—532no—
1189C22⋊C4—532no—
1190C22⋊C4—532no—
1191C22⋊C4—536no—
1192C22⋊C4—536no—
1193C22⋊C4—536no—
1194C22⋊C4—536no—
1195C22⋊C4C23×D5312yes—
1196C22⋊C4C23×D5316yes—
1197C22⋊C4C23×D5316yes—
1198C22⋊C4C23×D5316yes—
1199C22⋊C4C23×D5316yes—
1200C22⋊C4C23×D53112yes—
1201C42—533no—
1202C42—533no—
1203C42—533no—
1204C42—532no—
1205C42—536no—
1206C42—533no—
1207C42—533no—
1208C42—533no—
1209C42—533no—
1210C42—533no—
1211C42—533no—
1212C42—533no—
1213C42—533no—
1214C42—533no—
1215C42—536no—
1216C42—536no—
1217C42—5312no—
1218C42—5312no—
1219C42—536no—
1220C42C23×D5313yes—
1221C42C23×D5313yes—
1222C42C23×D5313yes—
1223C42C23×D5313yes—
1224C42C23×D5316yes—
1225C23—531no—
1226C23—531no—
1227C23—532no—
1228C23—1062no—
1229C23—1062no—
1230C23—1062no—
1231C23C24×D5316yes—
1232C23C24×D5311yescharacteristic
1233Q8—26no—
1234Q8—22no—
1235Q8—46no—
1236Q8—5312no—
1237Q8—10612no—
1238Q8—10612no—
1239Q8—1066no—
1240Q8—10612no—
1241Q8—1066no—
1242Q8—2126no—
1243Q8#41×D5314yes—
1244D4—212no—
1245D4—212no—
1246D4—26no—
1247D4—46no—
1248D4—1064no—
1249D4—1064no—
1250D4—10612no—
1251D4—10612no—
1252D4—10612no—
1253D4—1064no—
1254D4—1062no—
1255D4—2126no—
1256C2×C4—26no—
1257C2×C4—26no—
1258C2×C4—212no—
1259C2×C4—22no—
1260C2×C4—412no—
1261C2×C4—531no—
1262C2×C4—533no—
1263C2×C4—5312no—
1264C2×C4—534no—
1265C2×C4—531no—
1266C2×C4—533no—
1267C2×C4—536no—
1268C2×C4—533no—
1269C2×C4—536no—
1270C2×C4—532no—
1271C2×C4—533no—
1272C2×C4—1062no—
1273C2×C4—1066no—
1274C2×C4—1064no—
1275C2×C4—1062no—
1276C2×C4—1066no—
1277C2×C4—1062no—
1278C2×C4—1066no—
1279C2×C4—10624no—
1280C2×C4—10612no—
1281C2×C4—1066no—
1282C2×C4—1066no—
1283C2×C4—10612no—
1284C2×C4—1062no—
1285C2×C4—2123no—
1286C2×C4—2123no—
1287C2×C4—2123no—
1288C2×C4—2123no—
1289C2×C4—2126no—
1290C2×C4—2126no—
1291C2×C4C24×D5311yescharacteristic
1292C2×C4C24×D5313yes—
1293C2×C4C24×D5312yes—
1294C2×C4C24×D5312yes—
1295C2×C4C24×D5316yes—
1296C2×C4C24×D5313yes—
1297C2×C4C24×D5313yes—
1298C2×C4C24×D5313yes—
1299C2×C4C24×D5311yescharacteristic
1300C22—21no—
1301C22—21no—
1302C22—26no—
1303C22—26no—
1304C22—26no—
1305C22—532no—
1306C22—532no—
1307C22—1068no—
1308C22—1061no—
1309C22—1061no—
1310C22—1061no—
1311C22—1061no—
1312C22—1062no—
1313C22—1062no—
1314C22—1062no—
1315C22#1681145812yes—
1316C22C25×D5311yescharacteristic
1317C4—22no—
1318C4—23no—
1319C4—21no—
1320C4—22no—
1321C4—23no—
1322C4—23no—
1323C4—26no—
1324C4—536no—
1325C4—532no—
1326C4—1066no—
1327C4—1063no—
1328C4—1061no—
1329C4—1066no—
1330C4—1063no—
1331C4—1063no—
1332C4—1062no—
1333C4C2×#41×D5316yes—
1334C42−1+4×D5312yes—
1335C2—22no—
1336C2—46no—
1337C2—1062no—
1338C2—1062no—
1339C2—2122no—
1340C2C22×#41×D5311yescharacteristic
1341C2C2×2−1+4×D5311yescharacteristic
1342C2C2×#1681145811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3522C2
hypercenter#3522D53
hypocenterC53#62788
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3522

Complements

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

NH ≅ G/Ntype
1. #20288811C2semidirect
2. #20288809C2semidirect
3. #20288792C2semidirect
4. #20288702C2semidirect
5. #20288700C2semidirect
6. #20288578C2semidirect
7. #20288572C2semidirect
8. #20288524C2semidirect
9. #20288480C2semidirect
10. #20288417C2semidirect
11. #20288361C2semidirect
12. #20288331C2semidirect
13. #20288327C2semidirect
14. #20288314C2semidirect
15. #20288311C2semidirect
16. Q8×#11719949C2semidirect
17. #20288294C2semidirect
18. #20288141C2semidirect
19. #20288010C2semidirect
20. #20288009C2semidirect
21. #20287926C2semidirect
22. C2×C4×Q8×D53C2semidirect
23. C53×#3522C2semidirect
26. #16811359C22semidirect
27. #16811356C22semidirect
28. #16811353C22semidirect
29. #16811352C22semidirect
30. #16811352C22semidirect
31. #16811351C22semidirect
32. #16811351C22semidirect
33. #16811350C22semidirect
34. #16811349C22semidirect
35. #16811348C22semidirect
36. #16811346C22semidirect
37. #16811344C22semidirect
38. #16811343C22semidirect
39. #16811343C22semidirect
40. #16811342C22semidirect
41. #16811342C22semidirect
43. #16811334C22semidirect
44. #16811332C22semidirect
52. #16811310C22semidirect
54. #16811308C22semidirect
55. #16811307C22semidirect
56. #16811293C22semidirect
58. Q8×D212C22semidirect
60. D4×Dic106C22semidirect
65. #16811280C22semidirect
67. #16811279C22semidirect
71. #16811238C22semidirect
72. #16811237C22semidirect
73. #16811235C22semidirect
74. #16811231C22semidirect
75. #16811230C22semidirect
85. #16811178C22semidirect
88. #16811175C22semidirect
89. #16811175C22semidirect
103. #16811154C22semidirect
107. #16811152C22semidirect
110. #16811150C22semidirect
119. #16811102C22semidirect
120. #16811100C22semidirect
122. #16811099C22semidirect
124. #41×Dic53C22semidirect
131. C4×#11719947C22semidirect
135. C2×#13133182C22semidirect
144. C4×Q8×D53C22semidirect
147. C53×#559C22semidirect
148. Q82×C53C22semidirect
149. C53×#554C22semidirect
150. C53×#550C22semidirect
153. C53×#542C22semidirect
156. C53×#520C22semidirect
433. Q8×D53#41semidirect
620. C4×D532−1+4semidirect
667. #3522D53semidirect
699. #559C2×D53semidirect
701. Q82C2×D53semidirect
720. #554C2×D53semidirect
731. #550C2×D53semidirect
750. #542C2×D53semidirect
800. #520C2×D53semidirect
829. C53#62788semidirect

Maximal subgroups

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

subgroupindex
#202888112
#202888092
#202887922
#202887022
#202887002
#202885782
#202885722
#202885242
#202884802
#202884172
#202883612
#202883312
#202883272
#202883142
#202883112
Q8×#117199492
#202882942
#202881412
#202880102
#202880092
#202879262
C2×C4×Q8×D532
C53×#35222
#6278853