Finite Group Databasebeta

← #28293213

Subgroups — #28293213

Order 13568.

6806 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288541C211yesmaximal, characteristic, complemented
2#20288540C212yesmaximal, complemented
3#20288538C213yesmaximal, complemented
4#20288537C211yesmaximal, characteristic, complemented
5#20288536C213yesmaximal, complemented
6#20288535C216yesmaximal, complemented
7#20288533C212yesmaximal, complemented
8#20288531C213yesmaximal, complemented
9#20288530C213yesmaximal, complemented
10#20288528C211yesmaximal, characteristic, complemented
11#20288526C216yesmaximal, complemented
12#20288524C212yesmaximal, complemented
13#20288522C212yesmaximal, complemented
14#20288514C216yesmaximal, complemented
15#20288510C216yesmaximal, complemented
16#20288119C213yesmaximal, complemented
17#20288118C213yesmaximal, complemented
18C2×#16811250C213yesmaximal, complemented
19#544×D53C213yesmaximal, complemented
20#20287915C211yesmaximal, characteristic
21#20287914C211yesmaximal, characteristic
22#520×D53C211yesmaximal, characteristic
23C53×#3503C211yesmaximal, characteristic, complemented
24C2×#41×D53C2211yescharacteristic
25Q8×Dic106C2212yescomplemented
26#16811353C2216yescomplemented
27#16811353C2216yescomplemented
28#16811352C2212yescomplemented
29#16811351C2216yescomplemented
30#16811351C2216yescomplemented
31#16811350C2216yescomplemented
32#16811350C2216yescomplemented
33#16811349C2212yescomplemented
34#16811349C2212yescomplemented
35#16811349C2212yescomplemented
36#16811349C2212yescomplemented
37#16811348C2216yescomplemented
38#16811348C2216yescomplemented
39#16811334C2216yescomplemented
40#16811334C2216yescomplemented
41#16811333C2216yescomplemented
42#16811333C2216yescomplemented
43#16811332C2216yescomplemented
44#16811332C2216yescomplemented
45#16811332C2216yescomplemented
46#16811332C2216yescomplemented
47#16811331C22112yescomplemented
48#16811330C2216yescomplemented
49#16811329C2216yescomplemented
50#16811329C2216yescomplemented
51#16811328C22112yescomplemented
52#16811327C22112yescomplemented
53#16811327C22112yescomplemented
54#16811327C22112yescomplemented
55#16811327C22112yescomplemented
56D4×Dic106C2216yescomplemented
57#16811288C2216yescomplemented
58#16811288C2216yescomplemented
59Q8×C22⋊D53C22112yescomplemented
60#16811286C22112yescomplemented
61#16811254C2213yescomplemented
62#16811254C2213yescomplemented
63#16811253C2216yes—
64#16811253C2213yes—
65#16811253C2213yes—
66#16811253C2213yescomplemented
67#16811253C2216yescomplemented
68#16811253C2213yescomplemented
69#16811252C2216yescomplemented
70#16811252C22112yescomplemented
71#16811252C2216yescomplemented
72#16811251C2213yescomplemented
73#16811251C2213yescomplemented
74#16811251C2213yescomplemented
75#16811251C2213yescomplemented
76#16811250C2216yes—
77#16811250C2216yes—
78#16811250C2216yes—
79#16811250C2216yes—
80#16811250C2213yes—
81#16811250C2211yescharacteristic
82#16811250C2216yescomplemented
83#16811250C2216yescomplemented
84#16811250C2216yescomplemented
85#16811250C2213yescomplemented
86#16811250C2216yescomplemented
87#16811250C2216yescomplemented
88#16811250C2213yescomplemented
89#16811248C2216yes—
90#16811248C22112yes—
91#16811248C2216yes—
92#16811180C2213yescomplemented
93#16811179C2216yes—
94#16811179C2216yescomplemented
95#16811178C2216yes—
96#16811178C2216yescomplemented
97#16811177C2216yes—
98#16811177C2216yes—
99#16811177C2216yescomplemented
100#16811177C2216yescomplemented
101#16811176C2213yescomplemented
102#16811176C2213yescomplemented
103#16811175C22112yescomplemented
104C2×#13133216C2213yescomplemented
105C2×#13133215C2216yescomplemented
106C4⋊Q8×D53C2216yescomplemented
107C4⋊Q8×D53C2216yescomplemented
108C2×#13133209C2213yescomplemented
109C2×#13133208C2213yescomplemented
110C2×#13133207C2216yescomplemented
111#125×D53C2216yescomplemented
112#125×D53C2216yescomplemented
113C2×#13133195C2216yes—
114C2×#13133193C2216yes—
115C22⋊Q8×D53C22112yes—
116#16811106C2211yescharacteristic
117#16811106C2211yescharacteristic
118#16811105C2211yescharacteristic
119#16811105C2212yes—
120#16811105C2211yescharacteristic
121#16811104C2213yes—
122#16811104C2213yes—
123#16811103C2213yes—
124#16811103C2213yes—
125#16811102C2213yes—
126#16811102C2216yes—
127#16811102C2213yes—
128#16811099C2211yescharacteristic
129#16811099C2212yes—
130#16811099C2211yescharacteristic
131#16811095C2213yes—
132#16811095C2216yes—
133#16811095C2213yes—
134#41×Dic53C2211yescharacteristic
135C4×#11719949C2212yes—
136C4×#11719945C2213yes—
137#16811091C2213yes—
138C4×#11719947C2216yes—
139C4×Q8×D53C2212yes—
140C4×D4×D53C2216yes—
141C2×#13133175C2213yes—
142C2×#13133174C2213yes—
143#117×D53C2213yes—
144#117×D53C2213yes—
145#117×D53C2213yes—
146C2×C4⋊C4×D53C2213yes—
147Q82×C53C2212yescomplemented
148C53×#557C2212yescomplemented
149C53×#554C2216yescomplemented
150D4×Q8×C53C2216yescomplemented
151C53×#544C2213yescomplemented
152C53×#544C2213yescomplemented
153C53×#533C2213yescomplemented
154C2×C4⋊Q8×C53C2213yescomplemented
155C53×#520C2211yescharacteristic
156C53×#520C2211yescharacteristic
157C4×#41×C53C2211yescharacteristic
158C2×#11719949C2311yescharacteristic
159C2×#11719945C2313yes—
160C2×#11719947C2313yes—
161#41×D53Q8116yescomplemented
162C22×Dic106C2316yes—
163C2×Q8×D53C23112yes—
164C2×Q8×D53C2311yescharacteristic
165C2×D4×D53C2313yes—
166C22×C4×D53C2316yes—
167C22×C4×D53C2313yes—
168#13133217C2316yes—
169#13133217C2316yes—
170#13133217C2313yes—
171#13133217C2313yes—
172#13133216C2316yes—
173#13133216C23112yes—
174#13133216C2316yes—
175#13133216C2316yes—
176#13133216C2316yes—
177#13133216C2316yes—
178#13133216C2316yes—
179#13133216C2316yes—
180#13133216C2316yes—
181#13133216C2313yes—
182#13133216C2316yes—
183#13133216C2316yes—
184#13133216C2313yes—
185#13133216C2316yes—
186#13133216C2311yescharacteristic
187#13133216C2313yes—
188#13133215C23112yes—
189#13133215C2316yes—
190#13133215C23112yes—
191#13133215C23112yes—
192#13133215C2316yes—
193#13133215C23112yes—
194#13133215C2316yes—
195#13133215C2312yes—
196#13133209C2316yes—
197#13133209C2316yes—
198#13133209C2316yes—
199#13133209C2316yes—
200#13133209C2316yes—
201#13133209C2313yes—
202#13133209C2311yescharacteristic
203#13133208C2316yes—
204#13133208C2316yes—
205#13133208C2316yes—
206#13133208C2316yes—
207#13133208C2316yes—
208#13133208C2316yes—
209#13133208C2313yes—
210#13133208C2316yes—
211#13133208C2313yes—
212#13133208C2311yescharacteristic
213#13133208C2313yes—
214#13133207C2316yes—
215#13133207C2316yes—
216#13133207C23112yes—
217#13133207C2316yes—
218#13133207C23112yes—
219#13133207C23112yes—
220#13133207C23112yes—
221#13133207C2316yes—
222#13133207C2316yes—
223#13133207C23112yes—
224#13133207C2316yes—
225#13133207C2316yes—
226#13133207C2312yes—
227#13133197C2316yes—
228#13133197C23112yes—
229#13133197C2316yes—
230#13133197C2316yes—
231#13133197C2316yes—
232#13133196C2316yes—
233#13133196C23112yes—
234#13133196C23112yes—
235#13133196C2316yes—
236#13133195C23112yes—
237#13133195C23112yes—
238#13133195C2316yes—
239#13133195C2316yes—
240#13133195C23112yes—
241#13133195C2316yes—
242#13133195C23112yes—
243#13133195C2316yes—
244#13133195C2316yes—
245#13133195C23112yes—
246#13133195C2316yes—
247#13133195C2312yes—
248#13133195C2316yes—
249#13133194C2316yes—
250#13133194C23112yes—
251#13133194C2316yes—
252#13133194C23112yes—
253#13133194C2316yes—
254#13133194C23112yes—
255#13133194C23112yes—
256#13133194C2316yes—
257#13133193C2316yes—
258#13133193C23112yes—
259#13133193C23112yes—
260#13133193C23112yes—
261#13133193C2316yes—
262#13133193C23112yes—
263#13133193C2316yes—
264#13133193C2312yes—
265Q8×Dic53C23112yes—
266Q8×Dic53C2312yes—
267Q8×Dic53C2312yes—
268Q8×Dic53C2311yescharacteristic
269Q8×Dic53C2311yescharacteristic
270C4×Dic106C2316yes—
271C4×Dic106C2316yes—
272C4×Dic106C2316yes—
273C4×Dic106C2316yes—
274C4×Dic106C2316yes—
275C4×Dic106C2316yes—
276C4×Dic106C2316yes—
277C4×Dic106C2316yes—
278C4×Dic106C2313yes—
279C4×Dic106C2313yes—
280#13133182C23112yes—
281#13133182C23112yes—
282#13133182C23112yes—
283#13133182C2316yes—
284#13133182C2316yes—
285#13133182C2313yes—
286#13133182C2313yes—
287C4×D212C2313yes—
288C4×D212C2316yes—
289C4×D212C2316yes—
290C4×D212C2313yes—
291D4×Dic53C2313yes—
292D4×Dic53C2316yes—
293D4×Dic53C2313yes—
294D4×Dic53C2316yes—
295#13133179C2316yes—
296#13133179C2313yes—
297#13133179C2316yes—
298#13133179C2313yes—
299C4×C22⋊D53C23112yes—
300C4×C22⋊D53C2316yes—
301C4×C22⋊D53C23112yes—
302C4×C22⋊D53C2316yes—
303#13133177C2316yes—
304#13133177C23112yes—
305#13133177C23112yes—
306#13133177C2316yes—
307#13133176C2313yes—
308#13133176C2313yes—
309#13133176C2313yes—
310#13133175C2311yescharacteristic
311#13133175C2313yes—
312#13133175C2313yes—
313#13133175C2313yes—
314#13133175C2313yes—
315#13133175C2313yes—
316#13133175C2316yes—
317#13133175C2316yes—
318#13133175C2316yes—
319#13133174C2313yes—
320#13133174C2316yes—
321#13133174C2316yes—
322#13133174C2311yescharacteristic
323#13133174C2313yes—
324#13133174C2313yes—
325#13133174C2313yes—
326#13133174C2313yes—
327#13133174C2313yes—
328#13133174C2313yes—
329#13133173C2316yes—
330#13133173C2316yes—
331#13133173C2316yes—
332C2×C4⋊Dic53C2313yes—
333C2×C4⋊Dic53C2316yes—
334C2×C4⋊Dic53C2313yes—
335C2×#11719919C2316yes—
336C2×#11719919C2316yes—
337C2×#11719919C2316yes—
338C2×#11719919C2316yes—
339C2×#11719919C2316yes—
340C2×#11719919C2313yes—
341C2×#11719919C2313yes—
342C4⋊C4×D53C23112yes—
343C4⋊C4×D53C23112yes—
344C4⋊C4×D53C23112yes—
345C4⋊C4×D53C2313yes—
346C4⋊C4×D53C2316yes—
347C4⋊C4×D53C2316yes—
348C4⋊C4×D53C2316yes—
349C4⋊C4×D53C2311yescharacteristic
350C4⋊C4×D53C2313yes—
351C4⋊C4×D53C2313yes—
352C4⋊C4×D53C2313yes—
353C4⋊C4×D53C2313yes—
354C2×#11719921C2313yes—
355C2×#11719921C2313yes—
356C2×#11719921C2316yes—
357C22⋊C4×D53C2316yes—
358C22⋊C4×D53C2316yes—
359C22⋊C4×D53C2316yes—
360C2×C4×Dic53C2313yes—
361C2×C4×Dic53C2316yes—
362C42×D53C2316yes—
363C42×D53C2316yes—
364C42×D53C2316yes—
365C2×#41×C53C2311yescharacteristic
366C22×Q8×C53C2316yes—
367C4⋊Q8×C53C2316yes—
368C4⋊Q8×C53C2316yes—
369C4⋊Q8×C53C2313yes—
370C4⋊Q8×C53C2316yes—
371C4⋊Q8×C53C2316yes—
372C4⋊Q8×C53C2311yescharacteristic
373C4⋊Q8×C53C2316yes—
374#125×C53C2313yes—
375#125×C53C2313yes—
376#125×C53C2316yes—
377#125×C53C2316yes—
378C22⋊Q8×C53C23112yes—
379C22⋊Q8×C53C2316yes—
380C22⋊Q8×C53C2316yes—
381C22⋊Q8×C53C23112yes—
382C4×Q8×C53C2311yescharacteristic
383C4×Q8×C53C2311yescharacteristic
384C4×Q8×C53C2312yes—
385C4×Q8×C53C2312yes—
386C4×Q8×C53C2316yes—
387C4×Q8×C53C2316yes—
388C4×D4×C53C2316yes—
389C4×D4×C53C2313yes—
390C4×D4×C53C2313yes—
391C4×D4×C53C2316yes—
392#117×C53C2313yes—
393#117×C53C2313yes—
394#117×C53C2313yes—
395C2×C4⋊C4×C53C2313yes—
396C2×C4⋊C4×C53C2313yes—
397C2×C4⋊C4×C53C2316yes—
398C2×C42×C53C2313yes—
399C23×D53C2413yes—
400#41×C53C2×Q818yescomplemented
401C2×Q8×C53—86no—
402C2×Q8×C53C2412yes—
403C2×Q8×C53C2416yes—
404C2×Q8×C53C24112yes—
405C2×Q8×C53C2411yescharacteristic
406C2×D4×C53C2413yes—
407C22×C4×C53C2413yes—
408C22×C4×C53C2413yes—
409C22×C4×C53C2416yes—
410C22×C4×C53C2416yes—
411C22×C4×C53C2413yes—
412C2×C22⋊D53C2416yes—
413C22×Dic53C2413yes—
414C22×Dic53C2416yes—
415C22×Dic53C2413yes—
416C22×Dic53C2416yes—
417C22×Dic53C2413yes—
418#11719949C2×Q818yescomplemented
419Q8×D53—812no—
420Q8×D53C2×Q818yescomplemented
421#11719947C2×Q8124yescomplemented
422D4×D53C2×Q8124yescomplemented
423#11719945C2×Q8124yescomplemented
424C2×D212C2413yes—
425C2×C4×D53—86no—
426C2×C4×D53C2×Q8124yescomplemented
427C2×C4×D53C2412yes—
428C2×C4×D53C2416yes—
429C2×C4×D53C2416yes—
430C2×C4×D53C2416yes—
431C2×C4×D53C2416yes—
432C2×C4×D53C2416yes—
433C2×C4×D53C24112yes—
434C2×C4×D53C2413yes—
435C2×C4×D53C2413yes—
436C2×C4×D53C2413yes—
437C2×C4×D53C2411yescharacteristic
438C2×Dic106—86no—
439C2×Dic106C2416yes—
440C2×Dic106C2416yes—
441C2×Dic106C24112yes—
442C2×Dic106C2412yes—
443C2×Dic106C2416yes—
444C2×Dic106C2416yes—
445C2×Dic106C2416yes—
446C2×Dic106C2413yes—
447C4⋊C4×C53C2413yes—
448C4⋊C4×C53C2413yes—
449C4⋊C4×C53C2416yes—
450C4⋊C4×C53C2416yes—
451C4⋊C4×C53C2416yes—
452C4⋊C4×C53C24112yes—
453C4⋊C4×C53C2411yescharacteristic
454C4⋊C4×C53C2411yescharacteristic
455C4⋊C4×C53C2413yes—
456C4⋊C4×C53C2413yes—
457C4⋊C4×C53C2412yes—
458C4⋊C4×C53C2416yes—
459C4⋊C4×C53C2416yes—
460C4⋊C4×C53C2416yes—
461C4⋊C4×C53C2416yes—
462C22⋊C4×C53C2416yes—
463C22⋊C4×C53C2416yes—
464C22⋊C4×C53C2416yes—
465C42×C53C2411yescharacteristic
466C42×C53C2413yes—
467C42×C53C2413yes—
468C42×C53C2413yes—
469C42×C53C2416yes—
470C42×C53C2416yes—
471C22⋊Dic53C2416yes—
472C22⋊Dic53C2416yes—
473C22⋊Dic53C2416yes—
474#11719921C2412yes—
475#11719921C2413yes—
476#11719921C2413yes—
477#11719921C2416yes—
478#11719921C2416yes—
479#11719921C2416yes—
480#11719921C2411yescharacteristic
481#11719921C2411yescharacteristic
482#11719921C2413yes—
483#11719921C2413yes—
484#11719921C2413yes—
485#11719921C2413yes—
486#11719921C24112yes—
487C4⋊Dic53C2413yes—
488C4⋊Dic53C2411yescharacteristic
489C4⋊Dic53C2416yes—
490C4⋊Dic53C2416yes—
491C4⋊Dic53C2416yes—
492C4⋊Dic53C2413yes—
493C4⋊Dic53C24112yes—
494C4⋊Dic53C2411yescharacteristic
495C4⋊Dic53C2413yes—
496C4⋊Dic53C2413yes—
497C4⋊Dic53C2416yes—
498C4⋊Dic53C2416yes—
499C4⋊Dic53C2412yes—
500C4⋊Dic53C2416yes—
501C4⋊Dic53C2416yes—
502#11719919C2416yes—
503#11719919C2413yes—
504#11719919C2413yes—
505#11719919C24112yes—
506#11719919C2416yes—
507#11719919C2416yes—
508#11719919C24112yes—
509#11719919C24112yes—
510#11719919C24112yes—
511#11719919C24112yes—
512#11719919C2412yes—
513#11719919C2416yes—
514#11719919C2416yes—
515#11719919C2411yescharacteristic
516#11719919C2411yescharacteristic
517#11719919C2416yes—
518#11719919C2416yes—
519#11719919C2416yes—
520#11719919C2416yes—
521#11719919C2413yes—
522#11719919C2413yes—
523#11719919C2413yes—
524#11719919C2413yes—
525#11719919C2416yes—
526#11719919C2416yes—
527#11719919C2412yes—
528#11719919C2412yes—
529#11719919C2412yes—
530#11719919C2412yes—
531C4×Dic53C2412yes—
532C4×Dic53C2413yes—
533C4×Dic53C2416yes—
534C4×Dic53C2416yes—
535C4×Dic53C2416yes—
536C4×Dic53C2416yes—
537C4×Dic53C2416yes—
538C4×Dic53C2416yes—
539C4×Dic53C2416yes—
540C4×Dic53C2411yescharacteristic
541C4×Dic53C2413yes—
542C4×Dic53C2413yes—
543C4×Dic53C24112yes—
544C23×C53C2513yes—
545C22×D53—43no—
546C22×D53—43no—
547C22×D53C22×Q8112yes—
548C22×D53C2513yes—
549C22×D53C2511yescharacteristic
550Q8×C53—412no—
551Q8×C53—46no—
552Q8×C53—42no—
553Q8×C53C22×Q814yes—
554D4×C53C22×Q8112yes—
555C2×C4×C53—46no—
556C2×C4×C53—46no—
557C2×C4×C53—43no—
558C2×C4×C53—43no—
559C2×C4×C53C22×Q8112yes—
560C2×C4×C53C2516yes—
561C2×C4×C53C2512yes—
562C2×C4×C53C2513yes—
563C2×C4×C53C2513yes—
564C2×C4×C53C2516yes—
565C2×C4×C53C2512yes—
566C2×C4×C53C2511yescharacteristic
567C2×C4×C53C2511yescharacteristic
568C2×C4×C53C2513yes—
569C2×C4×C53C2511yescharacteristic
570C22⋊D53C22×Q8124yes—
571C2×Dic53—43no—
572C2×Dic53—46no—
573C2×Dic53—43no—
574C2×Dic53—46no—
575C2×Dic53C22×Q8112yes—
576C2×Dic53C2512yes—
577C2×Dic53C2513yes—
578C2×Dic53C2511yescharacteristic
579C2×Dic53C2516yes—
580C2×Dic53C2512yes—
581C2×Dic53C2513yes—
582C2×Dic53C2516yes—
583C2×Dic53C2511yescharacteristic
584C2×Dic53C2513yes—
585C2×Dic53C2511yescharacteristic
586D212C22×Q8112yes—
587C4×D53—46no—
588C4×D53—412no—
589C4×D53—42no—
590C4×D53—46no—
591C4×D53—46no—
592C4×D53—46no—
593C4×D53—46no—
594C4×D53C22×Q814yes—
595C4×D53C22×Q8112yes—
596C4×D53C22×Q8112yes—
597C4×D53C22×Q8112yes—
598Dic106—46no—
599Dic106—412no—
600Dic106—46no—
601Dic106—42no—
602Dic106—46no—
603Dic106—46no—
604Dic106—46no—
605Dic106C22×Q8112yes—
606#62854—531nomaximal, Sylow
607C22×C53—23no—
608C22×C53—23no—
609C22×C53C23×Q816yes—
610C22×C53C2611yescharacteristic
611C2×D53—23no—
612C2×D53—21no—
613C2×D53—23no—
614C2×D53—21no—
615C2×D53—412no—
616C2×D53C23×Q812yes—
617C2×D53C23×Q816yes—
618C4×C53—26no—
619C4×C53—23no—
620C4×C53—26no—
621C4×C53—21no—
622C4×C53—22no—
623C4×C53—23no—
624C4×C53—22no—
625C4×C53—21no—
626C4×C53C23×Q816yes—
627C4×C53C23×Q812yes—
628Dic53—22no—
629Dic53—23no—
630Dic53—21no—
631Dic53—26no—
632Dic53—22no—
633Dic53—23no—
634Dic53—26no—
635Dic53—21no—
636Dic53C23×Q816yes—
637Dic53C23×Q812yes—
638#3504—532no—
639#3504—536no—
640#3504—533no—
641#3504—533no—
642#3504—531no—
643#3504—531no—
644#3503—532no—
645#3503—536no—
646#3503—533no—
647#3503—533no—
648#3503—531no—
649#3503D5311yescharacteristic, complemented
650#3502—532no—
651#3502—532no—
652#3501—536no—
653#3501—536no—
654#3458—533no—
655#3458—533no—
656C2×#544—533no—
657C2×#544—533no—
658#3428—531no—
659#3428—531no—
660C2×#520—531no—
661C2×C53—26no—
662C2×C53C24×Q811yescharacteristic
663C2×C53H(7,𝔽2)11yescharacteristic
664C2×C532−1+611yescharacteristic
665D53—22no—
666D53—26no—
667C22×#41—531no—
668Q82—536no—
669Q82—536no—
670Q82—532no—
671Q82C2×D5312yescomplemented
672#557—536no—
673#557—536no—
674#557—536no—
675#557—536no—
676#557—532no—
677#557—532no—
678#557—532no—
679#557—532no—
680#557—536no—
681#557—536no—
682#557—532no—
683#557C2×D5312yescomplemented
684#554—536no—
685#554—536no—
686#554—536no—
687#554—536no—
688#554—5312no—
689#554—5312no—
690#554—5312no—
691#554—5312no—
692#554—5312no—
693#554—536no—
694#554—536no—
695#554—536no—
696#554—536no—
697#554—536no—
698#554—536no—
699#554—536no—
700#554—5312no—
701#554C2×D5316yescomplemented
702D4×Q8—5312no—
703D4×Q8—536no—
704D4×Q8—536no—
705D4×Q8—5312no—
706D4×Q8—536no—
707D4×Q8C2×D5316yescomplemented
708#544—536no—
709#544—533no—
710#544—536no—
711#544—536no—
712#544—536no—
713#544—536no—
714#544—536no—
715#544—536no—
716#544—536no—
717#544—531no—
718#544—536no—
719#544—533no—
720#544—533no—
721#544—533no—
722#544—536no—
723#544—533no—
724#544—533no—
725#544—536no—
726#544—533no—
727#544—5312no—
728#544—536no—
729#544—536no—
730#544—533no—
731#544—533no—
732#544—533no—
733#544—533no—
734#544—533no—
735#544—533no—
736#544C2×D5313yescomplemented
737#544C2×D5313yescomplemented
738#543—5312no—
739#543—536no—
740#543—536no—
741#533—536no—
742#533—536no—
743#533—536no—
744#533—536no—
745#533—5312no—
746#533—536no—
747#533—536no—
748#533—536no—
749#533—536no—
750#533—533no—
751#533—533no—
752#533—533no—
753#533C2×D5313yescomplemented
754C2×C4⋊Q8—536no—
755C2×C4⋊Q8—536no—
756C2×C4⋊Q8—536no—
757C2×C4⋊Q8—533no—
758C2×C4⋊Q8C2×D5313yescomplemented
759C2×#125—536no—
760C2×#125—536no—
761C2×#125—536no—
762C2×#125—533no—
763C2×#125—533no—
764C2×C22⋊Q8—536no—
765C2×C22⋊Q8—5312no—
766C2×C22⋊Q8—536no—
767#520—531no—
768#520—531no—
769#520—532no—
770#520—531no—
771#520—531no—
772#520—536no—
773#520—533no—
774#520—533no—
775#520—533no—
776#520—533no—
777#520—533no—
778#520—533no—
779#520C2×D5311yescharacteristic
780#520C2×D5311yescharacteristic
781#519—532no—
782#519—531no—
783#519—531no—
784#518—533no—
785#518—536no—
786#518—533no—
787C4×#41—531no—
788C4×#41—532no—
789C4×#41—536no—
790C4×#41—533no—
791C4×#41—533no—
792C4×#41C2×D5311yescharacteristic
793C2×C4×Q8—532no—
794C2×C4×D4—536no—
795C2×#117—533no—
796C2×#117—533no—
797C2×#117—533no—
798C2×#117—533no—
799C2×#117—533no—
800C22×C4⋊C4—533no—
801C53#6285411yescharacteristic, complemented, Sylow
802C2×#41—5316no—
803C2×#41—531no—
804C2×#41—533no—
805C2×#41—533no—
806C2×#41C22×D5311yescharacteristic
807C22×Q8—531no—
808C22×Q8—5312no—
809C22×Q8—536no—
810C22×Q8C22×D5316yes—
811C22×D4—533no—
812C23×C4—533no—
813C23×C4—536no—
814C4⋊Q8—5312no—
815C4⋊Q8—536no—
816C4⋊Q8—5312no—
817C4⋊Q8—5312no—
818C4⋊Q8—5312no—
819C4⋊Q8—532no—
820C4⋊Q8—536no—
821C4⋊Q8—536no—
822C4⋊Q8—536no—
823C4⋊Q8—536no—
824C4⋊Q8—533no—
825C4⋊Q8—533no—
826C4⋊Q8—5312no—
827C4⋊Q8—536no—
828C4⋊Q8—536no—
829C4⋊Q8—536no—
830C4⋊Q8—536no—
831C4⋊Q8—536no—
832C4⋊Q8—533no—
833C4⋊Q8—531no—
834C4⋊Q8—536no—
835C4⋊Q8—536no—
836C4⋊Q8—536no—
837C4⋊Q8—536no—
838C4⋊Q8—533no—
839C4⋊Q8—536no—
840C4⋊Q8—533no—
841C4⋊Q8—536no—
842C4⋊Q8C22×D5316yes—
843C4⋊Q8C22×D5316yes—
844C4⋊Q8C22×D5313yes—
845C4⋊Q8C22×D5316yes—
846C4⋊Q8C22×D5316yes—
847C4⋊Q8C22×D5316yes—
848C4⋊Q8C22×D5311yescharacteristic
849#125—5312no—
850#125—536no—
851#125—536no—
852#125—533no—
853#125—536no—
854#125—533no—
855#125—5312no—
856#125—5312no—
857#125—5312no—
858#125—5312no—
859#125—536no—
860#125—536no—
861#125—536no—
862#125—536no—
863#125—536no—
864#125—532no—
865#125—531no—
866#125—533no—
867#125—536no—
868#125—536no—
869#125—536no—
870#125—536no—
871#125—536no—
872#125—536no—
873#125—536no—
874#125—533no—
875#125—536no—
876#125—536no—
877#125—536no—
878#125—531no—
879#125—536no—
880#125C22×D5313yes—
881#125C22×D5316yes—
882#125C22×D5313yes—
883#125C22×D5316yes—
884C22⋊Q8—5312no—
885C22⋊Q8—536no—
886C22⋊Q8—5312no—
887C22⋊Q8—5312no—
888C22⋊Q8—532no—
889C22⋊Q8—5312no—
890C22⋊Q8—536no—
891C22⋊Q8—536no—
892C22⋊Q8—5312no—
893C22⋊Q8—5312no—
894C22⋊Q8—536no—
895C22⋊Q8—536no—
896C22⋊Q8—536no—
897C22⋊Q8—5312no—
898C22⋊Q8—536no—
899C22⋊Q8—536no—
900C22⋊Q8—5312no—
901C22⋊Q8—5312no—
902C22⋊Q8—536no—
903C22⋊Q8—532no—
904C22⋊Q8—536no—
905C22⋊Q8—5312no—
906C22⋊Q8—536no—
907C22⋊Q8—536no—
908C22⋊Q8—536no—
909C22⋊Q8—5312no—
910C22⋊Q8—536no—
911C22⋊Q8—536no—
912C22⋊Q8—536no—
913C22⋊Q8—5312no—
914C22⋊Q8—5312no—
915C22⋊Q8—5312no—
916C22⋊Q8—536no—
917C22⋊Q8—536no—
918C22⋊Q8—5312no—
919C22⋊Q8—536no—
920C22⋊Q8—5312no—
921C22⋊Q8—536no—
922C22⋊Q8C22×D53112yes—
923C22⋊Q8C22×D53112yes—
924C22⋊Q8C22×D5316yes—
925C22⋊Q8C22×D5316yes—
926C4×Q8—532no—
927C4×Q8—531no—
928C4×Q8—532no—
929C4×Q8—531no—
930C4×Q8—5312no—
931C4×Q8—536no—
932C4×Q8—533no—
933C4×Q8—533no—
934C4×Q8—536no—
935C4×Q8—5312no—
936C4×Q8—5312no—
937C4×Q8—5312no—
938C4×Q8—536no—
939C4×Q8—536no—
940C4×Q8—533no—
941C4×Q8—533no—
942C4×Q8—536no—
943C4×Q8—536no—
944C4×Q8—536no—
945C4×Q8—536no—
946C4×Q8—536no—
947C4×Q8—536no—
948C4×Q8C22×D5312yes—
949C4×Q8C22×D5312yes—
950C4×Q8C22×D5311yescharacteristic
951C4×Q8C22×D5311yescharacteristic
952C4×Q8C22×D5316yes—
953C4×Q8C22×D5316yes—
954C4×D4—536no—
955C4×D4—533no—
956C4×D4—533no—
957C4×D4—536no—
958C4×D4—5312no—
959C4×D4—5312no—
960C4×D4—536no—
961C4×D4—536no—
962C4×D4—536no—
963C4×D4—533no—
964C4×D4—536no—
965C4×D4—533no—
966C4×D4—5312no—
967C4×D4—536no—
968C4×D4—5312no—
969C4×D4—536no—
970C4×D4—536no—
971C4×D4—533no—
972C4×D4—536no—
973C4×D4—533no—
974C4×D4C22×D5316yes—
975C4×D4C22×D5316yes—
976C4×D4C22×D5313yes—
977C4×D4C22×D5313yes—
978#117—533no—
979#117—533no—
980#117—533no—
981#117—533no—
982#117—531no—
983#117—536no—
984#117—533no—
985#117—536no—
986#117—533no—
987#117—533no—
988#117—536no—
989#117—533no—
990#117—536no—
991#117—536no—
992#117—536no—
993#117—533no—
994#117—531no—
995#117—533no—
996#117—533no—
997#117—536no—
998#117—533no—
999#117—533no—
1000#117—536no—
1001#117—533no—
1002#117—533no—
1003#117C22×D5313yes—
1004#117C22×D5313yes—
1005#117C22×D5313yes—
1006C2×C4⋊C4—536no—
1007C2×C4⋊C4—533no—
1008C2×C4⋊C4—533no—
1009C2×C4⋊C4—533no—
1010C2×C4⋊C4—533no—
1011C2×C4⋊C4—536no—
1012C2×C4⋊C4—536no—
1013C2×C4⋊C4—536no—
1014C2×C4⋊C4—536no—
1015C2×C4⋊C4—536no—
1016C2×C4⋊C4—533no—
1017C2×C4⋊C4—536no—
1018C2×C4⋊C4—536no—
1019C2×C4⋊C4—536no—
1020C2×C4⋊C4—531no—
1021C2×C4⋊C4—533no—
1022C2×C4⋊C4—533no—
1023C2×C4⋊C4—533no—
1024C2×C4⋊C4—533no—
1025C2×C4⋊C4—5312no—
1026C2×C4⋊C4—5312no—
1027C2×C4⋊C4—5312no—
1028C2×C4⋊C4C22×D5313yes—
1029C2×C4⋊C4C22×D5313yes—
1030C2×C4⋊C4C22×D5316yes—
1031C2×C22⋊C4—536no—
1032C2×C22⋊C4—533no—
1033C2×C22⋊C4—533no—
1034C2×C22⋊C4—536no—
1035C2×C22⋊C4—536no—
1036C2×C22⋊C4—536no—
1037C2×C42—536no—
1038C2×C42—533no—
1039C2×C42—536no—
1040C2×C42—536no—
1041C2×C42—536no—
1042C2×C42C22×D5313yes—
1043C24—533no—
1044#41—538no—
1045#41—5324no—
1046#41—5324no—
1047#41Q8×D5318yescomplemented
1048C2×Q8—86no—
1049C2×Q8—538no—
1050C2×Q8—533no—
1051C2×Q8—536no—
1052C2×Q8—532no—
1053C2×Q8—536no—
1054C2×Q8—536no—
1055C2×Q8—5312no—
1056C2×Q8—536no—
1057C2×Q8—536no—
1058C2×Q8—4246no—
1059C2×Q8—42412no—
1060C2×Q8C23×D53112yes—
1061C2×Q8C23×D5312yes—
1062C2×Q8C23×D5316yes—
1063C2×Q8C23×D5311yescharacteristic
1064C2×D4—536no—
1065C2×D4—5324no—
1066C2×D4—533no—
1067C2×D4C23×D5313yes—
1068C22×C4—533no—
1069C22×C4—5324no—
1070C22×C4—533no—
1071C22×C4—533no—
1072C22×C4—533no—
1073C22×C4—531no—
1074C22×C4—533no—
1075C22×C4—536no—
1076C22×C4—533no—
1077C22×C4—536no—
1078C22×C4—532no—
1079C22×C4—536no—
1080C22×C4—536no—
1081C22×C4—536no—
1082C22×C4—536no—
1083C22×C4—536no—
1084C22×C4—5312no—
1085C22×C4—4246no—
1086C22×C4C23×D5316yes—
1087C22×C4C23×D5313yes—
1088C22×C4C23×D5313yes—
1089C22×C4C23×D5316yes—
1090C22×C4C23×D5313yes—
1091C4⋊C4—536no—
1092C4⋊C4—533no—
1093C4⋊C4—533no—
1094C4⋊C4—531no—
1095C4⋊C4—533no—
1096C4⋊C4—533no—
1097C4⋊C4—531no—
1098C4⋊C4—531no—
1099C4⋊C4—5312no—
1100C4⋊C4—536no—
1101C4⋊C4—5312no—
1102C4⋊C4—536no—
1103C4⋊C4—536no—
1104C4⋊C4—536no—
1105C4⋊C4—5312no—
1106C4⋊C4—536no—
1107C4⋊C4—5312no—
1108C4⋊C4—536no—
1109C4⋊C4—536no—
1110C4⋊C4—5312no—
1111C4⋊C4—5312no—
1112C4⋊C4—536no—
1113C4⋊C4—536no—
1114C4⋊C4—536no—
1115C4⋊C4—532no—
1116C4⋊C4—531no—
1117C4⋊C4—533no—
1118C4⋊C4—536no—
1119C4⋊C4—533no—
1120C4⋊C4—536no—
1121C4⋊C4—533no—
1122C4⋊C4—536no—
1123C4⋊C4—533no—
1124C4⋊C4—533no—
1125C4⋊C4—533no—
1126C4⋊C4—532no—
1127C4⋊C4—532no—
1128C4⋊C4—536no—
1129C4⋊C4—532no—
1130C4⋊C4—536no—
1131C4⋊C4—536no—
1132C4⋊C4—536no—
1133C4⋊C4—532no—
1134C4⋊C4—532no—
1135C4⋊C4C23×D5313yes—
1136C4⋊C4C23×D5311yescharacteristic
1137C4⋊C4C23×D5316yes—
1138C4⋊C4C23×D5316yes—
1139C4⋊C4C23×D5316yes—
1140C4⋊C4C23×D5313yes—
1141C4⋊C4C23×D53112yes—
1142C4⋊C4C23×D5311yescharacteristic
1143C4⋊C4C23×D5313yes—
1144C4⋊C4C23×D5313yes—
1145C4⋊C4C23×D5316yes—
1146C4⋊C4C23×D5316yes—
1147C4⋊C4C23×D5316yes—
1148C4⋊C4C23×D5316yes—
1149C4⋊C4C23×D5312yes—
1150C22⋊C4—536no—
1151C22⋊C4—536no—
1152C22⋊C4—536no—
1153C22⋊C4—536no—
1154C22⋊C4—533no—
1155C22⋊C4—531no—
1156C22⋊C4—533no—
1157C22⋊C4—532no—
1158C22⋊C4—531no—
1159C22⋊C4—536no—
1160C22⋊C4—5312no—
1161C22⋊C4—533no—
1162C22⋊C4—533no—
1163C22⋊C4—533no—
1164C22⋊C4—533no—
1165C22⋊C4—536no—
1166C22⋊C4C23×D5316yes—
1167C22⋊C4C23×D5316yes—
1168C22⋊C4C23×D5316yes—
1169C42—536no—
1170C42—532no—
1171C42—531no—
1172C42—533no—
1173C42—536no—
1174C42—5312no—
1175C42—536no—
1176C42—536no—
1177C42—536no—
1178C42—536no—
1179C42—533no—
1180C42—533no—
1181C42—536no—
1182C42C23×D5313yes—
1183C42C23×D5316yes—
1184C42C23×D5316yes—
1185C42C23×D5311yescharacteristic
1186C42C23×D5313yes—
1187C42C23×D5313yes—
1188C23—531no—
1189C23—533no—
1190C23—5312no—
1191C23—2123no—
1192C23—2123no—
1193C23C24×D5313yes—
1194Q8—46no—
1195Q8—412no—
1196Q8—42no—
1197Q8—5312no—
1198Q8—2126no—
1199Q8—2122no—
1200Q8—2126no—
1201Q8—2126no—
1202Q8—2126no—
1203Q8—21212no—
1204Q8—2126no—
1205Q8C2×Q8×D5314yes—
1206D4—5324no—
1207D4—5312no—
1208D4C2×Q8×D53112yes—
1209C2×C4—46no—
1210C2×C4—43no—
1211C2×C4—43no—
1212C2×C4—46no—
1213C2×C4—5312no—
1214C2×C4—533no—
1215C2×C4—531no—
1216C2×C4—534no—
1217C2×C4—5312no—
1218C2×C4—5312no—
1219C2×C4—5312no—
1220C2×C4—532no—
1221C2×C4—533no—
1222C2×C4—536no—
1223C2×C4—531no—
1224C2×C4—532no—
1225C2×C4—533no—
1226C2×C4—531no—
1227C2×C4—536no—
1228C2×C4—2126no—
1229C2×C4—2126no—
1230C2×C4—2122no—
1231C2×C4—2126no—
1232C2×C4—21212no—
1233C2×C4—2126no—
1234C2×C4—2126no—
1235C2×C4—2123no—
1236C2×C4—2126no—
1237C2×C4—2126no—
1238C2×C4—2123no—
1239C2×C4C2×Q8×D53112yes—
1240C2×C4C24×D5312yes—
1241C2×C4C24×D5316yes—
1242C2×C4C24×D5313yes—
1243C2×C4C24×D5313yes—
1244C2×C4C24×D5312yes—
1245C2×C4C24×D5316yes—
1246C2×C4C24×D5311yescharacteristic
1247C2×C4C24×D5311yescharacteristic
1248C2×C4C24×D5313yes—
1249C2×C4C24×D5311yescharacteristic
1250C22—23no—
1251C22—23no—
1252C22—532no—
1253C22—536no—
1254C22—1063no—
1255C22—1061no—
1256C22—1063no—
1257C22—1061no—
1258C22—21212no—
1259C22C22×Q8×D5316yes—
1260C22C25×D5311yescharacteristic
1261C4—21no—
1262C4—26no—
1263C4—26no—
1264C4—23no—
1265C4—21no—
1266C4—23no—
1267C4—22no—
1268C4—22no—
1269C4—532no—
1270C4—536no—
1271C4—1066no—
1272C4—1062no—
1273C4—1063no—
1274C4—1061no—
1275C4—1063no—
1276C4—1066no—
1277C4—1061no—
1278C4—1062no—
1279C4C22×Q8×D5312yes—
1280C4C22×Q8×D5316yes—
1281C2—26no—
1282C2—1062no—
1283C2—1066no—
1284C2C23×Q8×D5311yescharacteristic
1285C2#2028952511yescharacteristic
1286C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3503C2
prime radicalC2×#41×D53C22
hypercenter#3503D53
hypocenterC53#62854
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #20288541C2semidirect
2. #20288540C2semidirect
3. #20288538C2semidirect
4. #20288537C2semidirect
5. #20288536C2semidirect
6. #20288535C2semidirect
7. #20288533C2semidirect
8. #20288531C2semidirect
9. #20288530C2semidirect
10. #20288528C2semidirect
11. #20288526C2semidirect
12. #20288524C2semidirect
13. #20288522C2semidirect
14. #20288514C2semidirect
15. #20288510C2semidirect
16. #20288119C2semidirect
17. #20288118C2semidirect
18. C2×#16811250C2semidirect
19. #544×D53C2semidirect
23. C53×#3503C2semidirect
25. Q8×Dic106C22semidirect
26. #16811353C22semidirect
27. #16811353C22semidirect
28. #16811352C22semidirect
29. #16811351C22semidirect
30. #16811351C22semidirect
31. #16811350C22semidirect
32. #16811350C22semidirect
33. #16811349C22semidirect
34. #16811349C22semidirect
35. #16811349C22semidirect
36. #16811349C22semidirect
37. #16811348C22semidirect
38. #16811348C22semidirect
39. #16811334C22semidirect
40. #16811334C22semidirect
41. #16811333C22semidirect
42. #16811333C22semidirect
43. #16811332C22semidirect
44. #16811332C22semidirect
45. #16811332C22semidirect
46. #16811332C22semidirect
47. #16811331C22semidirect
48. #16811330C22semidirect
49. #16811329C22semidirect
50. #16811329C22semidirect
51. #16811328C22semidirect
52. #16811327C22semidirect
53. #16811327C22semidirect
54. #16811327C22semidirect
55. #16811327C22semidirect
56. D4×Dic106C22semidirect
57. #16811288C22semidirect
58. #16811288C22semidirect
59. Q8×C22⋊D53C22semidirect
60. #16811286C22semidirect
61. #16811254C22semidirect
62. #16811254C22semidirect
66. #16811253C22semidirect
67. #16811253C22semidirect
68. #16811253C22semidirect
69. #16811252C22semidirect
70. #16811252C22semidirect
71. #16811252C22semidirect
72. #16811251C22semidirect
73. #16811251C22semidirect
74. #16811251C22semidirect
75. #16811251C22semidirect
82. #16811250C22semidirect
83. #16811250C22semidirect
84. #16811250C22semidirect
85. #16811250C22semidirect
86. #16811250C22semidirect
87. #16811250C22semidirect
88. #16811250C22semidirect
92. #16811180C22semidirect
94. #16811179C22semidirect
96. #16811178C22semidirect
99. #16811177C22semidirect
100. #16811177C22semidirect
101. #16811176C22semidirect
102. #16811176C22semidirect
103. #16811175C22semidirect
104. C2×#13133216C22semidirect
105. C2×#13133215C22semidirect
106. C4⋊Q8×D53C22semidirect
107. C4⋊Q8×D53C22semidirect
108. C2×#13133209C22semidirect
109. C2×#13133208C22semidirect
110. C2×#13133207C22semidirect
111. #125×D53C22semidirect
112. #125×D53C22semidirect
147. Q82×C53C22semidirect
148. C53×#557C22semidirect
149. C53×#554C22semidirect
150. D4×Q8×C53C22semidirect
151. C53×#544C22semidirect
152. C53×#544C22semidirect
153. C53×#533C22semidirect
154. C2×C4⋊Q8×C53C22semidirect
161. #41×D53Q8semidirect
400. #41×C53C2×Q8semidirect
418. #11719949C2×Q8semidirect
420. Q8×D53C2×Q8semidirect
421. #11719947C2×Q8semidirect
422. D4×D53C2×Q8semidirect
423. #11719945C2×Q8semidirect
426. C2×C4×D53C2×Q8semidirect
649. #3503D53semidirect
671. Q82C2×D53semidirect
683. #557C2×D53semidirect
701. #554C2×D53semidirect
707. D4×Q8C2×D53semidirect
736. #544C2×D53semidirect
737. #544C2×D53semidirect
753. #533C2×D53semidirect
758. C2×C4⋊Q8C2×D53semidirect
801. C53#62854semidirect
1047. #41Q8×D53semidirect

Maximal subgroups

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

subgroupindex
#202885412
#202885402
#202885382
#202885372
#202885362
#202885352
#202885332
#202885312
#202885302
#202885282
#202885262
#202885242
#202885222
#202885142
#202885102
#202881192
#202881182
C2×#168112502
#544×D532
#202879152
#202879142
#520×D532
C53×#35032
#6285453