Finite Group Databasebeta

← D53×#3518 #28292352

Subgroups — D53×#3518 #28292352

Order 13568.

7118 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288733C211yesmaximal, characteristic, complemented
2#20288732C211yesmaximal, characteristic, complemented
3#20288731C213yesmaximal, complemented
4#20288730C213yesmaximal, complemented
5#20288729C213yesmaximal, complemented
6#20288728C216yesmaximal, complemented
7#20288727C211yesmaximal, characteristic, complemented
8#20288726C212yesmaximal, complemented
9#20288725C216yesmaximal, complemented
10#20288724C213yesmaximal, complemented
11#20288723C212yesmaximal, complemented
12Q82×D53C211yesmaximal, characteristic, complemented
13#556×D53C213yesmaximal, complemented
14#556×D53C216yesmaximal, complemented
15#555×D53C213yesmaximal, complemented
16D4×Q8×D53C211yesmaximal, characteristic, complemented
17#548×D53C212yesmaximal, complemented
18#542×D53C216yesmaximal, complemented
19#533×D53C213yesmaximal, complemented
20#529×D53C213yesmaximal, complemented
21#519×D53C212yesmaximal, complemented
22C4×#41×D53C211yesmaximal, characteristic, complemented
23C53×#3518C211yesmaximal, characteristic, complemented
24C2×#41×D53C2211yescharacteristic
25C22×Q8×D53C2212yes—
26Q8×Dic106C2212yescomplemented
27Q8×Dic106C2211yescharacteristic, complemented
28Q8×Dic106C2213yescomplemented
29#16811353C2213yescomplemented
30#16811353C2216yescomplemented
31#16811347C2213yescomplemented
32#16811347C2216yescomplemented
33#16811346C2216yescomplemented
34#16811346C2213yescomplemented
35#16811345C22112yescomplemented
36#16811345C2216yescomplemented
37#16811344C2216yescomplemented
38#16811344C2216yescomplemented
39#16811344C2216yescomplemented
40#16811343C2216yescomplemented
41#16811343C2213yescomplemented
42#16811342C2216yescomplemented
43#16811342C22112yescomplemented
44#16811341C2216yescomplemented
45#16811341C2216yescomplemented
46#16811341C2216yescomplemented
47#16811340C22112yescomplemented
48#16811340C22112yescomplemented
49#16811340C22112yescomplemented
50#16811339C2213yescomplemented
51#16811338C2213yescomplemented
52#16811338C2213yescomplemented
53#16811337C2216yescomplemented
54#16811337C2216yescomplemented
55#16811336C2216yescomplemented
56#16811336C2216yescomplemented
57#16811335C22112yescomplemented
58Q8×D212C2211yescharacteristic, complemented
59D4×Dic106C2213yescomplemented
60#16811288C2213yescomplemented
61Q8×C22⋊D53C2212yescomplemented
62#16811286C2216yescomplemented
63#16811285C2212yescomplemented
64#16811284C2212yescomplemented
65#16811283C2216yescomplemented
66#16811282C2216yescomplemented
67#16811281C2216yescomplemented
68#16811280C2212yescomplemented
69#16811279C2216yescomplemented
70#16811247C2216yescomplemented
71#16811246C2216yescomplemented
72#16811245C2216yescomplemented
73#16811244C2216yescomplemented
74#16811243C22112yescomplemented
75#16811242C2216yescomplemented
76#16811241C22112yescomplemented
77#16811240C2216yescomplemented
78#16811239C22112yescomplemented
79#16811238C2216yescomplemented
80#16811237C22112yescomplemented
81#16811180C2213yescomplemented
82#16811179C2216yescomplemented
83#16811178C2213yescomplemented
84#16811178C2213yescomplemented
85#16811177C2216yescomplemented
86#16811177C2216yescomplemented
87#16811176C2216yescomplemented
88#16811175C2216yescomplemented
89#16811175C2216yescomplemented
90C4⋊Q8×D53C2213yes—
91C4⋊Q8×D53C2213yes—
92C4⋊Q8×D53C2216yes—
93#16811160C2213yescomplemented
94#16811159C2213yescomplemented
95#16811158C2213yescomplemented
96#16811157C2213yescomplemented
97#16811156C2216yescomplemented
98#16811155C2213yescomplemented
99#16811154C2213yescomplemented
100#16811153C2216yescomplemented
101#16811152C2213yescomplemented
102#16811151C2216yescomplemented
103#16811150C2216yescomplemented
104#126×D53C22112yes—
105#126×D53C2216yes—
106#125×D53C2213yes—
107#124×D53C2216yes—
108#124×D53C22112yes—
109#124×D53C2211yescharacteristic
110#123×D53C2216yes—
111C22⋊Q8×D53C2216yes—
112C22⋊Q8×D53C2216yes—
113C22⋊Q8×D53C2213yes—
114C22⋊Q8×D53C2216yes—
115#121×D53C2216yes—
116#121×D53C2213yes—
117#16811101C2212yescomplemented
118#16811100C2216yescomplemented
119#16811100C2216yescomplemented
120#16811099C2212yescomplemented
121#16811099C2216yescomplemented
122#16811099C2216yescomplemented
123#16811099C2212yescomplemented
124#41×Dic53C2211yescharacteristic, complemented
125C4×#11719949C2211yescharacteristic, complemented
126C4×#11719949C2211yescharacteristic, complemented
127C4×#11719945C2213yescomplemented
128#16811091C2213yescomplemented
129C4×#11719947C2213yescomplemented
130C4×#11719947C2213yescomplemented
131C4×Q8×D53C2216yes—
132C4×Q8×D53C2216yes—
133C4×Q8×D53C2216yes—
134C4×Q8×D53C2213yes—
135C4×Q8×D53C2211yescharacteristic
136C4×Q8×D53C2212yes—
137C4×Q8×D53C2211yescharacteristic
138C4×D4×D53C2213yes—
139C4×D4×D53C2216yes—
140C4×D4×D53C2213yes—
141C4×D4×D53C2213yes—
142#117×D53C2216yes—
143#117×D53C2213yes—
144#117×D53C2216yes—
145#117×D53C2216yes—
146C2×C42×D53C2213yes—
147Q82×C53C2211yescharacteristic, complemented
148C53×#556C2216yescomplemented
149C53×#556C2213yescomplemented
150C53×#555C2213yescomplemented
151D4×Q8×C53C2211yescharacteristic, complemented
152C53×#548C2212yescomplemented
153C53×#542C2216yescomplemented
154C53×#533C2213yescomplemented
155C53×#529C2213yescomplemented
156C53×#519C2212yescomplemented
157C4×#41×C53C2211yescharacteristic, complemented
158C2×#11719949C2311yescharacteristic
159C2×#11719945C2313yes—
160C2×#11719947C2313yes—
161#41×D53—28no—
162C22×Dic106C2316yes—
163C2×Q8×D53—216no—
164C2×Q8×D53C2312yes—
165C2×Q8×D53C2316yes—
166C2×Q8×D53C2311yescharacteristic
167C2×Q8×D53C2316yes—
168C2×Q8×D53C2316yes—
169C2×Q8×D53C2311yescharacteristic
170C2×D4×D53C2311yescharacteristic
171C2×D4×D53C2313yes—
172C2×D4×D53C2316yes—
173C22×C4×D53C2313yes—
174C22×C4×D53C2313yes—
175C22×C4×D53C2316yes—
176C22×C4×D53C2313yes—
177#13133217C2313yes—
178#13133217C2313yes—
179#13133217C2316yes—
180#13133216C2316yes—
181#13133216C2316yes—
182#13133216C2316yes—
183#13133216C2316yes—
184#13133216C23112yes—
185#13133216C2316yes—
186#13133216C2316yes—
187#13133215C2316yes—
188#13133215C2316yes—
189#13133215C23112yes—
190#13133212C2316yes—
191#13133212C23112yes—
192#13133212C2316yes—
193#13133212C23112yes—
194#13133212C23112yes—
195#13133212C2316yes—
196#13133211C2316yes—
197#13133211C23112yes—
198#13133210C2316yes—
199#13133210C23112yes—
200#13133210C23112yes—
201#13133210C2316yes—
202#13133210C23112yes—
203#13133210C2316yes—
204#13133209C2313yes—
205#13133208C2313yes—
206#13133208C2313yes—
207#13133207C2316yes—
208#13133207C2316yes—
209#13133206C2316yes—
210#13133206C23112yes—
211#13133206C2311yescharacteristic
212#13133205C2316yes—
213#13133205C23112yes—
214#13133205C2311yescharacteristic
215#13133204C2316yes—
216#13133204C23112yes—
217#13133204C2311yescharacteristic
218#13133203C23112yes—
219#13133203C23112yes—
220#13133203C23112yes—
221#13133203C23112yes—
222#13133203C23112yes—
223#13133203C23112yes—
224#13133203C2312yes—
225#13133203C2312yes—
226#13133202C2316yes—
227#13133202C2316yes—
228#13133201C2316yes—
229#13133200C2316yes—
230#13133199C2316yes—
231#13133199C2316yes—
232#13133198C2316yes—
233#13133197C2316yes—
234#13133197C2316yes—
235#13133197C2313yes—
236#13133197C2316yes—
237#13133196C2316yes—
238#13133196C2316yes—
239#13133196C2313yes—
240#13133196C2316yes—
241#13133195C23112yes—
242#13133195C23112yes—
243#13133195C2316yes—
244#13133195C23112yes—
245#13133194C23112yes—
246#13133194C23112yes—
247#13133194C2316yes—
248#13133194C23112yes—
249#13133193C2316yes—
250#13133193C2316yes—
251#13133193C2313yes—
252#13133193C2316yes—
253#13133192C2316yes—
254#13133192C2313yes—
255#13133191C2316yes—
256#13133191C2313yes—
257#13133190C23112yes—
258#13133190C2316yes—
259#13133189C23112yes—
260#13133189C2316yes—
261#13133188C2316yes—
262#13133188C2313yes—
263Q8×Dic53C2312yes—
264Q8×Dic53C2311yescharacteristic
265Q8×Dic53C2316yes—
266Q8×Dic53C2316yes—
267Q8×Dic53C2313yes—
268Q8×Dic53C2311yescharacteristic
269Q8×Dic53C2316yes—
270C4×Dic106C2316yes—
271C4×Dic106C2313yes—
272C4×Dic106C2316yes—
273C4×Dic106C23112yes—
274C4×Dic106C23112yes—
275C4×Dic106C2316yes—
276C4×Dic106C2316yes—
277C4×Dic106C2313yes—
278C4×Dic106C2313yes—
279C4×Dic106C23112yes—
280C4×Dic106C2316yes—
281#13133182C2316yes—
282#13133182C2313yes—
283#13133182C23112yes—
284#13133182C2316yes—
285#13133182C2316yes—
286#13133182C23112yes—
287#13133182C2316yes—
288#13133182C2313yes—
289#13133182C2313yes—
290#13133182C2316yes—
291#13133182C23112yes—
292C4×D212C2316yes—
293C4×D212C2313yes—
294C4×D212C2313yes—
295C4×D212C2313yes—
296D4×Dic53C2316yes—
297D4×Dic53C2313yes—
298D4×Dic53C2313yes—
299D4×Dic53C2313yes—
300#13133179C2316yes—
301#13133179C2313yes—
302#13133179C2313yes—
303#13133179C2313yes—
304C4×C22⋊D53C2316yes—
305C4×C22⋊D53C2316yes—
306C4×C22⋊D53C2316yes—
307C4×C22⋊D53C2316yes—
308C4×C22⋊D53C2316yes—
309#13133177C2316yes—
310#13133177C2316yes—
311#13133177C2316yes—
312#13133177C2316yes—
313#13133177C2316yes—
314#13133176C2316yes—
315#13133176C2316yes—
316#13133176C2313yes—
317#13133176C2316yes—
318#13133175C2316yes—
319#13133175C2316yes—
320#13133175C2316yes—
321#13133175C2316yes—
322#13133175C2313yes—
323#13133175C2313yes—
324#13133175C2316yes—
325#13133175C2316yes—
326#13133174C23112yes—
327#13133174C23112yes—
328#13133174C2316yes—
329#13133174C2316yes—
330#13133174C2316yes—
331#13133173C23112yes—
332#13133173C23112yes—
333#13133173C2316yes—
334#13133173C2316yes—
335#13133173C2316yes—
336C4⋊C4×D53C2313yes—
337C4⋊C4×D53C2313yes—
338C4⋊C4×D53C2313yes—
339C4⋊C4×D53C2313yes—
340C4⋊C4×D53C2316yes—
341C4⋊C4×D53C2316yes—
342C4⋊C4×D53C2316yes—
343C4⋊C4×D53C2316yes—
344C4⋊C4×D53C2316yes—
345C4⋊C4×D53C2316yes—
346C22⋊C4×D53C2316yes—
347C22⋊C4×D53C2312yes—
348C22⋊C4×D53C2316yes—
349C22⋊C4×D53C23112yes—
350C22⋊C4×D53C2312yes—
351C22⋊C4×D53C2316yes—
352C22⋊C4×D53C2316yes—
353C2×C4×Dic53C2313yes—
354C2×C4×Dic53C2313yes—
355C2×C4×Dic53C2313yes—
356C42×D53C2311yescharacteristic
357C42×D53C2313yes—
358C42×D53C2313yes—
359C42×D53C2313yes—
360C42×D53C2313yes—
361C42×D53C2313yes—
362C42×D53C2313yes—
363C42×D53C2313yes—
364C42×D53C23112yes—
365C42×D53C2316yes—
366C2×#41×C53C2311yescharacteristic
367C22×Q8×C53C2312yes—
368C4⋊Q8×C53C2313yes—
369C4⋊Q8×C53C2313yes—
370C4⋊Q8×C53C2316yes—
371#126×C53C2316yes—
372#126×C53C23112yes—
373#125×C53C2313yes—
374#124×C53C2316yes—
375#124×C53C2311yescharacteristic
376#124×C53C23112yes—
377#123×C53C2316yes—
378C22⋊Q8×C53C2316yes—
379C22⋊Q8×C53C2316yes—
380C22⋊Q8×C53C2313yes—
381C22⋊Q8×C53C2316yes—
382#121×C53C2316yes—
383#121×C53C2313yes—
384C4×Q8×C53C2312yes—
385C4×Q8×C53C2311yescharacteristic
386C4×Q8×C53C2311yescharacteristic
387C4×Q8×C53C2316yes—
388C4×Q8×C53C2316yes—
389C4×Q8×C53C2313yes—
390C4×Q8×C53C2316yes—
391C4×D4×C53C2316yes—
392C4×D4×C53C2313yes—
393C4×D4×C53C2313yes—
394C4×D4×C53C2313yes—
395#117×C53C2313yes—
396#117×C53C2316yes—
397#117×C53C2316yes—
398#117×C53C2316yes—
399C2×C42×C53C2313yes—
400C23×D53C2412yes—
401C23×D53C2413yes—
402#41×C53—24no—
403C2×Q8×C53—28no—
404C2×Q8×C53C2411yescharacteristic
405C2×Q8×C53C2416yes—
406C2×Q8×C53C2416yes—
407C2×Q8×C53C2411yescharacteristic
408C2×D4×C53C2411yescharacteristic
409C2×D4×C53C2413yes—
410C2×D4×C53C2416yes—
411C22×C4×C53C2413yes—
412C22×C4×C53C2413yes—
413C22×C4×C53C2416yes—
414C22×C4×C53C2413yes—
415C2×C22⋊D53C2412yes—
416C2×C22⋊D53C2416yes—
417C2×C22⋊D53C2416yes—
418C2×C22⋊D53C2416yes—
419C22×Dic53C2413yes—
420C22×Dic53C2413yes—
421C22×Dic53C2416yes—
422C22×Dic53C2413yes—
423#11719949—24no—
424Q8×D53—28no—
425Q8×D53—224no—
426Q8×D53—24no—
427Q8×D53—224no—
428Q8×D53—412no—
429Q8×D53#4118yes—
430#11719947—212no—
431D4×D53—212no—
432D4×D53—24no—
433D4×D53—412no—
434#11719945—212no—
435C2×D212C2411yescharacteristic
436C2×D212C2413yes—
437C2×D212C2416yes—
438C2×C4×D53—224no—
439C2×C4×D53—212no—
440C2×C4×D53—212no—
441C2×C4×D53—46no—
442C2×C4×D53C2413yes—
443C2×C4×D53C2411yescharacteristic
444C2×C4×D53C2411yescharacteristic
445C2×C4×D53C2412yes—
446C2×C4×D53C2416yes—
447C2×C4×D53C2416yes—
448C2×C4×D53C2413yes—
449C2×C4×D53C2413yes—
450C2×C4×D53C2413yes—
451C2×C4×D53C2413yes—
452C2×C4×D53C2413yes—
453C2×C4×D53C2416yes—
454C2×C4×D53C2416yes—
455C2×C4×D53C2413yes—
456C2×C4×D53C2413yes—
457C2×C4×D53C2413yes—
458C2×C4×D53C2411yescharacteristic
459C2×Dic106—224no—
460C2×Dic106C2412yes—
461C2×Dic106C2411yescharacteristic
462C2×Dic106C24112yes—
463C2×Dic106C2416yes—
464C2×Dic106C24112yes—
465C2×Dic106C2416yes—
466C2×Dic106C2413yes—
467C4⋊C4×C53C2413yes—
468C4⋊C4×C53C2413yes—
469C4⋊C4×C53C2413yes—
470C4⋊C4×C53C2413yes—
471C4⋊C4×C53C2416yes—
472C4⋊C4×C53C2416yes—
473C4⋊C4×C53C2416yes—
474C4⋊C4×C53C2416yes—
475C4⋊C4×C53C2416yes—
476C4⋊C4×C53C2416yes—
477C22⋊C4×C53C2416yes—
478C22⋊C4×C53C2412yes—
479C22⋊C4×C53C2416yes—
480C22⋊C4×C53C24112yes—
481C22⋊C4×C53C2412yes—
482C22⋊C4×C53C2416yes—
483C22⋊C4×C53C2416yes—
484C42×C53C2411yescharacteristic
485C42×C53C2413yes—
486C42×C53C2413yes—
487C42×C53C2413yes—
488C42×C53C24112yes—
489C42×C53C2416yes—
490C22⋊Dic53C2416yes—
491C22⋊Dic53C2412yes—
492C22⋊Dic53C2416yes—
493C22⋊Dic53C24112yes—
494C22⋊Dic53C2412yes—
495C22⋊Dic53C2416yes—
496C22⋊Dic53C2416yes—
497#11719921C2416yes—
498#11719921C2416yes—
499#11719921C2412yes—
500#11719921C2412yes—
501#11719921C2416yes—
502#11719921C2416yes—
503#11719921C24112yes—
504#11719921C24112yes—
505#11719921C2412yes—
506#11719921C2416yes—
507#11719921C2416yes—
508#11719921C2412yes—
509#11719921C2416yes—
510#11719921C2416yes—
511C4⋊Dic53C2413yes—
512C4⋊Dic53C2413yes—
513C4⋊Dic53C2413yes—
514C4⋊Dic53C2413yes—
515C4⋊Dic53C2416yes—
516C4⋊Dic53C2416yes—
517C4⋊Dic53C2416yes—
518C4⋊Dic53C2416yes—
519C4⋊Dic53C2416yes—
520C4⋊Dic53C2416yes—
521#11719919C2416yes—
522#11719919C2416yes—
523#11719919C2416yes—
524#11719919C2416yes—
525#11719919C24112yes—
526#11719919C2416yes—
527#11719919C2416yes—
528#11719919C2416yes—
529#11719919C2416yes—
530#11719919C2416yes—
531#11719919C2416yes—
532#11719919C24112yes—
533#11719919C2416yes—
534#11719919C2416yes—
535C4×Dic53C2411yescharacteristic
536C4×Dic53C2411yescharacteristic
537C4×Dic53C2411yescharacteristic
538C4×Dic53C2413yes—
539C4×Dic53C2413yes—
540C4×Dic53C2413yes—
541C4×Dic53C2413yes—
542C4×Dic53C2413yes—
543C4×Dic53C2413yes—
544C4×Dic53C2413yes—
545C4×Dic53C2413yes—
546C4×Dic53C2413yes—
547C4×Dic53C24112yes—
548C4×Dic53C24112yes—
549C4×Dic53C24112yes—
550C4×Dic53C2416yes—
551C4×Dic53C2416yes—
552C4×Dic53C2416yes—
553C23×C53C2512yes—
554C23×C53C2513yes—
555C22×D53—24no—
556C22×D53—26no—
557C22×D53—26no—
558C22×D53—24no—
559C22×D53—26no—
560C22×D53—24no—
561C22×D53C2512yes—
562C22×D53C2513yes—
563C22×D53C2511yescharacteristic
564Q8×C53—212no—
565Q8×C53—22no—
566Q8×C53—46no—
567Q8×C53C2×#4114yes—
568D4×C53—26no—
569D4×C53—22no—
570D4×C53—46no—
571C2×C4×C53—212no—
572C2×C4×C53—26no—
573C2×C4×C53—26no—
574C2×C4×C53—43no—
575C2×C4×C53C2516yes—
576C2×C4×C53C2513yes—
577C2×C4×C53C2516yes—
578C2×C4×C53C2512yes—
579C2×C4×C53C2511yescharacteristic
580C2×C4×C53C2511yescharacteristic
581C2×C4×C53C2513yes—
582C2×C4×C53C2513yes—
583C2×C4×C53C2511yescharacteristic
584C22⋊D53—212no—
585C22⋊D53—24no—
586C22⋊D53—46no—
587C22⋊D53—46no—
588C2×Dic53—212no—
589C2×Dic53—26no—
590C2×Dic53—26no—
591C2×Dic53—43no—
592C2×Dic53C2516yes—
593C2×Dic53C2513yes—
594C2×Dic53C2516yes—
595C2×Dic53C2512yes—
596C2×Dic53C2511yescharacteristic
597C2×Dic53C2511yescharacteristic
598C2×Dic53C2513yes—
599C2×Dic53C2513yes—
600C2×Dic53C2511yescharacteristic
601D212—26no—
602D212—22no—
603D212—46no—
604C4×D53—22no—
605C4×D53—212no—
606C4×D53—26no—
607C4×D53—24no—
608C4×D53—22no—
609C4×D53—26no—
610C4×D53—212no—
611C4×D53—26no—
612C4×D53—212no—
613C4×D53—26no—
614C4×D53—26no—
615C4×D53—212no—
616C4×D53—26no—
617C4×D53—43no—
618C4×D53—43no—
619C4×D53C2×#41112yes—
620C4×D532−1+414yes—
621Dic106—212no—
622Dic106—22no—
623Dic106—224no—
624Dic106—24no—
625Dic106—412no—
626Dic106—46no—
627Dic106C2×#41112yes—
628C2×#3518—531nomaximal, Sylow
629C22×C53—22no—
630C22×C53—23no—
631C22×C53—23no—
632C22×C53—22no—
633C22×C53—23no—
634C22×C53—22no—
635C22×C53C2611yescharacteristic
636C2×D53—22no—
637C2×D53—23no—
638C2×D53—23no—
639C2×D53—22no—
640C2×D53—23no—
641C2×D53—22no—
642C2×D53—48no—
643C2×D53—412no—
644C2×D53C22×#4112yes—
645C2×D53C2×2−1+412yes—
646C2×D53#58512yes—
647C4×C53—26no—
648C4×C53—21no—
649C4×C53—22no—
650C4×C53—23no—
651C4×C53—23no—
652C4×C53—26no—
653C4×C53—21no—
654C4×C53C22×#4116yes—
655C4×C53C2×2−1+412yes—
656Dic53—26no—
657Dic53—21no—
658Dic53—22no—
659Dic53—23no—
660Dic53—23no—
661Dic53—26no—
662Dic53—21no—
663Dic53C22×#4116yes—
664Dic53C2×2−1+412yes—
665#3518—531no—
666#3518—536no—
667#3518—533no—
668#3518—533no—
669#3518—531no—
670#3518—532no—
671#3518—536no—
672#3518—533no—
673#3518—533no—
674#3518—532no—
675#3518—531no—
676#3518D5311yescharacteristic, direct product factor
677C2×Q82—531no—
678C2×#556—536no—
679C2×#556—533no—
680C2×#555—533no—
681C2×D4×Q8—531no—
682C2×#548—532no—
683C2×#542—536no—
684C2×#533—533no—
685C2×#529—533no—
686C2×#519—532no—
687C2×C4×#41—531no—
688C2×C53—42no—
689C2×C53—43no—
690C2×C53C23×#4111yescharacteristic
691C2×C53C22×2−1+411yescharacteristic
692C2×C53C2×#58511yescharacteristic
693D53—42no—
694D53—43no—
695D53#351814yesdirect product factor
696C22×#41—531no—
697C23×Q8—532no—
698Q82—536no—
699Q82—533no—
700Q82—532no—
701Q82—531no—
702Q82—533no—
703Q82C2×D5311yescharacteristic, complemented
704#556—536no—
705#556—533no—
706#556—5312no—
707#556—5312no—
708#556—5312no—
709#556—5312no—
710#556—536no—
711#556—536no—
712#556—536no—
713#556—536no—
714#556—5312no—
715#556—536no—
716#556—536no—
717#556—533no—
718#556—536no—
719#556—533no—
720#556—536no—
721#556—536no—
722#556—536no—
723#556C2×D5316yescomplemented
724#556C2×D5313yescomplemented
725#555—533no—
726#555—5312no—
727#555—536no—
728#555—536no—
729#555—533no—
730#555—533no—
731#555—536no—
732#555—536no—
733#555C2×D5313yescomplemented
734D4×Q8—532no—
735D4×Q8—533no—
736D4×Q8—536no—
737D4×Q8—531no—
738D4×Q8—533no—
739D4×Q8C2×D5311yescharacteristic, complemented
740#548—532no—
741#548—532no—
742#548—536no—
743#548—536no—
744#548—536no—
745#548—532no—
746#548—536no—
747#548C2×D5312yescomplemented
748#542—536no—
749#542—5312no—
750#542—5312no—
751#542—536no—
752#542—5312no—
753#542—5312no—
754#542—536no—
755#542—536no—
756#542—536no—
757#542—536no—
758#542—536no—
759#542C2×D5316yescomplemented
760#533—533no—
761#533—533no—
762#533—536no—
763#533—536no—
764#533—536no—
765#533—536no—
766#533—536no—
767#533—536no—
768#533—533no—
769#533C2×D5313yescomplemented
770C2×C4⋊Q8—533no—
771C2×C4⋊Q8—533no—
772C2×C4⋊Q8—536no—
773#529—536no—
774#529—533no—
775#529—533no—
776#529—536no—
777#529—533no—
778#529—533no—
779#529—533no—
780#529—536no—
781#529—533no—
782#529—536no—
783#529—533no—
784#529C2×D5313yescomplemented
785C2×#126—536no—
786C2×#126—5312no—
787C2×#125—533no—
788C2×#124—531no—
789C2×#124—536no—
790C2×#124—5312no—
791C2×#123—536no—
792C2×C22⋊Q8—533no—
793C2×C22⋊Q8—536no—
794C2×C22⋊Q8—536no—
795C2×C22⋊Q8—536no—
796C2×#121—533no—
797C2×#121—536no—
798#519—532no—
799#519—536no—
800#519—536no—
801#519—532no—
802#519—532no—
803#519—536no—
804#519—536no—
805#519C2×D5312yescomplemented
806C4×#41—531no—
807C4×#41—531no—
808C4×#41—531no—
809C4×#41—533no—
810C4×#41—533no—
811C4×#41—533no—
812C4×#41—533no—
813C4×#41C2×D5311yescharacteristic, complemented
814C2×C4×Q8—531no—
815C2×C4×Q8—531no—
816C2×C4×Q8—536no—
817C2×C4×Q8—532no—
818C2×C4×Q8—536no—
819C2×C4×Q8—533no—
820C2×C4×Q8—536no—
821C2×C4×D4—533no—
822C2×C4×D4—533no—
823C2×C4×D4—536no—
824C2×C4×D4—533no—
825C2×#117—533no—
826C2×#117—536no—
827C2×#117—536no—
828C2×#117—536no—
829C22×C42—533no—
830C53C2×#351811yescharacteristic, complemented, Sylow
831C2×#41—531no—
832C2×#41—533no—
833C2×#41—533no—
834C2×#41—1068no—
835C2×#41C22×D5311yescharacteristic
836C22×Q8—531no—
837C22×Q8—531no—
838C22×Q8—536no—
839C22×Q8—536no—
840C22×Q8—532no—
841C22×Q8—536no—
842C22×Q8—536no—
843C22×Q8—10616no—
844C22×Q8C22×D5312yes—
845C22×D4—531no—
846C22×D4—533no—
847C22×D4—536no—
848C23×C4—536no—
849C23×C4—533no—
850C23×C4—533no—
851C23×C4—533no—
852C4⋊Q8—536no—
853C4⋊Q8—536no—
854C4⋊Q8—5312no—
855C4⋊Q8—536no—
856C4⋊Q8—536no—
857C4⋊Q8—536no—
858C4⋊Q8—536no—
859C4⋊Q8—5312no—
860C4⋊Q8—536no—
861C4⋊Q8—536no—
862C4⋊Q8—533no—
863C4⋊Q8—533no—
864C4⋊Q8—536no—
865C4⋊Q8C22×D5313yes—
866C4⋊Q8C22×D5313yes—
867C4⋊Q8C22×D5316yes—
868#126—536no—
869#126—536no—
870#126—536no—
871#126—5312no—
872#126—5312no—
873#126—5312no—
874#126—536no—
875#126—536no—
876#126—536no—
877#126—5312no—
878#126—5312no—
879#126—5312no—
880#126—536no—
881#126—5312no—
882#126C22×D5316yes—
883#126C22×D53112yes—
884#125—536no—
885#125—536no—
886#125—533no—
887#125—533no—
888#125—533no—
889#125C22×D5313yes—
890#124—531no—
891#124—536no—
892#124—5312no—
893#124—531no—
894#124—536no—
895#124—5312no—
896#124—532no—
897#124—532no—
898#124—5312no—
899#124—5312no—
900#124—5312no—
901#124—5312no—
902#124—5312no—
903#124—5312no—
904#124—531no—
905#124—536no—
906#124—5312no—
907#124C22×D5311yescharacteristic
908#124C22×D5316yes—
909#124C22×D53112yes—
910#123—536no—
911#123—536no—
912#123—536no—
913#123—536no—
914#123—536no—
915#123—536no—
916#123—536no—
917#123C22×D5316yes—
918C22⋊Q8—533no—
919C22⋊Q8—536no—
920C22⋊Q8—536no—
921C22⋊Q8—536no—
922C22⋊Q8—533no—
923C22⋊Q8—536no—
924C22⋊Q8—536no—
925C22⋊Q8—536no—
926C22⋊Q8—536no—
927C22⋊Q8—533no—
928C22⋊Q8—5312no—
929C22⋊Q8—536no—
930C22⋊Q8—5312no—
931C22⋊Q8—536no—
932C22⋊Q8—5312no—
933C22⋊Q8—536no—
934C22⋊Q8—536no—
935C22⋊Q8—5312no—
936C22⋊Q8—5312no—
937C22⋊Q8—5312no—
938C22⋊Q8C22×D5313yes—
939C22⋊Q8C22×D5316yes—
940C22⋊Q8C22×D5316yes—
941C22⋊Q8C22×D5316yes—
942#121—533no—
943#121—536no—
944#121—536no—
945#121—5312no—
946#121—533no—
947#121—536no—
948#121—533no—
949#121—536no—
950#121—536no—
951#121—5312no—
952#121C22×D5313yes—
953#121C22×D5316yes—
954C4×Q8—531no—
955C4×Q8—531no—
956C4×Q8—536no—
957C4×Q8—532no—
958C4×Q8—536no—
959C4×Q8—533no—
960C4×Q8—536no—
961C4×Q8—533no—
962C4×Q8—533no—
963C4×Q8—5312no—
964C4×Q8—536no—
965C4×Q8—536no—
966C4×Q8—5312no—
967C4×Q8—536no—
968C4×Q8—536no—
969C4×Q8—533no—
970C4×Q8—536no—
971C4×Q8—5312no—
972C4×Q8—533no—
973C4×Q8—533no—
974C4×Q8—5312no—
975C4×Q8—536no—
976C4×Q8—536no—
977C4×Q8—536no—
978C4×Q8—5312no—
979C4×Q8—536no—
980C4×Q8—533no—
981C4×Q8—5312no—
982C4×Q8—536no—
983C4×Q8C22×D5311yescharacteristic
984C4×Q8C22×D5311yescharacteristic
985C4×Q8C22×D5316yes—
986C4×Q8C22×D5312yes—
987C4×Q8C22×D5316yes—
988C4×Q8C22×D5313yes—
989C4×Q8C22×D5316yes—
990C4×D4—533no—
991C4×D4—533no—
992C4×D4—536no—
993C4×D4—533no—
994C4×D4—536no—
995C4×D4—536no—
996C4×D4—536no—
997C4×D4—536no—
998C4×D4—536no—
999C4×D4—533no—
1000C4×D4—533no—
1001C4×D4—536no—
1002C4×D4—533no—
1003C4×D4—536no—
1004C4×D4—536no—
1005C4×D4—536no—
1006C4×D4—536no—
1007C4×D4—536no—
1008C4×D4—533no—
1009C4×D4—533no—
1010C4×D4—536no—
1011C4×D4—533no—
1012C4×D4C22×D5313yes—
1013C4×D4C22×D5313yes—
1014C4×D4C22×D5316yes—
1015C4×D4C22×D5313yes—
1016#117—533no—
1017#117—536no—
1018#117—536no—
1019#117—536no—
1020#117—533no—
1021#117—533no—
1022#117—536no—
1023#117—536no—
1024#117—536no—
1025#117—536no—
1026#117—536no—
1027#117—536no—
1028#117—536no—
1029#117—536no—
1030#117—536no—
1031#117—5312no—
1032#117—5312no—
1033#117—536no—
1034#117—536no—
1035#117—536no—
1036#117—5312no—
1037#117—5312no—
1038#117C22×D5313yes—
1039#117C22×D5316yes—
1040#117C22×D5316yes—
1041#117C22×D5316yes—
1042C2×C4⋊C4—533no—
1043C2×C4⋊C4—533no—
1044C2×C4⋊C4—533no—
1045C2×C4⋊C4—533no—
1046C2×C4⋊C4—536no—
1047C2×C4⋊C4—536no—
1048C2×C4⋊C4—536no—
1049C2×C4⋊C4—536no—
1050C2×C4⋊C4—536no—
1051C2×C4⋊C4—536no—
1052C2×C22⋊C4—536no—
1053C2×C22⋊C4—532no—
1054C2×C22⋊C4—536no—
1055C2×C22⋊C4—5312no—
1056C2×C22⋊C4—532no—
1057C2×C22⋊C4—536no—
1058C2×C22⋊C4—536no—
1059C2×C42—533no—
1060C2×C42—533no—
1061C2×C42—533no—
1062C2×C42—533no—
1063C2×C42—5312no—
1064C2×C42—533no—
1065C2×C42—536no—
1066C2×C42—533no—
1067C2×C42—533no—
1068C2×C42—533no—
1069C2×C42—533no—
1070C2×C42—533no—
1071C2×C42—531no—
1072C2×C42C22×D5313yes—
1073C24—532no—
1074C24—533no—
1075#41—24no—
1076#41—10612no—
1077#41—10612no—
1078#41—1064no—
1079C2×Q8—28no—
1080C2×Q8—538no—
1081C2×Q8—533no—
1082C2×Q8—532no—
1083C2×Q8—531no—
1084C2×Q8—5312no—
1085C2×Q8—536no—
1086C2×Q8—536no—
1087C2×Q8—5312no—
1088C2×Q8—10624no—
1089C2×Q8—1064no—
1090C2×Q8—10624no—
1091C2×Q8—10624no—
1092C2×Q8—1068no—
1093C2×Q8—21212no—
1094C2×Q8C23×D5311yescharacteristic
1095C2×Q8C23×D5316yes—
1096C2×Q8C23×D5316yes—
1097C2×Q8C23×D5311yescharacteristic
1098C2×D4—532no—
1099C2×D4—536no—
1100C2×D4—536no—
1101C2×D4—536no—
1102C2×D4—531no—
1103C2×D4—533no—
1104C2×D4—536no—
1105C2×D4—1064no—
1106C2×D4—10612no—
1107C2×D4—21212no—
1108C2×D4C23×D5311yescharacteristic
1109C2×D4C23×D5313yes—
1110C2×D4C23×D5316yes—
1111C22×C4—531no—
1112C22×C4—533no—
1113C22×C4—533no—
1114C22×C4—533no—
1115C22×C4—536no—
1116C22×C4—533no—
1117C22×C4—533no—
1118C22×C4—531no—
1119C22×C4—531no—
1120C22×C4—532no—
1121C22×C4—536no—
1122C22×C4—536no—
1123C22×C4—533no—
1124C22×C4—533no—
1125C22×C4—533no—
1126C22×C4—533no—
1127C22×C4—533no—
1128C22×C4—536no—
1129C22×C4—536no—
1130C22×C4—533no—
1131C22×C4—533no—
1132C22×C4—10612no—
1133C22×C4—10624no—
1134C22×C4—10612no—
1135C22×C4—2126no—
1136C22×C4C23×D5313yes—
1137C22×C4C23×D5313yes—
1138C22×C4C23×D5316yes—
1139C22×C4C23×D5313yes—
1140C4⋊C4—536no—
1141C4⋊C4—533no—
1142C4⋊C4—536no—
1143C4⋊C4—533no—
1144C4⋊C4—536no—
1145C4⋊C4—533no—
1146C4⋊C4—536no—
1147C4⋊C4—533no—
1148C4⋊C4—5312no—
1149C4⋊C4—536no—
1150C4⋊C4—536no—
1151C4⋊C4—536no—
1152C4⋊C4—536no—
1153C4⋊C4—536no—
1154C4⋊C4—536no—
1155C4⋊C4—536no—
1156C4⋊C4—536no—
1157C4⋊C4—536no—
1158C4⋊C4—536no—
1159C4⋊C4—5312no—
1160C4⋊C4—536no—
1161C4⋊C4—536no—
1162C4⋊C4—536no—
1163C4⋊C4—536no—
1164C4⋊C4C23×D5313yes—
1165C4⋊C4C23×D5313yes—
1166C4⋊C4C23×D5313yes—
1167C4⋊C4C23×D5313yes—
1168C4⋊C4C23×D5316yes—
1169C4⋊C4C23×D5316yes—
1170C4⋊C4C23×D5316yes—
1171C4⋊C4C23×D5316yes—
1172C4⋊C4C23×D5316yes—
1173C4⋊C4C23×D5316yes—
1174C22⋊C4—536no—
1175C22⋊C4—532no—
1176C22⋊C4—536no—
1177C22⋊C4—5312no—
1178C22⋊C4—532no—
1179C22⋊C4—536no—
1180C22⋊C4—536no—
1181C22⋊C4—536no—
1182C22⋊C4—536no—
1183C22⋊C4—532no—
1184C22⋊C4—532no—
1185C22⋊C4—536no—
1186C22⋊C4—536no—
1187C22⋊C4—5312no—
1188C22⋊C4—5312no—
1189C22⋊C4—532no—
1190C22⋊C4—532no—
1191C22⋊C4—536no—
1192C22⋊C4—536no—
1193C22⋊C4—536no—
1194C22⋊C4—536no—
1195C22⋊C4C23×D5316yes—
1196C22⋊C4C23×D5312yes—
1197C22⋊C4C23×D5316yes—
1198C22⋊C4C23×D53112yes—
1199C22⋊C4C23×D5312yes—
1200C22⋊C4C23×D5316yes—
1201C22⋊C4C23×D5316yes—
1202C42—531no—
1203C42—531no—
1204C42—531no—
1205C42—533no—
1206C42—533no—
1207C42—533no—
1208C42—533no—
1209C42—533no—
1210C42—533no—
1211C42—533no—
1212C42—533no—
1213C42—533no—
1214C42—5312no—
1215C42—5312no—
1216C42—5312no—
1217C42—536no—
1218C42—536no—
1219C42—536no—
1220C42C23×D5311yescharacteristic
1221C42C23×D5313yes—
1222C42C23×D5313yes—
1223C42C23×D5313yes—
1224C42C23×D53112yes—
1225C42C23×D5316yes—
1226C23—531no—
1227C23—532no—
1228C23—533no—
1229C23—1064no—
1230C23—1066no—
1231C23—1066no—
1232C23—1066no—
1233C23—1064no—
1234C23—1064no—
1235C23C24×D5312yes—
1236C23C24×D5313yes—
1237Q8—212no—
1238Q8—22no—
1239Q8—46no—
1240Q8—5312no—
1241Q8—1064no—
1242Q8—10624no—
1243Q8—10612no—
1244Q8—1062no—
1245Q8—2126no—
1246Q8—21212no—
1247Q8#41×D5314yes—
1248D4—26no—
1249D4—22no—
1250D4—46no—
1251D4—1064no—
1252D4—10612no—
1253D4—1066no—
1254D4—1062no—
1255D4—2126no—
1256D4—2126no—
1257D4—2126no—
1258C2×C4—212no—
1259C2×C4—26no—
1260C2×C4—26no—
1261C2×C4—43no—
1262C2×C4—531no—
1263C2×C4—533no—
1264C2×C4—5312no—
1265C2×C4—534no—
1266C2×C4—533no—
1267C2×C4—531no—
1268C2×C4—531no—
1269C2×C4—532no—
1270C2×C4—536no—
1271C2×C4—536no—
1272C2×C4—533no—
1273C2×C4—1066no—
1274C2×C4—10612no—
1275C2×C4—1066no—
1276C2×C4—1066no—
1277C2×C4—1062no—
1278C2×C4—10612no—
1279C2×C4—1062no—
1280C2×C4—1066no—
1281C2×C4—10612no—
1282C2×C4—1064no—
1283C2×C4—1066no—
1284C2×C4—10612no—
1285C2×C4—1066no—
1286C2×C4—10612no—
1287C2×C4—1066no—
1288C2×C4—1066no—
1289C2×C4—2123no—
1290C2×C4—2123no—
1291C2×C4—2123no—
1292C2×C4C24×D5313yes—
1293C2×C4C24×D5311yescharacteristic
1294C2×C4C24×D5311yescharacteristic
1295C2×C4C24×D5312yes—
1296C2×C4C24×D5316yes—
1297C2×C4C24×D5316yes—
1298C2×C4C24×D5313yes—
1299C2×C4C24×D5313yes—
1300C2×C4C24×D5311yescharacteristic
1301C22—22no—
1302C22—23no—
1303C22—23no—
1304C22—22no—
1305C22—23no—
1306C22—22no—
1307C22—532no—
1308C22—532no—
1309C22—532no—
1310C22—1062no—
1311C22—1063no—
1312C22—1063no—
1313C22—1062no—
1314C22—1063no—
1315C22—1062no—
1316C22—2128no—
1317C22—21212no—
1318C22C25×D5311yescharacteristic
1319C4—21no—
1320C4—26no—
1321C4—23no—
1322C4—22no—
1323C4—21no—
1324C4—23no—
1325C4—26no—
1326C4—536no—
1327C4—532no—
1328C4—1061no—
1329C4—1066no—
1330C4—1063no—
1331C4—1062no—
1332C4—1061no—
1333C4—1063no—
1334C4—1066no—
1335C4C2×#41×D5316yes—
1336C42−1+4×D5312yes—
1337C2—42no—
1338C2—43no—
1339C2—534no—
1340C2—2122no—
1341C2—2123no—
1342C2C22×#41×D5311yescharacteristic
1343C2C2×2−1+4×D5311yescharacteristic
1344C2#585×D5311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3518C2
hypercenter#3518D53
hypocenterC53C2×#3518
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3518

Complements

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

NH ≅ G/Ntype
1. #20288733C2semidirect
2. #20288732C2semidirect
3. #20288731C2semidirect
4. #20288730C2semidirect
5. #20288729C2semidirect
6. #20288728C2semidirect
7. #20288727C2semidirect
8. #20288726C2semidirect
9. #20288725C2semidirect
10. #20288724C2semidirect
11. #20288723C2semidirect
12. Q82×D53C2semidirect
13. #556×D53C2semidirect
14. #556×D53C2semidirect
15. #555×D53C2semidirect
16. D4×Q8×D53C2semidirect
17. #548×D53C2semidirect
18. #542×D53C2semidirect
19. #533×D53C2semidirect
20. #529×D53C2semidirect
21. #519×D53C2semidirect
22. C4×#41×D53C2semidirect
23. C53×#3518C2semidirect
26. Q8×Dic106C22semidirect
27. Q8×Dic106C22semidirect
28. Q8×Dic106C22semidirect
29. #16811353C22semidirect
30. #16811353C22semidirect
31. #16811347C22semidirect
32. #16811347C22semidirect
33. #16811346C22semidirect
34. #16811346C22semidirect
35. #16811345C22semidirect
36. #16811345C22semidirect
37. #16811344C22semidirect
38. #16811344C22semidirect
39. #16811344C22semidirect
40. #16811343C22semidirect
41. #16811343C22semidirect
42. #16811342C22semidirect
43. #16811342C22semidirect
44. #16811341C22semidirect
45. #16811341C22semidirect
46. #16811341C22semidirect
47. #16811340C22semidirect
48. #16811340C22semidirect
49. #16811340C22semidirect
50. #16811339C22semidirect
51. #16811338C22semidirect
52. #16811338C22semidirect
53. #16811337C22semidirect
54. #16811337C22semidirect
55. #16811336C22semidirect
56. #16811336C22semidirect
57. #16811335C22semidirect
58. Q8×D212C22semidirect
59. D4×Dic106C22semidirect
60. #16811288C22semidirect
61. Q8×C22⋊D53C22semidirect
62. #16811286C22semidirect
63. #16811285C22semidirect
64. #16811284C22semidirect
65. #16811283C22semidirect
66. #16811282C22semidirect
67. #16811281C22semidirect
68. #16811280C22semidirect
69. #16811279C22semidirect
70. #16811247C22semidirect
71. #16811246C22semidirect
72. #16811245C22semidirect
73. #16811244C22semidirect
74. #16811243C22semidirect
75. #16811242C22semidirect
76. #16811241C22semidirect
77. #16811240C22semidirect
78. #16811239C22semidirect
79. #16811238C22semidirect
80. #16811237C22semidirect
81. #16811180C22semidirect
82. #16811179C22semidirect
83. #16811178C22semidirect
84. #16811178C22semidirect
85. #16811177C22semidirect
86. #16811177C22semidirect
87. #16811176C22semidirect
88. #16811175C22semidirect
89. #16811175C22semidirect
93. #16811160C22semidirect
94. #16811159C22semidirect
95. #16811158C22semidirect
96. #16811157C22semidirect
97. #16811156C22semidirect
98. #16811155C22semidirect
99. #16811154C22semidirect
100. #16811153C22semidirect
101. #16811152C22semidirect
102. #16811151C22semidirect
103. #16811150C22semidirect
117. #16811101C22semidirect
118. #16811100C22semidirect
119. #16811100C22semidirect
120. #16811099C22semidirect
121. #16811099C22semidirect
122. #16811099C22semidirect
123. #16811099C22semidirect
124. #41×Dic53C22semidirect
125. C4×#11719949C22semidirect
126. C4×#11719949C22semidirect
127. C4×#11719945C22semidirect
128. #16811091C22semidirect
129. C4×#11719947C22semidirect
130. C4×#11719947C22semidirect
147. Q82×C53C22semidirect
148. C53×#556C22semidirect
149. C53×#556C22semidirect
150. C53×#555C22semidirect
151. D4×Q8×C53C22semidirect
152. C53×#548C22semidirect
153. C53×#542C22semidirect
154. C53×#533C22semidirect
155. C53×#529C22semidirect
156. C53×#519C22semidirect
157. C4×#41×C53C22semidirect
676. #3518D53direct (N × H)
695. D53#3518direct (N × H)
703. Q82C2×D53semidirect
723. #556C2×D53semidirect
724. #556C2×D53semidirect
733. #555C2×D53semidirect
739. D4×Q8C2×D53semidirect
747. #548C2×D53semidirect
759. #542C2×D53semidirect
769. #533C2×D53semidirect
784. #529C2×D53semidirect
805. #519C2×D53semidirect
813. C4×#41C2×D53semidirect
830. C53C2×#3518semidirect

Maximal subgroups

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

subgroupindex
#202887332
#202887322
#202887312
#202887302
#202887292
#202887282
#202887272
#202887262
#202887252
#202887242
#202887232
Q82×D532
#556×D532
#555×D532
D4×Q8×D532
#548×D532
#542×D532
#533×D532
#529×D532
#519×D532
C4×#41×D532
C53×#35182
C2×#351853