Finite Group Databasebeta

← C4×#11763550 #17197014

Subgroups — C4×#11763550 #17197014

Order 4352.

2568 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763550C211yesmaximal, characteristic
2#14531976C211yesmaximal, characteristic, complemented
3#14531973C211yesmaximal, characteristic, complemented
4#14531960C211yesmaximal, characteristic, complemented
5#14531939C213yesmaximal, complemented
6#14531937C213yesmaximal, complemented
7#14531931C213yesmaximal, complemented
8#14531924C213yesmaximal, complemented
9C4×#10587560C211yesmaximal, characteristic, complemented
10C4×#10587562C211yesmaximal, characteristic, complemented
11C4×#10587580C213yesmaximal, complemented
12C4×#10587581C213yesmaximal, complemented
13C4×#10587570C213yesmaximal, complemented
14C4×#10587568C213yesmaximal, complemented
15C4×C17×#126C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17#11763550C4116yesdirect product factor
18C2×#10587560C2211yescharacteristic
19C2×#10587562C2211yescharacteristic
20C2×#10587580C2213yes—
21C2×#10587581C2213yes—
22C2×#10587570C2213yes—
23C2×#10587568C2213yes—
24C2×C4×D68C2213yes—
25C2×C4×D68C2213yes—
26C2×C4×D68C2213yescomplemented
27C2×C4×C22⋊D17C2213yes—
28C2×C42×D17C2213yescomplemented
29#11762711C2213yes—
30#11762711C2213yescomplemented
31#11762710C2213yes—
32#11762709C2213yes—
33#11762708C2213yescomplemented
34#11762706C2213yescomplemented
35#11762702C2213yes—
36#11762701C2213yes—
37#11762701C2213yescomplemented
38#11762700C2213yes—
39#11762699C2213yes—
40#11762698C2213yes—
41#11762698C2213yescomplemented
42#11762696C2213yescomplemented
43#11762695C2213yescomplemented
44#11762693C2213yescomplemented
45#11762687C2213yes—
46#11762687C2213yes—
47#11762687C2213yes—
48#11762687C2213yes—
49#11762687C2213yescomplemented
50#11762687C2213yescomplemented
51#11762686C2213yes—
52#11762685C2213yes—
53#11762684C2213yes—
54#11762683C2213yes—
55#11762683C2213yes—
56#11762680C2213yescomplemented
57#11762679C2211yescharacteristic, complemented
58#11762677C2211yescharacteristic, complemented
59#11762671C2213yescomplemented
60#11762668C2213yescomplemented
61#11762666C2213yescomplemented
62#11762664C2213yes—
63C4×#63225C2213yescomplemented
64C4×#63227C2213yes—
65C4×#63227C2213yes—
66C4×#63227C2213yescomplemented
67C2×C17×#126C2211yescharacteristic
68C17×#388C2213yes—
69C17×#387C2213yescomplemented
70C17×#383C2211yescharacteristic, complemented
71C4×C4⋊C4×C17C2213yescomplemented
72C4×C22⋊C4×C17C2213yes—
73C43×C17C2211yescharacteristic, complemented
74C24×D17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C22×C22⋊D17C2313yes—
77C23×Dic17C2311yescharacteristic
78C22×D68C2313yes—
79C22×D68C2313yes—
80C22×D68C2313yes—
81C22×C4×D17—46no—
82C22×C4×D17C2313yes—
83C22×C4×D17C2311yescharacteristic
84C22×C4×D17C2311yescharacteristic
85C22×C4×D17C2313yes—
86C22×C4×D17C2311yescharacteristic
87C22×C4×D17C2311yescharacteristic
88C22×C4×D17C2313yes—
89C17×#126C2×C418yescomplemented
90C2×C4⋊C4×C17C2313yes—
91C2×C4⋊C4×C17C2313yes—
92C2×C22⋊C4×C17C2313yes—
93C2×C22⋊C4×C17C2313yes—
94C2×C42×C17C2313yes—
95C2×C42×C17C2313yes—
96C2×C42×C17C2313yes—
97C2×C42×C17C2311yescharacteristic
98C2×C22⋊Dic17C2313yes—
99C4×C22⋊D17—46no—
100C2×#63227C2313yes—
101C2×#63227C2313yes—
102C2×#63227C2313yes—
103C2×#63227C2313yes—
104C2×#63227C2313yes—
105C2×#63227C2313yes—
106C2×#63227C2313yes—
107C2×#63227C2313yes—
108C2×#63227C2313yes—
109C2×#63227C2313yes—
110C2×#63227C2313yes—
111C2×#63227C2313yes—
112C2×#63227C2313yes—
113C2×C4⋊Dic17C2313yes—
114C2×C4⋊Dic17C2313yes—
115C2×C4⋊Dic17C2313yes—
116C2×#63225C2313yes—
117C2×#63225C2313yes—
118C2×#63225C2313yes—
119C2×C4×Dic17C2313yes—
120C2×C4×Dic17C2313yes—
121C2×C4×Dic17C2313yes—
122#10587581C2×C4124yescomplemented
123#10587580C2×C4124yescomplemented
124#10587570C2×C4124yescomplemented
125#10587568C2×C4124yescomplemented
126#10587562C2×C418yescomplemented
127#10587560C2×C418yescomplemented
128C4×D68—46no—
129C4×D68—46no—
130C4×D68—46no—
131C42×D17—46no—
132C17×#95C2313yes—
133C17×#95C2313yes—
134C17×#95C2313yes—
135C17×#95C2313yes—
136#10587502C2313yes—
137#10587502C2313yes—
138#10587502C2313yes—
139#10587502C2313yes—
140#10587502C2313yes—
141#10587502C2313yes—
142#10587502C2313yes—
143#10587502C2313yes—
144C24×C17C2411yescharacteristic
145C23×D17—43no—
146C23×D17—43no—
147C23×D17C22×C414yes—
148C23×D17C2413yes—
149C23×D17C2411yescharacteristic
150C23×D17C2411yescharacteristic
151C22×C4×C17—26no—
152C22×C4×C17C2411yescharacteristic
153C22×C4×C17C2413yes—
154C22×C4×C17C2413yes—
155C22×C4×C17C2413yes—
156C22×C4×C17C2413yes—
157C22×C4×C17C2411yescharacteristic
158C2×C22⋊D17—43no—
159C2×C22⋊D17—43no—
160C2×C22⋊D17C22×C4112yes—
161C22×Dic17—43no—
162C22×Dic17C2411yescharacteristic
163C22×Dic17C2411yescharacteristic
164C22×Dic17C2413yes—
165C22×Dic17C2413yes—
166C22×Dic17C2413yes—
167C2×D68—43no—
168C2×D68—43no—
169C2×D68—43no—
170C2×D68—43no—
171C2×D68—43no—
172C2×D68—43no—
173C2×D68C22×C4112yes—
174C2×D68C22×C4112yes—
175C2×D68C22×C4112yescomplemented
176C2×C4×D17—26no—
177C2×C4×D17—26no—
178C2×C4×D17—26no—
179C2×C4×D17—26no—
180C2×C4×D17—26no—
181C2×C4×D17—43no—
182C2×C4×D17—43no—
183C2×C4×D17—43no—
184C2×C4×D17—43no—
185C2×C4×D17—43no—
186C2×C4×D17—43no—
187C2×C4×D17—43no—
188C2×C4×D17—416no—
189C2×C4×D17C22×C4112yescomplemented
190C4⋊C4×C17—43no—
191C4⋊C4×C17C22×C4112yescomplemented
192C22⋊C4×C17—43no—
193C22⋊C4×C17C22×C4112yes—
194C42×C17—26no—
195C42×C17—26no—
196C42×C17—43no—
197C42×C17C22×C414yescomplemented
198C22⋊Dic17—43no—
199#63227—43no—
200#63227—43no—
201#63227—43no—
202#63227—43no—
203#63227—43no—
204#63227—43no—
205#63227—43no—
206#63227—43no—
207#63227—43no—
208#63227—43no—
209#63227C22×C4112yes—
210#63227C22×C4112yes—
211#63227C22×C4112yescomplemented
212C4⋊Dic17—43no—
213C4⋊Dic17—43no—
214C4⋊Dic17—43no—
215#63225—43no—
216#63225—43no—
217#63225C22×C4112yescomplemented
218C4×Dic17—26no—
219C4×Dic17—43no—
220C4×Dic17—43no—
221C4×#560—171nomaximal, Sylow
222C23×C17—23no—
223C23×C17—23no—
224C23×C17C23×C412yes—
225C23×C17C2511yescharacteristic
226C22×D17—23no—
227C22×D17—23no—
228C22×D17—23no—
229C22×D17—23no—
230C22×D17—23no—
231C22×D17—23no—
232C22×D17—23no—
233C22×D17—23no—
234C22×D17—23no—
235C22×D17—23no—
236C22×D17—412no—
237C22×D17—44no—
238C22×D17—412no—
239C22×D17C23×C416yes—
240C22×D17C23×C412yes—
241C22×D17C23×C412yes—
242C2×C4×C17—23no—
243C2×C4×C17—23no—
244C2×C4×C17—23no—
245C2×C4×C17—23no—
246C2×C4×C17—23no—
247C2×C4×C17—23no—
248C2×C4×C17—23no—
249C2×C4×C17—23no—
250C2×C4×C17—23no—
251C2×C4×C17—23no—
252C2×C4×C17—23no—
253C2×C4×C17—44no—
254C2×C4×C17C23×C416yes—
255C2×C4×C17C23×C416yes—
256C2×C4×C17H(5,𝔽2)16yes—
257C22⋊D17—412no—
258C2×Dic17—23no—
259C2×Dic17—23no—
260C2×Dic17—23no—
261C2×Dic17—23no—
262C2×Dic17—23no—
263C2×Dic17—23no—
264C2×Dic17—23no—
265C2×Dic17—23no—
266C2×Dic17—23no—
267C2×Dic17—23no—
268C2×Dic17—44no—
269C2×Dic17C23×C416yes—
270D68—412no—
271D68—412no—
272D68—412no—
273C4×D17—412no—
274C4×D17—412no—
275C4×D17—44no—
276C4×D17—44no—
277C4×D17—412no—
278C4×D17—44no—
279C4×D17—44no—
280C2×#560—171no—
281#2383—171no—
282#2383—171no—
283#2380—171no—
284#2377—173no—
285#2377—173no—
286#2376—173no—
287#2375—173no—
288C4×#127—171no—
289C4×#126—171no—
290C4×#126D1711yescharacteristic, complemented
291C4×#123—173no—
292C4×#121—173no—
293C4×#121—173no—
294C4×#120—173no—
295C22×C17—26no—
296C22×C17—41no—
297C22×C17—43no—
298C22×C17C24×C411yescharacteristic
299C22×C17C2×H(5,𝔽2)13yes—
300C22×C17#58513yes—
301C2×D17—26no—
302C2×D17—26no—
303C2×D17—26no—
304C2×D17—26no—
305C2×D17—26no—
306C2×D17—416no—
307C2×D17—41no—
308C2×D17—41no—
309C2×D17—43no—
310C2×D17—43no—
311C2×D17—43no—
312C2×D17—43no—
313C2×D17—43no—
314C2×D17—43no—
315C4×C17—26no—
316C4×C17—26no—
317C4×C17—41no—
318C4×C17—43no—
319C4×C17—43no—
320C4×C17#56014yescomplemented
321Dic17—26no—
322Dic17—41no—
323Dic17—41no—
324Dic17—43no—
325Dic17—43no—
326C24×C4—171no—
327#560—1716no—
328C2×#127—171no—
329C2×#126—171no—
330C2×#126C2×D1711yescharacteristic
331C2×#123—173no—
332C2×#121—173no—
333C2×#121—173no—
334C2×#120—173no—
335C2×C4×D4—173no—
336C2×C4×D4—173no—
337C2×C4×D4—173no—
338C2×C4×D4—173no—
339C22×C42—173no—
340#390—173no—
341#390—173no—
342#390—173no—
343#390—173no—
344#389—173no—
345#389—173no—
346#388—173no—
347#388—173no—
348#388—173no—
349#388—173no—
350#388—173no—
351#388—173no—
352#388—173no—
353#388C2×D1713yes—
354#387—173no—
355#387—173no—
356#387—173no—
357#387C2×D1713yescomplemented
358#386—173no—
359#386—173no—
360#386—173no—
361#386—173no—
362#386—173no—
363#386—173no—
364#386—173no—
365#386—173no—
366#385—173no—
367#385—173no—
368#385—173no—
369#385—173no—
370#384—171no—
371#383—171no—
372#383C2×D1711yescharacteristic, complemented
373#381—173no—
374#380—173no—
375#380—173no—
376#379—173no—
377C4×C4⋊C4—173no—
378C4×C4⋊C4C2×D1713yescomplemented
379C4×C22⋊C4—173no—
380C4×C22⋊C4—173no—
381C4×C22⋊C4—173no—
382C4×C22⋊C4C2×D1713yes—
383C43C2×D1711yescharacteristic, complemented
384C2×C17—42no—
385C2×C17C4×H(5,𝔽2)13yes—
386C2×C17C2×#56011yescharacteristic
387C2×C17#352913yes—
388D17—46no—
389D17—42no—
390D17—42no—
391C25—171no—
392C22×D4—173no—
393C22×D4—173no—
394C22×D4—173no—
395C22×D4—173no—
396C23×C4—173no—
397C23×C4—171no—
398C23×C4—173no—
399C23×C4—171no—
400C23×C4—171no—
401C23×C4—171no—
402C23×C4—171no—
403C23×C4—173no—
404C23×C4—686no—
405C23×C4C22×D1711yescharacteristic
406#127—178no—
407#126—178no—
408#126C4×D1718yescomplemented
409#123—1724no—
410#121—1724no—
411#121—1724no—
412#120—1724no—
413C4×D4—686no—
414C4×D4—686no—
415C4×D4—686no—
416C4×D4—686no—
417C2×C4⋊C4—173no—
418C2×C4⋊C4—173no—
419C2×C4⋊C4—173no—
420C2×C4⋊C4—173no—
421C2×C4⋊C4—173no—
422C2×C4⋊C4—173no—
423C2×C4⋊C4C22×D1713yes—
424C2×C4⋊C4C22×D1713yes—
425C2×C22⋊C4—173no—
426C2×C22⋊C4—173no—
427C2×C22⋊C4—173no—
428C2×C22⋊C4—173no—
429C2×C22⋊C4—173no—
430C2×C22⋊C4—173no—
431C2×C22⋊C4—173no—
432C2×C22⋊C4—173no—
433C2×C22⋊C4—173no—
434C2×C22⋊C4—173no—
435C2×C22⋊C4—173no—
436C2×C22⋊C4—173no—
437C2×C22⋊C4—173no—
438C2×C22⋊C4—173no—
439C2×C22⋊C4C22×D1713yes—
440C2×C22⋊C4C22×D1713yes—
441C2×C42—173no—
442C2×C42—173no—
443C2×C42—173no—
444C2×C42—686no—
445C2×C42C22×D1713yes—
446C2×C42C22×D1713yes—
447C2×C42C22×D1713yes—
448C2×C42C22×D1711yescharacteristic
449#95—173no—
450#95—173no—
451#95—173no—
452#95—173no—
453#95—173no—
454#95—173no—
455#95—173no—
456#95—173no—
457#95C22×D1713yes—
458#95C22×D1713yes—
459#95C22×D1713yes—
460#95C22×D1713yes—
461C17C4×#56011yescharacteristic, complemented, Sylow
462C24—171no—
463C24—171no—
464C24—173no—
465C24—174no—
466C24—683no—
467C24—683no—
468C24C23×D1711yescharacteristic
469C2×D4—1712no—
470C2×D4—1712no—
471C2×D4—1712no—
472C2×D4—1712no—
473C2×D4—683no—
474C2×D4—683no—
475C2×D4—683no—
476C2×D4—683no—
477C2×D4—683no—
478C2×D4—683no—
479C2×D4—683no—
480C2×D4—683no—
481C22×C4—26no—
482C22×C4—173no—
483C22×C4—1712no—
484C22×C4—173no—
485C22×C4—171no—
486C22×C4—171no—
487C22×C4—173no—
488C22×C4—346no—
489C22×C4—346no—
490C22×C4—346no—
491C22×C4—346no—
492C22×C4—346no—
493C22×C4—683no—
494C22×C4—683no—
495C22×C4—683no—
496C22×C4—683no—
497C22×C4—683no—
498C22×C4—683no—
499C22×C4—683no—
500C22×C4—6816no—
501C22×C4—683no—
502C22×C4C23×D1713yes—
503C22×C4C23×D1713yes—
504C22×C4C23×D1711yescharacteristic
505C22×C4C23×D1713yes—
506C22×C4C23×D1713yes—
507C22×C4C23×D1711yescharacteristic
508C4⋊C4—43no—
509C4⋊C4—1712no—
510C4⋊C4—683no—
511C4⋊C4—683no—
512C4⋊C4—683no—
513C4⋊C4—683no—
514C4⋊C4—683no—
515C4⋊C4C2×C4×D17112yescomplemented
516C22⋊C4—43no—
517C22⋊C4—1712no—
518C22⋊C4—1712no—
519C22⋊C4—1712no—
520C22⋊C4—683no—
521C22⋊C4—683no—
522C22⋊C4—683no—
523C22⋊C4—683no—
524C22⋊C4—683no—
525C22⋊C4—683no—
526C22⋊C4—683no—
527C22⋊C4—683no—
528C22⋊C4—683no—
529C22⋊C4—683no—
530C22⋊C4—683no—
531C22⋊C4C2×C4×D17112yes—
532C42—26no—
533C42—26no—
534C42—43no—
535C42—346no—
536C42—683no—
537C42—683no—
538C42C2×C4×D1714yescomplemented
539C23—23no—
540C23—23no—
541C23—172no—
542C23—172no—
543C23—176no—
544C23—343no—
545C23—343no—
546C23—343no—
547C23—343no—
548C23—343no—
549C23—343no—
550C23—343no—
551C23—343no—
552C23—343no—
553C23—343no—
554C23—6812no—
555C23—684no—
556C23—6812no—
557C23C22×C4×D1712yes—
558C23C24×D1711yescharacteristic
559D4—6812no—
560D4—6812no—
561D4—6812no—
562D4—6812no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—23no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—44no—
575C2×C4—176no—
576C2×C4—343no—
577C2×C4—343no—
578C2×C4—343no—
579C2×C4—343no—
580C2×C4—343no—
581C2×C4—343no—
582C2×C4—343no—
583C2×C4—343no—
584C2×C4—343no—
585C2×C4—343no—
586C2×C4—6812no—
587C2×C4—684no—
588C2×C4—684no—
589C2×C4—6812no—
590C2×C4—684no—
591C2×C4—684no—
592C2×C4—684no—
593C2×C4—6812no—
594C2×C4C22×C4×D1716yes—
595C2×C4C22×C4×D1716yes—
596C2×C4#1058769616yes—
597C22—26no—
598C22—41no—
599C22—43no—
600C22—346no—
601C22—346no—
602C22—346no—
603C22—346no—
604C22—346no—
605C22—6816no—
606C22—681no—
607C22—681no—
608C22—683no—
609C22—683no—
610C22—683no—
611C22—683no—
612C22—683no—
613C22—683no—
614C22C23×C4×D1711yescharacteristic
615C22C2×#1058769613yes—
616C22#1176364513yes—
617C4—26no—
618C4—26no—
619C4—41no—
620C4—43no—
621C4—43no—
622C4—346no—
623C4—681no—
624C4—681no—
625C4—683no—
626C4—683no—
627C4#1176355014yesdirect product factor
628C2—42no—
629C2—682no—
630C2—682no—
631C2—686no—
632C2C4×#1058769613yes—
633C2C2×#1176355011yescharacteristic
634C2#1454292313yes—
subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC4×C17×#126C2
socle, cosocleC23×C17C25
prime radicalC2×#11763550C2
hypercenterC4×#126D17
hypocenterC17C4×#560
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
2. #14531976C2semidirect
3. #14531973C2semidirect
4. #14531960C2semidirect
5. #14531939C2semidirect
6. #14531937C2semidirect
7. #14531931C2semidirect
8. #14531924C2semidirect
9. C4×#10587560C2semidirect
10. C4×#10587562C2semidirect
11. C4×#10587580C2semidirect
12. C4×#10587581C2semidirect
13. C4×#10587570C2semidirect
14. C4×#10587568C2semidirect
15. C4×C17×#126C2semidirect
17. #11763550C4direct (N × H)
26. C2×C4×D68C22semidirect
28. C2×C42×D17C22semidirect
30. #11762711C22semidirect
33. #11762708C22semidirect
34. #11762706C22semidirect
37. #11762701C22semidirect
41. #11762698C22semidirect
42. #11762696C22semidirect
43. #11762695C22semidirect
44. #11762693C22semidirect
49. #11762687C22semidirect
50. #11762687C22semidirect
56. #11762680C22semidirect
57. #11762679C22semidirect
58. #11762677C22semidirect
59. #11762671C22semidirect
60. #11762668C22semidirect
61. #11762666C22semidirect
63. C4×#63225C22semidirect
66. C4×#63227C22semidirect
69. C17×#387C22semidirect
70. C17×#383C22semidirect
71. C4×C4⋊C4×C17C22semidirect
73. C43×C17C22semidirect
89. C17×#126C2×C4semidirect
122. #10587581C2×C4semidirect
123. #10587580C2×C4semidirect
124. #10587570C2×C4semidirect
125. #10587568C2×C4semidirect
126. #10587562C2×C4semidirect
127. #10587560C2×C4semidirect
175. C2×D68C22×C4semidirect
189. C2×C4×D17C22×C4semidirect
191. C4⋊C4×C17C22×C4semidirect
197. C42×C17C22×C4semidirect
211. #63227C22×C4semidirect
217. #63225C22×C4semidirect
290. C4×#126D17semidirect
320. C4×C17#560semidirect
357. #387C2×D17semidirect
372. #383C2×D17semidirect
378. C4×C4⋊C4C2×D17semidirect
383. C43C2×D17semidirect
408. #126C4×D17semidirect
461. C17C4×#560semidirect
515. C4⋊C4C2×C4×D17semidirect
538. C42C2×C4×D17semidirect
627. C4#11763550direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635502
#145319762
#145319732
#145319602
#145319392
#145319372
#145319312
#145319242
C4×#105875602
C4×#105875622
C4×#105875802
C4×#105875812
C4×#105875702
C4×#105875682
C4×C17×#1262
C4×#56017