Finite Group Databasebeta

← #17942719

Subgroups — #17942719

Order 4352.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542870C212yesmaximal, complemented
2#14542817C216yesmaximal, complemented
3#14542791C212yesmaximal, complemented
4#14542746C216yesmaximal, complemented
5#14542697C213yesmaximal, complemented
6#14542661C213yesmaximal, complemented
7#14542562C211yesmaximal, characteristic, complemented
8#14542522C216yesmaximal, complemented
9#14542454C212yesmaximal, complemented
10#14542411C212yesmaximal, complemented
11#14542395C216yesmaximal, complemented
12#14542384C212yesmaximal, complemented
13D4×#63256C216yesmaximal, complemented
14#14542207C216yesmaximal, complemented
15#14542081C213yesmaximal, complemented
16C2×#11763360C213yesmaximal, complemented
17#14541990C212yesmaximal, complemented
18C4×#41×D17C211yesmaximal, characteristic, complemented
19C17×#3503C211yesmaximal, characteristic, complemented
20C2×#10587696C2212yes—
21C22×#63256C2216yescomplemented
22C2×#41×D17C2211yescharacteristic
23#11763544C2216yescomplemented
24#11763544C2216yescomplemented
25#11763533C2216yescomplemented
26#11763525C2216yescomplemented
27#11763525C22112yescomplemented
28#11763520C2216yescomplemented
29#11763512C22112yescomplemented
30#11763512C22112yescomplemented
31#11763507C22112yescomplemented
32#11763486C22124yescomplemented
33#11763481C2212yescomplemented
34#11763481C2212yescomplemented
35#11763481C2216yescomplemented
36#11763481C2216yescomplemented
37#11763481C2214yescomplemented
38#11763471C2214yescomplemented
39#11763470C22112yescomplemented
40#11763462C22112yescomplemented
41#11763462C2216yescomplemented
42#11763454C22112yescomplemented
43#11763450C22112yescomplemented
44#11763450C22112yescomplemented
45#11763450C22124yescomplemented
46D4×D68C2216yescomplemented
47D4×D68C22112yescomplemented
48D4×D68C2216yescomplemented
49#11763433C22112yescomplemented
50#11763433C22112yescomplemented
51#11763415C22112yescomplemented
52#11763415C22112yescomplemented
53#11763399C22124yescomplemented
54#11763390C2216yescomplemented
55#11763378C2216yescomplemented
56#11763378C2216yescomplemented
57#11763364C2211yescharacteristic, complemented
58#11763364C2213yescomplemented
59#11763360C2213yescomplemented
60#11763360C2213yescomplemented
61#11763360C2216yescomplemented
62#11763360C2216yescomplemented
63#11763360C2216yescomplemented
64#11763360C2216yescomplemented
65#11763360C22112yescomplemented
66#11763360C2216yescomplemented
67#11763360C2216yescomplemented
68#11763360C2216yescomplemented
69#11763359C2213yescomplemented
70C2×#10587560C2213yescomplemented
71#11763346C2216yescomplemented
72#11763346C2216yescomplemented
73#11763345C2216yescomplemented
74#11763345C2216yescomplemented
75#11763344C2216yescomplemented
76#11763344C2216yescomplemented
77#11763344C22112yescomplemented
78C2×#10587633C2216yescomplemented
79#11763322C2216yescomplemented
80#11763322C2216yescomplemented
81#11763322C22124yescomplemented
82#11763321C2216yescomplemented
83C2×#10587581C2216yescomplemented
84C2×#10587581C2216yescomplemented
85#11763291C2214yescomplemented
86#11763290C2216yescomplemented
87#11763283C2216yescomplemented
88#11763281C22112yescomplemented
89#41×Dic17C2211yescharacteristic
90C4×#63256C2216yescomplemented
91C4×#63256C2216yescomplemented
92C4×#63256C2214yescomplemented
93C4×#63256C2211yescharacteristic, complemented
94C4×#63256C2211yescharacteristic, complemented
95C4×#63252C2213yescomplemented
96#11763277C2216yescomplemented
97#11763277C2213yescomplemented
98C4×#63254C2213yescomplemented
99C4×#63254C2213yescomplemented
100C4×Q8×D17C2211yescharacteristic, complemented
101C4×Q8×D17C2211yescharacteristic, complemented
102C2×#10587579C2216yescomplemented
103C2×#10587579C2216yescomplemented
104C4×D4×D17C22112yescomplemented
105C4×D4×D17C2213yescomplemented
106C4×D4×D17C2213yescomplemented
107#117×D17C2213yescomplemented
108C2×C42×D17C2213yescomplemented
109Q82×C17C2212yescomplemented
110C17×#557C2212yescomplemented
111C17×#554C2216yescomplemented
112D4×Q8×C17C2216yescomplemented
113C17×#544C2216yescomplemented
114C17×#533C2213yescomplemented
115C2×C17×C4⋊Q8C2213yescomplemented
116C17×#520C2212yes—
117C4×#41×C17C2211yescharacteristic
118C2×#41×C17C2311yescharacteristic
119C22×Q8×C17C2316yes—
120#10587696—216no—
121#41×D17—28no—
122C2×#63256—424no—
123C2×#63256C2314yes—
124C2×#63256C2311yescharacteristic
125C2×#63256C2316yes—
126C2×#63256C23112yes—
127C2×#63256C23112yes—
128C2×#63256C2316yes—
129C2×#63256C23112yes—
130C2×Q8×D17C2311yescharacteristic
131C2×#63254C2313yes—
132C2×D4×D17C2313yes—
133C2×D4×D17C23112yes—
134C2×#63252C2313yes—
135C2×#63252C2316yes—
136C22×D68C2316yes—
137C22×D68C2316yes—
138C22×D68C23112yes—
139C22×D68C2316yes—
140C22×C4×D17C2313yes—
141C22×C4×D17C2313yes—
142C22×C4×D17C2313yes—
143C22×C4×D17C23112yes—
144C17×C4⋊Q8C2316yes—
145C17×C4⋊Q8C23112yes—
146C17×C4⋊Q8C2313yes—
147C17×C4⋊Q8C2316yes—
148C17×C4⋊Q8C2316yes—
149C17×C4⋊Q8C2311yescharacteristic
150C17×#125C2316yes—
151C17×#125C23112yes—
152C17×C22⋊Q8C23124yes—
153C17×C22⋊Q8C2316yes—
154C17×C22⋊Q8C2316yes—
155C4×Q8×C17C2314yes—
156C4×Q8×C17C2311yescharacteristic
157C4×Q8×C17C2311yescharacteristic
158C4×Q8×C17C2316yes—
159C4×Q8×C17C2316yes—
160C4×D4×C17C2313yes—
161C4×D4×C17C2313yes—
162C4×D4×C17C23112yes—
163C17×#117C2313yes—
164C17×#117C2316yes—
165C2×C4⋊C4×C17C2316yes—
166C2×C4⋊C4×C17C2316yes—
167C2×C42×C17C2313yes—
168#10587633C23124yes—
169#10587633C23112yes—
170#10587633C23112yes—
171#10587633C2316yes—
172#10587633C2316yes—
173#10587633C23112yes—
174#10587632C2316yes—
175#10587632C23124yes—
176#10587632C2312yes—
177Q8×Dic17C2316yes—
178Q8×Dic17C2311yescharacteristic
179Q8×Dic17C2311yescharacteristic
180Q8×Dic17C2312yes—
181D4×Dic17C2313yes—
182D4×Dic17C2313yes—
183#10587616C2316yes—
184#10587616C23124yes—
185#10587616C2316yes—
186C4×C22⋊D17C2316yes—
187C4×C22⋊D17C23124yes—
188C4×C22⋊D17C2316yes—
189C2×#63227C23112yes—
190C2×#63227C23112yes—
191#10587612C2313yes—
192C2×C4×Dic17C2313yes—
193C2×C4×Dic17C2313yes—
194C2×C4×Dic17C2313yes—
195#10587584C23112yes—
196#10587584C23124yes—
197#10587584C23112yes—
198#10587583C23112yes—
199#10587583C2312yes—
200#10587583C2316yes—
201#10587581C23112yes—
202#10587581C23112yes—
203#10587581C23112yes—
204#10587581C2316yes—
205#10587581C23112yes—
206#10587581C23112yes—
207#10587581C23112yes—
208#10587581C23124yes—
209#10587581C23124yes—
210#10587581C23112yes—
211#10587581C2316yes—
212#10587581C2316yes—
213#10587581C23112yes—
214#10587581C23112yes—
215#10587581C2316yes—
216#10587580C23112yes—
217#10587580C23124yes—
218#10587580C23124yes—
219#10587580C23124yes—
220#10587580C23112yes—
221#10587579C23112yes—
222#10587579C23112yes—
223#10587579C23112yes—
224#10587579C23112yes—
225#10587579C2313yes—
226#10587579C2313yes—
227#10587579C2316yes—
228#10587579C2316yes—
229#10587579C23112yes—
230#10587579C23112yes—
231#10587579C23112yes—
232#10587579C2316yes—
233#10587579C2316yes—
234#10587579C23112yes—
235#10587578C23112yes—
236#10587578C2316yes—
237#10587578C2313yes—
238#10587578C23112yes—
239#10587578C2313yes—
240#10587578C2312yes—
241#10587578C23112yes—
242C4⋊C4×D17C2313yes—
243C4⋊C4×D17C23112yes—
244C4⋊C4×D17C2313yes—
245#10587576C2316yes—
246#10587576C2312yes—
247#10587573C2313yes—
248#10587573C2313yes—
249#10587573C2312yes—
250#10587573C2316yes—
251#10587572C23112yes—
252#10587568C23124yes—
253#10587568C23112yes—
254#10587568C23124yes—
255#10587567C23112yes—
256#10587567C2316yes—
257#10587567C2316yes—
258#10587567C23112yes—
259C22⋊C4×D17C23124yes—
260C22⋊C4×D17C2316yes—
261#10587563C2316yes—
262#10587561C23112yes—
263#10587561C2316yes—
264#10587560C23112yes—
265#10587560C2316yes—
266#10587560C2316yes—
267#10587560C2313yes—
268#10587560C2316yes—
269C4×D68C2313yes—
270C4×D68C23112yes—
271C4×D68C23112yes—
272C4×D68C2316yes—
273C4×D68C2313yes—
274C4×D68C23112yes—
275C4×D68C23112yes—
276C4×D68C2316yes—
277#10587558C2316yes—
278#10587558C23112yes—
279C42×D17C2311yescharacteristic
280C42×D17C2313yes—
281C42×D17C2313yes—
282C42×D17C2313yes—
283C42×D17C2313yes—
284C42×D17C2313yes—
285C42×D17C2313yes—
286C42×D17C2313yes—
287C42×D17C23112yes—
288#10587555C2311yescharacteristic
289C4×Dic34C2313yes—
290C4×Dic34C2313yes—
291C23×D17C2413yes—
292C23×D17C24112yes—
293#41×C17#4118yescomplemented
294C2×Q8×C17—412no—
295C2×Q8×C17C2412yes—
296C2×Q8×C17C2416yes—
297C2×Q8×C17C24112yes—
298C2×Q8×C17C2411yescharacteristic
299C2×D4×C17C2413yes—
300C22×C4×C17C2413yes—
301C22×C4×C17C2413yes—
302C22×C4×C17C24112yes—
303C22×C4×C17C2413yes—
304C2×C22⋊D17C24112yes—
305C2×C22⋊D17C2416yes—
306C22×Dic17C2413yes—
307C22×Dic17C2413yes—
308C22×Dic17C2413yes—
309#63256—24no—
310#63256—216no—
311#63256—224no—
312#63256—424no—
313#63256—424no—
314#63256—424no—
315#63256—412no—
316Q8×D17—24no—
317#63254—212no—
318D4×D17—212no—
319D4×D17—248no—
320#63252—212no—
321#63252—224no—
322C2×D68—224no—
323C2×D68—412no—
324C2×D68—412no—
325C2×D68—424no—
326C2×D68C2416yes—
327C2×D68C2416yes—
328C2×D68C24112yes—
329C2×D68C2416yes—
330C2×D68C24112yes—
331C2×D68C2413yes—
332C2×D68C24112yes—
333C2×D68C24124yes—
334C2×D68C24112yes—
335C2×D68C24112yes—
336C2×C4×D17—212no—
337C2×C4×D17—212no—
338C2×C4×D17—424no—
339C2×C4×D17—46no—
340C2×C4×D17C2411yescharacteristic
341C2×C4×D17C2411yescharacteristic
342C2×C4×D17C24112yes—
343C2×C4×D17C2413yes—
344C2×C4×D17C2413yes—
345C2×C4×D17C2413yes—
346C2×C4×D17C2413yes—
347C2×C4×D17C2413yes—
348C2×C4×D17C2413yes—
349C2×C4×D17C2413yes—
350C2×C4×D17C24112yes—
351C2×C4×D17C24124yes—
352C2×C4×D17C2413yes—
353C2×C4×D17C2413yes—
354C2×C4×D17C24112yes—
355C2×C4×D17C2411yescharacteristic
356C2×Dic34C2412yes—
357C2×Dic34C2413yes—
358C4⋊C4×C17C24112yes—
359C4⋊C4×C17C24112yes—
360C4⋊C4×C17C2412yes—
361C4⋊C4×C17C24112yes—
362C4⋊C4×C17C2416yes—
363C4⋊C4×C17C2413yes—
364C4⋊C4×C17C2412yes—
365C4⋊C4×C17C2416yes—
366C4⋊C4×C17C24112yes—
367C4⋊C4×C17C2413yes—
368C22⋊C4×C17C2416yes—
369C22⋊C4×C17C24112yes—
370C42×C17C2413yes—
371C42×C17C24112yes—
372C42×C17C2411yescharacteristic
373C42×C17C2413yes—
374C42×C17C2413yes—
375C22⋊Dic17C2416yes—
376#63227C24112yes—
377#63227C2416yes—
378#63227C2416yes—
379#63227C24112yes—
380#63227C2414yes—
381#63227C24112yes—
382#63227C24112yes—
383#63227C24112yes—
384#63227C24124yes—
385#63227C24112yes—
386#63227C24112yes—
387#63227C24124yes—
388C4⋊Dic17C2413yes—
389C4⋊Dic17C2413yes—
390C4⋊Dic17C2412yes—
391C4⋊Dic17C2412yes—
392C4⋊Dic17C2414yes—
393C4⋊Dic17C24112yes—
394#63225C2416yes—
395#63225C2416yes—
396#63225C2414yes—
397#63225C24112yes—
398C4×Dic17C2413yes—
399C4×Dic17C2413yes—
400C4×Dic17C2413yes—
401C4×Dic17C2411yescharacteristic
402C4×Dic17C2411yescharacteristic
403C4×Dic17C2411yescharacteristic
404C4×Dic17C2414yes—
405C4×Dic17C2413yes—
406C4×Dic17C2413yes—
407C4×Dic17C2413yes—
408C4×Dic17C2413yes—
409C4×Dic17C2413yes—
410C4×Dic17C2413yes—
411C4×Dic17C24112yes—
412#62800—171nomaximal, Sylow
413C23×C17C2513yes—
414C22×D17—26no—
415C22×D17—224no—
416C22×D17—26no—
417C22×D17—43no—
418C22×D17—412no—
419C22×D17—412no—
420C22×D17C2513yes—
421C22×D17C25112yes—
422C22×D17C2511yescharacteristic
423Q8×C17—212no—
424Q8×C17—24no—
425Q8×C17—412no—
426Q8×C17C2×#4114yescomplemented
427D4×C17C2×#41112yescomplemented
428C2×C4×C17—26no—
429C2×C4×C17—26no—
430C2×C4×C17—412no—
431C2×C4×C17C2×#41112yescomplemented
432C2×C4×C17C2514yes—
433C2×C4×C17C2513yes—
434C2×C4×C17C2513yes—
435C2×C4×C17C25112yes—
436C2×C4×C17C2513yes—
437C2×C4×C17C2511yescharacteristic
438C2×C4×C17C2511yescharacteristic
439C2×C4×C17C2511yescharacteristic
440C22⋊D17—224no—
441C22⋊D17—212no—
442C2×Dic17—26no—
443C2×Dic17—26no—
444C2×Dic17—43no—
445C2×Dic17C2513yes—
446C2×Dic17C2513yes—
447C2×Dic17C2513yes—
448C2×Dic17C2514yes—
449C2×Dic17C2511yescharacteristic
450C2×Dic17C2511yescharacteristic
451C2×Dic17C2511yescharacteristic
452D68—224no—
453D68—212no—
454D68—224no—
455D68—26no—
456D68—212no—
457D68—212no—
458D68—412no—
459D68—412no—
460D68—424no—
461D68—412no—
462C4×D17—26no—
463C4×D17—22no—
464C4×D17—26no—
465C4×D17—26no—
466C4×D17—26no—
467C4×D17—224no—
468C4×D17—26no—
469C4×D17—22no—
470C4×D17—26no—
471C4×D17—26no—
472C4×D17—224no—
473C4×D17—43no—
474C4×D17—43no—
475C4×D17—424no—
476C4×D17—412no—
477C4×D17H(5,𝔽2)14yescomplemented
478Dic34—24no—
479Dic34—26no—
480#3522—172no—
481#3519—176no—
482#3517—172no—
483#3514—176no—
484#3511—173no—
485#3508—173no—
486#3503D1711yescharacteristic, complemented
487#3498—171no—
488#3494—176no—
489#3488—172no—
490#3483—172no—
491#3481—176no—
492#3480—172no—
493D4×#41—176no—
494#3460—176no—
495#3444—173no—
496C2×#532—173no—
497C4×H(5,𝔽2)—172no—
498C2×C4×#41—171no—
499C22×C17—23no—
500C22×C17—23no—
501C22×C17C22×#4116yes—
502C22×C17C2611yescharacteristic
503C2×D17—21no—
504C2×D17—21no—
505C2×D17—23no—
506C2×D17—212no—
507C2×D17—23no—
508C2×D17—212no—
509C2×D17—23no—
510C2×D17—212no—
511C2×D17—412no—
512C2×D17—824no—
513C2×D17C2×H(5,𝔽2)12yes—
514C4×C17—23no—
515C4×C17—212no—
516C4×C17—24no—
517C4×C17—23no—
518C4×C17C22×#4112yes—
519C4×C17C22×#4116yes—
520C4×C17C2×H(5,𝔽2)12yes—
521C4×C17#58512yes—
522Dic17—23no—
523Dic17—24no—
524Dic17—21no—
525Dic17—23no—
526Dic17—23no—
527Dic17—21no—
528Dic17C2×H(5,𝔽2)12yes—
529C2×H(5,𝔽2)—172no—
530C22×#41—171no—
531C22×#41—176no—
532#559—176no—
533#559—176no—
534Q82C2×D1712yescomplemented
535#557C2×D1712yescomplemented
536#556—176no—
537#555—1712no—
538#555—176no—
539#554—176no—
540#554C2×D1716yescomplemented
541#553—1712no—
542#553—1712no—
543#553—1712no—
544#551—1724no—
545#550—176no—
546#550—172no—
547#550—174no—
548#550—172no—
549#550—176no—
550D4×Q8C2×D1716yescomplemented
551#548—1712no—
552#548—174no—
553#547—1712no—
554#547—176no—
555#546—1724no—
556#546—1712no—
557#546—1712no—
558#546—1712no—
559D42—1712no—
560D42—176no—
561D42—176no—
562#544C2×D1716yescomplemented
563#542—1712no—
564#542—1712no—
565#540—1712no—
566#540—1712no—
567#538—1724no—
568#537—176no—
569#535—176no—
570#535—176no—
571#533—171no—
572#533—173no—
573#533C2×D1713yescomplemented
574#532—173no—
575#532—176no—
576#532—176no—
577#532—176no—
578#532—176no—
579#532—176no—
580#532—176no—
581#532—176no—
582#532—173no—
583#532—1712no—
584#532—173no—
585C2×C4⋊Q8C2×D1713yescomplemented
586C2×#127—173no—
587#529—176no—
588#529—176no—
589#529—1712no—
590#529—176no—
591#529—176no—
592#529—176no—
593#529—176no—
594C2×#124—176no—
595#525—176no—
596#525—176no—
597#525—1724no—
598#525—176no—
599C2×#121—176no—
600C2×#121—176no—
601#520—174no—
602#520—176no—
603#520C2×D1712yes—
604#518—1712no—
605#518—176no—
606C4×#41—171no—
607C4×#41—171no—
608C4×#41—171no—
609C4×#41—174no—
610C4×#41—176no—
611C4×#41—176no—
612C4×#41—173no—
613C4×#41—173no—
614C4×#41—173no—
615C4×#41—176no—
616C4×#41—173no—
617C4×#41C2×D1711yescharacteristic
618C2×C4×Q8—171no—
619C2×C4×Q8—171no—
620C2×C4×D4—173no—
621C2×C4×D4—173no—
622C2×C4×D4—1712no—
623C2×C4×D4—176no—
624C2×C4×D4—176no—
625C2×#117—173no—
626C22×C42—173no—
627C2×C17—26no—
628C2×C17C23×#4111yescharacteristic
629C2×C17C22×H(5,𝔽2)11yescharacteristic
630C2×C17C2×#58511yescharacteristic
631D17—22no—
632D17—43no—
633D17—412no—
634H(5,𝔽2)—3416no—
635C2×#41—171no—
636C2×#41—174no—
637C2×#41—176no—
638C2×#41—176no—
639C2×#41—1712no—
640C2×#41—1712no—
641C2×#41—1712no—
642C2×#41—173no—
643C2×#41—173no—
644C2×#41—176no—
645C2×#41—348no—
646C2×#41—6824no—
647C2×#41C22×D1711yescharacteristic
648C22×Q8—171no—
649C22×Q8C22×D1716yes—
650C22×D4—173no—
651C22×D4—1712no—
652C22×D4—176no—
653C22×D4—176no—
654C22×D4—1712no—
655C22×D4—176no—
656C23×C4—173no—
657C23×C4—173no—
658C23×C4—1712no—
659C23×C4—173no—
660C4⋊Q8—171no—
661C4⋊Q8C22×D1713yes—
662C4⋊Q8C22×D1716yes—
663C4⋊Q8C22×D1716yes—
664C4⋊Q8C22×D1716yes—
665C4⋊Q8C22×D1711yescharacteristic
666C4⋊Q8C22×D17112yes—
667#127—173no—
668#127—176no—
669#127—176no—
670#127—176no—
671#127—1712no—
672#126—1712no—
673#126—1712no—
674#126—1724no—
675#125—172no—
676#125—176no—
677#125C22×D1716yes—
678#125C22×D17112yes—
679#124—176no—
680#124—1712no—
681#124—1712no—
682#124—1712no—
683#124—176no—
684#124—1724no—
685#124—176no—
686#124—1712no—
687#123—1712no—
688#123—1712no—
689#123—1724no—
690#123—1724no—
691#123—1724no—
692#123—1712no—
693C22⋊Q8—172no—
694C22⋊Q8—176no—
695C22⋊Q8—1724no—
696C22⋊Q8—172no—
697C22⋊Q8—176no—
698C22⋊Q8—1712no—
699C22⋊Q8C22×D1716yes—
700C22⋊Q8C22×D1716yes—
701C22⋊Q8C22×D17124yes—
702#121—176no—
703#121—176no—
704#121—1724no—
705#121—176no—
706#121—176no—
707#121—1712no—
708#121—1712no—
709#121—1712no—
710#121—1712no—
711#121—1712no—
712#121—1712no—
713#121—176no—
714#121—176no—
715#121—1724no—
716#121—1712no—
717#121—1712no—
718#121—1712no—
719#121—1724no—
720#120—1712no—
721#120—1724no—
722#120—1724no—
723C4×Q8—171no—
724C4×Q8—171no—
725C4×Q8—172no—
726C4×Q8—176no—
727C4×Q8—173no—
728C4×Q8—173no—
729C4×Q8—172no—
730C4×Q8—176no—
731C4×Q8—173no—
732C4×Q8—173no—
733C4×Q8C22×D1711yescharacteristic
734C4×Q8C22×D1711yescharacteristic
735C4×Q8C22×D1714yes—
736C4×Q8C22×D1716yes—
737C4×Q8C22×D1716yes—
738C4×D4—173no—
739C4×D4—173no—
740C4×D4—176no—
741C4×D4—176no—
742C4×D4—1724no—
743C4×D4—1712no—
744C4×D4—176no—
745C4×D4—176no—
746C4×D4—173no—
747C4×D4—173no—
748C4×D4—1712no—
749C4×D4—1712no—
750C4×D4—1712no—
751C4×D4—1712no—
752C4×D4—1712no—
753C4×D4—176no—
754C4×D4—1712no—
755C4×D4—1712no—
756C4×D4—176no—
757C4×D4—1712no—
758C4×D4—176no—
759C4×D4—176no—
760C4×D4—1712no—
761C4×D4—173no—
762C4×D4—173no—
763C4×D4—1712no—
764C4×D4—1712no—
765C4×D4—1712no—
766C4×D4—1712no—
767C4×D4—176no—
768C4×D4—176no—
769C4×D4C22×D1713yes—
770C4×D4C22×D1713yes—
771C4×D4C22×D17112yes—
772#117—173no—
773#117—173no—
774#117—173no—
775#117—172no—
776#117—1712no—
777#117—1712no—
778#117—176no—
779#117—1712no—
780#117—176no—
781#117—176no—
782#117—1712no—
783#117C22×D1713yes—
784#117C22×D1716yes—
785C2×C4⋊C4—173no—
786C2×C4⋊C4—173no—
787C2×C4⋊C4—1712no—
788C2×C4⋊C4C22×D1716yes—
789C2×C4⋊C4C22×D1716yes—
790C2×C22⋊C4—1712no—
791C2×C22⋊C4—1712no—
792C2×C22⋊C4—176no—
793C2×C22⋊C4—1724no—
794C2×C42—173no—
795C2×C42—173no—
796C2×C42—173no—
797C2×C42—173no—
798C2×C42—173no—
799C2×C42—173no—
800C2×C42—1712no—
801C2×C42—173no—
802C2×C42—173no—
803C2×C42—173no—
804C2×C42—173no—
805C2×C42—171no—
806C2×C42C22×D1713yes—
807C17#6280011yescharacteristic, complemented, Sylow
808C24—173no—
809C24—1712no—
810#41—3424no—
811#41—344no—
812#41—3416no—
813#41—3412no—
814#41—3412no—
815#41—3424no—
816#41—6824no—
817#41—6824no—
818#41—6812no—
819#41—6824no—
820#41#6325618yescomplemented
821C2×Q8—412no—
822C2×Q8—173no—
823C2×Q8—172no—
824C2×Q8—344no—
825C2×Q8C23×D1712yes—
826C2×Q8C23×D1716yes—
827C2×Q8C23×D17112yes—
828C2×Q8C23×D1711yescharacteristic
829C2×D4—176no—
830C2×D4—1712no—
831C2×D4—176no—
832C2×D4—1712no—
833C2×D4—176no—
834C2×D4—173no—
835C2×D4—1712no—
836C2×D4—176no—
837C2×D4—1712no—
838C2×D4—1712no—
839C2×D4—1712no—
840C2×D4—1724no—
841C2×D4—3412no—
842C2×D4—3448no—
843C2×D4—3424no—
844C2×D4—6812no—
845C2×D4—6812no—
846C2×D4—6824no—
847C2×D4C23×D1713yes—
848C22×C4—171no—
849C22×C4—173no—
850C22×C4—173no—
851C22×C4—173no—
852C22×C4—171no—
853C22×C4—171no—
854C22×C4—173no—
855C22×C4—173no—
856C22×C4—173no—
857C22×C4—173no—
858C22×C4—173no—
859C22×C4—173no—
860C22×C4—173no—
861C22×C4—1712no—
862C22×C4—1712no—
863C22×C4—173no—
864C22×C4—173no—
865C22×C4—1712no—
866C22×C4—1724no—
867C22×C4—3412no—
868C22×C4—3412no—
869C22×C4—686no—
870C22×C4—6824no—
871C22×C4C23×D1713yes—
872C22×C4C23×D1713yes—
873C22×C4C23×D17112yes—
874C22×C4C23×D1713yes—
875C4⋊C4—173no—
876C4⋊C4—1712no—
877C4⋊C4—173no—
878C4⋊C4—176no—
879C4⋊C4—176no—
880C4⋊C4—172no—
881C4⋊C4—174no—
882C4⋊C4—174no—
883C4⋊C4—172no—
884C4⋊C4—1712no—
885C4⋊C4C23×D17112yes—
886C4⋊C4C23×D1713yes—
887C4⋊C4C23×D1713yes—
888C4⋊C4C23×D1716yes—
889C4⋊C4C23×D1716yes—
890C4⋊C4C23×D17112yes—
891C4⋊C4C23×D1712yes—
892C4⋊C4C23×D17112yes—
893C4⋊C4C23×D17112yes—
894C4⋊C4C23×D1712yes—
895C22⋊C4—176no—
896C22⋊C4—1712no—
897C22⋊C4—1712no—
898C22⋊C4—1724no—
899C22⋊C4—1712no—
900C22⋊C4—176no—
901C22⋊C4—176no—
902C22⋊C4—1724no—
903C22⋊C4—174no—
904C22⋊C4—1712no—
905C22⋊C4—1712no—
906C22⋊C4—1712no—
907C22⋊C4—1712no—
908C22⋊C4C23×D17112yes—
909C22⋊C4C23×D1716yes—
910C42—171no—
911C42—173no—
912C42—171no—
913C42—171no—
914C42—173no—
915C42—173no—
916C42—174no—
917C42—173no—
918C42—173no—
919C42—173no—
920C42—173no—
921C42—173no—
922C42—173no—
923C42—1712no—
924C42C23×D1711yescharacteristic
925C42C23×D1713yes—
926C42C23×D1713yes—
927C42C23×D1713yes—
928C42C23×D17112yes—
929C23—171no—
930C23—1712no—
931C23—173no—
932C23—346no—
933C23—346no—
934C23—3424no—
935C23—683no—
936C23—6812no—
937C23—6812no—
938C23C24×D1713yes—
939Q8—212no—
940Q8—24no—
941Q8—412no—
942Q8—346no—
943Q8—344no—
944Q8C2×#6325614yescomplemented
945D4—3424no—
946D4—3424no—
947D4—3412no—
948D4—3424no—
949D4—3412no—
950D4—346no—
951D4—3412no—
952D4—3412no—
953D4—6812no—
954D4—6824no—
955D4—6812no—
956D4—6812no—
957D4C2×#63256112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—412no—
961C2×C4—171no—
962C2×C4—174no—
963C2×C4—171no—
964C2×C4—171no—
965C2×C4—173no—
966C2×C4—173no—
967C2×C4—174no—
968C2×C4—173no—
969C2×C4—346no—
970C2×C4—3424no—
971C2×C4—346no—
972C2×C4—346no—
973C2×C4—346no—
974C2×C4—342no—
975C2×C4—346no—
976C2×C4—346no—
977C2×C4—346no—
978C2×C4—3424no—
979C2×C4—346no—
980C2×C4—342no—
981C2×C4—346no—
982C2×C4—6824no—
983C2×C4—683no—
984C2×C4—683no—
985C2×C4—6812no—
986C2×C4—683no—
987C2×C4C2×#63256112yescomplemented
988C2×C4C24×D1713yes—
989C2×C4C24×D1713yes—
990C2×C4C24×D1714yes—
991C2×C4C24×D17112yes—
992C2×C4C24×D1711yescharacteristic
993C2×C4C24×D1713yes—
994C2×C4C24×D1711yescharacteristic
995C2×C4C24×D1711yescharacteristic
996C22—23no—
997C22—23no—
998C22—172no—
999C22—341no—
1000C22—341no—
1001C22—343no—
1002C22—3412no—
1003C22—343no—
1004C22—3412no—
1005C22—343no—
1006C22—3412no—
1007C22—6812no—
1008C22—13624no—
1009C22C22×#6325616yes—
1010C22C25×D1711yescharacteristic
1011C4—23no—
1012C4—212no—
1013C4—23no—
1014C4—24no—
1015C4—172no—
1016C4—341no—
1017C4—344no—
1018C4—343no—
1019C4—343no—
1020C4—341no—
1021C4—343no—
1022C4C22×#6325616yes—
1023C4C22×#6325612yes—
1024C4H(5,𝔽2)×D1712yes—
1025C4#1176364612yes—
1026C2—26no—
1027C2—342no—
1028C2—683no—
1029C2—6812no—
1030C2C23×#6325611yescharacteristic
1031C2C2×H(5,𝔽2)×D1711yescharacteristic
1032C2C2×#1176364611yescharacteristic
subgroupG/H
center, FrattiniC22C25×D17
commutator, socle, cosocleC22×C17C26
FittingC17×#3503C2
hypercenter#3503D17
hypocenterC17#62800
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #14542870C2semidirect
2. #14542817C2semidirect
3. #14542791C2semidirect
4. #14542746C2semidirect
5. #14542697C2semidirect
6. #14542661C2semidirect
7. #14542562C2semidirect
8. #14542522C2semidirect
9. #14542454C2semidirect
10. #14542411C2semidirect
11. #14542395C2semidirect
12. #14542384C2semidirect
13. D4×#63256C2semidirect
14. #14542207C2semidirect
15. #14542081C2semidirect
16. C2×#11763360C2semidirect
17. #14541990C2semidirect
18. C4×#41×D17C2semidirect
19. C17×#3503C2semidirect
21. C22×#63256C22semidirect
23. #11763544C22semidirect
24. #11763544C22semidirect
25. #11763533C22semidirect
26. #11763525C22semidirect
27. #11763525C22semidirect
28. #11763520C22semidirect
29. #11763512C22semidirect
30. #11763512C22semidirect
31. #11763507C22semidirect
32. #11763486C22semidirect
33. #11763481C22semidirect
34. #11763481C22semidirect
35. #11763481C22semidirect
36. #11763481C22semidirect
37. #11763481C22semidirect
38. #11763471C22semidirect
39. #11763470C22semidirect
40. #11763462C22semidirect
41. #11763462C22semidirect
42. #11763454C22semidirect
43. #11763450C22semidirect
44. #11763450C22semidirect
45. #11763450C22semidirect
46. D4×D68C22semidirect
47. D4×D68C22semidirect
48. D4×D68C22semidirect
49. #11763433C22semidirect
50. #11763433C22semidirect
51. #11763415C22semidirect
52. #11763415C22semidirect
53. #11763399C22semidirect
54. #11763390C22semidirect
55. #11763378C22semidirect
56. #11763378C22semidirect
57. #11763364C22semidirect
58. #11763364C22semidirect
59. #11763360C22semidirect
60. #11763360C22semidirect
61. #11763360C22semidirect
62. #11763360C22semidirect
63. #11763360C22semidirect
64. #11763360C22semidirect
65. #11763360C22semidirect
66. #11763360C22semidirect
67. #11763360C22semidirect
68. #11763360C22semidirect
69. #11763359C22semidirect
70. C2×#10587560C22semidirect
71. #11763346C22semidirect
72. #11763346C22semidirect
73. #11763345C22semidirect
74. #11763345C22semidirect
75. #11763344C22semidirect
76. #11763344C22semidirect
77. #11763344C22semidirect
78. C2×#10587633C22semidirect
79. #11763322C22semidirect
80. #11763322C22semidirect
81. #11763322C22semidirect
82. #11763321C22semidirect
83. C2×#10587581C22semidirect
84. C2×#10587581C22semidirect
85. #11763291C22semidirect
86. #11763290C22semidirect
87. #11763283C22semidirect
88. #11763281C22semidirect
90. C4×#63256C22semidirect
91. C4×#63256C22semidirect
92. C4×#63256C22semidirect
93. C4×#63256C22semidirect
94. C4×#63256C22semidirect
95. C4×#63252C22semidirect
96. #11763277C22semidirect
97. #11763277C22semidirect
98. C4×#63254C22semidirect
99. C4×#63254C22semidirect
100. C4×Q8×D17C22semidirect
101. C4×Q8×D17C22semidirect
102. C2×#10587579C22semidirect
103. C2×#10587579C22semidirect
104. C4×D4×D17C22semidirect
105. C4×D4×D17C22semidirect
106. C4×D4×D17C22semidirect
107. #117×D17C22semidirect
108. C2×C42×D17C22semidirect
109. Q82×C17C22semidirect
110. C17×#557C22semidirect
111. C17×#554C22semidirect
112. D4×Q8×C17C22semidirect
113. C17×#544C22semidirect
114. C17×#533C22semidirect
115. C2×C17×C4⋊Q8C22semidirect
293. #41×C17#41semidirect
426. Q8×C17C2×#41semidirect
427. D4×C17C2×#41semidirect
431. C2×C4×C17C2×#41semidirect
477. C4×D17H(5,𝔽2)semidirect
486. #3503D17semidirect
534. Q82C2×D17semidirect
535. #557C2×D17semidirect
540. #554C2×D17semidirect
550. D4×Q8C2×D17semidirect
562. #544C2×D17semidirect
573. #533C2×D17semidirect
585. C2×C4⋊Q8C2×D17semidirect
807. C17#62800semidirect
820. #41#63256semidirect
944. Q8C2×#63256semidirect
957. D4C2×#63256semidirect
987. C2×C4C2×#63256semidirect

Maximal subgroups

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

subgroupindex
#145428702
#145428172
#145427912
#145427462
#145426972
#145426612
#145425622
#145425222
#145424542
#145424112
#145423952
#145423842
D4×#632562
#145422072
#145420812
C2×#117633602
#145419902
C4×#41×D172
C17×#35032
#6280017