Finite Group Databasebeta

← #17197609

Subgroups — #17197609

Order 4352.

2118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763344C211yesmaximal, characteristic
2#14531975C212yesmaximal, complemented
3#14531974C212yesmaximal, complemented
4#14531781C212yesmaximal, complemented
5#14531769C212yesmaximal, complemented
6#14531723C212yesmaximal, complemented
7#14531693C212yesmaximal, complemented
8#14531673C212yesmaximal, complemented
9#14531643C212yesmaximal, complemented
10#14531597C211yesmaximal, characteristic, complemented
11#14531594C211yesmaximal, characteristic, complemented
12#14531590C211yesmaximal, characteristic, complemented
13#14531513C212yesmaximal, complemented
14#14531483C212yesmaximal
15#14531433C212yesmaximal, complemented
16#14531416C212yesmaximal, complemented
17#14531188C211yesmaximal, characteristic, complemented
18D17×#383C211yesmaximal, characteristic, complemented
19C17×#2336C211yesmaximal, characteristic, complemented
20#11763344C4116yescomplemented
21C2×#10587584C2212yes—
22C2×#10587561C2211yescharacteristic
23C2×#10587580C2212yes—
24C2×#10587583C2211yescharacteristic
25C2×#10587581C2211yescharacteristic
26C2×#10587573C2211yescharacteristic
27C2×C4×D68C2212yes—
28C2×#10587579C2212yes—
29C2×#10587579C2211yescharacteristic
30C2×#10587579C2212yes—
31C2×#10587578C2212yes—
32C2×#10587558C2211yescharacteristic
33C2×#10587558C2211yescharacteristic
34C2×C42×D17C2211yescharacteristic
35#11762713C2212yes—
36#11762713C2212yes—
37#11762708C2212yes—
38#11762707C2212yes—
39#11762706C2212yes—
40#11762705C2212yes—
41#11762704C2212yes—
42#11762701C2212yes—
43#11762700C2212yes—
44#11762700C2212yes—
45#11762700C2212yes—
46#11762699C2212yes—
47#11762698C2212yes—
48#11762698C2212yes—
49#11762698C2212yes—
50#11762695C2212yes—
51#11762695C2212yes—
52#11762695C2212yes—
53#11762695C2212yes—
54#11762694C2212yes—
55#11762693C2212yes—
56#11762692C2212yes—
57#11762691C2212yes—
58#11762687C2212yes—
59#11762687C2212yes—
60#11762687C2212yes—
61#11762687C2212yes—
62#11762683C2212yes—
63#11762683C2212yes—
64#11762683C2212yes—
65#11762683C2212yes—
66#11762680C2212yes—
67#11762680C2212yes—
68#11762680C2212yes—
69#11762680C2212yes—
70#11762678C2212yes—
71#11762677C2211yescharacteristic
72#11762676C2212yes—
73#11762676C2212yes—
74#11762676C2212yes—
75#11762676C2211yescharacteristic
76#11762676C2211yescharacteristic
77#11762674C2212yes—
78#11762673C2212yes—
79#11762671C2212yes—
80#11762668C2212yes—
81#11762666C2212yes—
82#11762666C2212yes—
83C4⋊C4×Dic17C2212yes—
84C4×#63225C2211yescharacteristic
85C4×#63225C2211yescharacteristic
86C4×#63225C2212yes—
87C4×C4⋊Dic17C2211yescharacteristic
88C4×#63227C2212yes—
89C4×#63227C2212yes—
90C4×#63227C2212yes—
91#11762656C2212yes—
92#11762656C2212yes—
93#11762654C2212yes—
94#95×D17C2212yes—
95#95×D17C2211yescharacteristic
96#95×D17C2211yescharacteristic
97#95×D17C2212yes—
98#95×D17C2212yes—
99C2×C17×#125C2211yescharacteristic
100C17×#389C2212yes—
101C17×#387C2212yes—
102C17×#387C2212yes—
103C17×#387C2212yes—
104C17×#387C2212yes—
105C17×#383C2211yescharacteristic
106C4×C4⋊C4×C17C2211yescharacteristic
107C4×C4⋊C4×C17C2212yes—
108C22×D68C2312yes—
109C22×D68C2311yescharacteristic
110C22×C4×D17C2311yescharacteristic
111C22×C4×D17C2312yes—
112C22×C4×D17C2312yes—
113C22×C4×D17C2312yes—
114C22×C4×D17C2312yes—
115C22×C4×D17C2311yescharacteristic
116C22×C4×D17C2311yescharacteristic
117C22×C4×D17C2312yes—
118C22×Dic34C2311yescharacteristic
119C17×#125C2×C418yescomplemented
120C2×C4⋊C4×C17C2312yes—
121C2×C4⋊C4×C17C2312yes—
122C2×C4⋊C4×C17C2312yes—
123C2×C4⋊C4×C17C2311yescharacteristic
124C2×C4⋊C4×C17C2311yescharacteristic
125C2×C4⋊C4×C17C2312yes—
126C2×C4⋊C4×C17C2312yes—
127C2×C42×C17C2312yes—
128C2×C42×C17C2311yescharacteristic
129C2×C42×C17C2312yes—
130C2×C42×C17C2311yescharacteristic
131C2×C42×C17C2311yescharacteristic
132C2×#63227C2312yes—
133C2×#63227C2312yes—
134C2×#63227C2312yes—
135C2×#63227C2312yes—
136C2×#63227C2312yes—
137C2×#63227C2312yes—
138C2×#63227C2312yes—
139C2×#63227C2312yes—
140C2×#63227C2312yes—
141C2×#63227C2312yes—
142C2×#63227C2312yes—
143C2×#63227C2312yes—
144C2×#63227C2312yes—
145C2×C4⋊Dic17C2312yes—
146C2×C4⋊Dic17C2312yes—
147C2×C4⋊Dic17C2312yes—
148C2×C4⋊Dic17C2312yes—
149C2×#63225C2312yes—
150C2×#63225C2312yes—
151C2×#63225C2312yes—
152C2×#63225C2312yes—
153C2×#63225C2312yes—
154C2×#63225C2312yes—
155C2×#63225C2312yes—
156C2×C4×Dic17C2312yes—
157C2×C4×Dic17C2312yes—
158C2×C4×Dic17C2312yes—
159C2×C4×Dic17C2312yes—
160C2×C4×Dic17C2311yescharacteristic
161C2×C4×Dic17C2311yescharacteristic
162C2×C4×Dic17C2311yescharacteristic
163C2×C4×Dic17C2311yescharacteristic
164C2×C4×Dic17C2311yescharacteristic
165C2×C4×Dic17C2312yes—
166#10587584C2×C4116yescomplemented
167#10587583C2×C418yescomplemented
168#10587581C2×C418yes—
169#10587580C2×C4116yescomplemented
170#10587579—44no—
171#10587579C2×C418yescomplemented
172#10587579C2×C4116yescomplemented
173#10587578C2×C4116yescomplemented
174#10587573C2×C418yescomplemented
175#10587561C2×C418yescomplemented
176C4×D68—44no—
177#10587558—42no—
178#10587558—42no—
179C42×D17C2×C418yescomplemented
180C17×#95C2312yes—
181C17×#95C2312yes—
182C17×#95C2312yes—
183C17×#95C2312yes—
184C17×#95C2312yes—
185C17×#95C2311yescharacteristic
186C17×#95C2312yes—
187C17×#95C2312yes—
188C17×#95C2311yescharacteristic
189#10587502C2312yes—
190#10587502C2312yes—
191#10587502C2312yes—
192#10587502C2312yes—
193#10587502C2312yes—
194#10587502C2312yes—
195#10587502C2312yes—
196#10587502C2312yes—
197#10587502C2312yes—
198#10587502C2312yes—
199#10587502C2312yes—
200#10587502C2311yescharacteristic
201#10587502C2312yes—
202#10587502C2312yes—
203#10587502C2312yes—
204#10587502C2312yes—
205#10587502C2311yescharacteristic
206#10587502C2312yes—
207#10587502C2312yes—
208#10587502C2312yes—
209#10587502C2312yes—
210C23×D17C2412yes—
211C23×D17C2411yescharacteristic
212C22×C4×C17C2412yes—
213C22×C4×C17C2412yes—
214C22×C4×C17C2412yes—
215C22×C4×C17C2412yes—
216C22×C4×C17C2411yescharacteristic
217C22×C4×C17C2411yescharacteristic
218C22×C4×C17C2412yes—
219C22×C4×C17C2411yescharacteristic
220C22×C4×C17C2412yes—
221C22×Dic17C2412yes—
222C22×Dic17C2412yes—
223C22×Dic17C2412yes—
224C22×Dic17C2412yes—
225C22×Dic17C2412yes—
226C22×Dic17C2411yescharacteristic
227C22×Dic17C2411yescharacteristic
228C22×Dic17C2411yescharacteristic
229C2×D68—24no—
230C2×D68—24no—
231C2×D68—42no—
232C2×D68C22×C418yes—
233C2×D68C22×C414yes—
234C2×C4×D17—22no—
235C2×C4×D17—22no—
236C2×C4×D17—24no—
237C2×C4×D17—24no—
238C2×C4×D17—42no—
239C2×C4×D17—42no—
240C2×C4×D17—42no—
241C2×C4×D17—42no—
242C2×C4×D17—42no—
243C2×C4×D17—42no—
244C2×C4×D17—42no—
245C2×C4×D17—42no—
246C2×C4×D17—42no—
247C2×C4×D17—42no—
248C2×C4×D17—42no—
249C2×C4×D17—42no—
250C2×C4×D17—42no—
251C2×C4×D17—42no—
252C2×C4×D17C22×C414yes—
253C2×C4×D17C22×C414yes—
254C2×C4×D17C22×C414yes—
255C2×C4×D17C22×C418yes—
256C2×Dic34—42no—
257C2×Dic34C22×C414yes—
258C4⋊C4×C17—42no—
259C4⋊C4×C17—42no—
260C4⋊C4×C17—42no—
261C4⋊C4×C17C22×C414yes—
262C4⋊C4×C17C22×C418yes—
263C4⋊C4×C17C22×C414yes—
264C4⋊C4×C17C22×C418yes—
265C42×C17—41no—
266C42×C17—41no—
267C42×C17—42no—
268C42×C17—42no—
269C42×C17C22×C414yes—
270#63227—24no—
271#63227—24no—
272#63227—42no—
273#63227—42no—
274#63227—42no—
275#63227—42no—
276#63227—42no—
277#63227—42no—
278#63227C22×C418yes—
279#63227C22×C418yes—
280#63227C22×C418yes—
281#63227C22×C418yes—
282#63227C22×C418yes—
283C4⋊Dic17—42no—
284C4⋊Dic17—42no—
285C4⋊Dic17—42no—
286C4⋊Dic17C22×C418yes—
287#63225—42no—
288#63225—42no—
289#63225—42no—
290#63225—42no—
291#63225—42no—
292#63225—42no—
293#63225C22×C418yes—
294C4×Dic17—41no—
295C4×Dic17—41no—
296C4×Dic17—42no—
297C4×Dic17—42no—
298C4×Dic17—42no—
299C4×Dic17—42no—
300C4×Dic17C22×C414yes—
301C4×Dic17C22×C414yes—
302C4×Dic17C22×C414yes—
303C4×Dic17C22×C418yes—
304#34401—171nomaximal, Sylow
305C23×C17C2511yescharacteristic
306C22×D17—22no—
307C22×D17—22no—
308C22×D17—22no—
309C22×D17—22no—
310C22×D17—22no—
311C22×D17—22no—
312C22×D17—22no—
313C22×D17—22no—
314C22×D17C23×C414yes—
315C22×D17C23×C412yes—
316C22×D17H(5,𝔽2)12yes—
317C22×D172−1+412yes—
318C2×C4×C17—21no—
319C2×C4×C17—22no—
320C2×C4×C17—21no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17C23×C412yes—
339C2×C4×C17C23×C412yes—
340C2×C4×C17C23×C412yes—
341C2×C4×C17C23×C414yes—
342C2×C4×C17C23×C414yes—
343C2×Dic17—21no—
344C2×Dic17—21no—
345C2×Dic17—22no—
346C2×Dic17—22no—
347C2×Dic17—22no—
348C2×Dic17—22no—
349C2×Dic17—22no—
350C2×Dic17—22no—
351C2×Dic17—22no—
352C2×Dic17—22no—
353C2×Dic17—22no—
354C2×Dic17—22no—
355C2×Dic17—22no—
356C2×Dic17—22no—
357C2×Dic17—22no—
358C2×Dic17—22no—
359C2×Dic17—22no—
360C2×Dic17—22no—
361C2×Dic17C23×C414yes—
362C2×Dic17C23×C412yes—
363C2×Dic17C23×C412yes—
364C2×Dic17C23×C412yes—
365D68—216no—
366D68—44no—
367C4×D17—28no—
368C4×D17—44no—
369C4×D17—48no—
370C4×D17—44no—
371C4×D17—84no—
372C4×D17—84no—
373C4×D17—84no—
374C4×D17—84no—
375Dic34—44no—
376C2×#529—171no—
377#2383—172no—
378#2383—172no—
379#2359—172no—
380#2359—172no—
381#2353—172no—
382#2349—172no—
383#2347—172no—
384#2343—172no—
385#2337—171no—
386#2337—171no—
387#2336—171no—
388#2336D1711yescharacteristic, complemented
389#2329—172no—
390#2325—172no—
391#2320—172no—
392#2318—172no—
393#2285—171no—
394C2×#383—171no—
395C22×C17C24×C411yescharacteristic
396C22×C17C2×H(5,𝔽2)11yescharacteristic
397C22×C17C2×2−1+411yescharacteristic
398C22×C17#58512yes—
399C22×C17#58512yes—
400C2×D17—22no—
401C2×D17—22no—
402C2×D17—24no—
403C2×D17—24no—
404C2×D17—24no—
405C2×D17—24no—
406C2×D17—24no—
407C2×D17—42no—
408C2×D17—42no—
409C2×D17—42no—
410C2×D17—42no—
411C2×D17#52014yes—
412C4×C17—22no—
413C4×C17—24no—
414C4×C17—22no—
415C4×C17—24no—
416C4×C17—22no—
417C4×C17—42no—
418C4×C17—42no—
419C4×C17—42no—
420C4×C17—42no—
421Dic17—22no—
422Dic17—24no—
423Dic17—22no—
424Dic17—22no—
425Dic17—42no—
426Dic17—42no—
427Dic17—42no—
428Dic17—42no—
429#529—1716no—
430C2×#126—172no—
431C2×#125C2×D1711yescharacteristic
432C2×#124—171no—
433C2×#123—172no—
434C2×C22⋊Q8—171no—
435C2×#121—171no—
436C2×C4×Q8—171no—
437C2×C4×D4—171no—
438C2×C4×D4—172no—
439C2×C4×D4—172no—
440C2×C4×D4—172no—
441C2×#117—172no—
442C2×#117—171no—
443C2×#117—171no—
444C22×C42—171no—
445#391—172no—
446#391—172no—
447#389—172no—
448#389—172no—
449#389—172no—
450#389—172no—
451#389—172no—
452#389C2×D1712yes—
453#388—172no—
454#388—172no—
455#388—172no—
456#388—172no—
457#388—172no—
458#388—172no—
459#388—172no—
460#388—172no—
461#387—172no—
462#387—172no—
463#387—172no—
464#387—172no—
465#387—172no—
466#387—172no—
467#387—172no—
468#387—172no—
469#387C2×D1712yes—
470#387C2×D1712yes—
471#387C2×D1712yes—
472#387C2×D1712yes—
473#386—172no—
474#386—172no—
475#386—172no—
476#386—172no—
477#385—172no—
478#385—172no—
479#385—172no—
480#385—172no—
481#385—172no—
482#385—172no—
483#385—172no—
484#385—172no—
485#384—172no—
486#383—171no—
487#383—172no—
488#383—172no—
489#383—172no—
490#383—171no—
491#383—171no—
492#383C2×D1711yescharacteristic
493#382—172no—
494#382—172no—
495#381—172no—
496#380—172no—
497#380—172no—
498#380—172no—
499C4×C4⋊C4—172no—
500C4×C4⋊C4—172no—
501C4×C4⋊C4—171no—
502C4×C4⋊C4—171no—
503C4×C4⋊C4—171no—
504C4×C4⋊C4C2×D1711yescharacteristic
505C4×C4⋊C4C2×D1712yes—
506C4×C22⋊C4—172no—
507C4×C22⋊C4—172no—
508C4×C22⋊C4—172no—
509C4×C22⋊C4—172no—
510C4×C22⋊C4—172no—
511#376—172no—
512C2×#95—172no—
513C2×#95—172no—
514C2×#95—171no—
515C2×#95—171no—
516C2×#95—172no—
517C2×C17C2×#52011yescharacteristic
518C2×C17#342811yescharacteristic
519C2×C17#342811yescharacteristic
520C2×C17#356012yes—
521C2×C17#356412yes—
522D17—24no—
523D17—44no—
524C22×Q8—171no—
525C22×D4—172no—
526C22×D4—171no—
527C23×C4—171no—
528C23×C4—172no—
529C23×C4—171no—
530C23×C4—171no—
531C23×C4—172no—
532C23×C4—172no—
533C23×C4—172no—
534C23×C4—172no—
535#126—1716no—
536#125C4×D1718yescomplemented
537#124—178no—
538#123—1716no—
539C22⋊Q8—178no—
540#121—178no—
541C4×Q8—178no—
542C4×D4—178no—
543C4×D4—1716no—
544C4×D4—684no—
545C4×D4—684no—
546#117—1716no—
547#117—682no—
548#117—682no—
549C2×C4⋊C4—172no—
550C2×C4⋊C4—172no—
551C2×C4⋊C4—172no—
552C2×C4⋊C4—172no—
553C2×C4⋊C4—172no—
554C2×C4⋊C4—172no—
555C2×C4⋊C4—172no—
556C2×C4⋊C4—172no—
557C2×C4⋊C4—172no—
558C2×C4⋊C4—172no—
559C2×C4⋊C4—172no—
560C2×C4⋊C4C22×D1712yes—
561C2×C4⋊C4C22×D1712yes—
562C2×C4⋊C4C22×D1712yes—
563C2×C4⋊C4C22×D1712yes—
564C2×C4⋊C4C22×D1711yescharacteristic
565C2×C4⋊C4C22×D1712yes—
566C2×C4⋊C4C22×D1711yescharacteristic
567C2×C22⋊C4—172no—
568C2×C22⋊C4—172no—
569C2×C22⋊C4—172no—
570C2×C22⋊C4—172no—
571C2×C22⋊C4—172no—
572C2×C22⋊C4—172no—
573C2×C22⋊C4—172no—
574C2×C22⋊C4—172no—
575C2×C22⋊C4—172no—
576C2×C22⋊C4—172no—
577C2×C22⋊C4—172no—
578C2×C22⋊C4—172no—
579C2×C22⋊C4—172no—
580C2×C42—171no—
581C2×C42—172no—
582C2×C42—171no—
583C2×C42—171no—
584C2×C42—178no—
585C2×C42—171no—
586C2×C42—171no—
587C2×C42—172no—
588C2×C42—172no—
589C2×C42—172no—
590C2×C42—172no—
591C2×C42C22×D1711yescharacteristic
592C2×C42C22×D1711yescharacteristic
593C2×C42C22×D1712yes—
594C2×C42C22×D1712yes—
595C2×C42C22×D1711yescharacteristic
596#95—172no—
597#95—172no—
598#95—172no—
599#95—172no—
600#95—171no—
601#95—172no—
602#95—172no—
603#95—172no—
604#95—172no—
605#95—172no—
606#95—171no—
607#95—172no—
608#95—172no—
609#95—172no—
610#95—172no—
611#95—172no—
612#95—172no—
613#95—172no—
614#95—172no—
615#95—172no—
616#95—172no—
617#95C22×D1712yes—
618#95C22×D1711yescharacteristic
619#95C22×D1712yes—
620#95C22×D1711yescharacteristic
621#95C22×D1712yes—
622#95C22×D1712yes—
623#95C22×D1712yes—
624#95C22×D1712yes—
625#95C22×D1712yes—
626C17#3440111yescharacteristic, complemented, Sylow
627C24—171no—
628C24—172no—
629C2×Q8—174no—
630C2×Q8—682no—
631C2×D4—178no—
632C2×D4—174no—
633C2×D4—344no—
634C2×D4—344no—
635C2×D4—682no—
636C22×C4—171no—
637C22×C4—172no—
638C22×C4—171no—
639C22×C4—171no—
640C22×C4—174no—
641C22×C4—174no—
642C22×C4—174no—
643C22×C4—178no—
644C22×C4—172no—
645C22×C4—172no—
646C22×C4—172no—
647C22×C4—172no—
648C22×C4—342no—
649C22×C4—342no—
650C22×C4—344no—
651C22×C4—344no—
652C22×C4—682no—
653C22×C4—682no—
654C22×C4—682no—
655C22×C4—682no—
656C22×C4—682no—
657C22×C4—682no—
658C22×C4—682no—
659C22×C4—682no—
660C22×C4—682no—
661C22×C4—682no—
662C22×C4—682no—
663C22×C4—682no—
664C22×C4—682no—
665C22×C4—682no—
666C22×C4C23×D1712yes—
667C22×C4C23×D1712yes—
668C22×C4C23×D1712yes—
669C22×C4C23×D1712yes—
670C22×C4C23×D1711yescharacteristic
671C22×C4C23×D1711yescharacteristic
672C22×C4C23×D1712yes—
673C22×C4C23×D1712yes—
674C22×C4C23×D1711yescharacteristic
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—178no—
679C4⋊C4—178no—
680C4⋊C4—682no—
681C4⋊C4—682no—
682C4⋊C4—682no—
683C4⋊C4—682no—
684C4⋊C4—682no—
685C4⋊C4—682no—
686C4⋊C4—682no—
687C4⋊C4—682no—
688C4⋊C4—682no—
689C4⋊C4C2×C4×D1718yes—
690C4⋊C4C2×C4×D1714yes—
691C4⋊C4C2×C4×D1718yes—
692C4⋊C4C2×C4×D1714yes—
693C22⋊C4—178no—
694C22⋊C4—178no—
695C22⋊C4—178no—
696C22⋊C4—178no—
697C22⋊C4—178no—
698C22⋊C4—344no—
699C22⋊C4—344no—
700C22⋊C4—682no—
701C22⋊C4—682no—
702C22⋊C4—682no—
703C22⋊C4—682no—
704C22⋊C4—682no—
705C22⋊C4—682no—
706C42—42no—
707C42—41no—
708C42—41no—
709C42—42no—
710C42—174no—
711C42—174no—
712C42—174no—
713C42—178no—
714C42—681no—
715C42—681no—
716C42—682no—
717C42—682no—
718C42—682no—
719C42—682no—
720C42C2×C4×D1714yes—
721C23—172no—
722C23—172no—
723C23—172no—
724C23—174no—
725C23—342no—
726C23—342no—
727C23—342no—
728C23—342no—
729C23—342no—
730C23—342no—
731C23—342no—
732C23—342no—
733C23C24×D1711yescharacteristic
734Q8—684no—
735D4—3416no—
736D4—684no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—172no—
758C2×C4—172no—
759C2×C4—172no—
760C2×C4—174no—
761C2×C4—348no—
762C2×C4—341no—
763C2×C4—341no—
764C2×C4—342no—
765C2×C4—342no—
766C2×C4—342no—
767C2×C4—342no—
768C2×C4—342no—
769C2×C4—342no—
770C2×C4—342no—
771C2×C4—342no—
772C2×C4—342no—
773C2×C4—342no—
774C2×C4—342no—
775C2×C4—342no—
776C2×C4—342no—
777C2×C4—342no—
778C2×C4—342no—
779C2×C4—342no—
780C2×C4—684no—
781C2×C4—688no—
782C2×C4—684no—
783C2×C4—1364no—
784C2×C4—1364no—
785C2×C4—1364no—
786C2×C4—1364no—
787C2×C4C22×C4×D1712yes—
788C2×C4C22×C4×D1712yes—
789C2×C4C22×C4×D1712yes—
790C2×C4C22×C4×D1714yes—
791C2×C4C22×C4×D1714yes—
792C22—174no—
793C22—344no—
794C22—342no—
795C22—342no—
796C22—344no—
797C22—344no—
798C22—344no—
799C22—344no—
800C22—682no—
801C22—682no—
802C22—682no—
803C22—682no—
804C22C23×C4×D1711yescharacteristic
805C22H(5,𝔽2)×D1711yescharacteristic
806C222−1+4×D1711yescharacteristic
807C22#1176364512yes—
808C22#1176364612yes—
809C4—22no—
810C4—24no—
811C4—24no—
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—342no—
819C4—342no—
820C4—342no—
821C4—344no—
822C4—682no—
823C4—682no—
824C4—682no—
825C4—682no—
826C2—344no—
827C2—684no—
828C2D17×#52011yescharacteristic
829C2#1454198311yescharacteristic
830C2#1454198611yescharacteristic
831C2#1454333712yes—
832C2#1454339712yes—
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2336C2
socle, cosocleC23×C17C25
prime radicalC2×#10587581C22
hypercenter#2336D17
hypocenterC17#34401
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
2. #14531975C2semidirect
3. #14531974C2semidirect
4. #14531781C2semidirect
5. #14531769C2semidirect
6. #14531723C2semidirect
7. #14531693C2semidirect
8. #14531673C2semidirect
9. #14531643C2semidirect
10. #14531597C2semidirect
11. #14531594C2semidirect
12. #14531590C2semidirect
13. #14531513C2semidirect
15. #14531433C2semidirect
16. #14531416C2semidirect
17. #14531188C2semidirect
18. D17×#383C2semidirect
19. C17×#2336C2semidirect
20. #11763344C4semidirect
119. C17×#125C2×C4semidirect
166. #10587584C2×C4semidirect
167. #10587583C2×C4semidirect
169. #10587580C2×C4semidirect
171. #10587579C2×C4semidirect
172. #10587579C2×C4semidirect
173. #10587578C2×C4semidirect
174. #10587573C2×C4semidirect
175. #10587561C2×C4semidirect
179. C42×D17C2×C4semidirect
388. #2336D17semidirect
536. #125C4×D17semidirect
626. C17#34401semidirect

Maximal subgroups

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

subgroupindex
C2×#117633442
#145319752
#145319742
#145317812
#145317692
#145317232
#145316932
#145316732
#145316432
#145315972
#145315942
#145315902
#145315132
#145314832
#145314332
#145314162
#145311882
D17×#3832
C17×#23362
#3440117