Finite Group Databasebeta

← #17196997

Subgroups — #17196997

Order 4352.

2106 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763345C211yesmaximal, characteristic
2#14531975C212yesmaximal, complemented
3#14531974C212yesmaximal, complemented
4#14531967C212yesmaximal, complemented
5#14531956C212yesmaximal, complemented
6#14531950C211yesmaximal, characteristic, complemented
7#14531943C211yesmaximal, characteristic
8#14531938C211yesmaximal, characteristic
9#14531930C212yesmaximal, complemented
10#14531930C212yesmaximal, complemented
11#14531276C212yesmaximal, complemented
12#14531265C212yesmaximal, complemented
13#14531259C212yesmaximal, complemented
14#14531244C212yesmaximal, complemented
15#14531226C212yesmaximal, complemented
16#14531222C212yesmaximal, complemented
17#14531186C211yesmaximal, characteristic, complemented
18#14531175C211yesmaximal, characteristic, complemented
19C17×#2378C211yesmaximal, characteristic, complemented
20#11763345C4116yescomplemented
21C2×#10587584C2212yes—
22C2×#10587576C2211yescharacteristic
23C2×#10587633C2211yescharacteristic
24C2×#10587572C2212yes—
25C2×#10587616C2211yescharacteristic
26C2×Q8×Dic17C2211yescharacteristic
27C2×#10587579C2211yescharacteristic
28C2×#10587567C2212yes—
29C2×#10587578C2212yes—
30C2×#10587578C2212yes—
31C2×#10587563C2211yescharacteristic
32C2×#10587563C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C2×C42×D17C2212yes—
35#11762716C2212yes—
36#11762709C2212yes—
37#11762709C2212yes—
38#11762708C2212yes—
39#11762707C2212yes—
40#11762707C2212yes—
41#11762706C2212yes—
42#11762705C2212yes—
43#11762705C2212yes—
44#11762704C2212yes—
45#11762702C2212yes—
46#11762702C2212yes—
47#11762701C2212yes—
48#11762700C2212yes—
49#11762700C2212yes—
50#11762700C2212yes—
51#11762699C2212yes—
52#11762698C2212yes—
53#11762698C2212yes—
54#11762698C2212yes—
55#11762695C2212yes—
56#11762695C2212yes—
57#11762694C2212yes—
58#11762694C2212yes—
59#11762694C2212yes—
60#11762693C2212yes—
61#11762692C2212yes—
62#11762692C2212yes—
63#11762692C2212yes—
64#11762691C2212yes—
65#11762687C2212yes—
66#11762687C2212yes—
67#11762685C2212yes—
68#11762685C2212yes—
69#11762683C2212yes—
70#11762683C2212yes—
71#11762683C2212yes—
72#11762683C2212yes—
73#11762680C2212yes—
74#11762680C2212yes—
75#11762680C2212yes—
76#11762680C2212yes—
77#11762678C2212yes—
78#11762676C2211yescharacteristic
79#11762676C2211yescharacteristic
80#11762673C2212yes—
81#11762673C2212yes—
82#11762672C2211yescharacteristic
83#11762669C2211yescharacteristic
84#11762667C2212yes—
85#11762667C2211yescharacteristic
86#11762667C2211yescharacteristic
87C4⋊C4×Dic17C2212yes—
88C4⋊C4×Dic17C2212yes—
89#11762660C2211yescharacteristic
90#11762660C2211yescharacteristic
91#11762660C2212yes—
92#11762660C2212yes—
93C22⋊C4×Dic17C2212yes—
94#11762656C2212yes—
95#11762656C2212yes—
96#11762654C2212yes—
97#11762654C2212yes—
98C42×Dic17C2212yes—
99C2×C17×C22⋊Q8C2211yescharacteristic
100C17×#391C2212yes—
101C17×#389C2212yes—
102C17×#388C2212yes—
103C17×#388C2212yes—
104C17×#387C2212yes—
105C17×#387C2212yes—
106C17×#381C2211yescharacteristic
107C17×#380C2211yescharacteristic
108C22×Q8×C17C2311yescharacteristic
109C23×C4×C17C2311yescharacteristic
110C22×C22⋊D17C2312yes—
111C23×Dic17C2311yescharacteristic
112C23×Dic17C2311yescharacteristic
113C22×D68C2311yescharacteristic
114C22×C4×D17C2312yes—
115C22×C4×D17C2312yes—
116C22×C4×D17C2312yes—
117C17×C22⋊Q8C2×C418yescomplemented
118C2×C4⋊C4×C17C2312yes—
119C2×C4⋊C4×C17C2312yes—
120C2×C4⋊C4×C17C2312yes—
121C2×C4⋊C4×C17C2311yescharacteristic
122C2×C4⋊C4×C17C2312yes—
123C2×C22⋊C4×C17C2311yescharacteristic
124C2×C22⋊C4×C17C2312yes—
125C2×C22⋊C4×C17C2311yescharacteristic
126C2×C22⋊C4×C17C2312yes—
127C2×C42×C17C2312yes—
128C2×C42×C17C2312yes—
129C2×C22⋊Dic17C2311yescharacteristic
130C2×C22⋊Dic17C2312yes—
131C2×C22⋊Dic17C2311yescharacteristic
132#10587633C2×C418yes—
133Q8×Dic17C2×C418yescomplemented
134#10587616C2×C418yes—
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⋊Dic17C2311yescharacteristic
149C2×C4⋊Dic17C2312yes—
150C2×C4⋊Dic17C2312yes—
151C2×#63225C2312yes—
152C2×#63225C2312yes—
153C2×#63225C2312yes—
154C2×#63225C2312yes—
155C2×#63225C2312yes—
156C2×#63225C2312yes—
157C2×#63225C2312yes—
158C2×#63225C2312yes—
159C2×#63225C2312yes—
160C2×C4×Dic17C2×C418yescomplemented
161C2×C4×Dic17C2312yes—
162C2×C4×Dic17C2312yes—
163C2×C4×Dic17C2312yes—
164C2×C4×Dic17C2312yes—
165C2×C4×Dic17C2312yes—
166C2×C4×Dic17C2312yes—
167C2×C4×Dic17C2312yes—
168C2×C4×Dic17C2312yes—
169C2×C4×Dic17C2311yescharacteristic
170C2×C4×Dic17C2311yescharacteristic
171C2×C4×Dic17C2311yescharacteristic
172C2×C4×Dic17C2311yescharacteristic
173C2×C4×Dic17C2312yes—
174#10587584C2×C4116yescomplemented
175#10587579C2×C418yes—
176#10587578—44no—
177#10587578C2×C4116yescomplemented
178#10587576C2×C418yescomplemented
179#10587572C2×C4116yescomplemented
180#10587567C2×C4116yescomplemented
181#10587563—42no—
182#10587563—42no—
183C42×D17—44no—
184C17×#95C2312yes—
185C17×#95C2312yes—
186C17×#95C2312yes—
187C17×#95C2312yes—
188C17×#95C2312yes—
189C17×#95C2312yes—
190C17×#95C2311yescharacteristic
191C17×#95C2311yescharacteristic
192#10587502C2312yes—
193#10587502C2312yes—
194#10587502C2312yes—
195#10587502C2312yes—
196#10587502C2312yes—
197#10587502C2312yes—
198#10587502C2312yes—
199#10587502C2312yes—
200#10587502C2312yes—
201#10587502C2312yes—
202#10587502C2312yes—
203#10587502C2312yes—
204#10587502C2312yes—
205#10587502C2312yes—
206#10587502C2312yes—
207#10587502C2312yes—
208#10587502C2311yescharacteristic
209#10587502C2311yescharacteristic
210C24×C17C2411yescharacteristic
211C23×D17C2412yes—
212C2×Q8×C17—42no—
213C2×Q8×C17C22×C414yes—
214C22×C4×C17—42no—
215C22×C4×C17C22×C414yes—
216C22×C4×C17C2412yes—
217C22×C4×C17C2412yes—
218C22×C4×C17C2412yes—
219C22×C4×C17C2412yes—
220C22×C4×C17C2412yes—
221C22×C4×C17C2411yescharacteristic
222C22×C4×C17C2411yescharacteristic
223C22×C4×C17C2412yes—
224C2×C22⋊D17—42no—
225C2×C22⋊D17—42no—
226C2×C22⋊D17C22×C418yes—
227C22×Dic17—22no—
228C22×Dic17—22no—
229C22×Dic17—42no—
230C22×Dic17C22×C414yes—
231C22×Dic17C22×C414yes—
232C22×Dic17C2412yes—
233C22×Dic17C2412yes—
234C22×Dic17C2412yes—
235C22×Dic17C2412yes—
236C22×Dic17C2411yescharacteristic
237C22×Dic17C2411yescharacteristic
238C22×Dic17C2411yescharacteristic
239C22×Dic17C2412yes—
240C22×Dic17C2411yescharacteristic
241C2×D68—42no—
242C2×D68C22×C414yes—
243C2×C4×D17—24no—
244C2×C4×D17—24no—
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×D17C22×C418yes—
252C4⋊C4×C17—42no—
253C4⋊C4×C17—42no—
254C4⋊C4×C17—42no—
255C4⋊C4×C17C22×C414yes—
256C4⋊C4×C17C22×C418yes—
257C22⋊C4×C17—41no—
258C22⋊C4×C17—41no—
259C22⋊C4×C17—42no—
260C22⋊C4×C17C22×C418yes—
261C42×C17—42no—
262C42×C17—42no—
263C22⋊Dic17—41no—
264C22⋊Dic17—41no—
265C22⋊Dic17—42no—
266#63227—42no—
267#63227—42no—
268#63227—42no—
269#63227—42no—
270#63227—42no—
271#63227—42no—
272#63227C22×C418yes—
273#63227C22×C418yes—
274#63227C22×C418yes—
275#63227C22×C418yes—
276C4⋊Dic17—42no—
277C4⋊Dic17—42no—
278C4⋊Dic17—42no—
279C4⋊Dic17C22×C418yes—
280C4⋊Dic17C22×C418yes—
281C4⋊Dic17C22×C414yes—
282#63225—42no—
283#63225—42no—
284#63225—42no—
285#63225—42no—
286#63225—42no—
287#63225—42no—
288#63225—42no—
289#63225—42no—
290#63225C22×C418yes—
291C4×Dic17—24no—
292C4×Dic17—24no—
293C4×Dic17—24no—
294C4×Dic17—24no—
295C4×Dic17—42no—
296C4×Dic17—42no—
297C4×Dic17—42no—
298C4×Dic17—42no—
299C4×Dic17C22×C418yes—
300C4×Dic17C22×C414yes—
301C4×Dic17C22×C414yes—
302C4×Dic17C22×C414yes—
303C4×Dic17C22×C414yes—
304#34350—171nomaximal, Sylow
305C23×C17—21no—
306C23×C17—21no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17C23×C412yes—
310C23×C17C2511yescharacteristic
311C22×D17—22no—
312C22×D17—22no—
313C22×D17—22no—
314C22×D17—22no—
315C22×D17—22no—
316C22×D17—22no—
317C22×D17C23×C414yes—
318Q8×C17—44no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
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—44no—
338C2×C4×C17C23×C414yes—
339C2×C4×C17C23×C414yes—
340C2×C4×C17C23×C412yes—
341C2×C4×C17C23×C412yes—
342C22⋊D17—48no—
343C2×Dic17—21no—
344C2×Dic17—21no—
345C2×Dic17—22no—
346C2×Dic17—22no—
347C2×Dic17—22no—
348C2×Dic17—22no—
349C2×Dic17—28no—
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×Dic17—22no—
362C2×Dic17—44no—
363C2×Dic17C23×C412yes—
364C2×Dic17C23×C412yes—
365C2×Dic17C23×C412yes—
366C2×Dic17C23×C414yes—
367C2×Dic17C23×C412yes—
368C2×Dic17H(5,𝔽2)12yes—
369C2×Dic172−1+412yes—
370D68—44no—
371C4×D17—216no—
372C4×D17—48no—
373C4×D17—48no—
374C2×#529—171no—
375#2383—172no—
376#2383—172no—
377#2382—172no—
378#2379—172no—
379#2378—171no—
380#2378D1711yescharacteristic, complemented
381#2377—171no—
382#2377—171no—
383#2376—172no—
384#2376—172no—
385#2298—172no—
386#2296—172no—
387#2295—172no—
388#2293—172no—
389#2290—172no—
390#2290—172no—
391#2285—171no—
392#2283—171no—
393C22×C17—22no—
394C22×C17—22no—
395C22×C17—22no—
396C22×C17—42no—
397C22×C17—42no—
398C22×C17C24×C411yescharacteristic
399C22×C17C2×H(5,𝔽2)11yescharacteristic
400C22×C17C2×2−1+411yescharacteristic
401C22×C17#58512yes—
402C22×C17#58512yes—
403C2×D17—24no—
404C2×D17—24no—
405C2×D17—24no—
406C2×D17—42no—
407C2×D17—42no—
408C2×D17—42no—
409C2×D17—42no—
410C4×C17—24no—
411C4×C17—22no—
412C4×C17—22no—
413C4×C17—24no—
414C4×C17—42no—
415C4×C17—42no—
416C4×C17—42no—
417C4×C17—42no—
418Dic17—22no—
419Dic17—22no—
420Dic17—22no—
421Dic17—24no—
422Dic17—42no—
423Dic17—42no—
424Dic17—42no—
425Dic17—42no—
426Dic17#52014yes—
427#529—1716no—
428C2×#126—172no—
429C2×#125—171no—
430C2×#124—171no—
431C2×#123—172no—
432C2×C22⋊Q8C2×D1711yescharacteristic
433C2×#121—171no—
434C2×C4×Q8—171no—
435C2×C4×D4—171no—
436C2×C4×D4—172no—
437C2×#117—172no—
438C2×#117—172no—
439C2×#117—171no—
440C2×#117—171no—
441C22×C42—171no—
442C22×C42—172no—
443#391—172no—
444#391C2×D1712yes—
445#390—172no—
446#390—172no—
447#389—172no—
448#389—172no—
449#389—172no—
450#389—172no—
451#389—172no—
452#389—172no—
453#389—172no—
454#389C2×D1712yes—
455#388—172no—
456#388—172no—
457#388—172no—
458#388—172no—
459#388—172no—
460#388—172no—
461#388—172no—
462#388—172no—
463#388—172no—
464#388—172no—
465#388C2×D1712yes—
466#388C2×D1712yes—
467#387—172no—
468#387—172no—
469#387—172no—
470#387—172no—
471#387—172no—
472#387—172no—
473#387—172no—
474#387—172no—
475#387—172no—
476#387—172no—
477#387C2×D1712yes—
478#387C2×D1712yes—
479#386—172no—
480#386—172no—
481#386—172no—
482#386—172no—
483#385—172no—
484#385—172no—
485#385—172no—
486#385—172no—
487#385—172no—
488#385—172no—
489#385—172no—
490#385—172no—
491#384—172no—
492#383—171no—
493#383—171no—
494#382—172no—
495#382—172no—
496#381—171no—
497#381C2×D1711yescharacteristic
498#380—171no—
499#380—172no—
500#380—171no—
501#380—171no—
502#380C2×D1711yescharacteristic
503C4×C4⋊C4—172no—
504C4×C4⋊C4—172no—
505C4×C4⋊C4—171no—
506C4×C4⋊C4—171no—
507C4×C4⋊C4—172no—
508C4×C4⋊C4—172no—
509C4×C22⋊C4—172no—
510C4×C22⋊C4—172no—
511C4×C22⋊C4—172no—
512#376—172no—
513#376—172no—
514C43—172no—
515C2×C17—42no—
516C2×C17C2×#52011yescharacteristic
517C2×C17#342811yescharacteristic
518C2×C17#342811yescharacteristic
519C2×C17#352912yes—
520C2×C17#353112yes—
521D17—44no—
522C22×Q8C22×D1711yescharacteristic
523C22×D4—172no—
524C22×D4—171no—
525C23×C4—171no—
526C23×C4—171no—
527C23×C4—172no—
528C23×C4—172no—
529C23×C4—172no—
530C23×C4C22×D1711yescharacteristic
531#126—1716no—
532#125—178no—
533#124—178no—
534#123—1716no—
535C22⋊Q8C4×D1718yescomplemented
536#121—178no—
537C4×Q8—178no—
538C4×D4—178no—
539C4×D4—1716no—
540#117—1716no—
541#117—682no—
542#117—682no—
543#117—684no—
544C2×C4⋊C4—172no—
545C2×C4⋊C4—172no—
546C2×C4⋊C4—171no—
547C2×C4⋊C4—172no—
548C2×C4⋊C4—172no—
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⋊C4C22×D1712yes—
560C2×C4⋊C4C22×D1712yes—
561C2×C4⋊C4C22×D1712yes—
562C2×C4⋊C4C22×D1712yes—
563C2×C4⋊C4C22×D1711yescharacteristic
564C2×C22⋊C4—172no—
565C2×C22⋊C4—172no—
566C2×C22⋊C4—172no—
567C2×C22⋊C4—172no—
568C2×C22⋊C4—171no—
569C2×C22⋊C4—171no—
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⋊C4C22×D1711yescharacteristic
578C2×C22⋊C4C22×D1711yescharacteristic
579C2×C22⋊C4C22×D1712yes—
580C2×C22⋊C4C22×D1712yes—
581C2×C42—178no—
582C2×C42—171no—
583C2×C42—172no—
584C2×C42—171no—
585C2×C42—171no—
586C2×C42—171no—
587C2×C42—172no—
588C2×C42—172no—
589C2×C42—172no—
590C2×C42—172no—
591C2×C42—172no—
592C2×C42—172no—
593C2×C42—172no—
594C2×C42—172no—
595C2×C42—684no—
596C2×C42C22×D1712yes—
597C2×C42C22×D1712yes—
598#95—172no—
599#95—172no—
600#95—172no—
601#95—172no—
602#95—172no—
603#95—172no—
604#95—172no—
605#95—172no—
606#95—172no—
607#95—172no—
608#95—172no—
609#95—172no—
610#95—172no—
611#95—171no—
612#95—171no—
613#95—172no—
614#95—172no—
615#95—172no—
616#95C22×D1712yes—
617#95C22×D1712yes—
618#95C22×D1712yes—
619#95C22×D1712yes—
620#95C22×D1712yes—
621#95C22×D1711yescharacteristic
622#95C22×D1711yescharacteristic
623#95C22×D1712yes—
624C17#3435011yescharacteristic, complemented, Sylow
625C24—172no—
626C24C23×D1711yescharacteristic
627C2×Q8—42no—
628C2×Q8C2×C4×D1714yes—
629C2×D4—178no—
630C2×D4—174no—
631C2×D4—682no—
632C2×D4—682no—
633C2×D4—682no—
634C22×C4—42no—
635C22×C4—171no—
636C22×C4—174no—
637C22×C4—172no—
638C22×C4—171no—
639C22×C4—171no—
640C22×C4—171no—
641C22×C4—174no—
642C22×C4—178no—
643C22×C4—172no—
644C22×C4—172no—
645C22×C4—172no—
646C22×C4—172no—
647C22×C4—344no—
648C22×C4—344no—
649C22×C4—342no—
650C22×C4—342no—
651C22×C4—682no—
652C22×C4—682no—
653C22×C4—682no—
654C22×C4—682no—
655C22×C4—682no—
656C22×C4—682no—
657C22×C4—682no—
658C22×C4C2×C4×D1714yes—
659C22×C4C23×D1712yes—
660C22×C4C23×D1712yes—
661C22×C4C23×D1712yes—
662C22×C4C23×D1712yes—
663C22×C4C23×D1711yescharacteristic
664C22×C4C23×D1712yes—
665C22×C4C23×D1711yescharacteristic
666C22×C4C23×D1712yes—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—178no—
671C4⋊C4—178no—
672C4⋊C4—174no—
673C4⋊C4—178no—
674C4⋊C4—682no—
675C4⋊C4—682no—
676C4⋊C4—682no—
677C4⋊C4—682no—
678C4⋊C4—682no—
679C4⋊C4—682no—
680C4⋊C4—682no—
681C4⋊C4—682no—
682C4⋊C4—682no—
683C4⋊C4—682no—
684C4⋊C4—682no—
685C4⋊C4C2×C4×D1718yes—
686C4⋊C4C2×C4×D1714yes—
687C22⋊C4—42no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—178no—
691C22⋊C4—178no—
692C22⋊C4—178no—
693C22⋊C4—178no—
694C22⋊C4—682no—
695C22⋊C4—682no—
696C22⋊C4—682no—
697C22⋊C4—682no—
698C22⋊C4—682no—
699C22⋊C4—682no—
700C22⋊C4—682no—
701C22⋊C4—681no—
702C22⋊C4—681no—
703C22⋊C4C2×C4×D1718yes—
704C42—42no—
705C42—42no—
706C42—174no—
707C42—174no—
708C42—174no—
709C42—174no—
710C42—178no—
711C42—344no—
712C42—344no—
713C42—344no—
714C42—344no—
715C42—682no—
716C42—682no—
717C42—682no—
718C42—682no—
719C23—21no—
720C23—21no—
721C23—22no—
722C23—22no—
723C23—174no—
724C23—342no—
725C23—342no—
726C23—342no—
727C23—342no—
728C23—342no—
729C23—342no—
730C23C22×C4×D1712yes—
731C23C24×D1711yescharacteristic
732Q8—44no—
733D4—684no—
734D4—688no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
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—44no—
754C2×C4—172no—
755C2×C4—172no—
756C2×C4—172no—
757C2×C4—172no—
758C2×C4—172no—
759C2×C4—172no—
760C2×C4—174no—
761C2×C4—3416no—
762C2×C4—348no—
763C2×C4—341no—
764C2×C4—341no—
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—342no—
781C2×C4—688no—
782C2×C4—688no—
783C2×C4—684no—
784C2×C4C22×C4×D1712yes—
785C2×C4C22×C4×D1712yes—
786C2×C4C22×C4×D1714yes—
787C2×C4C22×C4×D1714yes—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—42no—
792C22—42no—
793C22—344no—
794C22—344no—
795C22—344no—
796C22—682no—
797C22—682no—
798C22—682no—
799C22—682no—
800C22C23×C4×D1711yescharacteristic
801C22H(5,𝔽2)×D1711yescharacteristic
802C222−1+4×D1711yescharacteristic
803C22#1176364412yes—
804C22#1176364612yes—
805C4—24no—
806C4—22no—
807C4—22no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—174no—
814C4—342no—
815C4—342no—
816C4—342no—
817C4—344no—
818C4—682no—
819C4—682no—
820C4—682no—
821C4—682no—
822C2—42no—
823C2—684no—
824C2D17×#52011yescharacteristic
825C2#1454198211yescharacteristic
826C2#1454198611yescharacteristic
827C2#1454292112yes—
828C2#1454293012yes—
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2378C2
socle, cosocleC23×C17C25
prime radicalC2×#10587616C22
hypercenter#2378D17
hypocenterC17#34350
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2378

Complements

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

NH ≅ G/Ntype
2. #14531975C2semidirect
3. #14531974C2semidirect
4. #14531967C2semidirect
5. #14531956C2semidirect
6. #14531950C2semidirect
9. #14531930C2semidirect
10. #14531930C2semidirect
11. #14531276C2semidirect
12. #14531265C2semidirect
13. #14531259C2semidirect
14. #14531244C2semidirect
15. #14531226C2semidirect
16. #14531222C2semidirect
17. #14531186C2semidirect
18. #14531175C2semidirect
19. C17×#2378C2semidirect
20. #11763345C4semidirect
117. C17×C22⋊Q8C2×C4semidirect
133. Q8×Dic17C2×C4semidirect
160. C2×C4×Dic17C2×C4semidirect
174. #10587584C2×C4semidirect
177. #10587578C2×C4semidirect
178. #10587576C2×C4semidirect
179. #10587572C2×C4semidirect
180. #10587567C2×C4semidirect
380. #2378D17semidirect
535. C22⋊Q8C4×D17semidirect
624. C17#34350semidirect

Maximal subgroups

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

subgroupindex
C2×#117633452
#145319752
#145319742
#145319672
#145319562
#145319502
#145319432
#145319382
#145319302
#145312762
#145312652
#145312592
#145312442
#145312262
#145312222
#145311862
#145311752
C17×#23782
#3435017