Finite Group Databasebeta

← #17200475

Subgroups — #17200475

Order 4352.

2008 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763559C211yesmaximal, characteristic
2#14531969C211yesmaximal, characteristic, complemented
3#14531969C211yesmaximal, characteristic, complemented
4#14531902C212yesmaximal, complemented
5#14531899C212yesmaximal, complemented
6#14531865C212yesmaximal, complemented
7#14531841C212yesmaximal, complemented
8#14531814C212yesmaximal, complemented
9#14531782C212yesmaximal
10#14531575C212yesmaximal
11#14531560C212yesmaximal, complemented
12#14531557C212yesmaximal, complemented
13#14531527C212yesmaximal, complemented
14#14531515C212yesmaximal, complemented
15#14531463C212yesmaximal, complemented
16#14531339C211yesmaximal, characteristic, complemented
17#14531339C211yesmaximal, characteristic, complemented
18#124×Dic17C211yesmaximal, characteristic
19C17×#2379C211yesmaximal, characteristic
20#11763559C4116yescomplemented
21C2×#10587630C2212yes—
22C2×#10587565C2212yes—
23C2×#10587565C2212yes—
24C2×#10587556C2211yescharacteristic
25C2×#10587556C2211yescharacteristic
26C2×#10587621C2212yes—
27C2×#10587564C2212yes—
28C2×#10587564C2212yes—
29C2×Q8×Dic17C2211yescharacteristic
30C2×C4×Dic34C2212yes—
31C2×D4×Dic17C2211yescharacteristic
32C2×#10587563C2212yes—
33#11762716C2211yescharacteristic
34#11762714C2212yes—
35#11762713C2212yes—
36#11762713C2212yes—
37#11762712C2211yescharacteristic
38#11762706C2212yes—
39#11762706C2212yes—
40#11762706C2212yes—
41#11762705C2211yescharacteristic
42#11762705C2211yescharacteristic
43#11762705C2211yescharacteristic
44#11762705C2211yescharacteristic
45#11762704C2212yes—
46#11762704C2212yes—
47#11762704C2212yes—
48#11762703C2212yes—
49#11762703C2212yes—
50#11762703C2212yes—
51#11762703C2212yes—
52#11762702C2212yes—
53#11762702C2212yes—
54#11762697C2212yes—
55#11762697C2212yes—
56#11762696C2212yes—
57#11762696C2212yes—
58#11762696C2212yes—
59#11762694C2212yes—
60#11762694C2212yes—
61#11762693C2212yes—
62#11762692C2212yes—
63#11762692C2212yes—
64#11762691C2212yes—
65#11762691C2212yes—
66#11762691C2212yes—
67#11762691C2212yes—
68#11762691C2212yes—
69#11762690C2212yes—
70#11762690C2212yes—
71#11762690C2212yes—
72#11762682C2212yes—
73#11762681C2212yes—
74#11762681C2212yes—
75#11762675C2211yescharacteristic
76#11762673C2212yes—
77#11762667C2212yes—
78C4⋊C4×Dic17C2212yes—
79C4⋊C4×Dic17C2211yescharacteristic
80C4⋊C4×Dic17C2211yescharacteristic
81C4⋊C4×Dic17C2211yescharacteristic
82C4⋊C4×Dic17C2211yescharacteristic
83C4×#63225C2212yes—
84C4×#63225C2212yes—
85#11762660C2212yes—
86#11762660C2212yes—
87#11762660C2212yes—
88#11762660C2212yes—
89#11762660C2212yes—
90C22⋊C4×Dic17C2212yes—
91C22⋊C4×Dic17C2212yes—
92C22⋊C4×Dic17C2212yes—
93C22⋊C4×Dic17C2212yes—
94C4×C22⋊Dic17C2212yes—
95C4×C22⋊Dic17C2212yes—
96#11762654C2212yes—
97C2×#10587502C2212yes—
98C42×Dic17C2211yescharacteristic
99C2×C17×#124C2211yescharacteristic
100C17×#391C2212yes—
101C17×#388C2212yes—
102C17×#388C2212yes—
103C17×#386C2212yes—
104C17×#385C2212yes—
105C17×#385C2212yes—
106C17×#382C2211yescharacteristic
107C17×#382C2211yescharacteristic
108C22×Q8×C17C2311yescharacteristic
109C22×D4×C17C2311yescharacteristic
110C23×C4×C17C2312yes—
111C23×Dic17C2312yes—
112C23×Dic17C2312yes—
113C22×Dic34C2312yes—
114C17×#124C2×C418yes—
115C2×C4⋊C4×C17C2311yescharacteristic
116C2×C4⋊C4×C17C2311yescharacteristic
117C2×C4⋊C4×C17C2312yes—
118C2×C4⋊C4×C17C2311yescharacteristic
119C2×C4⋊C4×C17C2311yescharacteristic
120C2×C22⋊C4×C17C2312yes—
121C2×C22⋊C4×C17C2312yes—
122C2×C22⋊C4×C17C2312yes—
123C2×C22⋊C4×C17C2312yes—
124C2×C22⋊C4×C17C2312yes—
125C2×C42×C17C2312yes—
126C2×C42×C17C2311yescharacteristic
127C2×C22⋊Dic17C2312yes—
128C2×C22⋊Dic17C2312yes—
129C2×C22⋊Dic17C2312yes—
130C2×C22⋊Dic17C2312yes—
131C2×C22⋊Dic17C2312yes—
132C2×C22⋊Dic17C2312yes—
133Q8×Dic17—42no—
134#10587630C2×C4116yescomplemented
135#10587621C2×C4116yes—
136D4×Dic17—42no—
137C2×C4⋊Dic17C2312yes—
138C2×C4⋊Dic17C2311yescharacteristic
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141C2×C4⋊Dic17C2311yescharacteristic
142C2×C4⋊Dic17C2311yescharacteristic
143C2×C4⋊Dic17C2311yescharacteristic
144C2×#63225C2312yes—
145C2×#63225C2312yes—
146C2×#63225C2312yes—
147C2×#63225C2312yes—
148C2×#63225C2312yes—
149C2×#63225C2312yes—
150C2×#63225C2312yes—
151C2×#63225C2312yes—
152C2×#63225C2312yes—
153C2×#63225C2312yes—
154C2×#63225C2312yes—
155C2×#63225C2312yes—
156C2×#63225C2312yes—
157C2×#63225C2312yes—
158C2×C4×Dic17C2311yescharacteristic
159C2×C4×Dic17C2311yescharacteristic
160C2×C4×Dic17C2312yes—
161C2×C4×Dic17C2311yescharacteristic
162C2×C4×Dic17C2312yes—
163C2×C4×Dic17C2312yes—
164C2×C4×Dic17C2312yes—
165C2×C4×Dic17C2312yes—
166C2×C4×Dic17C2311yescharacteristic
167C2×C4×Dic17C2311yescharacteristic
168C2×C4×Dic17C2312yes—
169C2×C4×Dic17C2312yes—
170C2×C4×Dic17C2312yes—
171C2×C4×Dic17C2312yes—
172C2×C4×Dic17C2311yescharacteristic
173C2×C4×Dic17C2312yes—
174#10587565C2×C4116yescomplemented
175#10587565C2×C4116yescomplemented
176#10587564C2×C4116yescomplemented
177#10587564C2×C4116yescomplemented
178#10587563—44no—
179#10587556C2×C418yescomplemented
180#10587556C2×C418yescomplemented
181C4×Dic34—44no—
182C17×#95C2312yes—
183C17×#95C2312yes—
184C17×#95C2312yes—
185C17×#95C2312yes—
186C17×#95C2312yes—
187C17×#95C2312yes—
188#10587502C2312yes—
189#10587502C2312yes—
190#10587502C2312yes—
191#10587502C2312yes—
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—
208C24×C17C2412yes—
209C2×Q8×C17—41no—
210C2×Q8×C17—41no—
211C2×Q8×C17C22×C414yes—
212C2×D4×C17—41no—
213C2×D4×C17—41no—
214C2×D4×C17C22×C414yes—
215C22×C4×C17—42no—
216C22×C4×C17—42no—
217C22×C4×C17—42no—
218C22×C4×C17C2412yes—
219C22×C4×C17C2412yes—
220C22×C4×C17C2412yes—
221C22×C4×C17C2412yes—
222C22×C4×C17C2412yes—
223C22×C4×C17C2411yescharacteristic
224C22×C4×C17C2411yescharacteristic
225C22×C4×C17C2411yescharacteristic
226C22×Dic17—24no—
227C22×Dic17—42no—
228C22×Dic17—42no—
229C22×Dic17—42no—
230C22×Dic17—42no—
231C22×Dic17C22×C418yes—
232C22×Dic17C2412yes—
233C22×Dic17C2411yescharacteristic
234C22×Dic17C2412yes—
235C22×Dic17C2412yes—
236C22×Dic17C2412yes—
237C22×Dic17C2412yes—
238C22×Dic17C2412yes—
239C22×Dic17C2411yescharacteristic
240C22×Dic17C2411yescharacteristic
241C22×Dic17C2411yescharacteristic
242C2×Dic34—42no—
243C2×Dic34—42no—
244C2×Dic34C22×C418yes—
245C4⋊C4×C17—41no—
246C4⋊C4×C17—41no—
247C4⋊C4×C17—41no—
248C4⋊C4×C17—41no—
249C4⋊C4×C17—42no—
250C22⋊C4×C17—42no—
251C22⋊C4×C17—42no—
252C22⋊C4×C17—42no—
253C22⋊C4×C17C22×C418yes—
254C22⋊C4×C17C22×C418yes—
255C42×C17—42no—
256C42×C17C22×C414yes—
257C22⋊Dic17—24no—
258C22⋊Dic17—24no—
259C22⋊Dic17—42no—
260C22⋊Dic17C22×C418yes—
261C22⋊Dic17C22×C418yes—
262C22⋊Dic17C22×C418yes—
263C4⋊Dic17—24no—
264C4⋊Dic17—41no—
265C4⋊Dic17—41no—
266C4⋊Dic17C22×C414yes—
267C4⋊Dic17C22×C414yes—
268C4⋊Dic17C22×C414yes—
269C4⋊Dic17C22×C414yes—
270#63225—24no—
271#63225—24no—
272#63225—42no—
273#63225—42no—
274#63225—42no—
275#63225—42no—
276#63225—42no—
277#63225—42no—
278#63225C22×C418yes—
279#63225C22×C418yes—
280#63225C22×C418yes—
281#63225C22×C418yes—
282#63225C22×C418yes—
283#63225C22×C418yes—
284C4×Dic17—24no—
285C4×Dic17—22no—
286C4×Dic17—22no—
287C4×Dic17—24no—
288C4×Dic17—22no—
289C4×Dic17—42no—
290C4×Dic17—42no—
291C4×Dic17—42no—
292C4×Dic17—41no—
293C4×Dic17—42no—
294C4×Dic17—41no—
295C4×Dic17—41no—
296C4×Dic17—42no—
297C4×Dic17—42no—
298C4×Dic17—42no—
299C4×Dic17C22×C418yes—
300#34528—171nomaximal, Sylow
301C23×C17—22no—
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
307C23×C17C23×C414yes—
308C23×C17C2511yescharacteristic
309Q8×C17—44no—
310D4×C17—44no—
311C2×C4×C17—22no—
312C2×C4×C17—21no—
313C2×C4×C17—21no—
314C2×C4×C17—21no—
315C2×C4×C17—21no—
316C2×C4×C17—21no—
317C2×C4×C17—22no—
318C2×C4×C17—21no—
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—84no—
332C2×C4×C17C23×C412yes—
333C2×C4×C17C23×C412yes—
334C2×C4×C17C23×C412yes—
335C2×C4×C17C23×C414yes—
336C2×Dic17—22no—
337C2×Dic17—22no—
338C2×Dic17—21no—
339C2×Dic17—22no—
340C2×Dic17—21no—
341C2×Dic17—21no—
342C2×Dic17—22no—
343C2×Dic17—22no—
344C2×Dic17—22no—
345C2×Dic17—21no—
346C2×Dic17—21no—
347C2×Dic17—21no—
348C2×Dic17—22no—
349C2×Dic17—22no—
350C2×Dic17—22no—
351C2×Dic17—22no—
352C2×Dic17—22no—
353C2×Dic17—22no—
354C2×Dic17—21no—
355C2×Dic17—22no—
356C2×Dic17—22no—
357C2×Dic17—21no—
358C2×Dic17—21no—
359C2×Dic17—48no—
360C2×Dic17—84no—
361C2×Dic17C23×C414yes—
362C2×Dic17C23×C414yes—
363C2×Dic17C23×C414yes—
364C2×Dic17C23×C414yes—
365C2×Dic17H(5,𝔽2)12yes—
366C2×Dic172−1+412yes—
367C2×Dic172−1+412yes—
368Dic34—48no—
369C2×#563—171no—
370#2382—171no—
371#2382—171no—
372#2379D1711yescharacteristic
373#2373—172no—
374#2373—172no—
375#2368—172no—
376#2365—172no—
377#2362—172no—
378#2359—172no—
379#2335—172no—
380#2334—172no—
381#2334—172no—
382#2331—172no—
383#2329—172no—
384#2323—172no—
385C4×#125—171no—
386C4×#125—171no—
387C4×#124—171no—
388C22×C17—24no—
389C22×C17—24no—
390C22×C17—24no—
391C22×C17—42no—
392C22×C17—42no—
393C22×C17—42no—
394C22×C17—42no—
395C22×C17C24×C411yescharacteristic
396C22×C17C2×H(5,𝔽2)11yescharacteristic
397C22×C17C2×2−1+411yescharacteristic
398C22×C17C2×2−1+411yescharacteristic
399C22×C17#58511yescharacteristic
400C22×C17#58511yescharacteristic
401C22×C17#58511yescharacteristic
402C4×C17—24no—
403C4×C17—22no—
404C4×C17—22no—
405C4×C17—22no—
406C4×C17—42no—
407C4×C17—42no—
408C4×C17—42no—
409C4×C17—42no—
410Dic17—24no—
411Dic17—24no—
412Dic17—24no—
413Dic17—24no—
414Dic17—22no—
415Dic17—22no—
416Dic17—22no—
417Dic17—42no—
418Dic17—42no—
419Dic17—41no—
420#563—1716no—
421C2×C4⋊Q8—172no—
422C2×#126—172no—
423C2×#126—172no—
424C2×#125—171no—
425C2×#125—171no—
426C2×#124C2×D1711yescharacteristic
427C2×#123—172no—
428C2×C22⋊Q8—172no—
429C2×C22⋊Q8—172no—
430C2×C4×Q8—171no—
431C2×C4×Q8—172no—
432C2×C4×D4—171no—
433C2×#117—172no—
434#391—171no—
435#391—172no—
436#391—172no—
437#391—172no—
438#391C2×D1712yes—
439#390—171no—
440#389—171no—
441#389—171no—
442#389—171no—
443#389—171no—
444#389—172no—
445#389—172no—
446#389—172no—
447#389—172no—
448#389—172no—
449#389—172no—
450#388—172no—
451#388—172no—
452#388—172no—
453#388—172no—
454#388—172no—
455#388—172no—
456#388—172no—
457#388—172no—
458#388C2×D1712yes—
459#388C2×D1712yes—
460#387—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#387—172no—
470#387—172no—
471#387—172no—
472#387—172no—
473#387—172no—
474#387—172no—
475#387—172no—
476#386C2×D1712yes—
477#385—172no—
478#385—172no—
479#385—172no—
480#385C2×D1712yes—
481#385C2×D1712yes—
482#382—171no—
483#382—172no—
484#382C2×D1711yescharacteristic
485#382C2×D1711yescharacteristic
486#380—172no—
487C4×C4⋊C4—171no—
488C4×C4⋊C4—171no—
489C4×C4⋊C4—171no—
490C4×C4⋊C4—171no—
491C4×C4⋊C4—172no—
492C4×C4⋊C4—172no—
493C4×C4⋊C4—172no—
494C4×C4⋊C4—172no—
495C4×C4⋊C4—172no—
496C4×C4⋊C4—172no—
497C4×C4⋊C4—172no—
498C4×C4⋊C4—172no—
499C4×C22⋊C4—172no—
500C4×C22⋊C4—172no—
501C4×C22⋊C4—172no—
502C4×C22⋊C4—172no—
503C4×C22⋊C4—172no—
504C4×C22⋊C4—172no—
505#376—172no—
506C2×#95—172no—
507C43—171no—
508C2×C17—44no—
509C2×C17C4×H(5,𝔽2)11yescharacteristic
510C2×C17C4×2−1+411yescharacteristic
511C2×C17C4×2−1+411yescharacteristic
512C2×C17#355911yescharacteristic
513C2×C17#356111yescharacteristic
514C2×C17#356311yescharacteristic
515C2×C17#356811yescharacteristic
516C22×Q8—172no—
517C22×Q8C22×D1711yescharacteristic
518C22×D4C22×D1711yescharacteristic
519C23×C4—172no—
520C23×C4—172no—
521C23×C4C22×D1712yes—
522C4⋊Q8—1716no—
523#126—1716no—
524#126—1716no—
525#125—178no—
526#125—178no—
527#124C4×D1718yes—
528#123—1716no—
529C22⋊Q8—1716no—
530C22⋊Q8—1716no—
531C4×Q8—684no—
532C4×Q8—682no—
533C4×D4—682no—
534#117—684no—
535C2×C4⋊C4—171no—
536C2×C4⋊C4—171no—
537C2×C4⋊C4—172no—
538C2×C4⋊C4—172no—
539C2×C4⋊C4—172no—
540C2×C4⋊C4—172no—
541C2×C4⋊C4—172no—
542C2×C4⋊C4—172no—
543C2×C4⋊C4—171no—
544C2×C4⋊C4—171no—
545C2×C4⋊C4—172no—
546C2×C4⋊C4—172no—
547C2×C4⋊C4—172no—
548C2×C4⋊C4—172no—
549C2×C4⋊C4—171no—
550C2×C4⋊C4—172no—
551C2×C4⋊C4—171no—
552C2×C4⋊C4—172no—
553C2×C4⋊C4—172no—
554C2×C4⋊C4—172no—
555C2×C4⋊C4—172no—
556C2×C4⋊C4C22×D1711yescharacteristic
557C2×C4⋊C4C22×D1711yescharacteristic
558C2×C4⋊C4C22×D1711yescharacteristic
559C2×C4⋊C4C22×D1711yescharacteristic
560C2×C4⋊C4C22×D1712yes—
561C2×C22⋊C4—172no—
562C2×C22⋊C4—172no—
563C2×C22⋊C4—172no—
564C2×C22⋊C4—172no—
565C2×C22⋊C4—172no—
566C2×C22⋊C4—172no—
567C2×C22⋊C4C22×D1712yes—
568C2×C22⋊C4C22×D1712yes—
569C2×C22⋊C4C22×D1712yes—
570C2×C22⋊C4C22×D1712yes—
571C2×C22⋊C4C22×D1712yes—
572C2×C42—172no—
573C2×C42—172no—
574C2×C42—171no—
575C2×C42—171no—
576C2×C42—171no—
577C2×C42—172no—
578C2×C42—172no—
579C2×C42—172no—
580C2×C42—172no—
581C2×C42—171no—
582C2×C42—171no—
583C2×C42—171no—
584C2×C42—172no—
585C2×C42—172no—
586C2×C42—172no—
587C2×C42—172no—
588C2×C42C22×D1712yes—
589C2×C42C22×D1711yescharacteristic
590#95—172no—
591#95—172no—
592#95—172no—
593#95—172no—
594#95—172no—
595#95—172no—
596#95—172no—
597#95—172no—
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#95C22×D1712yes—
611#95C22×D1712yes—
612#95C22×D1712yes—
613#95C22×D1712yes—
614#95C22×D1712yes—
615#95C22×D1712yes—
616C17#3452811yescharacteristic, complemented, Sylow
617C24C23×D1712yes—
618C2×Q8—41no—
619C2×Q8—41no—
620C2×Q8—178no—
621C2×Q8—682no—
622C2×Q8—682no—
623C2×Q8C2×C4×D1714yes—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4C2×C4×D1714yes—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—171no—
631C22×C4—171no—
632C22×C4—172no—
633C22×C4—172no—
634C22×C4—172no—
635C22×C4—172no—
636C22×C4—171no—
637C22×C4—178no—
638C22×C4—172no—
639C22×C4—172no—
640C22×C4—171no—
641C22×C4—344no—
642C22×C4—682no—
643C22×C4—682no—
644C22×C4—682no—
645C22×C4—682no—
646C22×C4C23×D1712yes—
647C22×C4C23×D1712yes—
648C22×C4C23×D1712yes—
649C22×C4C23×D1712yes—
650C22×C4C23×D1711yescharacteristic
651C22×C4C23×D1711yescharacteristic
652C22×C4C23×D1712yes—
653C22×C4C23×D1711yescharacteristic
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—42no—
659C4⋊C4—174no—
660C4⋊C4—174no—
661C4⋊C4—178no—
662C4⋊C4—178no—
663C4⋊C4—178no—
664C4⋊C4—178no—
665C4⋊C4—178no—
666C4⋊C4—178no—
667C4⋊C4—174no—
668C4⋊C4—174no—
669C4⋊C4—344no—
670C4⋊C4—344no—
671C4⋊C4—344no—
672C4⋊C4—682no—
673C4⋊C4—681no—
674C4⋊C4—682no—
675C4⋊C4—681no—
676C4⋊C4—682no—
677C4⋊C4—682no—
678C4⋊C4—682no—
679C4⋊C4—682no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—178no—
684C22⋊C4—178no—
685C22⋊C4—178no—
686C22⋊C4—344no—
687C22⋊C4—344no—
688C22⋊C4—682no—
689C22⋊C4C2×C4×D1718yes—
690C22⋊C4C2×C4×D1718yes—
691C42—42no—
692C42—178no—
693C42—344no—
694C42—342no—
695C42—342no—
696C42—342no—
697C42—344no—
698C42—682no—
699C42—682no—
700C42—682no—
701C42—681no—
702C42—681no—
703C42—681no—
704C42—682no—
705C42—682no—
706C42—682no—
707C42—682no—
708C42C2×C4×D1714yes—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23C22×C4×D1714yes—
716C23C24×D1711yescharacteristic
717Q8—44no—
718Q8—688no—
719D4—44no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—84no—
741C2×C4—174no—
742C2×C4—174no—
743C2×C4—174no—
744C2×C4—174no—
745C2×C4—172no—
746C2×C4—172no—
747C2×C4—172no—
748C2×C4—341no—
749C2×C4—342no—
750C2×C4—342no—
751C2×C4—341no—
752C2×C4—342no—
753C2×C4—341no—
754C2×C4—342no—
755C2×C4—341no—
756C2×C4—341no—
757C2×C4—342no—
758C2×C4—342no—
759C2×C4—341no—
760C2×C4—342no—
761C2×C4—342no—
762C2×C4—342no—
763C2×C4—342no—
764C2×C4—342no—
765C2×C4—342no—
766C2×C4—341no—
767C2×C4—342no—
768C2×C4—341no—
769C2×C4—341no—
770C2×C4—342no—
771C2×C4—688no—
772C2×C4—1364no—
773C2×C4C22×C4×D1714yes—
774C2×C4C22×C4×D1712yes—
775C2×C4C22×C4×D1712yes—
776C2×C4C22×C4×D1712yes—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22C23×C4×D1711yescharacteristic
785C22H(5,𝔽2)×D1711yescharacteristic
786C222−1+4×D1711yescharacteristic
787C222−1+4×D1711yescharacteristic
788C22#1176364411yescharacteristic
789C22#1176364411yescharacteristic
790C22#1176364411yescharacteristic
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—342no—
800C4—344no—
801C4—344no—
802C4—344no—
803C4—344no—
804C4—342no—
805C4—342no—
806C4—681no—
807C4—682no—
808C4—682no—
809C2—44no—
810C2#1454198811yescharacteristic
811C2#1454199511yescharacteristic
812C2#1454199511yescharacteristic
813C2#1454331211yescharacteristic
814C2#1454334611yescharacteristic
815C2#1454338411yescharacteristic
816C2#1454347811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2379C2
socle, cosocleC23×C17C25
prime radicalC22×D4×C17C23
hypercenter#2379D17
hypocenterC17#34528
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2379

Complements

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

NH ≅ G/Ntype
2. #14531969C2semidirect
3. #14531969C2semidirect
4. #14531902C2semidirect
5. #14531899C2semidirect
6. #14531865C2semidirect
7. #14531841C2semidirect
8. #14531814C2semidirect
11. #14531560C2semidirect
12. #14531557C2semidirect
13. #14531527C2semidirect
14. #14531515C2semidirect
15. #14531463C2semidirect
16. #14531339C2semidirect
17. #14531339C2semidirect
20. #11763559C4semidirect
134. #10587630C2×C4semidirect
174. #10587565C2×C4semidirect
175. #10587565C2×C4semidirect
176. #10587564C2×C4semidirect
177. #10587564C2×C4semidirect
179. #10587556C2×C4semidirect
180. #10587556C2×C4semidirect
616. C17#34528semidirect

Maximal subgroups

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

subgroupindex
C2×#117635592
#145319692
#145319022
#145318992
#145318652
#145318412
#145318142
#145317822
#145315752
#145315602
#145315572
#145315272
#145315152
#145314632
#145313392
#124×Dic172
C17×#23792
#3452817