Finite Group Databasebeta

← #17193982

Subgroups — #17193982

Order 4352.

2322 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763361C211yesmaximal, characteristic
2#14531881C212yesmaximal, complemented
3#14531875C212yesmaximal, complemented
4#14531872C212yesmaximal, complemented
5#14531869C211yesmaximal, characteristic
6#14531867C211yesmaximal, characteristic
7#14531864C211yesmaximal, characteristic
8#14531839C212yesmaximal, complemented
9#14531790C212yesmaximal
10#14531784C212yesmaximal
11#14531263C212yesmaximal
12#14531259C212yesmaximal, complemented
13#14531257C212yesmaximal, complemented
14#14531257C212yesmaximal, complemented
15C4×#10587573C212yesmaximal, complemented
16C4×#10587563C212yesmaximal
17C4×#10587563C211yesmaximal, characteristic
18C2×#11762660C211yesmaximal, characteristic
19C17×#2368C211yesmaximal, characteristic
20#11763361C4116yescomplemented
21C2×#10587574C2211yescharacteristic
22C2×#10587630C2211yescharacteristic
23C2×#10587575C2212yes—
24C2×#10587610C2211yescharacteristic
25C2×#10587564C2212yes—
26C2×Q8×Dic17C2211yescharacteristic
27C2×C4×Dic34C2212yes—
28C2×#10587573C2212yes—
29C2×#10587573C2212yes—
30C2×#10587573C2211yescharacteristic
31C2×#10587563C2211yescharacteristic
32C2×#10587563C2212yes—
33C2×#10587563C2211yescharacteristic
34C22×#63225C2212yes—
35C22×C4×Dic17C2212yes—
36C22×C4×Dic17C2211yescharacteristic
37#11762716C2212yes—
38#11762713C2212yes—
39#11762713C2212yes—
40#11762713C2212yes—
41#11762713C2212yes—
42#11762707C2212yes—
43#11762706C2212yes—
44#11762706C2212yes—
45#11762706C2212yes—
46#11762706C2212yes—
47#11762705C2212yes—
48#11762704C2212yes—
49#11762704C2212yes—
50#11762704C2212yes—
51#11762704C2212yes—
52#11762695C2212yes—
53#11762695C2212yes—
54#11762694C2212yes—
55#11762694C2212yes—
56#11762693C2212yes—
57#11762693C2212yes—
58#11762692C2212yes—
59#11762692C2212yes—
60#11762691C2212yes—
61#11762691C2212yes—
62#11762684C2212yes—
63#11762682C2212yes—
64#11762681C2212yes—
65C4⋊C4×Dic17C2212yes—
66C4⋊C4×Dic17C2212yes—
67C4⋊C4×Dic17C2212yes—
68C4×#63225C2212yes—
69C4×#63225C2212yes—
70C4×#63225C2212yes—
71C4×#63225C2212yes—
72C4×#63225C2212yes—
73#11762660C2212yes—
74#11762660C2212yes—
75#11762660C2212yes—
76#11762660C2212yes—
77#11762660C2212yes—
78#11762660C2211yescharacteristic
79#11762660C2212yes—
80#11762660C2211yescharacteristic
81#11762660C2211yescharacteristic
82#11762660C2211yescharacteristic
83#11762660C2212yes—
84#11762660C2212yes—
85#11762660C2212yes—
86C22⋊C4×Dic17C2212yes—
87C22⋊C4×Dic17C2212yes—
88C22⋊C4×Dic17C2211yescharacteristic
89C22⋊C4×Dic17C2211yescharacteristic
90C4×C22⋊Dic17C2211yescharacteristic
91C4×C22⋊Dic17C2212yes—
92#11762654C2212yes—
93#11762654C2212yes—
94#11762654C2212yes—
95C2×#10587502C2211yescharacteristic
96C42×Dic17C2212yes—
97C42×Dic17C2212yes—
98C42×Dic17C2212yes—
99C2×C17×C22⋊Q8C2211yescharacteristic
100C17×#391C2212yes—
101C17×#387C2212yes—
102C17×#387C2212yes—
103C17×#385C2212yes—
104C4×C4⋊C4×C17C2212yes—
105C4×C22⋊C4×C17C2211yescharacteristic
106C4×C22⋊C4×C17C2212yes—
107C2×C17×#95C2211yescharacteristic
108C22×Q8×C17C2311yescharacteristic
109C23×C4×C17C2312yes—
110C23×C4×C17C2311yescharacteristic
111C23×Dic17C2312yes—
112C23×Dic17C2311yescharacteristic
113C23×Dic17C2311yescharacteristic
114C22×Dic34C2312yes—
115C22×Dic34C2311yescharacteristic
116C17×C22⋊Q8C2×C418yes—
117C2×C4⋊C4×C17C2312yes—
118C2×C4⋊C4×C17C2312yes—
119C2×C4⋊C4×C17C2311yescharacteristic
120C2×C4⋊C4×C17C2312yes—
121C2×C22⋊C4×C17C2311yescharacteristic
122C2×C22⋊C4×C17C2312yes—
123C2×C22⋊C4×C17C2311yescharacteristic
124C2×C42×C17C2312yes—
125C2×C42×C17C2312yes—
126C2×C42×C17C2312yes—
127C2×C22⋊Dic17C2311yescharacteristic
128C2×C22⋊Dic17C2312yes—
129C2×C22⋊Dic17C2311yescharacteristic
130Q8×Dic17C2×C418yescomplemented
131#10587630C2×C418yescomplemented
132C2×C4⋊Dic17C2312yes—
133C2×C4⋊Dic17C2312yes—
134C2×C4⋊Dic17C2311yescharacteristic
135C2×C4⋊Dic17C2312yes—
136#10587610C2×C418yes—
137C2×#63225—28no—
138C2×#63225C2312yes—
139C2×#63225C2312yes—
140C2×#63225C2312yes—
141C2×#63225C2312yes—
142C2×#63225C2312yes—
143C2×#63225C2312yes—
144C2×#63225C2312yes—
145C2×#63225C2312yes—
146C2×#63225C2312yes—
147C2×#63225C2312yes—
148C2×#63225C2312yes—
149C2×#63225C2312yes—
150C2×#63225C2312yes—
151C2×#63225C2312yes—
152C2×#63225C2312yes—
153C2×C4×Dic17—28no—
154C2×C4×Dic17C2×C418yes—
155C2×C4×Dic17C2312yes—
156C2×C4×Dic17C2312yes—
157C2×C4×Dic17C2312yes—
158C2×C4×Dic17C2312yes—
159C2×C4×Dic17C2312yes—
160C2×C4×Dic17C2312yes—
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—
174C2×C4×Dic17C2312yes—
175C2×C4×Dic17C2312yes—
176#10587575C2×C4116yescomplemented
177#10587574C2×C418yescomplemented
178#10587573—28no—
179#10587573C2×C418yescomplemented
180#10587573C2×C4116yescomplemented
181#10587564C2×C4116yes—
182#10587563—24no—
183#10587563C2×C4116yes—
184#10587563Q818yescomplemented
185C4×Dic34—28no—
186C17×#95C2311yescharacteristic
187C17×#95C2312yes—
188C17×#95C2312yes—
189C17×#95C2312yes—
190C17×#95C2312yes—
191C17×#95C2312yes—
192C17×#95C2312yes—
193C17×#95C2311yescharacteristic
194#10587502C2312yes—
195#10587502C2312yes—
196#10587502C2312yes—
197#10587502C2312yes—
198#10587502C2312yes—
199#10587502C2312yes—
200#10587502C2312yes—
201#10587502C2312yes—
202#10587502C2312yes—
203#10587502C2312yes—
204#10587502C2311yescharacteristic
205#10587502C2312yes—
206#10587502C2312yes—
207#10587502C2312yes—
208#10587502C2312yes—
209#10587502C2312yes—
210#10587502C2312yes—
211#10587502C2311yescharacteristic
212C24×C17C2411yescharacteristic
213C2×Q8×C17—42no—
214C2×Q8×C17C22×C414yes—
215C22×C4×C17—24no—
216C22×C4×C17—24no—
217C22×C4×C17—42no—
218C22×C4×C17—42no—
219C22×C4×C17C22×C414yes—
220C22×C4×C17C2412yes—
221C22×C4×C17C2412yes—
222C22×C4×C17C2411yescharacteristic
223C22×C4×C17C2412yes—
224C22×C4×C17C2411yescharacteristic
225C22×C4×C17C2412yes—
226C22×C4×C17C2412yes—
227C22×C4×C17C2412yes—
228C22×Dic17—24no—
229C22×Dic17—24no—
230C22×Dic17—24no—
231C22×Dic17—42no—
232C22×Dic17C22×C414yes—
233C22×Dic17C22×C414yes—
234C22×Dic17C2×Q814yes—
235C22×Dic17#4114yes—
236C22×Dic17C2412yes—
237C22×Dic17C2412yes—
238C22×Dic17C2412yes—
239C22×Dic17C2412yes—
240C22×Dic17C2411yescharacteristic
241C22×Dic17C2412yes—
242C22×Dic17C2412yes—
243C22×Dic17C2411yescharacteristic
244C22×Dic17C2411yescharacteristic
245C22×Dic17C2411yescharacteristic
246C2×Dic34—24no—
247C2×Dic34—24no—
248C2×Dic34—42no—
249C2×Dic34C22×C418yes—
250C2×Dic34C22×C414yes—
251C4⋊C4×C17—24no—
252C4⋊C4×C17—42no—
253C4⋊C4×C17C22×C414yes—
254C4⋊C4×C17C22×C418yes—
255C22⋊C4×C17—22no—
256C22⋊C4×C17C22×C418yes—
257C22⋊C4×C17C2×Q814yes—
258C42×C17—24no—
259C42×C17—42no—
260C42×C17—42no—
261C22⋊Dic17—22no—
262C22⋊Dic17C22×C418yes—
263C22⋊Dic17C2×Q814yes—
264C4⋊Dic17—24no—
265C4⋊Dic17—42no—
266C4⋊Dic17C22×C418yes—
267C4⋊Dic17C22×C414yes—
268#63225—24no—
269#63225—24no—
270#63225—24no—
271#63225—24no—
272#63225—24no—
273#63225—24no—
274#63225—42no—
275#63225—42no—
276#63225C22×C418yes—
277#63225C22×C418yes—
278#63225C22×C418yes—
279#63225C22×C418yes—
280#63225C22×C418yes—
281#63225C2×Q818yes—
282#63225#4118yes—
283C4×Dic17—24no—
284C4×Dic17—24no—
285C4×Dic17—24no—
286C4×Dic17—24no—
287C4×Dic17—24no—
288C4×Dic17—24no—
289C4×Dic17—24no—
290C4×Dic17—24no—
291C4×Dic17—24no—
292C4×Dic17—24no—
293C4×Dic17—42no—
294C4×Dic17—42no—
295C4×Dic17—42no—
296C4×Dic17—42no—
297C4×Dic17C22×C418yes—
298C4×Dic17C22×C418yes—
299C4×Dic17C22×C414yes—
300C4×Dic17C22×C414yes—
301C4×Dic17C22×C414yes—
302C4×Dic17C22×C414yes—
303C4×Dic17C2×Q818yes—
304#34145—171nomaximal, Sylow
305C23×C17—22no—
306C23×C17—22no—
307C23×C17C23×C412yes—
308C23×C17C22×Q812yes—
309C23×C17C2×#4112yes—
310C23×C17C2511yescharacteristic
311Q8×C17—44no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
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—44no—
329C2×C4×C17—48no—
330C2×C4×C17C23×C414yes—
331C2×C4×C17C23×C414yes—
332C2×C4×C17C23×C412yes—
333C2×C4×C17C23×C412yes—
334C2×C4×C17C22×Q814yes—
335C2×C4×C17C2×#4114yes—
336C2×Dic17—22no—
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—22no—
340C2×Dic17—22no—
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—22no—
344C2×Dic17—22no—
345C2×Dic17—28no—
346C2×Dic17—22no—
347C2×Dic17—22no—
348C2×Dic17—22no—
349C2×Dic17—22no—
350C2×Dic17—22no—
351C2×Dic17—22no—
352C2×Dic17—48no—
353C2×Dic17C4×Q8116yescomplemented
354C2×Dic17C23×C414yes—
355C2×Dic17C23×C414yes—
356C2×Dic17C23×C412yes—
357C2×Dic17C23×C412yes—
358C2×Dic17C23×C412yes—
359C2×Dic17C23×C412yes—
360C2×Dic17C22×Q814yes—
361C2×Dic17C22×Q812yes—
362C2×Dic17C22×Q812yes—
363C2×Dic17C2×#4114yes—
364C2×Dic17C2×#4112yes—
365C2×Dic17C2×#4112yes—
366C2×Dic17C2×#4114yes—
367Dic34—216no—
368Dic34—44no—
369C2×#533—171no—
370#2370—172no—
371#2370—172no—
372#2369—172no—
373#2368—171no—
374#2368—171no—
375#2368—171no—
376#2368D1711yescharacteristic
377#2365—172no—
378#2360—172no—
379#2360—172no—
380#2296—172no—
381#2295—172no—
382#2295—172no—
383#2295—172no—
384C42×Q8—172no—
385C4×#117—172no—
386C4×#117—171no—
387C2×C4×C4⋊C4—171no—
388C22×C17—22no—
389C22×C17—22no—
390C22×C17—24no—
391C22×C17—24no—
392C22×C17C2×C4×Q814yes—
393C22×C17C24×C411yescharacteristic
394C22×C17C23×Q811yescharacteristic
395C22×C17C22×#4111yescharacteristic
396C22×C17C22×#4112yes—
397C22×C17#58512yes—
398C4×C17—24no—
399C4×C17—22no—
400C4×C17—22no—
401C4×C17—24no—
402C4×C17—24no—
403C4×C17—24no—
404C4×C17—42no—
405C4×C17—42no—
406Dic17—24no—
407Dic17—22no—
408Dic17—24no—
409Dic17—24no—
410Dic17—24no—
411Dic17—42no—
412Dic17—42no—
413Dic17C2×C4×Q814yes—
414Dic17C2×C4×Q814yes—
415Dic17C4×#4114yes—
416#533—1716no—
417C2×C4⋊Q8—171no—
418C2×C4⋊Q8—171no—
419C2×#125—172no—
420C2×C22⋊Q8—171no—
421C2×C22⋊Q8—172no—
422C2×C22⋊Q8C2×D1711yescharacteristic
423C2×C4×Q8—171no—
424C2×C4×Q8—172no—
425C2×C4×Q8—171no—
426C2×C4×Q8—172no—
427C2×C4×Q8—172no—
428C2×#117—172no—
429C2×#117—171no—
430C2×#117—171no—
431C22×C4⋊C4—172no—
432C22×C42—171no—
433C22×C42—172no—
434#391—172no—
435#391—172no—
436#391—172no—
437#391—172no—
438#391—172no—
439#391C2×D1712yes—
440#389—172no—
441#389—172no—
442#389—172no—
443#389—172no—
444#389—172no—
445#389—172no—
446#389—172no—
447#389—172no—
448#389—172no—
449#389—172no—
450#387—172no—
451#387—172no—
452#387—172no—
453#387—172no—
454#387—172no—
455#387—172no—
456#387—172no—
457#387—172no—
458#387—172no—
459#387—172no—
460#387C2×D1712yes—
461#387C2×D1712yes—
462#385—172no—
463#385—172no—
464#385—172no—
465#385C2×D1712yes—
466C4×C4⋊C4—172no—
467C4×C4⋊C4—172no—
468C4×C4⋊C4—172no—
469C4×C4⋊C4—172no—
470C4×C4⋊C4—172no—
471C4×C4⋊C4—172no—
472C4×C4⋊C4—172no—
473C4×C4⋊C4—172no—
474C4×C4⋊C4—172no—
475C4×C4⋊C4—172no—
476C4×C4⋊C4—172no—
477C4×C4⋊C4—172no—
478C4×C4⋊C4—172no—
479C4×C4⋊C4—172no—
480C4×C4⋊C4—171no—
481C4×C4⋊C4—171no—
482C4×C4⋊C4—171no—
483C4×C4⋊C4—171no—
484C4×C4⋊C4—172no—
485C4×C4⋊C4—172no—
486C4×C4⋊C4—172no—
487C4×C4⋊C4C2×D1712yes—
488C4×C22⋊C4—172no—
489C4×C22⋊C4—171no—
490C4×C22⋊C4—171no—
491C4×C22⋊C4—171no—
492C4×C22⋊C4—172no—
493C4×C22⋊C4—172no—
494C4×C22⋊C4C2×D1712yes—
495C4×C22⋊C4C2×D1711yescharacteristic
496#376—172no—
497#376—172no—
498#376—172no—
499C2×#95—171no—
500C2×#95C2×D1711yescharacteristic
501C43—172no—
502C43—172no—
503C43—172no—
504C2×C17—24no—
505C2×C17C22×C4×Q811yescharacteristic
506C2×C17C2×C4×#4111yescharacteristic
507C2×C17#342811yescharacteristic
508C2×C17#347512yes—
509C2×C17Q8×#4112yes—
510C22×Q8—172no—
511C22×Q8—171no—
512C22×Q8C22×D1711yescharacteristic
513C23×C4—171no—
514C23×C4—171no—
515C23×C4—172no—
516C23×C4C22×D1712yes—
517C23×C4C22×D1711yescharacteristic
518C4⋊Q8—178no—
519C4⋊Q8—178no—
520#125—1716no—
521C22⋊Q8—178no—
522C22⋊Q8—1716no—
523C22⋊Q8C4×D1718yes—
524C4×Q8—178no—
525C4×Q8—178no—
526C4×Q8—1716no—
527C4×Q8—348no—
528C4×Q8—348no—
529#117—1716no—
530#117—178no—
531#117—344no—
532C2×C4⋊C4—172no—
533C2×C4⋊C4—172no—
534C2×C4⋊C4—172no—
535C2×C4⋊C4—172no—
536C2×C4⋊C4—172no—
537C2×C4⋊C4—172no—
538C2×C4⋊C4—172no—
539C2×C4⋊C4—172no—
540C2×C4⋊C4—171no—
541C2×C4⋊C4—172no—
542C2×C4⋊C4—172no—
543C2×C4⋊C4—172no—
544C2×C4⋊C4—172no—
545C2×C4⋊C4—172no—
546C2×C4⋊C4—172no—
547C2×C4⋊C4—172no—
548C2×C4⋊C4—172no—
549C2×C4⋊C4—172no—
550C2×C4⋊C4—172no—
551C2×C4⋊C4—348no—
552C2×C4⋊C4C22×D1712yes—
553C2×C4⋊C4C22×D1712yes—
554C2×C4⋊C4C22×D1712yes—
555C2×C4⋊C4C22×D1711yescharacteristic
556C2×C22⋊C4—172no—
557C2×C22⋊C4—171no—
558C2×C22⋊C4—171no—
559C2×C22⋊C4C22×D1711yescharacteristic
560C2×C22⋊C4C22×D1712yes—
561C2×C22⋊C4C22×D1711yescharacteristic
562C2×C42—178no—
563C2×C42—172no—
564C2×C42—172no—
565C2×C42—172no—
566C2×C42—171no—
567C2×C42—171no—
568C2×C42—171no—
569C2×C42—171no—
570C2×C42—172no—
571C2×C42—172no—
572C2×C42—172no—
573C2×C42—172no—
574C2×C42—172no—
575C2×C42—172no—
576C2×C42—172no—
577C2×C42—172no—
578C2×C42—172no—
579C2×C42—172no—
580C2×C42—172no—
581C2×C42—172no—
582C2×C42—172no—
583C2×C42—172no—
584C2×C42—348no—
585C2×C42C22×D1712yes—
586C2×C42C22×D1712yes—
587C2×C42C22×D1712yes—
588#95—171no—
589#95—171no—
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#95C22×D1711yescharacteristic
607#95C22×D1711yescharacteristic
608#95C22×D1712yes—
609#95C22×D1712yes—
610#95C22×D1712yes—
611#95C22×D1712yes—
612#95C22×D1712yes—
613#95C22×D1712yes—
614C17#3414511yescharacteristic, complemented, Sylow
615C24C23×D1711yescharacteristic
616C2×Q8—42no—
617C2×Q8—178no—
618C2×Q8—174no—
619C2×Q8—344no—
620C2×Q8—344no—
621C2×Q8—682no—
622C2×Q8C2×C4×D1714yes—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—174no—
628C22×C4—174no—
629C22×C4—174no—
630C22×C4—171no—
631C22×C4—171no—
632C22×C4—171no—
633C22×C4—174no—
634C22×C4—172no—
635C22×C4—172no—
636C22×C4—172no—
637C22×C4—172no—
638C22×C4—171no—
639C22×C4—172no—
640C22×C4—172no—
641C22×C4—344no—
642C22×C4—344no—
643C22×C4—344no—
644C22×C4—682no—
645C22×C4C2×C4×D1714yes—
646C22×C4C23×D1712yes—
647C22×C4C23×D1712yes—
648C22×C4C23×D1711yescharacteristic
649C22×C4C23×D1711yescharacteristic
650C22×C4C23×D1712yes—
651C22×C4C23×D1712yes—
652C22×C4C23×D1712yes—
653C22×C4C23×D1712yes—
654C4⋊C4—24no—
655C4⋊C4—42no—
656C4⋊C4—178no—
657C4⋊C4—178no—
658C4⋊C4—178no—
659C4⋊C4—178no—
660C4⋊C4—178no—
661C4⋊C4—178no—
662C4⋊C4—174no—
663C4⋊C4—178no—
664C4⋊C4—178no—
665C4⋊C4—344no—
666C4⋊C4—344no—
667C4⋊C4—344no—
668C4⋊C4—344no—
669C4⋊C4—344no—
670C4⋊C4—344no—
671C4⋊C4—344no—
672C4⋊C4—682no—
673C4⋊C4—682no—
674C4⋊C4—682no—
675C4⋊C4C2×C4×D1718yes—
676C4⋊C4C2×C4×D1714yes—
677C22⋊C4—22no—
678C22⋊C4—178no—
679C22⋊C4—174no—
680C22⋊C4—342no—
681C22⋊C4C2×C4×D1718yes—
682C22⋊C4Q8×D1714yes—
683C42—24no—
684C42—42no—
685C42—42no—
686C42—174no—
687C42—174no—
688C42—174no—
689C42—174no—
690C42—178no—
691C42—178no—
692C42—178no—
693C42—344no—
694C42—344no—
695C42—344no—
696C42—344no—
697C42—344no—
698C42—344no—
699C42—344no—
700C42—344no—
701C42—344no—
702C42—344no—
703C42—682no—
704C42—682no—
705C42—682no—
706C42—682no—
707C23—22no—
708C23—22no—
709C23C22×C4×D1712yes—
710C23C2×Q8×D1712yes—
711C23#41×D1712yes—
712C23C24×D1711yescharacteristic
713Q8—44no—
714Q8—3416no—
715Q8—684no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—44no—
733C2×C4—48no—
734C2×C4—1716no—
735C2×C4—172no—
736C2×C4—172no—
737C2×C4—172no—
738C2×C4—172no—
739C2×C4—172no—
740C2×C4—172no—
741C2×C4—172no—
742C2×C4—174no—
743C2×C4—172no—
744C2×C4—174no—
745C2×C4—174no—
746C2×C4—174no—
747C2×C4—174no—
748C2×C4—348no—
749C2×C4—342no—
750C2×C4—342no—
751C2×C4—342no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—342no—
756C2×C4—342no—
757C2×C4—342no—
758C2×C4—342no—
759C2×C4—342no—
760C2×C4—342no—
761C2×C4—342no—
762C2×C4—342no—
763C2×C4—342no—
764C2×C4—688no—
765C2×C4C22×C4×D1712yes—
766C2×C4C22×C4×D1712yes—
767C2×C4C22×C4×D1714yes—
768C2×C4C22×C4×D1714yes—
769C2×C4C2×Q8×D1714yes—
770C2×C4#41×D1714yes—
771C22—24no—
772C22—24no—
773C22—22no—
774C22—22no—
775C22C4×Q8×D1714yes—
776C22C23×C4×D1711yescharacteristic
777C22C22×Q8×D1711yescharacteristic
778C22C2×#41×D1711yescharacteristic
779C22C2×#41×D1712yes—
780C22#1176364412yes—
781C4—24no—
782C4—24no—
783C4—24no—
784C4—22no—
785C4—22no—
786C4—24no—
787C4—42no—
788C4—42no—
789C4—174no—
790C4—174no—
791C4—174no—
792C4—344no—
793C4—344no—
794C4—342no—
795C4—344no—
796C4—344no—
797C4—682no—
798C4—682no—
799C2—24no—
800C2C2×C4×Q8×D1711yescharacteristic
801C2C4×#41×D1711yescharacteristic
802C2#1454198211yescharacteristic
803C2#1454233912yes—
804C2#1454236312yes—
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2368C2
socle, cosocleC23×C17C25
prime radicalC24×C17C24
hypercenter#2368D17
hypocenterC17#34145
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2368

Complements

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

NH ≅ G/Ntype
2. #14531881C2semidirect
3. #14531875C2semidirect
4. #14531872C2semidirect
8. #14531839C2semidirect
12. #14531259C2semidirect
13. #14531257C2semidirect
14. #14531257C2semidirect
15. C4×#10587573C2semidirect
20. #11763361C4semidirect
130. Q8×Dic17C2×C4semidirect
131. #10587630C2×C4semidirect
176. #10587575C2×C4semidirect
177. #10587574C2×C4semidirect
179. #10587573C2×C4semidirect
180. #10587573C2×C4semidirect
184. #10587563Q8semidirect
353. C2×Dic17C4×Q8semidirect
614. C17#34145semidirect

Maximal subgroups

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

subgroupindex
C2×#117633612
#145318812
#145318752
#145318722
#145318692
#145318672
#145318642
#145318392
#145317902
#145317842
#145312632
#145312592
#145312572
C4×#105875732
C4×#105875632
C2×#117626602
C17×#23682
#3414517