Finite Group Databasebeta

← #16960849

Subgroups — #16960849

Order 4352.

2134 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587571C211yesmaximal, characteristic
2C2×#11762713C212yesmaximal, complemented
3C2×#11762709C212yesmaximal
4C2×#11762678C211yesmaximal, characteristic, complemented
5C2×#11762654C211yesmaximal, characteristic, complemented
6#14527030C211yesmaximal, characteristic, complemented
7#14527029C211yesmaximal, characteristic, complemented
8#14527028C212yesmaximal, complemented
9#14527027C212yesmaximal, complemented
10#14527026C211yesmaximal, characteristic, complemented
11C17×#1439C211yesmaximal, characteristic, complemented
12C23×Dic34C2211yescharacteristic
13C23×C22⋊D17C2211yescharacteristic
14C2×#10587571—24no—
15C2×#10587571—24no—
16C2×#10587571C418yescomplemented
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2212yes—
19C22×#63225C2212yes—
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2212yes—
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2212yes—
25C22×#63227C2212yes—
26C22×C4×Dic17C2212yes—
27C22×C4×Dic17C2211yescharacteristic
28#11762713—28no—
29#11762709—28no—
30#11762678—24no—
31#11762654—24no—
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C22×C4⋊C4×C17C2211yescharacteristic
38C22×C22⋊C4×C17C2211yescharacteristic
39C22×C22⋊C4×C17C2212yes—
40C2×C17×#95C2211yescharacteristic
41C2×C17×#95C2212yes—
42C25×C17C2311yescharacteristic
43C24×D17C2311yescharacteristic
44C23×C4×C17C2312yes—
45C23×C4×C17C2311yescharacteristic
46C23×C4×C17C2312yes—
47C23×C4×C17C2311yescharacteristic
48C22×C22⋊D17—24no—
49C22×C22⋊D17—22no—
50C22×C22⋊D17—22no—
51C22×C22⋊D17—24no—
52C22×C22⋊D17C2×C414yes—
53C23×Dic17C2312yes—
54C23×Dic17C2311yescharacteristic
55C23×Dic17C2312yes—
56C23×Dic17C2311yescharacteristic
57C23×Dic17C2311yescharacteristic
58C22×Dic34—24no—
59C22×Dic34—22no—
60C22×Dic34—22no—
61C22×Dic34—24no—
62C22×Dic34C2×C414yes—
63C2×C4⋊C4×C17—22no—
64C2×C4⋊C4×C17—42no—
65C2×C22⋊C4×C17—22no—
66C2×C22⋊C4×C17—22no—
67C2×C22⋊C4×C17—24no—
68C2×C22⋊C4×C17—42no—
69C2×C22⋊C4×C17—42no—
70C2×C22⋊C4×C17C2×C414yes—
71C2×C22⋊Dic17—22no—
72C2×C22⋊Dic17—22no—
73C2×C22⋊Dic17—24no—
74C2×C22⋊Dic17—42no—
75C2×C22⋊Dic17—42no—
76C2×C22⋊Dic17C2×C414yes—
77C2×#63227—22no—
78C2×#63227—22no—
79C2×#63227—24no—
80C2×#63227—22no—
81C2×#63227—22no—
82C2×#63227—24no—
83C2×#63227—42no—
84C2×#63227—42no—
85C2×#63227—42no—
86C2×#63227—42no—
87C2×#63227C2×C414yes—
88C2×#63227C2×C414yes—
89C2×C4⋊Dic17—22no—
90C2×C4⋊Dic17—42no—
91C2×#63225—24no—
92C2×#63225—24no—
93C2×#63225—24no—
94C2×#63225—24no—
95C2×#63225—42no—
96C2×#63225—42no—
97C2×C4×Dic17—24no—
98C2×C4×Dic17—24no—
99C2×C4×Dic17C2×C414yes—
100C2×C4×Dic17D418yes—
101C2×C4×Dic17D414yes—
102C2×C4×Dic17D414yes—
103#10587571—232no—
104C17×#95—24no—
105C17×#95—22no—
106#10587502—24no—
107#10587502—22no—
108#10587502—24no—
109#10587502—24no—
110#10587502—24no—
111C24×C17—21no—
112C24×C17—21no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17—21no—
116C24×C17—22no—
117C24×C17—21no—
118C24×C17—21no—
119C24×C17—22no—
120C24×C17—21no—
121C24×C17C22×C412yes—
122C24×C17C2411yescharacteristic
123C23×D17—21no—
124C23×D17—21no—
125C23×D17—22no—
126C23×D17—22no—
127C23×D17—22no—
128C23×D17—21no—
129C23×D17—21no—
130C23×D17—21no—
131C23×D17—22no—
132C23×D17—21no—
133C23×D17C22×C412yes—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—21no—
138C22×C4×C17—21no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—22no—
144C22×C4×C17—22no—
145C22×C4×C17—22no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17—22no—
153C22×C4×C17C22×C412yes—
154C22×C4×C17C22×C412yes—
155C22×C4×C17C2×D414yes—
156C22×C4×C17C2×D412yes—
157C22×C4×C17C2×D412yes—
158C2×C22⋊D17—28no—
159C2×C22⋊D17—216no—
160C2×C22⋊D17—48no—
161C2×C22⋊D17—44no—
162C2×C22⋊D17—44no—
163C22×Dic17—21no—
164C22×Dic17—21no—
165C22×Dic17—21no—
166C22×Dic17—21no—
167C22×Dic17—22no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17C22×C412yes—
185C22×Dic17C22×C412yes—
186C22×Dic17C22×C412yes—
187C22×Dic17C2×D414yes—
188C22×Dic17C2×D412yes—
189C22×Dic17C2×D412yes—
190C22×Dic17C2×D412yes—
191C22×Dic17C2×D412yes—
192C22×Dic17C2×D414yes—
193C22×Dic17#4114yes—
194C2×Dic34—28no—
195C2×Dic34—216no—
196C2×Dic34—48no—
197C2×Dic34—44no—
198C2×Dic34—44no—
199C4⋊C4×C17—44no—
200C22⋊C4×C17—28no—
201C22⋊C4×C17—48no—
202C22⋊Dic17—28no—
203C22⋊Dic17—48no—
204#63227—28no—
205#63227—28no—
206#63227—48no—
207#63227—48no—
208C4⋊Dic17—44no—
209#63225—48no—
210#63225—48no—
211C4×Dic17—216no—
212C4×Dic17C22⋊C4116yescomplemented
213#14273—171nomaximal, Sylow
214C23×C17—22no—
215C23×C17—24no—
216C23×C17—24no—
217C23×C17—22no—
218C23×C17—22no—
219C23×C17—42no—
220C23×C17—41no—
221C23×C17—41no—
222C23×C17—42no—
223C23×C17—42no—
224C23×C17—41no—
225C23×C17—41no—
226C23×C17—41no—
227C23×C17—42no—
228C23×C17—41no—
229C23×C17—42no—
230C23×C17—42no—
231C23×C17—41no—
232C23×C17—41no—
233C23×C17—42no—
234C23×C17—42no—
235C23×C17—42no—
236C23×C17—42no—
237C23×C17C23×C411yescharacteristic
238C23×C17C22×D411yescharacteristic
239C23×C17C22×D411yescharacteristic
240C23×C17C22×D412yes—
241C23×C17C2×#4112yes—
242C23×C17H(5,𝔽2)12yes—
243C23×C17H(5,𝔽2)11yescharacteristic
244C23×C17H(5,𝔽2)11yescharacteristic
245C23×C172−1+411yescharacteristic
246C23×C172−1+412yes—
247C23×C172−1+411yescharacteristic
248C22×D17—22no—
249C22×D17—24no—
250C22×D17—24no—
251C22×D17—22no—
252C22×D17—22no—
253C22×D17—42no—
254C22×D17—41no—
255C22×D17—41no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—42no—
259C22×D17—42no—
260C22×D17—41no—
261C22×D17—42no—
262C22×D17—41no—
263C22×D17—42no—
264C22×D17—42no—
265C22×D17—41no—
266C22×D17—41no—
267C22×D17—42no—
268C22×D17—42no—
269C22×D17—42no—
270C22×D17—42no—
271C2×C4×C17—24no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—24no—
275C2×C4×C17—22no—
276C2×C4×C17—24no—
277C2×C4×C17—24no—
278C2×C4×C17—24no—
279C2×C4×C17—24no—
280C2×C4×C17—42no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—42no—
284C2×C4×C17—42no—
285C2×C4×C17—42no—
286C2×C4×C17—42no—
287C2×C4×C17—42no—
288C2×C4×C17—42no—
289C2×C4×C17—42no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17C2×C22⋊C414yes—
295C22⋊D17—416no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—24no—
304C2×Dic17—24no—
305C2×Dic17—24no—
306C2×Dic17—24no—
307C2×Dic17—42no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—42no—
311C2×Dic17—42no—
312C2×Dic17—42no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17C2×C22⋊C414yes—
322C2×Dic17C2×C22⋊C414yes—
323C2×Dic17C4×D418yes—
324C2×Dic17#12118yes—
325C2×Dic17#12414yes—
326C2×Dic17#12714yes—
327Dic34—416no—
328C22×#124—171no—
329C2×#391—172no—
330C2×#390—172no—
331C2×#384—171no—
332C2×#376—171no—
333#1439—172no—
334#1439—171no—
335#1439—171no—
336#1439—172no—
337#1439—171no—
338#1439D1711yescharacteristic, complemented
339C22×C17—42no—
340C22×C17—42no—
341C22×C17—44no—
342C22×C17—44no—
343C22×C17—42no—
344C22×C17—82no—
345C22×C17—82no—
346C22×C17—81no—
347C22×C17—81no—
348C22×C17—81no—
349C22×C17—81no—
350C22×C17C22×C22⋊C411yescharacteristic
351C22×C17C2×C4×D412yes—
352C22×C17#52012yes—
353C22×C17#52011yescharacteristic
354C22×C17#52011yescharacteristic
355C22×C17C2×#12112yes—
356C22×C17C2×#12411yescharacteristic
357C22×C17C2×#12711yescharacteristic
358C22×C17#53511yescharacteristic
359C22×C17#53512yes—
360C22×C17#53511yescharacteristic
361C22×C17#53512yes—
362C22×C17#53611yescharacteristic
363C22×C17#53612yes—
364C22×C17#53611yescharacteristic
365C22×C17#53612yes—
366C22×C17#53712yes—
367C22×C17#53711yescharacteristic
368C22×C17#53711yescharacteristic
369C22×C17#54212yes—
370C22×C17#54212yes—
371C22×C17#54212yes—
372C22×C17#54212yes—
373C2×D17—42no—
374C2×D17—42no—
375C2×D17—44no—
376C2×D17—44no—
377C2×D17—42no—
378C2×D17—82no—
379C2×D17—82no—
380C2×D17—81no—
381C2×D17—81no—
382C2×D17—81no—
383C2×D17—81no—
384C4×C17—24no—
385C4×C17—44no—
386C4×C17—42no—
387C4×C17—82no—
388Dic17—24no—
389Dic17—44no—
390Dic17—42no—
391Dic17—82no—
392Dic17#39018yes—
393C23×Q8—171no—
394C23×D4—171no—
395C2×#124—178no—
396C2×#124—344no—
397C2×#124—344no—
398C22×C4⋊C4—172no—
399C22×C4⋊C4—172no—
400C22×C4⋊C4—171no—
401C22×C4⋊C4C2×D1711yescharacteristic
402C22×C22⋊C4—171no—
403C22×C22⋊C4—171no—
404C22×C22⋊C4—171no—
405C22×C22⋊C4—172no—
406C22×C22⋊C4—172no—
407C22×C22⋊C4—172no—
408C22×C22⋊C4C2×D1711yescharacteristic
409C22×C22⋊C4C2×D1712yes—
410C22×C42—171no—
411C22×C42—172no—
412#391—348no—
413#390—348no—
414#384—344no—
415#376—344no—
416C2×#95—172no—
417C2×#95—171no—
418C2×#95—172no—
419C2×#95—172no—
420C2×#95—172no—
421C2×#95C2×D1711yescharacteristic
422C2×#95C2×D1712yes—
423C2×C17—82no—
424C2×C17C2×#39011yescharacteristic
425C2×C17#231111yescharacteristic
426C2×C17#231111yescharacteristic
427C2×C17#232612yes—
428C2×C17#232612yes—
429C2×C17#262012yes—
430C2×C17#262012yes—
431C2×C17#264011yescharacteristic
432C2×C17#264011yescharacteristic
433C2×C17#265711yescharacteristic
434C2×C17#265811yescharacteristic
435D17—82no—
436C25—171no—
437C25C22×D1711yescharacteristic
438C22×Q8—174no—
439C22×Q8—342no—
440C22×Q8—342no—
441C22×Q8—344no—
442C22×Q8—344no—
443C22×D4—174no—
444C22×D4—342no—
445C22×D4—342no—
446C22×D4—344no—
447C22×D4—344no—
448C23×C4—171no—
449C23×C4—171no—
450C23×C4—171no—
451C23×C4—172no—
452C23×C4—172no—
453C23×C4C22×D1712yes—
454C23×C4C22×D1711yescharacteristic
455C23×C4C22×D1712yes—
456C23×C4C22×D1711yescharacteristic
457#124—3432no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—344no—
461C2×C4⋊C4—344no—
462C2×C4⋊C4—344no—
463C2×C4⋊C4—344no—
464C2×C4⋊C4—342no—
465C2×C4⋊C4—682no—
466C2×C4⋊C4—682no—
467C2×C4⋊C4—682no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—174no—
474C2×C22⋊C4—174no—
475C2×C22⋊C4—174no—
476C2×C22⋊C4—342no—
477C2×C22⋊C4—342no—
478C2×C22⋊C4—342no—
479C2×C22⋊C4—342no—
480C2×C22⋊C4—342no—
481C2×C22⋊C4—342no—
482C2×C22⋊C4—344no—
483C2×C22⋊C4—344no—
484C2×C22⋊C4—344no—
485C2×C22⋊C4—682no—
486C2×C22⋊C4—682no—
487C2×C22⋊C4—682no—
488C2×C22⋊C4—682no—
489C2×C22⋊C4—682no—
490C2×C22⋊C4—682no—
491C2×C22⋊C4C4×D1714yes—
492C2×C42—174no—
493C2×C42—174no—
494C2×C42—174no—
495C2×C42—178no—
496C2×C42—344no—
497C2×C42—344no—
498#95—22no—
499#95—24no—
500#95—344no—
501#95—344no—
502#95—344no—
503#95—342no—
504#95—344no—
505C17#1427311yescharacteristic, complemented, Sylow
506C24—21no—
507C24—21no—
508C24—22no—
509C24—21no—
510C24—22no—
511C24—21no—
512C24—22no—
513C24—21no—
514C24—22no—
515C24—21no—
516C24—172no—
517C24—341no—
518C24—341no—
519C24—342no—
520C24—342no—
521C24—341no—
522C24—341no—
523C24—342no—
524C24—341no—
525C24—342no—
526C24—341no—
527C24C2×C4×D1712yes—
528C24C23×D1711yescharacteristic
529C2×Q8—348no—
530C2×Q8—3416no—
531C2×Q8—688no—
532C2×Q8—684no—
533C2×Q8—684no—
534C2×D4—348no—
535C2×D4—3416no—
536C2×D4—688no—
537C2×D4—684no—
538C2×D4—684no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—172no—
559C22×C4—172no—
560C22×C4—172no—
561C22×C4—174no—
562C22×C4—174no—
563C22×C4—172no—
564C22×C4—172no—
565C22×C4—172no—
566C22×C4—172no—
567C22×C4—174no—
568C22×C4—341no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—342no—
573C22×C4—342no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—342no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4C2×C4×D1712yes—
590C22×C4C2×C4×D1712yes—
591C22×C4D4×D1714yes—
592C22×C4D4×D1712yes—
593C22×C4D4×D1712yes—
594C4⋊C4—44no—
595C4⋊C4—684no—
596C4⋊C4—688no—
597C4⋊C4—688no—
598C22⋊C4—28no—
599C22⋊C4—48no—
600C22⋊C4—348no—
601C22⋊C4—348no—
602C22⋊C4—348no—
603C22⋊C4—688no—
604C22⋊C4—688no—
605C22⋊C4—688no—
606C42—1716no—
607C42—3416no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23—42no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—41no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—342no—
632C23—344no—
633C23—344no—
634C23—342no—
635C23—342no—
636C23—682no—
637C23—681no—
638C23—681no—
639C23—682no—
640C23—681no—
641C23—682no—
642C23—681no—
643C23—681no—
644C23—682no—
645C23—681no—
646C23—682no—
647C23—682no—
648C23—681no—
649C23—681no—
650C23—682no—
651C23—682no—
652C23—682no—
653C23—682no—
654C23C22×C4×D1711yescharacteristic
655C23C2×D4×D1711yescharacteristic
656C23C2×D4×D1711yescharacteristic
657C23C2×D4×D1712yes—
658C23#1058769112yes—
659C23#1058769111yescharacteristic
660C23#1058769411yescharacteristic
661C23#41×D1712yes—
662C23#1058769611yescharacteristic
663C23#1058769712yes—
664C23#1058769711yescharacteristic
665Q8—6816no—
666D4—6816no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—174no—
691C2×C4—178no—
692C2×C4—178no—
693C2×C4—174no—
694C2×C4—174no—
695C2×C4—174no—
696C2×C4—342no—
697C2×C4—342no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—342no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—344no—
704C2×C4—344no—
705C2×C4—344no—
706C2×C4—344no—
707C2×C4—682no—
708C2×C4—681no—
709C2×C4—681no—
710C2×C4—682no—
711C2×C4—682no—
712C2×C4—682no—
713C2×C4—682no—
714C2×C4—682no—
715C2×C4—682no—
716C2×C4—682no—
717C2×C4—682no—
718C2×C4—682no—
719C2×C4—682no—
720C2×C4—682no—
721C2×C4C22⋊C4×D1714yes—
722C22—42no—
723C22—42no—
724C22—44no—
725C22—42no—
726C22—44no—
727C22—81no—
728C22—81no—
729C22—82no—
730C22—82no—
731C22—81no—
732C22—81no—
733C22—682no—
734C22—682no—
735C22—684no—
736C22—682no—
737C22—684no—
738C22—1361no—
739C22—1361no—
740C22—1362no—
741C22—1362no—
742C22—1361no—
743C22—1361no—
744C22C2×C22⋊C4×D1711yescharacteristic
745C22C4×D4×D1712yes—
746C22#1176328812yes—
747C22#1176328911yescharacteristic
748C22#1176329011yescharacteristic
749C22#121×D1712yes—
750C22#124×D1711yescharacteristic
751C22#127×D1711yescharacteristic
752C22#1176337411yescharacteristic
753C22#1176337412yes—
754C22#1176337511yescharacteristic
755C22#1176337512yes—
756C22#1176338111yescharacteristic
757C22#1176338112yes—
758C22#1176338211yescharacteristic
759C22#1176338212yes—
760C22#1176338612yes—
761C22#1176338811yescharacteristic
762C22#1176338911yescharacteristic
763C22#1176342312yes—
764C22#1176342512yes—
765C22#1176342712yes—
766C22#1176342912yes—
767C4—24no—
768C4—44no—
769C4—42no—
770C4—82no—
771C4—178no—
772C4—344no—
773C4—684no—
774C4—682no—
775C4—1362no—
776C2—82no—
777C2—1362no—
778C2D17×#39011yescharacteristic
779C2#1453137111yescharacteristic
780C2#1453137311yescharacteristic
781C2#1453149012yes—
782C2#1453149312yes—
783C2#1453454012yes—
784C2#1453454312yes—
785C2#1453471911yescharacteristic
786C2#1453472211yescharacteristic
787C2#1453488911yescharacteristic
788C2#1453489311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1439D17
hypocenterC17#14273
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#11762713C2semidirect
4. C2×#11762678C2semidirect
5. C2×#11762654C2semidirect
6. #14527030C2semidirect
7. #14527029C2semidirect
8. #14527028C2semidirect
9. #14527027C2semidirect
10. #14527026C2semidirect
11. C17×#1439C2semidirect
16. C2×#10587571C4semidirect
212. C4×Dic17C22⋊C4semidirect
338. #1439D17semidirect
505. C17#14273semidirect

Maximal subgroups

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

subgroupindex
C22×#105875712
C2×#117627132
C2×#117627092
C2×#117626782
C2×#117626542
#145270302
#145270292
#145270282
#145270272
#145270262
C17×#14392
#1427317