Finite Group Databasebeta

← #16956413

Subgroups — #16956413

Order 4352.

2330 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762695C212yesmaximal, complemented
2C2×#11762669C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
4#14527029C212yesmaximal, complemented
5#14527025C212yesmaximal
6#14527021C212yesmaximal, complemented
7#14527011C211yesmaximal, characteristic, complemented
8#14527011C211yesmaximal, characteristic, complemented
9#14527007C211yesmaximal, characteristic, complemented
10#14527007C211yesmaximal, characteristic, complemented
11C22×C4×D4×C17C211yesmaximal, characteristic
12C22×C4⋊Dic17C2212yes—
13C22×C22⋊Dic17C2212yes—
14C22×C22⋊Dic17C2212yes—
15C22×C22⋊Dic17C2212yes—
16C22×C22⋊Dic17C2212yes—
17C22×C4×Dic17C2212yes—
18#11762695—28no—
19#11762669—24no—
20C4×C22⋊Dic17—24no—
21C2×#10587502C2211yescharacteristic
22C2×#10587502C2211yescharacteristic
23C2×#10587502C2211yescharacteristic
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2211yescharacteristic
31C23×D4×C17C2211yescharacteristic
32C24×C4×C17C2211yescharacteristic
33C24×C4×C17C2211yescharacteristic
34C2×C4×D4×C17—28no—
35C2×C4×D4×C17C418yescomplemented
36C22×C4⋊C4×C17C2211yescharacteristic
37C22×C22⋊C4×C17C2211yescharacteristic
38C22×C22⋊C4×C17C2211yescharacteristic
39C22×C42×C17C2211yescharacteristic
40C25×C17C2311yescharacteristic
41C25×C17C2311yescharacteristic
42C22×D4×C17—24no—
43C22×D4×C17—22no—
44C22×D4×C17—22no—
45C22×D4×C17—24no—
46C22×D4×C17C2×C414yes—
47C23×C4×C17—24no—
48C23×C4×C17—24no—
49C23×C4×C17—22no—
50C23×C4×C17—22no—
51C23×C4×C17—22no—
52C23×C4×C17—22no—
53C23×C4×C17—42no—
54C23×C4×C17—42no—
55C23×C4×C17C2×C414yes—
56C23×C4×C17C2×C414yes—
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×Dic17C2312yes—
63C23×Dic17C2312yes—
64C23×Dic17C2312yes—
65C23×Dic17C2312yes—
66C4×D4×C17—232no—
67C2×C4⋊C4×C17C2×C414yes—
68C2×C4⋊C4×C17D418yes—
69C2×C22⋊C4×C17—24no—
70C2×C22⋊C4×C17—24no—
71C2×C22⋊C4×C17C2×C414yes—
72C2×C22⋊C4×C17C2×C414yes—
73C2×C42×C17—24no—
74C2×C42×C17C2×C414yes—
75C2×C22⋊Dic17—24no—
76C2×C22⋊Dic17—24no—
77C2×C22⋊Dic17—24no—
78C2×C22⋊Dic17—24no—
79C2×C22⋊Dic17—24no—
80C2×C22⋊Dic17—24no—
81C2×C22⋊Dic17—24no—
82C2×C22⋊Dic17—24no—
83C2×C22⋊Dic17—42no—
84C2×C22⋊Dic17—42no—
85C2×C22⋊Dic17—42no—
86C2×C22⋊Dic17—42no—
87C2×C4⋊Dic17—24no—
88C2×C4⋊Dic17—24no—
89C2×C4⋊Dic17—42no—
90C2×C4×Dic17—24no—
91C2×C4×Dic17—24no—
92C2×C4×Dic17—42no—
93#10587502—24no—
94#10587502—24no—
95#10587502—24no—
96#10587502—24no—
97#10587502—22no—
98#10587502—22no—
99#10587502—22no—
100#10587502—24no—
101#10587502—42no—
102#10587502D414yescomplemented
103C24×C17—22no—
104C24×C17—22no—
105C24×C17—21no—
106C24×C17—21no—
107C24×C17—21no—
108C24×C17—21no—
109C24×C17—22no—
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—22no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17—22no—
116C24×C17—21no—
117C24×C17—21no—
118C24×C17—21no—
119C24×C17—21no—
120C24×C17C22×C412yes—
121C24×C17C22×C412yes—
122C24×C17#4114yes—
123C24×C17#4112yes—
124C24×C17#4112yes—
125C24×C17C2411yescharacteristic
126C2×D4×C17—216no—
127C2×D4×C17—216no—
128C2×D4×C17—28no—
129C2×D4×C17—28no—
130C2×D4×C17—28no—
131C22×C4×C17—22no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
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—21no—
145C22×C4×C17—21no—
146C22×C4×C17—28no—
147C22×C4×C17—28no—
148C22×C4×C17—28no—
149C22×C4×C17—28no—
150C22×C4×C17—44no—
151C22×C4×C17—44no—
152C22×C4×C17—48no—
153C22×C4×C17—48no—
154C22×C4×C17—48no—
155C22×C4×C17—48no—
156C22×C4×C17C22×C412yes—
157C22×C4×C17C22×C412yes—
158C22×C4×C17C22×C412yes—
159C22×C4×C17C22×C412yes—
160C22×C4×C17C22×C412yes—
161C22×C4×C17C2×D412yes—
162C22×C4×C17C2×D414yes—
163C22×C4×C17C2×D414yes—
164C22×C4×C17C2×D414yes—
165C22×C4×C17#4112yes—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17—22no—
169C22×Dic17—22no—
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×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17C2×D414yes—
193C22×Dic17#4114yes—
194C4⋊C4×C17C22⋊C4116yescomplemented
195C22⋊C4×C17—28no—
196C22⋊C4×C17—28no—
197C42×C17—28no—
198C22⋊Dic17—216no—
199C22⋊Dic17—48no—
200C22⋊Dic17—48no—
201C22⋊Dic17—48no—
202C4⋊Dic17—48no—
203C4×Dic17—48no—
204#13890—171nomaximal, Sylow
205C23×C17—22no—
206C23×C17—22no—
207C23×C17—22no—
208C23×C17—22no—
209C23×C17—22no—
210C23×C17—22no—
211C23×C17—22no—
212C23×C17—22no—
213C23×C17—22no—
214C23×C17—22no—
215C23×C17—22no—
216C23×C17—22no—
217C23×C17—24no—
218C23×C17—24no—
219C23×C17—24no—
220C23×C17—24no—
221C23×C17—24no—
222C23×C17—24no—
223C23×C17—24no—
224C23×C17—24no—
225C23×C17—22no—
226C23×C17—22no—
227C23×C17—24no—
228C23×C17—22no—
229C23×C17—22no—
230C23×C17—24no—
231C23×C17—42no—
232C23×C17—42no—
233C23×C17—42no—
234C23×C17—42no—
235C23×C17—42no—
236C23×C17—42no—
237C23×C17—42no—
238C23×C17—42no—
239C23×C17—41no—
240C23×C17—42no—
241C23×C17—42no—
242C23×C17—41no—
243C23×C17—42no—
244C23×C17—42no—
245C23×C17—42no—
246C23×C17—41no—
247C23×C17—41no—
248C23×C17—42no—
249C23×C17#11714yes—
250C23×C17#11714yes—
251C23×C17C23×C411yescharacteristic
252C23×C17C22×D411yescharacteristic
253C23×C17C22×D412yes—
254C23×C17C2×#4112yes—
255C23×C17C2×#4111yescharacteristic
256C23×C17C2×#4111yescharacteristic
257C23×C17C2×#4111yescharacteristic
258C23×C17C2×#4112yes—
259C23×C17H(5,𝔽2)12yes—
260C23×C17H(5,𝔽2)11yescharacteristic
261C23×C172−1+411yescharacteristic
262D4×C17—232no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—24no—
272C2×C4×C17—24no—
273C2×C4×C17—24no—
274C2×C4×C17—24no—
275C2×C4×C17—24no—
276C2×C4×C17—24no—
277C2×C4×C17—24no—
278C2×C4×C17—24no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—416no—
283C2×C4×C17—416no—
284C2×C4×C17—42no—
285C2×C4×C17—42no—
286C2×C4×C17C2×C22⋊C414yes—
287C2×C4×C17C2×C22⋊C414yes—
288C2×C4×C17C2×C22⋊C414yes—
289C2×C4×C17C4×D414yes—
290C2×Dic17—24no—
291C2×Dic17—24no—
292C2×Dic17—24no—
293C2×Dic17—24no—
294C2×Dic17—24no—
295C2×Dic17—24no—
296C2×Dic17—42no—
297C2×Dic17—42no—
298C2×Dic17—42no—
299C2×Dic17—42no—
300C2×Dic17—42no—
301C2×Dic17—42no—
302C2×Dic17—42no—
303C2×Dic17—42no—
304C2×Dic17—42no—
305C2×Dic17—42no—
306C2×Dic17—42no—
307C2×Dic17—42no—
308C2×Dic17—42no—
309C2×Dic17—42no—
310C2×Dic17—42no—
311C2×Dic17—42no—
312C2×Dic17—42no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C22×C4×D4D1711yescharacteristic
319C2×#387—172no—
320C2×#380—171no—
321C2×C4×C22⋊C4—171no—
322#1439—172no—
323#1438—172no—
324#1437—172no—
325#1434—171no—
326#1434—171no—
327C22⋊#95—171no—
328C22⋊#95—171no—
329C22×C17—24no—
330C22×C17—24no—
331C22×C17—24no—
332C22×C17—24no—
333C22×C17—24no—
334C22×C17—24no—
335C22×C17—42no—
336C22×C17—42no—
337C22×C17—42no—
338C22×C17—42no—
339C22×C17—42no—
340C22×C17—42no—
341C22×C17—42no—
342C22×C17—44no—
343C22×C17—44no—
344C22×C17—44no—
345C22×C17—44no—
346C22×C17—44no—
347C22×C17—44no—
348C22×C17—44no—
349C22×C17—44no—
350C22×C17—42no—
351C22×C17C22×C22⋊C411yescharacteristic
352C22×C17C2×#11711yescharacteristic
353C22×C17C2×#11711yescharacteristic
354C22×C17C2×C4×D411yescharacteristic
355C22×C17C4×#4111yescharacteristic
356C22×C17#51811yescharacteristic
357C22×C17#52011yescharacteristic
358C22×C17#52512yes—
359C22×C17#52512yes—
360C22×C17#52512yes—
361C22×C17#52912yes—
362C22×C17#53812yes—
363C22×C17#53912yes—
364C22×C17D4212yes—
365C22×C17#54612yes—
366C22×C17#54611yescharacteristic
367C22×C17#54812yes—
368C22×C17#54811yescharacteristic
369C22×C17#55012yes—
370C22×C17#55112yes—
371C22×C17#55211yescharacteristic
372C22×C17#55311yescharacteristic
373C22×C17#55312yes—
374C4×C17—24no—
375C4×C17—24no—
376C4×C17—24no—
377C4×C17—24no—
378C4×C17—42no—
379Dic17—44no—
380Dic17—44no—
381Dic17—82no—
382Dic17—82no—
383C23×D4C2×D1711yescharacteristic
384C24×C4C2×D1711yescharacteristic
385C24×C4C2×D1711yescharacteristic
386C2×C4×D4—28no—
387C2×C4×D4Dic1718yescomplemented
388C22×C4⋊C4—172no—
389C22×C4⋊C4C2×D1711yescharacteristic
390C22×C22⋊C4—172no—
391C22×C22⋊C4—172no—
392C22×C22⋊C4—172no—
393C22×C22⋊C4—172no—
394C22×C22⋊C4C2×D1711yescharacteristic
395C22×C22⋊C4C2×D1711yescharacteristic
396C22×C42—172no—
397C22×C42C2×D1711yescharacteristic
398#387—348no—
399#380—344no—
400C4×C22⋊C4—344no—
401C2×#95—171no—
402C2×#95—171no—
403C2×#95—171no—
404C2×#95—171no—
405C2×#95—172no—
406C2×#95—172no—
407C2×#95—172no—
408C2×#95—172no—
409C2×#95—172no—
410C2×#95—172no—
411C2×C17—44no—
412C2×C17—44no—
413C2×C17#228011yescharacteristic
414C2×C17#229011yescharacteristic
415C2×C17#231811yescharacteristic
416C2×C17D4×C22⋊C411yescharacteristic
417C2×C17#234111yescharacteristic
418C2×C17#235211yescharacteristic
419C2×C17#235311yescharacteristic
420C2×C17#245612yes—
421C2×C17#246012yes—
422C2×C17#246312yes—
423C2×C17#246712yes—
424C25C22×D1711yescharacteristic
425C25C22×D1711yescharacteristic
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—24no—
429C22×D4—24no—
430C22×D4C2×Dic1714yes—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—24no—
436C23×C4—24no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—172no—
440C23×C4—172no—
441C23×C4—172no—
442C23×C4—172no—
443C23×C4C2×Dic1714yes—
444C23×C4C2×Dic1714yes—
445C23×C4C22×D1711yescharacteristic
446C23×C4C22×D1711yescharacteristic
447C23×C4C22×D1711yescharacteristic
448C23×C4C22×D1711yescharacteristic
449C23×C4C22×D1711yescharacteristic
450C4×D4—232no—
451C2×C4⋊C4—344no—
452C2×C4⋊C4—344no—
453C2×C4⋊C4—682no—
454C2×C4⋊C4C2×Dic1714yes—
455C2×C4⋊C4C22⋊D1718yes—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—344no—
459C2×C22⋊C4—344no—
460C2×C22⋊C4—344no—
461C2×C22⋊C4—344no—
462C2×C22⋊C4—344no—
463C2×C22⋊C4—344no—
464C2×C22⋊C4—344no—
465C2×C22⋊C4—344no—
466C2×C22⋊C4—682no—
467C2×C22⋊C4—682no—
468C2×C22⋊C4—682no—
469C2×C22⋊C4—682no—
470C2×C22⋊C4C2×Dic1714yes—
471C2×C22⋊C4C2×Dic1714yes—
472C2×C42—24no—
473C2×C42—344no—
474C2×C42—344no—
475C2×C42—682no—
476C2×C42C2×Dic1714yes—
477#95—174no—
478#95—344no—
479#95—342no—
480#95—342no—
481#95—342no—
482#95—344no—
483#95—344no—
484#95—344no—
485#95—344no—
486#95—682no—
487C17#1389011yescharacteristic, complemented, Sylow
488C24—21no—
489C24—21no—
490C24—22no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24#6325212yes—
506C24#6325212yes—
507C24#6325214yes—
508C24C22×Dic1712yes—
509C24C22×Dic1712yes—
510C24C23×D1711yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—174no—
542C22×C4—174no—
543C22×C4—342no—
544C22×C4—342no—
545C22×C4—342no—
546C22×C4—342no—
547C22×C4—342no—
548C22×C4—342no—
549C22×C4—342no—
550C22×C4—342no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—342no—
554C22×C4—342no—
555C22×C4—342no—
556C22×C4—342no—
557C22×C4—342no—
558C22×C4—342no—
559C22×C4—342no—
560C22×C4—342no—
561C22×C4—342no—
562C22×C4—342no—
563C22×C4—342no—
564C22×C4—342no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4D4×D1712yes—
570C22×C4#6325412yes—
571C22×C4C22×Dic1712yes—
572C22×C4C22×Dic1712yes—
573C22×C4C22×Dic1712yes—
574C22×C4C22×Dic1712yes—
575C22×C4C22×Dic1712yes—
576C22×C4C2×C22⋊D1714yes—
577C22×C4C2×C22⋊D1714yes—
578C22×C4C2×C22⋊D1714yes—
579C4⋊C4—688no—
580C4⋊C4C22⋊Dic17116yescomplemented
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—3416no—
584C22⋊C4—688no—
585C22⋊C4—688no—
586C22⋊C4—688no—
587C42—28no—
588C42—688no—
589C23—22no—
590C23—24no—
591C23—22no—
592C23—22no—
593C23—24no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—42no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23#1058761214yes—
634C23#1058761214yes—
635C23C2×#6325211yescharacteristic
636C23C2×#6325211yescharacteristic
637C23C2×#6325212yes—
638C23C2×D4×D1711yescharacteristic
639C23C2×#6325411yescharacteristic
640C23#1058769112yes—
641C23#41×D1712yes—
642C23#1058769611yescharacteristic
643C23#1058769711yescharacteristic
644C23C23×Dic1711yescharacteristic
645C23C22×C22⋊D1712yes—
646D4—232no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—416no—
667C2×C4—416no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—344no—
671C2×C4—344no—
672C2×C4—344no—
673C2×C4—344no—
674C2×C4—344no—
675C2×C4—344no—
676C2×C4—682no—
677C2×C4—682no—
678C2×C4—682no—
679C2×C4—682no—
680C2×C4—682no—
681C2×C4—682no—
682C2×C4—682no—
683C2×C4—682no—
684C2×C4—682no—
685C2×C4—682no—
686C2×C4—682no—
687C2×C4—682no—
688C2×C4—682no—
689C2×C4—682no—
690C2×C4—682no—
691C2×C4—682no—
692C2×C4—682no—
693C2×C4—682no—
694C2×C4—682no—
695C2×C4—682no—
696C2×C4—682no—
697C2×C4—682no—
698C2×C4D4×Dic1714yes—
699C2×C4C2×C22⋊Dic1714yes—
700C2×C4C2×C22⋊Dic1714yes—
701C2×C4C2×C22⋊Dic1714yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—44no—
713C22—44no—
714C22—42no—
715C22—44no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22C22×C22⋊Dic1711yescharacteristic
725C22C2×#1058761211yescharacteristic
726C22C2×#1058761211yescharacteristic
727C22C2×D4×Dic1711yescharacteristic
728C22#41×Dic1711yescharacteristic
729C22#1176328411yescharacteristic
730C22#1176329211yescharacteristic
731C22#1176331812yes—
732C22#1176332012yes—
733C22#1176332012yes—
734C22#1176333912yes—
735C22#1176339212yes—
736C22#1176340112yes—
737C22D4×C22⋊D1712yes—
738C22#1176345312yes—
739C22#1176345511yescharacteristic
740C22#1176346612yes—
741C22#1176346811yescharacteristic
742C22#1176347812yes—
743C22#1176348812yes—
744C22#1176349911yescharacteristic
745C22#1176350511yescharacteristic
746C22#1176350812yes—
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—684no—
753C4—684no—
754C4—1362no—
755C4—1362no—
756C2—44no—
757C2—44no—
758C2#1453116711yescharacteristic
759C2#1453122911yescharacteristic
760C2#1453141711yescharacteristic
761C2D4×C22⋊Dic1711yescharacteristic
762C2#1453162511yescharacteristic
763C2#1453171311yescharacteristic
764C2#1453172411yescharacteristic
765C2#1453267012yes—
766C2#1453273012yes—
767C2#1453277512yes—
768C2#1453282912yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C4×D4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC22×C4×D4D17
hypocenterC17#13890
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11762695C2semidirect
2. C2×#11762669C2semidirect
3. C2×C4×C22⋊Dic17C2semidirect
4. #14527029C2semidirect
6. #14527021C2semidirect
7. #14527011C2semidirect
8. #14527011C2semidirect
9. #14527007C2semidirect
10. #14527007C2semidirect
35. C2×C4×D4×C17C4semidirect
102. #10587502D4semidirect
194. C4⋊C4×C17C22⋊C4semidirect
387. C2×C4×D4Dic17semidirect
487. C17#13890semidirect
580. C4⋊C4C22⋊Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117626952
C2×#117626692
C2×C4×C22⋊Dic172
#145270292
#145270252
#145270212
#145270112
#145270072
C22×C4×D4×C172
#1389017