Finite Group Databasebeta

← #16956369

Subgroups — #16956369

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×#11762702C212yesmaximal, complemented
2C2×#11762672C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
4#14527029C212yesmaximal, complemented
5#14527025C212yesmaximal
6#14527016C212yesmaximal, complemented
7#14527014C211yesmaximal, 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#11762702—28no—
19#11762672—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—24no—
44C22×D4×C17—22no—
45C22×D4×C17—22no—
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×C17—24no—
68C2×C4⋊C4×C17C2×C414yes—
69C2×C22⋊C4×C17—24no—
70C2×C22⋊C4×C17C2×C414yes—
71C2×C22⋊C4×C17C2×C414yes—
72C2×C22⋊C4×C17D418yes—
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—22no—
96#10587502—22no—
97#10587502—24no—
98#10587502—24no—
99#10587502—22no—
100#10587502—24no—
101#10587502—42no—
102#10587502D414yescomplemented
103C24×C17—22no—
104C24×C17—21no—
105C24×C17—21no—
106C24×C17—21no—
107C24×C17—21no—
108C24×C17—22no—
109C24×C17—21no—
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—21no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17—22no—
116C24×C17—22no—
117C24×C17—21no—
118C24×C17—21no—
119C24×C17—21no—
120C24×C17—21no—
121C24×C17C22×C412yes—
122C24×C17C22×C412yes—
123C24×C17C2×D414yes—
124C24×C17#4114yes—
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—22no—
134C22×C4×C17—21no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—28no—
142C22×C4×C17—21no—
143C22×C4×C17—22no—
144C22×C4×C17—21no—
145C22×C4×C17—22no—
146C22×C4×C17—28no—
147C22×C4×C17—28no—
148C22×C4×C17—28no—
149C22×C4×C17—44no—
150C22×C4×C17—44no—
151C22×C4×C17—48no—
152C22×C4×C17—48no—
153C22×C4×C17—48no—
154C22×C4×C17—48no—
155C22×C4×C17C22×C412yes—
156C22×C4×C17C22×C412yes—
157C22×C4×C17C22×C412yes—
158C22×C4×C17C22×C412yes—
159C22×C4×C17C22×C412yes—
160C22×C4×C17C2×D412yes—
161C22×C4×C17C2×D414yes—
162C22×C4×C17C2×D414yes—
163C22×C4×C17#4112yes—
164C22×C4×C17#4112yes—
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×C17—28no—
195C22⋊C4×C17—28no—
196C22⋊C4×C17C22⋊C4116yescomplemented
197C42×C17—28no—
198C22⋊Dic17—216no—
199C22⋊Dic17—48no—
200C22⋊Dic17—48no—
201C22⋊Dic17—48no—
202C4⋊Dic17—48no—
203C4×Dic17—48no—
204#13886—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—24no—
226C23×C17—24no—
227C23×C17—24no—
228C23×C17—24no—
229C23×C17—42no—
230C23×C17—42no—
231C23×C17—42no—
232C23×C17—42no—
233C23×C17—42no—
234C23×C17—42no—
235C23×C17—42no—
236C23×C17—42no—
237C23×C17—41no—
238C23×C17—41no—
239C23×C17—41no—
240C23×C17—41no—
241C23×C17—42no—
242C23×C17—42no—
243C23×C17—41no—
244C23×C17—41no—
245C23×C17—41no—
246C23×C17—41no—
247C23×C17—42no—
248C23×C17—42no—
249C23×C17C2×C22⋊C414yes—
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×C17#11714yes—
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×#388—172no—
320C2×#381—171no—
321C2×C4×C22⋊C4—171no—
322#1439—172no—
323#1438—172no—
324#1436—172no—
325C4⋊#95—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#54612yes—
367C22×C17#54712yes—
368C22×C17#54711yescharacteristic
369C22×C17#55011yescharacteristic
370C22×C17#55312yes—
371C22×C17#55511yescharacteristic
372C22×C17#55611yescharacteristic
373C22×C17#55912yes—
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#388—348no—
399#381—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#233911yescharacteristic
418C2×C17#235411yescharacteristic
419C2×C17#235711yescharacteristic
420C2×C17#245512yes—
421C2×C17#245612yes—
422C2×C17#245912yes—
423C2×C17#246612yes—
424C25C22×D1711yescharacteristic
425C25C22×D1711yescharacteristic
426C22×D4—24no—
427C22×D4—24no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4C2×Dic1714yes—
431C23×C4—24no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
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—24no—
452C2×C4⋊C4—344no—
453C2×C4⋊C4—344no—
454C2×C4⋊C4—682no—
455C2×C4⋊C4C2×Dic1714yes—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—344no—
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—682no—
466C2×C22⋊C4—682no—
467C2×C22⋊C4—682no—
468C2×C22⋊C4—682no—
469C2×C22⋊C4C2×Dic1714yes—
470C2×C22⋊C4C2×Dic1714yes—
471C2×C22⋊C4C22⋊D1718yes—
472C2×C42—24no—
473C2×C42—344no—
474C2×C42—344no—
475C2×C42—682no—
476C2×C42C2×Dic1714yes—
477#95—174no—
478#95—344no—
479#95—344no—
480#95—344no—
481#95—342no—
482#95—342no—
483#95—342no—
484#95—344no—
485#95—344no—
486#95—682no—
487C17#1388611yescharacteristic, complemented, Sylow
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—22no—
506C24#6325214yes—
507C24C22×Dic1712yes—
508C24C22×Dic1712yes—
509C24C2×C22⋊D1714yes—
510C24C23×D1711yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—174no—
541C22×C4—174no—
542C22×C4—342no—
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#6325212yes—
569C22×C4#6325212yes—
570C22×C4D4×D1712yes—
571C22×C4#6325412yes—
572C22×C4C22×Dic1712yes—
573C22×C4C22×Dic1712yes—
574C22×C4C22×Dic1712yes—
575C22×C4C22×Dic1712yes—
576C22×C4C22×Dic1712yes—
577C22×C4C2×C22⋊D1714yes—
578C22×C4C2×C22⋊D1714yes—
579C4⋊C4—28no—
580C4⋊C4—688no—
581C22⋊C4—28no—
582C22⋊C4—3416no—
583C22⋊C4—688no—
584C22⋊C4—688no—
585C22⋊C4—688no—
586C22⋊C4C22⋊Dic17116yescomplemented
587C42—28no—
588C42—688no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23#1058761214yes—
634C23C2×C22⋊Dic1714yes—
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—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
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×C4#1058761214yes—
699C2×C4D4×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—44no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—42no—
715C22—44no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
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#1176344712yes—
739C22#1176345312yes—
740C22#1176345812yes—
741C22#1176346411yescharacteristic
742C22#1176348011yescharacteristic
743C22#1176350912yes—
744C22#1176352411yescharacteristic
745C22#1176352911yescharacteristic
746C22#1176354212yes—
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#1453161411yescharacteristic
763C2#1453173311yescharacteristic
764C2#1453175711yescharacteristic
765C2#1453266112yes—
766C2#1453267612yes—
767C2#1453271512yes—
768C2#1453281412yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C4×D4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC22×C4×D4D17
hypocenterC17#13886
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×#11762702C2semidirect
2. C2×#11762672C2semidirect
3. C2×C4×C22⋊Dic17C2semidirect
4. #14527029C2semidirect
6. #14527016C2semidirect
7. #14527014C2semidirect
8. #14527011C2semidirect
9. #14527007C2semidirect
10. #14527007C2semidirect
35. C2×C4×D4×C17C4semidirect
102. #10587502D4semidirect
196. C22⋊C4×C17C22⋊C4semidirect
387. C2×C4×D4Dic17semidirect
487. C17#13886semidirect
586. C22⋊C4C22⋊Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117627022
C2×#117626722
C2×C4×C22⋊Dic172
#145270292
#145270252
#145270162
#145270142
#145270112
#145270072
C22×C4×D4×C172
#1388617