Finite Group Databasebeta

← #16964982

Subgroups — #16964982

Order 4352.

1910 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762718C211yesmaximal, characteristic
2C2×#11762711C211yesmaximal, characteristic, complemented
3#14527040C211yesmaximal, characteristic, complemented
4#14527032C212yesmaximal, complemented
5#14527029C211yesmaximal, characteristic, complemented
6#14527026C212yesmaximal, complemented
7#14527024C211yesmaximal, characteristic, complemented
8#14527023C212yesmaximal, complemented
9#14527023C212yesmaximal, complemented
10#14527011C211yesmaximal, characteristic, complemented
11C2×C17×#388C211yesmaximal, characteristic, complemented
12C23×D68C2211yescharacteristic
13C23×C22⋊D17C2212yes—
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C22⋊Dic17C2212yes—
16C22×#63227C2212yes—
17C22×#63227C2212yes—
18C22×#63227C2212yes—
19C22×#63227C2212yes—
20C22×#63227C2212yes—
21#11762718C418yescomplemented
22#11762711—24no—
23C2×#10587502C2211yescharacteristic
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2211yescharacteristic
30C22×C4⋊C4×C17C2211yescharacteristic
31C22×C22⋊C4×C17C2211yescharacteristic
32C22×C22⋊C4×C17C2211yescharacteristic
33C22×C22⋊C4×C17C2211yescharacteristic
34C22×C42×C17C2211yescharacteristic
35C17×#388—24no—
36C2×C17×#95C2211yescharacteristic
37C2×C17×#95C2211yescharacteristic
38C25×C17C2311yescharacteristic
39C24×D17C2312yes—
40C23×C4×C17C2311yescharacteristic
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2311yescharacteristic
44C23×C4×C17C2311yescharacteristic
45C23×C4×C17C2311yescharacteristic
46C22×C22⋊D17—42no—
47C22×C22⋊D17—42no—
48C22×C22⋊D17—42no—
49C22×C22⋊D17—42no—
50C22×C22⋊D17—42no—
51C22×C22⋊D17—42no—
52C22×C22⋊D17C2×C418yes—
53C23×Dic17C2312yes—
54C23×Dic17C2312yes—
55C23×Dic17C2312yes—
56C22×D68—22no—
57C22×D68—22no—
58C22×D68—42no—
59C22×D68—42no—
60C22×D68C2×C414yes—
61C2×C4⋊C4×C17—22no—
62C2×C4⋊C4×C17—42no—
63C2×C22⋊C4×C17—22no—
64C2×C22⋊C4×C17—22no—
65C2×C22⋊C4×C17—22no—
66C2×C22⋊C4×C17—22no—
67C2×C22⋊C4×C17—42no—
68C2×C22⋊C4×C17—42no—
69C2×C22⋊C4×C17C2×C414yes—
70C2×C42×C17—42no—
71C2×C42×C17D414yescomplemented
72C2×C22⋊Dic17—42no—
73C2×C22⋊Dic17—42no—
74C2×C22⋊Dic17—42no—
75C2×#63227—24no—
76C2×#63227—24no—
77C2×#63227—42no—
78C2×#63227—42no—
79C2×#63227—42no—
80C2×#63227—42no—
81C2×#63227—42no—
82C2×#63227—42no—
83C2×#63227—42no—
84C2×#63227—42no—
85C2×#63227—42no—
86C2×#63227—42no—
87C2×#63227—42no—
88C2×#63227—42no—
89C2×#63227C2×C418yes—
90C2×C4⋊Dic17—22no—
91C2×C4⋊Dic17—42no—
92C17×#95—22no—
93C17×#95—22no—
94#10587502—22no—
95#10587502—42no—
96#10587502—42no—
97#10587502—42no—
98#10587502—42no—
99#10587502—42no—
100#10587502C2×C414yes—
101C24×C17—21no—
102C24×C17—21no—
103C24×C17—21no—
104C24×C17—21no—
105C24×C17—22no—
106C24×C17—22no—
107C24×C17—22no—
108C24×C17—22no—
109C24×C17—21no—
110C24×C17—21no—
111C24×C17C22×C412yes—
112C24×C17C2411yescharacteristic
113C23×D17—22no—
114C23×D17—22no—
115C23×D17—22no—
116C23×D17—22no—
117C23×D17—22no—
118C23×D17—22no—
119C23×D17—22no—
120C23×D17—22no—
121C23×D17—22no—
122C23×D17—22no—
123C23×D17—22no—
124C23×D17—22no—
125C23×D17—22no—
126C23×D17—22no—
127C23×D17C22×C414yes—
128C22×C4×C17—22no—
129C22×C4×C17—22no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—22no—
134C22×C4×C17—22no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—22no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—21no—
152C22×C4×C17C22×C412yes—
153C22×C4×C17C22×C412yes—
154C22×C4×C17C2×D412yes—
155C22×C4×C17C2×D412yes—
156C22×C4×C17C2×D412yes—
157C22×C4×C17#4112yes—
158C2×C22⋊D17—48no—
159C2×C22⋊D17—48no—
160C2×C22⋊D17—48no—
161C2×C22⋊D17—48no—
162C2×C22⋊D17—48no—
163C2×C22⋊D17—48no—
164C2×C22⋊D17—48no—
165C22×Dic17—22no—
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×Dic17C22×C414yes—
186C2×D68—28no—
187C2×D68—48no—
188C2×D68—44no—
189C2×D68—44no—
190C2×D68—48no—
191C4⋊C4×C17—44no—
192C22⋊C4×C17—28no—
193C22⋊C4×C17—44no—
194C22⋊C4×C17—44no—
195C42×C17—44no—
196C22⋊Dic17—48no—
197#63227—48no—
198#63227—48no—
199#63227—48no—
200#63227—48no—
201#63227—48no—
202C4⋊Dic17—44no—
203#14623—171nomaximal, Sylow
204C23×C17—22no—
205C23×C17—22no—
206C23×C17—24no—
207C23×C17—24no—
208C23×C17—22no—
209C23×C17—41no—
210C23×C17—41no—
211C23×C17—41no—
212C23×C17—41no—
213C23×C17—41no—
214C23×C17—41no—
215C23×C17—42no—
216C23×C17—42no—
217C23×C17—41no—
218C23×C17—41no—
219C23×C17—42no—
220C23×C17—42no—
221C23×C17—42no—
222C23×C17—42no—
223C23×C17—42no—
224C23×C17—42no—
225C23×C17—42no—
226C23×C17—42no—
227C23×C17C23×C411yescharacteristic
228C23×C17C22×D411yescharacteristic
229C23×C17C2×#4111yescharacteristic
230C23×C17H(5,𝔽2)12yes—
231C23×C17H(5,𝔽2)12yes—
232C23×C17H(5,𝔽2)12yes—
233C23×C17H(5,𝔽2)12yes—
234C23×C17H(5,𝔽2)11yescharacteristic
235C23×C17H(5,𝔽2)11yescharacteristic
236C23×C17H(5,𝔽2)11yescharacteristic
237C23×C172−1+411yescharacteristic
238C22×D17—24no—
239C22×D17—24no—
240C22×D17—24no—
241C22×D17—24no—
242C22×D17—24no—
243C22×D17—24no—
244C22×D17—24no—
245C22×D17—42no—
246C22×D17—42no—
247C22×D17—42no—
248C22×D17—42no—
249C22×D17—42no—
250C22×D17—42no—
251C22×D17—42no—
252C22×D17—42no—
253C22×D17—42no—
254C22×D17—42no—
255C22×D17—42no—
256C22×D17—42no—
257C22×D17—42no—
258C22×D17—42no—
259C22×D17—42no—
260C22×D17—42no—
261C22×D17—42no—
262C22×D17—42no—
263C22×D17—42no—
264C22×D17—42no—
265C22×D17—42no—
266C22×D17—42no—
267C22×D17—42no—
268C22×D17—42no—
269C22×D17—42no—
270C22×D17—42no—
271C22×D17—42no—
272C22×D17—42no—
273C2×C4×C17—24no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—24no—
277C2×C4×C17—22no—
278C2×C4×C17—24no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—42no—
288C2×C4×C17—42no—
289C2×C4×C17—42no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—41no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17—42no—
301C2×C4×C17—42no—
302C2×C4×C17C4×D414yes—
303C22⋊D17—432no—
304C2×Dic17—24no—
305C2×Dic17—24no—
306C2×Dic17—24no—
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—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325D68—416no—
326C2×#392—171no—
327C2×#390—171no—
328C2×#388D1711yescharacteristic, complemented
329#1442—171no—
330#1440—172no—
331#1439—172no—
332#1439—171no—
333#1438—171no—
334#1438—172no—
335#1438—172no—
336#1434—171no—
337C22×C17—42no—
338C22×C17—42no—
339C22×C17—42no—
340C22×C17—44no—
341C22×C17—44no—
342C22×C17—81no—
343C22×C17—81no—
344C22×C17—82no—
345C22×C17—82no—
346C22×C17—81no—
347C22×C17—81no—
348C22×C17C2×C4×D411yescharacteristic
349C22×C17#51812yes—
350C22×C17#51812yes—
351C22×C17#51811yescharacteristic
352C22×C17#52011yescharacteristic
353C22×C17#53411yescharacteristic
354C22×C17#53511yescharacteristic
355C22×C17#53511yescharacteristic
356C22×C17#53511yescharacteristic
357C22×C17#53511yescharacteristic
358C22×C17#53711yescharacteristic
359C22×C17#53812yes—
360C22×C17#54012yes—
361C22×C17#54011yescharacteristic
362C22×C17#54211yescharacteristic
363C22×C17#56012yes—
364C22×C17#56012yes—
365C22×C17#56012yes—
366C22×C17#56012yes—
367C22×C17#56012yes—
368C22×C17H(3,𝔽4)12yes—
369C22×C17#56212yes—
370C22×C17#56212yes—
371C2×D17—44no—
372C2×D17—44no—
373C2×D17—44no—
374C2×D17—44no—
375C2×D17—44no—
376C2×D17—44no—
377C2×D17—44no—
378C2×D17—82no—
379C2×D17—82no—
380C2×D17—82no—
381C2×D17—82no—
382C2×D17—82no—
383C2×D17—82no—
384C2×D17—82no—
385C2×D17—82no—
386C4×C17—24no—
387C4×C17—42no—
388C4×C17—42no—
389C4×C17—42no—
390C4×C17—81no—
391C4×C17—81no—
392Dic17—44no—
393Dic17—82no—
394Dic17—82no—
395C23×D4—172no—
396C23×D4—171no—
397C22×C4⋊C4—171no—
398C22×C4⋊C4C2×D1711yescharacteristic
399C22×C22⋊C4—172no—
400C22×C22⋊C4—172no—
401C22×C22⋊C4—172no—
402C22×C22⋊C4—172no—
403C22×C22⋊C4—172no—
404C22×C22⋊C4—172no—
405C22×C22⋊C4C2×D1711yescharacteristic
406C22×C22⋊C4C2×D1711yescharacteristic
407C22×C22⋊C4C2×D1711yescharacteristic
408C22×C42C2×D1711yescharacteristic
409#392—178no—
410#390—344no—
411#388—24no—
412C2×#95—171no—
413C2×#95—171no—
414C2×#95—172no—
415C2×#95—172no—
416C2×#95—172no—
417C2×#95—172no—
418C2×#95—172no—
419C2×#95C2×D1711yescharacteristic
420C2×#95C2×D1711yescharacteristic
421C2×C17—82no—
422C2×C17#232111yescharacteristic
423C2×C17#232411yescharacteristic
424C2×C17#232811yescharacteristic
425C2×C17#237512yes—
426C2×C17#237712yes—
427C2×C17#281311yescharacteristic
428C2×C17#281511yescharacteristic
429C2×C17#281811yescharacteristic
430C2×C17#281911yescharacteristic
431C2×C17#282812yes—
432C2×C17#282912yes—
433D17—84no—
434C25—172no—
435C25C22×D1711yescharacteristic
436C22×D4—178no—
437C22×D4—174no—
438C22×D4—342no—
439C22×D4—342no—
440C22×D4—682no—
441C22×D4—682no—
442C22×D4—682no—
443C22×D4—682no—
444C22×D4—682no—
445C22×D4—682no—
446C22×D4—682no—
447C22×D4—682no—
448C23×C4—172no—
449C23×C4—172no—
450C23×C4—172no—
451C23×C4C22×D1711yescharacteristic
452C23×C4C22×D1711yescharacteristic
453C23×C4C22×D1711yescharacteristic
454C23×C4C22×D1711yescharacteristic
455C23×C4C22×D1711yescharacteristic
456C23×C4C22×D1711yescharacteristic
457C2×C4⋊C4—22no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—342no—
460C2×C4⋊C4—682no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—178no—
468C2×C22⋊C4—344no—
469C2×C22⋊C4—344no—
470C2×C22⋊C4—682no—
471C2×C22⋊C4—682no—
472C2×C22⋊C4—682no—
473C2×C22⋊C4—682no—
474C2×C22⋊C4—682no—
475C2×C22⋊C4—682no—
476C2×C22⋊C4—682no—
477C2×C22⋊C4—682no—
478C2×C22⋊C4—682no—
479C2×C22⋊C4—682no—
480C2×C22⋊C4—682no—
481C2×C22⋊C4—682no—
482C2×C22⋊C4—682no—
483C2×C22⋊C4—682no—
484C2×C22⋊C4—682no—
485C2×C22⋊C4C4×D1714yes—
486C2×C42—42no—
487C2×C42C22⋊D1714yescomplemented
488#95—22no—
489#95—22no—
490#95—174no—
491#95—342no—
492#95—682no—
493#95—682no—
494#95—682no—
495#95—682no—
496#95—682no—
497C17#1462311yescharacteristic, complemented, Sylow
498C24—21no—
499C24—22no—
500C24—22no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—174no—
509C24—342no—
510C24—342no—
511C24—342no—
512C24—342no—
513C24—342no—
514C24—342no—
515C24—342no—
516C24—342no—
517C24—342no—
518C24—342no—
519C24—342no—
520C24—342no—
521C24—342no—
522C24—342no—
523C24C2×C4×D1712yes—
524C24C23×D1711yescharacteristic
525C2×D4—348no—
526C2×D4—688no—
527C2×D4—684no—
528C2×D4—684no—
529C2×D4—688no—
530C2×D4—688no—
531C2×D4—688no—
532C2×D4—688no—
533C2×D4—688no—
534C2×D4—688no—
535C2×D4—688no—
536C2×D4—688no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—174no—
562C22×C4—342no—
563C22×C4—342no—
564C22×C4—342no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—342no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4C2×C4×D1712yes—
583C22×C4C2×C4×D1712yes—
584C22×C4#6325212yes—
585C22×C4C2×C22⋊D1712yes—
586C22×C4C2×C22⋊D1712yes—
587C22×C4C2×C22⋊D1712yes—
588C4⋊C4—44no—
589C4⋊C4—684no—
590C22⋊C4—28no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—688no—
594C22⋊C4—688no—
595C22⋊C4—688no—
596C22⋊C4—688no—
597C22⋊C4—688no—
598C22⋊C4—688no—
599C42—44no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—344no—
624C23—344no—
625C23—344no—
626C23—344no—
627C23—344no—
628C23—344no—
629C23—344no—
630C23—682no—
631C23—682no—
632C23—682no—
633C23—682no—
634C23—682no—
635C23—682no—
636C23—682no—
637C23—682no—
638C23—682no—
639C23—682no—
640C23—682no—
641C23—682no—
642C23—682no—
643C23—682no—
644C23—682no—
645C23—682no—
646C23—682no—
647C23—682no—
648C23—682no—
649C23—682no—
650C23—682no—
651C23—682no—
652C23—682no—
653C23—682no—
654C23—682no—
655C23—682no—
656C23—682no—
657C23—682no—
658C23C22×C4×D1711yescharacteristic
659C23C2×#6325211yescharacteristic
660C23#1058769112yes—
661C23#1058769112yes—
662C23#1058769612yes—
663C23#1058769612yes—
664C23#1058769611yescharacteristic
665C23#1058769611yescharacteristic
666C23#1058769611yescharacteristic
667C23#1058769711yescharacteristic
668C23C22×C22⋊D1711yescharacteristic
669D4—6816no—
670D4—6832no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—344no—
701C2×C4—344no—
702C2×C4—344no—
703C2×C4—682no—
704C2×C4—682no—
705C2×C4—682no—
706C2×C4—682no—
707C2×C4—682no—
708C2×C4—682no—
709C2×C4—682no—
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×C4C4×C22⋊D1714yes—
722C22—44no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—82no—
732C22—82no—
733C22—684no—
734C22—684no—
735C22—684no—
736C22—684no—
737C22—684no—
738C22—684no—
739C22—684no—
740C22—1362no—
741C22—1362no—
742C22—1362no—
743C22—1362no—
744C22—1362no—
745C22—1362no—
746C22—1362no—
747C22—1362no—
748C22C2×C4×C22⋊D1711yescharacteristic
749C22#1176328112yes—
750C22#1176328112yes—
751C22#1176328311yescharacteristic
752C22#1176328911yescharacteristic
753C22#1176336811yescharacteristic
754C22#1176337311yescharacteristic
755C22#1176337311yescharacteristic
756C22#1176337311yescharacteristic
757C22#1176337611yescharacteristic
758C22#1176338711yescharacteristic
759C22#1176339212yes—
760C22#1176341012yes—
761C22#1176341411yescharacteristic
762C22#1176343011yescharacteristic
763C22#1176354712yes—
764C22#1176354712yes—
765C22#1176354912yes—
766C22#1176355012yes—
767C22#1176355012yes—
768C22#1176355112yes—
769C22#1176355312yes—
770C22#1176355612yes—
771C4—24no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—81no—
776C4—81no—
777C4—684no—
778C4—1362no—
779C4—1362no—
780C2—82no—
781C2—1364no—
782C2#1453143811yescharacteristic
783C2#1453147711yescharacteristic
784C2#1453150611yescharacteristic
785C2#1453192412yes—
786C2#1453193712yes—
787C2#1453678611yescharacteristic
788C2#1453680611yescharacteristic
789C2#1453682411yescharacteristic
790C2#1453682911yescharacteristic
791C2#1453690112yes—
792C2#1453691012yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC2×#11762718C2
hypercenterC2×#388D17
hypocenterC17#14623
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11762711C2semidirect
3. #14527040C2semidirect
4. #14527032C2semidirect
5. #14527029C2semidirect
6. #14527026C2semidirect
7. #14527024C2semidirect
8. #14527023C2semidirect
9. #14527023C2semidirect
10. #14527011C2semidirect
11. C2×C17×#388C2semidirect
21. #11762718C4semidirect
71. C2×C42×C17D4semidirect
328. C2×#388D17semidirect
487. C2×C42C22⋊D17semidirect
497. C17#14623semidirect

Maximal subgroups

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

subgroupindex
C2×#117627182
C2×#117627112
#145270402
#145270322
#145270292
#145270262
#145270242
#145270232
#145270112
C2×C17×#3882
#1462317