Finite Group Databasebeta

← #16964983

Subgroups — #16964983

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×#11762717C211yesmaximal, characteristic
2C2×#11762700C211yesmaximal, characteristic, complemented
3#14527043C211yesmaximal, characteristic, complemented
4#14527031C212yesmaximal, complemented
5#14527027C212yesmaximal, complemented
6#14527026C211yesmaximal, characteristic, complemented
7#14527025C211yesmaximal, characteristic, complemented
8#14527023C212yesmaximal, complemented
9#14527023C212yesmaximal, complemented
10#14527011C211yesmaximal, characteristic, complemented
11C2×C17×#390C211yesmaximal, characteristic, complemented
12C23×C22⋊D17C2212yes—
13C22×#63225C2211yescharacteristic
14C22×C22⋊Dic17C2212yes—
15C22×C22⋊Dic17C2212yes—
16C22×C22⋊Dic17C2212yes—
17C22×#63227C2211yescharacteristic
18C22×#63227C2211yescharacteristic
19C22×#63227C2211yescharacteristic
20C22×#63227C2212yes—
21#11762717C418yescomplemented
22#11762700—24no—
23C2×#10587502C2211yescharacteristic
24C2×#10587502C2211yescharacteristic
25C2×#10587502C2211yescharacteristic
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2211yescharacteristic
32C23×D4×C17C2211yescharacteristic
33C22×C4⋊C4×C17C2211yescharacteristic
34C22×C22⋊C4×C17C2212yes—
35C22×C22⋊C4×C17C2212yes—
36C22×C42×C17C2211yescharacteristic
37C17×#390—24no—
38C25×C17C2312yes—
39C24×D17C2311yescharacteristic
40C22×D4×C17—22no—
41C22×D4×C17—22no—
42C22×D4×C17—42no—
43C22×D4×C17—42no—
44C22×D4×C17C2×C414yes—
45C23×C4×C17C2312yes—
46C23×C4×C17C2311yescharacteristic
47C23×C4×C17C2311yescharacteristic
48C23×C4×C17C2311yescharacteristic
49C22×C22⋊D17—42no—
50C22×C22⋊D17—42no—
51C22×C22⋊D17—42no—
52C22×C22⋊D17—42no—
53C22×C22⋊D17—42no—
54C22×C22⋊D17—42no—
55C22×C22⋊D17C2×C418yes—
56C23×Dic17C2311yescharacteristic
57C23×Dic17C2311yescharacteristic
58C23×Dic17C2312yes—
59C23×Dic17C2311yescharacteristic
60C23×Dic17C2312yes—
61C2×C4⋊C4×C17—22no—
62C2×C4⋊C4×C17—42no—
63C2×C22⋊C4×C17—24no—
64C2×C22⋊C4×C17—24no—
65C2×C22⋊C4×C17—42no—
66C2×C22⋊C4×C17—42no—
67C2×C22⋊C4×C17—42no—
68C2×C22⋊C4×C17—42no—
69C2×C42×C17—42no—
70C2×C42×C17D414yescomplemented
71C2×C22⋊Dic17—42no—
72C2×C22⋊Dic17—42no—
73C2×C22⋊Dic17—42no—
74C2×C22⋊Dic17—42no—
75C2×C22⋊Dic17—42no—
76C2×C22⋊Dic17—42no—
77C2×C22⋊Dic17—42no—
78C2×C22⋊Dic17—42no—
79C2×C22⋊Dic17C2×C418yes—
80C2×#63227—22no—
81C2×#63227—22no—
82C2×#63227—22no—
83C2×#63227—22no—
84C2×#63227—42no—
85C2×#63227—42no—
86C2×#63227—42no—
87C2×#63227—42no—
88C2×#63227—42no—
89C2×#63227C2×C414yes—
90C2×#63225—22no—
91C2×#63225—42no—
92#10587502—22no—
93#10587502—22no—
94#10587502—22no—
95#10587502—42no—
96#10587502—42no—
97#10587502—42no—
98#10587502—42no—
99#10587502—42no—
100#10587502C2×C414yes—
101C24×C17—22no—
102C24×C17—22no—
103C24×C17—22no—
104C24×C17—22no—
105C24×C17—22no—
106C24×C17—22no—
107C24×C17—22no—
108C24×C17—22no—
109C24×C17—22no—
110C24×C17—22no—
111C24×C17—22no—
112C24×C17—22no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17C22×C414yes—
116C24×C17C2411yescharacteristic
117C23×D17—21no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—21no—
121C23×D17—22no—
122C23×D17—22no—
123C23×D17—22no—
124C23×D17—22no—
125C23×D17—21no—
126C23×D17—21no—
127C23×D17C22×C412yes—
128C2×D4×C17—28no—
129C2×D4×C17—48no—
130C2×D4×C17—44no—
131C2×D4×C17—44no—
132C2×D4×C17—48no—
133C22×C4×C17—22no—
134C22×C4×C17—22no—
135C22×C4×C17—21no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—22no—
142C22×C4×C17—21no—
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×C17C22×C412yes—
151C22×C4×C17C2×D412yes—
152C22×C4×C17C2×D412yes—
153C22×C4×C17C2×D412yes—
154C22×C4×C17#4112yes—
155C2×C22⋊D17—48no—
156C2×C22⋊D17—48no—
157C2×C22⋊D17—48no—
158C2×C22⋊D17—48no—
159C2×C22⋊D17—48no—
160C2×C22⋊D17—48no—
161C2×C22⋊D17—48no—
162C22×Dic17—21no—
163C22×Dic17—21no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—21no—
173C22×Dic17—21no—
174C22×Dic17—22no—
175C22×Dic17—21no—
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—21no—
186C22×Dic17—21no—
187C22×Dic17—22no—
188C22×Dic17—21no—
189C22×Dic17C22×C414yes—
190C22×Dic17C22×C412yes—
191C4⋊C4×C17—44no—
192C22⋊C4×C17—48no—
193C22⋊C4×C17—48no—
194C42×C17—44no—
195C22⋊Dic17—48no—
196C22⋊Dic17—48no—
197C22⋊Dic17—48no—
198#63227—28no—
199#63227—44no—
200#63227—44no—
201#63227—48no—
202#63225—44no—
203#14623—171nomaximal, Sylow
204C23×C17—24no—
205C23×C17—24no—
206C23×C17—24no—
207C23×C17—24no—
208C23×C17—24no—
209C23×C17—24no—
210C23×C17—24no—
211C23×C17—42no—
212C23×C17—42no—
213C23×C17—42no—
214C23×C17—42no—
215C23×C17—42no—
216C23×C17—42no—
217C23×C17—42no—
218C23×C17—42no—
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×C17—42no—
228C23×C17—42no—
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—42no—
238C23×C17—42no—
239C23×C17C23×C411yescharacteristic
240C23×C17C22×D411yescharacteristic
241C23×C17C2×#4111yescharacteristic
242C23×C17H(5,𝔽2)12yes—
243C23×C17H(5,𝔽2)12yes—
244C23×C17H(5,𝔽2)12yes—
245C23×C17H(5,𝔽2)11yescharacteristic
246C23×C17H(5,𝔽2)11yescharacteristic
247C23×C17H(5,𝔽2)12yes—
248C23×C17H(5,𝔽2)11yescharacteristic
249C23×C172−1+411yescharacteristic
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—24no—
253C22×D17—24no—
254C22×D17—22no—
255C22×D17—41no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—42no—
262C22×D17—41no—
263C22×D17—42no—
264C22×D17—41no—
265C22×D17—42no—
266C22×D17—42no—
267C22×D17—42no—
268C22×D17—42no—
269C22×D17—42no—
270C22×D17—42no—
271C22×D17—42no—
272C22×D17—42no—
273D4×C17—416no—
274C2×C4×C17—24no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—24no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
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×C17—42no—
295C2×C4×C17C4×D414yes—
296C22⋊D17—432no—
297C2×Dic17—22no—
298C2×Dic17—24no—
299C2×Dic17—24no—
300C2×Dic17—24no—
301C2×Dic17—24no—
302C2×Dic17—41no—
303C2×Dic17—41no—
304C2×Dic17—42no—
305C2×Dic17—42no—
306C2×Dic17—42no—
307C2×Dic17—42no—
308C2×Dic17—42no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
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—
325C2×Dic17—42no—
326C2×#392—171no—
327C2×#390D1711yescharacteristic, complemented
328C2×#388—171no—
329#1442—171no—
330#1440—172no—
331#1439—171no—
332#1439—172no—
333#1438—171no—
334#1438—172no—
335#1438—172no—
336#1434—171no—
337C22×C17—44no—
338C22×C17—44no—
339C22×C17—44no—
340C22×C17—44no—
341C22×C17—44no—
342C22×C17—44no—
343C22×C17—44no—
344C22×C17—82no—
345C22×C17—82no—
346C22×C17—82no—
347C22×C17—82no—
348C22×C17—82no—
349C22×C17—82no—
350C22×C17—82no—
351C22×C17—82no—
352C22×C17C2×C4×D411yescharacteristic
353C22×C17#51811yescharacteristic
354C22×C17#51812yes—
355C22×C17#51812yes—
356C22×C17#52011yescharacteristic
357C22×C17#53411yescharacteristic
358C22×C17#53511yescharacteristic
359C22×C17#53511yescharacteristic
360C22×C17#53511yescharacteristic
361C22×C17#53511yescharacteristic
362C22×C17#53711yescharacteristic
363C22×C17#53812yes—
364C22×C17#54011yescharacteristic
365C22×C17#54012yes—
366C22×C17#54211yescharacteristic
367C22×C17#56012yes—
368C22×C17#56012yes—
369C22×C17#56012yes—
370C22×C17#56012yes—
371C22×C17#56012yes—
372C22×C17H(3,𝔽4)12yes—
373C22×C17#56212yes—
374C22×C17#56212yes—
375C2×D17—42no—
376C2×D17—42no—
377C2×D17—42no—
378C2×D17—44no—
379C2×D17—44no—
380C2×D17—81no—
381C2×D17—81no—
382C2×D17—82no—
383C2×D17—82no—
384C2×D17—81no—
385C2×D17—81no—
386C4×C17—24no—
387C4×C17—42no—
388C4×C17—42no—
389C4×C17—82no—
390Dic17—42no—
391Dic17—44no—
392Dic17—81no—
393Dic17—82no—
394Dic17—81no—
395C23×D4—172no—
396C23×D4C2×D1711yescharacteristic
397C22×C4⋊C4—171no—
398C22×C4⋊C4C2×D1711yescharacteristic
399C22×C22⋊C4—171no—
400C22×C22⋊C4—172no—
401C22×C22⋊C4—171no—
402C22×C22⋊C4—171no—
403C22×C22⋊C4—172no—
404C22×C22⋊C4—172no—
405C22×C22⋊C4—172no—
406C22×C22⋊C4C2×D1712yes—
407C22×C22⋊C4C2×D1712yes—
408C22×C42C2×D1711yescharacteristic
409#392—178no—
410#390—24no—
411#388—344no—
412C2×#95—171no—
413C2×#95—171no—
414C2×#95—171no—
415C2×#95—171no—
416C2×#95—172no—
417C2×#95—172no—
418C2×#95—172no—
419C2×#95—172no—
420C2×#95—172no—
421C2×C17—84no—
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—82no—
434C25—171no—
435C25C22×D1712yes—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—42no—
439C22×D4—42no—
440C22×D4—178no—
441C22×D4—682no—
442C22×D4—682no—
443C22×D4—682no—
444C22×D4—682no—
445C22×D4—682no—
446C22×D4—682no—
447C22×D4C4×D1714yes—
448C23×C4—171no—
449C23×C4—172no—
450C23×C4—171no—
451C23×C4—172no—
452C23×C4—171no—
453C23×C4C22×D1712yes—
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—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—174no—
468C2×C22⋊C4—178no—
469C2×C22⋊C4—342no—
470C2×C22⋊C4—342no—
471C2×C22⋊C4—342no—
472C2×C22⋊C4—342no—
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⋊C4—682no—
486C2×C42—42no—
487C2×C42C22⋊D1714yescomplemented
488#95—174no—
489#95—342no—
490#95—342no—
491#95—342no—
492#95—682no—
493#95—682no—
494#95—682no—
495#95—682no—
496#95—682no—
497C17#1462311yescharacteristic, complemented, Sylow
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—172no—
513C24—341no—
514C24—341no—
515C24—342no—
516C24—342no—
517C24—342no—
518C24—341no—
519C24—342no—
520C24—341no—
521C24—341no—
522C24—341no—
523C24C2×C4×D1714yes—
524C24C23×D1711yescharacteristic
525C2×D4—28no—
526C2×D4—48no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—48no—
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—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—174no—
555C22×C4—172no—
556C22×C4—341no—
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—341no—
566C22×C4—342no—
567C22×C4—341no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—341no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—341no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—341no—
581C22×C4—341no—
582C22×C4—341no—
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—48no—
591C22⋊C4—48no—
592C22⋊C4—348no—
593C22⋊C4—684no—
594C22⋊C4—684no—
595C22⋊C4—688no—
596C22⋊C4—688no—
597C22⋊C4—688no—
598C22⋊C4—688no—
599C42—44no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—342no—
636C23—342no—
637C23—344no—
638C23—344no—
639C23—342no—
640C23—682no—
641C23—682no—
642C23—682no—
643C23—682no—
644C23—682no—
645C23—682no—
646C23—682no—
647C23—682no—
648C23—681no—
649C23—681no—
650C23—681no—
651C23—681no—
652C23—681no—
653C23—681no—
654C23—682no—
655C23—681no—
656C23—682no—
657C23—681no—
658C23C22×C4×D1711yescharacteristic
659C23C2×#6325211yescharacteristic
660C23#1058769111yescharacteristic
661C23#1058769112yes—
662C23#1058769112yes—
663C23#1058769112yes—
664C23#1058769111yescharacteristic
665C23#1058769611yescharacteristic
666C23#1058769612yes—
667C23#1058769711yescharacteristic
668C23C22×C22⋊D1711yescharacteristic
669D4—416no—
670D4—6832no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
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—42no—
691C2×C4—42no—
692C2×C4—342no—
693C2×C4—344no—
694C2×C4—344no—
695C2×C4—344no—
696C2×C4—344no—
697C2×C4—682no—
698C2×C4—682no—
699C2×C4—682no—
700C2×C4—682no—
701C2×C4—681no—
702C2×C4—681no—
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—681no—
713C2×C4—681no—
714C2×C4—681no—
715C2×C4—681no—
716C2×C4—681no—
717C2×C4—681no—
718C2×C4—682no—
719C2×C4—682no—
720C2×C4—682no—
721C2×C4C4×C22⋊D1714yes—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22—82no—
737C22—684no—
738C22—684no—
739C22—682no—
740C22—682no—
741C22—682no—
742C22—1361no—
743C22—1361no—
744C22—1361no—
745C22—1361no—
746C22—1362no—
747C22—1362no—
748C22C2×C4×C22⋊D1711yescharacteristic
749C22#1176328111yescharacteristic
750C22#1176328112yes—
751C22#1176328212yes—
752C22#1176328811yescharacteristic
753C22#1176336811yescharacteristic
754C22#1176337311yescharacteristic
755C22#1176337611yescharacteristic
756C22#1176337611yescharacteristic
757C22#1176337611yescharacteristic
758C22#1176338711yescharacteristic
759C22#1176339712yes—
760C22#1176341011yescharacteristic
761C22#1176341012yes—
762C22#1176342411yescharacteristic
763C22#1176354612yes—
764C22#1176354612yes—
765C22#1176354712yes—
766C22#1176354712yes—
767C22#1176354712yes—
768C22#1176355112yes—
769C22#1176355312yes—
770C22#1176355412yes—
771C4—24no—
772C4—42no—
773C4—42no—
774C4—82no—
775C4—684no—
776C4—682no—
777C4—1361no—
778C4—1361no—
779C4—1362no—
780C2—84no—
781C2—1362no—
782C2#1453144211yescharacteristic
783C2#1453147111yescharacteristic
784C2#1453150611yescharacteristic
785C2#1453192112yes—
786C2#1453193512yes—
787C2#1453678411yescharacteristic
788C2#1453680611yescharacteristic
789C2#1453682511yescharacteristic
790C2#1453682911yescharacteristic
791C2#1453690312yes—
792C2#1453691212yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#390C2
socle, cosocleC24×C17C24
prime radicalC2×#11762717C2
hypercenterC2×#390D17
hypocenterC17#14623
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#11762700C2semidirect
3. #14527043C2semidirect
4. #14527031C2semidirect
5. #14527027C2semidirect
6. #14527026C2semidirect
7. #14527025C2semidirect
8. #14527023C2semidirect
9. #14527023C2semidirect
10. #14527011C2semidirect
11. C2×C17×#390C2semidirect
21. #11762717C4semidirect
70. C2×C42×C17D4semidirect
327. C2×#390D17semidirect
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×#117627172
C2×#117627002
#145270432
#145270312
#145270272
#145270262
#145270252
#145270232
#145270112
C2×C17×#3902
#1462317