Finite Group Databasebeta

← C4×#11762736 #16956144

Subgroups — C4×#11762736 #16956144

Order 4352.

1790 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762736C211yesmaximal, characteristic
2C2×C4×C4⋊Dic17C211yesmaximal, characteristic, complemented
3C2×C4×#63227C212yesmaximal
4C2×C4×#63227C211yesmaximal, characteristic
5#14527053C211yesmaximal, characteristic, complemented
6#14527044C212yesmaximal, complemented
7#14527041C211yesmaximal, characteristic, complemented
8#14527032C212yesmaximal
9#14527030C211yesmaximal, characteristic
10C4×#10587502C212yesmaximal, complemented
11C4×C17×#95C211yesmaximal, characteristic, complemented
12C23×C4×D17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C4⋊Dic17C2211yescharacteristic
15C22×#63227C2212yes—
16C22×#63227C2211yescharacteristic
17C22×#63227C2211yescharacteristic
18C22×#63227C2212yes—
19C22×C4×Dic17C2211yescharacteristic
20C22×C4×Dic17C2212yes—
21#11762736C418yesdirect product factor
22C4×C4⋊Dic17—24no—
23C4×#63227—24no—
24C4×#63227—28no—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C22×C42×C17C2212yes—
35C22×C42×C17C2211yescharacteristic
36C2×C17×#95C2211yescharacteristic
37C2×C17×#95C2212yes—
38C2×C17×#95C2211yescharacteristic
39C24×D17C2311yescharacteristic
40C23×C4×C17C2312yes—
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2312yes—
43C23×C4×C17C2311yescharacteristic
44C23×C4×C17C2311yescharacteristic
45C23×Dic17C2312yes—
46C23×Dic17C2311yescharacteristic
47C23×Dic17C2311yescharacteristic
48C23×Dic17C2312yes—
49C23×Dic17C2311yescharacteristic
50C22×C4×D17—22no—
51C22×C4×D17—22no—
52C22×C4×D17—24no—
53C22×C4×D17—24no—
54C22×C4×D17D414yes—
55C2×C42×C17—24no—
56C2×C42×C17—24no—
57C2×C42×C17—24no—
58C2×C42×C17—24no—
59C2×C42×C17D414yes—
60C2×#63227—24no—
61C2×#63227—24no—
62C2×#63227—22no—
63C2×#63227—24no—
64C2×#63227—22no—
65C2×#63227—22no—
66C2×#63227—24no—
67C2×#63227—22no—
68C2×#63227—22no—
69C2×#63227—24no—
70C2×#63227C2×C414yes—
71C2×#63227C2×C418yes—
72C2×C4⋊Dic17—22no—
73C2×C4⋊Dic17—22no—
74C2×C4⋊Dic17—22no—
75C2×C4⋊Dic17—24no—
76C2×C4⋊Dic17C2×C414yescomplemented
77C2×C4×Dic17—22no—
78C2×C4×Dic17—24no—
79C2×C4×Dic17—24no—
80C2×C4×Dic17—24no—
81C2×C4×Dic17—24no—
82C17×#95—24no—
83C17×#95—22no—
84C17×#95C2×C414yescomplemented
85#10587502—22no—
86#10587502—22no—
87#10587502—24no—
88#10587502—24no—
89#10587502—24no—
90#10587502—24no—
91#10587502—24no—
92#10587502—24no—
93#10587502C2×C418yescomplemented
94C24×C17C2411yescharacteristic
95C23×D17—21no—
96C23×D17—22no—
97C23×D17—22no—
98C23×D17—21no—
99C23×D17—21no—
100C23×D17—22no—
101C23×D17—22no—
102C23×D17—21no—
103C23×D17C22×C412yes—
104C23×D17C2×D412yes—
105C23×D17#4112yes—
106C22×C4×C17—22no—
107C22×C4×C17—22no—
108C22×C4×C17—22no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—21no—
117C22×C4×C17—21no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17C22×C414yes—
125C22×C4×C17C22×C412yes—
126C22×C4×C17C2×D412yes—
127C22×C4×C17C2×D412yes—
128C22×C4×C17C2×D412yes—
129C22×C4×C17C2×D412yes—
130C22×C4×C17#4114yes—
131C22×C4×C17#4112yes—
132C22×C4×C17#4114yes—
133C22×C4×C17#4114yes—
134C22×C4×C17#4112yes—
135C22×Dic17—21no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—22no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—21no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—21no—
156C22×Dic17—22no—
157C22×Dic17—22no—
158C22×Dic17—21no—
159C22×Dic17C22×C412yes—
160C22×Dic17C22×C414yes—
161C22×Dic17C2×D412yes—
162C22×Dic17#4112yes—
163C22×Dic17#4114yes—
164C2×C4×D17—28no—
165C2×C4×D17—216no—
166C2×C4×D17—44no—
167C2×C4×D17—44no—
168C2×C4×D17—48no—
169C42×C17—28no—
170C42×C17—48no—
171#63227—28no—
172#63227—216no—
173#63227—216no—
174#63227—28no—
175C4⋊Dic17—28no—
176C4⋊Dic17—28no—
177C4×Dic17—48no—
178C4×Dic17—44no—
179C4×#397—171nomaximal, Sylow
180C23×C17C23×C411yescharacteristic
181C23×C17C22×D411yescharacteristic
182C23×C17C22×D411yescharacteristic
183C23×C17C2×#4111yescharacteristic
184C23×C17C2×#4112yes—
185C23×C17C2×#4112yes—
186C23×C17C2×#4112yes—
187C23×C17C2×#4111yescharacteristic
188C23×C17C2×#4111yescharacteristic
189C23×C17C2×#4112yes—
190C23×C17C2×#4111yescharacteristic
191C22×D17—22no—
192C22×D17—24no—
193C22×D17—24no—
194C22×D17—22no—
195C22×D17—22no—
196C22×D17—24no—
197C22×D17—24no—
198C22×D17—22no—
199C22×D17—24no—
200C22×D17—24no—
201C22×D17—22no—
202C22×D17—22no—
203C22×D17—41no—
204C22×D17—41no—
205C22×D17—41no—
206C22×D17—42no—
207C22×D17—42no—
208C22×D17—42no—
209C22×D17—42no—
210C22×D17—42no—
211C22×D17—42no—
212C22×D17—41no—
213C22×D17C4×D414yes—
214C2×C4×C17—24no—
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—24no—
218C2×C4×C17—24no—
219C2×C4×C17—24no—
220C2×C4×C17—24no—
221C2×C4×C17—22no—
222C2×C4×C17—22no—
223C2×C4×C17—24no—
224C2×C4×C17—24no—
225C2×C4×C17—24no—
226C2×C4×C17—22no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
229C2×C4×C17—42no—
230C2×C4×C17—42no—
231C2×C4×C17—42no—
232C2×C4×C17—42no—
233C2×C4×C17—42no—
234C2×C4×C17—42no—
235C2×C4×C17—42no—
236C2×C4×C17—42no—
237C2×C4×C17C4×D414yes—
238C2×C4×C17#12114yes—
239C2×C4×C17#12318yes—
240C2×C4×C17#12314yes—
241C2×C4×C17#12414yes—
242C2×C4×C17#12618yes—
243C2×Dic17—24no—
244C2×Dic17—24no—
245C2×Dic17—22no—
246C2×Dic17—24no—
247C2×Dic17—24no—
248C2×Dic17—22no—
249C2×Dic17—24no—
250C2×Dic17—24no—
251C2×Dic17—24no—
252C2×Dic17—22no—
253C2×Dic17—24no—
254C2×Dic17—24no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—41no—
258C2×Dic17—42no—
259C2×Dic17—41no—
260C2×Dic17—42no—
261C2×Dic17—41no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—42no—
265C2×Dic17—42no—
266C2×Dic17—42no—
267C2×Dic17—42no—
268C2×Dic17—42no—
269C2×Dic17—42no—
270C2×Dic17—42no—
271C2×Dic17—41no—
272C4×D17—416no—
273C2×#397—171no—
274C2×C4×C4⋊C4—171no—
275C2×C4×C22⋊C4—171no—
276C2×C4×C22⋊C4—172no—
277#1445—171no—
278#1443—172no—
279#1442—171no—
280#1440—172no—
281#1439—171no—
282C4×#95—172no—
283C4×#95D1711yescharacteristic, complemented
284C22×C17C2×C4×D411yescharacteristic
285C22×C17C2×C4×D411yescharacteristic
286C22×C17C4×#4112yes—
287C22×C17C4×#4112yes—
288C22×C17C4×#4111yescharacteristic
289C22×C17C2×#12111yescharacteristic
290C22×C17C2×#12312yes—
291C22×C17C2×#12311yescharacteristic
292C22×C17#52512yes—
293C22×C17#52511yescharacteristic
294C22×C17#52511yescharacteristic
295C22×C17C2×#12411yescharacteristic
296C22×C17C2×#12612yes—
297C22×C17#52912yes—
298C22×C17#52912yes—
299C22×C17#52912yes—
300C22×C17#52912yes—
301C22×C17#52912yes—
302C22×C17#52912yes—
303C22×C17#52912yes—
304C22×C17#52911yescharacteristic
305C22×C17#53211yescharacteristic
306C22×C17#53211yescharacteristic
307C2×D17—24no—
308C2×D17—28no—
309C2×D17—44no—
310C2×D17—42no—
311C2×D17—42no—
312C2×D17—42no—
313C2×D17—44no—
314C2×D17—42no—
315C2×D17—44no—
316C2×D17—42no—
317C2×D17—42no—
318C4×C17—24no—
319C4×C17—42no—
320C4×C17—44no—
321C4×C17—44no—
322C4×C17#39718yescomplemented
323Dic17—42no—
324Dic17—44no—
325Dic17—42no—
326Dic17—44no—
327Dic17—42no—
328C24×C4—171no—
329C22×C4⋊C4—171no—
330C22×C4⋊C4—171no—
331C22×C22⋊C4—171no—
332C22×C22⋊C4—172no—
333C22×C22⋊C4—172no—
334C22×C22⋊C4—171no—
335C22×C42—171no—
336C22×C42—172no—
337C22×C42C2×D1712yes—
338C22×C42C2×D1711yescharacteristic
339#397—178no—
340C4×C4⋊C4—344no—
341C4×C22⋊C4—348no—
342C4×C22⋊C4—344no—
343C2×#95—172no—
344C2×#95—172no—
345C2×#95—172no—
346C2×#95—172no—
347C2×#95—172no—
348C2×#95—172no—
349C2×#95—171no—
350C2×#95—171no—
351C2×#95—172no—
352C2×#95C2×D1711yescharacteristic
353C2×#95C2×D1712yes—
354C2×#95C2×D1711yescharacteristic
355C2×C17C4×#12111yescharacteristic
356C2×C17C4×#12312yes—
357C2×C17C4×#12311yescharacteristic
358C2×C17C4×#12411yescharacteristic
359C2×C17C4×#12612yes—
360C2×C17C2×#39711yescharacteristic
361C2×C17#239211yescharacteristic
362C2×C17#239511yescharacteristic
363C2×C17#239512yes—
364C2×C17#239811yescharacteristic
365C2×C17#240112yes—
366D17—44no—
367C25—171no—
368C23×C4—172no—
369C23×C4—172no—
370C23×C4—171no—
371C23×C4—171no—
372C23×C4—171no—
373C23×C4—174no—
374C23×C4—342no—
375C23×C4—344no—
376C23×C4—344no—
377C23×C4—342no—
378C23×C4C22×D1712yes—
379C23×C4C22×D1711yescharacteristic
380C23×C4C22×D1712yes—
381C23×C4C22×D1711yescharacteristic
382C23×C4C22×D1711yescharacteristic
383C2×C4⋊C4—174no—
384C2×C4⋊C4—344no—
385C2×C4⋊C4—342no—
386C2×C4⋊C4—342no—
387C2×C4⋊C4—342no—
388C2×C22⋊C4—178no—
389C2×C22⋊C4—174no—
390C2×C22⋊C4—342no—
391C2×C22⋊C4—344no—
392C2×C22⋊C4—344no—
393C2×C22⋊C4—344no—
394C2×C22⋊C4—344no—
395C2×C22⋊C4—342no—
396C2×C22⋊C4—342no—
397C2×C22⋊C4—342no—
398C2×C22⋊C4—344no—
399C2×C22⋊C4—342no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—342no—
405C2×C42—344no—
406C2×C42—344no—
407C2×C42—344no—
408C2×C42—344no—
409C2×C42D6814yes—
410#95—24no—
411#95—22no—
412#95—178no—
413#95—344no—
414#95—344no—
415#95—344no—
416#95—344no—
417#95—342no—
418#95—342no—
419#95—344no—
420#95—344no—
421#95C4×D1714yescomplemented
422C17C4×#39711yescharacteristic, complemented, Sylow
423C24—172no—
424C24—172no—
425C24—172no—
426C24—341no—
427C24—341no—
428C24—342no—
429C24—342no—
430C24—342no—
431C24—341no—
432C24—342no—
433C24—341no—
434C24C23×D1711yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—172no—
454C22×C4—174no—
455C22×C4—172no—
456C22×C4—172no—
457C22×C4—174no—
458C22×C4—341no—
459C22×C4—341no—
460C22×C4—341no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4—342no—
467C22×C4—341no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—341no—
477C22×C4—342no—
478C22×C4—342no—
479C22×C4—342no—
480C22×C4—341no—
481C22×C4—342no—
482C22×C4—3416no—
483C22×C4—348no—
484C22×C4—684no—
485C22×C4—684no—
486C22×C4—688no—
487C22×C4C2×C4×D1714yes—
488C22×C4C2×C4×D1712yes—
489C22×C4C2×D6812yes—
490C22×C4C2×D6812yes—
491C22×C4C2×D6812yes—
492C22×C4#6325214yes—
493C22×C4#6325212yes—
494C22×C4#6325214yes—
495C22×C4D4×D1712yes—
496C22×C4#6325414yes—
497C22×C4#6325612yes—
498C4⋊C4—348no—
499C4⋊C4—348no—
500C22⋊C4—3416no—
501C22⋊C4—3416no—
502C22⋊C4—348no—
503C22⋊C4—348no—
504C42—28no—
505C42—48no—
506C42—684no—
507C42—688no—
508C23—174no—
509C23—342no—
510C23—344no—
511C23—344no—
512C23—342no—
513C23—342no—
514C23—344no—
515C23—344no—
516C23—342no—
517C23—344no—
518C23—344no—
519C23—342no—
520C23—342no—
521C23—681no—
522C23—681no—
523C23—681no—
524C23—682no—
525C23—682no—
526C23—682no—
527C23—682no—
528C23—682no—
529C23—682no—
530C23—681no—
531C23C22×C4×D1711yescharacteristic
532C23C22×D6811yescharacteristic
533C23C2×#6325211yescharacteristic
534C23C2×#6325212yes—
535C23C2×#6325212yes—
536C23C2×D4×D1711yescharacteristic
537C23C2×#6325412yes—
538C23C2×#6325611yescharacteristic
539C23#41×D1711yescharacteristic
540C23#41×D1712yes—
541C23#41×D1711yescharacteristic
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—344no—
566C2×C4—342no—
567C2×C4—344no—
568C2×C4—344no—
569C2×C4—344no—
570C2×C4—342no—
571C2×C4—344no—
572C2×C4—344no—
573C2×C4—342no—
574C2×C4—344no—
575C2×C4—344no—
576C2×C4—344no—
577C2×C4—682no—
578C2×C4—682no—
579C2×C4—681no—
580C2×C4—682no—
581C2×C4—682no—
582C2×C4—681no—
583C2×C4—681no—
584C2×C4—681no—
585C2×C4—681no—
586C2×C4—682no—
587C2×C4—682no—
588C2×C4—682no—
589C2×C4—682no—
590C2×C4—682no—
591C2×C4—682no—
592C2×C4—681no—
593C2×C4—682no—
594C2×C4—6816no—
595C2×C4C4×D6814yes—
596C2×C4#1058756114yes—
597C2×C4#1058756918yes—
598C2×C4#1058757214yes—
599C2×C4#1058758114yes—
600C2×C4#1058758418yes—
601C22—344no—
602C22—348no—
603C22—682no—
604C22—684no—
605C22—682no—
606C22—682no—
607C22—682no—
608C22—684no—
609C22—682no—
610C22—682no—
611C22—684no—
612C22C4×D4×D1711yescharacteristic
613C22C2×C4×D6811yescharacteristic
614C22C4×#6325412yes—
615C22C4×#6325212yes—
616C22C4×#6325611yescharacteristic
617C22C2×#1058758111yescharacteristic
618C22C2×#1058756912yes—
619C22C2×#1058757211yescharacteristic
620C22#1176331812yes—
621C22#1176332111yescharacteristic
622C22#1176332111yescharacteristic
623C22C2×#1058756111yescharacteristic
624C22C2×#1058758412yes—
625C22#1176333712yes—
626C22#1176333712yes—
627C22#1176333912yes—
628C22#1176333912yes—
629C22#1176334112yes—
630C22#1176334312yes—
631C22#1176334612yes—
632C22#1176334611yescharacteristic
633C22#1176335611yescharacteristic
634C22#1176335911yescharacteristic
635C4—24no—
636C4—42no—
637C4—44no—
638C4—44no—
639C4—682no—
640C4—682no—
641C4—684no—
642C4—684no—
643C4—682no—
644C4#1176273618yesdirect product factor
645C2—684no—
646C2C4×#1058758111yescharacteristic
647C2C4×#1058756912yes—
648C2C4×#1058757211yescharacteristic
649C2C4×#1058756111yescharacteristic
650C2C4×#1058758412yes—
651C2C2×#1176273611yescharacteristic
652C2#1453202411yescharacteristic
653C2#1453204411yescharacteristic
654C2#1453204512yes—
655C2#1453207011yescharacteristic
656C2#1453208512yes—
subgroupG/H
centerC23×C4C22×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC4×C17×#95C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenterC4×#95D17
hypocenterC17C4×#397
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic17C2semidirect
5. #14527053C2semidirect
6. #14527044C2semidirect
7. #14527041C2semidirect
10. C4×#10587502C2semidirect
11. C4×C17×#95C2semidirect
21. #11762736C4direct (N × H)
76. C2×C4⋊Dic17C2×C4semidirect
84. C17×#95C2×C4semidirect
93. #10587502C2×C4semidirect
283. C4×#95D17semidirect
322. C4×C17#397semidirect
421. #95C4×D17semidirect
422. C17C4×#397semidirect
644. C4#11762736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117627362
C2×C4×C4⋊Dic172
C2×C4×#632272
#145270532
#145270442
#145270412
#145270322
#145270302
C4×#105875022
C4×C17×#952
C4×#39717