Finite Group Databasebeta

← #16940755

Subgroups — #16940755

Order 4352.

966 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762827C211yesmaximal, characteristic
2C2×#11762808C211yesmaximal, characteristic
3C2×#11762782C211yesmaximal, characteristic
4C2×#11762579C211yesmaximal, characteristic, complemented
5#14528503C211yesmaximal, characteristic, complemented
6C2×#11762565C211yesmaximal, characteristic, complemented
7C17×#2274C211yesmaximal, characteristic, complemented
8C22×#63252C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C22×#63223C2211yescharacteristic
11C2×#10587612C2211yescharacteristic
12#11762827—22no—
13#11762827C414yescomplemented
14C2×#10587476—22no—
15#11762808—22no—
16#11762808—22no—
17C2×#10587481C412yescomplemented
18C2×#10587480C412yescomplemented
19#11762782—22no—
20#11762782C414yescomplemented
21C2×#10587477—22no—
22#11762579—22no—
23#11762571—22no—
24#11762565—22no—
25C2×C17×#117C2211yescharacteristic
26C2×C17×#117C2211yescharacteristic
27C22×C4⋊C4×C17C2211yescharacteristic
28C4×C4⋊C4×C17—22no—
29C4×C4⋊C4×C17—22no—
30C4×C22⋊C4×C17—22no—
31C23×C4×C17—21no—
32C23×C4×C17C2311yescharacteristic
33C22×C22⋊D17—21no—
34C2×#63252—21no—
35C2×#63252—21no—
36C2×#63252—21no—
37C2×#63252—21no—
38C2×#63252—21no—
39C2×#63252—21no—
40C2×#63252—21no—
41C2×#63252—21no—
42C2×#63252—21no—
43C2×#63252—21no—
44C2×#63252C2×C412yes—
45C2×#63252C2×C412yes—
46C22×D68C2×C411yescharacteristic
47C22×C4×D17—21no—
48C22×Dic34C2×C411yescharacteristic
49C17×#117—21no—
50C17×#117—21no—
51C17×#117—21no—
52C17×#117—21no—
53C17×#117C2×C412yes—
54C17×#117C2×C412yes—
55C17×#117D412yes—
56C17×#117D412yes—
57C2×C4⋊C4×C17—21no—
58C2×C4⋊C4×C17—21no—
59C2×C4⋊C4×C17—21no—
60C2×C4⋊C4×C17—21no—
61C2×C4⋊C4×C17—21no—
62C2×C4⋊C4×C17C2×C412yes—
63C2×C4⋊C4×C17D412yes—
64C2×C4⋊C4×C17D412yes—
65C2×C22⋊C4×C17—21no—
66C2×C22⋊C4×C17D412yes—
67C2×C42×C17—21no—
68C2×C42×C17—24no—
69C2×C42×C17D412yes—
70C2×C22⋊Dic17—21no—
71#10587612—21no—
72#10587612—21no—
73#10587612—21no—
74#10587612C2×C412yes—
75C2×C4⋊Dic17—21no—
76C2×C4×Dic17—21no—
77C2×#63223—21no—
78C2×#63223—21no—
79C2×#63223—21no—
80C2×#63223—21no—
81C2×#63223—21no—
82C2×#63223—21no—
83C2×#63223—21no—
84C2×#63223—21no—
85C2×#63223—21no—
86C2×#63223—21no—
87C2×#63223—21no—
88C2×#63223C2×C412yes—
89C22×#3622—21no—
90C22×#3622C2×C412yes—
91C17×#95—24no—
92#10587481—24no—
93#10587480—24no—
94#10587477—28no—
95#10587476—28no—
96C24×C17C2×D411yescharacteristic
97C23×D17—21no—
98C22×C4×C17—22no—
99C22×C4×C17—22no—
100C22×C4×C17—22no—
101C22×C4×C17—22no—
102C22×C4×C17—22no—
103C22×C4×C17—82no—
104C22×C4×C17C22×C411yescharacteristic
105C22×C4×C17C22×C411yescharacteristic
106C22×C4×C17C22×C411yescharacteristic
107C22×C4×C17C2×D411yescharacteristic
108C22×C4×C17C2×D411yescharacteristic
109C22×C4×C17C2×D411yescharacteristic
110C22×C4×C17C2×D411yescharacteristic
111C22×C4×C17C2×D411yescharacteristic
112C22×C4×C17#4111yescharacteristic
113C22×C4×C17#4111yescharacteristic
114C22×C4×C17#4111yescharacteristic
115C22×C4×C17#4111yescharacteristic
116C22×C4×C17#4111yescharacteristic
117C22×C4×C17#4111yescharacteristic
118C2×C22⋊D17—22no—
119C2×C22⋊D17—22no—
120C2×C22⋊D17—41no—
121C2×C22⋊D17—41no—
122C2×C22⋊D17—41no—
123C2×C22⋊D17—41no—
124C22×Dic17—21no—
125C22×Dic17—41no—
126#63252—22no—
127#63252—22no—
128#63252—22no—
129#63252—22no—
130#63252—22no—
131#63252—22no—
132#63252—22no—
133#63252—22no—
134#63252—41no—
135#63252—41no—
136#63252—41no—
137#63252—41no—
138#63252—41no—
139#63252—41no—
140#63252—41no—
141#63252—41no—
142C2×D68—21no—
143C2×D68—21no—
144C2×D68—21no—
145C2×D68—21no—
146C2×D68—21no—
147C2×D68C4212yescomplemented
148C2×C4×D17—22no—
149C2×C4×D17—22no—
150C2×C4×D17—41no—
151C2×C4×D17—41no—
152C2×C4×D17—41no—
153C2×C4×D17—41no—
154C2×Dic34—21no—
155C2×Dic34—21no—
156C2×Dic34—21no—
157C2×Dic34—21no—
158C2×Dic34—21no—
159C2×Dic34C4212yescomplemented
160C4⋊C4×C17—22no—
161C4⋊C4×C17—22no—
162C4⋊C4×C17—22no—
163C4⋊C4×C17—22no—
164C4⋊C4×C17—22no—
165C4⋊C4×C17—22no—
166C4⋊C4×C17—22no—
167C4⋊C4×C17C22⋊C414yes—
168C22⋊C4×C17—22no—
169C22⋊C4×C17—22no—
170C22⋊C4×C17—22no—
171C22⋊C4×C17C22⋊C414yes—
172C42×C17—22no—
173C42×C17—22no—
174C42×C17—22no—
175C42×C17—84no—
176C42×C17C22⋊C414yes—
177C22⋊Dic17—22no—
178C22⋊Dic17—41no—
179C4⋊Dic17—22no—
180C4⋊Dic17—41no—
181C4×Dic17—22no—
182C4×Dic17—41no—
183#63223—22no—
184#63223—22no—
185#63223—41no—
186#63223—41no—
187#63223—41no—
188#63223—41no—
189#63223—41no—
190#63223—41no—
191C2×#3622—22no—
192C2×#3622—22no—
193C2×#3622—22no—
194C2×#3622—22no—
195C2×#3622—41no—
196C2×#3622—41no—
197#10954—171nomaximal, Sylow
198C23×C17—41no—
199C23×C17—41no—
200C23×C17C2×C22⋊C411yescharacteristic
201C23×C17C4×D411yescharacteristic
202C23×C17C4×D411yescharacteristic
203C23×C17#12011yescharacteristic
204C23×C17#12111yescharacteristic
205C23×C17#12111yescharacteristic
206C23×C17#12311yescharacteristic
207C22×D17—22no—
208C22×D17—41no—
209C22×D17—41no—
210C22×D17—81no—
211C22×D17—81no—
212C2×C4×C17—24no—
213C2×C4×C17—24no—
214C2×C4×C17—24no—
215C2×C4×C17—42no—
216C2×C4×C17—42no—
217C2×C4×C17—44no—
218C2×C4×C17—42no—
219C2×C4×C17—42no—
220C2×C4×C17—82no—
221C2×C4×C17—82no—
222C2×C4×C17C2×C4211yescharacteristic
223C2×C4×C17C2×C22⋊C411yescharacteristic
224C2×C4×C17C2×C22⋊C411yescharacteristic
225C2×C4×C17#11711yescharacteristic
226C2×C4×C17#11711yescharacteristic
227C2×C4×C17#11711yescharacteristic
228C2×C4×C17C4×D411yescharacteristic
229C2×C4×C17C4×D411yescharacteristic
230C2×C4×C17C4×D411yescharacteristic
231C2×C4×C17C4×D411yescharacteristic
232C2×C4×C17C4×D411yescharacteristic
233C2×C4×C17C4×D411yescharacteristic
234C2×C4×C17C4×D411yescharacteristic
235C2×C4×C17C4×D411yescharacteristic
236C2×C4×C17C4×D411yescharacteristic
237C2×C4×C17C4×D411yescharacteristic
238C2×C4×C17#12111yescharacteristic
239C2×C4×C17#12111yescharacteristic
240C2×C4×C17#12111yescharacteristic
241C2×C4×C17#12111yescharacteristic
242C2×C4×C17#12311yescharacteristic
243C2×C4×C17#12311yescharacteristic
244C2×C4×C17#12411yescharacteristic
245C2×C4×C17#12411yescharacteristic
246C2×C4×C17#12411yescharacteristic
247C2×C4×C17#12611yescharacteristic
248C2×C4×C17#12611yescharacteristic
249C2×C4×C17#12711yescharacteristic
250C22⋊D17—42no—
251C22⋊D17—42no—
252C22⋊D17—42no—
253C22⋊D17—42no—
254C2×Dic17—22no—
255C2×Dic17—41no—
256C2×Dic17—41no—
257C2×Dic17—42no—
258C2×Dic17—81no—
259C2×Dic17—81no—
260D68—22no—
261D68—22no—
262D68—41no—
263D68—41no—
264C4×D17—42no—
265C4×D17—42no—
266C4×D17—42no—
267C4×D17—42no—
268Dic34—22no—
269Dic34—22no—
270Dic34—41no—
271Dic34—41no—
272#3622—42no—
273#3622—42no—
274C2×#421—171no—
275C2×#417—171no—
276C2×#410—171no—
277#2274D1711yescharacteristic, complemented
278C2×#344—171no—
279#1736—171no—
280C2×H(3,ℤ/4)—171no—
281C22×C17—21no—
282C22×C17—21no—
283C22×C17—21no—
284C22×C17—21no—
285C22×C17—21no—
286C22×C17—21no—
287C22×C17—41no—
288C22×C17—41no—
289C22×C17—41no—
290C22×C17—41no—
291C22×C17C4×C22⋊C411yescharacteristic
292C22×C17#38611yescharacteristic
293C22×C17#38611yescharacteristic
294C22×C17#38611yescharacteristic
295C22×C17#38811yescharacteristic
296C22×C17#38811yescharacteristic
297C22×C17#39011yescharacteristic
298C2×D17—42no—
299C2×D17—82no—
300C2×D17—81no—
301C2×D17—81no—
302C2×D17—82no—
303C4×C17—44no—
304C4×C17—44no—
305C4×C17—44no—
306C4×C17C4×C22⋊C411yescharacteristic
307C4×C17C4×C22⋊C411yescharacteristic
308C4×C17#38811yescharacteristic
309C4×C17#38811yescharacteristic
310C4×C17#38811yescharacteristic
311C4×C17#38811yescharacteristic
312C4×C17#39011yescharacteristic
313C4×C17#39011yescharacteristic
314Dic17—42no—
315Dic17—82no—
316C22×#41—171no—
317C22×M16—171no—
318C22×M16—171no—
319C2×#117—171no—
320C2×#117C2×D1711yescharacteristic
321C2×#117C2×D1711yescharacteristic
322C22×C4⋊C4C2×D1711yescharacteristic
323#421—174no—
324#421—342no—
325C2×#104—342no—
326#417—342no—
327#417—342no—
328C2×#103—172no—
329C2×#102—172no—
330#410—174no—
331#410—342no—
332C2×#99—342no—
333C4×C4⋊C4—22no—
334C4×C4⋊C4—22no—
335C4×C22⋊C4—22no—
336#344—342no—
337#340—342no—
338H(3,ℤ/4)—342no—
339C2×C17—21no—
340C2×C17—21no—
341C2×C17—21no—
342C2×C17—21no—
343C2×C17—21no—
344C2×C17—21no—
345C2×C17#143711yescharacteristic
346C2×C17#190411yescharacteristic
347C2×C17#190511yescharacteristic
348D17—82no—
349C2×#41—172no—
350C2×#41—172no—
351C2×#41—341no—
352C2×#41—341no—
353C2×#41—341no—
354C2×#41—341no—
355C2×#41—341no—
356C2×#41—341no—
357C2×#41—341no—
358C2×#41—341no—
359C2×#41—341no—
360C2×#41—341no—
361C22×Q8—171no—
362C22×D4—171no—
363C22×D4—341no—
364C23×C4—21no—
365C23×C4—341no—
366C23×C4C22×D1711yescharacteristic
367C2×M16—172no—
368C2×M16—341no—
369C2×M16—341no—
370C2×M16—341no—
371C2×M16—341no—
372C2×M16—341no—
373C2×M16—341no—
374C2×M16—341no—
375C2×M16—341no—
376C2×M16—341no—
377C2×M16—341no—
378C2×M16—341no—
379C22×C8—172no—
380C22×C8—341no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—172no—
386#117—341no—
387#117—341no—
388#117—341no—
389#117C4×D1712yes—
390#117C4×D1712yes—
391#117D6812yes—
392#117D6812yes—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—341no—
399C2×C4⋊C4C4×D1712yes—
400C2×C4⋊C4D6812yes—
401C2×C4⋊C4C22⋊D1712yes—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—341no—
404C2×C22⋊C4C22⋊D1712yes—
405C2×C42—21no—
406C2×C42—24no—
407C2×C42—341no—
408C2×C42C22⋊D1712yes—
409#104—348no—
410#103—344no—
411#102—344no—
412#99—348no—
413#95—24no—
414C17#1095411yescharacteristic, complemented, Sylow
415C24—341no—
416C24C2×C22⋊D1711yescharacteristic
417#41—342no—
418#41—342no—
419#41—342no—
420#41—342no—
421#41—342no—
422#41—342no—
423#41—342no—
424#41—342no—
425#41—681no—
426#41—681no—
427#41—681no—
428#41—681no—
429#41—681no—
430#41—681no—
431#41—681no—
432#41—681no—
433C2×Q8—172no—
434C2×Q8—341no—
435C2×Q8—341no—
436C2×Q8—341no—
437C2×Q8—341no—
438C2×Q8—341no—
439C2×D4—172no—
440C2×D4—342no—
441C2×D4—342no—
442C2×D4—341no—
443C2×D4—341no—
444C2×D4—341no—
445C2×D4—341no—
446C2×D4—341no—
447C2×D4—681no—
448C2×D4—681no—
449C2×D4—681no—
450C2×D4—681no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—82no—
457C22×C4—341no—
458C22×C4—342no—
459C22×C4—342no—
460C22×C4—681no—
461C22×C4—681no—
462C22×C4—681no—
463C22×C4—681no—
464C22×C4—681no—
465C22×C4C2×C4×D1711yescharacteristic
466C22×C4C2×C4×D1711yescharacteristic
467C22×C4C2×C4×D1711yescharacteristic
468C22×C4C2×D6811yescharacteristic
469C22×C4C2×D6811yescharacteristic
470C22×C4C2×D6811yescharacteristic
471C22×C4#6325211yescharacteristic
472C22×C4#6325211yescharacteristic
473C22×C4#6325211yescharacteristic
474C22×C4#6325211yescharacteristic
475C22×C4#6325211yescharacteristic
476C22×C4#6325211yescharacteristic
477C22×C4C2×C22⋊D1711yescharacteristic
478C22×C4C2×C22⋊D1711yescharacteristic
479M16—342no—
480M16—342no—
481M16—681no—
482M16—681no—
483M16—681no—
484M16—681no—
485M16—681no—
486M16—681no—
487C2×C8—342no—
488C2×C8—342no—
489C2×C8—342no—
490C2×C8—342no—
491C2×C8—681no—
492C2×C8—681no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—342no—
501C4⋊C4—681no—
502C4⋊C4#6322714yes—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—342no—
507C22⋊C4—681no—
508C22⋊C4#6322714yes—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—84no—
513C42—342no—
514C42—681no—
515C42#6322714yes—
516C23—41no—
517C23—41no—
518C23—342no—
519C23—681no—
520C23—681no—
521C23—1361no—
522C23—1361no—
523C23C2×#6322711yescharacteristic
524C23C4×C22⋊D1711yescharacteristic
525C23C4×C22⋊D1711yescharacteristic
526C23#1058761511yescharacteristic
527C23#1058761611yescharacteristic
528C23#1058761611yescharacteristic
529C23#1058763911yescharacteristic
530Q8—342no—
531Q8—342no—
532Q8—681no—
533Q8—681no—
534D4—342no—
535D4—342no—
536D4—682no—
537D4—682no—
538D4—682no—
539D4—682no—
540D4—681no—
541D4—681no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—342no—
553C2×C4—681no—
554C2×C4—681no—
555C2×C4—682no—
556C2×C4—682no—
557C2×C4—682no—
558C2×C4—682no—
559C2×C4—682no—
560C2×C4—1361no—
561C2×C4—1361no—
562C2×C4C42×D1711yescharacteristic
563C2×C4#1058755811yescharacteristic
564C2×C4#1058755811yescharacteristic
565C2×C4#1058755811yescharacteristic
566C2×C4C4×D6811yescharacteristic
567C2×C4C4×D6811yescharacteristic
568C2×C4C4×D6811yescharacteristic
569C2×C4C4×D6811yescharacteristic
570C2×C4C4×D6811yescharacteristic
571C2×C4C4×D6811yescharacteristic
572C2×C4#1058756011yescharacteristic
573C2×C4#1058756111yescharacteristic
574C2×C4#1058756111yescharacteristic
575C2×C4#1058756111yescharacteristic
576C2×C4#1058756211yescharacteristic
577C2×C4#1058756211yescharacteristic
578C2×C4C2×#6322711yescharacteristic
579C2×C4C2×#6322711yescharacteristic
580C2×C4C4×C22⋊D1711yescharacteristic
581C2×C4C4×C22⋊D1711yescharacteristic
582C2×C4C4×C22⋊D1711yescharacteristic
583C2×C4C4×C22⋊D1711yescharacteristic
584C2×C4#1058761511yescharacteristic
585C2×C4#1058761511yescharacteristic
586C2×C4#1058761611yescharacteristic
587C2×C4#1058761611yescharacteristic
588C2×C4#1058761611yescharacteristic
589C2×C4#1058761611yescharacteristic
590C8—682no—
591C8—682no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—682no—
603C22—1362no—
604C22—1362no—
605C22—1361no—
606C22—1361no—
607C22C4×#6322711yescharacteristic
608C22#1176268811yescharacteristic
609C22#1176268811yescharacteristic
610C22#1176268811yescharacteristic
611C22#1176270011yescharacteristic
612C22#1176270011yescharacteristic
613C22#1176271111yescharacteristic
614C4—44no—
615C4—44no—
616C4—44no—
617C4—682no—
618C4—1362no—
619C4C4×#6322711yescharacteristic
620C4C4×#6322711yescharacteristic
621C4#1176270011yescharacteristic
622C4#1176270011yescharacteristic
623C4#1176270011yescharacteristic
624C4#1176270011yescharacteristic
625C4#1176271111yescharacteristic
626C4#1176271111yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—1362no—
634C2#1452702211yescharacteristic
635C2#1452927111yescharacteristic
636C2#1452927811yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC17×#2274C2
socleC22×C17#386
prime radicalC22×#63252C22
cosocleC23×C4×C17C23
hypercenter#2274D17
hypocenterC17#10954
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
4. C2×#11762579C2semidirect
5. #14528503C2semidirect
6. C2×#11762565C2semidirect
7. C17×#2274C2semidirect
13. #11762827C4semidirect
17. C2×#10587481C4semidirect
18. C2×#10587480C4semidirect
20. #11762782C4semidirect
147. C2×D68C42semidirect
159. C2×Dic34C42semidirect
277. #2274D17semidirect
414. C17#10954semidirect

Maximal subgroups

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

subgroupindex
C2×#117628272
C2×#117628082
C2×#117627822
C2×#117625792
#145285032
C2×#117625652
C17×#22742
#1095417