Finite Group Databasebeta

← #16942177

Subgroups — #16942177

Order 4352.

962 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587496C211yesmaximal, characteristic
2C2×#11762808C211yesmaximal, characteristic
3#14531372C211yesmaximal, characteristic
4C2×#11762577C211yesmaximal, characteristic, complemented
5C2×#11762568C211yesmaximal, characteristic, complemented
6#14527013C211yesmaximal, characteristic, complemented
7C17×#1736C211yesmaximal, characteristic, complemented
8C22×#63252C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C22×C4⋊Dic17C2211yescharacteristic
11C22×C4×Dic17C2211yescharacteristic
12C2×#10587496—22no—
13C2×#10587496—22no—
14C2×#10587496—22no—
15#11762808—22no—
16#11762808C414yescomplemented
17C2×#10587481—21no—
18C2×#10587480—21no—
19#11762715—21no—
20#11762711—21no—
21#11762686—22no—
22#11762666—21no—
23#11762666—21no—
24C2×#10587502—22no—
25#11762577—22no—
26#11762568—22no—
27C22×M16×C17C2211yescharacteristic
28C2×C17×#117C2211yescharacteristic
29C22×C4⋊C4×C17C2211yescharacteristic
30C17×#340—21no—
31C17×#340—21no—
32C23×C4×C17—21no—
33C23×C4×C17C2311yescharacteristic
34C22×C22⋊D17—21no—
35C23×Dic17—21no—
36C23×Dic17D412yes—
37C2×#63252—21no—
38C2×#63252—21no—
39C2×#63252—21no—
40C2×#63252—21no—
41C2×#63252—21no—
42C2×#63252—21no—
43C2×#63252—21no—
44C2×#63252—21no—
45C2×#63252—21no—
46C2×#63252—21no—
47C2×#63252C2×C412yes—
48C2×#63252D412yes—
49C22×D68D411yescharacteristic
50C22×C4×D17—21no—
51C22×Dic34D411yescharacteristic
52C2×M16×C17—21no—
53C2×M16×C17—21no—
54C2×M16×C17—21no—
55C2×M16×C17—21no—
56C2×M16×C17—21no—
57C2×M16×C17D412yes—
58C22×C8×C17—21no—
59C17×#117—21no—
60C17×#117—21no—
61C17×#117—21no—
62C17×#117—21no—
63C2×C4⋊C4×C17—21no—
64C2×C4⋊C4×C17—21no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17—21no—
67C2×C4⋊C4×C17—21no—
68C2×C4⋊C4×C17C2×C412yes—
69C2×C4⋊C4×C17D411yescharacteristic
70C2×C4⋊C4×C17D411yescharacteristic
71C2×C22⋊C4×C17—21no—
72C2×C42×C17—21no—
73C2×#63227—22no—
74C2×#63227—22no—
75C2×C4⋊Dic17—21no—
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17—21no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17—21no—
80C2×C4⋊Dic17—21no—
81C2×C4×Dic17—21no—
82C2×C4×Dic17—21no—
83C2×C4×Dic17—21no—
84C2×C4×Dic17—21no—
85C2×C4×Dic17—21no—
86C2×C4×Dic17D412yes—
87C2×#63223—21no—
88C2×#63223—21no—
89C2×#63223—21no—
90C2×#63223—21no—
91C2×#63223—21no—
92C2×#63223C2×C412yes—
93C22×#3622—21no—
94#10587502—22no—
95#10587502—22no—
96#10587502—44no—
97#10587496—28no—
98#10587481—24no—
99#10587480—24no—
100C24×C17C2×D411yescharacteristic
101C23×D17—21no—
102C22×C4×C17—22no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—42no—
106C22×C4×C17—42no—
107C22×C4×C17—41no—
108C22×C4×C17—41no—
109C22×C4×C17C22×C411yescharacteristic
110C22×C4×C17C2×D411yescharacteristic
111C22×C4×C17C2×D411yescharacteristic
112C22×C4×C17C2×D411yescharacteristic
113C22×C4×C17C2×D411yescharacteristic
114C22×C4×C17C2×D411yescharacteristic
115C22×C4×C17#4111yescharacteristic
116C22×C4×C17#4111yescharacteristic
117C22×C4×C17#4111yescharacteristic
118C22×C4×C17#4111yescharacteristic
119C22×C4×C17#4111yescharacteristic
120C22×C4×C17#4111yescharacteristic
121C22×C4×C17#4111yescharacteristic
122C22×C4×C17#4111yescharacteristic
123C2×C22⋊D17—22no—
124C2×C22⋊D17—22no—
125C2×C22⋊D17—41no—
126C2×C22⋊D17—41no—
127C2×C22⋊D17—41no—
128C2×C22⋊D17—41no—
129C22×Dic17—22no—
130C22×Dic17—22no—
131C22×Dic17—21no—
132C22×Dic17—22no—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—41no—
137C22×Dic17—41no—
138C22×Dic17—41no—
139C22×Dic17—41no—
140C22×Dic17—42no—
141C22×Dic17—42no—
142#63252—22no—
143#63252—22no—
144#63252—22no—
145#63252—22no—
146#63252—22no—
147#63252—22no—
148#63252—22no—
149#63252—22no—
150#63252—41no—
151#63252—41no—
152#63252—41no—
153#63252—41no—
154#63252—41no—
155#63252—41no—
156#63252—41no—
157#63252—41no—
158C2×D68—21no—
159C2×D68—21no—
160C2×D68—21no—
161C2×D68—21no—
162C2×D68—21no—
163C2×D68C22⋊C412yes—
164C2×C4×D17—22no—
165C2×C4×D17—22no—
166C2×C4×D17—41no—
167C2×C4×D17—41no—
168C2×C4×D17—41no—
169C2×C4×D17—41no—
170C2×Dic34—21no—
171C2×Dic34—21no—
172C2×Dic34—21no—
173C2×Dic34—21no—
174C2×Dic34—21no—
175C2×Dic34C22⋊C412yes—
176M16×C17—22no—
177M16×C17—22no—
178M16×C17—41no—
179M16×C17—41no—
180C2×C8×C17—22no—
181C2×C8×C17—41no—
182C2×C8×C17—41no—
183C4⋊C4×C17—22no—
184C4⋊C4×C17—22no—
185C4⋊C4×C17—21no—
186C4⋊C4×C17—21no—
187C4⋊C4×C17—21no—
188C4⋊C4×C17—21no—
189C4⋊C4×C17—41no—
190C4⋊C4×C17—41no—
191C22⋊C4×C17—41no—
192C22⋊C4×C17—41no—
193C42×C17—41no—
194C42×C17—41no—
195#63227—82no—
196#63227—82no—
197C4⋊Dic17—41no—
198C4⋊Dic17—41no—
199C4⋊Dic17—41no—
200C4⋊Dic17—41no—
201C4×Dic17—22no—
202C4×Dic17—22no—
203C4×Dic17—41no—
204C4×Dic17—41no—
205#63223—22no—
206#63223—22no—
207#63223—41no—
208#63223—41no—
209C2×#3622—22no—
210C2×#3622—41no—
211C2×#3622—41no—
212#11195—171nomaximal, Sylow
213C23×C17—21no—
214C23×C17—21no—
215C23×C17—21no—
216C23×C17—21no—
217C23×C17C4×D411yescharacteristic
218C23×C17#12011yescharacteristic
219C23×C17#12111yescharacteristic
220C23×C17#12111yescharacteristic
221C23×C17#12111yescharacteristic
222C23×C17#12311yescharacteristic
223C23×C17#12411yescharacteristic
224C22×D17—22no—
225C22×D17—41no—
226C22×D17—41no—
227C22×D17—41no—
228C22×D17—41no—
229C22×D17—41no—
230C22×D17—41no—
231C2×C4×C17—44no—
232C2×C4×C17—42no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—41no—
236C2×C4×C17—41no—
237C2×C4×C17—41no—
238C2×C4×C17—41no—
239C2×C4×C17—82no—
240C2×C4×C17—81no—
241C2×C4×C17—81no—
242C2×C4×C17C2×C22⋊C411yescharacteristic
243C2×C4×C17#11711yescharacteristic
244C2×C4×C17#11711yescharacteristic
245C2×C4×C17C4×D411yescharacteristic
246C2×C4×C17C4×D411yescharacteristic
247C2×C4×C17C4×D411yescharacteristic
248C2×C4×C17#12011yescharacteristic
249C2×C4×C17#12111yescharacteristic
250C2×C4×C17#12111yescharacteristic
251C2×C4×C17#12111yescharacteristic
252C2×C4×C17#12111yescharacteristic
253C2×C4×C17#12111yescharacteristic
254C2×C4×C17#12311yescharacteristic
255C2×C4×C17#12311yescharacteristic
256C2×C4×C17#12311yescharacteristic
257C2×C4×C17#12311yescharacteristic
258C2×C4×C17#12311yescharacteristic
259C2×C4×C17#12311yescharacteristic
260C2×C4×C17#12311yescharacteristic
261C2×C4×C17#12311yescharacteristic
262C2×C4×C17#12311yescharacteristic
263C2×C4×C17#12411yescharacteristic
264C2×C4×C17#12411yescharacteristic
265C2×C4×C17#12411yescharacteristic
266C2×C4×C17#12611yescharacteristic
267C2×C4×C17#12611yescharacteristic
268C2×C4×C17#12611yescharacteristic
269C2×C4×C17#12611yescharacteristic
270C22⋊D17—42no—
271C22⋊D17—42no—
272C22⋊D17—42no—
273C22⋊D17—42no—
274C2×Dic17—24no—
275C2×Dic17—22no—
276C2×Dic17—42no—
277C2×Dic17—42no—
278C2×Dic17—42no—
279C2×Dic17—42no—
280C2×Dic17—42no—
281C2×Dic17—41no—
282C2×Dic17—41no—
283C2×Dic17—42no—
284C2×Dic17—44no—
285C2×Dic17—42no—
286C2×Dic17—42no—
287C2×Dic17—42no—
288C2×Dic17—82no—
289D68—22no—
290D68—22no—
291D68—41no—
292D68—41no—
293C4×D17—42no—
294C4×D17—42no—
295C4×D17—42no—
296C4×D17—42no—
297Dic34—22no—
298Dic34—22no—
299Dic34—41no—
300Dic34—41no—
301C8×C17—42no—
302#3622—42no—
303C22×#104—171no—
304C2×#417—171no—
305#2311—171no—
306C2×#343—171no—
307#1736D1711yescharacteristic, complemented
308C2×#339—171no—
309C4⋊#95—171no—
310C22×C17—21no—
311C22×C17—21no—
312C22×C17—21no—
313C22×C17—21no—
314C22×C17—21no—
315C22×C17—21no—
316C22×C17—21no—
317C22×C17—21no—
318C22×C17—21no—
319C22×C17—21no—
320C22×C17—21no—
321C22×C17—21no—
322C22×C17#38611yescharacteristic
323C22×C17#38811yescharacteristic
324C22×C17#38811yescharacteristic
325C22×C17#39411yescharacteristic
326C22×C17#39411yescharacteristic
327C22×C17#39411yescharacteristic
328C22×C17#39711yescharacteristic
329C22×C17#45311yescharacteristic
330C22×C17#45411yescharacteristic
331C22×C17#45511yescharacteristic
332C22×C17#45611yescharacteristic
333C2×D17—42no—
334C2×D17—42no—
335C2×D17—42no—
336C2×D17—81no—
337C2×D17—81no—
338C2×D17—81no—
339C2×D17—81no—
340C4×C17—82no—
341C4×C17—81no—
342C4×C17—81no—
343C4×C17#38111yescharacteristic
344C4×C17#38611yescharacteristic
345C4×C17#38811yescharacteristic
346C4×C17#38811yescharacteristic
347C4×C17#39411yescharacteristic
348C4×C17#39711yescharacteristic
349C4×C17#39711yescharacteristic
350C4×C17#39711yescharacteristic
351Dic17—44no—
352Dic17—42no—
353Dic17—82no—
354C22×#41—171no—
355C22×M16—171no—
356C22×M16C2×D1711yescharacteristic
357C2×#117C2×D1711yescharacteristic
358C22×C4⋊C4—171no—
359C22×C4⋊C4C2×D1711yescharacteristic
360C22×C42—171no—
361C2×#104—342no—
362C2×#104—342no—
363C2×#104—342no—
364#417—174no—
365#417—342no—
366C2×#103—341no—
367C2×#102—341no—
368#391—341no—
369#390—341no—
370#386—342no—
371#380—341no—
372#380—341no—
373C2×#95—342no—
374#343—342no—
375#340—21no—
376#340—21no—
377#339—342no—
378C2×C17—21no—
379C2×C17—21no—
380C2×C17—21no—
381C2×C17—21no—
382C2×C17#144011yescharacteristic
383C2×C17#188211yescharacteristic
384C2×C17#188311yescharacteristic
385C2×C17#203711yescharacteristic
386C2×C17#203811yescharacteristic
387C2×C17#203911yescharacteristic
388C2×C17#204011yescharacteristic
389D17—82no—
390C2×#41—172no—
391C2×#41—172no—
392C2×#41—341no—
393C2×#41—341no—
394C2×#41—341no—
395C2×#41—341no—
396C2×#41—341no—
397C2×#41—341no—
398C2×#41—341no—
399C2×#41—341no—
400C2×#41—341no—
401C2×#41—341no—
402C22×Q8—171no—
403C22×D4—171no—
404C22×D4—341no—
405C23×C4—21no—
406C23×C4—172no—
407C23×C4—341no—
408C23×C4—341no—
409C23×C4C22×D1711yescharacteristic
410C2×M16—21no—
411C2×M16—21no—
412C2×M16—21no—
413C2×M16—21no—
414C2×M16—21no—
415C2×M16—172no—
416C2×M16—341no—
417C2×M16—341no—
418C2×M16—341no—
419C2×M16—341no—
420C2×M16—341no—
421C2×M16D6812yes—
422C22×C8—21no—
423C22×C8—341no—
424#117—21no—
425#117—21no—
426#117—21no—
427#117—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—341no—
434C2×C4⋊C4—341no—
435C2×C4⋊C4—341no—
436C2×C4⋊C4—341no—
437C2×C4⋊C4—341no—
438C2×C4⋊C4—341no—
439C2×C4⋊C4C4×D1712yes—
440C2×C4⋊C4C22⋊D1711yescharacteristic
441C2×C4⋊C4C22⋊D1711yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—342no—
444C2×C22⋊C4—342no—
445C2×C42—21no—
446C2×C42—172no—
447C2×C42—341no—
448C2×C42—341no—
449C2×C42—341no—
450C2×C42—341no—
451C2×C42—341no—
452#104—348no—
453#103—344no—
454#102—344no—
455#95—342no—
456#95—342no—
457#95—684no—
458C17#1119511yescharacteristic, complemented, Sylow
459C24—341no—
460C24D4×D1711yescharacteristic
461#41—342no—
462#41—342no—
463#41—342no—
464#41—342no—
465#41—342no—
466#41—342no—
467#41—342no—
468#41—342no—
469#41—681no—
470#41—681no—
471#41—681no—
472#41—681no—
473#41—681no—
474#41—681no—
475#41—681no—
476#41—681no—
477C2×Q8—172no—
478C2×Q8—341no—
479C2×Q8—341no—
480C2×Q8—341no—
481C2×Q8—341no—
482C2×Q8—341no—
483C2×D4—172no—
484C2×D4—342no—
485C2×D4—342no—
486C2×D4—341no—
487C2×D4—341no—
488C2×D4—341no—
489C2×D4—341no—
490C2×D4—341no—
491C2×D4—681no—
492C2×D4—681no—
493C2×D4—681no—
494C2×D4—681no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—342no—
503C22×C4—342no—
504C22×C4—342no—
505C22×C4—341no—
506C22×C4—342no—
507C22×C4—342no—
508C22×C4—342no—
509C22×C4—342no—
510C22×C4—342no—
511C22×C4—681no—
512C22×C4—681no—
513C22×C4—681no—
514C22×C4—681no—
515C22×C4—681no—
516C22×C4—681no—
517C22×C4—681no—
518C22×C4—681no—
519C22×C4—682no—
520C22×C4—682no—
521C22×C4C2×C4×D1711yescharacteristic
522C22×C4C2×D6811yescharacteristic
523C22×C4#6325211yescharacteristic
524C22×C4#6325211yescharacteristic
525C22×C4#6325211yescharacteristic
526C22×C4#6325211yescharacteristic
527C22×C4D4×D1711yescharacteristic
528C22×C4D4×D1711yescharacteristic
529C22×C4D4×D1711yescharacteristic
530C22×C4#6325411yescharacteristic
531C22×C4#6325411yescharacteristic
532C22×C4#6325611yescharacteristic
533C22×C4#6325611yescharacteristic
534C22×C4C2×C22⋊D1711yescharacteristic
535M16—22no—
536M16—22no—
537M16—41no—
538M16—41no—
539M16—342no—
540M16—342no—
541M16—681no—
542M16—681no—
543C2×C8—22no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—342no—
547C2×C8—681no—
548C2×C8—681no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—681no—
558C4⋊C4—681no—
559C4⋊C4—681no—
560C4⋊C4—681no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—1362no—
564C22⋊C4—1362no—
565C42—41no—
566C42—41no—
567C42—342no—
568C42—342no—
569C42—681no—
570C42—681no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—342no—
576C23—681no—
577C23—681no—
578C23—681no—
579C23—681no—
580C23—681no—
581C23—681no—
582C23#1058756711yescharacteristic
583C23#1058757011yescharacteristic
584C23#1058757011yescharacteristic
585C23#1058757111yescharacteristic
586C23#1058758011yescharacteristic
587C23#1058758111yescharacteristic
588C23#1058762311yescharacteristic
589Q8—342no—
590Q8—342no—
591Q8—681no—
592Q8—681no—
593D4—342no—
594D4—342no—
595D4—682no—
596D4—682no—
597D4—682no—
598D4—682no—
599D4—681no—
600D4—681no—
601C2×C4—44no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—82no—
610C2×C4—81no—
611C2×C4—81no—
612C2×C4—344no—
613C2×C4—342no—
614C2×C4—682no—
615C2×C4—682no—
616C2×C4—682no—
617C2×C4—682no—
618C2×C4—682no—
619C2×C4—681no—
620C2×C4—681no—
621C2×C4—682no—
622C2×C4—682no—
623C2×C4—682no—
624C2×C4—682no—
625C2×C4—682no—
626C2×C4—684no—
627C2×C4—682no—
628C2×C4—682no—
629C2×C4—682no—
630C2×C4—1362no—
631C2×C4#1058755811yescharacteristic
632C2×C4C4×D6811yescharacteristic
633C2×C4#1058756111yescharacteristic
634C2×C4#1058756211yescharacteristic
635C2×C4C22⋊C4×D1711yescharacteristic
636C2×C4#1058756811yescharacteristic
637C2×C4#1058756911yescharacteristic
638C2×C4#1058756911yescharacteristic
639C2×C4#1058756911yescharacteristic
640C2×C4#1058757011yescharacteristic
641C2×C4#1058757111yescharacteristic
642C2×C4#1058757211yescharacteristic
643C2×C4#1058757811yescharacteristic
644C2×C4#1058757911yescharacteristic
645C2×C4#1058758011yescharacteristic
646C2×C4#1058758011yescharacteristic
647C2×C4#1058758011yescharacteristic
648C2×C4#1058758011yescharacteristic
649C2×C4#1058758111yescharacteristic
650C2×C4#1058758411yescharacteristic
651C2×C4#1058758411yescharacteristic
652C2×C4#1058758411yescharacteristic
653C2×C4C4×C22⋊D1711yescharacteristic
654C2×C4#1058761511yescharacteristic
655C2×C4#1058761611yescharacteristic
656C2×C4#1058762411yescharacteristic
657C2×C4#1058762511yescharacteristic
658C2×C4#1058763311yescharacteristic
659C8—42no—
660C8—682no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—682no—
674C22—682no—
675C22—682no—
676C22—1361no—
677C22—1361no—
678C22—1361no—
679C22—1361no—
680C22#1176268511yescharacteristic
681C22#1176269811yescharacteristic
682C22#1176270111yescharacteristic
683C22#1176272411yescharacteristic
684C22#1176272611yescharacteristic
685C22#1176272711yescharacteristic
686C22#1176273811yescharacteristic
687C22#1176297511yescharacteristic
688C22#1176298011yescharacteristic
689C22#1176298511yescharacteristic
690C22#1176299011yescharacteristic
691C4—82no—
692C4—81no—
693C4—81no—
694C4—684no—
695C4—682no—
696C4—1362no—
697C4#1176267111yescharacteristic
698C4#1176268711yescharacteristic
699C4#1176269911yescharacteristic
700C4#1176270011yescharacteristic
701C4#1176272511yescharacteristic
702C4#1176273511yescharacteristic
703C4#1176273611yescharacteristic
704C4#1176273811yescharacteristic
705C2—21no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—1362no—
710C2#1452703211yescharacteristic
711C2#1452915011yescharacteristic
712C2#1452915711yescharacteristic
713C2#1452999611yescharacteristic
714C2#1453000311yescharacteristic
715C2#1453000611yescharacteristic
716C2#1453001111yescharacteristic
subgroupG/H
centerC23#10587623
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#1736C2
socleC23×C17#120
prime radicalC22×#63252C22
cosocleC23×C4×C17C23
hypercenter#1736D17
hypocenterC17#11195
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C2×#11762577C2semidirect
5. C2×#11762568C2semidirect
6. #14527013C2semidirect
7. C17×#1736C2semidirect
16. #11762808C4semidirect
307. #1736D17semidirect
458. C17#11195semidirect

Maximal subgroups

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

subgroupindex
C22×#105874962
C2×#117628082
#145313722
C2×#117625772
C2×#117625682
#145270132
C17×#17362
#1119517