Finite Group Databasebeta

← #17064316

Subgroups — #17064316

Order 4352.

880 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10587624C211yesmaximal, characteristic
2#14531188C211yesmaximal, characteristic, complemented
3#14530344C211yesmaximal, characteristic, complemented
4#14530310C211yesmaximal, characteristic, complemented
5#14530259C211yesmaximal, characteristic, complemented
6#14530211C211yesmaximal, characteristic, complemented
7#14530209C211yesmaximal, characteristic, complemented
8#14530190C211yesmaximal, characteristic, complemented
9#14529965C211yesmaximal, characteristic
10#14529964C211yesmaximal, characteristic
11C4×#10587478C211yesmaximal, characteristic, complemented
12C4×#10587489C211yesmaximal, characteristic, complemented
13C4×#10587503C211yesmaximal, characteristic, complemented
14C4×#10587491C211yesmaximal, characteristic, complemented
15C4×C17×#102C211yesmaximal, characteristic, complemented
16C2×#10587624C2211yescharacteristic
17C2×C4×C22⋊D17—21no—
18C2×#10587558—21no—
19C2×C42×D17C2211yescharacteristic
20C2×#10587489C2211yescharacteristic
21C2×#10587489C2211yescharacteristic
22C2×#10587478C2211yescharacteristic
23C2×#10587478C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×#10587491C2211yescharacteristic
27C2×#10587491C2211yescharacteristic
28C2×C4×#3622C2211yescharacteristic
29#11762712C2211yescharacteristic
30#11762705C2211yescharacteristic
31#11762697—21no—
32#11762685—21no—
33#11762678C2211yescharacteristic
34#11762678C2211yescharacteristic
35#11762673—21no—
36#11762668—21no—
37#11762666C2211yescharacteristic
38#11762666C2211yescharacteristic
39#11762666C2211yescharacteristic
40C4×#63225—21no—
41C4×C4⋊Dic17C2211yescharacteristic
42C4×C4⋊Dic17C2211yescharacteristic
43C4×C22⋊Dic17—21no—
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52C2×C4×D4×C17C2211yescharacteristic
53C2×C17×#102C2211yescharacteristic
54C2×C17×#102C2211yescharacteristic
55C2×C4×C8×C17C2211yescharacteristic
56C4×C4⋊C4×C17C2211yescharacteristic
57C17×#340C2211yescharacteristic
58C17×#340C2211yescharacteristic
59C22×D4×C17C2311yescharacteristic
60C23×C4×C17—21no—
61C22×C22⋊D17—21no—
62C22×C4×D17D411yescharacteristic
63C22×C4×D17D411yescharacteristic
64C22×C4×D17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C4×D4×C17—22no—
68C4×D4×C17—22no—
69C2×C4⋊C4×C17C2311yescharacteristic
70C2×C4⋊C4×C17C2311yescharacteristic
71C2×C4⋊C4×C17C2311yescharacteristic
72C2×C22⋊C4×C17—21no—
73C2×C42×C17—21no—
74C2×C42×C17C2311yescharacteristic
75C2×C22⋊Dic17—21no—
76C2×C22⋊Dic17—21no—
77C2×C22⋊Dic17—21no—
78#10587624—22no—
79#10587624—22no—
80C4×C22⋊D17—44no—
81C2×#63227—21no—
82C2×#63227—21no—
83C2×#63227—21no—
84C2×C4⋊Dic17C2311yescharacteristic
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×C4⋊Dic17C2311yescharacteristic
88C2×#63225—21no—
89C2×#63225—21no—
90C2×#63225—21no—
91C2×#63225—21no—
92C2×#63225—21no—
93C2×C4×Dic17—21no—
94C2×C4×Dic17—21no—
95C2×C4×Dic17D411yescharacteristic
96C2×C4×Dic17D411yescharacteristic
97C2×C4×Dic17C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C22×#3622C2311yescharacteristic
100#10587558—44no—
101C42×D17—22no—
102C42×D17—22no—
103C17×#102—22no—
104C17×#102—22no—
105C4×C8×C17—22no—
106C17×#95—21no—
107#10587503—22no—
108#10587503—22no—
109#10587502—21no—
110#10587502—21no—
111#10587502—21no—
112#10587502—21no—
113#10587502—21no—
114#10587502—21no—
115#10587491—22no—
116#10587491—22no—
117#10587489—22no—
118#10587489—22no—
119#10587478—22no—
120#10587478—22no—
121C4×#3622—22no—
122C24×C17—21no—
123C23×D17C2×D411yescharacteristic
124C2×D4×C17—21no—
125C2×D4×C17—21no—
126C2×D4×C17—21no—
127C2×D4×C17—21no—
128C2×D4×C17—21no—
129C2×D4×C17#4112yes—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—42no—
134C22×C4×C17—42no—
135C22×C4×C17—42no—
136C22×C4×C17C2×D411yescharacteristic
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2411yescharacteristic
139C2×C22⋊D17—24no—
140C2×C22⋊D17—42no—
141C2×C22⋊D17—42no—
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17C2×D411yescharacteristic
147C22×Dic17C2×D411yescharacteristic
148C22×Dic17C2×D411yescharacteristic
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—22no—
152C2×C4×D17—21no—
153C2×C4×D17—21no—
154C2×C4×D17—21no—
155C2×C4×D17—21no—
156C2×C4×D17—21no—
157C2×C4×D17—21no—
158C2×C4×D17—22no—
159C2×C4×D17—41no—
160C2×C4×D17D814yes—
161C2×C8×C17—21no—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17#4112yes—
167C4⋊C4×C17—21no—
168C4⋊C4×C17—21no—
169C4⋊C4×C17—21no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17—21no—
172C4⋊C4×C17—21no—
173C22⋊C4×C17—42no—
174C42×C17—42no—
175C42×C17#4112yes—
176C42×C17#4112yes—
177C22⋊Dic17—24no—
178C22⋊Dic17—42no—
179C22⋊Dic17—42no—
180#63227—42no—
181#63227—42no—
182#63227—42no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17—21no—
188C4⋊Dic17—21no—
189C4⋊Dic17—21no—
190C4⋊Dic17#4112yes—
191#63225—42no—
192#63225—42no—
193#63225—42no—
194#63225—42no—
195#63225—42no—
196C4×Dic17—22no—
197C4×Dic17—22no—
198C4×Dic17—21no—
199C4×Dic17—21no—
200C4×Dic17—42no—
201C4×Dic17—42no—
202C2×#3622—21no—
203C2×#3622—21no—
204C2×#3622—21no—
205C2×#3622—21no—
206C2×#3622—21no—
207C2×#3622#4112yes—
208#23754—171nomaximal, Sylow
209C23×C17—22no—
210C23×C17—41no—
211C23×C17—41no—
212C23×C17—41no—
213C23×C17—41no—
214C23×C17—41no—
215C23×C17—41no—
216C23×C17C22×D411yescharacteristic
217C22×D17—21no—
218C22×D17—21no—
219C22×D17—21no—
220C22×D17—21no—
221C22×D17—21no—
222C22×D17—21no—
223C22×D17C2×D812yes—
224D4×C17—22no—
225D4×C17—22no—
226D4×C17—41no—
227D4×C17—41no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—41no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
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—84no—
240C2×C4×C17#12312yes—
241C2×C4×C17#12312yes—
242C2×C4×C17C2×D812yes—
243C2×C4×C17#13712yes—
244C2×C4×C17C2×#4111yescharacteristic
245C2×C4×C17C2×#4111yescharacteristic
246C2×C4×C17C2×#4111yescharacteristic
247C2×C4×C17C2×#4111yescharacteristic
248C2×C4×C17C2×#4111yescharacteristic
249C2×C4×C17C2×#4111yescharacteristic
250C22⋊D17—48no—
251C2×Dic17—21no—
252C2×Dic17—21no—
253C2×Dic17—21no—
254C2×Dic17—21no—
255C2×Dic17—21no—
256C2×Dic17—21no—
257C2×Dic17—22no—
258C2×Dic17—21no—
259C2×Dic17—41no—
260C2×Dic17—41no—
261C2×Dic17—41no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—41no—
265C2×Dic17—41no—
266C2×Dic17—41no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17C2×D812yes—
271C2×Dic17#13512yes—
272C4×D17—28no—
273C4×D17—44no—
274C4×D17—41no—
275C4×D17—41no—
276C4×D17—41no—
277C4×D17—41no—
278C8×C17—22no—
279C8×C17—41no—
280#3622—22no—
281#3622—41no—
282C4×#121—171no—
283#2285—171no—
284#2099—171no—
285#2093—171no—
286#2083—171no—
287#2075—171no—
288#2075—171no—
289#2071—171no—
290#2033—171no—
291#2033—171no—
292C4×#107—171no—
293C4×#107—171no—
294C4×#102—171no—
295C4×#102D1711yescharacteristic, complemented
296C4×C22⋊C8—171no—
297C22×C17—42no—
298C22×C17—42no—
299C22×C17—42no—
300C22×C17—81no—
301C22×C17—81no—
302C22×C17—81no—
303C22×C17—81no—
304C22×C17C2×#12311yescharacteristic
305C22×C17#52511yescharacteristic
306C22×C17#53211yescharacteristic
307C22×C17C22×D811yescharacteristic
308C22×C17C2×#13511yescharacteristic
309C22×C17C2×#13711yescharacteristic
310C22×C17#57511yescharacteristic
311C2×D17—22no—
312C2×D17—22no—
313C2×D17—22no—
314C2×D17—41no—
315C2×D17—41no—
316C2×D17—41no—
317C2×D17—41no—
318C4×C17—22no—
319C4×C17—81no—
320C4×C17—81no—
321C4×C17—81no—
322C4×C17#48014yes—
323C4×C17#52911yescharacteristic
324C4×C17#52911yescharacteristic
325C4×C17#52911yescharacteristic
326C4×C17#52911yescharacteristic
327Dic17—22no—
328Dic17—22no—
329Dic17—42no—
330Dic17—41no—
331Dic17—81no—
332Dic17—81no—
333Dic17—81no—
334C2×#121—171no—
335C2×C4×D4—341no—
336C2×C4×D4C2×D1711yescharacteristic
337C2×#117—341no—
338C22×C42—171no—
339C2×#107—171no—
340C2×#107—171no—
341C2×#107—171no—
342C2×#107—171no—
343C2×#102—171no—
344C2×#102—171no—
345C2×#102C2×D1711yescharacteristic
346C2×#102C2×D1711yescharacteristic
347C2×C22⋊C8—171no—
348C2×C22⋊C8—171no—
349C2×C4×C8—171no—
350C2×C4×C8C2×D1711yescharacteristic
351#390—171no—
352#389—171no—
353#388—341no—
354#386—341no—
355#384—171no—
356#384—171no—
357#382—341no—
358#380—171no—
359#380—171no—
360#380—171no—
361#380—341no—
362C4×C4⋊C4—171no—
363C4×C4⋊C4—171no—
364C4×C4⋊C4—341no—
365C4×C4⋊C4C2×D1711yescharacteristic
366C4×C22⋊C4—341no—
367#340—171no—
368#340—171no—
369#340—171no—
370#340—171no—
371#340—171no—
372#340—171no—
373#340C2×D1711yescharacteristic
374#340C2×D1711yescharacteristic
375#336—171no—
376#336—171no—
377C2×C17—82no—
378C2×C17#239511yescharacteristic
379C2×C17C2×#48011yescharacteristic
380C2×C17#309111yescharacteristic
381C2×C17#310011yescharacteristic
382C2×C17#310711yescharacteristic
383C2×C17#316911yescharacteristic
384C2×C17#317211yescharacteristic
385D17—42no—
386C22×D4—341no—
387C22×D4C22×D1711yescharacteristic
388C23×C4—21no—
389C23×C4—171no—
390C23×C4—171no—
391C23×C4—171no—
392C22×C8—171no—
393C22×C8—171no—
394C22×C8C22×D1711yescharacteristic
395C22×C8C22×D1711yescharacteristic
396#121—342no—
397#121—342no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—684no—
401#117—684no—
402C2×C4⋊C4—171no—
403C2×C4⋊C4—171no—
404C2×C4⋊C4—171no—
405C2×C4⋊C4—171no—
406C2×C4⋊C4—341no—
407C2×C4⋊C4—341no—
408C2×C4⋊C4—341no—
409C2×C4⋊C4—341no—
410C2×C4⋊C4—341no—
411C2×C4⋊C4C22×D1711yescharacteristic
412C2×C4⋊C4C22×D1711yescharacteristic
413C2×C4⋊C4C22×D1711yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—341no—
416C2×C22⋊C4—341no—
417C2×C22⋊C4—341no—
418C2×C22⋊C4—341no—
419C2×C22⋊C4—341no—
420C2×C22⋊C4—341no—
421C2×C42—21no—
422C2×C42—171no—
423C2×C42—171no—
424C2×C42—171no—
425C2×C42—342no—
426C2×C42—342no—
427C2×C42—341no—
428C2×C42—341no—
429C2×C42C22×D1711yescharacteristic
430#107—342no—
431#107—342no—
432#107—342no—
433#107—342no—
434#102—22no—
435#102—22no—
436#102—342no—
437#102—342no—
438C22⋊C8—342no—
439C22⋊C8—342no—
440C4×C8—22no—
441C4×C8—342no—
442#95—21no—
443#95—341no—
444#95—341no—
445#95—341no—
446#95—341no—
447#95—341no—
448#95—341no—
449C17#2375411yescharacteristic, complemented, Sylow
450C24—21no—
451C24—171no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—344no—
458C2×D4—682no—
459C2×D4—682no—
460C2×D4#6325212yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—171no—
468C22×C4—171no—
469C22×C4—174no—
470C22×C4—171no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—341no—
475C22×C4—341no—
476C22×C4—341no—
477C22×C4—341no—
478C22×C4—341no—
479C22×C4—341no—
480C22×C4—341no—
481C22×C4—342no—
482C22×C4—341no—
483C22×C4—341no—
484C22×C4—341no—
485C22×C4—681no—
486C22×C4D4×D1711yescharacteristic
487C22×C4D4×D1711yescharacteristic
488C22×C4C23×D1711yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—172no—
495C2×C8—341no—
496C2×C8—341no—
497C2×C8—341no—
498C2×C8—341no—
499C2×C8—341no—
500C2×C8#6325212yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—172no—
508C4⋊C4—341no—
509C4⋊C4—341no—
510C4⋊C4—341no—
511C4⋊C4—341no—
512C4⋊C4—341no—
513C4⋊C4—341no—
514C4⋊C4—341no—
515C4⋊C4—682no—
516C4⋊C4—682no—
517C4⋊C4—682no—
518C4⋊C4—682no—
519C4⋊C4—682no—
520C22⋊C4—42no—
521C22⋊C4—344no—
522C22⋊C4—682no—
523C22⋊C4—682no—
524C22⋊C4—682no—
525C22⋊C4—682no—
526C22⋊C4—682no—
527C42—42no—
528C42—341no—
529C42—341no—
530C42—342no—
531C42—342no—
532C42—682no—
533C42—682no—
534C42#6325212yes—
535C42#6325412yes—
536C23—22no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—172no—
544C23—341no—
545C23—341no—
546C23—341no—
547C23—341no—
548C23—341no—
549C23—341no—
550C23C2×D4×D1711yescharacteristic
551D4—22no—
552D4—22no—
553D4—41no—
554D4—41no—
555D4—688no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—172no—
569C2×C4—172no—
570C2×C4—341no—
571C2×C4—341no—
572C2×C4—341no—
573C2×C4—341no—
574C2×C4—348no—
575C2×C4—341no—
576C2×C4—341no—
577C2×C4—342no—
578C2×C4—341no—
579C2×C4—684no—
580C2×C4—681no—
581C2×C4—681no—
582C2×C4—681no—
583C2×C4—681no—
584C2×C4—681no—
585C2×C4—681no—
586C2×C4—681no—
587C2×C4—681no—
588C2×C4—681no—
589C2×C4—681no—
590C2×C4—681no—
591C2×C4—681no—
592C2×C4—681no—
593C2×C4—681no—
594C2×C4—681no—
595C2×C4#1058756912yes—
596C2×C4#1058756912yes—
597C2×C4D8×D1712yes—
598C2×C4#1058760112yes—
599C2×C4C2×#6325211yescharacteristic
600C2×C4C2×#6325211yescharacteristic
601C2×C4C2×#6325211yescharacteristic
602C2×C4C2×#6325411yescharacteristic
603C2×C4#41×D1711yescharacteristic
604C2×C4#41×D1711yescharacteristic
605C8—22no—
606C8—41no—
607C8—342no—
608C8—681no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—342no—
617C22—342no—
618C22—342no—
619C22—681no—
620C22—681no—
621C22—681no—
622C22—681no—
623C22C2×#1058756911yescharacteristic
624C22#1176331811yescharacteristic
625C22#1176335611yescharacteristic
626C22C2×D8×D1711yescharacteristic
627C22#135×D1711yescharacteristic
628C22C2×#1058760111yescharacteristic
629C22#1176360611yescharacteristic
630C4—22no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—342no—
635C4—342no—
636C4—682no—
637C4—681no—
638C4—1361no—
639C4—1361no—
640C4—1361no—
641C4#1176312114yes—
642C4#1176333711yescharacteristic
643C4#1176333911yescharacteristic
644C4#1176333911yescharacteristic
645C4#1176334311yescharacteristic
646C2—82no—
647C2—682no—
648C2#1453204511yescharacteristic
649C2C2×#1176312111yescharacteristic
650C2#1453869511yescharacteristic
651C2#1453878211yescharacteristic
652C2#1453885111yescharacteristic
653C2#1453936011yescharacteristic
654C2#1453938611yescharacteristic
subgroupG/H
centerC22×C4D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC4×C17×#102C2
socleC23×C17C22×D4
prime radicalC2×#10587624C22
hypercenterC4×#102D17
hypocenterC17#23754
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #14531188C2semidirect
3. #14530344C2semidirect
4. #14530310C2semidirect
5. #14530259C2semidirect
6. #14530211C2semidirect
7. #14530209C2semidirect
8. #14530190C2semidirect
11. C4×#10587478C2semidirect
12. C4×#10587489C2semidirect
13. C4×#10587503C2semidirect
14. C4×#10587491C2semidirect
15. C4×C17×#102C2semidirect
295. C4×#102D17semidirect
449. C17#23754semidirect

Maximal subgroups

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

subgroupindex
C4×#105876242
#145311882
#145303442
#145303102
#145302592
#145302112
#145302092
#145301902
#145299652
#145299642
C4×#105874782
C4×#105874892
C4×#105875032
C4×#105874912
C4×C17×#1022
#2375417