Finite Group Databasebeta

← #17102829

Subgroups — #17102829

Order 4352.

832 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533300C211yesmaximal, characteristic, complemented
2#14530187C211yesmaximal, characteristic, complemented
3#14530172C211yesmaximal, characteristic, complemented
4#14530015C211yesmaximal, characteristic
5#14530015C211yesmaximal, characteristic
6#14529470C211yesmaximal, characteristic, complemented
7#14529401C211yesmaximal, characteristic, complemented
8#14529355C211yesmaximal, characteristic, complemented
9#14529355C211yesmaximal, characteristic, complemented
10#14529343C211yesmaximal, characteristic, complemented
11#14529031C211yesmaximal, characteristic, complemented
12#14529031C211yesmaximal, characteristic, complemented
13#14528784C211yesmaximal, characteristic, complemented
14C4×#10587503C211yesmaximal, characteristic, complemented
15C17×#2366C211yesmaximal, characteristic
16C2×#10587575—21no—
17C2×#10587478C2211yescharacteristic
18C2×#10587478C2211yescharacteristic
19C2×C4⋊#3622C2211yescharacteristic
20C2×#10587503C2211yescharacteristic
21C2×#10587503C2211yescharacteristic
22C2×#10587503C2211yescharacteristic
23C2×#10587503C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×#10587503C2211yescharacteristic
28C2×C4×#3622C2211yescharacteristic
29#11762749—21no—
30#11762739—21no—
31#11762707C2211yescharacteristic
32#11762707C2211yescharacteristic
33#11762707C2211yescharacteristic
34#11762707C2211yescharacteristic
35#11762694—21no—
36#11762679C2211yescharacteristic
37C4×C4⋊Dic17C2211yescharacteristic
38#11762571C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762564C2211yescharacteristic
45#11762564C2211yescharacteristic
46#11762564C2211yescharacteristic
47#11762564C2211yescharacteristic
48C2×C17×#127C2211yescharacteristic
49C2×C4×D4×C17—21no—
50C2×C4×D4×C17C2211yescharacteristic
51C2×C4×D4×C17C2211yescharacteristic
52C17×#390—21no—
53C17×#390C2211yescharacteristic
54C17×#390C2211yescharacteristic
55C17×#386—21no—
56C17×#386—21no—
57C4×C4⋊C4×C17C2211yescharacteristic
58C4×C4⋊C4×C17C2211yescharacteristic
59C22×D4×C17—21no—
60C22×D4×C17—21no—
61C22×D4×C17C2311yescharacteristic
62C22×D4×C17C2311yescharacteristic
63C23×C4×C17—21no—
64C23×C4×C17—21no—
65C17×#127—22no—
66C17×#127—22no—
67C4×D4×C17—22no—
68C4×D4×C17—22no—
69C4×D4×C17—41no—
70C4×D4×C17—41no—
71C4×D4×C17—44no—
72C2×C4⋊C4×C17D411yescharacteristic
73C2×C4⋊C4×C17D411yescharacteristic
74C2×C4⋊C4×C17C2311yescharacteristic
75C2×C4⋊C4×C17C2311yescharacteristic
76C2×C22⋊C4×C17—21no—
77C2×C22⋊C4×C17—21no—
78C2×C22⋊C4×C17—21no—
79C2×C22⋊C4×C17—21no—
80C2×C22⋊C4×C17—21no—
81C2×C22⋊C4×C17—21no—
82C2×C42×C17—21no—
83C2×C42×C17C2311yescharacteristic
84C2×C42×C17C2311yescharacteristic
85C2×C42×C17C2311yescharacteristic
86C2×C4⋊Dic17—21no—
87C2×C4⋊Dic17—21no—
88C2×C4⋊Dic17C2311yescharacteristic
89C2×C4⋊Dic17C2311yescharacteristic
90C2×C4⋊Dic17C2311yescharacteristic
91C2×C4⋊Dic17C2311yescharacteristic
92C2×#63225—21no—
93C2×#63225—21no—
94C2×#63225—21no—
95C2×#63225—21no—
96C2×C4×Dic17—21no—
97C22×#3622C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C22×#3622C2311yescharacteristic
100C22×#3622C2311yescharacteristic
101#10587575—44no—
102C17×#95—21no—
103C17×#95D411yescharacteristic
104C17×#95D411yescharacteristic
105#10587503—22no—
106#10587503—22no—
107#10587503—22no—
108#10587503—22no—
109#10587503—22no—
110#10587503—22no—
111#10587503—41no—
112#10587503—41no—
113#10587502—21no—
114#10587502—21no—
115#10587502—21no—
116#10587502—21no—
117#10587502—21no—
118#10587478—22no—
119#10587478—22no—
120C4⋊#3622—41no—
121C4×#3622—41no—
122C24×C17—21no—
123C24×C17—21no—
124C2×D4×C17—24no—
125C2×D4×C17—24no—
126C2×D4×C17—21no—
127C2×D4×C17—21no—
128C2×D4×C17—21no—
129C2×D4×C17—21no—
130C2×D4×C17—21no—
131C2×D4×C17—21no—
132C2×D4×C17—21no—
133C2×D4×C17—21no—
134C2×D4×C17—21no—
135C2×D4×C17—21no—
136C2×D4×C17—42no—
137C2×D4×C17—42no—
138C2×D4×C17—81no—
139C2×D4×C17—81no—
140C2×D4×C17#4112yes—
141C2×D4×C17#4112yes—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—42no—
145C22×C4×C17—42no—
146C22×C4×C17—42no—
147C22×C4×C17—42no—
148C22×C4×C17—81no—
149C22×C4×C17—81no—
150C22×C4×C17C2×D411yescharacteristic
151C22×C4×C17C2×D411yescharacteristic
152C22×C4×C17C2×D411yescharacteristic
153C22×C4×C17C2×D411yescharacteristic
154C22×C4×C17C2×D411yescharacteristic
155C22×C4×C17C2×D411yescharacteristic
156C22×C4×C17C2411yescharacteristic
157C22×Dic17—21no—
158C22×Dic17—21no—
159C22×Dic17—21no—
160C22×Dic17—21no—
161C4⋊C4×C17—21no—
162C4⋊C4×C17—21no—
163C4⋊C4×C17—21no—
164C4⋊C4×C17—41no—
165C4⋊C4×C17D814yes—
166C4⋊C4×C17#4112yes—
167C22⋊C4×C17—42no—
168C22⋊C4×C17—42no—
169C22⋊C4×C17—42no—
170C22⋊C4×C17—42no—
171C22⋊C4×C17—81no—
172C22⋊C4×C17—81no—
173C42×C17—21no—
174C42×C17—21no—
175C42×C17—21no—
176C42×C17—21no—
177C42×C17—21no—
178C42×C17—21no—
179C42×C17—42no—
180C4⋊Dic17—21no—
181C4⋊Dic17—21no—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17—42no—
188C4⋊Dic17—42no—
189C4⋊Dic17#4112yes—
190#63225—42no—
191#63225—42no—
192#63225—42no—
193#63225—42no—
194C4×Dic17—42no—
195C2×#3622—21no—
196C2×#3622—21no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203C2×#3622—21no—
204C2×#3622—21no—
205C2×#3622—21no—
206C2×#3622—21no—
207#26752—171nomaximal, Sylow
208C23×C17—22no—
209C23×C17—22no—
210C23×C17—41no—
211C23×C17—41no—
212C23×C17—41no—
213C23×C17—41no—
214C23×C17—41no—
215C23×C17—41no—
216C23×C17—41no—
217C23×C17—41no—
218C23×C17—41no—
219C23×C17—41no—
220C23×C17—41no—
221C23×C17—41no—
222C23×C17C22×D411yescharacteristic
223D4×C17—22no—
224D4×C17—22no—
225D4×C17—22no—
226D4×C17—22no—
227D4×C17—48no—
228D4×C17—41no—
229D4×C17—41no—
230D4×C17—41no—
231D4×C17—41no—
232D4×C17—84no—
233C2×C4×C17—21no—
234C2×C4×C17—21no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—21no—
239C2×C4×C17—21no—
240C2×C4×C17—21no—
241C2×C4×C17—21no—
242C2×C4×C17—22no—
243C2×C4×C17—21no—
244C2×C4×C17—21no—
245C2×C4×C17—21no—
246C2×C4×C17—21no—
247C2×C4×C17—21no—
248C2×C4×C17—21no—
249C2×C4×C17—41no—
250C2×C4×C17—41no—
251C2×C4×C17—41no—
252C2×C4×C17—41no—
253C2×C4×C17—41no—
254C2×C4×C17—84no—
255C2×C4×C17—84no—
256C2×C4×C17C2×D812yes—
257C2×C4×C17C2×D812yes—
258C2×C4×C17C2×D812yes—
259C2×C4×C17C2×#4111yescharacteristic
260C2×C4×C17C2×#4111yescharacteristic
261C2×C4×C17C2×#4111yescharacteristic
262C2×C4×C17C2×#4111yescharacteristic
263C2×C4×C17H(5,𝔽2)11yescharacteristic
264C2×C4×C172−1+411yescharacteristic
265C2×Dic17—22no—
266C2×Dic17—41no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17—41no—
271C2×Dic17—41no—
272C2×Dic17—41no—
273C2×Dic17—41no—
274C2×Dic17—41no—
275C2×Dic17—41no—
276C2×Dic17—41no—
277#3622—41no—
278#3622—41no—
279#3622—41no—
280#3622—41no—
281#2506—171no—
282#2366D1711yescharacteristic
283#2071—171no—
284#2067—171no—
285#2041—171no—
286#2041—171no—
287#1934—171no—
288#1925—171no—
289#1918—171no—
290#1918—171no—
291#1916—171no—
292#1862—171no—
293#1862—171no—
294#1802—171no—
295C4×#102—171no—
296C22×C17—42no—
297C22×C17—42no—
298C22×C17—42no—
299C22×C17—42no—
300C22×C17—42no—
301C22×C17—42no—
302C22×C17—81no—
303C22×C17—81no—
304C22×C17—81no—
305C22×C17—81no—
306C22×C17—81no—
307C22×C17—81no—
308C22×C17—81no—
309C22×C17—81no—
310C22×C17#52511yescharacteristic
311C22×C17#54611yescharacteristic
312C22×C17#54811yescharacteristic
313C22×C17C22×D811yescharacteristic
314C22×C17#57511yescharacteristic
315C22×C17#57711yescharacteristic
316C22×C17#57711yescharacteristic
317C4×C17—22no—
318C4×C17—22no—
319C4×C17—22no—
320C4×C17—41no—
321C4×C17—42no—
322C4×C17—41no—
323C4×C17—41no—
324C4×C17—81no—
325C4×C17#52911yescharacteristic
326C4×C17#53911yescharacteristic
327C4×C17#55211yescharacteristic
328C4×C17#55311yescharacteristic
329Dic17—42no—
330Dic17—81no—
331Dic17—81no—
332Dic17—81no—
333C2×#127C2×D1711yescharacteristic
334C2×#125—341no—
335C2×C4×D4—21no—
336C2×C4×D4C2×D1711yescharacteristic
337C2×C4×D4C2×D1711yescharacteristic
338C2×#107—171no—
339C2×#107—171no—
340C2×C4⋊C8—171no—
341C2×#102—171no—
342C2×#102—171no—
343C2×#102—171no—
344C2×#102—171no—
345C2×#102—171no—
346C2×#102—171no—
347C2×#102—171no—
348C2×#102—171no—
349C2×C4×C8—171no—
350#400—341no—
351#398—341no—
352#390—21no—
353#390C2×D1711yescharacteristic
354#390C2×D1711yescharacteristic
355#389—171no—
356#389—171no—
357#389—171no—
358#389—171no—
359#387—341no—
360#386—21no—
361#386—21no—
362#384—171no—
363C4×C4⋊C4—171no—
364C4×C4⋊C4C2×D1711yescharacteristic
365C4×C4⋊C4C2×D1711yescharacteristic
366#340—171no—
367#340—171no—
368#340—171no—
369#340—171no—
370#340—171no—
371#340—171no—
372#336—171no—
373#336—171no—
374#336—171no—
375#336—171no—
376C2×C17—82no—
377C2×C17—82no—
378C2×C17#246011yescharacteristic
379C2×C17#310011yescharacteristic
380C2×C17#312311yescharacteristic
381C2×C17#329411yescharacteristic
382C2×C17#331711yescharacteristic
383C2×C17#335811yescharacteristic
384C2×C17#337111yescharacteristic
385C22×D4—21no—
386C22×D4—21no—
387C22×D4C22×D1711yescharacteristic
388C22×D4C22×D1711yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C22×C8—171no—
392C22×C8—171no—
393C22×C8—171no—
394C22×C8—171no—
395#127—22no—
396#127—22no—
397#125—684no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—41no—
401C4×D4—41no—
402C4×D4—44no—
403C2×C4⋊C4—171no—
404C2×C4⋊C4—171no—
405C2×C4⋊C4—171no—
406C2×C4⋊C4—171no—
407C2×C4⋊C4—341no—
408C2×C4⋊C4—341no—
409C2×C4⋊C4—341no—
410C2×C4⋊C4—341no—
411C2×C4⋊C4—341no—
412C2×C4⋊C4—341no—
413C2×C4⋊C4C22⋊D1711yescharacteristic
414C2×C4⋊C4C22⋊D1711yescharacteristic
415C2×C4⋊C4C22×D1711yescharacteristic
416C2×C4⋊C4C22×D1711yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C42—21no—
424C2×C42—341no—
425C2×C42C22×D1711yescharacteristic
426C2×C42C22×D1711yescharacteristic
427C2×C42C22×D1711yescharacteristic
428#107—342no—
429#107—342no—
430C4⋊C8—681no—
431#102—342no—
432#102—342no—
433#102—342no—
434#102—342no—
435#102—342no—
436#102—342no—
437#102—681no—
438#102—681no—
439C4×C8—681no—
440#95—21no—
441#95—341no—
442#95—341no—
443#95—341no—
444#95—341no—
445#95—341no—
446#95C22⋊D1711yescharacteristic
447#95C22⋊D1711yescharacteristic
448C17#2675211yescharacteristic, complemented, Sylow
449C24—21no—
450C24—21no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—81no—
466C2×D4—81no—
467C2×D4#6325212yes—
468C2×D4#6325212yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—81no—
476C22×C4—81no—
477C22×C4—341no—
478C22×C4—341no—
479C22×C4—341no—
480C22×C4—341no—
481C22×C4C2×C22⋊D1711yescharacteristic
482C22×C4C2×C22⋊D1711yescharacteristic
483C22×C4C2×C22⋊D1711yescharacteristic
484C22×C4C2×C22⋊D1711yescharacteristic
485C22×C4C2×C22⋊D1711yescharacteristic
486C22×C4C2×C22⋊D1711yescharacteristic
487C22×C4C23×D1711yescharacteristic
488C2×C8—341no—
489C2×C8—341no—
490C2×C8—341no—
491C2×C8—341no—
492C2×C8—341no—
493C2×C8—341no—
494C2×C8—341no—
495C2×C8—341no—
496C2×C8—341no—
497C2×C8—341no—
498C2×C8—341no—
499C2×C8—341no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—172no—
505C4⋊C4—341no—
506C4⋊C4—341no—
507C4⋊C4—341no—
508C4⋊C4—341no—
509C4⋊C4—341no—
510C4⋊C4—341no—
511C4⋊C4—341no—
512C4⋊C4—682no—
513C4⋊C4—682no—
514C4⋊C4—682no—
515C4⋊C4—682no—
516C4⋊C4—682no—
517C4⋊C4—682no—
518C4⋊C4#6322814yes—
519C4⋊C4#6325412yes—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—81no—
525C22⋊C4—81no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—42no—
533C42—682no—
534C23—22no—
535C23—22no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23C22×C22⋊D1711yescharacteristic
549D4—22no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4—48no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—84no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4—84no—
582C2×C4—342no—
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×C4C2×#6322812yes—
595C2×C4C2×#6322812yes—
596C2×C4C2×#6322812yes—
597C2×C4C2×#6325211yescharacteristic
598C2×C4C2×#6325211yescharacteristic
599C2×C4C2×#6325411yescharacteristic
600C2×C4#1058769111yescharacteristic
601C2×C4#41×D1711yescharacteristic
602C2×C4#1058769711yescharacteristic
603C8—681no—
604C8—681no—
605C8—681no—
606C8—681no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22#1176332011yescharacteristic
622C22#1176345311yescharacteristic
623C22#1176346611yescharacteristic
624C22C22×#6322811yescharacteristic
625C22#1176360711yescharacteristic
626C22#1176362011yescharacteristic
627C22#1176362011yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—41no—
635C4—81no—
636C4—682no—
637C4—1361no—
638C4—1361no—
639C4—1361no—
640C4#1176333911yescharacteristic
641C4#1176340111yescharacteristic
642C4#1176349911yescharacteristic
643C4#1176350811yescharacteristic
644C2—82no—
645C2—82no—
646C2#1453273011yescharacteristic
647C2#1453878411yescharacteristic
648C2#1453903611yescharacteristic
649C2#1454059711yescharacteristic
650C2#1454091011yescharacteristic
651C2#1454141511yescharacteristic
652C2#1454154611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2366C2
socleC23×C17C22×D4
prime radicalC2×C17×#127C22
hypercenter#2366D17
hypocenterC17#26752
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. #14533300C2semidirect
2. #14530187C2semidirect
3. #14530172C2semidirect
6. #14529470C2semidirect
7. #14529401C2semidirect
8. #14529355C2semidirect
9. #14529355C2semidirect
10. #14529343C2semidirect
11. #14529031C2semidirect
12. #14529031C2semidirect
13. #14528784C2semidirect
14. C4×#10587503C2semidirect
448. C17#26752semidirect

Maximal subgroups

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

subgroupindex
#145333002
#145301872
#145301722
#145300152
#145294702
#145294012
#145293552
#145293432
#145290312
#145287842
C4×#105875032
C17×#23662
#2675217