Finite Group Databasebeta

← #17102874

Subgroups — #17102874

Order 4352.

804 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533333C211yesmaximal, characteristic, complemented
2#14530197C211yesmaximal, characteristic, complemented
3#14530158C211yesmaximal, characteristic, complemented
4#14530015C211yesmaximal, characteristic
5#14530015C211yesmaximal, characteristic
6#14529470C211yesmaximal, characteristic, complemented
7#14529408C211yesmaximal, characteristic, complemented
8#14529376C211yesmaximal, characteristic, complemented
9#14529362C211yesmaximal, characteristic, complemented
10#14529343C211yesmaximal, characteristic, complemented
11#14529031C211yesmaximal, characteristic, complemented
12#14529031C211yesmaximal, characteristic, complemented
13#14528794C211yesmaximal, characteristic, complemented
14C4×#10587503C211yesmaximal, characteristic, complemented
15C17×#2366C211yesmaximal, characteristic
16C2×#10587478C2211yescharacteristic
17C2×#10587479C2211yescharacteristic
18C2×C4⋊#3622C2211yescharacteristic
19C2×#10587503C2211yescharacteristic
20C2×#10587503C2211yescharacteristic
21C2×#10587503C2211yescharacteristic
22C2×#10587503C2211yescharacteristic
23C2×#10587503C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×C4×#3622C2211yescharacteristic
28#11762750—21no—
29#11762747—21no—
30#11762707C2211yescharacteristic
31#11762707C2211yescharacteristic
32#11762707C2211yescharacteristic
33#11762707C2211yescharacteristic
34#11762704—21no—
35#11762691—21no—
36#11762675C2211yescharacteristic
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⋊Dic17C2311yescharacteristic
87C2×C4⋊Dic17C2311yescharacteristic
88C2×C4⋊Dic17C2311yescharacteristic
89C2×C4⋊Dic17C2311yescharacteristic
90C2×#63225—21no—
91C2×#63225—21no—
92C2×#63225—21no—
93C2×#63225—21no—
94C2×C4×Dic17—21no—
95C22×#3622C2311yescharacteristic
96C22×#3622C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C17×#95—21no—
100C17×#95D411yescharacteristic
101C17×#95D411yescharacteristic
102#10587503—22no—
103#10587503—22no—
104#10587503—22no—
105#10587503—22no—
106#10587503—22no—
107#10587503—22no—
108#10587503—41no—
109#10587503—41no—
110#10587502—21no—
111#10587502—21no—
112#10587502—21no—
113#10587502—21no—
114#10587502—21no—
115#10587502—21no—
116#10587502—21no—
117#10587479—22no—
118#10587478—22no—
119C4⋊#3622—41no—
120C4×#3622—41no—
121C24×C17—21no—
122C24×C17—21no—
123C2×D4×C17—24no—
124C2×D4×C17—24no—
125C2×D4×C17—21no—
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—42no—
136C2×D4×C17—42no—
137C2×D4×C17—81no—
138C2×D4×C17—81no—
139C2×D4×C17#4112yes—
140C2×D4×C17#4112yes—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—42no—
144C22×C4×C17—42no—
145C22×C4×C17—42no—
146C22×C4×C17—42no—
147C22×C4×C17—81no—
148C22×C4×C17—81no—
149C22×C4×C17C2×D411yescharacteristic
150C22×C4×C17C2×D411yescharacteristic
151C22×C4×C17C2×D411yescharacteristic
152C22×C4×C17C2×D411yescharacteristic
153C22×C4×C17C2×D411yescharacteristic
154C22×C4×C17C2×D411yescharacteristic
155C22×C4×C17C2411yescharacteristic
156C22×Dic17—21no—
157C22×Dic17—21no—
158C22×Dic17—21no—
159C22×Dic17—21no—
160C4⋊C4×C17—22no—
161C4⋊C4×C17—22no—
162C4⋊C4×C17—21no—
163C4⋊C4×C17—21no—
164C4⋊C4×C17—21no—
165C4⋊C4×C17#4112yes—
166C22⋊C4×C17—42no—
167C22⋊C4×C17—42no—
168C22⋊C4×C17—42no—
169C22⋊C4×C17—42no—
170C22⋊C4×C17—81no—
171C22⋊C4×C17—81no—
172C42×C17—21no—
173C42×C17—21no—
174C42×C17—21no—
175C42×C17—21no—
176C42×C17—21no—
177C42×C17—21no—
178C42×C17—42no—
179C4⋊Dic17—21no—
180C4⋊Dic17—21no—
181C4⋊Dic17—21no—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17#4112yes—
187#63225—42no—
188#63225—42no—
189#63225—81no—
190#63225—81no—
191C4×Dic17—81no—
192C2×#3622—21no—
193C2×#3622—21no—
194C2×#3622—21no—
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—
204#26755—171nomaximal, Sylow
205C23×C17—22no—
206C23×C17—22no—
207C23×C17—41no—
208C23×C17—41no—
209C23×C17—41no—
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×C17C22×D411yescharacteristic
220D4×C17—22no—
221D4×C17—22no—
222D4×C17—22no—
223D4×C17—22no—
224D4×C17—48no—
225D4×C17—41no—
226D4×C17—41no—
227D4×C17—41no—
228D4×C17—41no—
229D4×C17—84no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17—21no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—22no—
239C2×C4×C17—21no—
240C2×C4×C17—21no—
241C2×C4×C17—21no—
242C2×C4×C17—21no—
243C2×C4×C17—21no—
244C2×C4×C17—21no—
245C2×C4×C17—21no—
246C2×C4×C17—21no—
247C2×C4×C17—41no—
248C2×C4×C17—41no—
249C2×C4×C17—41no—
250C2×C4×C17—41no—
251C2×C4×C17—41no—
252C2×C4×C17—84no—
253C2×C4×C17—84no—
254C2×C4×C17#13512yes—
255C2×C4×C17AGL(1,ℤ/8)12yes—
256C2×C4×C17C2×#4111yescharacteristic
257C2×C4×C17C2×#4111yescharacteristic
258C2×C4×C17C2×#4111yescharacteristic
259C2×C4×C17C2×#4111yescharacteristic
260C2×C4×C17H(5,𝔽2)11yescharacteristic
261C2×C4×C172−1+411yescharacteristic
262C2×Dic17—22no—
263C2×Dic17—41no—
264C2×Dic17—41no—
265C2×Dic17—41no—
266C2×Dic17—41no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17—41no—
271C2×Dic17—41no—
272C2×Dic17—41no—
273C2×Dic17—41no—
274#3622—41no—
275#3622—41no—
276#3622—41no—
277#3622—41no—
278#2509—171no—
279#2366D1711yescharacteristic
280#2073—171no—
281#2065—171no—
282#2041—171no—
283#2041—171no—
284#1934—171no—
285#1926—171no—
286#1921—171no—
287#1919—171no—
288#1916—171no—
289#1862—171no—
290#1862—171no—
291#1804—171no—
292C4×#102—171no—
293C22×C17—42no—
294C22×C17—42no—
295C22×C17—42no—
296C22×C17—42no—
297C22×C17—42no—
298C22×C17—42no—
299C22×C17—81no—
300C22×C17—81no—
301C22×C17—81no—
302C22×C17—81no—
303C22×C17—81no—
304C22×C17—81no—
305C22×C17—81no—
306C22×C17—81no—
307C22×C17#52511yescharacteristic
308C22×C17#54611yescharacteristic
309C22×C17#54811yescharacteristic
310C22×C17C2×#13511yescharacteristic
311C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C17#57611yescharacteristic
313C22×C17#57711yescharacteristic
314C4×C17—22no—
315C4×C17—22no—
316C4×C17—41no—
317C4×C17—41no—
318C4×C17—41no—
319C4×C17—41no—
320C4×C17—42no—
321C4×C17—81no—
322C4×C17#52911yescharacteristic
323C4×C17#53911yescharacteristic
324C4×C17#55211yescharacteristic
325C4×C17#55311yescharacteristic
326Dic17—42no—
327Dic17—81no—
328Dic17—81no—
329Dic17—81no—
330C2×#127C2×D1711yescharacteristic
331C2×C4×D4—21no—
332C2×C4×D4C2×D1711yescharacteristic
333C2×C4×D4C2×D1711yescharacteristic
334C2×#107—171no—
335C2×#106—171no—
336C2×C4⋊C8—171no—
337C2×#102—171no—
338C2×#102—171no—
339C2×#102—171no—
340C2×#102—171no—
341C2×#102—171no—
342C2×#102—171no—
343C2×#102—171no—
344C2×#102—171no—
345C2×C4×C8—171no—
346#400—341no—
347#400—341no—
348#390—21no—
349#390C2×D1711yescharacteristic
350#390C2×D1711yescharacteristic
351#389—171no—
352#389—171no—
353#389—171no—
354#389—171no—
355#389—341no—
356#387—341no—
357#386—21no—
358#386—21no—
359#382—171no—
360C4×C4⋊C4—171no—
361C4×C4⋊C4C2×D1711yescharacteristic
362C4×C4⋊C4C2×D1711yescharacteristic
363#340—171no—
364#340—171no—
365#340—171no—
366#340—171no—
367#340—171no—
368#340—171no—
369#336—171no—
370#336—171no—
371#336—171no—
372#336—171no—
373C2×C17—82no—
374C2×C17—82no—
375C2×C17#246011yescharacteristic
376C2×C17#310511yescharacteristic
377C2×C17#311811yescharacteristic
378C2×C17#330411yescharacteristic
379C2×C17#331811yescharacteristic
380C2×C17#336111yescharacteristic
381C2×C17#336811yescharacteristic
382C22×D4—21no—
383C22×D4—21no—
384C22×D4C22×D1711yescharacteristic
385C22×D4C22×D1711yescharacteristic
386C23×C4—21no—
387C23×C4—21no—
388C22×C8—171no—
389C22×C8—171no—
390C22×C8—171no—
391C22×C8—171no—
392#127—22no—
393#127—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—41no—
397C4×D4—41no—
398C4×D4—44no—
399C2×C4⋊C4—171no—
400C2×C4⋊C4—171no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4—171no—
403C2×C4⋊C4—341no—
404C2×C4⋊C4—341no—
405C2×C4⋊C4—341no—
406C2×C4⋊C4—341no—
407C2×C4⋊C4C22⋊D1711yescharacteristic
408C2×C4⋊C4C22⋊D1711yescharacteristic
409C2×C4⋊C4C22×D1711yescharacteristic
410C2×C4⋊C4C22×D1711yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C42—21no—
418C2×C42—341no—
419C2×C42C22×D1711yescharacteristic
420C2×C42C22×D1711yescharacteristic
421C2×C42C22×D1711yescharacteristic
422#107—342no—
423#106—342no—
424C4⋊C8—681no—
425#102—342no—
426#102—342no—
427#102—342no—
428#102—342no—
429#102—342no—
430#102—342no—
431#102—681no—
432#102—681no—
433C4×C8—681no—
434#95—21no—
435#95—341no—
436#95—341no—
437#95—341no—
438#95—341no—
439#95—341no—
440#95—341no—
441#95—341no—
442#95C22⋊D1711yescharacteristic
443#95C22⋊D1711yescharacteristic
444C17#2675511yescharacteristic, complemented, Sylow
445C24—21no—
446C24—21no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—81no—
462C2×D4—81no—
463C2×D4#6325212yes—
464C2×D4#6325212yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—341no—
474C22×C4—341no—
475C22×C4—341no—
476C22×C4—341no—
477C22×C4C2×C22⋊D1711yescharacteristic
478C22×C4C2×C22⋊D1711yescharacteristic
479C22×C4C2×C22⋊D1711yescharacteristic
480C22×C4C2×C22⋊D1711yescharacteristic
481C22×C4C2×C22⋊D1711yescharacteristic
482C22×C4C2×C22⋊D1711yescharacteristic
483C22×C4C23×D1711yescharacteristic
484C2×C8—341no—
485C2×C8—341no—
486C2×C8—341no—
487C2×C8—341no—
488C2×C8—341no—
489C2×C8—341no—
490C2×C8—341no—
491C2×C8—341no—
492C2×C8—341no—
493C2×C8—341no—
494C2×C8—341no—
495C2×C8—341no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—172no—
502C4⋊C4—341no—
503C4⋊C4—341no—
504C4⋊C4—341no—
505C4⋊C4—341no—
506C4⋊C4—341no—
507C4⋊C4—341no—
508C4⋊C4—341no—
509C4⋊C4—682no—
510C4⋊C4—682no—
511C4⋊C4—1361no—
512C4⋊C4—1361no—
513C4⋊C4#6325412yes—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—81no—
519C22⋊C4—81no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—42no—
527C42—1361no—
528C23—22no—
529C23—22no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23C22×C22⋊D1711yescharacteristic
543D4—22no—
544D4—22no—
545D4—22no—
546D4—22no—
547D4—48no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—84no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
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—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—84no—
577C2×C4—342no—
578C2×C4—681no—
579C2×C4—681no—
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#1058761812yes—
590C2×C4#1058763612yes—
591C2×C4C2×#6325211yescharacteristic
592C2×C4C2×#6325211yescharacteristic
593C2×C4C2×#6325411yescharacteristic
594C2×C4#1058769111yescharacteristic
595C2×C4#41×D1711yescharacteristic
596C2×C4#1058769711yescharacteristic
597C8—681no—
598C8—681no—
599C8—681no—
600C8—681no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22#1176332011yescharacteristic
616C22#1176345311yescharacteristic
617C22#1176346611yescharacteristic
618C22C2×#1058763611yescharacteristic
619C22C2×#1058761811yescharacteristic
620C22#1176361211yescharacteristic
621C22#1176362011yescharacteristic
622C4—22no—
623C4—22no—
624C4—41no—
625C4—42no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—81no—
630C4—682no—
631C4—1361no—
632C4—1361no—
633C4—1361no—
634C4#1176333911yescharacteristic
635C4#1176340111yescharacteristic
636C4#1176349911yescharacteristic
637C4#1176350811yescharacteristic
638C2—82no—
639C2—82no—
640C2#1453273011yescharacteristic
641C2#1453883111yescharacteristic
642C2#1453896811yescharacteristic
643C2#1454072311yescharacteristic
644C2#1454092511yescharacteristic
645C2#1454144011yescharacteristic
646C2#1454150911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2366C2
socleC23×C17C22×D4
prime radicalC2×C17×#127C22
hypercenter#2366D17
hypocenterC17#26755
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. #14533333C2semidirect
2. #14530197C2semidirect
3. #14530158C2semidirect
6. #14529470C2semidirect
7. #14529408C2semidirect
8. #14529376C2semidirect
9. #14529362C2semidirect
10. #14529343C2semidirect
11. #14529031C2semidirect
12. #14529031C2semidirect
13. #14528794C2semidirect
14. C4×#10587503C2semidirect
444. C17#26755semidirect

Maximal subgroups

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

subgroupindex
#145333332
#145301972
#145301582
#145300152
#145294702
#145294082
#145293762
#145293622
#145293432
#145290312
#145287942
C4×#105875032
C17×#23662
#2675517