Finite Group Databasebeta

← #17044935

Subgroups — #17044935

Order 4352.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531407C211yesmaximal, characteristic
2#14531393C211yesmaximal, characteristic
3#14529554C211yesmaximal, characteristic, complemented
4#14529554C211yesmaximal, characteristic, complemented
5#14529548C211yesmaximal, characteristic, complemented
6#14529543C211yesmaximal, characteristic, complemented
7#14528985C211yesmaximal, characteristic
8#14528985C211yesmaximal, characteristic
9#14528979C211yesmaximal, characteristic
10#14528974C211yesmaximal, characteristic
11#14528952C211yesmaximal, characteristic, complemented
12#14528948C211yesmaximal, characteristic, complemented
13#14528918C211yesmaximal, characteristic, complemented
14#14528912C211yesmaximal, characteristic, complemented
15C2×C17×#433C211yesmaximal, characteristic
16C2×#10587612C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C2×#10587489C2211yescharacteristic
19C2×#10587489C2211yescharacteristic
20C2×#10587489C2211yescharacteristic
21C2×#10587489C2211yescharacteristic
22C2×#10587488C2211yescharacteristic
23C2×#10587488C2211yescharacteristic
24C2×#10587488C2211yescharacteristic
25C2×#10587488C2211yescharacteristic
26#11762708—21no—
27#11762708—21no—
28#11762702—21no—
29#11762702—21no—
30#11762695—21no—
31#11762695—21no—
32#11762684—21no—
33#11762684—21no—
34#11762679C2211yescharacteristic
35#11762679C2211yescharacteristic
36#11762679C2211yescharacteristic
37#11762675C2211yescharacteristic
38#11762675C2211yescharacteristic
39#11762675C2211yescharacteristic
40#11762669C2211yescharacteristic
41#11762669C2211yescharacteristic
42C4×C4⋊Dic17C2211yescharacteristic
43C4×C4⋊Dic17C2211yescharacteristic
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52C2×C17×#117C2211yescharacteristic
53C17×#433C418yescomplemented
54C2×C17×C4⋊C8C2211yescharacteristic
55C2×C17×C4⋊C8C2211yescharacteristic
56C2×C17×C22⋊C8C2211yescharacteristic
57C2×C17×C22⋊C8C2211yescharacteristic
58C2×C17×#97C2211yescharacteristic
59C2×C4×C8×C17C2211yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17—21no—
62C22×C8×C17C2311yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C17×#117C2×C414yes—
67C17×#117Q814yes—
68C2×C4⋊C4×C17D411yescharacteristic
69C2×C4⋊C4×C17D411yescharacteristic
70C2×C22⋊C4×C17D411yescharacteristic
71C2×C22⋊C4×C17D411yescharacteristic
72C2×C42×C17C2311yescharacteristic
73C2×C42×C17C2311yescharacteristic
74C2×C22⋊Dic17—21no—
75C2×C22⋊Dic17—21no—
76C2×C22⋊Dic17—21no—
77#10587612—41no—
78#10587612—41no—
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⋊Dic17—41no—
87C2×C4⋊Dic17—41no—
88C2×C4⋊Dic17C2311yescharacteristic
89C2×C4⋊Dic17C2311yescharacteristic
90C2×C4⋊Dic17C2311yescharacteristic
91C2×C4⋊Dic17C2311yescharacteristic
92C2×C4⋊Dic17C2311yescharacteristic
93C2×C4⋊Dic17C2311yescharacteristic
94C2×C4⋊Dic17C2311yescharacteristic
95C2×C4⋊Dic17C2311yescharacteristic
96C2×C4×Dic17—21no—
97C2×C4×Dic17—21no—
98C2×C4×Dic17—21no—
99C17×C4⋊C8C2×C414yescomplemented
100C17×C4⋊C8C2×C414yescomplemented
101C17×C22⋊C8C2×C414yes—
102C17×C22⋊C8C2×C414yes—
103C17×#97C2×C414yescomplemented
104C4×C8×C17C2×C414yescomplemented
105#10587502—21no—
106#10587502—21no—
107#10587502—21no—
108#10587502—21no—
109#10587502—21no—
110#10587502—21no—
111#10587502—21no—
112#10587502—21no—
113#10587502—21no—
114#10587502—21no—
115#10587489—41no—
116#10587489—41no—
117#10587489—41no—
118#10587489—41no—
119#10587488—41no—
120#10587488—41no—
121#10587488—41no—
122#10587488—41no—
123C24×C17C2×D411yescharacteristic
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17C22×C412yes—
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2×D411yescharacteristic
131C22×C4×C17C2×D411yescharacteristic
132C22×C4×C17C2×D411yescharacteristic
133C22×C4×C17C2×D411yescharacteristic
134C22×C4×C17C2×Q812yes—
135C22×C4×C17C2411yescharacteristic
136C22×Dic17—21no—
137C22×Dic17—21no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—42no—
145C22×Dic17—81no—
146C22×Dic17—81no—
147C2×C8×C17—21no—
148C2×C8×C17—21no—
149C2×C8×C17—21no—
150C2×C8×C17—21no—
151C2×C8×C17—21no—
152C2×C8×C17—21no—
153C2×C8×C17—21no—
154C2×C8×C17—21no—
155C2×C8×C17C22×C412yes—
156C2×C8×C17C22×C412yes—
157C2×C8×C17C22×C412yes—
158C2×C8×C17C22×C412yes—
159C4⋊C4×C17C4⋊C414yes—
160C4⋊C4×C17C4⋊C414yes—
161C22⋊C4×C17C4⋊C414yes—
162C22⋊C4×C17C4⋊C414yes—
163C42×C17C22×C412yes—
164C42×C17C22×C412yes—
165C42×C17C2×Q812yes—
166C42×C17C2×Q812yes—
167C22⋊Dic17—42no—
168C22⋊Dic17—81no—
169C22⋊Dic17—81no—
170C4⋊Dic17—21no—
171C4⋊Dic17—21no—
172C4⋊Dic17—21no—
173C4⋊Dic17—21no—
174C4⋊Dic17—21no—
175C4⋊Dic17—21no—
176C4⋊Dic17—21no—
177C4⋊Dic17—21no—
178C4⋊Dic17—21no—
179C4⋊Dic17—21no—
180C4⋊Dic17—21no—
181C4⋊Dic17—21no—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—42no—
187C4⋊Dic17—81no—
188C4⋊Dic17—81no—
189C4⋊Dic17—81no—
190C4⋊Dic17—81no—
191C4⋊Dic17—81no—
192C4⋊Dic17—81no—
193C4×Dic17—42no—
194C4×Dic17—81no—
195C4×Dic17—81no—
196#21992—171nomaximal, Sylow
197C23×C17—21no—
198C23×C17—21no—
199C23×C17—21no—
200C23×C17—21no—
201C23×C17—21no—
202C23×C17—21no—
203C23×C17C2×C4⋊C412yes—
204C23×C17C22×D411yescharacteristic
205C2×C4×C17—21no—
206C2×C4×C17—21no—
207C2×C4×C17—21no—
208C2×C4×C17—21no—
209C2×C4×C17—21no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—21no—
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—22no—
218C2×C4×C17—22no—
219C2×C4×C17C2×C4⋊C412yes—
220C2×C4×C17C2×C4⋊C412yes—
221C2×C4×C17C2×C4⋊C412yes—
222C2×C4×C17C2×C4⋊C412yes—
223C2×C4×C17C2×C4⋊C412yes—
224C2×C4×C17C23×C411yescharacteristic
225C2×C4×C17C22×Q811yescharacteristic
226C2×C4×C17H(5,𝔽2)11yescharacteristic
227C2×C4×C17H(5,𝔽2)11yescharacteristic
228C2×C4×C172−1+411yescharacteristic
229C2×C4×C172−1+411yescharacteristic
230C2×Dic17—41no—
231C2×Dic17—41no—
232C2×Dic17—41no—
233C2×Dic17—41no—
234C2×Dic17—41no—
235C2×Dic17—41no—
236C2×Dic17—41no—
237C2×Dic17—41no—
238C2×Dic17—41no—
239C2×Dic17—41no—
240C2×Dic17—41no—
241C2×Dic17—41no—
242C2×Dic17—41no—
243C2×Dic17—41no—
244C2×Dic17—41no—
245C2×Dic17—41no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—41no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251C2×Dic17—41no—
252C2×Dic17—41no—
253C2×Dic17—41no—
254C2×Dic17—84no—
255C8×C17—22no—
256C8×C17—22no—
257C8×C17—22no—
258C8×C17—22no—
259C2×#433D1711yescharacteristic
260#2317—171no—
261#2314—171no—
262#1949—171no—
263#1949—171no—
264#1948—171no—
265#1947—171no—
266#1854—171no—
267#1854—171no—
268#1853—171no—
269#1852—171no—
270#1847—171no—
271#1846—171no—
272#1836—171no—
273#1834—171no—
274C22×C17—22no—
275C22×C17—22no—
276C22×C17—22no—
277C22×C17—41no—
278C22×C17—41no—
279C22×C17—41no—
280C22×C17—41no—
281C22×C17C22×C4⋊C411yescharacteristic
282C22×C17#53511yescharacteristic
283C22×C17#53611yescharacteristic
284C22×C17#57611yescharacteristic
285C22×C17#57711yescharacteristic
286C22×C17#57711yescharacteristic
287C22×C17#57811yescharacteristic
288C4×C17—22no—
289C4×C17—22no—
290C4×C17—22no—
291C4×C17—22no—
292C4×C17—22no—
293C4×C17#52011yescharacteristic
294C4×C17#52011yescharacteristic
295C4×C17#54411yescharacteristic
296C4×C17#54411yescharacteristic
297Dic17—81no—
298Dic17—81no—
299Dic17—81no—
300Dic17—81no—
301Dic17—81no—
302Dic17—81no—
303Dic17—81no—
304Dic17—81no—
305C2×#117—171no—
306C2×#117C2×D1711yescharacteristic
307C22×C4⋊C4—171no—
308#433Dic1718yescomplemented
309C2×#107—171no—
310C2×#107—171no—
311C2×#107—171no—
312C2×#107—171no—
313C2×#106—171no—
314C2×#106—171no—
315C2×#106—171no—
316C2×#106—171no—
317C2×C4⋊C8C2×D1711yescharacteristic
318C2×C4⋊C8C2×D1711yescharacteristic
319C2×C22⋊C8C2×D1711yescharacteristic
320C2×C22⋊C8C2×D1711yescharacteristic
321C2×#97C2×D1711yescharacteristic
322C2×C4×C8C2×D1711yescharacteristic
323#389—341no—
324#389—341no—
325#388—341no—
326#388—341no—
327#387—341no—
328#387—341no—
329#385—341no—
330#385—341no—
331#384—171no—
332#384—171no—
333#384—171no—
334#382—171no—
335#382—171no—
336#382—171no—
337#380—171no—
338#380—171no—
339C4×C4⋊C4—171no—
340C4×C4⋊C4—171no—
341#340—171no—
342#340—171no—
343#340—171no—
344#340—171no—
345#340—171no—
346#340—171no—
347#340—171no—
348#340—171no—
349C2×C17—42no—
350C2×C17#231711yescharacteristic
351C2×C17#291211yescharacteristic
352C2×C17#291311yescharacteristic
353C2×C17#322411yescharacteristic
354C2×C17#322511yescharacteristic
355C2×C17#324111yescharacteristic
356C2×C17#324211yescharacteristic
357C23×C4—341no—
358C23×C4C22×D1711yescharacteristic
359C22×C8C22×D1711yescharacteristic
360C22×C8C22×D1711yescharacteristic
361C22×C8C22×D1711yescharacteristic
362C22×C8C22×D1711yescharacteristic
363#117—681no—
364#117—681no—
365#117Dic3414yes—
366#117C2×Dic1714yes—
367C2×C4⋊C4—171no—
368C2×C4⋊C4—171no—
369C2×C4⋊C4—171no—
370C2×C4⋊C4—171no—
371C2×C4⋊C4—171no—
372C2×C4⋊C4—171no—
373C2×C4⋊C4—171no—
374C2×C4⋊C4—171no—
375C2×C4⋊C4—341no—
376C2×C4⋊C4—341no—
377C2×C4⋊C4—341no—
378C2×C4⋊C4—341no—
379C2×C4⋊C4—341no—
380C2×C4⋊C4—341no—
381C2×C4⋊C4—341no—
382C2×C4⋊C4—681no—
383C2×C4⋊C4—681no—
384C2×C4⋊C4D6811yescharacteristic
385C2×C4⋊C4D6811yescharacteristic
386C2×C22⋊C4—341no—
387C2×C22⋊C4—341no—
388C2×C22⋊C4—341no—
389C2×C22⋊C4D6811yescharacteristic
390C2×C22⋊C4D6811yescharacteristic
391C2×C42—341no—
392C2×C42—341no—
393C2×C42—341no—
394C2×C42C22×D1711yescharacteristic
395C2×C42C22×D1711yescharacteristic
396#107—681no—
397#107—681no—
398#107—681no—
399#107—681no—
400#106—681no—
401#106—681no—
402#106—681no—
403#106—681no—
404C4⋊C8C2×Dic1714yescomplemented
405C4⋊C8C2×Dic1714yescomplemented
406C22⋊C8C2×Dic1714yes—
407C22⋊C8C2×Dic1714yes—
408#97C2×Dic1714yescomplemented
409C4×C8C2×Dic1714yescomplemented
410#95—341no—
411#95—341no—
412#95—341no—
413#95—341no—
414#95—341no—
415#95—341no—
416#95—341no—
417#95—341no—
418#95—341no—
419#95—341no—
420C17#2199211yescharacteristic, complemented, Sylow
421C24C2×D6811yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—341no—
427C22×C4—341no—
428C22×C4—341no—
429C22×C4—341no—
430C22×C4—341no—
431C22×C4—341no—
432C22×C4—341no—
433C22×C4—341no—
434C22×C4—682no—
435C22×C4—1361no—
436C22×C4—1361no—
437C22×C4C2×Dic3412yes—
438C22×C4C2×D6811yescharacteristic
439C22×C4C2×D6811yescharacteristic
440C22×C4C2×D6811yescharacteristic
441C22×C4C2×D6811yescharacteristic
442C22×C4C2×D6811yescharacteristic
443C22×C4C22×Dic1712yes—
444C22×C4C23×D1711yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8C22×Dic1712yes—
454C2×C8C22×Dic1712yes—
455C2×C8C22×Dic1712yes—
456C2×C8C22×Dic1712yes—
457C4⋊C4—341no—
458C4⋊C4—341no—
459C4⋊C4—341no—
460C4⋊C4—341no—
461C4⋊C4—341no—
462C4⋊C4—341no—
463C4⋊C4—341no—
464C4⋊C4—341no—
465C4⋊C4—341no—
466C4⋊C4—341no—
467C4⋊C4—341no—
468C4⋊C4—341no—
469C4⋊C4—341no—
470C4⋊C4—341no—
471C4⋊C4—341no—
472C4⋊C4—341no—
473C4⋊C4—682no—
474C4⋊C4—1361no—
475C4⋊C4—1361no—
476C4⋊C4—1361no—
477C4⋊C4—1361no—
478C4⋊C4—1361no—
479C4⋊C4—1361no—
480C4⋊C4C4⋊Dic1714yes—
481C4⋊C4C4⋊Dic1714yes—
482C22⋊C4—682no—
483C22⋊C4—1361no—
484C22⋊C4—1361no—
485C22⋊C4C4⋊Dic1714yes—
486C22⋊C4C4⋊Dic1714yes—
487C42—682no—
488C42—1361no—
489C42—1361no—
490C42C2×Dic3412yes—
491C42C2×Dic3412yes—
492C42C22×Dic1712yes—
493C42C22×Dic1712yes—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C2×C4⋊Dic1712yes—
501C23C22×D6811yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—681no—
517C2×C4—681no—
518C2×C4—681no—
519C2×C4—681no—
520C2×C4—681no—
521C2×C4—681no—
522C2×C4—681no—
523C2×C4—681no—
524C2×C4—681no—
525C2×C4—681no—
526C2×C4—681no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4—681no—
530C2×C4—681no—
531C2×C4—681no—
532C2×C4—681no—
533C2×C4—681no—
534C2×C4—681no—
535C2×C4—681no—
536C2×C4—681no—
537C2×C4—681no—
538C2×C4—681no—
539C2×C4—681no—
540C2×C4—1364no—
541C2×C4C2×C4⋊Dic1712yes—
542C2×C4C2×C4⋊Dic1712yes—
543C2×C4C2×C4⋊Dic1712yes—
544C2×C4C2×C4⋊Dic1712yes—
545C2×C4C2×C4⋊Dic1712yes—
546C2×C4C22×Dic3411yescharacteristic
547C2×C4#1058769611yescharacteristic
548C2×C4#1058769611yescharacteristic
549C2×C4#1058769711yescharacteristic
550C2×C4#1058769711yescharacteristic
551C2×C4C23×Dic1711yescharacteristic
552C8—22no—
553C8—22no—
554C8—22no—
555C8—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C22×C4⋊Dic1711yescharacteristic
564C22#1176337811yescharacteristic
565C22#1176338511yescharacteristic
566C22#1176361411yescharacteristic
567C22#1176362111yescharacteristic
568C22#1176362111yescharacteristic
569C22#1176362611yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—1361no—
576C4—1361no—
577C4—1361no—
578C4—1361no—
579C4—1361no—
580C4—1361no—
581C4—1361no—
582C4—1361no—
583C4#1176329211yescharacteristic
584C4#1176329211yescharacteristic
585C4#1176343711yescharacteristic
586C4#1176343711yescharacteristic
587C2—42no—
588C2#1453140711yescharacteristic
589C2#1453737911yescharacteristic
590C2#1453738411yescharacteristic
591C2#1453988011yescharacteristic
592C2#1453989511yescharacteristic
593C2#1454003911yescharacteristic
594C2#1454005411yescharacteristic
subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#433C2
socleC23×C17C22×D4
prime radicalC24×C17C2×D4
cosocleC22×C4×C17C24
hypercenterC2×#433D17
hypocenterC17#21992
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #14529554C2semidirect
4. #14529554C2semidirect
5. #14529548C2semidirect
6. #14529543C2semidirect
11. #14528952C2semidirect
12. #14528948C2semidirect
13. #14528918C2semidirect
14. #14528912C2semidirect
53. C17×#433C4semidirect
99. C17×C4⋊C8C2×C4semidirect
100. C17×C4⋊C8C2×C4semidirect
103. C17×#97C2×C4semidirect
104. C4×C8×C17C2×C4semidirect
308. #433Dic17semidirect
404. C4⋊C8C2×Dic17semidirect
405. C4⋊C8C2×Dic17semidirect
408. #97C2×Dic17semidirect
409. C4×C8C2×Dic17semidirect
420. C17#21992semidirect

Maximal subgroups

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

subgroupindex
#145314072
#145313932
#145295542
#145295482
#145295432
#145289852
#145289792
#145289742
#145289522
#145289482
#145289182
#145289122
C2×C17×#4332
#2199217