Finite Group Databasebeta

← #17046339

Subgroups — #17046339

Order 4352.

786 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762940C211yesmaximal, characteristic, complemented
2C2×#11762864C211yesmaximal, characteristic
3C4×#10587632C211yesmaximal, characteristic
4#14529507C211yesmaximal, characteristic, complemented
5#14529506C211yesmaximal, characteristic, complemented
6#14529501C211yesmaximal, characteristic, complemented
7#14529398C211yesmaximal, characteristic
8#14529395C211yesmaximal, characteristic
9#14529391C211yesmaximal, characteristic
10#14529388C211yesmaximal, characteristic
11#14529346C211yesmaximal, characteristic, complemented
12#14529339C211yesmaximal, characteristic, complemented
13#14528761C211yesmaximal, characteristic
14#14528661C211yesmaximal, characteristic, complemented
15C17×#1985C211yesmaximal, characteristic, complemented
16C2×#10587632C411yescharacteristic
17C2×C42×D17C2211yescharacteristic
18#11762940—24no—
19#11762864—24no—
20C2×C4⋊#3622C2211yescharacteristic
21C2×C4⋊#3622C2211yescharacteristic
22C2×C4⋊#3622C2211yescharacteristic
23C2×#10587485C2211yescharacteristic
24C2×#10587485C2211yescharacteristic
25C2×#10587485C2211yescharacteristic
26C2×#10587485C2211yescharacteristic
27C2×#10587491C2211yescharacteristic
28C2×#10587491C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587474C2211yescharacteristic
32C2×#10587474C2211yescharacteristic
33C2×#10587486C2211yescharacteristic
34C2×C4×#3622C2211yescharacteristic
35C2×C8×Dic17C2211yescharacteristic
36#11762716C411yescharacteristic
37#11762705C411yescharacteristic
38#11762690C411yescharacteristic
39#11762690C411yescharacteristic
40#11762680C411yescharacteristic
41#11762680C411yescharacteristic
42#11762666C411yescharacteristic
43C4×#63225C2211yescharacteristic
44C4×#63225C2211yescharacteristic
45C4×C4⋊Dic17C2211yescharacteristic
46C4×#63227C2211yescharacteristic
47C4×#63227C2211yescharacteristic
48#11762563C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53#11762563C2211yescharacteristic
54C2×C4×Q8×C17C2211yescharacteristic
55C2×C17×C4⋊C8C2211yescharacteristic
56C2×C17×#97C2211yescharacteristic
57C17×#336C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C17×#336C2211yescharacteristic
60C17×#336C2211yescharacteristic
61C22×Q8×C17C2×C411yescharacteristic
62C22×C4×D17C2×C411yescharacteristic
63C22×C4×D17C2×C411yescharacteristic
64C22×C4×D17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C22×C8×C17C2311yescharacteristic
69C4×Q8×C17—22no—
70C4×Q8×C17—22no—
71C2×C4⋊C4×C17C2×C411yescharacteristic
72C2×C4⋊C4×C17C2×C411yescharacteristic
73C2×C4⋊C4×C17C2×C411yescharacteristic
74C2×C42×C17C2311yescharacteristic
75C2×C42×C17C2311yescharacteristic
76C2×C42×C17C2311yescharacteristic
77#10587632—24no—
78C2×#63227C2×C411yescharacteristic
79C2×#63227C2×C411yescharacteristic
80C2×#63227C2×C411yescharacteristic
81C2×#63227C2×C411yescharacteristic
82C2×C4⋊Dic17C2×C411yescharacteristic
83C2×C4⋊Dic17C2×C411yescharacteristic
84C2×#63225C2×C411yescharacteristic
85C2×#63225C2×C411yescharacteristic
86C2×#63225C2×C411yescharacteristic
87C2×#63225C2×C411yescharacteristic
88C2×C4×Dic17C2×C411yescharacteristic
89C2×C4×Dic17C2×C411yescharacteristic
90C2×C4×Dic17C2311yescharacteristic
91C2×C4×Dic17C2311yescharacteristic
92C2×C4×Dic17C2311yescharacteristic
93C22×#3622C2311yescharacteristic
94C22×#3622C2311yescharacteristic
95C22×#3622C2311yescharacteristic
96C22×#3622C2311yescharacteristic
97C42×D17—22no—
98C42×D17—22no—
99C17×C4⋊C8—22no—
100C17×#97—22no—
101#10587502C2×C411yescharacteristic
102#10587502C2×C411yescharacteristic
103#10587502C2×C411yescharacteristic
104#10587502C2×C411yescharacteristic
105#10587502C2×C411yescharacteristic
106#10587502C2×C411yescharacteristic
107#10587502C2×C411yescharacteristic
108#10587502C2×C411yescharacteristic
109#10587502C2×C411yescharacteristic
110#10587502C2×C411yescharacteristic
111#10587491—22no—
112#10587491—22no—
113#10587491—41no—
114#10587491—41no—
115#10587486—41no—
116#10587485—22no—
117#10587485—22no—
118#10587485—41no—
119#10587485—41no—
120C8×Dic17—41no—
121C4⋊#3622—22no—
122C4⋊#3622—22no—
123C4⋊#3622—22no—
124#10587474—22no—
125#10587474D414yes—
126C4×#3622—22no—
127C23×D17C22×C411yescharacteristic
128C2×Q8×C17—22no—
129C2×Q8×C17—22no—
130C2×Q8×C17—41no—
131C22×C4×C17C22×C411yescharacteristic
132C22×C4×C17C22×C411yescharacteristic
133C22×C4×C17C22×C411yescharacteristic
134C22×C4×C17C22×C411yescharacteristic
135C22×C4×C17C22×C411yescharacteristic
136C22×C4×C17C22×C411yescharacteristic
137C22×C4×C17C2411yescharacteristic
138C22×Dic17C22×C411yescharacteristic
139C22×Dic17C22×C411yescharacteristic
140C22×Dic17C22×C411yescharacteristic
141C22×Dic17C22×C411yescharacteristic
142C22×Dic17C22×C411yescharacteristic
143C22×Dic17C22×C411yescharacteristic
144C22×Dic17C22×C411yescharacteristic
145C2×C4×D17—22no—
146C2×C4×D17—22no—
147C2×C4×D17—22no—
148C2×C4×D17—21no—
149C2×C4×D17—21no—
150C2×C4×D17—21no—
151C2×C4×D17—21no—
152C2×C4×D17—21no—
153C2×C4×D17—21no—
154C2×C4×D17—22no—
155C2×C4×D17—41no—
156C2×C4×D17—41no—
157C2×C8×C17—21no—
158C2×C8×C17—21no—
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C2×C8×C17—21no—
169C4⋊C4×C17—22no—
170C4⋊C4×C17—22no—
171C4⋊C4×C17—22no—
172C42×C17—21no—
173C42×C17—21no—
174C42×C17—21no—
175C42×C17—21no—
176C42×C17C2×D412yes—
177C42×C17#4112yes—
178#63227—22no—
179#63227—41no—
180#63227—41no—
181#63227M1614yes—
182C4⋊Dic17—22no—
183C4⋊Dic17—41no—
184#63225—22no—
185#63225—22no—
186#63225—22no—
187#63225—22no—
188C4×Dic17—22no—
189C4×Dic17—22no—
190C4×Dic17—21no—
191C4×Dic17—21no—
192C4×Dic17—21no—
193C4×Dic17—21no—
194C4×Dic17—21no—
195C4×Dic17—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×#3622C2×D412yes—
207C2×#3622C2×D412yes—
208#22108—171nomaximal, Sylow
209C23×C17C23×C411yescharacteristic
210C22×D17—21no—
211C22×D17—21no—
212C22×D17—21no—
213C22×D17—21no—
214C22×D17—21no—
215C22×D17—21no—
216C22×D17C2×M1612yes—
217Q8×C17—44no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17C4×D412yes—
234C2×C4×C17C4×D412yes—
235C2×C4×C17C2×M1612yes—
236C2×C4×C17C22×D411yescharacteristic
237C2×C4×C17C2×#4111yescharacteristic
238C2×C4×C17H(5,𝔽2)11yescharacteristic
239C2×C4×C172−1+411yescharacteristic
240C2×C4×C172−1+411yescharacteristic
241C2×C4×C172−1+411yescharacteristic
242C2×Dic17—21no—
243C2×Dic17—21no—
244C2×Dic17—21no—
245C2×Dic17—21no—
246C2×Dic17—21no—
247C2×Dic17—21no—
248C2×Dic17—21no—
249C2×Dic17—21no—
250C2×Dic17—21no—
251C2×Dic17—21no—
252C2×Dic17—21no—
253C2×Dic17—21no—
254C2×Dic17—21no—
255C2×Dic17—21no—
256C2×Dic17—21no—
257C2×Dic17—21no—
258C2×Dic17—21no—
259C2×Dic17—21no—
260C2×Dic17—21no—
261C2×Dic17C2×M1612yes—
262C2×Dic17#13112yes—
263C4×D17—44no—
264C4×D17—44no—
265C4×D17—41no—
266C4×D17—41no—
267C4×D17—41no—
268C4×D17—41no—
269C8×C17—41no—
270C8×C17—41no—
271C8×C17—41no—
272C8×C17—41no—
273#3622—22no—
274#3622—22no—
275#3622—41no—
276#3622—41no—
277C2×#446—171no—
278C2×#432—171no—
279C4×C22⋊Q8—171no—
280#1985D1711yescharacteristic, complemented
281#1940—171no—
282#1940—171no—
283#1939—171no—
284#1924—171no—
285#1924—171no—
286#1923—171no—
287#1923—171no—
288#1917—171no—
289#1916—171no—
290#1797—171no—
291#1771—171no—
292C22×C17C2×C4×D411yescharacteristic
293C22×C17#51911yescharacteristic
294C22×C17#52011yescharacteristic
295C22×C17C22×M1611yescharacteristic
296C22×C17C2×#13111yescharacteristic
297C22×C17#56811yescharacteristic
298C22×C17#56811yescharacteristic
299C2×D17—22no—
300C2×D17—22no—
301C2×D17—22no—
302C2×D17—41no—
303C2×D17—41no—
304C2×D17—41no—
305C2×D17—41no—
306C4×C17—22no—
307C4×C17—22no—
308C4×C17—22no—
309C4×C17—41no—
310C4×C17—41no—
311C4×C17—41no—
312C4×C17#53611yescharacteristic
313C4×C17#53711yescharacteristic
314C4×C17#54111yescharacteristic
315C4×C17#54211yescharacteristic
316Dic17—22no—
317Dic17—22no—
318Dic17—41no—
319Dic17—41no—
320Dic17—41no—
321Dic17—41no—
322Dic17—41no—
323C2×C22⋊Q8—171no—
324C2×C4×Q8C2×D1711yescharacteristic
325C22×C42—171no—
326#446—344no—
327#432—344no—
328C2×C4⋊C8—171no—
329C2×C4⋊C8—171no—
330C2×C4⋊C8—171no—
331C2×C4⋊C8—171no—
332C2×C4⋊C8—171no—
333C2×C4⋊C8—171no—
334C2×C4⋊C8—171no—
335C2×C4⋊C8C2×D1711yescharacteristic
336C2×C22⋊C8—171no—
337C2×C22⋊C8—171no—
338C2×C22⋊C8—171no—
339C2×C22⋊C8—171no—
340C2×#97—171no—
341C2×#97—171no—
342C2×#97—171no—
343C2×#97C2×D1711yescharacteristic
344C2×C4×C8—171no—
345C2×C4×C8—171no—
346#391—171no—
347#389—171no—
348#387—171no—
349#387—171no—
350#385—171no—
351#385—171no—
352#380—171no—
353C4×C4⋊C4—171no—
354C4×C4⋊C4—171no—
355C4×C4⋊C4—171no—
356C4×C22⋊C4—171no—
357C4×C22⋊C4—171no—
358#336—171no—
359#336—171no—
360#336—171no—
361#336—171no—
362#336—171no—
363#336—171no—
364#336C2×D1711yescharacteristic
365#336C2×D1711yescharacteristic
366#336C2×D1711yescharacteristic
367#336C2×D1711yescharacteristic
368C2×C17#232311yescharacteristic
369C2×C17#293311yescharacteristic
370C2×C17D4×M1611yescharacteristic
371C2×C17#298311yescharacteristic
372C2×C17#298511yescharacteristic
373C2×C17#299011yescharacteristic
374C2×C17#299511yescharacteristic
375D17—42no—
376C22×Q8C4×D1711yescharacteristic
377C23×C4—171no—
378C23×C4—171no—
379C23×C4—171no—
380C22×C8—171no—
381C22×C8—171no—
382C22×C8—171no—
383C22×C8—171no—
384C22×C8C22×D1711yescharacteristic
385C22×C8C22×D1711yescharacteristic
386C22×C8C22×D1711yescharacteristic
387C22×C8C22×D1711yescharacteristic
388C22⋊Q8—344no—
389C4×Q8—22no—
390C4×Q8—22no—
391C2×C4⋊C4—171no—
392C2×C4⋊C4—171no—
393C2×C4⋊C4—171no—
394C2×C4⋊C4—171no—
395C2×C4⋊C4—171no—
396C2×C4⋊C4—171no—
397C2×C4⋊C4C4×D1711yescharacteristic
398C2×C4⋊C4C4×D1711yescharacteristic
399C2×C4⋊C4C4×D1711yescharacteristic
400C2×C22⋊C4—171no—
401C2×C22⋊C4—171no—
402C2×C22⋊C4—171no—
403C2×C22⋊C4—171no—
404C2×C42—171no—
405C2×C42—171no—
406C2×C42—171no—
407C2×C42—171no—
408C2×C42—171no—
409C2×C42—342no—
410C2×C42—342no—
411C2×C42C22×D1711yescharacteristic
412C2×C42C22×D1711yescharacteristic
413C2×C42C22×D1711yescharacteristic
414C4⋊C8—22no—
415C4⋊C8—342no—
416C4⋊C8—342no—
417C4⋊C8—342no—
418C4⋊C8—342no—
419C4⋊C8—342no—
420C4⋊C8—681no—
421C4⋊C8—681no—
422C22⋊C8—342no—
423C22⋊C8—342no—
424C22⋊C8—681no—
425C22⋊C8—681no—
426#97—22no—
427#97—174no—
428#97—342no—
429#97—681no—
430C4×C8—342no—
431C4×C8—681no—
432#95—171no—
433#95—171no—
434#95—171no—
435#95—171no—
436#95—171no—
437#95—171no—
438#95—171no—
439#95—171no—
440#95—171no—
441#95—171no—
442C17#2210811yescharacteristic, complemented, Sylow
443C24—171no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—41no—
447C22×C4—171no—
448C22×C4—171no—
449C22×C4—171no—
450C22×C4—171no—
451C22×C4—171no—
452C22×C4—171no—
453C22×C4—171no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—341no—
457C22×C4—341no—
458C22×C4—341no—
459C22×C4—341no—
460C22×C4—341no—
461C22×C4—341no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—681no—
465C22×C4—681no—
466C22×C4C2×C4×D1711yescharacteristic
467C22×C4C2×C4×D1711yescharacteristic
468C22×C4C2×C4×D1711yescharacteristic
469C22×C4C2×C4×D1711yescharacteristic
470C22×C4C2×C4×D1711yescharacteristic
471C22×C4C2×C4×D1711yescharacteristic
472C22×C4C23×D1711yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—172no—
486C2×C8—172no—
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—
496C2×C8—341no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—342no—
501C4⋊C4—342no—
502C4⋊C4—342no—
503C4⋊C4—342no—
504C4⋊C4—342no—
505C4⋊C4—681no—
506C22⋊C4—174no—
507C22⋊C4—342no—
508C22⋊C4—681no—
509C22⋊C4—681no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—341no—
515C42—341no—
516C42—341no—
517C42—341no—
518C42—341no—
519C42—341no—
520C42—342no—
521C42—342no—
522C42D4×D1712yes—
523C42#6325412yes—
524C23—172no—
525C23—341no—
526C23—341no—
527C23—341no—
528C23—341no—
529C23—341no—
530C23—341no—
531C23C22×C4×D1711yescharacteristic
532Q8—44no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—172no—
549C2×C4—172no—
550C2×C4—341no—
551C2×C4—341no—
552C2×C4—341no—
553C2×C4—341no—
554C2×C4—341no—
555C2×C4—341no—
556C2×C4—341no—
557C2×C4—341no—
558C2×C4—341no—
559C2×C4—341no—
560C2×C4—341no—
561C2×C4—341no—
562C2×C4—341no—
563C2×C4—341no—
564C2×C4—341no—
565C2×C4—341no—
566C2×C4—341no—
567C2×C4—341no—
568C2×C4—341no—
569C2×C4—684no—
570C2×C4—684no—
571C2×C4—681no—
572C2×C4—681no—
573C2×C4—681no—
574C2×C4—681no—
575C2×C4#1058756712yes—
576C2×C4#1058756712yes—
577C2×C4M16×D1712yes—
578C2×C4C2×D4×D1711yescharacteristic
579C2×C4C2×#6325411yescharacteristic
580C2×C4#1058769411yescharacteristic
581C2×C4#1058769411yescharacteristic
582C2×C4#1058769611yescharacteristic
583C2×C4#1058769711yescharacteristic
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—342no—
589C8—342no—
590C8—681no—
591C8—681no—
592C22—342no—
593C22—342no—
594C22—342no—
595C22—681no—
596C22—681no—
597C22—681no—
598C22—681no—
599C22C2×#1058756711yescharacteristic
600C22#1176328511yescharacteristic
601C22#1176329111yescharacteristic
602C22C2×M16×D1711yescharacteristic
603C22#131×D1711yescharacteristic
604C22#1176357411yescharacteristic
605C22#1176357511yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—342no—
613C4—342no—
614C4—681no—
615C4—681no—
616C4—681no—
617C4—681no—
618C4—681no—
619C4#1176338211yescharacteristic
620C4#1176338911yescharacteristic
621C4#1176342011yescharacteristic
622C4#1176342811yescharacteristic
623C2—682no—
624C2#1453146911yescharacteristic
625C2#1453751411yescharacteristic
626C2#1453751611yescharacteristic
627C2#1453786611yescharacteristic
628C2#1453787711yescharacteristic
629C2#1453790811yescharacteristic
630C2#1453795311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1985C2
prime radicalC23×D17C22×C4
cosocleC22×C4×C17C24
hypercenter#1985D17
hypocenterC17#22108
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
1. C2×#11762940C2semidirect
4. #14529507C2semidirect
5. #14529506C2semidirect
6. #14529501C2semidirect
11. #14529346C2semidirect
12. #14529339C2semidirect
14. #14528661C2semidirect
15. C17×#1985C2semidirect
280. #1985D17semidirect
442. C17#22108semidirect

Maximal subgroups

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

subgroupindex
C2×#117629402
C2×#117628642
C4×#105876322
#145295072
#145295062
#145295012
#145293982
#145293952
#145293912
#145293882
#145293462
#145293392
#145287612
#145286612
C17×#19852
#2210817