Finite Group Databasebeta

← #17043882

Subgroups — #17043882

Order 4352.

970 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763436C211yesmaximal, characteristic
2C2×#11762869C211yesmaximal, characteristic
3#14531389C211yesmaximal, characteristic
4#14529755C211yesmaximal, characteristic, complemented
5#14529751C211yesmaximal, characteristic, complemented
6#14529747C211yesmaximal, characteristic, complemented
7#14529743C211yesmaximal, characteristic, complemented
8#14529741C211yesmaximal, characteristic, complemented
9#14529739C211yesmaximal, characteristic, complemented
10#14529733C211yesmaximal, characteristic, complemented
11#14528878C211yesmaximal, characteristic
12#14528877C211yesmaximal, characteristic
13#14528873C211yesmaximal, characteristic
14#14528869C211yesmaximal, characteristic
15C17×#1988C211yesmaximal, characteristic, complemented
16#11763436—24no—
17#11763436C418yescomplemented
18C2×#10587574C2211yescharacteristic
19C2×#10587630—21no—
20C2×#10587556C2211yescharacteristic
21C2×#10587576C2211yescharacteristic
22C2×#10587575—21no—
23C2×#10587582—21no—
24C2×#10587632—21no—
25C2×#10587578C2211yescharacteristic
26C2×#10587558C2211yescharacteristic
27C2×C4⋊C4×D17C2211yescharacteristic
28#11762869—24no—
29C2×C4⋊#3622C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587486C2211yescharacteristic
33C2×C8×Dic17C2211yescharacteristic
34#11762700—21no—
35#11762698—21no—
36#11762693—21no—
37#11762691—21no—
38#11762678C2211yescharacteristic
39#11762674C2211yescharacteristic
40#11762666C2211yescharacteristic
41#11762666C2211yescharacteristic
42C4×C4⋊Dic17C2211yescharacteristic
43#11762572C2211yescharacteristic
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53#11762571C2211yescharacteristic
54#11762571C2211yescharacteristic
55C2×C17×C4⋊Q8C2211yescharacteristic
56C2×C17×C4⋊C8C2211yescharacteristic
57C4×C4⋊C4×C17C2211yescharacteristic
58C17×#340C2211yescharacteristic
59C17×#340C2211yescharacteristic
60C17×#340C2211yescharacteristic
61C17×#340C2211yescharacteristic
62C22×Q8×C17—21no—
63C22×C4×D17—21no—
64C22×C4×D17C2311yescharacteristic
65C22×Dic34—21no—
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C17×C4⋊Q8—22no—
69C17×C4⋊Q8C2×C414yes—
70C2×C4⋊C4×C17—21no—
71C2×C4⋊C4×C17C2311yescharacteristic
72C2×C4⋊C4×C17C2311yescharacteristic
73C2×C4⋊C4×C17C2311yescharacteristic
74C2×C4⋊C4×C17C2311yescharacteristic
75C2×C42×C17—21no—
76C2×C42×C17C2311yescharacteristic
77#10587632—28no—
78#10587630—28no—
79C2×#63227—21no—
80C2×#63227—21no—
81C2×#63227—21no—
82C2×#63227D411yescharacteristic
83C2×#63227D411yescharacteristic
84C2×C4⋊Dic17—21no—
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×C4⋊Dic17C2311yescharacteristic
88C2×C4⋊Dic17C2311yescharacteristic
89C2×#63225—21no—
90C2×#63225—21no—
91C2×#63225—21no—
92C2×#63225—21no—
93C2×#63225—21no—
94C2×#63225—21no—
95C2×#63225—21no—
96C2×#63225D411yescharacteristic
97C2×#63225D411yescharacteristic
98C2×C4×Dic17—21no—
99C2×C4×Dic17—21no—
100C2×C4×Dic17C2311yescharacteristic
101C22×#3622C2311yescharacteristic
102C22×#3622C2311yescharacteristic
103#10587582—28no—
104#10587578—22no—
105#10587578C2×C414yes—
106C4⋊C4×D17—22no—
107C4⋊C4×D17C2×C414yes—
108#10587576—22no—
109#10587576C2×C414yes—
110#10587575—28no—
111#10587574—22no—
112#10587574C2×C414yes—
113#10587558C2×C414yes—
114#10587558D414yes—
115#10587556—22no—
116#10587556C2×C414yes—
117C17×C4⋊C8—22no—
118C17×#95—21no—
119#10587502—21no—
120#10587502—21no—
121#10587502—21no—
122#10587502—21no—
123#10587502—21no—
124#10587491—22no—
125#10587491—22no—
126#10587486—22no—
127C8×Dic17—22no—
128C4⋊#3622—22no—
129C23×D17C2×D411yescharacteristic
130C2×Q8×C17—24no—
131C2×Q8×C17—81no—
132C2×Q8×C17—81no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2×D411yescharacteristic
139C22×C4×C17C2411yescharacteristic
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17C2×D411yescharacteristic
145C22×Dic17C2×D411yescharacteristic
146C22×Dic17C2×D411yescharacteristic
147C2×C4×D17—21no—
148C2×C4×D17—21no—
149C2×C4×D17—21no—
150C2×C4×D17—21no—
151C2×C4×D17—24no—
152C2×C4×D17—81no—
153C2×C4×D17—81no—
154C2×C4×D17C22×C412yes—
155C2×C4×D17C2×D412yes—
156C2×Dic34—24no—
157C2×Dic34—81no—
158C2×Dic34—81no—
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17—21no—
165C4⋊C4×C17—24no—
166C4⋊C4×C17—21no—
167C4⋊C4×C17—21no—
168C4⋊C4×C17—21no—
169C4⋊C4×C17—21no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17—21no—
172C4⋊C4×C17C22×C412yes—
173C4⋊C4×C17C22×C412yes—
174C42×C17—81no—
175C42×C17C22×C412yes—
176C42×C17C2×D412yes—
177#63227—24no—
178#63227—81no—
179#63227—81no—
180#63227C22⋊C414yes—
181#63227C22⋊C414yes—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4⋊Dic17—24no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17—21no—
188C4⋊Dic17—21no—
189C4⋊Dic17C22×C412yes—
190C4⋊Dic17C22×C412yes—
191#63225—24no—
192#63225—24no—
193#63225—24no—
194#63225—24no—
195#63225—24no—
196#63225—81no—
197#63225—81no—
198#63225C22⋊C414yes—
199#63225C22⋊C414yes—
200C4×Dic17—24no—
201C4×Dic17—81no—
202C4×Dic17C22×C412yes—
203C4×Dic17C2×D412yes—
204C2×#3622—21no—
205C2×#3622—21no—
206C2×#3622—21no—
207C2×#3622—21no—
208C2×#3622—21no—
209C2×#3622—21no—
210#21843—171nomaximal, Sylow
211C23×C17C22×D411yescharacteristic
212C22×D17—21no—
213C22×D17—21no—
214C22×D17—21no—
215C22×D17—21no—
216C22×D17—21no—
217C22×D17—21no—
218C22×D17C2×C22⋊C412yes—
219Q8×C17—84no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—22no—
225C2×C4×C17—22no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
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×C17C2×C22⋊C412yes—
237C2×C4×C17C2×C22⋊C412yes—
238C2×C4×C17C23×C411yescharacteristic
239C2×C4×C17C22×D411yescharacteristic
240C2×C4×C172−1+411yescharacteristic
241C2×C4×C172−1+411yescharacteristic
242C2×C4×C172−1+411yescharacteristic
243C2×C4×C172−1+411yescharacteristic
244C2×Dic17—21no—
245C2×Dic17—21no—
246C2×Dic17—21no—
247C2×Dic17—21no—
248C2×Dic17—21no—
249C2×Dic17—21no—
250C2×Dic17—22no—
251C2×Dic17—22no—
252C2×Dic17—41no—
253C2×Dic17—41no—
254C2×Dic17—41no—
255C2×Dic17—41no—
256C2×Dic17—41no—
257C2×Dic17—41no—
258C2×Dic17—41no—
259C2×Dic17—41no—
260C2×Dic17—41no—
261C2×Dic17—41no—
262C2×Dic17C2×C22⋊C412yes—
263C2×Dic17C2×C22⋊C412yes—
264C2×Dic17C2×C22⋊C412yes—
265C4×D17—22no—
266C4×D17—22no—
267C4×D17—22no—
268C4×D17—22no—
269C4×D17—84no—
270Dic34—84no—
271C8×C17—41no—
272C8×C17—41no—
273#3622—41no—
274#3622—41no—
275C2×#544—171no—
276C2×#433—171no—
277#2314—171no—
278#1993—171no—
279#1992—171no—
280#1991—171no—
281#1990—171no—
282#1989—171no—
283#1989—171no—
284#1988D1711yescharacteristic, complemented
285#1987—171no—
286#1825—171no—
287#1825—171no—
288#1824—171no—
289#1823—171no—
290C22×C17C22×C22⋊C411yescharacteristic
291C22×C17#53611yescharacteristic
292C22×C17#53611yescharacteristic
293C22×C17#57611yescharacteristic
294C22×C17#57711yescharacteristic
295C22×C17#57711yescharacteristic
296C22×C17#57811yescharacteristic
297C2×D17—22no—
298C2×D17—22no—
299C2×D17—22no—
300C2×D17—41no—
301C2×D17—41no—
302C2×D17—41no—
303C2×D17—41no—
304C4×C17—22no—
305C4×C17—22no—
306C4×C17—42no—
307C4×C17—42no—
308C4×C17—81no—
309C4×C17—81no—
310C4×C17#51911yescharacteristic
311C4×C17#51911yescharacteristic
312C4×C17#53611yescharacteristic
313C4×C17#53611yescharacteristic
314Dic17—22no—
315Dic17—22no—
316Dic17—22no—
317Dic17—42no—
318Dic17—42no—
319Dic17—81no—
320Dic17—81no—
321#544—178no—
322#544—344no—
323C2×C4⋊Q8—171no—
324C2×C4⋊Q8—341no—
325C2×C4⋊Q8C2×D1711yescharacteristic
326C2×#125—171no—
327C2×#125—171no—
328C2×#125—341no—
329C2×C22⋊Q8—341no—
330C2×C22⋊Q8—341no—
331C2×#117—171no—
332C2×#117—171no—
333C22×C4⋊C4—171no—
334#433—344no—
335C2×C4⋊C8—171no—
336C2×C4⋊C8C2×D1711yescharacteristic
337C2×C22⋊C8—171no—
338C2×C22⋊C8—171no—
339C2×#97—171no—
340C2×C4×C8—171no—
341#388—341no—
342#388—341no—
343#387—341no—
344#387—341no—
345#384—171no—
346#382—171no—
347#380—171no—
348#380—171no—
349C4×C4⋊C4—171no—
350C4×C4⋊C4C2×D1711yescharacteristic
351#340—171no—
352#340—171no—
353#340—171no—
354#340—171no—
355#340—171no—
356#340—171no—
357#340—171no—
358#340—171no—
359#340—171no—
360#340—171no—
361#340—171no—
362#340—171no—
363#340C2×D1711yescharacteristic
364#340C2×D1711yescharacteristic
365#340C2×D1711yescharacteristic
366#340C2×D1711yescharacteristic
367C2×C17#231011yescharacteristic
368C2×C17#289711yescharacteristic
369C2×C17#289811yescharacteristic
370C2×C17#324111yescharacteristic
371C2×C17#324211yescharacteristic
372C2×C17#324311yescharacteristic
373C2×C17#324411yescharacteristic
374D17—42no—
375C22×Q8—21no—
376C22×Q8—341no—
377C23×C4—171no—
378C23×C4—341no—
379C22×C8—171no—
380C22×C8—171no—
381C22×C8C22×D1711yescharacteristic
382C22×C8C22×D1711yescharacteristic
383C4⋊Q8—22no—
384C4⋊Q8—174no—
385C4⋊Q8—342no—
386C4⋊Q8—348no—
387C4⋊Q8C4×D1714yes—
388#125—174no—
389#125—174no—
390#125—342no—
391#125—348no—
392#125—342no—
393C22⋊Q8—348no—
394C22⋊Q8—348no—
395#117—174no—
396#117—174no—
397#117—174no—
398#117—342no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—171no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4—171no—
403C2×C4⋊C4—171no—
404C2×C4⋊C4—174no—
405C2×C4⋊C4—171no—
406C2×C4⋊C4—171no—
407C2×C4⋊C4—342no—
408C2×C4⋊C4—341no—
409C2×C4⋊C4—341no—
410C2×C4⋊C4—341no—
411C2×C4⋊C4—341no—
412C2×C4⋊C4—341no—
413C2×C4⋊C4—341no—
414C2×C4⋊C4—341no—
415C2×C4⋊C4—341no—
416C2×C4⋊C4C22×D1711yescharacteristic
417C2×C4⋊C4C22×D1711yescharacteristic
418C2×C4⋊C4C22×D1711yescharacteristic
419C2×C4⋊C4C22×D1711yescharacteristic
420C2×C22⋊C4—171no—
421C2×C22⋊C4—171no—
422C2×C22⋊C4—341no—
423C2×C22⋊C4—341no—
424C2×C22⋊C4—341no—
425C2×C42—21no—
426C2×C42—171no—
427C2×C42—341no—
428C2×C42—341no—
429C2×C42C22×D1711yescharacteristic
430C4⋊C8—22no—
431C4⋊C8—342no—
432C22⋊C8—342no—
433C22⋊C8—342no—
434#97—342no—
435C4×C8—342no—
436#95—21no—
437#95—341no—
438#95—341no—
439#95—341no—
440#95—341no—
441#95—341no—
442C17#2184311yescharacteristic, complemented, Sylow
443C24—171no—
444C2×Q8—24no—
445C2×Q8—81no—
446C2×Q8—81no—
447C2×Q8—344no—
448C2×Q8—1361no—
449C2×Q8—1361no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—171no—
455C22×C4—171no—
456C22×C4—171no—
457C22×C4—172no—
458C22×C4—172no—
459C22×C4—344no—
460C22×C4—341no—
461C22×C4—341no—
462C22×C4—341no—
463C22×C4—341no—
464C22×C4—341no—
465C22×C4—341no—
466C22×C4—341no—
467C22×C4—341no—
468C22×C4—1361no—
469C22×C4—1361no—
470C22×C4D4×D1711yescharacteristic
471C22×C4D4×D1711yescharacteristic
472C22×C4C23×D1711yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—341no—
480C2×C8—341no—
481C2×C8—341no—
482C2×C8—341no—
483C2×C8—341no—
484C2×C8—341no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—174no—
493C4⋊C4—174no—
494C4⋊C4—172no—
495C4⋊C4—172no—
496C4⋊C4—344no—
497C4⋊C4—344no—
498C4⋊C4—344no—
499C4⋊C4—344no—
500C4⋊C4—341no—
501C4⋊C4—341no—
502C4⋊C4—344no—
503C4⋊C4—344no—
504C4⋊C4—341no—
505C4⋊C4—341no—
506C4⋊C4—341no—
507C4⋊C4—341no—
508C4⋊C4—1361no—
509C4⋊C4—1361no—
510C4⋊C4C2×C4×D1712yes—
511C4⋊C4C2×C4×D1712yes—
512C22⋊C4—174no—
513C22⋊C4—174no—
514C22⋊C4—344no—
515C22⋊C4—1361no—
516C22⋊C4—1361no—
517C42—81no—
518C42—172no—
519C42—172no—
520C42—344no—
521C42—1361no—
522C42C2×C4×D1712yes—
523C42D4×D1712yes—
524C23—172no—
525C23—341no—
526C23—341no—
527C23—341no—
528C23—341no—
529C23—341no—
530C23—341no—
531C23C2×D4×D1711yescharacteristic
532Q8—84no—
533Q8—1364no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—172no—
551C2×C4—172no—
552C2×C4—172no—
553C2×C4—341no—
554C2×C4—341no—
555C2×C4—341no—
556C2×C4—341no—
557C2×C4—341no—
558C2×C4—341no—
559C2×C4—342no—
560C2×C4—342no—
561C2×C4—342no—
562C2×C4—342no—
563C2×C4—342no—
564C2×C4—342no—
565C2×C4—681no—
566C2×C4—681no—
567C2×C4—681no—
568C2×C4—681no—
569C2×C4—681no—
570C2×C4—681no—
571C2×C4—681no—
572C2×C4—681no—
573C2×C4—681no—
574C2×C4—681no—
575C2×C4—1364no—
576C2×C4C22⋊C4×D1712yes—
577C2×C4C22⋊C4×D1712yes—
578C2×C4C22×C4×D1711yescharacteristic
579C2×C4C2×D4×D1711yescharacteristic
580C2×C4#1058769411yescharacteristic
581C2×C4#1058769411yescharacteristic
582C2×C4#1058769711yescharacteristic
583C2×C4#1058769711yescharacteristic
584C8—41no—
585C8—41no—
586C8—681no—
587C8—681no—
588C22—342no—
589C22—342no—
590C22—342no—
591C22—681no—
592C22—681no—
593C22—681no—
594C22—681no—
595C22C2×C22⋊C4×D1711yescharacteristic
596C22#1176338211yescharacteristic
597C22#1176338211yescharacteristic
598C22#1176361011yescharacteristic
599C22#1176361511yescharacteristic
600C22#1176361811yescharacteristic
601C22#1176362511yescharacteristic
602C4—22no—
603C4—22no—
604C4—42no—
605C4—42no—
606C4—81no—
607C4—81no—
608C4—342no—
609C4—342no—
610C4—342no—
611C4—682no—
612C4—682no—
613C4—1361no—
614C4—1361no—
615C4#1176328511yescharacteristic
616C4#1176328511yescharacteristic
617C4#1176337911yescharacteristic
618C4#1176338411yescharacteristic
619C2—682no—
620C2#1453136711yescharacteristic
621C2#1453730511yescharacteristic
622C2#1453731611yescharacteristic
623C2#1454004411yescharacteristic
624C2#1454005911yescharacteristic
625C2#1454006411yescharacteristic
626C2#1454008711yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1988C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
cosocleC22×C4×C17C24
hypercenter#1988D17
hypocenterC17#21843
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
4. #14529755C2semidirect
5. #14529751C2semidirect
6. #14529747C2semidirect
7. #14529743C2semidirect
8. #14529741C2semidirect
9. #14529739C2semidirect
10. #14529733C2semidirect
15. C17×#1988C2semidirect
17. #11763436C4semidirect
284. #1988D17semidirect
442. C17#21843semidirect

Maximal subgroups

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

subgroupindex
C2×#117634362
C2×#117628692
#145313892
#145297552
#145297512
#145297472
#145297432
#145297412
#145297392
#145297332
#145288782
#145288772
#145288732
#145288692
C17×#19882
#2184317