Finite Group Databasebeta

← #17038927

Subgroups — #17038927

Order 4352.

1134 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763436C211yesmaximal, characteristic
2C2×#11762763C211yesmaximal, characteristic
3#14531405C211yesmaximal, characteristic
4#14529758C211yesmaximal, characteristic, complemented
5#14529755C211yesmaximal, characteristic, complemented
6#14529752C211yesmaximal, characteristic, complemented
7#14529751C211yesmaximal, characteristic, complemented
8#14529749C211yesmaximal, characteristic, complemented
9#14529747C211yesmaximal, characteristic, complemented
10#14529743C211yesmaximal, characteristic, complemented
11#14528502C211yesmaximal, characteristic
12#14528502C211yesmaximal, characteristic
13#14528499C211yesmaximal, characteristic
14D17×#340C211yesmaximal, characteristic
15C17×#1990C211yesmaximal, characteristic, complemented
16C22×#63218C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18#11763436—24no—
19#11763436C418yescomplemented
20C2×#10587574C2211yescharacteristic
21C2×#10587630—21no—
22C2×#10587556C2211yescharacteristic
23C2×#10587576C2211yescharacteristic
24C2×#10587575—21no—
25C2×#10587582—21no—
26C2×#10587632—21no—
27C2×#10587578C2211yescharacteristic
28C2×#10587578C2211yescharacteristic
29C2×#10587558C2211yescharacteristic
30C2×C4⋊C4×D17C2211yescharacteristic
31C2×C4⋊C4×D17C2211yescharacteristic
32#11762763—24no—
33C2×#10587474C2211yescharacteristic
34C2×#10587486C2211yescharacteristic
35C2×C8×Dic17C2211yescharacteristic
36#11762704—21no—
37#11762704—21no—
38#11762680—21no—
39#11762680—21no—
40#11762678C2211yescharacteristic
41#11762675C2211yescharacteristic
42#11762674C2211yescharacteristic
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×C4×C8×C17C2211yescharacteristic
57C17×#384C2211yescharacteristic
58C17×#340C2211yescharacteristic
59C17×#340C2211yescharacteristic
60C17×#340C2211yescharacteristic
61C17×#340C2211yescharacteristic
62C22×Q8×C17—21no—
63C22×C4×D17—21no—
64C22×C4×D17—21no—
65C22×C4×D17C2311yescharacteristic
66C22×Dic34—21no—
67C22×C8×C17C2311yescharacteristic
68C22×C8×C17C2311yescharacteristic
69C17×C4⋊Q8—22no—
70C17×C4⋊Q8C2×C414yescomplemented
71C2×C4⋊C4×C17—21no—
72C2×C4⋊C4×C17—21no—
73C2×C4⋊C4×C17—21no—
74C2×C4⋊C4×C17C2311yescharacteristic
75C2×C4⋊C4×C17C2311yescharacteristic
76C2×C4⋊C4×C17C2311yescharacteristic
77C2×C4⋊C4×C17C2311yescharacteristic
78C2×C42×C17C2311yescharacteristic
79#10587632—28no—
80#10587630—28no—
81C2×#63227—21no—
82C2×#63227—21no—
83C2×#63227D411yescharacteristic
84C2×#63227D411yescharacteristic
85C2×C4⋊Dic17—21no—
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×#63225—21no—
95C2×#63225—21no—
96C2×#63225—21no—
97C2×#63225—21no—
98C2×#63225D411yescharacteristic
99C2×#63225D411yescharacteristic
100C2×C4×Dic17—21no—
101C2×C4×Dic17—21no—
102C2×C4×Dic17C2311yescharacteristic
103C22×#3622C2311yescharacteristic
104C22×#3622C2311yescharacteristic
105C2×#63218—22no—
106C2×#63218—22no—
107C2×#63218Q814yescomplemented
108C2×C8×D17—22no—
109C2×C8×D17—22no—
110C2×C8×D17Q814yescomplemented
111#10587582—28no—
112#10587578—22no—
113#10587578—22no—
114#10587578—22no—
115#10587578C2×C414yes—
116C4⋊C4×D17—22no—
117C4⋊C4×D17—22no—
118C4⋊C4×D17—22no—
119C4⋊C4×D17C2×C414yes—
120#10587576—22no—
121#10587576C2×C414yescomplemented
122#10587575—28no—
123#10587574—22no—
124#10587574C2×C414yescomplemented
125#10587558C2×C414yes—
126#10587558D414yes—
127#10587556—22no—
128#10587556C2×C414yescomplemented
129C4×C8×C17—22no—
130#10587502—21no—
131#10587502—21no—
132#10587502—21no—
133#10587502—21no—
134#10587486—22no—
135C8×Dic17—22no—
136#10587474—22no—
137C23×D17C2×D411yescharacteristic
138C2×Q8×C17—24no—
139C2×Q8×C17—81no—
140C2×Q8×C17—81no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17C2×D411yescharacteristic
146C22×C4×C17C2×D411yescharacteristic
147C22×C4×C17C2411yescharacteristic
148C22×Dic17—21no—
149C22×Dic17—21no—
150C22×Dic17—21no—
151C22×Dic17—21no—
152C22×Dic17C2×D411yescharacteristic
153C22×Dic17C2×D411yescharacteristic
154C22×Dic17C2×D411yescharacteristic
155C2×C4×D17—24no—
156C2×C4×D17—42no—
157C2×C4×D17—81no—
158C2×C4×D17—81no—
159C2×C4×D17—81no—
160C2×C4×D17—81no—
161C2×C4×D17C22×C412yes—
162C2×C4×D17C2×D412yes—
163C2×C4×D17C2×Q812yes—
164C2×C4×D17C2×Q812yes—
165C2×C4×D17#4112yes—
166C2×C4×D17#4112yes—
167C2×Dic34—24no—
168C2×Dic34—81no—
169C2×Dic34—81no—
170C2×C8×C17—21no—
171C2×C8×C17—21no—
172C2×C8×C17—21no—
173C2×C8×C17—21no—
174C2×C8×C17C2×Q812yes—
175C2×C8×C17C2×Q812yes—
176C4⋊C4×C17—24no—
177C4⋊C4×C17—21no—
178C4⋊C4×C17—21no—
179C4⋊C4×C17—21no—
180C4⋊C4×C17—21no—
181C4⋊C4×C17—21no—
182C4⋊C4×C17—21no—
183C4⋊C4×C17—81no—
184C4⋊C4×C17—81no—
185C4⋊C4×C17C22×C412yes—
186C4⋊C4×C17C22×C412yes—
187C42×C17C22×C412yes—
188C42×C17C2×D412yes—
189#63227—24no—
190#63227—42no—
191#63227C22⋊C414yes—
192#63227C22⋊C414yes—
193C4⋊Dic17—21no—
194C4⋊Dic17—21no—
195C4⋊Dic17—24no—
196C4⋊Dic17—21no—
197C4⋊Dic17—21no—
198C4⋊Dic17—21no—
199C4⋊Dic17—21no—
200C4⋊Dic17C22×C412yes—
201C4⋊Dic17C22×C412yes—
202#63225—24no—
203#63225—24no—
204#63225—24no—
205#63225—24no—
206#63225—24no—
207#63225—42no—
208#63225—81no—
209#63225—81no—
210#63225C22⋊C414yes—
211#63225C22⋊C414yes—
212C4×Dic17—24no—
213C4×Dic17—42no—
214C4×Dic17C22×C412yes—
215C4×Dic17C2×D412yes—
216C2×#3622—21no—
217C2×#3622—21no—
218C2×#3622—21no—
219C2×#3622—21no—
220C2×#3622C2×Q812yes—
221C2×#3622C2×Q812yes—
222#63218—28no—
223C8×D17—28no—
224#21326—171nomaximal, Sylow
225C23×C17C22×D411yescharacteristic
226C22×D17—21no—
227C22×D17—21no—
228C22×D17—21no—
229C22×D17—21no—
230C22×D17C2×C22⋊C412yes—
231C22×D17#12412yes—
232C22×D17C4⋊Q812yes—
233Q8×C17—84no—
234C2×C4×C17—21no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—22no—
239C2×C4×C17—22no—
240C2×C4×C17—41no—
241C2×C4×C17—41no—
242C2×C4×C17—41no—
243C2×C4×C17—41no—
244C2×C4×C17—41no—
245C2×C4×C17—41no—
246C2×C4×C17—41no—
247C2×C4×C17—41no—
248C2×C4×C17—41no—
249C2×C4×C17—41no—
250C2×C4×C17C2×C22⋊C412yes—
251C2×C4×C17C2×C22⋊C412yes—
252C2×C4×C17C23×C411yescharacteristic
253C2×C4×C17C22×D411yescharacteristic
254C2×C4×C17C22×Q811yescharacteristic
255C2×C4×C17C22×Q811yescharacteristic
256C2×C4×C17C2×#4111yescharacteristic
257C2×C4×C17C2×#4111yescharacteristic
258C2×Dic17—21no—
259C2×Dic17—21no—
260C2×Dic17—21no—
261C2×Dic17—21no—
262C2×Dic17—22no—
263C2×Dic17—22no—
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—
274C2×Dic17C2×C22⋊C412yes—
275C2×Dic17C2×C22⋊C412yes—
276C2×Dic17C2×C22⋊C412yes—
277C2×Dic17#12412yes—
278C2×Dic17C4⋊Q812yes—
279C4×D17—84no—
280C4×D17—84no—
281C4×D17C4×Q814yes—
282C4×D17C4×Q814yes—
283C4×D17C22⋊Q814yes—
284C4×D17C22⋊Q814yes—
285Dic34—84no—
286C8×C17—22no—
287C8×C17—22no—
288#3622—22no—
289#3622—22no—
290C2×#544—171no—
291C2×#405—171no—
292#2317—171no—
293#1993—171no—
294#1993—171no—
295#1992—171no—
296#1992—171no—
297#1991—171no—
298#1991—171no—
299#1990—171no—
300#1990D1711yescharacteristic, complemented
301#1736—171no—
302#1736—171no—
303#1735—171no—
304C2×#340—171no—
305C22×C17C22×C22⋊C411yescharacteristic
306C22×C17C2×#12411yescharacteristic
307C22×C17C2×C4⋊Q811yescharacteristic
308C22×C17#57611yescharacteristic
309C22×C17#57711yescharacteristic
310C22×C17#57711yescharacteristic
311C22×C17#57811yescharacteristic
312C2×D17—22no—
313C2×D17—22no—
314C2×D17—22no—
315C2×D17—22no—
316C2×D17—22no—
317C2×D17—22no—
318C2×D17#39114yes—
319C4×C17—22no—
320C4×C17—22no—
321C4×C17—42no—
322C4×C17—42no—
323C4×C17—81no—
324C4×C17—81no—
325C4×C17C2×C4×Q811yescharacteristic
326C4×C17C2×C4×Q811yescharacteristic
327C4×C17C2×C22⋊Q811yescharacteristic
328C4×C17C2×C22⋊Q811yescharacteristic
329Dic17—22no—
330Dic17—22no—
331Dic17—42no—
332Dic17—42no—
333Dic17—81no—
334Dic17—81no—
335Dic17#39114yes—
336C22×M16—171no—
337C23×C8—171no—
338#544—178no—
339#544—344no—
340C2×C4⋊Q8—171no—
341C2×C4⋊Q8—341no—
342C2×C4⋊Q8C2×D1711yescharacteristic
343C2×#125—171no—
344C2×#125—171no—
345C2×#125—341no—
346C2×C22⋊Q8—341no—
347C2×C22⋊Q8—341no—
348C2×#117—171no—
349C2×#117—171no—
350C2×#117—171no—
351C22×C4⋊C4—171no—
352C22×C4⋊C4—171no—
353#405—344no—
354C2×#97—171no—
355C2×#97—171no—
356C2×C4×C8—171no—
357C2×C4×C8C2×D1711yescharacteristic
358#389—341no—
359#389—341no—
360#385—341no—
361#385—341no—
362#384—171no—
363#384C2×D1711yescharacteristic
364#382—171no—
365#382—171no—
366#340—171no—
367#340—171no—
368#340—171no—
369#340—171no—
370#340—171no—
371#340—171no—
372#340—171no—
373#340—171no—
374#340—171no—
375#340—171no—
376#340—171no—
377#340—171no—
378#340C2×D1711yescharacteristic
379#340C2×D1711yescharacteristic
380#340C2×D1711yescharacteristic
381#340C2×D1711yescharacteristic
382C2×C17C2×#39111yescharacteristic
383C2×C17#289711yescharacteristic
384C2×C17#289811yescharacteristic
385C2×C17#313611yescharacteristic
386C2×C17#313711yescharacteristic
387C2×C17#316311yescharacteristic
388C2×C17#316411yescharacteristic
389D17—24no—
390C22×Q8—21no—
391C22×Q8—341no—
392C23×C4—171no—
393C23×C4—341no—
394C23×C4—341no—
395C2×M16—174no—
396C2×M16—342no—
397C2×M16—342no—
398C22×C8—171no—
399C22×C8—171no—
400C22×C8—174no—
401C22×C8—342no—
402C22×C8—342no—
403C22×C8C22×D1711yescharacteristic
404C22×C8C22×D1711yescharacteristic
405C4⋊Q8—22no—
406C4⋊Q8—174no—
407C4⋊Q8—342no—
408C4⋊Q8—348no—
409C4⋊Q8C4×D1714yescomplemented
410#125—174no—
411#125—174no—
412#125—342no—
413#125—348no—
414#125—342no—
415C22⋊Q8—348no—
416C22⋊Q8—348no—
417#117—174no—
418#117—174no—
419#117—174no—
420#117—342no—
421#117—342no—
422#117—342no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—171no—
427C2×C4⋊C4—171no—
428C2×C4⋊C4—171no—
429C2×C4⋊C4—171no—
430C2×C4⋊C4—174no—
431C2×C4⋊C4—171no—
432C2×C4⋊C4—171no—
433C2×C4⋊C4—342no—
434C2×C4⋊C4—342no—
435C2×C4⋊C4—342no—
436C2×C4⋊C4—341no—
437C2×C4⋊C4—341no—
438C2×C4⋊C4—341no—
439C2×C4⋊C4—341no—
440C2×C4⋊C4—341no—
441C2×C4⋊C4—341no—
442C2×C4⋊C4—341no—
443C2×C4⋊C4—341no—
444C2×C4⋊C4—341no—
445C2×C4⋊C4C22×D1711yescharacteristic
446C2×C4⋊C4C22×D1711yescharacteristic
447C2×C4⋊C4C22×D1711yescharacteristic
448C2×C4⋊C4C22×D1711yescharacteristic
449C2×C22⋊C4—171no—
450C2×C22⋊C4—171no—
451C2×C22⋊C4—341no—
452C2×C22⋊C4—341no—
453C2×C42—171no—
454C2×C42—341no—
455C2×C42—341no—
456C2×C42C22×D1711yescharacteristic
457#97—342no—
458#97—342no—
459C4×C8—22no—
460C4×C8—342no—
461#95—341no—
462#95—341no—
463#95—341no—
464#95—341no—
465C17#2132611yescharacteristic, complemented, Sylow
466C24—171no—
467C2×Q8—24no—
468C2×Q8—81no—
469C2×Q8—81no—
470C2×Q8—344no—
471C2×Q8—1361no—
472C2×Q8—1361no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—171no—
478C22×C4—172no—
479C22×C4—172no—
480C22×C4—172no—
481C22×C4—172no—
482C22×C4—172no—
483C22×C4—172no—
484C22×C4—171no—
485C22×C4—171no—
486C22×C4—344no—
487C22×C4—341no—
488C22×C4—341no—
489C22×C4—341no—
490C22×C4—341no—
491C22×C4—682no—
492C22×C4—1361no—
493C22×C4—1361no—
494C22×C4—1361no—
495C22×C4—1361no—
496C22×C4D4×D1711yescharacteristic
497C22×C4D4×D1711yescharacteristic
498C22×C4C23×D1711yescharacteristic
499M16—348no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—172no—
505C2×C8—172no—
506C2×C8—348no—
507C2×C8—341no—
508C2×C8—341no—
509C2×C8—341no—
510C2×C8—341no—
511C2×C8Q8×D1712yes—
512C2×C8Q8×D1712yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—24no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—81no—
521C4⋊C4—81no—
522C4⋊C4—174no—
523C4⋊C4—174no—
524C4⋊C4—172no—
525C4⋊C4—172no—
526C4⋊C4—344no—
527C4⋊C4—344no—
528C4⋊C4—344no—
529C4⋊C4—344no—
530C4⋊C4—341no—
531C4⋊C4—341no—
532C4⋊C4—344no—
533C4⋊C4—344no—
534C4⋊C4—341no—
535C4⋊C4—341no—
536C4⋊C4—341no—
537C4⋊C4—341no—
538C4⋊C4—682no—
539C4⋊C4—1361no—
540C4⋊C4—1361no—
541C4⋊C4C2×C4×D1712yes—
542C4⋊C4C2×C4×D1712yes—
543C22⋊C4—174no—
544C22⋊C4—174no—
545C22⋊C4—344no—
546C22⋊C4—682no—
547C42—172no—
548C42—172no—
549C42—344no—
550C42—682no—
551C42C2×C4×D1712yes—
552C42D4×D1712yes—
553C23—172no—
554C23—172no—
555C23—172no—
556C23—341no—
557C23—341no—
558C23—341no—
559C23—341no—
560C23C2×D4×D1711yescharacteristic
561Q8—84no—
562Q8—1364no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—172no—
580C2×C4—172no—
581C2×C4—172no—
582C2×C4—174no—
583C2×C4—174no—
584C2×C4—174no—
585C2×C4—174no—
586C2×C4—172no—
587C2×C4—172no—
588C2×C4—341no—
589C2×C4—341no—
590C2×C4—341no—
591C2×C4—341no—
592C2×C4—342no—
593C2×C4—342no—
594C2×C4—681no—
595C2×C4—681no—
596C2×C4—681no—
597C2×C4—681no—
598C2×C4—681no—
599C2×C4—681no—
600C2×C4—681no—
601C2×C4—681no—
602C2×C4—681no—
603C2×C4—681no—
604C2×C4—1364no—
605C2×C4—1364no—
606C2×C4C22⋊C4×D1712yes—
607C2×C4C22⋊C4×D1712yes—
608C2×C4C22×C4×D1711yescharacteristic
609C2×C4C2×D4×D1711yescharacteristic
610C2×C4C2×Q8×D1711yescharacteristic
611C2×C4C2×Q8×D1711yescharacteristic
612C2×C4#41×D1711yescharacteristic
613C2×C4#41×D1711yescharacteristic
614C8—22no—
615C8—22no—
616C8—342no—
617C8—342no—
618C22—174no—
619C22—342no—
620C22—342no—
621C22—342no—
622C22—342no—
623C22—342no—
624C22—342no—
625C22C2×C22⋊C4×D1711yescharacteristic
626C22#124×D1711yescharacteristic
627C22C4⋊Q8×D1711yescharacteristic
628C22#1176361011yescharacteristic
629C22#1176361511yescharacteristic
630C22#1176361511yescharacteristic
631C22#1176362211yescharacteristic
632C4—22no—
633C4—22no—
634C4—42no—
635C4—42no—
636C4—81no—
637C4—81no—
638C4—174no—
639C4—342no—
640C4—342no—
641C4—682no—
642C4—682no—
643C4—1361no—
644C4—1361no—
645C4C4×Q8×D1711yescharacteristic
646C4C4×Q8×D1711yescharacteristic
647C4C22⋊Q8×D1711yescharacteristic
648C4C22⋊Q8×D1711yescharacteristic
649C2—344no—
650C2D17×#39111yescharacteristic
651C2#1453730511yescharacteristic
652C2#1453731211yescharacteristic
653C2#1453913311yescharacteristic
654C2#1453914411yescharacteristic
655C2#1453930911yescharacteristic
656C2#1453931711yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1990C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
cosocleC22×C4×C17C24
hypercenter#1990D17
hypocenterC17#21326
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #14529758C2semidirect
5. #14529755C2semidirect
6. #14529752C2semidirect
7. #14529751C2semidirect
8. #14529749C2semidirect
9. #14529747C2semidirect
10. #14529743C2semidirect
15. C17×#1990C2semidirect
19. #11763436C4semidirect
70. C17×C4⋊Q8C2×C4semidirect
107. C2×#63218Q8semidirect
110. C2×C8×D17Q8semidirect
121. #10587576C2×C4semidirect
124. #10587574C2×C4semidirect
128. #10587556C2×C4semidirect
300. #1990D17semidirect
409. C4⋊Q8C4×D17semidirect
465. C17#21326semidirect

Maximal subgroups

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

subgroupindex
C2×#117634362
C2×#117627632
#145314052
#145297582
#145297552
#145297522
#145297512
#145297492
#145297472
#145297432
#145285022
#145284992
D17×#3402
C17×#19902
#2132617