Finite Group Databasebeta

← #17034529

Subgroups — #17034529

Order 4352.

894 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762766C211yesmaximal, characteristic
2#14531409C211yesmaximal, characteristic
3#14531405C211yesmaximal, characteristic
4#14528918C211yesmaximal, characteristic, complemented
5#14528916C211yesmaximal, characteristic, complemented
6#14528916C211yesmaximal, characteristic, complemented
7#14528914C211yesmaximal, characteristic, complemented
8#14528913C211yesmaximal, characteristic, complemented
9#14528911C211yesmaximal, characteristic, complemented
10#14528910C211yesmaximal, characteristic, complemented
11#14528502C211yesmaximal, characteristic
12#14528502C211yesmaximal, characteristic
13#14528499C211yesmaximal, characteristic
14D17×#340C211yesmaximal, characteristic
15C17×#1836C211yesmaximal, characteristic, complemented
16C22×#63218C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18C2×#10587578C2211yescharacteristic
19C2×#10587578C2211yescharacteristic
20C2×#10587558C2211yescharacteristic
21C2×C4⋊C4×D17C2211yescharacteristic
22C2×C4⋊C4×D17C2211yescharacteristic
23#11762766C418yescomplemented
24C2×#10587486C2211yescharacteristic
25C2×C4×#3622C2211yescharacteristic
26C2×C8×Dic17C2211yescharacteristic
27#11762706—21no—
28#11762706—21no—
29#11762704—21no—
30#11762704—21no—
31#11762683—21no—
32#11762683—21no—
33#11762680—21no—
34#11762680—21no—
35#11762679C2211yescharacteristic
36#11762678C2211yescharacteristic
37#11762678C2211yescharacteristic
38#11762675C2211yescharacteristic
39#11762674C2211yescharacteristic
40#11762674C2211yescharacteristic
41#11762572C2211yescharacteristic
42#11762572C2211yescharacteristic
43#11762572C2211yescharacteristic
44#11762572C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53C2×C17×#97C2211yescharacteristic
54C17×#384C2211yescharacteristic
55C17×#382C2211yescharacteristic
56C17×#340C2211yescharacteristic
57C17×#340C2211yescharacteristic
58C17×#340C2211yescharacteristic
59C17×#340C2211yescharacteristic
60C22×C4×D17—21no—
61C22×C4×D17—21no—
62C22×C4×D17C2311yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17—21no—
67C2×C4⋊C4×C17C2311yescharacteristic
68C2×C4⋊C4×C17C2311yescharacteristic
69C2×C4⋊C4×C17C2311yescharacteristic
70C2×C4⋊C4×C17C2311yescharacteristic
71C2×C42×C17C2311yescharacteristic
72C2×#63227—21no—
73C2×#63227—21no—
74C2×#63227D411yescharacteristic
75C2×#63227D411yescharacteristic
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17—21no—
78C2×C4⋊Dic17C2311yescharacteristic
79C2×C4⋊Dic17C2311yescharacteristic
80C2×C4⋊Dic17C2311yescharacteristic
81C2×C4⋊Dic17C2311yescharacteristic
82C2×#63225—21no—
83C2×#63225—21no—
84C2×#63225—21no—
85C2×#63225—21no—
86C2×#63225—21no—
87C2×#63225—21no—
88C2×#63225D411yescharacteristic
89C2×#63225D411yescharacteristic
90C2×C4×Dic17—21no—
91C2×C4×Dic17—21no—
92C2×C4×Dic17C2311yescharacteristic
93C22×#3622C2311yescharacteristic
94C22×#3622C2311yescharacteristic
95C2×#63218—22no—
96C2×#63218—22no—
97C2×#63218C2×C414yes—
98C2×C8×D17—22no—
99C2×C8×D17—22no—
100C2×C8×D17C2×C414yes—
101#10587578—22no—
102#10587578—22no—
103#10587578—22no—
104#10587578—22no—
105C4⋊C4×D17—22no—
106C4⋊C4×D17—22no—
107C4⋊C4×D17—22no—
108C4⋊C4×D17—22no—
109#10587558C2×C414yes—
110#10587558Q814yes—
111C17×#97C2×C414yescomplemented
112C17×#95—21no—
113C17×#95—21no—
114#10587502—21no—
115#10587502—21no—
116#10587502—21no—
117#10587502—21no—
118#10587502—21no—
119#10587502—21no—
120#10587486C2×C414yescomplemented
121C8×Dic17C2×C414yescomplemented
122C4×#3622C2×C414yescomplemented
123C23×D17C2×D411yescharacteristic
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17C2×D411yescharacteristic
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2411yescharacteristic
131C22×Dic17—21no—
132C22×Dic17—21no—
133C22×Dic17—21no—
134C22×Dic17—21no—
135C22×Dic17C2×D411yescharacteristic
136C22×Dic17C2×D411yescharacteristic
137C22×Dic17C2×D411yescharacteristic
138C2×C4×D17—42no—
139C2×C4×D17—42no—
140C2×C4×D17—81no—
141C2×C4×D17—81no—
142C2×C4×D17—81no—
143C2×C4×D17—81no—
144C2×C4×D17C22×C412yes—
145C2×C4×D17C2×Q812yes—
146C2×C4×D17#4112yes—
147C2×C4×D17#4112yes—
148C2×C4×D17#4112yes—
149C2×C4×D17#4112yes—
150C2×C8×C17—21no—
151C2×C8×C17—21no—
152C2×C8×C17—21no—
153C2×C8×C17—21no—
154C2×C8×C17C22×C412yes—
155C2×C8×C17C22×C412yes—
156C4⋊C4×C17—21no—
157C4⋊C4×C17—21no—
158C4⋊C4×C17—21no—
159C4⋊C4×C17—21no—
160C4⋊C4×C17—21no—
161C4⋊C4×C17—21no—
162C4⋊C4×C17—21no—
163C4⋊C4×C17—21no—
164C4⋊C4×C17—81no—
165C4⋊C4×C17—81no—
166C42×C17C22×C412yes—
167C42×C17C2×Q812yes—
168#63227—42no—
169#63227—42no—
170#63227C4⋊C414yes—
171#63227C4⋊C414yes—
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—81no—
181C4⋊Dic17—81no—
182#63225—42no—
183#63225—42no—
184#63225—81no—
185#63225—81no—
186#63225—81no—
187#63225—81no—
188#63225C4⋊C414yes—
189#63225C4⋊C414yes—
190C4×Dic17—42no—
191C4×Dic17—42no—
192C4×Dic17C22×C412yes—
193C4×Dic17C2×Q812yes—
194C2×#3622—21no—
195C2×#3622—21no—
196C2×#3622—21no—
197C2×#3622—21no—
198C2×#3622C22×C412yes—
199C2×#3622C22×C412yes—
200#63218—28no—
201C8×D17—28no—
202#20763—171nomaximal, Sylow
203C23×C17C22×D411yescharacteristic
204C22×D17—21no—
205C22×D17—21no—
206C22×D17—21no—
207C22×D17—21no—
208C22×D17C2×C4⋊C412yes—
209C22×D17#12412yes—
210C22×D17#12412yes—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—21no—
215C2×C4×C17—41no—
216C2×C4×C17—41no—
217C2×C4×C17—41no—
218C2×C4×C17—41no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17—41no—
222C2×C4×C17—41no—
223C2×C4×C17—41no—
224C2×C4×C17—41no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17C2×C4⋊C412yes—
228C2×C4×C17C2×C4⋊C412yes—
229C2×C4×C17C23×C411yescharacteristic
230C2×C4×C17C22×Q811yescharacteristic
231C2×C4×C17C2×#4111yescharacteristic
232C2×C4×C17C2×#4111yescharacteristic
233C2×C4×C17C2×#4111yescharacteristic
234C2×C4×C17C2×#4111yescharacteristic
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238C2×Dic17—21no—
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×Dic17C2×C4⋊C412yes—
252C2×Dic17C2×C4⋊C412yes—
253C2×Dic17C2×C4⋊C412yes—
254C2×Dic17#12412yes—
255C2×Dic17#12412yes—
256C4×D17—84no—
257C4×D17—84no—
258C4×D17#11714yes—
259C4×D17#11714yes—
260C4×D17#12514yes—
261C4×D17#12514yes—
262C8×C17—22no—
263C8×C17—22no—
264#3622—22no—
265#3622—22no—
266C2×#405—171no—
267#2317—171no—
268#2317—171no—
269#1836—171no—
270#1836—171no—
271#1836—171no—
272#1836D1711yescharacteristic, complemented
273#1835—171no—
274#1835—171no—
275#1834—171no—
276#1834—171no—
277#1736—171no—
278#1736—171no—
279#1735—171no—
280C2×#340—171no—
281C22×C17C22×C4⋊C411yescharacteristic
282C22×C17C2×#12411yescharacteristic
283C22×C17C2×#12411yescharacteristic
284C22×C17#57611yescharacteristic
285C22×C17#57711yescharacteristic
286C22×C17#57711yescharacteristic
287C22×C17#57811yescharacteristic
288C2×D17—22no—
289C2×D17—22no—
290C2×D17—22no—
291C2×D17—22no—
292C2×D17—22no—
293C2×D17—22no—
294C2×D17#38214yes—
295C4×C17—22no—
296C4×C17—22no—
297C4×C17—81no—
298C4×C17—81no—
299C4×C17—81no—
300C4×C17—81no—
301C4×C17C2×#11711yescharacteristic
302C4×C17C2×#11711yescharacteristic
303C4×C17C2×#12511yescharacteristic
304C4×C17C2×#12511yescharacteristic
305Dic17—22no—
306Dic17—22no—
307Dic17—81no—
308Dic17—81no—
309Dic17—81no—
310Dic17—81no—
311Dic17#38214yes—
312C22×M16—171no—
313C23×C8—171no—
314C2×#117—171no—
315C2×#117—171no—
316C2×#117—171no—
317C22×C4⋊C4—171no—
318C22×C4⋊C4—171no—
319#405—178no—
320C2×#97—171no—
321C2×#97C2×D1711yescharacteristic
322C2×C4×C8—171no—
323C2×C4×C8—171no—
324#389—341no—
325#389—341no—
326#389—341no—
327#389—341no—
328#385—341no—
329#385—341no—
330#385—341no—
331#385—341no—
332#384—171no—
333#384—171no—
334#384—171no—
335#384C2×D1711yescharacteristic
336#382—171no—
337#382—171no—
338#382—171no—
339#382C2×D1711yescharacteristic
340#340—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—
349#340—171no—
350#340—171no—
351#340—171no—
352#340C2×D1711yescharacteristic
353#340C2×D1711yescharacteristic
354#340C2×D1711yescharacteristic
355#340C2×D1711yescharacteristic
356C2×C17C2×#38211yescharacteristic
357C2×C17#291211yescharacteristic
358C2×C17#291311yescharacteristic
359C2×C17#313611yescharacteristic
360C2×C17#313611yescharacteristic
361C2×C17#313711yescharacteristic
362C2×C17#313711yescharacteristic
363D17—24no—
364C23×C4—171no—
365C23×C4—341no—
366C23×C4—341no—
367C2×M16—174no—
368C2×M16—342no—
369C2×M16—342no—
370C22×C8—171no—
371C22×C8—171no—
372C22×C8—174no—
373C22×C8—342no—
374C22×C8—342no—
375C22×C8C22×D1711yescharacteristic
376C22×C8C22×D1711yescharacteristic
377#117—174no—
378#117—174no—
379#117—342no—
380#117—342no—
381#117—342no—
382#117—342no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—171no—
386C2×C4⋊C4—171no—
387C2×C4⋊C4—171no—
388C2×C4⋊C4—171no—
389C2×C4⋊C4—171no—
390C2×C4⋊C4—171no—
391C2×C4⋊C4—342no—
392C2×C4⋊C4—342no—
393C2×C4⋊C4—342no—
394C2×C4⋊C4—342no—
395C2×C4⋊C4—341no—
396C2×C4⋊C4—341no—
397C2×C4⋊C4—341no—
398C2×C4⋊C4—341no—
399C2×C4⋊C4—341no—
400C2×C4⋊C4—341no—
401C2×C4⋊C4—341no—
402C2×C4⋊C4—341no—
403C2×C4⋊C4C22×D1711yescharacteristic
404C2×C4⋊C4C22×D1711yescharacteristic
405C2×C4⋊C4C22×D1711yescharacteristic
406C2×C4⋊C4C22×D1711yescharacteristic
407C2×C22⋊C4—171no—
408C2×C22⋊C4—171no—
409C2×C22⋊C4—341no—
410C2×C22⋊C4—341no—
411C2×C42—171no—
412C2×C42—341no—
413C2×C42—341no—
414C2×C42C22×D1711yescharacteristic
415#97—174no—
416#97C4×D1714yescomplemented
417C4×C8—174no—
418C4×C8—174no—
419#95—21no—
420#95—21no—
421#95—341no—
422#95—341no—
423#95—341no—
424#95—341no—
425#95—341no—
426#95—341no—
427C17#2076311yescharacteristic, complemented, Sylow
428C24—171no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—171no—
434C22×C4—172no—
435C22×C4—172no—
436C22×C4—172no—
437C22×C4—172no—
438C22×C4—172no—
439C22×C4—172no—
440C22×C4—171no—
441C22×C4—171no—
442C22×C4—341no—
443C22×C4—341no—
444C22×C4—341no—
445C22×C4—341no—
446C22×C4—682no—
447C22×C4—682no—
448C22×C4—1361no—
449C22×C4—1361no—
450C22×C4—1361no—
451C22×C4—1361no—
452C22×C4D4×D1711yescharacteristic
453C22×C4D4×D1711yescharacteristic
454C22×C4C23×D1711yescharacteristic
455M16—348no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—172no—
461C2×C8—172no—
462C2×C8—348no—
463C2×C8—341no—
464C2×C8—341no—
465C2×C8—341no—
466C2×C8—341no—
467C2×C8C2×C4×D1712yes—
468C2×C8C2×C4×D1712yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—174no—
480C4⋊C4—174no—
481C4⋊C4—341no—
482C4⋊C4—341no—
483C4⋊C4—341no—
484C4⋊C4—341no—
485C4⋊C4—341no—
486C4⋊C4—341no—
487C4⋊C4—341no—
488C4⋊C4—341no—
489C4⋊C4—682no—
490C4⋊C4—682no—
491C4⋊C4—1361no—
492C4⋊C4—1361no—
493C4⋊C4—1361no—
494C4⋊C4—1361no—
495C4⋊C4—1361no—
496C4⋊C4—1361no—
497C22⋊C4—174no—
498C22⋊C4—174no—
499C22⋊C4—682no—
500C22⋊C4—682no—
501C42—172no—
502C42—172no—
503C42—682no—
504C42—682no—
505C42C2×C4×D1712yes—
506C42Q8×D1712yes—
507C23—172no—
508C23—172no—
509C23—172no—
510C23—341no—
511C23—341no—
512C23—341no—
513C23—341no—
514C23C2×D4×D1711yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—172no—
532C2×C4—172no—
533C2×C4—172no—
534C2×C4—174no—
535C2×C4—174no—
536C2×C4—174no—
537C2×C4—174no—
538C2×C4—172no—
539C2×C4—172no—
540C2×C4—341no—
541C2×C4—341no—
542C2×C4—341no—
543C2×C4—341no—
544C2×C4—681no—
545C2×C4—681no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4—681no—
552C2×C4—681no—
553C2×C4—681no—
554C2×C4—681no—
555C2×C4—681no—
556C2×C4—1364no—
557C2×C4—1364no—
558C2×C4C4⋊C4×D1712yes—
559C2×C4C4⋊C4×D1712yes—
560C2×C4C22×C4×D1711yescharacteristic
561C2×C4C2×Q8×D1711yescharacteristic
562C2×C4#41×D1711yescharacteristic
563C2×C4#41×D1711yescharacteristic
564C2×C4#41×D1711yescharacteristic
565C2×C4#41×D1711yescharacteristic
566C8—22no—
567C8—22no—
568C8—342no—
569C8—342no—
570C22—174no—
571C22—342no—
572C22—342no—
573C22—342no—
574C22—342no—
575C22—342no—
576C22—342no—
577C22C2×C4⋊C4×D1711yescharacteristic
578C22#124×D1711yescharacteristic
579C22#124×D1711yescharacteristic
580C22#1176361311yescharacteristic
581C22#1176361811yescharacteristic
582C22#1176361911yescharacteristic
583C22#1176362511yescharacteristic
584C4—22no—
585C4—22no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—174no—
591C4—342no—
592C4—342no—
593C4—1361no—
594C4—1361no—
595C4—1361no—
596C4—1361no—
597C4#117×D1711yescharacteristic
598C4#117×D1711yescharacteristic
599C4#125×D1711yescharacteristic
600C4#125×D1711yescharacteristic
601C2—344no—
602C2D17×#38211yescharacteristic
603C2#1453737811yescharacteristic
604C2#1453738311yescharacteristic
605C2#1453913511yescharacteristic
606C2#1453913911yescharacteristic
607C2#1453914611yescharacteristic
608C2#1453915011yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1836C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
cosocleC22×C4×C17C24
hypercenter#1836D17
hypocenterC17#20763
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
4. #14528918C2semidirect
5. #14528916C2semidirect
6. #14528916C2semidirect
7. #14528914C2semidirect
8. #14528913C2semidirect
9. #14528911C2semidirect
10. #14528910C2semidirect
15. C17×#1836C2semidirect
23. #11762766C4semidirect
111. C17×#97C2×C4semidirect
120. #10587486C2×C4semidirect
121. C8×Dic17C2×C4semidirect
122. C4×#3622C2×C4semidirect
272. #1836D17semidirect
416. #97C4×D17semidirect
427. C17#20763semidirect

Maximal subgroups

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

subgroupindex
C2×#117627662
#145314092
#145314052
#145289182
#145289162
#145289142
#145289132
#145289112
#145289102
#145285022
#145284992
D17×#3402
C17×#18362
#2076317