Finite Group Databasebeta

← #17036513

Subgroups — #17036513

Order 4352.

898 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×#11762850C211yesmaximal, characteristic
2#14531406C211yesmaximal, characteristic
3#14531138C211yesmaximal, characteristic
4#14529378C211yesmaximal, characteristic, complemented
5#14529373C211yesmaximal, characteristic, complemented
6#14529370C211yesmaximal, characteristic, complemented
7#14529367C211yesmaximal, characteristic, complemented
8#14529362C211yesmaximal, characteristic, complemented
9#14529361C211yesmaximal, characteristic, complemented
10#14529358C211yesmaximal, characteristic, complemented
11#14528502C211yesmaximal, characteristic
12#14528499C211yesmaximal, characteristic
13D17×#340C211yesmaximal, characteristic
14#14528479C211yesmaximal, characteristic
15C17×#1918C211yesmaximal, characteristic, complemented
16C22×#63218C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18C2×#10587578C2211yescharacteristic
19C2×#10587578C2211yescharacteristic
20C2×#10587558C2211yescharacteristic
21C2×C4⋊C4×D17C2211yescharacteristic
22C2×C4⋊C4×D17C2211yescharacteristic
23#11762850C418yescomplemented
24C2×#10587478C2211yescharacteristic
25C2×#10587488C2211yescharacteristic
26C2×#10587479C2211yescharacteristic
27#11762708C2211yescharacteristic
28#11762707C2211yescharacteristic
29#11762705C2211yescharacteristic
30#11762683—21no—
31#11762680—21no—
32#11762678—21no—
33#11762673—21no—
34C4⋊C4×Dic17C2211yescharacteristic
35C4⋊C4×Dic17C2211yescharacteristic
36C4×#63225—21no—
37C4×C4⋊Dic17C2211yescharacteristic
38#11762660—21no—
39C4×#63227—21no—
40#11762656—21no—
41#11762572C2211yescharacteristic
42#11762572C2211yescharacteristic
43#11762572C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762564C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53C2×C17×#107C2211yescharacteristic
54C17×#389C2211yescharacteristic
55C4×C4⋊C4×C17C2211yescharacteristic
56C17×#340C2211yescharacteristic
57C17×#340C2211yescharacteristic
58C17×#340C2211yescharacteristic
59C17×#336C2211yescharacteristic
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×C17C2311yescharacteristic
67C2×C4⋊C4×C17C2311yescharacteristic
68C2×C4⋊C4×C17C2311yescharacteristic
69C2×C4⋊C4×C17C2311yescharacteristic
70C2×C42×C17—21no—
71C2×C42×C17C2311yescharacteristic
72C2×#63227—21no—
73C2×#63227—21no—
74C2×#63227D411yescharacteristic
75C2×#63227D411yescharacteristic
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17C2311yescharacteristic
78C2×C4⋊Dic17C2311yescharacteristic
79C2×C4⋊Dic17C2311yescharacteristic
80C2×C4⋊Dic17C2311yescharacteristic
81C2×#63225—21no—
82C2×#63225—21no—
83C2×#63225—21no—
84C2×#63225—21no—
85C2×#63225D411yescharacteristic
86C2×#63225D411yescharacteristic
87C2×C4×Dic17—21no—
88C2×C4×Dic17—21no—
89C2×C4×Dic17—21no—
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×D17—22no—
101#10587578—22no—
102#10587578—22no—
103#10587578C2×C414yes—
104#10587578Q814yes—
105C4⋊C4×D17—22no—
106C4⋊C4×D17—22no—
107C4⋊C4×D17—22no—
108C4⋊C4×D17C2×C414yes—
109#10587558—22no—
110#10587558—22no—
111C17×#107C2×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#10587488C2×C414yescomplemented
121#10587479C2×C414yescomplemented
122#10587478C2×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—24no—
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×C17—21no—
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—81no—
162C4⋊C4×C17C22×C412yes—
163C4⋊C4×C17C22×C412yes—
164C4⋊C4×C17C2×Q812yes—
165C42×C17—21no—
166C42×C17—21no—
167C42×C17—81no—
168#63227—24no—
169#63227—24no—
170#63227—22no—
171#63227—22no—
172C4⋊Dic17—21no—
173C4⋊Dic17—21no—
174C4⋊Dic17—21no—
175C4⋊Dic17—21no—
176C4⋊Dic17—21no—
177C4⋊Dic17—81no—
178C4⋊Dic17C22×C412yes—
179C4⋊Dic17C22×C412yes—
180C4⋊Dic17C2×Q812yes—
181#63225—24no—
182#63225—22no—
183#63225—22no—
184#63225—42no—
185#63225—81no—
186#63225—81no—
187C4×Dic17—21no—
188C4×Dic17—21no—
189C4×Dic17—24no—
190C4×Dic17—24no—
191C4×Dic17—81no—
192C4×Dic17—81no—
193C4×Dic17—81no—
194C2×#3622—21no—
195C2×#3622—21no—
196C2×#3622—21no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622C22×C412yes—
200#63218—28no—
201C8×D17—44no—
202#21035—171nomaximal, Sylow
203C23×C17C22×D411yescharacteristic
204C22×D17—21no—
205C22×D17—21no—
206C22×D17—21no—
207C22×D17—21no—
208C22×D17C4×D412yes—
209C22×D17C22⋊Q812yes—
210C22×D17#12312yes—
211C2×C4×C17—22no—
212C2×C4×C17—22no—
213C2×C4×C17—22no—
214C2×C4×C17—21no—
215C2×C4×C17—21no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
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×C17—41no—
228C2×C4×C17—41no—
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—22no—
236C2×Dic17—22no—
237C2×Dic17—22no—
238C2×Dic17—21no—
239C2×Dic17—21no—
240C2×Dic17—21no—
241C2×Dic17—21no—
242C2×Dic17—21no—
243C2×Dic17—21no—
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×Dic17C4×D412yes—
254C2×Dic17C22⋊Q812yes—
255C2×Dic17#12312yes—
256C4×D17—84no—
257C4×D17—84no—
258C4×D17#11714yes—
259C4×D17C4×Q814yes—
260C4×D17#12514yes—
261C4×D17#12614yes—
262C8×C17—22no—
263C8×C17—41no—
264#3622—22no—
265#3622—41no—
266C2×#428—171no—
267#2317—171no—
268#2274—171no—
269#1921—171no—
270#1921—171no—
271#1920—171no—
272#1920—171no—
273#1919—171no—
274#1919—171no—
275#1918—171no—
276#1918D1711yescharacteristic, complemented
277#1736—171no—
278#1735—171no—
279C2×#340—171no—
280#1729—171no—
281C22×C17C2×C4×D411yescharacteristic
282C22×C17C2×C22⋊Q811yescharacteristic
283C22×C17C2×#12311yescharacteristic
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#38714yes—
295C4×C17—42no—
296C4×C17—41no—
297C4×C17—41no—
298C4×C17—42no—
299C4×C17—42no—
300C4×C17—81no—
301C4×C17C2×#11711yescharacteristic
302C4×C17C2×C4×Q811yescharacteristic
303C4×C17C2×#12511yescharacteristic
304C4×C17C2×#12611yescharacteristic
305Dic17—42no—
306Dic17—41no—
307Dic17—41no—
308Dic17—42no—
309Dic17—42no—
310Dic17—81no—
311Dic17#38714yes—
312C22×M16—171no—
313C23×C8—171no—
314C2×#117—171no—
315C2×#117—171no—
316C2×#117—171no—
317C22×C4⋊C4—171no—
318C22×C4⋊C4—171no—
319#428—178no—
320C2×#107—171no—
321C2×#107C2×D1711yescharacteristic
322C2×#106—171no—
323C2×#106—171no—
324#389—171no—
325#389—171no—
326#389—171no—
327#389C2×D1711yescharacteristic
328#385—341no—
329#385—341no—
330#384—341no—
331#382—341no—
332C4×C4⋊C4—171no—
333C4×C4⋊C4—171no—
334C4×C4⋊C4—171no—
335C4×C4⋊C4—341no—
336C4×C4⋊C4—341no—
337C4×C4⋊C4C2×D1711yescharacteristic
338C4×C22⋊C4—341no—
339C4×C22⋊C4—341no—
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#340C2×D1711yescharacteristic
350#340C2×D1711yescharacteristic
351#340C2×D1711yescharacteristic
352#336—171no—
353#336—171no—
354#336—171no—
355#336C2×D1711yescharacteristic
356C2×C17C2×#38711yescharacteristic
357C2×C17#294611yescharacteristic
358C2×C17#294711yescharacteristic
359C2×C17#308311yescharacteristic
360C2×C17#308411yescharacteristic
361C2×C17#309611yescharacteristic
362C2×C17#309711yescharacteristic
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—342no—
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—171no—
385C2×C4⋊C4—171no—
386C2×C4⋊C4—171no—
387C2×C4⋊C4—174no—
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—341no—
395C2×C4⋊C4—341no—
396C2×C4⋊C4—341no—
397C2×C4⋊C4—341no—
398C2×C4⋊C4—341no—
399C2×C4⋊C4C22×D1711yescharacteristic
400C2×C4⋊C4C22×D1711yescharacteristic
401C2×C4⋊C4C22×D1711yescharacteristic
402C2×C4⋊C4C22×D1711yescharacteristic
403C2×C22⋊C4—171no—
404C2×C22⋊C4—171no—
405C2×C22⋊C4—341no—
406C2×C22⋊C4—341no—
407C2×C42—21no—
408C2×C42—171no—
409C2×C42—341no—
410C2×C42—341no—
411C2×C42—341no—
412C2×C42—341no—
413C2×C42—341no—
414C2×C42C22×D1711yescharacteristic
415#107—174no—
416#107C4×D1714yescomplemented
417#106—174no—
418#106—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#2103511yescharacteristic, 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—344no—
443C22×C4—341no—
444C22×C4—341no—
445C22×C4—341no—
446C22×C4—341no—
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—21no—
461C2×C8—172no—
462C2×C8—341no—
463C2×C8—341no—
464C2×C8—341no—
465C2×C8—341no—
466C2×C8—341no—
467C2×C8—684no—
468C2×C8C2×C4×D1712yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—81no—
475C4⋊C4—172no—
476C4⋊C4—172no—
477C4⋊C4—172no—
478C4⋊C4—344no—
479C4⋊C4—342no—
480C4⋊C4—342no—
481C4⋊C4—341no—
482C4⋊C4—341no—
483C4⋊C4—341no—
484C4⋊C4—341no—
485C4⋊C4—341no—
486C4⋊C4—682no—
487C4⋊C4—1361no—
488C4⋊C4—1361no—
489C4⋊C4—1361no—
490C4⋊C4C2×C4×D1712yes—
491C4⋊C4C2×C4×D1712yes—
492C4⋊C4Q8×D1712yes—
493C22⋊C4—342no—
494C22⋊C4—342no—
495C22⋊C4—344no—
496C22⋊C4—344no—
497C42—21no—
498C42—21no—
499C42—81no—
500C42—344no—
501C42—344no—
502C42—341no—
503C42—341no—
504C42—1361no—
505C42—1361no—
506C42—1361no—
507C23—172no—
508C23—172no—
509C23—172no—
510C23—341no—
511C23—341no—
512C23—341no—
513C23—341no—
514C23C2×D4×D1711yescharacteristic
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—172no—
534C2×C4—172no—
535C2×C4—172no—
536C2×C4—174no—
537C2×C4—174no—
538C2×C4—174no—
539C2×C4—174no—
540C2×C4—342no—
541C2×C4—342no—
542C2×C4—342no—
543C2×C4—341no—
544C2×C4—341no—
545C2×C4—341no—
546C2×C4—341no—
547C2×C4—341no—
548C2×C4—341no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4—681no—
552C2×C4—681no—
553C2×C4—681no—
554C2×C4—681no—
555C2×C4—681no—
556C2×C4—681no—
557C2×C4—681no—
558C2×C4—1364no—
559C2×C4—1364no—
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—41no—
568C8—342no—
569C8—681no—
570C22—174no—
571C22—342no—
572C22—342no—
573C22—342no—
574C22—342no—
575C22—342no—
576C22—342no—
577C22C4×D4×D1711yescharacteristic
578C22C22⋊Q8×D1711yescharacteristic
579C22#123×D1711yescharacteristic
580C22#1176361011yescharacteristic
581C22#1176361611yescharacteristic
582C22#1176361811yescharacteristic
583C22#1176362511yescharacteristic
584C4—42no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—174no—
591C4—682no—
592C4—682no—
593C4—682no—
594C4—681no—
595C4—681no—
596C4—1361no—
597C4#117×D1711yescharacteristic
598C4C4×Q8×D1711yescharacteristic
599C4#125×D1711yescharacteristic
600C4#126×D1711yescharacteristic
601C2—344no—
602C2D17×#38711yescharacteristic
603C2#1453760911yescharacteristic
604C2#1453762611yescharacteristic
605C2#1453863011yescharacteristic
606C2#1453864911yescharacteristic
607C2#1453873511yescharacteristic
608C2#1453875011yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1918C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
cosocleC22×C4×C17C24
hypercenter#1918D17
hypocenterC17#21035
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. #14529378C2semidirect
5. #14529373C2semidirect
6. #14529370C2semidirect
7. #14529367C2semidirect
8. #14529362C2semidirect
9. #14529361C2semidirect
10. #14529358C2semidirect
15. C17×#1918C2semidirect
23. #11762850C4semidirect
111. C17×#107C2×C4semidirect
120. #10587488C2×C4semidirect
121. #10587479C2×C4semidirect
122. #10587478C2×C4semidirect
276. #1918D17semidirect
416. #107C4×D17semidirect
427. C17#21035semidirect

Maximal subgroups

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

subgroupindex
C2×#117628502
#145314062
#145311382
#145293782
#145293732
#145293702
#145293672
#145293622
#145293612
#145293582
#145285022
#145284992
D17×#3402
#145284792
C17×#19182
#2103517