Finite Group Databasebeta

← #17042096

Subgroups — #17042096

Order 4352.

876 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763100C211yesmaximal, characteristic
2#14531532C211yesmaximal, characteristic, complemented
3#14531146C211yesmaximal, characteristic
4#14529735C211yesmaximal, characteristic, complemented
5#14529554C211yesmaximal, characteristic, complemented
6#14529370C211yesmaximal, characteristic, complemented
7#14529363C211yesmaximal, characteristic, complemented
8#14529048C211yesmaximal, characteristic
9#14529034C211yesmaximal, characteristic
10#14528795C211yesmaximal, characteristic
11#14528681C211yesmaximal, characteristic, complemented
12C4×#10587488C211yesmaximal, characteristic, complemented
13#14528610C211yesmaximal, characteristic
14C4×#10587492C211yesmaximal, characteristic
15C17×#1768C211yesmaximal, characteristic, complemented
16C2×#10587555C2211yescharacteristic
17C2×C4×D68C2211yescharacteristic
18C2×C4×D68C2211yescharacteristic
19C2×C4×D68C2211yescharacteristic
20#11763100C418yescomplemented
21C2×#10587489C2211yescharacteristic
22C2×#10587488C2211yescharacteristic
23C2×#10587488C2211yescharacteristic
24C2×#10587488C2211yescharacteristic
25C2×#10587492C2211yescharacteristic
26C2×#10587492C2211yescharacteristic
27C2×#10587492C2211yescharacteristic
28C2×#10587492C2211yescharacteristic
29#11762713—21no—
30#11762713—21no—
31#11762707C2211yescharacteristic
32#11762707C2211yescharacteristic
33#11762692—21no—
34#11762692—21no—
35#11762675C2211yescharacteristic
36C4×C4⋊Dic17C2211yescharacteristic
37C4×C4⋊Dic17C2211yescharacteristic
38C4×C4⋊Dic17C2211yescharacteristic
39C4×C4⋊Dic17C2211yescharacteristic
40C4×C4⋊Dic17C2211yescharacteristic
41#11762656—21no—
42#11762656—21no—
43#11762656—21no—
44#95×D17—21no—
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52#11762572C2211yescharacteristic
53C2×C17×C4⋊C8C2211yescharacteristic
54C2×C17×C4⋊C8C2211yescharacteristic
55C2×C17×#97C2211yescharacteristic
56C2×C4×C8×C17C2211yescharacteristic
57C17×#376C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C17×#336C2211yescharacteristic
60C22×D68C2311yescharacteristic
61C22×C4×D17—21no—
62C22×C4×D17—21no—
63C22×C4×D17—21no—
64C22×Dic34—21no—
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C22×C8×C17C2311yescharacteristic
69C2×C42×C17C2311yescharacteristic
70C2×C42×C17C2311yescharacteristic
71C2×C42×C17C2311yescharacteristic
72C2×#63227—21no—
73C2×#63227—21no—
74C2×#63227—21no—
75C2×C4⋊Dic17—21no—
76C2×C4⋊Dic17C2311yescharacteristic
77C2×C4⋊Dic17C2311yescharacteristic
78C2×C4⋊Dic17C2311yescharacteristic
79C2×C4⋊Dic17C2311yescharacteristic
80C2×C4⋊Dic17C2311yescharacteristic
81C2×C4⋊Dic17C2311yescharacteristic
82C2×C4⋊Dic17C2311yescharacteristic
83C2×#63225—21no—
84C2×#63225—21no—
85C2×C4×Dic17—21no—
86C2×C4×Dic17—21no—
87C2×C4×Dic17—21no—
88C2×C4×Dic17—21no—
89C2×C4×Dic17—21no—
90C4×D68—22no—
91C4×D68—22no—
92C4×D68—22no—
93C4×D68—22no—
94C4×D68C2×C414yes—
95C4×D68Q814yescomplemented
96#10587555—22no—
97#10587555C2×C414yescomplemented
98C17×C4⋊C8—22no—
99C17×C4⋊C8C2×C414yescomplemented
100C17×#97—22no—
101C4×C8×C17—22no—
102C17×#95D411yescharacteristic
103C17×#95D411yescharacteristic
104C17×#95D411yescharacteristic
105C17×#95D411yescharacteristic
106#10587502—21no—
107#10587502—21no—
108#10587502—21no—
109#10587502—21no—
110#10587502—21no—
111#10587502—21no—
112#10587502—21no—
113#10587502—21no—
114#10587502—21no—
115#10587492—22no—
116#10587492—22no—
117#10587492C2×C414yes—
118#10587492C2×C414yes—
119#10587489—22no—
120#10587488—22no—
121#10587488C2×C414yescomplemented
122#10587488C2×C414yescomplemented
123C23×D17—21no—
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2×D411yescharacteristic
126C22×C4×C17C2×D411yescharacteristic
127C22×C4×C17C2×D411yescharacteristic
128C22×C4×C17C2×D411yescharacteristic
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2411yescharacteristic
131C22×Dic17—21no—
132C22×Dic17—21no—
133C22×Dic17—21no—
134C22×Dic17—21no—
135C22×Dic17—21no—
136C22×Dic17—21no—
137C22×Dic17—21no—
138C2×D68—21no—
139C2×D68—21no—
140C2×D68—21no—
141C2×D68C22×C412yes—
142C2×D68C2×Q812yes—
143C2×D68#4112yes—
144C2×C4×D17—24no—
145C2×C4×D17—24no—
146C2×C4×D17—24no—
147C2×C4×D17—81no—
148C2×C4×D17—81no—
149C2×C4×D17—81no—
150C2×C4×D17—81no—
151C2×C4×D17—81no—
152C2×C4×D17—81no—
153C2×Dic34—24no—
154C2×Dic34—81no—
155C2×Dic34—81no—
156C2×C8×C17—21no—
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×C17C22×C412yes—
167C2×C8×C17C22×C412yes—
168C42×C17—21no—
169C42×C17—21no—
170C42×C17C22×C412yes—
171C42×C17C2×Q812yes—
172C42×C17#4112yes—
173C42×C17#4112yes—
174#63227—24no—
175#63227—24no—
176#63227—24no—
177C4⋊Dic17—24no—
178C4⋊Dic17—21no—
179C4⋊Dic17—21no—
180C4⋊Dic17—21no—
181C4⋊Dic17—21no—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17C22×C412yes—
188C4⋊Dic17C22×C412yes—
189C4⋊Dic17C22×C412yes—
190C4⋊Dic17C2×Q812yes—
191C4⋊Dic17#4112yes—
192#63225—81no—
193#63225—81no—
194C4×Dic17—81no—
195C4×Dic17—81no—
196C4×Dic17—81no—
197C4×Dic17—81no—
198C4×Dic17—81no—
199#21623—171nomaximal, Sylow
200C23×C17C22×D411yescharacteristic
201C22×D17—22no—
202C22×D17—22no—
203C22×D17—22no—
204C22×D17—41no—
205C22×D17—41no—
206C22×D17—41no—
207C22×D17—41no—
208C2×C4×C17—21no—
209C2×C4×C17—21no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
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—21no—
221C2×C4×C17—21no—
222C2×C4×C17C4×D412yes—
223C2×C4×C17C4×D412yes—
224C2×C4×C17C22⋊Q812yes—
225C2×C4×C17C22⋊Q812yes—
226C2×C4×C17C23×C411yescharacteristic
227C2×C4×C17C22×Q811yescharacteristic
228C2×C4×C17C2×#4111yescharacteristic
229C2×C4×C17C2×#4111yescharacteristic
230C2×C4×C17C2×#4111yescharacteristic
231C2×C4×C17C2×#4111yescharacteristic
232C2×Dic17—22no—
233C2×Dic17—22no—
234C2×Dic17—22no—
235C2×Dic17—22no—
236C2×Dic17—22no—
237C2×Dic17—41no—
238C2×Dic17—41no—
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×Dic17—41no—
252C2×Dic17—41no—
253D68—22no—
254D68—22no—
255D68—22no—
256D68C4×Q814yes—
257C4×D17—84no—
258C4×D17—84no—
259C4×D17—84no—
260Dic34—84no—
261C8×C17—22no—
262C8×C17—22no—
263C8×C17—41no—
264C8×C17—41no—
265C2×#476—171no—
266#2331—171no—
267#2275—171no—
268#1988—171no—
269#1949—171no—
270#1920—171no—
271#1919—171no—
272#1864—171no—
273#1862—171no—
274#1804—171no—
275#1776—171no—
276C4×#106—171no—
277#1768D1711yescharacteristic, complemented
278#1762—171no—
279C4×#102—171no—
280C22×C17C2×C4×D411yescharacteristic
281C22×C17C2×C22⋊Q811yescharacteristic
282C22×C17#52511yescharacteristic
283C22×C17#57611yescharacteristic
284C22×C17#57711yescharacteristic
285C22×C17#57711yescharacteristic
286C22×C17#57711yescharacteristic
287C2×D17—24no—
288C2×D17—42no—
289C2×D17—42no—
290C2×D17—42no—
291C2×D17—42no—
292C2×D17—42no—
293C2×D17—42no—
294C4×C17—22no—
295C4×C17—22no—
296C4×C17—22no—
297C4×C17—22no—
298C4×C17—41no—
299C4×C17—41no—
300C4×C17C2×C4×Q811yescharacteristic
301C4×C17C4×#4111yescharacteristic
302C4×C17#52911yescharacteristic
303C4×C17#53311yescharacteristic
304Dic17—42no—
305Dic17—42no—
306Dic17—42no—
307Dic17—42no—
308Dic17—42no—
309Dic17—81no—
310Dic17—81no—
311C2×C4⋊Q8—171no—
312C2×C4×D4—171no—
313C2×C4×D4—171no—
314C2×C4×D4—171no—
315#476—178no—
316C2×#107—171no—
317C2×#106—171no—
318C2×#106—171no—
319C2×#106—171no—
320C2×C4⋊C8C2×D1711yescharacteristic
321C2×C4⋊C8C2×D1711yescharacteristic
322C2×#102—171no—
323C2×#102—171no—
324C2×#102—171no—
325C2×#102—171no—
326C2×#97C2×D1711yescharacteristic
327C2×C4×C8C2×D1711yescharacteristic
328#391—341no—
329#391—341no—
330#389—171no—
331#389—171no—
332#387—341no—
333#387—341no—
334#382—171no—
335C4×C4⋊C4—171no—
336C4×C4⋊C4—171no—
337C4×C4⋊C4—171no—
338C4×C4⋊C4—171no—
339C4×C4⋊C4—171no—
340C4×C22⋊C4—341no—
341C4×C22⋊C4—341no—
342C4×C22⋊C4—341no—
343#376C2×D1711yescharacteristic
344C2×#95—341no—
345#340—171no—
346#340—171no—
347#340—171no—
348#340—171no—
349#340—171no—
350#340—171no—
351#340—171no—
352#340—171no—
353#336C2×D1711yescharacteristic
354#336C2×D1711yescharacteristic
355C2×C17C4×C22⋊Q811yescharacteristic
356C2×C17#294611yescharacteristic
357C2×C17#294911yescharacteristic
358C2×C17#308111yescharacteristic
359C2×C17#308411yescharacteristic
360C2×C17#311811yescharacteristic
361C2×C17#312511yescharacteristic
362D17—44no—
363C22×Q8—341no—
364C22×D4—171no—
365C23×C4—341no—
366C23×C4—341no—
367C23×C4—341no—
368C22×C8C22×D1711yescharacteristic
369C22×C8C22×D1711yescharacteristic
370C22×C8C22×D1711yescharacteristic
371C22×C8C22×D1711yescharacteristic
372C4⋊Q8—174no—
373C4⋊Q8—342no—
374C4×D4—174no—
375C4×D4—174no—
376C4×D4—342no—
377C4×D4—342no—
378C4×D4—342no—
379C4×D4—342no—
380C2×C4⋊C4—171no—
381C2×C4⋊C4—171no—
382C2×C4⋊C4—171no—
383C2×C4⋊C4—171no—
384C2×C4⋊C4—171no—
385C2×C4⋊C4—171no—
386C2×C4⋊C4—171no—
387C2×C4⋊C4—341no—
388C2×C4⋊C4—341no—
389C2×C4⋊C4—341no—
390C2×C22⋊C4—341no—
391C2×C22⋊C4—341no—
392C2×C22⋊C4—341no—
393C2×C42—341no—
394C2×C42—341no—
395C2×C42—341no—
396C2×C42—341no—
397C2×C42—341no—
398C2×C42C22×D1711yescharacteristic
399C2×C42C22×D1711yescharacteristic
400C2×C42C22×D1711yescharacteristic
401#107—342no—
402#106—174no—
403#106—174no—
404#106—342no—
405C4⋊C8—22no—
406C4⋊C8C4×D1714yescomplemented
407#102—174no—
408#102—174no—
409#102—342no—
410#102—342no—
411#97—22no—
412C4×C8—22no—
413#95—341no—
414#95—341no—
415#95—341no—
416#95—341no—
417#95—341no—
418#95—341no—
419#95—341no—
420#95—341no—
421#95—341no—
422#95D6811yescharacteristic
423#95D6811yescharacteristic
424#95D6811yescharacteristic
425#95D6811yescharacteristic
426C17#2162311yescharacteristic, complemented, Sylow
427C24—341no—
428C2×Q8—344no—
429C2×Q8—1361no—
430C2×Q8—1361no—
431C2×D4—172no—
432C2×D4—172no—
433C2×D4—172no—
434C2×D4—341no—
435C2×D4—341no—
436C2×D4—341no—
437C22×C4—344no—
438C22×C4—341no—
439C22×C4—341no—
440C22×C4—341no—
441C22×C4—341no—
442C22×C4—341no—
443C22×C4—344no—
444C22×C4—344no—
445C22×C4—341no—
446C22×C4—341no—
447C22×C4—1361no—
448C22×C4—1361no—
449C22×C4—1361no—
450C22×C4—1361no—
451C22×C4—1361no—
452C22×C4—1361no—
453C22×C4C2×D6811yescharacteristic
454C22×C4C2×D6811yescharacteristic
455C22×C4C2×D6811yescharacteristic
456C22×C4C2×D6811yescharacteristic
457C22×C4C2×D6811yescharacteristic
458C22×C4C2×D6811yescharacteristic
459C22×C4C23×D1711yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×C4×D1712yes—
471C2×C8C2×C4×D1712yes—
472C4⋊C4—172no—
473C4⋊C4—172no—
474C4⋊C4—172no—
475C4⋊C4—172no—
476C4⋊C4—172no—
477C4⋊C4—341no—
478C4⋊C4—341no—
479C4⋊C4—341no—
480C4⋊C4—341no—
481C4⋊C4—341no—
482C4⋊C4—344no—
483C4⋊C4—341no—
484C4⋊C4—341no—
485C4⋊C4—341no—
486C4⋊C4—341no—
487C4⋊C4—1361no—
488C4⋊C4—1361no—
489C22⋊C4—344no—
490C22⋊C4—344no—
491C22⋊C4—344no—
492C42—21no—
493C42—21no—
494C42—1361no—
495C42—1361no—
496C42—1361no—
497C42—1361no—
498C42—1361no—
499C42C2×C4×D1712yes—
500C42#6325212yes—
501C42#6325412yes—
502C42Q8×D1712yes—
503C23—342no—
504C23—342no—
505C23—342no—
506C23—681no—
507C23—681no—
508C23—681no—
509C23—681no—
510C23C22×D6811yescharacteristic
511Q8—1364no—
512D4—174no—
513D4—342no—
514D4—342no—
515D4—342no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—342no—
531C2×C4—342no—
532C2×C4—342no—
533C2×C4—342no—
534C2×C4—342no—
535C2×C4—681no—
536C2×C4—681no—
537C2×C4—681no—
538C2×C4—681no—
539C2×C4—681no—
540C2×C4—681no—
541C2×C4—681no—
542C2×C4—681no—
543C2×C4—681no—
544C2×C4—681no—
545C2×C4—681no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4—1364no—
552C2×C4—1364no—
553C2×C4—1364no—
554C2×C4C4×D6812yes—
555C2×C4C4×D6812yes—
556C2×C4#1058758312yes—
557C2×C4#1058758312yes—
558C2×C4C22×C4×D1711yescharacteristic
559C2×C4C2×#6325211yescharacteristic
560C2×C4C2×#6325411yescharacteristic
561C2×C4C2×Q8×D1711yescharacteristic
562C2×C4#41×D1711yescharacteristic
563C2×C4#41×D1711yescharacteristic
564C8—22no—
565C8—22no—
566C8—41no—
567C8—41no—
568C22—344no—
569C22—682no—
570C22—682no—
571C22—682no—
572C22—682no—
573C22—682no—
574C22—682no—
575C22C2×C4×D6811yescharacteristic
576C22C2×#1058758311yescharacteristic
577C22#1176332111yescharacteristic
578C22#1176361411yescharacteristic
579C22#1176362111yescharacteristic
580C22#1176362111yescharacteristic
581C22#1176362111yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—682no—
589C4—682no—
590C4—682no—
591C4—682no—
592C4—682no—
593C4—1361no—
594C4—1361no—
595C4C4×Q8×D1711yescharacteristic
596C4C4×#6325411yescharacteristic
597C4#1176334111yescharacteristic
598C4#1176336311yescharacteristic
599C2—684no—
600C2C4×#1058758311yescharacteristic
601C2#1453761811yescharacteristic
602C2#1453764511yescharacteristic
603C2#1453861611yescharacteristic
604C2#1453864811yescharacteristic
605C2#1453897011yescharacteristic
606C2#1453906311yescharacteristic
subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1768C2
socleC23×C17C22×D4
prime radicalC22×D68C23
cosocleC22×C4×C17C24
hypercenter#1768D17
hypocenterC17#21623
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
2. #14531532C2semidirect
4. #14529735C2semidirect
5. #14529554C2semidirect
6. #14529370C2semidirect
7. #14529363C2semidirect
11. #14528681C2semidirect
12. C4×#10587488C2semidirect
15. C17×#1768C2semidirect
20. #11763100C4semidirect
95. C4×D68Q8semidirect
97. #10587555C2×C4semidirect
99. C17×C4⋊C8C2×C4semidirect
121. #10587488C2×C4semidirect
122. #10587488C2×C4semidirect
277. #1768D17semidirect
406. C4⋊C8C4×D17semidirect
426. C17#21623semidirect

Maximal subgroups

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

subgroupindex
C2×#117631002
#145315322
#145311462
#145297352
#145295542
#145293702
#145293632
#145290482
#145290342
#145287952
#145286812
C4×#105874882
#145286102
C4×#105874922
C17×#17682
#2162317