Finite Group Databasebeta

← #17037445

Subgroups — #17037445

Order 4352.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762907C211yesmaximal, characteristic
2#14531428C211yesmaximal, characteristic
3#14529411C211yesmaximal, characteristic
4#14529404C211yesmaximal, characteristic
5#14529376C211yesmaximal, characteristic, complemented
6#14529355C211yesmaximal, characteristic, complemented
7#14529139C211yesmaximal, characteristic
8#14529139C211yesmaximal, characteristic
9#14529052C211yesmaximal, characteristic, complemented
10#14529038C211yesmaximal, characteristic, complemented
11#14528682C211yesmaximal, characteristic, complemented
12C4×#10587506C211yesmaximal, characteristic, complemented
13C4×#10587480C211yesmaximal, characteristic
14#14528536C211yesmaximal, characteristic, complemented
15C17×#2276C211yesmaximal, characteristic, complemented
16C22×#63230C2211yescharacteristic
17C2×C4×D68C2211yescharacteristic
18#11762907C418yescomplemented
19C2×#10587478C2211yescharacteristic
20C2×#10587478C2211yescharacteristic
21C2×#10587479C2211yescharacteristic
22C2×#10587506C2211yescharacteristic
23C2×#10587506C2211yescharacteristic
24C2×#10587506C2211yescharacteristic
25C2×#10587480C2211yescharacteristic
26C2×#10587480C2211yescharacteristic
27C2×#10587480C2211yescharacteristic
28C2×#10587474C2211yescharacteristic
29C2×C4×#3622C2211yescharacteristic
30#11762711C2211yescharacteristic
31#11762711C2211yescharacteristic
32#11762707C2211yescharacteristic
33#11762707C2211yescharacteristic
34#11762698—21no—
35#11762698—21no—
36#11762671—21no—
37#11762668—21no—
38C4×C4⋊Dic17C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762564C2211yescharacteristic
46#11762564C2211yescharacteristic
47#11762564C2211yescharacteristic
48#11762564C2211yescharacteristic
49C2×C4×Q8×C17C2211yescharacteristic
50C2×C4×Q8×C17C2211yescharacteristic
51C2×C4×Q8×C17C2211yescharacteristic
52C4×C4⋊C4×C17—21no—
53C4×C4⋊C4×C17—21no—
54C4×C4⋊C4×C17—21no—
55C4×C4⋊C4×C17C2211yescharacteristic
56C4×C4⋊C4×C17C2211yescharacteristic
57C4×C4⋊C4×C17C2211yescharacteristic
58C17×#376—21no—
59C17×#376C2211yescharacteristic
60C22×Q8×C17C2311yescharacteristic
61C22×D68C2311yescharacteristic
62C22×C4×D17—21no—
63C4×Q8×C17—22no—
64C4×Q8×C17—22no—
65C4×Q8×C17—22no—
66C4×Q8×C17—22no—
67C4×Q8×C17—22no—
68C4×Q8×C17C2×C414yes—
69C2×C4⋊C4×C17—21no—
70C2×C4⋊C4×C17—21no—
71C2×C4⋊C4×C17—21no—
72C2×C4⋊C4×C17C2311yescharacteristic
73C2×C4⋊C4×C17C2311yescharacteristic
74C2×C4⋊C4×C17C2311yescharacteristic
75C2×C42×C17—21no—
76C2×C42×C17—21no—
77C2×C42×C17—21no—
78C2×C42×C17—21no—
79C2×C42×C17—21no—
80C2×C42×C17—21no—
81C2×C42×C17C2311yescharacteristic
82C2×C42×C17C2311yescharacteristic
83C2×C42×C17C2311yescharacteristic
84C2×#63230—22no—
85C2×#63230—22no—
86C2×#63230C2×C414yes—
87C2×#63227—21no—
88C2×#63227—21no—
89C2×#63227—21no—
90C2×#63227—21no—
91C2×#63227—21no—
92C2×C4⋊Dic17C2311yescharacteristic
93C2×C4⋊Dic17C2311yescharacteristic
94C2×C4⋊Dic17C2311yescharacteristic
95C2×#63225—21no—
96C2×#63225—21no—
97C2×C4×Dic17—21no—
98C22×#3622C2311yescharacteristic
99C22×#3622C2311yescharacteristic
100C22×#3622C2311yescharacteristic
101C22×#3622C2311yescharacteristic
102C4×D68—22no—
103C4×D68C2×C414yes—
104C17×#95—21no—
105C17×#95—21no—
106C17×#95—21no—
107C17×#95D411yescharacteristic
108C17×#95D411yescharacteristic
109C17×#95D411yescharacteristic
110C17×#95D411yescharacteristic
111#10587506—22no—
112#10587506—22no—
113#10587506C2×C414yes—
114#10587502—21no—
115#10587502—21no—
116#10587502—21no—
117#10587480—22no—
118#10587480—22no—
119#10587480C2×C414yes—
120#10587479—22no—
121#10587478—22no—
122#10587478C2×C414yes—
123#10587474C2×C414yes—
124C4×#3622—22no—
125C23×D17—21no—
126C2×Q8×C17—21no—
127C2×Q8×C17—21no—
128C2×Q8×C17—21no—
129C2×Q8×C17C22×C412yes—
130C2×Q8×C17#4112yes—
131C2×Q8×C17#4112yes—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17C2×D411yescharacteristic
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2×D411yescharacteristic
139C22×C4×C17C2×D411yescharacteristic
140C22×C4×C17C2×D411yescharacteristic
141C22×C4×C17C2×D411yescharacteristic
142C22×C4×C17C2411yescharacteristic
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C2×D68—21no—
147C2×D68—21no—
148C2×D68—21no—
149C2×D68—21no—
150C2×D68—21no—
151C2×D68C22×C412yes—
152C2×C4×D17—24no—
153C2×C4×D17—81no—
154C2×C4×D17—81no—
155C4⋊C4×C17—24no—
156C4⋊C4×C17—24no—
157C4⋊C4×C17—24no—
158C4⋊C4×C17—21no—
159C4⋊C4×C17—21no—
160C4⋊C4×C17—21no—
161C4⋊C4×C17C22×C412yes—
162C4⋊C4×C17#4112yes—
163C4⋊C4×C17#4112yes—
164C42×C17—24no—
165C42×C17—24no—
166C42×C17—24no—
167C42×C17—21no—
168C42×C17—21no—
169C42×C17—21no—
170C42×C17—21no—
171C42×C17—81no—
172C42×C17—81no—
173C42×C17—81no—
174C42×C17C22×C412yes—
175C42×C17#4112yes—
176#63230—28no—
177#63227—24no—
178#63227—81no—
179#63227—81no—
180#63227—81no—
181#63227—81no—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17C22×C412yes—
188#63225—81no—
189#63225—81no—
190C4×Dic17—81no—
191C2×#3622—21no—
192C2×#3622—21no—
193C2×#3622—21no—
194C2×#3622—21no—
195C2×#3622—21no—
196C2×#3622—21no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622C22×C412yes—
202C2×#3622C22×C412yes—
203#21128—171nomaximal, Sylow
204C23×C17C22×D411yescharacteristic
205C22×D17—22no—
206C22×D17—41no—
207C22×D17—41no—
208C22×D17—41no—
209C22×D17—41no—
210C22×D17—41no—
211C22×D17—41no—
212Q8×C17—22no—
213Q8×C17—22no—
214Q8×C17—22no—
215Q8×C17#11714yes—
216C2×C4×C17—22no—
217C2×C4×C17—22no—
218C2×C4×C17—22no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—22no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—22no—
229C2×C4×C17—22no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17—21no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—41no—
239C2×C4×C17—41no—
240C2×C4×C17—41no—
241C2×C4×C17—41no—
242C2×C4×C17—41no—
243C2×C4×C17—41no—
244C2×C4×C17C4×D412yes—
245C2×C4×C17C4×D412yes—
246C2×C4×C17C23×C411yescharacteristic
247C2×C4×C17C2×#4111yescharacteristic
248C2×C4×C17C2×#4111yescharacteristic
249C2×C4×C17C2×#4111yescharacteristic
250C2×C4×C17C2×#4111yescharacteristic
251C2×C4×C17C2×#4111yescharacteristic
252C2×Dic17—22no—
253C2×Dic17—41no—
254C2×Dic17—41no—
255C2×Dic17—41no—
256C2×Dic17—41no—
257C2×Dic17—41no—
258C2×Dic17—41no—
259C2×Dic17—41no—
260C2×Dic17—41no—
261D68—22no—
262D68—22no—
263D68—41no—
264D68—41no—
265C4×D17—84no—
266#3622—22no—
267#3622—22no—
268#3622—41no—
269#3622—41no—
270C2×#440—171no—
271#2319—171no—
272#2276D1711yescharacteristic, complemented
273#1926—171no—
274#1925—171no—
275#1921—171no—
276#1918—171no—
277#1880—171no—
278#1880—171no—
279#1865—171no—
280#1863—171no—
281#1776—171no—
282C4×#103—171no—
283C4×#102—171no—
284#1746—171no—
285C22×C17C2×C4×D411yescharacteristic
286C22×C17#52511yescharacteristic
287C22×C17#52511yescharacteristic
288C22×C17#57611yescharacteristic
289C22×C17#57711yescharacteristic
290C22×C17#57711yescharacteristic
291C22×C17#57811yescharacteristic
292C2×D17—42no—
293C2×D17—42no—
294C2×D17—42no—
295C2×D17—81no—
296C2×D17—81no—
297C2×D17—81no—
298C2×D17—81no—
299C4×C17—22no—
300C4×C17—22no—
301C4×C17—24no—
302C4×C17—41no—
303C4×C17—42no—
304C4×C17—41no—
305C4×C17—41no—
306C4×C17—42no—
307C4×C17—41no—
308C4×C17—42no—
309C4×C17C2×#11711yescharacteristic
310C4×C17C4×#4111yescharacteristic
311C4×C17#52911yescharacteristic
312C4×C17#52911yescharacteristic
313Dic17—42no—
314Dic17—81no—
315Dic17—81no—
316C22×SD16—171no—
317C2×C4×Q8C2×D1711yescharacteristic
318C2×C4×Q8C2×D1711yescharacteristic
319C2×C4×Q8C2×D1711yescharacteristic
320C2×C4×D4—171no—
321#440—178no—
322C2×#107—171no—
323C2×#107—171no—
324C2×#106—171no—
325C2×#103—171no—
326C2×#103—171no—
327C2×#103—171no—
328C2×#102—171no—
329C2×#102—171no—
330C2×#102—171no—
331C2×#97—171no—
332C2×C4×C8—171no—
333#390—171no—
334#390—171no—
335#389—171no—
336#389—171no—
337#388—341no—
338#388—341no—
339#381—341no—
340#380—341no—
341C4×C4⋊C4—21no—
342C4×C4⋊C4—21no—
343C4×C4⋊C4—21no—
344C4×C4⋊C4—171no—
345C4×C4⋊C4C2×D1711yescharacteristic
346C4×C4⋊C4C2×D1711yescharacteristic
347C4×C4⋊C4C2×D1711yescharacteristic
348#376—21no—
349#376C2×D1711yescharacteristic
350#340—171no—
351#340—171no—
352#340—171no—
353#340—171no—
354#340—171no—
355#340—171no—
356#336—171no—
357#336—171no—
358#336—171no—
359#336—171no—
360C2×C17#229011yescharacteristic
361C2×C17#294611yescharacteristic
362C2×C17#294711yescharacteristic
363C2×C17#311911yescharacteristic
364C2×C17#312111yescharacteristic
365C2×C17#312411yescharacteristic
366C2×C17#312611yescharacteristic
367D17—82no—
368C22×Q8C22×D1711yescharacteristic
369C22×D4—171no—
370C23×C4—341no—
371C2×SD16—174no—
372C2×SD16—342no—
373C2×SD16—342no—
374C22×C8—171no—
375C22×C8—171no—
376C22×C8—171no—
377C22×C8—171no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8C4×D1714yes—
384C4×D4—174no—
385C4×D4—342no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—171no—
390C2×C4⋊C4—171no—
391C2×C4⋊C4—171no—
392C2×C4⋊C4—341no—
393C2×C4⋊C4—341no—
394C2×C4⋊C4C22×D1711yescharacteristic
395C2×C4⋊C4C22×D1711yescharacteristic
396C2×C4⋊C4C22×D1711yescharacteristic
397C2×C22⋊C4—341no—
398C2×C22⋊C4—341no—
399C2×C22⋊C4—341no—
400C2×C22⋊C4—341no—
401C2×C22⋊C4—341no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—341no—
409C2×C42C22×D1711yescharacteristic
410C2×C42C22×D1711yescharacteristic
411C2×C42C22×D1711yescharacteristic
412#107—174no—
413#107—342no—
414#106—342no—
415#103—174no—
416#103—342no—
417#103—342no—
418#102—174no—
419#102—342no—
420#102—342no—
421#97—174no—
422C4×C8—342no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—341no—
427#95—341no—
428#95—341no—
429#95C22⋊D1711yescharacteristic
430#95C22⋊D1711yescharacteristic
431#95C22⋊D1711yescharacteristic
432#95C22⋊D1711yescharacteristic
433C17#2112811yescharacteristic, complemented, Sylow
434C24—341no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×C4×D1712yes—
439C2×Q8#6325212yes—
440C2×Q8#6325212yes—
441C2×D4—172no—
442C2×D4—341no—
443C2×D4—341no—
444C2×D4—341no—
445C2×D4—341no—
446C2×D4—341no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—341no—
452C22×C4—344no—
453C22×C4—341no—
454C22×C4—341no—
455C22×C4—1361no—
456C22×C4—1361no—
457C22×C4C2×C22⋊D1711yescharacteristic
458C22×C4C2×C22⋊D1711yescharacteristic
459C22×C4C2×C22⋊D1711yescharacteristic
460C22×C4C2×C22⋊D1711yescharacteristic
461C22×C4C2×C22⋊D1711yescharacteristic
462C22×C4C2×C22⋊D1711yescharacteristic
463C22×C4C23×D1711yescharacteristic
464SD16—348no—
465C2×C8—172no—
466C2×C8—172no—
467C2×C8—341no—
468C2×C8—341no—
469C2×C8—341no—
470C2×C8—341no—
471C2×C8—341no—
472C2×C8—341no—
473C2×C8—341no—
474C2×C8—341no—
475C2×C8—341no—
476C2×C8—341no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—24no—
483C4⋊C4—172no—
484C4⋊C4—341no—
485C4⋊C4—341no—
486C4⋊C4—341no—
487C4⋊C4—341no—
488C4⋊C4—341no—
489C4⋊C4—1361no—
490C4⋊C4—1361no—
491C4⋊C4C2×C4×D1712yes—
492C4⋊C4#6325212yes—
493C4⋊C4#6325212yes—
494C22⋊C4—344no—
495C22⋊C4—1361no—
496C22⋊C4—1361no—
497C22⋊C4—1361no—
498C22⋊C4—1361no—
499C42—24no—
500C42—24no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—24no—
506C42—81no—
507C42—81no—
508C42—81no—
509C42—1361no—
510C42C2×C4×D1712yes—
511C42#6325212yes—
512C23—342no—
513C23—681no—
514C23—681no—
515C23—681no—
516C23—681no—
517C23—681no—
518C23—681no—
519C23C22×C22⋊D1711yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8#1058755814yes—
524D4—342no—
525D4—342no—
526D4—681no—
527D4—681no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—342no—
557C2×C4—681no—
558C2×C4—681no—
559C2×C4—681no—
560C2×C4—681no—
561C2×C4—681no—
562C2×C4—681no—
563C2×C4—681no—
564C2×C4—681no—
565C2×C4—1364no—
566C2×C4C4×C22⋊D1712yes—
567C2×C4C4×C22⋊D1712yes—
568C2×C4C22×C4×D1711yescharacteristic
569C2×C4C2×#6325211yescharacteristic
570C2×C4C2×#6325211yescharacteristic
571C2×C4C2×#6325211yescharacteristic
572C2×C4C2×#6325211yescharacteristic
573C2×C4C2×#6325211yescharacteristic
574C8—342no—
575C8—342no—
576C8—681no—
577C8—681no—
578C22—682no—
579C22—682no—
580C22—682no—
581C22—1361no—
582C22—1361no—
583C22—1361no—
584C22—1361no—
585C22C2×C4×C22⋊D1711yescharacteristic
586C22#1176332011yescharacteristic
587C22#1176332011yescharacteristic
588C22#1176361211yescharacteristic
589C22#1176361711yescharacteristic
590C22#1176361711yescharacteristic
591C22#1176362411yescharacteristic
592C4—22no—
593C4—24no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—42no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—42no—
602C4—682no—
603C4—1361no—
604C4—1361no—
605C4C2×#1058755811yescharacteristic
606C4C4×#6325211yescharacteristic
607C4#1176334311yescharacteristic
608C4#1176334311yescharacteristic
609C2—1362no—
610C2#1453122711yescharacteristic
611C2#1453761211yescharacteristic
612C2#1453762711yescharacteristic
613C2#1453898311yescharacteristic
614C2#1453901311yescharacteristic
615C2#1453904611yescharacteristic
616C2#1453907511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2276C2
socleC23×C17C22×D4
prime radicalC22×D68C23
cosocleC22×C4×C17C24
hypercenter#2276D17
hypocenterC17#21128
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ #376 ◁ #2276

Complements

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

NH ≅ G/Ntype
5. #14529376C2semidirect
6. #14529355C2semidirect
9. #14529052C2semidirect
10. #14529038C2semidirect
11. #14528682C2semidirect
12. C4×#10587506C2semidirect
14. #14528536C2semidirect
15. C17×#2276C2semidirect
18. #11762907C4semidirect
272. #2276D17semidirect
433. C17#21128semidirect

Maximal subgroups

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

subgroupindex
C2×#117629072
#145314282
#145294112
#145294042
#145293762
#145293552
#145291392
#145290522
#145290382
#145286822
C4×#105875062
C4×#105874802
#145285362
C17×#22762
#2112817