Finite Group Databasebeta

← #16942174

Subgroups — #16942174

Order 4352.

822 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537301C211yesmaximal, characteristic
2C2×#11762806C211yesmaximal, characteristic
3#14537228C211yesmaximal, characteristic
4C2×#11762580C211yesmaximal, characteristic, complemented
5C2×#11762574C211yesmaximal, characteristic, complemented
6#14528493C211yesmaximal, characteristic, complemented
7C17×#1729C211yesmaximal, characteristic, complemented
8C22×#63252C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C22×#63223C2211yescharacteristic
11C2×#10587612C2211yescharacteristic
12#11762817—21no—
13#11762813—21no—
14#11762808C414yescomplemented
15#11762806—22no—
16#11762806—22no—
17#11762803—22no—
18C2×#10587487—21no—
19C2×#10587492—21no—
20#11762777—22no—
21#11762775—22no—
22#11762772—22no—
23#11762580—22no—
24#11762574—22no—
25#11762568—22no—
26C22×M16×C17C2211yescharacteristic
27C23×C8×C17C2211yescharacteristic
28C2×C17×#117C2211yescharacteristic
29C17×#336—22no—
30C23×C4×C17C2311yescharacteristic
31C22×C22⋊D17—21no—
32C2×#63252—21no—
33C2×#63252—21no—
34C2×#63252—21no—
35C2×#63252—21no—
36C2×#63252—21no—
37C2×#63252—21no—
38C2×#63252—21no—
39C2×#63252—21no—
40C2×#63252—21no—
41C2×#63252—21no—
42C2×#63252C2×C412yes—
43C2×#63252D412yes—
44C22×D68D411yescharacteristic
45C22×C4×D17—21no—
46C22×Dic34D411yescharacteristic
47C2×M16×C17—21no—
48C2×M16×C17—21no—
49C2×M16×C17—21no—
50C2×M16×C17—21no—
51C2×M16×C17—21no—
52C2×M16×C17—21no—
53C22×C8×C17—21no—
54C22×C8×C17—21no—
55C22×C8×C17—21no—
56C22×C8×C17—21no—
57C22×C8×C17—21no—
58C22×C8×C17—21no—
59C22×C8×C17D412yes—
60C22×C8×C17D412yes—
61C17×#117—21no—
62C17×#117—21no—
63C17×#117—21no—
64C17×#117—21no—
65C2×C4⋊C4×C17C2×C412yes—
66C2×C22⋊C4×C17—21no—
67C2×C42×C17—21no—
68C2×C22⋊Dic17—21no—
69#10587612—21no—
70#10587612—21no—
71#10587612—21no—
72#10587612D412yes—
73C2×C4⋊Dic17—21no—
74C2×C4×Dic17—21no—
75C2×#63223—21no—
76C2×#63223—21no—
77C2×#63223—21no—
78C2×#63223—21no—
79C2×#63223—21no—
80C2×#63223—21no—
81C2×#63223—21no—
82C2×#63223—21no—
83C2×#63223—21no—
84C2×#63223—21no—
85C2×#63223C2×C412yes—
86C2×#63223D412yes—
87C22×#3622—21no—
88C22×#3622—21no—
89#10587492—24no—
90#10587491—28no—
91#10587487—24no—
92#10587481—24no—
93#10587480—24no—
94C24×C17#4111yescharacteristic
95C23×D17—21no—
96C22×C4×C17—22no—
97C22×C4×C17C22×C411yescharacteristic
98C22×C4×C17C2×D411yescharacteristic
99C22×C4×C17C2×D411yescharacteristic
100C22×C4×C17C2×D411yescharacteristic
101C22×C4×C17C2×D411yescharacteristic
102C22×C4×C17C2×D411yescharacteristic
103C22×C4×C17C2×D411yescharacteristic
104C22×C4×C17#4111yescharacteristic
105C22×C4×C17#4111yescharacteristic
106C22×C4×C17#4111yescharacteristic
107C22×C4×C17#4111yescharacteristic
108C22×C4×C17#4111yescharacteristic
109C22×C4×C17#4111yescharacteristic
110C22×C4×C17#4111yescharacteristic
111C2×C22⋊D17—22no—
112C2×C22⋊D17—22no—
113C2×C22⋊D17—41no—
114C2×C22⋊D17—41no—
115C2×C22⋊D17—41no—
116C2×C22⋊D17—41no—
117C22×Dic17—21no—
118C22×Dic17—41no—
119#63252—22no—
120#63252—22no—
121#63252—22no—
122#63252—22no—
123#63252—22no—
124#63252—22no—
125#63252—22no—
126#63252—22no—
127#63252—41no—
128#63252—41no—
129#63252—41no—
130#63252—41no—
131#63252—41no—
132#63252—41no—
133#63252—41no—
134#63252—41no—
135C2×D68—21no—
136C2×D68—21no—
137C2×D68—21no—
138C2×D68—21no—
139C2×D68—21no—
140C2×D68C22⋊C412yes—
141C2×C4×D17—22no—
142C2×C4×D17—22no—
143C2×C4×D17—41no—
144C2×C4×D17—41no—
145C2×C4×D17—41no—
146C2×C4×D17—41no—
147C2×Dic34—21no—
148C2×Dic34—21no—
149C2×Dic34—21no—
150C2×Dic34—21no—
151C2×Dic34—21no—
152C2×Dic34C22⋊C412yes—
153M16×C17—41no—
154M16×C17—41no—
155M16×C17—41no—
156M16×C17—41no—
157C2×C8×C17—22no—
158C2×C8×C17—22no—
159C2×C8×C17—22no—
160C2×C8×C17—22no—
161C2×C8×C17—22no—
162C2×C8×C17—22no—
163C2×C8×C17—41no—
164C2×C8×C17—41no—
165C2×C8×C17—41no—
166C2×C8×C17—41no—
167C4⋊C4×C17—22no—
168C4⋊C4×C17—22no—
169C22⋊C4×C17—41no—
170C22⋊C4×C17—41no—
171C42×C17—41no—
172C42×C17—41no—
173C22⋊Dic17—22no—
174C22⋊Dic17—41no—
175C4⋊Dic17—22no—
176C4⋊Dic17—41no—
177C4×Dic17—22no—
178C4×Dic17—41no—
179#63223—22no—
180#63223—22no—
181#63223—22no—
182#63223—22no—
183#63223—41no—
184#63223—41no—
185#63223—41no—
186#63223—41no—
187C2×#3622—22no—
188C2×#3622—22no—
189C2×#3622—41no—
190C2×#3622—41no—
191C2×#3622—41no—
192C2×#3622—41no—
193#11194—171nomaximal, Sylow
194C23×C17—42no—
195C23×C17C4×D411yescharacteristic
196C23×C17#12111yescharacteristic
197C23×C17#12311yescharacteristic
198C23×C17#12311yescharacteristic
199C23×C17#12411yescharacteristic
200C23×C17#12611yescharacteristic
201C23×C17#12611yescharacteristic
202C22×D17—22no—
203C22×D17—41no—
204C22×D17—41no—
205C22×D17—82no—
206C2×C4×C17—44no—
207C2×C4×C17—42no—
208C2×C4×C17C2×C22⋊C411yescharacteristic
209C2×C4×C17#11711yescharacteristic
210C2×C4×C17#11711yescharacteristic
211C2×C4×C17C4×D411yescharacteristic
212C2×C4×C17C4×D411yescharacteristic
213C2×C4×C17C4×D411yescharacteristic
214C2×C4×C17#12011yescharacteristic
215C2×C4×C17#12011yescharacteristic
216C2×C4×C17#12111yescharacteristic
217C2×C4×C17#12111yescharacteristic
218C2×C4×C17#12111yescharacteristic
219C2×C4×C17#12111yescharacteristic
220C2×C4×C17#12111yescharacteristic
221C2×C4×C17#12111yescharacteristic
222C2×C4×C17#12111yescharacteristic
223C2×C4×C17#12311yescharacteristic
224C2×C4×C17#12311yescharacteristic
225C2×C4×C17#12311yescharacteristic
226C2×C4×C17#12311yescharacteristic
227C2×C4×C17#12311yescharacteristic
228C2×C4×C17#12311yescharacteristic
229C2×C4×C17#12311yescharacteristic
230C2×C4×C17#12311yescharacteristic
231C2×C4×C17#12411yescharacteristic
232C2×C4×C17#12411yescharacteristic
233C2×C4×C17#12411yescharacteristic
234C2×C4×C17#12611yescharacteristic
235C2×C4×C17#12611yescharacteristic
236C22⋊D17—42no—
237C22⋊D17—42no—
238C22⋊D17—42no—
239C22⋊D17—42no—
240C2×Dic17—22no—
241C2×Dic17—41no—
242C2×Dic17—41no—
243C2×Dic17—42no—
244C2×Dic17—82no—
245D68—22no—
246D68—22no—
247D68—41no—
248D68—41no—
249C4×D17—42no—
250C4×D17—42no—
251C4×D17—42no—
252C4×D17—42no—
253Dic34—22no—
254Dic34—22no—
255Dic34—41no—
256Dic34—41no—
257C8×C17—42no—
258C8×C17—42no—
259#3622—42no—
260#3622—42no—
261#2896—171no—
262C2×#416—171no—
263#2879—171no—
264C2×#344—171no—
265C2×#341—171no—
266#1733—171no—
267#1729D1711yescharacteristic, complemented
268C22×C17—22no—
269C22×C17—22no—
270C22×C17—22no—
271C22×C17—41no—
272C22×C17—41no—
273C22×C17—41no—
274C22×C17—41no—
275C22×C17#38611yescharacteristic
276C22×C17#38811yescharacteristic
277C22×C17#38811yescharacteristic
278C22×C17#39411yescharacteristic
279C22×C17#39711yescharacteristic
280C22×C17#39711yescharacteristic
281C22×C17#39711yescharacteristic
282C2×D17—44no—
283C2×D17—42no—
284C2×D17—82no—
285C2×D17—82no—
286C4×C17—82no—
287C4×C17#38111yescharacteristic
288C4×C17#38611yescharacteristic
289C4×C17#38811yescharacteristic
290C4×C17#38811yescharacteristic
291C4×C17#39411yescharacteristic
292C4×C17#39411yescharacteristic
293C4×C17#39411yescharacteristic
294C4×C17#39711yescharacteristic
295Dic17—42no—
296Dic17—82no—
297C22×#41—171no—
298C22×M16—171no—
299C22×M16—171no—
300C22×M16C2×D1711yescharacteristic
301C23×C8C2×D1711yescharacteristic
302C2×#117—171no—
303C2×#117C2×D1711yescharacteristic
304#419—341no—
305#418—341no—
306#417—174no—
307#416—342no—
308#416—342no—
309#416—342no—
310C2×#103—341no—
311C2×#102—341no—
312#408—342no—
313#408—342no—
314#407—342no—
315#344—342no—
316#341—342no—
317#339—342no—
318#336—22no—
319C2×C17—21no—
320C2×C17—21no—
321C2×C17—21no—
322C2×C17—21no—
323C2×C17—21no—
324C2×C17—21no—
325C2×C17#144011yescharacteristic
326C2×C17#188112yes—
327D17—82no—
328C2×#41—172no—
329C2×#41—172no—
330C2×#41—341no—
331C2×#41—341no—
332C2×#41—341no—
333C2×#41—341no—
334C2×#41—341no—
335C2×#41—341no—
336C2×#41—341no—
337C2×#41—341no—
338C2×#41—341no—
339C2×#41—341no—
340C22×Q8—171no—
341C22×D4—171no—
342C22×D4—341no—
343C23×C4—341no—
344C23×C4C22×D1711yescharacteristic
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—172no—
352C2×M16—172no—
353C2×M16—341no—
354C2×M16—341no—
355C2×M16—341no—
356C2×M16—341no—
357C2×M16—341no—
358C2×M16—341no—
359C2×M16—341no—
360C2×M16—341no—
361C2×M16—341no—
362C2×M16—341no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—341no—
370C22×C8—341no—
371C22×C8D6812yes—
372C22×C8C22⋊D1712yes—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—172no—
378#117—341no—
379#117—341no—
380#117—341no—
381C2×C4⋊C4—341no—
382C2×C4⋊C4C4×D1712yes—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—341no—
385C2×C42—21no—
386C2×C42—341no—
387#103—344no—
388#103—344no—
389#102—344no—
390#102—344no—
391C22⋊C8—348no—
392C17#1119411yescharacteristic, complemented, Sylow
393C24—341no—
394C24#6325211yescharacteristic
395#41—342no—
396#41—342no—
397#41—342no—
398#41—342no—
399#41—342no—
400#41—342no—
401#41—342no—
402#41—342no—
403#41—681no—
404#41—681no—
405#41—681no—
406#41—681no—
407#41—681no—
408#41—681no—
409#41—681no—
410#41—681no—
411C2×Q8—172no—
412C2×Q8—341no—
413C2×Q8—341no—
414C2×Q8—341no—
415C2×Q8—341no—
416C2×Q8—341no—
417C2×D4—172no—
418C2×D4—342no—
419C2×D4—342no—
420C2×D4—341no—
421C2×D4—341no—
422C2×D4—341no—
423C2×D4—341no—
424C2×D4—341no—
425C2×D4—681no—
426C2×D4—681no—
427C2×D4—681no—
428C2×D4—681no—
429C22×C4—22no—
430C22×C4—341no—
431C22×C4—342no—
432C22×C4—342no—
433C22×C4—681no—
434C22×C4—681no—
435C22×C4—681no—
436C22×C4—681no—
437C22×C4—681no—
438C22×C4C2×C4×D1711yescharacteristic
439C22×C4C2×D6811yescharacteristic
440C22×C4#6325211yescharacteristic
441C22×C4#6325211yescharacteristic
442C22×C4#6325211yescharacteristic
443C22×C4D4×D1711yescharacteristic
444C22×C4D4×D1711yescharacteristic
445C22×C4D4×D1711yescharacteristic
446C22×C4D4×D1711yescharacteristic
447C22×C4#6325411yescharacteristic
448C22×C4#6325411yescharacteristic
449C22×C4#6325611yescharacteristic
450C22×C4#6325611yescharacteristic
451C22×C4C2×C22⋊D1711yescharacteristic
452M16—41no—
453M16—41no—
454M16—41no—
455M16—41no—
456M16—342no—
457M16—342no—
458M16—342no—
459M16—342no—
460M16—681no—
461M16—681no—
462M16—681no—
463M16—681no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—342no—
475C2×C8—342no—
476C2×C8—681no—
477C2×C8—681no—
478C2×C8—681no—
479C2×C8—681no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—342no—
483C4⋊C4—681no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—342no—
487C22⋊C4—681no—
488C42—41no—
489C42—41no—
490C42—342no—
491C42—681no—
492C23—42no—
493C23—342no—
494C23—681no—
495C23—681no—
496C23—1362no—
497C23#1058756111yescharacteristic
498C23#1058756211yescharacteristic
499C23#1058756911yescharacteristic
500C23#1058757011yescharacteristic
501C23#1058758011yescharacteristic
502C23#1058758411yescharacteristic
503C23C4×C22⋊D1711yescharacteristic
504Q8—342no—
505Q8—342no—
506Q8—681no—
507Q8—681no—
508D4—342no—
509D4—342no—
510D4—682no—
511D4—682no—
512D4—682no—
513D4—682no—
514D4—681no—
515D4—681no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—342no—
519C2×C4—681no—
520C2×C4—681no—
521C2×C4—682no—
522C2×C4—682no—
523C2×C4—682no—
524C2×C4—682no—
525C2×C4—682no—
526C2×C4—1362no—
527C2×C4#1058755811yescharacteristic
528C2×C4C4×D6811yescharacteristic
529C2×C4C22⋊C4×D1711yescharacteristic
530C2×C4#1058756711yescharacteristic
531C2×C4#1058756811yescharacteristic
532C2×C4#1058756911yescharacteristic
533C2×C4#1058756911yescharacteristic
534C2×C4#1058757011yescharacteristic
535C2×C4#1058757011yescharacteristic
536C2×C4#1058757111yescharacteristic
537C2×C4#1058757111yescharacteristic
538C2×C4#1058757211yescharacteristic
539C2×C4#1058757811yescharacteristic
540C2×C4#1058757911yescharacteristic
541C2×C4#1058758011yescharacteristic
542C2×C4#1058758011yescharacteristic
543C2×C4#1058758011yescharacteristic
544C2×C4#1058758011yescharacteristic
545C2×C4#1058758111yescharacteristic
546C2×C4#1058758111yescharacteristic
547C2×C4#1058758411yescharacteristic
548C2×C4#1058758411yescharacteristic
549C2×C4#1058761511yescharacteristic
550C2×C4#1058761611yescharacteristic
551C2×C4#1058762311yescharacteristic
552C2×C4#1058762411yescharacteristic
553C2×C4#1058762511yescharacteristic
554C2×C4#1058763311yescharacteristic
555C8—42no—
556C8—42no—
557C8—682no—
558C8—682no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—682no—
567C22—684no—
568C22—1362no—
569C22—1362no—
570C22#1176268511yescharacteristic
571C22#1176269911yescharacteristic
572C22#1176270011yescharacteristic
573C22#1176272711yescharacteristic
574C22#1176273611yescharacteristic
575C22#1176273811yescharacteristic
576C22#1176273811yescharacteristic
577C4—82no—
578C4—682no—
579C4—1362no—
580C4#1176267111yescharacteristic
581C4#1176268711yescharacteristic
582C4#1176269811yescharacteristic
583C4#1176270111yescharacteristic
584C4#1176272411yescharacteristic
585C4#1176272511yescharacteristic
586C4#1176272611yescharacteristic
587C4#1176273511yescharacteristic
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—21no—
593C2—21no—
594C2—1362no—
595C2#1452703211yescharacteristic
596C2#1452914912yes—
subgroupG/H
centerC2×C4#10587623
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#1729C2
socleC22×C17#386
prime radicalC22×#63252C22
cosocleC23×C4×C17C23
hypercenter#1729D17
hypocenterC17#11194
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1729

Complements

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

NH ≅ G/Ntype
4. C2×#11762580C2semidirect
5. C2×#11762574C2semidirect
6. #14528493C2semidirect
7. C17×#1729C2semidirect
14. #11762808C4semidirect
267. #1729D17semidirect
392. C17#11194semidirect

Maximal subgroups

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

subgroupindex
#145373012
C2×#117628062
#145372282
C2×#117625802
C2×#117625742
#145284932
C17×#17292
#1119417