Finite Group Databasebeta

← #17963084

Subgroups — #17963084

Order 4352.

1326 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×#11763758C212yesmaximal
2#14543964C212yesmaximal
3#14543963C212yesmaximal
4#14543963C212yesmaximal
5#14543961C212yesmaximal
6#14543960C211yesmaximal, characteristic
7#14543960C211yesmaximal, characteristic
8#14543959C212yesmaximal
9D17×#389C211yesmaximal, characteristic
10C22×C4⋊#595C2212yes—
11C22×C4×#595C2212yes—
12C22×C4×#595C2212yes—
13#11763758C4116yescomplemented
14C2×(C2×#595)⋊C4C2211yescharacteristic
15C2×(C2×#595)⋊C4C2212yes—
16C2×(C2×#595)⋊C4C2212yes—
17C2×(C2×#595)⋊C4C2212yes—
18C2×(C2×#595)⋊C4C2211yescharacteristic
19C2×(C2×#595)⋊C4C2212yes—
20C2×(C2×#595)⋊C4C2211yescharacteristic
21C2×(C2×#595)⋊C4C2211yescharacteristic
22C2×(C2×#595)⋊C4C2212yes—
23C2×(C2×#595)⋊C4C2212yes—
24C2×(C2×#595)⋊C4C2212yes—
25C2×(C2×#595)⋊C4C2212yes—
26C2×(C2×#595)⋊C4C2212yes—
27C2×C4⋊C4×D17C2212yes—
28C2×C4⋊C4×D17C2211yescharacteristic
29C2×C4⋊C4×D17C2211yescharacteristic
30C2×C42×D17C2211yescharacteristic
31#11762708C411yescharacteristic, complemented
32#11762707C411yescharacteristic, complemented
33#11762706C412yescomplemented
34#11762705C411yescharacteristic, complemented
35#11762704C412yescomplemented
36#95×D17C2212yes—
37C17×#389C411yescharacteristic, complemented
38C23×#595C2312yes—
39C23×#595C2312yes—
40C23×#595C2312yes—
41C23×#595C2312yes—
42C22×C4×D17C2311yescharacteristic
43C22×C4×D17C2311yescharacteristic
44C22×C4×D17C2312yes—
45C22×C4×D17C2311yescharacteristic
46C22×C4×D17C2312yes—
47C2×C4⋊#595—42no—
48C2×C4⋊#595—42no—
49C2×C4⋊#595C2×C418yes—
50C2×C4×#595—42no—
51C2×C4×#595—42no—
52C2×C4×#595—42no—
53C2×C4×#595—42no—
54C2×C4×#595—42no—
55C2×C4×#595C2×C418yes—
56C2×C4⋊C4×C17C2×C412yes—
57C2×C4⋊C4×C17C2×C411yescharacteristic
58C2×C4⋊C4×C17C2×C411yescharacteristic
59C2×C42×C17C2×C411yescharacteristic
60C2×C4⋊Dic17C2×C412yes—
61C2×C4⋊Dic17C2×C411yescharacteristic
62C2×C4⋊Dic17C2×C411yescharacteristic
63C2×#63225C2×C412yes—
64C2×#63225C2×C412yes—
65C2×#63225C2×C412yes—
66C2×#63225C2×C412yes—
67C2×C4×Dic17C2×C411yescharacteristic
68C2×C4×Dic17C2×C411yescharacteristic
69C2×C4×Dic17C2×C411yescharacteristic
70C4⋊C4×D17—42no—
71C4⋊C4×D17—42no—
72C4⋊C4×D17—42no—
73C4⋊C4×D17C2×C418yes—
74C42×D17—42no—
75(C2×#595)⋊C4—42no—
76(C2×#595)⋊C4—41no—
77(C2×#595)⋊C4—41no—
78(C2×#595)⋊C4—41no—
79(C2×#595)⋊C4—41no—
80(C2×#595)⋊C4—42no—
81(C2×#595)⋊C4—42no—
82(C2×#595)⋊C4—42no—
83(C2×#595)⋊C4—42no—
84(C2×#595)⋊C4C2×C418yes—
85(C2×#595)⋊C4C2×C418yes—
86(C2×#595)⋊C4C2×C418yes—
87(C2×#595)⋊C4C2×C418yes—
88C17×#95C2×C412yes—
89#10587502C2×C412yes—
90#10587502C2×C412yes—
91#10587502C2×C412yes—
92C23×D17C2411yescharacteristic
93C22×#595—22no—
94C22×#595—22no—
95C22×#595—22no—
96C22×#595—22no—
97C22×#595—22no—
98C22×#595—22no—
99C22×#595—22no—
100C22×#595—22no—
101C22×#595—22no—
102C22×#595—22no—
103C22×#595—22no—
104C22×#595—22no—
105C22×#595—22no—
106C22×#595—22no—
107C22×#595—22no—
108C22×#595—22no—
109C22×#595—22no—
110C22×#595—22no—
111C22×#595—22no—
112C22×#595—22no—
113C22×#595—22no—
114C22×#595—22no—
115C22×#595—22no—
116C22×#595—22no—
117C22×#595C22×C414yes—
118C22×#595C22×C414yes—
119C22×#595C22×C414yes—
120C22×#595C22×C414yes—
121C22×C4×C17C22×C411yescharacteristic
122C22×C4×C17C22×C412yes—
123C22×C4×C17C22×C411yescharacteristic
124C22×C4×C17C22×C412yes—
125C22×C4×C17C22×C411yescharacteristic
126C22×Dic17C22×C411yescharacteristic
127C22×Dic17C22×C412yes—
128C22×Dic17C22×C411yescharacteristic
129C22×Dic17C22×C412yes—
130C22×Dic17C22×C411yescharacteristic
131C2×C4×D17—22no—
132C2×C4×D17—22no—
133C2×C4×D17—22no—
134C2×C4×D17—22no—
135C2×C4×D17—21no—
136C2×C4×D17—21no—
137C2×C4×D17—22no—
138C2×C4×D17—22no—
139C2×C4×D17—22no—
140C2×C4×D17—22no—
141C2×C4×D17—21no—
142C2×C4×D17—21no—
143C2×C4×D17—22no—
144C2×C4×D17—22no—
145C2×C4×D17—22no—
146C2×C4×D17—22no—
147C2×C4×D17—22no—
148C2×C4×D17—21no—
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—21no—
152C2×C4×D17C22×C414yes—
153C2×C4×D17C22×C414yes—
154C2×C4×D17C22×C414yes—
155C4⋊#595—48no—
156C4×#595—48no—
157C4×#595—48no—
158C4⋊C4×C17—41no—
159C4⋊C4×C17—42no—
160C4⋊C4×C17C4214yescomplemented
161C42×C17—41no—
162C4⋊Dic17—42no—
163C4⋊Dic17—41no—
164C4⋊Dic17C4214yescomplemented
165#63225—42no—
166#63225—42no—
167#63225—42no—
168#63225C4218yescomplemented
169C4×Dic17—41no—
170C4×Dic17—41no—
171C4×Dic17—41no—
172#13833—171nomaximal, Sylow
173C23×C17C23×C411yescharacteristic
174C22×D17C23×C412yes—
175C22×D17H(5,𝔽2)11yescharacteristic
176C22×D17H(5,𝔽2)12yes—
177C22×D17H(5,𝔽2)11yescharacteristic
178C22×D17H(5,𝔽2)12yes—
179C22×D172−1+411yescharacteristic
180C22×D172−1+412yes—
181C22×D172−1+411yescharacteristic
182C22×D172−1+411yescharacteristic
183C22×D172−1+411yescharacteristic
184C2×#595—24no—
185C2×#595—24no—
186C2×#595—24no—
187C2×#595—24no—
188C2×#595—24no—
189C2×#595—24no—
190C2×#595—24no—
191C2×#595—24no—
192C2×#595—24no—
193C2×#595—24no—
194C2×#595—24no—
195C2×#595—24no—
196C2×#595—42no—
197C2×#595—42no—
198C2×#595—42no—
199C2×#595—42no—
200C2×#595—42no—
201C2×#595—42no—
202C2×#595—42no—
203C2×#595—42no—
204C2×#595—42no—
205C2×#595—42no—
206C2×#595—42no—
207C2×#595—42no—
208C2×#595—42no—
209C2×#595—42no—
210C2×#595—42no—
211C2×#595—42no—
212C2×C4×C17—21no—
213C2×C4×C17—22no—
214C2×C4×C17—21no—
215C2×C4×C17—22no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—22no—
220C2×C4×C17—22no—
221C2×C4×C17—21no—
222C2×C4×C17—22no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17C2×C4214yes—
226C2×C4×C17C2×C4212yes—
227C2×Dic17—21no—
228C2×Dic17—22no—
229C2×Dic17—21no—
230C2×Dic17—22no—
231C2×Dic17—21no—
232C2×Dic17—21no—
233C2×Dic17—21no—
234C2×Dic17—22no—
235C2×Dic17—22no—
236C2×Dic17—21no—
237C2×Dic17—22no—
238C2×Dic17—21no—
239C2×Dic17—21no—
240C2×Dic17C2×C4212yes—
241C2×Dic17C2×C4214yes—
242C4×D17—24no—
243C4×D17—24no—
244C4×D17—24no—
245C4×D17—24no—
246C4×D17—24no—
247C4×D17—24no—
248C4×D17—42no—
249C4×D17—42no—
250C4×D17—42no—
251C4×D17—42no—
252C4×D17—42no—
253C4×D17—42no—
254C4×D17—42no—
255C4×D17—42no—
256C2×#389—171no—
257C2×#387—172no—
258#1436—172no—
259#1436—172no—
260#1436—172no—
261C4⋊#95—172no—
262#1434—172no—
263#1434—171no—
264#1434—171no—
265C22×C17C22×C4211yescharacteristic
266C22×C17#51811yescharacteristic
267C22×C17#51811yescharacteristic
268C22×C17#51911yescharacteristic
269C22×C17#51911yescharacteristic
270C22×C17#52011yescharacteristic
271C22×C17#52011yescharacteristic
272C2×D17#51812yes—
273C2×D17#51912yes—
274C2×D17#52012yes—
275C2×D17#52012yes—
276C2×D17#52012yes—
277C2×D17#52012yes—
278C2×D17#56012yes—
279C2×D17#56211yescharacteristic
280C2×D17#56212yes—
281C2×D17#56212yes—
282C2×D17#56312yes—
283C2×D17#56311yescharacteristic
284C2×D17#56312yes—
285C2×D17#56312yes—
286C2×D17#56311yescharacteristic
287C2×D17#56411yescharacteristic
288#595—44no—
289#595—44no—
290#595—44no—
291#595—44no—
292C4×C17—22no—
293C4×C17—24no—
294C4×C17—42no—
295C4×C17—41no—
296C4×C17—41no—
297Dic17—22no—
298Dic17—24no—
299Dic17—42no—
300Dic17—41no—
301Dic17—41no—
302C22×C4⋊C4—171no—
303C22×C4⋊C4—172no—
304C22×C4⋊C4—172no—
305C22×C4⋊C4—171no—
306C22×C42—172no—
307C22×C42—171no—
308C22×C42—172no—
309#389—172no—
310#389—171no—
311#389—171no—
312#389—171no—
313#389—172no—
314#389#59511yescharacteristic, complemented
315#387—1716no—
316C2×#95—172no—
317C2×#95—172no—
318C2×#95—172no—
319C2×#95—172no—
320C2×#95—172no—
321C2×#95—171no—
322C2×#95—172no—
323C2×#95—171no—
324C2×#95—172no—
325C2×#95—172no—
326C2×#95—171no—
327C2×#95—172no—
328C2×#95—171no—
329C2×#95—172no—
330C2×C17#227411yescharacteristic
331C2×C17#227511yescharacteristic
332C2×C17#227611yescharacteristic
333C2×C17#237711yescharacteristic
334C2×C17#237811yescharacteristic
335C2×C17#238111yescharacteristic
336C2×C17#238211yescharacteristic
337D17#237612yes—
338D17#237812yes—
339D17#238212yes—
340D17#238312yes—
341C23×C4—172no—
342C23×C4—171no—
343C23×C4—172no—
344C23×C4—172no—
345C23×C4—172no—
346C23×C4—172no—
347C23×C4—172no—
348C23×C4—171no—
349C23×C4—171no—
350C2×C4⋊C4—172no—
351C2×C4⋊C4—171no—
352C2×C4⋊C4—178no—
353C2×C4⋊C4—178no—
354C2×C4⋊C4—172no—
355C2×C4⋊C4—172no—
356C2×C4⋊C4—172no—
357C2×C4⋊C4—171no—
358C2×C4⋊C4—172no—
359C2×C4⋊C4—682no—
360C2×C4⋊C4—682no—
361C2×C4⋊C4—682no—
362C2×C4⋊C4—682no—
363C2×C4⋊C4—682no—
364C2×C4⋊C4C2×#59511yescharacteristic
365C2×C4⋊C4C2×#59512yes—
366C2×C4⋊C4C2×#59511yescharacteristic
367C2×C42—178no—
368C2×C42—171no—
369C2×C42—171no—
370C2×C42—171no—
371C2×C42—682no—
372C2×C42—682no—
373C2×C42—682no—
374C2×C42—682no—
375C2×C42—682no—
376C2×C42—682no—
377C2×C42C2×#59511yescharacteristic
378#95—178no—
379#95—178no—
380#95—178no—
381#95—178no—
382#95—172no—
383#95—172no—
384#95—172no—
385#95—681no—
386#95—681no—
387#95—681no—
388#95—681no—
389#95—682no—
390#95—682no—
391#95—682no—
392#95—682no—
393#95—682no—
394#95C2×#59512yes—
395C17#1383311yescharacteristic, complemented, Sylow
396C24—171no—
397C22×C4—172no—
398C22×C4—171no—
399C22×C4—174no—
400C22×C4—174no—
401C22×C4—174no—
402C22×C4—174no—
403C22×C4—174no—
404C22×C4—174no—
405C22×C4—174no—
406C22×C4—171no—
407C22×C4—172no—
408C22×C4—171no—
409C22×C4—342no—
410C22×C4—342no—
411C22×C4—342no—
412C22×C4—342no—
413C22×C4—341no—
414C22×C4—341no—
415C22×C4—342no—
416C22×C4—341no—
417C22×C4—341no—
418C22×C4—342no—
419C22×C4—342no—
420C22×C4—342no—
421C22×C4—342no—
422C22×C4—342no—
423C22×C4—342no—
424C22×C4—342no—
425C22×C4—342no—
426C22×C4—342no—
427C22×C4—341no—
428C22×C4—342no—
429C22×C4—341no—
430C22×C4—342no—
431C22×C4—342no—
432C22×C4—342no—
433C22×C4—342no—
434C22×C4—342no—
435C22×C4—342no—
436C22×C4—342no—
437C22×C4—342no—
438C22×C4—342no—
439C22×C4—342no—
440C22×C4—342no—
441C22×C4—342no—
442C22×C4—342no—
443C22×C4—342no—
444C22×C4—342no—
445C22×C4—342no—
446C22×C4—342no—
447C22×C4—342no—
448C22×C4—342no—
449C22×C4—342no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—342no—
453C22×C4—342no—
454C22×C4C22×#59511yescharacteristic
455C22×C4C22×#59512yes—
456C22×C4C22×#59511yescharacteristic
457C22×C4C22×#59512yes—
458C22×C4C22×#59511yescharacteristic
459C4⋊C4—41no—
460C4⋊C4—42no—
461C4⋊C4—178no—
462C4⋊C4—174no—
463C4⋊C4—682no—
464C4⋊C4—682no—
465C4⋊C4—682no—
466C4⋊C4—681no—
467C4⋊C4—682no—
468C4⋊C4—688no—
469C4⋊C4C4×#59514yescomplemented
470C42—41no—
471C42—681no—
472C42—681no—
473C42—681no—
474C42—688no—
475C42—688no—
476C23—172no—
477C23—172no—
478C23—172no—
479C23—171no—
480C23—171no—
481C23—172no—
482C23—171no—
483C23—171no—
484C23—171no—
485C23—171no—
486C23C23×#59511yescharacteristic
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—172no—
501C2×C4—174no—
502C2×C4—344no—
503C2×C4—344no—
504C2×C4—344no—
505C2×C4—344no—
506C2×C4—344no—
507C2×C4—344no—
508C2×C4—341no—
509C2×C4—342no—
510C2×C4—341no—
511C2×C4—342no—
512C2×C4—344no—
513C2×C4—344no—
514C2×C4—344no—
515C2×C4—344no—
516C2×C4—344no—
517C2×C4—344no—
518C2×C4—344no—
519C2×C4—344no—
520C2×C4—344no—
521C2×C4—344no—
522C2×C4—344no—
523C2×C4—344no—
524C2×C4—341no—
525C2×C4—341no—
526C2×C4—341no—
527C2×C4—342no—
528C2×C4—342no—
529C2×C4—341no—
530C2×C4—342no—
531C2×C4—341no—
532C2×C4—341no—
533C2×C4—682no—
534C2×C4—682no—
535C2×C4—682no—
536C2×C4—682no—
537C2×C4—682no—
538C2×C4—682no—
539C2×C4—682no—
540C2×C4—682no—
541C2×C4—682no—
542C2×C4—682no—
543C2×C4—682no—
544C2×C4—682no—
545C2×C4—682no—
546C2×C4—682no—
547C2×C4—682no—
548C2×C4—682no—
549C2×C4—682no—
550C2×C4—682no—
551C2×C4—682no—
552C2×C4—682no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
556C2×C4—682no—
557C2×C4C2×C4×#59512yes—
558C2×C4C2×C4×#59514yes—
559C22—172no—
560C22—172no—
561C22—172no—
562C22—172no—
563C22—172no—
564C22—172no—
565C22—172no—
566C22—172no—
567C22—172no—
568C22—172no—
569C22—172no—
570C22—172no—
571C22—171no—
572C22—171no—
573C22—171no—
574C22—171no—
575C22C22×C4×#59511yescharacteristic
576C22#1176387611yescharacteristic
577C22#1176387611yescharacteristic
578C22#1176387711yescharacteristic
579C22#1176387711yescharacteristic
580C22#1176387811yescharacteristic
581C22#1176387811yescharacteristic
582C4—22no—
583C4—24no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—342no—
588C4—344no—
589C4—684no—
590C4—684no—
591C4—684no—
592C4—684no—
593C4—681no—
594C4—682no—
595C4—681no—
596C2—172no—
597C2—172no—
598C2—172no—
599C2—172no—
600C2#1454522211yescharacteristic
601C2#1454522311yescharacteristic
602C2#1454522411yescharacteristic
603C2#1454532511yescharacteristic
604C2#1454532611yescharacteristic
605C2#1454532911yescharacteristic
606C2#1454533011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#389C4
socleC23×C17C23×C4
prime radical, cosocleC23×D17C24
hypercenter#389#595
hypocenterC17#13833
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
13. #11763758C4semidirect
31. #11762708C4semidirect
32. #11762707C4semidirect
33. #11762706C4semidirect
34. #11762705C4semidirect
35. #11762704C4semidirect
37. C17×#389C4semidirect
160. C4⋊C4×C17C42semidirect
164. C4⋊Dic17C42semidirect
168. #63225C42semidirect
314. #389#595semidirect
395. C17#13833semidirect
469. C4⋊C4C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637582
#145439642
#145439632
#145439612
#145439602
#145439592
D17×#3892
#1383317