Finite Group Databasebeta

← #16965373

Subgroups — #16965373

Order 4352.

1334 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
1C22×#10587575C211yesmaximal, characteristic
2C2×#11762674C211yesmaximal, characteristic
3C2×#11762673C211yesmaximal, characteristic
4#14527050C212yesmaximal
5#14527050C212yesmaximal
6#14527038C211yesmaximal, characteristic
7#14527037C211yesmaximal, characteristic
8#14527036C212yesmaximal
9#14527035C212yesmaximal
10#14527034C211yesmaximal, characteristic
11C17×#1441C211yesmaximal, characteristic
12C2×#10587575—24no—
13C2×#10587575—24no—
14C2×#10587575C418yescomplemented
15C22×C4⋊Dic17C2211yescharacteristic
16C22×C4⋊Dic17C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2212yes—
22C22×C4×Dic17C2211yescharacteristic
23#11762674—24no—
24#11762673—24no—
25C2×#10587502C2211yescharacteristic
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C22×C4⋊C4×C17C2211yescharacteristic
36C22×C4⋊C4×C17C2211yescharacteristic
37C2×C17×#95C2211yescharacteristic
38C2×C17×#95C2212yes—
39C2×C17×#95C2212yes—
40C23×C4×C17C2312yes—
41C23×C4×C17C2312yes—
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2311yescharacteristic
44C23×C4×C17C2311yescharacteristic
45C23×Dic17C2312yes—
46C23×Dic17C2312yes—
47C23×Dic17C2311yescharacteristic
48C23×Dic17C2311yescharacteristic
49C23×Dic17C2311yescharacteristic
50C23×Dic17C2311yescharacteristic
51C2×C4⋊C4×C17—22no—
52C2×C4⋊C4×C17—22no—
53C2×C4⋊C4×C17—22no—
54C2×C4⋊C4×C17—42no—
55C2×C4⋊C4×C17C2×C414yes—
56C2×C4⋊Dic17—22no—
57C2×C4⋊Dic17—22no—
58C2×C4⋊Dic17—22no—
59C2×C4⋊Dic17—42no—
60C2×C4⋊Dic17C2×C414yes—
61C2×#63225—22no—
62C2×#63225—22no—
63C2×#63225—22no—
64C2×#63225—22no—
65C2×#63225—22no—
66C2×#63225—22no—
67C2×#63225—22no—
68C2×#63225—22no—
69C2×#63225—24no—
70C2×#63225—42no—
71C2×#63225—42no—
72C2×#63225C2×C414yes—
73C2×#63225C2×C414yes—
74C2×#63225C2×C414yes—
75C2×#63225C2×C414yes—
76C2×C4×Dic17C2×C414yes—
77C2×C4×Dic17D414yes—
78C2×C4×Dic17D414yes—
79#10587575—232no—
80C17×#95—22no—
81C17×#95—42no—
82C17×#95—42no—
83#10587502—22no—
84#10587502—24no—
85#10587502—24no—
86#10587502—24no—
87#10587502—42no—
88#10587502—42no—
89#10587502—42no—
90#10587502—42no—
91#10587502—42no—
92#10587502—42no—
93C24×C17C2411yescharacteristic
94C22×C4×C17—22no—
95C22×C4×C17—22no—
96C22×C4×C17—21no—
97C22×C4×C17—21no—
98C22×C4×C17—21no—
99C22×C4×C17—21no—
100C22×C4×C17—21no—
101C22×C4×C17—22no—
102C22×C4×C17—21no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—22no—
106C22×C4×C17—22no—
107C22×C4×C17—22no—
108C22×C4×C17—22no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17C22×C412yes—
121C22×C4×C17C22×C412yes—
122C22×C4×C17C22×C412yes—
123C22×C4×C17C2×D412yes—
124C22×C4×C17C2×D412yes—
125C22×Dic17—21no—
126C22×Dic17—21no—
127C22×Dic17—22no—
128C22×Dic17—21no—
129C22×Dic17—22no—
130C22×Dic17—21no—
131C22×Dic17—21no—
132C22×Dic17—21no—
133C22×Dic17—21no—
134C22×Dic17—21no—
135C22×Dic17—22no—
136C22×Dic17—21no—
137C22×Dic17—21no—
138C22×Dic17—21no—
139C22×Dic17—22no—
140C22×Dic17—21no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17C22×C412yes—
156C22×Dic17C22×C412yes—
157C22×Dic17C22×C412yes—
158C22×Dic17C22×C412yes—
159C22×Dic17C2×D412yes—
160C22×Dic17C2×D412yes—
161C22×Dic17C2×D412yes—
162C22×Dic17C2×D412yes—
163C4⋊C4×C17—28no—
164C4⋊C4×C17—44no—
165C4⋊Dic17—28no—
166C4⋊Dic17—44no—
167#63225—28no—
168#63225—28no—
169#63225—28no—
170#63225—28no—
171#63225—48no—
172C4×Dic17C22⋊C4116yes—
173#14664—171nomaximal, Sylow
174C23×C17C23×C411yescharacteristic
175C23×C17C22×D411yescharacteristic
176C23×C17C22×D411yescharacteristic
177C23×C17H(5,𝔽2)12yes—
178C23×C17H(5,𝔽2)11yescharacteristic
179C23×C17H(5,𝔽2)11yescharacteristic
180C23×C172−1+412yes—
181C23×C172−1+411yescharacteristic
182C23×C172−1+412yes—
183C23×C172−1+412yes—
184C23×C172−1+411yescharacteristic
185C2×C4×C17—24no—
186C2×C4×C17—22no—
187C2×C4×C17—22no—
188C2×C4×C17—24no—
189C2×C4×C17—22no—
190C2×C4×C17—22no—
191C2×C4×C17—24no—
192C2×C4×C17—22no—
193C2×C4×C17—22no—
194C2×C4×C17—41no—
195C2×C4×C17—41no—
196C2×C4×C17—41no—
197C2×C4×C17—41no—
198C2×C4×C17—42no—
199C2×C4×C17—41no—
200C2×C4×C17—41no—
201C2×C4×C17—42no—
202C2×C4×C17—42no—
203C2×C4×C17—42no—
204C2×C4×C17—42no—
205C2×C4×C17—42no—
206C2×C4×C17—42no—
207C2×C4×C17—42no—
208C2×C4×C17—42no—
209C2×C4×C17—42no—
210C2×C4×C17—42no—
211C2×C4×C17—42no—
212C2×C4×C17—42no—
213C2×C4×C17—42no—
214C2×C4×C17—42no—
215C2×C4×C17C2×C22⋊C414yes—
216C2×Dic17—24no—
217C2×Dic17—22no—
218C2×Dic17—22no—
219C2×Dic17—22no—
220C2×Dic17—22no—
221C2×Dic17—24no—
222C2×Dic17—22no—
223C2×Dic17—22no—
224C2×Dic17—22no—
225C2×Dic17—22no—
226C2×Dic17—22no—
227C2×Dic17—22no—
228C2×Dic17—24no—
229C2×Dic17—22no—
230C2×Dic17—22no—
231C2×Dic17—41no—
232C2×Dic17—41no—
233C2×Dic17—41no—
234C2×Dic17—41no—
235C2×Dic17—42no—
236C2×Dic17—41no—
237C2×Dic17—41no—
238C2×Dic17—42no—
239C2×Dic17—42no—
240C2×Dic17—42no—
241C2×Dic17—42no—
242C2×Dic17—42no—
243C2×Dic17—42no—
244C2×Dic17—42no—
245C2×Dic17—42no—
246C2×Dic17—42no—
247C2×Dic17—42no—
248C2×Dic17—42no—
249C2×Dic17—42no—
250C2×Dic17—42no—
251C2×Dic17—42no—
252C2×Dic17C2×C22⋊C414yes—
253C2×Dic17C2×C22⋊C414yes—
254C22×#125—171no—
255C2×#382—171no—
256C2×#382—171no—
257#1445—172no—
258#1445—172no—
259#1441—172no—
260#1441—172no—
261#1441—171no—
262#1441—171no—
263#1441—171no—
264#1441D1711yescharacteristic
265C22×C17C22×C22⋊C411yescharacteristic
266C22×C17#51912yes—
267C22×C17#52012yes—
268C22×C17#52011yescharacteristic
269C22×C17#52011yescharacteristic
270C22×C17#53511yescharacteristic
271C22×C17#53511yescharacteristic
272C22×C17#53611yescharacteristic
273C22×C17#53611yescharacteristic
274C22×C17#53612yes—
275C22×C17#53611yescharacteristic
276C22×C17#53611yescharacteristic
277C22×C17#53712yes—
278C22×C17#53711yescharacteristic
279C22×C17#53711yescharacteristic
280C22×C17#56212yes—
281C22×C17#56212yes—
282C22×C17#56312yes—
283C22×C17#56312yes—
284C22×C17#56312yes—
285C22×C17#56312yes—
286C22×C17#56412yes—
287C22×C17#56412yes—
288C4×C17—24no—
289C4×C17—42no—
290C4×C17—42no—
291C4×C17—82no—
292C4×C17—82no—
293Dic17—24no—
294Dic17—24no—
295Dic17—42no—
296Dic17—42no—
297Dic17—82no—
298Dic17—82no—
299C2×#125—178no—
300C2×#125—344no—
301C2×#125—344no—
302C22×C4⋊C4—171no—
303C22×C4⋊C4—171no—
304C22×C4⋊C4—171no—
305C22×C4⋊C4—171no—
306C22×C4⋊C4—171no—
307C22×C4⋊C4—172no—
308C22×C4⋊C4—171no—
309C22×C4⋊C4C2×D1711yescharacteristic
310C22×C4⋊C4C2×D1711yescharacteristic
311C22×C42—171no—
312#382—344no—
313#382—344no—
314C2×#95—172no—
315C2×#95—171no—
316C2×#95—172no—
317C2×#95—172no—
318C2×#95—172no—
319C2×#95—172no—
320C2×#95—172no—
321C2×#95—172no—
322C2×#95—172no—
323C2×#95—172no—
324C2×#95C2×D1711yescharacteristic
325C2×#95C2×D1712yes—
326C2×#95C2×D1712yes—
327C2×C17#231011yescharacteristic
328C2×C17#231111yescharacteristic
329C2×C17#231111yescharacteristic
330C2×C17#238212yes—
331C2×C17#238212yes—
332C2×C17#282012yes—
333C2×C17#282011yescharacteristic
334C2×C17#282011yescharacteristic
335C2×C17#282212yes—
336C2×C17#282211yescharacteristic
337C2×C17#282211yescharacteristic
338C23×C4—171no—
339C23×C4—171no—
340C23×C4—171no—
341C23×C4—171no—
342C23×C4—172no—
343C23×C4—172no—
344C23×C4C22×D1712yes—
345C23×C4C22×D1712yes—
346C23×C4C22×D1711yescharacteristic
347C23×C4C22×D1711yescharacteristic
348C23×C4C22×D1711yescharacteristic
349#125—3432no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—174no—
355C2×C4⋊C4—174no—
356C2×C4⋊C4—174no—
357C2×C4⋊C4—174no—
358C2×C4⋊C4—174no—
359C2×C4⋊C4—342no—
360C2×C4⋊C4—342no—
361C2×C4⋊C4—342no—
362C2×C4⋊C4—342no—
363C2×C4⋊C4—342no—
364C2×C4⋊C4—342no—
365C2×C4⋊C4—342no—
366C2×C4⋊C4—342no—
367C2×C4⋊C4—342no—
368C2×C4⋊C4—342no—
369C2×C4⋊C4—344no—
370C2×C4⋊C4—342no—
371C2×C4⋊C4—682no—
372C2×C4⋊C4—682no—
373C2×C4⋊C4—682no—
374C2×C4⋊C4C4×D1714yes—
375C2×C42—174no—
376C2×C42—174no—
377C2×C42—174no—
378#95—22no—
379#95—42no—
380#95—42no—
381#95—344no—
382#95—344no—
383#95—344no—
384#95—342no—
385#95—682no—
386#95—682no—
387#95—682no—
388#95—682no—
389#95—682no—
390#95—682no—
391C17#1466411yescharacteristic, complemented, Sylow
392C24C23×D1711yescharacteristic
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—172no—
420C22×C4—172no—
421C22×C4—172no—
422C22×C4—172no—
423C22×C4—172no—
424C22×C4—172no—
425C22×C4—172no—
426C22×C4—172no—
427C22×C4—341no—
428C22×C4—342no—
429C22×C4—341no—
430C22×C4—341no—
431C22×C4—342no—
432C22×C4—341no—
433C22×C4—341no—
434C22×C4—341no—
435C22×C4—341no—
436C22×C4—341no—
437C22×C4—342no—
438C22×C4—341no—
439C22×C4—341no—
440C22×C4—341no—
441C22×C4—342no—
442C22×C4—341no—
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×C4—342no—
455C22×C4—342no—
456C22×C4—342no—
457C22×C4C2×C4×D1712yes—
458C22×C4C2×C4×D1712yes—
459C22×C4C2×C4×D1712yes—
460C22×C4D4×D1712yes—
461C22×C4D4×D1712yes—
462C4⋊C4—28no—
463C4⋊C4—44no—
464C4⋊C4—348no—
465C4⋊C4—348no—
466C4⋊C4—348no—
467C4⋊C4—348no—
468C4⋊C4—348no—
469C4⋊C4—684no—
470C4⋊C4—688no—
471C42—1716no—
472C23C22×C4×D1711yescharacteristic
473C23C2×D4×D1711yescharacteristic
474C23C2×D4×D1711yescharacteristic
475C23#1058769112yes—
476C23#1058769111yescharacteristic
477C23#1058769412yes—
478C23#1058769411yescharacteristic
479C23#1058769611yescharacteristic
480C23#1058769712yes—
481C23#1058769712yes—
482C23#1058769711yescharacteristic
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—174no—
514C2×C4—174no—
515C2×C4—344no—
516C2×C4—342no—
517C2×C4—342no—
518C2×C4—342no—
519C2×C4—342no—
520C2×C4—344no—
521C2×C4—342no—
522C2×C4—342no—
523C2×C4—342no—
524C2×C4—342no—
525C2×C4—342no—
526C2×C4—342no—
527C2×C4—344no—
528C2×C4—342no—
529C2×C4—342no—
530C2×C4—681no—
531C2×C4—681no—
532C2×C4—681no—
533C2×C4—681no—
534C2×C4—682no—
535C2×C4—681no—
536C2×C4—681no—
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×C4C22⋊C4×D1714yes—
552C22C2×C22⋊C4×D1711yescharacteristic
553C22#1176328512yes—
554C22#1176328812yes—
555C22#1176328911yescharacteristic
556C22#1176329011yescharacteristic
557C22#1176337411yescharacteristic
558C22#1176337511yescharacteristic
559C22#1176337911yescharacteristic
560C22#1176338111yescharacteristic
561C22#1176338212yes—
562C22#1176338211yescharacteristic
563C22#1176338411yescharacteristic
564C22#1176338612yes—
565C22#1176338811yescharacteristic
566C22#1176338911yescharacteristic
567C22#1176355412yes—
568C22#1176355512yes—
569C22#1176355812yes—
570C22#1176356012yes—
571C22#1176356112yes—
572C22#1176356212yes—
573C22C17⋊#56412yes—
574C22C17⋊#56412yes—
575C4—24no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4—82no—
580C4—344no—
581C4—344no—
582C4—682no—
583C4—682no—
584C4—1362no—
585C4—1362no—
586C2#1453136711yescharacteristic
587C2#1453137111yescharacteristic
588C2#1453137311yescharacteristic
589C2#1453196612yes—
590C2#1453196812yes—
591C2#1453683312yes—
592C2#1453683711yescharacteristic
593C2#1453683911yescharacteristic
594C2#1453685012yes—
595C2#1453685311yescharacteristic
596C2#1453685411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1441C2
socle, prime radical, cosocleC24×C17C24
hypercenter#1441D17
hypocenterC17#14664
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
14. C2×#10587575C4semidirect
391. C17#14664semidirect

Maximal subgroups

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

subgroupindex
C22×#105875752
C2×#117626742
C2×#117626732
#145270502
#145270382
#145270372
#145270362
#145270352
#145270342
C17×#14412
#1466417