Finite Group Databasebeta

← #16960927

Subgroups — #16960927

Order 4352.

1502 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587575C211yesmaximal, characteristic
2C2×#11762678C211yesmaximal, characteristic
3C2×#11762654C211yesmaximal, characteristic
4#14527038C211yesmaximal, characteristic
5#14527037C211yesmaximal, characteristic
6#14527036C212yesmaximal
7#14527035C212yesmaximal
8#14527034C211yesmaximal, characteristic
9#14527012C212yesmaximal
10#14527012C212yesmaximal
11C17×#1441C211yesmaximal, characteristic
12C2×#10587575—24no—
13C2×#10587575—24no—
14C2×#10587575C418yescomplemented
15C22×C4⋊Dic17C2211yescharacteristic
16C22×C4⋊Dic17C2211yescharacteristic
17C22×#63225C2212yes—
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2212yes—
23C22×C4×Dic17C2212yes—
24C22×C4×Dic17C2211yescharacteristic
25#11762678—24no—
26#11762654—24no—
27C2×#10587502C2211yescharacteristic
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×C17C2311yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2312yes—
44C23×C4×C17C2311yescharacteristic
45C23×Dic17C2312yes—
46C23×Dic17C2311yescharacteristic
47C23×Dic17C2311yescharacteristic
48C23×Dic17C2312yes—
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—24no—
71C2×#63225—24no—
72C2×#63225—24no—
73C2×#63225—42no—
74C2×#63225—42no—
75C2×#63225C2×C414yes—
76C2×#63225C2×C414yes—
77C2×#63225C2×C414yes—
78C2×#63225C2×C414yes—
79C2×C4×Dic17—24no—
80C2×C4×Dic17—24no—
81C2×C4×Dic17C2×C414yes—
82C2×C4×Dic17D414yes—
83C2×C4×Dic17D414yes—
84C2×C4×Dic17Q818yes—
85#10587575—232no—
86C17×#95—22no—
87C17×#95—42no—
88C17×#95—42no—
89#10587502—22no—
90#10587502—24no—
91#10587502—42no—
92#10587502—42no—
93#10587502—42no—
94#10587502—42no—
95#10587502—42no—
96#10587502—42no—
97C24×C17C2411yescharacteristic
98C22×C4×C17—22no—
99C22×C4×C17—22no—
100C22×C4×C17—22no—
101C22×C4×C17—21no—
102C22×C4×C17—21no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—22no—
106C22×C4×C17—21no—
107C22×C4×C17—22no—
108C22×C4×C17—22no—
109C22×C4×C17—22no—
110C22×C4×C17—21no—
111C22×C4×C17—21no—
112C22×C4×C17—21no—
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×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17C22×C412yes—
124C22×C4×C17C22×C412yes—
125C22×C4×C17C22×C412yes—
126C22×C4×C17C2×D412yes—
127C22×C4×C17C2×D412yes—
128C22×C4×C17C2×Q814yes—
129C22×Dic17—21no—
130C22×Dic17—21no—
131C22×Dic17—21no—
132C22×Dic17—21no—
133C22×Dic17—22no—
134C22×Dic17—21no—
135C22×Dic17—21no—
136C22×Dic17—21no—
137C22×Dic17—21no—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—21no—
141C22×Dic17—22no—
142C22×Dic17—21no—
143C22×Dic17—22no—
144C22×Dic17—21no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—21no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17C22×C412yes—
157C22×Dic17C22×C412yes—
158C22×Dic17C22×C412yes—
159C22×Dic17C22×C412yes—
160C22×Dic17C2×D412yes—
161C22×Dic17C2×D412yes—
162C22×Dic17C2×D412yes—
163C22×Dic17C2×D412yes—
164C22×Dic17C2×Q814yes—
165C22×Dic17C2×Q814yes—
166C22×Dic17#4114yes—
167C4⋊C4×C17—28no—
168C4⋊C4×C17—44no—
169C4⋊Dic17—28no—
170C4⋊Dic17—44no—
171#63225—28no—
172#63225—28no—
173#63225—28no—
174#63225—28no—
175#63225—48no—
176#63225—48no—
177C4×Dic17—216no—
178C4×Dic17C22⋊C4116yes—
179#14283—171nomaximal, Sylow
180C23×C17C23×C411yescharacteristic
181C23×C17C22×D411yescharacteristic
182C23×C17C22×D411yescharacteristic
183C23×C17C22×Q812yes—
184C23×C17C2×#4112yes—
185C23×C17H(5,𝔽2)12yes—
186C23×C17H(5,𝔽2)11yescharacteristic
187C23×C17H(5,𝔽2)11yescharacteristic
188C23×C172−1+411yescharacteristic
189C23×C172−1+412yes—
190C23×C172−1+411yescharacteristic
191C2×C4×C17—24no—
192C2×C4×C17—22no—
193C2×C4×C17—22no—
194C2×C4×C17—24no—
195C2×C4×C17—22no—
196C2×C4×C17—22no—
197C2×C4×C17—24no—
198C2×C4×C17—22no—
199C2×C4×C17—22no—
200C2×C4×C17—24no—
201C2×C4×C17—24no—
202C2×C4×C17—24no—
203C2×C4×C17—41no—
204C2×C4×C17—41no—
205C2×C4×C17—41no—
206C2×C4×C17—41no—
207C2×C4×C17—42no—
208C2×C4×C17—42no—
209C2×C4×C17—41no—
210C2×C4×C17—42no—
211C2×C4×C17—41no—
212C2×C4×C17—42no—
213C2×C4×C17—42no—
214C2×C4×C17—42no—
215C2×C4×C17—42no—
216C2×C4×C17—42no—
217C2×C4×C17—42no—
218C2×C4×C17—42no—
219C2×C4×C17—42no—
220C2×C4×C17—42no—
221C2×C4×C17C2×C22⋊C414yes—
222C2×Dic17—22no—
223C2×Dic17—22no—
224C2×Dic17—22no—
225C2×Dic17—22no—
226C2×Dic17—22no—
227C2×Dic17—22no—
228C2×Dic17—22no—
229C2×Dic17—22no—
230C2×Dic17—24no—
231C2×Dic17—22no—
232C2×Dic17—22no—
233C2×Dic17—24no—
234C2×Dic17—24no—
235C2×Dic17—24no—
236C2×Dic17—41no—
237C2×Dic17—41no—
238C2×Dic17—41no—
239C2×Dic17—41no—
240C2×Dic17—42no—
241C2×Dic17—42no—
242C2×Dic17—41no—
243C2×Dic17—41no—
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×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17C2×C22⋊C414yes—
255C2×Dic17C2×C22⋊C414yes—
256C2×Dic17C4×Q818yes—
257C2×Dic17C22⋊Q818yes—
258C2×Dic17#12414yes—
259C2×Dic17C4⋊Q814yes—
260C22×#125—171no—
261C2×#384—171no—
262C2×#376—171no—
263#1441—172no—
264#1441—172no—
265#1441—171no—
266#1441—171no—
267#1441—171no—
268#1441D1711yescharacteristic
269C4⋊#95—172no—
270C4⋊#95—172no—
271C22×C17C22×C22⋊C411yescharacteristic
272C22×C17C2×C4×Q812yes—
273C22×C17#52012yes—
274C22×C17#52011yescharacteristic
275C22×C17#52011yescharacteristic
276C22×C17C2×C22⋊Q812yes—
277C22×C17C2×#12411yescharacteristic
278C22×C17C2×C4⋊Q811yescharacteristic
279C22×C17#53511yescharacteristic
280C22×C17#53511yescharacteristic
281C22×C17#53611yescharacteristic
282C22×C17#53611yescharacteristic
283C22×C17#53712yes—
284C22×C17#53711yescharacteristic
285C22×C17#53711yescharacteristic
286C22×C17#54012yes—
287C22×C17#54012yes—
288C22×C17#54112yes—
289C22×C17#54112yes—
290C22×C17#54412yes—
291C22×C17#54412yes—
292C22×C17#54412yes—
293C22×C17#54412yes—
294C4×C17—24no—
295C4×C17—42no—
296C4×C17—42no—
297C4×C17—44no—
298C4×C17—82no—
299Dic17—24no—
300Dic17—42no—
301Dic17—42no—
302Dic17—44no—
303Dic17—82no—
304Dic17#39118yes—
305C2×#125—178no—
306C2×#125—344no—
307C2×#125—344no—
308C22×C4⋊C4—171no—
309C22×C4⋊C4—171no—
310C22×C4⋊C4—171no—
311C22×C4⋊C4—171no—
312C22×C4⋊C4—171no—
313C22×C4⋊C4—172no—
314C22×C4⋊C4—172no—
315C22×C4⋊C4—171no—
316C22×C4⋊C4C2×D1711yescharacteristic
317C22×C4⋊C4C2×D1711yescharacteristic
318C22×C42—171no—
319C22×C42—172no—
320#384—344no—
321#376—344no—
322C2×#95—172no—
323C2×#95—171no—
324C2×#95—172no—
325C2×#95—172no—
326C2×#95—172no—
327C2×#95—172no—
328C2×#95—172no—
329C2×#95—172no—
330C2×#95C2×D1711yescharacteristic
331C2×#95C2×D1712yes—
332C2×#95C2×D1712yes—
333C2×C17C2×#39111yescharacteristic
334C2×C17#231111yescharacteristic
335C2×C17#231111yescharacteristic
336C2×C17#233012yes—
337C2×C17#233012yes—
338C2×C17#262912yes—
339C2×C17#262912yes—
340C2×C17#264111yescharacteristic
341C2×C17#264211yescharacteristic
342C2×C17#266011yescharacteristic
343C2×C17#266011yescharacteristic
344C23×C4—171no—
345C23×C4—171no—
346C23×C4—171no—
347C23×C4—171no—
348C23×C4—172no—
349C23×C4—172no—
350C23×C4C22×D1712yes—
351C23×C4C22×D1711yescharacteristic
352C23×C4C22×D1711yescharacteristic
353C23×C4C22×D1712yes—
354C23×C4C22×D1711yescharacteristic
355#125—3432no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—174no—
361C2×C4⋊C4—174no—
362C2×C4⋊C4—174no—
363C2×C4⋊C4—174no—
364C2×C4⋊C4—174no—
365C2×C4⋊C4—342no—
366C2×C4⋊C4—342no—
367C2×C4⋊C4—342no—
368C2×C4⋊C4—342no—
369C2×C4⋊C4—342no—
370C2×C4⋊C4—342no—
371C2×C4⋊C4—342no—
372C2×C4⋊C4—342no—
373C2×C4⋊C4—342no—
374C2×C4⋊C4—342no—
375C2×C4⋊C4—344no—
376C2×C4⋊C4—344no—
377C2×C4⋊C4—344no—
378C2×C4⋊C4—344no—
379C2×C4⋊C4—342no—
380C2×C4⋊C4—682no—
381C2×C4⋊C4—682no—
382C2×C4⋊C4—682no—
383C2×C4⋊C4C4×D1714yes—
384C2×C42—174no—
385C2×C42—174no—
386C2×C42—174no—
387C2×C42—178no—
388C2×C42—344no—
389C2×C42—344no—
390#95—22no—
391#95—42no—
392#95—42no—
393#95—344no—
394#95—342no—
395#95—682no—
396#95—682no—
397#95—682no—
398#95—682no—
399#95—682no—
400#95—682no—
401C17#1428311yescharacteristic, complemented, Sylow
402C24C23×D1711yescharacteristic
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—172no—
429C22×C4—172no—
430C22×C4—172no—
431C22×C4—174no—
432C22×C4—174no—
433C22×C4—172no—
434C22×C4—172no—
435C22×C4—172no—
436C22×C4—172no—
437C22×C4—172no—
438C22×C4—174no—
439C22×C4—341no—
440C22×C4—341no—
441C22×C4—341no—
442C22×C4—341no—
443C22×C4—342no—
444C22×C4—341no—
445C22×C4—341no—
446C22×C4—341no—
447C22×C4—341no—
448C22×C4—342no—
449C22×C4—341no—
450C22×C4—342no—
451C22×C4—341no—
452C22×C4—342no—
453C22×C4—342no—
454C22×C4—341no—
455C22×C4—342no—
456C22×C4—342no—
457C22×C4—341no—
458C22×C4—342no—
459C22×C4—342no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4C2×C4×D1712yes—
467C22×C4C2×C4×D1712yes—
468C22×C4C2×C4×D1712yes—
469C22×C4D4×D1712yes—
470C22×C4D4×D1712yes—
471C22×C4Q8×D1714yes—
472C4⋊C4—28no—
473C4⋊C4—44no—
474C4⋊C4—348no—
475C4⋊C4—348no—
476C4⋊C4—348no—
477C4⋊C4—348no—
478C4⋊C4—348no—
479C4⋊C4—684no—
480C4⋊C4—688no—
481C4⋊C4—688no—
482C42—1716no—
483C42—3416no—
484C23C22×C4×D1711yescharacteristic
485C23C2×D4×D1711yescharacteristic
486C23C2×D4×D1711yescharacteristic
487C23#1058769112yes—
488C23#1058769111yescharacteristic
489C23C2×Q8×D1712yes—
490C23#1058769411yescharacteristic
491C23#41×D1712yes—
492C23#1058769611yescharacteristic
493C23#1058769712yes—
494C23#1058769711yescharacteristic
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—174no—
526C2×C4—178no—
527C2×C4—178no—
528C2×C4—174no—
529C2×C4—174no—
530C2×C4—174no—
531C2×C4—342no—
532C2×C4—342no—
533C2×C4—342no—
534C2×C4—342no—
535C2×C4—342no—
536C2×C4—342no—
537C2×C4—342no—
538C2×C4—342no—
539C2×C4—344no—
540C2×C4—342no—
541C2×C4—342no—
542C2×C4—344no—
543C2×C4—344no—
544C2×C4—344no—
545C2×C4—681no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—682no—
550C2×C4—682no—
551C2×C4—681no—
552C2×C4—681no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
556C2×C4—682no—
557C2×C4—682no—
558C2×C4—682no—
559C2×C4—682no—
560C2×C4—682no—
561C2×C4—682no—
562C2×C4—682no—
563C2×C4C22⋊C4×D1714yes—
564C22C2×C22⋊C4×D1711yescharacteristic
565C22C4×Q8×D1712yes—
566C22#1176328812yes—
567C22#1176328911yescharacteristic
568C22#1176329011yescharacteristic
569C22C22⋊Q8×D1712yes—
570C22#124×D1711yescharacteristic
571C22C4⋊Q8×D1711yescharacteristic
572C22#1176337411yescharacteristic
573C22#1176337511yescharacteristic
574C22#1176338111yescharacteristic
575C22#1176338211yescharacteristic
576C22#1176338612yes—
577C22#1176338811yescharacteristic
578C22#1176338911yescharacteristic
579C22#1176340912yes—
580C22#1176341112yes—
581C22#1176341612yes—
582C22#1176341812yes—
583C22#1176343612yes—
584C22#1176343812yes—
585C22#1176343812yes—
586C22#1176343912yes—
587C4—24no—
588C4—42no—
589C4—42no—
590C4—44no—
591C4—82no—
592C4—178no—
593C4—344no—
594C4—682no—
595C4—682no—
596C4—684no—
597C4—1362no—
598C2D17×#39111yescharacteristic
599C2#1453137111yescharacteristic
600C2#1453137311yescharacteristic
601C2#1453152012yes—
602C2#1453152212yes—
603C2#1453461312yes—
604C2#1453461612yes—
605C2#1453472611yescharacteristic
606C2#1453473111yescharacteristic
607C2#1453490211yescharacteristic
608C2#1453490711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1441C2
socle, prime radical, cosocleC24×C17C24
hypercenter#1441D17
hypocenterC17#14283
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
14. C2×#10587575C4semidirect
401. C17#14283semidirect

Maximal subgroups

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

subgroupindex
C22×#105875752
C2×#117626782
C2×#117626542
#145270382
#145270372
#145270362
#145270352
#145270342
#145270122
C17×#14412
#1428317