Finite Group Databasebeta

← #16956939

Subgroups — #16956939

Order 4352.

1486 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#63227C211yesmaximal, characteristic
2#14527045C212yesmaximal, complemented
3#14527032C212yesmaximal
4#14527020C212yesmaximal
5#14527011C211yesmaximal, characteristic, complemented
6#14527009C211yesmaximal, characteristic, complemented
7#14527008C212yesmaximal, complemented
8#14527005C211yesmaximal, characteristic
9#14527005C211yesmaximal, characteristic
10#95×Dic17C211yesmaximal, characteristic, complemented
11C17×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D17C2211yescharacteristic
13C22×#63227C2212yes—
14C22×#63227C2212yes—
15C22×#63227C2211yescharacteristic
16C22×#63227C2211yescharacteristic
17C22×C4×Dic17C2212yes—
18C22×C4×Dic17C2211yescharacteristic
19C4×#63227C418yescomplemented
20C2×#10587502C2211yescharacteristic
21C2×#10587502C2212yes—
22C2×#10587502C2211yescharacteristic
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C22×C42×C17C2211yescharacteristic
32C2×C17×#95C2211yescharacteristic
33C2×C17×#95C2211yescharacteristic
34C2×C17×#95C2212yes—
35C2×C17×#95C2212yes—
36C24×D17C2311yescharacteristic
37C23×C4×C17C2312yes—
38C23×C4×C17C2311yescharacteristic
39C23×C4×C17C2311yescharacteristic
40C23×C4×C17C2312yes—
41C23×C4×C17C2311yescharacteristic
42C23×Dic17C2312yes—
43C23×Dic17C2311yescharacteristic
44C23×Dic17C2311yescharacteristic
45C23×Dic17C2312yes—
46C23×Dic17C2311yescharacteristic
47C22×C4×D17—22no—
48C22×C4×D17—22no—
49C22×C4×D17—42no—
50C22×C4×D17—42no—
51C22×C4×D17C2×C414yes—
52C2×C42×C17—42no—
53C2×C42×C17C2×C414yes—
54C2×#63227—22no—
55C2×#63227—22no—
56C2×#63227—24no—
57C2×#63227—24no—
58C2×#63227—24no—
59C2×#63227—22no—
60C2×#63227—22no—
61C2×#63227—24no—
62C2×#63227—42no—
63C2×#63227—42no—
64C2×#63227C2×C414yes—
65C2×#63227C2×C414yes—
66C2×C4×Dic17—24no—
67C2×C4×Dic17—24no—
68C2×C4×Dic17—42no—
69C2×C4×Dic17—42no—
70C2×C4×Dic17C2×C414yes—
71C17×#95—22no—
72C17×#95—24no—
73C17×#95—22no—
74C17×#95—42no—
75#10587502—22no—
76#10587502—22no—
77#10587502—24no—
78#10587502—24no—
79#10587502—24no—
80#10587502—42no—
81#10587502—42no—
82#10587502—42no—
83#10587502—42no—
84#10587502C2×C414yes—
85#10587502C2×C414yes—
86C24×C17C2411yescharacteristic
87C23×D17—21no—
88C23×D17—21no—
89C23×D17—22no—
90C23×D17—21no—
91C23×D17—21no—
92C23×D17—22no—
93C23×D17—22no—
94C23×D17—22no—
95C23×D17C22×C412yes—
96C23×D17#4112yes—
97C23×D17#4112yes—
98C22×C4×C17—22no—
99C22×C4×C17—22no—
100C22×C4×C17—22no—
101C22×C4×C17—22no—
102C22×C4×C17—22no—
103C22×C4×C17—22no—
104C22×C4×C17—22no—
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
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×C17—22no—
121C22×C4×C17C22×C412yes—
122C22×C4×C17C22×C412yes—
123C22×C4×C17C22×C412yes—
124C22×C4×C17#4114yes—
125C22×C4×C17#4112yes—
126C22×C4×C17#4112yes—
127C22×Dic17—22no—
128C22×Dic17—22no—
129C22×Dic17—21no—
130C22×Dic17—21no—
131C22×Dic17—22no—
132C22×Dic17—22no—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—21no—
136C22×Dic17—21no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—22no—
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×Dic17C22×C412yes—
151C22×Dic17C22×C412yes—
152C22×Dic17C22×C412yes—
153C22×Dic17#4114yes—
154C22×Dic17#4112yes—
155C22×Dic17#4112yes—
156C2×C4×D17—28no—
157C2×C4×D17—44no—
158C2×C4×D17—44no—
159C2×C4×D17—48no—
160C2×C4×D17—48no—
161C42×C17—44no—
162#63227—28no—
163#63227—28no—
164#63227—48no—
165#63227—48no—
166C4×Dic17—44no—
167C4×Dic17—48no—
168#13947—171nomaximal, Sylow
169C23×C17C23×C411yescharacteristic
170C23×C17C2×#4112yes—
171C23×C17C2×#4111yescharacteristic
172C23×C17C2×#4111yescharacteristic
173C23×C17C2×#4111yescharacteristic
174C23×C17C2×#4111yescharacteristic
175C23×C17C2×#4111yescharacteristic
176C23×C17C2×#4111yescharacteristic
177C23×C17C2×#4112yes—
178C23×C17H(5,𝔽2)12yes—
179C23×C17H(5,𝔽2)12yes—
180C22×D17—22no—
181C22×D17—22no—
182C22×D17—22no—
183C22×D17—22no—
184C22×D17—22no—
185C22×D17—22no—
186C22×D17—22no—
187C22×D17—22no—
188C22×D17—22no—
189C22×D17—22no—
190C22×D17—24no—
191C22×D17—24no—
192C22×D17—24no—
193C22×D17—24no—
194C22×D17—42no—
195C22×D17—42no—
196C22×D17—42no—
197C22×D17—42no—
198C22×D17—42no—
199C22×D17—42no—
200C22×D17—42no—
201C22×D17—42no—
202C22×D17#11714yes—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—24no—
206C2×C4×C17—24no—
207C2×C4×C17—22no—
208C2×C4×C17—22no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17—22no—
212C2×C4×C17—22no—
213C2×C4×C17—24no—
214C2×C4×C17—24no—
215C2×C4×C17—24no—
216C2×C4×C17—42no—
217C2×C4×C17—42no—
218C2×C4×C17—42no—
219C2×C4×C17—42no—
220C2×C4×C17—42no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17—42no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
229C2×C4×C17—42no—
230C2×C4×C17—42no—
231C2×C4×C17#11714yes—
232C2×Dic17—22no—
233C2×Dic17—22no—
234C2×Dic17—24no—
235C2×Dic17—24no—
236C2×Dic17—22no—
237C2×Dic17—22no—
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—22no—
241C2×Dic17—22no—
242C2×Dic17—24no—
243C2×Dic17—24no—
244C2×Dic17—24no—
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×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—42no—
259C2×Dic17—42no—
260C2×Dic17#11714yes—
261C4×D17—416no—
262C2×C4×C22⋊C4—171no—
263#1443—172no—
264#1440—172no—
265#1437—172no—
266#1434—171no—
267#1434—172no—
268#1434—171no—
269#1434D1711yescharacteristic, complemented
270C22⋊#95—171no—
271C22⋊#95—171no—
272C4×#95—171no—
273C22×C17C2×#11711yescharacteristic
274C22×C17C2×#11711yescharacteristic
275C22×C17C2×#11711yescharacteristic
276C22×C17C4×#4111yescharacteristic
277C22×C17C4×#4111yescharacteristic
278C22×C17#51811yescharacteristic
279C22×C17#51811yescharacteristic
280C22×C17#52911yescharacteristic
281C22×C17#52911yescharacteristic
282C22×C17#52912yes—
283C22×C17#52911yescharacteristic
284C22×C17#52911yescharacteristic
285C22×C17#52912yes—
286C22×C17#53812yes—
287C22×C17#53812yes—
288C22×C17#55112yes—
289C22×C17#55112yes—
290C22×C17#55112yes—
291C22×C17#55312yes—
292C22×C17#55312yes—
293C22×C17#55312yes—
294C22×C17#55312yes—
295C22×C17#55912yes—
296C2×D17—24no—
297C2×D17—24no—
298C2×D17—24no—
299C2×D17—42no—
300C2×D17—44no—
301C2×D17—44no—
302C2×D17—44no—
303C2×D17—44no—
304C2×D17—42no—
305C2×D17—42no—
306C2×D17—42no—
307C4×C17—24no—
308C4×C17—44no—
309C4×C17—42no—
310C4×C17—42no—
311C4×C17—82no—
312Dic17—24no—
313Dic17—42no—
314Dic17—44no—
315Dic17—42no—
316Dic17—82no—
317C24×C4—171no—
318C22×C22⋊C4—171no—
319C22×C22⋊C4—171no—
320C22×C22⋊C4—172no—
321C22×C22⋊C4—172no—
322C22×C42—171no—
323C22×C42—172no—
324C22×C42C2×D1711yescharacteristic
325C4×C22⋊C4—178no—
326C2×#95—171no—
327C2×#95—171no—
328C2×#95—171no—
329C2×#95—172no—
330C2×#95—171no—
331C2×#95—172no—
332C2×#95—172no—
333C2×#95—172no—
334C2×#95—172no—
335C2×#95—172no—
336C2×#95—172no—
337C2×#95C2×D1711yescharacteristic
338C2×#95C2×D1711yescharacteristic
339C2×#95C2×D1712yes—
340C2×#95C2×D1712yes—
341C2×C17#228311yescharacteristic
342C2×C17#229811yescharacteristic
343C2×C17#231211yescharacteristic
344C2×C17#235311yescharacteristic
345C2×C17#235311yescharacteristic
346C2×C17#235311yescharacteristic
347C2×C17#235711yescharacteristic
348C2×C17#257612yes—
349C2×C17#257812yes—
350C2×C17#259512yes—
351C2×C17#259712yes—
352D17—44no—
353C25—171no—
354C23×C4—171no—
355C23×C4—171no—
356C23×C4—172no—
357C23×C4—171no—
358C23×C4—174no—
359C23×C4—172no—
360C23×C4—342no—
361C23×C4—342no—
362C23×C4—682no—
363C23×C4—682no—
364C23×C4C22×D1712yes—
365C23×C4C22×D1711yescharacteristic
366C23×C4C22×D1711yescharacteristic
367C23×C4C22×D1712yes—
368C23×C4C22×D1711yescharacteristic
369C2×C22⋊C4—174no—
370C2×C22⋊C4—174no—
371C2×C22⋊C4—342no—
372C2×C22⋊C4—342no—
373C2×C22⋊C4—342no—
374C2×C22⋊C4—342no—
375C2×C22⋊C4—344no—
376C2×C22⋊C4—344no—
377C2×C22⋊C4—344no—
378C2×C22⋊C4—344no—
379C2×C22⋊C4—682no—
380C2×C22⋊C4—682no—
381C2×C42—42no—
382C2×C42—174no—
383C2×C42—344no—
384C2×C42—344no—
385C2×C42—682no—
386C2×C42—682no—
387C2×C42C4×D1714yes—
388#95—24no—
389#95—22no—
390#95—22no—
391#95—42no—
392#95—174no—
393#95—174no—
394#95—344no—
395#95—344no—
396#95—344no—
397#95—342no—
398#95—342no—
399#95—682no—
400#95—682no—
401#95—682no—
402#95—682no—
403C17#1394711yescharacteristic, complemented, Sylow
404C24—172no—
405C24—172no—
406C24—172no—
407C24—342no—
408C24—341no—
409C24—342no—
410C24—341no—
411C24—342no—
412C24—341no—
413C24—341no—
414C24—342no—
415C24C23×D1711yescharacteristic
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
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—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—172no—
440C22×C4—172no—
441C22×C4—172no—
442C22×C4—172no—
443C22×C4—172no—
444C22×C4—174no—
445C22×C4—342no—
446C22×C4—342no—
447C22×C4—342no—
448C22×C4—341no—
449C22×C4—342no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—341no—
453C22×C4—342no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—341no—
457C22×C4—341no—
458C22×C4—342no—
459C22×C4—342no—
460C22×C4—342no—
461C22×C4—348no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4—342no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—684no—
470C22×C4—684no—
471C22×C4—688no—
472C22×C4—688no—
473C22×C4C2×C4×D1712yes—
474C22×C4C2×C4×D1712yes—
475C22×C4C2×C4×D1712yes—
476C22×C4#6325214yes—
477C22×C4#6325412yes—
478C22×C4#6325612yes—
479C22⋊C4—348no—
480C22⋊C4—348no—
481C22⋊C4—688no—
482C22⋊C4—688no—
483C42—44no—
484C42—684no—
485C42—688no—
486C23—174no—
487C23—344no—
488C23—344no—
489C23—344no—
490C23—344no—
491C23—342no—
492C23—342no—
493C23—342no—
494C23—342no—
495C23—342no—
496C23—342no—
497C23—342no—
498C23—342no—
499C23—342no—
500C23—342no—
501C23—682no—
502C23—682no—
503C23—682no—
504C23—682no—
505C23—682no—
506C23—682no—
507C23—682no—
508C23—682no—
509C23C22×C4×D1711yescharacteristic
510C23C2×#6325212yes—
511C23C2×#6325411yescharacteristic
512C23#1058769112yes—
513C23C2×#6325611yescharacteristic
514C23#41×D1711yescharacteristic
515C23#41×D1711yescharacteristic
516C23#41×D1712yes—
517C23#41×D1711yescharacteristic
518C23#41×D1711yescharacteristic
519C23#1058769612yes—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—174no—
549C2×C4—344no—
550C2×C4—344no—
551C2×C4—342no—
552C2×C4—342no—
553C2×C4—344no—
554C2×C4—344no—
555C2×C4—342no—
556C2×C4—342no—
557C2×C4—342no—
558C2×C4—342no—
559C2×C4—342no—
560C2×C4—342no—
561C2×C4—344no—
562C2×C4—6816no—
563C2×C4—682no—
564C2×C4—682no—
565C2×C4—682no—
566C2×C4—682no—
567C2×C4—682no—
568C2×C4—682no—
569C2×C4—682no—
570C2×C4—682no—
571C2×C4—682no—
572C2×C4—682no—
573C2×C4—682no—
574C2×C4—682no—
575C2×C4—682no—
576C2×C4—682no—
577C2×C4—682no—
578C2×C4#1058757814yes—
579C22—344no—
580C22—344no—
581C22—344no—
582C22—682no—
583C22—682no—
584C22—684no—
585C22—682no—
586C22—684no—
587C22—682no—
588C22—684no—
589C22—684no—
590C22#117×D1711yescharacteristic
591C22#117×D1711yescharacteristic
592C22C2×#1058757811yescharacteristic
593C22#1176327711yescharacteristic
594C22C4×#6325211yescharacteristic
595C22#1176328211yescharacteristic
596C22#1176328311yescharacteristic
597C22#1176333811yescharacteristic
598C22#1176333811yescharacteristic
599C22#1176333912yes—
600C22#1176334411yescharacteristic
601C22#1176334411yescharacteristic
602C22#1176334612yes—
603C22#1176339612yes—
604C22#1176339912yes—
605C22#1176348312yes—
606C22#1176348412yes—
607C22#1176348812yes—
608C22#1176350312yes—
609C22#1176350412yes—
610C22#1176350912yes—
611C22#1176351012yes—
612C22#1176354312yes—
613C4—24no—
614C4—42no—
615C4—42no—
616C4—44no—
617C4—82no—
618C4—344no—
619C4—682no—
620C4—682no—
621C4—684no—
622C4—1362no—
623C2—684no—
624C2#1453117711yescharacteristic
625C2#1453127711yescharacteristic
626C2#1453138111yescharacteristic
627C2#1453171711yescharacteristic
628C2#1453172511yescharacteristic
629C2#1453172711yescharacteristic
630C2#1453175211yescharacteristic
631C2#1453409312yes—
632C2#1453412512yes—
633C2#1453431012yes—
634C2#1453434212yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1434D17
hypocenterC17#13947
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #14527045C2semidirect
5. #14527011C2semidirect
6. #14527009C2semidirect
7. #14527008C2semidirect
10. #95×Dic17C2semidirect
11. C17×#1434C2semidirect
19. C4×#63227C4semidirect
269. #1434D17semidirect
403. C17#13947semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#632272
#145270452
#145270322
#145270202
#145270112
#145270092
#145270082
#145270052
#95×Dic172
C17×#14342
#1394717