Finite Group Databasebeta

← #17044358

Subgroups — #17044358

Order 4352.

1094 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Dic17C211yesmaximal, characteristic
2#14529400C212yesmaximal, complemented
3#14529394C212yesmaximal, complemented
4#14529393C212yesmaximal, complemented
5#14529387C212yesmaximal, complemented
6#14528762C211yesmaximal, characteristic, complemented
7#14528762C211yesmaximal, characteristic, complemented
8#14528694C211yesmaximal, characteristic
9#14528548C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic17C211yesmaximal, characteristic, complemented
11C17×#1779C211yesmaximal, characteristic
12C22×C22⋊Dic17C411yescharacteristic
13C22×C22⋊Dic17C411yescharacteristic
14C22×C4×Dic17C2211yescharacteristic
15C22×C4×Dic17C2211yescharacteristic
16C2×#10587485C2212yescomplemented
17C2×#10587485C2212yescomplemented
18C2×C22⋊#3622C2211yescharacteristic
19C2×C22⋊#3622C2211yescharacteristic
20C2×C22⋊#3622C2212yes—
21C2×C22⋊#3622C2212yes—
22C2×#10587486C2212yescomplemented
23C2×C8×Dic17C2212yescomplemented
24C4×C22⋊Dic17C411yescharacteristic
25C4×C22⋊Dic17C411yescharacteristic
26C4×C22⋊Dic17C411yescharacteristic
27C4×C22⋊Dic17C411yescharacteristic
28C4×C22⋊Dic17C2211yescharacteristic
29C4×C22⋊Dic17C2211yescharacteristic
30C4×C22⋊Dic17C2211yescharacteristic
31C4×C22⋊Dic17C2211yescharacteristic
32C2×#10587502C411yescharacteristic
33C2×#10587502C411yescharacteristic
34#11762563C2212yescomplemented
35#11762563C2212yescomplemented
36#11762563C2212yescomplemented
37#11762563C2212yescomplemented
38C24×C4×C17C2211yescharacteristic
39C2×C17×C22⋊C8C2211yescharacteristic
40C2×C17×C22⋊C8C2211yescharacteristic
41C2×C17×C22⋊C8C2212yes—
42C2×C17×C22⋊C8C2212yes—
43C25×C17C2×C411yescharacteristic
44C23×C4×C17—22no—
45C23×C4×C17—22no—
46C23×C4×C17—42no—
47C23×C4×C17—42no—
48C23×C4×C17C2×C411yescharacteristic
49C23×C4×C17C2×C411yescharacteristic
50C23×C4×C17C2×C411yescharacteristic
51C23×C4×C17C2311yescharacteristic
52C23×C4×C17C2311yescharacteristic
53C23×C4×C17C2311yescharacteristic
54C23×Dic17C2×C411yescharacteristic
55C23×Dic17C2×C411yescharacteristic
56C23×Dic17C2×C411yescharacteristic
57C23×Dic17C2×C411yescharacteristic
58C22×C8×C17C2312yes—
59C22×C8×C17C2312yes—
60C2×C22⋊Dic17—24no—
61C2×C22⋊Dic17—24no—
62C2×C22⋊Dic17C2×C411yescharacteristic
63C2×C22⋊Dic17C2×C411yescharacteristic
64C2×C22⋊Dic17C2×C411yescharacteristic
65C2×C22⋊Dic17C2×C411yescharacteristic
66C2×C22⋊Dic17C2×C411yescharacteristic
67C2×C22⋊Dic17C2×C411yescharacteristic
68C2×C22⋊Dic17C2×C411yescharacteristic
69C2×C22⋊Dic17C2×C411yescharacteristic
70C2×C4×Dic17—42no—
71C2×C4×Dic17—42no—
72C2×C4×Dic17C2×C411yescharacteristic
73C2×C4×Dic17C2×C411yescharacteristic
74C2×C4×Dic17C2×C411yescharacteristic
75C2×C4×Dic17C2×C411yescharacteristic
76C2×C4×Dic17C2311yescharacteristic
77C2×C4×Dic17C2311yescharacteristic
78C2×C4×Dic17C2311yescharacteristic
79C2×C4×Dic17C2311yescharacteristic
80C22×#3622C2312yes—
81C22×#3622C2312yes—
82C17×C22⋊C8—22no—
83C17×C22⋊C8—22no—
84C17×C22⋊C8—42no—
85C17×C22⋊C8—42no—
86#10587502C2×C411yescharacteristic
87#10587502C2×C411yescharacteristic
88#10587502C2×C411yescharacteristic
89#10587502C2×C411yescharacteristic
90#10587502C2×C411yescharacteristic
91#10587502C2×C411yescharacteristic
92#10587502C2×C411yescharacteristic
93#10587502C2×C411yescharacteristic
94C22⋊#3622—22no—
95C22⋊#3622—22no—
96C22⋊#3622—42no—
97C22⋊#3622—42no—
98#10587486—42no—
99#10587485—42no—
100#10587485—42no—
101C8×Dic17—42no—
102C24×C17—22no—
103C24×C17—22no—
104C24×C17—22no—
105C24×C17—22no—
106C24×C17—22no—
107C24×C17—41no—
108C24×C17—41no—
109C24×C17C22×C411yescharacteristic
110C24×C17C22×C411yescharacteristic
111C24×C17C22×C411yescharacteristic
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—21no—
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17—21no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17—22no—
125C22×C4×C17—41no—
126C22×C4×C17—41no—
127C22×C4×C17—41no—
128C22×C4×C17—41no—
129C22×C4×C17—41no—
130C22×C4×C17—41no—
131C22×C4×C17—48no—
132C22×C4×C17—48no—
133C22×C4×C17C22×C411yescharacteristic
134C22×C4×C17C22×C411yescharacteristic
135C22×C4×C17C22×C411yescharacteristic
136C22×C4×C17#4112yes—
137C22×C4×C17#4112yes—
138C22×C4×C17C2411yescharacteristic
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—41no—
148C22×Dic17—41no—
149C22×Dic17—41no—
150C22×Dic17—41no—
151C22×Dic17C22×C411yescharacteristic
152C22×Dic17C22×C411yescharacteristic
153C22×Dic17C22×C411yescharacteristic
154C22×Dic17C22×C411yescharacteristic
155C22×Dic17C22×C411yescharacteristic
156C22×Dic17C22×C411yescharacteristic
157C22×Dic17C22×C411yescharacteristic
158C22×Dic17C22×C411yescharacteristic
159C2×C8×C17—22no—
160C2×C8×C17—22no—
161C2×C8×C17—22no—
162C2×C8×C17—22no—
163C2×C8×C17—22no—
164C2×C8×C17—22no—
165C22⋊Dic17—22no—
166C22⋊Dic17—22no—
167C22⋊Dic17—22no—
168C22⋊Dic17—22no—
169C22⋊Dic17—22no—
170C22⋊Dic17—22no—
171C22⋊Dic17M1614yes—
172C22⋊Dic17M1614yes—
173C4×Dic17—22no—
174C4×Dic17—22no—
175C4×Dic17—22no—
176C4×Dic17—22no—
177C4×Dic17—41no—
178C4×Dic17—41no—
179C4×Dic17—41no—
180C4×Dic17—41no—
181C2×#3622—22no—
182C2×#3622—22no—
183C2×#3622—22no—
184C2×#3622—22no—
185C2×#3622—22no—
186C2×#3622—22no—
187#21904—171nomaximal, Sylow
188C23×C17—21no—
189C23×C17—21no—
190C23×C17—21no—
191C23×C17—21no—
192C23×C17—28no—
193C23×C17—21no—
194C23×C17—21no—
195C23×C17—21no—
196C23×C17—21no—
197C23×C17—21no—
198C23×C17—21no—
199C23×C17—21no—
200C23×C17—21no—
201C23×C17—21no—
202C23×C17—21no—
203C23×C17—21no—
204C23×C17—21no—
205C23×C17—44no—
206C23×C17—44no—
207C23×C17—44no—
208C23×C17—44no—
209C23×C17—44no—
210C23×C17—44no—
211C23×C17#11712yes—
212C23×C17C2×M1612yes—
213C23×C17C2×M1612yes—
214C23×C17#13112yes—
215C23×C17#13112yes—
216C23×C17C23×C411yescharacteristic
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—24no—
220C2×C4×C17—24no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—44no—
228C2×C4×C17—44no—
229C2×C4×C17—44no—
230C2×C4×C17—42no—
231C2×C4×C17—42no—
232C2×C4×C17—42no—
233C2×C4×C17—42no—
234C2×C4×C17#11712yes—
235C2×C4×C17C2×#4111yescharacteristic
236C2×C4×C17C2×#4111yescharacteristic
237C2×C4×C17H(5,𝔽2)12yes—
238C2×C4×C17H(5,𝔽2)12yes—
239C2×Dic17—21no—
240C2×Dic17—21no—
241C2×Dic17—21no—
242C2×Dic17—21no—
243C2×Dic17—21no—
244C2×Dic17—21no—
245C2×Dic17—21no—
246C2×Dic17—21no—
247C2×Dic17—21no—
248C2×Dic17—21no—
249C2×Dic17—21no—
250C2×Dic17—21no—
251C2×Dic17—21no—
252C2×Dic17—21no—
253C2×Dic17—21no—
254C2×Dic17—21no—
255C2×Dic17—21no—
256C2×Dic17—21no—
257C2×Dic17—21no—
258C2×Dic17—21no—
259C2×Dic17—44no—
260C2×Dic17—44no—
261C2×Dic17—44no—
262C2×Dic17—44no—
263C2×Dic17C2×M1612yes—
264C2×Dic17C2×M1612yes—
265C2×Dic17C2×M1612yes—
266C2×Dic17C2×M1612yes—
267C8×C17—42no—
268C8×C17—42no—
269#3622—42no—
270#3622—42no—
271C2×C4×C22⋊C4—171no—
272#1924—172no—
273#1924—172no—
274#1923—172no—
275#1923—172no—
276#1797—171no—
277#1797—171no—
278#1779—171no—
279#1779D1711yescharacteristic
280#1749—171no—
281C4×C22⋊C8—171no—
282C22×C17—22no—
283C22×C17—22no—
284C22×C17—22no—
285C22×C17—22no—
286C22×C17—22no—
287C22×C17—22no—
288C22×C17—22no—
289C22×C17—22no—
290C22×C17—22no—
291C22×C17—22no—
292C22×C17—22no—
293C22×C17—22no—
294C22×C17—416no—
295C22×C17—41no—
296C22×C17—41no—
297C22×C17—41no—
298C22×C17—41no—
299C22×C17—41no—
300C22×C17—41no—
301C22×C17—41no—
302C22×C17—41no—
303C22×C17#43314yes—
304C22×C17C2×#11711yescharacteristic
305C22×C17#51811yescharacteristic
306C22×C17#51811yescharacteristic
307C22×C17C22×M1611yescharacteristic
308C22×C17C22×M1611yescharacteristic
309C22×C17C2×#13111yescharacteristic
310C22×C17C2×#13111yescharacteristic
311C4×C17—22no—
312C4×C17—41no—
313C4×C17—41no—
314C4×C17#53812yes—
315C4×C17#53812yes—
316Dic17—22no—
317Dic17—22no—
318Dic17—22no—
319Dic17—22no—
320Dic17—41no—
321Dic17—41no—
322Dic17—41no—
323Dic17—41no—
324C24×C4C2×D1711yescharacteristic
325C22×C22⋊C4—171no—
326C22×C22⋊C4—171no—
327C22×C42—171no—
328C22×C42—171no—
329C2×C4⋊C8—172no—
330C2×C4⋊C8—172no—
331C2×C22⋊C8—171no—
332C2×C22⋊C8—171no—
333C2×C22⋊C8—172no—
334C2×C22⋊C8—172no—
335C2×C22⋊C8C2×D1711yescharacteristic
336C2×C22⋊C8C2×D1711yescharacteristic
337C2×C22⋊C8C2×D1712yes—
338C2×C22⋊C8C2×D1712yes—
339C2×#97—172no—
340C2×C4×C8—172no—
341C4×C22⋊C4—171no—
342C4×C22⋊C4—171no—
343C4×C22⋊C4—171no—
344C4×C22⋊C4—171no—
345C4×C22⋊C4—171no—
346C4×C22⋊C4—171no—
347C4×C22⋊C4—171no—
348C4×C22⋊C4—171no—
349C2×#95—171no—
350C2×#95—171no—
351#336—172no—
352#336—172no—
353#336—172no—
354#336—172no—
355C2×C17—24no—
356C2×C17—42no—
357C2×C17—42no—
358C2×C17#231211yescharacteristic
359C2×C17C2×#43311yescharacteristic
360C2×C17#292011yescharacteristic
361C2×C17#297411yescharacteristic
362C2×C17#297411yescharacteristic
363C2×C17#297411yescharacteristic
364C2×C17#297411yescharacteristic
365C25C4×D1711yescharacteristic
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4—171no—
371C23×C4—171no—
372C23×C4—171no—
373C23×C4—171no—
374C23×C4C4×D1711yescharacteristic
375C23×C4C4×D1711yescharacteristic
376C23×C4C4×D1711yescharacteristic
377C23×C4C22×D1711yescharacteristic
378C23×C4C22×D1711yescharacteristic
379C23×C4C22×D1711yescharacteristic
380C22×C8—172no—
381C22×C8—172no—
382C22×C8C22×D1712yes—
383C22×C8C22×D1712yes—
384C2×C22⋊C4—171no—
385C2×C22⋊C4—171no—
386C2×C22⋊C4—171no—
387C2×C22⋊C4—171no—
388C2×C22⋊C4—171no—
389C2×C22⋊C4—171no—
390C2×C22⋊C4—171no—
391C2×C22⋊C4—171no—
392C2×C22⋊C4—344no—
393C2×C22⋊C4—344no—
394C2×C42—171no—
395C2×C42—171no—
396C2×C42—171no—
397C2×C42—171no—
398C2×C42—171no—
399C2×C42—171no—
400C2×C42—171no—
401C2×C42—171no—
402C2×C42—682no—
403C2×C42—682no—
404C4⋊C8—682no—
405C4⋊C8—682no—
406C22⋊C8—22no—
407C22⋊C8—22no—
408C22⋊C8—42no—
409C22⋊C8—42no—
410C22⋊C8—342no—
411C22⋊C8—342no—
412C22⋊C8—682no—
413C22⋊C8—682no—
414#97—682no—
415C4×C8—682no—
416#95—171no—
417#95—171no—
418#95—171no—
419#95—171no—
420#95—171no—
421#95—171no—
422#95—171no—
423#95—171no—
424C17#2190411yescharacteristic, complemented, Sylow
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—41no—
431C24—41no—
432C24C2×C4×D1711yescharacteristic
433C24C2×C4×D1711yescharacteristic
434C24C2×C4×D1711yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—48no—
455C22×C4—48no—
456C22×C4—171no—
457C22×C4—171no—
458C22×C4—171no—
459C22×C4—171no—
460C22×C4—171no—
461C22×C4—171no—
462C22×C4—171no—
463C22×C4—171no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4—342no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—681no—
473C22×C4—681no—
474C22×C4—681no—
475C22×C4—681no—
476C22×C4C2×C4×D1711yescharacteristic
477C22×C4C2×C4×D1711yescharacteristic
478C22×C4C2×C4×D1711yescharacteristic
479C22×C4#6325412yes—
480C22×C4#6325412yes—
481C22×C4C23×D1711yescharacteristic
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—342no—
489C2×C8—342no—
490C2×C8—342no—
491C2×C8—342no—
492C2×C8—342no—
493C2×C8—342no—
494C22⋊C4—174no—
495C22⋊C4—174no—
496C22⋊C4—342no—
497C22⋊C4—342no—
498C22⋊C4—342no—
499C22⋊C4—342no—
500C22⋊C4—342no—
501C22⋊C4—342no—
502C42—342no—
503C42—342no—
504C42—342no—
505C42—342no—
506C42—681no—
507C42—681no—
508C42—681no—
509C42—681no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—28no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23—44no—
532C23—44no—
533C23#1058756312yes—
534C23#1058758712yes—
535C23M16×D1712yes—
536C23M16×D1712yes—
537C23#1058759312yes—
538C23C22×C4×D1711yescharacteristic
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—172no—
557C2×C4—172no—
558C2×C4—172no—
559C2×C4—172no—
560C2×C4—341no—
561C2×C4—341no—
562C2×C4—341no—
563C2×C4—341no—
564C2×C4—341no—
565C2×C4—341no—
566C2×C4—341no—
567C2×C4—341no—
568C2×C4—341no—
569C2×C4—341no—
570C2×C4—341no—
571C2×C4—341no—
572C2×C4—341no—
573C2×C4—341no—
574C2×C4—341no—
575C2×C4—341no—
576C2×C4—341no—
577C2×C4—341no—
578C2×C4—341no—
579C2×C4—341no—
580C2×C4—684no—
581C2×C4—684no—
582C2×C4—684no—
583C2×C4—684no—
584C2×C4#1058756312yes—
585C2×C4C2×#6325411yescharacteristic
586C2×C4C2×#6325411yescharacteristic
587C2×C4#1058769112yes—
588C2×C4#1058769112yes—
589C8—42no—
590C8—42no—
591C8—682no—
592C8—682no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—416no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22#1176286714yes—
615C22C2×#1058756311yescharacteristic
616C22#1176328211yescharacteristic
617C22#1176328211yescharacteristic
618C22C2×M16×D1711yescharacteristic
619C22C2×M16×D1711yescharacteristic
620C22C2×#1058758711yescharacteristic
621C22C2×#1058759311yescharacteristic
622C4—22no—
623C4—41no—
624C4—41no—
625C4—342no—
626C4—342no—
627C4—342no—
628C4—342no—
629C4—681no—
630C4—681no—
631C4—681no—
632C4—681no—
633C4#1176339412yes—
634C4#1176339412yes—
635C2—24no—
636C2—42no—
637C2—42no—
638C2#1453138011yescharacteristic
639C2C2×#1176286711yescharacteristic
640C2#1453741311yescharacteristic
641C2#1453781511yescharacteristic
642C2#1453781511yescharacteristic
643C2#1453782011yescharacteristic
644C2#1453782011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1779C2
prime radicalC25×C17C2×C4
cosocleC22×C4×C17C24
hypercenter#1779D17
hypocenterC17#21904
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. #14529400C2semidirect
3. #14529394C2semidirect
4. #14529393C2semidirect
5. #14529387C2semidirect
6. #14528762C2semidirect
7. #14528762C2semidirect
9. #14528548C2semidirect
10. C22⋊C8×Dic17C2semidirect
16. C2×#10587485C22semidirect
17. C2×#10587485C22semidirect
22. C2×#10587486C22semidirect
23. C2×C8×Dic17C22semidirect
34. #11762563C22semidirect
35. #11762563C22semidirect
36. #11762563C22semidirect
37. #11762563C22semidirect
424. C17#21904semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic172
#145294002
#145293942
#145293932
#145293872
#145287622
#145286942
#145285482
C22⋊C8×Dic172
C17×#17792
#2190417