Finite Group Databasebeta

← #17000144

Subgroups — #17000144

Order 4352.

1278 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763290C211yesmaximal, characteristic
2#14537806C212yesmaximal, complemented
3#14527106C212yesmaximal, complemented
4#14527101C212yesmaximal, complemented
5#14527100C212yesmaximal, complemented
6#14527097C212yesmaximal, complemented
7C2×#11762535C211yesmaximal, characteristic, complemented
8D17×#324C212yesmaximal, complemented
9C2×C17×#324C211yesmaximal, characteristic, complemented
10C22×#63252C411yescharacteristic
11#11763290—24no—
12#11763290—24no—
13C2×#10587573C411yescharacteristic
14C2×#10587573C2211yescharacteristic
15C2×#10587579C411yescharacteristic
16C2×#10587579C2211yescharacteristic
17C2×C4×C22⋊D17C411yescharacteristic
18C2×C4×C22⋊D17C411yescharacteristic
19C2×C4×C22⋊D17C2211yescharacteristic
20C2×C4×C22⋊D17C2211yescharacteristic
21C2×#10587612C411yescharacteristic
22C2×#10587578C411yescharacteristic
23C2×#10587578C2211yescharacteristic
24C2×C4⋊C4×D17C411yescharacteristic
25C2×C4⋊C4×D17C2211yescharacteristic
26C8×C22⋊D17—24no—
27#11762872—24no—
28#11762859C2214yes—
29C2×C22⋊#3622C2212yes—
30C22⋊C8×D17C2214yes—
31#11762535C2212yes—
32#11762535C2212yes—
33#11762534C2214yes—
34#11762532C2214yes—
35C22×C4⋊C4×C17C2211yescharacteristic
36C2×C17×C22⋊C8C2212yes—
37C17×#324C2212yes—
38C17×#324C2212yes—
39C23×C4×C17C2×C411yescharacteristic
40C23×C4×C17C2×C411yescharacteristic
41C23×C4×C17C2311yescharacteristic
42C22×C22⋊D17C2×C411yescharacteristic
43C22×C22⋊D17C2×C411yescharacteristic
44C2×#63252—22no—
45C2×#63252—22no—
46C2×#63252—24no—
47C2×#63252C818yescomplemented
48C22×D68C2×C411yescharacteristic
49C22×C4×D17C2×C411yescharacteristic
50C22×C4×D17C2×C411yescharacteristic
51C22×C4×D17C2×C411yescharacteristic
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17C2311yescharacteristic
55C22×Dic34C2×C411yescharacteristic
56C22×C8×C17—22no—
57C2×C4⋊C4×C17—22no—
58C2×C4⋊C4×C17—22no—
59C2×C4⋊C4×C17C2×C411yescharacteristic
60C2×C4⋊C4×C17C2×C411yescharacteristic
61C2×C4⋊C4×C17C2311yescharacteristic
62C2×C4⋊C4×C17C2311yescharacteristic
63C2×C22⋊Dic17C2×C411yescharacteristic
64C2×C22⋊Dic17C2×C411yescharacteristic
65C4×C22⋊D17—22no—
66C4×C22⋊D17—22no—
67C4×C22⋊D17—22no—
68C4×C22⋊D17—22no—
69C4×C22⋊D17—22no—
70C4×C22⋊D17—22no—
71C4×C22⋊D17D414yes—
72C4×C22⋊D17D414yes—
73C2×#63227C2×C411yescharacteristic
74C2×#63227C2×C411yescharacteristic
75C2×#63227C2×C411yescharacteristic
76C2×#63227C2311yescharacteristic
77#10587612—22no—
78#10587612—22no—
79C2×C4⋊Dic17C2×C411yescharacteristic
80C2×C4⋊Dic17C2×C411yescharacteristic
81C2×#63225C2×C411yescharacteristic
82C2×#63225C2×C411yescharacteristic
83C2×#63225C2×C411yescharacteristic
84C2×#63225C2311yescharacteristic
85C2×C4×Dic17C2×C411yescharacteristic
86C2×C4×Dic17C2×C411yescharacteristic
87C2×C4×Dic17C2×C411yescharacteristic
88C2×C4×Dic17C2×C411yescharacteristic
89C2×C4×Dic17C2×C411yescharacteristic
90C2×C4×Dic17C2311yescharacteristic
91C22×#3622—22no—
92C2×C8×D17—24no—
93#10587579—24no—
94#10587579—24no—
95#10587578—24no—
96#10587578—24no—
97C4⋊C4×D17—24no—
98C4⋊C4×D17—24no—
99#10587573—24no—
100#10587573—24no—
101C17×C22⋊C8—22no—
102C17×C22⋊C8C2314yes—
103C22⋊#3622—22no—
104C22⋊#3622C2314yes—
105#10587491—24no—
106#10587485—24no—
107C8×Dic17—24no—
108C24×C17C22×C411yescharacteristic
109C23×D17C22×C411yescharacteristic
110C23×D17C22×C411yescharacteristic
111C22×C4×C17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—22no—
114C22×C4×C17—21no—
115C22×C4×C17—21no—
116C22×C4×C17—81no—
117C22×C4×C17—81no—
118C22×C4×C17C2×C814yescomplemented
119C22×C4×C17C22×C411yescharacteristic
120C22×C4×C17C22×C411yescharacteristic
121C22×C4×C17C22×C411yescharacteristic
122C22×C4×C17C22×C411yescharacteristic
123C22×C4×C17C22×C411yescharacteristic
124C22×C4×C17C2×D412yes—
125C22×C4×C17C2×D412yes—
126C22×C4×C17C2411yescharacteristic
127C2×C22⋊D17—21no—
128C2×C22⋊D17—21no—
129C2×C22⋊D17—22no—
130C2×C22⋊D17C22⋊C412yes—
131C2×C22⋊D17C22⋊C412yes—
132C2×C22⋊D17C2×C814yes—
133C2×C22⋊D17C2×C814yescomplemented
134C2×C22⋊D17M1614yes—
135C22×Dic17C22×C411yescharacteristic
136C22×Dic17C22×C411yescharacteristic
137C22×Dic17C22×C411yescharacteristic
138C22×Dic17C22×C411yescharacteristic
139C22×Dic17C22×C411yescharacteristic
140C22×Dic17C22×C411yescharacteristic
141#63252—216no—
142#63252—216no—
143C2×D68—22no—
144C2×D68—22no—
145C2×D68C2×C814yescomplemented
146C2×C4×D17—22no—
147C2×C4×D17—22no—
148C2×C4×D17—22no—
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—22no—
152C2×C4×D17—22no—
153C2×C4×D17—81no—
154C2×C4×D17—81no—
155C2×C4×D17—81no—
156C2×C4×D17—81no—
157C2×C4×D17C2×C814yescomplemented
158C2×C4×D17C2×C814yescomplemented
159C2×C4×D17C2×D414yes—
160C2×Dic34—22no—
161C2×Dic34—22no—
162C2×Dic34C2×C814yescomplemented
163C2×C8×C17—24no—
164C2×C8×C17—82no—
165C4⋊C4×C17—22no—
166C4⋊C4×C17—22no—
167C4⋊C4×C17—22no—
168C4⋊C4×C17—22no—
169C22⋊Dic17—21no—
170C22⋊Dic17—21no—
171C22⋊Dic17C22⋊C412yes—
172C22⋊Dic17C22⋊C412yes—
173#63227—22no—
174#63227—22no—
175#63227—22no—
176#63227C22⋊C414yes—
177C4⋊Dic17—22no—
178C4⋊Dic17—22no—
179#63225—22no—
180#63225—22no—
181#63225—22no—
182#63225C22⋊C414yes—
183C4×Dic17—22no—
184C4×Dic17—22no—
185C4×Dic17—22no—
186C4×Dic17—22no—
187C4×Dic17—22no—
188C4×Dic17C2×D414yes—
189C2×#3622—24no—
190C2×#3622—82no—
191C8×D17—84no—
192#17351—171nomaximal, Sylow
193C23×C17—41no—
194C23×C17—41no—
195C23×C17C2×C22⋊C411yescharacteristic
196C23×C17C2×C22⋊C411yescharacteristic
197C23×C17C22×C812yes—
198C23×C17C2×M1612yes—
199C23×C17C23×C411yescharacteristic
200C22×D17—21no—
201C22×D17—21no—
202C22×D17—41no—
203C22×D17—41no—
204C22×D17—41no—
205C22×D17—41no—
206C22×D17C2×C22⋊C412yes—
207C22×D17C22×C812yes—
208C22×D17C22×C812yes—
209C22×D17C2×M1612yes—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—24no—
215C2×C4×C17—24no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
218C2×C4×C17—42no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17—42no—
222C2×C4×C17—41no—
223C2×C4×C17—41no—
224C2×C4×C17—81no—
225C2×C4×C17—81no—
226C2×C4×C17C2×C22⋊C412yes—
227C2×C4×C17C22×C812yes—
228C2×C4×C17C22×C812yes—
229C2×C4×C17C22×D412yes—
230C22⋊D17—24no—
231C22⋊D17—24no—
232C22⋊D17C22⋊C818yes—
233C22⋊D17C22⋊C818yes—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238C2×Dic17—41no—
239C2×Dic17—41no—
240C2×Dic17—41no—
241C2×Dic17—41no—
242C2×Dic17C2×C22⋊C412yes—
243C2×Dic17C2×C22⋊C412yes—
244C2×Dic17C2×C22⋊C412yes—
245C2×Dic17C22×C812yes—
246C2×Dic17C22×C812yes—
247C2×Dic17C2×M1612yes—
248D68—28no—
249C4×D17—28no—
250C4×D17—28no—
251C4×D17—44no—
252C4×D17—82no—
253C4×D17—82no—
254C4×D17—82no—
255Dic34—28no—
256C8×C17—44no—
257#3622—44no—
258C2×#520—171no—
259#2972—172no—
260#1461—172no—
261#1459—172no—
262#1459—172no—
263#1458—172no—
264C2×#324—172no—
265C2×#324—171no—
266C2×#324D1711yescharacteristic, complemented
267C22×C17—21no—
268C22×C17—21no—
269C22×C17—21no—
270C22×C17—21no—
271C22×C17—21no—
272C22×C17—21no—
273C22×C17—42no—
274C22×C17—42no—
275C22×C17C2×C22⋊C812yes—
276C22×C17C2×C22⋊C812yes—
277C22×C17C22×C22⋊C411yescharacteristic
278C22×C17C23×C811yescharacteristic
279C22×C17C22×M1611yescharacteristic
280C2×D17—22no—
281C2×D17—22no—
282C2×D17—22no—
283C2×D17—42no—
284C2×D17—42no—
285C2×D17—42no—
286C2×D17—41no—
287C2×D17—41no—
288C2×D17—42no—
289C2×D17C2×C22⋊C814yes—
290C4×C17—22no—
291C4×C17—22no—
292C4×C17—22no—
293C4×C17—22no—
294C4×C17—41no—
295C4×C17—41no—
296Dic17—22no—
297Dic17—22no—
298Dic17—22no—
299Dic17—41no—
300Dic17—41no—
301Dic17C2×C22⋊C814yes—
302C22×#41—171no—
303#520—344no—
304#520—344no—
305C2×C4×Q8—171no—
306C2×C4×Q8—171no—
307C2×C4×D4—171no—
308C2×C4×D4—171no—
309C2×C4×D4—171no—
310C2×C4×D4—171no—
311C2×C4×D4—171no—
312C2×C4×D4—171no—
313C2×#117—171no—
314C2×#117—171no—
315C2×#117—171no—
316C22×C4⋊C4—171no—
317C22×C4⋊C4—171no—
318C22×C4⋊C4C2×D1711yescharacteristic
319C8×D4—344no—
320C8×D4—344no—
321#431—174no—
322C2×C22⋊C8—172no—
323C2×C22⋊C8—174no—
324C2×C22⋊C8C2×D1712yes—
325#324—172no—
326#324—172no—
327#324—174no—
328#324C2×D1712yes—
329#324C2×D1712yes—
330#323—174no—
331C2×C17—21no—
332C2×C17—21no—
333C2×C17—22no—
334C2×C17—22no—
335C2×C17C22×C22⋊C811yescharacteristic
336C2×C17#288311yescharacteristic
337C2×C17#288911yescharacteristic
338D17—24no—
339D17—42no—
340C2×#41—178no—
341C2×#41—342no—
342C2×#41—342no—
343C2×#41—344no—
344C22×Q8—171no—
345C22×D4—171no—
346C22×D4—171no—
347C22×D4—171no—
348C23×C4—171no—
349C23×C4—171no—
350C23×C4—171no—
351C23×C4—171no—
352C23×C4—171no—
353C23×C4—171no—
354C23×C4C4×D1711yescharacteristic
355C23×C4C4×D1711yescharacteristic
356C23×C4C22×D1711yescharacteristic
357C22×C8—22no—
358C22×C8—344no—
359C22×C8—342no—
360C4×Q8—344no—
361C4×Q8—344no—
362C4×D4—174no—
363C4×D4—174no—
364C4×D4—344no—
365C4×D4—342no—
366C4×D4—342no—
367C4×D4—344no—
368C4×D4—342no—
369C4×D4—342no—
370C4×D4—342no—
371C4×D4—342no—
372#117—344no—
373#117—344no—
374#117—342no—
375#117—342no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—171no—
379C2×C4⋊C4—171no—
380C2×C4⋊C4—171no—
381C2×C4⋊C4—171no—
382C2×C4⋊C4—171no—
383C2×C4⋊C4—171no—
384C2×C4⋊C4—344no—
385C2×C4⋊C4—344no—
386C2×C4⋊C4C4×D1711yescharacteristic
387C2×C4⋊C4C4×D1711yescharacteristic
388C2×C4⋊C4C22×D1711yescharacteristic
389C2×C4⋊C4C22×D1711yescharacteristic
390C2×C22⋊C4—171no—
391C2×C22⋊C4—171no—
392C2×C22⋊C4—171no—
393C2×C22⋊C4—171no—
394C2×C22⋊C4—171no—
395C2×C22⋊C4—171no—
396C2×C42—171no—
397C2×C42—171no—
398C2×C42—171no—
399C2×C42—171no—
400C2×C42—171no—
401C2×C42—171no—
402C4⋊C8—344no—
403C22⋊C8—22no—
404C22⋊C8—174no—
405C22⋊C8—344no—
406C22⋊C8—342no—
407C22⋊C8C22×D1714yes—
408C4×C8—344no—
409C17#1735111yescharacteristic, complemented, Sylow
410C24—171no—
411C24—171no—
412C24C2×C4×D1711yescharacteristic
413#41—3416no—
414#41—3416no—
415C2×Q8—174no—
416C2×Q8—342no—
417C2×Q8—342no—
418C2×D4—172no—
419C2×D4—172no—
420C2×D4—174no—
421C2×D4—174no—
422C2×D4—174no—
423C2×D4—174no—
424C2×D4—342no—
425C2×D4—342no—
426C2×D4—341no—
427C2×D4—341no—
428C2×D4—342no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4—171no—
437C22×C4—171no—
438C22×C4—171no—
439C22×C4—171no—
440C22×C4—174no—
441C22×C4—174no—
442C22×C4—174no—
443C22×C4—171no—
444C22×C4—171no—
445C22×C4—342no—
446C22×C4—342no—
447C22×C4—342no—
448C22×C4—342no—
449C22×C4—342no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—1361no—
453C22×C4—1361no—
454C22×C4—1361no—
455C22×C4—1361no—
456C22×C4C8×D1714yescomplemented
457C22×C4C2×C4×D1711yescharacteristic
458C22×C4C2×C4×D1711yescharacteristic
459C22×C4C2×C4×D1711yescharacteristic
460C22×C4C2×C4×D1711yescharacteristic
461C22×C4C2×C4×D1711yescharacteristic
462C22×C4D4×D1712yes—
463C22×C4D4×D1712yes—
464C22×C4C23×D1711yescharacteristic
465C2×C8—24no—
466C2×C8—82no—
467C2×C8—344no—
468C2×C8—1364no—
469C2×C8—1362no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—174no—
475C4⋊C4—342no—
476C4⋊C4—342no—
477C4⋊C4—342no—
478C4⋊C4—342no—
479C4⋊C4—342no—
480C22⋊C4—172no—
481C22⋊C4—172no—
482C22⋊C4—174no—
483C22⋊C4—342no—
484C22⋊C4—342no—
485C22⋊C4—341no—
486C22⋊C4—341no—
487C22⋊C4—342no—
488C42—174no—
489C42—342no—
490C42—342no—
491C42—342no—
492C42—342no—
493C42—342no—
494C23—41no—
495C23—41no—
496C23—172no—
497C23—172no—
498C23—172no—
499C23—172no—
500C23—341no—
501C23—341no—
502C23—681no—
503C23—681no—
504C23—681no—
505C23—681no—
506C23C22⋊C4×D1711yescharacteristic
507C23C22⋊C4×D1711yescharacteristic
508C23C2×C8×D1712yes—
509C23M16×D1712yes—
510C23C22×C4×D1711yescharacteristic
511Q8—348no—
512D4—178no—
513D4—178no—
514D4—348no—
515D4—344no—
516D4—344no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—172no—
534C2×C4—172no—
535C2×C4—172no—
536C2×C4—172no—
537C2×C4—172no—
538C2×C4—172no—
539C2×C4—348no—
540C2×C4—348no—
541C2×C4—341no—
542C2×C4—341no—
543C2×C4—341no—
544C2×C4—341no—
545C2×C4—684no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—1362no—
551C2×C4—1362no—
552C2×C4—1362no—
553C2×C4C22⋊C4×D1712yes—
554C2×C4C2×C8×D1712yes—
555C2×C4C2×C8×D1712yes—
556C2×C4C2×D4×D1712yes—
557C8—44no—
558C8—684no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—42no—
566C22—42no—
567C22—174no—
568C22—342no—
569C22—342no—
570C22—342no—
571C22—682no—
572C22—682no—
573C22—682no—
574C22—682no—
575C22—681no—
576C22—681no—
577C22C22⋊C8×D1712yes—
578C22C22⋊C8×D1712yes—
579C22C2×C22⋊C4×D1711yescharacteristic
580C22C22×C8×D1711yescharacteristic
581C22C2×M16×D1711yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—174no—
589C4—342no—
590C4—342no—
591C4—342no—
592C4—681no—
593C4—681no—
594C2—21no—
595C2—21no—
596C2—22no—
597C2—22no—
598C2—344no—
599C2—682no—
600C2C2×C22⋊C8×D1711yescharacteristic
601C2#1453724211yescharacteristic
602C2#1453726411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D17
commutatorC22×C17C23×C8
FrattiniC22×C4C23×D17
FittingC2×C17×#324C2
socleC22×C17C22×C22⋊C4
prime radicalC22×#63252C4
cosocleC22×C4×C17C24
hypercenterC2×#324D17
hypocenterC17#17351
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #14537806C2semidirect
3. #14527106C2semidirect
4. #14527101C2semidirect
5. #14527100C2semidirect
6. #14527097C2semidirect
7. C2×#11762535C2semidirect
8. D17×#324C2semidirect
9. C2×C17×#324C2semidirect
47. C2×#63252C8semidirect
118. C22×C4×C17C2×C8semidirect
133. C2×C22⋊D17C2×C8semidirect
145. C2×D68C2×C8semidirect
157. C2×C4×D17C2×C8semidirect
158. C2×C4×D17C2×C8semidirect
162. C2×Dic34C2×C8semidirect
266. C2×#324D17semidirect
409. C17#17351semidirect
456. C22×C4C8×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#117632902
#145378062
#145271062
#145271012
#145271002
#145270972
C2×#117625352
D17×#3242
C2×C17×#3242
#1735117