Finite Group Databasebeta

← #16957440

Subgroups — #16957440

Order 4352.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587569C211yesmaximal, characteristic
2C2×#11762685C211yesmaximal, characteristic
3C2×#11762685C211yesmaximal, characteristic
4C2×#11762680C211yesmaximal, characteristic, complemented
5C2×#11762671C211yesmaximal, characteristic, complemented
6C2×#11762656C211yesmaximal, characteristic, complemented
7C2×#95×D17C211yesmaximal, characteristic, complemented
8#14527051C211yesmaximal, characteristic, complemented
9#14527050C211yesmaximal, characteristic, complemented
10#14527027C211yesmaximal, characteristic, complemented
11#14527021C211yesmaximal, characteristic, complemented
12#14527021C211yesmaximal, characteristic, complemented
13#14527013C211yesmaximal, characteristic, complemented
14#14527012C211yesmaximal, characteristic, complemented
15C17×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C2×#10587569—24no—
21C2×#10587569—24no—
22C2×#10587569C418yescomplemented
23C22×C4⋊Dic17C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34#11762685—24no—
35#11762685—24no—
36#11762680—24no—
37#11762671—24no—
38#11762656—24no—
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52#95×D17—24no—
53C22×C4⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C22⋊C4×C17C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C24×D17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C22×C22⋊D17—22no—
69C22×C22⋊D17—22no—
70C22×C22⋊D17—22no—
71C22×C22⋊D17—22no—
72C22×C22⋊D17—22no—
73C22×C22⋊D17—22no—
74C22×C22⋊D17C2×C414yes—
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—22no—
85C22×C4×D17—22no—
86C22×C4×D17—22no—
87C22×C4×D17—22no—
88C22×C4×D17—22no—
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—22no—
94C22×C4×D17—22no—
95C22×C4×D17—22no—
96C22×C4×D17—22no—
97C22×C4×D17—41no—
98C22×C4×D17—41no—
99C22×C4×D17—41no—
100C22×C4×D17—41no—
101C22×C4×D17C2×C414yes—
102C22×C4×D17D414yes—
103C2×C4⋊C4×C17—22no—
104C2×C4⋊C4×C17—22no—
105C2×C4⋊C4×C17—41no—
106C2×C22⋊C4×C17—22no—
107C2×C22⋊C4×C17—22no—
108C2×C22⋊C4×C17—22no—
109C2×C22⋊C4×C17—22no—
110C2×C22⋊C4×C17—22no—
111C2×C22⋊C4×C17—41no—
112C2×C22⋊C4×C17—41no—
113C2×C22⋊C4×C17—41no—
114C2×C22⋊C4×C17C2×C414yescomplemented
115C2×C22⋊Dic17—22no—
116C2×C22⋊Dic17—22no—
117C2×C22⋊Dic17—22no—
118C2×C22⋊Dic17—22no—
119C2×C22⋊Dic17—22no—
120C2×C22⋊Dic17—22no—
121C2×C22⋊Dic17—22no—
122C2×C22⋊Dic17—41no—
123C2×C22⋊Dic17C2×C414yescomplemented
124C2×#63227—22no—
125C2×#63227—22no—
126C2×#63227—22no—
127C2×#63227—22no—
128C2×#63227—22no—
129C2×#63227C2×C414yes—
130C2×#63227D414yes—
131C2×#63227D414yes—
132C2×#63227D414yes—
133C2×C4⋊Dic17—22no—
134C2×C4⋊Dic17—22no—
135C2×C4⋊Dic17C2×C414yescomplemented
136C2×#63225—22no—
137C2×#63225—22no—
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225—41no—
141C2×#63225C2×C414yescomplemented
142C2×C4×Dic17—22no—
143C2×C4×Dic17—22no—
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—41no—
147C2×C4×Dic17—41no—
148#10587569—232no—
149C17×#95—22no—
150C17×#95—22no—
151C17×#95—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—22no—
156#10587502—22no—
157#10587502—22no—
158#10587502—22no—
159#10587502—22no—
160#10587502—22no—
161#10587502—22no—
162#10587502—22no—
163#10587502—22no—
164#10587502—22no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17—21no—
173C24×C17—21no—
174C24×C17—21no—
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17—21no—
179C24×C17C22×C412yes—
180C24×C17C2411yescharacteristic
181C23×D17—21no—
182C23×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C23×D17C22×C412yes—
190C23×D17C2×D412yes—
191C23×D17C2×D412yes—
192C23×D17C2×D412yes—
193C23×D17C2×D412yes—
194C23×D17#4112yes—
195C23×D17#4112yes—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17C22×C412yes—
232C22×C4×C17C22×C412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17C2×D412yes—
236C22×C4×C17C2×D412yes—
237C22×C4×C17#4112yes—
238C2×C22⋊D17—28no—
239C2×C22⋊D17—28no—
240C2×C22⋊D17—28no—
241C2×C22⋊D17—44no—
242C2×C22⋊D17—44no—
243C2×C22⋊D17—44no—
244C2×C22⋊D17—44no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17C22×C412yes—
285C22×Dic17C22×C412yes—
286C22×Dic17C22×C412yes—
287C22×Dic17C2×D412yes—
288C22×Dic17C2×D412yes—
289C22×Dic17C2×D412yes—
290C22×Dic17C2×D412yes—
291C22×Dic17#4112yes—
292C22×Dic17#4112yes—
293C22×Dic17#4112yes—
294C2×C4×D17—28no—
295C2×C4×D17—28no—
296C2×C4×D17—28no—
297C2×C4×D17—28no—
298C2×C4×D17—28no—
299C2×C4×D17—28no—
300C2×C4×D17—44no—
301C2×C4×D17—44no—
302C2×C4×D17—44no—
303C2×C4×D17—44no—
304C2×C4×D17—44no—
305C2×C4×D17—44no—
306C2×C4×D17—44no—
307C2×C4×D17—44no—
308C2×C4×D17—44no—
309C2×C4×D17—44no—
310C2×C4×D17—44no—
311C2×C4×D17—44no—
312C2×C4×D17—44no—
313C2×C4×D17—44no—
314C2×C4×D17—44no—
315C4⋊C4×C17—44no—
316C22⋊C4×C17—28no—
317C22⋊C4×C17—44no—
318C22⋊C4×C17—44no—
319C22⋊Dic17—28no—
320C22⋊Dic17—44no—
321C22⋊Dic17—44no—
322#63227—28no—
323#63227—44no—
324#63227C22⋊C4116yescomplemented
325C4⋊Dic17—28no—
326#63225—28no—
327#63225—44no—
328C4×Dic17—44no—
329C4×Dic17—44no—
330#13996—171nomaximal, Sylow
331C23×C17—22no—
332C23×C17—22no—
333C23×C17—22no—
334C23×C17—22no—
335C23×C17—22no—
336C23×C17—22no—
337C23×C17—22no—
338C23×C17—41no—
339C23×C17—41no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17—41no—
345C23×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17—41no—
350C23×C17—41no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17—41no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17C23×C411yescharacteristic
367C23×C17C22×D411yescharacteristic
368C23×C17C22×D411yescharacteristic
369C23×C17C22×D411yescharacteristic
370C23×C17C22×D411yescharacteristic
371C23×C17C2×#4111yescharacteristic
372C23×C17C2×#4111yescharacteristic
373C23×C17C2×#4111yescharacteristic
374C23×C17C2×#4111yescharacteristic
375C23×C17C2×#4111yescharacteristic
376C23×C17C2×#4111yescharacteristic
377C23×C17H(5,𝔽2)11yescharacteristic
378C23×C17H(5,𝔽2)11yescharacteristic
379C23×C172−1+411yescharacteristic
380C23×C172−1+411yescharacteristic
381C22×D17—22no—
382C22×D17—22no—
383C22×D17—22no—
384C22×D17—22no—
385C22×D17—22no—
386C22×D17—22no—
387C22×D17—22no—
388C22×D17—22no—
389C22×D17—22no—
390C22×D17—22no—
391C22×D17—22no—
392C22×D17—22no—
393C22×D17—22no—
394C22×D17—22no—
395C22×D17—22no—
396C22×D17—22no—
397C22×D17—22no—
398C22×D17—22no—
399C22×D17—22no—
400C22×D17—22no—
401C22×D17—22no—
402C22×D17—22no—
403C22×D17—22no—
404C22×D17—22no—
405C22×D17—22no—
406C22×D17—22no—
407C22×D17—22no—
408C22×D17—22no—
409C22×D17C2×C22⋊C414yes—
410C22×D17C4×D414yes—
411C22×D17C4×D414yes—
412C22×D17#12114yes—
413C22×D17#12114yes—
414C22×D17#12414yes—
415C22×D17#12714yes—
416C2×C4×C17—22no—
417C2×C4×C17—22no—
418C2×C4×C17—22no—
419C2×C4×C17—22no—
420C2×C4×C17—22no—
421C2×C4×C17—22no—
422C2×C4×C17—22no—
423C2×C4×C17—22no—
424C2×C4×C17—22no—
425C2×C4×C17—22no—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—22no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×C4×C17—41no—
445C2×C4×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17—41no—
448C2×C4×C17—41no—
449C2×C4×C17—41no—
450C2×C4×C17—41no—
451C2×C4×C17—41no—
452C2×C4×C17—41no—
453C2×C4×C17—41no—
454C2×C4×C17—41no—
455C2×C4×C17—41no—
456C2×C4×C17—41no—
457C2×C4×C17C2×C22⋊C414yes—
458C22⋊D17—416no—
459C2×Dic17—22no—
460C2×Dic17—22no—
461C2×Dic17—22no—
462C2×Dic17—22no—
463C2×Dic17—22no—
464C2×Dic17—22no—
465C2×Dic17—22no—
466C2×Dic17—22no—
467C2×Dic17—22no—
468C2×Dic17—22no—
469C2×Dic17—22no—
470C2×Dic17—22no—
471C2×Dic17—22no—
472C2×Dic17—22no—
473C2×Dic17—22no—
474C2×Dic17—22no—
475C2×Dic17—22no—
476C2×Dic17—22no—
477C2×Dic17—22no—
478C2×Dic17—22no—
479C2×Dic17—22no—
480C2×Dic17—22no—
481C2×Dic17—22no—
482C2×Dic17—22no—
483C2×Dic17—41no—
484C2×Dic17—41no—
485C2×Dic17—41no—
486C2×Dic17—41no—
487C2×Dic17—41no—
488C2×Dic17—41no—
489C2×Dic17—41no—
490C2×Dic17—41no—
491C2×Dic17—41no—
492C2×Dic17—41no—
493C2×Dic17—41no—
494C2×Dic17—41no—
495C2×Dic17—41no—
496C2×Dic17—41no—
497C2×Dic17—41no—
498C2×Dic17—41no—
499C2×Dic17—41no—
500C2×Dic17—41no—
501C2×Dic17—41no—
502C2×Dic17—41no—
503C2×Dic17—41no—
504C2×Dic17—41no—
505C2×Dic17—41no—
506C2×Dic17C2×C22⋊C414yes—
507C2×Dic17#12314yescomplemented
508C4×D17—416no—
509C4×D17—416no—
510C4×D17—416no—
511C22×#123—171no—
512C2×#386—171no—
513C2×#386—171no—
514C2×#385—171no—
515C2×#381—171no—
516C2×C4×C22⋊C4—171no—
517C22×#95—171no—
518#1445—171no—
519#1445—171no—
520#1439—171no—
521#1439D1711yescharacteristic, complemented
522#1437—171no—
523#1437—171no—
524C4⋊#95—171no—
525C4⋊#95—171no—
526C22×C17—42no—
527C22×C17—42no—
528C22×C17—42no—
529C22×C17—42no—
530C22×C17—42no—
531C22×C17—42no—
532C22×C17—42no—
533C22×C17—81no—
534C22×C17—81no—
535C22×C17—81no—
536C22×C17—81no—
537C22×C17—81no—
538C22×C17—81no—
539C22×C17—81no—
540C22×C17—81no—
541C22×C17C22×C22⋊C411yescharacteristic
542C22×C17C2×C4×D411yescharacteristic
543C22×C17C2×C4×D411yescharacteristic
544C22×C17C4×#4111yescharacteristic
545C22×C17C4×#4111yescharacteristic
546C22×C17#52011yescharacteristic
547C22×C17#52011yescharacteristic
548C22×C17C2×#12111yescharacteristic
549C22×C17C2×#12111yescharacteristic
550C22×C17C2×#12311yescharacteristic
551C22×C17#52511yescharacteristic
552C22×C17C2×#12411yescharacteristic
553C22×C17#52911yescharacteristic
554C22×C17#52911yescharacteristic
555C22×C17C2×#12711yescharacteristic
556C22×C17#53411yescharacteristic
557C22×C17#53611yescharacteristic
558C22×C17#53911yescharacteristic
559C22×C17#53911yescharacteristic
560C22×C17#54611yescharacteristic
561C22×C17#54611yescharacteristic
562C22×C17#54611yescharacteristic
563C22×C17#54611yescharacteristic
564C22×C17#54611yescharacteristic
565C22×C17#54611yescharacteristic
566C22×C17#54711yescharacteristic
567C22×C17#54711yescharacteristic
568C22×C17#54711yescharacteristic
569C22×C17#54711yescharacteristic
570C22×C17#54711yescharacteristic
571C22×C17#54711yescharacteristic
572C22×C17#55111yescharacteristic
573C22×C17#55111yescharacteristic
574C22×C17#55211yescharacteristic
575C22×C17#55211yescharacteristic
576C2×D17—24no—
577C2×D17—24no—
578C2×D17—24no—
579C2×D17—24no—
580C2×D17—24no—
581C2×D17—24no—
582C2×D17—24no—
583C2×D17—24no—
584C2×D17—24no—
585C2×D17—24no—
586C2×D17—24no—
587C2×D17—24no—
588C2×D17—24no—
589C2×D17—24no—
590C2×D17#39018yes—
591C4×C17—24no—
592C4×C17—42no—
593C4×C17—42no—
594C4×C17—42no—
595C4×C17—42no—
596C4×C17—81no—
597Dic17—24no—
598Dic17—24no—
599Dic17—42no—
600Dic17—42no—
601Dic17—42no—
602Dic17—42no—
603Dic17—81no—
604C23×D4—171no—
605C24×C4—171no—
606C24×C4—171no—
607C24×C4—171no—
608C2×#123—178no—
609C2×#123—344no—
610C2×#123—344no—
611C22×C4⋊C4—171no—
612C22×C4⋊C4—171no—
613C22×C4⋊C4—171no—
614C22×C4⋊C4C2×D1711yescharacteristic
615C22×C22⋊C4—171no—
616C22×C22⋊C4—171no—
617C22×C22⋊C4—171no—
618C22×C22⋊C4—171no—
619C22×C22⋊C4—171no—
620C22×C22⋊C4—171no—
621C22×C22⋊C4C2×D1711yescharacteristic
622C22×C22⋊C4C2×D1711yescharacteristic
623C22×C22⋊C4C2×D1711yescharacteristic
624C22×C42—171no—
625C22×C42—171no—
626#386—344no—
627#386—344no—
628#385—344no—
629#381—344no—
630C4×C22⋊C4—344no—
631C2×#95—171no—
632C2×#95—171no—
633C2×#95—171no—
634C2×#95—171no—
635C2×#95—171no—
636C2×#95—171no—
637C2×#95—171no—
638C2×#95—171no—
639C2×#95—171no—
640C2×#95—171no—
641C2×#95—171no—
642C2×#95—171no—
643C2×#95—171no—
644C2×#95—344no—
645C2×#95C2×D1711yescharacteristic
646C2×#95C2×D1711yescharacteristic
647C2×#95C2×D1711yescharacteristic
648C2×C17—82no—
649C2×C17C2×#39011yescharacteristic
650C2×C17C4×#12311yescharacteristic
651C2×C17#232211yescharacteristic
652C2×C17#233911yescharacteristic
653C2×C17#233911yescharacteristic
654C2×C17#235911yescharacteristic
655C2×C17#235911yescharacteristic
656C2×C17#241211yescharacteristic
657C2×C17#241311yescharacteristic
658C2×C17#242511yescharacteristic
659C2×C17#242511yescharacteristic
660C2×C17#248811yescharacteristic
661C2×C17#248811yescharacteristic
662C2×C17#250111yescharacteristic
663C2×C17#253911yescharacteristic
664D17—28no—
665C25—171no—
666C25C22×D1711yescharacteristic
667C22×D4—174no—
668C22×D4—342no—
669C22×D4—342no—
670C22×D4—342no—
671C22×D4—342no—
672C22×D4—342no—
673C22×D4—342no—
674C23×C4—171no—
675C23×C4—171no—
676C23×C4—171no—
677C23×C4—171no—
678C23×C4—171no—
679C23×C4—171no—
680C23×C4—174no—
681C23×C4—174no—
682C23×C4—171no—
683C23×C4—342no—
684C23×C4—342no—
685C23×C4—342no—
686C23×C4—342no—
687C23×C4—342no—
688C23×C4—342no—
689C23×C4—342no—
690C23×C4—342no—
691C23×C4—342no—
692C23×C4—342no—
693C23×C4—342no—
694C23×C4—342no—
695C23×C4—342no—
696C23×C4—342no—
697C23×C4—342no—
698C23×C4—681no—
699C23×C4—681no—
700C23×C4—681no—
701C23×C4—681no—
702C23×C4C22×D1711yescharacteristic
703C23×C4C22×D1711yescharacteristic
704C23×C4C22×D1711yescharacteristic
705C23×C4C22×D1711yescharacteristic
706C23×C4C22×D1711yescharacteristic
707C23×C4C22×D1711yescharacteristic
708#123—3432no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—41no—
712C2×C4⋊C4—174no—
713C2×C4⋊C4—174no—
714C2×C4⋊C4—342no—
715C2×C4⋊C4—342no—
716C2×C4⋊C4—342no—
717C2×C4⋊C4—342no—
718C2×C4⋊C4—342no—
719C2×C4⋊C4—342no—
720C2×C4⋊C4—681no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—174no—
730C2×C22⋊C4—174no—
731C2×C22⋊C4—174no—
732C2×C22⋊C4—174no—
733C2×C22⋊C4—174no—
734C2×C22⋊C4—342no—
735C2×C22⋊C4—342no—
736C2×C22⋊C4—342no—
737C2×C22⋊C4—342no—
738C2×C22⋊C4—342no—
739C2×C22⋊C4—342no—
740C2×C22⋊C4—342no—
741C2×C22⋊C4—342no—
742C2×C22⋊C4—342no—
743C2×C22⋊C4—342no—
744C2×C22⋊C4—342no—
745C2×C22⋊C4—342no—
746C2×C22⋊C4—681no—
747C2×C22⋊C4C4×D1714yescomplemented
748C2×C42—342no—
749C2×C42—342no—
750C2×C42—342no—
751C2×C42—342no—
752C2×C42—681no—
753C2×C42—681no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—342no—
758#95—342no—
759#95—342no—
760#95—342no—
761#95—342no—
762#95—342no—
763#95—342no—
764#95—342no—
765#95—342no—
766#95—342no—
767#95—342no—
768#95—342no—
769#95—342no—
770C17#1399611yescharacteristic, complemented, Sylow
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—172no—
786C24—172no—
787C24—172no—
788C24—172no—
789C24—172no—
790C24—172no—
791C24—172no—
792C24—341no—
793C24—341no—
794C24—341no—
795C24—341no—
796C24—341no—
797C24—341no—
798C24—341no—
799C24—341no—
800C24C2×C4×D1712yes—
801C24C23×D1711yescharacteristic
802C2×D4—348no—
803C2×D4—348no—
804C2×D4—348no—
805C2×D4—684no—
806C2×D4—684no—
807C2×D4—684no—
808C2×D4—684no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—172no—
845C22×C4—172no—
846C22×C4—172no—
847C22×C4—172no—
848C22×C4—172no—
849C22×C4—172no—
850C22×C4—172no—
851C22×C4—172no—
852C22×C4—172no—
853C22×C4—172no—
854C22×C4—348no—
855C22×C4—348no—
856C22×C4—348no—
857C22×C4—348no—
858C22×C4—348no—
859C22×C4—348no—
860C22×C4—341no—
861C22×C4—341no—
862C22×C4—341no—
863C22×C4—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—341no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4—341no—
874C22×C4—341no—
875C22×C4—341no—
876C22×C4—341no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—341no—
883C22×C4—341no—
884C22×C4—341no—
885C22×C4—341no—
886C22×C4—341no—
887C22×C4—341no—
888C22×C4—341no—
889C22×C4—341no—
890C22×C4—341no—
891C22×C4—341no—
892C22×C4—341no—
893C22×C4—341no—
894C22×C4—341no—
895C22×C4—341no—
896C22×C4—341no—
897C22×C4—341no—
898C22×C4—341no—
899C22×C4—684no—
900C22×C4—684no—
901C22×C4—684no—
902C22×C4—684no—
903C22×C4—684no—
904C22×C4—684no—
905C22×C4—684no—
906C22×C4—684no—
907C22×C4—684no—
908C22×C4—684no—
909C22×C4—684no—
910C22×C4—684no—
911C22×C4—684no—
912C22×C4—684no—
913C22×C4—684no—
914C22×C4C2×C4×D1712yes—
915C22×C4C2×C4×D1712yes—
916C22×C4D4×D1712yes—
917C22×C4D4×D1712yes—
918C22×C4D4×D1712yes—
919C22×C4D4×D1712yes—
920C22×C4#6325412yes—
921C4⋊C4—44no—
922C4⋊C4—348no—
923C4⋊C4—348no—
924C4⋊C4—684no—
925C22⋊C4—28no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—1716no—
929C22⋊C4—348no—
930C22⋊C4—348no—
931C22⋊C4—684no—
932C22⋊C4—684no—
933C22⋊C4—684no—
934C42—684no—
935C42—684no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—174no—
972C23—174no—
973C23—174no—
974C23—174no—
975C23—174no—
976C23—174no—
977C23—174no—
978C23—342no—
979C23—342no—
980C23—342no—
981C23—342no—
982C23—342no—
983C23—342no—
984C23—342no—
985C23—342no—
986C23—342no—
987C23—342no—
988C23—342no—
989C23—342no—
990C23—342no—
991C23—342no—
992C23—342no—
993C23—342no—
994C23—342no—
995C23—342no—
996C23—342no—
997C23—342no—
998C23—342no—
999C23—342no—
1000C23—342no—
1001C23—342no—
1002C23—342no—
1003C23—342no—
1004C23—342no—
1005C23—342no—
1006C23C22×C4×D1711yescharacteristic
1007C23C2×D4×D1711yescharacteristic
1008C23C2×D4×D1711yescharacteristic
1009C23C2×D4×D1711yescharacteristic
1010C23C2×D4×D1711yescharacteristic
1011C23C2×#6325411yescharacteristic
1012C23#1058769111yescharacteristic
1013C23#1058769111yescharacteristic
1014C23#1058769411yescharacteristic
1015C23#41×D1711yescharacteristic
1016C23#41×D1711yescharacteristic
1017C23#41×D1711yescharacteristic
1018C23#41×D1711yescharacteristic
1019C23#41×D1711yescharacteristic
1020C23#1058769711yescharacteristic
1021D4—6816no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—174no—
1064C2×C4—174no—
1065C2×C4—342no—
1066C2×C4—342no—
1067C2×C4—342no—
1068C2×C4—342no—
1069C2×C4—342no—
1070C2×C4—342no—
1071C2×C4—342no—
1072C2×C4—342no—
1073C2×C4—342no—
1074C2×C4—342no—
1075C2×C4—342no—
1076C2×C4—342no—
1077C2×C4—342no—
1078C2×C4—342no—
1079C2×C4—342no—
1080C2×C4—342no—
1081C2×C4—342no—
1082C2×C4—342no—
1083C2×C4—342no—
1084C2×C4—342no—
1085C2×C4—342no—
1086C2×C4—342no—
1087C2×C4—342no—
1088C2×C4—342no—
1089C2×C4—6816no—
1090C2×C4—6816no—
1091C2×C4—6816no—
1092C2×C4—681no—
1093C2×C4—681no—
1094C2×C4—681no—
1095C2×C4—681no—
1096C2×C4—681no—
1097C2×C4—681no—
1098C2×C4—681no—
1099C2×C4—681no—
1100C2×C4—681no—
1101C2×C4—681no—
1102C2×C4—681no—
1103C2×C4—681no—
1104C2×C4—681no—
1105C2×C4—681no—
1106C2×C4—681no—
1107C2×C4—681no—
1108C2×C4—681no—
1109C2×C4—681no—
1110C2×C4—681no—
1111C2×C4—681no—
1112C2×C4—681no—
1113C2×C4—681no—
1114C2×C4—681no—
1115C2×C4C22⋊C4×D1714yes—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—178no—
1132C22—344no—
1133C22—344no—
1134C22—344no—
1135C22—344no—
1136C22—344no—
1137C22—344no—
1138C22—344no—
1139C22—344no—
1140C22—344no—
1141C22—344no—
1142C22—344no—
1143C22—344no—
1144C22—344no—
1145C22—344no—
1146C22C2×C22⋊C4×D1711yescharacteristic
1147C22C4×D4×D1711yescharacteristic
1148C22C4×D4×D1711yescharacteristic
1149C22C4×#6325411yescharacteristic
1150C22#1176327711yescharacteristic
1151C22#1176328811yescharacteristic
1152C22#1176329011yescharacteristic
1153C22#121×D1711yescharacteristic
1154C22#121×D1711yescharacteristic
1155C22#123×D1711yescharacteristic
1156C22#1176331911yescharacteristic
1157C22#124×D1711yescharacteristic
1158C22#1176333811yescharacteristic
1159C22#1176334211yescharacteristic
1160C22#127×D1711yescharacteristic
1161C22#1176336911yescharacteristic
1162C22#1176338211yescharacteristic
1163C22#1176340211yescharacteristic
1164C22#1176340511yescharacteristic
1165C22#1176344611yescharacteristic
1166C22#1176344611yescharacteristic
1167C22#1176344811yescharacteristic
1168C22#1176345611yescharacteristic
1169C22#1176345611yescharacteristic
1170C22#1176345611yescharacteristic
1171C22#1176345711yescharacteristic
1172C22#1176345711yescharacteristic
1173C22#1176345911yescharacteristic
1174C22#1176346111yescharacteristic
1175C22#1176346111yescharacteristic
1176C22#1176346111yescharacteristic
1177C22#1176348711yescharacteristic
1178C22#1176348911yescharacteristic
1179C22#1176349311yescharacteristic
1180C22#1176349511yescharacteristic
1181C4—24no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—81no—
1187C4—344no—
1188C4—344no—
1189C4—682no—
1190C4—682no—
1191C4—682no—
1192C4—682no—
1193C4—1361no—
1194C2—82no—
1195C2—348no—
1196C2D17×#39011yescharacteristic
1197C2#1453131111yescharacteristic
1198C2#1453145111yescharacteristic
1199C2#1453161011yescharacteristic
1200C2#1453161211yescharacteristic
1201C2#1453177311yescharacteristic
1202C2#1453177911yescharacteristic
1203C2#1453217511yescharacteristic
1204C2#1453218611yescharacteristic
1205C2#1453233011yescharacteristic
1206C2#1453233611yescharacteristic
1207C2#1453310311yescharacteristic
1208C2#1453311311yescharacteristic
1209C2#1453325011yescharacteristic
1210C2#1453370911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1439D17
hypocenterC17#13996
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. C2×#11762680C2semidirect
5. C2×#11762671C2semidirect
6. C2×#11762656C2semidirect
7. C2×#95×D17C2semidirect
8. #14527051C2semidirect
9. #14527050C2semidirect
10. #14527027C2semidirect
11. #14527021C2semidirect
12. #14527021C2semidirect
13. #14527013C2semidirect
14. #14527012C2semidirect
15. C17×#1439C2semidirect
22. C2×#10587569C4semidirect
114. C2×C22⋊C4×C17C2×C4semidirect
123. C2×C22⋊Dic17C2×C4semidirect
135. C2×C4⋊Dic17C2×C4semidirect
141. C2×#63225C2×C4semidirect
324. #63227C22⋊C4semidirect
507. C2×Dic17#123semidirect
521. #1439D17semidirect
747. C2×C22⋊C4C4×D17semidirect
770. C17#13996semidirect

Maximal subgroups

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

subgroupindex
C22×#105875692
C2×#117626852
C2×#117626802
C2×#117626712
C2×#117626562
C2×#95×D172
#145270512
#145270502
#145270272
#145270212
#145270132
#145270122
C17×#14392
#1399617