Finite Group Databasebeta

← #16957727

Subgroups — #16957727

Order 4352.

2538 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×C4⋊C4×D17C211yesmaximal, characteristic, complemented
2C2×#11762702C211yesmaximal, characteristic, complemented
3C2×#11762697C211yesmaximal, characteristic, complemented
4C2×#11762685C211yesmaximal, characteristic
5C2×#11762685C211yesmaximal, characteristic
6C2×#11762685C211yesmaximal, characteristic
7C2×#11762656C211yesmaximal, characteristic, complemented
8#14527043C211yesmaximal, characteristic, complemented
9#14527039C211yesmaximal, characteristic, complemented
10#14527027C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C2×C4⋊C4×D17—24no—
24C2×C4⋊C4×D17—24no—
25C2×C4⋊C4×D17—24no—
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34#11762702—24no—
35#11762697—24no—
36#11762685—24no—
37#11762685—24no—
38#11762685C418yescomplemented
39#11762656—24no—
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
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—22no—
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×#63227—22no—
130C2×#63227—22no—
131C2×#63227C2×C414yes—
132C2×#63227D414yes—
133C2×C4⋊Dic17—22no—
134C2×C4⋊Dic17—22no—
135C2×C4⋊Dic17D414yescomplemented
136C2×#63225—22no—
137C2×#63225—22no—
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225—22no—
141C2×#63225D414yescomplemented
142C2×C4×Dic17—22no—
143C2×C4×Dic17—22no—
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—41no—
147C2×C4×Dic17—41no—
148C4⋊C4×D17—232no—
149C17×#95—22no—
150C17×#95—22no—
151C17×#95—41no—
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—41no—
163#10587502C2×C414yescomplemented
164#10587502C2×C414yescomplemented
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×D17#4112yes—
193C23×D17#4112yes—
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×Dic17C2×D412yes—
292C22×Dic17C2×D412yes—
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—28no—
301C2×C4×D17—28no—
302C2×C4×D17—28no—
303C2×C4×D17—28no—
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—28no—
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—28no—
324#63227—44no—
325C4⋊Dic17—28no—
326#63225—28no—
327#63225—28no—
328C4×Dic17—44no—
329C4×Dic17—44no—
330#14019—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×D17#11714yes—
410C22×D17C4×D414yes—
411C22×D17C4×D414yes—
412C22×D17#12114yes—
413C22×D17#12314yes—
414C22×D17#12414yes—
415C22×D17#12614yes—
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×C17C4×D414yes—
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×Dic17C4×D414yes—
507C2×Dic17#12014yes—
508C4×D17—232no—
509C4×D17—416no—
510C4×D17—416no—
511C23×C4⋊C4—171no—
512C2×#388—171no—
513C2×#388—171no—
514C2×#386—171no—
515C2×#386—171no—
516C2×#386—171no—
517C2×C4×C22⋊C4—171no—
518#1442—171no—
519#1442—171no—
520#1439—171no—
521#1439D1711yescharacteristic, complemented
522#1436—171no—
523#1436—171no—
524C22⋊#95—171no—
525C22⋊#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×C17C2×#11711yescharacteristic
542C22×C17C2×C4×D411yescharacteristic
543C22×C17C2×C4×D411yescharacteristic
544C22×C17C2×C4×D411yescharacteristic
545C22×C17C2×C4×D411yescharacteristic
546C22×C17#52011yescharacteristic
547C22×C17#52011yescharacteristic
548C22×C17C2×#12011yescharacteristic
549C22×C17C2×#12111yescharacteristic
550C22×C17C2×#12311yescharacteristic
551C22×C17#52511yescharacteristic
552C22×C17#52511yescharacteristic
553C22×C17#52511yescharacteristic
554C22×C17C2×#12411yescharacteristic
555C22×C17C2×#12611yescharacteristic
556C22×C17#53411yescharacteristic
557C22×C17#53611yescharacteristic
558C22×C17#53911yescharacteristic
559C22×C17#53911yescharacteristic
560C22×C17D4211yescharacteristic
561C22×C17D4211yescharacteristic
562C22×C17#54611yescharacteristic
563C22×C17#54611yescharacteristic
564C22×C17#54711yescharacteristic
565C22×C17#54711yescharacteristic
566C22×C17#54811yescharacteristic
567C22×C17#54811yescharacteristic
568C22×C17#54811yescharacteristic
569C22×C17#54811yescharacteristic
570C22×C17#55211yescharacteristic
571C22×C17#55211yescharacteristic
572C22×C17#55311yescharacteristic
573C22×C17#55311yescharacteristic
574C22×C17#55311yescharacteristic
575C22×C17#55311yescharacteristic
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#38818yescomplemented
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—
608C22×C4⋊C4—171no—
609C22×C4⋊C4—171no—
610C22×C4⋊C4—171no—
611C22×C4⋊C4—344no—
612C22×C4⋊C4—344no—
613C22×C4⋊C4—344no—
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#388—344no—
627#388—344no—
628#386—178no—
629#386—344no—
630#386—344no—
631C4×C22⋊C4—344no—
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—171no—
645C2×#95C2×D1711yescharacteristic
646C2×#95C2×D1711yescharacteristic
647C2×#95C2×D1711yescharacteristic
648C2×C17—82no—
649C2×C17C2×#38811yescharacteristic
650C2×C17C4×#12011yescharacteristic
651C2×C17#232211yescharacteristic
652C2×C17#235211yescharacteristic
653C2×C17#235211yescharacteristic
654C2×C17#236111yescharacteristic
655C2×C17#236111yescharacteristic
656C2×C17#241011yescharacteristic
657C2×C17#241311yescharacteristic
658C2×C17#243611yescharacteristic
659C2×C17#244311yescharacteristic
660C2×C17#244311yescharacteristic
661C2×C17#248111yescharacteristic
662C2×C17#248111yescharacteristic
663C2×C17#259111yescharacteristic
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
708C2×C4⋊C4—22no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—174no—
712C2×C4⋊C4—174no—
713C2×C4⋊C4—3432no—
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—342no—
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—342no—
733C2×C22⋊C4—342no—
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—41no—
757#95—174no—
758#95—174no—
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—681no—
770C17#1401911yescharacteristic, 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—348no—
861C22×C4—348no—
862C22×C4—348no—
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—348no—
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—341no—
900C22×C4—341no—
901C22×C4—341no—
902C22×C4—341no—
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—28no—
922C4⋊C4—348no—
923C4⋊C4—348no—
924C4⋊C4—348no—
925C22⋊C4—28no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—348no—
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—3432no—
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—342no—
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×C4#1058756714yes—
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—
1146C22#117×D1711yescharacteristic
1147C22C4×D4×D1711yescharacteristic
1148C22C4×D4×D1711yescharacteristic
1149C22C4×D4×D1711yescharacteristic
1150C22C2×#1058756711yescharacteristic
1151C22#1176328811yescharacteristic
1152C22#1176329011yescharacteristic
1153C22#120×D1711yescharacteristic
1154C22#121×D1711yescharacteristic
1155C22#123×D1711yescharacteristic
1156C22#1176331711yescharacteristic
1157C22#1176331911yescharacteristic
1158C22#1176331911yescharacteristic
1159C22#124×D1711yescharacteristic
1160C22#126×D1711yescharacteristic
1161C22#1176336911yescharacteristic
1162C22#1176338211yescharacteristic
1163C22#1176340211yescharacteristic
1164C22#1176340511yescharacteristic
1165C22#1176344111yescharacteristic
1166C22#1176344411yescharacteristic
1167C22#1176344811yescharacteristic
1168C22#1176345611yescharacteristic
1169C22#1176345911yescharacteristic
1170C22#1176346111yescharacteristic
1171C22#1176346711yescharacteristic
1172C22#1176346711yescharacteristic
1173C22#1176346911yescharacteristic
1174C22#1176346911yescharacteristic
1175C22#1176349311yescharacteristic
1176C22#1176349511yescharacteristic
1177C22#1176350411yescharacteristic
1178C22#1176350411yescharacteristic
1179C22#1176350611yescharacteristic
1180C22#1176350611yescharacteristic
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×#38811yescharacteristic
1197C2#1453128911yescharacteristic
1198C2#1453145111yescharacteristic
1199C2#1453170611yescharacteristic
1200C2#1453171211yescharacteristic
1201C2#1453180311yescharacteristic
1202C2#1453180511yescharacteristic
1203C2#1453215111yescharacteristic
1204C2#1453218611yescharacteristic
1205C2#1453243711yescharacteristic
1206C2#1453251211yescharacteristic
1207C2#1453252211yescharacteristic
1208C2#1453304011yescharacteristic
1209C2#1453304611yescharacteristic
1210C2#1453425811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1439D17
hypocenterC17#14019
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊C4×D17C2semidirect
2. C2×#11762702C2semidirect
3. C2×#11762697C2semidirect
7. C2×#11762656C2semidirect
8. #14527043C2semidirect
9. #14527039C2semidirect
10. #14527027C2semidirect
11. #14527018C2semidirect
12. #14527015C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1439C2semidirect
38. #11762685C4semidirect
114. C2×C22⋊C4×C17C2×C4semidirect
123. C2×C22⋊Dic17C2×C4semidirect
135. C2×C4⋊Dic17D4semidirect
141. C2×#63225D4semidirect
163. #10587502C2×C4semidirect
164. #10587502C2×C4semidirect
521. #1439D17semidirect
590. C2×D17#388semidirect
747. C2×C22⋊C4C4×D17semidirect
770. C17#14019semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D172
C2×#117627022
C2×#117626972
C2×#117626852
C2×#117626562
#145270432
#145270392
#145270272
#145270182
#145270152
#145270052
C17×#14392
#1401917