Finite Group Databasebeta

← #16959669

Subgroups — #16959669

Order 4352.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587567C211yesmaximal, characteristic
2C2×#11762724C211yesmaximal, characteristic
3C2×#11762700C211yesmaximal, characteristic, complemented
4C2×#11762681C211yesmaximal, characteristic, complemented
5C2×#11762680C211yesmaximal, characteristic, complemented
6C2×C4×#63225C211yesmaximal, characteristic, complemented
7#14527047C211yesmaximal, characteristic, complemented
8#14527035C211yesmaximal, characteristic, complemented
9#14527023C211yesmaximal, characteristic
10#14527021C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527008C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C2×#10587567—24no—
20C2×#10587567—24no—
21C2×#10587567—24no—
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762724C418yescomplemented
36#11762700—24no—
37#11762681—24no—
38#11762680—24no—
39C4×#63225—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
52C22×C4⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C42×C17C2211yescharacteristic
57C17×#388—24no—
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×Dic17—22no—
76C23×Dic17—22no—
77C23×Dic17—22no—
78C23×Dic17—22no—
79C23×Dic17—22no—
80C23×Dic17—41no—
81C23×Dic17—41no—
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—22no—
94C22×C4×D17—41no—
95C22×C4×D17—41no—
96C2×C4⋊C4×C17—22no—
97C2×C4⋊C4×C17—22no—
98C2×C4⋊C4×C17—41no—
99C2×C22⋊C4×C17—22no—
100C2×C22⋊C4×C17—22no—
101C2×C22⋊C4×C17—22no—
102C2×C22⋊C4×C17—22no—
103C2×C22⋊C4×C17—22no—
104C2×C22⋊C4×C17—22no—
105C2×C22⋊C4×C17—41no—
106C2×C22⋊C4×C17C2×C414yescomplemented
107C2×C22⋊C4×C17D414yes—
108C2×C42×C17—22no—
109C2×C42×C17—22no—
110C2×C42×C17—22no—
111C2×C22⋊Dic17—22no—
112C2×C22⋊Dic17—22no—
113C2×C22⋊Dic17—22no—
114C2×C22⋊Dic17—22no—
115C2×C22⋊Dic17—41no—
116C2×C22⋊Dic17C2×C414yescomplemented
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—22no—
122C2×#63227—22no—
123C2×#63227—22no—
124C2×#63227—22no—
125C2×#63227—22no—
126C2×#63227—22no—
127C2×#63227—41no—
128C2×#63227—41no—
129C2×#63227C2×C414yescomplemented
130C2×#63227C2×C414yescomplemented
131C2×#63227D414yes—
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—22no—
135C2×#63225—22no—
136C2×#63225—22no—
137C2×#63225—22no—
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225—22no—
141C2×#63225—41no—
142C2×#63225C2×C414yescomplemented
143C2×#63225D414yescomplemented
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147C2×C4×Dic17—22no—
148C2×C4×Dic17—22no—
149C2×C4×Dic17D414yes—
150#10587567—232no—
151C17×#95—22no—
152C17×#95—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#10587502—41no—
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×C17C22×C412yes—
178C24×C17C2×D412yes—
179C24×C17#4112yes—
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×D17—21no—
190C23×D17—21no—
191C23×D17—21no—
192C23×D17—21no—
193C23×D17C22×C412yes—
194C23×D17C2×D412yes—
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×C17C2×D412yes—
238C2×C22⋊D17—28no—
239C2×C22⋊D17—28no—
240C2×C22⋊D17—28no—
241C2×C22⋊D17—28no—
242C2×C22⋊D17—28no—
243C2×C22⋊D17—28no—
244C2×C22⋊D17—28no—
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—28no—
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—44no—
284C22×Dic17—44no—
285C22×Dic17—44no—
286C22×Dic17—44no—
287C22×Dic17—44no—
288C22×Dic17—44no—
289C22×Dic17C22×C412yes—
290C22×Dic17C22×C412yes—
291C22×Dic17C22×C412yes—
292C22×Dic17C2×D412yes—
293C22×Dic17C2×D412yes—
294C22×Dic17C2×D412yes—
295C22×Dic17C2×D412yes—
296C22×Dic17C2×D412yes—
297C22×Dic17#4112yes—
298C22×Dic17#4112yes—
299C22×Dic17#4112yes—
300C22×Dic17#4112yes—
301C2×C4×D17—28no—
302C2×C4×D17—44no—
303C2×C4×D17—44no—
304C2×C4×D17—44no—
305C2×C4×D17—44no—
306C2×C4×D17—44no—
307C2×C4×D17—44no—
308C4⋊C4×C17—44no—
309C22⋊C4×C17—28no—
310C22⋊C4×C17—28no—
311C22⋊C4×C17—44no—
312C42×C17—44no—
313C22⋊Dic17—28no—
314C22⋊Dic17—44no—
315#63227—28no—
316#63227—28no—
317#63227—28no—
318#63227—44no—
319#63227—44no—
320#63225—28no—
321#63225—28no—
322#63225—28no—
323#63225—44no—
324C4×Dic17—28no—
325C4×Dic17—28no—
326#14176—171nomaximal, Sylow
327C23×C17—22no—
328C23×C17—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—22no—
332C23×C17—22no—
333C23×C17—22no—
334C23×C17—22no—
335C23×C17—22no—
336C23×C17—22no—
337C23×C17—22no—
338C23×C17—22no—
339C23×C17—22no—
340C23×C17—22no—
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
344C23×C17—22no—
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×C17C4×D414yes—
362C23×C17C23×C411yescharacteristic
363C23×C17C22×D411yescharacteristic
364C23×C17C22×D411yescharacteristic
365C23×C17C22×D411yescharacteristic
366C23×C17C22×D411yescharacteristic
367C23×C17C2×#4111yescharacteristic
368C23×C17C2×#4111yescharacteristic
369C23×C17C2×#4111yescharacteristic
370C23×C17C2×#4111yescharacteristic
371C23×C17C2×#4111yescharacteristic
372C23×C17C2×#4111yescharacteristic
373C23×C17H(5,𝔽2)11yescharacteristic
374C23×C17H(5,𝔽2)11yescharacteristic
375C23×C172−1+411yescharacteristic
376C23×C172−1+411yescharacteristic
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—22no—
380C22×D17—22no—
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—41no—
396C22×D17—41no—
397C22×D17—41no—
398C22×D17—41no—
399C22×D17—41no—
400C22×D17—41no—
401C22×D17—41no—
402C22×D17—41no—
403C22×D17—41no—
404C22×D17—41no—
405C22×D17—41no—
406C22×D17—41no—
407C22×D17—41no—
408C22×D17—41no—
409C22×D17—41no—
410C22×D17—41no—
411C22×D17C4×D414yes—
412C2×C4×C17—22no—
413C2×C4×C17—22no—
414C2×C4×C17—22no—
415C2×C4×C17—22no—
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—41no—
431C2×C4×C17—41no—
432C2×C4×C17—41no—
433C2×C4×C17—41no—
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#12014yes—
454C22⋊D17—232no—
455C2×Dic17—22no—
456C2×Dic17—22no—
457C2×Dic17—22no—
458C2×Dic17—22no—
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—416no—
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×Dic17C4×D414yes—
503C2×Dic17C4×D414yescomplemented
504C2×Dic17#12114yes—
505C4×D17—416no—
506C22×C4×D4—171no—
507C2×#394—171no—
508C2×#388—171no—
509C2×#388D1711yescharacteristic, complemented
510C2×#385—171no—
511C2×#385—171no—
512C2×C4×C4⋊C4—171no—
513#1444—171no—
514#1441—171no—
515#1438—171no—
516#1437—171no—
517#1437—171no—
518#1434—171no—
519C22⋊#95—171no—
520C22⋊#95—171no—
521C22×C17—24no—
522C22×C17—24no—
523C22×C17—24no—
524C22×C17—42no—
525C22×C17—42no—
526C22×C17—42no—
527C22×C17—42no—
528C22×C17—42no—
529C22×C17—42no—
530C22×C17—42no—
531C22×C17—42no—
532C22×C17—42no—
533C22×C17—42no—
534C22×C17—42no—
535C22×C17—42no—
536C22×C17C2×C4×D411yescharacteristic
537C22×C17C2×C4×D411yescharacteristic
538C22×C17C2×C4×D411yescharacteristic
539C22×C17C2×C4×D411yescharacteristic
540C22×C17C4×#4111yescharacteristic
541C22×C17#52011yescharacteristic
542C22×C17#52011yescharacteristic
543C22×C17C2×#12011yescharacteristic
544C22×C17C2×#12111yescharacteristic
545C22×C17#52511yescharacteristic
546C22×C17#52511yescharacteristic
547C22×C17#52511yescharacteristic
548C22×C17#52511yescharacteristic
549C22×C17#52911yescharacteristic
550C22×C17#53211yescharacteristic
551C22×C17#53511yescharacteristic
552C22×C17#53611yescharacteristic
553C22×C17#54211yescharacteristic
554C22×C17#54211yescharacteristic
555C22×C17D4211yescharacteristic
556C22×C17D4211yescharacteristic
557C22×C17#54611yescharacteristic
558C22×C17#54611yescharacteristic
559C22×C17#54711yescharacteristic
560C22×C17#54711yescharacteristic
561C22×C17#54711yescharacteristic
562C22×C17#54711yescharacteristic
563C22×C17#54811yescharacteristic
564C22×C17#54811yescharacteristic
565C22×C17#55111yescharacteristic
566C22×C17#55111yescharacteristic
567C22×C17#55211yescharacteristic
568C22×C17#55211yescharacteristic
569C22×C17#55311yescharacteristic
570C22×C17#55311yescharacteristic
571C2×D17—24no—
572C2×D17—24no—
573C2×D17—24no—
574C2×D17—42no—
575C2×D17—42no—
576C2×D17—42no—
577C2×D17—42no—
578C2×D17—42no—
579C2×D17—42no—
580C2×D17—42no—
581C2×D17—42no—
582C2×D17—42no—
583C2×D17—42no—
584C2×D17—42no—
585C2×D17—42no—
586C4×C17—24no—
587C4×C17—42no—
588C4×C17—42no—
589C4×C17—42no—
590C4×C17—42no—
591C4×C17—81no—
592Dic17—24no—
593Dic17—24no—
594Dic17—24no—
595Dic17—42no—
596Dic17—42no—
597Dic17—42no—
598Dic17—81no—
599C23×D4—171no—
600C24×C4—171no—
601C24×C4—171no—
602C2×C4×D4—344no—
603C2×C4×D4—344no—
604C2×C4×D4—344no—
605C22×C4⋊C4—171no—
606C22×C4⋊C4—171no—
607C22×C4⋊C4—171no—
608C22×C4⋊C4—171no—
609C22×C4⋊C4C2×D1711yescharacteristic
610C22×C22⋊C4—171no—
611C22×C22⋊C4—171no—
612C22×C22⋊C4—171no—
613C22×C22⋊C4—171no—
614C22×C22⋊C4—171no—
615C22×C22⋊C4—171no—
616C22×C22⋊C4—171no—
617C22×C22⋊C4C2×D1711yescharacteristic
618C22×C22⋊C4C2×D1711yescharacteristic
619C22×C22⋊C4C2×D1711yescharacteristic
620C22×C42—171no—
621C22×C42—171no—
622C22×C42C2×D1711yescharacteristic
623#394—178no—
624#388—24no—
625#388—344no—
626#385—344no—
627#385—344no—
628C4×C4⋊C4—344no—
629C2×#95—171no—
630C2×#95—171no—
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×#95C2×D1711yescharacteristic
642C2×#95C2×D1711yescharacteristic
643C2×C17—44no—
644C2×C17C4×#12011yescharacteristic
645C2×C17C4×#12111yescharacteristic
646C2×C17#232611yescharacteristic
647C2×C17#235911yescharacteristic
648C2×C17#235911yescharacteristic
649C2×C17#236111yescharacteristic
650C2×C17#236111yescharacteristic
651C2×C17#240611yescharacteristic
652C2×C17#240811yescharacteristic
653C2×C17#246111yescharacteristic
654C2×C17#246111yescharacteristic
655C2×C17#246811yescharacteristic
656C2×C17#246811yescharacteristic
657C2×C17#253611yescharacteristic
658C2×C17#259811yescharacteristic
659D17—44no—
660C25—171no—
661C25C22×D1711yescharacteristic
662C22×D4—174no—
663C22×D4—342no—
664C22×D4—342no—
665C22×D4—342no—
666C22×D4—342no—
667C22×D4—342no—
668C22×D4—342no—
669C23×C4—171no—
670C23×C4—171no—
671C23×C4—171no—
672C23×C4—171no—
673C23×C4—171no—
674C23×C4—171no—
675C23×C4—171no—
676C23×C4—342no—
677C23×C4—342no—
678C23×C4—342no—
679C23×C4—342no—
680C23×C4—342no—
681C23×C4—342no—
682C23×C4—342no—
683C23×C4—342no—
684C23×C4—342no—
685C23×C4—342no—
686C23×C4—681no—
687C23×C4—681no—
688C23×C4—681no—
689C23×C4—681no—
690C23×C4C22×D1711yescharacteristic
691C23×C4C22×D1711yescharacteristic
692C23×C4C22×D1711yescharacteristic
693C23×C4C22×D1711yescharacteristic
694C23×C4C22×D1711yescharacteristic
695C23×C4C22×D1711yescharacteristic
696C4×D4—3432no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—41no—
700C2×C4⋊C4—174no—
701C2×C4⋊C4—174no—
702C2×C4⋊C4—342no—
703C2×C4⋊C4—342no—
704C2×C4⋊C4—342no—
705C2×C4⋊C4—342no—
706C2×C4⋊C4—342no—
707C2×C4⋊C4—342no—
708C2×C4⋊C4—342no—
709C2×C4⋊C4—342no—
710C2×C4⋊C4—342no—
711C2×C4⋊C4—681no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—174no—
720C2×C22⋊C4—174no—
721C2×C22⋊C4—174no—
722C2×C22⋊C4—174no—
723C2×C22⋊C4—342no—
724C2×C22⋊C4—342no—
725C2×C22⋊C4—342no—
726C2×C22⋊C4—342no—
727C2×C22⋊C4—342no—
728C2×C22⋊C4—342no—
729C2×C22⋊C4—342no—
730C2×C22⋊C4—342no—
731C2×C22⋊C4—342no—
732C2×C22⋊C4—342no—
733C2×C22⋊C4—342no—
734C2×C22⋊C4—342no—
735C2×C22⋊C4—342no—
736C2×C22⋊C4—342no—
737C2×C22⋊C4—681no—
738C2×C22⋊C4—681no—
739C2×C22⋊C4—681no—
740C2×C22⋊C4C4×D1714yescomplemented
741C2×C22⋊C4C22⋊D1714yes—
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—22no—
745C2×C42—174no—
746C2×C42—342no—
747C2×C42—342no—
748C2×C42—342no—
749C2×C42—342no—
750C2×C42—342no—
751#95—22no—
752#95—22no—
753#95—174no—
754#95—342no—
755#95—342no—
756#95—342no—
757#95—342no—
758#95—342no—
759#95—342no—
760#95—342no—
761#95—342no—
762#95—342no—
763#95—681no—
764#95—681no—
765C17#1417611yescharacteristic, complemented, Sylow
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—172no—
779C24—172no—
780C24—172no—
781C24—341no—
782C24—341no—
783C24—341no—
784C24—341no—
785C24—341no—
786C24—341no—
787C24—341no—
788C24—341no—
789C24—341no—
790C24—341no—
791C24—341no—
792C24—341no—
793C24C2×C4×D1712yes—
794C24#6325212yes—
795C24C2×C22⋊D1712yes—
796C24C23×D1711yescharacteristic
797C2×D4—348no—
798C2×D4—348no—
799C2×D4—348no—
800C2×D4—348no—
801C2×D4—348no—
802C2×D4—348no—
803C2×D4—348no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
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—172no—
840C22×C4—172no—
841C22×C4—172no—
842C22×C4—172no—
843C22×C4—172no—
844C22×C4—172no—
845C22×C4—172no—
846C22×C4—172no—
847C22×C4—172no—
848C22×C4—172no—
849C22×C4—172no—
850C22×C4—172no—
851C22×C4—348no—
852C22×C4—341no—
853C22×C4—341no—
854C22×C4—341no—
855C22×C4—341no—
856C22×C4—341no—
857C22×C4—341no—
858C22×C4—341no—
859C22×C4—341no—
860C22×C4—341no—
861C22×C4—341no—
862C22×C4—341no—
863C22×C4—341no—
864C22×C4—348no—
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—684no—
891C22×C4—684no—
892C22×C4—684no—
893C22×C4—684no—
894C22×C4—684no—
895C22×C4—684no—
896C22×C4—684no—
897C22×C4—684no—
898C22×C4—684no—
899C22×C4—684no—
900C22×C4—684no—
901C22×C4—684no—
902C22×C4C2×C4×D1712yes—
903C22×C4C2×C4×D1712yes—
904C22×C4D4×D1712yes—
905C22×C4D4×D1712yes—
906C22×C4D4×D1712yes—
907C22×C4C2×C22⋊D1712yes—
908C22×C4C2×C22⋊D1712yes—
909C4⋊C4—44no—
910C4⋊C4—348no—
911C4⋊C4—348no—
912C4⋊C4—348no—
913C4⋊C4—684no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—44no—
917C22⋊C4—348no—
918C22⋊C4—348no—
919C22⋊C4—348no—
920C22⋊C4—348no—
921C22⋊C4—684no—
922C22⋊C4—684no—
923C22⋊C4—684no—
924C42—44no—
925C42—348no—
926C42—348no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
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—174no—
962C23—342no—
963C23—342no—
964C23—342no—
965C23—342no—
966C23—342no—
967C23—342no—
968C23—342no—
969C23—342no—
970C23—342no—
971C23—342no—
972C23—342no—
973C23—342no—
974C23—342no—
975C23—342no—
976C23—342no—
977C23—342no—
978C23—342no—
979C23—342no—
980C23—681no—
981C23—681no—
982C23—681no—
983C23—681no—
984C23—681no—
985C23—681no—
986C23—681no—
987C23—681no—
988C23—681no—
989C23—681no—
990C23—681no—
991C23—681no—
992C23—681no—
993C23—681no—
994C23—681no—
995C23—681no—
996C23C4×C22⋊D1714yes—
997C23C22×C4×D1711yescharacteristic
998C23C2×#6325211yescharacteristic
999C23C2×D4×D1711yescharacteristic
1000C23C2×D4×D1711yescharacteristic
1001C23C2×D4×D1711yescharacteristic
1002C23#1058769111yescharacteristic
1003C23#41×D1711yescharacteristic
1004C23#41×D1711yescharacteristic
1005C23#41×D1711yescharacteristic
1006C23#41×D1711yescharacteristic
1007C23#41×D1711yescharacteristic
1008C23#1058769611yescharacteristic
1009C23#1058769711yescharacteristic
1010C23#1058769711yescharacteristic
1011C23C22×C22⋊D1711yescharacteristic
1012D4—3432no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
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—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
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—174no—
1055C2×C4—174no—
1056C2×C4—174no—
1057C2×C4—342no—
1058C2×C4—342no—
1059C2×C4—342no—
1060C2×C4—342no—
1061C2×C4—342no—
1062C2×C4—342no—
1063C2×C4—342no—
1064C2×C4—342no—
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—6816no—
1085C2×C4—6816no—
1086C2×C4—681no—
1087C2×C4—681no—
1088C2×C4—681no—
1089C2×C4—681no—
1090C2×C4—681no—
1091C2×C4—681no—
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#1058762314yes—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—344no—
1122C22—344no—
1123C22—344no—
1124C22—682no—
1125C22—682no—
1126C22—682no—
1127C22—682no—
1128C22—682no—
1129C22—682no—
1130C22—682no—
1131C22—682no—
1132C22—682no—
1133C22—682no—
1134C22—682no—
1135C22—682no—
1136C22C4×D4×D1711yescharacteristic
1137C22C4×D4×D1711yescharacteristic
1138C22C4×D4×D1711yescharacteristic
1139C22C2×C4×C22⋊D1711yescharacteristic
1140C22#1176327711yescharacteristic
1141C22#1176328811yescharacteristic
1142C22#1176328911yescharacteristic
1143C22C2×#1058762311yescharacteristic
1144C22#121×D1711yescharacteristic
1145C22#1176331611yescharacteristic
1146C22#1176331711yescharacteristic
1147C22#1176331811yescharacteristic
1148C22#1176331811yescharacteristic
1149C22#1176334211yescharacteristic
1150C22#1176335811yescharacteristic
1151C22#1176337511yescharacteristic
1152C22#1176338111yescharacteristic
1153C22#1176342311yescharacteristic
1154C22#1176342511yescharacteristic
1155C22D4×C22⋊D1711yescharacteristic
1156C22#1176344311yescharacteristic
1157C22#1176344711yescharacteristic
1158C22#1176345611yescharacteristic
1159C22#1176345711yescharacteristic
1160C22#1176345711yescharacteristic
1161C22#1176345811yescharacteristic
1162C22#1176345811yescharacteristic
1163C22#1176346711yescharacteristic
1164C22#1176346811yescharacteristic
1165C22#1176348311yescharacteristic
1166C22#1176348911yescharacteristic
1167C22#1176349211yescharacteristic
1168C22#1176349511yescharacteristic
1169C22#1176350811yescharacteristic
1170C22#1176351011yescharacteristic
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—81no—
1177C4—344no—
1178C4—344no—
1179C4—344no—
1180C4—682no—
1181C4—682no—
1182C4—682no—
1183C4—1361no—
1184C2—44no—
1185C2—684no—
1186C2C4×#1058762311yescharacteristic
1187C2#1453129611yescharacteristic
1188C2#1453149311yescharacteristic
1189C2#1453177311yescharacteristic
1190C2#1453177611yescharacteristic
1191C2#1453179711yescharacteristic
1192C2#1453180111yescharacteristic
1193C2#1453211611yescharacteristic
1194C2#1453213611yescharacteristic
1195C2#1453274711yescharacteristic
1196C2#1453275511yescharacteristic
1197C2#1453284611yescharacteristic
1198C2#1453285411yescharacteristic
1199C2#1453369211yescharacteristic
1200C2#1453434811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#388D17
hypocenterC17#14176
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×#11762700C2semidirect
4. C2×#11762681C2semidirect
5. C2×#11762680C2semidirect
6. C2×C4×#63225C2semidirect
7. #14527047C2semidirect
8. #14527035C2semidirect
10. #14527021C2semidirect
11. #14527020C2semidirect
12. #14527008C2semidirect
13. #14527006C2semidirect
14. #14527005C2semidirect
15. C2×C17×#388C2semidirect
35. #11762724C4semidirect
106. C2×C22⋊C4×C17C2×C4semidirect
116. C2×C22⋊Dic17C2×C4semidirect
129. C2×#63227C2×C4semidirect
130. C2×#63227C2×C4semidirect
142. C2×#63225C2×C4semidirect
143. C2×#63225D4semidirect
164. #10587502C2×C4semidirect
503. C2×Dic17C4×D4semidirect
509. C2×#388D17semidirect
740. C2×C22⋊C4C4×D17semidirect
765. C17#14176semidirect

Maximal subgroups

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

subgroupindex
C22×#105875672
C2×#117627242
C2×#117627002
C2×#117626812
C2×#117626802
C2×C4×#632252
#145270472
#145270352
#145270232
#145270212
#145270202
#145270082
#145270062
#145270052
C2×C17×#3882
#1417617