Finite Group Databasebeta

← #16958021

Subgroups — #16958021

Order 4352.

2366 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D17C211yesmaximal, characteristic
2C2×#11762706C211yesmaximal, characteristic, complemented
3C2×#11762705C211yesmaximal, characteristic, complemented
4C2×#11762683C211yesmaximal, characteristic
5C2×#11762680C211yesmaximal, characteristic
6C2×#11762680C211yesmaximal, characteristic
7C2×#11762656C211yesmaximal, characteristic
8#14527047C211yesmaximal, characteristic, complemented
9#14527036C211yesmaximal, characteristic, complemented
10#14527034C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic
14#14527005C211yesmaximal, characteristic
15C17×#1444C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C2×C4⋊C4×D17—24no—
27C2×C4⋊C4×D17—24no—
28C2×C4⋊C4×D17—24no—
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762706—24no—
36#11762705—24no—
37#11762683C418yescomplemented
38#11762680—24no—
39#11762680—24no—
40#11762656—24no—
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×C4⋊C4×C17C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C24×D17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C22×C4×D17—22no—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
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—41no—
91C22×C4×D17—41no—
92C22×C4×D17—41no—
93C22×C4×D17—41no—
94C22×C4×D17C2×C414yes—
95C22×C4×D17D414yes—
96C2×C4⋊C4×C17—22no—
97C2×C4⋊C4×C17—22no—
98C2×C4⋊C4×C17—22no—
99C2×C4⋊C4×C17—22no—
100C2×C4⋊C4×C17—22no—
101C2×C4⋊C4×C17—22no—
102C2×C4⋊C4×C17—41no—
103C2×C4⋊C4×C17—41no—
104C2×C4⋊C4×C17—41no—
105C2×#63227—22no—
106C2×#63227—22no—
107C2×#63227—22no—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227C2×C414yes—
113C2×#63227C2×C414yes—
114C2×#63227D414yes—
115C2×#63227Q814yes—
116C2×#63227Q814yes—
117C2×C4⋊Dic17—22no—
118C2×C4⋊Dic17—22no—
119C2×C4⋊Dic17—22no—
120C2×C4⋊Dic17—22no—
121C2×C4⋊Dic17C2×C414yescomplemented
122C2×C4⋊Dic17D414yes—
123C2×#63225—22no—
124C2×#63225—22no—
125C2×#63225—22no—
126C2×#63225—22no—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—22no—
135C2×#63225—41no—
136C2×#63225C2×C414yescomplemented
137C2×#63225D414yes—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—41no—
143C2×C4×Dic17—41no—
144C4⋊C4×D17—232no—
145C17×#95—22no—
146C17×#95—22no—
147C17×#95—41no—
148C17×#95C2×C414yescomplemented
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—22no—
156#10587502—22no—
157#10587502—22no—
158#10587502—22no—
159#10587502—41no—
160#10587502C2×C414yescomplemented
161C24×C17C2411yescharacteristic
162C23×D17—21no—
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17C22×C412yes—
171C23×D17C2×D412yes—
172C23×D17C2×D412yes—
173C23×D17C2×Q812yes—
174C23×D17C2×Q812yes—
175C23×D17#4112yes—
176C23×D17#4112yes—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
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×C17C22×C412yes—
217C22×C4×C17C22×C412yes—
218C22×C4×C17C22×C412yes—
219C22×C4×C17C2×D412yes—
220C22×C4×C17C2×D412yes—
221C22×C4×C17C2×D412yes—
222C22×C4×C17C2×D412yes—
223C22×C4×C17C2×Q812yes—
224C22×C4×C17C2×Q812yes—
225C22×C4×C17#4112yes—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
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×Dic17C22×C412yes—
264C22×Dic17C22×C412yes—
265C22×Dic17C22×C412yes—
266C22×Dic17C2×D412yes—
267C22×Dic17C2×D412yes—
268C22×Dic17C2×D412yes—
269C22×Dic17C2×D412yes—
270C22×Dic17C2×D412yes—
271C22×Dic17C2×D412yes—
272C22×Dic17C2×Q812yes—
273C22×Dic17C2×Q812yes—
274C22×Dic17#4112yes—
275C2×C4×D17—28no—
276C2×C4×D17—28no—
277C2×C4×D17—28no—
278C2×C4×D17—28no—
279C2×C4×D17—28no—
280C2×C4×D17—28no—
281C2×C4×D17—28no—
282C2×C4×D17—28no—
283C2×C4×D17—28no—
284C2×C4×D17—28no—
285C2×C4×D17—44no—
286C2×C4×D17—44no—
287C2×C4×D17—44no—
288C2×C4×D17—44no—
289C2×C4×D17—44no—
290C2×C4×D17—44no—
291C2×C4×D17—44no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C2×C4×D17—44no—
295C2×C4×D17—44no—
296C4⋊C4×C17—28no—
297C4⋊C4×C17—44no—
298C4⋊C4×C17—44no—
299#63227—28no—
300#63227—28no—
301#63227—44no—
302#63227C4⋊C4116yescomplemented
303C4⋊Dic17—28no—
304C4⋊Dic17—28no—
305#63225—28no—
306#63225—28no—
307#63225—28no—
308#63225—44no—
309#63225—44no—
310C4×Dic17—44no—
311C4×Dic17—44no—
312#14043—171nomaximal, Sylow
313C23×C17C23×C411yescharacteristic
314C23×C17C22×D411yescharacteristic
315C23×C17C22×D411yescharacteristic
316C23×C17C22×D411yescharacteristic
317C23×C17C22×D411yescharacteristic
318C23×C17C22×Q811yescharacteristic
319C23×C17C22×Q811yescharacteristic
320C23×C17C2×#4111yescharacteristic
321C23×C17C2×#4111yescharacteristic
322C23×C17C2×#4111yescharacteristic
323C23×C17C2×#4111yescharacteristic
324C23×C17H(5,𝔽2)11yescharacteristic
325C23×C17H(5,𝔽2)11yescharacteristic
326C23×C172−1+411yescharacteristic
327C23×C172−1+411yescharacteristic
328C22×D17—22no—
329C22×D17—22no—
330C22×D17—22no—
331C22×D17—22no—
332C22×D17—22no—
333C22×D17—22no—
334C22×D17—22no—
335C22×D17—22no—
336C22×D17—22no—
337C22×D17—22no—
338C22×D17—22no—
339C22×D17—22no—
340C22×D17—22no—
341C22×D17—22no—
342C22×D17—22no—
343C22×D17—22no—
344C22×D17—22no—
345C22×D17—22no—
346C22×D17—22no—
347C22×D17—22no—
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—22no—
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—22no—
355C22×D17—22no—
356C22×D17C2×C4⋊C414yes—
357C22×D17C4×D414yes—
358C22×D17C4×Q814yes—
359C22×D17#12114yes—
360C22×D17C22⋊Q814yes—
361C22×D17#12514yes—
362C22×D17C4⋊Q814yes—
363C2×C4×C17—22no—
364C2×C4×C17—22no—
365C2×C4×C17—22no—
366C2×C4×C17—22no—
367C2×C4×C17—22no—
368C2×C4×C17—22no—
369C2×C4×C17—22no—
370C2×C4×C17—22no—
371C2×C4×C17—22no—
372C2×C4×C17—22no—
373C2×C4×C17—22no—
374C2×C4×C17—22no—
375C2×C4×C17—22no—
376C2×C4×C17—22no—
377C2×C4×C17—22no—
378C2×C4×C17—22no—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—22no—
382C2×C4×C17—22no—
383C2×C4×C17—22no—
384C2×C4×C17—22no—
385C2×C4×C17—22no—
386C2×C4×C17—22no—
387C2×C4×C17—41no—
388C2×C4×C17—41no—
389C2×C4×C17—41no—
390C2×C4×C17—41no—
391C2×C4×C17—41no—
392C2×C4×C17—41no—
393C2×C4×C17—41no—
394C2×C4×C17—41no—
395C2×C4×C17—41no—
396C2×C4×C17—41no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
402C2×C4×C17—41no—
403C2×C4×C17—41no—
404C2×C4×C17—41no—
405C2×C4×C17—41no—
406C2×C4×C17—41no—
407C2×C4×C17—41no—
408C2×C4×C17—41no—
409C2×C4×C17—41no—
410C2×C4×C17C2×C4⋊C414yescomplemented
411C2×C4×C17C4×D414yes—
412C2×Dic17—22no—
413C2×Dic17—22no—
414C2×Dic17—22no—
415C2×Dic17—22no—
416C2×Dic17—22no—
417C2×Dic17—22no—
418C2×Dic17—22no—
419C2×Dic17—22no—
420C2×Dic17—22no—
421C2×Dic17—22no—
422C2×Dic17—22no—
423C2×Dic17—22no—
424C2×Dic17—22no—
425C2×Dic17—22no—
426C2×Dic17—22no—
427C2×Dic17—22no—
428C2×Dic17—22no—
429C2×Dic17—22no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
437C2×Dic17—22no—
438C2×Dic17—22no—
439C2×Dic17—41no—
440C2×Dic17—41no—
441C2×Dic17—41no—
442C2×Dic17—41no—
443C2×Dic17—41no—
444C2×Dic17—41no—
445C2×Dic17—41no—
446C2×Dic17—41no—
447C2×Dic17—41no—
448C2×Dic17—41no—
449C2×Dic17—41no—
450C2×Dic17—41no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17C2×C4⋊C414yescomplemented
459C2×Dic17C4×D414yes—
460C2×Dic17#12014yes—
461C4×D17—232no—
462C4×D17—416no—
463C4×D17—416no—
464C23×C4⋊C4—171no—
465C2×#389—171no—
466C2×#389—171no—
467C2×#385—171no—
468C2×#385—171no—
469C2×#385—171no—
470C2×C4×C22⋊C4—171no—
471#1444—171no—
472#1444D1711yescharacteristic, complemented
473#1441—171no—
474#1441—171no—
475#1436—171no—
476#1436—171no—
477C22⋊#95—171no—
478C22⋊#95—171no—
479C22×C17C22×C4⋊C411yescharacteristic
480C22×C17C2×C4×D411yescharacteristic
481C22×C17C2×C4×D411yescharacteristic
482C22×C17C2×C4×D411yescharacteristic
483C22×C17C2×C4×Q811yescharacteristic
484C22×C17#52011yescharacteristic
485C22×C17#52011yescharacteristic
486C22×C17C2×#12011yescharacteristic
487C22×C17C2×#12111yescharacteristic
488C22×C17C2×C22⋊Q811yescharacteristic
489C22×C17#52511yescharacteristic
490C22×C17#52511yescharacteristic
491C22×C17#52511yescharacteristic
492C22×C17C2×#12511yescharacteristic
493C22×C17C2×C4⋊Q811yescharacteristic
494C22×C17#53411yescharacteristic
495C22×C17#53611yescharacteristic
496C22×C17#53911yescharacteristic
497C22×C17#53911yescharacteristic
498C22×C17D4211yescharacteristic
499C22×C17D4211yescharacteristic
500C22×C17#54611yescharacteristic
501C22×C17#54611yescharacteristic
502C22×C17#54711yescharacteristic
503C22×C17#54711yescharacteristic
504C22×C17D4×Q811yescharacteristic
505C22×C17D4×Q811yescharacteristic
506C22×C17D4×Q811yescharacteristic
507C22×C17D4×Q811yescharacteristic
508C22×C17#55211yescharacteristic
509C22×C17#55211yescharacteristic
510C22×C17#55411yescharacteristic
511C22×C17#55411yescharacteristic
512C22×C17#55411yescharacteristic
513C22×C17#55411yescharacteristic
514C2×D17—24no—
515C2×D17—24no—
516C2×D17—24no—
517C2×D17—24no—
518C2×D17—24no—
519C2×D17—24no—
520C2×D17—24no—
521C2×D17—24no—
522C2×D17—24no—
523C2×D17—24no—
524C2×D17—24no—
525C2×D17—24no—
526C2×D17—24no—
527C2×D17—24no—
528C2×D17#38918yescomplemented
529C4×C17—24no—
530C4×C17—24no—
531C4×C17—42no—
532C4×C17—42no—
533C4×C17—42no—
534C4×C17—42no—
535C4×C17—81no—
536Dic17—24no—
537Dic17—24no—
538Dic17—24no—
539Dic17—42no—
540Dic17—42no—
541Dic17—42no—
542Dic17—81no—
543C24×C4—171no—
544C24×C4—171no—
545C24×C4—171no—
546C22×C4⋊C4—171no—
547C22×C4⋊C4—171no—
548C22×C4⋊C4—171no—
549C22×C4⋊C4—171no—
550C22×C4⋊C4—171no—
551C22×C4⋊C4—171no—
552C22×C4⋊C4—171no—
553C22×C4⋊C4—344no—
554C22×C4⋊C4—344no—
555C22×C4⋊C4—344no—
556C22×C4⋊C4C2×D1711yescharacteristic
557C22×C4⋊C4C2×D1711yescharacteristic
558C22×C4⋊C4C2×D1711yescharacteristic
559C22×C22⋊C4—171no—
560C22×C22⋊C4—171no—
561C22×C22⋊C4—171no—
562C22×C22⋊C4—171no—
563C22×C42—171no—
564C22×C42—171no—
565#389—344no—
566#389—344no—
567#385—178no—
568#385—344no—
569#385—344no—
570C4×C22⋊C4—344no—
571C2×#95—171no—
572C2×#95—171no—
573C2×#95—171no—
574C2×#95—171no—
575C2×#95—171no—
576C2×#95—171no—
577C2×#95—171no—
578C2×#95—171no—
579C2×#95—171no—
580C2×#95—171no—
581C2×#95—171no—
582C2×#95—171no—
583C2×#95C2×D1711yescharacteristic
584C2×#95C2×D1711yescharacteristic
585C2×#95C2×D1711yescharacteristic
586C2×#95C2×D1711yescharacteristic
587C2×C17C2×#38911yescharacteristic
588C2×C17C4×#12011yescharacteristic
589C2×C17#232211yescharacteristic
590C2×C17D4×C4⋊C411yescharacteristic
591C2×C17D4×C4⋊C411yescharacteristic
592C2×C17#236011yescharacteristic
593C2×C17#236011yescharacteristic
594C2×C17#241011yescharacteristic
595C2×C17#241311yescharacteristic
596C2×C17#243411yescharacteristic
597C2×C17#244911yescharacteristic
598C2×C17#244911yescharacteristic
599C2×C17#247311yescharacteristic
600C2×C17#247311yescharacteristic
601C2×C17#258311yescharacteristic
602D17—28no—
603C25—171no—
604C23×C4—171no—
605C23×C4—171no—
606C23×C4—171no—
607C23×C4—171no—
608C23×C4—171no—
609C23×C4—171no—
610C23×C4—174no—
611C23×C4—174no—
612C23×C4—171no—
613C23×C4—342no—
614C23×C4—342no—
615C23×C4—342no—
616C23×C4—342no—
617C23×C4—342no—
618C23×C4—342no—
619C23×C4—342no—
620C23×C4—342no—
621C23×C4—342no—
622C23×C4—342no—
623C23×C4—342no—
624C23×C4—342no—
625C23×C4—342no—
626C23×C4—342no—
627C23×C4—342no—
628C23×C4—681no—
629C23×C4—681no—
630C23×C4—681no—
631C23×C4—681no—
632C23×C4C22×D1711yescharacteristic
633C23×C4C22×D1711yescharacteristic
634C23×C4C22×D1711yescharacteristic
635C23×C4C22×D1711yescharacteristic
636C23×C4C22×D1711yescharacteristic
637C23×C4C22×D1711yescharacteristic
638C23×C4C22×D1711yescharacteristic
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—174no—
649C2×C4⋊C4—174no—
650C2×C4⋊C4—174no—
651C2×C4⋊C4—174no—
652C2×C4⋊C4—3432no—
653C2×C4⋊C4—342no—
654C2×C4⋊C4—342no—
655C2×C4⋊C4—342no—
656C2×C4⋊C4—342no—
657C2×C4⋊C4—342no—
658C2×C4⋊C4—342no—
659C2×C4⋊C4—342no—
660C2×C4⋊C4—342no—
661C2×C4⋊C4—342no—
662C2×C4⋊C4—342no—
663C2×C4⋊C4—342no—
664C2×C4⋊C4—342no—
665C2×C4⋊C4—342no—
666C2×C4⋊C4—342no—
667C2×C4⋊C4—342no—
668C2×C4⋊C4—342no—
669C2×C4⋊C4—681no—
670C2×C22⋊C4—174no—
671C2×C22⋊C4—174no—
672C2×C22⋊C4—174no—
673C2×C22⋊C4—174no—
674C2×C22⋊C4—174no—
675C2×C22⋊C4—342no—
676C2×C22⋊C4—342no—
677C2×C22⋊C4—342no—
678C2×C22⋊C4—342no—
679C2×C22⋊C4—342no—
680C2×C22⋊C4—342no—
681C2×C22⋊C4—342no—
682C2×C42—342no—
683C2×C42—342no—
684C2×C42—342no—
685C2×C42—342no—
686C2×C42—681no—
687C2×C42—681no—
688#95—22no—
689#95—22no—
690#95—41no—
691#95—174no—
692#95—342no—
693#95—342no—
694#95—342no—
695#95—342no—
696#95—342no—
697#95—342no—
698#95—342no—
699#95—342no—
700#95—342no—
701#95—342no—
702#95—681no—
703#95C4×D1714yescomplemented
704C17#1404311yescharacteristic, complemented, Sylow
705C24—172no—
706C24—172no—
707C24—172no—
708C24—172no—
709C24—172no—
710C24—172no—
711C24—172no—
712C24—341no—
713C24—341no—
714C24—341no—
715C24—341no—
716C24—341no—
717C24—341no—
718C24—341no—
719C24—341no—
720C24C23×D1711yescharacteristic
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—172no—
761C22×C4—172no—
762C22×C4—172no—
763C22×C4—172no—
764C22×C4—172no—
765C22×C4—172no—
766C22×C4—172no—
767C22×C4—172no—
768C22×C4—172no—
769C22×C4—172no—
770C22×C4—172no—
771C22×C4—172no—
772C22×C4—348no—
773C22×C4—348no—
774C22×C4—348no—
775C22×C4—348no—
776C22×C4—348no—
777C22×C4—348no—
778C22×C4—348no—
779C22×C4—348no—
780C22×C4—348no—
781C22×C4—341no—
782C22×C4—341no—
783C22×C4—341no—
784C22×C4—341no—
785C22×C4—341no—
786C22×C4—341no—
787C22×C4—341no—
788C22×C4—341no—
789C22×C4—341no—
790C22×C4—341no—
791C22×C4—341no—
792C22×C4—341no—
793C22×C4—348no—
794C22×C4—341no—
795C22×C4—341no—
796C22×C4—341no—
797C22×C4—341no—
798C22×C4—341no—
799C22×C4—341no—
800C22×C4—341no—
801C22×C4—341no—
802C22×C4—341no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—684no—
820C22×C4—684no—
821C22×C4—684no—
822C22×C4—684no—
823C22×C4—684no—
824C22×C4—684no—
825C22×C4—684no—
826C22×C4—684no—
827C22×C4—684no—
828C22×C4—684no—
829C22×C4—684no—
830C22×C4C2×C4×D1712yes—
831C22×C4C2×C4×D1712yes—
832C22×C4C2×C4×D1712yes—
833C22×C4D4×D1712yes—
834C22×C4D4×D1712yes—
835C22×C4D4×D1712yes—
836C22×C4D4×D1712yes—
837C22×C4Q8×D1712yes—
838C22×C4Q8×D1712yes—
839C22×C4#6325612yes—
840C4⋊C4—28no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—348no—
844C4⋊C4—348no—
845C4⋊C4—348no—
846C4⋊C4—348no—
847C4⋊C4—348no—
848C4⋊C4—684no—
849C4⋊C4—684no—
850C22⋊C4—1716no—
851C22⋊C4—348no—
852C22⋊C4—348no—
853C22⋊C4—684no—
854C42—684no—
855C42—684no—
856C23—174no—
857C23—174no—
858C23—174no—
859C23—174no—
860C23—174no—
861C23—174no—
862C23—174no—
863C23—342no—
864C23—342no—
865C23—342no—
866C23—342no—
867C23—342no—
868C23—342no—
869C23—342no—
870C23—342no—
871C23—342no—
872C23—342no—
873C23—342no—
874C23—342no—
875C23—342no—
876C23—342no—
877C23—342no—
878C23—342no—
879C23—342no—
880C23—342no—
881C23—342no—
882C23—342no—
883C23—342no—
884C23—342no—
885C23—342no—
886C23—342no—
887C23—342no—
888C23—342no—
889C23—342no—
890C23—342no—
891C23C22×C4×D1711yescharacteristic
892C23C2×D4×D1711yescharacteristic
893C23C2×D4×D1711yescharacteristic
894C23C2×D4×D1711yescharacteristic
895C23C2×D4×D1711yescharacteristic
896C23#1058769111yescharacteristic
897C23#1058769111yescharacteristic
898C23C2×Q8×D1711yescharacteristic
899C23C2×Q8×D1711yescharacteristic
900C23C2×#6325611yescharacteristic
901C23#1058769411yescharacteristic
902C23#41×D1711yescharacteristic
903C23#41×D1711yescharacteristic
904C23#41×D1711yescharacteristic
905C23#1058769711yescharacteristic
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—174no—
954C2×C4—174no—
955C2×C4—174no—
956C2×C4—3432no—
957C2×C4—342no—
958C2×C4—342no—
959C2×C4—342no—
960C2×C4—342no—
961C2×C4—342no—
962C2×C4—342no—
963C2×C4—342no—
964C2×C4—342no—
965C2×C4—342no—
966C2×C4—342no—
967C2×C4—342no—
968C2×C4—342no—
969C2×C4—342no—
970C2×C4—342no—
971C2×C4—342no—
972C2×C4—342no—
973C2×C4—342no—
974C2×C4—342no—
975C2×C4—342no—
976C2×C4—342no—
977C2×C4—342no—
978C2×C4—342no—
979C2×C4—342no—
980C2×C4—342no—
981C2×C4—342no—
982C2×C4—342no—
983C2×C4—342no—
984C2×C4—6816no—
985C2×C4—6816no—
986C2×C4—681no—
987C2×C4—681no—
988C2×C4—681no—
989C2×C4—681no—
990C2×C4—681no—
991C2×C4—681no—
992C2×C4—681no—
993C2×C4—681no—
994C2×C4—681no—
995C2×C4—681no—
996C2×C4—681no—
997C2×C4—681no—
998C2×C4—681no—
999C2×C4—681no—
1000C2×C4—681no—
1001C2×C4—681no—
1002C2×C4—681no—
1003C2×C4—681no—
1004C2×C4—681no—
1005C2×C4C4⋊C4×D1714yescomplemented
1006C2×C4#1058757914yes—
1007C22—178no—
1008C22—344no—
1009C22—344no—
1010C22—344no—
1011C22—344no—
1012C22—344no—
1013C22—344no—
1014C22—344no—
1015C22—344no—
1016C22—344no—
1017C22—344no—
1018C22—344no—
1019C22—344no—
1020C22—344no—
1021C22—344no—
1022C22C2×C4⋊C4×D1711yescharacteristic
1023C22C4×D4×D1711yescharacteristic
1024C22C4×D4×D1711yescharacteristic
1025C22C2×#1058757911yescharacteristic
1026C22C4×Q8×D1711yescharacteristic
1027C22#1176328811yescharacteristic
1028C22#1176329011yescharacteristic
1029C22#120×D1711yescharacteristic
1030C22#121×D1711yescharacteristic
1031C22C22⋊Q8×D1711yescharacteristic
1032C22#1176331711yescharacteristic
1033C22#1176332211yescharacteristic
1034C22#1176332211yescharacteristic
1035C22#125×D1711yescharacteristic
1036C22C4⋊Q8×D1711yescharacteristic
1037C22#1176336911yescharacteristic
1038C22#1176338211yescharacteristic
1039C22#1176340211yescharacteristic
1040C22#1176340511yescharacteristic
1041C22#1176344111yescharacteristic
1042C22#1176344411yescharacteristic
1043C22#1176344811yescharacteristic
1044C22#1176345611yescharacteristic
1045C22#1176345711yescharacteristic
1046C22#1176346211yescharacteristic
1047C22#1176347211yescharacteristic
1048C22#1176347211yescharacteristic
1049C22#1176347411yescharacteristic
1050C22#1176347411yescharacteristic
1051C22#1176349111yescharacteristic
1052C22#1176349711yescharacteristic
1053C22#1176351311yescharacteristic
1054C22#1176351311yescharacteristic
1055C22#1176352011yescharacteristic
1056C22#1176352011yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—344no—
1065C4—344no—
1066C4—344no—
1067C4—682no—
1068C4—682no—
1069C4—682no—
1070C4—1361no—
1071C2—348no—
1072C2D17×#38911yescharacteristic
1073C2#1453128511yescharacteristic
1074C2#1453145111yescharacteristic
1075C2#1453168211yescharacteristic
1076C2#1453168411yescharacteristic
1077C2#1453178611yescharacteristic
1078C2#1453178811yescharacteristic
1079C2#1453215111yescharacteristic
1080C2#1453218411yescharacteristic
1081C2#1453242311yescharacteristic
1082C2#1453258611yescharacteristic
1083C2#1453259611yescharacteristic
1084C2#1453291811yescharacteristic
1085C2#1453292811yescharacteristic
1086C2#1453416011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1444C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1444D17
hypocenterC17#14043
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
2. C2×#11762706C2semidirect
3. C2×#11762705C2semidirect
8. #14527047C2semidirect
9. #14527036C2semidirect
10. #14527034C2semidirect
11. #14527018C2semidirect
12. #14527015C2semidirect
15. C17×#1444C2semidirect
37. #11762683C4semidirect
121. C2×C4⋊Dic17C2×C4semidirect
136. C2×#63225C2×C4semidirect
148. C17×#95C2×C4semidirect
160. #10587502C2×C4semidirect
302. #63227C4⋊C4semidirect
410. C2×C4×C17C2×C4⋊C4semidirect
458. C2×Dic17C2×C4⋊C4semidirect
472. #1444D17semidirect
528. C2×D17#389semidirect
703. #95C4×D17semidirect
704. C17#14043semidirect
1005. C2×C4C4⋊C4×D17semidirect

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×#117627062
C2×#117627052
C2×#117626832
C2×#117626802
C2×#117626562
#145270472
#145270362
#145270342
#145270182
#145270152
#145270052
C17×#14442
#1404317