Finite Group Databasebeta

← #16957692

Subgroups — #16957692

Order 4352.

2590 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587579C211yesmaximal, characteristic
2C2×#11762687C211yesmaximal, characteristic
3C2×#11762687C211yesmaximal, characteristic
4C2×#11762683C211yesmaximal, characteristic, complemented
5C2×#95×D17C211yesmaximal, characteristic, complemented
6#14527043C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527028C211yesmaximal, characteristic, complemented
9#14527018C211yesmaximal, characteristic, complemented
10#14527015C211yesmaximal, characteristic, complemented
11#14527005C211yesmaximal, characteristic, complemented
12#14527005C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1442C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C2×#10587579—24no—
22C2×#10587579—24no—
23C2×#10587579—24no—
24C22×C4⋊Dic17C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762687—24no—
36#11762687C418yescomplemented
37#11762683—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50#95×D17—24no—
51C22×C4⋊C4×C17C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C24×D17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C22×D68—22no—
74C22×D68—22no—
75C22×D68—22no—
76C22×D68—22no—
77C22×D68C2×C414yes—
78C22×D68D414yes—
79C22×D68Q814yes—
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—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—22no—
94C22×C4×D17—22no—
95C22×C4×D17—22no—
96C22×C4×D17—41no—
97C22×C4×D17—41no—
98C22×C4×D17—41no—
99C22×C4×D17—41no—
100C22×C4×D17—41no—
101C22×C4×D17—41no—
102C22×C4×D17—41no—
103C22×C4×D17—41no—
104C22×C4×D17—41no—
105C22×C4×D17—41no—
106C22×C4×D17C2×C414yescomplemented
107C22×C4×D17D414yes—
108C2×C4⋊C4×C17—22no—
109C2×C4⋊C4×C17—22no—
110C2×C4⋊C4×C17—22no—
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
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—41no—
126C2×#63227—41no—
127C2×#63227—41no—
128C2×#63227—41no—
129C2×#63227—41no—
130C2×#63227—41no—
131C2×#63227C2×C414yescomplemented
132C2×#63227C2×C414yescomplemented
133C2×#63227C2×C414yescomplemented
134C2×#63227D414yes—
135C2×C4⋊Dic17—22no—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—41no—
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225—41no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—22no—
143C2×C4×Dic17—22no—
144#10587579—232no—
145C17×#95—22no—
146C17×#95—22no—
147C17×#95—22no—
148C17×#95—41no—
149C17×#95—41no—
150C17×#95C2×C414yescomplemented
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—22no—
156#10587502—22no—
157#10587502—22no—
158#10587502—41no—
159#10587502—41no—
160#10587502—41no—
161#10587502—41no—
162#10587502C2×C414yescomplemented
163C24×C17C2411yescharacteristic
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17—21no—
180C23×D17—21no—
181C23×D17—21no—
182C23×D17—21no—
183C23×D17—21no—
184C23×D17C22×C412yes—
185C23×D17C22×C412yes—
186C23×D17C2×D412yes—
187C23×D17C2×D412yes—
188C23×D17C2×D412yes—
189C23×D17C2×D412yes—
190C23×D17C2×Q812yes—
191C23×D17C2×Q812yes—
192C23×D17#4112yes—
193C23×D17#4112yes—
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×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×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17—21no—
235C22×C4×C17C22×C412yes—
236C22×C4×C17C22×C412yes—
237C22×C4×C17C22×C412yes—
238C22×C4×C17C2×D412yes—
239C22×C4×C17C2×D412yes—
240C22×C4×C17C2×D412yes—
241C22×C4×C17C2×Q812yes—
242C22×C4×C17#4112yes—
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×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×Dic17C22×C412yes—
279C22×Dic17C22×C412yes—
280C22×Dic17C2×D412yes—
281C22×Dic17C2×D412yes—
282C22×Dic17#4112yes—
283C22×Dic17#4112yes—
284C22×Dic17#4112yes—
285C2×D68—28no—
286C2×D68—28no—
287C2×D68—28no—
288C2×D68—28no—
289C2×D68—28no—
290C2×D68—28no—
291C2×D68C4⋊C4116yescomplemented
292C2×C4×D17—28no—
293C2×C4×D17—28no—
294C2×C4×D17—28no—
295C2×C4×D17—28no—
296C2×C4×D17—28no—
297C2×C4×D17—44no—
298C2×C4×D17—44no—
299C2×C4×D17—44no—
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—
315C2×C4×D17—44no—
316C2×C4×D17—44no—
317C2×C4×D17—44no—
318C2×C4×D17—44no—
319C2×C4×D17—44no—
320C4⋊C4×C17—28no—
321#63227—28no—
322#63227—28no—
323#63227—28no—
324#63227—44no—
325#63227—44no—
326#63227—44no—
327#63227—44no—
328#63227—44no—
329C4⋊Dic17—44no—
330#63225—44no—
331C4×Dic17—28no—
332#14016—171nomaximal, Sylow
333C23×C17C23×C411yescharacteristic
334C23×C17C22×D411yescharacteristic
335C23×C17C22×D411yescharacteristic
336C23×C17C22×D411yescharacteristic
337C23×C17C22×Q811yescharacteristic
338C23×C17C2×#4111yescharacteristic
339C23×C17C2×#4111yescharacteristic
340C23×C17C2×#4111yescharacteristic
341C23×C17C2×#4111yescharacteristic
342C23×C17C2×#4111yescharacteristic
343C23×C17C2×#4111yescharacteristic
344C23×C17H(5,𝔽2)11yescharacteristic
345C23×C17H(5,𝔽2)11yescharacteristic
346C23×C17H(5,𝔽2)11yescharacteristic
347C23×C17H(5,𝔽2)11yescharacteristic
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×D17—22no—
357C22×D17—22no—
358C22×D17—22no—
359C22×D17—22no—
360C22×D17—22no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
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—41no—
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×D17C2×C4⋊C414yes—
411C22×D17C2×C4⋊C414yes—
412C22×D17C4×D414yes—
413C22×D17C4×D414yes—
414C22×D17#12014yes—
415C22×D17C22⋊Q814yes—
416C22×D17C22⋊Q814yes—
417C22×D17#12314yes—
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—22no—
435C2×C4×C17—22no—
436C2×C4×C17—22no—
437C2×C4×C17—22no—
438C2×C4×C17—22no—
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×C17—41no—
458C2×C4×C17—41no—
459C2×C4×C17—41no—
460C2×C4×C17—41no—
461C2×C4×C17—41no—
462C2×C4×C17—41no—
463C2×C4×C17—41no—
464C2×C4×C17—41no—
465C2×C4×C17—41no—
466C2×C4×C17C2×C4⋊C414yes—
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—22no—
484C2×Dic17—22no—
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×Dic17—41no—
507C2×Dic17—41no—
508C2×Dic17#12314yes—
509D68—232no—
510C4×D17—416no—
511C4×D17—416no—
512C4×D17—416no—
513C4×D17—416no—
514C22×C4×D4—171no—
515C2×#386—171no—
516C2×#386—171no—
517C2×#385—171no—
518C22×#95—171no—
519#1442—171no—
520#1442D1711yescharacteristic, complemented
521#1439—171no—
522#1439—171no—
523#1436—171no—
524#1436—171no—
525C22⋊#95—171no—
526C22⋊#95—171no—
527C22⋊#95—171no—
528C22⋊#95—171no—
529C22×C17C22×C4⋊C411yescharacteristic
530C22×C17C2×C4×D411yescharacteristic
531C22×C17C2×C4×D411yescharacteristic
532C22×C17C4×#4111yescharacteristic
533C22×C17C4×#4111yescharacteristic
534C22×C17#51811yescharacteristic
535C22×C17#51811yescharacteristic
536C22×C17C2×#12011yescharacteristic
537C22×C17C2×C22⋊Q811yescharacteristic
538C22×C17C2×C22⋊Q811yescharacteristic
539C22×C17C2×#12311yescharacteristic
540C22×C17C2×#12311yescharacteristic
541C22×C17#52511yescharacteristic
542C22×C17#52911yescharacteristic
543C22×C17#52911yescharacteristic
544C22×C17#53411yescharacteristic
545C22×C17#53511yescharacteristic
546C22×C17#53811yescharacteristic
547C22×C17#53811yescharacteristic
548C22×C17#54611yescharacteristic
549C22×C17#54611yescharacteristic
550C22×C17#54611yescharacteristic
551C22×C17#54611yescharacteristic
552C22×C17#54611yescharacteristic
553C22×C17#54611yescharacteristic
554C22×C17#54611yescharacteristic
555C22×C17#54611yescharacteristic
556C22×C17#55311yescharacteristic
557C22×C17#55311yescharacteristic
558C22×C17#55311yescharacteristic
559C22×C17#55311yescharacteristic
560C22×C17#55411yescharacteristic
561C22×C17#55411yescharacteristic
562C22×C17#55411yescharacteristic
563C22×C17#55411yescharacteristic
564C2×D17—24no—
565C2×D17—24no—
566C2×D17—24no—
567C2×D17—24no—
568C2×D17—24no—
569C2×D17—24no—
570C2×D17—24no—
571C2×D17—24no—
572C2×D17—24no—
573C2×D17—24no—
574C2×D17—24no—
575C2×D17—24no—
576C2×D17—24no—
577C2×D17—24no—
578C2×D17—24no—
579C2×D17—24no—
580C2×D17—24no—
581C2×D17—42no—
582C2×D17—42no—
583C2×D17—42no—
584C2×D17—42no—
585C2×D17—42no—
586C2×D17—42no—
587C2×D17—42no—
588C2×D17—42no—
589C2×D17—42no—
590C2×D17—42no—
591C2×D17—42no—
592C2×D17—42no—
593C2×D17#38518yes—
594C4×C17—24no—
595C4×C17—42no—
596C4×C17—42no—
597C4×C17—42no—
598C4×C17—42no—
599C4×C17—42no—
600C4×C17—81no—
601Dic17—24no—
602Dic17—42no—
603Dic17—42no—
604Dic17—42no—
605Dic17—42no—
606Dic17—81no—
607C23×D4—171no—
608C24×C4—171no—
609C24×C4—171no—
610C24×C4—171no—
611C24×C4—171no—
612C2×C4×D4—344no—
613C2×C4×D4—344no—
614C2×C4×D4—344no—
615C22×C4⋊C4—171no—
616C22×C4⋊C4—171no—
617C22×C4⋊C4C2×D1711yescharacteristic
618C22×C22⋊C4—171no—
619C22×C22⋊C4—171no—
620C22×C22⋊C4—171no—
621C22×C22⋊C4—171no—
622C22×C22⋊C4—171no—
623C22×C22⋊C4—171no—
624C22×C22⋊C4—171no—
625C22×C22⋊C4—171no—
626C22×C42—171no—
627#386—178no—
628#386—344no—
629#385—344no—
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×#95—171no—
642C2×#95—344no—
643C2×#95C2×D1711yescharacteristic
644C2×#95C2×D1711yescharacteristic
645C2×#95C2×D1711yescharacteristic
646C2×#95C2×D1711yescharacteristic
647C2×#95C2×D1711yescharacteristic
648C2×#95C2×D1711yescharacteristic
649C2×C17C2×#38511yescharacteristic
650C2×C17C4×#12311yescharacteristic
651C2×C17#232111yescharacteristic
652C2×C17#234911yescharacteristic
653C2×C17#234911yescharacteristic
654C2×C17#236411yescharacteristic
655C2×C17#236411yescharacteristic
656C2×C17#240411yescharacteristic
657C2×C17#240511yescharacteristic
658C2×C17#244411yescharacteristic
659C2×C17#244411yescharacteristic
660C2×C17#245011yescharacteristic
661C2×C17#245011yescharacteristic
662C2×C17#248711yescharacteristic
663C2×C17#257911yescharacteristic
664D17—28no—
665D17—44no—
666C25—171no—
667C25—171no—
668C22×D4—174no—
669C22×D4—174no—
670C22×D4—174no—
671C22×D4—342no—
672C22×D4—342no—
673C22×D4—342no—
674C22×D4—342no—
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—342no—
699C23×C4—681no—
700C23×C4—681no—
701C23×C4—681no—
702C23×C4—681no—
703C23×C4—681no—
704C23×C4—681no—
705C23×C4—681no—
706C23×C4—681no—
707C23×C4—681no—
708C23×C4—681no—
709C23×C4C22×D1711yescharacteristic
710C23×C4C22×D1711yescharacteristic
711C23×C4C22×D1711yescharacteristic
712C23×C4C22×D1711yescharacteristic
713C23×C4C22×D1711yescharacteristic
714C23×C4C22×D1711yescharacteristic
715C23×C4C22×D1711yescharacteristic
716C4×D4—3432no—
717C2×C4⋊C4—22no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—342no—
721C2×C4⋊C4—342no—
722C2×C4⋊C4—342no—
723C2×C4⋊C4—342no—
724C2×C4⋊C4—681no—
725C2×C4⋊C4—681no—
726C2×C22⋊C4—174no—
727C2×C22⋊C4—174no—
728C2×C22⋊C4—174no—
729C2×C22⋊C4—174no—
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—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—681no—
745C2×C22⋊C4—681no—
746C2×C22⋊C4—681no—
747C2×C22⋊C4—681no—
748C2×C22⋊C4—681no—
749C2×C22⋊C4—681no—
750C2×C42—342no—
751C2×C42—342no—
752C2×C42—342no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—41no—
757#95—41no—
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—681no—
767#95—681no—
768#95—681no—
769#95—681no—
770#95C4×D1714yescomplemented
771C17#1401611yescharacteristic, complemented, Sylow
772C24—172no—
773C24—172no—
774C24—172no—
775C24—172no—
776C24—172no—
777C24—172no—
778C24—172no—
779C24—172no—
780C24—172no—
781C24—172no—
782C24—341no—
783C24—341no—
784C24—341no—
785C24—341no—
786C24—341no—
787C24—341no—
788C24—341no—
789C24—341no—
790C24—341no—
791C24—341no—
792C24—341no—
793C24—341no—
794C24—341no—
795C24—341no—
796C24—341no—
797C24—341no—
798C24—341no—
799C24—341no—
800C24—341no—
801C24—341no—
802C24C23×D1711yescharacteristic
803C2×D4—1716no—
804C2×D4—348no—
805C2×D4—348no—
806C2×D4—348no—
807C2×D4—348no—
808C2×D4—348no—
809C2×D4—348no—
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—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—172no—
852C22×C4—172no—
853C22×C4—172no—
854C22×C4—172no—
855C22×C4—172no—
856C22×C4—172no—
857C22×C4—172no—
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—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—684no—
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×C4—684no—
915C22×C4—684no—
916C22×C4—684no—
917C22×C4—684no—
918C22×C4—684no—
919C22×C4—684no—
920C22×C4—684no—
921C22×C4C2×C4×D1712yes—
922C22×C4C2×C4×D1712yes—
923C22×C4C2×C4×D1712yes—
924C22×C4D4×D1712yes—
925C22×C4D4×D1712yes—
926C22×C4D4×D1712yes—
927C22×C4Q8×D1712yes—
928C22×C4#6325612yes—
929C4⋊C4—28no—
930C4⋊C4—684no—
931C4⋊C4—684no—
932C22⋊C4—348no—
933C22⋊C4—348no—
934C22⋊C4—348no—
935C22⋊C4—684no—
936C22⋊C4—684no—
937C22⋊C4—684no—
938C22⋊C4—684no—
939C22⋊C4—684no—
940C42—348no—
941C23—174no—
942C23—174no—
943C23—174no—
944C23—174no—
945C23—174no—
946C23—174no—
947C23—174no—
948C23—174no—
949C23—342no—
950C23—342no—
951C23—342no—
952C23—342no—
953C23—342no—
954C23—342no—
955C23—342no—
956C23—342no—
957C23—342no—
958C23—342no—
959C23—342no—
960C23—342no—
961C23—342no—
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—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—681no—
996C23—681no—
997C23—681no—
998C23—681no—
999C23—681no—
1000C23—681no—
1001C23—681no—
1002C23—681no—
1003C23—681no—
1004C23—681no—
1005C23—681no—
1006C23—681no—
1007C23—681no—
1008C23—681no—
1009C23—681no—
1010C23—681no—
1011C23C22×C4×D1711yescharacteristic
1012C23C2×D4×D1711yescharacteristic
1013C23C2×D4×D1711yescharacteristic
1014C23C2×D4×D1711yescharacteristic
1015C23#1058769111yescharacteristic
1016C23C2×Q8×D1711yescharacteristic
1017C23C2×#6325611yescharacteristic
1018C23#41×D1711yescharacteristic
1019C23#41×D1711yescharacteristic
1020C23#41×D1711yescharacteristic
1021C23#41×D1711yescharacteristic
1022C23#41×D1711yescharacteristic
1023C23#1058769611yescharacteristic
1024C23#1058769611yescharacteristic
1025C23#1058769611yescharacteristic
1026D4—3432no—
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—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
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—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—174no—
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—342no—
1091C2×C4—342no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—6816no—
1095C2×C4—6816no—
1096C2×C4—6816no—
1097C2×C4—6816no—
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—681no—
1116C2×C4—681no—
1117C2×C4—681no—
1118C2×C4—681no—
1119C2×C4—681no—
1120C2×C4—681no—
1121C2×C4C4⋊C4×D1714yes—
1122C22—178no—
1123C22—344no—
1124C22—344no—
1125C22—344no—
1126C22—344no—
1127C22—344no—
1128C22—344no—
1129C22—344no—
1130C22—344no—
1131C22—344no—
1132C22—344no—
1133C22—344no—
1134C22—344no—
1135C22—344no—
1136C22—344no—
1137C22—344no—
1138C22—344no—
1139C22—344no—
1140C22—682no—
1141C22—682no—
1142C22—682no—
1143C22—682no—
1144C22—682no—
1145C22—682no—
1146C22—682no—
1147C22—682no—
1148C22—682no—
1149C22—682no—
1150C22—682no—
1151C22—682no—
1152C22C2×C4⋊C4×D1711yescharacteristic
1153C22C4×D4×D1711yescharacteristic
1154C22C4×D4×D1711yescharacteristic
1155C22#1176327711yescharacteristic
1156C22C4×#6325611yescharacteristic
1157C22#1176328111yescharacteristic
1158C22#1176328311yescharacteristic
1159C22#120×D1711yescharacteristic
1160C22C22⋊Q8×D1711yescharacteristic
1161C22C22⋊Q8×D1711yescharacteristic
1162C22#123×D1711yescharacteristic
1163C22#123×D1711yescharacteristic
1164C22#1176332211yescharacteristic
1165C22#1176334211yescharacteristic
1166C22#1176334411yescharacteristic
1167C22#1176336711yescharacteristic
1168C22#1176337711yescharacteristic
1169C22#1176339511yescharacteristic
1170C22#1176339811yescharacteristic
1171C22#1176344811yescharacteristic
1172C22#1176345011yescharacteristic
1173C22#1176345011yescharacteristic
1174C22#1176345111yescharacteristic
1175C22#1176345211yescharacteristic
1176C22#1176345211yescharacteristic
1177C22#1176345211yescharacteristic
1178C22#1176345611yescharacteristic
1179C22#1176350411yescharacteristic
1180C22#1176351011yescharacteristic
1181C22#1176351011yescharacteristic
1182C22#1176351211yescharacteristic
1183C22#1176351511yescharacteristic
1184C22#1176351511yescharacteristic
1185C22#1176351511yescharacteristic
1186C22#1176352011yescharacteristic
1187C4—24no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—81no—
1194C4—344no—
1195C4—682no—
1196C4—682no—
1197C4—682no—
1198C4—682no—
1199C4—1361no—
1200C2—348no—
1201C2—684no—
1202C2D17×#38511yescharacteristic
1203C2#1453130511yescharacteristic
1204C2#1453143711yescharacteristic
1205C2#1453169211yescharacteristic
1206C2#1453169311yescharacteristic
1207C2#1453182811yescharacteristic
1208C2#1453183011yescharacteristic
1209C2#1453210411yescharacteristic
1210C2#1453210611yescharacteristic
1211C2#1453253511yescharacteristic
1212C2#1453253711yescharacteristic
1213C2#1453260911yescharacteristic
1214C2#1453261111yescharacteristic
1215C2#1453309611yescharacteristic
1216C2#1453413211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1442C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1442D17
hypocenterC17#14016
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
4. C2×#11762683C2semidirect
5. C2×#95×D17C2semidirect
6. #14527043C2semidirect
7. #14527030C2semidirect
8. #14527028C2semidirect
9. #14527018C2semidirect
10. #14527015C2semidirect
11. #14527005C2semidirect
12. #14527005C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1442C2semidirect
36. #11762687C4semidirect
106. C22×C4×D17C2×C4semidirect
131. C2×#63227C2×C4semidirect
132. C2×#63227C2×C4semidirect
133. C2×#63227C2×C4semidirect
150. C17×#95C2×C4semidirect
162. #10587502C2×C4semidirect
291. C2×D68C4⋊C4semidirect
520. #1442D17semidirect
770. #95C4×D17semidirect
771. C17#14016semidirect

Maximal subgroups

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

subgroupindex
C22×#105875792
C2×#117626872
C2×#117626832
C2×#95×D172
#145270432
#145270302
#145270282
#145270182
#145270152
#145270052
C17×#14422
#1401617