Finite Group Databasebeta

← #16959794

Subgroups — #16959794

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×#10587579C211yesmaximal, characteristic
2C2×#11762726C211yesmaximal, characteristic
3C2×#11762699C211yesmaximal, characteristic, complemented
4C2×#11762680C211yesmaximal, characteristic, complemented
5C2×#11762680C211yesmaximal, characteristic, complemented
6C2×C4×#63227C211yesmaximal, characteristic, complemented
7#14527032C211yesmaximal, characteristic, complemented
8#14527026C211yesmaximal, characteristic, complemented
9#14527024C211yesmaximal, characteristic
10#14527022C211yesmaximal, characteristic, complemented
11#14527016C211yesmaximal, characteristic, complemented
12#14527016C211yesmaximal, characteristic, complemented
13#14527015C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C2×C17×#389C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C2×#10587579—24no—
20C2×#10587579—24no—
21C2×#10587579—24no—
22C22×#63225C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762726C418yescomplemented
36#11762699—24no—
37#11762680—24no—
38#11762680—24no—
39C4×#63227—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×C4⋊C4×C17C2211yescharacteristic
54C22×C4⋊C4×C17C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C22×C42×C17C2211yescharacteristic
57C17×#389—24no—
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C24×D17C2311yescharacteristic
61C24×D17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C22×D68—22no—
76C22×D68—22no—
77C22×D68—22no—
78C22×D68—22no—
79C22×D68—22no—
80C22×D68—22no—
81C22×D68C2×C414yes—
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—41no—
92C22×C4×D17—41no—
93C22×C4×D17—41no—
94C22×C4×D17—41no—
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—22no—
103C2×C4⋊C4×C17—22no—
104C2×C4⋊C4×C17—22no—
105C2×C4⋊C4×C17—41no—
106C2×C4⋊C4×C17C2×C414yescomplemented
107C2×C4⋊C4×C17D414yes—
108C2×C42×C17—22no—
109C2×C42×C17—22no—
110C2×C42×C17—41no—
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—22no—
126C2×#63227—22no—
127C2×#63227—22no—
128C2×#63227—22no—
129C2×#63227—22no—
130C2×#63227—22no—
131C2×#63227—22no—
132C2×#63227—41no—
133C2×#63227—41no—
134C2×#63227—41no—
135C2×#63227—41no—
136C2×#63227C2×C414yescomplemented
137C2×#63227C2×C414yescomplemented
138C2×#63227C2×C414yescomplemented
139C2×#63227C2×C414yescomplemented
140C2×#63227D414yes—
141C2×#63225—22no—
142C2×#63225—22no—
143C2×#63225—22no—
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147C2×C4×Dic17—22no—
148C2×C4×Dic17—22no—
149C2×C4×Dic17—41no—
150#10587579—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#10587502C2×C414yescomplemented
164#10587502D414yescomplemented
165C24×C17C2411yescharacteristic
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×D17—21no—
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C23×D17—21no—
190C23×D17C22×C412yes—
191C23×D17C22×C412yes—
192C23×D17C2×D412yes—
193C23×D17C2×D412yes—
194C23×D17#4112yes—
195C23×D17#4112yes—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17C22×C412yes—
234C22×C4×C17C22×C412yes—
235C22×C4×C17C22×C412yes—
236C22×C4×C17C2×D412yes—
237C22×C4×C17C2×D412yes—
238C22×C4×C17C2×D412yes—
239C22×C4×C17C2×D412yes—
240C22×C4×C17C2×D412yes—
241C22×C4×C17C2×D412yes—
242C22×C4×C17#4112yes—
243C22×C4×C17#4112yes—
244C22×C4×C17#4112yes—
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×Dic17C22×C412yes—
281C22×Dic17C22×C412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17C2×D412yes—
286C22×Dic17#4112yes—
287C2×D68—28no—
288C2×D68—28no—
289C2×D68—28no—
290C2×D68—28no—
291C2×D68—28no—
292C2×D68—28no—
293C2×D68—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—
308C4⋊C4×C17—28no—
309C4⋊C4×C17—28no—
310C4⋊C4×C17—44no—
311C4⋊C4×C17—44no—
312C42×C17—44no—
313#63227—28no—
314#63227—28no—
315#63227—28no—
316#63227—28no—
317#63227—28no—
318#63227—28no—
319#63227—28no—
320#63227—44no—
321#63227—44no—
322#63227—44no—
323#63225—44no—
324C4×Dic17—28no—
325C4×Dic17—44no—
326#14185—171nomaximal, Sylow
327C23×C17C23×C411yescharacteristic
328C23×C17C22×D411yescharacteristic
329C23×C17C22×D411yescharacteristic
330C23×C17C22×D411yescharacteristic
331C23×C17C22×D411yescharacteristic
332C23×C17C2×#4111yescharacteristic
333C23×C17C2×#4111yescharacteristic
334C23×C17C2×#4111yescharacteristic
335C23×C17C2×#4111yescharacteristic
336C23×C17C2×#4111yescharacteristic
337C23×C17C2×#4111yescharacteristic
338C23×C17H(5,𝔽2)11yescharacteristic
339C23×C17H(5,𝔽2)11yescharacteristic
340C23×C172−1+411yescharacteristic
341C23×C172−1+411yescharacteristic
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×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—41no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17—41no—
382C22×D17—41no—
383C22×D17—41no—
384C22×D17—41no—
385C22×D17—41no—
386C22×D17—41no—
387C22×D17—41no—
388C22×D17—41no—
389C22×D17—41no—
390C22×D17—41no—
391C22×D17—41no—
392C22×D17—41no—
393C22×D17—41no—
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×D17C4×D414yes—
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—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×C17C4×D414yes—
459C2×C4×C17C4×D414yescomplemented
460C2×C4×C17#12014yes—
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—41no—
480C2×Dic17—41no—
481C2×Dic17—41no—
482C2×Dic17—41no—
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#12114yes—
503D68—232no—
504C4×D17—416no—
505C4×D17—416no—
506C22×C4×D4—171no—
507C2×#394—171no—
508C2×#389D1711yescharacteristic, complemented
509C2×#388—171no—
510C2×#385—171no—
511C2×#385—171no—
512C2×C4×C22⋊C4—171no—
513#1440—171no—
514#1439—171no—
515#1438—171no—
516#1437—171no—
517#1436—171no—
518#1436—171no—
519#1436—171no—
520C22⋊#95—171no—
521C22×C17C2×C4×D411yescharacteristic
522C22×C17C2×C4×D411yescharacteristic
523C22×C17C2×C4×D411yescharacteristic
524C22×C17C2×C4×D411yescharacteristic
525C22×C17C4×#4111yescharacteristic
526C22×C17#52011yescharacteristic
527C22×C17#52011yescharacteristic
528C22×C17C2×#12011yescharacteristic
529C22×C17C2×#12111yescharacteristic
530C22×C17#52511yescharacteristic
531C22×C17#52511yescharacteristic
532C22×C17#52511yescharacteristic
533C22×C17#52511yescharacteristic
534C22×C17#52911yescharacteristic
535C22×C17#53211yescharacteristic
536C22×C17#53411yescharacteristic
537C22×C17#53611yescharacteristic
538C22×C17#53911yescharacteristic
539C22×C17#53911yescharacteristic
540C22×C17D4211yescharacteristic
541C22×C17D4211yescharacteristic
542C22×C17#54611yescharacteristic
543C22×C17#54611yescharacteristic
544C22×C17#54711yescharacteristic
545C22×C17#54711yescharacteristic
546C22×C17#54711yescharacteristic
547C22×C17#54811yescharacteristic
548C22×C17#54811yescharacteristic
549C22×C17#54811yescharacteristic
550C22×C17#55111yescharacteristic
551C22×C17#55211yescharacteristic
552C22×C17#55311yescharacteristic
553C22×C17#55311yescharacteristic
554C22×C17#55611yescharacteristic
555C22×C17#55911yescharacteristic
556C2×D17—24no—
557C2×D17—24no—
558C2×D17—24no—
559C2×D17—24no—
560C2×D17—24no—
561C2×D17—24no—
562C2×D17—42no—
563C2×D17—42no—
564C2×D17—42no—
565C2×D17—42no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—42no—
569C2×D17—42no—
570C2×D17—42no—
571C2×D17—42no—
572C2×D17—42no—
573C2×D17—42no—
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—24no—
588C4×C17—24no—
589C4×C17—42no—
590C4×C17—42no—
591C4×C17—42no—
592C4×C17—81no—
593Dic17—24no—
594Dic17—42no—
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⋊C4C2×D1711yescharacteristic
607C22×C4⋊C4C2×D1711yescharacteristic
608C22×C4⋊C4C2×D1711yescharacteristic
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⋊C4—171no—
618C22×C22⋊C4—171no—
619C22×C22⋊C4—171no—
620C22×C42—171no—
621C22×C42—171no—
622C22×C42C2×D1711yescharacteristic
623#394—178no—
624#389—24no—
625#388—344no—
626#385—344no—
627#385—344no—
628C4×C22⋊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×C17C4×#12011yescharacteristic
644C2×C17C4×#12111yescharacteristic
645C2×C17#232211yescharacteristic
646C2×C17#235911yescharacteristic
647C2×C17#236111yescharacteristic
648C2×C17#236111yescharacteristic
649C2×C17#236711yescharacteristic
650C2×C17#241011yescharacteristic
651C2×C17#241511yescharacteristic
652C2×C17#243211yescharacteristic
653C2×C17#245511yescharacteristic
654C2×C17#246011yescharacteristic
655C2×C17#246311yescharacteristic
656C2×C17#246611yescharacteristic
657C2×C17#260211yescharacteristic
658D17—44no—
659D17—44no—
660C25—171no—
661C25—171no—
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—174no—
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—681no—
686C23×C4—681no—
687C23×C4—681no—
688C23×C4—681no—
689C23×C4C22×D1711yescharacteristic
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—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—41no—
707C2×C4⋊C4—342no—
708C2×C4⋊C4—342no—
709C2×C4⋊C4—342no—
710C2×C4⋊C4C4×D1714yescomplemented
711C2×C4⋊C4C22⋊D1714yes—
712C2×C22⋊C4—174no—
713C2×C22⋊C4—174no—
714C2×C22⋊C4—174no—
715C2×C22⋊C4—174no—
716C2×C22⋊C4—174no—
717C2×C22⋊C4—342no—
718C2×C22⋊C4—342no—
719C2×C22⋊C4—342no—
720C2×C22⋊C4—342no—
721C2×C22⋊C4—342no—
722C2×C22⋊C4—342no—
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—342no—
738C2×C22⋊C4—681no—
739C2×C22⋊C4—681no—
740C2×C22⋊C4—681no—
741C2×C22⋊C4—681no—
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—41no—
745C2×C42—342no—
746C2×C42—342no—
747C2×C42—342no—
748C2×C42—342no—
749C2×C42—342no—
750C2×C42—681no—
751#95—22no—
752#95—22no—
753#95—174no—
754#95—174no—
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—342no—
764#95—681no—
765C17#1418511yescharacteristic, complemented, Sylow
766C24—172no—
767C24—172no—
768C24—172no—
769C24—172no—
770C24—172no—
771C24—172no—
772C24—341no—
773C24—341no—
774C24—341no—
775C24—341no—
776C24—341no—
777C24—341no—
778C24—341no—
779C24—341no—
780C24—341no—
781C24—341no—
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—
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—21no—
840C22×C4—21no—
841C22×C4—172no—
842C22×C4—172no—
843C22×C4—172no—
844C22×C4—172no—
845C22×C4—172no—
846C22×C4—172no—
847C22×C4—172no—
848C22×C4—348no—
849C22×C4—348no—
850C22×C4—341no—
851C22×C4—341no—
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—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—348no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—341no—
883C22×C4—341no—
884C22×C4—341no—
885C22×C4—341no—
886C22×C4—684no—
887C22×C4—684no—
888C22×C4—684no—
889C22×C4—684no—
890C22×C4—684no—
891C22×C4—684no—
892C22×C4—684no—
893C22×C4—684no—
894C22×C4—684no—
895C22×C4—684no—
896C22×C4—684no—
897C22×C4C2×C4×D1712yes—
898C22×C4C2×C4×D1712yes—
899C22×C4C2×C4×D1712yes—
900C22×C4#6325212yes—
901C22×C4D4×D1712yes—
902C22×C4D4×D1712yes—
903C22×C4D4×D1712yes—
904C22×C4#6325612yes—
905C22×C4#6325612yes—
906C22×C4C2×C22⋊D1712yes—
907C22×C4C2×C22⋊D1712yes—
908C22×C4C2×C22⋊D1712yes—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—684no—
914C22⋊C4—348no—
915C22⋊C4—348no—
916C22⋊C4—348no—
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—684no—
927C23—174no—
928C23—174no—
929C23—342no—
930C23—342no—
931C23—342no—
932C23—342no—
933C23—342no—
934C23—342no—
935C23—342no—
936C23—342no—
937C23—342no—
938C23—342no—
939C23—342no—
940C23—342no—
941C23—342no—
942C23—342no—
943C23—342no—
944C23—342no—
945C23—342no—
946C23—342no—
947C23—342no—
948C23—342no—
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—681no—
966C23—681no—
967C23—681no—
968C23—681no—
969C23—681no—
970C23—681no—
971C23—681no—
972C23—681no—
973C23—681no—
974C23—681no—
975C23—681no—
976C23—681no—
977C23—681no—
978C23—681no—
979C23—681no—
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—
996C23—681no—
997C23C22×C4×D1711yescharacteristic
998C23C2×#6325211yescharacteristic
999C23C2×D4×D1711yescharacteristic
1000C23C2×D4×D1711yescharacteristic
1001C23C2×D4×D1711yescharacteristic
1002C23#1058769111yescharacteristic
1003C23C2×#6325611yescharacteristic
1004C23C2×#6325611yescharacteristic
1005C23#1058769411yescharacteristic
1006C23#1058769411yescharacteristic
1007C23#41×D1711yescharacteristic
1008C23#41×D1711yescharacteristic
1009C23#41×D1711yescharacteristic
1010C23#1058769611yescharacteristic
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—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—174no—
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—6816no—
1079C2×C4—6816no—
1080C2×C4—681no—
1081C2×C4—681no—
1082C2×C4—681no—
1083C2×C4—681no—
1084C2×C4—681no—
1085C2×C4—681no—
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#1058757914yescomplemented
1104C2×C4C4×C22⋊D1714yes—
1105C2×C4#1058762314yes—
1106C22—344no—
1107C22—344no—
1108C22—344no—
1109C22—344no—
1110C22—344no—
1111C22—344no—
1112C22—682no—
1113C22—682no—
1114C22—682no—
1115C22—682no—
1116C22—682no—
1117C22—682no—
1118C22—682no—
1119C22—682no—
1120C22—682no—
1121C22—682no—
1122C22—682no—
1123C22—682no—
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
1138C22C2×C4×C22⋊D1711yescharacteristic
1139C22C2×#1058757911yescharacteristic
1140C22C4×#6325611yescharacteristic
1141C22#1176329011yescharacteristic
1142C22#1176329111yescharacteristic
1143C22C2×#1058762311yescharacteristic
1144C22#121×D1711yescharacteristic
1145C22#1176331611yescharacteristic
1146C22#1176331811yescharacteristic
1147C22#1176331811yescharacteristic
1148C22#1176332211yescharacteristic
1149C22#1176334411yescharacteristic
1150C22#1176336011yescharacteristic
1151C22#1176336711yescharacteristic
1152C22#1176338411yescharacteristic
1153C22#1176340511yescharacteristic
1154C22#1176340711yescharacteristic
1155C22D4×C22⋊D1711yescharacteristic
1156C22#1176344311yescharacteristic
1157C22#1176344711yescharacteristic
1158C22#1176344811yescharacteristic
1159C22#1176346011yescharacteristic
1160C22#1176346211yescharacteristic
1161C22#1176346211yescharacteristic
1162C22#1176346911yescharacteristic
1163C22#1176347011yescharacteristic
1164C22#1176347011yescharacteristic
1165C22#1176348611yescharacteristic
1166C22#1176349111yescharacteristic
1167C22#1176350711yescharacteristic
1168C22#1176351211yescharacteristic
1169C22#1176353111yescharacteristic
1170C22#1176354411yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—24no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—81no—
1178C4—344no—
1179C4—682no—
1180C4—682no—
1181C4—682no—
1182C4—682no—
1183C4—1361no—
1184C2—684no—
1185C2—684no—
1186C2C4×#1058762311yescharacteristic
1187C2#1453129211yescharacteristic
1188C2#1453144811yescharacteristic
1189C2#1453177111yescharacteristic
1190C2#1453179911yescharacteristic
1191C2#1453180011yescharacteristic
1192C2#1453185111yescharacteristic
1193C2#1453215511yescharacteristic
1194C2#1453221211yescharacteristic
1195C2#1453240911yescharacteristic
1196C2#1453266811yescharacteristic
1197C2#1453273211yescharacteristic
1198C2#1453277711yescharacteristic
1199C2#1453282611yescharacteristic
1200C2#1453439511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#389C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenterC2×#389D17
hypocenterC17#14185
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. C2×#11762699C2semidirect
4. C2×#11762680C2semidirect
5. C2×#11762680C2semidirect
6. C2×C4×#63227C2semidirect
7. #14527032C2semidirect
8. #14527026C2semidirect
10. #14527022C2semidirect
11. #14527016C2semidirect
12. #14527016C2semidirect
13. #14527015C2semidirect
14. #14527005C2semidirect
15. C2×C17×#389C2semidirect
35. #11762726C4semidirect
106. C2×C4⋊C4×C17C2×C4semidirect
136. C2×#63227C2×C4semidirect
137. C2×#63227C2×C4semidirect
138. C2×#63227C2×C4semidirect
139. C2×#63227C2×C4semidirect
163. #10587502C2×C4semidirect
164. #10587502D4semidirect
459. C2×C4×C17C4×D4semidirect
508. C2×#389D17semidirect
710. C2×C4⋊C4C4×D17semidirect
765. C17#14185semidirect
1103. C2×C4#10587579semidirect

Maximal subgroups

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

subgroupindex
C22×#105875792
C2×#117627262
C2×#117626992
C2×#117626802
C2×C4×#632272
#145270322
#145270262
#145270242
#145270222
#145270162
#145270152
#145270052
C2×C17×#3892
#1418517