Finite Group Databasebeta

← #16962723

Subgroups — #16962723

Order 4352.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762710C211yesmaximal, characteristic
2C2×#11762687C211yesmaximal, characteristic
3C2×#11762687C211yesmaximal, characteristic
4C2×#11762683C211yesmaximal, characteristic, complemented
5C2×#11762680C211yesmaximal, characteristic, complemented
6#14527037C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527028C211yesmaximal, characteristic, complemented
9#14527028C211yesmaximal, characteristic, complemented
10#14527026C211yesmaximal, characteristic, complemented
11#14527012C211yesmaximal, characteristic, complemented
12#14527010C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1441C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762710C418yescomplemented
34#11762687—24no—
35#11762687—24no—
36#11762683—24no—
37#11762680—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C4⋊C4×C17C2211yescharacteristic
50C22×C4⋊C4×C17C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×D68—41no—
72C22×D68—41no—
73C22×D68—41no—
74C22×D68—41no—
75C22×D68C2×C414yes—
76C22×D68D414yes—
77C22×D68Q814yes—
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—41no—
85C22×C4×D17—41no—
86C22×C4×D17—41no—
87C22×C4×D17—41no—
88C22×C4×D17—41no—
89C22×C4×D17—41no—
90C22×C4×D17—41no—
91C22×C4×D17—41no—
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17—41no—
94C2×C4⋊C4×C17—41no—
95C2×C4⋊C4×C17—41no—
96C2×C4⋊C4×C17—41no—
97C2×C4⋊C4×C17C2×C414yescomplemented
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
106C2×#63227—22no—
107C2×#63227—22no—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227—41no—
117C2×#63227—41no—
118C2×#63227—41no—
119C2×#63227—41no—
120C2×#63227—41no—
121C2×#63227—41no—
122C2×#63227—41no—
123C2×#63227—41no—
124C2×#63227C2×C414yescomplemented
125C2×#63227C2×C414yescomplemented
126C2×#63227C2×C414yescomplemented
127C2×#63227C2×C414yescomplemented
128C2×C4⋊Dic17—22no—
129C2×C4⋊Dic17—41no—
130C2×C4⋊Dic17—41no—
131C2×#63225—22no—
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—22no—
135C2×#63225—41no—
136C2×#63225—41no—
137C2×C4×Dic17—41no—
138C2×C4×Dic17—41no—
139C2×C4×Dic17C2×C414yescomplemented
140C17×#95—22no—
141C17×#95—22no—
142C17×#95—22no—
143C17×#95—41no—
144C17×#95—41no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—41no—
150#10587502—41no—
151#10587502—41no—
152#10587502—41no—
153#10587502—41no—
154#10587502—41no—
155#10587502D414yescomplemented
156C24×C17C2411yescharacteristic
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
160C23×D17—21no—
161C23×D17—21no—
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×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×D17C22×C412yes—
182C23×D17C22×C412yes—
183C23×D17C2×D412yes—
184C23×D17C2×D412yes—
185C23×D17C2×Q812yes—
186C23×D17C2×Q812yes—
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×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×C17C22×C412yes—
230C22×C4×C17C22×C412yes—
231C22×C4×C17C22×C412yes—
232C22×C4×C17C2×D412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2×Q812yes—
235C22×C4×C17#4112yes—
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×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×Dic17C22×C412yes—
273C22×Dic17C22×C412yes—
274C22×Dic17C2×D412yes—
275C22×Dic17C2×D412yes—
276C22×Dic17#4112yes—
277C22×Dic17#4112yes—
278C2×D68—44no—
279C2×D68—44no—
280C2×D68—44no—
281C2×D68—44no—
282C2×D68—44no—
283C2×D68—44no—
284C2×D68C4⋊C4116yescomplemented
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—
296C2×C4×D17—44no—
297C2×C4×D17—44no—
298C2×C4×D17—44no—
299C4⋊C4×C17—44no—
300C4⋊C4×C17—44no—
301#63227—28no—
302#63227—28no—
303#63227—44no—
304#63227—44no—
305#63227—44no—
306#63227—44no—
307#63227—44no—
308#63227—44no—
309#63227—44no—
310#63227—44no—
311C4⋊Dic17—44no—
312#63225—44no—
313#63225—44no—
314C4×Dic17—44no—
315#14438—171nomaximal, Sylow
316C23×C17C23×C411yescharacteristic
317C23×C17C22×D411yescharacteristic
318C23×C17C22×D411yescharacteristic
319C23×C17C22×Q811yescharacteristic
320C23×C17C2×#4111yescharacteristic
321C23×C17C2×#4111yescharacteristic
322C23×C17C2×#4111yescharacteristic
323C23×C17H(5,𝔽2)11yescharacteristic
324C23×C17H(5,𝔽2)11yescharacteristic
325C23×C17H(5,𝔽2)11yescharacteristic
326C23×C17H(5,𝔽2)11yescharacteristic
327C23×C17H(5,𝔽2)11yescharacteristic
328C23×C17H(5,𝔽2)11yescharacteristic
329C23×C17H(5,𝔽2)11yescharacteristic
330C23×C172−1+411yescharacteristic
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×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—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C22×D17—41no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17—41no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
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×D17C2×C4⋊C414yes—
400C22×D17C2×C4⋊C414yes—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
404C2×C4×C17—22no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
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—41no—
420C2×C4×C17—41no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×C4×C17—41no—
429C2×C4×C17—41no—
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×C17C2×C4⋊C414yes—
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—22no—
453C2×Dic17—22no—
454C2×Dic17—22no—
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—41no—
466C2×Dic17—41no—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×Dic17—41no—
470C2×Dic17—41no—
471C2×Dic17—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17—41no—
475C2×Dic17—41no—
476C2×Dic17—41no—
477C2×Dic17—41no—
478C2×Dic17—41no—
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×Dic17C4×D414yes—
492D68—416no—
493C4×D17—416no—
494C4×D17—416no—
495C2×#390—171no—
496C2×#386—171no—
497C2×#386—171no—
498C2×#385—171no—
499C2×#385—171no—
500#1441—171no—
501#1441D1711yescharacteristic, complemented
502#1439—171no—
503#1439—171no—
504#1439—171no—
505#1439—171no—
506C4⋊#95—171no—
507#1434—171no—
508C22⋊#95—171no—
509C22⋊#95—171no—
510C22×C17C22×C4⋊C411yescharacteristic
511C22×C17C2×C4×D411yescharacteristic
512C22×C17C4×#4111yescharacteristic
513C22×C17#51811yescharacteristic
514C22×C17#51811yescharacteristic
515C22×C17#51811yescharacteristic
516C22×C17#52011yescharacteristic
517C22×C17#53411yescharacteristic
518C22×C17#53411yescharacteristic
519C22×C17#53511yescharacteristic
520C22×C17#53511yescharacteristic
521C22×C17#53811yescharacteristic
522C22×C17#53811yescharacteristic
523C22×C17#54011yescharacteristic
524C22×C17#54011yescharacteristic
525C22×C17#54211yescharacteristic
526C22×C17#54211yescharacteristic
527C22×C17#54311yescharacteristic
528C22×C17#54311yescharacteristic
529C22×C17D4211yescharacteristic
530C22×C17#54611yescharacteristic
531C22×C17#54611yescharacteristic
532C22×C17#54611yescharacteristic
533C22×C17#54611yescharacteristic
534C22×C17#54711yescharacteristic
535C22×C17D4×Q811yescharacteristic
536C22×C17#55311yescharacteristic
537C22×C17#55311yescharacteristic
538C22×C17#55411yescharacteristic
539C22×C17#55411yescharacteristic
540C22×C17#55411yescharacteristic
541C22×C17#56011yescharacteristic
542C22×C17#56011yescharacteristic
543C22×C17#56211yescharacteristic
544C22×C17#56211yescharacteristic
545C2×D17—24no—
546C2×D17—24no—
547C2×D17—24no—
548C2×D17—24no—
549C2×D17—24no—
550C2×D17—24no—
551C2×D17—42no—
552C2×D17—42no—
553C2×D17—42no—
554C2×D17—42no—
555C2×D17—42no—
556C2×D17—42no—
557C2×D17—42no—
558C2×D17—42no—
559C2×D17—42no—
560C2×D17—42no—
561C2×D17—42no—
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—
575C4×C17—24no—
576C4×C17—42no—
577C4×C17—42no—
578C4×C17—42no—
579C4×C17—42no—
580C4×C17—81no—
581C4×C17—81no—
582Dic17—24no—
583Dic17—42no—
584Dic17—42no—
585Dic17—42no—
586Dic17—81no—
587Dic17—81no—
588C23×D4—171no—
589C24×C4—171no—
590C24×C4—171no—
591C22×C4⋊C4—171no—
592C22×C4⋊C4—171no—
593C22×C4⋊C4—171no—
594C22×C4⋊C4C2×D1711yescharacteristic
595C22×C4⋊C4C2×D1711yescharacteristic
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C22⋊C4—171no—
599C22×C22⋊C4—171no—
600C22×C22⋊C4—171no—
601C22×C22⋊C4—171no—
602C22×C22⋊C4—171no—
603C22×C22⋊C4—171no—
604C22×C22⋊C4—171no—
605C22×C22⋊C4—171no—
606C22×C42—171no—
607#390—178no—
608#386—344no—
609#386—344no—
610#385—344no—
611#385—344no—
612C2×#95—171no—
613C2×#95—171no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95C2×D1711yescharacteristic
624C2×#95C2×D1711yescharacteristic
625C2×#95C2×D1711yescharacteristic
626C2×#95C2×D1711yescharacteristic
627C2×#95C2×D1711yescharacteristic
628C2×C17#231511yescharacteristic
629C2×C17#232811yescharacteristic
630C2×C17#233711yescharacteristic
631C2×C17D4×C4⋊C411yescharacteristic
632C2×C17#234911yescharacteristic
633C2×C17#236411yescharacteristic
634C2×C17#237711yescharacteristic
635C2×C17#267811yescharacteristic
636C2×C17#267811yescharacteristic
637C2×C17#269211yescharacteristic
638C2×C17#269211yescharacteristic
639C2×C17#270111yescharacteristic
640C2×C17#270111yescharacteristic
641C2×C17#278011yescharacteristic
642C2×C17#278011yescharacteristic
643D17—44no—
644D17—44no—
645C25—171no—
646C25—171no—
647C22×D4—174no—
648C22×D4—174no—
649C22×D4—174no—
650C22×D4—681no—
651C22×D4—681no—
652C22×D4—681no—
653C22×D4—681no—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—171no—
657C23×C4—171no—
658C23×C4—171no—
659C23×C4—171no—
660C23×C4—342no—
661C23×C4—342no—
662C23×C4—342no—
663C23×C4—342no—
664C23×C4—342no—
665C23×C4—342no—
666C23×C4—681no—
667C23×C4—681no—
668C23×C4—681no—
669C23×C4—681no—
670C23×C4—681no—
671C23×C4—681no—
672C23×C4—681no—
673C23×C4—681no—
674C23×C4C22×D1711yescharacteristic
675C23×C4C22×D1711yescharacteristic
676C23×C4C22×D1711yescharacteristic
677C23×C4C22×D1711yescharacteristic
678C23×C4C22×D1711yescharacteristic
679C23×C4C22×D1711yescharacteristic
680C23×C4C22×D1711yescharacteristic
681C2×C4⋊C4—22no—
682C2×C4⋊C4—41no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—342no—
687C2×C4⋊C4—342no—
688C2×C4⋊C4—342no—
689C2×C4⋊C4—342no—
690C2×C4⋊C4—342no—
691C2×C4⋊C4—681no—
692C2×C4⋊C4—681no—
693C2×C4⋊C4—681no—
694C2×C4⋊C4—681no—
695C2×C4⋊C4C4×D1714yescomplemented
696C2×C22⋊C4—174no—
697C2×C22⋊C4—174no—
698C2×C22⋊C4—174no—
699C2×C22⋊C4—174no—
700C2×C22⋊C4—342no—
701C2×C22⋊C4—342no—
702C2×C22⋊C4—342no—
703C2×C22⋊C4—342no—
704C2×C22⋊C4—342no—
705C2×C22⋊C4—342no—
706C2×C22⋊C4—342no—
707C2×C22⋊C4—342no—
708C2×C22⋊C4—342no—
709C2×C22⋊C4—342no—
710C2×C22⋊C4—342no—
711C2×C22⋊C4—342no—
712C2×C22⋊C4—342no—
713C2×C22⋊C4—342no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4—681no—
718C2×C22⋊C4—681no—
719C2×C22⋊C4—681no—
720C2×C22⋊C4—681no—
721C2×C22⋊C4—681no—
722C2×C22⋊C4—681no—
723C2×C22⋊C4—681no—
724C2×C22⋊C4—681no—
725C2×C22⋊C4—681no—
726C2×C42—174no—
727C2×C42—681no—
728C2×C42—681no—
729#95—22no—
730#95—22no—
731#95—22no—
732#95—41no—
733#95—41no—
734#95—174no—
735#95—342no—
736#95—342no—
737#95—342no—
738#95—342no—
739#95—681no—
740#95—681no—
741#95—681no—
742#95—681no—
743#95—681no—
744#95—681no—
745C17#1443811yescharacteristic, complemented, Sylow
746C24—172no—
747C24—172no—
748C24—172no—
749C24—172no—
750C24—172no—
751C24—172no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24—341no—
756C24—341no—
757C24—341no—
758C24—341no—
759C24—341no—
760C24—341no—
761C24—341no—
762C24—341no—
763C24—341no—
764C24—341no—
765C24—341no—
766C24—341no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24—341no—
775C24—341no—
776C24C23×D1711yescharacteristic
777C2×D4—1716no—
778C2×D4—684no—
779C2×D4—684no—
780C2×D4—684no—
781C2×D4—684no—
782C2×D4—684no—
783C2×D4—684no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
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—172no—
827C22×C4—172no—
828C22×C4—172no—
829C22×C4—172no—
830C22×C4—172no—
831C22×C4—172no—
832C22×C4—341no—
833C22×C4—341no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
837C22×C4—341no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—341no—
844C22×C4—341no—
845C22×C4—341no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—341no—
849C22×C4—341no—
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—684no—
869C22×C4—684no—
870C22×C4—684no—
871C22×C4—684no—
872C22×C4—684no—
873C22×C4—684no—
874C22×C4—684no—
875C22×C4—684no—
876C22×C4—684no—
877C22×C4—684no—
878C22×C4—684no—
879C22×C4—684no—
880C22×C4—684no—
881C22×C4—684no—
882C22×C4C2×C4×D1712yes—
883C22×C4C2×C4×D1712yes—
884C22×C4C2×C4×D1712yes—
885C22×C4D4×D1712yes—
886C22×C4D4×D1712yes—
887C22×C4Q8×D1712yes—
888C22×C4#6325612yes—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—684no—
892C4⋊C4—684no—
893C4⋊C4—684no—
894C22⋊C4—348no—
895C22⋊C4—348no—
896C22⋊C4—684no—
897C22⋊C4—684no—
898C22⋊C4—684no—
899C22⋊C4—684no—
900C22⋊C4—684no—
901C22⋊C4—684no—
902C22⋊C4—684no—
903C22⋊C4—684no—
904C42—684no—
905C23—174no—
906C23—174no—
907C23—342no—
908C23—342no—
909C23—342no—
910C23—342no—
911C23—342no—
912C23—342no—
913C23—342no—
914C23—342no—
915C23—342no—
916C23—342no—
917C23—342no—
918C23—342no—
919C23—342no—
920C23—342no—
921C23—342no—
922C23—342no—
923C23—342no—
924C23—342no—
925C23—342no—
926C23—342no—
927C23—342no—
928C23—342no—
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—681no—
944C23—681no—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23—681no—
955C23—681no—
956C23—681no—
957C23—681no—
958C23—681no—
959C23—681no—
960C23—681no—
961C23—681no—
962C23—681no—
963C23—681no—
964C23—681no—
965C23—681no—
966C23—681no—
967C23—681no—
968C23—681no—
969C23—681no—
970C23—681no—
971C23—681no—
972C23—681no—
973C23—681no—
974C23—681no—
975C23C22×C4×D1711yescharacteristic
976C23C2×D4×D1711yescharacteristic
977C23C2×D4×D1711yescharacteristic
978C23#1058769111yescharacteristic
979C23#1058769111yescharacteristic
980C23#1058769111yescharacteristic
981C23C2×Q8×D1711yescharacteristic
982C23C2×#6325611yescharacteristic
983C23#1058769411yescharacteristic
984C23#41×D1711yescharacteristic
985C23#41×D1711yescharacteristic
986C23#1058769611yescharacteristic
987C23#1058769611yescharacteristic
988C23#1058769611yescharacteristic
989C23#1058769611yescharacteristic
990D4—6816no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
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—174no—
1040C2×C4—342no—
1041C2×C4—342no—
1042C2×C4—342no—
1043C2×C4—342no—
1044C2×C4—342no—
1045C2×C4—342no—
1046C2×C4—342no—
1047C2×C4—342no—
1048C2×C4—342no—
1049C2×C4—342no—
1050C2×C4—342no—
1051C2×C4—342no—
1052C2×C4—342no—
1053C2×C4—342no—
1054C2×C4—342no—
1055C2×C4—6816no—
1056C2×C4—6816no—
1057C2×C4—681no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4—681no—
1061C2×C4—681no—
1062C2×C4—681no—
1063C2×C4—681no—
1064C2×C4—681no—
1065C2×C4—681no—
1066C2×C4—681no—
1067C2×C4—681no—
1068C2×C4—681no—
1069C2×C4—681no—
1070C2×C4—681no—
1071C2×C4—681no—
1072C2×C4—681no—
1073C2×C4—681no—
1074C2×C4—681no—
1075C2×C4—681no—
1076C2×C4—681no—
1077C2×C4—681no—
1078C2×C4—681no—
1079C2×C4—681no—
1080C2×C4—681no—
1081C2×C4—681no—
1082C2×C4—681no—
1083C2×C4C4⋊C4×D1714yes—
1084C22—344no—
1085C22—344no—
1086C22—344no—
1087C22—344no—
1088C22—344no—
1089C22—344no—
1090C22—682no—
1091C22—682no—
1092C22—682no—
1093C22—682no—
1094C22—682no—
1095C22—682no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22—682no—
1103C22—682no—
1104C22—682no—
1105C22—682no—
1106C22—682no—
1107C22—682no—
1108C22—682no—
1109C22—682no—
1110C22—682no—
1111C22—682no—
1112C22—682no—
1113C22—682no—
1114C22C2×C4⋊C4×D1711yescharacteristic
1115C22C4×D4×D1711yescharacteristic
1116C22C4×#6325611yescharacteristic
1117C22#1176328111yescharacteristic
1118C22#1176328211yescharacteristic
1119C22#1176328311yescharacteristic
1120C22#1176329111yescharacteristic
1121C22#1176336711yescharacteristic
1122C22#1176336711yescharacteristic
1123C22#1176337411yescharacteristic
1124C22#1176337511yescharacteristic
1125C22#1176339311yescharacteristic
1126C22#1176339911yescharacteristic
1127C22#1176340911yescharacteristic
1128C22#1176341111yescharacteristic
1129C22#1176342911yescharacteristic
1130C22#1176343311yescharacteristic
1131C22#1176343411yescharacteristic
1132C22#1176343411yescharacteristic
1133C22#1176344311yescharacteristic
1134C22#1176345011yescharacteristic
1135C22#1176345011yescharacteristic
1136C22#1176345111yescharacteristic
1137C22#1176345611yescharacteristic
1138C22#1176346111yescharacteristic
1139C22#1176347411yescharacteristic
1140C22#1176351011yescharacteristic
1141C22#1176351211yescharacteristic
1142C22#1176351511yescharacteristic
1143C22#1176351511yescharacteristic
1144C22#1176352011yescharacteristic
1145C22#1176354911yescharacteristic
1146C22#1176355011yescharacteristic
1147C22#1176355511yescharacteristic
1148C22#1176355711yescharacteristic
1149C4—24no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—81no—
1156C4—344no—
1157C4—682no—
1158C4—682no—
1159C4—682no—
1160C4—1361no—
1161C4—1361no—
1162C2—684no—
1163C2—684no—
1164C2#1453139711yescharacteristic
1165C2#1453150511yescharacteristic
1166C2#1453159611yescharacteristic
1167C2#1453168511yescharacteristic
1168C2#1453169311yescharacteristic
1169C2#1453183011yescharacteristic
1170C2#1453193911yescharacteristic
1171C2#1453511411yescharacteristic
1172C2#1453511511yescharacteristic
1173C2#1453528211yescharacteristic
1174C2#1453528711yescharacteristic
1175C2#1453539011yescharacteristic
1176C2#1453539611yescharacteristic
1177C2#1453643111yescharacteristic
1178C2#1453643811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1441C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1441D17
hypocenterC17#14438
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
4. C2×#11762683C2semidirect
5. C2×#11762680C2semidirect
6. #14527037C2semidirect
7. #14527030C2semidirect
8. #14527028C2semidirect
9. #14527028C2semidirect
10. #14527026C2semidirect
11. #14527012C2semidirect
12. #14527010C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1441C2semidirect
33. #11762710C4semidirect
97. C2×C4⋊C4×C17C2×C4semidirect
124. C2×#63227C2×C4semidirect
125. C2×#63227C2×C4semidirect
126. C2×#63227C2×C4semidirect
127. C2×#63227C2×C4semidirect
139. C2×C4×Dic17C2×C4semidirect
155. #10587502D4semidirect
284. C2×D68C4⋊C4semidirect
501. #1441D17semidirect
695. C2×C4⋊C4C4×D17semidirect
745. C17#14438semidirect

Maximal subgroups

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

subgroupindex
C2×#117627102
C2×#117626872
C2×#117626832
C2×#117626802
#145270372
#145270302
#145270282
#145270262
#145270122
#145270102
#145270052
C17×#14412
#1443817