Finite Group Databasebeta

← #16962332

Subgroups — #16962332

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×#11762666C211yesmaximal, characteristic, complemented
6#14527043C211yesmaximal, characteristic, complemented
7#14527028C211yesmaximal, characteristic, complemented
8#14527026C211yesmaximal, characteristic, complemented
9#14527026C211yesmaximal, characteristic, complemented
10#14527026C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1444C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762710—24no—
33#11762687—24no—
34#11762687C418yescomplemented
35#11762683—24no—
36#11762666—24no—
37C2×#10587502C2211yescharacteristic
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
51C22×C4⋊C4×C17C2211yescharacteristic
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—41no—
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×D17C2×C414yescomplemented
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17—22no—
94C2×C4⋊C4×C17—41no—
95C2×C4⋊C4×C17—41no—
96C2×C4⋊C4×C17—41no—
97C2×C4⋊C4×C17—41no—
98C2×C4⋊C4×C17—41no—
99C2×C4⋊C4×C17—41no—
100C2×C4⋊C4×C17—41no—
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—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
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×#63227—41no—
125C2×#63227—41no—
126C2×#63227—41no—
127C2×#63227—41no—
128C2×#63227C2×C414yes—
129C2×#63227C2×C414yes—
130C2×#63227C2×C414yescomplemented
131C2×C4⋊Dic17—41no—
132C2×C4⋊Dic17—41no—
133C2×C4⋊Dic17D414yescomplemented
134C2×#63225—22no—
135C2×#63225—22no—
136C2×#63225—41no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—41no—
139C2×C4×Dic17—41no—
140C17×#95—22no—
141C17×#95—22no—
142C17×#95—41no—
143C17×#95C2×C414yescomplemented
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—41no—
151#10587502—41no—
152#10587502—41no—
153#10587502—41no—
154#10587502—41no—
155#10587502C2×C414yescomplemented
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×C17C22×C412yes—
229C22×C4×C17C22×C412yes—
230C22×C4×C17C22×C412yes—
231C22×C4×C17C2×D412yes—
232C22×C4×C17C2×D412yes—
233C22×C4×C17C2×Q812yes—
234C22×C4×C17#4112yes—
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×Dic17—21no—
273C22×Dic17C22×C412yes—
274C22×Dic17C22×C412yes—
275C22×Dic17C2×D412yes—
276C22×Dic17C2×D412yes—
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—28no—
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—
301C4⋊C4×C17—44no—
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—
311#63227—44no—
312C4⋊Dic17—44no—
313#63225—44no—
314C4×Dic17—44no—
315#14407—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×C17C2×C4⋊C414yes—
449C2×C4×C17C4×D414yes—
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×Dic17—41no—
492D68—416no—
493C4×D17—416no—
494C4×D17—416no—
495C2×#390—171no—
496C2×#386—171no—
497C2×#386—171no—
498C2×#385—171no—
499C2×#380—171no—
500#1444D1711yescharacteristic, complemented
501#1442—171no—
502#1439—171no—
503#1439—171no—
504#1439—171no—
505#1439—171no—
506#1436—171no—
507#1436—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#53411yescharacteristic
520C22×C17#53511yescharacteristic
521C22×C17#53811yescharacteristic
522C22×C17#53811yescharacteristic
523C22×C17#53811yescharacteristic
524C22×C17#53911yescharacteristic
525C22×C17#54011yescharacteristic
526C22×C17#54211yescharacteristic
527C22×C17#54311yescharacteristic
528C22×C17#54311yescharacteristic
529C22×C17D4211yescharacteristic
530C22×C17#54611yescharacteristic
531C22×C17#54611yescharacteristic
532C22×C17#54611yescharacteristic
533C22×C17#54711yescharacteristic
534C22×C17D4×Q811yescharacteristic
535C22×C17#55011yescharacteristic
536C22×C17#55311yescharacteristic
537C22×C17#55411yescharacteristic
538C22×C17#55411yescharacteristic
539C22×C17#55411yescharacteristic
540C22×C17#55511yescharacteristic
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—24no—
577C4×C17—42no—
578C4×C17—42no—
579C4×C17—81no—
580C4×C17—81no—
581C4×C17—81no—
582Dic17—42no—
583Dic17—42no—
584Dic17—42no—
585Dic17—42no—
586Dic17—42no—
587Dic17—81no—
588C23×D4—171no—
589C24×C4—171no—
590C24×C4—171no—
591C22×C4⋊C4—171no—
592C22×C4⋊C4—171no—
593C22×C4⋊C4C2×D1711yescharacteristic
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—344no—
608#386—178no—
609#386—344no—
610#385—344no—
611#380—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×#95—171no—
624C2×#95C2×D1711yescharacteristic
625C2×#95C2×D1711yescharacteristic
626C2×#95C2×D1711yescharacteristic
627C2×#95C2×D1711yescharacteristic
628C2×C17#231511yescharacteristic
629C2×C17#232111yescharacteristic
630C2×C17#233511yescharacteristic
631C2×C17D4×C4⋊C411yescharacteristic
632C2×C17#234911yescharacteristic
633C2×C17#236311yescharacteristic
634C2×C17#237711yescharacteristic
635C2×C17#266811yescharacteristic
636C2×C17#267311yescharacteristic
637C2×C17#268611yescharacteristic
638C2×C17#269211yescharacteristic
639C2×C17#270811yescharacteristic
640C2×C17#273211yescharacteristic
641C2×C17#278011yescharacteristic
642C2×C17#278411yescharacteristic
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—174no—
660C23×C4—171no—
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—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—174no—
691C2×C4⋊C4—342no—
692C2×C4⋊C4—342no—
693C2×C4⋊C4—681no—
694C2×C4⋊C4—681no—
695C2×C4⋊C4—681no—
696C2×C22⋊C4—174no—
697C2×C22⋊C4—174no—
698C2×C22⋊C4—174no—
699C2×C22⋊C4—342no—
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—342no—
727C2×C42—681no—
728C2×C42—681no—
729#95—22no—
730#95—22no—
731#95—41no—
732#95—174no—
733#95—342no—
734#95—342no—
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#95C4×D1714yescomplemented
745C17#1440711yescharacteristic, 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—172no—
826C22×C4—172no—
827C22×C4—172no—
828C22×C4—172no—
829C22×C4—172no—
830C22×C4—341no—
831C22×C4—341no—
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—348no—
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×C4C2×C4×D1712yes—
882C22×C4C2×C4×D1712yes—
883C22×C4C2×C4×D1712yes—
884C22×C4D4×D1712yes—
885C22×C4D4×D1712yes—
886C22×C4Q8×D1712yes—
887C22×C4#6325612yes—
888C22×C4#6325612yes—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—684no—
893C4⋊C4—684no—
894C22⋊C4—348no—
895C22⋊C4—684no—
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
981C23#1058769111yescharacteristic
982C23C2×Q8×D1711yescharacteristic
983C23C2×#6325611yescharacteristic
984C23C2×#6325611yescharacteristic
985C23#1058769411yescharacteristic
986C23#41×D1711yescharacteristic
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—342no—
1039C2×C4—342no—
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—6816no—
1054C2×C4—6816no—
1055C2×C4—681no—
1056C2×C4—681no—
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×C4C4⋊C4×D1714yes—
1083C2×C4#1058757914yes—
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
1115C22C2×#1058757911yescharacteristic
1116C22C4×#6325611yescharacteristic
1117C22#1176328111yescharacteristic
1118C22#1176328111yescharacteristic
1119C22#1176328111yescharacteristic
1120C22#1176329011yescharacteristic
1121C22#1176336911yescharacteristic
1122C22#1176337011yescharacteristic
1123C22#1176337011yescharacteristic
1124C22#1176337411yescharacteristic
1125C22#1176339911yescharacteristic
1126C22#1176339911yescharacteristic
1127C22#1176339911yescharacteristic
1128C22#1176340711yescharacteristic
1129C22#1176340911yescharacteristic
1130C22#1176343311yescharacteristic
1131C22#1176343411yescharacteristic
1132C22#1176343411yescharacteristic
1133C22#1176344411yescharacteristic
1134C22#1176345011yescharacteristic
1135C22#1176345011yescharacteristic
1136C22#1176345611yescharacteristic
1137C22#1176346211yescharacteristic
1138C22#1176347411yescharacteristic
1139C22#1176347711yescharacteristic
1140C22#1176351211yescharacteristic
1141C22#1176351511yescharacteristic
1142C22#1176352011yescharacteristic
1143C22#1176352011yescharacteristic
1144C22#1176352511yescharacteristic
1145C22#1176354811yescharacteristic
1146C22#1176354911yescharacteristic
1147C22#1176355511yescharacteristic
1148C22#1176355511yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—682no—
1157C4—682no—
1158C4—682no—
1159C4—682no—
1160C4—682no—
1161C4—1361no—
1162C2—684no—
1163C2—684no—
1164C2#1453139511yescharacteristic
1165C2#1453144111yescharacteristic
1166C2#1453157711yescharacteristic
1167C2#1453168411yescharacteristic
1168C2#1453169311yescharacteristic
1169C2#1453182111yescharacteristic
1170C2#1453194011yescharacteristic
1171C2#1453499311yescharacteristic
1172C2#1453505511yescharacteristic
1173C2#1453519711yescharacteristic
1174C2#1453528711yescharacteristic
1175C2#1453550911yescharacteristic
1176C2#1453580511yescharacteristic
1177C2#1453643811yescharacteristic
1178C2#1453648711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1444C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1444D17
hypocenterC17#14407
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. C2×#11762683C2semidirect
5. C2×#11762666C2semidirect
6. #14527043C2semidirect
7. #14527028C2semidirect
8. #14527026C2semidirect
9. #14527026C2semidirect
10. #14527026C2semidirect
11. #14527018C2semidirect
12. #14527015C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1444C2semidirect
34. #11762687C4semidirect
91. C22×C4×D17C2×C4semidirect
130. C2×#63227C2×C4semidirect
133. C2×C4⋊Dic17D4semidirect
143. C17×#95C2×C4semidirect
155. #10587502C2×C4semidirect
284. C2×D68C4⋊C4semidirect
500. #1444D17semidirect
744. #95C4×D17semidirect
745. C17#14407semidirect

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×#117626662
#145270432
#145270282
#145270262
#145270182
#145270152
#145270052
C17×#14442
#1440717