Finite Group Databasebeta

← #16962616

Subgroups — #16962616

Order 4352.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762711C211yesmaximal, characteristic
2C2×#11762694C211yesmaximal, characteristic, complemented
3C2×#11762687C211yesmaximal, characteristic
4#14527051C211yesmaximal, characteristic, complemented
5#14527032C211yesmaximal, characteristic, complemented
6#14527032C211yesmaximal, characteristic, complemented
7#14527028C211yesmaximal, characteristic, complemented
8#14527028C211yesmaximal, characteristic, complemented
9#14527024C211yesmaximal, characteristic
10#14527020C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527011C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1434C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762711C418yescomplemented
33#11762694—24no—
34#11762687—24no—
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C22×C42×C17C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C24×D17C2311yescharacteristic
55C24×D17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C22×D68—22no—
70C22×D68—22no—
71C22×D68—22no—
72C22×D68—22no—
73C22×D68—41no—
74C22×D68—41no—
75C22×D68C2×C414yes—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—22no—
79C22×C4×D17—41no—
80C22×C4×D17—41no—
81C22×C4×D17—41no—
82C22×C4×D17—41no—
83C2×C42×C17—41no—
84C2×C42×C17—41no—
85C2×C42×C17C2×C414yescomplemented
86C2×#63227—22no—
87C2×#63227—22no—
88C2×#63227—22no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227—22no—
93C2×#63227—22no—
94C2×#63227—22no—
95C2×#63227—41no—
96C2×#63227—41no—
97C2×#63227—41no—
98C2×#63227—41no—
99C2×#63227—41no—
100C2×#63227—41no—
101C2×#63227—41no—
102C2×#63227—41no—
103C2×#63227—41no—
104C2×#63227—41no—
105C2×#63227—41no—
106C2×#63227—41no—
107C2×#63227—41no—
108C2×#63227—41no—
109C2×#63227—41no—
110C2×#63227—41no—
111C2×#63227—41no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227C2×C414yes—
116C2×#63227C2×C414yes—
117C2×#63227C2×C414yescomplemented
118C2×#63227C2×C414yescomplemented
119C2×C4⋊Dic17—22no—
120C2×C4⋊Dic17—22no—
121C2×C4⋊Dic17C2×C414yescomplemented
122C2×#63225—22no—
123C2×#63225—41no—
124C2×#63225—41no—
125C2×C4×Dic17—22no—
126C2×C4×Dic17—41no—
127C2×C4×Dic17—41no—
128C17×#95—22no—
129C17×#95—41no—
130C17×#95—41no—
131C17×#95—41no—
132C17×#95—41no—
133C17×#95D414yes—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—41no—
141#10587502—41no—
142#10587502—41no—
143#10587502—41no—
144#10587502—41no—
145#10587502—41no—
146C24×C17C2411yescharacteristic
147C23×D17—21no—
148C23×D17—21no—
149C23×D17—21no—
150C23×D17—21no—
151C23×D17—21no—
152C23×D17—21no—
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
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×D17C22×C412yes—
174C23×D17C22×C412yes—
175C23×D17#4112yes—
176C23×D17#4112yes—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17C22×C412yes—
220C22×C4×C17C22×C412yes—
221C22×C4×C17C22×C412yes—
222C22×C4×C17C2×D412yes—
223C22×C4×C17C2×D412yes—
224C22×C4×C17C2×D412yes—
225C22×C4×C17#4112yes—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17C22×C412yes—
265C22×Dic17C22×C412yes—
266C22×Dic17#4112yes—
267C22×Dic17#4112yes—
268C2×D68—28no—
269C2×D68—28no—
270C2×D68—44no—
271C2×D68—44no—
272C2×D68—44no—
273C2×D68—44no—
274C2×D68—44no—
275C2×C4×D17—44no—
276C2×C4×D17—44no—
277C2×C4×D17—44no—
278C2×C4×D17—44no—
279C2×C4×D17—44no—
280C2×C4×D17—44no—
281C2×C4×D17—44no—
282C42×C17—44no—
283#63227—44no—
284#63227—44no—
285#63227—44no—
286#63227—44no—
287#63227—44no—
288#63227—44no—
289#63227—44no—
290#63227—44no—
291#63227—44no—
292#63227—44no—
293#63227—44no—
294C4⋊Dic17—28no—
295#63225—44no—
296C4×Dic17—44no—
297#14431—171nomaximal, Sylow
298C23×C17C23×C411yescharacteristic
299C23×C17C22×D411yescharacteristic
300C23×C17C2×#4111yescharacteristic
301C23×C17C2×#4111yescharacteristic
302C23×C17C2×#4111yescharacteristic
303C23×C17C2×#4111yescharacteristic
304C23×C17C2×#4111yescharacteristic
305C23×C17H(5,𝔽2)11yescharacteristic
306C23×C17H(5,𝔽2)11yescharacteristic
307C23×C17H(5,𝔽2)11yescharacteristic
308C23×C17H(5,𝔽2)11yescharacteristic
309C23×C17H(5,𝔽2)11yescharacteristic
310C23×C17H(5,𝔽2)11yescharacteristic
311C23×C17H(5,𝔽2)11yescharacteristic
312C23×C172−1+411yescharacteristic
313C22×D17—22no—
314C22×D17—22no—
315C22×D17—22no—
316C22×D17—22no—
317C22×D17—22no—
318C22×D17—22no—
319C22×D17—22no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
329C22×D17—22no—
330C22×D17—22no—
331C22×D17—22no—
332C22×D17—22no—
333C22×D17—22no—
334C22×D17—22no—
335C22×D17—22no—
336C22×D17—22no—
337C22×D17—22no—
338C22×D17—41no—
339C22×D17—41no—
340C22×D17—41no—
341C22×D17—41no—
342C22×D17—41no—
343C22×D17—41no—
344C22×D17—41no—
345C22×D17—41no—
346C22×D17—41no—
347C22×D17—41no—
348C22×D17—41no—
349C22×D17—41no—
350C22×D17—41no—
351C22×D17—41no—
352C22×D17—41no—
353C22×D17—41no—
354C22×D17—41no—
355C22×D17—41no—
356C22×D17—41no—
357C22×D17—41no—
358C22×D17—41no—
359C22×D17—41no—
360C22×D17—41no—
361C22×D17—41no—
362C22×D17—41no—
363C22×D17—41no—
364C22×D17—41no—
365C22×D17—41no—
366C22×D17—41no—
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#11714yes—
383C2×C4×C17—22no—
384C2×C4×C17—22no—
385C2×C4×C17—22no—
386C2×C4×C17—22no—
387C2×C4×C17—22no—
388C2×C4×C17—22no—
389C2×C4×C17—22no—
390C2×C4×C17—22no—
391C2×C4×C17—22no—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
399C2×C4×C17—22no—
400C2×C4×C17—22no—
401C2×C4×C17—41no—
402C2×C4×C17—41no—
403C2×C4×C17—41no—
404C2×C4×C17—41no—
405C2×C4×C17—41no—
406C2×C4×C17—41no—
407C2×C4×C17—41no—
408C2×C4×C17—41no—
409C2×C4×C17—41no—
410C2×C4×C17—41no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
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×C17C4×D414yes—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
437C2×Dic17—22no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—41no—
445C2×Dic17—41no—
446C2×Dic17—41no—
447C2×Dic17—41no—
448C2×Dic17—41no—
449C2×Dic17—41no—
450C2×Dic17—41no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
461C2×Dic17—41no—
462C2×Dic17—41no—
463C2×Dic17—41no—
464C2×Dic17—41no—
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—
474D68—416no—
475C4×D17—416no—
476C2×#390—171no—
477C2×#387—171no—
478C2×#386—171no—
479#1445—171no—
480#1440—171no—
481#1440—171no—
482#1439—171no—
483#1439—171no—
484#1438—171no—
485#1437—171no—
486#1437—171no—
487#1434—171no—
488#1434D1711yescharacteristic, complemented
489C22⋊#95—171no—
490C22⋊#95—171no—
491C22×C17C2×#11711yescharacteristic
492C22×C17C2×C4×D411yescharacteristic
493C22×C17C4×#4111yescharacteristic
494C22×C17#51811yescharacteristic
495C22×C17#51811yescharacteristic
496C22×C17#51811yescharacteristic
497C22×C17#52011yescharacteristic
498C22×C17#53511yescharacteristic
499C22×C17#53511yescharacteristic
500C22×C17#53811yescharacteristic
501C22×C17#53811yescharacteristic
502C22×C17#53811yescharacteristic
503C22×C17#53811yescharacteristic
504C22×C17#53911yescharacteristic
505C22×C17#53911yescharacteristic
506C22×C17#54011yescharacteristic
507C22×C17#54011yescharacteristic
508C22×C17#54011yescharacteristic
509C22×C17#54011yescharacteristic
510C22×C17#54611yescharacteristic
511C22×C17#54611yescharacteristic
512C22×C17#54611yescharacteristic
513C22×C17#54811yescharacteristic
514C22×C17#55111yescharacteristic
515C22×C17#55111yescharacteristic
516C22×C17#55111yescharacteristic
517C22×C17#55111yescharacteristic
518C22×C17#55311yescharacteristic
519C22×C17#55311yescharacteristic
520C22×C17#55611yescharacteristic
521C22×C17#55911yescharacteristic
522C22×C17#56011yescharacteristic
523C22×C17#56011yescharacteristic
524C22×C17#56211yescharacteristic
525C22×C17#56211yescharacteristic
526C2×D17—24no—
527C2×D17—24no—
528C2×D17—24no—
529C2×D17—42no—
530C2×D17—42no—
531C2×D17—42no—
532C2×D17—42no—
533C2×D17—42no—
534C2×D17—42no—
535C2×D17—42no—
536C2×D17—42no—
537C2×D17—42no—
538C2×D17—42no—
539C2×D17—42no—
540C2×D17—42no—
541C2×D17—42no—
542C2×D17—42no—
543C2×D17—42no—
544C2×D17—42no—
545C2×D17—42no—
546C2×D17—42no—
547C2×D17—42no—
548C2×D17—81no—
549C2×D17—81no—
550C2×D17—81no—
551C2×D17—81no—
552C2×D17—81no—
553C2×D17—81no—
554C2×D17—81no—
555C2×D17—81no—
556C4×C17—24no—
557C4×C17—42no—
558C4×C17—42no—
559C4×C17—42no—
560C4×C17—42no—
561C4×C17—81no—
562C4×C17—81no—
563Dic17—42no—
564Dic17—42no—
565Dic17—42no—
566Dic17—42no—
567Dic17—81no—
568Dic17—81no—
569C23×D4—171no—
570C24×C4—171no—
571C22×C4⋊C4—171no—
572C22×C4⋊C4—171no—
573C22×C22⋊C4—171no—
574C22×C22⋊C4—171no—
575C22×C22⋊C4—171no—
576C22×C22⋊C4—171no—
577C22×C22⋊C4—171no—
578C22×C22⋊C4—171no—
579C22×C22⋊C4—171no—
580C22×C22⋊C4—171no—
581C22×C22⋊C4—171no—
582C22×C22⋊C4—171no—
583C22×C22⋊C4—171no—
584C22×C42—171no—
585C22×C42C2×D1711yescharacteristic
586#390—178no—
587#387—344no—
588#386—344no—
589C2×#95—171no—
590C2×#95—171no—
591C2×#95—171no—
592C2×#95—171no—
593C2×#95—171no—
594C2×#95—171no—
595C2×#95—171no—
596C2×#95—171no—
597C2×#95—171no—
598C2×#95—171no—
599C2×#95—171no—
600C2×#95—171no—
601C2×#95C2×D1711yescharacteristic
602C2×#95C2×D1711yescharacteristic
603C2×#95C2×D1711yescharacteristic
604C2×#95C2×D1711yescharacteristic
605C2×#95C2×D1711yescharacteristic
606C2×#95C2×D1711yescharacteristic
607C2×C17#231811yescharacteristic
608C2×C17#232811yescharacteristic
609C2×C17#233311yescharacteristic
610C2×C17#234211yescharacteristic
611C2×C17#235311yescharacteristic
612C2×C17#236711yescharacteristic
613C2×C17#237711yescharacteristic
614C2×C17#268511yescharacteristic
615C2×C17#269611yescharacteristic
616C2×C17#270311yescharacteristic
617C2×C17#271111yescharacteristic
618C2×C17#274011yescharacteristic
619C2×C17#275211yescharacteristic
620C2×C17#278611yescharacteristic
621C2×C17#279711yescharacteristic
622D17—44no—
623D17—82no—
624C25—171no—
625C25—171no—
626C22×D4—174no—
627C22×D4—342no—
628C22×D4—342no—
629C22×D4—342no—
630C22×D4—342no—
631C22×D4—681no—
632C22×D4—681no—
633C23×C4—171no—
634C23×C4—171no—
635C23×C4—171no—
636C23×C4—171no—
637C23×C4—171no—
638C23×C4—171no—
639C23×C4—342no—
640C23×C4—342no—
641C23×C4—342no—
642C23×C4—681no—
643C23×C4—681no—
644C23×C4—681no—
645C23×C4—681no—
646C23×C4C22×D1711yescharacteristic
647C23×C4C22×D1711yescharacteristic
648C23×C4C22×D1711yescharacteristic
649C23×C4C22×D1711yescharacteristic
650C23×C4C22×D1711yescharacteristic
651C23×C4C22×D1711yescharacteristic
652C23×C4C22×D1711yescharacteristic
653C2×C4⋊C4—174no—
654C2×C4⋊C4—342no—
655C2×C4⋊C4—342no—
656C2×C4⋊C4—342no—
657C2×C4⋊C4—681no—
658C2×C4⋊C4—681no—
659C2×C22⋊C4—174no—
660C2×C22⋊C4—174no—
661C2×C22⋊C4—174no—
662C2×C22⋊C4—174no—
663C2×C22⋊C4—342no—
664C2×C22⋊C4—342no—
665C2×C22⋊C4—342no—
666C2×C22⋊C4—342no—
667C2×C22⋊C4—342no—
668C2×C22⋊C4—342no—
669C2×C22⋊C4—342no—
670C2×C22⋊C4—342no—
671C2×C22⋊C4—342no—
672C2×C22⋊C4—681no—
673C2×C22⋊C4—681no—
674C2×C22⋊C4—681no—
675C2×C22⋊C4—681no—
676C2×C22⋊C4—681no—
677C2×C22⋊C4—681no—
678C2×C22⋊C4—681no—
679C2×C22⋊C4—681no—
680C2×C22⋊C4—681no—
681C2×C22⋊C4—681no—
682C2×C22⋊C4—681no—
683C2×C22⋊C4—681no—
684C2×C22⋊C4—681no—
685C2×C22⋊C4—681no—
686C2×C22⋊C4—681no—
687C2×C22⋊C4—681no—
688C2×C22⋊C4—681no—
689C2×C22⋊C4—681no—
690C2×C22⋊C4—681no—
691C2×C22⋊C4—681no—
692C2×C42—41no—
693C2×C42—41no—
694C2×C42—342no—
695C2×C42—681no—
696C2×C42—681no—
697C2×C42C4×D1714yescomplemented
698#95—22no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—342no—
704#95—342no—
705#95—342no—
706#95—342no—
707#95—342no—
708#95—342no—
709#95—681no—
710#95—681no—
711#95—681no—
712#95—681no—
713#95—681no—
714#95—681no—
715#95D6814yes—
716C17#1443111yescharacteristic, complemented, Sylow
717C24—172no—
718C24—172no—
719C24—172no—
720C24—172no—
721C24—341no—
722C24—341no—
723C24—341no—
724C24—341no—
725C24—341no—
726C24—341no—
727C24—341no—
728C24—341no—
729C24—341no—
730C24—341no—
731C24—341no—
732C24—341no—
733C24—341no—
734C24—341no—
735C24—341no—
736C24—341no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
741C24—341no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24—341no—
747C24C23×D1711yescharacteristic
748C2×D4—348no—
749C2×D4—348no—
750C2×D4—684no—
751C2×D4—684no—
752C2×D4—684no—
753C2×D4—684no—
754C2×D4—684no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
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—172no—
798C22×C4—172no—
799C22×C4—172no—
800C22×C4—172no—
801C22×C4—341no—
802C22×C4—341no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4—341no—
825C22×C4—341no—
826C22×C4—341no—
827C22×C4—341no—
828C22×C4—341no—
829C22×C4—341no—
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—684no—
840C22×C4—684no—
841C22×C4—684no—
842C22×C4—684no—
843C22×C4—684no—
844C22×C4—684no—
845C22×C4—684no—
846C22×C4C2×C4×D1712yes—
847C22×C4C2×C4×D1712yes—
848C22×C4C2×C4×D1712yes—
849C22×C4C2×D6812yes—
850C22×C4C2×D6812yes—
851C22×C4C2×D6812yes—
852C22×C4#6325212yes—
853C4⋊C4—348no—
854C4⋊C4—684no—
855C22⋊C4—684no—
856C22⋊C4—684no—
857C22⋊C4—684no—
858C22⋊C4—684no—
859C22⋊C4—684no—
860C22⋊C4—684no—
861C22⋊C4—684no—
862C22⋊C4—684no—
863C22⋊C4—684no—
864C22⋊C4—684no—
865C22⋊C4—684no—
866C42—44no—
867C42—684no—
868C23—174no—
869C23—342no—
870C23—342no—
871C23—342no—
872C23—342no—
873C23—342no—
874C23—342no—
875C23—342no—
876C23—342no—
877C23—342no—
878C23—342no—
879C23—342no—
880C23—342no—
881C23—342no—
882C23—342no—
883C23—342no—
884C23—342no—
885C23—342no—
886C23—342no—
887C23—342no—
888C23—342no—
889C23—342no—
890C23—342no—
891C23—342no—
892C23—342no—
893C23—342no—
894C23—681no—
895C23—681no—
896C23—681no—
897C23—681no—
898C23—681no—
899C23—681no—
900C23—681no—
901C23—681no—
902C23—681no—
903C23—681no—
904C23—681no—
905C23—681no—
906C23—681no—
907C23—681no—
908C23—681no—
909C23—681no—
910C23—681no—
911C23—681no—
912C23—681no—
913C23—681no—
914C23—681no—
915C23—681no—
916C23—681no—
917C23—681no—
918C23—681no—
919C23—681no—
920C23—681no—
921C23—681no—
922C23—681no—
923C23—681no—
924C23—681no—
925C23—681no—
926C23—681no—
927C23—681no—
928C23—681no—
929C23—681no—
930C23—681no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23C22×C4×D1711yescharacteristic
939C23C22×D6811yescharacteristic
940C23C2×#6325211yescharacteristic
941C23#1058769111yescharacteristic
942C23#1058769111yescharacteristic
943C23#1058769111yescharacteristic
944C23#1058769411yescharacteristic
945C23#41×D1711yescharacteristic
946C23#41×D1711yescharacteristic
947C23#41×D1711yescharacteristic
948C23#41×D1711yescharacteristic
949C23#1058769611yescharacteristic
950C23#1058769611yescharacteristic
951C23#1058769611yescharacteristic
952C23#1058769611yescharacteristic
953D4—6816no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—342no—
1003C2×C4—342no—
1004C2×C4—342no—
1005C2×C4—342no—
1006C2×C4—342no—
1007C2×C4—342no—
1008C2×C4—342no—
1009C2×C4—342no—
1010C2×C4—342no—
1011C2×C4—342no—
1012C2×C4—342no—
1013C2×C4—342no—
1014C2×C4—6816no—
1015C2×C4—681no—
1016C2×C4—681no—
1017C2×C4—681no—
1018C2×C4—681no—
1019C2×C4—681no—
1020C2×C4—681no—
1021C2×C4—681no—
1022C2×C4—681no—
1023C2×C4—681no—
1024C2×C4—681no—
1025C2×C4—681no—
1026C2×C4—681no—
1027C2×C4—681no—
1028C2×C4—681no—
1029C2×C4—681no—
1030C2×C4—681no—
1031C2×C4—681no—
1032C2×C4—681no—
1033C2×C4—681no—
1034C2×C4—681no—
1035C2×C4—681no—
1036C2×C4—681no—
1037C2×C4—681no—
1038C2×C4—681no—
1039C2×C4—681no—
1040C2×C4—681no—
1041C2×C4—681no—
1042C2×C4—681no—
1043C2×C4—681no—
1044C2×C4—681no—
1045C2×C4C4×D6814yes—
1046C22—344no—
1047C22—344no—
1048C22—344no—
1049C22—682no—
1050C22—682no—
1051C22—682no—
1052C22—682no—
1053C22—682no—
1054C22—682no—
1055C22—682no—
1056C22—682no—
1057C22—682no—
1058C22—682no—
1059C22—682no—
1060C22—682no—
1061C22—682no—
1062C22—682no—
1063C22—682no—
1064C22—682no—
1065C22—682no—
1066C22—682no—
1067C22—682no—
1068C22—1361no—
1069C22—1361no—
1070C22—1361no—
1071C22—1361no—
1072C22—1361no—
1073C22—1361no—
1074C22—1361no—
1075C22—1361no—
1076C22#117×D1711yescharacteristic
1077C22C2×C4×D6811yescharacteristic
1078C22#1176327711yescharacteristic
1079C22#1176328211yescharacteristic
1080C22#1176328311yescharacteristic
1081C22#1176328311yescharacteristic
1082C22#1176329011yescharacteristic
1083C22#1176337811yescharacteristic
1084C22#1176337811yescharacteristic
1085C22#1176339311yescharacteristic
1086C22#1176339311yescharacteristic
1087C22#1176339511yescharacteristic
1088C22#1176339511yescharacteristic
1089C22#1176340711yescharacteristic
1090C22#1176340711yescharacteristic
1091C22#1176341111yescharacteristic
1092C22#1176341111yescharacteristic
1093C22#1176341411yescharacteristic
1094C22#1176341411yescharacteristic
1095C22#1176345411yescharacteristic
1096C22#1176345411yescharacteristic
1097C22#1176345411yescharacteristic
1098C22#1176347111yescharacteristic
1099C22#1176348411yescharacteristic
1100C22#1176348411yescharacteristic
1101C22#1176348811yescharacteristic
1102C22#1176348811yescharacteristic
1103C22#1176351011yescharacteristic
1104C22#1176351011yescharacteristic
1105C22#1176353111yescharacteristic
1106C22#1176354211yescharacteristic
1107C22#1176354711yescharacteristic
1108C22#1176354711yescharacteristic
1109C22#1176355511yescharacteristic
1110C22#1176355511yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—81no—
1117C4—81no—
1118C4—682no—
1119C4—682no—
1120C4—682no—
1121C4—682no—
1122C4—1361no—
1123C4—1361no—
1124C2—684no—
1125C2—1362no—
1126C2#1453142011yescharacteristic
1127C2#1453150911yescharacteristic
1128C2#1453154611yescharacteristic
1129C2#1453163611yescharacteristic
1130C2#1453171711yescharacteristic
1131C2#1453185511yescharacteristic
1132C2#1453193811yescharacteristic
1133C2#1453517311yescharacteristic
1134C2#1453533211yescharacteristic
1135C2#1453542511yescharacteristic
1136C2#1453553911yescharacteristic
1137C2#1453588111yescharacteristic
1138C2#1453604911yescharacteristic
1139C2#1453649511yescharacteristic
1140C2#1453664411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1434D17
hypocenterC17#14431
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#11762694C2semidirect
4. #14527051C2semidirect
5. #14527032C2semidirect
6. #14527032C2semidirect
7. #14527028C2semidirect
8. #14527028C2semidirect
10. #14527020C2semidirect
11. #14527020C2semidirect
12. #14527011C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1434C2semidirect
32. #11762711C4semidirect
85. C2×C42×C17C2×C4semidirect
117. C2×#63227C2×C4semidirect
118. C2×#63227C2×C4semidirect
121. C2×C4⋊Dic17C2×C4semidirect
488. #1434D17semidirect
697. C2×C42C4×D17semidirect
716. C17#14431semidirect

Maximal subgroups

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

subgroupindex
C2×#117627112
C2×#117626942
C2×#117626872
#145270512
#145270322
#145270282
#145270242
#145270202
#145270112
#145270052
C17×#14342
#1443117