Finite Group Databasebeta

← #16965384

Subgroups — #16965384

Order 4352.

1602 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762687C211yesmaximal, characteristic
2#14527045C211yesmaximal, characteristic, complemented
3#14527042C211yesmaximal, characteristic, complemented
4#14527041C211yesmaximal, characteristic, complemented
5#14527032C211yesmaximal, characteristic, complemented
6#14527032C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527030C211yesmaximal, characteristic, complemented
9#14527028C211yesmaximal, characteristic, complemented
10#14527028C211yesmaximal, characteristic, complemented
11#14527024C211yesmaximal, characteristic
12#14527024C211yesmaximal, characteristic
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1443C211yesmaximal, 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
31#11762687C418yescomplemented
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×C17×#95C2211yescharacteristic
46C2×C17×#95C2211yescharacteristic
47C2×C17×#95C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C24×D17C2311yescharacteristic
53C24×D17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17C2311yescharacteristic
62C23×Dic17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C22×D68—22no—
68C22×D68—22no—
69C22×D68—41no—
70C22×D68—41no—
71C22×D68—41no—
72C22×D68—41no—
73C22×D68C2×C414yes—
74C22×C4×D17—41no—
75C22×C4×D17—41no—
76C22×C4×D17—41no—
77C22×C4×D17—41no—
78C22×C4×D17—41no—
79C22×C4×D17—41no—
80C22×C4×D17C2×C414yes—
81C2×#63227—22no—
82C2×#63227—22no—
83C2×#63227—22no—
84C2×#63227—22no—
85C2×#63227—41no—
86C2×#63227—41no—
87C2×#63227—41no—
88C2×#63227—41no—
89C2×#63227—41no—
90C2×#63227—41no—
91C2×#63227—41no—
92C2×#63227—41no—
93C2×#63227—41no—
94C2×#63227—41no—
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×#63227C2×C414yes—
112C2×#63227C2×C414yes—
113C2×#63227C2×C414yes—
114C2×C4⋊Dic17—41no—
115C2×C4⋊Dic17—41no—
116C2×C4⋊Dic17—41no—
117C2×#63225—41no—
118C2×#63225—41no—
119C2×#63225—41no—
120C17×#95—41no—
121C17×#95—41no—
122C17×#95—41no—
123C17×#95—41no—
124C17×#95—41no—
125C17×#95—41no—
126C17×#95C2×C414yes—
127#10587502—41no—
128#10587502—41no—
129#10587502—41no—
130#10587502—41no—
131#10587502—41no—
132#10587502—41no—
133#10587502—41no—
134#10587502—41no—
135#10587502—41no—
136#10587502—41no—
137#10587502—41no—
138#10587502—41no—
139#10587502C2×C414yes—
140C24×C17C2411yescharacteristic
141C23×D17—21no—
142C23×D17—21no—
143C23×D17—21no—
144C23×D17—21no—
145C23×D17—21no—
146C23×D17—21no—
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×D17C22×C412yes—
168C23×D17C22×C412yes—
169C23×D17#4112yes—
170C23×D17#4112yes—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
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×C17C22×C412yes—
218C22×C4×C17C22×C412yes—
219C22×C4×C17C22×C412yes—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
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×Dic17C22×C412yes—
261C22×Dic17C22×C412yes—
262C2×D68—28no—
263C2×D68—44no—
264C2×D68—44no—
265C2×D68—44no—
266C2×D68—44no—
267C2×D68—44no—
268C2×D68—44no—
269C2×C4×D17—44no—
270C2×C4×D17—44no—
271C2×C4×D17—44no—
272C2×C4×D17—44no—
273C2×C4×D17—44no—
274C2×C4×D17—44no—
275C2×C4×D17—44no—
276#63227—44no—
277#63227—44no—
278#63227—44no—
279#63227—44no—
280#63227—44no—
281#63227—44no—
282#63227—44no—
283#63227—44no—
284#63227—44no—
285#63227—44no—
286#63227—44no—
287C4⋊Dic17—44no—
288#63225—44no—
289#14666—171nomaximal, Sylow
290C23×C17C23×C411yescharacteristic
291C23×C17C2×#4111yescharacteristic
292C23×C17C2×#4111yescharacteristic
293C23×C17H(5,𝔽2)11yescharacteristic
294C23×C17H(5,𝔽2)11yescharacteristic
295C23×C17H(5,𝔽2)11yescharacteristic
296C23×C17H(5,𝔽2)11yescharacteristic
297C23×C17H(5,𝔽2)11yescharacteristic
298C23×C17H(5,𝔽2)11yescharacteristic
299C23×C17H(5,𝔽2)11yescharacteristic
300C23×C17H(5,𝔽2)11yescharacteristic
301C23×C17H(5,𝔽2)11yescharacteristic
302C23×C17H(5,𝔽2)11yescharacteristic
303C23×C172−1+411yescharacteristic
304C23×C172−1+411yescharacteristic
305C22×D17—22no—
306C22×D17—22no—
307C22×D17—22no—
308C22×D17—22no—
309C22×D17—22no—
310C22×D17—22no—
311C22×D17—22no—
312C22×D17—22no—
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—41no—
331C22×D17—41no—
332C22×D17—41no—
333C22×D17—41no—
334C22×D17—41no—
335C22×D17—41no—
336C22×D17—41no—
337C22×D17—41no—
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#11714yes—
375C2×C4×C17—22no—
376C2×C4×C17—22no—
377C2×C4×C17—22no—
378C2×C4×C17—22no—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—22no—
382C2×C4×C17—22no—
383C2×C4×C17—22no—
384C2×C4×C17—41no—
385C2×C4×C17—41no—
386C2×C4×C17—41no—
387C2×C4×C17—41no—
388C2×C4×C17—41no—
389C2×C4×C17—41no—
390C2×C4×C17—41no—
391C2×C4×C17—41no—
392C2×C4×C17—41no—
393C2×C4×C17—41no—
394C2×C4×C17—41no—
395C2×C4×C17—41no—
396C2×C4×C17—41no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
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×Dic17—22no—
425C2×Dic17—22no—
426C2×Dic17—22no—
427C2×Dic17—22no—
428C2×Dic17—22no—
429C2×Dic17—22no—
430C2×Dic17—41no—
431C2×Dic17—41no—
432C2×Dic17—41no—
433C2×Dic17—41no—
434C2×Dic17—41no—
435C2×Dic17—41no—
436C2×Dic17—41no—
437C2×Dic17—41no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17—41no—
441C2×Dic17—41no—
442C2×Dic17—41no—
443C2×Dic17—41no—
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—
466D68—416no—
467C4×D17—416no—
468C2×#386—171no—
469#1443—171no—
470#1443D1711yescharacteristic, complemented
471#1442—171no—
472#1442—171no—
473#1440—171no—
474#1440—171no—
475#1439—171no—
476#1439—171no—
477#1439—171no—
478#1439—171no—
479#1438—171no—
480#1438—171no—
481C22⋊#95—171no—
482C22⋊#95—171no—
483C22×C17C2×#11711yescharacteristic
484C22×C17#51811yescharacteristic
485C22×C17#51811yescharacteristic
486C22×C17#51811yescharacteristic
487C22×C17#51811yescharacteristic
488C22×C17#52011yescharacteristic
489C22×C17#52011yescharacteristic
490C22×C17#53811yescharacteristic
491C22×C17#53811yescharacteristic
492C22×C17#53811yescharacteristic
493C22×C17#53811yescharacteristic
494C22×C17#53811yescharacteristic
495C22×C17#53811yescharacteristic
496C22×C17#53811yescharacteristic
497C22×C17#53811yescharacteristic
498C22×C17#53911yescharacteristic
499C22×C17#53911yescharacteristic
500C22×C17#53911yescharacteristic
501C22×C17#53911yescharacteristic
502C22×C17#56011yescharacteristic
503C22×C17#56011yescharacteristic
504C22×C17#56011yescharacteristic
505C22×C17#56011yescharacteristic
506C22×C17#56011yescharacteristic
507C22×C17#56011yescharacteristic
508C22×C17#56011yescharacteristic
509C22×C17#56011yescharacteristic
510C22×C17H(3,𝔽4)11yescharacteristic
511C22×C17#56211yescharacteristic
512C22×C17#56211yescharacteristic
513C22×C17#56211yescharacteristic
514C22×C17#56211yescharacteristic
515C22×C17#56211yescharacteristic
516C22×C17#56211yescharacteristic
517C22×C17#56311yescharacteristic
518C2×D17—24no—
519C2×D17—24no—
520C2×D17—24no—
521C2×D17—42no—
522C2×D17—42no—
523C2×D17—42no—
524C2×D17—42no—
525C2×D17—42no—
526C2×D17—42no—
527C2×D17—42no—
528C2×D17—42no—
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—81no—
541C2×D17—81no—
542C2×D17—81no—
543C2×D17—81no—
544C2×D17—81no—
545C2×D17—81no—
546C2×D17—81no—
547C2×D17—81no—
548C4×C17—42no—
549C4×C17—42no—
550C4×C17—42no—
551C4×C17—81no—
552C4×C17—81no—
553C4×C17—81no—
554C4×C17—81no—
555Dic17—42no—
556Dic17—42no—
557Dic17—81no—
558Dic17—81no—
559Dic17—81no—
560Dic17—81no—
561C23×D4—171no—
562C24×C4—171no—
563C22×C4⋊C4—171no—
564C22×C4⋊C4—171no—
565C22×C22⋊C4—171no—
566C22×C22⋊C4—171no—
567C22×C22⋊C4—171no—
568C22×C22⋊C4—171no—
569C22×C22⋊C4—171no—
570C22×C22⋊C4—171no—
571C22×C22⋊C4—171no—
572C22×C22⋊C4—171no—
573C22×C22⋊C4—171no—
574C22×C22⋊C4—171no—
575C22×C22⋊C4—171no—
576#386—178no—
577C2×#95—171no—
578C2×#95—171no—
579C2×#95—171no—
580C2×#95—171no—
581C2×#95—171no—
582C2×#95—171no—
583C2×#95—171no—
584C2×#95—171no—
585C2×#95—171no—
586C2×#95—171no—
587C2×#95—171no—
588C2×#95—171no—
589C2×#95—171no—
590C2×#95C2×D1711yescharacteristic
591C2×#95C2×D1711yescharacteristic
592C2×#95C2×D1711yescharacteristic
593C2×#95C2×D1711yescharacteristic
594C2×#95C2×D1711yescharacteristic
595C2×#95C2×D1711yescharacteristic
596C2×#95C2×D1711yescharacteristic
597C2×C17#231211yescharacteristic
598C2×C17#231811yescharacteristic
599C2×C17#231811yescharacteristic
600C2×C17#237511yescharacteristic
601C2×C17#237611yescharacteristic
602C2×C17#237711yescharacteristic
603C2×C17#237711yescharacteristic
604C2×C17#282411yescharacteristic
605C2×C17#282411yescharacteristic
606C2×C17#282511yescharacteristic
607C2×C17#282511yescharacteristic
608C2×C17#282611yescharacteristic
609C2×C17#282611yescharacteristic
610C2×C17#282711yescharacteristic
611C2×C17#282711yescharacteristic
612D17—44no—
613D17—82no—
614C25—171no—
615C25—171no—
616C22×D4—174no—
617C22×D4—342no—
618C22×D4—342no—
619C22×D4—681no—
620C22×D4—681no—
621C22×D4—681no—
622C22×D4—681no—
623C23×C4—171no—
624C23×C4—171no—
625C23×C4—174no—
626C23×C4—171no—
627C23×C4—171no—
628C23×C4—171no—
629C23×C4—171no—
630C23×C4—681no—
631C23×C4—681no—
632C23×C4—681no—
633C23×C4—681no—
634C23×C4—681no—
635C23×C4—681no—
636C23×C4C22×D1711yescharacteristic
637C23×C4C22×D1711yescharacteristic
638C23×C4C22×D1711yescharacteristic
639C23×C4C22×D1711yescharacteristic
640C23×C4C22×D1711yescharacteristic
641C23×C4C22×D1711yescharacteristic
642C23×C4C22×D1711yescharacteristic
643C2×C4⋊C4—681no—
644C2×C4⋊C4—681no—
645C2×C4⋊C4—681no—
646C2×C4⋊C4—681no—
647C2×C4⋊C4—681no—
648C2×C4⋊C4—681no—
649C2×C22⋊C4—174no—
650C2×C22⋊C4—174no—
651C2×C22⋊C4—174no—
652C2×C22⋊C4—342no—
653C2×C22⋊C4—342no—
654C2×C22⋊C4—342no—
655C2×C22⋊C4—342no—
656C2×C22⋊C4—681no—
657C2×C22⋊C4—681no—
658C2×C22⋊C4—681no—
659C2×C22⋊C4—681no—
660C2×C22⋊C4—681no—
661C2×C22⋊C4—681no—
662C2×C22⋊C4—681no—
663C2×C22⋊C4—681no—
664C2×C22⋊C4—681no—
665C2×C22⋊C4—681no—
666C2×C22⋊C4—681no—
667C2×C22⋊C4—681no—
668C2×C22⋊C4—681no—
669C2×C22⋊C4—681no—
670C2×C22⋊C4—681no—
671C2×C22⋊C4—681no—
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—
682#95—41no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—41no—
687#95—41no—
688#95—174no—
689#95—681no—
690#95—681no—
691#95—681no—
692#95—681no—
693#95—681no—
694#95—681no—
695#95—681no—
696#95—681no—
697#95—681no—
698#95—681no—
699#95—681no—
700#95—681no—
701#95C4×D1714yes—
702C17#1466611yescharacteristic, complemented, Sylow
703C24—172no—
704C24—172no—
705C24—172no—
706C24—172no—
707C24—341no—
708C24—341no—
709C24—341no—
710C24—341no—
711C24—341no—
712C24—341no—
713C24—341no—
714C24—341no—
715C24—341no—
716C24—341no—
717C24—341no—
718C24—341no—
719C24—341no—
720C24—341no—
721C24—341no—
722C24—341no—
723C24—341no—
724C24—341no—
725C24—341no—
726C24—341no—
727C24—341no—
728C24—341no—
729C24—341no—
730C24—341no—
731C24—341no—
732C24—341no—
733C24C23×D1711yescharacteristic
734C2×D4—348no—
735C2×D4—684no—
736C2×D4—684no—
737C2×D4—684no—
738C2×D4—684no—
739C2×D4—684no—
740C2×D4—684no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
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—172no—
788C22×C4—172no—
789C22×C4—341no—
790C22×C4—341no—
791C22×C4—341no—
792C22×C4—341no—
793C22×C4—341no—
794C22×C4—341no—
795C22×C4—341no—
796C22×C4—341no—
797C22×C4—341no—
798C22×C4—341no—
799C22×C4—341no—
800C22×C4—341no—
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—684no—
830C22×C4—684no—
831C22×C4—684no—
832C22×C4—684no—
833C22×C4—684no—
834C22×C4—684no—
835C22×C4—684no—
836C22×C4C2×C4×D1712yes—
837C22×C4C2×C4×D1712yes—
838C22×C4C2×C4×D1712yes—
839C4⋊C4—684no—
840C4⋊C4—684no—
841C22⋊C4—684no—
842C22⋊C4—684no—
843C22⋊C4—684no—
844C22⋊C4—684no—
845C22⋊C4—684no—
846C22⋊C4—684no—
847C22⋊C4—684no—
848C22⋊C4—684no—
849C22⋊C4—684no—
850C22⋊C4—684no—
851C22⋊C4—684no—
852C23—174no—
853C23—342no—
854C23—342no—
855C23—342no—
856C23—342no—
857C23—342no—
858C23—342no—
859C23—342no—
860C23—342no—
861C23—342no—
862C23—342no—
863C23—342no—
864C23—342no—
865C23—342no—
866C23—342no—
867C23—342no—
868C23—342no—
869C23—342no—
870C23—342no—
871C23—342no—
872C23—342no—
873C23—342no—
874C23—342no—
875C23—342no—
876C23—342no—
877C23—342no—
878C23—681no—
879C23—681no—
880C23—681no—
881C23—681no—
882C23—681no—
883C23—681no—
884C23—681no—
885C23—681no—
886C23—681no—
887C23—681no—
888C23—681no—
889C23—681no—
890C23—681no—
891C23—681no—
892C23—681no—
893C23—681no—
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—
922C23C22×C4×D1711yescharacteristic
923C23#1058769111yescharacteristic
924C23#1058769111yescharacteristic
925C23#1058769111yescharacteristic
926C23#1058769411yescharacteristic
927C23#41×D1711yescharacteristic
928C23#41×D1711yescharacteristic
929C23#1058769611yescharacteristic
930C23#1058769611yescharacteristic
931C23#1058769611yescharacteristic
932C23#1058769611yescharacteristic
933C23#1058769611yescharacteristic
934C23#1058769611yescharacteristic
935C23#1058769611yescharacteristic
936C23#1058769711yescharacteristic
937D4—6816no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
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—342no—
988C2×C4—342no—
989C2×C4—342no—
990C2×C4—342no—
991C2×C4—342no—
992C2×C4—342no—
993C2×C4—6816no—
994C2×C4—681no—
995C2×C4—681no—
996C2×C4—681no—
997C2×C4—681no—
998C2×C4—681no—
999C2×C4—681no—
1000C2×C4—681no—
1001C2×C4—681no—
1002C2×C4—681no—
1003C2×C4—681no—
1004C2×C4—681no—
1005C2×C4—681no—
1006C2×C4—681no—
1007C2×C4—681no—
1008C2×C4—681no—
1009C2×C4—681no—
1010C2×C4—681no—
1011C2×C4—681no—
1012C2×C4—681no—
1013C2×C4—681no—
1014C2×C4—681no—
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—
1030C22—344no—
1031C22—344no—
1032C22—344no—
1033C22—682no—
1034C22—682no—
1035C22—682no—
1036C22—682no—
1037C22—682no—
1038C22—682no—
1039C22—682no—
1040C22—682no—
1041C22—682no—
1042C22—682no—
1043C22—682no—
1044C22—682no—
1045C22—682no—
1046C22—682no—
1047C22—682no—
1048C22—682no—
1049C22—682no—
1050C22—682no—
1051C22—682no—
1052C22—1361no—
1053C22—1361no—
1054C22—1361no—
1055C22—1361no—
1056C22—1361no—
1057C22—1361no—
1058C22—1361no—
1059C22—1361no—
1060C22#117×D1711yescharacteristic
1061C22#1176328111yescharacteristic
1062C22#1176328111yescharacteristic
1063C22#1176328111yescharacteristic
1064C22#1176328311yescharacteristic
1065C22#1176328911yescharacteristic
1066C22#1176329111yescharacteristic
1067C22#1176339111yescharacteristic
1068C22#1176339311yescharacteristic
1069C22#1176339511yescharacteristic
1070C22#1176339511yescharacteristic
1071C22#1176339811yescharacteristic
1072C22#1176339811yescharacteristic
1073C22#1176339811yescharacteristic
1074C22#1176339811yescharacteristic
1075C22#1176340011yescharacteristic
1076C22#1176340011yescharacteristic
1077C22#1176340511yescharacteristic
1078C22#1176340711yescharacteristic
1079C22#1176354711yescharacteristic
1080C22#1176354711yescharacteristic
1081C22#1176354911yescharacteristic
1082C22#1176354911yescharacteristic
1083C22#1176355011yescharacteristic
1084C22#1176355011yescharacteristic
1085C22#1176355011yescharacteristic
1086C22#1176355011yescharacteristic
1087C22#1176355111yescharacteristic
1088C22#1176355311yescharacteristic
1089C22#1176355511yescharacteristic
1090C22#1176355511yescharacteristic
1091C22#1176355611yescharacteristic
1092C22#1176355611yescharacteristic
1093C22#1176355711yescharacteristic
1094C22#1176356311yescharacteristic
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—682no—
1103C4—682no—
1104C4—1361no—
1105C4—1361no—
1106C4—1361no—
1107C4—1361no—
1108C2—684no—
1109C2—1362no—
1110C2#1453137811yescharacteristic
1111C2#1453141511yescharacteristic
1112C2#1453141611yescharacteristic
1113C2#1453192411yescharacteristic
1114C2#1453193111yescharacteristic
1115C2#1453193711yescharacteristic
1116C2#1453193911yescharacteristic
1117C2#1453686211yescharacteristic
1118C2#1453686511yescharacteristic
1119C2#1453687111yescharacteristic
1120C2#1453687411yescharacteristic
1121C2#1453687611yescharacteristic
1122C2#1453687811yescharacteristic
1123C2#1453689111yescharacteristic
1124C2#1453689511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1443C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1443D17
hypocenterC17#14666
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. #14527045C2semidirect
3. #14527042C2semidirect
4. #14527041C2semidirect
5. #14527032C2semidirect
6. #14527032C2semidirect
7. #14527030C2semidirect
8. #14527030C2semidirect
9. #14527028C2semidirect
10. #14527028C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1443C2semidirect
31. #11762687C4semidirect
470. #1443D17semidirect
702. C17#14666semidirect

Maximal subgroups

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

subgroupindex
C2×#117626872
#145270452
#145270422
#145270412
#145270322
#145270302
#145270282
#145270242
#145270052
C17×#14432
#1466617