Finite Group Databasebeta

← #16965382

Subgroups — #16965382

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×#11762685C211yesmaximal, characteristic
2#14527045C211yesmaximal, characteristic, complemented
3#14527044C211yesmaximal, characteristic, complemented
4#14527042C211yesmaximal, characteristic, complemented
5#14527040C211yesmaximal, characteristic, complemented
6#14527031C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527029C211yesmaximal, characteristic, complemented
9#14527028C211yesmaximal, characteristic, complemented
10#14527027C211yesmaximal, characteristic, complemented
11#14527023C211yesmaximal, characteristic
12#14527023C211yesmaximal, characteristic
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28#11762685C418yescomplemented
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
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
45C22×C22⋊C4×C17C2211yescharacteristic
46C22×C22⋊C4×C17C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C25×C17C2311yescharacteristic
53C24×D17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C22×C22⋊D17—22no—
61C22×C22⋊D17—22no—
62C22×C22⋊D17—41no—
63C22×C22⋊D17—41no—
64C22×C22⋊D17—41no—
65C22×C22⋊D17—41no—
66C22×C22⋊D17C2×C414yes—
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
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×C22⋊C4×C17—41no—
82C2×C22⋊C4×C17—41no—
83C2×C22⋊C4×C17—41no—
84C2×C22⋊C4×C17—41no—
85C2×C22⋊C4×C17—41no—
86C2×C22⋊C4×C17—41no—
87C2×C22⋊C4×C17—41no—
88C2×C22⋊C4×C17—41no—
89C2×C22⋊C4×C17C2×C414yes—
90C2×C22⋊Dic17—41no—
91C2×C22⋊Dic17—41no—
92C2×C22⋊Dic17—41no—
93C2×C22⋊Dic17—41no—
94C2×C22⋊Dic17—41no—
95C2×C22⋊Dic17—41no—
96C2×C22⋊Dic17—41no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17C2×C414yes—
99C2×#63227—22no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
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×#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—
124#10587502—41no—
125#10587502—41no—
126#10587502—41no—
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#10587502C2×C414yes—
139#10587502C2×C414yes—
140C24×C17—21no—
141C24×C17—21no—
142C24×C17—21no—
143C24×C17—21no—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17—21no—
151C24×C17—21no—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17C22×C412yes—
155C24×C17C2411yescharacteristic
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×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×C17C22×C412yes—
212C22×C4×C17C22×C412yes—
213C2×C22⋊D17—28no—
214C2×C22⋊D17—44no—
215C2×C22⋊D17—44no—
216C2×C22⋊D17—44no—
217C2×C22⋊D17—44no—
218C2×C22⋊D17—44no—
219C2×C22⋊D17—44no—
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×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17C22×C412yes—
267C22×Dic17C22×C412yes—
268C22×Dic17C22×C412yes—
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—
276C22⋊C4×C17—44no—
277C22⋊C4×C17—44no—
278C22⋊C4×C17—44no—
279C22⋊Dic17—44no—
280C22⋊Dic17—44no—
281C22⋊Dic17—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×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—41no—
298C23×C17—41no—
299C23×C17—41no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17—41no—
309C23×C17—41no—
310C23×C17—41no—
311C23×C17—41no—
312C23×C17—41no—
313C23×C17—41no—
314C23×C17—41no—
315C23×C17—41no—
316C23×C17—41no—
317C23×C17—41no—
318C23×C17—41no—
319C23×C17—41no—
320C23×C17—41no—
321C23×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17C23×C411yescharacteristic
326C23×C17C2×#4111yescharacteristic
327C23×C17C2×#4111yescharacteristic
328C23×C17H(5,𝔽2)11yescharacteristic
329C23×C17H(5,𝔽2)11yescharacteristic
330C23×C17H(5,𝔽2)11yescharacteristic
331C23×C17H(5,𝔽2)11yescharacteristic
332C23×C17H(5,𝔽2)11yescharacteristic
333C23×C17H(5,𝔽2)11yescharacteristic
334C23×C17H(5,𝔽2)11yescharacteristic
335C23×C17H(5,𝔽2)11yescharacteristic
336C23×C17H(5,𝔽2)11yescharacteristic
337C23×C17H(5,𝔽2)11yescharacteristic
338C23×C172−1+411yescharacteristic
339C23×C172−1+411yescharacteristic
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—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—41no—
382C2×C4×C17—41no—
383C2×C4×C17—41no—
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—
417C22⋊D17—416no—
418C2×Dic17—22no—
419C2×Dic17—22no—
420C2×Dic17—22no—
421C2×Dic17—22no—
422C2×Dic17—22no—
423C2×Dic17—22no—
424C2×Dic17—22no—
425C2×Dic17—22no—
426C2×Dic17—22no—
427C2×Dic17—41no—
428C2×Dic17—41no—
429C2×Dic17—41no—
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—
466C2×Dic17—41no—
467C4×D17—416no—
468C2×#386—171no—
469#1443—171no—
470#1443—171no—
471#1442—171no—
472#1442—171no—
473#1440—171no—
474#1440D1711yescharacteristic, complemented
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×C17—42no—
484C22×C17—42no—
485C22×C17—42no—
486C22×C17—42no—
487C22×C17—42no—
488C22×C17—42no—
489C22×C17—42no—
490C22×C17—81no—
491C22×C17—81no—
492C22×C17—81no—
493C22×C17—81no—
494C22×C17—81no—
495C22×C17—81no—
496C22×C17—81no—
497C22×C17—81no—
498C22×C17C2×#11711yescharacteristic
499C22×C17#51811yescharacteristic
500C22×C17#51811yescharacteristic
501C22×C17#51811yescharacteristic
502C22×C17#51811yescharacteristic
503C22×C17#52011yescharacteristic
504C22×C17#52011yescharacteristic
505C22×C17#53811yescharacteristic
506C22×C17#53811yescharacteristic
507C22×C17#53811yescharacteristic
508C22×C17#53811yescharacteristic
509C22×C17#53811yescharacteristic
510C22×C17#53811yescharacteristic
511C22×C17#53811yescharacteristic
512C22×C17#53811yescharacteristic
513C22×C17#53911yescharacteristic
514C22×C17#53911yescharacteristic
515C22×C17#53911yescharacteristic
516C22×C17#53911yescharacteristic
517C22×C17#56011yescharacteristic
518C22×C17#56011yescharacteristic
519C22×C17#56011yescharacteristic
520C22×C17#56011yescharacteristic
521C22×C17#56011yescharacteristic
522C22×C17#56011yescharacteristic
523C22×C17#56011yescharacteristic
524C22×C17#56011yescharacteristic
525C22×C17H(3,𝔽4)11yescharacteristic
526C22×C17#56211yescharacteristic
527C22×C17#56211yescharacteristic
528C22×C17#56211yescharacteristic
529C22×C17#56211yescharacteristic
530C22×C17#56211yescharacteristic
531C22×C17#56211yescharacteristic
532C22×C17#56311yescharacteristic
533C2×D17—24no—
534C2×D17—24no—
535C2×D17—24no—
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—
548C4×C17—42no—
549C4×C17—42no—
550C4×C17—81no—
551C4×C17—81no—
552C4×C17—81no—
553C4×C17—81no—
554Dic17—42no—
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⋊C4C2×D1711yescharacteristic
574C22×C22⋊C4C2×D1711yescharacteristic
575C22×C22⋊C4C2×D1711yescharacteristic
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×#95—171no—
591C2×#95—171no—
592C2×#95—171no—
593C2×#95C2×D1711yescharacteristic
594C2×#95C2×D1711yescharacteristic
595C2×#95C2×D1711yescharacteristic
596C2×#95C2×D1711yescharacteristic
597C2×C17—82no—
598C2×C17#231211yescharacteristic
599C2×C17#231811yescharacteristic
600C2×C17#231811yescharacteristic
601C2×C17#237511yescharacteristic
602C2×C17#237611yescharacteristic
603C2×C17#237711yescharacteristic
604C2×C17#237711yescharacteristic
605C2×C17#282411yescharacteristic
606C2×C17#282411yescharacteristic
607C2×C17#282511yescharacteristic
608C2×C17#282511yescharacteristic
609C2×C17#282611yescharacteristic
610C2×C17#282611yescharacteristic
611C2×C17#282711yescharacteristic
612C2×C17#282711yescharacteristic
613D17—44no—
614C25—171no—
615C25C22×D1711yescharacteristic
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—171no—
626C23×C4—174no—
627C23×C4—171no—
628C23×C4—171no—
629C23×C4—171no—
630C23×C4—171no—
631C23×C4—681no—
632C23×C4—681no—
633C23×C4—681no—
634C23×C4—681no—
635C23×C4—681no—
636C23×C4—681no—
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—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—174no—
658C2×C22⋊C4—174no—
659C2×C22⋊C4—342no—
660C2×C22⋊C4—342no—
661C2×C22⋊C4—342no—
662C2×C22⋊C4—342no—
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⋊C4C4×D1714yes—
682#95—41no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—174no—
687#95—174no—
688#95—681no—
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#95—681no—
702C17#1466611yescharacteristic, complemented, Sylow
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—172no—
718C24—172no—
719C24—172no—
720C24—341no—
721C24—341no—
722C24—341no—
723C24—341no—
724C24—341no—
725C24—341no—
726C24—341no—
727C24—341no—
728C24—341no—
729C24—341no—
730C24—341no—
731C24—341no—
732C24C2×C4×D1712yes—
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—172no—
782C22×C4—172no—
783C22×C4—172no—
784C22×C4—341no—
785C22×C4—341no—
786C22×C4—341no—
787C22×C4—341no—
788C22×C4—341no—
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—341no—
830C22×C4—684no—
831C22×C4—684no—
832C22×C4—684no—
833C22×C4—684no—
834C22×C4—684no—
835C22×C4—684no—
836C22×C4—684no—
837C22×C4C2×C4×D1712yes—
838C22×C4C2×C4×D1712yes—
839C4⋊C4—684no—
840C4⋊C4—684no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
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—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—174no—
888C23—342no—
889C23—342no—
890C23—342no—
891C23—342no—
892C23—342no—
893C23—342no—
894C23—342no—
895C23—342no—
896C23—342no—
897C23—342no—
898C23—342no—
899C23—342no—
900C23—342no—
901C23—342no—
902C23—342no—
903C23—342no—
904C23—342no—
905C23—342no—
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#1058769111yescharacteristic
927C23#1058769111yescharacteristic
928C23#1058769111yescharacteristic
929C23#41×D1711yescharacteristic
930C23#41×D1711yescharacteristic
931C23#1058769611yescharacteristic
932C23#1058769611yescharacteristic
933C23#1058769611yescharacteristic
934C23#1058769611yescharacteristic
935C23#1058769711yescharacteristic
936C23#1058769711yescharacteristic
937D4—6816no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
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—342no—
981C2×C4—342no—
982C2×C4—342no—
983C2×C4—342no—
984C2×C4—342no—
985C2×C4—342no—
986C2×C4—342no—
987C2×C4—342no—
988C2×C4—342no—
989C2×C4—6816no—
990C2×C4—681no—
991C2×C4—681no—
992C2×C4—681no—
993C2×C4—681no—
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—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—344no—
1046C22—344no—
1047C22—344no—
1048C22—682no—
1049C22—682no—
1050C22—682no—
1051C22—682no—
1052C22—682no—
1053C22—682no—
1054C22—682no—
1055C22—682no—
1056C22—682no—
1057C22—682no—
1058C22—682no—
1059C22—682no—
1060C22#117×D1711yescharacteristic
1061C22#1176328111yescharacteristic
1062C22#1176328111yescharacteristic
1063C22#1176328111yescharacteristic
1064C22#1176328211yescharacteristic
1065C22#1176328811yescharacteristic
1066C22#1176328911yescharacteristic
1067C22#1176339111yescharacteristic
1068C22#1176339111yescharacteristic
1069C22#1176339311yescharacteristic
1070C22#1176339311yescharacteristic
1071C22#1176339511yescharacteristic
1072C22#1176339511yescharacteristic
1073C22#1176339511yescharacteristic
1074C22#1176339811yescharacteristic
1075C22#1176340011yescharacteristic
1076C22#1176340211yescharacteristic
1077C22#1176340211yescharacteristic
1078C22#1176340211yescharacteristic
1079C22#1176354711yescharacteristic
1080C22#1176354711yescharacteristic
1081C22#1176354711yescharacteristic
1082C22#1176354711yescharacteristic
1083C22#1176354811yescharacteristic
1084C22#1176354911yescharacteristic
1085C22#1176354911yescharacteristic
1086C22#1176355011yescharacteristic
1087C22#1176355211yescharacteristic
1088C22#1176355311yescharacteristic
1089C22#1176355311yescharacteristic
1090C22#1176355411yescharacteristic
1091C22#1176355411yescharacteristic
1092C22#1176355611yescharacteristic
1093C22#1176355611yescharacteristic
1094C22#1176356111yescharacteristic
1095C4—42no—
1096C4—42no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—682no—
1102C4—682no—
1103C4—682no—
1104C4—1361no—
1105C4—1361no—
1106C4—1361no—
1107C4—1361no—
1108C2—82no—
1109C2—684no—
1110C2#1453137811yescharacteristic
1111C2#1453141311yescharacteristic
1112C2#1453141411yescharacteristic
1113C2#1453192211yescharacteristic
1114C2#1453192611yescharacteristic
1115C2#1453193611yescharacteristic
1116C2#1453193711yescharacteristic
1117C2#1453686011yescharacteristic
1118C2#1453686011yescharacteristic
1119C2#1453686911yescharacteristic
1120C2#1453687411yescharacteristic
1121C2#1453687611yescharacteristic
1122C2#1453688011yescharacteristic
1123C2#1453688911yescharacteristic
1124C2#1453689711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1440C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1440D17
hypocenterC17#14666
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. #14527045C2semidirect
3. #14527044C2semidirect
4. #14527042C2semidirect
5. #14527040C2semidirect
6. #14527031C2semidirect
7. #14527030C2semidirect
8. #14527029C2semidirect
9. #14527028C2semidirect
10. #14527027C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1440C2semidirect
28. #11762685C4semidirect
474. #1440D17semidirect
702. C17#14666semidirect

Maximal subgroups

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

subgroupindex
C2×#117626852
#145270452
#145270442
#145270422
#145270402
#145270312
#145270302
#145270292
#145270282
#145270272
#145270232
#145270052
C17×#14402
#1466617