Finite Group Databasebeta

← #16965222

Subgroups — #16965222

Order 4352.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14527052C211yesmaximal, characteristic, complemented
2#14527046C211yesmaximal, characteristic, complemented
3#14527037C211yesmaximal, characteristic, complemented
4#14527033C211yesmaximal, characteristic, complemented
5#14527033C211yesmaximal, characteristic, complemented
6#14527029C211yesmaximal, characteristic, complemented
7#14527029C211yesmaximal, characteristic, complemented
8#14527029C211yesmaximal, characteristic, complemented
9#14527029C211yesmaximal, characteristic, complemented
10#14527025C211yesmaximal, characteristic
11#14527025C211yesmaximal, characteristic
12#14527021C211yesmaximal, characteristic, complemented
13#14527021C211yesmaximal, characteristic, complemented
14#14527018C211yesmaximal, characteristic, complemented
15C2×C17×#394C211yesmaximal, characteristic
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C22⋊Dic17C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2211yescharacteristic
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
44C23×D4×C17C2211yescharacteristic
45C22×C4⋊C4×C17C2211yescharacteristic
46C22×C22⋊C4×C17C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C22×C22⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C17×#394C418yescomplemented
51C2×C17×#95C2211yescharacteristic
52C25×C17C2311yescharacteristic
53C25×C17C2311yescharacteristic
54C22×D4×C17—41no—
55C22×D4×C17—41no—
56C22×D4×C17—41no—
57C22×D4×C17—41no—
58C22×D4×C17—41no—
59C22×D4×C17—41no—
60C22×D4×C17C2×C414yes—
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C2×C4⋊C4×C17—41no—
75C2×C4⋊C4×C17—41no—
76C2×C4⋊C4×C17C2×C414yes—
77C2×C22⋊C4×C17—41no—
78C2×C22⋊C4×C17—41no—
79C2×C22⋊C4×C17—41no—
80C2×C22⋊C4×C17—41no—
81C2×C22⋊C4×C17—41no—
82C2×C22⋊C4×C17—41no—
83C2×C22⋊C4×C17—41no—
84C2×C22⋊C4×C17—41no—
85C2×C22⋊C4×C17C2×C414yes—
86C2×C22⋊C4×C17C2×C414yes—
87C2×C22⋊C4×C17C2×C414yes—
88C2×C22⋊C4×C17C2×C414yes—
89C2×C22⋊Dic17—22no—
90C2×C22⋊Dic17—22no—
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17—22no—
93C2×C22⋊Dic17—41no—
94C2×C22⋊Dic17—41no—
95C2×C22⋊Dic17—41no—
96C2×C22⋊Dic17—41no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17—41no—
99C2×C22⋊Dic17—41no—
100C2×C22⋊Dic17—41no—
101C2×C22⋊Dic17—41no—
102C2×C22⋊Dic17—41no—
103C2×C22⋊Dic17—41no—
104C2×C22⋊Dic17—41no—
105C2×C22⋊Dic17—41no—
106C2×C22⋊Dic17—41no—
107C2×C22⋊Dic17—41no—
108C2×C22⋊Dic17—41no—
109C2×C22⋊Dic17—41no—
110C2×C22⋊Dic17—41no—
111C2×C22⋊Dic17—41no—
112C2×C22⋊Dic17—41no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—41no—
115C2×C4⋊Dic17—41no—
116C2×C4⋊Dic17—41no—
117C2×C4⋊Dic17—41no—
118C2×C4⋊Dic17—41no—
119C2×C4×Dic17—41no—
120C2×C4×Dic17—41no—
121C2×C4×Dic17—41no—
122C17×#95C2×C414yes—
123#10587502—22no—
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#10587502—41no—
139#10587502—41no—
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×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17C22×C412yes—
169C24×C17C22×C412yes—
170C24×C17C2411yescharacteristic
171C2×D4×C17—44no—
172C2×D4×C17—44no—
173C2×D4×C17—44no—
174C2×D4×C17—44no—
175C2×D4×C17—44no—
176C2×D4×C17—44no—
177C2×D4×C17—44no—
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×C17C22×C412yes—
209C22×C4×C17C22×C412yes—
210C22×C4×C17C22×C412yes—
211C22×C4×C17C22×C412yes—
212C22×C4×C17C22×C412yes—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
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×Dic17—21no—
267C22×Dic17#4112yes—
268C22×Dic17#4112yes—
269C4⋊C4×C17—44no—
270C22⋊C4×C17—44no—
271C22⋊C4×C17—44no—
272C22⋊C4×C17—44no—
273C22⋊C4×C17—44no—
274C22⋊Dic17—44no—
275C22⋊Dic17—44no—
276C22⋊Dic17—44no—
277C22⋊Dic17—44no—
278C22⋊Dic17—44no—
279C22⋊Dic17—44no—
280C22⋊Dic17—44no—
281C22⋊Dic17—44no—
282C4⋊Dic17—44no—
283C4⋊Dic17—44no—
284C4×Dic17—44no—
285#14645—171nomaximal, Sylow
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—22no—
298C23×C17—22no—
299C23×C17—22no—
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×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—41no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17—41no—
337C23×C17—41no—
338C23×C17—41no—
339C23×C17—41no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17—41no—
345C23×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17—41no—
350C23×C17—41no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17C23×C411yescharacteristic
357C23×C17C2×#4111yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17H(5,𝔽2)11yescharacteristic
360C23×C17H(5,𝔽2)11yescharacteristic
361C23×C17H(5,𝔽2)11yescharacteristic
362C23×C17H(5,𝔽2)11yescharacteristic
363C23×C17H(5,𝔽2)11yescharacteristic
364C23×C17H(5,𝔽2)11yescharacteristic
365C23×C17H(5,𝔽2)11yescharacteristic
366C23×C17H(5,𝔽2)11yescharacteristic
367C23×C17H(5,𝔽2)11yescharacteristic
368C23×C17H(5,𝔽2)11yescharacteristic
369C23×C172−1+411yescharacteristic
370C23×C172−1+411yescharacteristic
371D4×C17—416no—
372C2×C4×C17—22no—
373C2×C4×C17—22no—
374C2×C4×C17—22no—
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—22no—
385C2×C4×C17—22no—
386C2×C4×C17—22no—
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×Dic17—22no—
408C2×Dic17—22no—
409C2×Dic17—22no—
410C2×Dic17—22no—
411C2×Dic17—22no—
412C2×Dic17—22no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
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×#394D1711yescharacteristic
464#1445—171no—
465#1443—171no—
466#1441—171no—
467#1440—171no—
468#1440—171no—
469#1439—171no—
470#1439—171no—
471#1439—171no—
472#1439—171no—
473#1438—171no—
474#1438—171no—
475#1437—171no—
476#1437—171no—
477#1436—171no—
478C22×C17—42no—
479C22×C17—42no—
480C22×C17—42no—
481C22×C17—42no—
482C22×C17—42no—
483C22×C17—42no—
484C22×C17—42no—
485C22×C17—42no—
486C22×C17—42no—
487C22×C17—42no—
488C22×C17—42no—
489C22×C17—42no—
490C22×C17—42no—
491C22×C17—42no—
492C22×C17—81no—
493C22×C17—81no—
494C22×C17—81no—
495C22×C17—81no—
496C22×C17—81no—
497C22×C17—81no—
498C22×C17—81no—
499C22×C17—81no—
500C22×C17—81no—
501C22×C17—81no—
502C22×C17—81no—
503C22×C17—81no—
504C22×C17—81no—
505C22×C17—81no—
506C22×C17—81no—
507C22×C17—81no—
508C22×C17C4×#4111yescharacteristic
509C22×C17#51811yescharacteristic
510C22×C17#51811yescharacteristic
511C22×C17#51811yescharacteristic
512C22×C17#51811yescharacteristic
513C22×C17#52011yescharacteristic
514C22×C17#52011yescharacteristic
515C22×C17#53811yescharacteristic
516C22×C17#53811yescharacteristic
517C22×C17#53811yescharacteristic
518C22×C17#53811yescharacteristic
519C22×C17#53811yescharacteristic
520C22×C17#53911yescharacteristic
521C22×C17#54011yescharacteristic
522C22×C17#54011yescharacteristic
523C22×C17#54011yescharacteristic
524C22×C17#54211yescharacteristic
525C22×C17#54211yescharacteristic
526C22×C17#54211yescharacteristic
527C22×C17#56011yescharacteristic
528C22×C17#56011yescharacteristic
529C22×C17#56011yescharacteristic
530C22×C17#56011yescharacteristic
531C22×C17#56011yescharacteristic
532C22×C17#56011yescharacteristic
533C22×C17#56011yescharacteristic
534C22×C17#56011yescharacteristic
535C22×C17H(3,𝔽4)11yescharacteristic
536C22×C17#56211yescharacteristic
537C22×C17#56211yescharacteristic
538C22×C17#56211yescharacteristic
539C22×C17#56211yescharacteristic
540C22×C17#56211yescharacteristic
541C22×C17#56211yescharacteristic
542C22×C17#56311yescharacteristic
543C4×C17—42no—
544C4×C17—42no—
545C4×C17—42no—
546C4×C17—42no—
547C4×C17—42no—
548Dic17—42no—
549Dic17—42no—
550Dic17—81no—
551Dic17—81no—
552Dic17—81no—
553Dic17—81no—
554Dic17—81no—
555Dic17—81no—
556C23×D4C2×D1711yescharacteristic
557C22×C4⋊C4—171no—
558C22×C4⋊C4—171no—
559C22×C4⋊C4C2×D1711yescharacteristic
560C22×C22⋊C4—171no—
561C22×C22⋊C4—171no—
562C22×C22⋊C4—171no—
563C22×C22⋊C4—171no—
564C22×C22⋊C4—171no—
565C22×C22⋊C4—171no—
566C22×C22⋊C4—171no—
567C22×C22⋊C4—171no—
568C22×C22⋊C4C2×D1711yescharacteristic
569C22×C22⋊C4C2×D1711yescharacteristic
570C22×C22⋊C4C2×D1711yescharacteristic
571C22×C22⋊C4C2×D1711yescharacteristic
572C22×C42—171no—
573#394Dic1718yescomplemented
574C2×#95—171no—
575C2×#95—171no—
576C2×#95—171no—
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×#95C2×D1711yescharacteristic
592C2×C17—82no—
593C2×C17—82no—
594C2×C17#233311yescharacteristic
595C2×C17#233511yescharacteristic
596C2×C17#233711yescharacteristic
597C2×C17#237511yescharacteristic
598C2×C17#237611yescharacteristic
599C2×C17#237711yescharacteristic
600C2×C17#237711yescharacteristic
601C2×C17#282511yescharacteristic
602C2×C17#282611yescharacteristic
603C2×C17#282811yescharacteristic
604C2×C17#282911yescharacteristic
605C2×C17#282911yescharacteristic
606C2×C17#282911yescharacteristic
607C2×C17#283211yescharacteristic
608C2×C17#283711yescharacteristic
609C25C22×D1711yescharacteristic
610C25C22×D1711yescharacteristic
611C22×D4—41no—
612C22×D4—41no—
613C22×D4—41no—
614C22×D4—41no—
615C22×D4—41no—
616C22×D4—41no—
617C22×D4C2×Dic1714yes—
618C23×C4—171no—
619C23×C4—171no—
620C23×C4—171no—
621C23×C4—171no—
622C23×C4—171no—
623C23×C4—171no—
624C23×C4—171no—
625C23×C4—171no—
626C23×C4C22×D1711yescharacteristic
627C23×C4C22×D1711yescharacteristic
628C23×C4C22×D1711yescharacteristic
629C23×C4C22×D1711yescharacteristic
630C23×C4C22×D1711yescharacteristic
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—342no—
634C2×C4⋊C4—681no—
635C2×C4⋊C4—681no—
636C2×C4⋊C4—681no—
637C2×C4⋊C4—681no—
638C2×C4⋊C4—681no—
639C2×C4⋊C4C2×Dic1714yes—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4—41no—
643C2×C22⋊C4—41no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—342no—
649C2×C22⋊C4—342no—
650C2×C22⋊C4—342no—
651C2×C22⋊C4—342no—
652C2×C22⋊C4—681no—
653C2×C22⋊C4—681no—
654C2×C22⋊C4—681no—
655C2×C22⋊C4—681no—
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⋊C4C2×Dic1714yes—
673C2×C22⋊C4C2×Dic1714yes—
674C2×C22⋊C4C2×Dic1714yes—
675C2×C22⋊C4C2×Dic1714yes—
676C2×C42—681no—
677C2×C42—681no—
678C2×C42—681no—
679#95—342no—
680#95—681no—
681#95—681no—
682#95—681no—
683#95—681no—
684#95—681no—
685#95—681no—
686#95—681no—
687#95—681no—
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#95C2×Dic1714yes—
697C17#1464511yescharacteristic, complemented, Sylow
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
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—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24C22×Dic1712yes—
727C24C22×Dic1712yes—
728C24C23×D1711yescharacteristic
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
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—172no—
767C22×C4—172no—
768C22×C4—341no—
769C22×C4—341no—
770C22×C4—341no—
771C22×C4—341no—
772C22×C4—341no—
773C22×C4—341no—
774C22×C4—341no—
775C22×C4—341no—
776C22×C4—341no—
777C22×C4—341no—
778C22×C4—341no—
779C22×C4—341no—
780C22×C4—341no—
781C22×C4—341no—
782C22×C4—341no—
783C22×C4—341no—
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×C4C22×Dic1712yes—
823C22×C4C22×Dic1712yes—
824C22×C4C22×Dic1712yes—
825C22×C4C22×Dic1712yes—
826C22×C4C22×Dic1712yes—
827C4⋊C4—44no—
828C4⋊C4—684no—
829C4⋊C4—684no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—684no—
835C22⋊C4—684no—
836C22⋊C4—684no—
837C22⋊C4—684no—
838C22⋊C4—684no—
839C22⋊C4—684no—
840C22⋊C4—684no—
841C22⋊C4—684no—
842C42—684no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—41no—
858C23—41no—
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—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23#1058769111yescharacteristic
914C23#1058769111yescharacteristic
915C23#1058769111yescharacteristic
916C23#1058769111yescharacteristic
917C23#1058769111yescharacteristic
918C23#1058769111yescharacteristic
919C23#1058769111yescharacteristic
920C23#1058769111yescharacteristic
921C23#41×D1711yescharacteristic
922C23#41×D1711yescharacteristic
923C23#1058769611yescharacteristic
924C23#1058769611yescharacteristic
925C23#1058769711yescharacteristic
926C23#1058769711yescharacteristic
927C23C23×Dic1711yescharacteristic
928D4—416no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
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—342no—
965C2×C4—342no—
966C2×C4—342no—
967C2×C4—342no—
968C2×C4—342no—
969C2×C4—342no—
970C2×C4—681no—
971C2×C4—681no—
972C2×C4—681no—
973C2×C4—681no—
974C2×C4—681no—
975C2×C4—681no—
976C2×C4—681no—
977C2×C4—681no—
978C2×C4—681no—
979C2×C4—681no—
980C2×C4—681no—
981C2×C4—681no—
982C2×C4—681no—
983C2×C4—681no—
984C2×C4—681no—
985C2×C4—681no—
986C2×C4—681no—
987C2×C4—681no—
988C2×C4—681no—
989C2×C4—681no—
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—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—81no—
1035C22—81no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22#41×Dic1711yescharacteristic
1051C22#1176328411yescharacteristic
1052C22#1176328411yescharacteristic
1053C22#1176328411yescharacteristic
1054C22#1176328411yescharacteristic
1055C22#1176329211yescharacteristic
1056C22#1176329211yescharacteristic
1057C22#1176339111yescharacteristic
1058C22#1176339111yescharacteristic
1059C22#1176339311yescharacteristic
1060C22#1176339311yescharacteristic
1061C22#1176339511yescharacteristic
1062C22#1176340211yescharacteristic
1063C22#1176340911yescharacteristic
1064C22#1176340911yescharacteristic
1065C22#1176341111yescharacteristic
1066C22#1176342311yescharacteristic
1067C22#1176342311yescharacteristic
1068C22#1176342711yescharacteristic
1069C22#1176354711yescharacteristic
1070C22#1176354711yescharacteristic
1071C22#1176354711yescharacteristic
1072C22#1176354711yescharacteristic
1073C22#1176354811yescharacteristic
1074C22#1176354811yescharacteristic
1075C22#1176354811yescharacteristic
1076C22#1176354911yescharacteristic
1077C22#1176355211yescharacteristic
1078C22#1176355411yescharacteristic
1079C22#1176355411yescharacteristic
1080C22#1176355411yescharacteristic
1081C22#1176355411yescharacteristic
1082C22#1176355611yescharacteristic
1083C22#1176355611yescharacteristic
1084C22#1176356211yescharacteristic
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—682no—
1091C4—682no—
1092C4—1361no—
1093C4—1361no—
1094C4—1361no—
1095C4—1361no—
1096C4—1361no—
1097C4—1361no—
1098C2—82no—
1099C2—82no—
1100C2#1453155111yescharacteristic
1101C2#1453157811yescharacteristic
1102C2#1453159911yescharacteristic
1103C2#1453192511yescharacteristic
1104C2#1453193211yescharacteristic
1105C2#1453194111yescharacteristic
1106C2#1453194111yescharacteristic
1107C2#1453686911yescharacteristic
1108C2#1453688011yescharacteristic
1109C2#1453690411yescharacteristic
1110C2#1453690911yescharacteristic
1111C2#1453691111yescharacteristic
1112C2#1453691911yescharacteristic
1113C2#1453695011yescharacteristic
1114C2#1453700111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#394C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC2×#394D17
hypocenterC17#14645
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #14527052C2semidirect
2. #14527046C2semidirect
3. #14527037C2semidirect
4. #14527033C2semidirect
5. #14527033C2semidirect
6. #14527029C2semidirect
7. #14527029C2semidirect
8. #14527029C2semidirect
9. #14527029C2semidirect
12. #14527021C2semidirect
13. #14527021C2semidirect
14. #14527018C2semidirect
50. C17×#394C4semidirect
573. #394Dic17semidirect
697. C17#14645semidirect

Maximal subgroups

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

subgroupindex
#145270522
#145270462
#145270372
#145270332
#145270292
#145270252
#145270212
#145270182
C2×C17×#3942
#1464517