Finite Group Databasebeta

← #16964970

Subgroups — #16964970

Order 4352.

1694 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×#11762725C211yesmaximal, characteristic
2C2×#11762685C211yesmaximal, characteristic
3C2×#11762683C211yesmaximal, characteristic, complemented
4#14527053C211yesmaximal, characteristic, complemented
5#14527040C211yesmaximal, characteristic, complemented
6#14527039C211yesmaximal, characteristic, complemented
7#14527036C211yesmaximal, characteristic, complemented
8#14527032C211yesmaximal, characteristic, complemented
9#14527029C211yesmaximal, characteristic, complemented
10#14527028C211yesmaximal, characteristic, complemented
11#14527027C211yesmaximal, characteristic, complemented
12#14527027C211yesmaximal, characteristic, complemented
13#14527023C211yesmaximal, characteristic
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30#11762725C418yescomplemented
31#11762685—24no—
32#11762683—24no—
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×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C22×C22⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C24×D17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C22×C22⋊D17—22no—
63C22×C22⋊D17—22no—
64C22×C22⋊D17—41no—
65C22×C22⋊D17—41no—
66C22×C22⋊D17—41no—
67C22×C22⋊D17—41no—
68C22×C22⋊D17C2×C414yes—
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C22×C4×D17—41no—
77C22×C4×D17—41no—
78C22×C4×D17—41no—
79C22×C4×D17—41no—
80C22×C4×D17—41no—
81C22×C4×D17—41no—
82C22×C4×D17D414yes—
83C2×C22⋊C4×C17—22no—
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×C17—41no—
90C2×C22⋊C4×C17—41no—
91C2×C22⋊C4×C17C2×C414yescomplemented
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⋊Dic17C2×C414yescomplemented
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
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×#63227C2×C414yes—
115C2×#63227C2×C414yes—
116C2×C4⋊Dic17—22no—
117C2×C4⋊Dic17—41no—
118C2×C4⋊Dic17—41no—
119C2×C4⋊Dic17—41no—
120C2×C4⋊Dic17—41no—
121C2×C4⋊Dic17C2×C414yescomplemented
122C2×#63225—22no—
123C2×#63225—41no—
124C2×#63225—41no—
125C2×#63225—41no—
126C2×#63225—41no—
127C2×#63225—41no—
128C17×#95—22no—
129C17×#95—41no—
130C17×#95—41no—
131C17×#95—41no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—41no—
136#10587502—41no—
137#10587502—41no—
138#10587502—41no—
139#10587502—41no—
140#10587502—41no—
141#10587502—41no—
142#10587502—41no—
143#10587502—41no—
144#10587502—41no—
145#10587502C2×C414yescomplemented
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×C17C22×C412yes—
161C24×C17C2411yescharacteristic
162C23×D17—21no—
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
174C23×D17C22×C412yes—
175C23×D17C2×D412yes—
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×C17C22×C412yes—
217C22×C4×C17C22×C412yes—
218C22×C4×C17C2×D412yes—
219C2×C22⋊D17—28no—
220C2×C22⋊D17—44no—
221C2×C22⋊D17—44no—
222C2×C22⋊D17—44no—
223C2×C22⋊D17—44no—
224C2×C22⋊D17—44no—
225C2×C22⋊D17—44no—
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—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17C22×C412yes—
272C22×Dic17C22×C412yes—
273C22×Dic17C22×C412yes—
274C22×Dic17C2×D412yes—
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—
282C22⋊C4×C17—44no—
283C22⋊C4×C17—44no—
284C22⋊C4×C17—44no—
285C22⋊Dic17—44no—
286C22⋊Dic17—44no—
287C22⋊Dic17—44no—
288#63227—28no—
289#63227—44no—
290#63227—44no—
291#63227—44no—
292#63227—44no—
293C4⋊Dic17—44no—
294C4⋊Dic17—44no—
295#63225—44no—
296#63225—44no—
297#14622—171nomaximal, Sylow
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—22no—
301C23×C17—22no—
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
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×C17C23×C411yescharacteristic
334C23×C17C22×D411yescharacteristic
335C23×C17C2×#4111yescharacteristic
336C23×C17H(5,𝔽2)11yescharacteristic
337C23×C17H(5,𝔽2)11yescharacteristic
338C23×C17H(5,𝔽2)11yescharacteristic
339C23×C17H(5,𝔽2)11yescharacteristic
340C23×C17H(5,𝔽2)11yescharacteristic
341C23×C17H(5,𝔽2)11yescharacteristic
342C23×C17H(5,𝔽2)11yescharacteristic
343C23×C17H(5,𝔽2)11yescharacteristic
344C23×C17H(5,𝔽2)11yescharacteristic
345C23×C172−1+411yescharacteristic
346C23×C172−1+411yescharacteristic
347C23×C172−1+411yescharacteristic
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—22no—
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—22no—
355C22×D17—22no—
356C22×D17—22no—
357C22×D17—22no—
358C22×D17—22no—
359C22×D17—22no—
360C22×D17—22no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—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×D17C4×D414yes—
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—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×C4×C17—41no—
425C22⋊D17—416no—
426C2×Dic17—22no—
427C2×Dic17—22no—
428C2×Dic17—22no—
429C2×Dic17—22no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
437C2×Dic17—22no—
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—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×Dic17—41no—
470C2×Dic17—41no—
471C2×Dic17—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17—41no—
475C4×D17—416no—
476C2×#394—171no—
477C2×#386—171no—
478C2×#385—171no—
479#1445—171no—
480#1442—171no—
481#1442—171no—
482#1441—171no—
483#1440—171no—
484#1440D1711yescharacteristic, complemented
485#1439—171no—
486#1439—171no—
487#1439—171no—
488#1439—171no—
489#1438—171no—
490C22⋊#95—171no—
491C22×C17—42no—
492C22×C17—42no—
493C22×C17—42no—
494C22×C17—42no—
495C22×C17—42no—
496C22×C17—42no—
497C22×C17—42no—
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×C17C2×C4×D411yescharacteristic
507C22×C17#51811yescharacteristic
508C22×C17#51811yescharacteristic
509C22×C17#51811yescharacteristic
510C22×C17#52011yescharacteristic
511C22×C17#52011yescharacteristic
512C22×C17#52011yescharacteristic
513C22×C17#53411yescharacteristic
514C22×C17#53411yescharacteristic
515C22×C17#53411yescharacteristic
516C22×C17#53511yescharacteristic
517C22×C17#53611yescharacteristic
518C22×C17#53711yescharacteristic
519C22×C17#53811yescharacteristic
520C22×C17#53811yescharacteristic
521C22×C17#53811yescharacteristic
522C22×C17#53911yescharacteristic
523C22×C17#53911yescharacteristic
524C22×C17#53911yescharacteristic
525C22×C17#56011yescharacteristic
526C22×C17#56011yescharacteristic
527C22×C17#56011yescharacteristic
528C22×C17#56011yescharacteristic
529C22×C17#56011yescharacteristic
530C22×C17H(3,𝔽4)11yescharacteristic
531C22×C17#56211yescharacteristic
532C22×C17#56211yescharacteristic
533C22×C17#56211yescharacteristic
534C22×C17#56211yescharacteristic
535C22×C17#56211yescharacteristic
536C22×C17#56211yescharacteristic
537C22×C17#56211yescharacteristic
538C22×C17#56211yescharacteristic
539C22×C17#56311yescharacteristic
540C22×C17#56311yescharacteristic
541C2×D17—24no—
542C2×D17—24no—
543C2×D17—24no—
544C2×D17—42no—
545C2×D17—42no—
546C2×D17—42no—
547C2×D17—42no—
548C2×D17—42no—
549C2×D17—42no—
550C2×D17—42no—
551C2×D17—42no—
552C2×D17—42no—
553C2×D17—42no—
554C2×D17—42no—
555C2×D17—42no—
556C4×C17—42no—
557C4×C17—42no—
558C4×C17—42no—
559C4×C17—81no—
560C4×C17—81no—
561C4×C17—81no—
562Dic17—42no—
563Dic17—42no—
564Dic17—42no—
565Dic17—42no—
566Dic17—81no—
567Dic17—81no—
568Dic17—81no—
569C23×D4—171no—
570C24×C4—171no—
571C22×C4⋊C4—171no—
572C22×C4⋊C4—171no—
573C22×C4⋊C4—171no—
574C22×C4⋊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⋊C4C2×D1711yescharacteristic
584C22×C22⋊C4C2×D1711yescharacteristic
585C22×C22⋊C4C2×D1711yescharacteristic
586#394—178no—
587#386—344no—
588#385—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×#95—171no—
602C2×#95—171no—
603C2×#95C2×D1711yescharacteristic
604C2×#95C2×D1711yescharacteristic
605C2×#95C2×D1711yescharacteristic
606C2×#95C2×D1711yescharacteristic
607C2×C17—82no—
608C2×C17#232111yescharacteristic
609C2×C17#232211yescharacteristic
610C2×C17#232511yescharacteristic
611C2×C17#237611yescharacteristic
612C2×C17#237711yescharacteristic
613C2×C17#237711yescharacteristic
614C2×C17#237911yescharacteristic
615C2×C17#281211yescharacteristic
616C2×C17#281311yescharacteristic
617C2×C17#281411yescharacteristic
618C2×C17#281611yescharacteristic
619C2×C17#282411yescharacteristic
620C2×C17#282611yescharacteristic
621C2×C17#282711yescharacteristic
622C2×C17#282711yescharacteristic
623D17—44no—
624C25—171no—
625C25C22×D1711yescharacteristic
626C22×D4—174no—
627C22×D4—342no—
628C22×D4—342no—
629C22×D4—681no—
630C22×D4—681no—
631C22×D4—681no—
632C22×D4—681no—
633C23×C4—171no—
634C23×C4—171no—
635C23×C4—171no—
636C23×C4—171no—
637C23×C4—174no—
638C23×C4—171no—
639C23×C4—171no—
640C23×C4—171no—
641C23×C4—681no—
642C23×C4—681no—
643C23×C4—681no—
644C23×C4—681no—
645C23×C4—681no—
646C23×C4—681no—
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—681no—
657C2×C4⋊C4—681no—
658C2×C4⋊C4—681no—
659C2×C4⋊C4—681no—
660C2×C4⋊C4—681no—
661C2×C4⋊C4—681no—
662C2×C4⋊C4—681no—
663C2×C4⋊C4—681no—
664C2×C4⋊C4—681no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—174no—
674C2×C22⋊C4—174no—
675C2×C22⋊C4—174no—
676C2×C22⋊C4—342no—
677C2×C22⋊C4—342no—
678C2×C22⋊C4—342no—
679C2×C22⋊C4—342no—
680C2×C22⋊C4—342no—
681C2×C22⋊C4—342no—
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×C22⋊C4—681no—
693C2×C22⋊C4—681no—
694C2×C22⋊C4—681no—
695C2×C22⋊C4—681no—
696C2×C22⋊C4—681no—
697C2×C22⋊C4C4×D1714yescomplemented
698#95—22no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—174no—
703#95—342no—
704#95—342no—
705#95—342no—
706#95—681no—
707#95—681no—
708#95—681no—
709#95—681no—
710#95—681no—
711#95—681no—
712#95—681no—
713#95—681no—
714#95—681no—
715#95—681no—
716C17#1462211yescharacteristic, complemented, Sylow
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—172no—
732C24—172no—
733C24—172no—
734C24—341no—
735C24—341no—
736C24—341no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
741C24—341no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24C2×C4×D1712yes—
747C24C23×D1711yescharacteristic
748C2×D4—348no—
749C2×D4—684no—
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—172no—
795C22×C4—172no—
796C22×C4—172no—
797C22×C4—172no—
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—341no—
831C22×C4—341no—
832C22×C4—341no—
833C22×C4—341no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
837C22×C4—341no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—684no—
844C22×C4—684no—
845C22×C4—684no—
846C22×C4—684no—
847C22×C4—684no—
848C22×C4—684no—
849C22×C4—684no—
850C22×C4C2×C4×D1712yes—
851C22×C4C2×C4×D1712yes—
852C22×C4D4×D1712yes—
853C4⋊C4—684no—
854C4⋊C4—684no—
855C4⋊C4—684no—
856C4⋊C4—684no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—348no—
861C22⋊C4—684no—
862C22⋊C4—684no—
863C22⋊C4—684no—
864C22⋊C4—684no—
865C22⋊C4—684no—
866C22⋊C4—684no—
867C22⋊C4—684no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
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—174no—
904C23—342no—
905C23—342no—
906C23—342no—
907C23—342no—
908C23—342no—
909C23—342no—
910C23—342no—
911C23—342no—
912C23—342no—
913C23—342no—
914C23—342no—
915C23—342no—
916C23—342no—
917C23—342no—
918C23—342no—
919C23—342no—
920C23—342no—
921C23—342no—
922C23—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
939C23C2×D4×D1711yescharacteristic
940C23#1058769111yescharacteristic
941C23#1058769111yescharacteristic
942C23#1058769111yescharacteristic
943C23#1058769111yescharacteristic
944C23#1058769111yescharacteristic
945C23#41×D1711yescharacteristic
946C23#1058769611yescharacteristic
947C23#1058769611yescharacteristic
948C23#1058769611yescharacteristic
949C23#1058769611yescharacteristic
950C23#1058769711yescharacteristic
951C23#1058769711yescharacteristic
952C23#1058769711yescharacteristic
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—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—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—342no—
997C2×C4—342no—
998C2×C4—342no—
999C2×C4—342no—
1000C2×C4—342no—
1001C2×C4—342no—
1002C2×C4—342no—
1003C2×C4—342no—
1004C2×C4—342no—
1005C2×C4—342no—
1006C2×C4—342no—
1007C2×C4—342no—
1008C2×C4—6816no—
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—
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×C4—681no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—344no—
1062C22—344no—
1063C22—344no—
1064C22—682no—
1065C22—682no—
1066C22—682no—
1067C22—682no—
1068C22—682no—
1069C22—682no—
1070C22—682no—
1071C22—682no—
1072C22—682no—
1073C22—682no—
1074C22—682no—
1075C22—682no—
1076C22C4×D4×D1711yescharacteristic
1077C22#1176328111yescharacteristic
1078C22#1176328211yescharacteristic
1079C22#1176328311yescharacteristic
1080C22#1176328811yescharacteristic
1081C22#1176328811yescharacteristic
1082C22#1176328911yescharacteristic
1083C22#1176336711yescharacteristic
1084C22#1176336911yescharacteristic
1085C22#1176337011yescharacteristic
1086C22#1176337511yescharacteristic
1087C22#1176337911yescharacteristic
1088C22#1176338811yescharacteristic
1089C22#1176339111yescharacteristic
1090C22#1176339311yescharacteristic
1091C22#1176339811yescharacteristic
1092C22#1176340011yescharacteristic
1093C22#1176340211yescharacteristic
1094C22#1176340211yescharacteristic
1095C22#1176354711yescharacteristic
1096C22#1176354711yescharacteristic
1097C22#1176354811yescharacteristic
1098C22#1176354911yescharacteristic
1099C22#1176354911yescharacteristic
1100C22#1176355111yescharacteristic
1101C22#1176355311yescharacteristic
1102C22#1176355411yescharacteristic
1103C22#1176355411yescharacteristic
1104C22#1176355611yescharacteristic
1105C22#1176355611yescharacteristic
1106C22#1176355611yescharacteristic
1107C22#1176355611yescharacteristic
1108C22#1176355611yescharacteristic
1109C22#1176356111yescharacteristic
1110C22#1176356111yescharacteristic
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—682no—
1118C4—682no—
1119C4—682no—
1120C4—682no—
1121C4—1361no—
1122C4—1361no—
1123C4—1361no—
1124C2—82no—
1125C2—684no—
1126C2#1453144611yescharacteristic
1127C2#1453145411yescharacteristic
1128C2#1453148611yescharacteristic
1129C2#1453193011yescharacteristic
1130C2#1453194211yescharacteristic
1131C2#1453194311yescharacteristic
1132C2#1453195311yescharacteristic
1133C2#1453678011yescharacteristic
1134C2#1453679111yescharacteristic
1135C2#1453679811yescharacteristic
1136C2#1453681511yescharacteristic
1137C2#1453686211yescharacteristic
1138C2#1453688011yescharacteristic
1139C2#1453688911yescharacteristic
1140C2#1453689711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1440C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1440D17
hypocenterC17#14622
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. C2×#11762683C2semidirect
4. #14527053C2semidirect
5. #14527040C2semidirect
6. #14527039C2semidirect
7. #14527036C2semidirect
8. #14527032C2semidirect
9. #14527029C2semidirect
10. #14527028C2semidirect
11. #14527027C2semidirect
12. #14527027C2semidirect
14. #14527005C2semidirect
15. C17×#1440C2semidirect
30. #11762725C4semidirect
91. C2×C22⋊C4×C17C2×C4semidirect
100. C2×C22⋊Dic17C2×C4semidirect
121. C2×C4⋊Dic17C2×C4semidirect
145. #10587502C2×C4semidirect
484. #1440D17semidirect
697. C2×C22⋊C4C4×D17semidirect
716. C17#14622semidirect

Maximal subgroups

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

subgroupindex
C2×#117627252
C2×#117626852
C2×#117626832
#145270532
#145270402
#145270392
#145270362
#145270322
#145270292
#145270282
#145270272
#145270232
#145270052
C17×#14402
#1462217