Finite Group Databasebeta

← #16964380

Subgroups — #16964380

Order 4352.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762727C211yesmaximal, characteristic
2C2×#11762701C211yesmaximal, characteristic, complemented
3C2×#11762699C211yesmaximal, characteristic, complemented
4C2×#11762687C211yesmaximal, characteristic
5C2×#11762687C211yesmaximal, characteristic
6#14527050C211yesmaximal, characteristic, complemented
7#14527041C211yesmaximal, characteristic, complemented
8#14527030C211yesmaximal, characteristic, complemented
9#14527026C211yesmaximal, characteristic, complemented
10#14527015C211yesmaximal, characteristic, complemented
11#14527005C211yesmaximal, characteristic, complemented
12#14527005C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1442C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762727C418yescomplemented
33#11762701—24no—
34#11762699—24no—
35#11762687—24no—
36#11762687—24no—
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C4⋊C4×C17C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×D68—22no—
72C22×D68—22no—
73C22×D68—22no—
74C22×D68—22no—
75C22×D68—41no—
76C22×D68—41no—
77C22×D68C2×C414yes—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—41no—
85C22×C4×D17—41no—
86C22×C4×D17—41no—
87C22×C4×D17—41no—
88C22×C4×D17—41no—
89C22×C4×D17—41no—
90C22×C4×D17—41no—
91C22×C4×D17—41no—
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17—41no—
94C2×C4⋊C4×C17—41no—
95C2×#63227—22no—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
106C2×#63227—22no—
107C2×#63227—41no—
108C2×#63227—41no—
109C2×#63227—41no—
110C2×#63227—41no—
111C2×#63227—41no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227—41no—
117C2×#63227—41no—
118C2×#63227—41no—
119C2×#63227C2×C414yescomplemented
120C2×#63227C2×C414yescomplemented
121C2×#63227C2×C414yescomplemented
122C2×#63227C2×C414yescomplemented
123C2×#63227D414yes—
124C2×#63227D414yes—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17—41no—
127C2×C4⋊Dic17—41no—
128C2×#63225—41no—
129C2×#63225—41no—
130C2×#63225C2×C414yescomplemented
131C2×C4×Dic17—22no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—41no—
134C17×#95—22no—
135C17×#95—22no—
136C17×#95—22no—
137C17×#95—41no—
138C17×#95—41no—
139C17×#95C2×C414yescomplemented
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—41no—
148#10587502—41no—
149#10587502—41no—
150#10587502—41no—
151#10587502—41no—
152C24×C17C2411yescharacteristic
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
160C23×D17—21no—
161C23×D17—21no—
162C23×D17—21no—
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
177C23×D17C22×C412yes—
178C23×D17C22×C412yes—
179C23×D17C2×D412yes—
180C23×D17C2×D412yes—
181C23×D17#4112yes—
182C23×D17#4112yes—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17C22×C412yes—
227C22×C4×C17C22×C412yes—
228C22×C4×C17C22×C412yes—
229C22×C4×C17C2×D412yes—
230C22×C4×C17C2×D412yes—
231C22×C4×C17#4112yes—
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×Dic17C22×C412yes—
270C22×Dic17C22×C412yes—
271C22×Dic17C2×D412yes—
272C22×Dic17C2×D412yes—
273C22×Dic17#4112yes—
274C2×D68—28no—
275C2×D68—28no—
276C2×D68—44no—
277C2×D68—44no—
278C2×D68—44no—
279C2×D68—44no—
280C2×D68—44no—
281C2×C4×D17—44no—
282C2×C4×D17—44no—
283C2×C4×D17—44no—
284C2×C4×D17—44no—
285C2×C4×D17—44no—
286C2×C4×D17—44no—
287C2×C4×D17—44no—
288C2×C4×D17—44no—
289C2×C4×D17—44no—
290C2×C4×D17—44no—
291C2×C4×D17—44no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C2×C4×D17—44no—
295C4⋊C4×C17—44no—
296#63227—28no—
297#63227—28no—
298#63227—44no—
299#63227—44no—
300#63227—44no—
301#63227—44no—
302#63227—44no—
303#63227—44no—
304#63227—44no—
305#63227—44no—
306C4⋊Dic17—44no—
307#63225—44no—
308C4×Dic17—44no—
309#14571—171nomaximal, Sylow
310C23×C17C23×C411yescharacteristic
311C23×C17C22×D411yescharacteristic
312C23×C17C22×D411yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17C2×#4111yescharacteristic
315C23×C17C2×#4111yescharacteristic
316C23×C17C2×#4111yescharacteristic
317C23×C17H(5,𝔽2)11yescharacteristic
318C23×C17H(5,𝔽2)11yescharacteristic
319C23×C17H(5,𝔽2)11yescharacteristic
320C23×C17H(5,𝔽2)11yescharacteristic
321C23×C17H(5,𝔽2)11yescharacteristic
322C23×C17H(5,𝔽2)11yescharacteristic
323C23×C172−1+411yescharacteristic
324C23×C172−1+411yescharacteristic
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
329C22×D17—22no—
330C22×D17—22no—
331C22×D17—22no—
332C22×D17—22no—
333C22×D17—22no—
334C22×D17—22no—
335C22×D17—22no—
336C22×D17—22no—
337C22×D17—22no—
338C22×D17—22no—
339C22×D17—22no—
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—22no—
359C22×D17—22no—
360C22×D17—22no—
361C22×D17—41no—
362C22×D17—41no—
363C22×D17—41no—
364C22×D17—41no—
365C22×D17—41no—
366C22×D17—41no—
367C22×D17—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C22×D17—41no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17—41no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17—41no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17—41no—
382C22×D17—41no—
383C22×D17—41no—
384C22×D17—41no—
385C22×D17—41no—
386C22×D17—41no—
387C22×D17—41no—
388C22×D17—41no—
389C22×D17—41no—
390C22×D17—41no—
391C22×D17—41no—
392C22×D17—41no—
393C22×D17C4×D414yes—
394C22×D17C4×D414yes—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
399C2×C4×C17—22no—
400C2×C4×C17—22no—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
404C2×C4×C17—22no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
412C2×C4×C17—22no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
420C2×C4×C17—41no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×C4×C17—41no—
429C2×C4×C17—41no—
430C2×C4×C17—41no—
431C2×C4×C17—41no—
432C2×C4×C17—41no—
433C2×C4×C17—41no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—22no—
448C2×Dic17—22no—
449C2×Dic17—22no—
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—22no—
453C2×Dic17—22no—
454C2×Dic17—22no—
455C2×Dic17—22no—
456C2×Dic17—22no—
457C2×Dic17—22no—
458C2×Dic17—22no—
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—
475C2×Dic17—41no—
476C2×Dic17—41no—
477C2×Dic17—41no—
478C2×Dic17—41no—
479C2×Dic17—41no—
480C2×Dic17—41no—
481C2×Dic17—41no—
482C2×Dic17—41no—
483C2×Dic17—41no—
484C2×Dic17—41no—
485C2×Dic17—41no—
486D68—416no—
487C4×D17—416no—
488C4×D17—416no—
489C2×#394—171no—
490C2×#388—171no—
491C2×#388—171no—
492C2×#386—171no—
493C2×#386—171no—
494#1445—171no—
495#1442—171no—
496#1442D1711yescharacteristic, complemented
497#1439—171no—
498#1439—171no—
499#1436—171no—
500C22⋊#95—171no—
501C22⋊#95—171no—
502C22⋊#95—171no—
503C22⋊#95—171no—
504C22×C17C2×C4×D411yescharacteristic
505C22×C17C2×C4×D411yescharacteristic
506C22×C17C4×#4111yescharacteristic
507C22×C17#51811yescharacteristic
508C22×C17#51811yescharacteristic
509C22×C17#52011yescharacteristic
510C22×C17#52011yescharacteristic
511C22×C17#53411yescharacteristic
512C22×C17#53411yescharacteristic
513C22×C17#53711yescharacteristic
514C22×C17#53711yescharacteristic
515C22×C17#53811yescharacteristic
516C22×C17#53811yescharacteristic
517C22×C17#53811yescharacteristic
518C22×C17#53811yescharacteristic
519C22×C17#53911yescharacteristic
520C22×C17#53911yescharacteristic
521C22×C17#54011yescharacteristic
522C22×C17#54011yescharacteristic
523C22×C17D4211yescharacteristic
524C22×C17#54611yescharacteristic
525C22×C17#54611yescharacteristic
526C22×C17#54611yescharacteristic
527C22×C17#54611yescharacteristic
528C22×C17#54711yescharacteristic
529C22×C17#54711yescharacteristic
530C22×C17#55111yescharacteristic
531C22×C17#55111yescharacteristic
532C22×C17#55111yescharacteristic
533C22×C17#55211yescharacteristic
534C22×C17#55211yescharacteristic
535C22×C17H(3,𝔽4)11yescharacteristic
536C22×C17#56211yescharacteristic
537C22×C17#56211yescharacteristic
538C22×C17#56311yescharacteristic
539C2×D17—24no—
540C2×D17—24no—
541C2×D17—24no—
542C2×D17—24no—
543C2×D17—24no—
544C2×D17—24no—
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—
556C2×D17—42no—
557C2×D17—42no—
558C2×D17—42no—
559C2×D17—42no—
560C2×D17—42no—
561C2×D17—42no—
562C2×D17—42no—
563C2×D17—42no—
564C2×D17—42no—
565C2×D17—42no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—42no—
569C4×C17—42no—
570C4×C17—42no—
571C4×C17—42no—
572C4×C17—42no—
573C4×C17—42no—
574C4×C17—42no—
575C4×C17—81no—
576Dic17—42no—
577Dic17—42no—
578Dic17—42no—
579Dic17—42no—
580Dic17—42no—
581Dic17—81no—
582C23×D4—171no—
583C24×C4—171no—
584C24×C4—171no—
585C22×C4⋊C4—171no—
586C22×C4⋊C4—171no—
587C22×C4⋊C4C2×D1711yescharacteristic
588C22×C22⋊C4—171no—
589C22×C22⋊C4—171no—
590C22×C22⋊C4—171no—
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C22⋊C4—171no—
595C22×C22⋊C4—171no—
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C42—171no—
599#394—178no—
600#388—344no—
601#388—344no—
602#386—344no—
603#386—344no—
604C2×#95—171no—
605C2×#95—171no—
606C2×#95—171no—
607C2×#95—171no—
608C2×#95—171no—
609C2×#95—171no—
610C2×#95—171no—
611C2×#95—171no—
612C2×#95—171no—
613C2×#95—171no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95C2×D1711yescharacteristic
617C2×#95C2×D1711yescharacteristic
618C2×#95C2×D1711yescharacteristic
619C2×#95C2×D1711yescharacteristic
620C2×#95C2×D1711yescharacteristic
621C2×#95C2×D1711yescharacteristic
622C2×C17#232511yescharacteristic
623C2×C17#232511yescharacteristic
624C2×C17#233311yescharacteristic
625C2×C17#235811yescharacteristic
626C2×C17#235911yescharacteristic
627C2×C17#235911yescharacteristic
628C2×C17#237911yescharacteristic
629C2×C17#267111yescharacteristic
630C2×C17#267111yescharacteristic
631C2×C17#268411yescharacteristic
632C2×C17#268411yescharacteristic
633C2×C17#269511yescharacteristic
634C2×C17#269511yescharacteristic
635C2×C17#274311yescharacteristic
636C2×C17#274311yescharacteristic
637D17—44no—
638D17—44no—
639C25—171no—
640C25—171no—
641C22×D4—174no—
642C22×D4—342no—
643C22×D4—342no—
644C22×D4—342no—
645C22×D4—342no—
646C22×D4—681no—
647C22×D4—681no—
648C23×C4—171no—
649C23×C4—171no—
650C23×C4—171no—
651C23×C4—171no—
652C23×C4—171no—
653C23×C4—171no—
654C23×C4—342no—
655C23×C4—342no—
656C23×C4—342no—
657C23×C4—342no—
658C23×C4—342no—
659C23×C4—342no—
660C23×C4—681no—
661C23×C4—681no—
662C23×C4—681no—
663C23×C4—681no—
664C23×C4—681no—
665C23×C4—681no—
666C23×C4—681no—
667C23×C4—681no—
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C23×C4C22×D1711yescharacteristic
674C23×C4C22×D1711yescharacteristic
675C2×C4⋊C4—22no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—174no—
679C2×C4⋊C4—342no—
680C2×C4⋊C4—681no—
681C2×C4⋊C4—681no—
682C2×C4⋊C4—681no—
683C2×C4⋊C4—681no—
684C2×C22⋊C4—174no—
685C2×C22⋊C4—174no—
686C2×C22⋊C4—174no—
687C2×C22⋊C4—174no—
688C2×C22⋊C4—174no—
689C2×C22⋊C4—174no—
690C2×C22⋊C4—342no—
691C2×C22⋊C4—342no—
692C2×C22⋊C4—342no—
693C2×C22⋊C4—342no—
694C2×C22⋊C4—342no—
695C2×C22⋊C4—342no—
696C2×C22⋊C4—342no—
697C2×C22⋊C4—342no—
698C2×C22⋊C4—342no—
699C2×C22⋊C4—342no—
700C2×C22⋊C4—342no—
701C2×C22⋊C4—342no—
702C2×C22⋊C4—681no—
703C2×C22⋊C4—681no—
704C2×C22⋊C4—681no—
705C2×C22⋊C4—681no—
706C2×C22⋊C4—681no—
707C2×C22⋊C4—681no—
708C2×C22⋊C4—681no—
709C2×C22⋊C4—681no—
710C2×C22⋊C4—681no—
711C2×C22⋊C4—681no—
712C2×C22⋊C4—681no—
713C2×C22⋊C4—681no—
714C2×C42—342no—
715C2×C42—342no—
716C2×C42—681no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—41no—
721#95—41no—
722#95—342no—
723#95—342no—
724#95—342no—
725#95—342no—
726#95—342no—
727#95—342no—
728#95—342no—
729#95—681no—
730#95—681no—
731#95—681no—
732#95—681no—
733#95—681no—
734#95C4×D1714yescomplemented
735C17#1457111yescharacteristic, complemented, Sylow
736C24—172no—
737C24—172no—
738C24—172no—
739C24—172no—
740C24—172no—
741C24—172no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24—341no—
747C24—341no—
748C24—341no—
749C24—341no—
750C24—341no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24—341no—
756C24—341no—
757C24—341no—
758C24—341no—
759C24—341no—
760C24—341no—
761C24—341no—
762C24—341no—
763C24—341no—
764C24—341no—
765C24—341no—
766C24C23×D1711yescharacteristic
767C2×D4—348no—
768C2×D4—348no—
769C2×D4—684no—
770C2×D4—684no—
771C2×D4—684no—
772C2×D4—684no—
773C2×D4—684no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—172no—
818C22×C4—172no—
819C22×C4—172no—
820C22×C4—172no—
821C22×C4—172no—
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—341no—
844C22×C4—341no—
845C22×C4—341no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—341no—
849C22×C4—341no—
850C22×C4—341no—
851C22×C4—341no—
852C22×C4—341no—
853C22×C4—341no—
854C22×C4—341no—
855C22×C4—341no—
856C22×C4—341no—
857C22×C4—341no—
858C22×C4—341no—
859C22×C4—684no—
860C22×C4—684no—
861C22×C4—684no—
862C22×C4—684no—
863C22×C4—684no—
864C22×C4—684no—
865C22×C4—684no—
866C22×C4—684no—
867C22×C4—684no—
868C22×C4—684no—
869C22×C4—684no—
870C22×C4—684no—
871C22×C4—684no—
872C22×C4—684no—
873C22×C4C2×C4×D1712yes—
874C22×C4C2×C4×D1712yes—
875C22×C4C2×C4×D1712yes—
876C22×C4D4×D1712yes—
877C22×C4D4×D1712yes—
878C22×C4#6325612yes—
879C4⋊C4—44no—
880C4⋊C4—684no—
881C4⋊C4—684no—
882C22⋊C4—348no—
883C22⋊C4—348no—
884C22⋊C4—684no—
885C22⋊C4—684no—
886C22⋊C4—684no—
887C22⋊C4—684no—
888C22⋊C4—684no—
889C22⋊C4—684no—
890C22⋊C4—684no—
891C22⋊C4—684no—
892C42—684no—
893C23—174no—
894C23—174no—
895C23—342no—
896C23—342no—
897C23—342no—
898C23—342no—
899C23—342no—
900C23—342no—
901C23—342no—
902C23—342no—
903C23—342no—
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—342no—
923C23—342no—
924C23—342no—
925C23—342no—
926C23—342no—
927C23—342no—
928C23—342no—
929C23—342no—
930C23—342no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23—681no—
955C23—681no—
956C23—681no—
957C23—681no—
958C23—681no—
959C23—681no—
960C23—681no—
961C23—681no—
962C23—681no—
963C23C22×C4×D1711yescharacteristic
964C23C2×D4×D1711yescharacteristic
965C23C2×D4×D1711yescharacteristic
966C23#1058769111yescharacteristic
967C23#1058769111yescharacteristic
968C23C2×#6325611yescharacteristic
969C23#1058769411yescharacteristic
970C23#41×D1711yescharacteristic
971C23#41×D1711yescharacteristic
972C23#41×D1711yescharacteristic
973C23#1058769611yescharacteristic
974C23#1058769611yescharacteristic
975C23#1058769611yescharacteristic
976C23#1058769611yescharacteristic
977C23#1058769711yescharacteristic
978D4—6816no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—342no—
1029C2×C4—342no—
1030C2×C4—342no—
1031C2×C4—342no—
1032C2×C4—342no—
1033C2×C4—342no—
1034C2×C4—342no—
1035C2×C4—342no—
1036C2×C4—342no—
1037C2×C4—342no—
1038C2×C4—342no—
1039C2×C4—342no—
1040C2×C4—342no—
1041C2×C4—342no—
1042C2×C4—342no—
1043C2×C4—6816no—
1044C2×C4—6816no—
1045C2×C4—681no—
1046C2×C4—681no—
1047C2×C4—681no—
1048C2×C4—681no—
1049C2×C4—681no—
1050C2×C4—681no—
1051C2×C4—681no—
1052C2×C4—681no—
1053C2×C4—681no—
1054C2×C4—681no—
1055C2×C4—681no—
1056C2×C4—681no—
1057C2×C4—681no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4—681no—
1061C2×C4—681no—
1062C2×C4—681no—
1063C2×C4—681no—
1064C2×C4—681no—
1065C2×C4—681no—
1066C2×C4—681no—
1067C2×C4—681no—
1068C2×C4—681no—
1069C2×C4—681no—
1070C2×C4—681no—
1071C2×C4—681no—
1072C22—344no—
1073C22—344no—
1074C22—344no—
1075C22—344no—
1076C22—344no—
1077C22—344no—
1078C22—682no—
1079C22—682no—
1080C22—682no—
1081C22—682no—
1082C22—682no—
1083C22—682no—
1084C22—682no—
1085C22—682no—
1086C22—682no—
1087C22—682no—
1088C22—682no—
1089C22—682no—
1090C22—682no—
1091C22—682no—
1092C22—682no—
1093C22—682no—
1094C22—682no—
1095C22—682no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22C4×D4×D1711yescharacteristic
1103C22C4×D4×D1711yescharacteristic
1104C22C4×#6325611yescharacteristic
1105C22#1176328111yescharacteristic
1106C22#1176328311yescharacteristic
1107C22#1176328911yescharacteristic
1108C22#1176329011yescharacteristic
1109C22#1176336911yescharacteristic
1110C22#1176337011yescharacteristic
1111C22#1176338811yescharacteristic
1112C22#1176338911yescharacteristic
1113C22#1176339311yescharacteristic
1114C22#1176339511yescharacteristic
1115C22#1176339811yescharacteristic
1116C22#1176339911yescharacteristic
1117C22#1176340011yescharacteristic
1118C22#1176340511yescharacteristic
1119C22#1176341111yescharacteristic
1120C22#1176341511yescharacteristic
1121C22#1176344311yescharacteristic
1122C22#1176344811yescharacteristic
1123C22#1176345011yescharacteristic
1124C22#1176345111yescharacteristic
1125C22#1176345211yescharacteristic
1126C22#1176345711yescharacteristic
1127C22#1176346211yescharacteristic
1128C22#1176348411yescharacteristic
1129C22#1176348411yescharacteristic
1130C22#1176348611yescharacteristic
1131C22#1176349111yescharacteristic
1132C22#1176349711yescharacteristic
1133C22#1176355111yescharacteristic
1134C22#1176355311yescharacteristic
1135C22#1176355711yescharacteristic
1136C22#1176356311yescharacteristic
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—81no—
1144C4—682no—
1145C4—682no—
1146C4—682no—
1147C4—682no—
1148C4—682no—
1149C4—1361no—
1150C2—684no—
1151C2—684no—
1152C2#1453148111yescharacteristic
1153C2#1453148811yescharacteristic
1154C2#1453154811yescharacteristic
1155C2#1453176211yescharacteristic
1156C2#1453177111yescharacteristic
1157C2#1453178311yescharacteristic
1158C2#1453195511yescharacteristic
1159C2#1453502611yescharacteristic
1160C2#1453502711yescharacteristic
1161C2#1453516611yescharacteristic
1162C2#1453516711yescharacteristic
1163C2#1453532111yescharacteristic
1164C2#1453532411yescharacteristic
1165C2#1453592211yescharacteristic
1166C2#1453592811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1442C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1442D17
hypocenterC17#14571
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#11762701C2semidirect
3. C2×#11762699C2semidirect
6. #14527050C2semidirect
7. #14527041C2semidirect
8. #14527030C2semidirect
9. #14527026C2semidirect
10. #14527015C2semidirect
11. #14527005C2semidirect
12. #14527005C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1442C2semidirect
32. #11762727C4semidirect
119. C2×#63227C2×C4semidirect
120. C2×#63227C2×C4semidirect
121. C2×#63227C2×C4semidirect
122. C2×#63227C2×C4semidirect
130. C2×#63225C2×C4semidirect
139. C17×#95C2×C4semidirect
496. #1442D17semidirect
734. #95C4×D17semidirect
735. C17#14571semidirect

Maximal subgroups

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

subgroupindex
C2×#117627272
C2×#117627012
C2×#117626992
C2×#117626872
#145270502
#145270412
#145270302
#145270262
#145270152
#145270052
C17×#14422
#1457117