Finite Group Databasebeta

← #17050672

Subgroups — #17050672

Order 4352.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762881C211yesmaximal, characteristic, complemented
2#14531713C211yesmaximal, characteristic, complemented
3#14529758C211yesmaximal, characteristic, complemented
4#14529733C211yesmaximal, characteristic, complemented
5#14529223C211yesmaximal, characteristic, complemented
6#14529213C211yesmaximal, characteristic, complemented
7#14529107C211yesmaximal, characteristic, complemented
8#14529102C211yesmaximal, characteristic, complemented
9#14528874C211yesmaximal, characteristic, complemented
10#14528870C211yesmaximal, characteristic, complemented
11#14528794C211yesmaximal, characteristic, complemented
12#14528609C211yesmaximal, characteristic, complemented
13#14528503C211yesmaximal, characteristic, complemented
14C2×#11762571C211yesmaximal, characteristic, complemented
15C2×C17×#547C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C2×#10587612C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20#11762881—24no—
21C2×C4⋊#3622C2211yescharacteristic
22C2×#10587503C2211yescharacteristic
23C2×#10587503C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×C22⋊#3622C2211yescharacteristic
27C2×C22⋊#3622C2211yescharacteristic
28C2×#10587474C2211yescharacteristic
29#11762702—21no—
30#11762695—21no—
31#11762689—21no—
32#11762675C2211yescharacteristic
33#11762669C2211yescharacteristic
34#11762669C2211yescharacteristic
35C4×C4⋊Dic17C2211yescharacteristic
36C22⋊C4×Dic17—21no—
37#11762571C2211yescharacteristic
38#11762571C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49C22×#41×C17—21no—
50C17×#547—24no—
51C17×#547C418yescomplemented
52C2×C17×C4⋊Q8C2211yescharacteristic
53C2×C17×#123—21no—
54C2×C17×#123—21no—
55C2×C17×C22⋊Q8—21no—
56C2×C17×#121C2211yescharacteristic
57C2×C17×#121C2211yescharacteristic
58C2×C4×D4×C17C2211yescharacteristic
59C2×C4×D4×C17C2211yescharacteristic
60C22×C4⋊C4×C17C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C2×#41×C17—28no—
63C2×#41×C17—44no—
64C2×#41×C17—44no—
65C22×Q8×C17—21no—
66C22×D4×C17—21no—
67C22×D4×C17—21no—
68C22×D4×C17D411yescharacteristic
69C22×D4×C17C2311yescharacteristic
70C23×C4×C17—21no—
71C23×C4×C17—21no—
72C23×C4×C17—21no—
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×Dic17—21no—
76C17×C4⋊Q8—22no—
77C17×C4⋊Q8C2×C414yescomplemented
78C17×#123—28no—
79C17×#123—28no—
80C17×C22⋊Q8—28no—
81C17×#121—22no—
82C17×#121—22no—
83C17×#121C2×C414yes—
84C17×#121C2×C414yescomplemented
85C4×D4×C17—22no—
86C4×D4×C17C2×C414yes—
87C4×D4×C17C2×C414yescomplemented
88C4×D4×C17D414yes—
89C2×C4⋊C4×C17—21no—
90C2×C4⋊C4×C17—21no—
91C2×C4⋊C4×C17—22no—
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17—21no—
94C2×C4⋊C4×C17C2×C414yes—
95C2×C4⋊C4×C17C2×C414yescomplemented
96C2×C4⋊C4×C17D411yescharacteristic
97C2×C4⋊C4×C17C2311yescharacteristic
98C2×C4⋊C4×C17C2311yescharacteristic
99C2×C4⋊C4×C17C2311yescharacteristic
100C2×C22⋊C4×C17—21no—
101C2×C22⋊C4×C17—21no—
102C2×C22⋊C4×C17—21no—
103C2×C22⋊C4×C17D411yescharacteristic
104C2×C22⋊C4×C17D411yescharacteristic
105C2×C42×C17C2311yescharacteristic
106C2×C22⋊Dic17—21no—
107C2×C22⋊Dic17—21no—
108C2×C22⋊Dic17—21no—
109#10587612—22no—
110#10587612—41no—
111C2×C4⋊Dic17—21no—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—41no—
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4⋊Dic17C2311yescharacteristic
117C2×C4⋊Dic17C2311yescharacteristic
118C2×C4×Dic17—21no—
119C2×C4×Dic17—21no—
120C2×#63223—22no—
121C2×#63223—22no—
122C2×#63223—41no—
123C22×#3622—22no—
124C22×#3622—22no—
125C22×#3622—41no—
126C22×#3622C2311yescharacteristic
127C22×#3622C2311yescharacteristic
128C22×#3622C2311yescharacteristic
129C22×#3622C2311yescharacteristic
130#10587503—22no—
131#10587503—22no—
132#10587503—41no—
133#10587503—41no—
134#10587502—21no—
135#10587502—21no—
136#10587502—21no—
137#10587502—21no—
138#10587502—21no—
139C22⋊#3622—22no—
140C22⋊#3622—22no—
141C4⋊#3622—22no—
142#10587474—22no—
143C24×C17—21no—
144C24×C17C2×D411yescharacteristic
145C24×C17C2×D411yescharacteristic
146#41×C17—432no—
147C2×Q8×C17—24no—
148C2×Q8×C17—42no—
149C2×Q8×C17—42no—
150C2×D4×C17—22no—
151C2×D4×C17—22no—
152C2×D4×C17—24no—
153C2×D4×C17—24no—
154C2×D4×C17—21no—
155C2×D4×C17—21no—
156C2×D4×C17—21no—
157C2×D4×C17—21no—
158C2×D4×C17—21no—
159C2×D4×C17—42no—
160C2×D4×C17—42no—
161C2×D4×C17—42no—
162C2×D4×C17—42no—
163C2×D4×C17C22⋊C414yes—
164C2×D4×C17C22×C412yes—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—24no—
174C22×C4×C17—24no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—24no—
179C22×C4×C17—42no—
180C22×C4×C17—42no—
181C22×C4×C17—42no—
182C22×C4×C17—42no—
183C22×C4×C17—42no—
184C22×C4×C17—42no—
185C22×C4×C17C22×C412yes—
186C22×C4×C17C22×C412yes—
187C22×C4×C17C2×D411yescharacteristic
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D412yes—
192C22×C4×C17C2×D412yes—
193C22×C4×C17C2411yescharacteristic
194C22×Dic17—21no—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—42no—
199C22×Dic17—42no—
200C22×Dic17—81no—
201C4⋊C4×C17—24no—
202C4⋊C4×C17—24no—
203C4⋊C4×C17—24no—
204C4⋊C4×C17—21no—
205C4⋊C4×C17—21no—
206C4⋊C4×C17—21no—
207C4⋊C4×C17C22⋊C414yes—
208C4⋊C4×C17C22×C412yes—
209C4⋊C4×C17C22×C412yes—
210C4⋊C4×C17C22×C412yes—
211C22⋊C4×C17—24no—
212C22⋊C4×C17—24no—
213C22⋊C4×C17—24no—
214C22⋊C4×C17C22⋊C414yes—
215C22⋊C4×C17C22⋊C414yes—
216C42×C17C22×C412yes—
217C42×C17C2×D412yes—
218C22⋊Dic17—42no—
219C22⋊Dic17—42no—
220C22⋊Dic17—81no—
221C4⋊Dic17—21no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17—21no—
228C4⋊Dic17—42no—
229C4⋊Dic17#4112yescomplemented
230C4×Dic17—42no—
231C4×Dic17—81no—
232#63223—44no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622—21no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—21no—
243C2×#3622—21no—
244C2×#3622—44no—
245C2×#3622#4112yescomplemented
246#22495—171nomaximal, Sylow
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—21no—
253C23×C17—21no—
254C23×C17—21no—
255C23×C17—21no—
256C23×C17—21no—
257C23×C17—22no—
258C23×C17—41no—
259C23×C17—41no—
260C23×C17—41no—
261C23×C17—41no—
262C23×C17—41no—
263C23×C17—41no—
264C23×C17C2×C22⋊C412yes—
265C23×C17C2×C22⋊C412yes—
266C23×C17AGL(1,ℤ/8)12yes—
267C23×C17AGL(1,ℤ/8)12yes—
268C23×C17C22×D411yescharacteristic
269Q8×C17—48no—
270D4×C17—28no—
271D4×C17—22no—
272D4×C17—22no—
273D4×C17—48no—
274D4×C17—48no—
275D4×C17—41no—
276D4×C17—41no—
277C2×C4×C17—21no—
278C2×C4×C17—21no—
279C2×C4×C17—21no—
280C2×C4×C17—21no—
281C2×C4×C17—21no—
282C2×C4×C17—21no—
283C2×C4×C17—21no—
284C2×C4×C17—21no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—48no—
297C2×C4×C17—48no—
298C2×C4×C17—41no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—48no—
305C2×C4×C17C2×C22⋊C412yes—
306C2×C4×C17C2×C22⋊C412yes—
307C2×C4×C17C2×C22⋊C412yes—
308C2×C4×C17C2×C22⋊C412yes—
309C2×C4×C17C23×C411yescharacteristic
310C2×C4×C17C22×D411yescharacteristic
311C2×C4×C17C2×#4111yescharacteristic
312C2×C4×C17C2×#4111yescharacteristic
313C2×C4×C17H(5,𝔽2)11yescharacteristic
314C2×C4×C172−1+411yescharacteristic
315C2×Dic17—22no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—41no—
322C2×Dic17—41no—
323C2×Dic17—41no—
324C2×Dic17—41no—
325C2×Dic17—41no—
326C2×Dic17—41no—
327C2×Dic17—84no—
328#3622—22no—
329#3622—41no—
330#3622—41no—
331#3622—41no—
332C2×#547D1711yescharacteristic
333C2×#435—171no—
334#2352—171no—
335#1993—171no—
336#1987—171no—
337#1895—171no—
338#1893—171no—
339#1875—171no—
340#1874—171no—
341#1824—171no—
342#1823—171no—
343#1804—171no—
344#1762—171no—
345#1736—171no—
346C2×#340—171no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—22no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—41no—
357C22×C17—41no—
358C22×C17—41no—
359C22×C17—41no—
360C22×C17—42no—
361C22×C17—42no—
362C22×C17—42no—
363C22×C17—81no—
364C22×C17—81no—
365C22×C17—81no—
366C22×C17—81no—
367C22×C17#41814yes—
368C22×C17C22×C22⋊C411yescharacteristic
369C22×C17#54611yescharacteristic
370C22×C17#54711yescharacteristic
371C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C17#57711yescharacteristic
374C22×C17#57811yescharacteristic
375C4×C17—22no—
376C4×C17—22no—
377C4×C17—22no—
378C4×C17—22no—
379C4×C17—42no—
380C4×C17—42no—
381C4×C17—42no—
382C4×C17C4×#4111yescharacteristic
383C4×C17#52011yescharacteristic
384C4×C17#54611yescharacteristic
385C4×C17#54711yescharacteristic
386Dic17—42no—
387Dic17—81no—
388Dic17—81no—
389Dic17—81no—
390C22×#41—21no—
391C22×M16—171no—
392C23×C8—171no—
393#547—24no—
394#547Dic1718yescomplemented
395C2×C4⋊Q8C2×D1711yescharacteristic
396C2×#123—21no—
397C2×#123—21no—
398C2×C22⋊Q8—21no—
399C2×#121C2×D1711yescharacteristic
400C2×#121C2×D1711yescharacteristic
401C2×C4×D4C2×D1711yescharacteristic
402C2×C4×D4C2×D1711yescharacteristic
403C2×#117—171no—
404C22×C4⋊C4—171no—
405C22×C4⋊C4C2×D1711yescharacteristic
406C22×C4⋊C4C2×D1711yescharacteristic
407#435—344no—
408C2×C4⋊C8—171no—
409C2×#102—171no—
410C2×#102—171no—
411C2×#102—171no—
412C2×#102—171no—
413C2×C22⋊C8—171no—
414C2×C22⋊C8—171no—
415C2×#97—171no—
416#388—341no—
417#387—341no—
418#386—341no—
419#382—171no—
420#380—171no—
421#380—171no—
422C4×C4⋊C4—171no—
423C4×C22⋊C4—341no—
424#340—171no—
425#340—171no—
426#340—171no—
427#340—171no—
428#340—171no—
429#340—171no—
430#340—171no—
431#340—171no—
432#340—171no—
433#340—171no—
434#340—171no—
435#340—171no—
436C2×C17—24no—
437C2×C17—42no—
438C2×C17—82no—
439C2×C17#233911yescharacteristic
440C2×C17C2×#41811yescharacteristic
441C2×C17#289811yescharacteristic
442C2×C17#330611yescharacteristic
443C2×C17#330811yescharacteristic
444C2×C17#334311yescharacteristic
445C2×C17#334511yescharacteristic
446C2×#41—28no—
447C2×#41—44no—
448C2×#41—44no—
449C22×Q8—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C22⋊D1711yescharacteristic
453C22×D4C22×D1711yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—341no—
458C23×C4C22×D1711yescharacteristic
459C23×C4C22×D1711yescharacteristic
460C2×M16—342no—
461C2×M16—342no—
462C2×M16—681no—
463C22×C8—171no—
464C22×C8—171no—
465C22×C8—171no—
466C22×C8—171no—
467C22×C8—342no—
468C22×C8—342no—
469C22×C8—681no—
470C4⋊Q8—22no—
471C4⋊Q8C2×Dic1714yescomplemented
472#123—28no—
473#123—28no—
474C22⋊Q8—28no—
475#121—22no—
476#121—22no—
477#121C2×Dic1714yes—
478#121C2×Dic1714yescomplemented
479C4×D4—22no—
480C4×D4C2×Dic1714yes—
481C4×D4C2×Dic1714yescomplemented
482C4×D4C22⋊D1714yes—
483#117—342no—
484#117—681no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—171no—
491C2×C4⋊C4—171no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—342no—
495C2×C4⋊C4—341no—
496C2×C4⋊C4—681no—
497C2×C4⋊C4C2×Dic1714yes—
498C2×C4⋊C4C2×Dic1714yescomplemented
499C2×C4⋊C4C22⋊D1711yescharacteristic
500C2×C4⋊C4C22×D1711yescharacteristic
501C2×C4⋊C4C22×D1711yescharacteristic
502C2×C4⋊C4C22×D1711yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—341no—
507C2×C22⋊C4—341no—
508C2×C22⋊C4—341no—
509C2×C22⋊C4C22⋊D1711yescharacteristic
510C2×C22⋊C4C22⋊D1711yescharacteristic
511C2×C42—341no—
512C2×C42—341no—
513C2×C42C22×D1711yescharacteristic
514C4⋊C8—342no—
515#102—342no—
516#102—342no—
517#102—681no—
518#102—681no—
519C22⋊C8—342no—
520C22⋊C8—342no—
521#97—342no—
522#95—341no—
523#95—341no—
524#95—341no—
525#95—341no—
526#95—341no—
527C17#2249511yescharacteristic, complemented, Sylow
528C24—21no—
529C24C2×C22⋊D1711yescharacteristic
530C24C2×C22⋊D1711yescharacteristic
531#41—432no—
532C2×Q8—24no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4C22⋊Dic1714yes—
549C2×D4C22×Dic1712yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—682no—
575C22×C4—682no—
576C22×C4—1361no—
577C22×C4C22×Dic1712yes—
578C22×C4C22×Dic1712yes—
579C22×C4C2×C22⋊D1712yes—
580C22×C4C2×C22⋊D1712yes—
581C22×C4C2×C22⋊D1711yescharacteristic
582C22×C4C2×C22⋊D1711yescharacteristic
583C22×C4C2×C22⋊D1711yescharacteristic
584C22×C4C2×C22⋊D1711yescharacteristic
585C22×C4C23×D1711yescharacteristic
586M16—684no—
587C2×C8—172no—
588C2×C8—341no—
589C2×C8—341no—
590C2×C8—341no—
591C2×C8—341no—
592C2×C8—341no—
593C2×C8—341no—
594C2×C8—341no—
595C2×C8—341no—
596C2×C8—341no—
597C2×C8—341no—
598C2×C8—341no—
599C2×C8—684no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—172no—
607C4⋊C4—341no—
608C4⋊C4—341no—
609C4⋊C4—341no—
610C4⋊C4—341no—
611C4⋊C4—341no—
612C4⋊C4—341no—
613C4⋊C4—341no—
614C4⋊C4—682no—
615C4⋊C4C22⋊Dic1714yes—
616C4⋊C4C22×Dic1712yes—
617C4⋊C4C22×Dic1712yes—
618C4⋊C4C22×Dic1712yes—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—682no—
623C22⋊C4—682no—
624C22⋊C4—1361no—
625C22⋊C4C22⋊Dic1714yes—
626C22⋊C4C22⋊Dic1714yes—
627C42—682no—
628C42—1361no—
629C42C22×Dic1712yes—
630C42C2×C22⋊D1712yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23#1058761812yes—
649C23#1058761812yes—
650C23C2×C22⋊Dic1712yes—
651C23C2×C22⋊Dic1712yes—
652C23C22×C22⋊D1711yescharacteristic
653Q8—48no—
654D4—28no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—48no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—48no—
681C2×C4—48no—
682C2×C4—48no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—342no—
690C2×C4—681no—
691C2×C4—681no—
692C2×C4—681no—
693C2×C4—681no—
694C2×C4—681no—
695C2×C4—681no—
696C2×C4—681no—
697C2×C4—681no—
698C2×C4—681no—
699C2×C4—681no—
700C2×C4—681no—
701C2×C4—1364no—
702C2×C4C2×C22⋊Dic1712yes—
703C2×C4C2×C22⋊Dic1712yes—
704C2×C4C2×C22⋊Dic1712yes—
705C2×C4C2×C22⋊Dic1712yes—
706C2×C4#41×D1711yescharacteristic
707C2×C4#41×D1711yescharacteristic
708C2×C4#1058769611yescharacteristic
709C2×C4#1058769711yescharacteristic
710C2×C4C23×Dic1711yescharacteristic
711C2×C4C22×C22⋊D1711yescharacteristic
712C8—342no—
713C8—681no—
714C8—681no—
715C8—681no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22#1176281414yes—
737C22C22×C22⋊Dic1711yescharacteristic
738C22#1176344711yescharacteristic
739C22#1176345811yescharacteristic
740C22C2×#1058761811yescharacteristic
741C22C2×#1058761811yescharacteristic
742C22#1176361711yescharacteristic
743C22#1176362411yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—682no—
752C4—1361no—
753C4—1361no—
754C4—1361no—
755C4#41×Dic1711yescharacteristic
756C4#1176329211yescharacteristic
757C4#1176344711yescharacteristic
758C4#1176345811yescharacteristic
759C2—24no—
760C2—42no—
761C2—82no—
762C2#1453161411yescharacteristic
763C2C2×#1176281411yescharacteristic
764C2#1453731711yescharacteristic
765C2#1454073911yescharacteristic
766C2#1454076911yescharacteristic
767C2#1454121811yescharacteristic
768C2#1454125411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#547C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×#547D17
hypocenterC17#22495
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11762881C2semidirect
2. #14531713C2semidirect
3. #14529758C2semidirect
4. #14529733C2semidirect
5. #14529223C2semidirect
6. #14529213C2semidirect
7. #14529107C2semidirect
8. #14529102C2semidirect
9. #14528874C2semidirect
10. #14528870C2semidirect
11. #14528794C2semidirect
12. #14528609C2semidirect
13. #14528503C2semidirect
14. C2×#11762571C2semidirect
51. C17×#547C4semidirect
77. C17×C4⋊Q8C2×C4semidirect
84. C17×#121C2×C4semidirect
87. C4×D4×C17C2×C4semidirect
95. C2×C4⋊C4×C17C2×C4semidirect
229. C4⋊Dic17#41semidirect
245. C2×#3622#41semidirect
394. #547Dic17semidirect
471. C4⋊Q8C2×Dic17semidirect
478. #121C2×Dic17semidirect
481. C4×D4C2×Dic17semidirect
498. C2×C4⋊C4C2×Dic17semidirect
527. C17#22495semidirect

Maximal subgroups

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

subgroupindex
C2×#117628812
#145317132
#145297582
#145297332
#145292232
#145292132
#145291072
#145291022
#145288742
#145288702
#145287942
#145286092
#145285032
C2×#117625712
C2×C17×#5472
#2249517