Finite Group Databasebeta

← #16957416

Subgroups — #16957416

Order 4352.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762708C211yesmaximal, characteristic, complemented
2C2×#11762669C211yesmaximal, characteristic
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic17C211yesmaximal, characteristic
5#14527046C212yesmaximal, complemented
6#14527029C212yesmaximal
7#14527021C212yesmaximal
8#14527018C212yesmaximal, complemented
9#14527013C211yesmaximal, characteristic, complemented
10#14527013C211yesmaximal, characteristic, complemented
11C2×C17×#380C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2212yes—
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C22⋊Dic17C2211yescharacteristic
16C22×C22⋊Dic17C2212yes—
17C22×C22⋊Dic17C2211yescharacteristic
18C22×C4×Dic17C2211yescharacteristic
19C22×C4×Dic17C2211yescharacteristic
20C22×C4×Dic17C2212yes—
21#11762708—24no—
22#11762669—24no—
23C4⋊C4×Dic17—24no—
24C4×C22⋊Dic17—24no—
25C2×#10587502C2212yes—
26C2×#10587502C2211yescharacteristic
27C2×#10587502C2212yes—
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C24×C4×C17C2211yescharacteristic
35C22×C4⋊C4×C17C2211yescharacteristic
36C22×C4⋊C4×C17C2211yescharacteristic
37C22×C22⋊C4×C17C2212yes—
38C17×#380C418yescomplemented
39C2×C17×#95C2212yes—
40C25×C17C2311yescharacteristic
41C23×C4×C17—22no—
42C23×C4×C17—22no—
43C23×C4×C17—22no—
44C23×C4×C17—22no—
45C23×C4×C17—22no—
46C23×C4×C17—22no—
47C23×C4×C17C2×C414yes—
48C23×C4×C17C2312yes—
49C23×C4×C17C2312yes—
50C23×C4×C17C2311yescharacteristic
51C23×C4×C17C2311yescharacteristic
52C23×Dic17C2312yes—
53C23×Dic17C2312yes—
54C23×Dic17C2311yescharacteristic
55C23×Dic17C2311yescharacteristic
56C23×Dic17C2311yescharacteristic
57C23×Dic17C2311yescharacteristic
58C2×C4⋊C4×C17—22no—
59C2×C4⋊C4×C17—22no—
60C2×C4⋊C4×C17—22no—
61C2×C4⋊C4×C17—22no—
62C2×C4⋊C4×C17C2×C414yes—
63C2×C4⋊C4×C17C2×C414yes—
64C2×C22⋊C4×C17—42no—
65C2×C22⋊C4×C17—42no—
66C2×C22⋊C4×C17C2×C418yes—
67C2×C22⋊Dic17—22no—
68C2×C22⋊Dic17—22no—
69C2×C22⋊Dic17—22no—
70C2×C22⋊Dic17—22no—
71C2×C22⋊Dic17—22no—
72C2×C22⋊Dic17—24no—
73C2×C22⋊Dic17—24no—
74C2×C22⋊Dic17—42no—
75C2×C22⋊Dic17Q814yes—
76C2×C4⋊Dic17—22no—
77C2×C4⋊Dic17—22no—
78C2×C4⋊Dic17—22no—
79C2×C4⋊Dic17—22no—
80C2×C4⋊Dic17—22no—
81C2×C4⋊Dic17—24no—
82C2×C4⋊Dic17—24no—
83C2×C4⋊Dic17—42no—
84C2×C4⋊Dic17D414yes—
85C2×C4×Dic17—22no—
86C2×C4×Dic17—22no—
87C2×C4×Dic17—22no—
88C2×C4×Dic17—22no—
89C2×C4×Dic17—22no—
90C2×C4×Dic17—24no—
91C2×C4×Dic17—42no—
92C2×C4×Dic17—42no—
93C2×C4×Dic17D414yes—
94C17×#95C2×C418yes—
95#10587502—24no—
96#10587502—22no—
97#10587502—22no—
98#10587502—24no—
99#10587502—24no—
100#10587502—24no—
101#10587502—42no—
102#10587502—42no—
103#10587502—42no—
104C24×C17—21no—
105C24×C17—21no—
106C24×C17—21no—
107C24×C17—21no—
108C24×C17—21no—
109C24×C17—21no—
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—21no—
113C24×C17—21no—
114C24×C17—21no—
115C24×C17—21no—
116C24×C17C22×C412yes—
117C24×C17C2×Q812yes—
118C24×C17#4112yes—
119C24×C17C2411yescharacteristic
120C22×C4×C17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—22no—
129C22×C4×C17—22no—
130C22×C4×C17—22no—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—22no—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—28no—
139C22×C4×C17—28no—
140C22×C4×C17—28no—
141C22×C4×C17—44no—
142C22×C4×C17—44no—
143C22×C4×C17—44no—
144C22×C4×C17—44no—
145C22×C4×C17C22×C412yes—
146C22×C4×C17C22×C414yes—
147C22×C4×C17C22×C414yes—
148C22×C4×C17C22×C412yes—
149C22×C4×C17C2×D412yes—
150C22×C4×C17C2×D412yes—
151C22×C4×C17#4112yes—
152C22×C4×C17#4112yes—
153C22×C4×C17#4112yes—
154C22×C4×C17#4112yes—
155C22×Dic17—21no—
156C22×Dic17—21no—
157C22×Dic17—21no—
158C22×Dic17—21no—
159C22×Dic17—21no—
160C22×Dic17—22no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17—21no—
164C22×Dic17—21no—
165C22×Dic17—21no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17—21no—
171C22×Dic17—21no—
172C22×Dic17—22no—
173C22×Dic17—21no—
174C22×Dic17—21no—
175C22×Dic17—21no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—21no—
181C22×Dic17—21no—
182C22×Dic17—21no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17C2×D412yes—
191C22×Dic17C2×D414yes—
192C22×Dic17C2×D412yes—
193C22×Dic17C2×Q812yes—
194C22×Dic17C2×Q812yes—
195C22×Dic17#4112yes—
196C22×Dic17#4112yes—
197C4⋊C4×C17—28no—
198C4⋊C4×C17—28no—
199C22⋊C4×C17—48no—
200C22⋊Dic17—28no—
201C22⋊Dic17—28no—
202C22⋊Dic17—48no—
203C4⋊Dic17—28no—
204C4⋊Dic17—48no—
205C4⋊Dic17—44no—
206C4×Dic17—28no—
207C4×Dic17—48no—
208C4×Dic17—44no—
209#13993—171nomaximal, Sylow
210C23×C17—22no—
211C23×C17—22no—
212C23×C17—22no—
213C23×C17—22no—
214C23×C17—22no—
215C23×C17—22no—
216C23×C17—22no—
217C23×C17—22no—
218C23×C17—22no—
219C23×C17—22no—
220C23×C17—22no—
221C23×C17—22no—
222C23×C17—22no—
223C23×C17—22no—
224C23×C17—22no—
225C23×C17—22no—
226C23×C17—22no—
227C23×C17—22no—
228C23×C17—41no—
229C23×C17—41no—
230C23×C17—41no—
231C23×C17—41no—
232C23×C17—41no—
233C23×C17—41no—
234C23×C17—41no—
235C23×C17—41no—
236C23×C17—41no—
237C23×C17—41no—
238C23×C17—41no—
239C23×C17—41no—
240C23×C17—41no—
241C23×C17—41no—
242C23×C17—41no—
243C23×C17—41no—
244C23×C17C4×Q814yes—
245C23×C17C23×C411yescharacteristic
246C23×C17C22×D411yescharacteristic
247C23×C17C22×D411yescharacteristic
248C23×C17C22×Q811yescharacteristic
249C23×C17C2×#4111yescharacteristic
250C23×C17C2×#4111yescharacteristic
251C23×C17C2×#4111yescharacteristic
252C23×C17C2×#4111yescharacteristic
253C23×C17C2×#4111yescharacteristic
254C23×C17C2×#4111yescharacteristic
255C23×C17C2×#4111yescharacteristic
256C23×C17H(5,𝔽2)11yescharacteristic
257C23×C17H(5,𝔽2)11yescharacteristic
258C23×C17H(5,𝔽2)11yescharacteristic
259C23×C172−1+411yescharacteristic
260C2×C4×C17—22no—
261C2×C4×C17—24no—
262C2×C4×C17—24no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—24no—
266C2×C4×C17—24no—
267C2×C4×C17—24no—
268C2×C4×C17—24no—
269C2×C4×C17—41no—
270C2×C4×C17—41no—
271C2×C4×C17—41no—
272C2×C4×C17—41no—
273C2×C4×C17—42no—
274C2×C4×C17—42no—
275C2×C4×C17—42no—
276C2×C4×C17—42no—
277C2×C4×C17—42no—
278C2×C4×C17—42no—
279C2×C4×C17—42no—
280C2×C4×C17—42no—
281C2×C4×C17—416no—
282C2×C4×C17#11714yes—
283C2×C4×C17C4×D414yes—
284C2×C4×C17C4×D414yes—
285C2×C4×C17#12114yes—
286C2×C4×C17#12314yes—
287C2×C4×C17#12414yes—
288C2×C4×C17#12614yes—
289C2×Dic17—22no—
290C2×Dic17—22no—
291C2×Dic17—22no—
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—22no—
295C2×Dic17—24no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—24no—
302C2×Dic17—24no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—42no—
310C2×Dic17—41no—
311C2×Dic17—42no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—42no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—42no—
320C2×Dic17—41no—
321C2×Dic17—41no—
322C2×Dic17—41no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17—42no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17—42no—
330C2×Dic17C22⋊Q814yes—
331C2×#389—171no—
332C2×#380—171no—
333C2×#380D1711yescharacteristic
334C2×C4×C4⋊C4—171no—
335C2×C4×C22⋊C4—171no—
336#1443—172no—
337#1439—172no—
338#1437—172no—
339#1436—172no—
340C4⋊#95—171no—
341C4⋊#95—171no—
342C22×C17—24no—
343C22×C17—24no—
344C22×C17—24no—
345C22×C17—42no—
346C22×C17—42no—
347C22×C17—42no—
348C22×C17—42no—
349C22×C17—42no—
350C22×C17—42no—
351C22×C17—42no—
352C22×C17—42no—
353C22×C17—42no—
354C22×C17—42no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17C2×#11711yescharacteristic
358C22×C17C2×C4×D411yescharacteristic
359C22×C17C2×C4×D411yescharacteristic
360C22×C17C2×C4×Q811yescharacteristic
361C22×C17C4×#4111yescharacteristic
362C22×C17#51811yescharacteristic
363C22×C17#52011yescharacteristic
364C22×C17C2×#12111yescharacteristic
365C22×C17C2×C22⋊Q811yescharacteristic
366C22×C17C2×#12311yescharacteristic
367C22×C17#52511yescharacteristic
368C22×C17C2×#12411yescharacteristic
369C22×C17C2×#12611yescharacteristic
370C22×C17#52911yescharacteristic
371C22×C17#53311yescharacteristic
372C22×C17#53511yescharacteristic
373C22×C17#53711yescharacteristic
374C22×C17#54011yescharacteristic
375C22×C17#54211yescharacteristic
376C22×C17#54611yescharacteristic
377C22×C17#54611yescharacteristic
378C22×C17D4×Q811yescharacteristic
379C22×C17#55011yescharacteristic
380C22×C17#55211yescharacteristic
381C22×C17#55311yescharacteristic
382C22×C17#55311yescharacteristic
383C22×C17#55311yescharacteristic
384C22×C17#55311yescharacteristic
385C22×C17#55311yescharacteristic
386C22×C17#55411yescharacteristic
387C22×C17#55411yescharacteristic
388C22×C17#55411yescharacteristic
389C22×C17#55511yescharacteristic
390C22×C17#55611yescharacteristic
391C22×C17#55611yescharacteristic
392C4×C17—44no—
393C4×C17—44no—
394C4×C17—42no—
395C4×C17#38818yes—
396Dic17—24no—
397Dic17—42no—
398Dic17—44no—
399Dic17—42no—
400Dic17—42no—
401Dic17—82no—
402C24×C4C2×D1711yescharacteristic
403C22×C4⋊C4—171no—
404C22×C4⋊C4—171no—
405C22×C4⋊C4—172no—
406C22×C4⋊C4C2×D1711yescharacteristic
407C22×C4⋊C4C2×D1711yescharacteristic
408C22×C22⋊C4—171no—
409C22×C22⋊C4—171no—
410C22×C22⋊C4—172no—
411C22×C22⋊C4C2×D1712yes—
412C22×C42—171no—
413C22×C42—171no—
414C22×C42—172no—
415#389—344no—
416#380—344no—
417#380Dic1718yescomplemented
418C4×C4⋊C4—344no—
419C4×C22⋊C4—344no—
420C2×#95—172no—
421C2×#95—171no—
422C2×#95—172no—
423C2×#95—172no—
424C2×#95—172no—
425C2×#95—171no—
426C2×#95—172no—
427C2×#95—172no—
428C2×#95—172no—
429C2×#95C2×D1712yes—
430C2×C17—44no—
431C2×C17C2×#38811yescharacteristic
432C2×C17C4×C22⋊Q811yescharacteristic
433C2×C17#232411yescharacteristic
434C2×C17#234511yescharacteristic
435C2×C17#234711yescharacteristic
436C2×C17#236011yescharacteristic
437C2×C17#236311yescharacteristic
438C2×C17#248511yescharacteristic
439C2×C17#248711yescharacteristic
440C2×C17#249011yescharacteristic
441C2×C17#249211yescharacteristic
442C2×C17#249411yescharacteristic
443C2×C17#249711yescharacteristic
444C2×C17#253511yescharacteristic
445C2×C17#253811yescharacteristic
446C25C22×D1711yescharacteristic
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—171no—
454C23×C4—172no—
455C23×C4—171no—
456C23×C4—171no—
457C23×C4—171no—
458C23×C4—172no—
459C23×C4C2×Dic1714yes—
460C23×C4C22×D1712yes—
461C23×C4C22×D1712yes—
462C23×C4C22×D1711yescharacteristic
463C23×C4C22×D1711yescharacteristic
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—174no—
469C2×C4⋊C4—342no—
470C2×C4⋊C4—342no—
471C2×C4⋊C4—344no—
472C2×C4⋊C4—344no—
473C2×C4⋊C4—342no—
474C2×C4⋊C4—342no—
475C2×C4⋊C4—342no—
476C2×C4⋊C4—682no—
477C2×C4⋊C4C2×Dic1714yes—
478C2×C4⋊C4C2×Dic1714yes—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—174no—
482C2×C22⋊C4—342no—
483C2×C22⋊C4—342no—
484C2×C22⋊C4—342no—
485C2×C22⋊C4—342no—
486C2×C22⋊C4—342no—
487C2×C22⋊C4—344no—
488C2×C22⋊C4—344no—
489C2×C22⋊C4—682no—
490C2×C22⋊C4C2×Dic1718yes—
491C2×C42—174no—
492C2×C42—342no—
493C2×C42—342no—
494C2×C42—344no—
495C2×C42—342no—
496C2×C42—342no—
497C2×C42—342no—
498C2×C42—682no—
499C2×C42—682no—
500#95—344no—
501#95—342no—
502#95—342no—
503#95—344no—
504#95—344no—
505#95—344no—
506#95—682no—
507#95—682no—
508#95—682no—
509#95C2×Dic1718yes—
510C17#1399311yescharacteristic, complemented, Sylow
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24Q8×D1712yes—
524C24#6325612yes—
525C24C22×Dic1712yes—
526C24C23×D1711yescharacteristic
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—172no—
553C22×C4—172no—
554C22×C4—172no—
555C22×C4—172no—
556C22×C4—174no—
557C22×C4—172no—
558C22×C4—172no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—341no—
562C22×C4—341no—
563C22×C4—341no—
564C22×C4—341no—
565C22×C4—341no—
566C22×C4—342no—
567C22×C4—341no—
568C22×C4—341no—
569C22×C4—341no—
570C22×C4—342no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—342no—
576C22×C4—341no—
577C22×C4—341no—
578C22×C4—341no—
579C22×C4—342no—
580C22×C4—341no—
581C22×C4—341no—
582C22×C4—342no—
583C22×C4—341no—
584C22×C4—342no—
585C22×C4—341no—
586C22×C4—341no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—342no—
592C22×C4—342no—
593C22×C4—342no—
594C22×C4#6325212yes—
595C22×C4#6325212yes—
596C22×C4D4×D1712yes—
597C22×C4D4×D1712yes—
598C22×C4#6325412yes—
599C22×C4#6325412yes—
600C22×C4C22×Dic1712yes—
601C22×C4C22×Dic1714yes—
602C22×C4C22×Dic1714yes—
603C22×C4C22×Dic1712yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—348no—
607C4⋊C4—688no—
608C4⋊C4—684no—
609C22⋊C4—48no—
610C22⋊C4—348no—
611C22⋊C4—348no—
612C22⋊C4—688no—
613C42—348no—
614C42—688no—
615C42—684no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23Q8×Dic1714yes—
651C23C2×#6325211yescharacteristic
652C23C2×#6325211yescharacteristic
653C23C2×D4×D1711yescharacteristic
654C23C2×D4×D1711yescharacteristic
655C23C2×#6325411yescharacteristic
656C23C2×#6325411yescharacteristic
657C23#1058769111yescharacteristic
658C23#1058769111yescharacteristic
659C23C2×Q8×D1711yescharacteristic
660C23C2×#6325611yescharacteristic
661C23#41×D1711yescharacteristic
662C23#41×D1711yescharacteristic
663C23#1058769611yescharacteristic
664C23#1058769711yescharacteristic
665C23C23×Dic1711yescharacteristic
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—416no—
688C2×C4—174no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—342no—
694C2×C4—342no—
695C2×C4—342no—
696C2×C4—344no—
697C2×C4—342no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—344no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—342no—
704C2×C4—342no—
705C2×C4—342no—
706C2×C4—344no—
707C2×C4—681no—
708C2×C4—681no—
709C2×C4—682no—
710C2×C4—681no—
711C2×C4—682no—
712C2×C4—681no—
713C2×C4—681no—
714C2×C4—681no—
715C2×C4—681no—
716C2×C4—681no—
717C2×C4—681no—
718C2×C4—682no—
719C2×C4—682no—
720C2×C4—681no—
721C2×C4—681no—
722C2×C4—681no—
723C2×C4—682no—
724C2×C4—682no—
725C2×C4—682no—
726C2×C4—682no—
727C2×C4—682no—
728C2×C4—682no—
729C2×C4—682no—
730C2×C4#1058756514yes—
731C2×C4#1058756914yes—
732C2×C4#1058757014yes—
733C2×C4#1058757114yes—
734C2×C4#1058761214yes—
735C2×C4D4×Dic1714yes—
736C2×C4D4×Dic1714yes—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×#1058761211yescharacteristic
753C22C2×D4×Dic1711yescharacteristic
754C22C2×D4×Dic1711yescharacteristic
755C22C2×Q8×Dic1711yescharacteristic
756C22#41×Dic1711yescharacteristic
757C22#1176328411yescharacteristic
758C22#1176329211yescharacteristic
759C22C2×#1058757011yescharacteristic
760C22C22⋊Q8×D1711yescharacteristic
761C22C2×#1058756911yescharacteristic
762C22#1176332211yescharacteristic
763C22C2×#1058757111yescharacteristic
764C22C2×#1058756511yescharacteristic
765C22#1176334511yescharacteristic
766C22#1176336111yescharacteristic
767C22#1176337511yescharacteristic
768C22#1176338811yescharacteristic
769C22#1176341211yescharacteristic
770C22#1176342611yescharacteristic
771C22#1176345011yescharacteristic
772C22#1176345611yescharacteristic
773C22#1176347211yescharacteristic
774C22#1176347711yescharacteristic
775C22#1176350111yescharacteristic
776C22#1176350311yescharacteristic
777C22#1176350311yescharacteristic
778C22#1176350611yescharacteristic
779C22#1176350711yescharacteristic
780C22#1176350711yescharacteristic
781C22#1176351411yescharacteristic
782C22#1176351411yescharacteristic
783C22#1176351711yescharacteristic
784C22#1176352311yescharacteristic
785C22#1176352711yescharacteristic
786C22#1176352711yescharacteristic
787C4—42no—
788C4—44no—
789C4—44no—
790C4—344no—
791C4—682no—
792C4—684no—
793C4—682no—
794C4—682no—
795C4—1362no—
796C4#1176270218yes—
797C2—44no—
798C2C2×#1176270211yescharacteristic
799C2C22⋊Q8×Dic1711yescharacteristic
800C2#1453147911yescharacteristic
801C2#1453166111yescharacteristic
802C2#1453167711yescharacteristic
803C2#1453179311yescharacteristic
804C2#1453182611yescharacteristic
805C2#1453308311yescharacteristic
806C2#1453309711yescharacteristic
807C2#1453313211yescharacteristic
808C2#1453315411yescharacteristic
809C2#1453318611yescharacteristic
810C2#1453321911yescharacteristic
811C2#1453368711yescharacteristic
812C2#1453370811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#380C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#380D17
hypocenterC17#13993
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#11762708C2semidirect
3. C2×C4⋊C4×Dic17C2semidirect
5. #14527046C2semidirect
8. #14527018C2semidirect
9. #14527013C2semidirect
10. #14527013C2semidirect
38. C17×#380C4semidirect
417. #380Dic17semidirect
510. C17#13993semidirect

Maximal subgroups

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

subgroupindex
C2×#117627082
C2×#117626692
C2×C4⋊C4×Dic172
C2×C4×C22⋊Dic172
#145270462
#145270292
#145270212
#145270182
#145270132
C2×C17×#3802
#1399317