Finite Group Databasebeta

← #17050678

Subgroups — #17050678

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×#11763459C211yesmaximal, characteristic
2C2×#11762880C211yesmaximal, characteristic, complemented
3#14531715C211yesmaximal, characteristic, complemented
4#14529755C211yesmaximal, characteristic, complemented
5#14529730C211yesmaximal, characteristic, complemented
6#14529219C211yesmaximal, characteristic, complemented
7#14529103C211yesmaximal, characteristic, complemented
8#14529102C211yesmaximal, characteristic, complemented
9#14528873C211yesmaximal, characteristic, complemented
10#14528868C211yesmaximal, characteristic, complemented
11#14528792C211yesmaximal, characteristic, complemented
12#14528611C211yesmaximal, characteristic, complemented
13#14528502C211yesmaximal, characteristic, complemented
14C2×#11762572C211yesmaximal, characteristic, complemented
15C17×#1893C211yesmaximal, characteristic, complemented
16C22×#63254—21no—
17C22×#63218C2211yescharacteristic
18#11763459—24no—
19#11763459C418yescomplemented
20C2×#10587574C2211yescharacteristic
21C2×#10587569—21no—
22C2×#10587621—21no—
23C2×#10587564—21no—
24C2×#10587624C2211yescharacteristic
25C2×D4×Dic17C2211yescharacteristic
26C2×C4×C22⋊D17C2211yescharacteristic
27C2×#10587578C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29C22×C4⋊Dic17C2211yescharacteristic
30C2×C4⋊C4×D17C2211yescharacteristic
31#11762880—24no—
32C2×#10587485C2211yescharacteristic
33C2×#10587503C2211yescharacteristic
34C2×#10587503C2211yescharacteristic
35C2×C22⋊#3622C2211yescharacteristic
36C2×#10587491C2211yescharacteristic
37C2×#10587486C2211yescharacteristic
38#11762701—21no—
39#11762696—21no—
40#11762686—21no—
41#11762674C2211yescharacteristic
42#11762666C2211yescharacteristic
43C4⋊C4×Dic17C2211yescharacteristic
44C22⋊C4×Dic17—21no—
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53#11762571C2211yescharacteristic
54#11762571C2211yescharacteristic
55C23×C8×C17C2211yescharacteristic
56C2×C17×#121C2211yescharacteristic
57C2×C17×#102C2211yescharacteristic
58C2×C17×#102C2211yescharacteristic
59C17×#380C2211yescharacteristic
60C17×#340C2211yescharacteristic
61C17×#340C2211yescharacteristic
62C22×D4×C17—21no—
63C22×D4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C22×C22⋊D17—21no—
66C22×C22⋊D17D411yescharacteristic
67C23×Dic17—21no—
68C23×Dic17—21no—
69C23×Dic17—21no—
70C2×#63254—28no—
71C2×#63254—44no—
72C2×#63254—44no—
73C22×C4×D17—21no—
74C22×C4×D17C2311yescharacteristic
75C22×Dic34—21no—
76C22×C8×C17—22no—
77C22×C8×C17—22no—
78C22×C8×C17—41no—
79C22×C8×C17C2311yescharacteristic
80C22×C8×C17C2311yescharacteristic
81C17×#121—22no—
82C17×#121C2×C414yes—
83C2×C4⋊C4×C17C2311yescharacteristic
84C2×C4⋊C4×C17C2311yescharacteristic
85C2×C4⋊C4×C17C2311yescharacteristic
86C2×C22⋊C4×C17—21no—
87C2×C22⋊C4×C17—21no—
88C2×C22⋊Dic17—21no—
89C2×C22⋊Dic17—21no—
90C2×C22⋊Dic17D411yescharacteristic
91#10587624—22no—
92#10587624C2×C414yescomplemented
93#10587621—28no—
94D4×Dic17—22no—
95D4×Dic17C2×C414yescomplemented
96C4×C22⋊D17C2×C414yes—
97C4×C22⋊D17D414yes—
98C2×#63227—21no—
99C2×#63227—21no—
100C2×#63227D411yescharacteristic
101C2×C4⋊Dic17—22no—
102C2×C4⋊Dic17—21no—
103C2×C4⋊Dic17—21no—
104C2×C4⋊Dic17—22no—
105C2×C4⋊Dic17—41no—
106C2×C4⋊Dic17C2×C414yes—
107C2×C4⋊Dic17C2311yescharacteristic
108C2×C4⋊Dic17C2311yescharacteristic
109C2×C4⋊Dic17C2311yescharacteristic
110C2×C4⋊Dic17C2311yescharacteristic
111C2×#63225—21no—
112C2×#63225—21no—
113C2×#63225D411yescharacteristic
114C2×C4×Dic17—21no—
115C2×C4×Dic17—21no—
116C2×C4×Dic17C2311yescharacteristic
117C22×#3622C2311yescharacteristic
118C22×#3622C2311yescharacteristic
119C2×#63218—22no—
120C2×#63218—22no—
121C2×#63218—41no—
122#10587578—22no—
123#10587578—41no—
124C4⋊C4×D17—22no—
125C4⋊C4×D17C2×C414yescomplemented
126#10587574—22no—
127#10587574C2×C414yescomplemented
128#10587569—28no—
129#10587564—28no—
130C17×#102—22no—
131C17×#102—41no—
132C17×#95—21no—
133#10587503—22no—
134#10587503—41no—
135#10587502—21no—
136#10587502—21no—
137#10587502—21no—
138#10587502—21no—
139C22⋊#3622—22no—
140#10587491—22no—
141#10587486—22no—
142#10587485—22no—
143C24×C17—21no—
144C24×C17C2×D411yescharacteristic
145C23×D17C2×D411yescharacteristic
146C2×D4×C17—24no—
147C2×D4×C17—21no—
148C2×D4×C17—21no—
149C2×D4×C17—21no—
150C2×D4×C17—21no—
151C2×D4×C17—21no—
152C2×D4×C17—42no—
153C2×D4×C17—42no—
154C2×D4×C17C22×C412yes—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17C22×C412yes—
163C22×C4×C17C2×D411yescharacteristic
164C22×C4×C17C2×D412yes—
165C22×C4×C17C2411yescharacteristic
166C2×C22⋊D17—22no—
167C2×C22⋊D17—22no—
168C2×C22⋊D17—24no—
169C2×C22⋊D17—42no—
170C2×C22⋊D17—42no—
171C2×C22⋊D17C22⋊C414yes—
172C22×Dic17—24no—
173C22×Dic17—21no—
174C22×Dic17—21no—
175C22×Dic17—21no—
176C22×Dic17—24no—
177C22×Dic17—21no—
178C22×Dic17—42no—
179C22×Dic17—42no—
180C22×Dic17—42no—
181C22×Dic17—42no—
182C22×Dic17—42no—
183C22×Dic17—42no—
184C22×Dic17—81no—
185C22×Dic17C2×D411yescharacteristic
186C22×Dic17C2×D411yescharacteristic
187C22×Dic17C2×D411yescharacteristic
188#63254—432no—
189C2×C4×D17—21no—
190C2×C4×D17—21no—
191C2×C4×D17—21no—
192C2×C4×D17—21no—
193C2×C4×D17—24no—
194C2×C4×D17—42no—
195C2×C4×D17—42no—
196C2×C4×D17C22×C412yes—
197C2×C4×D17C2×D412yes—
198C2×Dic34—24no—
199C2×Dic34—42no—
200C2×Dic34—42no—
201C2×C8×C17—21no—
202C2×C8×C17—21no—
203C2×C8×C17—21no—
204C2×C8×C17—21no—
205C2×C8×C17—21no—
206C2×C8×C17—44no—
207C2×C8×C17#4112yescomplemented
208C4⋊C4×C17—21no—
209C4⋊C4×C17—21no—
210C4⋊C4×C17—21no—
211C4⋊C4×C17—21no—
212C4⋊C4×C17—21no—
213C4⋊C4×C17C22×C412yes—
214C22⋊C4×C17—24no—
215C22⋊C4×C17—42no—
216C22⋊Dic17—24no—
217C22⋊Dic17—24no—
218C22⋊Dic17C22⋊C414yes—
219#63227—42no—
220#63227—81no—
221#63227C22⋊C414yes—
222C4⋊Dic17—24no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17—21no—
228C4⋊Dic17—42no—
229C4⋊Dic17C22×C412yes—
230C4⋊Dic17C22×C412yes—
231C4⋊Dic17#4112yescomplemented
232#63225—24no—
233#63225—24no—
234#63225C22⋊C414yes—
235C4×Dic17—42no—
236C4×Dic17—81no—
237C4×Dic17C22×C412yes—
238C4×Dic17C2×D412yes—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—21no—
243C2×#3622—21no—
244C2×#3622—21no—
245#63218—44no—
246#22495—171nomaximal, Sylow
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—22no—
252C23×C17—41no—
253C23×C17—41no—
254C23×C17—41no—
255C23×C17—41no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17C2×C22⋊C412yes—
259C23×C17AGL(1,ℤ/8)12yes—
260C23×C17AGL(1,ℤ/8)12yes—
261C23×C17C22×D411yescharacteristic
262C22×D17—21no—
263C22×D17—21no—
264C22×D17—21no—
265C22×D17—21no—
266C22×D17—21no—
267C22×D17—21no—
268C22×D17C2×C22⋊C412yes—
269D4×C17—22no—
270D4×C17—22no—
271D4×C17—48no—
272D4×C17—41no—
273D4×C17—41no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17C2×C22⋊C412yes—
290C2×C4×C17C23×C411yescharacteristic
291C2×C4×C17C22×D411yescharacteristic
292C2×C4×C17C2×#4111yescharacteristic
293C2×C4×C17C2×#4111yescharacteristic
294C2×C4×C17H(5,𝔽2)11yescharacteristic
295C2×C4×C172−1+411yescharacteristic
296C22⋊D17—28no—
297C22⋊D17—48no—
298C2×Dic17—21no—
299C2×Dic17—21no—
300C2×Dic17—21no—
301C2×Dic17—21no—
302C2×Dic17—21no—
303C2×Dic17—21no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—48no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—48no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—84no—
319C2×Dic17C2×C22⋊C412yes—
320C2×Dic17C2×C22⋊C412yes—
321C2×Dic17C2×C22⋊C412yes—
322C4×D17—22no—
323C4×D17—22no—
324C4×D17—22no—
325C4×D17—22no—
326C4×D17—48no—
327Dic34—48no—
328C8×C17—22no—
329C8×C17—41no—
330#3622—41no—
331#3622—41no—
332C2×#547—171no—
333C2×#435—171no—
334#2352—171no—
335#1993—171no—
336#1987—171no—
337#1895—171no—
338#1893D1711yescharacteristic, complemented
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—42no—
354C22×C17—42no—
355C22×C17—42no—
356C22×C17—81no—
357C22×C17—81no—
358C22×C17—81no—
359C22×C17—81no—
360C22×C17#41814yes—
361C22×C17C22×C22⋊C411yescharacteristic
362C22×C17#54611yescharacteristic
363C22×C17#54711yescharacteristic
364C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C17#57711yescharacteristic
367C22×C17#57811yescharacteristic
368C2×D17—22no—
369C2×D17—22no—
370C2×D17—22no—
371C2×D17—41no—
372C2×D17—41no—
373C2×D17—41no—
374C2×D17—41no—
375C4×C17—22no—
376C4×C17—42no—
377C4×C17—81no—
378C4×C17—81no—
379C4×C17C4×#4111yescharacteristic
380C4×C17#52011yescharacteristic
381C4×C17#54611yescharacteristic
382C4×C17#54711yescharacteristic
383Dic17—22no—
384Dic17—22no—
385Dic17—22no—
386Dic17—42no—
387Dic17—42no—
388Dic17—42no—
389Dic17—81no—
390C22×#41—341no—
391C22×M16—171no—
392C23×C8C2×D1711yescharacteristic
393#547—178no—
394#547—344no—
395C2×C4⋊Q8—171no—
396C2×#123—341no—
397C2×#123—341no—
398C2×C22⋊Q8—341no—
399C2×#121—171no—
400C2×#121C2×D1711yescharacteristic
401C2×C4×D4—171no—
402C2×C4×D4—171no—
403C2×#117—171no—
404C22×C4⋊C4—171no—
405C22×C4⋊C4—171no—
406C22×C4⋊C4—171no—
407#435—344no—
408C2×C4⋊C8—171no—
409C2×#102—171no—
410C2×#102—171no—
411C2×#102C2×D1711yescharacteristic
412C2×#102C2×D1711yescharacteristic
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#380C2×D1711yescharacteristic
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#340C2×D1711yescharacteristic
435#340C2×D1711yescharacteristic
436C2×C17—24no—
437C2×C17—82no—
438C2×C17#233911yescharacteristic
439C2×C17C2×#41811yescharacteristic
440C2×C17#289811yescharacteristic
441C2×C17#330611yescharacteristic
442C2×C17#330811yescharacteristic
443C2×C17#334311yescharacteristic
444C2×C17#334511yescharacteristic
445D17—42no—
446C2×#41—348no—
447C2×#41—684no—
448C2×#41—684no—
449C22×Q8—341no—
450C22×D4—21no—
451C22×D4—171no—
452C22×D4—341no—
453C22×D4C22×D1711yescharacteristic
454C23×C4—171no—
455C23×C4—341no—
456C23×C4—341no—
457C23×C4—341no—
458C23×C4—341no—
459C23×C4C22×D1711yescharacteristic
460C2×M16—342no—
461C2×M16—342no—
462C2×M16—681no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—41no—
466C22×C8—171no—
467C22×C8—171no—
468C22×C8C22×D1711yescharacteristic
469C22×C8C22×D1711yescharacteristic
470C4⋊Q8—174no—
471C4⋊Q8—342no—
472#123—348no—
473#123—348no—
474C22⋊Q8—348no—
475#121—22no—
476#121—174no—
477#121—342no—
478#121C4×D1714yes—
479C4×D4—174no—
480C4×D4—174no—
481C4×D4—174no—
482C4×D4—342no—
483#117—342no—
484#117—681no—
485C2×C4⋊C4—171no—
486C2×C4⋊C4—174no—
487C2×C4⋊C4—171no—
488C2×C4⋊C4—171no—
489C2×C4⋊C4—171no—
490C2×C4⋊C4—174no—
491C2×C4⋊C4—171no—
492C2×C4⋊C4—342no—
493C2×C4⋊C4—342no—
494C2×C4⋊C4—341no—
495C2×C4⋊C4—341no—
496C2×C4⋊C4—341no—
497C2×C4⋊C4—342no—
498C2×C4⋊C4—341no—
499C2×C4⋊C4—681no—
500C2×C4⋊C4C22×D1711yescharacteristic
501C2×C4⋊C4C22×D1711yescharacteristic
502C2×C4⋊C4C22×D1711yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—171no—
506C2×C22⋊C4—171no—
507C2×C22⋊C4—341no—
508C2×C22⋊C4—341no—
509C2×C22⋊C4—341no—
510C2×C22⋊C4—341no—
511C2×C42—171no—
512C2×C42—341no—
513C2×C42—341no—
514C4⋊C8—342no—
515#102—22no—
516#102—41no—
517#102—342no—
518#102—681no—
519C22⋊C8—342no—
520C22⋊C8—342no—
521#97—342no—
522#95—21no—
523#95—341no—
524#95—341no—
525#95—341no—
526#95—341no—
527C17#2249511yescharacteristic, complemented, Sylow
528C24—21no—
529C24—171no—
530C24D4×D1711yescharacteristic
531#41—6832no—
532C2×Q8—344no—
533C2×Q8—682no—
534C2×Q8—682no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—174no—
544C2×D4—342no—
545C2×D4—342no—
546C2×D4—344no—
547C2×D4—682no—
548C2×D4—682no—
549C2×D4C2×C4×D1712yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—171no—
558C22×C4—171no—
559C22×C4—171no—
560C22×C4—172no—
561C22×C4—172no—
562C22×C4—344no—
563C22×C4—344no—
564C22×C4—341no—
565C22×C4—341no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—341no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—344no—
572C22×C4—341no—
573C22×C4—682no—
574C22×C4—682no—
575C22×C4—682no—
576C22×C4—682no—
577C22×C4—682no—
578C22×C4—682no—
579C22×C4—682no—
580C22×C4—682no—
581C22×C4—1361no—
582C22×C4C2×C4×D1712yes—
583C22×C4D4×D1712yes—
584C22×C4D4×D1711yescharacteristic
585C22×C4C23×D1711yescharacteristic
586M16—684no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—44no—
593C2×C8—341no—
594C2×C8—341no—
595C2×C8—341no—
596C2×C8—341no—
597C2×C8—341no—
598C2×C8—341no—
599C2×C8#6325412yescomplemented
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—174no—
606C4⋊C4—172no—
607C4⋊C4—172no—
608C4⋊C4—172no—
609C4⋊C4—344no—
610C4⋊C4—344no—
611C4⋊C4—341no—
612C4⋊C4—341no—
613C4⋊C4—341no—
614C4⋊C4—344no—
615C4⋊C4—341no—
616C4⋊C4—341no—
617C4⋊C4—682no—
618C4⋊C4C2×C4×D1712yes—
619C22⋊C4—24no—
620C22⋊C4—42no—
621C22⋊C4—174no—
622C22⋊C4—174no—
623C22⋊C4—344no—
624C22⋊C4—344no—
625C22⋊C4—682no—
626C22⋊C4—1361no—
627C42—172no—
628C42—172no—
629C42—682no—
630C42—1361no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—172no—
643C23—341no—
644C23—341no—
645C23—341no—
646C23—341no—
647C23—341no—
648C23—341no—
649C23C22⋊C4×D1712yes—
650C23#1058759712yes—
651C23#1058760012yes—
652C23C2×D4×D1711yescharacteristic
653Q8—688no—
654D4—22no—
655D4—22no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—348no—
660D4—688no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—172no—
677C2×C4—172no—
678C2×C4—172no—
679C2×C4—341no—
680C2×C4—341no—
681C2×C4—341no—
682C2×C4—341no—
683C2×C4—341no—
684C2×C4—341no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—688no—
693C2×C4—688no—
694C2×C4—688no—
695C2×C4—681no—
696C2×C4—681no—
697C2×C4—681no—
698C2×C4—681no—
699C2×C4—681no—
700C2×C4—681no—
701C2×C4—681no—
702C2×C4—681no—
703C2×C4—681no—
704C2×C4—1364no—
705C2×C4C22⋊C4×D1712yes—
706C2×C4C22×C4×D1711yescharacteristic
707C2×C4C2×D4×D1711yescharacteristic
708C2×C4C2×#6325411yescharacteristic
709C2×C4#1058769111yescharacteristic
710C2×C4#41×D1711yescharacteristic
711C2×C4#1058769711yescharacteristic
712C8—22no—
713C8—41no—
714C8—681no—
715C8—681no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—342no—
730C22—342no—
731C22—342no—
732C22—681no—
733C22—681no—
734C22—681no—
735C22—681no—
736C22#1176281214yes—
737C22C2×C22⋊C4×D1711yescharacteristic
738C22#1176344811yescharacteristic
739C22#1176345911yescharacteristic
740C22C2×#1058759711yescharacteristic
741C22C2×#1058760011yescharacteristic
742C22#1176361611yescharacteristic
743C22#1176362311yescharacteristic
744C4—22no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—342no—
749C4—342no—
750C4—342no—
751C4—682no—
752C4—682no—
753C4—682no—
754C4—1361no—
755C4C4×#6325411yescharacteristic
756C4#1176328811yescharacteristic
757C4#1176344611yescharacteristic
758C4#1176345711yescharacteristic
759C2—24no—
760C2—82no—
761C2—682no—
762C2#1453161011yescharacteristic
763C2C2×#1176281211yescharacteristic
764C2#1453731311yescharacteristic
765C2#1454075111yescharacteristic
766C2#1454078111yescharacteristic
767C2#1454123011yescharacteristic
768C2#1454126011yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1893C2
socleC23×C17C22×D4
prime radicalC2×#11763459C2
cosocleC22×C4×C17C24
hypercenter#1893D17
hypocenterC17#22495
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#11762880C2semidirect
3. #14531715C2semidirect
4. #14529755C2semidirect
5. #14529730C2semidirect
6. #14529219C2semidirect
7. #14529103C2semidirect
8. #14529102C2semidirect
9. #14528873C2semidirect
10. #14528868C2semidirect
11. #14528792C2semidirect
12. #14528611C2semidirect
13. #14528502C2semidirect
14. C2×#11762572C2semidirect
15. C17×#1893C2semidirect
19. #11763459C4semidirect
92. #10587624C2×C4semidirect
95. D4×Dic17C2×C4semidirect
125. C4⋊C4×D17C2×C4semidirect
127. #10587574C2×C4semidirect
207. C2×C8×C17#41semidirect
231. C4⋊Dic17#41semidirect
338. #1893D17semidirect
527. C17#22495semidirect
599. C2×C8#63254semidirect

Maximal subgroups

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

subgroupindex
C2×#117634592
C2×#117628802
#145317152
#145297552
#145297302
#145292192
#145291032
#145291022
#145288732
#145288682
#145287922
#145286112
#145285022
C2×#117625722
C17×#18932
#2249517