Finite Group Databasebeta

← #17050666

Subgroups — #17050666

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×#11763463C211yesmaximal, characteristic
2C2×#11762881C211yesmaximal, characteristic, complemented
3#14529756C211yesmaximal, characteristic, complemented
4#14529732C211yesmaximal, characteristic, complemented
5#14529220C211yesmaximal, characteristic, complemented
6#14529210C211yesmaximal, characteristic, complemented
7#14529106C211yesmaximal, characteristic, complemented
8#14529101C211yesmaximal, characteristic, complemented
9#14528872C211yesmaximal, characteristic, complemented
10#14528868C211yesmaximal, characteristic, complemented
11#14528791C211yesmaximal, characteristic, complemented
12#14528612C211yesmaximal, characteristic, complemented
13#14528505C211yesmaximal, characteristic, complemented
14C2×#11762571C211yesmaximal, characteristic, complemented
15C17×#2352C211yesmaximal, characteristic, complemented
16C22×#63254—21no—
17C22×#63223C2211yescharacteristic
18C23×#3622C2211yescharacteristic
19#11763463—24no—
20#11763463C418yescomplemented
21C2×#10587555C2211yescharacteristic
22C2×#10587572—21no—
23C2×#10587572—21no—
24C2×#10587583—21no—
25C2×#10587616C2211yescharacteristic
26C2×#10587616C2211yescharacteristic
27C2×C4×D68C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29C22×C4⋊Dic17C2211yescharacteristic
30#11762881—24no—
31C2×C4⋊#3622C2211yescharacteristic
32C2×#10587480C2211yescharacteristic
33C2×#10587480C2211yescharacteristic
34C2×#10587480C2211yescharacteristic
35C2×#10587480C2211yescharacteristic
36C2×C22⋊#3622C2211yescharacteristic
37C2×C22⋊#3622C2211yescharacteristic
38C2×#10587474C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51C2×C4×D4×C17C2211yescharacteristic
52C2×C17×#117C2211yescharacteristic
53C22×C4⋊C4×C17C2211yescharacteristic
54C17×#388—21no—
55C17×#387—21no—
56C17×#386—21no—
57C17×#382C2211yescharacteristic
58C17×#380C2211yescharacteristic
59C17×#380C2211yescharacteristic
60C4×C4⋊C4×C17C2211yescharacteristic
61C4×C22⋊C4×C17—21no—
62C22×D4×C17D411yescharacteristic
63C23×C4×C17—21no—
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C22×C22⋊D17—21no—
67C22×C22⋊D17—21no—
68C23×Dic17—21no—
69C23×Dic17—21no—
70C2×#63254—28no—
71C2×#63254—44no—
72C2×#63254—44no—
73C22×D68C2311yescharacteristic
74C22×C4×D17—21no—
75C22×Dic34—21no—
76C4×D4×C17C2×C414yes—
77C4×D4×C17D414yes—
78C17×#117—22no—
79C17×#117—41no—
80C2×C4⋊C4×C17—22no—
81C2×C4⋊C4×C17—21no—
82C2×C4⋊C4×C17—41no—
83C2×C4⋊C4×C17D411yescharacteristic
84C2×C4⋊C4×C17C2311yescharacteristic
85C2×C4⋊C4×C17C2311yescharacteristic
86C2×C4⋊C4×C17C2311yescharacteristic
87C2×C4⋊C4×C17C2311yescharacteristic
88C2×C22⋊C4×C17—21no—
89C2×C22⋊C4×C17—21no—
90C2×C22⋊C4×C17—21no—
91C2×C22⋊C4×C17D411yescharacteristic
92C2×C22⋊C4×C17D411yescharacteristic
93C2×C42×C17—21no—
94C2×C42×C17—21no—
95C2×C42×C17C2311yescharacteristic
96#10587616—22no—
97#10587616—22no—
98#10587616C2×C414yes—
99#10587616C2×C414yescomplemented
100C2×#63227—21no—
101C2×#63227—21no—
102C2×#63227—21no—
103C2×C4⋊Dic17—22no—
104C2×C4⋊Dic17—22no—
105C2×C4⋊Dic17—21no—
106C2×C4⋊Dic17—21no—
107C2×C4⋊Dic17—21no—
108C2×C4⋊Dic17C2×C414yes—
109C2×C4⋊Dic17C2×C414yescomplemented
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4⋊Dic17C2311yescharacteristic
112C2×C4⋊Dic17C2311yescharacteristic
113C2×#63223—22no—
114C2×#63223—22no—
115C2×#63223—41no—
116C22×#3622—22no—
117C22×#3622—22no—
118C22×#3622—41no—
119C22×#3622C2311yescharacteristic
120C22×#3622C2311yescharacteristic
121C22×#3622C2311yescharacteristic
122C22×#3622C2311yescharacteristic
123#10587583—28no—
124#10587572—28no—
125#10587572—28no—
126C4×D68—22no—
127C4×D68C2×C414yescomplemented
128#10587555—22no—
129#10587555C2×C414yescomplemented
130C17×#95—21no—
131C17×#95—21no—
132C17×#95—21no—
133C17×#95—21no—
134C17×#95—21no—
135C22⋊#3622—22no—
136C22⋊#3622—22no—
137#10587480—22no—
138#10587480—22no—
139#10587480—41no—
140#10587480—41no—
141C4⋊#3622—22no—
142#10587474—22no—
143C24×C17C2×D411yescharacteristic
144C24×C17C2×D411yescharacteristic
145C23×D17—21no—
146C2×D4×C17—22no—
147C2×D4×C17—22no—
148C2×D4×C17C22⋊C414yes—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
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—42no—
162C22×C4×C17—42no—
163C22×C4×C17—81no—
164C22×C4×C17C22×C412yes—
165C22×C4×C17C22×C412yes—
166C22×C4×C17C2×D412yes—
167C22×C4×C17C2×D412yes—
168C22×C4×C17C2×D411yescharacteristic
169C22×C4×C17C2×D411yescharacteristic
170C22×C4×C17C2×D411yescharacteristic
171C22×C4×C17C2×D411yescharacteristic
172C22×C4×C17C2411yescharacteristic
173C2×C22⋊D17—24no—
174C2×C22⋊D17—24no—
175C2×C22⋊D17—42no—
176C2×C22⋊D17—42no—
177C2×C22⋊D17—42no—
178C2×C22⋊D17—42no—
179C22×Dic17—24no—
180C22×Dic17—24no—
181C22×Dic17—21no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—42no—
185C22×Dic17—42no—
186C22×Dic17—42no—
187C22×Dic17—42no—
188#63254—432no—
189C2×D68—21no—
190C2×D68—21no—
191C2×D68—21no—
192C2×D68—21no—
193C2×D68—21no—
194C2×D68C22×C412yes—
195C2×C4×D17—24no—
196C2×C4×D17—42no—
197C2×C4×D17—42no—
198C2×Dic34—24no—
199C2×Dic34—42no—
200C2×Dic34—42no—
201C4⋊C4×C17—21no—
202C4⋊C4×C17—21no—
203C4⋊C4×C17—21no—
204C4⋊C4×C17—21no—
205C4⋊C4×C17—21no—
206C4⋊C4×C17—21no—
207C4⋊C4×C17—21no—
208C4⋊C4×C17—42no—
209C4⋊C4×C17C22⋊C414yes—
210C4⋊C4×C17#4112yescomplemented
211C22⋊C4×C17—42no—
212C22⋊C4×C17—42no—
213C22⋊C4×C17—81no—
214C22⋊C4×C17C22⋊C414yes—
215C22⋊C4×C17C22⋊C414yes—
216C42×C17—42no—
217C42×C17—81no—
218C42×C17C22×C412yes—
219C42×C17C2×D412yes—
220#63227—24no—
221#63227—24no—
222#63227—24no—
223C4⋊Dic17—24no—
224C4⋊Dic17—24no—
225C4⋊Dic17—24no—
226C4⋊Dic17—21no—
227C4⋊Dic17—21no—
228C4⋊Dic17—21no—
229C4⋊Dic17C22×C412yes—
230C4⋊Dic17C22×C412yes—
231C4⋊Dic17C22×C412yes—
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×C17C2×C22⋊C412yes—
258C23×C17C2×C22⋊C412yes—
259C23×C17AGL(1,ℤ/8)12yes—
260C23×C17AGL(1,ℤ/8)12yes—
261C23×C17C22×D411yescharacteristic
262C22×D17—22no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17—41no—
266C22×D17—41no—
267C22×D17—41no—
268C22×D17—41no—
269D4×C17—28no—
270C2×C4×C17—21no—
271C2×C4×C17—21no—
272C2×C4×C17—21no—
273C2×C4×C17—21no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17—41no—
291C2×C4×C17—41no—
292C2×C4×C17—41no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—84no—
299C2×C4×C17C2×C22⋊C412yes—
300C2×C4×C17C2×C22⋊C412yes—
301C2×C4×C17C2×C22⋊C412yes—
302C2×C4×C17C2×C22⋊C412yes—
303C2×C4×C17C23×C411yescharacteristic
304C2×C4×C17C22×D411yescharacteristic
305C2×C4×C17C2×#4111yescharacteristic
306C2×C4×C17C2×#4111yescharacteristic
307C2×C4×C17H(5,𝔽2)11yescharacteristic
308C2×C4×C172−1+411yescharacteristic
309C22⋊D17—48no—
310C22⋊D17—48no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—48no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—48no—
322D68—22no—
323D68—22no—
324D68—41no—
325D68—41no—
326C4×D17—48no—
327Dic34—48no—
328#3622—22no—
329#3622—41no—
330#3622—41no—
331#3622—41no—
332C2×#547—171no—
333C2×#435—171no—
334#2352D1711yescharacteristic, complemented
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#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—42no—
369C2×D17—42no—
370C2×D17—42no—
371C2×D17—81no—
372C2×D17—81no—
373C2×D17—81no—
374C2×D17—81no—
375C4×C17—22no—
376C4×C17—22no—
377C4×C17—22no—
378C4×C17—22no—
379C4×C17—42no—
380C4×C17—81no—
381C4×C17—81no—
382C4×C17—81no—
383C4×C17C4×#4111yescharacteristic
384C4×C17#52011yescharacteristic
385C4×C17#54611yescharacteristic
386C4×C17#54711yescharacteristic
387Dic17—42no—
388Dic17—42no—
389Dic17—42no—
390C22×#41—341no—
391C22×M16—171no—
392C23×C8—171no—
393#547—178no—
394#547—344no—
395C2×C4⋊Q8—171no—
396C2×#123—341no—
397C2×#123—341no—
398C2×C22⋊Q8—341no—
399C2×#121—171no—
400C2×#121—171no—
401C2×C4×D4—171no—
402C2×C4×D4C2×D1711yescharacteristic
403C2×#117C2×D1711yescharacteristic
404C22×C4⋊C4—171no—
405C22×C4⋊C4—171no—
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—21no—
417#387—21no—
418#386—21no—
419#382C2×D1711yescharacteristic
420#380C2×D1711yescharacteristic
421#380C2×D1711yescharacteristic
422C4×C4⋊C4C2×D1711yescharacteristic
423C4×C22⋊C4—21no—
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#233911yescharacteristic
439C2×C17C2×#41811yescharacteristic
440C2×C17#289811yescharacteristic
441C2×C17#330611yescharacteristic
442C2×C17#330811yescharacteristic
443C2×C17#334311yescharacteristic
444C2×C17#334511yescharacteristic
445D17—82no—
446C2×#41—348no—
447C2×#41—684no—
448C2×#41—684no—
449C22×Q8—341no—
450C22×D4—171no—
451C22×D4—341no—
452C22×D4—341no—
453C22×D4C22⋊D1711yescharacteristic
454C23×C4—21no—
455C23×C4—341no—
456C23×C4—341no—
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—174no—
471C4⋊Q8—342no—
472#123—348no—
473#123—348no—
474C22⋊Q8—348no—
475#121—174no—
476#121—174no—
477#121—342no—
478#121—342no—
479C4×D4—174no—
480C4×D4—342no—
481C4×D4C4×D1714yes—
482C4×D4D6814yes—
483#117—22no—
484#117—41no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4—174no—
489C2×C4⋊C4—174no—
490C2×C4⋊C4—171no—
491C2×C4⋊C4—171no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—342no—
494C2×C4⋊C4—342no—
495C2×C4⋊C4—341no—
496C2×C4⋊C4—341no—
497C2×C4⋊C4—341no—
498C2×C4⋊C4C22⋊D1711yescharacteristic
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—21no—
512C2×C42—21no—
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—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527C17#2249511yescharacteristic, complemented, Sylow
528C24—341no—
529C24C2×C22⋊D1711yescharacteristic
530C24C2×C22⋊D1711yescharacteristic
531#41—6832no—
532C2×Q8—344no—
533C2×Q8—682no—
534C2×Q8—682no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—172no—
538C2×D4—344no—
539C2×D4—344no—
540C2×D4—341no—
541C2×D4—341no—
542C2×D4—341no—
543C2×D4—341no—
544C2×D4—341no—
545C2×D4—682no—
546C2×D4—682no—
547C2×D4—682no—
548C2×D4—682no—
549C2×D4#6322714yes—
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—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—341no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—344no—
569C22×C4—344no—
570C22×C4—344no—
571C22×C4—682no—
572C22×C4—682no—
573C22×C4—682no—
574C22×C4—682no—
575C22×C4—682no—
576C22×C4—682no—
577C22×C4C2×C4×D1712yes—
578C22×C4C2×C4×D1712yes—
579C22×C4C2×D6812yes—
580C22×C4C2×D6812yes—
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—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—172no—
609C4⋊C4—172no—
610C4⋊C4—172no—
611C4⋊C4—341no—
612C4⋊C4—341no—
613C4⋊C4—341no—
614C4⋊C4—344no—
615C4⋊C4—344no—
616C4⋊C4—344no—
617C4⋊C4#6322714yes—
618C4⋊C4#6325412yescomplemented
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—344no—
623C22⋊C4—344no—
624C22⋊C4—344no—
625C22⋊C4#6322714yes—
626C22⋊C4#6322714yes—
627C42—42no—
628C42—81no—
629C42C2×C4×D1712yes—
630C42C2×D6812yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—342no—
642C23—681no—
643C23—681no—
644C23—681no—
645C23—681no—
646C23—681no—
647C23—681no—
648C23C2×#6322712yes—
649C23C2×#6322712yes—
650C23#1058763512yes—
651C23#1058763512yes—
652C23C22×C22⋊D1711yescharacteristic
653Q8—688no—
654D4—28no—
655D4—342no—
656D4—342no—
657D4—688no—
658D4—688no—
659D4—681no—
660D4—681no—
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—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—688no—
694C2×C4—688no—
695C2×C4—688no—
696C2×C4—681no—
697C2×C4—681no—
698C2×C4—681no—
699C2×C4—681no—
700C2×C4—681no—
701C2×C4—681no—
702C2×C4C2×#6322712yes—
703C2×C4C2×#6322712yes—
704C2×C4C2×#6322712yes—
705C2×C4C2×#6322712yes—
706C2×C4C22×C4×D1711yescharacteristic
707C2×C4C22×D6811yescharacteristic
708C2×C4C2×#6325411yescharacteristic
709C2×C4#1058769111yescharacteristic
710C2×C4#41×D1711yescharacteristic
711C2×C4#1058769711yescharacteristic
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—682no—
730C22—682no—
731C22—682no—
732C22—1361no—
733C22—1361no—
734C22—1361no—
735C22—1361no—
736C22#1176281314yes—
737C22C22×#6322711yescharacteristic
738C22#1176345311yescharacteristic
739C22#1176345811yescharacteristic
740C22C2×#1058763511yescharacteristic
741C22C2×#1058763511yescharacteristic
742C22#1176362011yescharacteristic
743C22#1176362411yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—682no—
753C4—682no—
754C4—682no—
755C4C4×#6325411yescharacteristic
756C4#1176328811yescharacteristic
757C4#1176345411yescharacteristic
758C4#1176346311yescharacteristic
759C2—24no—
760C2—42no—
761C2—1362no—
762C2#1453160911yescharacteristic
763C2C2×#1176281311yescharacteristic
764C2#1453731411yescharacteristic
765C2#1454074511yescharacteristic
766C2#1454077511yescharacteristic
767C2#1454122411yescharacteristic
768C2#1454124811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2352C2
socleC23×C17C22×D4
prime radicalC2×#11763463C2
cosocleC22×C4×C17C24
hypercenter#2352D17
hypocenterC17#22495
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#11762881C2semidirect
3. #14529756C2semidirect
4. #14529732C2semidirect
5. #14529220C2semidirect
6. #14529210C2semidirect
7. #14529106C2semidirect
8. #14529101C2semidirect
9. #14528872C2semidirect
10. #14528868C2semidirect
11. #14528791C2semidirect
12. #14528612C2semidirect
13. #14528505C2semidirect
14. C2×#11762571C2semidirect
15. C17×#2352C2semidirect
20. #11763463C4semidirect
99. #10587616C2×C4semidirect
109. C2×C4⋊Dic17C2×C4semidirect
127. C4×D68C2×C4semidirect
129. #10587555C2×C4semidirect
210. C4⋊C4×C17#41semidirect
245. C2×#3622#41semidirect
334. #2352D17semidirect
527. C17#22495semidirect
618. C4⋊C4#63254semidirect

Maximal subgroups

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

subgroupindex
C2×#117634632
C2×#117628812
#145297562
#145297322
#145292202
#145292102
#145291062
#145291012
#145288722
#145288682
#145287912
#145286122
#145285052
C2×#117625712
C17×#23522
#2249517