Finite Group Databasebeta

← #17050644

Subgroups — #17050644

Order 4352.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763505C211yesmaximal, characteristic
2D4×C4⋊Dic17C211yesmaximal, characteristic, complemented
3#14529753C211yesmaximal, characteristic, complemented
4#14529739C211yesmaximal, characteristic, complemented
5#14529222C211yesmaximal, characteristic, complemented
6#14529212C211yesmaximal, characteristic, complemented
7#14529099C211yesmaximal, characteristic, complemented
8#14529099C211yesmaximal, characteristic, complemented
9#14528880C211yesmaximal, characteristic, complemented
10#14528875C211yesmaximal, characteristic, complemented
11#14528785C211yesmaximal, characteristic, complemented
12#14528610C211yesmaximal, characteristic, complemented
13#14528504C211yesmaximal, characteristic, complemented
14C2×#11762572C211yesmaximal, characteristic, complemented
15C2×C17×#435C211yesmaximal, characteristic, complemented
16#11763505—24no—
17#11763505C418yescomplemented
18C2×#10587584—21no—
19C2×#10587556C2211yescharacteristic
20C2×#10587569—21no—
21C2×#10587616C2211yescharacteristic
22C2×#10587616C2211yescharacteristic
23C2×#10587625—21no—
24C2×C4×D68C2211yescharacteristic
25C2×D4×Dic17—21no—
26C2×#10587567—21no—
27C2×#10587612C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29C22×C4⋊Dic17C2211yescharacteristic
30C22×C4⋊Dic17C2211yescharacteristic
31C2×#10587492C2211yescharacteristic
32C2×#10587492C2211yescharacteristic
33C2×#10587492C2211yescharacteristic
34C2×#10587492C2211yescharacteristic
35#11762708—21no—
36#11762684—21no—
37#11762684—21no—
38#11762679C2211yescharacteristic
39#11762669C2211yescharacteristic
40#11762669C2211yescharacteristic
41C4×C4⋊Dic17C2211yescharacteristic
42#11762572C2211yescharacteristic
43#11762572C2211yescharacteristic
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52#11762572C2211yescharacteristic
53#11762572C2211yescharacteristic
54C22×M16×C17C2211yescharacteristic
55C23×C8×C17C2211yescharacteristic
56C2×C4×D4×C17C2211yescharacteristic
57C17×#435—24no—
58C2×C17×C4⋊C8C2211yescharacteristic
59C2×C17×C22⋊C8C2211yescharacteristic
60C2×C17×C22⋊C8C2211yescharacteristic
61C2×C17×#97C2211yescharacteristic
62C22×D4×C17D411yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C22×C22⋊D17—21no—
66C22×C22⋊D17—21no—
67C23×Dic17—21no—
68C23×Dic17—21no—
69C23×Dic17—21no—
70C22×D68C2311yescharacteristic
71C22×C4×D17—21no—
72C2×M16×C17—22no—
73C2×M16×C17—22no—
74C2×M16×C17—41no—
75C22×C8×C17—22no—
76C22×C8×C17—22no—
77C22×C8×C17—41no—
78C22×C8×C17C2311yescharacteristic
79C22×C8×C17C2311yescharacteristic
80C22×C8×C17C2311yescharacteristic
81C22×C8×C17C2311yescharacteristic
82C4×D4×C17C2×C414yes—
83C4×D4×C17D414yes—
84C2×C4⋊C4×C17D411yescharacteristic
85C2×C22⋊C4×C17D411yescharacteristic
86C2×C22⋊C4×C17D411yescharacteristic
87C2×C42×C17C2311yescharacteristic
88C2×C22⋊Dic17—21no—
89C2×C22⋊Dic17—21no—
90C2×C22⋊Dic17—21no—
91#10587625—28no—
92D4×Dic17—44no—
93#10587616—22no—
94#10587616—22no—
95#10587616C2×C414yescomplemented
96#10587616C2×C414yescomplemented
97C2×#63227—21no—
98C2×#63227—21no—
99C2×#63227—21no—
100#10587612—22no—
101#10587612C2×C414yescomplemented
102C2×C4⋊Dic17—22no—
103C2×C4⋊Dic17—21no—
104C2×C4⋊Dic17—21no—
105C2×C4⋊Dic17—21no—
106C2×C4⋊Dic17—21no—
107C2×C4⋊Dic17—21no—
108C2×C4⋊Dic17—22no—
109C2×C4⋊Dic17—22no—
110C2×C4⋊Dic17—41no—
111C2×C4⋊Dic17—41no—
112C2×C4⋊Dic17C2×C414yescomplemented
113C2×C4⋊Dic17C2311yescharacteristic
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4⋊Dic17C2311yescharacteristic
117C2×C4⋊Dic17C2311yescharacteristic
118C2×C4⋊Dic17C2311yescharacteristic
119C2×C4⋊Dic17C2311yescharacteristic
120C2×#63225—21no—
121C2×#63225—21no—
122C2×C4×Dic17—21no—
123C2×C4×Dic17—21no—
124#10587584—28no—
125#10587569—28no—
126#10587567—28no—
127C4×D68—22no—
128C4×D68C2×C414yescomplemented
129#10587556—22no—
130#10587556C2×C414yescomplemented
131C17×C4⋊C8—22no—
132C17×C22⋊C8—22no—
133C17×C22⋊C8—22no—
134C17×#97—22no—
135#10587502—21no—
136#10587502—21no—
137#10587502—21no—
138#10587492—22no—
139#10587492—22no—
140#10587492—41no—
141#10587492—41no—
142C24×C17C2×D411yescharacteristic
143C24×C17C2×D411yescharacteristic
144C23×D17—21no—
145C2×D4×C17—22no—
146C2×D4×C17—22no—
147C2×D4×C17C22⋊C414yes—
148C22×C4×C17—21no—
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×C17C22×C412yes—
157C22×C4×C17C22×C412yes—
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D411yescharacteristic
161C22×C4×C17C2×D411yescharacteristic
162C22×C4×C17C2×D412yes—
163C22×C4×C17C2×D412yes—
164C22×C4×C17C2411yescharacteristic
165C2×C22⋊D17—24no—
166C2×C22⋊D17—24no—
167C2×C22⋊D17—42no—
168C2×C22⋊D17—42no—
169C2×C22⋊D17—81no—
170C2×C22⋊D17—81no—
171C22×Dic17—21no—
172C22×Dic17—21no—
173C22×Dic17—21no—
174C22×Dic17—21no—
175C22×Dic17—24no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—42no—
180C22×Dic17—42no—
181C22×Dic17—42no—
182C22×Dic17—42no—
183C22×Dic17—81no—
184C22×Dic17—81no—
185C22×Dic17—81no—
186C22×Dic17—81no—
187C2×D68—21no—
188C2×D68—21no—
189C2×D68—21no—
190C2×D68—21no—
191C2×D68—21no—
192C2×D68C22×C412yes—
193C2×C4×D17—24no—
194C2×C4×D17—81no—
195C2×C4×D17—81no—
196M16×C17—44no—
197C2×C8×C17—21no—
198C2×C8×C17—21no—
199C2×C8×C17—21no—
200C2×C8×C17—21no—
201C2×C8×C17—21no—
202C2×C8×C17—21no—
203C2×C8×C17—21no—
204C2×C8×C17—21no—
205C2×C8×C17—21no—
206C2×C8×C17—21no—
207C2×C8×C17—21no—
208C2×C8×C17—44no—
209C2×C8×C17#4112yes—
210C4⋊C4×C17C22⋊C414yes—
211C22⋊C4×C17C22⋊C414yes—
212C22⋊C4×C17C22⋊C414yes—
213C42×C17C22×C412yes—
214C42×C17C2×D412yes—
215C22⋊Dic17—24no—
216C22⋊Dic17—42no—
217C22⋊Dic17—42no—
218#63227—24no—
219#63227—24no—
220#63227—24no—
221C4⋊Dic17—24no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17—21no—
228C4⋊Dic17—21no—
229C4⋊Dic17—21no—
230C4⋊Dic17—21no—
231C4⋊Dic17—21no—
232C4⋊Dic17—42no—
233C4⋊Dic17—42no—
234C4⋊Dic17—42no—
235C4⋊Dic17—81no—
236C4⋊Dic17C22×C412yes—
237C4⋊Dic17C22×C412yes—
238C4⋊Dic17C22×C412yes—
239C4⋊Dic17#4112yes—
240#63225—24no—
241#63225—24no—
242C4×Dic17—24no—
243C4×Dic17—42no—
244#22493—171nomaximal, Sylow
245C23×C17—21no—
246C23×C17—21no—
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×C17C2×C22⋊C412yes—
256C23×C17C2×C22⋊C412yes—
257C23×C17AGL(1,ℤ/8)12yes—
258C23×C17#13712yes—
259C23×C17C22×D411yescharacteristic
260C22×D17—22no—
261C22×D17—41no—
262C22×D17—41no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17—41no—
266C22×D17—41no—
267D4×C17—28no—
268C2×C4×C17—21no—
269C2×C4×C17—21no—
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—22no—
277C2×C4×C17—22no—
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×C17C2×C22⋊C412yes—
285C2×C4×C17C2×C22⋊C412yes—
286C2×C4×C17C2×C22⋊C412yes—
287C2×C4×C17C2×C22⋊C412yes—
288C2×C4×C17C23×C411yescharacteristic
289C2×C4×C17C22×D411yescharacteristic
290C2×C4×C17C2×#4111yescharacteristic
291C2×C4×C17C2×#4111yescharacteristic
292C2×C4×C17H(5,𝔽2)11yescharacteristic
293C2×C4×C172−1+411yescharacteristic
294C22⋊D17—48no—
295C22⋊D17—84no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—41no—
301C2×Dic17—41no—
302C2×Dic17—41no—
303C2×Dic17—41no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—84no—
318C2×Dic17—84no—
319C2×Dic17—84no—
320D68—22no—
321D68—22no—
322D68—41no—
323D68—41no—
324C4×D17—84no—
325C8×C17—22no—
326C8×C17—41no—
327C8×C17—41no—
328C8×C17—41no—
329C2×#553—171no—
330C2×#435D1711yescharacteristic, complemented
331D4×C4⋊C4—171no—
332#1992—171no—
333#1989—171no—
334#1895—171no—
335#1893—171no—
336#1874—171no—
337#1874—171no—
338#1825—171no—
339#1824—171no—
340#1802—171no—
341#1762—171no—
342#1736—171no—
343C2×#340—171no—
344C22×C17—22no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—22no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—41no—
354C22×C17—41no—
355C22×C17—41no—
356C22×C17—41no—
357C22×C17#41714yes—
358C22×C17C22×C22⋊C411yescharacteristic
359C22×C17#54611yescharacteristic
360C22×C17#54711yescharacteristic
361C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C17C2×#13711yescharacteristic
363C22×C17#57611yescharacteristic
364C22×C17#57711yescharacteristic
365C2×D17—42no—
366C2×D17—42no—
367C2×D17—42no—
368C2×D17—81no—
369C2×D17—81no—
370C2×D17—81no—
371C2×D17—81no—
372C4×C17—22no—
373C4×C17—22no—
374C4×C17—22no—
375C4×C17—22no—
376C4×C17C4×#4111yescharacteristic
377C4×C17#52011yescharacteristic
378C4×C17#54611yescharacteristic
379C4×C17#54711yescharacteristic
380Dic17—42no—
381Dic17—42no—
382Dic17—42no—
383Dic17—42no—
384Dic17—81no—
385Dic17—81no—
386Dic17—81no—
387C22×M16C2×D1711yescharacteristic
388C23×C8C2×D1711yescharacteristic
389#553—178no—
390#553—344no—
391C2×#126—341no—
392C2×#125—171no—
393C2×#123—341no—
394C2×#121—171no—
395C2×#121—171no—
396C2×#121—341no—
397C2×C4×D4—171no—
398C2×C4×D4—341no—
399C2×C4×D4—341no—
400C2×C4×D4C2×D1711yescharacteristic
401C2×#117—171no—
402C22×C4⋊C4—171no—
403C22×C4⋊C4—171no—
404C22×C4⋊C4—171no—
405#435—24no—
406C2×C4⋊C8C2×D1711yescharacteristic
407C2×#102—171no—
408C2×#102—171no—
409C2×#102—171no—
410C2×#102—171no—
411C2×C22⋊C8C2×D1711yescharacteristic
412C2×C22⋊C8C2×D1711yescharacteristic
413C2×#97C2×D1711yescharacteristic
414#389—341no—
415#385—341no—
416#385—341no—
417#384—171no—
418#380—171no—
419#380—171no—
420C4×C4⋊C4—171no—
421#340—171no—
422#340—171no—
423#340—171no—
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—
433C2×C17—24no—
434C2×C17—42no—
435C2×C17#233911yescharacteristic
436C2×C17C2×#41711yescharacteristic
437C2×C17#289711yescharacteristic
438C2×C17#331811yescharacteristic
439C2×C17#332011yescharacteristic
440C2×C17#334511yescharacteristic
441C2×C17#334611yescharacteristic
442D17—82no—
443C22×D4—171no—
444C22×D4—341no—
445C22×D4—341no—
446C22×D4D6811yescharacteristic
447C23×C4—341no—
448C23×C4—341no—
449C23×C4—341no—
450C23×C4—341no—
451C23×C4C22×D1711yescharacteristic
452C23×C4C22×D1711yescharacteristic
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—41no—
456C22×C8—22no—
457C22×C8—22no—
458C22×C8—41no—
459C22×C8C22×D1711yescharacteristic
460C22×C8C22×D1711yescharacteristic
461C22×C8C22×D1711yescharacteristic
462C22×C8C22×D1711yescharacteristic
463#126—348no—
464#125—174no—
465#125—342no—
466#123—348no—
467#121—174no—
468#121—174no—
469#121—348no—
470#121—342no—
471#121—342no—
472C4×D4—174no—
473C4×D4—348no—
474C4×D4—342no—
475C4×D4—684no—
476C4×D4C4×D1714yes—
477C4×D4C22⋊D1714yes—
478#117—174no—
479#117—342no—
480C2×C4⋊C4—174no—
481C2×C4⋊C4—171no—
482C2×C4⋊C4—171no—
483C2×C4⋊C4—171no—
484C2×C4⋊C4—171no—
485C2×C4⋊C4—171no—
486C2×C4⋊C4—171no—
487C2×C4⋊C4—171no—
488C2×C4⋊C4—342no—
489C2×C4⋊C4—342no—
490C2×C4⋊C4—341no—
491C2×C4⋊C4—341no—
492C2×C4⋊C4—341no—
493C2×C4⋊C4—342no—
494C2×C4⋊C4—341no—
495C2×C4⋊C4—341no—
496C2×C4⋊C4—341no—
497C2×C4⋊C4—341no—
498C2×C4⋊C4—681no—
499C2×C4⋊C4—681no—
500C2×C4⋊C4D6811yescharacteristic
501C2×C22⋊C4—341no—
502C2×C22⋊C4—341no—
503C2×C22⋊C4—341no—
504C2×C22⋊C4—341no—
505C2×C22⋊C4—341no—
506C2×C22⋊C4—341no—
507C2×C22⋊C4D6811yescharacteristic
508C2×C22⋊C4D6811yescharacteristic
509C2×C42—341no—
510C2×C42—341no—
511C2×C42C22×D1711yescharacteristic
512C4⋊C8—22no—
513#102—342no—
514#102—342no—
515#102—681no—
516#102—681no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519#97—22no—
520#95—341no—
521#95—341no—
522#95—341no—
523C17#2249311yescharacteristic, complemented, Sylow
524C24—341no—
525C24C2×D6811yescharacteristic
526C24C2×D6811yescharacteristic
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—172no—
530C2×D4—344no—
531C2×D4—344no—
532C2×D4—341no—
533C2×D4—341no—
534C2×D4—341no—
535C2×D4—341no—
536C2×D4—341no—
537C2×D4—682no—
538C2×D4—682no—
539C2×D4—1361no—
540C2×D4—1361no—
541C2×D4#6322714yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—341no—
551C22×C4—341no—
552C22×C4—341no—
553C22×C4—341no—
554C22×C4—344no—
555C22×C4—344no—
556C22×C4—341no—
557C22×C4—341no—
558C22×C4—341no—
559C22×C4—682no—
560C22×C4—682no—
561C22×C4—682no—
562C22×C4—682no—
563C22×C4—1361no—
564C22×C4—1361no—
565C22×C4—1361no—
566C22×C4—1361no—
567C22×C4—1361no—
568C22×C4—1361no—
569C22×C4C2×C4×D1712yes—
570C22×C4C2×C4×D1712yes—
571C22×C4C2×D6811yescharacteristic
572C22×C4C2×D6811yescharacteristic
573C22×C4C2×D6811yescharacteristic
574C22×C4C2×D6811yescharacteristic
575C22×C4C2×C22⋊D1712yes—
576C22×C4C2×C22⋊D1712yes—
577C22×C4C23×D1711yescharacteristic
578M16—44no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—44no—
591C2×C8#6325412yes—
592C4⋊C4—172no—
593C4⋊C4—172no—
594C4⋊C4—172no—
595C4⋊C4—172no—
596C4⋊C4—341no—
597C4⋊C4—341no—
598C4⋊C4—341no—
599C4⋊C4—341no—
600C4⋊C4—344no—
601C4⋊C4—344no—
602C4⋊C4—344no—
603C4⋊C4—341no—
604C4⋊C4—341no—
605C4⋊C4—341no—
606C4⋊C4—341no—
607C4⋊C4—341no—
608C4⋊C4—341no—
609C4⋊C4—682no—
610C4⋊C4—682no—
611C4⋊C4—682no—
612C4⋊C4—1361no—
613C4⋊C4#6322714yes—
614C22⋊C4—344no—
615C22⋊C4—344no—
616C22⋊C4—344no—
617C22⋊C4—344no—
618C22⋊C4—682no—
619C22⋊C4—682no—
620C22⋊C4#6322714yes—
621C22⋊C4#6322714yes—
622C42—344no—
623C42—682no—
624C42C2×C4×D1712yes—
625C42C2×C22⋊D1712yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—342no—
637C23—681no—
638C23—681no—
639C23—681no—
640C23—681no—
641C23—681no—
642C23—681no—
643C23#1058759412yes—
644C23#1058759512yes—
645C23C2×#6322712yes—
646C23C2×#6322712yes—
647C23C22×D6811yescharacteristic
648D4—28no—
649D4—342no—
650D4—342no—
651D4—688no—
652D4—681no—
653D4—681no—
654D4—1364no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—681no—
676C2×C4—681no—
677C2×C4—681no—
678C2×C4—681no—
679C2×C4—681no—
680C2×C4—681no—
681C2×C4—681no—
682C2×C4—681no—
683C2×C4—681no—
684C2×C4—681no—
685C2×C4—681no—
686C2×C4—681no—
687C2×C4—681no—
688C2×C4—681no—
689C2×C4—681no—
690C2×C4—681no—
691C2×C4—681no—
692C2×C4—1364no—
693C2×C4—1364no—
694C2×C4—1364no—
695C2×C4—1364no—
696C2×C4C2×#6322712yes—
697C2×C4C2×#6322712yes—
698C2×C4C2×#6322712yes—
699C2×C4C2×#6322712yes—
700C2×C4C22×C4×D1711yescharacteristic
701C2×C4C2×#6325411yescharacteristic
702C2×C4#1058769111yescharacteristic
703C2×C4#41×D1711yescharacteristic
704C2×C4#1058769711yescharacteristic
705C2×C4C22×C22⋊D1711yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—682no—
724C22—682no—
725C22—682no—
726C22—1361no—
727C22—1361no—
728C22—1361no—
729C22—1361no—
730C22#1176281114yes—
731C22C22×#6322711yescharacteristic
732C22#1176345411yescharacteristic
733C22#1176346311yescharacteristic
734C22C2×#1058759411yescharacteristic
735C22C2×#1058759511yescharacteristic
736C22#1176361411yescharacteristic
737C22#1176362111yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—682no—
743C4—682no—
744C4—682no—
745C4—682no—
746C4—1361no—
747C4—1361no—
748C4—1361no—
749C4C4×#6325411yescharacteristic
750C4#1176328811yescharacteristic
751C4#1176345311yescharacteristic
752C4#1176345811yescharacteristic
753C2—24no—
754C2—42no—
755C2—1362no—
756C2#1453160911yescharacteristic
757C2C2×#1176281111yescharacteristic
758C2#1453731111yescharacteristic
759C2#1454092711yescharacteristic
760C2#1454095711yescharacteristic
761C2#1454125611yescharacteristic
762C2#1454127111yescharacteristic
subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#435C2
socleC23×C17C22×D4
prime radicalC2×#11763505C2
cosocleC22×C4×C17C24
hypercenterC2×#435D17
hypocenterC17#22493
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. D4×C4⋊Dic17C2semidirect
3. #14529753C2semidirect
4. #14529739C2semidirect
5. #14529222C2semidirect
6. #14529212C2semidirect
7. #14529099C2semidirect
8. #14529099C2semidirect
9. #14528880C2semidirect
10. #14528875C2semidirect
11. #14528785C2semidirect
12. #14528610C2semidirect
13. #14528504C2semidirect
14. C2×#11762572C2semidirect
15. C2×C17×#435C2semidirect
17. #11763505C4semidirect
95. #10587616C2×C4semidirect
96. #10587616C2×C4semidirect
101. #10587612C2×C4semidirect
112. C2×C4⋊Dic17C2×C4semidirect
128. C4×D68C2×C4semidirect
130. #10587556C2×C4semidirect
330. C2×#435D17semidirect
523. C17#22493semidirect

Maximal subgroups

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

subgroupindex
C2×#117635052
D4×C4⋊Dic172
#145297532
#145297392
#145292222
#145292122
#145290992
#145288802
#145288752
#145287852
#145286102
#145285042
C2×#117625722
C2×C17×#4352
#2249317