Finite Group Databasebeta

← #17054630

Subgroups — #17054630

Order 4352.

1146 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×#11762910C211yesmaximal, characteristic, complemented
2C2×#11762805C211yesmaximal, characteristic, complemented
3#14531826C211yesmaximal, characteristic, complemented
4#14531625C211yesmaximal, characteristic, complemented
5#14529661C211yesmaximal, characteristic, complemented
6#14529483C211yesmaximal, characteristic, complemented
7#14529406C211yesmaximal, characteristic, complemented
8#14529213C211yesmaximal, characteristic, complemented
9#14529141C211yesmaximal, characteristic, complemented
10#14529134C211yesmaximal, characteristic, complemented
11#14529054C211yesmaximal, characteristic, complemented
12#14528985C211yesmaximal, characteristic, complemented
13#14528616C211yesmaximal, characteristic, complemented
14#14528563C211yesmaximal, characteristic, complemented
15C2×C17×#449C211yesmaximal, characteristic
16C23×#3622C2211yescharacteristic
17C2×Q8×Dic17C2211yescharacteristic
18C2×Q8×Dic17C2211yescharacteristic
19C2×D4×Dic17C2211yescharacteristic
20C2×#10587612C2211yescharacteristic
21#11762910—24no—
22C2×#10587489C2211yescharacteristic
23C2×#10587488C2211yescharacteristic
24#11762805—24no—
25C2×#10587506C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587503C2211yescharacteristic
28C2×#10587503C2211yescharacteristic
29C2×#10587503C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587486C2211yescharacteristic
32C2×#10587486C2211yescharacteristic
33#11762712—21no—
34#11762712—21no—
35#11762712—21no—
36#11762712C2211yescharacteristic
37#11762712C2211yescharacteristic
38#11762712C2211yescharacteristic
39#11762708C2211yescharacteristic
40#11762702—21no—
41#11762689—21no—
42#11762669—21no—
43#11762669C2211yescharacteristic
44C4⋊C4×Dic17C2211yescharacteristic
45C22⋊C4×Dic17—21no—
46C4×C22⋊Dic17—21no—
47C4×C22⋊Dic17C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762563C2211yescharacteristic
53#11762563C2211yescharacteristic
54C22×#41×C17C2211yescharacteristic
55C22×SD16×C17C2211yescharacteristic
56C22×D8×C17C2211yescharacteristic
57C2×C17×#121C2211yescharacteristic
58C17×#449C418yescomplemented
59C2×C17×#103C2211yescharacteristic
60C2×C17×#102C2211yescharacteristic
61C2×C17×C22⋊C8C2211yescharacteristic
62C2×#41×C17—22no—
63C2×#41×C17—22no—
64C2×#41×C17—22no—
65C2×#41×C17—41no—
66C2×#41×C17—41no—
67C2×#41×C17C2×C414yescomplemented
68C22×Q8×C17C2311yescharacteristic
69C22×D4×C17—21no—
70C22×D4×C17—21no—
71C22×D4×C17C2311yescharacteristic
72C22×D4×C17C2311yescharacteristic
73C23×C4×C17—21no—
74C23×C4×C17C2311yescharacteristic
75C23×Dic17—21no—
76C2×SD16×C17—22no—
77C2×SD16×C17—22no—
78C2×SD16×C17C2×C414yes—
79C2×D8×C17—41no—
80C2×D8×C17—41no—
81C2×D8×C17C2×C414yes—
82C22×C8×C17C2311yescharacteristic
83C22×C8×C17C2311yescharacteristic
84C17×#121—22no—
85C17×#121C2×C414yes—
86C2×C4⋊C4×C17C2311yescharacteristic
87C2×C22⋊C4×C17—21no—
88C2×C22⋊Dic17—21no—
89C2×C22⋊Dic17—21no—
90C2×C22⋊Dic17—21no—
91C2×C22⋊Dic17—21no—
92C2×C22⋊Dic17—21no—
93C2×C22⋊Dic17—21no—
94C2×C22⋊Dic17—21no—
95C2×C22⋊Dic17—21no—
96C2×C22⋊Dic17—21no—
97C2×C22⋊Dic17D411yescharacteristic
98C2×C22⋊Dic17D411yescharacteristic
99Q8×Dic17—22no—
100Q8×Dic17—22no—
101Q8×Dic17—41no—
102Q8×Dic17—41no—
103D4×Dic17—22no—
104D4×Dic17—41no—
105#10587612—22no—
106#10587612—41no—
107C2×C4⋊Dic17—21no—
108C2×C4⋊Dic17—21no—
109C2×C4⋊Dic17—21no—
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4⋊Dic17C2311yescharacteristic
112C2×C4⋊Dic17C2311yescharacteristic
113C2×C4⋊Dic17C2311yescharacteristic
114C2×C4×Dic17—21no—
115C2×C4×Dic17—21no—
116C2×C4×Dic17—21no—
117C2×C4×Dic17—21no—
118C2×C4×Dic17C2311yescharacteristic
119C2×C4×Dic17C2311yescharacteristic
120C22×#3622—22no—
121C22×#3622—22no—
122C22×#3622—41no—
123C22×#3622C2311yescharacteristic
124C22×#3622C2311yescharacteristic
125C17×#103C2×C414yescomplemented
126C17×#102C2×C414yescomplemented
127C17×C22⋊C8C2×C414yescomplemented
128#10587506—22no—
129#10587506D414yescomplemented
130#10587503—22no—
131#10587503—22no—
132#10587503—22no—
133#10587503—41no—
134#10587502—21no—
135#10587502—21no—
136#10587502—21no—
137#10587502D411yescharacteristic
138#10587502D411yescharacteristic
139#10587489—22no—
140#10587488—41no—
141#10587486—22no—
142#10587486—41no—
143C24×C17—21no—
144C24×C17—21no—
145C24×C17C2×D411yescharacteristic
146#41×C17—28no—
147#41×C17—44no—
148#41×C17—44no—
149#41×C17—44no—
150C2×Q8×C17—21no—
151C2×Q8×C17—21no—
152C2×Q8×C17—21no—
153C2×Q8×C17C22×C412yes—
154C2×Q8×C17C2×D412yes—
155C2×Q8×C17#4112yes—
156C2×D4×C17—24no—
157C2×D4×C17—24no—
158C2×D4×C17—21no—
159C2×D4×C17—21no—
160C2×D4×C17—21no—
161C2×D4×C17—21no—
162C2×D4×C17—21no—
163C2×D4×C17—21no—
164C2×D4×C17—21no—
165C2×D4×C17—21no—
166C2×D4×C17—21no—
167C2×D4×C17—21no—
168C2×D4×C17—42no—
169C2×D4×C17—42no—
170C2×D4×C17—81no—
171C2×D4×C17—81no—
172C2×D4×C17C22×C412yes—
173C2×D4×C17C22×C412yes—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—24no—
181C22×C4×C17—42no—
182C22×C4×C17—42no—
183C22×C4×C17C22×C412yes—
184C22×C4×C17C2×D411yescharacteristic
185C22×C4×C17#4112yes—
186C22×C4×C17C2411yescharacteristic
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—21no—
191C22×Dic17—42no—
192C22×Dic17—42no—
193C22×Dic17—81no—
194C22×Dic17C2×D411yescharacteristic
195C22×Dic17C2×D411yescharacteristic
196C22×Dic17C2×D411yescharacteristic
197C22×Dic17C2×D411yescharacteristic
198SD16×C17—28no—
199D8×C17—44no—
200C2×C8×C17—21no—
201C2×C8×C17—21no—
202C2×C8×C17—21no—
203C2×C8×C17—21no—
204C2×C8×C17C22×C412yes—
205C2×C8×C17C22×C412yes—
206C4⋊C4×C17—21no—
207C4⋊C4×C17C22×C412yes—
208C22⋊C4×C17—24no—
209C22⋊Dic17—41no—
210C22⋊Dic17—41no—
211C22⋊Dic17—42no—
212C22⋊Dic17—42no—
213C22⋊Dic17—42no—
214C22⋊Dic17—42no—
215C22⋊Dic17—42no—
216C22⋊Dic17—81no—
217C22⋊Dic17—81no—
218C22⋊Dic17—81no—
219C22⋊Dic17—81no—
220C4⋊Dic17—21no—
221C4⋊Dic17—21no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17—42no—
228C4⋊Dic17—42no—
229C4⋊Dic17—81no—
230C4⋊Dic17C2×D412yes—
231C4×Dic17—21no—
232C4×Dic17—21no—
233C4×Dic17—21no—
234C4×Dic17—21no—
235C4×Dic17—42no—
236C4×Dic17—42no—
237C4×Dic17—42no—
238C4×Dic17—81no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—21no—
243C2×#3622—21no—
244C2×#3622—44no—
245C2×#3622C2×D412yes—
246#22857—171nomaximal, Sylow
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—21no—
253C23×C17—22no—
254C23×C17—22no—
255C23×C17—41no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17—41no—
259C23×C17—41no—
260C23×C17—41no—
261C23×C17—41no—
262C23×C17—41no—
263C23×C17—41no—
264C23×C17—41no—
265C23×C17—41no—
266C23×C17—41no—
267C23×C17C4×D412yes—
268C23×C17C22×D411yescharacteristic
269Q8×C17—22no—
270Q8×C17—22no—
271Q8×C17—22no—
272Q8×C17C4×D414yes—
273D4×C17—22no—
274D4×C17—22no—
275D4×C17—22no—
276D4×C17—22no—
277D4×C17—48no—
278D4×C17—41no—
279D4×C17—41no—
280D4×C17—41no—
281D4×C17—41no—
282D4×C17—84no—
283C2×C4×C17—22no—
284C2×C4×C17—21no—
285C2×C4×C17—22no—
286C2×C4×C17—21no—
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—48no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17C4×D412yes—
297C2×C4×C17C23×C411yescharacteristic
298C2×C4×C17C22×D411yescharacteristic
299C2×C4×C17C2×#4111yescharacteristic
300C2×C4×C17C2×#4111yescharacteristic
301C2×C4×C17H(5,𝔽2)11yescharacteristic
302C2×C4×C17H(5,𝔽2)11yescharacteristic
303C2×Dic17—22no—
304C2×Dic17—21no—
305C2×Dic17—21no—
306C2×Dic17—21no—
307C2×Dic17—21no—
308C2×Dic17—21no—
309C2×Dic17—21no—
310C2×Dic17—21no—
311C2×Dic17—21no—
312C2×Dic17—21no—
313C2×Dic17—21no—
314C2×Dic17—21no—
315C2×Dic17—21no—
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—
328C8×C17—22no—
329C8×C17—22no—
330#3622—22no—
331#3622—41no—
332C2×#449D1711yescharacteristic
333C2×#440—171no—
334C2×#416—171no—
335#2363—171no—
336#2341—171no—
337#1972—171no—
338#1936—171no—
339#1925—171no—
340#1893—171no—
341#1880—171no—
342#1879—171no—
343#1865—171no—
344#1854—171no—
345#1763—171no—
346#1752—171no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—41no—
351C22×C17—41no—
352C22×C17—41no—
353C22×C17—41no—
354C22×C17—42no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17—42no—
358C22×C17—42no—
359C22×C17—42no—
360C22×C17—81no—
361C22×C17—81no—
362C22×C17—81no—
363C22×C17—81no—
364C22×C17—81no—
365C22×C17—81no—
366C22×C17—81no—
367C22×C17—81no—
368C22×C17C2×C4×D411yescharacteristic
369C22×C17D4211yescharacteristic
370C22×C17#54611yescharacteristic
371C22×C17#57511yescharacteristic
372C22×C17#57511yescharacteristic
373C22×C17#57611yescharacteristic
374C22×C17#57711yescharacteristic
375C4×C17—22no—
376C4×C17—24no—
377C4×C17—42no—
378C4×C17C2×C4×D411yescharacteristic
379C4×C17#51811yescharacteristic
380C4×C17#54611yescharacteristic
381C4×C17#55111yescharacteristic
382Dic17—41no—
383Dic17—42no—
384Dic17—41no—
385Dic17—41no—
386Dic17—41no—
387Dic17—81no—
388Dic17—81no—
389Dic17—81no—
390C22×#41C2×D1711yescharacteristic
391C22×SD16C2×D1711yescharacteristic
392C22×D8C2×D1711yescharacteristic
393C23×C8—171no—
394C2×#121C2×D1711yescharacteristic
395C2×C4×Q8—171no—
396C2×C4×Q8—171no—
397C2×C4×D4—171no—
398C2×#117—171no—
399#449Dic1718yescomplemented
400#440—344no—
401C2×#107—171no—
402C2×#106—171no—
403#416—344no—
404C2×#103—171no—
405C2×#103—171no—
406C2×#103C2×D1711yescharacteristic
407C2×#102—171no—
408C2×#102—171no—
409C2×#102—171no—
410C2×#102—171no—
411C2×#102C2×D1711yescharacteristic
412C2×C22⋊C8C2×D1711yescharacteristic
413C2×#97—171no—
414C2×#97—171no—
415#390—171no—
416#390—171no—
417#390—171no—
418#390—341no—
419#390—341no—
420#390—341no—
421#389—171no—
422#388—341no—
423#386—341no—
424#380—171no—
425#380—341no—
426C4×C4⋊C4—171no—
427C4×C22⋊C4—171no—
428C4×C22⋊C4—341no—
429C4×C22⋊C4—341no—
430#340—171no—
431#340—171no—
432#340—171no—
433#340—171no—
434#336—171no—
435#336—171no—
436C2×C17—42no—
437C2×C17—82no—
438C2×C17—82no—
439C2×C17#235811yescharacteristic
440C2×C17#294311yescharacteristic
441C2×C17#294611yescharacteristic
442C2×C17#326811yescharacteristic
443C2×C17#327111yescharacteristic
444C2×C17#330911yescharacteristic
445C2×C17#332111yescharacteristic
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—41no—
450C2×#41—41no—
451C2×#41C2×Dic1714yescomplemented
452C22×Q8C22×D1711yescharacteristic
453C22×D4—21no—
454C22×D4—21no—
455C22×D4C22×D1711yescharacteristic
456C22×D4C22×D1711yescharacteristic
457C23×C4—21no—
458C23×C4—341no—
459C23×C4C22×D1711yescharacteristic
460C2×SD16—22no—
461C2×SD16—22no—
462C2×SD16C2×Dic1714yes—
463C2×D8—41no—
464C2×D8—41no—
465C2×D8C2×Dic1714yes—
466C22×C8—171no—
467C22×C8—171no—
468C22×C8—342no—
469C22×C8—342no—
470C22×C8—681no—
471C22×C8C22×D1711yescharacteristic
472C22×C8C22×D1711yescharacteristic
473#121—22no—
474#121C2×Dic1714yes—
475C4×Q8—342no—
476C4×Q8—342no—
477C4×Q8—681no—
478C4×Q8—681no—
479C4×D4—342no—
480C4×D4—681no—
481#117—342no—
482#117—681no—
483C2×C4⋊C4—171no—
484C2×C4⋊C4—171no—
485C2×C4⋊C4—171no—
486C2×C4⋊C4—171no—
487C2×C4⋊C4—341no—
488C2×C4⋊C4—341no—
489C2×C4⋊C4—341no—
490C2×C4⋊C4C22×D1711yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—171no—
493C2×C22⋊C4—171no—
494C2×C22⋊C4—341no—
495C2×C22⋊C4—341no—
496C2×C22⋊C4—341no—
497C2×C22⋊C4—341no—
498C2×C22⋊C4—341no—
499C2×C22⋊C4—341no—
500C2×C22⋊C4—341no—
501C2×C22⋊C4—341no—
502C2×C22⋊C4—341no—
503C2×C42—171no—
504C2×C42—171no—
505C2×C42—341no—
506C2×C42—341no—
507C2×C42—341no—
508C2×C42—341no—
509#107—342no—
510#106—681no—
511#103—174no—
512#103—342no—
513#103C2×Dic1714yescomplemented
514#102—342no—
515#102—342no—
516#102—342no—
517#102—681no—
518#102C2×Dic1714yescomplemented
519C22⋊C8C2×Dic1714yescomplemented
520#97—342no—
521#97—681no—
522#95—171no—
523#95—171no—
524#95—341no—
525#95—341no—
526#95—341no—
527C17#2285711yescharacteristic, complemented, Sylow
528C24—21no—
529C24—21no—
530C24D4×D1711yescharacteristic
531#41—28no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8D4×D1712yes—
539C2×Q8#6325412yes—
540C2×Q8C22×Dic1712yes—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4C22×Dic1712yes—
558C2×D4C22×Dic1712yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—171no—
569C22×C4—171no—
570C22×C4—171no—
571C22×C4—171no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—682no—
577C22×C4—682no—
578C22×C4—1361no—
579C22×C4D4×D1711yescharacteristic
580C22×C4#6325412yes—
581C22×C4C22×Dic1712yes—
582C22×C4C23×D1711yescharacteristic
583SD16—28no—
584D8—44no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—172no—
590C2×C8—341no—
591C2×C8—341no—
592C2×C8—341no—
593C2×C8—341no—
594C2×C8—341no—
595C2×C8—684no—
596C2×C8C22×Dic1712yes—
597C2×C8C22×Dic1712yes—
598C4⋊C4—21no—
599C4⋊C4—172no—
600C4⋊C4—341no—
601C4⋊C4—341no—
602C4⋊C4—341no—
603C4⋊C4—341no—
604C4⋊C4—341no—
605C4⋊C4—341no—
606C4⋊C4—341no—
607C4⋊C4—682no—
608C4⋊C4—682no—
609C4⋊C4—1361no—
610C4⋊C4C22×Dic1712yes—
611C22⋊C4—24no—
612C22⋊C4—681no—
613C22⋊C4—681no—
614C22⋊C4—682no—
615C22⋊C4—682no—
616C22⋊C4—682no—
617C22⋊C4—682no—
618C22⋊C4—682no—
619C22⋊C4—1361no—
620C22⋊C4—1361no—
621C22⋊C4—1361no—
622C22⋊C4—1361no—
623C42—341no—
624C42—341no—
625C42—341no—
626C42—341no—
627C42—682no—
628C42—682no—
629C42—682no—
630C42—1361no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23D4×Dic1712yes—
652C23C2×D4×D1711yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8D4×Dic1714yes—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—48no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—84no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—341no—
681C2×C4—341no—
682C2×C4—341no—
683C2×C4—341no—
684C2×C4—341no—
685C2×C4—341no—
686C2×C4—341no—
687C2×C4—341no—
688C2×C4—341no—
689C2×C4—341no—
690C2×C4—342no—
691C2×C4—341no—
692C2×C4—341no—
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—681no—
702C2×C4—681no—
703C2×C4—681no—
704C2×C4—1364no—
705C2×C4D4×Dic1712yes—
706C2×C4C2×D4×D1711yescharacteristic
707C2×C4C2×#6325411yescharacteristic
708C2×C4C2×#6325411yescharacteristic
709C2×C4#1058769111yescharacteristic
710C2×C4#1058769111yescharacteristic
711C2×C4C23×Dic1711yescharacteristic
712C8—22no—
713C8—22no—
714C8—342no—
715C8—681no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22C2×D4×Dic1711yescharacteristic
738C22#1176344111yescharacteristic
739C22#1176344611yescharacteristic
740C22#1176360611yescharacteristic
741C22#1176360611yescharacteristic
742C22#1176361311yescharacteristic
743C22#1176361911yescharacteristic
744C4—22no—
745C4—24no—
746C4—42no—
747C4—681no—
748C4—682no—
749C4—681no—
750C4—681no—
751C4—681no—
752C4—1361no—
753C4—1361no—
754C4—1361no—
755C4C2×D4×Dic1711yescharacteristic
756C4#1176328411yescharacteristic
757C4#1176344611yescharacteristic
758C4#1176349011yescharacteristic
759C2—42no—
760C2—82no—
761C2—82no—
762C2#1453176811yescharacteristic
763C2#1453758511yescharacteristic
764C2#1453761711yescharacteristic
765C2#1454031711yescharacteristic
766C2#1454036211yescharacteristic
767C2#1454079411yescharacteristic
768C2#1454097411yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#449C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×#449D17
hypocenterC17#22857
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#11762910C2semidirect
2. C2×#11762805C2semidirect
3. #14531826C2semidirect
4. #14531625C2semidirect
5. #14529661C2semidirect
6. #14529483C2semidirect
7. #14529406C2semidirect
8. #14529213C2semidirect
9. #14529141C2semidirect
10. #14529134C2semidirect
11. #14529054C2semidirect
12. #14528985C2semidirect
13. #14528616C2semidirect
14. #14528563C2semidirect
58. C17×#449C4semidirect
67. C2×#41×C17C2×C4semidirect
125. C17×#103C2×C4semidirect
126. C17×#102C2×C4semidirect
127. C17×C22⋊C8C2×C4semidirect
129. #10587506D4semidirect
399. #449Dic17semidirect
451. C2×#41C2×Dic17semidirect
513. #103C2×Dic17semidirect
518. #102C2×Dic17semidirect
519. C22⋊C8C2×Dic17semidirect
527. C17#22857semidirect

Maximal subgroups

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

subgroupindex
C2×#117629102
C2×#117628052
#145318262
#145316252
#145296612
#145294832
#145294062
#145292132
#145291412
#145291342
#145290542
#145289852
#145286162
#145285632
C2×C17×#4492
#2285717