Finite Group Databasebeta

← #17044095

Subgroups — #17044095

Order 4352.

1086 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762870C211yesmaximal, characteristic, complemented
2#14531407C211yesmaximal, characteristic, complemented
3#14529758C211yesmaximal, characteristic, complemented
4#14529746C211yesmaximal, characteristic, complemented
5#14529601C211yesmaximal, characteristic, complemented
6#14529596C211yesmaximal, characteristic, complemented
7#14529107C211yesmaximal, characteristic
8#14529102C211yesmaximal, characteristic
9#14529097C211yesmaximal, characteristic, complemented
10#14529092C211yesmaximal, characteristic, complemented
11#14528799C211yesmaximal, characteristic, complemented
12#14528794C211yesmaximal, characteristic, complemented
13#14528789C211yesmaximal, characteristic, complemented
14#14528784C211yesmaximal, characteristic, complemented
15C2×C17×#542C211yesmaximal, characteristic
16C2×#10587612C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18#11762870—24no—
19C2×C4⋊#3622C2211yescharacteristic
20C2×C4⋊#3622C2211yescharacteristic
21C2×#10587506C2211yescharacteristic
22C2×#10587506C2211yescharacteristic
23C2×#10587506C2211yescharacteristic
24C2×#10587506C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×#10587503C2211yescharacteristic
28C2×#10587503C2211yescharacteristic
29C2×C22⋊#3622C2211yescharacteristic
30C2×C22⋊#3622C2211yescharacteristic
31C2×#10587474C2211yescharacteristic
32C2×C4×#3622C2211yescharacteristic
33#11762708—21no—
34#11762708—21no—
35#11762684—21no—
36#11762684—21no—
37#11762679C2211yescharacteristic
38#11762679C2211yescharacteristic
39#11762675C2211yescharacteristic
40#11762675C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49C17×#542—24no—
50C17×#542C418yescomplemented
51C2×C17×C4⋊Q8C2211yescharacteristic
52C2×C17×#126—21no—
53C2×C17×#124—21no—
54C2×C17×#124C2211yescharacteristic
55C2×C17×#123—21no—
56C2×C17×C22⋊Q8—21no—
57C2×C17×C22⋊Q8C2211yescharacteristic
58C2×C17×#121C2211yescharacteristic
59C2×C4×Q8×C17C2211yescharacteristic
60C2×C4×D4×C17C2211yescharacteristic
61C2×C17×#117C2211yescharacteristic
62C22×Q8×C17—21no—
63C22×Q8×C17C2311yescharacteristic
64C22×D4×C17—21no—
65C22×D4×C17C2311yescharacteristic
66C23×C4×C17—21no—
67C23×C4×C17C2311yescharacteristic
68C23×Dic17—21no—
69C17×C4⋊Q8—22no—
70C17×C4⋊Q8C2×C414yescomplemented
71C17×#126—28no—
72C17×#124—28no—
73C17×#124—22no—
74C17×#124C2×C414yescomplemented
75C17×#123—28no—
76C17×C22⋊Q8—22no—
77C17×C22⋊Q8—28no—
78C17×C22⋊Q8C2×C414yes—
79C17×#121—22no—
80C17×#121C2×C414yes—
81C4×Q8×C17—22no—
82C4×Q8×C17C2×C414yescomplemented
83C4×D4×C17—22no—
84C4×D4×C17C2×C414yescomplemented
85C17×#117C2×C414yes—
86C17×#117D414yes—
87C2×C4⋊C4×C17—21no—
88C2×C4⋊C4×C17—21no—
89C2×C4⋊C4×C17—21no—
90C2×C4⋊C4×C17D411yescharacteristic
91C2×C4⋊C4×C17D411yescharacteristic
92C2×C4⋊C4×C17C2311yescharacteristic
93C2×C4⋊C4×C17C2311yescharacteristic
94C2×C22⋊C4×C17—21no—
95C2×C22⋊C4×C17—21no—
96C2×C22⋊C4×C17—21no—
97C2×C22⋊C4×C17—21no—
98C2×C22⋊C4×C17—21no—
99C2×C22⋊C4×C17D411yescharacteristic
100C2×C22⋊C4×C17D411yescharacteristic
101C2×C42×C17—21no—
102C2×C42×C17C2311yescharacteristic
103C2×C42×C17C2311yescharacteristic
104C2×C22⋊Dic17—21no—
105#10587612—41no—
106#10587612—41no—
107C2×C4⋊Dic17—21no—
108C2×C4⋊Dic17—21no—
109C2×C4⋊Dic17—21no—
110C2×C4⋊Dic17—21no—
111C2×C4⋊Dic17—21no—
112C2×C4⋊Dic17—41no—
113C2×C4⋊Dic17—41no—
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4⋊Dic17C2311yescharacteristic
117C2×C4⋊Dic17C2311yescharacteristic
118C2×C4×Dic17—21no—
119C22×#3622C2311yescharacteristic
120C22×#3622C2311yescharacteristic
121C22×#3622C2311yescharacteristic
122C22×#3622C2311yescharacteristic
123#10587506—41no—
124#10587506—41no—
125#10587506—41no—
126#10587506—41no—
127#10587503—41no—
128#10587503—41no—
129#10587503—41no—
130#10587503—41no—
131#10587502—21no—
132#10587502—21no—
133#10587502—21no—
134#10587502—21no—
135C22⋊#3622—22no—
136C22⋊#3622—22no—
137C4⋊#3622—22no—
138C4⋊#3622—22no—
139#10587474—22no—
140C4×#3622—22no—
141C24×C17—21no—
142C24×C17C2×D411yescharacteristic
143C2×Q8×C17—24no—
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17—21no—
148C2×Q8×C17—21no—
149C2×Q8×C17—81no—
150C2×Q8×C17—81no—
151C2×Q8×C17C22×C412yes—
152C2×D4×C17—24no—
153C2×D4×C17—21no—
154C2×D4×C17—21no—
155C2×D4×C17—21no—
156C2×D4×C17—21no—
157C2×D4×C17—21no—
158C2×D4×C17—81no—
159C2×D4×C17—81no—
160C2×D4×C17C22×C412yes—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—24no—
169C22×C4×C17—81no—
170C22×C4×C17—81no—
171C22×C4×C17C22×C412yes—
172C22×C4×C17C2×D411yescharacteristic
173C22×C4×C17C2×D411yescharacteristic
174C22×C4×C17C2×D411yescharacteristic
175C22×C4×C17C2×D411yescharacteristic
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×D412yes—
178C22×C4×C17C2411yescharacteristic
179C22×Dic17—21no—
180C22×Dic17—21no—
181C22×Dic17—21no—
182C22×Dic17—21no—
183C22×Dic17—42no—
184C22×Dic17—81no—
185C22×Dic17—81no—
186C4⋊C4×C17—24no—
187C4⋊C4×C17—24no—
188C4⋊C4×C17—24no—
189C4⋊C4×C17—21no—
190C4⋊C4×C17—21no—
191C4⋊C4×C17C22⋊C414yes—
192C4⋊C4×C17C22⋊C414yes—
193C4⋊C4×C17C22×C412yes—
194C4⋊C4×C17C22×C412yes—
195C22⋊C4×C17—24no—
196C22⋊C4×C17—24no—
197C22⋊C4×C17—24no—
198C22⋊C4×C17—24no—
199C22⋊C4×C17—24no—
200C22⋊C4×C17C22⋊C414yes—
201C22⋊C4×C17C22⋊C414yes—
202C42×C17—24no—
203C42×C17C22×C412yes—
204C42×C17C22×C412yes—
205C42×C17C2×D412yes—
206C42×C17C2×D412yes—
207C22⋊Dic17—42no—
208C4⋊Dic17—21no—
209C4⋊Dic17—21no—
210C4⋊Dic17—21no—
211C4⋊Dic17—21no—
212C4⋊Dic17—21no—
213C4⋊Dic17—21no—
214C4⋊Dic17—21no—
215C4⋊Dic17—21no—
216C4⋊Dic17—42no—
217C4⋊Dic17—81no—
218C4⋊Dic17—81no—
219C4⋊Dic17—81no—
220C4⋊Dic17—81no—
221C4×Dic17—42no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234#21871—171nomaximal, Sylow
235C23×C17—21no—
236C23×C17—21no—
237C23×C17—21no—
238C23×C17—21no—
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—22no—
242C23×C17—41no—
243C23×C17—41no—
244C23×C17—41no—
245C23×C17—41no—
246C23×C17—41no—
247C23×C17—41no—
248C23×C17C2×C22⋊C412yes—
249C23×C17C22×D411yescharacteristic
250Q8×C17—22no—
251Q8×C17—22no—
252Q8×C17—41no—
253Q8×C17—41no—
254Q8×C17—84no—
255D4×C17—22no—
256D4×C17—22no—
257D4×C17—41no—
258D4×C17—41no—
259D4×C17—84no—
260C2×C4×C17—21no—
261C2×C4×C17—21no—
262C2×C4×C17—21no—
263C2×C4×C17—21no—
264C2×C4×C17—21no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—21no—
268C2×C4×C17—21no—
269C2×C4×C17—21no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—41no—
278C2×C4×C17—41no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—84no—
284C2×C4×C17C2×C22⋊C412yes—
285C2×C4×C17C2×C22⋊C412yes—
286C2×C4×C17C2×C22⋊C412yes—
287C2×C4×C17C2×C22⋊C412yes—
288C2×C4×C17C2×C22⋊C412yes—
289C2×C4×C17C23×C411yescharacteristic
290C2×C4×C17C22×D411yescharacteristic
291C2×C4×C17H(5,𝔽2)11yescharacteristic
292C2×C4×C17H(5,𝔽2)11yescharacteristic
293C2×C4×C172−1+411yescharacteristic
294C2×C4×C172−1+411yescharacteristic
295C2×Dic17—41no—
296C2×Dic17—41no—
297C2×Dic17—41no—
298C2×Dic17—41no—
299C2×Dic17—41no—
300C2×Dic17—41no—
301C2×Dic17—41no—
302C2×Dic17—41no—
303C2×Dic17—41no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—84no—
308#3622—41no—
309#3622—41no—
310#3622—41no—
311#3622—41no—
312C2×#542D1711yescharacteristic
313C2×#433—171no—
314#2317—171no—
315#1993—171no—
316#1990—171no—
317#1959—171no—
318#1958—171no—
319#1875—171no—
320#1874—171no—
321#1873—171no—
322#1872—171no—
323#1805—171no—
324#1804—171no—
325#1803—171no—
326#1802—171no—
327C22×C17—22no—
328C22×C17—22no—
329C22×C17—22no—
330C22×C17—41no—
331C22×C17—41no—
332C22×C17—41no—
333C22×C17—41no—
334C22×C17—42no—
335C22×C17—42no—
336C22×C17—42no—
337C22×C17—81no—
338C22×C17—81no—
339C22×C17—81no—
340C22×C17—81no—
341C22×C17C22×C22⋊C411yescharacteristic
342C22×C17#53511yescharacteristic
343C22×C17#53611yescharacteristic
344C22×C17#57611yescharacteristic
345C22×C17#57711yescharacteristic
346C22×C17#57711yescharacteristic
347C22×C17#57811yescharacteristic
348C4×C17—22no—
349C4×C17—22no—
350C4×C17—22no—
351C4×C17—22no—
352C4×C17—22no—
353C4×C17—42no—
354C4×C17—42no—
355C4×C17—42no—
356C4×C17#52011yescharacteristic
357C4×C17#52011yescharacteristic
358C4×C17#53711yescharacteristic
359C4×C17#53711yescharacteristic
360Dic17—81no—
361Dic17—81no—
362Dic17—81no—
363Dic17—81no—
364#542—24no—
365#542Dic1718yescomplemented
366C2×C4⋊Q8C2×D1711yescharacteristic
367C2×#126—21no—
368C2×#124—21no—
369C2×#124C2×D1711yescharacteristic
370C2×#123—21no—
371C2×C22⋊Q8—21no—
372C2×C22⋊Q8C2×D1711yescharacteristic
373C2×#121C2×D1711yescharacteristic
374C2×C4×Q8C2×D1711yescharacteristic
375C2×C4×D4C2×D1711yescharacteristic
376C2×#117—171no—
377C2×#117C2×D1711yescharacteristic
378C22×C4⋊C4—171no—
379#433—344no—
380C2×C4⋊C8—171no—
381C2×C4⋊C8—171no—
382C2×#103—171no—
383C2×#103—171no—
384C2×#103—171no—
385C2×#103—171no—
386C2×#102—171no—
387C2×#102—171no—
388C2×#102—171no—
389C2×#102—171no—
390C2×C22⋊C8—171no—
391C2×C22⋊C8—171no—
392C2×#97—171no—
393C2×C4×C8—171no—
394#389—341no—
395#389—341no—
396#385—341no—
397#385—341no—
398#384—171no—
399#384—171no—
400#382—171no—
401#382—171no—
402#340—171no—
403#340—171no—
404#340—171no—
405#340—171no—
406#340—171no—
407#340—171no—
408#340—171no—
409#340—171no—
410C2×C17—42no—
411C2×C17—82no—
412C2×C17#231111yescharacteristic
413C2×C17#289711yescharacteristic
414C2×C17#289811yescharacteristic
415C2×C17#322411yescharacteristic
416C2×C17#322511yescharacteristic
417C2×C17#324311yescharacteristic
418C2×C17#324411yescharacteristic
419C22×Q8—21no—
420C22×Q8C22×D1711yescharacteristic
421C22×D4—21no—
422C22×D4C22×D1711yescharacteristic
423C23×C4—21no—
424C23×C4—341no—
425C23×C4C22×D1711yescharacteristic
426C22×C8—171no—
427C22×C8—171no—
428C22×C8—171no—
429C22×C8—171no—
430C4⋊Q8—22no—
431C4⋊Q8C2×Dic1714yescomplemented
432#126—28no—
433#124—28no—
434#124—22no—
435#124C2×Dic1714yescomplemented
436#123—28no—
437C22⋊Q8—22no—
438C22⋊Q8—28no—
439C22⋊Q8C2×Dic1714yes—
440#121—22no—
441#121C2×Dic1714yes—
442C4×Q8—22no—
443C4×Q8C2×Dic1714yescomplemented
444C4×D4—22no—
445C4×D4C2×Dic1714yescomplemented
446#117—681no—
447#117—681no—
448#117C2×Dic1714yes—
449#117C22⋊D1714yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—171no—
454C2×C4⋊C4—171no—
455C2×C4⋊C4—171no—
456C2×C4⋊C4—171no—
457C2×C4⋊C4—341no—
458C2×C4⋊C4—341no—
459C2×C4⋊C4—341no—
460C2×C4⋊C4—341no—
461C2×C4⋊C4—341no—
462C2×C4⋊C4—681no—
463C2×C4⋊C4—681no—
464C2×C4⋊C4C22⋊D1711yescharacteristic
465C2×C4⋊C4C22⋊D1711yescharacteristic
466C2×C4⋊C4C22×D1711yescharacteristic
467C2×C4⋊C4C22×D1711yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—341no—
474C2×C22⋊C4C22⋊D1711yescharacteristic
475C2×C22⋊C4C22⋊D1711yescharacteristic
476C2×C42—21no—
477C2×C42—341no—
478C2×C42C22×D1711yescharacteristic
479C2×C42C22×D1711yescharacteristic
480C4⋊C8—342no—
481C4⋊C8—342no—
482#103—681no—
483#103—681no—
484#103—681no—
485#103—681no—
486#102—681no—
487#102—681no—
488#102—681no—
489#102—681no—
490C22⋊C8—342no—
491C22⋊C8—342no—
492#97—342no—
493C4×C8—342no—
494#95—341no—
495#95—341no—
496#95—341no—
497#95—341no—
498C17#2187111yescharacteristic, complemented, Sylow
499C24—21no—
500C24C2×C22⋊D1711yescharacteristic
501C2×Q8—21no—
502C2×Q8—24no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×Q8C22×Dic1712yes—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C22×Dic1712yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—341no—
530C22×C4—341no—
531C22×C4—341no—
532C22×C4—341no—
533C22×C4—682no—
534C22×C4—1361no—
535C22×C4—1361no—
536C22×C4C22×Dic1712yes—
537C22×C4C2×C22⋊D1712yes—
538C22×C4C2×C22⋊D1711yescharacteristic
539C22×C4C2×C22⋊D1711yescharacteristic
540C22×C4C2×C22⋊D1711yescharacteristic
541C22×C4C2×C22⋊D1711yescharacteristic
542C22×C4C2×C22⋊D1711yescharacteristic
543C22×C4C23×D1711yescharacteristic
544C2×C8—341no—
545C2×C8—341no—
546C2×C8—341no—
547C2×C8—341no—
548C2×C8—341no—
549C2×C8—341no—
550C2×C8—341no—
551C2×C8—341no—
552C2×C8—341no—
553C2×C8—341no—
554C2×C8—341no—
555C2×C8—341no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—341no—
562C4⋊C4—341no—
563C4⋊C4—341no—
564C4⋊C4—341no—
565C4⋊C4—341no—
566C4⋊C4—341no—
567C4⋊C4—341no—
568C4⋊C4—341no—
569C4⋊C4—682no—
570C4⋊C4—1361no—
571C4⋊C4—1361no—
572C4⋊C4—1361no—
573C4⋊C4—1361no—
574C4⋊C4C22⋊Dic1714yes—
575C4⋊C4C22⋊Dic1714yes—
576C4⋊C4C22×Dic1712yes—
577C4⋊C4C22×Dic1712yes—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—682no—
584C22⋊C4C22⋊Dic1714yes—
585C22⋊C4C22⋊Dic1714yes—
586C42—24no—
587C42—682no—
588C42C22×Dic1712yes—
589C42C22×Dic1712yes—
590C42C2×C22⋊D1712yes—
591C42C2×C22⋊D1712yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C2×C22⋊Dic1712yes—
606C23C22×C22⋊D1711yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—84no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—681no—
642C2×C4—681no—
643C2×C4—681no—
644C2×C4—681no—
645C2×C4—681no—
646C2×C4—681no—
647C2×C4—681no—
648C2×C4—681no—
649C2×C4—681no—
650C2×C4—681no—
651C2×C4—681no—
652C2×C4—681no—
653C2×C4—1364no—
654C2×C4C2×C22⋊Dic1712yes—
655C2×C4C2×C22⋊Dic1712yes—
656C2×C4C2×C22⋊Dic1712yes—
657C2×C4C2×C22⋊Dic1712yes—
658C2×C4C2×C22⋊Dic1712yes—
659C2×C4#1058769611yescharacteristic
660C2×C4#1058769611yescharacteristic
661C2×C4#1058769711yescharacteristic
662C2×C4#1058769711yescharacteristic
663C2×C4C23×Dic1711yescharacteristic
664C2×C4C22×C22⋊D1711yescharacteristic
665C8—681no—
666C8—681no—
667C8—681no—
668C8—681no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊Dic1711yescharacteristic
684C22#1176337311yescharacteristic
685C22#1176338011yescharacteristic
686C22#1176361211yescharacteristic
687C22#1176361711yescharacteristic
688C22#1176362011yescharacteristic
689C22#1176362411yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—1361no—
699C4—1361no—
700C4—1361no—
701C4—1361no—
702C4#1176329211yescharacteristic
703C4#1176329211yescharacteristic
704C4#1176338711yescharacteristic
705C4#1176338711yescharacteristic
706C2—42no—
707C2—82no—
708C2#1453137611yescharacteristic
709C2#1453731011yescharacteristic
710C2#1453731711yescharacteristic
711C2#1453987211yescharacteristic
712C2#1453988711yescharacteristic
713C2#1454006111yescharacteristic
714C2#1454007611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#542C2
socleC23×C17C22×D4
prime radicalC2×C17×#121C22
cosocleC22×C4×C17C24
hypercenterC2×#542D17
hypocenterC17#21871
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11762870C2semidirect
2. #14531407C2semidirect
3. #14529758C2semidirect
4. #14529746C2semidirect
5. #14529601C2semidirect
6. #14529596C2semidirect
9. #14529097C2semidirect
10. #14529092C2semidirect
11. #14528799C2semidirect
12. #14528794C2semidirect
13. #14528789C2semidirect
14. #14528784C2semidirect
50. C17×#542C4semidirect
70. C17×C4⋊Q8C2×C4semidirect
74. C17×#124C2×C4semidirect
82. C4×Q8×C17C2×C4semidirect
84. C4×D4×C17C2×C4semidirect
365. #542Dic17semidirect
431. C4⋊Q8C2×Dic17semidirect
435. #124C2×Dic17semidirect
443. C4×Q8C2×Dic17semidirect
445. C4×D4C2×Dic17semidirect
498. C17#21871semidirect

Maximal subgroups

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

subgroupindex
C2×#117628702
#145314072
#145297582
#145297462
#145296012
#145295962
#145291072
#145291022
#145290972
#145290922
#145287992
#145287942
#145287892
#145287842
C2×C17×#5422
#2187117