Finite Group Databasebeta

← #17050549

Subgroups — #17050549

Order 4352.

1162 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#3622C211yesmaximal, characteristic
2#14531713C211yesmaximal, characteristic
3#14529750C211yesmaximal, characteristic, complemented
4#14529742C211yesmaximal, characteristic, complemented
5#14529208C211yesmaximal, characteristic, complemented
6#14529208C211yesmaximal, characteristic, complemented
7#14529097C211yesmaximal, characteristic, complemented
8#14529092C211yesmaximal, characteristic, complemented
9#14528879C211yesmaximal, characteristic, complemented
10#14528870C211yesmaximal, characteristic, complemented
11#14528799C211yesmaximal, characteristic, complemented
12C4×#10587506C211yesmaximal, characteristic, complemented
13#14528500C211yesmaximal, characteristic, complemented
14C2×#11762571C211yesmaximal, characteristic, complemented
15C2×C17×#552C211yesmaximal, characteristic
16C23×#3622C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C2×#10587612C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20D4×#3622—24no—
21C2×C4⋊#3622C2211yescharacteristic
22C2×#10587506C2211yescharacteristic
23C2×#10587506C2211yescharacteristic
24C2×#10587506C2211yescharacteristic
25C2×#10587506C2211yescharacteristic
26C2×C22⋊#3622C2211yescharacteristic
27C2×C22⋊#3622C2211yescharacteristic
28C2×C4×#3622C2211yescharacteristic
29#11762702—21no—
30#11762695—21no—
31#11762689—21no—
32#11762675C2211yescharacteristic
33#11762669C2211yescharacteristic
34#11762669C2211yescharacteristic
35C4×C4⋊Dic17C2211yescharacteristic
36C22⋊C4×Dic17—21no—
37#11762571C2211yescharacteristic
38#11762571C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49C17×#552—24no—
50C17×#552C418yescomplemented
51C2×C17×#126—21no—
52C2×C17×#125—21no—
53C2×C17×#125C2211yescharacteristic
54C2×C17×#123—21no—
55C2×C17×C22⋊Q8C2211yescharacteristic
56C2×C17×C22⋊Q8C2211yescharacteristic
57C2×C4×Q8×C17C2211yescharacteristic
58C2×C4×D4×C17C2211yescharacteristic
59C2×C17×#117—21no—
60C2×C17×#117C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×Q8×C17C2311yescharacteristic
63C22×D4×C17D411yescharacteristic
64C23×C4×C17—21no—
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×Dic17—21no—
68C17×#126—28no—
69C17×#125—28no—
70C17×#125—22no—
71C17×#125C2×C414yescomplemented
72C17×#123—28no—
73C17×C22⋊Q8—22no—
74C17×C22⋊Q8—22no—
75C17×C22⋊Q8C2×C414yes—
76C17×C22⋊Q8C2×C414yescomplemented
77C4×Q8×C17—22no—
78C4×Q8×C17C2×C414yescomplemented
79C4×D4×C17C2×C414yes—
80C4×D4×C17D414yes—
81C17×#117—22no—
82C17×#117—28no—
83C17×#117C2×C414yescomplemented
84C2×C4⋊C4×C17—21no—
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—21no—
87C2×C4⋊C4×C17—21no—
88C2×C4⋊C4×C17—21no—
89C2×C4⋊C4×C17—21no—
90C2×C4⋊C4×C17—21no—
91C2×C4⋊C4×C17C2×C414yes—
92C2×C4⋊C4×C17D411yescharacteristic
93C2×C4⋊C4×C17C2311yescharacteristic
94C2×C4⋊C4×C17C2311yescharacteristic
95C2×C4⋊C4×C17C2311yescharacteristic
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×C17—21no—
103C2×C42×C17C2311yescharacteristic
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17—21no—
106C2×C22⋊Dic17—21no—
107#10587612—22no—
108#10587612—41no—
109C2×C4⋊Dic17—21no—
110C2×C4⋊Dic17—22no—
111C2×C4⋊Dic17—41no—
112C2×C4⋊Dic17C2311yescharacteristic
113C2×C4⋊Dic17C2311yescharacteristic
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4×Dic17—21no—
117C2×C4×Dic17—21no—
118C22×#3622—22no—
119C22×#3622—22no—
120C22×#3622—22no—
121C22×#3622—22no—
122C22×#3622—41no—
123C22×#3622—41no—
124C22×#3622C2311yescharacteristic
125C22×#3622C2311yescharacteristic
126C22×#3622C2311yescharacteristic
127C22×#3622C2311yescharacteristic
128#10587506—22no—
129#10587506—22no—
130#10587506—41no—
131#10587506—41no—
132#10587502—21no—
133#10587502—21no—
134#10587502—21no—
135#10587502—21no—
136#10587502—21no—
137C22⋊#3622—22no—
138C22⋊#3622—22no—
139C4⋊#3622—22no—
140C4×#3622—22no—
141C24×C17C2×D411yescharacteristic
142C24×C17C2×D411yescharacteristic
143C2×Q8×C17—21no—
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17—21no—
148C2×Q8×C17C22×C412yes—
149C2×D4×C17—22no—
150C2×D4×C17—22no—
151C2×D4×C17C22⋊C414yes—
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—24no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—42no—
166C22×C4×C17—42no—
167C22×C4×C17C22×C412yes—
168C22×C4×C17C22×C412yes—
169C22×C4×C17C2×D411yescharacteristic
170C22×C4×C17C2×D411yescharacteristic
171C22×C4×C17C2×D411yescharacteristic
172C22×C4×C17C2×D411yescharacteristic
173C22×C4×C17C2×D412yes—
174C22×C4×C17C2×D412yes—
175C22×C4×C17C2411yescharacteristic
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—42no—
181C22×Dic17—42no—
182C22×Dic17—81no—
183C4⋊C4×C17—24no—
184C4⋊C4×C17—24no—
185C4⋊C4×C17—24no—
186C4⋊C4×C17—24no—
187C4⋊C4×C17—24no—
188C4⋊C4×C17—24no—
189C4⋊C4×C17—21no—
190C4⋊C4×C17—21no—
191C4⋊C4×C17—21no—
192C4⋊C4×C17C22⋊C414yes—
193C4⋊C4×C17C22×C412yes—
194C4⋊C4×C17C22×C412yes—
195C4⋊C4×C17C22×C412yes—
196C22⋊C4×C17—24no—
197C22⋊C4×C17—24no—
198C22⋊C4×C17—24no—
199C22⋊C4×C17C22⋊C414yes—
200C22⋊C4×C17C22⋊C414yes—
201C42×C17—24no—
202C42×C17—24no—
203C42×C17C22×C412yes—
204C42×C17C2×D412yes—
205C22⋊Dic17—42no—
206C22⋊Dic17—42no—
207C22⋊Dic17—81no—
208C4⋊Dic17—21no—
209C4⋊Dic17—21no—
210C4⋊Dic17—21no—
211C4⋊Dic17—21no—
212C4⋊Dic17—21no—
213C4⋊Dic17—21no—
214C4⋊Dic17—21no—
215C4⋊Dic17—42no—
216C4⋊Dic17#4112yes—
217C4×Dic17—42no—
218C4×Dic17—81no—
219C2×#3622—21no—
220C2×#3622—21no—
221C2×#3622—21no—
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—44no—
231C2×#3622—44no—
232C2×#3622#4112yes—
233#22486—171nomaximal, Sylow
234C23×C17—21no—
235C23×C17—21no—
236C23×C17—21no—
237C23×C17—21no—
238C23×C17—21no—
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—21no—
244C23×C17C2×C22⋊C412yes—
245C23×C17C2×C22⋊C412yes—
246C23×C17#13512yes—
247C23×C17#13512yes—
248C23×C17C22×D411yescharacteristic
249Q8×C17—22no—
250Q8×C17—22no—
251Q8×C17—41no—
252Q8×C17—41no—
253D4×C17—28no—
254C2×C4×C17—21no—
255C2×C4×C17—21no—
256C2×C4×C17—21no—
257C2×C4×C17—21no—
258C2×C4×C17—21no—
259C2×C4×C17—21no—
260C2×C4×C17—21no—
261C2×C4×C17—21no—
262C2×C4×C17—22no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—41no—
275C2×C4×C17—41no—
276C2×C4×C17—41no—
277C2×C4×C17—41no—
278C2×C4×C17—41no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—48no—
283C2×C4×C17C2×C22⋊C412yes—
284C2×C4×C17C2×C22⋊C412yes—
285C2×C4×C17C2×C22⋊C412yes—
286C2×C4×C17C2×C22⋊C412yes—
287C2×C4×C17C23×C411yescharacteristic
288C2×C4×C17C22×D411yescharacteristic
289C2×C4×C17C2×#4111yescharacteristic
290C2×C4×C17C2×#4111yescharacteristic
291C2×C4×C17H(5,𝔽2)11yescharacteristic
292C2×C4×C172−1+411yescharacteristic
293C2×Dic17—22no—
294C2×Dic17—41no—
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—84no—
306#3622—22no—
307#3622—41no—
308#3622—41no—
309#3622—41no—
310C2×#552D1711yescharacteristic
311C2×C8×D4—171no—
312#2352—171no—
313#1991—171no—
314#1989—171no—
315#1892—171no—
316#1892—171no—
317#1873—171no—
318#1872—171no—
319#1825—171no—
320#1823—171no—
321#1805—171no—
322C4×#103—171no—
323#1735—171no—
324C2×#340—171no—
325C22×C17—22no—
326C22×C17—22no—
327C22×C17—22no—
328C22×C17—22no—
329C22×C17—22no—
330C22×C17—22no—
331C22×C17—22no—
332C22×C17—22no—
333C22×C17—22no—
334C22×C17—41no—
335C22×C17—41no—
336C22×C17—41no—
337C22×C17—41no—
338C22×C17#41614yes—
339C22×C17C22×C22⋊C411yescharacteristic
340C22×C17#54611yescharacteristic
341C22×C17#54711yescharacteristic
342C22×C17C2×#13511yescharacteristic
343C22×C17C2×#13511yescharacteristic
344C22×C17#57711yescharacteristic
345C22×C17#57811yescharacteristic
346C4×C17—22no—
347C4×C17—22no—
348C4×C17—22no—
349C4×C17—22no—
350C4×C17—42no—
351C4×C17—42no—
352C4×C17—42no—
353C4×C17—42no—
354C4×C17C4×#4111yescharacteristic
355C4×C17#52011yescharacteristic
356C4×C17#54611yescharacteristic
357C4×C17#54711yescharacteristic
358Dic17—42no—
359Dic17—81no—
360Dic17—81no—
361Dic17—81no—
362C23×C8—171no—
363C23×C8—171no—
364#552—24no—
365#552Dic1718yescomplemented
366C2×#126—21no—
367C2×#125—21no—
368C2×#125C2×D1711yescharacteristic
369C2×#123—21no—
370C2×C22⋊Q8C2×D1711yescharacteristic
371C2×C22⋊Q8C2×D1711yescharacteristic
372C2×C4×Q8C2×D1711yescharacteristic
373C2×C4×D4C2×D1711yescharacteristic
374C2×#117—21no—
375C2×#117—171no—
376C2×#117C2×D1711yescharacteristic
377C22×C4⋊C4—171no—
378C22×C4⋊C4C2×D1711yescharacteristic
379C8×D4—344no—
380C2×C4⋊C8—171no—
381C2×#103—171no—
382C2×#103—171no—
383C2×#103—171no—
384C2×#103—171no—
385C2×C22⋊C8—171no—
386C2×C22⋊C8—171no—
387C2×C4×C8—171no—
388#388—341no—
389#387—341no—
390#386—341no—
391#382—171no—
392#380—171no—
393#380—171no—
394C4×C4⋊C4—171no—
395C4×C22⋊C4—341no—
396#340—171no—
397#340—171no—
398#340—171no—
399#340—171no—
400#340—171no—
401#340—171no—
402#340—171no—
403#340—171no—
404#340—171no—
405#340—171no—
406#340—171no—
407#340—171no—
408C2×C17—24no—
409C2×C17—42no—
410C2×C17#233911yescharacteristic
411C2×C17C2×#41611yescharacteristic
412C2×C17#289811yescharacteristic
413C2×C17#329611yescharacteristic
414C2×C17#330011yescharacteristic
415C2×C17#333611yescharacteristic
416C2×C17#333711yescharacteristic
417C22×Q8C22×D1711yescharacteristic
418C22×D4C22⋊D1711yescharacteristic
419C23×C4—21no—
420C23×C4—341no—
421C23×C4C22×D1711yescharacteristic
422C23×C4C22×D1711yescharacteristic
423C22×C8—171no—
424C22×C8—171no—
425C22×C8—171no—
426C22×C8—171no—
427C22×C8—342no—
428C22×C8—342no—
429C22×C8—342no—
430C22×C8—342no—
431C22×C8—681no—
432C22×C8—681no—
433#126—28no—
434#125—28no—
435#125—22no—
436#125C2×Dic1714yescomplemented
437#123—28no—
438C22⋊Q8—22no—
439C22⋊Q8—22no—
440C22⋊Q8C2×Dic1714yes—
441C22⋊Q8C2×Dic1714yescomplemented
442C4×Q8—22no—
443C4×Q8C2×Dic1714yescomplemented
444C4×D4C2×Dic1714yes—
445C4×D4C22⋊D1714yes—
446#117—22no—
447#117—28no—
448#117—342no—
449#117—681no—
450#117C2×Dic1714yescomplemented
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—171no—
459C2×C4⋊C4—171no—
460C2×C4⋊C4—171no—
461C2×C4⋊C4—171no—
462C2×C4⋊C4—342no—
463C2×C4⋊C4—341no—
464C2×C4⋊C4—681no—
465C2×C4⋊C4C2×Dic1714yes—
466C2×C4⋊C4C22⋊D1711yescharacteristic
467C2×C4⋊C4C22×D1711yescharacteristic
468C2×C4⋊C4C22×D1711yescharacteristic
469C2×C4⋊C4C22×D1711yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—341no—
474C2×C22⋊C4—341no—
475C2×C22⋊C4—341no—
476C2×C22⋊C4C22⋊D1711yescharacteristic
477C2×C22⋊C4C22⋊D1711yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—341no—
481C2×C42—341no—
482C2×C42C22×D1711yescharacteristic
483C4⋊C8—342no—
484#103—342no—
485#103—342no—
486#103—681no—
487#103—681no—
488C22⋊C8—342no—
489C22⋊C8—342no—
490C4×C8—342no—
491#95—341no—
492#95—341no—
493#95—341no—
494#95—341no—
495#95—341no—
496C17#2248611yescharacteristic, complemented, Sylow
497C24C2×C22⋊D1711yescharacteristic
498C24C2×C22⋊D1711yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C22×Dic1712yes—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4C22⋊Dic1714yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—341no—
524C22×C4—341no—
525C22×C4—341no—
526C22×C4—341no—
527C22×C4—682no—
528C22×C4—682no—
529C22×C4—1361no—
530C22×C4C22×Dic1712yes—
531C22×C4C22×Dic1712yes—
532C22×C4C2×C22⋊D1712yes—
533C22×C4C2×C22⋊D1712yes—
534C22×C4C2×C22⋊D1711yescharacteristic
535C22×C4C2×C22⋊D1711yescharacteristic
536C22×C4C2×C22⋊D1711yescharacteristic
537C22×C4C2×C22⋊D1711yescharacteristic
538C22×C4C23×D1711yescharacteristic
539C2×C8—172no—
540C2×C8—341no—
541C2×C8—341no—
542C2×C8—341no—
543C2×C8—341no—
544C2×C8—341no—
545C2×C8—341no—
546C2×C8—341no—
547C2×C8—341no—
548C2×C8—341no—
549C2×C8—341no—
550C2×C8—341no—
551C2×C8—684no—
552C2×C8—684no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—172no—
563C4⋊C4—341no—
564C4⋊C4—341no—
565C4⋊C4—341no—
566C4⋊C4—341no—
567C4⋊C4—341no—
568C4⋊C4—341no—
569C4⋊C4—341no—
570C4⋊C4—682no—
571C4⋊C4C22⋊Dic1714yes—
572C4⋊C4C22×Dic1712yes—
573C4⋊C4C22×Dic1712yes—
574C4⋊C4C22×Dic1712yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—682no—
579C22⋊C4—682no—
580C22⋊C4—1361no—
581C22⋊C4C22⋊Dic1714yes—
582C22⋊C4C22⋊Dic1714yes—
583C42—24no—
584C42—24no—
585C42—682no—
586C42—1361no—
587C42C22×Dic1712yes—
588C42C2×C22⋊D1712yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23#1058763612yes—
600C23#1058763612yes—
601C23C2×C22⋊Dic1712yes—
602C23C2×C22⋊Dic1712yes—
603C23C22×C22⋊D1711yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608D4—28no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—48no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—342no—
639C2×C4—681no—
640C2×C4—681no—
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—1364no—
651C2×C4C2×C22⋊Dic1712yes—
652C2×C4C2×C22⋊Dic1712yes—
653C2×C4C2×C22⋊Dic1712yes—
654C2×C4C2×C22⋊Dic1712yes—
655C2×C4#41×D1711yescharacteristic
656C2×C4#41×D1711yescharacteristic
657C2×C4#1058769611yescharacteristic
658C2×C4#1058769711yescharacteristic
659C2×C4C23×Dic1711yescharacteristic
660C2×C4C22×C22⋊D1711yescharacteristic
661C8—342no—
662C8—681no—
663C8—681no—
664C8—681no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22#1176280514yes—
679C22C22×C22⋊Dic1711yescharacteristic
680C22#1176344711yescharacteristic
681C22#1176345811yescharacteristic
682C22C2×#1058763611yescharacteristic
683C22C2×#1058763611yescharacteristic
684C22#1176361711yescharacteristic
685C22#1176362411yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—682no—
695C4—1361no—
696C4—1361no—
697C4—1361no—
698C4#41×Dic1711yescharacteristic
699C4#1176329211yescharacteristic
700C4#1176344711yescharacteristic
701C4#1176345811yescharacteristic
702C2—24no—
703C2—42no—
704C2#1453161411yescharacteristic
705C2C2×#1176280511yescharacteristic
706C2#1453731711yescharacteristic
707C2#1454061311yescharacteristic
708C2#1454066511yescharacteristic
709C2#1454114611yescharacteristic
710C2#1454116311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#552C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
cosocleC22×C4×C17C24
hypercenterC2×#552D17
hypocenterC17#22486
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
3. #14529750C2semidirect
4. #14529742C2semidirect
5. #14529208C2semidirect
6. #14529208C2semidirect
7. #14529097C2semidirect
8. #14529092C2semidirect
9. #14528879C2semidirect
10. #14528870C2semidirect
11. #14528799C2semidirect
12. C4×#10587506C2semidirect
13. #14528500C2semidirect
14. C2×#11762571C2semidirect
50. C17×#552C4semidirect
71. C17×#125C2×C4semidirect
76. C17×C22⋊Q8C2×C4semidirect
78. C4×Q8×C17C2×C4semidirect
83. C17×#117C2×C4semidirect
365. #552Dic17semidirect
436. #125C2×Dic17semidirect
441. C22⋊Q8C2×Dic17semidirect
443. C4×Q8C2×Dic17semidirect
450. #117C2×Dic17semidirect
496. C17#22486semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#36222
#145317132
#145297502
#145297422
#145292082
#145290972
#145290922
#145288792
#145288702
#145287992
C4×#105875062
#145285002
C2×#117625712
C2×C17×#5522
#2248617