Finite Group Databasebeta

← #17050612

Subgroups — #17050612

Order 4352.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762881C211yesmaximal, characteristic
2D4×C4⋊Dic17C211yesmaximal, characteristic
3#14529754C211yesmaximal, characteristic, complemented
4#14529742C211yesmaximal, characteristic, complemented
5#14529218C211yesmaximal, characteristic, complemented
6#14529208C211yesmaximal, characteristic, complemented
7#14529092C211yesmaximal, characteristic, complemented
8#14529092C211yesmaximal, characteristic, complemented
9#14528879C211yesmaximal, characteristic, complemented
10#14528870C211yesmaximal, characteristic, complemented
11#14528789C211yesmaximal, characteristic, complemented
12#14528614C211yesmaximal, characteristic, complemented
13#14528505C211yesmaximal, characteristic, complemented
14C2×#11762571C211yesmaximal, characteristic, complemented
15C2×C17×#552C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C2×D4×Dic17—21no—
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21#11762881—24no—
22C2×C4⋊#3622C2211yescharacteristic
23C2×#10587506C2211yescharacteristic
24C2×#10587506C2211yescharacteristic
25C2×#10587506C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×C22⋊#3622C2211yescharacteristic
28C2×C22⋊#3622C2211yescharacteristic
29C2×#10587474C2211yescharacteristic
30#11762708—21no—
31#11762684—21no—
32#11762684—21no—
33#11762679C2211yescharacteristic
34#11762669C2211yescharacteristic
35#11762669C2211yescharacteristic
36C4×C4⋊Dic17C2211yescharacteristic
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—
68C23×Dic17—21no—
69C17×#126—28no—
70C17×#125—28no—
71C17×#125—22no—
72C17×#125C2×C414yescomplemented
73C17×#123—28no—
74C17×C22⋊Q8—22no—
75C17×C22⋊Q8—22no—
76C17×C22⋊Q8C2×C414yescomplemented
77C17×C22⋊Q8C2×C414yescomplemented
78C4×Q8×C17—22no—
79C4×Q8×C17C2×C414yescomplemented
80C4×D4×C17C2×C414yes—
81C4×D4×C17D414yes—
82C17×#117—22no—
83C17×#117—28no—
84C17×#117C2×C414yescomplemented
85C2×C4⋊C4×C17—21no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊C4×C17—21no—
88C2×C4⋊C4×C17—21no—
89C2×C4⋊C4×C17—21no—
90C2×C4⋊C4×C17—21no—
91C2×C4⋊C4×C17—21no—
92C2×C4⋊C4×C17C2×C414yescomplemented
93C2×C4⋊C4×C17D411yescharacteristic
94C2×C4⋊C4×C17C2311yescharacteristic
95C2×C4⋊C4×C17C2311yescharacteristic
96C2×C4⋊C4×C17C2311yescharacteristic
97C2×C22⋊C4×C17—21no—
98C2×C22⋊C4×C17—21no—
99C2×C22⋊C4×C17—21no—
100C2×C22⋊C4×C17D411yescharacteristic
101C2×C22⋊C4×C17D411yescharacteristic
102C2×C42×C17—21no—
103C2×C42×C17—21no—
104C2×C42×C17C2311yescharacteristic
105C2×C22⋊Dic17—21no—
106C2×C22⋊Dic17—21no—
107D4×Dic17—44no—
108C2×C4⋊Dic17—21no—
109C2×C4⋊Dic17—21no—
110C2×C4⋊Dic17—21no—
111C2×C4⋊Dic17—21no—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—41no—
115C2×C4⋊Dic17—41no—
116C2×C4⋊Dic17C2311yescharacteristic
117C2×C4⋊Dic17C2311yescharacteristic
118C2×C4⋊Dic17C2311yescharacteristic
119C2×C4⋊Dic17C2311yescharacteristic
120C2×C4×Dic17—21no—
121C2×#63223—22no—
122C2×#63223—22no—
123C2×#63223—41no—
124C22×#3622—22no—
125C22×#3622—22no—
126C22×#3622—41no—
127C22×#3622C2311yescharacteristic
128C22×#3622C2311yescharacteristic
129C22×#3622C2311yescharacteristic
130C22×#3622C2311yescharacteristic
131#10587506—22no—
132#10587506—22no—
133#10587506—41no—
134#10587506—41no—
135#10587502—21no—
136#10587502—21no—
137#10587502—21no—
138C22⋊#3622—22no—
139C22⋊#3622—22no—
140C4⋊#3622—22no—
141#10587474—22no—
142C24×C17C2×D411yescharacteristic
143C24×C17C2×D411yescharacteristic
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17—21no—
148C2×Q8×C17—21no—
149C2×Q8×C17C22×C412yes—
150C2×D4×C17—22no—
151C2×D4×C17—22no—
152C2×D4×C17C22⋊C414yes—
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—24no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—42no—
167C22×C4×C17—42no—
168C22×C4×C17C22×C412yes—
169C22×C4×C17C22×C412yes—
170C22×C4×C17C2×D411yescharacteristic
171C22×C4×C17C2×D411yescharacteristic
172C22×C4×C17C2×D411yescharacteristic
173C22×C4×C17C2×D411yescharacteristic
174C22×C4×C17C2×D412yes—
175C22×C4×C17C2×D412yes—
176C22×C4×C17C2411yescharacteristic
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—21no—
181C22×Dic17—42no—
182C22×Dic17—42no—
183C22×Dic17—42no—
184C22×Dic17—42no—
185C22×Dic17—81no—
186C22×Dic17—81no—
187C4⋊C4×C17—24no—
188C4⋊C4×C17—24no—
189C4⋊C4×C17—24no—
190C4⋊C4×C17—24no—
191C4⋊C4×C17—24no—
192C4⋊C4×C17—24no—
193C4⋊C4×C17—21no—
194C4⋊C4×C17—21no—
195C4⋊C4×C17—21no—
196C4⋊C4×C17C22⋊C414yes—
197C4⋊C4×C17C22×C412yes—
198C4⋊C4×C17C22×C412yes—
199C4⋊C4×C17C22×C412yes—
200C22⋊C4×C17—24no—
201C22⋊C4×C17—24no—
202C22⋊C4×C17—24no—
203C22⋊C4×C17C22⋊C414yes—
204C22⋊C4×C17C22⋊C414yes—
205C42×C17—24no—
206C42×C17—24no—
207C42×C17C22×C412yes—
208C42×C17C2×D412yes—
209C22⋊Dic17—42no—
210C22⋊Dic17—42no—
211C4⋊Dic17—21no—
212C4⋊Dic17—21no—
213C4⋊Dic17—21no—
214C4⋊Dic17—21no—
215C4⋊Dic17—21no—
216C4⋊Dic17—21no—
217C4⋊Dic17—21no—
218C4⋊Dic17—42no—
219C4⋊Dic17—42no—
220C4⋊Dic17—42no—
221C4⋊Dic17—81no—
222C4⋊Dic17#4112yes—
223C4×Dic17—42no—
224#63223—44no—
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—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—44no—
237C2×#3622#4112yes—
238#22491—171nomaximal, Sylow
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17C2×C22⋊C412yes—
250C23×C17C2×C22⋊C412yes—
251C23×C17AGL(1,ℤ/8)12yes—
252C23×C17#13712yes—
253C23×C17C22×D411yescharacteristic
254Q8×C17—22no—
255Q8×C17—22no—
256Q8×C17—41no—
257Q8×C17—41no—
258D4×C17—28no—
259C2×C4×C17—21no—
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—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—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—48no—
288C2×C4×C17C2×C22⋊C412yes—
289C2×C4×C17C2×C22⋊C412yes—
290C2×C4×C17C2×C22⋊C412yes—
291C2×C4×C17C2×C22⋊C412yes—
292C2×C4×C17C23×C411yescharacteristic
293C2×C4×C17C22×D411yescharacteristic
294C2×C4×C17C2×#4111yescharacteristic
295C2×C4×C17C2×#4111yescharacteristic
296C2×C4×C17H(5,𝔽2)11yescharacteristic
297C2×C4×C172−1+411yescharacteristic
298C2×Dic17—22no—
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—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—84no—
311C2×Dic17—84no—
312#3622—22no—
313#3622—41no—
314#3622—41no—
315#3622—41no—
316C2×#552D1711yescharacteristic
317C2×#435—171no—
318D4×C4⋊C4—171no—
319#1992—171no—
320#1989—171no—
321#1894—171no—
322#1892—171no—
323#1872—171no—
324#1872—171no—
325#1825—171no—
326#1823—171no—
327#1803—171no—
328#1763—171no—
329#1736—171no—
330C2×#340—171no—
331C22×C17—22no—
332C22×C17—22no—
333C22×C17—22no—
334C22×C17—22no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17—22no—
338C22×C17—22no—
339C22×C17—22no—
340C22×C17—41no—
341C22×C17—41no—
342C22×C17—41no—
343C22×C17—41no—
344C22×C17#41714yes—
345C22×C17C22×C22⋊C411yescharacteristic
346C22×C17#54611yescharacteristic
347C22×C17#54711yescharacteristic
348C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C17C2×#13711yescharacteristic
350C22×C17#57711yescharacteristic
351C22×C17#57811yescharacteristic
352C4×C17—22no—
353C4×C17—22no—
354C4×C17—22no—
355C4×C17—22no—
356C4×C17—42no—
357C4×C17—42no—
358C4×C17—42no—
359C4×C17—42no—
360C4×C17C4×#4111yescharacteristic
361C4×C17#52011yescharacteristic
362C4×C17#54611yescharacteristic
363C4×C17#54711yescharacteristic
364Dic17—42no—
365Dic17—81no—
366Dic17—81no—
367Dic17—81no—
368C22×M16—171no—
369C23×C8—171no—
370#552—24no—
371#552Dic1718yescomplemented
372C2×#126—21no—
373C2×#125—21no—
374C2×#125C2×D1711yescharacteristic
375C2×#123—21no—
376C2×C22⋊Q8C2×D1711yescharacteristic
377C2×C22⋊Q8C2×D1711yescharacteristic
378C2×C4×Q8C2×D1711yescharacteristic
379C2×C4×D4—341no—
380C2×C4×D4C2×D1711yescharacteristic
381C2×#117—21no—
382C2×#117C2×D1711yescharacteristic
383C22×C4⋊C4—171no—
384C22×C4⋊C4—171no—
385C22×C4⋊C4C2×D1711yescharacteristic
386#435—344no—
387C2×C4⋊C8—171no—
388C2×#103—171no—
389C2×#103—171no—
390C2×#103—171no—
391C2×#103—171no—
392C2×C22⋊C8—171no—
393C2×C22⋊C8—171no—
394C2×#97—171no—
395#389—341no—
396#385—341no—
397#385—341no—
398#384—171no—
399#380—171no—
400#380—171no—
401C4×C4⋊C4—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—
410#340—171no—
411#340—171no—
412#340—171no—
413#340—171no—
414C2×C17—24no—
415C2×C17—42no—
416C2×C17#233911yescharacteristic
417C2×C17C2×#41711yescharacteristic
418C2×C17#289811yescharacteristic
419C2×C17#331011yescharacteristic
420C2×C17#331211yescharacteristic
421C2×C17#334311yescharacteristic
422C2×C17#334411yescharacteristic
423C22×Q8C22×D1711yescharacteristic
424C22×D4C22⋊D1711yescharacteristic
425C23×C4—21no—
426C23×C4—341no—
427C23×C4—341no—
428C23×C4C22×D1711yescharacteristic
429C23×C4C22×D1711yescharacteristic
430C2×M16—342no—
431C2×M16—342no—
432C2×M16—681no—
433C22×C8—171no—
434C22×C8—171no—
435C22×C8—171no—
436C22×C8—171no—
437C22×C8—342no—
438C22×C8—342no—
439C22×C8—681no—
440#126—28no—
441#125—28no—
442#125—22no—
443#125C2×Dic1714yescomplemented
444#123—28no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8C2×Dic1714yescomplemented
448C22⋊Q8C2×Dic1714yescomplemented
449C4×Q8—22no—
450C4×Q8C2×Dic1714yescomplemented
451C4×D4—684no—
452C4×D4C2×Dic1714yes—
453C4×D4C22⋊D1714yes—
454#117—22no—
455#117—28no—
456#117C2×Dic1714yescomplemented
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—171no—
465C2×C4⋊C4—171no—
466C2×C4⋊C4—171no—
467C2×C4⋊C4—171no—
468C2×C4⋊C4—342no—
469C2×C4⋊C4—342no—
470C2×C4⋊C4—341no—
471C2×C4⋊C4—341no—
472C2×C4⋊C4—341no—
473C2×C4⋊C4—341no—
474C2×C4⋊C4—681no—
475C2×C4⋊C4—681no—
476C2×C4⋊C4C2×Dic1714yescomplemented
477C2×C4⋊C4C22⋊D1711yescharacteristic
478C2×C4⋊C4C22×D1711yescharacteristic
479C2×C4⋊C4C22×D1711yescharacteristic
480C2×C4⋊C4C22×D1711yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—341no—
485C2×C22⋊C4—341no—
486C2×C22⋊C4C22⋊D1711yescharacteristic
487C2×C22⋊C4C22⋊D1711yescharacteristic
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—341no—
491C2×C42C22×D1711yescharacteristic
492C4⋊C8—342no—
493#103—342no—
494#103—342no—
495#103—681no—
496#103—681no—
497C22⋊C8—342no—
498C22⋊C8—342no—
499#97—342no—
500#95—341no—
501#95—341no—
502#95—341no—
503C17#2249111yescharacteristic, complemented, Sylow
504C24C2×C22⋊D1711yescharacteristic
505C24C2×C22⋊D1711yescharacteristic
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8C22×Dic1712yes—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4C22⋊Dic1714yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—341no—
531C22×C4—341no—
532C22×C4—341no—
533C22×C4—341no—
534C22×C4—682no—
535C22×C4—682no—
536C22×C4—682no—
537C22×C4—682no—
538C22×C4—1361no—
539C22×C4—1361no—
540C22×C4C22×Dic1712yes—
541C22×C4C22×Dic1712yes—
542C22×C4C2×C22⋊D1712yes—
543C22×C4C2×C22⋊D1712yes—
544C22×C4C2×C22⋊D1711yescharacteristic
545C22×C4C2×C22⋊D1711yescharacteristic
546C22×C4C2×C22⋊D1711yescharacteristic
547C22×C4C2×C22⋊D1711yescharacteristic
548C22×C4C23×D1711yescharacteristic
549M16—684no—
550C2×C8—172no—
551C2×C8—341no—
552C2×C8—341no—
553C2×C8—341no—
554C2×C8—341no—
555C2×C8—341no—
556C2×C8—341no—
557C2×C8—341no—
558C2×C8—341no—
559C2×C8—341no—
560C2×C8—341no—
561C2×C8—341no—
562C2×C8—684no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—172no—
573C4⋊C4—341no—
574C4⋊C4—341no—
575C4⋊C4—341no—
576C4⋊C4—341no—
577C4⋊C4—341no—
578C4⋊C4—341no—
579C4⋊C4—341no—
580C4⋊C4—682no—
581C4⋊C4—682no—
582C4⋊C4—682no—
583C4⋊C4—1361no—
584C4⋊C4C22⋊Dic1714yes—
585C4⋊C4C22×Dic1712yes—
586C4⋊C4C22×Dic1712yes—
587C4⋊C4C22×Dic1712yes—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—682no—
592C22⋊C4—682no—
593C22⋊C4C22⋊Dic1714yes—
594C22⋊C4C22⋊Dic1714yes—
595C42—24no—
596C42—24no—
597C42—682no—
598C42C22×Dic1712yes—
599C42C2×C22⋊D1712yes—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23#1058763512yes—
611C23#1058763712yes—
612C23C2×C22⋊Dic1712yes—
613C23C2×C22⋊Dic1712yes—
614C23C22×C22⋊D1711yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—48no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—342no—
650C2×C4—681no—
651C2×C4—681no—
652C2×C4—681no—
653C2×C4—681no—
654C2×C4—681no—
655C2×C4—681no—
656C2×C4—681no—
657C2×C4—681no—
658C2×C4—681no—
659C2×C4—681no—
660C2×C4—681no—
661C2×C4—1364no—
662C2×C4—1364no—
663C2×C4C2×C22⋊Dic1712yes—
664C2×C4C2×C22⋊Dic1712yes—
665C2×C4C2×C22⋊Dic1712yes—
666C2×C4C2×C22⋊Dic1712yes—
667C2×C4#41×D1711yescharacteristic
668C2×C4#41×D1711yescharacteristic
669C2×C4#1058769611yescharacteristic
670C2×C4#1058769711yescharacteristic
671C2×C4C23×Dic1711yescharacteristic
672C2×C4C22×C22⋊D1711yescharacteristic
673C8—342no—
674C8—681no—
675C8—681no—
676C8—681no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1176281014yes—
691C22C22×C22⋊Dic1711yescharacteristic
692C22#1176344711yescharacteristic
693C22#1176345811yescharacteristic
694C22C2×#1058763511yescharacteristic
695C22C2×#1058763711yescharacteristic
696C22#1176361711yescharacteristic
697C22#1176362411yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—682no—
707C4—1361no—
708C4—1361no—
709C4—1361no—
710C4#41×Dic1711yescharacteristic
711C4#1176329211yescharacteristic
712C4#1176344711yescharacteristic
713C4#1176345811yescharacteristic
714C2—24no—
715C2—42no—
716C2#1453161411yescharacteristic
717C2C2×#1176281011yescharacteristic
718C2#1453731711yescharacteristic
719C2#1454079911yescharacteristic
720C2#1454082911yescharacteristic
721C2#1454122411yescharacteristic
722C2#1454123911yescharacteristic
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#22491
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. #14529754C2semidirect
4. #14529742C2semidirect
5. #14529218C2semidirect
6. #14529208C2semidirect
7. #14529092C2semidirect
8. #14529092C2semidirect
9. #14528879C2semidirect
10. #14528870C2semidirect
11. #14528789C2semidirect
12. #14528614C2semidirect
13. #14528505C2semidirect
14. C2×#11762571C2semidirect
50. C17×#552C4semidirect
72. C17×#125C2×C4semidirect
76. C17×C22⋊Q8C2×C4semidirect
77. C17×C22⋊Q8C2×C4semidirect
79. C4×Q8×C17C2×C4semidirect
84. C17×#117C2×C4semidirect
92. C2×C4⋊C4×C17C2×C4semidirect
371. #552Dic17semidirect
443. #125C2×Dic17semidirect
447. C22⋊Q8C2×Dic17semidirect
448. C22⋊Q8C2×Dic17semidirect
450. C4×Q8C2×Dic17semidirect
456. #117C2×Dic17semidirect
476. C2×C4⋊C4C2×Dic17semidirect
503. C17#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#117628812
D4×C4⋊Dic172
#145297542
#145297422
#145292182
#145292082
#145290922
#145288792
#145288702
#145287892
#145286142
#145285052
C2×#117625712
C2×C17×#5522
#2249117