Finite Group Databasebeta

← C2×#14532859 #17202530

Subgroups — C2×#14532859 #17202530

Order 4352.

2594 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
1C22×#10587584C211yesmaximal, characteristic
2#14532859C2116yesmaximal, direct product factor
3C2×#11762748C211yesmaximal, characteristic, complemented
4C2×#11762731C211yesmaximal, characteristic
5C2×#11762728C211yesmaximal, characteristic, complemented
6C2×#11762720C211yesmaximal, characteristic
7C2×#11762707C211yesmaximal, characteristic, complemented
8C2×#11762700C211yesmaximal, characteristic
9C2×#11762700C211yesmaximal, characteristic
10C2×#11762700C211yesmaximal, characteristic
11C2×#11762699C211yesmaximal, characteristic
12C2×#11762695C211yesmaximal, characteristic, complemented
13C2×#11762693C211yesmaximal, characteristic, complemented
14C2×#11762690C211yesmaximal, characteristic, complemented
15C2×C4×#63225C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C17C211yesmaximal, characteristic, complemented
17C2×#10587584—28no—
18C2×#10587584C2218yes—
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762748C2218yescomplemented
36#11762731C2218yes—
37#11762728C2218yescomplemented
38#11762720C2218yes—
39#11762707C2218yescomplemented
40#11762700C2218yes—
41#11762700C2218yes—
42#11762700C2218yes—
43#11762699C2218yes—
44#11762695C2218yescomplemented
45#11762693C2218yescomplemented
46#11762690C2218yescomplemented
47C4×#63225C2218yescomplemented
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C23×Q8×C17C2211yescharacteristic
61C2×C4×Q8×C17—28no—
62C2×C4×Q8×C17C2218yescomplemented
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C4⋊C4×C17C2211yescharacteristic
65C22×C4⋊C4×C17C2211yescharacteristic
66C22×C42×C17C2211yescharacteristic
67C22×C42×C17C2211yescharacteristic
68C22×C42×C17C2211yescharacteristic
69C24×D17C2311yescharacteristic
70C22×Q8×C17—24no—
71C22×Q8×C17—24no—
72C22×Q8×C17—24no—
73C22×Q8×C17C2314yes—
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C4×Q8×C17—232no—
89C2×C4⋊C4×C17—24no—
90C2×C4⋊C4×C17—24no—
91C2×C4⋊C4×C17D418yes—
92C2×C4⋊C4×C17C2314yes—
93C2×C4⋊C4×C17C2314yes—
94C2×C4⋊C4×C17C2314yes—
95C2×C42×C17—24no—
96C2×C42×C17—24no—
97C2×C42×C17—24no—
98C2×C42×C17C2314yes—
99C2×C42×C17C2314yes—
100C2×C42×C17C2314yes—
101C2×#63227—24no—
102C2×#63227—24no—
103C2×#63227—24no—
104C2×#63227—24no—
105C2×#63227—24no—
106C2×#63227—24no—
107C2×#63227—24no—
108C2×#63227C2314yes—
109C2×#63227C2314yes—
110C2×#63227C2314yes—
111C2×#63227C2314yes—
112C2×#63227C2314yes—
113C2×#63227C2314yes—
114C2×#63227C2314yes—
115C2×C4⋊Dic17—24no—
116C2×C4⋊Dic17—24no—
117C2×C4⋊Dic17C2314yes—
118C2×C4⋊Dic17C2314yes—
119C2×#63225—24no—
120C2×#63225—24no—
121C2×#63225—24no—
122C2×#63225—24no—
123C2×#63225—24no—
124C2×#63225C2314yes—
125C2×#63225C2314yes—
126C2×#63225C2314yes—
127C2×#63225C2314yes—
128C2×#63225C2314yes—
129C2×C4×Dic17—24no—
130C2×C4×Dic17—24no—
131C2×C4×Dic17C2314yes—
132C2×C4×Dic17C2314yes—
133#10587584—232no—
134#10587502C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144#10587502C2314yes—
145#10587502C2314yes—
146C24×C17C2411yescharacteristic
147C23×D17—22no—
148C23×D17—22no—
149C23×D17—22no—
150C23×D17—22no—
151C23×D17—22no—
152C23×D17—22no—
153C23×D17—22no—
154C23×D17C2412yes—
155C2×Q8×C17—232no—
156C2×Q8×C17—28no—
157C2×Q8×C17—28no—
158C2×Q8×C17—28no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—22no—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—22no—
172C22×C4×C17—22no—
173C22×C4×C17—22no—
174C22×C4×C17C2×D414yes—
175C22×C4×C17C2×D414yes—
176C22×C4×C17C2×D414yes—
177C22×C4×C17#4114yes—
178C22×C4×C17#4114yes—
179C22×C4×C17#4114yes—
180C22×C4×C17C2412yes—
181C22×C4×C17C2412yes—
182C22×C4×C17C2412yes—
183C22×C4×C17C2412yes—
184C22×C4×C17C2412yes—
185C22×C4×C17C2412yes—
186C22×C4×C17C2412yes—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—22no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17#4114yes—
208C22×Dic17C2412yes—
209C22×Dic17C2412yes—
210C22×Dic17C2412yes—
211C22×Dic17C2412yes—
212C22×Dic17C2412yes—
213C22×Dic17C2412yes—
214C22×Dic17C2412yes—
215C4⋊C4×C17—28no—
216C4⋊C4×C17—28no—
217C4⋊C4×C17C2×D4116yes—
218C42×C17—28no—
219C42×C17—28no—
220C42×C17—28no—
221#63227—28no—
222#63227—28no—
223#63227—28no—
224#63227—28no—
225#63227—28no—
226#63227—28no—
227#63227—28no—
228C4⋊Dic17—28no—
229C4⋊Dic17—28no—
230#63225—28no—
231#63225—28no—
232#63225—28no—
233#63225—28no—
234#63225—28no—
235C4×Dic17—28no—
236C4×Dic17—28no—
237C2×#2469—171nomaximal, Sylow
238C23×C17C22×D412yes—
239C23×C17C2×#4112yes—
240C23×C17C2×#4112yes—
241C23×C17C2×#4112yes—
242C23×C17C2×#4112yes—
243C23×C172−1+412yes—
244C23×C172−1+412yes—
245C23×C17C2511yescharacteristic
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—22no—
253C22×D17—44no—
254C22×D17—44no—
255C22×D17—44no—
256C22×D17—44no—
257C22×D17—44no—
258C22×D17—44no—
259C22×D17—44no—
260Q8×C17—232no—
261C2×C4×C17—28no—
262C2×C4×C17—28no—
263C2×C4×C17—28no—
264C2×C4×C17—28no—
265C2×C4×C17—28no—
266C2×C4×C17—28no—
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—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—44no—
283C2×C4×C17C22×D414yes—
284C2×C4×C17C22×D414yes—
285C2×C4×C17C22×D414yes—
286C2×C4×C17C2×#4114yes—
287C2×C4×C17C2×#4114yes—
288C2×C4×C17C2×#4114yes—
289C2×Dic17—28no—
290C2×Dic17—22no—
291C2×Dic17—22no—
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—22no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—44no—
311C2×Dic17—44no—
312C2×Dic17—44no—
313C2×Dic17—44no—
314C2×Dic17—44no—
315C2×Dic17—44no—
316C2×Dic17C2×#4114yes—
317C22×#126—171no—
318C22×C4×Q8D1711yescharacteristic, complemented
319#2469—1716no—
320C2×#400—171no—
321C2×#396—171no—
322C2×#395—171no—
323C2×#393—171no—
324C2×#389—171no—
325C2×#388—171no—
326C2×#388—171no—
327C2×#388—171no—
328C2×#388—171no—
329C2×#387—171no—
330C2×#387—171no—
331C2×#387—171no—
332C2×C4×C4⋊C4—171no—
333C22×C17#52514yes—
334C22×C17#52914yes—
335C22×C17#54114yes—
336C22×C17#54714yes—
337C22×C17#54814yes—
338C22×C17#55614yes—
339C22×C17#55614yes—
340C22×C17C23×D411yescharacteristic
341C22×C17C22×#4111yescharacteristic
342C22×C17C22×#4111yescharacteristic
343C22×C17C22×#4111yescharacteristic
344C22×C17C22×#4111yescharacteristic
345C22×C17C2×2−1+411yescharacteristic
346C22×C17C2×2−1+411yescharacteristic
347C2×D17—42no—
348C2×D17—42no—
349C2×D17—42no—
350C2×D17—42no—
351C2×D17—42no—
352C2×D17—42no—
353C2×D17—42no—
354C2×D17—88no—
355C4×C17—24no—
356C4×C17—24no—
357C4×C17—24no—
358C4×C17—24no—
359C4×C17—24no—
360C4×C17—24no—
361C4×C17—42no—
362Dic17—24no—
363Dic17—42no—
364Dic17—42no—
365Dic17—42no—
366Dic17—42no—
367Dic17—42no—
368Dic17—42no—
369C23×Q8C2×D1711yescharacteristic
370C2×#126—178no—
371C2×#126—348no—
372C2×C4×Q8—28no—
373C2×C4×Q8C2×D1718yescomplemented
374C22×C4⋊C4—171no—
375C22×C4⋊C4—171no—
376C22×C4⋊C4—171no—
377C22×C4⋊C4—171no—
378C22×C4⋊C4—171no—
379C22×C4⋊C4—171no—
380C22×C4⋊C4—171no—
381C22×C4⋊C4C2×D1711yescharacteristic
382C22×C4⋊C4C2×D1711yescharacteristic
383C22×C4⋊C4C2×D1711yescharacteristic
384C22×C22⋊C4—171no—
385C22×C22⋊C4—171no—
386C22×C22⋊C4—171no—
387C22×C22⋊C4—171no—
388C22×C22⋊C4—171no—
389C22×C22⋊C4—171no—
390C22×C22⋊C4—171no—
391C22×C42—171no—
392C22×C42—171no—
393C22×C42C2×D1711yescharacteristic
394C22×C42C2×D1711yescharacteristic
395C22×C42C2×D1711yescharacteristic
396#400—178no—
397#396—178no—
398#395—178no—
399#393—178no—
400#389—178no—
401#388—178no—
402#388—178no—
403#388—178no—
404#388—178no—
405#387—178no—
406#387—178no—
407#387—178no—
408C4×C4⋊C4—178no—
409C2×#95—171no—
410C2×#95—171no—
411C2×#95—171no—
412C2×#95—171no—
413C2×#95—171no—
414C2×#95—171no—
415C2×#95—171no—
416C2×#95—171no—
417C2×#95—171no—
418C2×#95—171no—
419C2×#95—171no—
420C2×#95—171no—
421C2×C17#246918yescomplemented
422C2×C17C2×#52511yescharacteristic
423C2×C17C2×#52911yescharacteristic
424C2×C17C2×#54111yescharacteristic
425C2×C17C2×#54711yescharacteristic
426C2×C17C2×#54811yescharacteristic
427C2×C17C2×#55611yescharacteristic
428C2×C17C2×#55611yescharacteristic
429D17—82no—
430C25—171no—
431C22×Q8—24no—
432C22×Q8—24no—
433C22×Q8—24no—
434C22×Q8C22×D1714yes—
435C23×C4—171no—
436C23×C4—171no—
437C23×C4—171no—
438C23×C4—171no—
439C23×C4—171no—
440C23×C4—171no—
441C23×C4—171no—
442C23×C4C22×D1711yescharacteristic
443C23×C4C22×D1711yescharacteristic
444C23×C4C22×D1711yescharacteristic
445C23×C4C22×D1711yescharacteristic
446C23×C4C22×D1711yescharacteristic
447C23×C4C22×D1711yescharacteristic
448C23×C4C22×D1711yescharacteristic
449#126—3432no—
450C4×Q8—232no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—174no—
454C2×C4⋊C4—174no—
455C2×C4⋊C4—174no—
456C2×C4⋊C4—174no—
457C2×C4⋊C4—174no—
458C2×C4⋊C4—174no—
459C2×C4⋊C4—174no—
460C2×C4⋊C4—344no—
461C2×C4⋊C4—344no—
462C2×C4⋊C4—344no—
463C2×C4⋊C4—344no—
464C2×C4⋊C4—344no—
465C2×C4⋊C4—344no—
466C2×C4⋊C4—344no—
467C2×C4⋊C4C22⋊D1718yes—
468C2×C4⋊C4C22×D1714yes—
469C2×C4⋊C4C22×D1714yes—
470C2×C4⋊C4C22×D1714yes—
471C2×C22⋊C4—174no—
472C2×C22⋊C4—174no—
473C2×C22⋊C4—174no—
474C2×C22⋊C4—174no—
475C2×C22⋊C4—174no—
476C2×C22⋊C4—174no—
477C2×C22⋊C4—174no—
478C2×C22⋊C4—344no—
479C2×C22⋊C4—344no—
480C2×C22⋊C4—344no—
481C2×C22⋊C4—344no—
482C2×C22⋊C4—344no—
483C2×C22⋊C4—344no—
484C2×C22⋊C4—344no—
485C2×C42—24no—
486C2×C42—24no—
487C2×C42—24no—
488C2×C42—174no—
489C2×C42—174no—
490C2×C42—344no—
491C2×C42—344no—
492C2×C42C22×D1714yes—
493C2×C42C22×D1714yes—
494C2×C42C22×D1714yes—
495#95—174no—
496#95—174no—
497#95—174no—
498#95—174no—
499#95—174no—
500#95—174no—
501#95—174no—
502#95—174no—
503#95—174no—
504#95—174no—
505#95—174no—
506#95—174no—
507C17C2×#246911yescharacteristic, complemented, Sylow
508C24—172no—
509C24—342no—
510C24—342no—
511C24—342no—
512C24—342no—
513C24—342no—
514C24—342no—
515C24—342no—
516C24C23×D1711yescharacteristic
517C2×Q8—232no—
518C2×Q8—28no—
519C2×Q8—28no—
520C2×Q8—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—174no—
537C22×C4—172no—
538C22×C4—172no—
539C22×C4—172no—
540C22×C4—172no—
541C22×C4—172no—
542C22×C4—172no—
543C22×C4—172no—
544C22×C4—342no—
545C22×C4—342no—
546C22×C4—342no—
547C22×C4—342no—
548C22×C4—342no—
549C22×C4—342no—
550C22×C4—342no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—342no—
554C22×C4—342no—
555C22×C4—342no—
556C22×C4—342no—
557C22×C4—342no—
558C22×C4—342no—
559C22×C4—342no—
560C22×C4—342no—
561C22×C4—342no—
562C22×C4—342no—
563C22×C4—342no—
564C22×C4#6325214yes—
565C22×C4#6325214yes—
566C22×C4#6325614yes—
567C22×C4C2×C22⋊D1714yes—
568C22×C4C2×C22⋊D1714yes—
569C22×C4C2×C22⋊D1714yes—
570C22×C4C23×D1712yes—
571C22×C4C23×D1712yes—
572C22×C4C23×D1712yes—
573C22×C4C23×D1712yes—
574C22×C4C23×D1712yes—
575C22×C4C23×D1712yes—
576C22×C4C23×D1712yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—348no—
580C4⋊C4—348no—
581C4⋊C4—348no—
582C4⋊C4—348no—
583C4⋊C4—348no—
584C4⋊C4—348no—
585C4⋊C4—348no—
586C4⋊C4C2×C22⋊D17116yes—
587C22⋊C4—348no—
588C22⋊C4—348no—
589C22⋊C4—348no—
590C22⋊C4—348no—
591C22⋊C4—348no—
592C22⋊C4—348no—
593C22⋊C4—348no—
594C42—28no—
595C42—28no—
596C42—28no—
597C42—348no—
598C42—348no—
599C23—342no—
600C23—342no—
601C23—342no—
602C23—342no—
603C23—342no—
604C23—342no—
605C23—342no—
606C23—684no—
607C23—684no—
608C23—684no—
609C23—684no—
610C23—684no—
611C23—684no—
612C23—684no—
613C23C2×#6325212yes—
614C23C2×#6325212yes—
615C23C2×#6325612yes—
616C23#1058769412yes—
617C23#41×D1712yes—
618C23#1058769712yes—
619C23C22×C22⋊D1712yes—
620C23C24×D1711yescharacteristic
621Q8—232no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—28no—
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—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—174no—
645C2×C4—348no—
646C2×C4—342no—
647C2×C4—342no—
648C2×C4—342no—
649C2×C4—342no—
650C2×C4—342no—
651C2×C4—342no—
652C2×C4—342no—
653C2×C4—342no—
654C2×C4—342no—
655C2×C4—342no—
656C2×C4—342no—
657C2×C4—342no—
658C2×C4—342no—
659C2×C4—342no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—342no—
663C2×C4—342no—
664C2×C4—342no—
665C2×C4—342no—
666C2×C4—684no—
667C2×C4—684no—
668C2×C4—684no—
669C2×C4—684no—
670C2×C4—684no—
671C2×C4—684no—
672C2×C4C2×#6325214yes—
673C2×C4C2×#6325214yes—
674C2×C4C2×#6325614yes—
675C2×C4C22×C22⋊D1714yes—
676C2×C4C22×C22⋊D1714yes—
677C2×C4C22×C22⋊D1714yes—
678C22—682no—
679C22—682no—
680C22—682no—
681C22—682no—
682C22—682no—
683C22—682no—
684C22—682no—
685C22—1368no—
686C22#1176332014yes—
687C22#1176334614yes—
688C22#1176341714yes—
689C22#1176345814yes—
690C22#1176347014yes—
691C22#1176353114yes—
692C22#1176353214yes—
693C22C23×C22⋊D1711yescharacteristic
694C22C2×#41×D1711yescharacteristic
695C22C22×#6325211yescharacteristic
696C22C22×#6325211yescharacteristic
697C22C22×#6325611yescharacteristic
698C22C2×#1058769711yescharacteristic
699C22C2×#1058769411yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—24no—
705C4—24no—
706C4—42no—
707C4—344no—
708C4—682no—
709C4—682no—
710C4—682no—
711C4—682no—
712C4—682no—
713C4—682no—
714C2—1362no—
715C2#1453285918yesdirect product factor
716C2C2×#1176332011yescharacteristic
717C2C2×#1176334611yescharacteristic
718C2C2×#1176341711yescharacteristic
719C2C2×#1176345811yescharacteristic
720C2C2×#1176347011yescharacteristic
721C2C2×#1176353111yescharacteristic
722C2C2×#1176353211yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC22×C4×Q8×C17C2
socleC24×C17C24
prime radicalC24×D17C23
hypercenterC22×C4×Q8D17
hypocenterC17C2×#2469
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #14532859C2direct (N × H)
3. C2×#11762748C2semidirect
5. C2×#11762728C2semidirect
7. C2×#11762707C2semidirect
12. C2×#11762695C2semidirect
13. C2×#11762693C2semidirect
14. C2×#11762690C2semidirect
15. C2×C4×#63225C2semidirect
16. C22×C4×Q8×C17C2semidirect
35. #11762748C22semidirect
37. #11762728C22semidirect
39. #11762707C22semidirect
44. #11762695C22semidirect
45. #11762693C22semidirect
46. #11762690C22semidirect
47. C4×#63225C22semidirect
62. C2×C4×Q8×C17C22semidirect
318. C22×C4×Q8D17semidirect
373. C2×C4×Q8C2×D17semidirect
421. C2×C17#2469semidirect
507. C17C2×#2469semidirect
715. C2#14532859direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875842
#145328592
C2×#117627482
C2×#117627312
C2×#117627282
C2×#117627202
C2×#117627072
C2×#117627002
C2×#117626992
C2×#117626952
C2×#117626932
C2×#117626902
C2×C4×#632252
C22×C4×Q8×C172
C2×#246917