Finite Group Databasebeta

← C2×#14531949 #17196930

Subgroups — C2×#14531949 #17196930

Order 4352.

2566 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×#10587582C211yesmaximal, characteristic
2#14531949C2116yesmaximal, direct product factor
3C2×#11762715C211yesmaximal, characteristic, complemented
4C2×#11762713C211yesmaximal, characteristic, complemented
5C2×#11762708C211yesmaximal, characteristic, complemented
6C2×#11762704C211yesmaximal, characteristic, complemented
7C2×#11762701C211yesmaximal, characteristic
8C2×#11762701C211yesmaximal, characteristic
9C2×#11762700C211yesmaximal, characteristic
10C2×#11762698C211yesmaximal, characteristic
11C2×#11762696C211yesmaximal, characteristic, complemented
12C2×#11762696C211yesmaximal, characteristic, complemented
13C2×#11762691C211yesmaximal, characteristic, complemented
14C2×#11762671C211yesmaximal, characteristic
15C2×#11762666C211yesmaximal, characteristic
16C2×C17×#387C211yesmaximal, characteristic, complemented
17C23×Dic34C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C2×#10587582C4116yescomplemented
20C2×#10587582C2218yes—
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37#11762715C2218yescomplemented
38#11762713C2218yescomplemented
39#11762708C2218yescomplemented
40#11762704C2218yescomplemented
41#11762701C2218yes—
42#11762701C2218yes—
43#11762700C2218yes—
44#11762698C2218yes—
45#11762696C2218yescomplemented
46#11762696C2218yescomplemented
47#11762691C2218yescomplemented
48#11762671C2218yes—
49#11762666C2218yes—
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C22×C4⋊C4×C17C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×C42×C17C2211yescharacteristic
63C17×#387C2218yescomplemented
64C2×C17×#95C2211yescharacteristic
65C2×C17×#95C2211yescharacteristic
66C2×C17×#95C2211yescharacteristic
67C2×C17×#95C2211yescharacteristic
68C24×D17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C22×C4×D17—42no—
84C22×C4×D17—42no—
85C22×C4×D17C2×C418yes—
86C22×C4×D17C2314yes—
87C22×Dic34—42no—
88C22×Dic34—42no—
89C22×Dic34C2×C418yes—
90C22×Dic34C2314yes—
91C2×C4⋊C4×C17—42no—
92C2×C4⋊C4×C17C2×C418yes—
93C2×C4⋊C4×C17C2314yes—
94C2×C4⋊C4×C17C2314yes—
95C2×C42×C17—42no—
96C2×C42×C17C2314yes—
97C2×#63227—42no—
98C2×#63227—42no—
99C2×#63227—42no—
100C2×#63227—42no—
101C2×#63227C2×C418yes—
102C2×#63227C2×C418yes—
103C2×#63227C2314yes—
104C2×#63227C2314yes—
105C2×#63227C2314yes—
106C2×#63227C2314yes—
107C2×#63227C2314yes—
108C2×#63227C2314yes—
109C2×C4⋊Dic17—42no—
110C2×C4⋊Dic17—42no—
111C2×C4⋊Dic17—42no—
112C2×C4⋊Dic17C2314yes—
113C2×C4⋊Dic17C2314yes—
114C2×C4⋊Dic17C2314yes—
115C2×#63225—42no—
116C2×#63225—42no—
117C2×#63225C2×C418yes—
118C2×#63225C2×C418yes—
119C2×#63225C2314yes—
120C2×#63225C2314yes—
121C2×#63225C2314yes—
122C2×#63225C2314yes—
123C2×C4×Dic17—42no—
124C2×C4×Dic17—42no—
125C2×C4×Dic17—42no—
126C2×C4×Dic17C2314yes—
127C2×C4×Dic17C2314yes—
128C2×C4×Dic17C2314yes—
129#10587582C2×C4164yescomplemented
130C17×#95C2314yes—
131C17×#95C2314yes—
132C17×#95C2314yes—
133C17×#95C2314yes—
134#10587502C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144C24×C17C2411yescharacteristic
145C23×D17—22no—
146C23×D17—22no—
147C23×D17—22no—
148C23×D17—22no—
149C23×D17—22no—
150C23×D17—22no—
151C23×D17C22×C414yes—
152C23×D17C2412yes—
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
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×C17C22×C414yes—
172C22×C4×C17C22×C414yes—
173C22×C4×C17C22×C414yes—
174C22×C4×C17C2412yes—
175C22×C4×C17C2412yes—
176C22×C4×C17C2412yes—
177C22×C4×C17C2412yes—
178C22×C4×C17C2412yes—
179C22×C4×C17C2412yes—
180C22×C4×C17C2412yes—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
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×Dic17C22×C414yes—
200C22×Dic17C22×C414yes—
201C22×Dic17C22×C414yes—
202C22×Dic17C2412yes—
203C22×Dic17C2412yes—
204C22×Dic17C2412yes—
205C22×Dic17C2412yes—
206C22×Dic17C2412yes—
207C22×Dic17C2412yes—
208C22×Dic17C2412yes—
209C2×C4×D17—416no—
210C2×C4×D17—44no—
211C2×C4×D17—44no—
212C2×C4×D17C22×C4116yes—
213C2×Dic34—416no—
214C2×Dic34—44no—
215C2×Dic34—44no—
216C2×Dic34C22×C4116yes—
217C4⋊C4×C17—44no—
218C4⋊C4×C17C22×C4116yes—
219C42×C17—44no—
220#63227—44no—
221#63227—44no—
222#63227—44no—
223#63227—44no—
224#63227C22×C4116yes—
225#63227C22×C4116yes—
226C4⋊Dic17—44no—
227C4⋊Dic17—44no—
228C4⋊Dic17—44no—
229#63225—44no—
230#63225—44no—
231#63225C22×C4116yes—
232#63225C22×C4116yes—
233C4×Dic17—44no—
234C4×Dic17—44no—
235C4×Dic17—44no—
236C2×#2378—171nomaximal, Sylow
237C23×C17C23×C412yes—
238C23×C17H(5,𝔽2)12yes—
239C23×C17H(5,𝔽2)12yes—
240C23×C17H(5,𝔽2)12yes—
241C23×C172−1+412yes—
242C23×C172−1+412yes—
243C23×C172−1+412yes—
244C23×C17C2511yescharacteristic
245C22×D17—28no—
246C22×D17—28no—
247C22×D17—28no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—22no—
253C22×D17—22no—
254C22×D17—44no—
255C22×D17—44no—
256C22×D17—44no—
257C22×D17—44no—
258C22×D17C23×C414yes—
259C2×C4×C17—28no—
260C2×C4×C17—28no—
261C2×C4×C17—28no—
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—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—44no—
281C2×C4×C17—44no—
282C2×C4×C17—44no—
283C2×C4×C17—44no—
284C2×C4×C17C23×C414yes—
285C2×C4×C17C23×C414yes—
286C2×C4×C17C23×C414yes—
287C2×Dic17—28no—
288C2×Dic17—28no—
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—44no—
309C2×Dic17—44no—
310C2×Dic17—44no—
311C2×Dic17—44no—
312C2×Dic17C23×C414yes—
313C2×Dic17C23×C414yes—
314C2×Dic17C23×C414yes—
315C4×D17—416no—
316Dic34—416no—
317C22×C22⋊Q8—171no—
318#2378—1716no—
319C2×#391—171no—
320C2×#391—171no—
321C2×#389—171no—
322C2×#389—171no—
323C2×#388—171no—
324C2×#388—171no—
325C2×#388—171no—
326C2×#388—171no—
327C2×#387—171no—
328C2×#387—171no—
329C2×#387—171no—
330C2×#387D1711yescharacteristic, complemented
331C2×#381—171no—
332C2×#380—171no—
333C22×C17#51814yes—
334C22×C17#51914yes—
335C22×C17#52014yes—
336C22×C17#56214yes—
337C22×C17#56214yes—
338C22×C17#56314yes—
339C22×C17#56314yes—
340C22×C17C24×C411yescharacteristic
341C22×C17C2×H(5,𝔽2)11yescharacteristic
342C22×C17C2×H(5,𝔽2)11yescharacteristic
343C22×C17C2×H(5,𝔽2)11yescharacteristic
344C22×C17C2×2−1+411yescharacteristic
345C22×C17C2×2−1+411yescharacteristic
346C22×C17C2×2−1+411yescharacteristic
347C2×D17—24no—
348C2×D17—24no—
349C2×D17—24no—
350C2×D17—416no—
351C2×D17—42no—
352C2×D17—42no—
353C2×D17—42no—
354C2×D17—42no—
355C4×C17—24no—
356C4×C17—24no—
357C4×C17—24no—
358C4×C17—42no—
359C4×C17—42no—
360C4×C17—42no—
361C4×C17—42no—
362Dic17—24no—
363Dic17—24no—
364Dic17—24no—
365Dic17—42no—
366Dic17—42no—
367Dic17—42no—
368Dic17—42no—
369C23×Q8—171no—
370C24×C4—171no—
371C2×C22⋊Q8—1716no—
372C2×C22⋊Q8—178no—
373C22×C4⋊C4—171no—
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⋊C4C2×D1711yescharacteristic
381C22×C4⋊C4C2×D1711yescharacteristic
382C22×C22⋊C4—171no—
383C22×C22⋊C4—171no—
384C22×C22⋊C4—171no—
385C22×C22⋊C4—171no—
386C22×C22⋊C4—171no—
387C22×C22⋊C4—171no—
388C22×C42—171no—
389C22×C42—171no—
390C22×C42—171no—
391C22×C42C2×D1711yescharacteristic
392#391—178no—
393#391—178no—
394#389—178no—
395#389—178no—
396#388—178no—
397#388—178no—
398#388—178no—
399#388—178no—
400#387—178no—
401#387—178no—
402#387—178no—
403#387C2×D1718yescomplemented
404#381—178no—
405#380—178no—
406C2×#95—171no—
407C2×#95—171no—
408C2×#95—171no—
409C2×#95—171no—
410C2×#95—171no—
411C2×#95—171no—
412C2×#95—171no—
413C2×#95—171no—
414C2×#95—171no—
415C2×#95—171no—
416C2×#95C2×D1711yescharacteristic
417C2×#95C2×D1711yescharacteristic
418C2×#95C2×D1711yescharacteristic
419C2×#95C2×D1711yescharacteristic
420C2×C17#237818yescomplemented
421C2×C17C2×#51811yescharacteristic
422C2×C17C2×#51911yescharacteristic
423C2×C17C2×#52011yescharacteristic
424C2×C17C2×#56211yescharacteristic
425C2×C17C2×#56211yescharacteristic
426C2×C17C2×#56311yescharacteristic
427C2×C17C2×#56311yescharacteristic
428D17—44no—
429C25—171no—
430C22×Q8—178no—
431C22×Q8—174no—
432C22×Q8—682no—
433C22×Q8—682no—
434C23×C4—171no—
435C23×C4—171no—
436C23×C4—171no—
437C23×C4—178no—
438C23×C4—174no—
439C23×C4—171no—
440C23×C4—171no—
441C23×C4—171no—
442C23×C4—171no—
443C23×C4—682no—
444C23×C4—682no—
445C23×C4C22×D1711yescharacteristic
446C23×C4C22×D1711yescharacteristic
447C23×C4C22×D1711yescharacteristic
448C23×C4C22×D1711yescharacteristic
449C23×C4C22×D1711yescharacteristic
450C23×C4C22×D1711yescharacteristic
451C23×C4C22×D1711yescharacteristic
452C22⋊Q8—1764no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—178no—
455C2×C4⋊C4—178no—
456C2×C4⋊C4—174no—
457C2×C4⋊C4—174no—
458C2×C4⋊C4—174no—
459C2×C4⋊C4—174no—
460C2×C4⋊C4—174no—
461C2×C4⋊C4—174no—
462C2×C4⋊C4—174no—
463C2×C4⋊C4—682no—
464C2×C4⋊C4—682no—
465C2×C4⋊C4—682no—
466C2×C4⋊C4—682no—
467C2×C4⋊C4—682no—
468C2×C4⋊C4C4×D1718yes—
469C2×C4⋊C4C22×D1714yes—
470C2×C4⋊C4C22×D1714yes—
471C2×C22⋊C4—178no—
472C2×C22⋊C4—178no—
473C2×C22⋊C4—174no—
474C2×C22⋊C4—174no—
475C2×C22⋊C4—174no—
476C2×C22⋊C4—174no—
477C2×C22⋊C4—174no—
478C2×C22⋊C4—174no—
479C2×C22⋊C4—682no—
480C2×C22⋊C4—682no—
481C2×C22⋊C4—682no—
482C2×C22⋊C4—682no—
483C2×C42—42no—
484C2×C42—174no—
485C2×C42—174no—
486C2×C42—174no—
487C2×C42—682no—
488C2×C42—682no—
489C2×C42—682no—
490C2×C42C22×D1714yes—
491#95—174no—
492#95—174no—
493#95—174no—
494#95—174no—
495#95—174no—
496#95—174no—
497#95—174no—
498#95—174no—
499#95—174no—
500#95—174no—
501#95C22×D1714yes—
502#95C22×D1714yes—
503#95C22×D1714yes—
504#95C22×D1714yes—
505C17C2×#237811yescharacteristic, complemented, Sylow
506C24—174no—
507C24—172no—
508C24—342no—
509C24—342no—
510C24—342no—
511C24—342no—
512C24—342no—
513C24—342no—
514C24C23×D1711yescharacteristic
515C2×Q8—1716no—
516C2×Q8—6816no—
517C2×Q8—684no—
518C2×Q8—684no—
519C22×C4—22no—
520C22×C4—22no—
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—22no—
537C22×C4—174no—
538C22×C4—174no—
539C22×C4—174no—
540C22×C4—172no—
541C22×C4—172no—
542C22×C4—172no—
543C22×C4—1716no—
544C22×C4—172no—
545C22×C4—172no—
546C22×C4—172no—
547C22×C4—172no—
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—342no—
565C22×C4—342no—
566C22×C4—6816no—
567C22×C4—684no—
568C22×C4—684no—
569C22×C4C2×C4×D1714yes—
570C22×C4C2×C4×D1714yes—
571C22×C4C2×C4×D1714yes—
572C22×C4C23×D1712yes—
573C22×C4C23×D1712yes—
574C22×C4C23×D1712yes—
575C22×C4C23×D1712yes—
576C22×C4C23×D1712yes—
577C22×C4C23×D1712yes—
578C22×C4C23×D1712yes—
579C4⋊C4—44no—
580C4⋊C4—1716no—
581C4⋊C4—1716no—
582C4⋊C4—684no—
583C4⋊C4—684no—
584C4⋊C4—684no—
585C4⋊C4—684no—
586C4⋊C4—684no—
587C4⋊C4C2×C4×D17116yes—
588C22⋊C4—1716no—
589C22⋊C4—1716no—
590C22⋊C4—684no—
591C22⋊C4—684no—
592C22⋊C4—684no—
593C22⋊C4—684no—
594C42—44no—
595C42—684no—
596C42—684no—
597C42—684no—
598C23—174no—
599C23—348no—
600C23—348no—
601C23—348no—
602C23—342no—
603C23—342no—
604C23—342no—
605C23—342no—
606C23—342no—
607C23—342no—
608C23—684no—
609C23—684no—
610C23—684no—
611C23—684no—
612C23C22×C4×D1712yes—
613C23#1058769112yes—
614C23#1058769412yes—
615C23#1058769612yes—
616C23#1058769612yes—
617C23#1058769712yes—
618C23#1058769712yes—
619C23C24×D1711yescharacteristic
620Q8—6816no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
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—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—174no—
647C2×C4—174no—
648C2×C4—174no—
649C2×C4—348no—
650C2×C4—348no—
651C2×C4—348no—
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—342no—
667C2×C4—342no—
668C2×C4—342no—
669C2×C4—342no—
670C2×C4—6816no—
671C2×C4—684no—
672C2×C4—684no—
673C2×C4—684no—
674C2×C4—684no—
675C2×C4C22×C4×D1714yes—
676C2×C4C22×C4×D1714yes—
677C2×C4C22×C4×D1714yes—
678C22—344no—
679C22—344no—
680C22—344no—
681C22—682no—
682C22—682no—
683C22—682no—
684C22—682no—
685C22—6816no—
686C22#1176328114yes—
687C22#1176328514yes—
688C22#1176328914yes—
689C22#1176355614yes—
690C22#1176355714yes—
691C22#1176356014yes—
692C22#1176356114yes—
693C22C23×C4×D1711yescharacteristic
694C22C2×#1058769111yescharacteristic
695C22C2×#1058769611yescharacteristic
696C22C2×#1058769611yescharacteristic
697C22C2×#1058769711yescharacteristic
698C22C2×#1058769711yescharacteristic
699C22C2×#1058769411yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—344no—
708C4—344no—
709C4—344no—
710C4—682no—
711C4—682no—
712C4—682no—
713C4—682no—
714C2—684no—
715C2#1453194918yesdirect product factor
716C2C2×#1176328111yescharacteristic
717C2C2×#1176328511yescharacteristic
718C2C2×#1176328911yescharacteristic
719C2C2×#1176355611yescharacteristic
720C2C2×#1176355711yescharacteristic
721C2C2×#1176356011yescharacteristic
722C2C2×#1176356111yescharacteristic
subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#387C2
socleC24×C17C24
prime radicalC24×D17C23
cosocleC23×C17C25
hypercenterC2×#387D17
hypocenterC17C2×#2378
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #14531949C2direct (N × H)
3. C2×#11762715C2semidirect
4. C2×#11762713C2semidirect
5. C2×#11762708C2semidirect
6. C2×#11762704C2semidirect
11. C2×#11762696C2semidirect
12. C2×#11762696C2semidirect
13. C2×#11762691C2semidirect
16. C2×C17×#387C2semidirect
19. C2×#10587582C4semidirect
37. #11762715C22semidirect
38. #11762713C22semidirect
39. #11762708C22semidirect
40. #11762704C22semidirect
45. #11762696C22semidirect
46. #11762696C22semidirect
47. #11762691C22semidirect
63. C17×#387C22semidirect
129. #10587582C2×C4semidirect
330. C2×#387D17semidirect
403. #387C2×D17semidirect
420. C2×C17#2378semidirect
505. C17C2×#2378semidirect
715. C2#14531949direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875822
#145319492
C2×#117627152
C2×#117627132
C2×#117627082
C2×#117627042
C2×#117627012
C2×#117627002
C2×#117626982
C2×#117626962
C2×#117626912
C2×#117626712
C2×#117626662
C2×C17×#3872
C2×#237817