Finite Group Databasebeta

← C2×#14531513 #17193142

Subgroups — C2×#14531513 #17193142

Order 4352.

2982 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587583C211yesmaximal, characteristic
2#14531513C2116yesmaximal, direct product factor
3C2×#11762713C211yesmaximal, characteristic, complemented
4C2×#11762713C211yesmaximal, characteristic, complemented
5C2×#11762707C211yesmaximal, characteristic, complemented
6C2×#11762705C211yesmaximal, characteristic, complemented
7C2×#11762695C211yesmaximal, characteristic, complemented
8C2×#11762694C211yesmaximal, characteristic, complemented
9C2×#11762692C211yesmaximal, characteristic, complemented
10C2×#11762683C211yesmaximal, characteristic
11C2×#11762680C211yesmaximal, characteristic
12C2×#11762668C211yesmaximal, characteristic
13C2×C4×#63227C211yesmaximal, characteristic
14C2×#11762656C211yesmaximal, characteristic
15C2×#95×D17C211yesmaximal, characteristic
16C2×C17×#387C211yesmaximal, characteristic, complemented
17C23×Dic34C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C2×#10587583C4116yescomplemented
22C2×#10587583C2218yes—
23C22×C4⋊Dic17C2211yescharacteristic
24C22×C4⋊Dic17C2211yescharacteristic
25C22×C4⋊Dic17C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37#11762713C2218yescomplemented
38#11762713C2218yescomplemented
39#11762707C2218yescomplemented
40#11762705C2218yescomplemented
41#11762695C2218yescomplemented
42#11762694C2218yescomplemented
43#11762692C2218yescomplemented
44#11762683C2218yes—
45#11762680C2218yes—
46#11762668C2218yes—
47C4×#63227C2218yes—
48#11762656C2218yes—
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59#95×D17C2218yes—
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—24no—
84C22×C4×D17—42no—
85C22×C4×D17—42no—
86C22×C4×D17—42no—
87C22×C4×D17—42no—
88C22×C4×D17—42no—
89C22×C4×D17—42no—
90C22×C4×D17C2×C418yes—
91C22×C4×D17Q818yescomplemented
92C22×C4×D17C2314yes—
93C22×C4×D17C2314yes—
94C22×C4×D17C2314yes—
95C22×Dic34—42no—
96C22×Dic34—42no—
97C22×Dic34C2×C418yescomplemented
98C22×Dic34C2314yes—
99C2×C4⋊C4×C17—42no—
100C2×C4⋊C4×C17C2×C418yescomplemented
101C2×C4⋊C4×C17C2314yes—
102C2×C4⋊C4×C17C2314yes—
103C2×C42×C17—42no—
104C2×C42×C17C2314yes—
105C2×#63227—24no—
106C2×#63227—24no—
107C2×#63227C2×C418yes—
108C2×#63227C2×C418yes—
109C2×#63227C2314yes—
110C2×#63227C2314yes—
111C2×#63227C2314yes—
112C2×#63227C2314yes—
113C2×C4⋊Dic17—42no—
114C2×C4⋊Dic17C2×C418yescomplemented
115C2×C4⋊Dic17C2×C418yescomplemented
116C2×C4⋊Dic17C2314yes—
117C2×C4⋊Dic17C2314yes—
118C2×C4⋊Dic17C2314yes—
119C2×#63225—42no—
120C2×#63225—42no—
121C2×#63225—42no—
122C2×#63225—42no—
123C2×#63225C2314yes—
124C2×#63225C2314yes—
125C2×#63225C2314yes—
126C2×#63225C2314yes—
127C2×C4×Dic17—42no—
128C2×C4×Dic17—42no—
129C2×C4×Dic17—42no—
130C2×C4×Dic17C2314yes—
131C2×C4×Dic17C2314yes—
132C2×C4×Dic17C2314yes—
133#10587583C2×C4164yescomplemented
134C17×#95C2314yes—
135C17×#95C2314yes—
136C17×#95C2314yes—
137C17×#95C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144#10587502C2314yes—
145#10587502C2314yes—
146#10587502C2314yes—
147#10587502C2314yes—
148C24×C17C2411yescharacteristic
149C23×D17—22no—
150C23×D17—22no—
151C23×D17—22no—
152C23×D17—22no—
153C23×D17C22×C414yes—
154C23×D17C2×Q814yes—
155C23×D17#4114yes—
156C23×D17C2412yes—
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×C17—22no—
172C22×C4×C17—22no—
173C22×C4×C17—22no—
174C22×C4×C17C22×C414yes—
175C22×C4×C17C22×C414yes—
176C22×C4×C17C22×C414yes—
177C22×C4×C17C2×Q814yes—
178C22×C4×C17C2412yes—
179C22×C4×C17C2412yes—
180C22×C4×C17C2412yes—
181C22×C4×C17C2412yes—
182C22×C4×C17C2412yes—
183C22×C4×C17C2412yes—
184C22×C4×C17C2412yes—
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×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17C22×C414yes—
203C22×Dic17C22×C414yes—
204C22×Dic17C22×C414yes—
205C22×Dic17C2×Q814yes—
206C22×Dic17C2412yes—
207C22×Dic17C2412yes—
208C22×Dic17C2412yes—
209C22×Dic17C2412yes—
210C22×Dic17C2412yes—
211C22×Dic17C2412yes—
212C22×Dic17C2412yes—
213C2×C4×D17—28no—
214C2×C4×D17—416no—
215C2×C4×D17—416no—
216C2×C4×D17—44no—
217C2×C4×D17—44no—
218C2×C4×D17—44no—
219C2×C4×D17—44no—
220C2×C4×D17—44no—
221C2×C4×D17—44no—
222C2×C4×D17—416no—
223C2×C4×D17C22×C4116yes—
224C2×C4×D17C2×Q8116yescomplemented
225C2×Dic34—416no—
226C2×Dic34—44no—
227C2×Dic34—44no—
228C2×Dic34C22×C4116yescomplemented
229C4⋊C4×C17—44no—
230C4⋊C4×C17C22×C4116yescomplemented
231C42×C17—44no—
232#63227—28no—
233#63227—28no—
234#63227C22×C4116yes—
235#63227C22×C4116yes—
236C4⋊Dic17—44no—
237C4⋊Dic17C22×C4116yescomplemented
238C4⋊Dic17C22×C4116yescomplemented
239#63225—44no—
240#63225—44no—
241#63225—44no—
242#63225—44no—
243C4×Dic17—44no—
244C4×Dic17—44no—
245C4×Dic17—44no—
246C2×#2329—171nomaximal, Sylow
247C23×C17C23×C412yes—
248C23×C17C22×Q812yes—
249C23×C17C2×#4112yes—
250C23×C17H(5,𝔽2)12yes—
251C23×C17H(5,𝔽2)12yes—
252C23×C17H(5,𝔽2)12yes—
253C23×C172−1+412yes—
254C23×C17C2511yescharacteristic
255C22×D17—28no—
256C22×D17—28no—
257C22×D17—28no—
258C22×D17—28no—
259C22×D17—28no—
260C22×D17—28no—
261C22×D17—22no—
262C22×D17—22no—
263C22×D17—22no—
264C22×D17—22no—
265C22×D17C4×Q8116yes—
266C22×D17C23×C414yes—
267C22×D17C22×Q814yes—
268C22×D17C2×#4114yes—
269C2×C4×C17—28no—
270C2×C4×C17—28no—
271C2×C4×C17—28no—
272C2×C4×C17—28no—
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—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—44no—
291C2×C4×C17—44no—
292C2×C4×C17—44no—
293C2×C4×C17C23×C414yes—
294C2×C4×C17C23×C414yes—
295C2×C4×C17C23×C414yes—
296C2×C4×C17C22×Q814yes—
297C2×Dic17—28no—
298C2×Dic17—28no—
299C2×Dic17—28no—
300C2×Dic17—28no—
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—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—44no—
319C2×Dic17—44no—
320C2×Dic17—44no—
321C2×Dic17C23×C414yes—
322C2×Dic17C23×C414yes—
323C2×Dic17C23×C414yes—
324C2×Dic17C22×Q814yes—
325C4×D17—416no—
326C4×D17—416no—
327C4×D17—416no—
328Dic34—416no—
329C22×C22⋊Q8—171no—
330#2329—1716no—
331C2×#391—171no—
332C2×#391—171no—
333C2×#389—171no—
334C2×#389—171no—
335C2×#387—171no—
336C2×#387—171no—
337C2×#387—171no—
338C2×#387D1711yescharacteristic, complemented
339C2×#385—171no—
340C2×#385—171no—
341C2×#380—171no—
342C2×C4×C22⋊C4—171no—
343C2×C4×C22⋊C4—171no—
344C22×#95—171no—
345C22×C17C2×C4×Q814yes—
346C22×C17#51814yes—
347C22×C17#52014yes—
348C22×C17#53814yes—
349C22×C17#53914yes—
350C22×C17#54314yes—
351C22×C17#54414yes—
352C22×C17C24×C411yescharacteristic
353C22×C17C23×Q811yescharacteristic
354C22×C17C22×#4111yescharacteristic
355C22×C17C2×H(5,𝔽2)11yescharacteristic
356C22×C17C2×H(5,𝔽2)11yescharacteristic
357C22×C17C2×H(5,𝔽2)11yescharacteristic
358C22×C17C2×2−1+411yescharacteristic
359C2×D17—232no—
360C2×D17—24no—
361C2×D17—24no—
362C2×D17—24no—
363C2×D17—24no—
364C2×D17—24no—
365C2×D17—24no—
366C2×D17C2×C4×Q818yes—
367C4×C17—24no—
368C4×C17—24no—
369C4×C17—24no—
370C4×C17—24no—
371C4×C17—42no—
372C4×C17—42no—
373C4×C17—42no—
374Dic17—24no—
375Dic17—24no—
376Dic17—24no—
377Dic17—24no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381C23×Q8—171no—
382C24×C4—171no—
383C24×C4—171no—
384C24×C4—171no—
385C2×C22⋊Q8—1716no—
386C2×C22⋊Q8—178no—
387C22×C4⋊C4—171no—
388C22×C4⋊C4—171no—
389C22×C4⋊C4—171no—
390C22×C4⋊C4—171no—
391C22×C4⋊C4—171no—
392C22×C4⋊C4—171no—
393C22×C4⋊C4—171no—
394C22×C4⋊C4C2×D1711yescharacteristic
395C22×C4⋊C4C2×D1711yescharacteristic
396C22×C22⋊C4—171no—
397C22×C22⋊C4—171no—
398C22×C22⋊C4—171no—
399C22×C22⋊C4—171no—
400C22×C42—171no—
401C22×C42—171no—
402C22×C42—171no—
403C22×C42C2×D1711yescharacteristic
404#391—178no—
405#391—178no—
406#389—178no—
407#389—178no—
408#387—178no—
409#387—178no—
410#387—178no—
411#387C2×D1718yescomplemented
412#385—178no—
413#385—178no—
414#380—178no—
415C4×C22⋊C4—178no—
416C4×C22⋊C4—178no—
417C2×#95—171no—
418C2×#95—171no—
419C2×#95—171no—
420C2×#95—171no—
421C2×#95—171no—
422C2×#95—171no—
423C2×#95—171no—
424C2×#95—171no—
425C2×#95—171no—
426C2×#95—171no—
427C2×#95—178no—
428C2×#95C2×D1711yescharacteristic
429C2×#95C2×D1711yescharacteristic
430C2×#95C2×D1711yescharacteristic
431C2×#95C2×D1711yescharacteristic
432C2×C17#232918yescomplemented
433C2×C17C22×C4×Q811yescharacteristic
434C2×C17C2×#51811yescharacteristic
435C2×C17C2×#52011yescharacteristic
436C2×C17C2×#53811yescharacteristic
437C2×C17C2×#53911yescharacteristic
438C2×C17C2×#54311yescharacteristic
439C2×C17C2×#54411yescharacteristic
440D17—28no—
441C25—171no—
442C22×Q8—178no—
443C22×Q8—174no—
444C22×Q8—682no—
445C22×Q8—682no—
446C23×C4—171no—
447C23×C4—171no—
448C23×C4—171no—
449C23×C4—171no—
450C23×C4—178no—
451C23×C4—178no—
452C23×C4—174no—
453C23×C4—174no—
454C23×C4—171no—
455C23×C4—171no—
456C23×C4—171no—
457C23×C4—174no—
458C23×C4—344no—
459C23×C4—682no—
460C23×C4—682no—
461C23×C4—682no—
462C23×C4—682no—
463C23×C4—682no—
464C23×C4—682no—
465C23×C4C22×D1711yescharacteristic
466C23×C4C22×D1711yescharacteristic
467C23×C4C22×D1711yescharacteristic
468C23×C4C22×D1711yescharacteristic
469C23×C4C22×D1711yescharacteristic
470C23×C4C22×D1711yescharacteristic
471C23×C4C22×D1711yescharacteristic
472C22⋊Q8—1764no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—178no—
475C2×C4⋊C4—178no—
476C2×C4⋊C4—174no—
477C2×C4⋊C4—174no—
478C2×C4⋊C4—174no—
479C2×C4⋊C4—174no—
480C2×C4⋊C4—174no—
481C2×C4⋊C4—174no—
482C2×C4⋊C4—174no—
483C2×C4⋊C4—682no—
484C2×C4⋊C4—682no—
485C2×C4⋊C4—682no—
486C2×C4⋊C4—682no—
487C2×C4⋊C4—682no—
488C2×C4⋊C4C4×D1718yescomplemented
489C2×C4⋊C4C22×D1714yes—
490C2×C4⋊C4C22×D1714yes—
491C2×C22⋊C4—178no—
492C2×C22⋊C4—178no—
493C2×C22⋊C4—174no—
494C2×C22⋊C4—174no—
495C2×C22⋊C4—174no—
496C2×C22⋊C4—174no—
497C2×C22⋊C4—344no—
498C2×C22⋊C4—344no—
499C2×C42—42no—
500C2×C42—174no—
501C2×C42—174no—
502C2×C42—174no—
503C2×C42—682no—
504C2×C42—682no—
505C2×C42—682no—
506C2×C42C22×D1714yes—
507#95—174no—
508#95—174no—
509#95—174no—
510#95—174no—
511#95—174no—
512#95—174no—
513#95—174no—
514#95—174no—
515#95—174no—
516#95—174no—
517#95C22×D1714yes—
518#95C22×D1714yes—
519#95C22×D1714yes—
520#95C22×D1714yes—
521C17C2×#232911yescharacteristic, complemented, Sylow
522C24—174no—
523C24—174no—
524C24—174no—
525C24—172no—
526C24—342no—
527C24—342no—
528C24—342no—
529C24—342no—
530C24C23×D1711yescharacteristic
531C2×Q8—1716no—
532C2×Q8—6816no—
533C2×Q8—684no—
534C2×Q8—684no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—174no—
553C22×C4—174no—
554C22×C4—174no—
555C22×C4—174no—
556C22×C4—172no—
557C22×C4—172no—
558C22×C4—172no—
559C22×C4—172no—
560C22×C4—1716no—
561C22×C4—1716no—
562C22×C4—172no—
563C22×C4—172no—
564C22×C4—172no—
565C22×C4—348no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—342no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—342no—
583C22×C4—6816no—
584C22×C4—684no—
585C22×C4—684no—
586C22×C4—684no—
587C22×C4—684no—
588C22×C4—6816no—
589C22×C4—684no—
590C22×C4—684no—
591C22×C4—6816no—
592C22×C4C2×C4×D1714yes—
593C22×C4C2×C4×D1714yes—
594C22×C4C2×C4×D1714yes—
595C22×C4Q8×D1714yes—
596C22×C4C23×D1712yes—
597C22×C4C23×D1712yes—
598C22×C4C23×D1712yes—
599C22×C4C23×D1712yes—
600C22×C4C23×D1712yes—
601C22×C4C23×D1712yes—
602C22×C4C23×D1712yes—
603C4⋊C4—44no—
604C4⋊C4—1716no—
605C4⋊C4—1716no—
606C4⋊C4—684no—
607C4⋊C4—684no—
608C4⋊C4—684no—
609C4⋊C4—684no—
610C4⋊C4—684no—
611C4⋊C4C2×C4×D17116yescomplemented
612C22⋊C4—1716no—
613C22⋊C4—1716no—
614C22⋊C4—348no—
615C22⋊C4—348no—
616C42—44no—
617C42—684no—
618C42—684no—
619C42—684no—
620C23—1716no—
621C23—174no—
622C23—174no—
623C23—174no—
624C23—348no—
625C23—348no—
626C23—342no—
627C23—342no—
628C23—342no—
629C23—342no—
630C23—348no—
631C23—348no—
632C23—348no—
633C23—348no—
634C23C22×C4×D1712yes—
635C23#1058769112yes—
636C23C2×Q8×D1712yes—
637C23#41×D1712yes—
638C23#1058769612yes—
639C23#1058769612yes—
640C23#1058769712yes—
641C23C24×D1711yescharacteristic
642Q8—6816no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—28no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—174no—
668C2×C4—174no—
669C2×C4—174no—
670C2×C4—174no—
671C2×C4—348no—
672C2×C4—348no—
673C2×C4—348no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—342no—
682C2×C4—348no—
683C2×C4—342no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—6816no—
693C2×C4—6816no—
694C2×C4—6816no—
695C2×C4—684no—
696C2×C4—684no—
697C2×C4—684no—
698C2×C4C22×C4×D1714yes—
699C2×C4C22×C4×D1714yes—
700C2×C4C22×C4×D1714yes—
701C2×C4C2×Q8×D1714yes—
702C22—178no—
703C22—344no—
704C22—344no—
705C22—344no—
706C22—344no—
707C22—344no—
708C22—344no—
709C22—3432no—
710C22C4×Q8×D1714yes—
711C22#1176328314yes—
712C22#1176328814yes—
713C22#1176339514yes—
714C22#1176340014yes—
715C22#1176343414yes—
716C22#1176343914yes—
717C22C23×C4×D1711yescharacteristic
718C22C22×Q8×D1711yescharacteristic
719C22C2×#41×D1711yescharacteristic
720C22C2×#1058769111yescharacteristic
721C22C2×#1058769611yescharacteristic
722C22C2×#1058769611yescharacteristic
723C22C2×#1058769711yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—344no—
732C4—344no—
733C4—344no—
734C4—344no—
735C4—682no—
736C4—682no—
737C4—682no—
738C2—348no—
739C2#1453151318yesdirect product factor
740C2C2×C4×Q8×D1711yescharacteristic
741C2C2×#1176328311yescharacteristic
742C2C2×#1176328811yescharacteristic
743C2C2×#1176339511yescharacteristic
744C2C2×#1176340011yescharacteristic
745C2C2×#1176343411yescharacteristic
746C2C2×#1176343911yescharacteristic
subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#387C2
socleC24×C17C24
prime radicalC24×D17C23
cosocleC23×C17C25
hypercenterC2×#387D17
hypocenterC17C2×#2329
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #14531513C2direct (N × H)
3. C2×#11762713C2semidirect
4. C2×#11762713C2semidirect
5. C2×#11762707C2semidirect
6. C2×#11762705C2semidirect
7. C2×#11762695C2semidirect
8. C2×#11762694C2semidirect
9. C2×#11762692C2semidirect
16. C2×C17×#387C2semidirect
21. C2×#10587583C4semidirect
37. #11762713C22semidirect
38. #11762713C22semidirect
39. #11762707C22semidirect
40. #11762705C22semidirect
41. #11762695C22semidirect
42. #11762694C22semidirect
43. #11762692C22semidirect
63. C17×#387C22semidirect
91. C22×C4×D17Q8semidirect
97. C22×Dic34C2×C4semidirect
100. C2×C4⋊C4×C17C2×C4semidirect
114. C2×C4⋊Dic17C2×C4semidirect
115. C2×C4⋊Dic17C2×C4semidirect
133. #10587583C2×C4semidirect
224. C2×C4×D17C2×Q8semidirect
228. C2×Dic34C22×C4semidirect
230. C4⋊C4×C17C22×C4semidirect
237. C4⋊Dic17C22×C4semidirect
238. C4⋊Dic17C22×C4semidirect
338. C2×#387D17semidirect
411. #387C2×D17semidirect
432. C2×C17#2329semidirect
488. C2×C4⋊C4C4×D17semidirect
521. C17C2×#2329semidirect
611. C4⋊C4C2×C4×D17semidirect
739. C2#14531513direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875832
#145315132
C2×#117627132
C2×#117627072
C2×#117627052
C2×#117626952
C2×#117626942
C2×#117626922
C2×#117626832
C2×#117626802
C2×#117626682
C2×C4×#632272
C2×#117626562
C2×#95×D172
C2×C17×#3872
C2×#232917