Finite Group Databasebeta

← C2×#14541224 #17912855

Subgroups — C2×#14541224 #17912855

Order 4352.

2094 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
1C2×#11763463C211yesmaximal, characteristic
2#14541224C2116yesmaximal, direct product factor
3C2×#11763219C211yesmaximal, characteristic, complemented
4C2×#11763142C211yesmaximal, characteristic, complemented
5C2×#11763133C211yesmaximal, characteristic, complemented
6C2×#11763137C211yesmaximal, characteristic, complemented
7C2×#11763122C211yesmaximal, characteristic, complemented
8C2×#11763104C211yesmaximal, characteristic, complemented
9C2×#11763106C211yesmaximal, characteristic, complemented
10C2×#11763057C211yesmaximal, characteristic, complemented
11C2×#11763040C211yesmaximal, characteristic, complemented
12C2×#11762907C211yesmaximal, characteristic, complemented
13C2×#11762881C211yesmaximal, characteristic, complemented
14C2×#11762852C211yesmaximal, characteristic, complemented
15C22×#10587478C211yesmaximal, characteristic, complemented
16C2×C17×#552C211yesmaximal, characteristic, complemented
17C22×#63254—21no—
18C22×#63230C2211yescharacteristic
19C22×#63223C2211yescharacteristic
20C23×#3622C2211yescharacteristic
21#11763463—24no—
22#11763463C2218yes—
23C2×#10587555C2211yescharacteristic
24C2×#10587572—21no—
25C2×#10587572—21no—
26C2×#10587583—21no—
27C2×#10587616C2211yescharacteristic
28C2×#10587616C2211yescharacteristic
29C2×C4×D68C2211yescharacteristic
30C22×C4⋊Dic17C2211yescharacteristic
31C22×C4⋊Dic17C2211yescharacteristic
32#11763219C2218yescomplemented
33#11763142C2218yescomplemented
34#11763137C2218yescomplemented
35#11763133C2218yescomplemented
36#11763122C2218yescomplemented
37#11763106C2218yescomplemented
38#11763104C2218yescomplemented
39#11763057C2218yescomplemented
40#11763040C2218yescomplemented
41#11762907C2218yescomplemented
42#11762881C2218yescomplemented
43#11762852C2218yescomplemented
44C2×#10587478C2211yescharacteristic
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587478C2211yescharacteristic
49C2×#10587478C2211yescharacteristic
50C2×#10587478C2218yescomplemented
51C2×#10587479C2211yescharacteristic
52C2×#10587479C2211yescharacteristic
53C2×#10587479C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587506C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C17×#552—24no—
65C17×#552C2218yescomplemented
66C2×C17×#126—21no—
67C2×C17×#125—21no—
68C2×C17×#125C2211yescharacteristic
69C2×C17×#123—21no—
70C2×C17×C22⋊Q8C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×D4×C17C2211yescharacteristic
74C2×C17×#117—21no—
75C2×C17×#117C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17D411yescharacteristic
79C23×C4×C17—21no—
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C22×C22⋊D17—21no—
83C22×C22⋊D17—21no—
84C23×Dic17—21no—
85C23×Dic17—21no—
86C2×#63254—28no—
87C2×#63254—48no—
88C22×D68C2311yescharacteristic
89C22×C4×D17—21no—
90C22×Dic34—21no—
91C17×#126—28no—
92C17×#125—28no—
93C17×#125—22no—
94C17×#125C2314yes—
95C17×#123—28no—
96C17×C22⋊Q8—22no—
97C17×C22⋊Q8—22no—
98C17×C22⋊Q8C2314yes—
99C17×C22⋊Q8C2314yes—
100C4×Q8×C17—22no—
101C4×Q8×C17C2314yes—
102C4×D4×C17D414yes—
103C4×D4×C17C2314yes—
104C17×#117—22no—
105C17×#117—28no—
106C17×#117C2314yes—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—22no—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17—21no—
111C2×C4⋊C4×C17—21no—
112C2×C4⋊C4×C17—21no—
113C2×C4⋊C4×C17—21no—
114C2×C4⋊C4×C17D411yescharacteristic
115C2×C4⋊C4×C17C2311yescharacteristic
116C2×C4⋊C4×C17C2311yescharacteristic
117C2×C4⋊C4×C17C2314yes—
118C2×C4⋊C4×C17C2311yescharacteristic
119C2×C22⋊C4×C17—21no—
120C2×C22⋊C4×C17—21no—
121C2×C22⋊C4×C17—21no—
122C2×C22⋊C4×C17D411yescharacteristic
123C2×C22⋊C4×C17D411yescharacteristic
124C2×C42×C17—21no—
125C2×C42×C17—21no—
126C2×C42×C17C2311yescharacteristic
127C2×#63230—24no—
128C2×#63230C2314yes—
129#10587616—22no—
130#10587616—22no—
131#10587616C2314yes—
132#10587616C2314yes—
133C2×#63227—21no—
134C2×#63227—21no—
135C2×#63227—21no—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—22no—
138C2×C4⋊Dic17—21no—
139C2×C4⋊Dic17—21no—
140C2×C4⋊Dic17—21no—
141C2×C4⋊Dic17C2314yes—
142C2×C4⋊Dic17C2314yes—
143C2×C4⋊Dic17C2311yescharacteristic
144C2×C4⋊Dic17C2311yescharacteristic
145C2×C4⋊Dic17C2311yescharacteristic
146C2×#63223—24no—
147C2×#63223C2314yes—
148C22×#3622—24no—
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152C22×#3622C2314yes—
153C22×#3622C2311yescharacteristic
154#10587583—28no—
155#10587572—28no—
156#10587572—28no—
157C4×D68—22no—
158C4×D68C2314yes—
159#10587555—22no—
160#10587555C2314yes—
161#10587506C2314yes—
162#10587506C2314yes—
163#10587506C2314yes—
164C22⋊#3622C2314yes—
165C22⋊#3622C2314yes—
166#10587480C2314yes—
167#10587480C2314yes—
168#10587480C2314yes—
169#10587479C2314yes—
170#10587479C2314yes—
171#10587479C2314yes—
172#10587478C2314yes—
173#10587478C2314yes—
174#10587478C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178C4⋊#3622C2314yes—
179#10587474C2314yes—
180C24×C17C2×D411yescharacteristic
181C24×C17C2×D411yescharacteristic
182C23×D17—21no—
183C2×Q8×C17—21no—
184C2×Q8×C17—22no—
185C2×Q8×C17—22no—
186C2×Q8×C17C2412yes—
187C2×D4×C17—24no—
188C2×D4×C17C2×D414yes—
189C22×C4×C17—22no—
190C22×C4×C17—22no—
191C22×C4×C17—22no—
192C22×C4×C17—22no—
193C22×C4×C17—24no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—44no—
199C22×C4×C17C2×D412yes—
200C22×C4×C17C2×D412yes—
201C22×C4×C17C2×D411yescharacteristic
202C22×C4×C17C2×D411yescharacteristic
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2×D411yescharacteristic
205C22×C4×C17C2412yes—
206C22×C4×C17C2412yes—
207C22×C4×C17C2411yescharacteristic
208C2×C22⋊D17—24no—
209C2×C22⋊D17—24no—
210C2×C22⋊D17—44no—
211C2×C22⋊D17—44no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—24no—
216C22×Dic17—24no—
217C22×Dic17—44no—
218C22×Dic17—44no—
219#63254—432no—
220C2×D68—22no—
221C2×D68—22no—
222C2×D68—21no—
223C2×D68C2412yes—
224C2×C4×D17—24no—
225C2×C4×D17—44no—
226C2×Dic34—24no—
227C2×Dic34—44no—
228C4⋊C4×C17—21no—
229C4⋊C4×C17—21no—
230C4⋊C4×C17—24no—
231C4⋊C4×C17—24no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17—24no—
234C4⋊C4×C17—24no—
235C4⋊C4×C17—24no—
236C4⋊C4×C17—21no—
237C4⋊C4×C17C2×D414yes—
238C4⋊C4×C17C2412yes—
239C4⋊C4×C17C2412yes—
240C4⋊C4×C17C2412yes—
241C22⋊C4×C17—24no—
242C22⋊C4×C17—24no—
243C22⋊C4×C17—24no—
244C22⋊C4×C17C2×D414yes—
245C22⋊C4×C17C2×D414yes—
246C42×C17—24no—
247C42×C17—24no—
248C42×C17C2×D412yes—
249C42×C17C2412yes—
250#63230—28no—
251#63227—24no—
252#63227—24no—
253#63227—24no—
254C4⋊Dic17—21no—
255C4⋊Dic17—21no—
256C4⋊Dic17—24no—
257C4⋊Dic17—21no—
258C4⋊Dic17—24no—
259C4⋊Dic17—24no—
260C4⋊Dic17C2412yes—
261C4⋊Dic17C2412yes—
262C4⋊Dic17C2412yes—
263#63223—28no—
264C2×#3622—22no—
265C2×#3622—22no—
266C2×#3622—22no—
267C2×#3622—28no—
268C2×#3622#4114yescomplemented
269C2×#3622C2412yes—
270C2×#3622C2412yes—
271C2×#3622C2412yes—
272C2×#3622C2412yes—
273C2×#3343—171nomaximal, Sylow
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—22no—
279C23×C17AGL(1,ℤ/8)14yes—
280C23×C17C22×D412yes—
281C23×C17C22×D412yes—
282C23×C17C22×D411yescharacteristic
283C22×D17—22no—
284C22×D17—42no—
285C22×D17—42no—
286C22×D17—42no—
287Q8×C17—22no—
288Q8×C17—22no—
289Q8×C17—42no—
290D4×C17—28no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—24no—
296C2×C4×C17—24no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—42no—
306C2×C4×C17—48no—
307C2×C4×C17—42no—
308C2×C4×C17—42no—
309C2×C4×C17—42no—
310C2×C4×C17C22×D412yes—
311C2×C4×C17C22×D412yes—
312C2×C4×C17C22×D412yes—
313C2×C4×C17C22×D412yes—
314C2×C4×C17C22×D411yescharacteristic
315C2×C4×C17C2×#4112yes—
316C2×C4×C172−1+412yes—
317C2×C4×C17C2511yescharacteristic
318C22⋊D17—48no—
319C22⋊D17—48no—
320C2×Dic17—22no—
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—48no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17—42no—
327C2×Dic17—48no—
328D68—22no—
329D68—22no—
330D68—42no—
331C4×D17—48no—
332Dic34—48no—
333#3622—22no—
334#3622—22no—
335#3622—22no—
336#3622C2×#4114yescomplemented
337C2×#552D1711yescharacteristic, complemented
338C2×#547—171no—
339#3343—1716no—
340C2×#501—171no—
341C2×#484—171no—
342C2×#482—171no—
343C2×#483—171no—
344C2×#480—171no—
345C2×#477—171no—
346C2×#478—171no—
347C2×#468—171no—
348C2×#465—171no—
349C2×#440—171no—
350C2×#435—171no—
351C2×#428—171no—
352C22×#107—171no—
353C22×C17—28no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—22no—
357C22×C17—22no—
358C22×C17—22no—
359C22×C17—44no—
360C22×C17#54712yes—
361C22×C17C2×AGL(1,ℤ/8)14yes—
362C22×C17C2×AGL(1,ℤ/8)12yes—
363C22×C17#57812yes—
364C22×C17C23×D411yescharacteristic
365C2×D17—42no—
366C2×D17—42no—
367C2×D17—42no—
368C2×D17—84no—
369C4×C17—22no—
370C4×C17—22no—
371C4×C17—22no—
372C4×C17—22no—
373C4×C17—42no—
374C4×C17—42no—
375C4×C17—42no—
376C4×C17—42no—
377C4×C17#54712yes—
378C4×C17C22×#4111yescharacteristic
379C4×C17C2×2−1+411yescharacteristic
380Dic17—42no—
381Dic17—42no—
382Dic17—42no—
383C22×#41—341no—
384C22×SD16—171no—
385C22×M16—171no—
386C23×C8—171no—
387#552—24no—
388#552C2×D1718yescomplemented
389#547—178no—
390#547—344no—
391C2×C4⋊Q8—171no—
392C2×#126—21no—
393C2×#125—21no—
394C2×#125C2×D1711yescharacteristic
395C2×#123—21no—
396C2×#123—341no—
397C2×#123—341no—
398C2×C22⋊Q8—341no—
399C2×C22⋊Q8C2×D1711yescharacteristic
400C2×C22⋊Q8C2×D1711yescharacteristic
401C2×#121—171no—
402C2×#121—171no—
403C2×C4×Q8C2×D1711yescharacteristic
404C2×C4×D4—171no—
405C2×C4×D4C2×D1711yescharacteristic
406C2×#117—21no—
407C2×#117C2×D1711yescharacteristic
408C22×C4⋊C4—171no—
409C22×C4⋊C4—171no—
410C22×C4⋊C4C2×D1711yescharacteristic
411#501—178no—
412#484—178no—
413#483—178no—
414#482—178no—
415#480—178no—
416#478—178no—
417#477—178no—
418#468—178no—
419#465—178no—
420#440—178no—
421#435—178no—
422#428—178no—
423C2×#107—171no—
424C2×#107—171no—
425C2×#107—171no—
426C2×#107—171no—
427C2×#107—178no—
428C2×#107—171no—
429C2×#107—171no—
430C2×#106—171no—
431C2×#106—171no—
432C2×#106—171no—
433C2×C4⋊C8—171no—
434C2×#103—171no—
435C2×#103—171no—
436C2×#103—171no—
437C2×#102—171no—
438C2×#102—171no—
439C2×#102—171no—
440C2×C22⋊C8—171no—
441C2×C22⋊C8—171no—
442C2×#97—171no—
443C2×C17—24no—
444C2×C17—42no—
445C2×C17#334314yescomplemented
446C2×C17C2×#54711yescharacteristic
447C2×C17C22×AGL(1,ℤ/8)11yescharacteristic
448C2×C17C2×#57811yescharacteristic
449D17—82no—
450C2×#41—348no—
451C2×#41—688no—
452C22×Q8—341no—
453C22×Q8C22×D1711yescharacteristic
454C22×D4—171no—
455C22×D4—341no—
456C22×D4—341no—
457C22×D4C22⋊D1711yescharacteristic
458C23×C4—21no—
459C23×C4—341no—
460C23×C4—341no—
461C23×C4—341no—
462C23×C4C22×D1711yescharacteristic
463C23×C4C22×D1711yescharacteristic
464C2×SD16—174no—
465C2×SD16—344no—
466C2×M16—174no—
467C2×M16—344no—
468C22×C8—171no—
469C22×C8—171no—
470C22×C8—174no—
471C22×C8—171no—
472C22×C8—171no—
473C22×C8—344no—
474C4⋊Q8—174no—
475C4⋊Q8—342no—
476#126—28no—
477#125—28no—
478#125—22no—
479#125C22×D1714yes—
480#123—28no—
481#123—348no—
482#123—348no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—348no—
486C22⋊Q8C22×D1714yes—
487C22⋊Q8C22×D1714yes—
488#121—174no—
489#121—174no—
490#121—342no—
491#121—342no—
492C4×Q8—22no—
493C4×Q8C22×D1714yes—
494C4×D4—174no—
495C4×D4—342no—
496C4×D4C22⋊D1714yes—
497C4×D4C22×D1714yes—
498#117—22no—
499#117—28no—
500#117C22×D1714yes—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—171no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—171no—
511C2×C4⋊C4—174no—
512C2×C4⋊C4—174no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4—342no—
516C2×C4⋊C4—342no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4C22⋊D1711yescharacteristic
519C2×C4⋊C4C22×D1711yescharacteristic
520C2×C4⋊C4C22×D1711yescharacteristic
521C2×C4⋊C4C22×D1714yes—
522C2×C4⋊C4C22×D1711yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4—341no—
528C2×C22⋊C4—341no—
529C2×C22⋊C4C22⋊D1711yescharacteristic
530C2×C22⋊C4C22⋊D1711yescharacteristic
531C2×C42—21no—
532C2×C42—21no—
533C2×C42C22×D1711yescharacteristic
534#107—174no—
535#107—174no—
536#107—174no—
537#107—174no—
538#107—174no—
539#107—174no—
540#106—174no—
541#106—174no—
542#106—174no—
543C4⋊C8—174no—
544#103—174no—
545#103—174no—
546#103—174no—
547#102—174no—
548#102—174no—
549#102—174no—
550C22⋊C8—174no—
551C22⋊C8—174no—
552#97—174no—
553C17C2×#334311yescharacteristic, complemented, Sylow
554C24—341no—
555C24C2×C22⋊D1711yescharacteristic
556C24C2×C22⋊D1711yescharacteristic
557#41—6832no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—344no—
562C2×Q8—684no—
563C2×Q8C23×D1712yes—
564C2×D4—24no—
565C2×D4—172no—
566C2×D4—344no—
567C2×D4—344no—
568C2×D4—342no—
569C2×D4—342no—
570C2×D4—341no—
571C2×D4—684no—
572C2×D4—684no—
573C2×D4C2×C22⋊D1714yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—44no—
584C22×C4—344no—
585C22×C4—344no—
586C22×C4—341no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—344no—
590C22×C4—684no—
591C22×C4—684no—
592C22×C4—684no—
593C22×C4C2×C22⋊D1712yes—
594C22×C4C2×C22⋊D1712yes—
595C22×C4C2×C22⋊D1711yescharacteristic
596C22×C4C2×C22⋊D1711yescharacteristic
597C22×C4C2×C22⋊D1711yescharacteristic
598C22×C4C2×C22⋊D1711yescharacteristic
599C22×C4C23×D1712yes—
600C22×C4C23×D1712yes—
601C22×C4C23×D1711yescharacteristic
602SD16—348no—
603M16—348no—
604C2×C8—174no—
605C2×C8—172no—
606C2×C8—172no—
607C2×C8—172no—
608C2×C8—172no—
609C2×C8—348no—
610C2×C8—342no—
611C2×C8—342no—
612C2×C8—342no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—172no—
623C4⋊C4—172no—
624C4⋊C4—172no—
625C4⋊C4—341no—
626C4⋊C4—341no—
627C4⋊C4—341no—
628C4⋊C4—344no—
629C4⋊C4—344no—
630C4⋊C4—344no—
631C4⋊C4C2×C22⋊D1714yes—
632C4⋊C4C23×D1712yes—
633C4⋊C4C23×D1712yes—
634C4⋊C4C23×D1712yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—344no—
639C22⋊C4—344no—
640C22⋊C4—344no—
641C22⋊C4C2×C22⋊D1714yes—
642C22⋊C4C2×C22⋊D1714yes—
643C42—24no—
644C42—24no—
645C42C2×C22⋊D1712yes—
646C42C23×D1712yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—342no—
653C23—682no—
654C23—682no—
655C23—682no—
656C23#1058763514yes—
657C23C22×C22⋊D1712yes—
658C23C22×C22⋊D1712yes—
659C23C22×C22⋊D1711yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—688no—
664D4—28no—
665D4—342no—
666D4—342no—
667D4—688no—
668D4—688no—
669D4—682no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—48no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—688no—
693C2×C4—688no—
694C2×C4—682no—
695C2×C4—682no—
696C2×C4—682no—
697C2×C4—688no—
698C2×C4#41×D1712yes—
699C2×C4#1058769712yes—
700C2×C4C22×C22⋊D1712yes—
701C2×C4C22×C22⋊D1712yes—
702C2×C4C22×C22⋊D1712yes—
703C2×C4C22×C22⋊D1712yes—
704C2×C4C22×C22⋊D1711yescharacteristic
705C2×C4C24×D1711yescharacteristic
706C8—174no—
707C8—342no—
708C8—342no—
709C8—342no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—682no—
718C22—682no—
719C22—682no—
720C22—1364no—
721C22#1176345812yes—
722C22C2×#1058763514yes—
723C22C2×#1058763512yes—
724C22#1176362412yes—
725C22C23×C22⋊D1711yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—682no—
735C4—682no—
736C4—682no—
737C4#1176345812yes—
738C4C2×#41×D1711yescharacteristic
739C4C2×#1058769711yescharacteristic
740C2—24no—
741C2—42no—
742C2—1362no—
743C2#1454122414yesdirect product factor
744C2C2×#1176345811yescharacteristic
745C2C22×#1058763511yescharacteristic
746C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#552C2
socleC23×C17C22×D4
prime radicalC2×#11763463C2
hypercenterC2×#552D17
hypocenterC17C2×#3343
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
2. #14541224C2direct (N × H)
3. C2×#11763219C2semidirect
4. C2×#11763142C2semidirect
5. C2×#11763133C2semidirect
6. C2×#11763137C2semidirect
7. C2×#11763122C2semidirect
8. C2×#11763104C2semidirect
9. C2×#11763106C2semidirect
10. C2×#11763057C2semidirect
11. C2×#11763040C2semidirect
12. C2×#11762907C2semidirect
13. C2×#11762881C2semidirect
14. C2×#11762852C2semidirect
15. C22×#10587478C2semidirect
16. C2×C17×#552C2semidirect
32. #11763219C22semidirect
33. #11763142C22semidirect
34. #11763137C22semidirect
35. #11763133C22semidirect
36. #11763122C22semidirect
37. #11763106C22semidirect
38. #11763104C22semidirect
39. #11763057C22semidirect
40. #11763040C22semidirect
41. #11762907C22semidirect
42. #11762881C22semidirect
43. #11762852C22semidirect
50. C2×#10587478C22semidirect
65. C17×#552C22semidirect
268. C2×#3622#41semidirect
336. #3622C2×#41semidirect
337. C2×#552D17semidirect
388. #552C2×D17semidirect
445. C2×C17#3343semidirect
553. C17C2×#3343semidirect
743. C2#14541224direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634632
#145412242
C2×#117632192
C2×#117631422
C2×#117631332
C2×#117631372
C2×#117631222
C2×#117631042
C2×#117631062
C2×#117630572
C2×#117630402
C2×#117629072
C2×#117628812
C2×#117628522
C22×#105874782
C2×C17×#5522
C2×#334317