Finite Group Databasebeta

← C2×#14541844 #17915324

Subgroups — C2×#14541844 #17915324

Order 4352.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763532C211yesmaximal, characteristic, complemented
2#14541844C2116yesmaximal, direct product factor
3C2×#11763204C211yesmaximal, characteristic, complemented
4C2×#11763196C211yesmaximal, characteristic
5C2×#11763191C211yesmaximal, characteristic, complemented
6C2×#11763031C211yesmaximal, characteristic, complemented
7C2×#11763028C211yesmaximal, characteristic, complemented
8C2×#11763006C211yesmaximal, characteristic, complemented
9C2×#11763024C211yesmaximal, characteristic, complemented
10C2×#11763021C211yesmaximal, characteristic, complemented
11C2×#11763014C211yesmaximal, characteristic, complemented
12C2×#11762940C211yesmaximal, characteristic, complemented
13C2×#11762919C211yesmaximal, characteristic, complemented
14C2×#11762914C211yesmaximal, characteristic, complemented
15C2×C4×#63229C211yesmaximal, characteristic, complemented
16C2×C17×#559C211yesmaximal, characteristic, complemented
17C22×#63231C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63229C2211yescharacteristic
20C22×#63229C2211yescharacteristic
21C22×#63229C2211yescharacteristic
22C22×#63229C2211yescharacteristic
23C22×#63230C2211yescharacteristic
24C22×#63228C2211yescharacteristic
25C22×#63228C2211yescharacteristic
26#11763532—24no—
27#11763532C2218yescomplemented
28C2×#10587555C2211yescharacteristic
29C2×#10587584—21no—
30C2×#10587584—21no—
31C2×#10587561C2211yescharacteristic
32C2×#10587561C2211yescharacteristic
33C2×#10587632—21no—
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×Dic34C2211yescharacteristic
36C2×C4×D68C2211yescharacteristic
37C2×#10587578—21no—
38#11763204C2218yescomplemented
39#11763196C2218yes—
40#11763191C2218yescomplemented
41#11763031C2218yescomplemented
42#11763028C2218yescomplemented
43#11763024C2218yescomplemented
44#11763021C2218yescomplemented
45#11763014C2218yescomplemented
46#11763006C2218yescomplemented
47#11762940C2218yescomplemented
48#11762919C2218yescomplemented
49#11762914C2218yescomplemented
50C4×#63229C2218yescomplemented
51C2×#10587479C2211yescharacteristic
52C2×C4⋊#3622C2211yescharacteristic
53C2×C4⋊#3622C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×#10587474C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#559—24no—
65C17×#559C2218yescomplemented
66C2×C17×#127C2211yescharacteristic
67C2×C17×#124—21no—
68C2×C17×#124C2211yescharacteristic
69C2×C17×#124C2211yescharacteristic
70C2×C17×#123—21no—
71C2×C17×#123—21no—
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×Q8×C17C2211yescharacteristic
74C2×C4×D4×C17—21no—
75C2×C4×D4×C17C2211yescharacteristic
76C2×C4×D4×C17C2211yescharacteristic
77C22×Q8×C17D411yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17—21no—
80C22×D4×C17—21no—
81C22×D4×C17C2311yescharacteristic
82C22×D4×C17C2311yescharacteristic
83C23×C4×C17—21no—
84C23×C4×C17—21no—
85C22×D68C2311yescharacteristic
86C22×C4×D17—21no—
87C22×Dic34C2311yescharacteristic
88C22×Dic34C2311yescharacteristic
89C17×#127—22no—
90C17×#127C2314yes—
91C17×#124—28no—
92C17×#124—22no—
93C17×#124—22no—
94C17×#124C2314yes—
95C17×#124C2314yes—
96C17×#123—28no—
97C17×#123—28no—
98C4×Q8×C17—22no—
99C4×Q8×C17D414yes—
100C4×Q8×C17C2314yes—
101C4×Q8×C17C2314yes—
102C4×D4×C17—28no—
103C4×D4×C17—22no—
104C4×D4×C17—22no—
105C4×D4×C17C2314yes—
106C4×D4×C17C2314yes—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17D411yescharacteristic
109C2×C4⋊C4×C17D411yescharacteristic
110C2×C4⋊C4×C17D411yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C22⋊C4×C17—21no—
113C2×C22⋊C4×C17—21no—
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17—21no—
118C2×C42×C17—21no—
119C2×C42×C17C2311yescharacteristic
120C2×C42×C17C2311yescharacteristic
121C2×C42×C17C2311yescharacteristic
122#10587632—28no—
123C2×#63231—24no—
124C2×#63231—42no—
125C2×#63231C2314yes—
126C2×#63231C2314yes—
127C2×#63230—42no—
128C2×#63230C2314yes—
129C2×#63229—24no—
130C2×#63229—42no—
131C2×#63229—42no—
132C2×#63229—42no—
133C2×#63229C2314yes—
134C2×#63229C2314yes—
135C2×#63229C2314yes—
136C2×#63229C2314yes—
137C2×#63228—24no—
138C2×#63228—42no—
139C2×#63228C2314yes—
140C2×#63228C2314yes—
141C2×#63227—21no—
142C2×#63227—21no—
143C2×#63227—21no—
144C2×#63227—21no—
145C2×#63227—21no—
146C2×C4⋊Dic17—21no—
147C2×C4⋊Dic17—21no—
148C2×C4⋊Dic17C2311yescharacteristic
149C2×#63225—21no—
150C2×#63225—21no—
151C2×C4×Dic17—21no—
152C2×C4×Dic17—21no—
153C22×#3622C2311yescharacteristic
154C22×#3622C2311yescharacteristic
155C22×#3622C2311yescharacteristic
156C22×#3622C2311yescharacteristic
157#10587584—28no—
158#10587584—28no—
159#10587578—28no—
160#10587561—22no—
161#10587561—22no—
162#10587561C2314yes—
163#10587561C2314yes—
164C4×D68—22no—
165C4×D68C2314yes—
166#10587555—22no—
167#10587555C2314yes—
168C4×Dic34—22no—
169C4×Dic34—22no—
170C4×Dic34C2314yes—
171C4×Dic34C2314yes—
172#10587506C2314yes—
173#10587503C2314yes—
174#10587503C2314yes—
175#10587481C2314yes—
176#10587481C2314yes—
177#10587480C2314yes—
178#10587479C2314yes—
179C4⋊#3622C2314yes—
180C4⋊#3622C2314yes—
181C4⋊#3622C2314yes—
182#10587474C2314yes—
183#10587474C2314yes—
184C4×#3622C2314yes—
185C24×C17—21no—
186C24×C17—21no—
187C23×D17—21no—
188C2×Q8×C17—21no—
189C2×Q8×C17—22no—
190C2×Q8×C17—22no—
191C2×Q8×C17—42no—
192C2×Q8×C17C2×D414yes—
193C2×Q8×C17C2412yes—
194C2×D4×C17—21no—
195C2×D4×C17—21no—
196C2×D4×C17—24no—
197C2×D4×C17—24no—
198C2×D4×C17—22no—
199C2×D4×C17—22no—
200C2×D4×C17—22no—
201C2×D4×C17—22no—
202C2×D4×C17—44no—
203C2×D4×C17—82no—
204C2×D4×C17C2412yes—
205C2×D4×C17C2412yes—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—24no—
209C22×C4×C17—24no—
210C22×C4×C17—82no—
211C22×C4×C17—82no—
212C22×C4×C17C2×D411yescharacteristic
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2×D411yescharacteristic
215C22×C4×C17C2×D411yescharacteristic
216C22×C4×C17C2×D411yescharacteristic
217C22×C4×C17C2×D411yescharacteristic
218C22×C4×C17C2411yescharacteristic
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C2×D68—22no—
223C2×D68—22no—
224C2×D68—21no—
225C2×D68C2412yes—
226C2×C4×D17—24no—
227C2×C4×D17—44no—
228C2×Dic34—22no—
229C2×Dic34—22no—
230C2×Dic34—22no—
231C2×Dic34—22no—
232C2×Dic34—21no—
233C2×Dic34—21no—
234C2×Dic34C2412yes—
235C2×Dic34C2412yes—
236C4⋊C4×C17—24no—
237C4⋊C4×C17—21no—
238C4⋊C4×C17C2×D414yes—
239C4⋊C4×C17C2×D414yes—
240C4⋊C4×C17C2×D414yes—
241C4⋊C4×C17C2412yes—
242C22⋊C4×C17—24no—
243C22⋊C4×C17—24no—
244C22⋊C4×C17—24no—
245C22⋊C4×C17—24no—
246C22⋊C4×C17—24no—
247C22⋊C4×C17—24no—
248C42×C17—24no—
249C42×C17C2×D412yes—
250C42×C17C2×D412yes—
251C42×C17C2×D412yes—
252C42×C17C2412yes—
253C42×C17C2412yes—
254C42×C17C2412yes—
255#63231—28no—
256#63231—44no—
257#63230—44no—
258#63229—28no—
259#63229—44no—
260#63229—44no—
261#63229—44no—
262#63228—28no—
263#63228—44no—
264#63227—24no—
265#63227—24no—
266#63227—24no—
267#63227—24no—
268#63227—24no—
269C4⋊Dic17—21no—
270C4⋊Dic17—24no—
271C4⋊Dic17—24no—
272C4⋊Dic17C2412yes—
273#63225—24no—
274#63225—24no—
275C4×Dic17—24no—
276C4×Dic17—24no—
277C2×#3622—22no—
278C2×#3622—22no—
279C2×#3622—22no—
280C2×#3622#4114yes—
281C2×#3622C2412yes—
282C2×#3622C2412yes—
283C2×#3622C2412yes—
284C2×#3622C2412yes—
285C2×#3401—171nomaximal, Sylow
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—42no—
289C23×C17—42no—
290C23×C17—42no—
291C23×C17—42no—
292C23×C17—42no—
293C23×C17—42no—
294C23×C17C22×D411yescharacteristic
295C22×D17—22no—
296C22×D17—42no—
297C22×D17—42no—
298C22×D17—42no—
299Q8×C17—22no—
300Q8×C17—22no—
301Q8×C17—44no—
302Q8×C17—42no—
303D4×C17—22no—
304D4×C17—22no—
305D4×C17—22no—
306D4×C17—22no—
307D4×C17—48no—
308D4×C17—42no—
309D4×C17—42no—
310D4×C17—84no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—42no—
320C2×C4×C17—42no—
321C2×C4×C17—84no—
322C2×C4×C17—84no—
323C2×C4×C17C22×D412yes—
324C2×C4×C17C22×D412yes—
325C2×C4×C17C22×D412yes—
326C2×C4×C17C22×D412yes—
327C2×C4×C17C22×D412yes—
328C2×C4×C17C22×D412yes—
329C2×C4×C17C22×D411yescharacteristic
330C2×C4×C17C2×#4112yes—
331C2×C4×C17H(5,𝔽2)12yes—
332C2×C4×C17C2511yescharacteristic
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—22no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338C2×Dic17—42no—
339D68—22no—
340D68—22no—
341D68—42no—
342C4×D17—48no—
343Dic34—22no—
344Dic34—22no—
345Dic34—22no—
346Dic34—22no—
347Dic34—42no—
348Dic34—42no—
349#3622—22no—
350#3622—22no—
351#3622—22no—
352#3622C2×#4114yes—
353C2×#559D1711yescharacteristic, complemented
354C2×#556—171no—
355#3401—1716no—
356C2×#497—171no—
357C2×#496—171no—
358C2×#495—171no—
359C2×#464—171no—
360C2×#464—171no—
361C2×#460—171no—
362C2×#463—171no—
363C2×#463—171no—
364C2×#461—171no—
365C2×#446—171no—
366C2×#442—171no—
367C2×#441—171no—
368C2×C4×SD16—171no—
369C22×C17—42no—
370C22×C17—42no—
371C22×C17—42no—
372C22×C17—42no—
373C22×C17—42no—
374C22×C17—42no—
375C22×C17—84no—
376C22×C17—84no—
377C22×C17#55012yes—
378C22×C17#57512yes—
379C22×C17#57712yes—
380C22×C17C23×D411yescharacteristic
381C2×D17—42no—
382C2×D17—42no—
383C2×D17—42no—
384C2×D17—84no—
385C4×C17—22no—
386C4×C17—22no—
387C4×C17—22no—
388C4×C17—22no—
389C4×C17—22no—
390C4×C17—22no—
391C4×C17—42no—
392C4×C17—42no—
393C4×C17#55012yes—
394C4×C17C22×#4111yescharacteristic
395C4×C17C2×H(5,𝔽2)11yescharacteristic
396Dic17—42no—
397Dic17—42no—
398Dic17—42no—
399C22×Q16—171no—
400C22×Q16—171no—
401C22×SD16—171no—
402C22×SD16—171no—
403C22×SD16—171no—
404C22×SD16—171no—
405C22×SD16—171no—
406C22×D8—171no—
407C22×D8—171no—
408#559—24no—
409#559C2×D1718yescomplemented
410#556—178no—
411#556—344no—
412C2×C4⋊Q8—171no—
413C2×#127C2×D1711yescharacteristic
414C2×#126—341no—
415C2×#126—341no—
416C2×#124—21no—
417C2×#124—171no—
418C2×#124—171no—
419C2×#124C2×D1711yescharacteristic
420C2×#124C2×D1711yescharacteristic
421C2×#123—21no—
422C2×#123—21no—
423C2×C22⋊Q8—341no—
424C2×C4×Q8—171no—
425C2×C4×Q8—171no—
426C2×C4×Q8C2×D1711yescharacteristic
427C2×C4×Q8C2×D1711yescharacteristic
428C2×C4×D4—21no—
429C2×C4×D4—171no—
430C2×C4×D4C2×D1711yescharacteristic
431C2×C4×D4C2×D1711yescharacteristic
432C2×#117—341no—
433#497—178no—
434#496—178no—
435#495—178no—
436#464—178no—
437#464—178no—
438#463—178no—
439#463—178no—
440#461—178no—
441#460—178no—
442#446—178no—
443#442—178no—
444#441—178no—
445C4×SD16—178no—
446C2×#106—171no—
447C2×C4⋊C8—171no—
448C2×C4⋊C8—171no—
449C2×C4⋊C8—171no—
450C2×#103—171no—
451C2×#103—171no—
452C2×#103—171no—
453C2×#102—171no—
454C2×#102—171no—
455C2×#102—171no—
456C2×#97—171no—
457C2×#97—171no—
458C2×C4×C8—171no—
459C2×C17—82no—
460C2×C17—82no—
461C2×C17#340114yescomplemented
462C2×C17C2×#55011yescharacteristic
463C2×C17C2×#57511yescharacteristic
464C2×C17C2×#57711yescharacteristic
465D17—82no—
466C22×Q8—171no—
467C22×Q8—171no—
468C22×Q8C22⋊D1711yescharacteristic
469C22×Q8C22×D1711yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—171no—
473C22×D4C22×D1711yescharacteristic
474C22×D4C22×D1711yescharacteristic
475C23×C4—21no—
476C23×C4—21no—
477C23×C4—341no—
478C2×Q16—174no—
479C2×Q16—174no—
480C2×Q16—344no—
481C2×Q16—682no—
482C2×SD16—174no—
483C2×SD16—174no—
484C2×SD16—174no—
485C2×SD16—174no—
486C2×SD16—174no—
487C2×SD16—344no—
488C2×SD16—682no—
489C2×SD16—682no—
490C2×SD16—682no—
491C2×SD16—682no—
492C2×D8—174no—
493C2×D8—174no—
494C2×D8—344no—
495C2×D8—682no—
496C22×C8—171no—
497C22×C8—171no—
498C22×C8—171no—
499C22×C8—171no—
500C4⋊Q8—174no—
501C4⋊Q8—342no—
502#127—22no—
503#127C22×D1714yes—
504#126—348no—
505#126—348no—
506#124—28no—
507#124—22no—
508#124—22no—
509#124—174no—
510#124—174no—
511#124—342no—
512#124—342no—
513#124C22×D1714yes—
514#124C22×D1714yes—
515#123—28no—
516#123—28no—
517C22⋊Q8—348no—
518C4×Q8—22no—
519C4×Q8—174no—
520C4×Q8—174no—
521C4×Q8—342no—
522C4×Q8—342no—
523C4×Q8C22⋊D1714yes—
524C4×Q8C22×D1714yes—
525C4×Q8C22×D1714yes—
526C4×D4—28no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—174no—
530C4×D4—342no—
531C4×D4C22×D1714yes—
532C4×D4C22×D1714yes—
533#117—348no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—171no—
536C2×C4⋊C4—341no—
537C2×C4⋊C4—341no—
538C2×C4⋊C4—341no—
539C2×C4⋊C4—341no—
540C2×C4⋊C4C22⋊D1711yescharacteristic
541C2×C4⋊C4C22⋊D1711yescharacteristic
542C2×C4⋊C4C22⋊D1711yescharacteristic
543C2×C4⋊C4C22×D1711yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—341no—
551C2×C22⋊C4—341no—
552C2×C22⋊C4—341no—
553C2×C22⋊C4—341no—
554C2×C22⋊C4—341no—
555C2×C42—21no—
556C2×C42—341no—
557C2×C42—341no—
558C2×C42C22×D1711yescharacteristic
559C2×C42C22×D1711yescharacteristic
560C2×C42C22×D1711yescharacteristic
561#106—174no—
562C4⋊C8—174no—
563C4⋊C8—174no—
564C4⋊C8—174no—
565#103—174no—
566#103—174no—
567#103—174no—
568#102—174no—
569#102—174no—
570#102—174no—
571#97—174no—
572#97—174no—
573C4×C8—174no—
574C17C2×#340111yescharacteristic, complemented, Sylow
575C24—21no—
576C24—21no—
577C24—341no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—42no—
582C2×Q8—172no—
583C2×Q8—172no—
584C2×Q8—341no—
585C2×Q8—341no—
586C2×Q8—342no—
587C2×Q8—342no—
588C2×Q8—342no—
589C2×Q8—342no—
590C2×Q8C2×C22⋊D1714yes—
591C2×Q8C23×D1712yes—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—44no—
601C2×D4—82no—
602C2×D4—172no—
603C2×D4—342no—
604C2×D4—342no—
605C2×D4—341no—
606C2×D4C23×D1712yes—
607C2×D4C23×D1712yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—341no—
615C22×C4—341no—
616C22×C4—341no—
617C22×C4—344no—
618C22×C4—684no—
619C22×C4C2×C22⋊D1711yescharacteristic
620C22×C4C2×C22⋊D1711yescharacteristic
621C22×C4C2×C22⋊D1711yescharacteristic
622C22×C4C2×C22⋊D1711yescharacteristic
623C22×C4C2×C22⋊D1711yescharacteristic
624C22×C4C2×C22⋊D1711yescharacteristic
625C22×C4C23×D1711yescharacteristic
626Q16—348no—
627Q16—684no—
628SD16—348no—
629SD16—684no—
630SD16—684no—
631SD16—684no—
632SD16—684no—
633D8—348no—
634D8—684no—
635C2×C8—174no—
636C2×C8—172no—
637C2×C8—172no—
638C2×C8—172no—
639C2×C8—172no—
640C2×C8—342no—
641C2×C8—342no—
642C2×C8—342no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—172no—
646C4⋊C4—341no—
647C4⋊C4—344no—
648C4⋊C4—344no—
649C4⋊C4—344no—
650C4⋊C4—344no—
651C4⋊C4C2×C22⋊D1714yes—
652C4⋊C4C2×C22⋊D1714yes—
653C4⋊C4C2×C22⋊D1714yes—
654C4⋊C4C23×D1712yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—344no—
662C22⋊C4—344no—
663C22⋊C4—344no—
664C22⋊C4—344no—
665C22⋊C4—344no—
666C42—24no—
667C42—344no—
668C42—344no—
669C42C2×C22⋊D1712yes—
670C42C2×C22⋊D1712yes—
671C42C2×C22⋊D1712yes—
672C42C23×D1712yes—
673C42C23×D1712yes—
674C42C23×D1712yes—
675C23—22no—
676C23—22no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—342no—
684C23—682no—
685C23—682no—
686C23—682no—
687C23C22×C22⋊D1711yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—44no—
691Q8—42no—
692Q8—342no—
693Q8—342no—
694Q8—342no—
695Q8—342no—
696Q8—682no—
697Q8—682no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—42no—
704D4—42no—
705D4—84no—
706D4—342no—
707D4—342no—
708D4—682no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4—342no—
722C2×C4—342no—
723C2×C4—342no—
724C2×C4—688no—
725C2×C4—682no—
726C2×C4—682no—
727C2×C4—682no—
728C2×C4#41×D1712yes—
729C2×C4#1058769612yes—
730C2×C4C22×C22⋊D1712yes—
731C2×C4C22×C22⋊D1712yes—
732C2×C4C22×C22⋊D1712yes—
733C2×C4C22×C22⋊D1712yes—
734C2×C4C22×C22⋊D1712yes—
735C2×C4C22×C22⋊D1712yes—
736C2×C4C22×C22⋊D1711yescharacteristic
737C2×C4C24×D1711yescharacteristic
738C8—174no—
739C8—342no—
740C8—342no—
741C8—342no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—84no—
750C22—682no—
751C22—682no—
752C22—682no—
753C22—1364no—
754C22#1176347812yes—
755C22#1176360712yes—
756C22#1176362012yes—
757C22C23×C22⋊D1711yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—682no—
767C4—682no—
768C4—682no—
769C4#1176347812yes—
770C4C2×#41×D1711yescharacteristic
771C4C2×#1058769611yescharacteristic
772C2—82no—
773C2—82no—
774C2—1362no—
775C2#1454184414yesdirect product factor
776C2C2×#1176347811yescharacteristic
777C2C2×#1176360711yescharacteristic
778C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#559C2
socleC23×C17C22×D4
prime radicalC2×#11763196C2
hypercenterC2×#559D17
hypocenterC17C2×#3401
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#11763532C2semidirect
2. #14541844C2direct (N × H)
3. C2×#11763204C2semidirect
5. C2×#11763191C2semidirect
6. C2×#11763031C2semidirect
7. C2×#11763028C2semidirect
8. C2×#11763006C2semidirect
9. C2×#11763024C2semidirect
10. C2×#11763021C2semidirect
11. C2×#11763014C2semidirect
12. C2×#11762940C2semidirect
13. C2×#11762919C2semidirect
14. C2×#11762914C2semidirect
15. C2×C4×#63229C2semidirect
16. C2×C17×#559C2semidirect
27. #11763532C22semidirect
38. #11763204C22semidirect
40. #11763191C22semidirect
41. #11763031C22semidirect
42. #11763028C22semidirect
43. #11763024C22semidirect
44. #11763021C22semidirect
45. #11763014C22semidirect
46. #11763006C22semidirect
47. #11762940C22semidirect
48. #11762919C22semidirect
49. #11762914C22semidirect
50. C4×#63229C22semidirect
65. C17×#559C22semidirect
353. C2×#559D17semidirect
409. #559C2×D17semidirect
461. C2×C17#3401semidirect
574. C17C2×#3401semidirect
775. C2#14541844direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635322
#145418442
C2×#117632042
C2×#117631962
C2×#117631912
C2×#117630312
C2×#117630282
C2×#117630062
C2×#117630242
C2×#117630212
C2×#117630142
C2×#117629402
C2×#117629192
C2×#117629142
C2×C4×#632292
C2×C17×#5592
C2×#340117