Finite Group Databasebeta

← C2×#14540189 #17907228

Subgroups — C2×#14540189 #17907228

Order 4352.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763430C211yesmaximal, characteristic, complemented
2#14540189C2116yesmaximal, direct product factor
3C2×#11763113C211yesmaximal, characteristic, complemented
4C2×#11763106C211yesmaximal, characteristic, complemented
5C2×#11763099C211yesmaximal, characteristic, complemented
6C2×#11763089C211yesmaximal, characteristic, complemented
7C2×#11763060C211yesmaximal, characteristic, complemented
8C2×#11763053C211yesmaximal, characteristic, complemented
9C2×#11763043C211yesmaximal, characteristic, complemented
10C2×#11763036C211yesmaximal, characteristic, complemented
11C2×#11763006C211yesmaximal, characteristic, complemented
12C2×#11763024C211yesmaximal, characteristic, complemented
13C2×#11763024C211yesmaximal, characteristic, complemented
14C2×#11763001C211yesmaximal, characteristic, complemented
15C2×#11762836C211yesmaximal, characteristic, complemented
16C2×C17×#540C211yesmaximal, characteristic, complemented
17C22×#63229C2211yescharacteristic
18C22×#63229C2211yescharacteristic
19C22×#63228C2211yescharacteristic
20C22×#63228C2211yescharacteristic
21C22×#63223C2211yescharacteristic
22C23×#3622C2211yescharacteristic
23#11763430—24no—
24#11763430C2218yescomplemented
25C2×#10587555C2211yescharacteristic
26C2×#10587584—21no—
27C2×#10587561C2211yescharacteristic
28C2×#10587571—21no—
29C2×#10587569—21no—
30C2×#10587610C2211yescharacteristic
31C2×#10587582—21no—
32C2×#10587616C2211yescharacteristic
33C2×C4×Dic34C2211yescharacteristic
34C2×C4×D68C2211yescharacteristic
35#11763113C2218yescomplemented
36#11763106C2218yescomplemented
37#11763099C2218yescomplemented
38#11763089C2218yescomplemented
39#11763060C2218yescomplemented
40#11763053C2218yescomplemented
41#11763043C2218yescomplemented
42#11763036C2218yescomplemented
43#11763024C2218yescomplemented
44#11763024C2218yescomplemented
45#11763006C2218yescomplemented
46#11763001C2218yescomplemented
47C2×#10587478C2211yescharacteristic
48C2×#10587478C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51#11762836C2218yescomplemented
52C2×C4⋊#3622C2211yescharacteristic
53C2×C4⋊#3622C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×C4⋊#3622C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×#10587503C2211yescharacteristic
61C2×#10587503C2211yescharacteristic
62C2×#10587480C2211yescharacteristic
63C2×#10587480C2211yescharacteristic
64C17×#540—24no—
65C17×#540C2218yescomplemented
66C2×C17×#127C2211yescharacteristic
67C2×C17×#125C2211yescharacteristic
68C2×C17×#123—21no—
69C2×C17×#123—21no—
70C2×C17×#121—21no—
71C2×C17×#121—21no—
72C2×C17×#121C2211yescharacteristic
73C2×C17×#121C2211yescharacteristic
74C2×C4×D4×C17C2211yescharacteristic
75C2×C4×D4×C17C2211yescharacteristic
76C2×C17×#117C2211yescharacteristic
77C22×D4×C17—21no—
78C22×D4×C17—21no—
79C22×D4×C17—21no—
80C22×D4×C17—21no—
81C22×D4×C17C2311yescharacteristic
82C22×D4×C17C2311yescharacteristic
83C23×C4×C17—21no—
84C23×C4×C17—21no—
85C23×C4×C17C2311yescharacteristic
86C22×C22⋊D17—21no—
87C22×D68C2311yescharacteristic
88C22×C4×D17—21no—
89C22×Dic34—21no—
90C22×Dic34C2311yescharacteristic
91C17×#127—22no—
92C17×#127C2314yes—
93C17×#125—22no—
94C17×#125C2314yes—
95C17×#123—28no—
96C17×#123—28no—
97C17×#121—22no—
98C17×#121—22no—
99C17×#121—28no—
100C17×#121—28no—
101C17×#121C2314yes—
102C17×#121C2314yes—
103C4×D4×C17—22no—
104C4×D4×C17—22no—
105C4×D4×C17C2314yes—
106C4×D4×C17C2314yes—
107C17×#117D414yes—
108C17×#117C2314yes—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17—21no—
111C2×C4⋊C4×C17D411yescharacteristic
112C2×C4⋊C4×C17D411yescharacteristic
113C2×C4⋊C4×C17C2311yescharacteristic
114C2×C4⋊C4×C17C2311yescharacteristic
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17—21no—
119C2×C22⋊C4×C17D411yescharacteristic
120C2×C22⋊C4×C17D411yescharacteristic
121C2×C42×C17C2311yescharacteristic
122C2×C42×C17C2311yescharacteristic
123C2×C22⋊Dic17—21no—
124C2×#63229—42no—
125C2×#63229—42no—
126C2×#63229C2314yes—
127C2×#63229C2314yes—
128C2×#63228—42no—
129C2×#63228—42no—
130C2×#63228C2314yes—
131C2×#63228C2314yes—
132#10587616—22no—
133#10587616C2314yes—
134C2×#63227—21no—
135C2×#63227—21no—
136C2×#63227—21no—
137C2×#63227—21no—
138C2×C4⋊Dic17—21no—
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141#10587610—22no—
142#10587610C2314yes—
143C2×#63225—21no—
144C2×#63225—21no—
145C2×C4×Dic17—21no—
146C2×#63223—42no—
147C2×#63223C2314yes—
148C22×#3622—42no—
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152C22×#3622C2311yescharacteristic
153C22×#3622C2314yes—
154#10587584—28no—
155#10587582—28no—
156#10587571—28no—
157#10587569—28no—
158#10587561—22no—
159#10587561C2314yes—
160C4×D68—22no—
161C4×D68C2314yes—
162#10587555—22no—
163#10587555C2314yes—
164C4×Dic34—22no—
165C4×Dic34C2314yes—
166#10587503C2314yes—
167#10587503C2314yes—
168#10587503C2314yes—
169#10587503C2314yes—
170#10587481C2314yes—
171#10587481C2314yes—
172#10587480C2314yes—
173#10587480C2314yes—
174#10587479C2314yes—
175#10587479C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178C4⋊#3622C2314yes—
179C4⋊#3622C2314yes—
180C4⋊#3622C2314yes—
181C4⋊#3622C2314yes—
182C24×C17—21no—
183C24×C17—21no—
184C24×C17C2×D411yescharacteristic
185C23×D17—21no—
186C2×D4×C17—24no—
187C2×D4×C17—24no—
188C2×D4×C17—21no—
189C2×D4×C17—21no—
190C2×D4×C17—24no—
191C2×D4×C17—24no—
192C2×D4×C17—22no—
193C2×D4×C17—22no—
194C2×D4×C17—22no—
195C2×D4×C17—22no—
196C2×D4×C17—82no—
197C2×D4×C17—82no—
198C2×D4×C17—82no—
199C2×D4×C17—82no—
200C2×D4×C17C2412yes—
201C2×D4×C17C2412yes—
202C22×C4×C17—22no—
203C22×C4×C17—22no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—24no—
207C22×C4×C17—24no—
208C22×C4×C17—82no—
209C22×C4×C17—82no—
210C22×C4×C17C2×D411yescharacteristic
211C22×C4×C17C2×D411yescharacteristic
212C22×C4×C17C2×D411yescharacteristic
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2×D412yes—
215C22×C4×C17C2×D411yescharacteristic
216C22×C4×C17C2412yes—
217C22×C4×C17C2411yescharacteristic
218C2×C22⋊D17—24no—
219C2×C22⋊D17—82no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C2×D68—22no—
224C2×D68—22no—
225C2×D68—21no—
226C2×D68C2412yes—
227C2×C4×D17—24no—
228C2×C4×D17—82no—
229C2×Dic34—22no—
230C2×Dic34—22no—
231C2×Dic34—21no—
232C2×Dic34—24no—
233C2×Dic34—82no—
234C2×Dic34C2412yes—
235C4⋊C4×C17—24no—
236C4⋊C4×C17—24no—
237C4⋊C4×C17—21no—
238C4⋊C4×C17—21no—
239C4⋊C4×C17C2×D414yes—
240C4⋊C4×C17C2×D414yes—
241C4⋊C4×C17C2412yes—
242C4⋊C4×C17C2412yes—
243C22⋊C4×C17—24no—
244C22⋊C4×C17—24no—
245C22⋊C4×C17—24no—
246C22⋊C4×C17—24no—
247C22⋊C4×C17C2×D414yes—
248C22⋊C4×C17C2×D414yes—
249C42×C17C2×D412yes—
250C42×C17C2×D412yes—
251C42×C17C2412yes—
252C42×C17C2412yes—
253C22⋊Dic17—24no—
254#63229—44no—
255#63229—44no—
256#63228—44no—
257#63228—44no—
258#63227—24no—
259#63227—24no—
260#63227—24no—
261#63227—24no—
262C4⋊Dic17—21no—
263C4⋊Dic17—21no—
264C4⋊Dic17—24no—
265C4⋊Dic17C2412yes—
266C4⋊Dic17C2412yes—
267#63225—24no—
268#63225—24no—
269C4×Dic17—24no—
270#63223—44no—
271C2×#3622—22no—
272C2×#3622—22no—
273C2×#3622—22no—
274C2×#3622—22no—
275C2×#3622—44no—
276C2×#3622C2412yes—
277C2×#3622C2412yes—
278C2×#3622C2412yes—
279C2×#3622C2412yes—
280C2×#3257—171nomaximal, Sylow
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—22no—
284C23×C17—22no—
285C23×C17—22no—
286C23×C17—42no—
287C23×C17—42no—
288C23×C17—42no—
289C23×C17—42no—
290C23×C17—42no—
291C23×C17—42no—
292C23×C17C22×D412yes—
293C23×C17C22×D411yescharacteristic
294C22×D17—22no—
295C22×D17—42no—
296C22×D17—42no—
297C22×D17—42no—
298D4×C17—22no—
299D4×C17—22no—
300D4×C17—22no—
301D4×C17—22no—
302D4×C17—42no—
303D4×C17—42no—
304D4×C17—84no—
305D4×C17—84no—
306D4×C17—84no—
307D4×C17—84no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—24no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—42no—
319C2×C4×C17—42no—
320C2×C4×C17—84no—
321C2×C4×C17—84no—
322C2×C4×C17C22×D412yes—
323C2×C4×C17C22×D412yes—
324C2×C4×C17C22×D412yes—
325C2×C4×C17C22×D412yes—
326C2×C4×C17C22×D412yes—
327C2×C4×C17C22×D411yescharacteristic
328C2×C4×C17H(5,𝔽2)12yes—
329C2×C4×C172−1+412yes—
330C2×C4×C17C2511yescharacteristic
331C22⋊D17—84no—
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—42no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338D68—22no—
339D68—22no—
340D68—42no—
341C4×D17—84no—
342Dic34—22no—
343Dic34—22no—
344Dic34—42no—
345Dic34—84no—
346#3622—22no—
347#3622—22no—
348#3622—22no—
349#3622—22no—
350C2×#542—171no—
351C2×#540D1711yescharacteristic, complemented
352#3257—1716no—
353C2×#479—171no—
354C2×#478—171no—
355C2×#476—171no—
356C2×#474—171no—
357C2×#469—171no—
358C2×#468—171no—
359C2×#466—171no—
360C2×#465—171no—
361C2×#460—171no—
362C2×#463—171no—
363C2×#463—171no—
364C2×#459—171no—
365C2×#424—171no—
366C22×C17—22no—
367C22×C17—22no—
368C22×C17—22no—
369C22×C17—44no—
370C22×C17—42no—
371C22×C17—42no—
372C22×C17—42no—
373C22×C17—42no—
374C22×C17—42no—
375C22×C17—42no—
376C22×C17—84no—
377C22×C17—84no—
378C22×C17#53712yes—
379C22×C17#57612yes—
380C22×C17#57712yes—
381C22×C17C23×D411yescharacteristic
382C2×D17—42no—
383C2×D17—42no—
384C2×D17—42no—
385C2×D17—84no—
386C4×C17—22no—
387C4×C17—22no—
388C4×C17—22no—
389C4×C17—22no—
390C4×C17—22no—
391C4×C17—42no—
392C4×C17—42no—
393C4×C17#53712yes—
394C4×C17C2×H(5,𝔽2)11yescharacteristic
395C4×C17C2×2−1+411yescharacteristic
396Dic17—42no—
397Dic17—42no—
398Dic17—42no—
399C22×SD16—171no—
400C22×SD16—171no—
401C22×D8—171no—
402C22×D8—171no—
403C22×M16—171no—
404C23×C8—171no—
405#542—178no—
406#542—344no—
407#540—24no—
408#540C2×D1718yescomplemented
409C2×C4⋊Q8—171no—
410C2×#127C2×D1711yescharacteristic
411C2×#126—341no—
412C2×#125C2×D1711yescharacteristic
413C2×#124—171no—
414C2×#124—341no—
415C2×#123—21no—
416C2×#123—21no—
417C2×#123—341no—
418C2×C22⋊Q8—171no—
419C2×C22⋊Q8—341no—
420C2×#121—21no—
421C2×#121—21no—
422C2×#121—171no—
423C2×#121C2×D1711yescharacteristic
424C2×#121C2×D1711yescharacteristic
425C2×C4×Q8—171no—
426C2×C4×D4—171no—
427C2×C4×D4C2×D1711yescharacteristic
428C2×C4×D4C2×D1711yescharacteristic
429C2×#117C2×D1711yescharacteristic
430#479—178no—
431#478—178no—
432#476—178no—
433#474—178no—
434#469—178no—
435#468—178no—
436#466—178no—
437#465—178no—
438#463—178no—
439#463—178no—
440#460—178no—
441#459—178no—
442C2×#107—171no—
443C2×#107—171no—
444C2×#106—171no—
445C2×#106—171no—
446#424—178no—
447C2×C4⋊C8—171no—
448C2×C4⋊C8—171no—
449C2×C4⋊C8—171no—
450C2×C4⋊C8—171no—
451C2×#103—171no—
452C2×#103—171no—
453C2×#102—171no—
454C2×#102—171no—
455C2×#102—171no—
456C2×#102—171no—
457C2×#102—171no—
458C2×#102—171no—
459C2×C17—42no—
460C2×C17—82no—
461C2×C17—82no—
462C2×C17#325714yescomplemented
463C2×C17C2×#53711yescharacteristic
464C2×C17C2×#57611yescharacteristic
465C2×C17C2×#57711yescharacteristic
466D17—82no—
467C22×Q8—171no—
468C22×Q8—341no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—171no—
474C22×D4—341no—
475C22×D4C22×D1711yescharacteristic
476C22×D4C22×D1711yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—341no—
480C23×C4C22×D1711yescharacteristic
481C2×SD16—174no—
482C2×SD16—174no—
483C2×SD16—682no—
484C2×SD16—682no—
485C2×D8—174no—
486C2×D8—174no—
487C2×D8—682no—
488C2×D8—682no—
489C2×M16—174no—
490C2×M16—682no—
491C22×C8—171no—
492C22×C8—171no—
493C22×C8—171no—
494C22×C8—171no—
495C22×C8—174no—
496C22×C8—682no—
497C4⋊Q8—174no—
498C4⋊Q8—342no—
499#127—22no—
500#127C22×D1714yes—
501#126—348no—
502#125—22no—
503#125C22×D1714yes—
504#124—174no—
505#124—348no—
506#124—342no—
507#123—28no—
508#123—28no—
509#123—348no—
510C22⋊Q8—174no—
511C22⋊Q8—342no—
512C22⋊Q8—348no—
513#121—22no—
514#121—22no—
515#121—28no—
516#121—28no—
517#121—174no—
518#121—342no—
519#121C22×D1714yes—
520#121C22×D1714yes—
521C4×Q8—174no—
522C4×Q8—342no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—174no—
526C4×D4—342no—
527C4×D4C22×D1714yes—
528C4×D4C22×D1714yes—
529#117C22⋊D1714yes—
530#117C22×D1714yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—171no—
534C2×C4⋊C4—171no—
535C2×C4⋊C4—341no—
536C2×C4⋊C4—341no—
537C2×C4⋊C4—341no—
538C2×C4⋊C4C22⋊D1711yescharacteristic
539C2×C4⋊C4C22⋊D1711yescharacteristic
540C2×C4⋊C4C22×D1711yescharacteristic
541C2×C4⋊C4C22×D1711yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—341no—
547C2×C22⋊C4—341no—
548C2×C22⋊C4—341no—
549C2×C22⋊C4—341no—
550C2×C22⋊C4—341no—
551C2×C22⋊C4C22⋊D1711yescharacteristic
552C2×C22⋊C4C22⋊D1711yescharacteristic
553C2×C42—341no—
554C2×C42C22×D1711yescharacteristic
555C2×C42C22×D1711yescharacteristic
556#107—174no—
557#107—174no—
558#106—174no—
559#106—174no—
560C4⋊C8—174no—
561C4⋊C8—174no—
562C4⋊C8—174no—
563C4⋊C8—174no—
564#103—174no—
565#103—174no—
566#102—174no—
567#102—174no—
568#102—174no—
569#102—174no—
570#102—174no—
571#102—174no—
572C17C2×#325711yescharacteristic, complemented, Sylow
573C24—21no—
574C24—21no—
575C24—341no—
576C24C2×C22⋊D1711yescharacteristic
577C2×Q8—172no—
578C2×Q8—341no—
579C2×Q8—344no—
580C2×Q8—342no—
581C2×Q8—342no—
582C2×Q8—1362no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—82no—
594C2×D4—82no—
595C2×D4—82no—
596C2×D4—82no—
597C2×D4—172no—
598C2×D4—344no—
599C2×D4—342no—
600C2×D4—342no—
601C2×D4—341no—
602C2×D4—1362no—
603C2×D4C23×D1712yes—
604C2×D4C23×D1712yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—341no—
614C22×C4—341no—
615C22×C4—341no—
616C22×C4—344no—
617C22×C4—1362no—
618C22×C4C2×C22⋊D1712yes—
619C22×C4C2×C22⋊D1711yescharacteristic
620C22×C4C2×C22⋊D1711yescharacteristic
621C22×C4C2×C22⋊D1711yescharacteristic
622C22×C4C2×C22⋊D1711yescharacteristic
623C22×C4C2×C22⋊D1711yescharacteristic
624C22×C4C23×D1712yes—
625C22×C4C23×D1711yescharacteristic
626SD16—684no—
627SD16—684no—
628D8—684no—
629D8—684no—
630M16—684no—
631C2×C8—172no—
632C2×C8—172no—
633C2×C8—172no—
634C2×C8—172no—
635C2×C8—342no—
636C2×C8—342no—
637C2×C8—342no—
638C2×C8—342no—
639C2×C8—684no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—172no—
645C4⋊C4—172no—
646C4⋊C4—341no—
647C4⋊C4—341no—
648C4⋊C4—344no—
649C4⋊C4—344no—
650C4⋊C4—344no—
651C4⋊C4C2×C22⋊D1714yes—
652C4⋊C4C2×C22⋊D1714yes—
653C4⋊C4C23×D1712yes—
654C4⋊C4C23×D1712yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—344no—
660C22⋊C4—344no—
661C22⋊C4—344no—
662C22⋊C4—344no—
663C22⋊C4—344no—
664C22⋊C4C2×C22⋊D1714yes—
665C22⋊C4C2×C22⋊D1714yes—
666C42—344no—
667C42C2×C22⋊D1712yes—
668C42C2×C22⋊D1712yes—
669C42C23×D1712yes—
670C42C23×D1712yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—342no—
683C23—682no—
684C23—682no—
685C23—682no—
686C23C22×C22⋊D1712yes—
687C23C22×C22⋊D1711yescharacteristic
688Q8—342no—
689Q8—342no—
690Q8—682no—
691Q8—1364no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—42no—
697D4—42no—
698D4—84no—
699D4—84no—
700D4—84no—
701D4—84no—
702D4—342no—
703D4—342no—
704D4—682no—
705D4—1364no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4—342no—
721C2×C4—342no—
722C2×C4—342no—
723C2×C4—682no—
724C2×C4—682no—
725C2×C4—682no—
726C2×C4—1364no—
727C2×C4#1058769612yes—
728C2×C4#1058769712yes—
729C2×C4C22×C22⋊D1712yes—
730C2×C4C22×C22⋊D1712yes—
731C2×C4C22×C22⋊D1712yes—
732C2×C4C22×C22⋊D1712yes—
733C2×C4C22×C22⋊D1712yes—
734C2×C4C22×C22⋊D1711yescharacteristic
735C2×C4C24×D1711yescharacteristic
736C8—342no—
737C8—342no—
738C8—342no—
739C8—342no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—84no—
751C22—84no—
752C22—682no—
753C22—682no—
754C22—682no—
755C22—1364no—
756C22#1176338712yes—
757C22#1176361212yes—
758C22#1176362012yes—
759C22C23×C22⋊D1711yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—682no—
768C4—682no—
769C4—682no—
770C4#1176338712yes—
771C4C2×#1058769611yescharacteristic
772C4C2×#1058769711yescharacteristic
773C2—42no—
774C2—82no—
775C2—82no—
776C2—1362no—
777C2#1454018914yesdirect product factor
778C2C2×#1176338711yescharacteristic
779C2C2×#1176361211yescharacteristic
780C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#540C2
socleC23×C17C22×D4
hypercenterC2×#540D17
hypocenterC17C2×#3257
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#11763430C2semidirect
2. #14540189C2direct (N × H)
3. C2×#11763113C2semidirect
4. C2×#11763106C2semidirect
5. C2×#11763099C2semidirect
6. C2×#11763089C2semidirect
7. C2×#11763060C2semidirect
8. C2×#11763053C2semidirect
9. C2×#11763043C2semidirect
10. C2×#11763036C2semidirect
11. C2×#11763006C2semidirect
12. C2×#11763024C2semidirect
13. C2×#11763024C2semidirect
14. C2×#11763001C2semidirect
15. C2×#11762836C2semidirect
16. C2×C17×#540C2semidirect
24. #11763430C22semidirect
35. #11763113C22semidirect
36. #11763106C22semidirect
37. #11763099C22semidirect
38. #11763089C22semidirect
39. #11763060C22semidirect
40. #11763053C22semidirect
41. #11763043C22semidirect
42. #11763036C22semidirect
43. #11763024C22semidirect
44. #11763024C22semidirect
45. #11763006C22semidirect
46. #11763001C22semidirect
51. #11762836C22semidirect
65. C17×#540C22semidirect
351. C2×#540D17semidirect
408. #540C2×D17semidirect
462. C2×C17#3257semidirect
572. C17C2×#3257semidirect
777. C2#14540189direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634302
#145401892
C2×#117631132
C2×#117631062
C2×#117630992
C2×#117630892
C2×#117630602
C2×#117630532
C2×#117630432
C2×#117630362
C2×#117630062
C2×#117630242
C2×#117630012
C2×#117628362
C2×C17×#5402
C2×#325717