Finite Group Databasebeta

← C2×#14538983 #17902571

Subgroups — C2×#14538983 #17902571

Order 4352.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763414C211yesmaximal, characteristic, complemented
2#14538983C2116yesmaximal, direct product factor
3C2×#11763127C211yesmaximal, characteristic, complemented
4C2×#11763122C211yesmaximal, characteristic, complemented
5C2×#11763116C211yesmaximal, characteristic, complemented
6C2×#11763109C211yesmaximal, characteristic, complemented
7C2×#11763009C211yesmaximal, characteristic, complemented
8C2×#11763004C211yesmaximal, characteristic, complemented
9C2×#11762954C211yesmaximal, characteristic, complemented
10C2×#11762954C211yesmaximal, characteristic, complemented
11C2×#11762919C211yesmaximal, characteristic, complemented
12C2×#11762907C211yesmaximal, characteristic, complemented
13C2×C4×#63230C211yesmaximal, characteristic, complemented
14C2×C4×#63228C211yesmaximal, characteristic, complemented
15C2×#11762870C211yesmaximal, characteristic, complemented
16C2×C17×#520C211yesmaximal, characteristic, complemented
17C22×#63230C2211yescharacteristic
18C22×#63230C2211yescharacteristic
19C22×#63228C2211yescharacteristic
20C22×#63228C2211yescharacteristic
21#11763414—24no—
22#11763414C2218yescomplemented
23C2×#10587560C2211yescharacteristic
24C2×#10587556C2211yescharacteristic
25C2×#10587580—21no—
26C2×#10587580—21no—
27C2×#10587616C2211yescharacteristic
28C2×#10587616C2211yescharacteristic
29C2×#10587570—21no—
30C2×#10587570—21no—
31C2×C4×D68C2211yescharacteristic
32C2×C4×D68C2211yescharacteristic
33#11763127C2218yescomplemented
34#11763122C2218yescomplemented
35#11763116C2218yescomplemented
36#11763109C2218yescomplemented
37#11763009C2218yescomplemented
38#11763004C2218yescomplemented
39#11762954C2218yescomplemented
40#11762954C2218yescomplemented
41#11762919C2218yescomplemented
42#11762907C2218yescomplemented
43C4×#63230C2218yescomplemented
44C4×#63228C2218yescomplemented
45#11762870C2218yescomplemented
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×C4⋊#3622C2211yescharacteristic
51C2×C4⋊#3622C2211yescharacteristic
52C2×#10587506C2211yescharacteristic
53C2×#10587506C2211yescharacteristic
54C2×#10587503C2211yescharacteristic
55C2×#10587503C2211yescharacteristic
56C2×#10587480C2211yescharacteristic
57C2×#10587480C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×C22⋊#3622C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C22×#41×C17C2211yescharacteristic
65C17×#520—24no—
66C17×#520C2218yescomplemented
67C2×C4×Q8×C17C2211yescharacteristic
68C2×C4×Q8×C17C2211yescharacteristic
69C2×C4×D4×C17—21no—
70C2×C4×D4×C17—21no—
71C2×C4×D4×C17C2211yescharacteristic
72C2×C4×D4×C17C2211yescharacteristic
73C2×C17×#117—21no—
74C2×C17×#117C2211yescharacteristic
75C22×C4⋊C4×C17—21no—
76C22×C4⋊C4×C17C2211yescharacteristic
77C2×#41×C17—24no—
78C2×#41×C17—24no—
79C2×#41×C17—22no—
80C2×#41×C17C2314yes—
81C22×Q8×C17C2311yescharacteristic
82C22×D4×C17—21no—
83C22×D4×C17C2311yescharacteristic
84C23×C4×C17—21no—
85C23×C4×C17—21no—
86C23×C4×C17—21no—
87C23×C4×C17—21no—
88C23×C4×C17C2311yescharacteristic
89C22×C22⋊D17—21no—
90C22×C22⋊D17—21no—
91C22×D68—21no—
92C22×D68—21no—
93C22×D68C2311yescharacteristic
94C22×D68C2311yescharacteristic
95C22×C4×D17—21no—
96C22×C4×D17—21no—
97C4×Q8×C17—22no—
98C4×Q8×C17—22no—
99C4×Q8×C17C2314yes—
100C4×Q8×C17C2314yes—
101C4×D4×C17—28no—
102C4×D4×C17—28no—
103C4×D4×C17—22no—
104C4×D4×C17—22no—
105C4×D4×C17C2314yes—
106C4×D4×C17C2314yes—
107C17×#117—28no—
108C17×#117D414yes—
109C17×#117C2314yes—
110C2×C4⋊C4×C17—21no—
111C2×C4⋊C4×C17—21no—
112C2×C4⋊C4×C17—21no—
113C2×C4⋊C4×C17—22no—
114C2×C4⋊C4×C17—28no—
115C2×C4⋊C4×C17D411yescharacteristic
116C2×C4⋊C4×C17D411yescharacteristic
117C2×C4⋊C4×C17C2311yescharacteristic
118C2×C4⋊C4×C17C2311yescharacteristic
119C2×C4⋊C4×C17C2314yes—
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×C42×C17C2311yescharacteristic
128C2×#63230—24no—
129C2×#63230—24no—
130C2×#63230C2314yes—
131C2×#63230C2314yes—
132C2×#63228—24no—
133C2×#63228—24no—
134C2×#63228C2314yes—
135C2×#63228C2314yes—
136#10587616—22no—
137#10587616—22no—
138#10587616C2314yes—
139#10587616C2314yes—
140C2×#63227—21no—
141C2×#63227—21no—
142C2×#63227—21no—
143C2×#63227—21no—
144C2×C4⋊Dic17C2311yescharacteristic
145C2×C4⋊Dic17C2311yescharacteristic
146C2×#63225—21no—
147C2×#63225—21no—
148C22×#3622C2311yescharacteristic
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152#10587580—28no—
153#10587580—28no—
154#10587570—28no—
155#10587570—28no—
156#10587560—22no—
157#10587560C2314yes—
158C4×D68—22no—
159C4×D68—22no—
160C4×D68C2314yes—
161C4×D68C2314yes—
162#10587556—22no—
163#10587556C2314yes—
164#10587506C2314yes—
165#10587506C2314yes—
166#10587503C2314yes—
167#10587503C2314yes—
168C22⋊#3622C2314yes—
169C22⋊#3622C2314yes—
170#10587480C2314yes—
171#10587480C2314yes—
172#10587480C2314yes—
173#10587480C2314yes—
174#10587479C2314yes—
175#10587479C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178C4⋊#3622C2314yes—
179C4⋊#3622C2314yes—
180#10587474C2314yes—
181C4×#3622C2314yes—
182C24×C17—21no—
183C24×C17C2×D411yescharacteristic
184C23×D17—21no—
185C23×D17—21no—
186#41×C17—216no—
187#41×C17—28no—
188#41×C17—28no—
189C2×Q8×C17—21no—
190C2×Q8×C17—22no—
191C2×Q8×C17#4114yes—
192C2×Q8×C17C2412yes—
193C2×D4×C17—28no—
194C2×D4×C17—24no—
195C2×D4×C17—21no—
196C2×D4×C17—22no—
197C2×D4×C17#4114yes—
198C2×D4×C17C2412yes—
199C22×C4×C17—28no—
200C22×C4×C17—21no—
201C22×C4×C17—24no—
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—24no—
209C22×C4×C17—82no—
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×D412yes—
218C22×C4×C17C2412yes—
219C22×C4×C17C2411yescharacteristic
220C2×C22⋊D17—24no—
221C2×C22⋊D17—24no—
222C2×C22⋊D17—82no—
223C2×C22⋊D17—82no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C2×D68—22no—
227C2×D68—22no—
228C2×D68—22no—
229C2×D68—22no—
230C2×D68—21no—
231C2×D68—21no—
232C2×D68—24no—
233C2×D68—24no—
234C2×D68—82no—
235C2×D68—82no—
236C2×D68C2412yes—
237C2×D68C2412yes—
238C2×C4×D17—24no—
239C2×C4×D17—24no—
240C2×C4×D17—82no—
241C2×C4×D17—82no—
242C4⋊C4×C17—24no—
243C4⋊C4×C17—24no—
244C4⋊C4×C17—24no—
245C4⋊C4×C17—21no—
246C4⋊C4×C17—21no—
247C4⋊C4×C17C2×D414yes—
248C4⋊C4×C17C2×D414yes—
249C4⋊C4×C17C2412yes—
250C4⋊C4×C17C2412yes—
251C22⋊C4×C17—24no—
252C22⋊C4×C17—24no—
253C22⋊C4×C17C2×D414yes—
254C22⋊C4×C17C2×D414yes—
255C42×C17—24no—
256C42×C17—24no—
257C42×C17C2×D412yes—
258C42×C17C2×D412yes—
259C42×C17C2412yes—
260C42×C17C2412yes—
261#63230—28no—
262#63230—28no—
263#63228—28no—
264#63228—28no—
265#63227—24no—
266#63227—24no—
267#63227—24no—
268#63227—24no—
269C4⋊Dic17—21no—
270C4⋊Dic17—21no—
271C4⋊Dic17C2412yes—
272C4⋊Dic17C2412yes—
273#63225—24no—
274#63225—24no—
275C2×#3622—22no—
276C2×#3622—22no—
277C2×#3622—22no—
278C2×#3622—22no—
279C2×#3622C2412yes—
280C2×#3622C2412yes—
281C2×#3622C2412yes—
282C2×#3622C2412yes—
283C2×#3119—171nomaximal, Sylow
284C23×C17—22no—
285C23×C17—24no—
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—22no—
289C23×C17—42no—
290C23×C17—42no—
291C23×C17C22×D412yes—
292C23×C17C22×D411yescharacteristic
293C22×D17—22no—
294C22×D17—22no—
295C22×D17—42no—
296C22×D17—42no—
297C22×D17—42no—
298C22×D17—42no—
299C22×D17—42no—
300C22×D17—42no—
301Q8×C17—24no—
302Q8×C17—22no—
303Q8×C17C2×#4114yes—
304D4×C17—216no—
305D4×C17—24no—
306D4×C17—22no—
307D4×C17C2×#4114yes—
308C2×C4×C17—216no—
309C2×C4×C17—22no—
310C2×C4×C17—24no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—24no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—42no—
322C2×C4×C17—42no—
323C2×C4×C17—84no—
324C2×C4×C17—84no—
325C2×C4×C17—84no—
326C2×C4×C17C22×D412yes—
327C2×C4×C17C22×D412yes—
328C2×C4×C17C22×D412yes—
329C2×C4×C17C22×D412yes—
330C2×C4×C17C22×D412yes—
331C2×C4×C17C22×D411yescharacteristic
332C2×C4×C17C2×#4112yes—
333C2×C4×C17C2×#4112yes—
334C2×C4×C17C2511yescharacteristic
335C22⋊D17—84no—
336C22⋊D17—84no—
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—42no—
340C2×Dic17—42no—
341D68—22no—
342D68—22no—
343D68—22no—
344D68—22no—
345D68—42no—
346D68—42no—
347D68—84no—
348D68—84no—
349C4×D17—84no—
350C4×D17—84no—
351#3622—22no—
352#3622—22no—
353#3622—22no—
354#3622—22no—
355C2×#540—171no—
356C2×#520D1711yescharacteristic, complemented
357#3119—1716no—
358C2×#481—171no—
359C2×#480—171no—
360C2×#479—171no—
361C2×#478—171no—
362C2×#460—171no—
363C2×#459—171no—
364C2×#449—171no—
365C2×#449—171no—
366C2×#442—171no—
367C2×#440—171no—
368C2×C4×SD16—171no—
369C2×C4×D8—171no—
370C2×#433—171no—
371C22×C17—22no—
372C22×C17—24no—
373C22×C17—22no—
374C22×C17—22no—
375C22×C17—44no—
376C22×C17—48no—
377C22×C17—42no—
378C22×C17—42no—
379C22×C17#52512yes—
380C22×C17#57612yes—
381C22×C17#57712yes—
382C22×C17C23×D411yescharacteristic
383C2×D17—42no—
384C2×D17—42no—
385C2×D17—42no—
386C2×D17—42no—
387C2×D17—42no—
388C2×D17—42no—
389C2×D17—84no—
390C2×D17—84no—
391C4×C17—22no—
392C4×C17—24no—
393C4×C17—22no—
394C4×C17—22no—
395C4×C17—22no—
396C4×C17—22no—
397C4×C17—42no—
398C4×C17—42no—
399C4×C17#52512yes—
400C4×C17C22×#4111yescharacteristic
401C4×C17C22×#4111yescharacteristic
402Dic17—42no—
403Dic17—42no—
404C22×#41C2×D1711yescharacteristic
405C22×SD16—171no—
406C22×SD16—171no—
407C22×D8—171no—
408C22×D8—171no—
409#540—178no—
410#540—344no—
411C2×#127—171no—
412C2×#125—171no—
413C2×#123—341no—
414C2×#123—341no—
415C2×#121—171no—
416C2×#121—171no—
417C2×#121—341no—
418C2×#121—341no—
419#520—24no—
420#520C2×D1718yescomplemented
421C2×C4×Q8C2×D1711yescharacteristic
422C2×C4×Q8C2×D1711yescharacteristic
423C2×C4×D4—21no—
424C2×C4×D4—21no—
425C2×C4×D4—171no—
426C2×C4×D4—171no—
427C2×C4×D4C2×D1711yescharacteristic
428C2×C4×D4C2×D1711yescharacteristic
429C2×#117—21no—
430C2×#117C2×D1711yescharacteristic
431C22×C4⋊C4—21no—
432C22×C4⋊C4C2×D1711yescharacteristic
433#481—178no—
434#480—178no—
435#479—178no—
436#478—178no—
437#460—178no—
438#459—178no—
439#449—178no—
440#449—178no—
441#442—178no—
442#440—178no—
443C4×SD16—178no—
444C4×D8—178no—
445#433—178no—
446C2×#107—171no—
447C2×#107—171no—
448C2×#106—171no—
449C2×#106—171no—
450C2×C4⋊C8—171no—
451C2×C4⋊C8—171no—
452C2×#103—171no—
453C2×#103—171no—
454C2×#102—171no—
455C2×#102—171no—
456C2×#102—171no—
457C2×#102—171no—
458C2×#102—171no—
459C2×#102—171no—
460C2×C22⋊C8—171no—
461C2×C22⋊C8—171no—
462C2×#97—171no—
463C2×C4×C8—171no—
464C2×C17—42no—
465C2×C17—44no—
466C2×C17#311914yescomplemented
467C2×C17C2×#52511yescharacteristic
468C2×C17C2×#57611yescharacteristic
469C2×C17C2×#57711yescharacteristic
470D17—82no—
471D17—82no—
472C2×#41—24no—
473C2×#41—24no—
474C2×#41—22no—
475C2×#41C22×D1714yes—
476C22×Q8C22×D1711yescharacteristic
477C22×D4—21no—
478C22×D4—171no—
479C22×D4—171no—
480C22×D4—341no—
481C22×D4—341no—
482C22×D4—341no—
483C22×D4—341no—
484C22×D4C22×D1711yescharacteristic
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—341no—
490C23×C4—341no—
491C23×C4C22×D1711yescharacteristic
492C2×SD16—174no—
493C2×SD16—174no—
494C2×SD16—344no—
495C2×SD16—344no—
496C2×D8—174no—
497C2×D8—174no—
498C2×D8—344no—
499C2×D8—344no—
500C22×C8—171no—
501C22×C8—171no—
502C22×C8—171no—
503C22×C8—171no—
504#127—174no—
505#127—342no—
506#125—174no—
507#125—342no—
508#123—348no—
509#123—348no—
510#121—174no—
511#121—174no—
512#121—342no—
513#121—342no—
514#121—348no—
515#121—348no—
516C4×Q8—22no—
517C4×Q8—22no—
518C4×Q8C22×D1714yes—
519C4×Q8C22×D1714yes—
520C4×D4—28no—
521C4×D4—28no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—174no—
525C4×D4—174no—
526C4×D4—342no—
527C4×D4—342no—
528C4×D4C22×D1714yes—
529C4×D4C22×D1714yes—
530#117—28no—
531#117C22⋊D1714yes—
532#117C22×D1714yes—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—28no—
538C2×C4⋊C4—171no—
539C2×C4⋊C4—171no—
540C2×C4⋊C4—341no—
541C2×C4⋊C4—341no—
542C2×C4⋊C4C22⋊D1711yescharacteristic
543C2×C4⋊C4C22⋊D1711yescharacteristic
544C2×C4⋊C4C22×D1711yescharacteristic
545C2×C4⋊C4C22×D1711yescharacteristic
546C2×C4⋊C4C22×D1714yes—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—341no—
550C2×C22⋊C4—341no—
551C2×C22⋊C4—341no—
552C2×C22⋊C4—341no—
553C2×C22⋊C4C22⋊D1711yescharacteristic
554C2×C22⋊C4C22⋊D1711yescharacteristic
555C2×C42—21no—
556C2×C42—21no—
557C2×C42C22×D1711yescharacteristic
558C2×C42C22×D1711yescharacteristic
559#107—174no—
560#107—174no—
561#106—174no—
562#106—174no—
563C4⋊C8—174no—
564C4⋊C8—174no—
565#103—174no—
566#103—174no—
567#102—174no—
568#102—174no—
569#102—174no—
570#102—174no—
571#102—174no—
572#102—174no—
573C22⋊C8—174no—
574C22⋊C8—174no—
575#97—174no—
576C4×C8—174no—
577C17C2×#311911yescharacteristic, complemented, Sylow
578C24—21no—
579C24—341no—
580C24—341no—
581C24C2×C22⋊D1711yescharacteristic
582#41—216no—
583#41—28no—
584#41—28no—
585C2×Q8—22no—
586C2×Q8—21no—
587C2×Q8#6325214yes—
588C2×Q8C23×D1712yes—
589C2×D4—28no—
590C2×D4—24no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—172no—
594C2×D4—172no—
595C2×D4—344no—
596C2×D4—344no—
597C2×D4—342no—
598C2×D4—342no—
599C2×D4—342no—
600C2×D4—342no—
601C2×D4—341no—
602C2×D4—341no—
603C2×D4—344no—
604C2×D4—344no—
605C2×D4—1362no—
606C2×D4—1362no—
607C2×D4—1362no—
608C2×D4—1362no—
609C2×D4#6325214yes—
610C2×D4C23×D1712yes—
611C22×C4—28no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—82no—
622C22×C4—82no—
623C22×C4—82no—
624C22×C4—341no—
625C22×C4—341no—
626C22×C4—344no—
627C22×C4—344no—
628C22×C4—1362no—
629C22×C4—1362no—
630C22×C4C2×C22⋊D1712yes—
631C22×C4C2×C22⋊D1711yescharacteristic
632C22×C4C2×C22⋊D1711yescharacteristic
633C22×C4C2×C22⋊D1711yescharacteristic
634C22×C4C2×C22⋊D1711yescharacteristic
635C22×C4C2×C22⋊D1711yescharacteristic
636C22×C4C23×D1712yes—
637C22×C4C23×D1711yescharacteristic
638SD16—348no—
639SD16—348no—
640D8—348no—
641D8—348no—
642C2×C8—172no—
643C2×C8—172no—
644C2×C8—172no—
645C2×C8—172no—
646C2×C8—342no—
647C2×C8—342no—
648C2×C8—342no—
649C2×C8—342no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—172no—
656C4⋊C4—172no—
657C4⋊C4—341no—
658C4⋊C4—341no—
659C4⋊C4—344no—
660C4⋊C4—344no—
661C4⋊C4C2×C22⋊D1714yes—
662C4⋊C4C2×C22⋊D1714yes—
663C4⋊C4C23×D1712yes—
664C4⋊C4C23×D1712yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—344no—
668C22⋊C4—344no—
669C22⋊C4—344no—
670C22⋊C4—344no—
671C22⋊C4C2×C22⋊D1714yes—
672C22⋊C4C2×C22⋊D1714yes—
673C42—24no—
674C42—24no—
675C42C2×C22⋊D1712yes—
676C42C2×C22⋊D1712yes—
677C42C23×D1712yes—
678C42C23×D1712yes—
679C23—22no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—342no—
687C23—342no—
688C23—682no—
689C23—682no—
690C23—682no—
691C23—682no—
692C23—682no—
693C23—682no—
694C23C22×C22⋊D1712yes—
695C23C22×C22⋊D1711yescharacteristic
696Q8—24no—
697Q8—22no—
698Q8C2×#6325214yes—
699D4—216no—
700D4—24no—
701D4—22no—
702D4—342no—
703D4—342no—
704D4—342no—
705D4—342no—
706D4—682no—
707D4—682no—
708D4—1364no—
709D4—1364no—
710D4—1364no—
711D4—1364no—
712D4C2×#6325214yes—
713C2×C4—216no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—342no—
732C2×C4—342no—
733C2×C4—682no—
734C2×C4—682no—
735C2×C4—1364no—
736C2×C4—1364no—
737C2×C4C2×#6325212yes—
738C2×C4C2×#6325212yes—
739C2×C4C22×C22⋊D1712yes—
740C2×C4C22×C22⋊D1712yes—
741C2×C4C22×C22⋊D1712yes—
742C2×C4C22×C22⋊D1712yes—
743C2×C4C22×C22⋊D1712yes—
744C2×C4C22×C22⋊D1711yescharacteristic
745C2×C4C24×D1711yescharacteristic
746C8—342no—
747C8—342no—
748C8—342no—
749C8—342no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—44no—
757C22—48no—
758C22—682no—
759C22—682no—
760C22—682no—
761C22—682no—
762C22—682no—
763C22—682no—
764C22—1364no—
765C22—1364no—
766C22#1176332012yes—
767C22#1176361212yes—
768C22#1176361712yes—
769C22C23×C22⋊D1711yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—682no—
779C4—682no—
780C4#1176332012yes—
781C4C22×#6325211yescharacteristic
782C4C22×#6325211yescharacteristic
783C2—42no—
784C2—44no—
785C2—1362no—
786C2—1362no—
787C2#1453898314yesdirect product factor
788C2C2×#1176332011yescharacteristic
789C2C2×#1176361211yescharacteristic
790C2C2×#1176361711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#520C2
socleC23×C17C22×D4
hypercenterC2×#520D17
hypocenterC17C2×#3119
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#11763414C2semidirect
2. #14538983C2direct (N × H)
3. C2×#11763127C2semidirect
4. C2×#11763122C2semidirect
5. C2×#11763116C2semidirect
6. C2×#11763109C2semidirect
7. C2×#11763009C2semidirect
8. C2×#11763004C2semidirect
9. C2×#11762954C2semidirect
10. C2×#11762954C2semidirect
11. C2×#11762919C2semidirect
12. C2×#11762907C2semidirect
13. C2×C4×#63230C2semidirect
14. C2×C4×#63228C2semidirect
15. C2×#11762870C2semidirect
16. C2×C17×#520C2semidirect
22. #11763414C22semidirect
33. #11763127C22semidirect
34. #11763122C22semidirect
35. #11763116C22semidirect
36. #11763109C22semidirect
37. #11763009C22semidirect
38. #11763004C22semidirect
39. #11762954C22semidirect
40. #11762954C22semidirect
41. #11762919C22semidirect
42. #11762907C22semidirect
43. C4×#63230C22semidirect
44. C4×#63228C22semidirect
45. #11762870C22semidirect
66. C17×#520C22semidirect
356. C2×#520D17semidirect
420. #520C2×D17semidirect
466. C2×C17#3119semidirect
577. C17C2×#3119semidirect
787. C2#14538983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634142
#145389832
C2×#117631272
C2×#117631222
C2×#117631162
C2×#117631092
C2×#117630092
C2×#117630042
C2×#117629542
C2×#117629192
C2×#117629072
C2×C4×#632302
C2×C4×#632282
C2×#117628702
C2×C17×#5202
C2×#311917