Finite Group Databasebeta

← C2×#14537622 #17898428

Subgroups — C2×#14537622 #17898428

Order 4352.

2730 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587604C211yesmaximal, characteristic
2C2×#11763291C211yesmaximal, characteristic
3C2×#11763285C211yesmaximal, characteristic, complemented
4#14537622C2116yesmaximal, direct product factor
5C2×#11762916C211yesmaximal, characteristic, complemented
6C2×#11762914C211yesmaximal, characteristic, complemented
7C2×#11762908C211yesmaximal, characteristic, complemented
8C2×#11762907C211yesmaximal, characteristic, complemented
9C2×#11762901C211yesmaximal, characteristic, complemented
10C2×C4×#63219C211yesmaximal, characteristic, complemented
11C2×#11762894C211yesmaximal, characteristic, complemented
12C2×#11762850C211yesmaximal, characteristic, complemented
13C2×#11762804C211yesmaximal, characteristic
14C2×#103×D17C211yesmaximal, characteristic, complemented
15C2×#11762763C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C17C211yesmaximal, characteristic, complemented
17C22×#63256C2211yescharacteristic
18C22×Q8×D17C2211yescharacteristic
19C2×#10587604C4116yescomplemented
20C2×#10587604C2218yes—
21C22×#63231C2211yescharacteristic
22C22×#63219C2211yescharacteristic
23C22×#63230C2211yescharacteristic
24C22×#63218C2211yescharacteristic
25C22×C8×D17C2211yescharacteristic
26#11763291—24no—
27#11763291C2218yes—
28#11763285—24no—
29#11763285C2218yescomplemented
30C2×Q8×Dic17C2211yescharacteristic
31C2×Q8×Dic17C2211yescharacteristic
32C2×C4×Dic34—21no—
33C2×C4×Dic34C2211yescharacteristic
34C2×#10587573—21no—
35C2×#10587573C2211yescharacteristic
36C2×C4×D68—21no—
37C2×C4×D68C2211yescharacteristic
38C2×#10587579—21no—
39C2×#10587579C2211yescharacteristic
40C2×#10587578—21no—
41C2×#10587578C2211yescharacteristic
42C2×#10587558—21no—
43C2×#10587558—21no—
44C2×#10587558C2211yescharacteristic
45C2×C4⋊C4×D17—21no—
46C2×C4⋊C4×D17C2211yescharacteristic
47#11762916C2218yescomplemented
48#11762914C2218yescomplemented
49#11762908C2218yescomplemented
50#11762907C2218yescomplemented
51#11762901C2218yescomplemented
52C4×#63219C2218yescomplemented
53#11762894C2218yescomplemented
54#11762850C2218yescomplemented
55C2×#10587478C2211yescharacteristic
56C2×#10587488C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58#11762804C2218yes—
59C2×#10587487C2211yescharacteristic
60C2×#10587506C2211yescharacteristic
61C2×#10587506C2211yescharacteristic
62C2×#10587481C2211yescharacteristic
63#103×D17C2218yescomplemented
64C2×#10587492C2211yescharacteristic
65C2×#10587480C2211yescharacteristic
66#11762763C2218yescomplemented
67C2×#10587474C2211yescharacteristic
68C2×#10587486C2211yescharacteristic
69C2×C8×Dic17C2211yescharacteristic
70C22×Q16×C17C2211yescharacteristic
71C2×C4×Q8×C17C2211yescharacteristic
72C2×C4×Q8×C17C2211yescharacteristic
73C4×Q16×C17C2218yescomplemented
74C2×C17×#107C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×#103C2211yescharacteristic
77C2×C4×C8×C17C2211yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C22×Q8×C17C2311yescharacteristic
80C2×#63256—22no—
81C2×#63256—24no—
82C2×#63256C2×C418yes—
83C2×#63256C2314yes—
84C2×Q8×D17—22no—
85C2×Q8×D17—24no—
86C2×Q8×D17C2×C418yescomplemented
87C2×Q8×D17C2314yes—
88C22×D68—21no—
89C22×D68C2311yescharacteristic
90C22×C4×D17—21no—
91C22×C4×D17—21no—
92C22×C4×D17—21no—
93C22×C4×D17—21no—
94C22×C4×D17—21no—
95C22×C4×D17C2311yescharacteristic
96C22×Dic34—21no—
97C22×Dic34C2311yescharacteristic
98C2×Q16×C17C2×C418yescomplemented
99C2×Q16×C17C2314yes—
100C22×C8×C17C2311yescharacteristic
101C22×C8×C17C2311yescharacteristic
102C4×Q8×C17—22no—
103C4×Q8×C17—22no—
104C4×Q8×C17C2314yes—
105C4×Q8×C17C2314yes—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17C2311yescharacteristic
109C2×C4⋊C4×C17C2311yescharacteristic
110C2×C42×C17—21no—
111C2×C42×C17—21no—
112C2×C42×C17C2311yescharacteristic
113Q8×Dic17—22no—
114Q8×Dic17—22no—
115Q8×Dic17C2314yes—
116Q8×Dic17C2314yes—
117C2×#63231C2×C418yescomplemented
118C2×#63231C2314yes—
119C2×#63230C2×C418yescomplemented
120C2×#63230C2314yes—
121C2×#63227—21no—
122C2×#63227—21no—
123C2×#63227—21no—
124C2×#63227D411yescharacteristic
125C2×#63227D411yescharacteristic
126C2×C4⋊Dic17—21no—
127C2×C4⋊Dic17—21no—
128C2×C4⋊Dic17C2311yescharacteristic
129C2×C4⋊Dic17C2311yescharacteristic
130C2×#63225—21no—
131C2×#63225—21no—
132C2×#63225—21no—
133C2×#63225D411yescharacteristic
134C2×#63225D411yescharacteristic
135C2×C4×Dic17—21no—
136C2×C4×Dic17—21no—
137C2×C4×Dic17—21no—
138C2×C4×Dic17—21no—
139C2×C4×Dic17—21no—
140C2×C4×Dic17C2311yescharacteristic
141C22×#3622C2311yescharacteristic
142C22×#3622C2311yescharacteristic
143#10587604C2×C4164yescomplemented
144C2×#63219C2×C418yescomplemented
145C2×#63219C2314yes—
146C2×#63218C2×C418yescomplemented
147C2×#63218C2314yes—
148C2×C8×D17—24no—
149C2×C8×D17C2314yes—
150#10587579—28no—
151#10587579—22no—
152#10587579C2314yes—
153#10587578—28no—
154#10587578—22no—
155#10587578C2314yes—
156C4⋊C4×D17—28no—
157C4⋊C4×D17—22no—
158C4⋊C4×D17C2314yes—
159#10587573—28no—
160#10587573—22no—
161#10587573C2314yes—
162C4×D68—28no—
163C4×D68—22no—
164C4×D68C2314yes—
165#10587558—28no—
166#10587558—28no—
167#10587558D414yes—
168#10587558C2314yes—
169C4×Dic34—28no—
170C4×Dic34—22no—
171C4×Dic34C2314yes—
172C17×#107C2314yes—
173C17×#103C2314yes—
174C17×#103C2314yes—
175C4×C8×C17C2314yes—
176#10587506C2314yes—
177#10587506C2314yes—
178#10587492C2314yes—
179#10587488C2314yes—
180#10587487C2314yes—
181#10587486C2314yes—
182C8×Dic17C2314yes—
183#10587481C2314yes—
184#10587480C2314yes—
185#10587479C2314yes—
186#10587478C2314yes—
187#10587474C2314yes—
188C23×D17—21no—
189C23×D17C2×D411yescharacteristic
190C2×Q8×C17—21no—
191C2×Q8×C17—21no—
192C2×Q8×C17—22no—
193C2×Q8×C17—22no—
194C2×Q8×C17C22×C414yes—
195C2×Q8×C17C22×C414yes—
196C2×Q8×C17C2412yes—
197C2×Q8×C17C2412yes—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17C2×D411yescharacteristic
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2411yescharacteristic
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17C2×D411yescharacteristic
209C22×Dic17C2×D411yescharacteristic
210C22×Dic17C2×D411yescharacteristic
211#63256—216no—
212#63256—28no—
213#63256C22×C4116yes—
214Q8×D17—216no—
215Q8×D17—28no—
216Q8×D17C22×C4116yescomplemented
217C2×D68—28no—
218C2×D68—24no—
219C2×D68—21no—
220C2×D68—22no—
221C2×D68C22×C414yes—
222C2×D68C2412yes—
223C2×C4×D17—28no—
224C2×C4×D17—24no—
225C2×C4×D17—28no—
226C2×C4×D17—24no—
227C2×C4×D17—24no—
228C2×C4×D17—24no—
229C2×C4×D17—24no—
230C2×C4×D17—82no—
231C2×C4×D17—82no—
232C2×C4×D17—82no—
233C2×C4×D17C22×C414yes—
234C2×C4×D17C2×D412yes—
235C2×C4×D17#4114yes—
236C2×C4×D17C2412yes—
237C2×Dic34—21no—
238C2×Dic34—22no—
239C2×Dic34—28no—
240C2×Dic34—24no—
241C2×Dic34C22×C414yes—
242C2×Dic34C2412yes—
243Q16×C17C22×C4116yescomplemented
244C2×C8×C17—22no—
245C2×C8×C17C22×C414yes—
246C2×C8×C17C2412yes—
247C2×C8×C17C2412yes—
248C4⋊C4×C17—24no—
249C4⋊C4×C17—21no—
250C4⋊C4×C17—24no—
251C4⋊C4×C17—21no—
252C4⋊C4×C17C2412yes—
253C4⋊C4×C17C2412yes—
254C42×C17—24no—
255C42×C17—24no—
256C42×C17C2×D412yes—
257C42×C17C2412yes—
258#63231C22×C4116yescomplemented
259#63230C22×C4116yescomplemented
260#63227—24no—
261#63227—24no—
262#63227—24no—
263#63227C2×D414yes—
264#63227C2×D414yes—
265C4⋊Dic17—21no—
266C4⋊Dic17—21no—
267C4⋊Dic17—24no—
268C4⋊Dic17—24no—
269C4⋊Dic17C2412yes—
270C4⋊Dic17C2412yes—
271#63225—24no—
272#63225—24no—
273#63225—24no—
274#63225C2×D414yes—
275#63225C2×D414yes—
276C4×Dic17—24no—
277C4×Dic17—24no—
278C4×Dic17—24no—
279C4×Dic17—24no—
280C4×Dic17—24no—
281C4×Dic17C2×D412yes—
282C4×Dic17C2412yes—
283C2×#3622—22no—
284C2×#3622C22×C414yes—
285C2×#3622C2412yes—
286C2×#3622C2412yes—
287#63219C22×C4116yescomplemented
288#63218C22×C4116yescomplemented
289C8×D17—28no—
290C2×#2947—171nomaximal, Sylow
291C23×C17C22×D411yescharacteristic
292C22×D17—22no—
293C22×D17—22no—
294C22×D17—24no—
295C22×D17—22no—
296C22×D17—42no—
297C22×D17—42no—
298C22×D17C4×D414yes—
299C22×D17C22×D412yes—
300Q8×C17—24no—
301Q8×C17—24no—
302Q8×C17—22no—
303Q8×C17—22no—
304Q8×C17C23×C414yes—
305Q8×C17C23×C414yes—
306C2×C4×C17—24no—
307C2×C4×C17—24no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—42no—
315C2×C4×C17—42no—
316C2×C4×C17C23×C412yes—
317C2×C4×C17C22×D412yes—
318C2×C4×C17C22×D412yes—
319C2×C4×C17C22×D411yescharacteristic
320C2×C4×C17C2×#4112yes—
321C2×C4×C17C2511yescharacteristic
322C2×Dic17—24no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—42no—
329C2×Dic17—42no—
330C2×Dic17C4×D414yes—
331C2×Dic17C22×D412yes—
332C2×Dic17C22×D412yes—
333C2×Dic17C22×D412yes—
334D68—216no—
335D68—24no—
336D68—22no—
337D68C23×C414yes—
338C4×D17—216no—
339C4×D17—216no—
340C4×D17—84no—
341C4×D17—84no—
342C4×D17—84no—
343C4×D17C4×D418yes—
344C4×D17C23×C414yes—
345C4×D17C2×#4114yes—
346Dic34—24no—
347Dic34—22no—
348Dic34—216no—
349Dic34C23×C414yes—
350C8×C17—22no—
351C8×C17C23×C414yes—
352#3622—22no—
353#3622C23×C414yes—
354C22×#137—171no—
355C2×#520—171no—
356C2×#519—171no—
357#2947—1716no—
358C2×#441—171no—
359C2×#441—171no—
360C2×#440—171no—
361C2×#440—171no—
362C2×C4×Q16—171no—
363C2×C4×Q16D1711yescharacteristic, complemented
364C2×C4×SD16—171no—
365C2×C4×SD16—171no—
366C2×#428—171no—
367C2×#416—171no—
368C22×#103—171no—
369C2×#405—171no—
370C22×C17C2×C4×D412yes—
371C22×C17#57712yes—
372C22×C17#57812yes—
373C22×C17C23×D411yescharacteristic
374C2×D17—28no—
375C2×D17—22no—
376C2×D17—22no—
377C2×D17—24no—
378C2×D17—48no—
379C2×D17—42no—
380C2×D17—42no—
381C2×D17C2×C4×D414yes—
382C4×C17—24no—
383C4×C17—24no—
384C4×C17—22no—
385C4×C17—22no—
386C4×C17—42no—
387C4×C17—42no—
388C4×C17C2×C4×D412yes—
389C4×C17C24×C411yescharacteristic
390C4×C17C22×#4111yescharacteristic
391Dic17—24no—
392Dic17—22no—
393Dic17—22no—
394Dic17—42no—
395Dic17—42no—
396Dic17C2×C4×D414yes—
397C22×#41—171no—
398C23×Q8—171no—
399C2×#137—1716no—
400C2×#137—178no—
401C22×Q16—171no—
402C22×Q16C2×D1711yescharacteristic
403C22×SD16—171no—
404C22×SD16—171no—
405C22×M16—171no—
406C23×C8—171no—
407#520—178no—
408#520—344no—
409#519—178no—
410#519—344no—
411C2×C4×Q8—171no—
412C2×C4×Q8—171no—
413C2×C4×Q8—171no—
414C2×C4×Q8—171no—
415C2×C4×Q8—341no—
416C2×C4×Q8—341no—
417C2×C4×Q8C2×D1711yescharacteristic
418C2×C4×Q8C2×D1711yescharacteristic
419C2×C4×D4—171no—
420C2×C4×D4—171no—
421C2×C4×D4—341no—
422C2×C4×D4—341no—
423C2×#117—171no—
424C2×#117—171no—
425C2×#117—341no—
426C2×#117—341no—
427C2×#117—341no—
428C22×C4⋊C4—171no—
429C22×C4⋊C4—341no—
430#441—178no—
431#441—178no—
432#440—178no—
433#440—178no—
434C4×Q16—178no—
435C4×Q16C2×D1718yescomplemented
436C4×SD16—178no—
437C4×SD16—178no—
438#428—178no—
439C2×#107—171no—
440C2×#107C2×D1711yescharacteristic
441C2×#106—171no—
442C2×#106—171no—
443#416—178no—
444C2×#103—171no—
445C2×#103—171no—
446C2×#103—171no—
447C2×#103—171no—
448C2×#103—178no—
449C2×#103C2×D1711yescharacteristic
450C2×#103C2×D1711yescharacteristic
451C2×#102—171no—
452C2×#102—171no—
453#405—178no—
454C2×#97—171no—
455C2×#97—171no—
456C2×C4×C8—171no—
457C2×C4×C8C2×D1711yescharacteristic
458C2×C17#294714yescomplemented
459C2×C17C22×C4×D411yescharacteristic
460C2×C17C2×#57711yescharacteristic
461C2×C17C2×#57811yescharacteristic
462D17—24no—
463D17—44no—
464C2×#41—178no—
465C2×#41—174no—
466C2×#41—342no—
467C2×#41—344no—
468C22×Q8—178no—
469C22×Q8—174no—
470C22×Q8—171no—
471C22×Q8—341no—
472C22×Q8—342no—
473C22×Q8—344no—
474C22×Q8C22×D1711yescharacteristic
475C22×Q8C22×D1711yescharacteristic
476C22×D4—171no—
477C22×D4—341no—
478C23×C4—171no—
479C23×C4—341no—
480C23×C4—341no—
481C23×C4—341no—
482C23×C4—341no—
483C23×C4—341no—
484#137—1764no—
485C2×Q16—178no—
486C2×Q16—174no—
487C2×Q16C4×D1718yescomplemented
488C2×Q16C22×D1714yes—
489C2×SD16—178no—
490C2×SD16—174no—
491C2×SD16—178no—
492C2×SD16—174no—
493C2×M16—178no—
494C2×M16—174no—
495C22×C8—171no—
496C22×C8—171no—
497C22×C8—174no—
498C22×C8—344no—
499C22×C8C22×D1711yescharacteristic
500C22×C8C22×D1711yescharacteristic
501C4×Q8—22no—
502C4×Q8—22no—
503C4×Q8—174no—
504C4×Q8—174no—
505C4×Q8—174no—
506C4×Q8—174no—
507C4×Q8—348no—
508C4×Q8—342no—
509C4×Q8—342no—
510C4×Q8—342no—
511C4×Q8—348no—
512C4×Q8—342no—
513C4×Q8C22×D1714yes—
514C4×Q8C22×D1714yes—
515C4×D4—174no—
516C4×D4—174no—
517C4×D4—348no—
518C4×D4—342no—
519C4×D4—348no—
520C4×D4—342no—
521#117—174no—
522#117—174no—
523#117—174no—
524#117—348no—
525#117—348no—
526#117—348no—
527#117—342no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—171no—
531C2×C4⋊C4—171no—
532C2×C4⋊C4—171no—
533C2×C4⋊C4—171no—
534C2×C4⋊C4—174no—
535C2×C4⋊C4—348no—
536C2×C4⋊C4—342no—
537C2×C4⋊C4—341no—
538C2×C4⋊C4—341no—
539C2×C4⋊C4—341no—
540C2×C4⋊C4—341no—
541C2×C4⋊C4—341no—
542C2×C4⋊C4C22×D1711yescharacteristic
543C2×C4⋊C4C22×D1711yescharacteristic
544C2×C22⋊C4—171no—
545C2×C22⋊C4—171no—
546C2×C22⋊C4—341no—
547C2×C22⋊C4—341no—
548C2×C22⋊C4—341no—
549C2×C42—21no—
550C2×C42—21no—
551C2×C42—171no—
552C2×C42—341no—
553C2×C42—341no—
554C2×C42—341no—
555C2×C42—341no—
556C2×C42—341no—
557C2×C42C22×D1711yescharacteristic
558#107—174no—
559#107C22×D1714yes—
560#106—174no—
561#106—174no—
562#103—174no—
563#103—174no—
564#103—174no—
565#103—174no—
566#103C22×D1714yes—
567#103C22×D1714yes—
568#102—174no—
569#102—174no—
570#97—174no—
571#97—174no—
572C4×C8—174no—
573C4×C8C22×D1714yes—
574C17C2×#294711yescharacteristic, complemented, Sylow
575C24—171no—
576C24—341no—
577#41—1716no—
578#41—3416no—
579#41—348no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—1716no—
585C2×Q8—174no—
586C2×Q8—172no—
587C2×Q8—344no—
588C2×Q8—348no—
589C2×Q8—3416no—
590C2×Q8—348no—
591C2×Q8—341no—
592C2×Q8—342no—
593C2×Q8C2×C4×D1714yes—
594C2×Q8C2×C4×D1714yes—
595C2×Q8C23×D1712yes—
596C2×Q8C23×D1712yes—
597C2×D4—174no—
598C2×D4—172no—
599C2×D4—344no—
600C2×D4—348no—
601C2×D4—341no—
602C2×D4—342no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—171no—
608C22×C4—174no—
609C22×C4—172no—
610C22×C4—174no—
611C22×C4—172no—
612C22×C4—171no—
613C22×C4—171no—
614C22×C4—344no—
615C22×C4—348no—
616C22×C4—344no—
617C22×C4—344no—
618C22×C4—348no—
619C22×C4—344no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—341no—
623C22×C4—344no—
624C22×C4—1362no—
625C22×C4—1362no—
626C22×C4—1362no—
627C22×C4D4×D1711yescharacteristic
628C22×C4D4×D1711yescharacteristic
629C22×C4C23×D1711yescharacteristic
630Q16—1716no—
631Q16C2×C4×D17116yescomplemented
632SD16—1716no—
633SD16—1716no—
634M16—1716no—
635C2×C8—22no—
636C2×C8—174no—
637C2×C8—172no—
638C2×C8—172no—
639C2×C8—348no—
640C2×C8—342no—
641C2×C8C2×C4×D1714yes—
642C2×C8C23×D1712yes—
643C2×C8C23×D1712yes—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—174no—
649C4⋊C4—174no—
650C4⋊C4—172no—
651C4⋊C4—172no—
652C4⋊C4—344no—
653C4⋊C4—344no—
654C4⋊C4—344no—
655C4⋊C4—344no—
656C4⋊C4—341no—
657C4⋊C4—341no—
658C4⋊C4—344no—
659C4⋊C4C23×D1712yes—
660C4⋊C4C23×D1712yes—
661C22⋊C4—174no—
662C22⋊C4—174no—
663C22⋊C4—344no—
664C22⋊C4—344no—
665C22⋊C4—344no—
666C42—24no—
667C42—24no—
668C42—172no—
669C42—172no—
670C42—344no—
671C42—344no—
672C42—344no—
673C42—344no—
674C42—344no—
675C42D4×D1712yes—
676C42C23×D1712yes—
677C23—174no—
678C23—172no—
679C23—342no—
680C23—342no—
681C23—344no—
682C23—342no—
683C23—682no—
684C23—682no—
685C23C2×D4×D1711yescharacteristic
686Q8—24no—
687Q8—24no—
688Q8—22no—
689Q8—22no—
690Q8—174no—
691Q8—3416no—
692Q8—344no—
693Q8—342no—
694Q8C22×C4×D1714yes—
695Q8C22×C4×D1714yes—
696D4—174no—
697D4—3416no—
698D4—344no—
699D4—342no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—174no—
711C2×C4—172no—
712C2×C4—178no—
713C2×C4—174no—
714C2×C4—174no—
715C2×C4—172no—
716C2×C4—172no—
717C2×C4—3416no—
718C2×C4—3416no—
719C2×C4—344no—
720C2×C4—342no—
721C2×C4—342no—
722C2×C4—342no—
723C2×C4—342no—
724C2×C4—342no—
725C2×C4—682no—
726C2×C4—682no—
727C2×C4—1364no—
728C2×C4—1364no—
729C2×C4—1364no—
730C2×C4C22×C4×D1712yes—
731C2×C4C2×D4×D1712yes—
732C2×C4C2×D4×D1712yes—
733C2×C4C2×D4×D1711yescharacteristic
734C2×C4#41×D1712yes—
735C2×C4C24×D1711yescharacteristic
736C8—22no—
737C8—174no—
738C8—342no—
739C8C22×C4×D1714yes—
740C22—174no—
741C22—348no—
742C22—342no—
743C22—342no—
744C22—344no—
745C22—688no—
746C22—682no—
747C22—682no—
748C22C4×D4×D1712yes—
749C22#1176361612yes—
750C22#1176362212yes—
751C22C22×D4×D1711yescharacteristic
752C4—24no—
753C4—24no—
754C4—22no—
755C4—22no—
756C4—42no—
757C4—42no—
758C4—174no—
759C4—344no—
760C4—342no—
761C4—342no—
762C4—682no—
763C4—682no—
764C4C4×D4×D1712yes—
765C4C23×C4×D1711yescharacteristic
766C4C2×#41×D1711yescharacteristic
767C2—344no—
768C2—684no—
769C2#1453762214yesdirect product factor
770C2C2×C4×D4×D1711yescharacteristic
771C2C2×#1176361611yescharacteristic
772C2C2×#1176362211yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C4×Q16×C17C2
socleC23×C17C22×D4
prime radicalC22×#63256C22
cosocleC2×C4×C17C25
hypercenterC2×C4×Q16D17
hypocenterC17C2×#2947
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×#11763285C2semidirect
4. #14537622C2direct (N × H)
5. C2×#11762916C2semidirect
6. C2×#11762914C2semidirect
7. C2×#11762908C2semidirect
8. C2×#11762907C2semidirect
9. C2×#11762901C2semidirect
10. C2×C4×#63219C2semidirect
11. C2×#11762894C2semidirect
12. C2×#11762850C2semidirect
14. C2×#103×D17C2semidirect
15. C2×#11762763C2semidirect
16. C2×C4×Q16×C17C2semidirect
19. C2×#10587604C4semidirect
29. #11763285C22semidirect
47. #11762916C22semidirect
48. #11762914C22semidirect
49. #11762908C22semidirect
50. #11762907C22semidirect
51. #11762901C22semidirect
52. C4×#63219C22semidirect
53. #11762894C22semidirect
54. #11762850C22semidirect
63. #103×D17C22semidirect
66. #11762763C22semidirect
73. C4×Q16×C17C22semidirect
86. C2×Q8×D17C2×C4semidirect
98. C2×Q16×C17C2×C4semidirect
117. C2×#63231C2×C4semidirect
119. C2×#63230C2×C4semidirect
143. #10587604C2×C4semidirect
144. C2×#63219C2×C4semidirect
146. C2×#63218C2×C4semidirect
216. Q8×D17C22×C4semidirect
243. Q16×C17C22×C4semidirect
258. #63231C22×C4semidirect
259. #63230C22×C4semidirect
287. #63219C22×C4semidirect
288. #63218C22×C4semidirect
363. C2×C4×Q16D17semidirect
435. C4×Q16C2×D17semidirect
458. C2×C17#2947semidirect
487. C2×Q16C4×D17semidirect
574. C17C2×#2947semidirect
631. Q16C2×C4×D17semidirect
769. C2#14537622direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876042
C2×#117632912
C2×#117632852
#145376222
C2×#117629162
C2×#117629142
C2×#117629082
C2×#117629072
C2×#117629012
C2×C4×#632192
C2×#117628942
C2×#117628502
C2×#117628042
C2×#103×D172
C2×#117627632
C2×C4×Q16×C172
C2×#294717