Finite Group Databasebeta

← C2×#14541052 #17911193

Subgroups — C2×#14541052 #17911193

Order 4352.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763499C211yesmaximal, characteristic, complemented
2#14541052C2116yesmaximal, direct product factor
3C2×#11763163C211yesmaximal, characteristic, complemented
4C2×#11763142C211yesmaximal, characteristic, complemented
5C2×#11763130C211yesmaximal, characteristic, complemented
6C2×#11763116C211yesmaximal, characteristic, complemented
7C2×#11763065C211yesmaximal, characteristic, complemented
8C2×#11763053C211yesmaximal, characteristic, complemented
9C2×#11763028C211yesmaximal, characteristic, complemented
10C2×#11762971C211yesmaximal, characteristic, complemented
11C2×#11762965C211yesmaximal, characteristic, complemented
12C2×C4×#63231C211yesmaximal, characteristic, complemented
13C2×#11762887C211yesmaximal, characteristic, complemented
14C2×#11762810C211yesmaximal, characteristic, complemented
15C2×#11762818C211yesmaximal, characteristic, complemented
16C2×C17×#548C211yesmaximal, characteristic
17C22×#63231C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63229C2211yescharacteristic
20C22×#63223C2211yescharacteristic
21C22×#63223C2211yescharacteristic
22#11763499—24no—
23#11763499C2218yescomplemented
24C2×#10587565—21no—
25C2×#10587556C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587621—21no—
28C2×#10587610C2211yescharacteristic
29C2×#10587610C2211yescharacteristic
30C2×C4×Dic34C2211yescharacteristic
31C2×#10587612C2211yescharacteristic
32C2×#10587563—21no—
33C22×C4⋊Dic17C2211yescharacteristic
34#11763163C2218yescomplemented
35#11763142C2218yescomplemented
36#11763130C2218yescomplemented
37#11763116C2218yescomplemented
38#11763065C2218yescomplemented
39#11763053C2218yescomplemented
40#11763028C2218yescomplemented
41#11762971C2218yescomplemented
42#11762965C2218yescomplemented
43C4×#63231C2218yescomplemented
44#11762887C2218yescomplemented
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49#11762818C2218yescomplemented
50#11762810C2218yescomplemented
51C2×#10587506C2211yescharacteristic
52C2×#10587506C2211yescharacteristic
53C2×#10587506C2211yescharacteristic
54C2×#10587506C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×#10587503C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C22×#41×C17C2211yescharacteristic
65C23×Q8×C17C2211yescharacteristic
66C17×#548—24no—
67C17×#548C2218yes—
68C2×C17×#124—21no—
69C2×C17×#124C2211yescharacteristic
70C2×C17×C22⋊Q8—21no—
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C17×#121—21no—
73C2×C17×#121C2211yescharacteristic
74C2×C4×Q8×C17C2211yescharacteristic
75C2×C4×D4×C17—21no—
76C2×C4×D4×C17C2211yescharacteristic
77C2×#41×C17—22no—
78C2×#41×C17—24no—
79C2×#41×C17—42no—
80C2×#41×C17C2314yes—
81C22×Q8×C17—21no—
82C22×Q8×C17—22no—
83C22×Q8×C17—24no—
84C22×Q8×C17—42no—
85C22×Q8×C17C2311yescharacteristic
86C22×Q8×C17C2314yes—
87C22×Q8×C17C2311yescharacteristic
88C22×D4×C17—21no—
89C22×D4×C17—21no—
90C22×D4×C17D411yescharacteristic
91C22×D4×C17C2311yescharacteristic
92C23×C4×C17—21no—
93C23×C4×C17—21no—
94C23×C4×C17C2311yescharacteristic
95C23×C4×C17C2311yescharacteristic
96C23×Dic17—21no—
97C22×Dic34C2311yescharacteristic
98C17×#124—28no—
99C17×#124—22no—
100C17×#124C2314yes—
101C17×C22⋊Q8—22no—
102C17×C22⋊Q8—28no—
103C17×C22⋊Q8C2314yes—
104C17×#121—28no—
105C17×#121—22no—
106C17×#121C2314yes—
107C4×Q8×C17—22no—
108C4×Q8×C17C2314yes—
109C4×D4×C17—28no—
110C4×D4×C17D414yes—
111C4×D4×C17C2314yes—
112C2×C4⋊C4×C17—21no—
113C2×C4⋊C4×C17—21no—
114C2×C4⋊C4×C17D411yescharacteristic
115C2×C4⋊C4×C17C2311yescharacteristic
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17—21no—
119C2×C22⋊C4×C17—21no—
120C2×C22⋊C4×C17D411yescharacteristic
121C2×C22⋊C4×C17D411yescharacteristic
122C2×C42×C17—21no—
123C2×C42×C17C2311yescharacteristic
124C2×C22⋊Dic17—21no—
125C2×C22⋊Dic17—21no—
126C2×C22⋊Dic17—21no—
127C2×#63231—24no—
128C2×#63231—42no—
129C2×#63231C2314yes—
130C2×#63231C2314yes—
131#10587621—28no—
132C2×#63229—42no—
133C2×#63229C2314yes—
134#10587612—22no—
135#10587612C2314yes—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—21no—
138C2×C4⋊Dic17C2314yes—
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141C2×C4⋊Dic17C2311yescharacteristic
142#10587610—22no—
143#10587610—22no—
144#10587610C2314yes—
145#10587610C2314yes—
146C2×#63225—21no—
147C2×#63225—21no—
148C2×#63225—21no—
149C2×#63225—21no—
150C2×#63225—21no—
151C2×C4×Dic17—21no—
152C2×C4×Dic17—21no—
153C2×#63223—42no—
154C2×#63223—42no—
155C2×#63223C2314yes—
156C2×#63223C2314yes—
157C22×#3622C2311yescharacteristic
158C22×#3622C2311yescharacteristic
159C22×#3622C2311yescharacteristic
160C22×#3622C2311yescharacteristic
161#10587575—28no—
162#10587565—28no—
163#10587563—28no—
164#10587556—22no—
165#10587556C2314yes—
166C4×Dic34—22no—
167C4×Dic34C2314yes—
168#10587506C2314yes—
169#10587506C2314yes—
170#10587506C2314yes—
171#10587506C2314yes—
172#10587506C2314yes—
173#10587506C2314yes—
174#10587503C2314yes—
175#10587503C2314yes—
176#10587503C2314yes—
177C22⋊#3622C2314yes—
178C22⋊#3622C2314yes—
179#10587481C2314yes—
180#10587479C2314yes—
181#10587478C2314yes—
182#10587478C2314yes—
183C4⋊#3622C2314yes—
184C4×#3622C2314yes—
185C24×C17—21no—
186C24×C17C2×D411yescharacteristic
187C24×C17C2×D411yescharacteristic
188#41×C17—28no—
189#41×C17—44no—
190#41×C17—48no—
191C2×Q8×C17—21no—
192C2×Q8×C17—24no—
193C2×Q8×C17—21no—
194C2×Q8×C17—22no—
195C2×Q8×C17—28no—
196C2×Q8×C17—22no—
197C2×Q8×C17—22no—
198C2×Q8×C17—44no—
199C2×Q8×C17—44no—
200C2×Q8×C17—48no—
201C2×Q8×C17#4114yes—
202C2×Q8×C17C2412yes—
203C2×Q8×C17C2412yes—
204C2×D4×C17—24no—
205C2×D4×C17—24no—
206C2×D4×C17—21no—
207C2×D4×C17—22no—
208C2×D4×C17—22no—
209C2×D4×C17—42no—
210C2×D4×C17—44no—
211C2×D4×C17—44no—
212C2×D4×C17C2×D414yes—
213C2×D4×C17C2412yes—
214C22×C4×C17—21no—
215C22×C4×C17—22no—
216C22×C4×C17—22no—
217C22×C4×C17—22no—
218C22×C4×C17—22no—
219C22×C4×C17—21no—
220C22×C4×C17—24no—
221C22×C4×C17—21no—
222C22×C4×C17—24no—
223C22×C4×C17—44no—
224C22×C4×C17—44no—
225C22×C4×C17C2×D412yes—
226C22×C4×C17C2×D411yescharacteristic
227C22×C4×C17C2×D411yescharacteristic
228C22×C4×C17C2×D412yes—
229C22×C4×C17C2×D411yescharacteristic
230C22×C4×C17C2×D411yescharacteristic
231C22×C4×C17C2412yes—
232C22×C4×C17C2412yes—
233C22×C4×C17C2411yescharacteristic
234C22×Dic17—21no—
235C22×Dic17—24no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—44no—
240C2×Dic34—22no—
241C2×Dic34—22no—
242C2×Dic34—21no—
243C2×Dic34C2412yes—
244C4⋊C4×C17—24no—
245C4⋊C4×C17—24no—
246C4⋊C4×C17—21no—
247C4⋊C4×C17C2×D414yes—
248C4⋊C4×C17C2412yes—
249C22⋊C4×C17—24no—
250C22⋊C4×C17—24no—
251C22⋊C4×C17—24no—
252C22⋊C4×C17—24no—
253C22⋊C4×C17C2×D414yes—
254C22⋊C4×C17C2×D414yes—
255C42×C17—24no—
256C42×C17C2×D412yes—
257C42×C17C2412yes—
258C22⋊Dic17—24no—
259C22⋊Dic17—24no—
260C22⋊Dic17—24no—
261#63231—28no—
262#63231—44no—
263#63229—44no—
264C4⋊Dic17—21no—
265C4⋊Dic17—21no—
266C4⋊Dic17—21no—
267C4⋊Dic17—24no—
268C4⋊Dic17C2412yes—
269C4⋊Dic17C2412yes—
270C4⋊Dic17C2412yes—
271#63225—24no—
272#63225—24no—
273#63225—24no—
274#63225—24no—
275#63225—24no—
276C4×Dic17—24no—
277C4×Dic17—24no—
278#63223—44no—
279#63223—44no—
280C2×#3622—22no—
281C2×#3622—22no—
282C2×#3622—22no—
283C2×#3622—22no—
284C2×#3622C2412yes—
285C2×#3622C2412yes—
286C2×#3622C2412yes—
287C2×#3622C2412yes—
288C2×#3327—171nomaximal, Sylow
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—42no—
297C23×C17—42no—
298C23×C17—42no—
299C23×C17C22×D412yes—
300C23×C17C22×D412yes—
301C23×C17C22×D411yescharacteristic
302Q8×C17—24no—
303Q8×C17—22no—
304Q8×C17—22no—
305Q8×C17—22no—
306Q8×C17—48no—
307Q8×C17—42no—
308Q8×C17C2×#4114yes—
309D4×C17—22no—
310D4×C17—22no—
311D4×C17—44no—
312D4×C17—48no—
313D4×C17—48no—
314D4×C17—42no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—24no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—24no—
322C2×C4×C17—24no—
323C2×C4×C17—22no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—48no—
330C2×C4×C17—48no—
331C2×C4×C17—42no—
332C2×C4×C17—42no—
333C2×C4×C17C22×D412yes—
334C2×C4×C17C22×D412yes—
335C2×C4×C17C22×D412yes—
336C2×C4×C17C22×D412yes—
337C2×C4×C17C22×D411yescharacteristic
338C2×C4×C17C2×#4112yes—
339C2×C4×C17H(5,𝔽2)12yes—
340C2×C4×C17C2511yescharacteristic
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—22no—
344C2×Dic17—22no—
345C2×Dic17—48no—
346C2×Dic17—42no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C2×Dic17—42no—
350Dic34—22no—
351Dic34—22no—
352Dic34—42no—
353#3622—22no—
354#3622—22no—
355#3622—22no—
356#3622—22no—
357C2×#552—171no—
358C2×#548D1711yescharacteristic
359#3327—1716no—
360C2×#488—171no—
361C2×#484—171no—
362C2×#482—171no—
363C2×#479—171no—
364C2×#470—171no—
365C2×#468—171no—
366C2×#464—171no—
367C2×#452—171no—
368C2×#451—171no—
369C2×C4×Q16—171no—
370C2×#436—171no—
371C2×#417—171no—
372C2×#419—171no—
373C22×C17—22no—
374C22×C17—22no—
375C22×C17—22no—
376C22×C17—22no—
377C22×C17—22no—
378C22×C17—22no—
379C22×C17—44no—
380C22×C17—44no—
381C22×C17—42no—
382C22×C17—42no—
383C22×C17—42no—
384C22×C17—84no—
385C22×C17#54612yes—
386C22×C17#57512yes—
387C22×C17#57812yes—
388C22×C17C23×D411yescharacteristic
389C4×C17—22no—
390C4×C17—22no—
391C4×C17—24no—
392C4×C17—22no—
393C4×C17—22no—
394C4×C17—42no—
395C4×C17—42no—
396C4×C17#54612yes—
397C4×C17C22×#4111yescharacteristic
398C4×C17C2×H(5,𝔽2)11yescharacteristic
399Dic17—42no—
400Dic17—42no—
401Dic17—42no—
402Dic17—42no—
403C22×#41C2×D1711yescharacteristic
404C23×Q8C2×D1711yescharacteristic
405C22×Q16—171no—
406C22×Q16—171no—
407C22×SD16—171no—
408C22×M16—171no—
409C22×M16—171no—
410#552—178no—
411#552—344no—
412#548—24no—
413#548C2×D1718yes—
414C2×#126—341no—
415C2×#125—171no—
416C2×#125—341no—
417C2×#124—21no—
418C2×#124C2×D1711yescharacteristic
419C2×#123—341no—
420C2×C22⋊Q8—21no—
421C2×C22⋊Q8—171no—
422C2×C22⋊Q8—171no—
423C2×C22⋊Q8C2×D1711yescharacteristic
424C2×#121—21no—
425C2×#121C2×D1711yescharacteristic
426C2×C4×Q8—171no—
427C2×C4×Q8C2×D1711yescharacteristic
428C2×C4×D4—21no—
429C2×C4×D4C2×D1711yescharacteristic
430C2×#117—171no—
431C2×#117—341no—
432C22×C4⋊C4—171no—
433#488—178no—
434#484—178no—
435#482—178no—
436#479—178no—
437#470—178no—
438#468—178no—
439#464—178no—
440#452—178no—
441#451—178no—
442C4×Q16—178no—
443#436—178no—
444C2×#107—171no—
445C2×#107—171no—
446C2×#106—171no—
447C2×C4⋊C8—171no—
448#419—178no—
449#417—178no—
450C2×#103—171no—
451C2×#103—171no—
452C2×#103—171no—
453C2×#103—171no—
454C2×#103—171no—
455C2×#103—171no—
456C2×#103—171no—
457C2×#102—171no—
458C2×#102—171no—
459C2×#102—171no—
460C2×C22⋊C8—171no—
461C2×C22⋊C8—171no—
462C2×C4×C8—171no—
463C2×C17—42no—
464C2×C17—42no—
465C2×C17—82no—
466C2×C17#332714yescomplemented
467C2×C17C2×#54611yescharacteristic
468C2×C17C2×#57511yescharacteristic
469C2×C17C2×#57811yescharacteristic
470C2×#41—22no—
471C2×#41—24no—
472C2×#41—42no—
473C2×#41C22×D1714yes—
474C22×Q8—21no—
475C22×Q8—22no—
476C22×Q8—24no—
477C22×Q8—42no—
478C22×Q8—171no—
479C22×Q8C22×D1711yescharacteristic
480C22×Q8C22×D1714yes—
481C22×Q8C22×D1711yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C22⋊D1711yescharacteristic
485C22×D4C22×D1711yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—341no—
489C23×C4C22×D1711yescharacteristic
490C23×C4C22×D1711yescharacteristic
491C2×Q16—174no—
492C2×Q16—174no—
493C2×Q16—344no—
494C2×Q16—682no—
495C2×SD16—174no—
496C2×SD16—682no—
497C2×M16—174no—
498C2×M16—174no—
499C2×M16—682no—
500C2×M16—682no—
501C22×C8—171no—
502C22×C8—171no—
503C22×C8—171no—
504C22×C8—171no—
505#126—348no—
506#125—174no—
507#125—348no—
508#125—342no—
509#124—28no—
510#124—22no—
511#124C22×D1714yes—
512#123—348no—
513C22⋊Q8—22no—
514C22⋊Q8—28no—
515C22⋊Q8—174no—
516C22⋊Q8—174no—
517C22⋊Q8—342no—
518C22⋊Q8—342no—
519C22⋊Q8C22×D1714yes—
520#121—28no—
521#121—22no—
522#121C22×D1714yes—
523C4×Q8—22no—
524C4×Q8—174no—
525C4×Q8—342no—
526C4×Q8C22×D1714yes—
527C4×D4—28no—
528C4×D4C22⋊D1714yes—
529C4×D4C22×D1714yes—
530#117—174no—
531#117—342no—
532#117—348no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—171no—
536C2×C4⋊C4—171no—
537C2×C4⋊C4—174no—
538C2×C4⋊C4—171no—
539C2×C4⋊C4—341no—
540C2×C4⋊C4—342no—
541C2×C4⋊C4—341no—
542C2×C4⋊C4—341no—
543C2×C4⋊C4—341no—
544C2×C4⋊C4—341no—
545C2×C4⋊C4—341no—
546C2×C4⋊C4C22⋊D1711yescharacteristic
547C2×C4⋊C4C22×D1711yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—341no—
553C2×C22⋊C4—341no—
554C2×C22⋊C4—341no—
555C2×C22⋊C4C22⋊D1711yescharacteristic
556C2×C22⋊C4C22⋊D1711yescharacteristic
557C2×C42—21no—
558C2×C42—341no—
559C2×C42—341no—
560C2×C42C22×D1711yescharacteristic
561#107—174no—
562#107—174no—
563#106—174no—
564C4⋊C8—174no—
565#103—174no—
566#103—174no—
567#103—174no—
568#103—174no—
569#103—174no—
570#103—174no—
571#103—174no—
572#102—174no—
573#102—174no—
574#102—174no—
575C22⋊C8—174no—
576C22⋊C8—174no—
577C4×C8—174no—
578C17C2×#332711yescharacteristic, complemented, Sylow
579C24—21no—
580C24C2×C22⋊D1711yescharacteristic
581C24C2×C22⋊D1711yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585C2×Q8—22no—
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—28no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—48no—
595C2×Q8—172no—
596C2×Q8—341no—
597C2×Q8—342no—
598C2×Q8—342no—
599C2×Q8#6325414yes—
600C2×Q8C23×D1712yes—
601C2×Q8C23×D1712yes—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—42no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4C2×C22⋊D1714yes—
611C2×D4C23×D1712yes—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—24no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—344no—
624C22×C4—341no—
625C22×C4—341no—
626C22×C4—341no—
627C22×C4—341no—
628C22×C4—684no—
629C22×C4C2×C22⋊D1712yes—
630C22×C4C2×C22⋊D1712yes—
631C22×C4C2×C22⋊D1711yescharacteristic
632C22×C4C2×C22⋊D1711yescharacteristic
633C22×C4C2×C22⋊D1711yescharacteristic
634C22×C4C2×C22⋊D1711yescharacteristic
635C22×C4C23×D1712yes—
636C22×C4C23×D1712yes—
637C22×C4C23×D1711yescharacteristic
638Q16—348no—
639Q16—684no—
640SD16—684no—
641M16—684no—
642M16—684no—
643C2×C8—172no—
644C2×C8—172no—
645C2×C8—172no—
646C2×C8—172no—
647C2×C8—342no—
648C2×C8—342no—
649C2×C8—342no—
650C2×C8—342no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—172no—
655C4⋊C4—172no—
656C4⋊C4—172no—
657C4⋊C4—341no—
658C4⋊C4—341no—
659C4⋊C4—344no—
660C4⋊C4—341no—
661C4⋊C4—344no—
662C4⋊C4—344no—
663C4⋊C4—344no—
664C4⋊C4—344no—
665C4⋊C4—344no—
666C4⋊C4C2×C22⋊D1714yes—
667C4⋊C4C23×D1712yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—344no—
673C22⋊C4—344no—
674C22⋊C4—344no—
675C22⋊C4C2×C22⋊D1714yes—
676C22⋊C4C2×C22⋊D1714yes—
677C42—24no—
678C42—344no—
679C42—344no—
680C42C2×C22⋊D1712yes—
681C42C23×D1712yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23C22×C22⋊D1712yes—
693C23C22×C22⋊D1712yes—
694C23C22×C22⋊D1711yescharacteristic
695Q8—22no—
696Q8—24no—
697Q8—22no—
698Q8—22no—
699Q8—48no—
700Q8—42no—
701Q8—342no—
702Q8—342no—
703Q8—682no—
704Q8C2×#6325414yes—
705D4—22no—
706D4—22no—
707D4—44no—
708D4—48no—
709D4—48no—
710D4—42no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—342no—
730C2×C4—342no—
731C2×C4—342no—
732C2×C4—342no—
733C2×C4—688no—
734C2×C4—682no—
735C2×C4—682no—
736C2×C4—682no—
737C2×C4—682no—
738C2×C4C2×#6325412yes—
739C2×C4#1058769112yes—
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—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22#1176345312yes—
763C22#1176360712yes—
764C22#1176362412yes—
765C22C23×C22⋊D1711yescharacteristic
766C4—22no—
767C4—22no—
768C4—24no—
769C4—22no—
770C4—22no—
771C4—42no—
772C4—42no—
773C4—682no—
774C4—682no—
775C4—682no—
776C4—682no—
777C4#1176345312yes—
778C4C22×#6325411yescharacteristic
779C4C2×#1058769111yescharacteristic
780C2—42no—
781C2—42no—
782C2—82no—
783C2#1454105214yesdirect product factor
784C2C2×#1176345311yescharacteristic
785C2C2×#1176360711yescharacteristic
786C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
Fitting, prime radicalC2×C17×#548C2
socleC23×C17C22×D4
hypercenterC2×#548D17
hypocenterC17C2×#3327
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#11763499C2semidirect
2. #14541052C2direct (N × H)
3. C2×#11763163C2semidirect
4. C2×#11763142C2semidirect
5. C2×#11763130C2semidirect
6. C2×#11763116C2semidirect
7. C2×#11763065C2semidirect
8. C2×#11763053C2semidirect
9. C2×#11763028C2semidirect
10. C2×#11762971C2semidirect
11. C2×#11762965C2semidirect
12. C2×C4×#63231C2semidirect
13. C2×#11762887C2semidirect
14. C2×#11762810C2semidirect
15. C2×#11762818C2semidirect
23. #11763499C22semidirect
34. #11763163C22semidirect
35. #11763142C22semidirect
36. #11763130C22semidirect
37. #11763116C22semidirect
38. #11763065C22semidirect
39. #11763053C22semidirect
40. #11763028C22semidirect
41. #11762971C22semidirect
42. #11762965C22semidirect
43. C4×#63231C22semidirect
44. #11762887C22semidirect
49. #11762818C22semidirect
50. #11762810C22semidirect
466. C2×C17#3327semidirect
578. C17C2×#3327semidirect
783. C2#14541052direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634992
#145410522
C2×#117631632
C2×#117631422
C2×#117631302
C2×#117631162
C2×#117630652
C2×#117630532
C2×#117630282
C2×#117629712
C2×#117629652
C2×C4×#632312
C2×#117628872
C2×#117628102
C2×#117628182
C2×C17×#5482
C2×#332717