Finite Group Databasebeta

← C2×#14540949 #17910940

Subgroups — C2×#14540949 #17910940

Order 4352.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic34C211yesmaximal, characteristic, complemented
2#14540949C2116yesmaximal, direct product factor
3C2×#11763179C211yesmaximal, characteristic, complemented
4C2×#11763144C211yesmaximal, characteristic, complemented
5C2×#11763150C211yesmaximal, characteristic, complemented
6C2×#11763113C211yesmaximal, characteristic, complemented
7C2×#11763053C211yesmaximal, characteristic, complemented
8C2×#11763036C211yesmaximal, characteristic, complemented
9C2×#11763014C211yesmaximal, characteristic, complemented
10C2×#11762947C211yesmaximal, characteristic, complemented
11C2×#11762947C211yesmaximal, characteristic, complemented
12C2×#11762909C211yesmaximal, characteristic, complemented
13C2×#11762881C211yesmaximal, characteristic, complemented
14C2×#11762817C211yesmaximal, characteristic, complemented
15C22×#10587481C211yesmaximal, characteristic, complemented
16C2×C17×#553C211yesmaximal, characteristic
17C23×Dic34C2211yescharacteristic
18C23×Dic34C2211yescharacteristic
19C22×#63229C2211yescharacteristic
20C22×#63229C2211yescharacteristic
21C22×#63229C2211yescharacteristic
22C22×#63223C2211yescharacteristic
23C23×#3622C2211yescharacteristic
24D4×Dic34—24no—
25D4×Dic34C2218yescomplemented
26C2×#10587555C2211yescharacteristic
27C2×#10587574—21no—
28C2×#10587610C2211yescharacteristic
29C2×#10587610C2211yescharacteristic
30C2×#10587564—21no—
31C2×#10587564—21no—
32C2×C4×Dic34C2211yescharacteristic
33C2×D4×Dic17—21no—
34#11763179C2218yescomplemented
35#11763150C2218yescomplemented
36#11763144C2218yescomplemented
37#11763113C2218yescomplemented
38#11763053C2218yescomplemented
39#11763036C2218yescomplemented
40#11763014C2218yescomplemented
41#11762947C2218yescomplemented
42#11762947C2218yescomplemented
43#11762909C2218yescomplemented
44#11762881C2218yescomplemented
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49#11762817C2218yescomplemented
50C2×#10587481C2211yescharacteristic
51C2×#10587481C2211yescharacteristic
52C2×#10587481C2211yescharacteristic
53C2×#10587481C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587481C2211yescharacteristic
59C2×#10587481C2218yescomplemented
60C2×#10587503C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C17×#553—24no—
65C17×#553C2218yes—
66C2×C17×#126—21no—
67C2×C17×#125C2211yescharacteristic
68C2×C17×#123—21no—
69C2×C17×#121—21no—
70C2×C17×#121C2211yescharacteristic
71C2×C17×#121C2211yescharacteristic
72C2×C4×D4×C17—21no—
73C2×C4×D4×C17C2211yescharacteristic
74C2×C4×D4×C17C2211yescharacteristic
75C2×C17×#117C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×D4×C17—21no—
78C22×D4×C17—21no—
79C22×D4×C17D411yescharacteristic
80C22×D4×C17C2311yescharacteristic
81C23×C4×C17—21no—
82C23×C4×C17—21no—
83C23×C4×C17C2311yescharacteristic
84C23×C4×C17C2311yescharacteristic
85C23×Dic17—21no—
86C23×Dic17—21no—
87C22×Dic34—24no—
88C22×Dic34—24no—
89C22×Dic34—22no—
90C22×Dic34—22no—
91C22×Dic34—21no—
92C22×Dic34—21no—
93C22×Dic34—42no—
94C22×Dic34—42no—
95C22×Dic34C2311yescharacteristic
96C22×Dic34C2311yescharacteristic
97C22×Dic34C2314yes—
98C22×Dic34C2314yes—
99C22×Dic34C2311yescharacteristic
100C17×#126—28no—
101C17×#125—22no—
102C17×#125C2314yes—
103C17×#123—28no—
104C17×#121—28no—
105C17×#121—22no—
106C17×#121—22no—
107C17×#121C2314yes—
108C17×#121C2314yes—
109C4×D4×C17—28no—
110C4×D4×C17—22no—
111C4×D4×C17D414yes—
112C4×D4×C17C2314yes—
113C4×D4×C17C2314yes—
114C17×#117—22no—
115C17×#117C2314yes—
116C2×C4⋊C4×C17—21no—
117C2×C4⋊C4×C17—22no—
118C2×C4⋊C4×C17—21no—
119C2×C4⋊C4×C17—21no—
120C2×C4⋊C4×C17D411yescharacteristic
121C2×C4⋊C4×C17C2311yescharacteristic
122C2×C4⋊C4×C17C2311yescharacteristic
123C2×C4⋊C4×C17C2314yes—
124C2×C4⋊C4×C17C2311yescharacteristic
125C2×C22⋊C4×C17—21no—
126C2×C22⋊C4×C17—21no—
127C2×C22⋊C4×C17—21no—
128C2×C22⋊C4×C17—21no—
129C2×C22⋊C4×C17D411yescharacteristic
130C2×C22⋊C4×C17D411yescharacteristic
131C2×C42×C17—21no—
132C2×C42×C17C2311yescharacteristic
133C2×C22⋊Dic17—21no—
134C2×C22⋊Dic17—21no—
135D4×Dic17—28no—
136C2×#63229—24no—
137C2×#63229—42no—
138C2×#63229—42no—
139C2×#63229C2314yes—
140C2×#63229C2314yes—
141C2×#63229C2314yes—
142C2×C4⋊Dic17—21no—
143C2×C4⋊Dic17—21no—
144C2×C4⋊Dic17C2311yescharacteristic
145#10587610—22no—
146#10587610—22no—
147#10587610C2314yes—
148#10587610C2314yes—
149C2×#63225—21no—
150C2×#63225—21no—
151C2×#63225—21no—
152C2×C4×Dic17—21no—
153C2×#63223—42no—
154C2×#63223C2314yes—
155C22×#3622—42no—
156C22×#3622C2311yescharacteristic
157C22×#3622C2311yescharacteristic
158C22×#3622C2311yescharacteristic
159C22×#3622C2311yescharacteristic
160C22×#3622C2314yes—
161#10587574—28no—
162#10587564—28no—
163#10587564—28no—
164#10587555—22no—
165#10587555C2314yes—
166C4×Dic34—22no—
167C4×Dic34C2314yes—
168#10587503C2314yes—
169C22⋊#3622C2314yes—
170C22⋊#3622C2314yes—
171#10587481C2314yes—
172#10587481C2314yes—
173#10587481C2314yes—
174#10587481C2314yes—
175#10587481C2314yes—
176#10587481C2314yes—
177#10587481C2314yes—
178#10587481C2314yes—
179#10587481C2314yes—
180#10587479C2314yes—
181#10587478C2314yes—
182#10587478C2314yes—
183C4⋊#3622C2314yes—
184#10587474C2314yes—
185C24×C17—21no—
186C24×C17C2×D411yescharacteristic
187C24×C17C2×D411yescharacteristic
188C2×D4×C17—24no—
189C2×D4×C17—24no—
190C2×D4×C17—24no—
191C2×D4×C17—21no—
192C2×D4×C17—22no—
193C2×D4×C17—22no—
194C2×D4×C17—44no—
195C2×D4×C17—82no—
196C2×D4×C17C2×D414yes—
197C2×D4×C17C2412yes—
198C22×C4×C17—22no—
199C22×C4×C17—22no—
200C22×C4×C17—22no—
201C22×C4×C17—22no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—24no—
206C22×C4×C17—24no—
207C22×C4×C17—82no—
208C22×C4×C17—82no—
209C22×C4×C17C2×D411yescharacteristic
210C22×C4×C17C2×D411yescharacteristic
211C22×C4×C17C2×D412yes—
212C22×C4×C17C2×D412yes—
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2×D411yescharacteristic
215C22×C4×C17C2412yes—
216C22×C4×C17C2412yes—
217C22×C4×C17C2411yescharacteristic
218C22×Dic17—21no—
219C22×Dic17—24no—
220C22×Dic17—24no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—44no—
225C22×Dic17—44no—
226C2×Dic34—21no—
227C2×Dic34—22no—
228C2×Dic34—22no—
229C2×Dic34—22no—
230C2×Dic34—22no—
231C2×Dic34—22no—
232C2×Dic34—28no—
233C2×Dic34—28no—
234C2×Dic34—21no—
235C2×Dic34—21no—
236C2×Dic34—24no—
237C2×Dic34—24no—
238C2×Dic34—44no—
239C2×Dic34—44no—
240C2×Dic34—48no—
241C2×Dic34—48no—
242C2×Dic34—44no—
243C2×Dic34—44no—
244C2×Dic34#4114yes—
245C2×Dic34C2412yes—
246C2×Dic34C2412yes—
247C2×Dic34C2412yes—
248C4⋊C4×C17—24no—
249C4⋊C4×C17—24no—
250C4⋊C4×C17—21no—
251C4⋊C4×C17—21no—
252C4⋊C4×C17—24no—
253C4⋊C4×C17—21no—
254C4⋊C4×C17C2×D414yes—
255C4⋊C4×C17C2412yes—
256C4⋊C4×C17C2412yes—
257C4⋊C4×C17C2412yes—
258C22⋊C4×C17—24no—
259C22⋊C4×C17—24no—
260C22⋊C4×C17—24no—
261C22⋊C4×C17—24no—
262C22⋊C4×C17C2×D414yes—
263C22⋊C4×C17C2×D414yes—
264C42×C17—24no—
265C42×C17C2×D412yes—
266C42×C17C2412yes—
267C22⋊Dic17—24no—
268C22⋊Dic17—24no—
269#63229—28no—
270#63229—44no—
271#63229—44no—
272C4⋊Dic17—21no—
273C4⋊Dic17—24no—
274C4⋊Dic17—24no—
275C4⋊Dic17C2412yes—
276#63225—24no—
277#63225—24no—
278#63225—24no—
279C4×Dic17—24no—
280#63223—44no—
281C2×#3622—22no—
282C2×#3622—22no—
283C2×#3622—22no—
284C2×#3622—22no—
285C2×#3622—44no—
286C2×#3622C2412yes—
287C2×#3622C2412yes—
288C2×#3622C2412yes—
289C2×#3622C2412yes—
290C2×#3320—171nomaximal, Sylow
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—42no—
298C23×C17—42no—
299C23×C17—42no—
300C23×C17#13714yes—
301C23×C17C22×D412yes—
302C23×C17C22×D412yes—
303C23×C17C22×D411yescharacteristic
304D4×C17—28no—
305D4×C17—22no—
306D4×C17—22no—
307D4×C17—48no—
308D4×C17—42no—
309D4×C17—84no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—24no—
315C2×C4×C17—24no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—42no—
324C2×C4×C17—42no—
325C2×C4×C17—42no—
326C2×C4×C17—84no—
327C2×C4×C17—84no—
328C2×C4×C17C22×D412yes—
329C2×C4×C17C22×D412yes—
330C2×C4×C17C22×D412yes—
331C2×C4×C17C22×D412yes—
332C2×C4×C17C22×D411yescharacteristic
333C2×C4×C17C2×#4112yes—
334C2×C4×C17H(5,𝔽2)12yes—
335C2×C4×C17C2511yescharacteristic
336C2×Dic17—24no—
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—22no—
340C2×Dic17—22no—
341C2×Dic17—48no—
342C2×Dic17—48no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346Dic34—24no—
347Dic34—22no—
348Dic34—22no—
349Dic34—22no—
350Dic34—22no—
351Dic34—22no—
352Dic34—48no—
353Dic34—48no—
354Dic34—42no—
355Dic34—42no—
356Dic34C2×#4114yes—
357#3622—22no—
358#3622—22no—
359#3622—22no—
360#3622—22no—
361C2×#553D1711yescharacteristic
362C2×D4×Q8—171no—
363#3320—1716no—
364C2×#491—171no—
365C2×#484—171no—
366C2×#485—171no—
367C2×#479—171no—
368C2×#468—171no—
369C2×#465—171no—
370C2×#461—171no—
371C2×#448—171no—
372C2×#448—171no—
373C2×#440—171no—
374C2×#435—171no—
375C2×#419—171no—
376C22×#103—171no—
377C22×C17—22no—
378C22×C17—28no—
379C22×C17—22no—
380C22×C17—22no—
381C22×C17—22no—
382C22×C17—22no—
383C22×C17—44no—
384C22×C17—42no—
385C22×C17—42no—
386C22×C17—42no—
387C22×C17—84no—
388C22×C17#54612yes—
389C22×C17C2×#13714yes—
390C22×C17C2×#13712yes—
391C22×C17#57712yes—
392C22×C17C23×D411yescharacteristic
393C4×C17—22no—
394C4×C17—22no—
395C4×C17—22no—
396C4×C17—22no—
397C4×C17—42no—
398C4×C17—42no—
399C4×C17—42no—
400C4×C17#54612yes—
401C4×C17C22×#4111yescharacteristic
402C4×C17C2×H(5,𝔽2)11yescharacteristic
403Dic17—24no—
404Dic17—42no—
405Dic17—42no—
406Dic17—42no—
407C23×Q8—171no—
408C23×Q8—171no—
409C22×SD16—171no—
410C22×SD16—171no—
411C22×SD16—171no—
412C22×M16—171no—
413C23×C8—171no—
414#553—24no—
415#553C2×D1718yes—
416D4×Q8—178no—
417D4×Q8—344no—
418C2×C4⋊Q8—171no—
419C2×C4⋊Q8—341no—
420C2×#126—21no—
421C2×#125C2×D1711yescharacteristic
422C2×#123—21no—
423C2×C22⋊Q8—171no—
424C2×C22⋊Q8—171no—
425C2×C22⋊Q8—341no—
426C2×C22⋊Q8—341no—
427C2×#121—21no—
428C2×#121C2×D1711yescharacteristic
429C2×#121C2×D1711yescharacteristic
430C2×C4×Q8—171no—
431C2×C4×D4—21no—
432C2×C4×D4—341no—
433C2×C4×D4C2×D1711yescharacteristic
434C2×C4×D4C2×D1711yescharacteristic
435C2×#117C2×D1711yescharacteristic
436C22×C4⋊C4C2×D1711yescharacteristic
437#491—178no—
438#485—178no—
439#484—178no—
440#479—178no—
441#468—178no—
442#465—178no—
443#461—178no—
444#448—178no—
445#448—178no—
446#440—178no—
447#435—178no—
448C2×#107—171no—
449C2×#107—171no—
450C2×#106—171no—
451C2×C4⋊C8—171no—
452#419—178no—
453C2×#103—171no—
454C2×#103—171no—
455C2×#103—171no—
456C2×#103—171no—
457C2×#103—171no—
458C2×#103—171no—
459C2×#103—171no—
460C2×#103—171no—
461C2×#103—171no—
462C2×#103—178no—
463C2×#102—171no—
464C2×C22⋊C8—171no—
465C2×C22⋊C8—171no—
466C2×#97—171no—
467C2×C17—24no—
468C2×C17—42no—
469C2×C17—82no—
470C2×C17#332014yescomplemented
471C2×C17C2×#54611yescharacteristic
472C2×C17C22×#13711yescharacteristic
473C2×C17C2×#57711yescharacteristic
474C22×Q8—171no—
475C22×Q8—171no—
476C22×Q8—171no—
477C22×Q8—174no—
478C22×Q8—174no—
479C22×Q8—344no—
480C22×Q8—344no—
481C22×Q8—341no—
482C22×Q8—341no—
483C22×Q8—342no—
484C22×Q8—342no—
485C22×Q8—682no—
486C22×Q8—682no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4C22⋊D1711yescharacteristic
490C22×D4C22×D1711yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—341no—
494C23×C4—341no—
495C23×C4C22×D1711yescharacteristic
496C23×C4C22×D1711yescharacteristic
497C2×SD16—174no—
498C2×SD16—174no—
499C2×SD16—174no—
500C2×SD16—344no—
501C2×SD16—682no—
502C2×SD16—682no—
503C2×M16—174no—
504C2×M16—682no—
505C22×C8—171no—
506C22×C8—171no—
507C22×C8—171no—
508C22×C8—171no—
509C22×C8—174no—
510C22×C8—682no—
511C4⋊Q8—174no—
512C4⋊Q8—348no—
513C4⋊Q8—342no—
514#126—28no—
515#125—22no—
516#125C22×D1714yes—
517#123—28no—
518C22⋊Q8—174no—
519C22⋊Q8—174no—
520C22⋊Q8—342no—
521C22⋊Q8—342no—
522C22⋊Q8—348no—
523C22⋊Q8—348no—
524#121—28no—
525#121—22no—
526#121—22no—
527#121C22×D1714yes—
528#121C22×D1714yes—
529C4×Q8—174no—
530C4×Q8—342no—
531C4×D4—28no—
532C4×D4—22no—
533C4×D4—348no—
534C4×D4C22⋊D1714yes—
535C4×D4C22×D1714yes—
536C4×D4C22×D1714yes—
537#117—22no—
538#117C22×D1714yes—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—171no—
544C2×C4⋊C4—341no—
545C2×C4⋊C4—341no—
546C2×C4⋊C4—341no—
547C2×C4⋊C4—341no—
548C2×C4⋊C4—341no—
549C2×C4⋊C4C22⋊D1711yescharacteristic
550C2×C4⋊C4C22×D1711yescharacteristic
551C2×C4⋊C4C22×D1711yescharacteristic
552C2×C4⋊C4C22×D1714yes—
553C2×C4⋊C4C22×D1711yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—341no—
559C2×C22⋊C4—341no—
560C2×C22⋊C4C22⋊D1711yescharacteristic
561C2×C22⋊C4C22⋊D1711yescharacteristic
562C2×C42—21no—
563C2×C42—341no—
564C2×C42C22×D1711yescharacteristic
565#107—174no—
566#107—174no—
567#106—174no—
568C4⋊C8—174no—
569#103—174no—
570#103—174no—
571#103—174no—
572#103—174no—
573#103—174no—
574#103—174no—
575#103—174no—
576#103—174no—
577#103—174no—
578#102—174no—
579C22⋊C8—174no—
580C22⋊C8—174no—
581#97—174no—
582C17C2×#332011yescharacteristic, complemented, Sylow
583C24—21no—
584C24C2×C22⋊D1711yescharacteristic
585C24C2×C22⋊D1711yescharacteristic
586C2×Q8—174no—
587C2×Q8—172no—
588C2×Q8—172no—
589C2×Q8—172no—
590C2×Q8—348no—
591C2×Q8—348no—
592C2×Q8—342no—
593C2×Q8—341no—
594C2×Q8—344no—
595C2×Q8—344no—
596C2×Q8—341no—
597C2×Q8—341no—
598C2×Q8—342no—
599C2×Q8—342no—
600C2×Q8—342no—
601C2×Q8—342no—
602C2×Q8—684no—
603C2×Q8—684no—
604C2×Q8—684no—
605C2×Q8—684no—
606C2×Q8—688no—
607C2×Q8—688no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—44no—
615C2×D4—82no—
616C2×D4C2×C22⋊D1714yes—
617C2×D4C23×D1712yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—82no—
628C22×C4—82no—
629C22×C4—341no—
630C22×C4—344no—
631C22×C4—344no—
632C22×C4—341no—
633C22×C4—341no—
634C22×C4—341no—
635C22×C4—684no—
636C22×C4—684no—
637C22×C4C2×C22⋊D1712yes—
638C22×C4C2×C22⋊D1712yes—
639C22×C4C2×C22⋊D1711yescharacteristic
640C22×C4C2×C22⋊D1711yescharacteristic
641C22×C4C2×C22⋊D1711yescharacteristic
642C22×C4C2×C22⋊D1711yescharacteristic
643C22×C4C23×D1712yes—
644C22×C4C23×D1712yes—
645C22×C4C23×D1711yescharacteristic
646SD16—348no—
647SD16—684no—
648SD16—684no—
649M16—684no—
650C2×C8—172no—
651C2×C8—172no—
652C2×C8—172no—
653C2×C8—172no—
654C2×C8—342no—
655C2×C8—342no—
656C2×C8—342no—
657C2×C8—342no—
658C2×C8—684no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—21no—
665C4⋊C4—172no—
666C4⋊C4—341no—
667C4⋊C4—344no—
668C4⋊C4—344no—
669C4⋊C4—344no—
670C4⋊C4—344no—
671C4⋊C4—344no—
672C4⋊C4C2×C22⋊D1714yes—
673C4⋊C4C23×D1712yes—
674C4⋊C4C23×D1712yes—
675C4⋊C4C23×D1712yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—344no—
681C22⋊C4—344no—
682C22⋊C4C2×C22⋊D1714yes—
683C22⋊C4C2×C22⋊D1714yes—
684C42—24no—
685C42—344no—
686C42C2×C22⋊D1712yes—
687C42C23×D1712yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23#1058763714yes—
698C23C22×C22⋊D1712yes—
699C23C22×C22⋊D1712yes—
700C23C22×C22⋊D1711yescharacteristic
701Q8—174no—
702Q8—342no—
703Q8—344no—
704Q8—342no—
705Q8—342no—
706Q8—342no—
707Q8—342no—
708Q8—688no—
709Q8—688no—
710Q8—682no—
711Q8—682no—
712D4—28no—
713D4—22no—
714D4—22no—
715D4—48no—
716D4—42no—
717D4—84no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—342no—
737C2×C4—344no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—688no—
742C2×C4—688no—
743C2×C4—682no—
744C2×C4—682no—
745C2×C4—682no—
746C2×C4#41×D1712yes—
747C2×C4#1058769612yes—
748C2×C4C22×C22⋊D1712yes—
749C2×C4C22×C22⋊D1712yes—
750C2×C4C22×C22⋊D1712yes—
751C2×C4C22×C22⋊D1712yes—
752C2×C4C22×C22⋊D1711yescharacteristic
753C2×C4C24×D1711yescharacteristic
754C8—342no—
755C8—342no—
756C8—342no—
757C8—342no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22#1176344712yes—
770C22C2×#1058763714yes—
771C22C2×#1058763712yes—
772C22#1176362012yes—
773C22C23×C22⋊D1711yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—344no—
782C4—682no—
783C4—682no—
784C4—682no—
785C4#1176344712yes—
786C4C2×#41×D1711yescharacteristic
787C4C2×#1058769611yescharacteristic
788C2—24no—
789C2—42no—
790C2—82no—
791C2#1454094914yesdirect product factor
792C2C2×#1176344711yescharacteristic
793C2C22×#1058763711yescharacteristic
794C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
Fitting, prime radicalC2×C17×#553C2
socleC23×C17C22×D4
hypercenterC2×#553D17
hypocenterC17C2×#3320
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic34C2semidirect
2. #14540949C2direct (N × H)
3. C2×#11763179C2semidirect
4. C2×#11763144C2semidirect
5. C2×#11763150C2semidirect
6. C2×#11763113C2semidirect
7. C2×#11763053C2semidirect
8. C2×#11763036C2semidirect
9. C2×#11763014C2semidirect
10. C2×#11762947C2semidirect
11. C2×#11762947C2semidirect
12. C2×#11762909C2semidirect
13. C2×#11762881C2semidirect
14. C2×#11762817C2semidirect
15. C22×#10587481C2semidirect
25. D4×Dic34C22semidirect
34. #11763179C22semidirect
35. #11763150C22semidirect
36. #11763144C22semidirect
37. #11763113C22semidirect
38. #11763053C22semidirect
39. #11763036C22semidirect
40. #11763014C22semidirect
41. #11762947C22semidirect
42. #11762947C22semidirect
43. #11762909C22semidirect
44. #11762881C22semidirect
49. #11762817C22semidirect
59. C2×#10587481C22semidirect
470. C2×C17#3320semidirect
582. C17C2×#3320semidirect
791. C2#14540949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic342
#145409492
C2×#117631792
C2×#117631442
C2×#117631502
C2×#117631132
C2×#117630532
C2×#117630362
C2×#117630142
C2×#117629472
C2×#117629092
C2×#117628812
C2×#117628172
C22×#105874812
C2×C17×#5532
C2×#332017