Finite Group Databasebeta

← #17049828

Subgroups — #17049828

Order 4352.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763468C211yesmaximal, characteristic
2C2×#11762881C211yesmaximal, characteristic, complemented
3C2×#11762808C211yesmaximal, characteristic, complemented
4C22×#10587481C211yesmaximal, characteristic, complemented
5#14529716C211yesmaximal, characteristic, complemented
6#14529598C211yesmaximal, characteristic, complemented
7#14529215C211yesmaximal, characteristic, complemented
8#14529210C211yesmaximal, characteristic, complemented
9#14529101C211yesmaximal, characteristic, complemented
10#14529091C211yesmaximal, characteristic, complemented
11#14528786C211yesmaximal, characteristic, complemented
12#14528722C211yesmaximal, characteristic, complemented
13#14528718C211yesmaximal, characteristic, complemented
14#14528617C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C17C211yesmaximal, characteristic, complemented
16C22×#63252C2211yescharacteristic
17C23×Dic34C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C23×#3622C2211yescharacteristic
20#11763468—24no—
21#11763468C418yescomplemented
22C2×#10587561C2211yescharacteristic
23C2×#10587571—21no—
24C2×#10587610C2211yescharacteristic
25C2×#10587582—21no—
26C2×#10587616C2211yescharacteristic
27C2×#10587625—21no—
28C2×C4×Dic34C2211yescharacteristic
29C2×#10587567—21no—
30#11762881—24no—
31C2×C4⋊#3622C2211yescharacteristic
32#11762808—24no—
33C2×#10587481—24no—
34C2×#10587481C2211yescharacteristic
35C2×#10587481C2211yescharacteristic
36C2×#10587481C2211yescharacteristic
37C2×#10587481C2211yescharacteristic
38C2×#10587481C2211yescharacteristic
39C2×#10587481C2211yescharacteristic
40C2×#10587481C2211yescharacteristic
41C2×#10587481C2211yescharacteristic
42C2×#10587480C2211yescharacteristic
43C2×#10587480C2211yescharacteristic
44C2×#10587480C2211yescharacteristic
45C2×#10587480C2211yescharacteristic
46C2×C22⋊#3622C2211yescharacteristic
47C2×C22⋊#3622C2211yescharacteristic
48C2×#10587474C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53C2×C4×D4×C17—21no—
54C2×C4×D4×C17C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C22×C4⋊C4×C17C2211yescharacteristic
57C17×#389—21no—
58C17×#385—21no—
59C17×#385—21no—
60C17×#384C2211yescharacteristic
61C17×#380C2211yescharacteristic
62C17×#380C2211yescharacteristic
63C4×C4⋊C4×C17C2211yescharacteristic
64C22×D4×C17D411yescharacteristic
65C23×C4×C17—21no—
66C23×C4×C17—21no—
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C22×C22⋊D17—21no—
70C22×C22⋊D17—21no—
71C23×Dic17—21no—
72C2×#63252—22no—
73C2×#63252—22no—
74C2×#63252—22no—
75C2×#63252—41no—
76C2×#63252—41no—
77C2×#63252C2×C414yescomplemented
78C22×D68C2311yescharacteristic
79C22×C4×D17—21no—
80C22×Dic34—22no—
81C22×Dic34—22no—
82C22×Dic34—22no—
83C22×Dic34—21no—
84C22×Dic34—41no—
85C22×Dic34—41no—
86C22×Dic34C2×C414yescomplemented
87C22×Dic34C2311yescharacteristic
88C22×Dic34C2311yescharacteristic
89C4×D4×C17—44no—
90C4×D4×C17C2×C414yes—
91C4×D4×C17D414yes—
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17—22no—
94C2×C4⋊C4×C17—21no—
95C2×C4⋊C4×C17—21no—
96C2×C4⋊C4×C17—21no—
97C2×C4⋊C4×C17—21no—
98C2×C4⋊C4×C17—41no—
99C2×C4⋊C4×C17—41no—
100C2×C4⋊C4×C17D411yescharacteristic
101C2×C4⋊C4×C17C2311yescharacteristic
102C2×C4⋊C4×C17C2311yescharacteristic
103C2×C4⋊C4×C17C2311yescharacteristic
104C2×C4⋊C4×C17C2311yescharacteristic
105C2×C22⋊C4×C17—21no—
106C2×C22⋊C4×C17—21no—
107C2×C22⋊C4×C17D411yescharacteristic
108C2×C22⋊C4×C17D411yescharacteristic
109C2×C42×C17—21no—
110C2×C42×C17C2311yescharacteristic
111C2×C22⋊Dic17—21no—
112#10587625—28no—
113#10587616—22no—
114#10587616C2×C414yescomplemented
115C2×#63227—21no—
116C2×#63227—21no—
117C2×#63227—21no—
118C2×C4⋊Dic17C2311yescharacteristic
119#10587610—22no—
120#10587610C2×C414yescomplemented
121C2×#63225—21no—
122C2×#63225—21no—
123C2×C4×Dic17—21no—
124C2×#63223—22no—
125C2×#63223—22no—
126C2×#63223—41no—
127C22×#3622—22no—
128C22×#3622—22no—
129C22×#3622—41no—
130C22×#3622C2311yescharacteristic
131C22×#3622C2311yescharacteristic
132C22×#3622C2311yescharacteristic
133C22×#3622C2311yescharacteristic
134#10587582—28no—
135#10587571—28no—
136#10587567—28no—
137#10587561—22no—
138#10587561C2×C414yescomplemented
139C4×Dic34—22no—
140C4×Dic34C2×C414yescomplemented
141C17×#95—21no—
142C17×#95—21no—
143C17×#95—21no—
144C22⋊#3622—22no—
145C22⋊#3622—22no—
146#10587481—22no—
147#10587481—22no—
148#10587481—22no—
149#10587481—22no—
150#10587481—22no—
151#10587481—41no—
152#10587481—41no—
153#10587481D414yescomplemented
154#10587480—22no—
155#10587480—22no—
156#10587480—41no—
157#10587480—41no—
158C4⋊#3622—22no—
159#10587474—22no—
160C24×C17C2×D411yescharacteristic
161C24×C17C2×D411yescharacteristic
162C23×D17—21no—
163C2×D4×C17—22no—
164C2×D4×C17—22no—
165C2×D4×C17C22⋊C414yes—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—42no—
179C22×C4×C17—42no—
180C22×C4×C17—42no—
181C22×C4×C17—42no—
182C22×C4×C17—81no—
183C22×C4×C17—81no—
184C22×C4×C17C22×C412yes—
185C22×C4×C17C22×C412yes—
186C22×C4×C17C2×D412yes—
187C22×C4×C17C2×D412yes—
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2411yescharacteristic
193C2×C22⋊D17—24no—
194C2×C22⋊D17—24no—
195C2×C22⋊D17—42no—
196C2×C22⋊D17—42no—
197C2×C22⋊D17—42no—
198C2×C22⋊D17—42no—
199C22×Dic17—21no—
200C22×Dic17—24no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—42no—
204C22×Dic17—42no—
205#63252—28no—
206#63252—44no—
207#63252—44no—
208#63252—44no—
209C2×D68—21no—
210C2×D68—21no—
211C2×D68—21no—
212C2×D68—21no—
213C2×D68—21no—
214C2×D68C22×C412yes—
215C2×C4×D17—24no—
216C2×C4×D17—42no—
217C2×C4×D17—42no—
218C2×Dic34—21no—
219C2×Dic34—21no—
220C2×Dic34—21no—
221C2×Dic34—21no—
222C2×Dic34—21no—
223C2×Dic34—21no—
224C2×Dic34—21no—
225C2×Dic34—28no—
226C2×Dic34—24no—
227C2×Dic34—21no—
228C2×Dic34—44no—
229C2×Dic34—44no—
230C2×Dic34—44no—
231C2×Dic34—42no—
232C2×Dic34—42no—
233C2×Dic34C22×C412yes—
234C2×Dic34C22×C412yes—
235C2×Dic34C2×D412yes—
236C2×Dic34#4112yes—
237C4⋊C4×C17—21no—
238C4⋊C4×C17—21no—
239C4⋊C4×C17—21no—
240C4⋊C4×C17—21no—
241C4⋊C4×C17—21no—
242C4⋊C4×C17—21no—
243C4⋊C4×C17—21no—
244C4⋊C4×C17—42no—
245C4⋊C4×C17—42no—
246C4⋊C4×C17—42no—
247C4⋊C4×C17—81no—
248C4⋊C4×C17C22⋊C414yes—
249C4⋊C4×C17C2×D412yes—
250C22⋊C4×C17—42no—
251C22⋊C4×C17—42no—
252C22⋊C4×C17C22⋊C414yes—
253C22⋊C4×C17C22⋊C414yes—
254C42×C17—42no—
255C42×C17C22×C412yes—
256C42×C17C2×D412yes—
257C22⋊Dic17—24no—
258#63227—24no—
259#63227—24no—
260#63227—24no—
261C4⋊Dic17—21no—
262C4⋊Dic17C22×C412yes—
263#63225—24no—
264#63225—24no—
265C4×Dic17—24no—
266#63223—44no—
267C2×#3622—21no—
268C2×#3622—21no—
269C2×#3622—21no—
270C2×#3622—21no—
271C2×#3622—21no—
272C2×#3622—21no—
273C2×#3622—21no—
274C2×#3622—21no—
275C2×#3622—21no—
276C2×#3622—21no—
277C2×#3622—21no—
278C2×#3622—44no—
279C2×#3622C2×D412yes—
280#22421—171nomaximal, Sylow
281C23×C17—21no—
282C23×C17—21no—
283C23×C17—21no—
284C23×C17—21no—
285C23×C17—21no—
286C23×C17—21no—
287C23×C17—21no—
288C23×C17—21no—
289C23×C17—21no—
290C23×C17—21no—
291C23×C17C2×C22⋊C412yes—
292C23×C17C2×C22⋊C412yes—
293C23×C17AGL(1,ℤ/8)12yes—
294C23×C17#13712yes—
295C23×C17C22×D411yescharacteristic
296C22×D17—22no—
297C22×D17—41no—
298C22×D17—41no—
299C22×D17—41no—
300C22×D17—41no—
301C22×D17—41no—
302C22×D17—41no—
303D4×C17—28no—
304C2×C4×C17—21no—
305C2×C4×C17—21no—
306C2×C4×C17—21no—
307C2×C4×C17—21no—
308C2×C4×C17—21no—
309C2×C4×C17—21no—
310C2×C4×C17—21no—
311C2×C4×C17—21no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—41no—
322C2×C4×C17—41no—
323C2×C4×C17—41no—
324C2×C4×C17—41no—
325C2×C4×C17—41no—
326C2×C4×C17—41no—
327C2×C4×C17—41no—
328C2×C4×C17—41no—
329C2×C4×C17—41no—
330C2×C4×C17—41no—
331C2×C4×C17—41no—
332C2×C4×C17—84no—
333C2×C4×C17—84no—
334C2×C4×C17C2×C22⋊C412yes—
335C2×C4×C17C2×C22⋊C412yes—
336C2×C4×C17C2×C22⋊C412yes—
337C2×C4×C17C2×C22⋊C412yes—
338C2×C4×C17C23×C411yescharacteristic
339C2×C4×C17C22×D411yescharacteristic
340C2×C4×C17C22×D411yescharacteristic
341C2×C4×C17C2×#4111yescharacteristic
342C2×C4×C17H(5,𝔽2)11yescharacteristic
343C2×C4×C17H(5,𝔽2)11yescharacteristic
344C22⋊D17—48no—
345C22⋊D17—48no—
346C2×Dic17—22no—
347C2×Dic17—22no—
348C2×Dic17—22no—
349C2×Dic17—22no—
350C2×Dic17—22no—
351C2×Dic17—48no—
352C2×Dic17—41no—
353C2×Dic17—41no—
354C2×Dic17—41no—
355C2×Dic17—41no—
356D68—22no—
357D68—22no—
358D68—41no—
359D68—41no—
360C4×D17—48no—
361Dic34—22no—
362Dic34—22no—
363Dic34—22no—
364Dic34—22no—
365Dic34—22no—
366Dic34—48no—
367Dic34—41no—
368Dic34—41no—
369Dic34C4×D414yescomplemented
370#3622—22no—
371#3622—41no—
372#3622—41no—
373#3622—41no—
374C2×#548—171no—
375C2×#435—171no—
376C2×#417—171no—
377C22×#103—171no—
378D4×C4⋊C4D1711yescharacteristic, complemented
379#1983—171no—
380#1959—171no—
381#1894—171no—
382#1893—171no—
383#1874—171no—
384#1872—171no—
385#1803—171no—
386#1788—171no—
387#1787—171no—
388#1763—171no—
389C22×C17—22no—
390C22×C17—22no—
391C22×C17—22no—
392C22×C17—22no—
393C22×C17—22no—
394C22×C17—22no—
395C22×C17—22no—
396C22×C17—22no—
397C22×C17—22no—
398C22×C17—41no—
399C22×C17—41no—
400C22×C17—41no—
401C22×C17—41no—
402C22×C17#41714yescomplemented
403C22×C17C22×C22⋊C411yescharacteristic
404C22×C17D4211yescharacteristic
405C22×C17#54611yescharacteristic
406C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C17C2×#13711yescharacteristic
408C22×C17#57711yescharacteristic
409C22×C17#57811yescharacteristic
410C2×D17—42no—
411C2×D17—42no—
412C2×D17—42no—
413C2×D17—81no—
414C2×D17—81no—
415C2×D17—81no—
416C2×D17—81no—
417C4×C17—22no—
418C4×C17—22no—
419C4×C17—22no—
420C4×C17—22no—
421C4×C17—42no—
422C4×C17—81no—
423C4×C17—81no—
424C4×C17—81no—
425C4×C17C2×C4×D411yescharacteristic
426C4×C17#51811yescharacteristic
427C4×C17D4211yescharacteristic
428C4×C17#54611yescharacteristic
429Dic17—24no—
430Dic17—42no—
431Dic17—42no—
432C22×#41—171no—
433C23×Q8—171no—
434C22×M16—171no—
435C23×C8—171no—
436#548—178no—
437#548—344no—
438C2×#124—171no—
439C2×#124—341no—
440C2×C22⋊Q8—171no—
441C2×C22⋊Q8—341no—
442C2×#121—171no—
443C2×#121—341no—
444C2×C4×Q8—171no—
445C2×C4×D4—21no—
446C2×C4×D4—341no—
447C2×C4×D4C2×D1711yescharacteristic
448C22×C4⋊C4C2×D1711yescharacteristic
449C22×C4⋊C4C2×D1711yescharacteristic
450#435—344no—
451C2×C4⋊C8—171no—
452#417—344no—
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—344no—
462C2×#102—171no—
463C2×#102—171no—
464C2×#102—171no—
465C2×#102—171no—
466C2×C22⋊C8—171no—
467C2×C22⋊C8—171no—
468C2×#97—171no—
469#389—21no—
470#385—21no—
471#385—21no—
472#384C2×D1711yescharacteristic
473#380C2×D1711yescharacteristic
474#380C2×D1711yescharacteristic
475C4×C4⋊C4C2×D1711yescharacteristic
476#340—171no—
477#340—171no—
478#340—171no—
479#340—171no—
480C2×C17—24no—
481C2×C17—42no—
482C2×C17D4×C22⋊C411yescharacteristic
483C2×C17C2×#41711yescharacteristic
484C2×C17#289811yescharacteristic
485C2×C17#326511yescharacteristic
486C2×C17#327011yescharacteristic
487C2×C17#330811yescharacteristic
488C2×C17#331611yescharacteristic
489D17—82no—
490C2×#41—174no—
491C2×#41—342no—
492C2×#41—342no—
493C2×#41—342no—
494C2×#41—681no—
495C2×#41—681no—
496C22×Q8—174no—
497C22×Q8—171no—
498C22×Q8—171no—
499C22×Q8—342no—
500C22×Q8—342no—
501C22×Q8—342no—
502C22×Q8—341no—
503C22×Q8—681no—
504C22×Q8—681no—
505C22×D4—171no—
506C22×D4—341no—
507C22×D4—341no—
508C22×D4C22⋊D1711yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—341no—
512C23×C4—341no—
513C23×C4C22×D1711yescharacteristic
514C23×C4C22×D1711yescharacteristic
515C2×M16—342no—
516C2×M16—342no—
517C2×M16—681no—
518C22×C8—171no—
519C22×C8—171no—
520C22×C8—171no—
521C22×C8—171no—
522C22×C8—342no—
523C22×C8—342no—
524C22×C8—681no—
525#124—174no—
526#124—348no—
527#124—342no—
528C22⋊Q8—174no—
529C22⋊Q8—342no—
530C22⋊Q8—348no—
531#121—174no—
532#121—348no—
533#121—342no—
534C4×Q8—174no—
535C4×Q8—342no—
536C4×D4—44no—
537C4×D4—348no—
538C4×D4C4×D1714yes—
539C4×D4D6814yes—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—171no—
549C2×C4⋊C4—341no—
550C2×C4⋊C4—341no—
551C2×C4⋊C4C22⋊D1711yescharacteristic
552C2×C4⋊C4C22×D1711yescharacteristic
553C2×C4⋊C4C22×D1711yescharacteristic
554C2×C4⋊C4C22×D1711yescharacteristic
555C2×C4⋊C4C22×D1711yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—341no—
559C2×C22⋊C4—341no—
560C2×C22⋊C4—341no—
561C2×C22⋊C4—341no—
562C2×C22⋊C4C22⋊D1711yescharacteristic
563C2×C22⋊C4C22⋊D1711yescharacteristic
564C2×C42—21no—
565C2×C42—341no—
566C2×C42C22×D1711yescharacteristic
567C4⋊C8—342no—
568#103—174no—
569#103—342no—
570#103—342no—
571#103—342no—
572#103—342no—
573#103—342no—
574#103—681no—
575#103—681no—
576#102—342no—
577#102—342no—
578#102—681no—
579#102—681no—
580C22⋊C8—342no—
581C22⋊C8—342no—
582#97—342no—
583#95—21no—
584#95—21no—
585#95—21no—
586C17#2242111yescharacteristic, complemented, Sylow
587C24—341no—
588C24C2×C22⋊D1711yescharacteristic
589C24C2×C22⋊D1711yescharacteristic
590#41—348no—
591#41—684no—
592#41—684no—
593#41—684no—
594C2×Q8—172no—
595C2×Q8—172no—
596C2×Q8—172no—
597C2×Q8—172no—
598C2×Q8—348no—
599C2×Q8—341no—
600C2×Q8—341no—
601C2×Q8—341no—
602C2×Q8—341no—
603C2×Q8—344no—
604C2×Q8—341no—
605C2×Q8—341no—
606C2×Q8—341no—
607C2×Q8—341no—
608C2×Q8—682no—
609C2×Q8—682no—
610C2×Q8—684no—
611C2×Q8—684no—
612C2×Q8—684no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—172no—
616C2×D4—344no—
617C2×D4—344no—
618C2×D4—341no—
619C2×D4—341no—
620C2×D4—341no—
621C2×D4—341no—
622C2×D4—341no—
623C2×D4—682no—
624C2×D4—682no—
625C2×D4—682no—
626C2×D4—682no—
627C2×D4#6322714yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4—341no—
647C22×C4—341no—
648C22×C4—341no—
649C22×C4—344no—
650C22×C4—344no—
651C22×C4—682no—
652C22×C4—682no—
653C22×C4—682no—
654C22×C4—682no—
655C22×C4C2×C4×D1712yes—
656C22×C4C2×C4×D1712yes—
657C22×C4C2×D6812yes—
658C22×C4C2×D6812yes—
659C22×C4C2×C22⋊D1711yescharacteristic
660C22×C4C2×C22⋊D1711yescharacteristic
661C22×C4C2×C22⋊D1711yescharacteristic
662C22×C4C2×C22⋊D1711yescharacteristic
663C22×C4C23×D1711yescharacteristic
664M16—684no—
665C2×C8—172no—
666C2×C8—341no—
667C2×C8—341no—
668C2×C8—341no—
669C2×C8—341no—
670C2×C8—341no—
671C2×C8—341no—
672C2×C8—341no—
673C2×C8—341no—
674C2×C8—341no—
675C2×C8—341no—
676C2×C8—341no—
677C2×C8—684no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—81no—
689C4⋊C4—172no—
690C4⋊C4—341no—
691C4⋊C4—344no—
692C4⋊C4—344no—
693C4⋊C4#6322714yes—
694C4⋊C4D4×D1712yes—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—344no—
698C22⋊C4—344no—
699C22⋊C4—344no—
700C22⋊C4—344no—
701C22⋊C4#6322714yes—
702C22⋊C4#6322714yes—
703C42—42no—
704C42—344no—
705C42C2×C4×D1712yes—
706C42C2×D6812yes—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—342no—
718C23—681no—
719C23—681no—
720C23—681no—
721C23—681no—
722C23—681no—
723C23—681no—
724C23C2×#6322712yes—
725C23C2×#6322712yes—
726C23#1058761812yes—
727C23#1058762812yes—
728C23C22×C22⋊D1711yescharacteristic
729Q8—174no—
730Q8—342no—
731Q8—342no—
732Q8—342no—
733Q8—342no—
734Q8—342no—
735Q8—688no—
736Q8—681no—
737Q8—681no—
738D4—28no—
739D4—342no—
740D4—342no—
741D4—688no—
742D4—688no—
743D4—681no—
744D4—681no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—342no—
776C2×C4—342no—
777C2×C4—342no—
778C2×C4—342no—
779C2×C4—342no—
780C2×C4—688no—
781C2×C4—688no—
782C2×C4—681no—
783C2×C4—681no—
784C2×C4—681no—
785C2×C4—681no—
786C2×C4C2×#6322712yes—
787C2×C4C2×#6322712yes—
788C2×C4C2×#6322712yes—
789C2×C4C2×#6322712yes—
790C2×C4C22×C4×D1711yescharacteristic
791C2×C4C22×D6811yescharacteristic
792C2×C4C2×D4×D1711yescharacteristic
793C2×C4#1058769111yescharacteristic
794C2×C4#41×D1711yescharacteristic
795C2×C4#1058769611yescharacteristic
796C8—342no—
797C8—681no—
798C8—681no—
799C8—681no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—682no—
814C22—682no—
815C22—682no—
816C22—1361no—
817C22—1361no—
818C22—1361no—
819C22—1361no—
820C22#1176280814yescomplemented
821C22C22×#6322711yescharacteristic
822C22D4×C22⋊D1711yescharacteristic
823C22#1176344711yescharacteristic
824C22C2×#1058761811yescharacteristic
825C22C2×#1058762811yescharacteristic
826C22#1176362011yescharacteristic
827C22#1176362411yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—344no—
837C4—682no—
838C4—682no—
839C4C4×D4×D1711yescharacteristic
840C4#1176328111yescharacteristic
841C4D4×D6811yescharacteristic
842C4#1176345411yescharacteristic
843C2—24no—
844C2—42no—
845C2—1362no—
846C2D4×#6322711yescharacteristic
847C2C2×#1176280811yescharacteristic
848C2#1453731411yescharacteristic
849C2#1454027511yescharacteristic
850C2#1454035511yescharacteristic
851C2#1454076911yescharacteristic
852C2#1454088911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingD4×C4⋊C4×C17C2
socleC23×C17C22×D4
prime radicalC2×#11763468C2
cosocleC22×C4×C17C24
hypercenterD4×C4⋊C4D17
hypocenterC17#22421
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11762881C2semidirect
3. C2×#11762808C2semidirect
4. C22×#10587481C2semidirect
5. #14529716C2semidirect
6. #14529598C2semidirect
7. #14529215C2semidirect
8. #14529210C2semidirect
9. #14529101C2semidirect
10. #14529091C2semidirect
11. #14528786C2semidirect
12. #14528722C2semidirect
13. #14528718C2semidirect
14. #14528617C2semidirect
15. D4×C4⋊C4×C17C2semidirect
21. #11763468C4semidirect
77. C2×#63252C2×C4semidirect
86. C22×Dic34C2×C4semidirect
114. #10587616C2×C4semidirect
120. #10587610C2×C4semidirect
138. #10587561C2×C4semidirect
140. C4×Dic34C2×C4semidirect
153. #10587481D4semidirect
369. Dic34C4×D4semidirect
378. D4×C4⋊C4D17semidirect
402. C22×C17#417semidirect
586. C17#22421semidirect
820. C22#11762808semidirect

Maximal subgroups

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

subgroupindex
C2×#117634682
C2×#117628812
C2×#117628082
C22×#105874812
#145297162
#145295982
#145292152
#145292102
#145291012
#145290912
#145287862
#145287222
#145287182
#145286172
D4×C4⋊C4×C172
#2242117