Finite Group Databasebeta

← #440×#595 #17968814

Subgroups — #440×#595 #17968814

Order 4352.

1206 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763848C211yesmaximal, characteristic
2C2×SD16×#595C211yesmaximal, characteristic
3C4×Q8×#595C211yesmaximal, characteristic, complemented
4C4×D4×#595C211yesmaximal, characteristic
5#14544599C211yesmaximal, characteristic, complemented
6#14544598C211yesmaximal, characteristic, complemented
7#107×#595C211yesmaximal, characteristic, complemented
8#14544557C211yesmaximal, characteristic, complemented
9#14544556C211yesmaximal, characteristic, complemented
10#14544555C211yesmaximal, characteristic
11#14544554C211yesmaximal, characteristic
12#103×#595C211yesmaximal, characteristic, complemented
13#102×#595C211yesmaximal, characteristic
14#97×#595C211yesmaximal, characteristic, complemented
15D17×#440C211yesmaximal, characteristic
16C2×Q8×#595C2211yescharacteristic
17C2×Q8×#595C2211yescharacteristic
18C2×D4×#595C2211yescharacteristic
19C2×D4×#595C2211yescharacteristic
20C22×C4×#595—21no—
21#11763848C418yescomplemented
22SD16×#595C418yescomplemented
23C2×#10587534C2211yescharacteristic
24C2×#10587533C2211yescharacteristic
25C2×#10587549C2211yescharacteristic
26C2×#10587549C2211yescharacteristic
27C2×#10587547C2211yescharacteristic
28C2×#10587547C2211yescharacteristic
29#11763768C2211yescharacteristic
30C2×#10587532C2211yescharacteristic
31C2×#10587532C2211yescharacteristic
32C2×C8×#595C2211yescharacteristic
33C2×C8×#595C2211yescharacteristic
34C4⋊C4×#595—21no—
35C4⋊C4×#595—21no—
36C4⋊C4×#595C2211yescharacteristic
37C4⋊C4×#595C2211yescharacteristic
38C4⋊C4×#595C2211yescharacteristic
39C4⋊C4×#595C2211yescharacteristic
40C4×C4⋊#595—21no—
41C4×C4⋊#595C2211yescharacteristic
42C4×C4⋊#595C2211yescharacteristic
43C22⋊C4×#595—21no—
44C22⋊C4×#595—21no—
45C4×C22⋊#595—21no—
46C42×#595—21no—
47C42×#595C2211yescharacteristic
48#11763683C2211yescharacteristic
49#11763683C2211yescharacteristic
50#11763682C2211yescharacteristic
51#11763682C2211yescharacteristic
52#11763682C2211yescharacteristic
53#11763682C2211yescharacteristic
54C2×SD16×D17C2211yescharacteristic
55C4×Q8×D17C2211yescharacteristic
56C4×D4×D17C2211yescharacteristic
57#11762912C411yescharacteristic, complemented
58#11762911C411yescharacteristic, complemented
59#11762910C411yescharacteristic, complemented
60#11762909C411yescharacteristic, complemented
61#11762908C411yescharacteristic, complemented
62#11762907C411yescharacteristic, complemented
63#11762906C411yescharacteristic, complemented
64#107×D17C2211yescharacteristic
65#103×D17C2211yescharacteristic
66#102×D17C2211yescharacteristic
67#97×D17C2211yescharacteristic
68C17×#440C411yescharacteristic, complemented
69C23×#595—21no—
70C23×#595—21no—
71C2×Q8×D17C2311yescharacteristic
72C2×D4×D17C2311yescharacteristic
73C22×C4×D17—21no—
74C2×C22⋊#595—21no—
75C2×C22⋊#595—21no—
76Q8×#595—22no—
77Q8×#595—22no—
78Q8×#595C2×C414yescomplemented
79Q8×#595C2×C414yescomplemented
80D4×#595—22no—
81D4×#595—22no—
82D4×#595C2×C414yes—
83D4×#595C2×C414yes—
84C2×C4⋊#595—21no—
85C2×C4⋊#595—21no—
86C2×C4⋊#595C2311yescharacteristic
87C2×C4⋊#595C2311yescharacteristic
88C2×C4⋊#595C2311yescharacteristic
89C2×C4⋊#595C2311yescharacteristic
90C2×C4×#595—21no—
91C2×C4×#595—21no—
92C2×C4×#595—21no—
93C2×C4×#595—21no—
94C2×C4×#595—21no—
95C2×C4×#595—21no—
96C2×C4×#595—21no—
97C2×C4×#595—21no—
98C2×C4×#595—44no—
99C2×C4×#595D411yescharacteristic
100C2×C4×#595D411yescharacteristic
101C2×C4×#595D411yescharacteristic
102C2×C4×#595D411yescharacteristic
103C2×C4×#595C2311yescharacteristic
104C2×C4×#595C2311yescharacteristic
105C2×#63242C2311yescharacteristic
106C2×#63242C2311yescharacteristic
107C2×SD16×C17C2×C411yescharacteristic
108C4×Q8×C17C2×C411yescharacteristic, complemented
109C4×D4×C17C2×C411yescharacteristic
110Q8×Dic17C2×C411yescharacteristic, complemented
111C2×#63230C2×C411yescharacteristic
112D4×Dic17C2×C411yescharacteristic
113C2×#63229C2×C411yescharacteristic
114C4×C22⋊D17—21no—
115SD16×D17C2×C414yes—
116SD16×D17C2×C414yes—
117C2×#63219C2×C411yescharacteristic
118C2×C8×D17C2311yescharacteristic
119C2×C8×D17C2311yescharacteristic
120#10587579C2×C411yescharacteristic
121C4⋊C4×D17—21no—
122C4⋊C4×D17C2311yescharacteristic
123C4⋊C4×D17C2311yescharacteristic
124#10587573—21no—
125#10587573C2×C411yescharacteristic, complemented
126#10587567—21no—
127C22⋊C4×D17—21no—
128C4×D68C2×C411yescharacteristic
129C42×D17—21no—
130C42×D17C2311yescharacteristic
131C4×Dic34—21no—
132C4×Dic34C2×C411yescharacteristic, complemented
133#10587549C2×C414yescomplemented
134#10587549C2×C414yescomplemented
135#10587547C2×C414yes—
136#10587547C2×C414yes—
137(C2×#595)⋊C4—21no—
138(C2×#595)⋊C4—21no—
139(C2×#595)⋊C4—21no—
140(C2×#595)⋊C4—21no—
141(C2×#595)⋊C4—21no—
142(C2×#595)⋊C4—21no—
143#10587542—21no—
144#10587542—21no—
145#10587534C2×C414yescomplemented
146#10587533C2×C414yescomplemented
147#10587532—22no—
148#10587532C2×C414yescomplemented
149C8×#595—22no—
150C8×#595C2×C414yescomplemented
151C17×#107C2×C411yescharacteristic, complemented
152C17×#103C2×C411yescharacteristic, complemented
153C17×#102C2×C411yescharacteristic
154C17×#97C2×C411yescharacteristic, complemented
155#10587506C2×C411yescharacteristic, complemented
156#10587503C2×C411yescharacteristic
157#10587492C2×C411yescharacteristic
158#10587489C2×C411yescharacteristic, complemented
159#10587487C2×C411yescharacteristic, complemented
160#10587486C2×C411yescharacteristic, complemented
161#10587486C2×C411yescharacteristic, complemented
162#10587481C2×C411yescharacteristic, complemented
163#10587480C2×C411yescharacteristic
164#10587478C2×C411yescharacteristic, complemented
165#10587478C2×C411yescharacteristic, complemented
166#10587474C2×C411yescharacteristic, complemented
167C23×D17—21no—
168C22×#595—21no—
169C22×#595—21no—
170C22×#595—21no—
171C22×#595—21no—
172C22×#595—24no—
173C22×#595—24no—
174C22×#595—42no—
175C22×#595—42no—
176C22×#595—42no—
177C22×#595—42no—
178C22×#595C2×D411yescharacteristic
179C22×#595C2×D411yescharacteristic
180C22×#595C2×D411yescharacteristic
181C22×#595C2×D411yescharacteristic
182C2×Q8×C17C22×C411yescharacteristic
183C2×D4×C17C22×C411yescharacteristic
184C22×C4×C17—21no—
185C2×C22⋊D17—21no—
186C22×Dic17—21no—
187Q8×D17—21no—
188Q8×D17—21no—
189Q8×D17C22×C412yes—
190Q8×D17C22×C412yes—
191D4×D17—21no—
192D4×D17—21no—
193D4×D17C22×C412yes—
194D4×D17C22×C412yes—
195C2×D68C22×C411yescharacteristic
196C2×C4×D17—21no—
197C2×C4×D17—21no—
198C2×C4×D17—21no—
199C2×C4×D17—21no—
200C2×C4×D17—21no—
201C2×C4×D17—42no—
202C2×C4×D17—42no—
203C2×C4×D17C2×D411yescharacteristic
204C2×C4×D17C2×D411yescharacteristic
205C2×C4×D17C2411yescharacteristic
206C2×Dic34—21no—
207C2×Dic34C22×C411yescharacteristic
208C22⋊#595—24no—
209C22⋊#595—24no—
210C2×#3624—21no—
211C2×#3624—21no—
212C4⋊#595—24no—
213C4⋊#595—24no—
214C4⋊#595—21no—
215C4⋊#595—21no—
216C4⋊#595—21no—
217C4⋊#595—21no—
218C4⋊#595C22×C412yes—
219C4⋊#595C22×C412yes—
220C4⋊#595C22×C412yes—
221C4⋊#595C22×C412yes—
222C4×#595—24no—
223C4×#595—24no—
224C4×#595—22no—
225C4×#595—22no—
226C4×#595—41no—
227C4×#595—41no—
228C4×#595—42no—
229C4×#595—42no—
230C4×#595—42no—
231C4×#595—42no—
232C4×#595—42no—
233C4×#595—42no—
234C4×#595C22×C412yes—
235C4×#595C22×C412yes—
236C4×#595#4112yes—
237C4×#595#4112yes—
238#63242—21no—
239#63242—21no—
240#63242C22×C412yes—
241#63242C22×C412yes—
242SD16×C17C4214yescomplemented
243C2×C8×C17C22×C411yescharacteristic
244C2×C8×C17C22×C411yescharacteristic
245C4⋊C4×C17—21no—
246C4⋊C4×C17C22×C411yescharacteristic
247C4⋊C4×C17C22×C411yescharacteristic
248C22⋊C4×C17—21no—
249C42×C17—21no—
250C42×C17C22×C411yescharacteristic
251C22⋊Dic17—21no—
252#63230C4214yescomplemented
253#63229C4214yescomplemented
254#63227—21no—
255#63227—21no—
256C4⋊Dic17—21no—
257C4⋊Dic17C22×C411yescharacteristic
258C4⋊Dic17C22×C411yescharacteristic
259#63225—21no—
260#63225—21no—
261#63225—21no—
262#63225—21no—
263C4×Dic17—21no—
264C4×Dic17—21no—
265C4×Dic17—21no—
266C4×Dic17C22×C411yescharacteristic
267C4×Dic17#4111yescharacteristic
268C4×Dic17#4111yescharacteristic
269C2×#3622C22×C411yescharacteristic
270C2×#3622C22×C411yescharacteristic
271#63219C4214yescomplemented
272C8×D17—21no—
273C8×D17—21no—
274C8×D17C22×C412yes—
275C8×D17C22×C412yes—
276C4×#440—171nomaximal, Sylow
277C23×C17—21no—
278C22×D17—21no—
279C22×D17—22no—
280C22×D17—22no—
281C22×D17—41no—
282C22×D17—41no—
283C22×D17—41no—
284C22×D17—41no—
285C22×D17C22×D411yescharacteristic
286C2×#595—21no—
287C2×#595—21no—
288C2×#595—21no—
289C2×#595—21no—
290C2×#595—21no—
291C2×#595—21no—
292C2×#595—22no—
293C2×#595—22no—
294C2×#595—22no—
295C2×#595—22no—
296C2×#595—48no—
297C2×#595—41no—
298C2×#595—41no—
299C2×#595—41no—
300C2×#595—41no—
301C2×#595—41no—
302C2×#595—41no—
303C2×#595—41no—
304C2×#595—41no—
305C2×#595—48no—
306C2×#595C4×D412yes—
307C2×#595C4×D412yes—
308C2×#595C4×D412yes—
309C2×#595C4×D412yes—
310C2×#595AGL(1,ℤ/8)12yes—
311C2×#595#13712yes—
312Q8×C17—21no—
313Q8×C17C2×C4212yescomplemented
314D4×C17—21no—
315D4×C17C2×C4212yes—
316C2×C4×C17—21no—
317C2×C4×C17—21no—
318C2×C4×C17—21no—
319C2×C4×C17—42no—
320C2×C4×C17C4×D411yescharacteristic
321C2×C4×C17C4×D411yescharacteristic
322C2×C4×C17C23×C411yescharacteristic
323C22⋊D17—22no—
324C22⋊D17—22no—
325C2×Dic17—21no—
326C2×Dic17—21no—
327C2×Dic17—21no—
328C2×Dic17—42no—
329C2×Dic17C4×D411yescharacteristic
330C2×Dic17C4×D411yescharacteristic
331C2×Dic17C2×#4111yescharacteristic
332D68—21no—
333D68C2×C4212yes—
334C4×D17—22no—
335C4×D17—22no—
336C4×D17—21no—
337C4×D17—21no—
338C4×D17—21no—
339C4×D17—21no—
340C4×D17—42no—
341C4×D17—42no—
342C4×D17—41no—
343C4×D17—41no—
344C4×D17—41no—
345C4×D17—41no—
346C4×D17C23×C411yescharacteristic
347C4×D17C23×C411yescharacteristic
348C4×D17C2×#4111yescharacteristic
349C4×D17C2×#4111yescharacteristic
350Dic34—21no—
351Dic34—22no—
352Dic34—22no—
353Dic34C2×C4212yescomplemented
354#3624—22no—
355#3624—22no—
356C8×C17—21no—
357C8×C17C2×C4212yescomplemented
358#3622—21no—
359#3622C2×C4212yescomplemented
360C2×#440—171no—
361C2×#440—171no—
362C2×C4×SD16—171no—
363C42×Q8—171no—
364C42×D4—171no—
365#1776—171no—
366#1776—171no—
367C4×#107—171no—
368#1763—171no—
369#1763—171no—
370#1762—171no—
371#1762—171no—
372C4×#103—171no—
373C4×#102—171no—
374C4×#97—171no—
375C22×C17—22no—
376C22×C17—41no—
377C22×C17—41no—
378C22×C17C2×C4×D411yescharacteristic
379C2×D17—22no—
380C2×D17—41no—
381C2×D17—41no—
382C2×D17—42no—
383C2×D17—42no—
384C2×D17—42no—
385C2×D17—42no—
386C2×D17C2×C4×D411yescharacteristic
387C2×D17C2×C4×D411yescharacteristic
388C2×D17C2×AGL(1,ℤ/8)11yescharacteristic
389C2×D17C2×#13711yescharacteristic
390C2×D17#57511yescharacteristic
391C2×D17#57511yescharacteristic
392#595—22no—
393#595—22no—
394#595—22no—
395#595—42no—
396#595—42no—
397#595—42no—
398#595—42no—
399#595#44014yesdirect product factor
400C4×C17—21no—
401C4×C17—21no—
402C4×C17—22no—
403C4×C17—41no—
404C4×C17—41no—
405C4×C17C22×C4211yescharacteristic
406C4×C17C4×#4111yescharacteristic
407Dic17—21no—
408Dic17—21no—
409Dic17—22no—
410Dic17—41no—
411Dic17—41no—
412Dic17C4×#4111yescharacteristic
413Dic17C4×#4111yescharacteristic
414C22×SD16—171no—
415C2×C4×Q8—171no—
416C2×C4×Q8—171no—
417C2×C4×Q8—171no—
418C2×C4×D4—171no—
419C2×C4×D4—171no—
420C2×C4×D4—171no—
421C22×C42—341no—
422#440—178no—
423#440—171no—
424#440—171no—
425#440—171no—
426#440—171no—
427#440—171no—
428#440—171no—
429#440—171no—
430#440#59511yescharacteristic, direct product factor
431C4×SD16—178no—
432C2×#107—171no—
433C2×#107—171no—
434C2×#106—171no—
435C2×#103—171no—
436C2×#103—171no—
437C2×#103—171no—
438C2×#102—171no—
439C2×#102—171no—
440C2×#102—171no—
441C2×#97—171no—
442C2×#97—171no—
443C2×#97—171no—
444C2×#97—171no—
445C2×C4×C8—171no—
446C2×C4×C8—171no—
447C4×C4⋊C4—171no—
448C4×C4⋊C4—171no—
449C4×C4⋊C4—171no—
450C4×C4⋊C4—171no—
451C4×C4⋊C4—171no—
452C4×C4⋊C4—171no—
453C4×C4⋊C4—341no—
454C4×C4⋊C4—341no—
455C4×C4⋊C4—341no—
456C4×C22⋊C4—341no—
457C4×C22⋊C4—341no—
458C4×C22⋊C4—341no—
459C43—171no—
460C43—341no—
461#340—171no—
462#340—171no—
463#340—171no—
464#340—171no—
465#340—171no—
466#340—171no—
467C2×C17—42no—
468C2×C17C42×D411yescharacteristic
469C2×C17C4×AGL(1,ℤ/8)11yescharacteristic
470C2×C17C4×#13711yescharacteristic
471D17—42no—
472D17C2×#44011yescharacteristic
473D17#294311yescharacteristic
474D17C4×AGL(1,ℤ/8)11yescharacteristic
475D17C4×#13711yescharacteristic
476C22×Q8—171no—
477C22×D4—171no—
478C23×C4—341no—
479C23×C4—341no—
480C23×C4—341no—
481C2×SD16—171no—
482C2×SD16—171no—
483C2×SD16—174no—
484C2×SD16—174no—
485C2×SD16—171no—
486C2×SD16C2×#59511yescharacteristic
487C22×C8—171no—
488C22×C8—171no—
489C22×C8—171no—
490C22×C8—171no—
491C4×Q8—174no—
492C4×Q8—174no—
493C4×Q8—171no—
494C4×Q8—171no—
495C4×Q8—171no—
496C4×Q8—341no—
497C4×Q8—341no—
498C4×Q8—342no—
499C4×Q8—342no—
500C4×Q8C2×#59511yescharacteristic, complemented
501C4×D4—174no—
502C4×D4—174no—
503C4×D4—171no—
504C4×D4—171no—
505C4×D4—171no—
506C4×D4—341no—
507C4×D4—341no—
508C4×D4—342no—
509C4×D4—342no—
510C4×D4C2×#59511yescharacteristic
511C2×C4⋊C4—171no—
512C2×C4⋊C4—171no—
513C2×C4⋊C4—171no—
514C2×C4⋊C4—171no—
515C2×C4⋊C4—171no—
516C2×C4⋊C4—171no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4—341no—
519C2×C4⋊C4—341no—
520C2×C22⋊C4—341no—
521C2×C22⋊C4—341no—
522C2×C22⋊C4—341no—
523C2×C42—171no—
524C2×C42—171no—
525C2×C42—171no—
526C2×C42—171no—
527C2×C42—171no—
528C2×C42—171no—
529C2×C42—171no—
530C2×C42—341no—
531C2×C42—341no—
532C2×C42—341no—
533C2×C42—341no—
534C2×C42—341no—
535C2×C42—341no—
536C2×C42—341no—
537C2×C42—341no—
538C2×C42—341no—
539C2×C42—684no—
540#107—174no—
541#107—171no—
542#107—171no—
543#107—171no—
544#107C2×#59511yescharacteristic, complemented
545#106—174no—
546#103—174no—
547#103—174no—
548#103—171no—
549#103—171no—
550#103—171no—
551#103C2×#59511yescharacteristic, complemented
552#102—174no—
553#102—174no—
554#102—171no—
555#102—171no—
556#102—171no—
557#102C2×#59511yescharacteristic
558#97—174no—
559#97—171no—
560#97—171no—
561#97—171no—
562#97—342no—
563#97—341no—
564#97—341no—
565#97C2×#59511yescharacteristic, complemented
566C4×C8—174no—
567C4×C8—342no—
568#95—341no—
569#95—341no—
570#95—341no—
571#95—341no—
572#95—341no—
573#95—341no—
574C17C4×#44011yescharacteristic, complemented, Sylow
575C24—341no—
576C2×Q8—172no—
577C2×Q8—172no—
578C2×Q8—171no—
579C2×Q8—341no—
580C2×Q8—341no—
581C2×Q8—341no—
582C2×Q8C22×#59511yescharacteristic
583C2×D4—172no—
584C2×D4—172no—
585C2×D4—171no—
586C2×D4—341no—
587C2×D4—341no—
588C2×D4—341no—
589C2×D4C22×#59511yescharacteristic
590C22×C4—21no—
591C22×C4—171no—
592C22×C4—171no—
593C22×C4—171no—
594C22×C4—171no—
595C22×C4—171no—
596C22×C4—171no—
597C22×C4—171no—
598C22×C4—341no—
599C22×C4—341no—
600C22×C4—341no—
601C22×C4—341no—
602C22×C4—341no—
603C22×C4—344no—
604C22×C4—344no—
605C22×C4—341no—
606C22×C4—341no—
607C22×C4—341no—
608C22×C4—341no—
609C22×C4—341no—
610C22×C4—682no—
611C22×C4—682no—
612C22×C4—682no—
613C22×C4—682no—
614C22×C4—682no—
615C22×C4—682no—
616SD16—174no—
617SD16—174no—
618SD16—174no—
619SD16C4×#59514yescomplemented
620C2×C8—171no—
621C2×C8—172no—
622C2×C8—172no—
623C2×C8—172no—
624C2×C8—172no—
625C2×C8—171no—
626C2×C8—341no—
627C2×C8—341no—
628C2×C8—341no—
629C2×C8—341no—
630C2×C8—341no—
631C2×C8—341no—
632C2×C8C22×#59511yescharacteristic
633C2×C8C22×#59511yescharacteristic
634C4⋊C4—21no—
635C4⋊C4—172no—
636C4⋊C4—172no—
637C4⋊C4—172no—
638C4⋊C4—172no—
639C4⋊C4—171no—
640C4⋊C4—171no—
641C4⋊C4—341no—
642C4⋊C4—341no—
643C4⋊C4—341no—
644C4⋊C4—341no—
645C4⋊C4—341no—
646C4⋊C4—341no—
647C4⋊C4—341no—
648C4⋊C4—341no—
649C4⋊C4—344no—
650C4⋊C4—344no—
651C4⋊C4—341no—
652C4⋊C4C22×#59511yescharacteristic
653C4⋊C4C22×#59511yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—341no—
656C22⋊C4—341no—
657C22⋊C4—344no—
658C22⋊C4—344no—
659C22⋊C4—341no—
660C42—21no—
661C42—172no—
662C42—172no—
663C42—172no—
664C42—172no—
665C42—171no—
666C42—171no—
667C42—171no—
668C42—341no—
669C42—341no—
670C42—342no—
671C42—342no—
672C42—344no—
673C42—344no—
674C42—341no—
675C42—682no—
676C42—682no—
677C42—681no—
678C42—681no—
679C42—682no—
680C42—682no—
681C42—682no—
682C42—682no—
683C42C22×#59511yescharacteristic
684C23—21no—
685C23—171no—
686C23—342no—
687C23—342no—
688C23—341no—
689C23—681no—
690C23—681no—
691C23—681no—
692C23—681no—
693Q8—21no—
694Q8—172no—
695Q8—342no—
696Q8—342no—
697Q8—341no—
698Q8C2×C4×#59512yescomplemented
699D4—21no—
700D4—172no—
701D4—342no—
702D4—342no—
703D4—341no—
704D4C2×C4×#59512yes—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—42no—
709C2×C4—172no—
710C2×C4—172no—
711C2×C4—172no—
712C2×C4—171no—
713C2×C4—171no—
714C2×C4—171no—
715C2×C4—171no—
716C2×C4—171no—
717C2×C4—172no—
718C2×C4—172no—
719C2×C4—172no—
720C2×C4—171no—
721C2×C4—171no—
722C2×C4—341no—
723C2×C4—342no—
724C2×C4—342no—
725C2×C4—341no—
726C2×C4—341no—
727C2×C4—341no—
728C2×C4—341no—
729C2×C4—341no—
730C2×C4—341no—
731C2×C4—341no—
732C2×C4—341no—
733C2×C4—341no—
734C2×C4—341no—
735C2×C4—342no—
736C2×C4—342no—
737C2×C4—342no—
738C2×C4—342no—
739C2×C4—341no—
740C2×C4—341no—
741C2×C4—682no—
742C2×C4—682no—
743C2×C4—681no—
744C2×C4—681no—
745C2×C4—681no—
746C2×C4—681no—
747C2×C4—688no—
748C2×C4—682no—
749C2×C4—688no—
750C2×C4—681no—
751C2×C4—681no—
752C2×C4—681no—
753C2×C4—681no—
754C2×C4—681no—
755C2×C4—681no—
756C2×C4—681no—
757C2×C4—681no—
758C2×C4D4×#59511yescharacteristic
759C2×C4D4×#59511yescharacteristic
760C2×C4C23×#59511yescharacteristic
761C8—21no—
762C8—172no—
763C8—342no—
764C8—342no—
765C8—341no—
766C8C2×C4×#59512yescomplemented
767C22—22no—
768C22—41no—
769C22—41no—
770C22—171no—
771C22—171no—
772C22—171no—
773C22—171no—
774C22—171no—
775C22—171no—
776C22—342no—
777C22—682no—
778C22—682no—
779C22—682no—
780C22—682no—
781C22—681no—
782C22—681no—
783C22C2×D4×#59511yescharacteristic
784C4—22no—
785C4—21no—
786C4—21no—
787C4—41no—
788C4—41no—
789C4—174no—
790C4—171no—
791C4—171no—
792C4—342no—
793C4—342no—
794C4—342no—
795C4—342no—
796C4—341no—
797C4—341no—
798C4—682no—
799C4—682no—
800C4—682no—
801C4—682no—
802C4—681no—
803C4—681no—
804C4C22×C4×#59511yescharacteristic
805C4#41×#59511yescharacteristic
806C2—42no—
807C2—171no—
808C2—171no—
809C2—171no—
810C2—171no—
811C2—682no—
812C2C4×D4×#59511yescharacteristic
813C2AGL(1,ℤ/8)×#59511yescharacteristic
814C2#137×#59511yescharacteristic
subgroupG/H
centerC22C2×D4×#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC17×#440C4
socleC22×C17C2×C4×D4
prime radicalC2×D4×D17C23
cosocleC2×C4×D17C24
hypercenter#440#595
hypocenterC17C4×#440
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. C4×Q8×#595C2semidirect
5. #14544599C2semidirect
6. #14544598C2semidirect
7. #107×#595C2semidirect
8. #14544557C2semidirect
9. #14544556C2semidirect
12. #103×#595C2semidirect
14. #97×#595C2semidirect
21. #11763848C4semidirect
22. SD16×#595C4semidirect
57. #11762912C4semidirect
58. #11762911C4semidirect
59. #11762910C4semidirect
60. #11762909C4semidirect
61. #11762908C4semidirect
62. #11762907C4semidirect
63. #11762906C4semidirect
68. C17×#440C4semidirect
78. Q8×#595C2×C4semidirect
79. Q8×#595C2×C4semidirect
108. C4×Q8×C17C2×C4semidirect
110. Q8×Dic17C2×C4semidirect
125. #10587573C2×C4semidirect
132. C4×Dic34C2×C4semidirect
133. #10587549C2×C4semidirect
134. #10587549C2×C4semidirect
145. #10587534C2×C4semidirect
146. #10587533C2×C4semidirect
148. #10587532C2×C4semidirect
150. C8×#595C2×C4semidirect
151. C17×#107C2×C4semidirect
152. C17×#103C2×C4semidirect
154. C17×#97C2×C4semidirect
155. #10587506C2×C4semidirect
158. #10587489C2×C4semidirect
159. #10587487C2×C4semidirect
160. #10587486C2×C4semidirect
161. #10587486C2×C4semidirect
162. #10587481C2×C4semidirect
164. #10587478C2×C4semidirect
165. #10587478C2×C4semidirect
166. #10587474C2×C4semidirect
242. SD16×C17C42semidirect
252. #63230C42semidirect
253. #63229C42semidirect
271. #63219C42semidirect
313. Q8×C17C2×C42semidirect
353. Dic34C2×C42semidirect
357. C8×C17C2×C42semidirect
359. #3622C2×C42semidirect
399. #595#440direct (N × H)
430. #440#595direct (N × H)
500. C4×Q8C2×#595semidirect
544. #107C2×#595semidirect
551. #103C2×#595semidirect
565. #97C2×#595semidirect
574. C17C4×#440semidirect
619. SD16C4×#595semidirect
698. Q8C2×C4×#595semidirect
766. C8C2×C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117638482
C2×SD16×#5952
C4×Q8×#5952
C4×D4×#5952
#145445992
#145445982
#107×#5952
#145445572
#145445562
#145445552
#145445542
#103×#5952
#102×#5952
#97×#5952
D17×#4402
C4×#44017