Finite Group Databasebeta

← C4×#11763052 #17040947

Subgroups — C4×#11763052 #17040947

Order 4352.

1086 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763052C211yesmaximal, characteristic
2C2×C4×#63218C211yesmaximal, characteristic, complemented
3C4×#10587632C211yesmaximal, characteristic, complemented
4C4×#10587624C211yesmaximal, characteristic
5#14529667C211yesmaximal, characteristic, complemented
6#14529520C211yesmaximal, characteristic, complemented
7#14529478C211yesmaximal, characteristic, complemented
8#14529471C211yesmaximal, characteristic, complemented
9#14529219C211yesmaximal, characteristic
10#14529214C211yesmaximal, characteristic, complemented
11#14528814C211yesmaximal, characteristic, complemented
12C4×#10587489C211yesmaximal, characteristic, complemented
13C4×#10587506C211yesmaximal, characteristic, complemented
14C4×#10587503C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C17C211yesmaximal, characteristic, complemented
16C22×#63218C2211yescharacteristic
17C22×#63218C2211yescharacteristic
18C2×#10587632C2211yescharacteristic
19C2×#10587624C2211yescharacteristic
20C2×C4×C22⋊D17—21no—
21C2×C42×D17C2211yescharacteristic
22#11763052C418yesdirect product factor
23C2×#10587489C2211yescharacteristic
24C2×#10587489C2211yescharacteristic
25C2×#10587506C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587503C2211yescharacteristic
28C2×#10587503C2211yescharacteristic
29C4×#63218—24no—
30C2×#10587486C2211yescharacteristic
31C2×#10587486C2211yescharacteristic
32C2×C4×#3622C2211yescharacteristic
33#11762716C2211yescharacteristic
34#11762712C2211yescharacteristic
35#11762705C2211yescharacteristic
36#11762705C2211yescharacteristic
37#11762697—21no—
38#11762690—21no—
39#11762685—21no—
40#11762680—21no—
41#11762666C2211yescharacteristic
42#11762666C2211yescharacteristic
43C4×#63225—21no—
44C4×C4⋊Dic17C2211yescharacteristic
45C4×C4⋊Dic17C2211yescharacteristic
46C4×#63227—21no—
47C4×C22⋊Dic17—21no—
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53#11762571C2211yescharacteristic
54C22×SD16×C17C2211yescharacteristic
55C2×C4×Q8×C17C2211yescharacteristic
56C2×C4×D4×C17C2211yescharacteristic
57C4×SD16×C17—24no—
58C2×C17×#106C2211yescharacteristic
59C2×C17×#103C2211yescharacteristic
60C2×C17×#102C2211yescharacteristic
61C2×C4×C8×C17C2211yescharacteristic
62C22×Q8×C17C2311yescharacteristic
63C22×D4×C17C2311yescharacteristic
64C23×C4×C17—21no—
65C22×C22⋊D17—21no—
66C22×C4×D17D411yescharacteristic
67C22×C4×D17D411yescharacteristic
68C22×C4×D17C2311yescharacteristic
69C2×SD16×C17—22no—
70C2×SD16×C17—22no—
71C2×SD16×C17C2×C414yescomplemented
72C22×C8×C17C2311yescharacteristic
73C22×C8×C17C2311yescharacteristic
74C4×Q8×C17—22no—
75C4×Q8×C17—22no—
76C4×D4×C17—22no—
77C4×D4×C17—22no—
78C2×C4⋊C4×C17—21no—
79C2×C4⋊C4×C17C2311yescharacteristic
80C2×C4⋊C4×C17C2311yescharacteristic
81C2×C22⋊C4×C17—21no—
82C2×C42×C17—21no—
83C2×C42×C17C2311yescharacteristic
84C2×C22⋊Dic17—21no—
85C2×C22⋊Dic17—21no—
86C2×C22⋊Dic17—21no—
87#10587632—22no—
88#10587632C2×C414yescomplemented
89#10587624—22no—
90#10587624C2×C414yes—
91C4×C22⋊D17—44no—
92C2×#63227—21no—
93C2×#63227—21no—
94C2×#63227—21no—
95C2×C4⋊Dic17C2311yescharacteristic
96C2×C4⋊Dic17C2311yescharacteristic
97C2×C4⋊Dic17C2311yescharacteristic
98C2×C4⋊Dic17C2311yescharacteristic
99C2×#63225—21no—
100C2×#63225—21no—
101C2×#63225—21no—
102C2×C4×Dic17—21no—
103C2×C4×Dic17—21no—
104C2×C4×Dic17D411yescharacteristic
105C2×C4×Dic17D411yescharacteristic
106C2×C4×Dic17C2311yescharacteristic
107C22×#3622C2311yescharacteristic
108C22×#3622C2311yescharacteristic
109C2×#63218—22no—
110C2×#63218—22no—
111C2×#63218—22no—
112C2×#63218—22no—
113C2×#63218—22no—
114C2×#63218C2×C414yescomplemented
115C42×D17—22no—
116C42×D17—22no—
117C17×#106—22no—
118C17×#103—22no—
119C17×#102—22no—
120C4×C8×C17D414yescomplemented
121#10587506—22no—
122#10587506C2×C414yescomplemented
123#10587503—22no—
124#10587503C2×C414yescomplemented
125#10587502—21no—
126#10587502—21no—
127#10587502—21no—
128#10587502—21no—
129#10587502—21no—
130#10587502—21no—
131#10587502—21no—
132#10587502—21no—
133#10587489—22no—
134#10587489C2×C414yescomplemented
135#10587486—22no—
136#10587486—22no—
137C4×#3622—22no—
138C24×C17—21no—
139C23×D17C2×D411yescharacteristic
140C2×Q8×C17—21no—
141C2×Q8×C17—21no—
142C2×Q8×C17—21no—
143C2×Q8×C17—21no—
144C2×Q8×C17—21no—
145C2×Q8×C17C22×C412yes—
146C2×D4×C17—21no—
147C2×D4×C17—21no—
148C2×D4×C17—21no—
149C2×D4×C17—21no—
150C2×D4×C17—21no—
151C2×D4×C17C22×C412yes—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—42no—
156C22×C4×C17—42no—
157C22×C4×C17—42no—
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2411yescharacteristic
161C2×C22⋊D17—24no—
162C2×C22⋊D17—42no—
163C2×C22⋊D17—42no—
164C22×Dic17—21no—
165C22×Dic17—21no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17C2×D411yescharacteristic
169C22×Dic17C2×D411yescharacteristic
170C22×Dic17C2×D411yescharacteristic
171C2×C4×D17—21no—
172C2×C4×D17—21no—
173C2×C4×D17—21no—
174C2×C4×D17—21no—
175C2×C4×D17—22no—
176C2×C4×D17—22no—
177C2×C4×D17—22no—
178C2×C4×D17—22no—
179C2×C4×D17—41no—
180C2×C4×D17—41no—
181C2×C4×D17C22×C412yes—
182C2×C4×D17#4112yes—
183SD16×C17—28no—
184C2×C8×C17—21no—
185C2×C8×C17—21no—
186C2×C8×C17C22×C412yes—
187C2×C8×C17C2×D412yes—
188C2×C8×C17C2×D412yes—
189C2×C8×C17#4112yes—
190C4⋊C4×C17—21no—
191C4⋊C4×C17—21no—
192C4⋊C4×C17—21no—
193C4⋊C4×C17—21no—
194C4⋊C4×C17—42no—
195C22⋊C4×C17—42no—
196C42×C17—42no—
197C42×C17C2×D412yes—
198C42×C17#4112yes—
199C22⋊Dic17—24no—
200C22⋊Dic17—42no—
201C22⋊Dic17—42no—
202#63227—24no—
203#63227—42no—
204#63227—42no—
205C4⋊Dic17—21no—
206C4⋊Dic17—21no—
207C4⋊Dic17—21no—
208C4⋊Dic17—21no—
209C4⋊Dic17—21no—
210C4⋊Dic17—21no—
211C4⋊Dic17C22×C412yes—
212C4⋊Dic17C22×C412yes—
213#63225—24no—
214#63225—42no—
215#63225—42no—
216C4×Dic17—22no—
217C4×Dic17—22no—
218C4×Dic17—21no—
219C4×Dic17—21no—
220C4×Dic17—42no—
221C4×Dic17—42no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622C22×C412yes—
227C2×#3622#4112yes—
228#63218—28no—
229#63218—28no—
230C4×#468—171nomaximal, Sylow
231C23×C17—22no—
232C23×C17—41no—
233C23×C17—41no—
234C23×C17—41no—
235C23×C17—41no—
236C23×C17—41no—
237C23×C17—41no—
238C23×C17C22×D411yescharacteristic
239C22×D17—21no—
240C22×D17—21no—
241C22×D17—21no—
242C22×D17—21no—
243C22×D17—21no—
244C22×D17—21no—
245C22×D17C4×D412yes—
246Q8×C17—22no—
247Q8×C17—22no—
248Q8×C17—41no—
249Q8×C17—41no—
250D4×C17—22no—
251D4×C17—22no—
252D4×C17—41no—
253D4×C17—41no—
254C2×C4×C17—21no—
255C2×C4×C17—21no—
256C2×C4×C17—22no—
257C2×C4×C17—41no—
258C2×C4×C17—41no—
259C2×C4×C17—41no—
260C2×C4×C17—41no—
261C2×C4×C17—41no—
262C2×C4×C17—41no—
263C2×C4×C17—41no—
264C2×C4×C17—41no—
265C2×C4×C17—84no—
266C2×C4×C17#12112yes—
267C2×C4×C17#12112yes—
268C2×C4×C17AGL(1,ℤ/8)12yes—
269C2×C4×C17#13712yes—
270C2×C4×C17C23×C411yescharacteristic
271C2×C4×C17C22×D411yescharacteristic
272C2×C4×C17C2×#4111yescharacteristic
273C2×C4×C17C2×#4111yescharacteristic
274C2×C4×C17C2×#4111yescharacteristic
275C2×C4×C17C2×#4111yescharacteristic
276C22⋊D17—48no—
277C2×Dic17—21no—
278C2×Dic17—21no—
279C2×Dic17—22no—
280C2×Dic17—22no—
281C2×Dic17—21no—
282C2×Dic17—21no—
283C2×Dic17—21no—
284C2×Dic17—21no—
285C2×Dic17—21no—
286C2×Dic17—21no—
287C2×Dic17—41no—
288C2×Dic17—41no—
289C2×Dic17—41no—
290C2×Dic17—41no—
291C2×Dic17—41no—
292C2×Dic17—41no—
293C2×Dic17—41no—
294C2×Dic17—41no—
295C2×Dic17—41no—
296C2×Dic17—41no—
297C2×Dic17C4×D412yes—
298C4×D17—22no—
299C4×D17—22no—
300C4×D17—22no—
301C4×D17—22no—
302C4×D17—44no—
303C4×D17—44no—
304C8×C17—22no—
305C8×C17C4×D414yescomplemented
306#3622—22no—
307#3622—22no—
308C2×#468—171no—
309C2×C4×SD16D1711yescharacteristic, complemented
310C2×C4×M16—171no—
311C4×C22⋊Q8—171no—
312C4×#121—171no—
313#1973—171no—
314#1943—171no—
315#1936—171no—
316#1935—171no—
317#1895—171no—
318#1894—171no—
319#1809—171no—
320C4×#107—171no—
321C4×#103—171no—
322C4×#102—171no—
323C22×C17—42no—
324C22×C17—42no—
325C22×C17—42no—
326C22×C17—81no—
327C22×C17—81no—
328C22×C17—81no—
329C22×C17—81no—
330C22×C17C2×C4×D411yescharacteristic
331C22×C17C2×#12111yescharacteristic
332C22×C17#53211yescharacteristic
333C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C17C2×#13711yescharacteristic
335C22×C17#57511yescharacteristic
336C22×C17#57511yescharacteristic
337C2×D17—22no—
338C2×D17—22no—
339C2×D17—22no—
340C2×D17—41no—
341C2×D17—41no—
342C2×D17—41no—
343C2×D17—41no—
344C4×C17—22no—
345C4×C17—42no—
346C4×C17—81no—
347C4×C17—81no—
348C4×C17#46814yescomplemented
349C4×C17C2×C4×D411yescharacteristic
350C4×C17C4×#4111yescharacteristic
351C4×C17#52511yescharacteristic
352C4×C17#52911yescharacteristic
353Dic17—22no—
354Dic17—42no—
355Dic17—42no—
356Dic17—41no—
357Dic17—41no—
358Dic17—81no—
359Dic17—81no—
360C22×SD16C2×D1711yescharacteristic
361C22×M16—171no—
362C22×M16—171no—
363C2×C22⋊Q8—171no—
364C2×#121—171no—
365C2×C4×Q8C2×D1711yescharacteristic
366C2×C4×D4—341no—
367C2×C4×D4C2×D1711yescharacteristic
368C22×C42—171no—
369#468—178no—
370C4×SD16—24no—
371C2×#107—171no—
372C2×#107—171no—
373C2×#106C2×D1711yescharacteristic
374C2×#103—171no—
375C2×#103—171no—
376C2×#103C2×D1711yescharacteristic
377C2×#102—171no—
378C2×#102—171no—
379C2×#102C2×D1711yescharacteristic
380C4×M16—344no—
381C2×#97—171no—
382C2×#97—171no—
383C2×C4×C8—171no—
384C2×C4×C8C2×D1711yescharacteristic
385#391—171no—
386#390—171no—
387#389—171no—
388#389—171no—
389#388—341no—
390#387—341no—
391#386—341no—
392#385—341no—
393#380—171no—
394#380—171no—
395C4×C4⋊C4—171no—
396C4×C4⋊C4—171no—
397C4×C4⋊C4—341no—
398C4×C22⋊C4—341no—
399C4×C22⋊C4—341no—
400#340—171no—
401#340—171no—
402#340—171no—
403#340—171no—
404#340—171no—
405#340—171no—
406C2×C17—82no—
407C2×C17C4×#12111yescharacteristic
408C2×C17C4×AGL(1,ℤ/8)11yescharacteristic
409C2×C17C4×#13711yescharacteristic
410C2×C17C2×#46811yescharacteristic
411C2×C17#305411yescharacteristic
412C2×C17#317111yescharacteristic
413C2×C17#317211yescharacteristic
414D17—42no—
415C22×Q8C22×D1711yescharacteristic
416C22×D4—341no—
417C22×D4C22×D1711yescharacteristic
418C23×C4—21no—
419C23×C4—171no—
420C23×C4—171no—
421C23×C4—171no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16C4×D1714yescomplemented
425C2×M16—174no—
426C2×M16—342no—
427C2×M16—342no—
428C2×M16—342no—
429C2×M16—342no—
430C2×M16—342no—
431C22×C8—171no—
432C22×C8—171no—
433C22×C8C22×D1711yescharacteristic
434C22×C8C22×D1711yescharacteristic
435C22⋊Q8—174no—
436C22⋊Q8—342no—
437#121—174no—
438#121—342no—
439C4×Q8—22no—
440C4×Q8—22no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—684no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—171no—
446C2×C4⋊C4—171no—
447C2×C4⋊C4—171no—
448C2×C4⋊C4—171no—
449C2×C4⋊C4—341no—
450C2×C4⋊C4—341no—
451C2×C4⋊C4—341no—
452C2×C4⋊C4C22×D1711yescharacteristic
453C2×C4⋊C4C22×D1711yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—341no—
456C2×C22⋊C4—341no—
457C2×C22⋊C4—341no—
458C2×C22⋊C4—341no—
459C2×C22⋊C4—341no—
460C2×C22⋊C4—341no—
461C2×C42—21no—
462C2×C42—171no—
463C2×C42—171no—
464C2×C42—171no—
465C2×C42—342no—
466C2×C42—342no—
467C2×C42—341no—
468C2×C42—341no—
469C2×C42C22×D1711yescharacteristic
470#107—174no—
471#107—342no—
472#106—22no—
473#103—22no—
474#103—174no—
475#103—342no—
476#102—22no—
477#102—174no—
478#102—342no—
479#97—342no—
480#97—342no—
481C4×C8—342no—
482C4×C8C22⋊D1714yescomplemented
483#95—341no—
484#95—341no—
485#95—341no—
486#95—341no—
487#95—341no—
488#95—341no—
489#95—341no—
490#95—341no—
491C17C4×#46811yescharacteristic, complemented, Sylow
492C24—21no—
493C24—171no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4×D1712yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—344no—
506C2×D4—682no—
507C2×D4—682no—
508C2×D4C2×C4×D1712yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—171no—
516C22×C4—172no—
517C22×C4—172no—
518C22×C4—171no—
519C22×C4—171no—
520C22×C4—341no—
521C22×C4—341no—
522C22×C4—341no—
523C22×C4—341no—
524C22×C4—341no—
525C22×C4—341no—
526C22×C4—342no—
527C22×C4—342no—
528C22×C4—342no—
529C22×C4—342no—
530C22×C4—341no—
531C22×C4—341no—
532C22×C4—681no—
533C22×C4—681no—
534C22×C4D4×D1711yescharacteristic
535C22×C4D4×D1711yescharacteristic
536C22×C4C23×D1711yescharacteristic
537SD16—28no—
538M16—348no—
539M16—348no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—172no—
543C2×C8—172no—
544C2×C8—341no—
545C2×C8—341no—
546C2×C8—341no—
547C2×C8—341no—
548C2×C8C2×C4×D1712yes—
549C2×C8#6325212yes—
550C2×C8C2×C22⋊D1712yes—
551C2×C8C2×C22⋊D1712yes—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—172no—
558C4⋊C4—172no—
559C4⋊C4—344no—
560C4⋊C4—341no—
561C4⋊C4—341no—
562C4⋊C4—341no—
563C4⋊C4—341no—
564C4⋊C4—341no—
565C4⋊C4—341no—
566C4⋊C4—682no—
567C4⋊C4—682no—
568C22⋊C4—42no—
569C22⋊C4—344no—
570C22⋊C4—344no—
571C22⋊C4—682no—
572C22⋊C4—682no—
573C22⋊C4—682no—
574C22⋊C4—682no—
575C42—42no—
576C42—341no—
577C42—341no—
578C42—342no—
579C42—342no—
580C42—682no—
581C42—682no—
582C42#6325412yes—
583C42C2×C22⋊D1712yes—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—172no—
592C23—341no—
593C23—341no—
594C23—341no—
595C23—341no—
596C23—341no—
597C23—341no—
598C23C2×D4×D1711yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—41no—
606D4—41no—
607D4—688no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—84no—
620C2×C4—172no—
621C2×C4—341no—
622C2×C4—341no—
623C2×C4—342no—
624C2×C4—342no—
625C2×C4—342no—
626C2×C4—342no—
627C2×C4—342no—
628C2×C4—342no—
629C2×C4—341no—
630C2×C4—341no—
631C2×C4—341no—
632C2×C4—341no—
633C2×C4—341no—
634C2×C4—341no—
635C2×C4—684no—
636C2×C4—681no—
637C2×C4—681no—
638C2×C4—681no—
639C2×C4—681no—
640C2×C4—684no—
641C2×C4—681no—
642C2×C4—681no—
643C2×C4—681no—
644C2×C4—681no—
645C2×C4—681no—
646C2×C4—681no—
647C2×C4#1058760012yes—
648C2×C4#1058760112yes—
649C2×C4#1058762412yes—
650C2×C4#1058762412yes—
651C2×C4C22×C4×D1711yescharacteristic
652C2×C4C2×#6325211yescharacteristic
653C2×C4C2×#6325411yescharacteristic
654C2×C4#41×D1711yescharacteristic
655C2×C4#41×D1711yescharacteristic
656C2×C4C22×C22⋊D1711yescharacteristic
657C8—22no—
658C8—342no—
659C8—342no—
660C8C4×C22⋊D1714yescomplemented
661C22—42no—
662C22—42no—
663C22—42no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—342no—
669C22—342no—
670C22—342no—
671C22—681no—
672C22—681no—
673C22—681no—
674C22—681no—
675C22C4×D4×D1711yescharacteristic
676C22C2×#1058762411yescharacteristic
677C22#1176335611yescharacteristic
678C22C2×#1058760011yescharacteristic
679C22C2×#1058760111yescharacteristic
680C22#1176360611yescharacteristic
681C22#1176360611yescharacteristic
682C4—22no—
683C4—42no—
684C4—81no—
685C4—81no—
686C4—342no—
687C4—682no—
688C4—682no—
689C4—681no—
690C4—681no—
691C4—1361no—
692C4—1361no—
693C4#1176305214yesdirect product factor
694C4C2×C4×C22⋊D1711yescharacteristic
695C4C4×#6325411yescharacteristic
696C4#1176331611yescharacteristic
697C4#1176334111yescharacteristic
698C2—82no—
699C2—682no—
700C2C4×#1058762411yescharacteristic
701C2C4×#1058760011yescharacteristic
702C2C4×#1058760111yescharacteristic
703C2C2×#1176305211yescharacteristic
704C2#1453838911yescharacteristic
705C2#1453937511yescharacteristic
706C2#1453938611yescharacteristic
subgroupG/H
centerC22×C4D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C4×SD16×C17C2
socleC23×C17C22×D4
prime radicalC2×#10587624C22
cosocleC22×C4×C17C24
hypercenterC2×C4×SD16D17
hypocenterC17C4×#468
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#63218C2semidirect
3. C4×#10587632C2semidirect
5. #14529667C2semidirect
6. #14529520C2semidirect
7. #14529478C2semidirect
8. #14529471C2semidirect
10. #14529214C2semidirect
11. #14528814C2semidirect
12. C4×#10587489C2semidirect
13. C4×#10587506C2semidirect
14. C4×#10587503C2semidirect
15. C2×C4×SD16×C17C2semidirect
22. #11763052C4direct (N × H)
71. C2×SD16×C17C2×C4semidirect
88. #10587632C2×C4semidirect
114. C2×#63218C2×C4semidirect
120. C4×C8×C17D4semidirect
122. #10587506C2×C4semidirect
124. #10587503C2×C4semidirect
134. #10587489C2×C4semidirect
305. C8×C17C4×D4semidirect
309. C2×C4×SD16D17semidirect
348. C4×C17#468semidirect
424. C2×SD16C4×D17semidirect
482. C4×C8C22⋊D17semidirect
491. C17C4×#468semidirect
660. C8C4×C22⋊D17semidirect
693. C4#11763052direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117630522
C2×C4×#632182
C4×#105876322
C4×#105876242
#145296672
#145295202
#145294782
#145294712
#145292192
#145292142
#145288142
C4×#105874892
C4×#105875062
C4×#105875032
C2×C4×SD16×C172
C4×#46817