Finite Group Databasebeta

← D17×#3499 #17942732

Subgroups — D17×#3499 #17942732

Order 4352.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D17C212yesmaximal, complemented
2#14542569C211yesmaximal, characteristic, complemented
3#14542568C214yesmaximal, complemented
4#14542567C213yesmaximal, complemented
5#14542566C216yesmaximal, complemented
6#14542565C212yesmaximal, complemented
7#14542564C213yesmaximal, complemented
8#14542563C2112yesmaximal, complemented
9D4×Q8×D17C214yesmaximal, complemented
10D17×#547C2112yesmaximal, complemented
11D17×#536C216yesmaximal, complemented
12D17×#532C213yesmaximal, complemented
13C2×C4⋊Q8×D17C213yesmaximal, complemented
14C4×#41×D17C211yesmaximal, characteristic, complemented
15C17×#3499C211yesmaximal, characteristic, complemented
16C2×#10587694C2216yescomplemented
17C2×#10587694C2214yescomplemented
18C2×#10587697C22112yescomplemented
19C2×#10587697C2216yescomplemented
20C2×#10587697C2212yescomplemented
212−1+4×D17—232no—
22C2×#41×D17C2216yes—
23C2×#41×D17C22112yes—
24C2×#41×D17C2211yescharacteristic
25C22×Q8×D17C2216yes—
26C22×Q8×D17C2214yes—
27Q8×D68C2214yescomplemented
28D4×Dic34C22112yescomplemented
29#11763474C22112yescomplemented
30Q8×C22⋊D17C2218yescomplemented
31#11763472C22124yescomplemented
32#11763464C22112yescomplemented
33#11763463C22112yescomplemented
34#11763462C22112yescomplemented
35#11763461C22124yescomplemented
36#11763460C22124yescomplemented
37#11763459C22124yescomplemented
38#11763458C22124yescomplemented
39#11763457C22148yescomplemented
40#11763385C2216yescomplemented
41#11763384C22112yescomplemented
42#11763383C2216yescomplemented
43#11763382C22124yescomplemented
44#11763381C22124yescomplemented
45#11763380C2216yescomplemented
46#11763379C22112yescomplemented
47#11763360C2213yescomplemented
48#11763359C2213yescomplemented
49#11763358C2216yescomplemented
50#11763357C2213yescomplemented
51#11763356C22112yescomplemented
52#11763355C2216yescomplemented
53#11763354C22112yescomplemented
54C2×#10587555C2213yescomplemented
55C2×#10587574C22112yescomplemented
56C2×#10587630C2216yescomplemented
57C4⋊Q8×D17C2216yes—
58C4⋊Q8×D17C22112yes—
59C4⋊Q8×D17C2213yes—
60C4⋊Q8×D17C22112yescomplemented
61C4⋊Q8×D17C2216yescomplemented
62C4⋊Q8×D17C2216yescomplemented
63#127×D17C2211yescharacteristic
64#124×D17C2216yes—
65#123×D17C22124yes—
66C22⋊Q8×D17C22124yes—
67#121×D17C22112yes—
68#41×Dic17C2211yescharacteristic, complemented
69C4×#63256C2212yescomplemented
70C4×#63252C2213yescomplemented
71#11763277C2213yescomplemented
72C4×#63254C2216yescomplemented
73C4×Q8×D17C2212yes—
74C4×D4×D17C2216yes—
75C4×D4×D17C22112yes—
76#117×D17C2213yes—
77C2×C4⋊C4×D17C22112yes—
78C2×C42×D17C2213yes—
79C2×C17×2−1+4C2212yescomplemented
80D4×Q8×C17C2214yescomplemented
81C17×#547C22112yescomplemented
82C17×#536C2216yescomplemented
83C17×#532C2213yescomplemented
84C2×C17×C4⋊Q8C2213yescomplemented
85C4×#41×C17C2211yescharacteristic, complemented
86C17×2−1+4—216no—
87C2×#41×C17C23112yes—
88C2×#41×C17C2316yes—
89C2×#41×C17C2311yescharacteristic
90C22×Q8×C17C2314yes—
91C22×Q8×C17C2316yes—
92#10587697—216no—
93#10587697—296no—
94#10587697—248no—
95#41×D17—296no—
96#41×D17—248no—
97#41×D17D4116yescomplemented
98#10587694—232no—
99#10587694—248no—
100C2×#63256C23112yes—
101C2×#63256C2316yes—
102C2×#63256C2311yescharacteristic
103C2×Q8×D17—232no—
104C2×Q8×D17—248no—
105C2×Q8×D17C23112yes—
106C2×Q8×D17C2314yes—
107C2×Q8×D17C23112yes—
108C2×Q8×D17C2316yes—
109C2×Q8×D17C23112yes—
110C2×Q8×D17C23112yes—
111C2×Q8×D17C2311yescharacteristic
112C2×#63254C23124yes—
113C2×#63254C23112yes—
114C2×#63254C23112yes—
115C2×#63254C2316yes—
116C2×#63254C2313yes—
117C2×D4×D17C2314yes—
118C2×D4×D17C23112yes—
119C2×D4×D17C2312yes—
120C2×D4×D17C2313yes—
121C2×#63252C23124yes—
122C2×#63252C23112yes—
123C2×#63252C2316yes—
124C2×#63252C23112yes—
125C2×#63252C2313yes—
126C22×C4×D17C2316yes—
127C22×C4×D17C23112yes—
128C22×C4×D17C23112yes—
129C22×C4×D17C2313yes—
130C22×Dic34C23112yes—
131C22×Dic34C2316yes—
132C22×Dic34C23112yes—
133C17×C4⋊Q8C23112yes—
134C17×C4⋊Q8C2313yes—
135C17×C4⋊Q8C2316yes—
136C17×#127C2311yescharacteristic
137C17×#124C2316yes—
138C17×#123C23124yes—
139C17×C22⋊Q8C23124yes—
140C17×#121C23112yes—
141C4×Q8×C17C2312yes—
142C4×D4×C17C2316yes—
143C4×D4×C17C23112yes—
144C17×#117C2313yes—
145C2×C4⋊C4×C17C23112yes—
146C2×C42×C17C2313yes—
147#10587633C2316yes—
148#10587632C23124yes—
149Q8×Dic17C2312yes—
150#10587630C23124yes—
151#10587630C2316yes—
152#10587630C23112yes—
153#10587626C2314yes—
154#10587626C2312yes—
155#10587625C23124yes—
156#10587624C23112yes—
157#10587622C2316yes—
158#10587621C23124yes—
159D4×Dic17C2316yes—
160D4×Dic17C23112yes—
161#10587616C23112yes—
162#10587615C23124yes—
163C4×C22⋊D17C23124yes—
164C4×C22⋊D17C23112yes—
165#10587612C2313yes—
166C2×C4⋊Dic17C23112yes—
167#10587610C23124yes—
168C2×#63225C23124yes—
169C2×C4×Dic17C2316yes—
170C2×C4×Dic17C2313yes—
171#10587583C23124yes—
172#10587582C23148yes—
173#10587581C23112yes—
174#10587580C23148yes—
175#10587579C23112yes—
176#10587579C2316yes—
177#10587578C2316yes—
178C4⋊C4×D17C23124yes—
179C4⋊C4×D17C23124yes—
180C4⋊C4×D17C23112yes—
181C4⋊C4×D17C23124yes—
182C4⋊C4×D17C2316yes—
183#10587574C23124yes—
184#10587574C23124yes—
185#10587574C23112yes—
186#10587574C23124yes—
187#10587573C2316yes—
188#10587572C23124yes—
189#10587571C23124yes—
190#10587570C23124yes—
191#10587569C23148yes—
192#10587567C23112yes—
193#10587567C23124yes—
194C22⋊C4×D17C2316yes—
195C22⋊C4×D17C23124yes—
196#10587564C23148yes—
197#10587563C2316yes—
198#10587561C2316yes—
199#10587560C2311yescharacteristic
200C4×D68C2316yes—
201C4×D68C23112yes—
202#10587558C2316yes—
203C42×D17C2311yescharacteristic
204C42×D17C2313yes—
205C42×D17C2316yes—
206C42×D17C2316yes—
207C42×D17C2313yes—
208C42×D17C2313yes—
209#10587555C23112yes—
210#10587555C2313yes—
211#10587555C2316yes—
212C4×Dic34C2316yes—
213C23×D17C2414yes—
214C23×D17C2413yes—
215#41×C17—248no—
216#41×C17—224no—
217#41×C17C2×D418yescomplemented
218C2×Q8×C17—216no—
219C2×Q8×C17—224no—
220C2×Q8×C17C24112yes—
221C2×Q8×C17C2416yes—
222C2×Q8×C17C2411yescharacteristic
223C2×D4×C17C24112yes—
224C2×D4×C17C2412yes—
225C2×D4×C17C2414yes—
226C2×D4×C17C2413yes—
227C22×C4×C17C24112yes—
228C22×C4×C17C24112yes—
229C22×C4×C17C2416yes—
230C22×C4×C17C2413yes—
231C2×C22⋊D17C24112yes—
232C2×C22⋊D17C2414yes—
233C2×C22⋊D17C24112yes—
234C2×C22⋊D17C2418yes—
235C2×C22⋊D17C2416yes—
236C22×Dic17C24112yes—
237C22×Dic17C24112yes—
238C22×Dic17C2416yes—
239C22×Dic17C2413yes—
240#63256—248no—
241#63256—224no—
242#63256C2×D418yescomplemented
243Q8×D17—216no—
244Q8×D17—248no—
245Q8×D17—224no—
246Q8×D17—248no—
247Q8×D17—248no—
248Q8×D17—248no—
249Q8×D17C2×D418yes—
250#63254—248no—
251#63254—296no—
252#63254—248no—
253#63254—224no—
254#63254C2×D4124yescomplemented
255D4×D17—248no—
256D4×D17—28no—
257D4×D17—216no—
258D4×D17C2×D4124yes—
259#63252—224no—
260#63252—296no—
261#63252—248no—
262#63252—248no—
263#63252C2×D4124yescomplemented
264C2×D68C2412yes—
265C2×D68C24112yes—
266C2×D68C2414yes—
267C2×D68C2413yes—
268C2×C4×D17—248no—
269C2×C4×D17—248no—
270C2×C4×D17—224no—
271C2×C4×D17C2×D4124yes—
272C2×C4×D17C24112yes—
273C2×C4×D17C24112yes—
274C2×C4×D17C24112yes—
275C2×C4×D17C24124yes—
276C2×C4×D17C2416yes—
277C2×C4×D17C2416yes—
278C2×C4×D17C2416yes—
279C2×C4×D17C2413yes—
280C2×C4×D17C2411yescharacteristic
281C2×C4×D17C2413yes—
282C2×C4×D17C2413yes—
283C2×C4×D17C2412yes—
284C2×Dic34—224no—
285C2×Dic34—248no—
286C2×Dic34—248no—
287C2×Dic34C2416yes—
288C2×Dic34C24112yes—
289C2×Dic34C24124yes—
290C2×Dic34C24112yes—
291C2×Dic34C2413yes—
292C4⋊C4×C17C2416yes—
293C4⋊C4×C17C24124yes—
294C4⋊C4×C17C24112yes—
295C22⋊C4×C17C24124yes—
296C22⋊C4×C17C2416yes—
297C42×C17C2413yes—
298C42×C17C2411yescharacteristic
299C42×C17C2416yes—
300C22⋊Dic17C2416yes—
301C22⋊Dic17C24124yes—
302#63227C24112yes—
303#63227C24124yes—
304#63227C24124yes—
305C4⋊Dic17C2416yes—
306C4⋊Dic17C24112yes—
307C4⋊Dic17C24124yes—
308#63225C24112yes—
309#63225C24148yes—
310#63225C24124yes—
311C4×Dic17C2416yes—
312C4×Dic17C2412yes—
313C4×Dic17C2411yescharacteristic
314C4×Dic17C2413yes—
315C4×Dic17C2416yes—
316C4×Dic17C2416yes—
317C4×Dic17C2416yes—
318C2×#3499—171nomaximal, Sylow
319C23×C17C2514yes—
320C23×C17C2513yes—
321C22×D17—212no—
322C22×D17—28no—
323C22×D17—216no—
324C22×D17C22×D4112yes—
325C22×D17C2514yes—
326C22×D17C2513yes—
327C22×D17C2511yescharacteristic
328Q8×C17—212no—
329Q8×C17—224no—
330Q8×C17C22×D414yes—
331D4×C17—224no—
332D4×C17—24no—
333D4×C17—28no—
334D4×C17C22×D4112yes—
335C2×C4×C17—224no—
336C2×C4×C17—224no—
337C2×C4×C17—212no—
338C2×C4×C17C22×D4112yes—
339C2×C4×C17C2516yes—
340C2×C4×C17C25112yes—
341C2×C4×C17C2511yescharacteristic
342C2×C4×C17C2513yes—
343C2×C4×C17C2512yes—
344C22⋊D17—224no—
345C22⋊D17—224no—
346C22⋊D17—28no—
347C22⋊D17—216no—
348C22⋊D17C22×D4124yes—
349C2×Dic17—224no—
350C2×Dic17—224no—
351C2×Dic17—212no—
352C2×Dic17C22×D4112yes—
353C2×Dic17C2516yes—
354C2×Dic17C25112yes—
355C2×Dic17C2511yescharacteristic
356C2×Dic17C2513yes—
357C2×Dic17C2512yes—
358D68—224no—
359D68—24no—
360D68—28no—
361D68C22×D4112yes—
362C4×D17—224no—
363C4×D17—248no—
364C4×D17—212no—
365C4×D17—224no—
366C4×D17—212no—
367C4×D17—224no—
368C4×D17—212no—
369C4×D17C22×D4112yes—
370C4×D17C22×D414yes—
371C4×D17C22×D4112yes—
372C4×D17C22×D4112yes—
373C4×D172−1+418yescomplemented
374Dic34—212no—
375Dic34—224no—
376Dic34—224no—
377Dic34—248no—
378Dic34C22×D4112yes—
379C22×2−1+4—172no—
380#3499—172no—
381#3499—174no—
382#3499—1712no—
383#3499—176no—
384#3499—173no—
385#3499—173no—
386#3499—171no—
387#3499D1711yescharacteristic, direct product factor
388C2×D4×Q8—174no—
389C2×#547—1712no—
390C2×#536—176no—
391C2×#532—173no—
392C22×C4⋊Q8—173no—
393C2×C4×#41—171no—
394C22×C17—26no—
395C22×C17—24no—
396C22×C17—28no—
397C22×C17C23×D416yes—
398C22×C17C2611yescharacteristic
399C2×D17—26no—
400C2×D17—224no—
401C2×D17—24no—
402C2×D17—28no—
403C2×D17—416no—
404C2×D17C23×D416yes—
405C2×D17C23×D412yes—
406C2×D17C2×2−1+414yes—
407C4×C17—212no—
408C4×C17—26no—
409C4×C17C23×D412yes—
410C4×C17C23×D416yes—
411C4×C17C2×2−1+414yescomplemented
412Dic17—212no—
413Dic17—26no—
414Dic17C23×D412yes—
415Dic17C23×D416yes—
416Dic17C2×2−1+414yescomplemented
417C2×2−1+4—176no—
418C2×2−1+4—1712no—
419C2×2−1+4—172no—
420C2×2−1+4—174no—
421C2×2−1+4—176no—
422C2×2−1+4—3432no—
423C2×2−1+4C2×D1712yescomplemented
424C22×#41—171no—
425C22×#41—176no—
426C22×#41—1712no—
427C23×Q8—176no—
428C23×Q8—174no—
429D4×Q8—178no—
430D4×Q8—1712no—
431D4×Q8—1724no—
432D4×Q8—174no—
433D4×Q8—1712no—
434D4×Q8C2×D1714yescomplemented
435#547—1724no—
436#547—1712no—
437#547—1748no—
438#547—1724no—
439#547—1724no—
440#547—1712no—
441#547—1712no—
442#547—1724no—
443#547C2×D17112yescomplemented
444#536—176no—
445#536—176no—
446#536—1712no—
447#536—1712no—
448#536—1724no—
449#536—1724no—
450#536—176no—
451#536C2×D1716yescomplemented
452#532—176no—
453#532—173no—
454#532—173no—
455#532—176no—
456#532—1712no—
457#532—1712no—
458#532—173no—
459#532C2×D1713yescomplemented
460C2×C4⋊Q8—176no—
461C2×C4⋊Q8—173no—
462C2×C4⋊Q8—176no—
463C2×C4⋊Q8—1712no—
464C2×C4⋊Q8—176no—
465C2×C4⋊Q8—176no—
466C2×C4⋊Q8—1712no—
467C2×C4⋊Q8—1712no—
468C2×C4⋊Q8—173no—
469C2×C4⋊Q8C2×D1713yescomplemented
470C2×#127—171no—
471C2×#124—176no—
472C2×#123—1724no—
473C2×C22⋊Q8—1724no—
474C2×#121—1712no—
475C4×#41—171no—
476C4×#41—172no—
477C4×#41—176no—
478C4×#41—173no—
479C4×#41—173no—
480C4×#41C2×D1711yescharacteristic, complemented
481C2×C4×Q8—172no—
482C2×C4×D4—176no—
483C2×C4×D4—1712no—
484C2×#117—173no—
485C22×C4⋊C4—1712no—
486C22×C42—173no—
487C2×C17—26no—
488C2×C17—44no—
489C2×C17C24×D411yescharacteristic
490C2×C17C22×2−1+412yes—
491D17—26no—
492D17—44no—
493D17#349914yesdirect product factor
4942−1+4—216no—
4952−1+4—3432no—
4962−1+4—3448no—
4972−1+4—3496no—
4982−1+4—3448no—
4992−1+4—3416no—
500C2×#41—1716no—
501C2×#41—171no—
502C2×#41—176no—
503C2×#41—1712no—
504C2×#41—173no—
505C2×#41—1712no—
506C2×#41—176no—
507C2×#41—1712no—
508C2×#41—1724no—
509C2×#41—173no—
510C2×#41—1712no—
511C2×#41—176no—
512C2×#41—1712no—
513C2×#41—1724no—
514C2×#41—3448no—
515C2×#41—3496no—
516C2×#41C22×D1716yes—
517C2×#41C22×D17112yes—
518C2×#41C22×D1711yescharacteristic
519C22×Q8—171no—
520C22×Q8—1712no—
521C22×Q8—176no—
522C22×Q8—1712no—
523C22×Q8—1712no—
524C22×Q8—1712no—
525C22×Q8—174no—
526C22×Q8—1712no—
527C22×Q8—176no—
528C22×Q8—1712no—
529C22×Q8—3448no—
530C22×Q8—3432no—
531C22×Q8C22×D1716yes—
532C22×Q8C22×D1714yes—
533C22×D4—173no—
534C22×D4—174no—
535C22×D4—1712no—
536C22×D4—172no—
537C23×C4—173no—
538C23×C4—176no—
539C23×C4—1712no—
540C23×C4—1712no—
541C4⋊Q8—176no—
542C4⋊Q8—1712no—
543C4⋊Q8—1724no—
544C4⋊Q8—1712no—
545C4⋊Q8—1724no—
546C4⋊Q8—1724no—
547C4⋊Q8—1724no—
548C4⋊Q8—173no—
549C4⋊Q8—176no—
550C4⋊Q8—1712no—
551C4⋊Q8C22×D1713yes—
552C4⋊Q8C22×D1716yes—
553C4⋊Q8C22×D17112yes—
554#127—172no—
555#127—174no—
556#127—171no—
557#127C22×D1711yescharacteristic
558#124—176no—
559#124—176no—
560#124—1724no—
561#124—176no—
562#124C22×D1716yes—
563#123—1724no—
564#123—1724no—
565#123—1748no—
566#123—1748no—
567#123—1724no—
568#123C22×D17124yes—
569C22⋊Q8—1724no—
570C22⋊Q8—1724no—
571C22⋊Q8—1748no—
572C22⋊Q8—1724no—
573C22⋊Q8—1748no—
574C22⋊Q8C22×D17124yes—
575#121—1712no—
576#121—1724no—
577#121—1712no—
578#121—1712no—
579#121—1724no—
580#121C22×D17112yes—
581C4×Q8—172no—
582C4×Q8—176no—
583C4×Q8—176no—
584C4×Q8C22×D1712yes—
585C4×D4—176no—
586C4×D4—1712no—
587C4×D4—1712no—
588C4×D4—1724no—
589C4×D4—176no—
590C4×D4—1712no—
591C4×D4—1712no—
592C4×D4—1724no—
593C4×D4—176no—
594C4×D4—1712no—
595C4×D4C22×D1716yes—
596C4×D4C22×D17112yes—
597#117—173no—
598#117—176no—
599#117—176no—
600#117—176no—
601#117C22×D1713yes—
602C2×C4⋊C4—1724no—
603C2×C4⋊C4—1712no—
604C2×C4⋊C4—1712no—
605C2×C4⋊C4—1724no—
606C2×C4⋊C4—1724no—
607C2×C4⋊C4—1724no—
608C2×C4⋊C4—176no—
609C2×C4⋊C4C22×D17112yes—
610C2×C22⋊C4—176no—
611C2×C22⋊C4—1724no—
612C2×C42—176no—
613C2×C42—173no—
614C2×C42—173no—
615C2×C42—176no—
616C2×C42—176no—
617C2×C42—173no—
618C2×C42—173no—
619C2×C42—171no—
620C2×C42C22×D1713yes—
621C17C2×#349911yescharacteristic, complemented, Sylow
622C24—173no—
623C24—174no—
624#41—248no—
625#41—224no—
626#41—178no—
627#41—1724no—
628#41—1724no—
629#41—3448no—
630#41—3496no—
631#41—3448no—
632#41—3448no—
633#41—3424no—
634#41—3424no—
635#41—3496no—
636#41—3448no—
637#41—3448no—
638#41—3424no—
639#41D4×D1718yescomplemented
640C2×Q8—216no—
641C2×Q8—224no—
642C2×Q8—178no—
643C2×Q8—173no—
644C2×Q8—1724no—
645C2×Q8—1712no—
646C2×Q8—1712no—
647C2×Q8—176no—
648C2×Q8—3448no—
649C2×Q8—3448no—
650C2×Q8—3424no—
651C2×Q8—3448no—
652C2×Q8—3448no—
653C2×Q8—3448no—
654C2×Q8—3448no—
655C2×Q8—3416no—
656C2×Q8—3424no—
657C2×Q8C23×D17112yes—
658C2×Q8C23×D1716yes—
659C2×Q8C23×D1711yescharacteristic
660C2×D4—176no—
661C2×D4—1724no—
662C2×D4—178no—
663C2×D4—1712no—
664C2×D4—1712no—
665C2×D4—174no—
666C2×D4—173no—
667C2×D4—174no—
668C2×D4—1712no—
669C2×D4—172no—
670C2×D4—3416no—
671C2×D4—348no—
672C2×D4—3448no—
673C2×D4C23×D1714yes—
674C2×D4C23×D17112yes—
675C2×D4C23×D1712yes—
676C2×D4C23×D1713yes—
677C22×C4—173no—
678C22×C4—1724no—
679C22×C4—172no—
680C22×C4—171no—
681C22×C4—173no—
682C22×C4—173no—
683C22×C4—173no—
684C22×C4—176no—
685C22×C4—1712no—
686C22×C4—1712no—
687C22×C4—176no—
688C22×C4—176no—
689C22×C4—176no—
690C22×C4—1712no—
691C22×C4—1724no—
692C22×C4—1712no—
693C22×C4—1712no—
694C22×C4—3424no—
695C22×C4—3448no—
696C22×C4—3448no—
697C22×C4C23×D1716yes—
698C22×C4C23×D17112yes—
699C22×C4C23×D17112yes—
700C22×C4C23×D1713yes—
701C4⋊C4—1724no—
702C4⋊C4—1712no—
703C4⋊C4—1748no—
704C4⋊C4—1724no—
705C4⋊C4—1712no—
706C4⋊C4—176no—
707C4⋊C4C23×D17112yes—
708C4⋊C4C23×D17124yes—
709C4⋊C4C23×D1716yes—
710C22⋊C4—176no—
711C22⋊C4—1724no—
712C22⋊C4—1712no—
713C22⋊C4—1724no—
714C22⋊C4—1724no—
715C22⋊C4C23×D1716yes—
716C22⋊C4C23×D17124yes—
717C42—171no—
718C42—172no—
719C42—176no—
720C42—173no—
721C42—176no—
722C42—176no—
723C42—176no—
724C42C23×D1711yescharacteristic
725C42C23×D1713yes—
726C42C23×D1716yes—
727C23—171no—
728C23—1712no—
729C23—173no—
730C23—174no—
731C23—3412no—
732C23—348no—
733C23—3416no—
734C23C24×D1714yes—
735C23C24×D1713yes—
736Q8—224no—
737Q8—212no—
738Q8—1712no—
739Q8—3424no—
740Q8—3448no—
741Q8—3424no—
742Q8—3412no—
743Q8C2×D4×D1714yes—
744D4—224no—
745D4—24no—
746D4—28no—
747D4—1724no—
748D4—1712no—
749D4—3424no—
750D4—348no—
751D4—3416no—
752D4—3424no—
753D4—3424no—
754D4—344no—
755D4—348no—
756D4C2×D4×D17112yes—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—212no—
760C2×C4—1712no—
761C2×C4—172no—
762C2×C4—171no—
763C2×C4—173no—
764C2×C4—174no—
765C2×C4—1712no—
766C2×C4—1712no—
767C2×C4—1712no—
768C2×C4—178no—
769C2×C4—176no—
770C2×C4—1712no—
771C2×C4—3424no—
772C2×C4—3412no—
773C2×C4—3424no—
774C2×C4—3448no—
775C2×C4—3412no—
776C2×C4—3424no—
777C2×C4—3412no—
778C2×C4—3424no—
779C2×C4—3424no—
780C2×C4—3412no—
781C2×C4C2×D4×D17112yes—
782C2×C4C24×D1716yes—
783C2×C4C24×D17112yes—
784C2×C4C24×D1711yescharacteristic
785C2×C4C24×D1713yes—
786C2×C4C24×D1712yes—
787C22—26no—
788C22—24no—
789C22—28no—
790C22—172no—
791C22—174no—
792C22—176no—
793C22—3424no—
794C22—346no—
795C22—344no—
796C22—348no—
797C22—6816no—
798C22C22×D4×D1716yes—
799C22C25×D1711yescharacteristic
800C4—212no—
801C4—26no—
802C4—172no—
803C4—176no—
804C4—174no—
805C4—3412no—
806C4—346no—
807C4C22×D4×D1716yes—
808C4C22×D4×D1712yes—
809C42−1+4×D1714yescomplemented
810C2—26no—
811C2—44no—
812C2—174no—
813C2—346no—
814C2—684no—
815C2C23×D4×D1711yescharacteristic
816C2C2×2−1+4×D1712yes—
subgroupG/H
center, FrattiniC22C25×D17
commutator, socle, cosocleC22×C17C26
FittingC17×#3499C2
hypercenter#3499D17
hypocenterC17C2×#3499
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D17C2semidirect
2. #14542569C2semidirect
3. #14542568C2semidirect
4. #14542567C2semidirect
5. #14542566C2semidirect
6. #14542565C2semidirect
7. #14542564C2semidirect
8. #14542563C2semidirect
9. D4×Q8×D17C2semidirect
10. D17×#547C2semidirect
11. D17×#536C2semidirect
12. D17×#532C2semidirect
13. C2×C4⋊Q8×D17C2semidirect
14. C4×#41×D17C2semidirect
15. C17×#3499C2semidirect
16. C2×#10587694C22semidirect
17. C2×#10587694C22semidirect
18. C2×#10587697C22semidirect
19. C2×#10587697C22semidirect
20. C2×#10587697C22semidirect
27. Q8×D68C22semidirect
28. D4×Dic34C22semidirect
29. #11763474C22semidirect
30. Q8×C22⋊D17C22semidirect
31. #11763472C22semidirect
32. #11763464C22semidirect
33. #11763463C22semidirect
34. #11763462C22semidirect
35. #11763461C22semidirect
36. #11763460C22semidirect
37. #11763459C22semidirect
38. #11763458C22semidirect
39. #11763457C22semidirect
40. #11763385C22semidirect
41. #11763384C22semidirect
42. #11763383C22semidirect
43. #11763382C22semidirect
44. #11763381C22semidirect
45. #11763380C22semidirect
46. #11763379C22semidirect
47. #11763360C22semidirect
48. #11763359C22semidirect
49. #11763358C22semidirect
50. #11763357C22semidirect
51. #11763356C22semidirect
52. #11763355C22semidirect
53. #11763354C22semidirect
54. C2×#10587555C22semidirect
55. C2×#10587574C22semidirect
56. C2×#10587630C22semidirect
60. C4⋊Q8×D17C22semidirect
61. C4⋊Q8×D17C22semidirect
62. C4⋊Q8×D17C22semidirect
68. #41×Dic17C22semidirect
69. C4×#63256C22semidirect
70. C4×#63252C22semidirect
71. #11763277C22semidirect
72. C4×#63254C22semidirect
79. C2×C17×2−1+4C22semidirect
80. D4×Q8×C17C22semidirect
81. C17×#547C22semidirect
82. C17×#536C22semidirect
83. C17×#532C22semidirect
84. C2×C17×C4⋊Q8C22semidirect
85. C4×#41×C17C22semidirect
97. #41×D17D4semidirect
217. #41×C17C2×D4semidirect
242. #63256C2×D4semidirect
254. #63254C2×D4semidirect
263. #63252C2×D4semidirect
373. C4×D172−1+4semidirect
387. #3499D17direct (N × H)
411. C4×C17C2×2−1+4semidirect
416. Dic17C2×2−1+4semidirect
423. C2×2−1+4C2×D17semidirect
434. D4×Q8C2×D17semidirect
443. #547C2×D17semidirect
451. #536C2×D17semidirect
459. #532C2×D17semidirect
469. C2×C4⋊Q8C2×D17semidirect
480. C4×#41C2×D17semidirect
493. D17#3499direct (N × H)
621. C17C2×#3499semidirect
639. #41D4×D17semidirect
809. C42−1+4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D172
#145425692
#145425682
#145425672
#145425662
#145425652
#145425642
#145425632
D4×Q8×D172
D17×#5472
D17×#5362
D17×#5322
C2×C4⋊Q8×D172
C4×#41×D172
C17×#34992
C2×#349917