Finite Group Databasebeta

← D17×#3550 #17942128

Subgroups — D17×#3550 #17942128

Order 4352.

7074 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14543198C211yesmaximal, characteristic, complemented
2#14543197C214yesmaximal, complemented
3#14543196C212yesmaximal, complemented
4#14543195C212yesmaximal, complemented
5#14543194C214yesmaximal, complemented
6#14543193C214yesmaximal, complemented
7#14543192C218yesmaximal, complemented
8#14543191C214yesmaximal, complemented
9#14543190C212yesmaximal, complemented
10D17×#563C214yesmaximal, complemented
11D17×#559C212yesmaximal, complemented
12Q82×D17C212yesmaximal, complemented
13D17×#556C214yesmaximal, complemented
14D4×Q8×D17C214yesmaximal, complemented
15D17×#542C218yesmaximal, complemented
16D17×#536C214yesmaximal, complemented
17D17×#533C212yesmaximal, complemented
18D17×#532C211yesmaximal, characteristic
19C17×#3550C211yesmaximal, characteristic, complemented
20C2×#41×D17C2212yes—
21C22×Q8×D17C2214yes—
22#11763563C2218yescomplemented
23#11763562C2218yescomplemented
24#11763561C22116yescomplemented
25#11763560C22116yescomplemented
26#11763559C2214yescomplemented
27#11763558C2218yescomplemented
28#11763545C2212yescomplemented
29#11763544C2214yescomplemented
30#11763543C2218yescomplemented
31#11763542C2218yescomplemented
32#11763541C2218yescomplemented
33Q8×Dic34C2218yescomplemented
34Q8×Dic34C2214yescomplemented
35#11763539C2212yescomplemented
36#11763539C2218yescomplemented
37#11763539C2218yescomplemented
38#11763533C2214yescomplemented
39#11763532C2214yescomplemented
40#11763531C2218yescomplemented
41#11763530C2218yescomplemented
42#11763529C2214yescomplemented
43#11763528C2218yescomplemented
44#11763527C2218yescomplemented
45#11763526C22116yescomplemented
46Q8×D68C2214yescomplemented
47D4×Dic34C2218yescomplemented
48D4×Dic34C2214yescomplemented
49#11763474C2218yescomplemented
50#11763474C2214yescomplemented
51Q8×C22⋊D17C2218yescomplemented
52#11763472C22116yescomplemented
53#11763472C2218yescomplemented
54#11763433C2218yescomplemented
55#11763432C2218yescomplemented
56#11763431C2218yescomplemented
57#11763430C2218yescomplemented
58#11763429C22116yescomplemented
59#11763428C2218yescomplemented
60#11763427C22116yescomplemented
61#11763426C2218yescomplemented
62#11763425C22116yescomplemented
63#11763424C2218yescomplemented
64#11763423C22116yescomplemented
65#11763385C2214yescomplemented
66#11763384C2218yescomplemented
67#11763383C2214yescomplemented
68#11763382C2218yescomplemented
69#11763382C2218yescomplemented
70#11763381C2218yescomplemented
71#11763381C2218yescomplemented
72#11763380C2214yescomplemented
73#11763379C2218yescomplemented
74#11763366C2212yescomplemented
75#11763365C2214yescomplemented
76#11763364C2212yescomplemented
77#11763364C2212yescomplemented
78#11763363C2214yescomplemented
79#11763363C2214yescomplemented
80#11763362C2214yescomplemented
81#11763361C2214yescomplemented
82#11763361C2214yescomplemented
83#11763360C2211yescharacteristic
84#11763359C2211yescharacteristic
85#11763358C2212yes—
86#11763357C2211yescharacteristic
87#11763356C2214yes—
88#11763355C2212yes—
89#11763354C2214yes—
90C4⋊Q8×D17C2218yes—
91C4⋊Q8×D17C2211yescharacteristic
92C4⋊Q8×D17C2218yes—
93C4⋊Q8×D17C2212yes—
94C4⋊Q8×D17C2212yes—
95#127×D17C2211yescharacteristic
96#126×D17C22116yes—
97#125×D17C2214yes—
98#124×D17C2218yes—
99#124×D17C2218yes—
100#124×D17C2212yes—
101#123×D17C2218yes—
102#123×D17C2218yes—
103C22⋊Q8×D17C2214yes—
104C22⋊Q8×D17C2218yes—
105C22⋊Q8×D17C22116yes—
106C22⋊Q8×D17C2214yes—
107#121×D17C2214yes—
108C4×Q8×D17C2214yes—
109C4×Q8×D17C2218yes—
110C4×Q8×D17C2214yes—
111C4×D4×D17C2218yes—
112C4×D4×D17C2214yes—
113#117×D17C2214yes—
114#117×D17C2214yes—
115C2×C42×D17C2211yescharacteristic
116C17×#563C2214yescomplemented
117C17×#559C2212yescomplemented
118Q82×C17C2212yescomplemented
119C17×#556C2214yescomplemented
120D4×Q8×C17C2214yescomplemented
121C17×#542C2218yescomplemented
122C17×#536C2214yescomplemented
123C17×#533C2212yescomplemented
124C17×#532C2211yescharacteristic
125C2×#41×C17C2312yes—
126C22×Q8×C17C2314yes—
127#41×D17—48no—
128C2×#63256C2312yes—
129C2×Q8×D17—416no—
130C2×Q8×D17C2314yes—
131C2×Q8×D17C2314yes—
132C2×Q8×D17C2318yes—
133C2×Q8×D17C2318yes—
134C2×Q8×D17C2318yes—
135C2×Q8×D17C2312yes—
136C2×#63254C2314yes—
137C2×#63254C2312yes—
138C2×D4×D17C2314yes—
139C2×D4×D17C2314yes—
140C2×D4×D17C2312yes—
141C2×#63252C2312yes—
142C2×#63252C2314yes—
143C22×C4×D17C2312yes—
144C22×C4×D17C2311yescharacteristic
145C22×C4×D17C2314yes—
146C22×C4×D17C2318yes—
147C22×Dic34C2314yes—
148C22×Dic34C2318yes—
149C17×C4⋊Q8C2312yes—
150C17×C4⋊Q8C2318yes—
151C17×C4⋊Q8C2311yescharacteristic
152C17×C4⋊Q8C2312yes—
153C17×C4⋊Q8C2318yes—
154C17×#127C2311yescharacteristic
155C17×#126C23116yes—
156C17×#125C2314yes—
157C17×#124C2312yes—
158C17×#124C2318yes—
159C17×#124C2318yes—
160C17×#123C2318yes—
161C17×#123C2318yes—
162C17×C22⋊Q8C2318yes—
163C17×C22⋊Q8C23116yes—
164C17×C22⋊Q8C2314yes—
165C17×C22⋊Q8C2314yes—
166C17×#121C2314yes—
167C4×Q8×C17C2314yes—
168C4×Q8×C17C2314yes—
169C4×Q8×C17C2318yes—
170C4×D4×C17C2314yes—
171C4×D4×C17C2318yes—
172C17×#117C2314yes—
173C17×#117C2314yes—
174C2×C42×C17C2311yescharacteristic
175#10587633C2318yes—
176#10587633C2312yes—
177#10587633C2318yes—
178#10587632C2318yes—
179#10587632C23116yes—
180#10587632C2314yes—
181#10587632C2314yes—
182Q8×Dic17C2314yes—
183Q8×Dic17C2318yes—
184Q8×Dic17C2314yes—
185#10587630C2314yes—
186#10587630C23116yes—
187#10587630C2314yes—
188#10587630C2312yes—
189#10587630C2318yes—
190#10587630C2318yes—
191#10587626C2314yes—
192#10587626C2312yes—
193#10587625C2318yes—
194#10587624C2314yes—
195#10587622C2318yes—
196#10587622C2312yes—
197#10587622C2318yes—
198#10587621C2318yes—
199#10587621C2318yes—
200D4×Dic17C2314yes—
201D4×Dic17C2318yes—
202#10587616C2314yes—
203#10587615C2318yes—
204#10587615C2318yes—
205C4×C22⋊D17C2318yes—
206C4×C22⋊D17C23116yes—
207#10587612C2314yes—
208#10587612C2314yes—
209#10587610C2318yes—
210#10587610C23116yes—
211#10587610C2314yes—
212#10587610C2314yes—
213C2×C4×Dic17C2312yes—
214C2×C4×Dic17C2311yescharacteristic
215#10587584C23116yes—
216#10587584C23116yes—
217#10587584C23116yes—
218#10587583C2318yes—
219#10587583C23116yes—
220#10587583C2314yes—
221#10587583C2314yes—
222#10587582C23116yes—
223#10587582C23116yes—
224#10587582C23116yes—
225#10587582C2318yes—
226#10587582C2318yes—
227#10587581C2314yes—
228#10587580C23116yes—
229#10587580C23116yes—
230#10587579C2314yes—
231#10587579C2318yes—
232#10587578C2318yes—
233#10587578C2314yes—
234#10587578C2314yes—
235C4⋊C4×D17C2314yes—
236C4⋊C4×D17C2314yes—
237C4⋊C4×D17C2314yes—
238C4⋊C4×D17C2314yes—
239C4⋊C4×D17C2314yes—
240C4⋊C4×D17C2318yes—
241C4⋊C4×D17C23116yes—
242C4⋊C4×D17C2318yes—
243#10587576C2314yes—
244#10587576C2314yes—
245#10587575C2318yes—
246#10587575C2318yes—
247#10587574C2314yes—
248#10587574C23116yes—
249#10587574C2314yes—
250#10587574C2318yes—
251#10587574C2318yes—
252#10587574C2314yes—
253#10587574C2314yes—
254#10587574C2314yes—
255#10587574C23116yes—
256#10587574C23116yes—
257#10587573C2318yes—
258#10587573C2314yes—
259#10587573C23116yes—
260#10587573C2318yes—
261#10587573C2314yes—
262#10587573C2318yes—
263#10587572C2318yes—
264#10587572C2318yes—
265#10587571C23116yes—
266#10587571C23116yes—
267#10587571C2318yes—
268#10587571C23116yes—
269#10587571C23116yes—
270#10587570C2318yes—
271#10587569C23116yes—
272#10587569C23116yes—
273#10587567C2318yes—
274#10587567C23116yes—
275C22⋊C4×D17C2318yes—
276C22⋊C4×D17C2318yes—
277C22⋊C4×D17C2318yes—
278C22⋊C4×D17C23116yes—
279#10587565C23116yes—
280#10587565C23116yes—
281#10587565C23116yes—
282#10587564C23116yes—
283#10587564C23116yes—
284#10587564C23116yes—
285#10587564C2318yes—
286#10587564C2318yes—
287#10587563C2318yes—
288#10587563C2318yes—
289#10587562C23116yes—
290#10587561C2318yes—
291#10587561C2312yes—
292#10587561C2318yes—
293#10587560C2311yescharacteristic
294C4×D68C2314yes—
295C4×D68C2318yes—
296#10587558C2318yes—
297#10587558C2318yes—
298C42×D17C2312yes—
299C42×D17C2311yescharacteristic
300C42×D17C2311yescharacteristic
301C42×D17C2312yes—
302C42×D17C2311yescharacteristic
303C42×D17C2311yescharacteristic
304C42×D17C2318yes—
305C42×D17C2318yes—
306#10587556C2314yes—
307#10587555C2312yes—
308#10587555C2318yes—
309#10587555C2312yes—
310#10587555C2311yescharacteristic
311#10587555C2318yes—
312C4×Dic34C2318yes—
313C4×Dic34C2314yes—
314C4×Dic34C23116yes—
315C4×Dic34C2318yes—
316C4×Dic34C2318yes—
317C4×Dic34C2314yes—
318C23×D17C2414yes—
319C23×D17C2411yescharacteristic
320#41×C17—44no—
321C2×Q8×C17—48no—
322C2×Q8×C17C2414yes—
323C2×Q8×C17C2414yes—
324C2×Q8×C17C2418yes—
325C2×Q8×C17C2412yes—
326C2×D4×C17C2414yes—
327C2×D4×C17C2412yes—
328C2×D4×C17C2414yes—
329C22×C4×C17C2411yescharacteristic
330C22×C4×C17C2414yes—
331C22×C4×C17C2412yes—
332C22×C4×C17C2418yes—
333C2×C22⋊D17C2418yes—
334C2×C22⋊D17C2414yes—
335C2×C22⋊D17C2414yes—
336C2×C22⋊D17C2414yes—
337C22×Dic17C2414yes—
338C22×Dic17C2411yescharacteristic
339C22×Dic17C2412yes—
340C22×Dic17C2418yes—
341#63256—44no—
342Q8×D17—216no—
343Q8×D17—216no—
344Q8×D17—416no—
345Q8×D17—416no—
346Q8×D17—416no—
347Q8×D17—44no—
348#63254—44no—
349#63254—48no—
350D4×D17—216no—
351D4×D17—44no—
352D4×D17—48no—
353#63252—48no—
354#63252—44no—
355C2×D68C2414yes—
356C2×D68C2412yes—
357C2×D68C2414yes—
358C2×C4×D17—216no—
359C2×C4×D17—24no—
360C2×C4×D17—28no—
361C2×C4×D17—416no—
362C2×C4×D17C2418yes—
363C2×C4×D17C2411yescharacteristic
364C2×C4×D17C2414yes—
365C2×C4×D17C2411yescharacteristic
366C2×C4×D17C2414yes—
367C2×C4×D17C2411yescharacteristic
368C2×C4×D17C2414yes—
369C2×C4×D17C2412yes—
370C2×C4×D17C2412yes—
371C2×C4×D17C2412yes—
372C2×C4×D17C2418yes—
373C2×C4×D17C24116yes—
374C2×C4×D17C2411yescharacteristic
375C2×C4×D17C2412yes—
376C2×Dic34—416no—
377C2×Dic34—48no—
378C2×Dic34C2414yes—
379C2×Dic34C2418yes—
380C2×Dic34C2414yes—
381C2×Dic34C2418yes—
382C2×Dic34C2418yes—
383C2×Dic34C24116yes—
384C2×Dic34C2414yes—
385C2×Dic34C2412yes—
386C4⋊C4×C17C2414yes—
387C4⋊C4×C17C2418yes—
388C4⋊C4×C17C2414yes—
389C4⋊C4×C17C24116yes—
390C4⋊C4×C17C2418yes—
391C4⋊C4×C17C2414yes—
392C4⋊C4×C17C2414yes—
393C4⋊C4×C17C2414yes—
394C22⋊C4×C17C2418yes—
395C22⋊C4×C17C24116yes—
396C22⋊C4×C17C2418yes—
397C22⋊C4×C17C2418yes—
398C42×C17C2411yescharacteristic
399C42×C17C2418yes—
400C42×C17C2418yes—
401C42×C17C2411yescharacteristic
402C42×C17C2412yes—
403C22⋊Dic17C2418yes—
404C22⋊Dic17C2418yes—
405C22⋊Dic17C2418yes—
406C22⋊Dic17C24116yes—
407#63227C2418yes—
408#63227C24116yes—
409#63227C2418yes—
410#63227C24116yes—
411#63227C2418yes—
412#63227C24116yes—
413#63227C2418yes—
414C4⋊Dic17C2414yes—
415C4⋊Dic17C2414yes—
416C4⋊Dic17C24116yes—
417C4⋊Dic17C2418yes—
418C4⋊Dic17C2414yes—
419C4⋊Dic17C2418yes—
420C4⋊Dic17C2414yes—
421C4⋊Dic17C2414yes—
422#63225C2418yes—
423#63225C2418yes—
424#63225C2418yes—
425#63225C2418yes—
426#63225C2418yes—
427#63225C24116yes—
428#63225C24116yes—
429#63225C2418yes—
430#63225C2418yes—
431#63225C2418yes—
432#63225C2418yes—
433C4×Dic17C2412yes—
434C4×Dic17C2412yes—
435C4×Dic17C2418yes—
436C4×Dic17C24116yes—
437C4×Dic17C2418yes—
438C4×Dic17C2412yes—
439C4×Dic17C2412yes—
440C4×Dic17C2411yescharacteristic
441C4×Dic17C2412yes—
442C4×Dic17C2411yescharacteristic
443C4×Dic17C2418yes—
444C4×Dic17C2418yes—
445C2×#3550—171nomaximal, Sylow
446C23×C17C2514yes—
447C23×C17C2511yescharacteristic
448C22×D17—28no—
449C22×D17—22no—
450C22×D17—24no—
451C22×D17—216no—
452C22×D17C2514yes—
453C22×D17C2511yescharacteristic
454C22×D17C2511yescharacteristic
455Q8×C17—28no—
456Q8×C17—28no—
457Q8×C17—48no—
458Q8×C17—42no—
459D4×C17—28no—
460D4×C17—44no—
461D4×C17—42no—
462C2×C4×C17—28no—
463C2×C4×C17—22no—
464C2×C4×C17—24no—
465C2×C4×C17—48no—
466C2×C4×C17C2518yes—
467C2×C4×C17C2512yes—
468C2×C4×C17C2514yes—
469C2×C4×C17C2511yescharacteristic
470C2×C4×C17C2518yes—
471C2×C4×C17C2511yescharacteristic
472C2×C4×C17C2512yes—
473C22⋊D17—216no—
474C22⋊D17—44no—
475C22⋊D17—44no—
476C22⋊D17—44no—
477C2×Dic17—28no—
478C2×Dic17—22no—
479C2×Dic17—24no—
480C2×Dic17—48no—
481C2×Dic17C2518yes—
482C2×Dic17C2512yes—
483C2×Dic17C2518yes—
484C2×Dic17C2514yes—
485C2×Dic17C2511yescharacteristic
486C2×Dic17C2511yescharacteristic
487C2×Dic17C2512yes—
488D68—28no—
489D68—44no—
490D68—42no—
491C4×D17—22no—
492C4×D17—28no—
493C4×D17—216no—
494C4×D17—24no—
495C4×D17—216no—
496C4×D17—22no—
497C4×D17—28no—
498C4×D17—24no—
499C4×D17—22no—
500C4×D17—28no—
501C4×D17—24no—
502C4×D17—416no—
503C4×D17H(5,𝔽2)14yes—
504C4×D172−1+418yes—
505Dic34—28no—
506Dic34—28no—
507Dic34—216no—
508Dic34—216no—
509Dic34—48no—
510Dic34—416no—
511Dic34—42no—
512Dic34—44no—
513#3550—174no—
514#3550—172no—
515#3550—172no—
516#3550—174no—
517#3550—174no—
518#3550—178no—
519#3550—174no—
520#3550—172no—
521#3550—171no—
522#3550D1711yescharacteristic, direct product factor
523C2×#563—174no—
524C2×#559—172no—
525C2×Q82—172no—
526C2×#556—174no—
527C2×D4×Q8—174no—
528C2×#542—178no—
529C2×#536—174no—
530C2×#533—172no—
531C2×#532—171no—
532C22×C17—24no—
533C22×C17—21no—
534C22×C17—22no—
535C22×C17—28no—
536C22×C17C2611yescharacteristic
537C2×D17—24no—
538C2×D17—21no—
539C2×D17—22no—
540C2×D17—28no—
541C2×D17—416no—
542C2×D17—44no—
543C2×D17C2×H(5,𝔽2)12yes—
544C2×D17C2×2−1+414yes—
545C4×C17—28no—
546C4×C17—24no—
547C4×C17—21no—
548C4×C17—28no—
549C4×C17—22no—
550C4×C17C2×H(5,𝔽2)12yes—
551C4×C17C2×2−1+414yes—
552Dic17—28no—
553Dic17—24no—
554Dic17—21no—
555Dic17—28no—
556Dic17—22no—
557Dic17C2×H(5,𝔽2)12yes—
558Dic17C2×2−1+414yes—
559C22×#41—172no—
560C23×Q8—174no—
561#563—178no—
562#563—1716no—
563#563—178no—
564#563—174no—
565#563—178no—
566#563—1716no—
567#563C2×D1714yescomplemented
568#559—172no—
569#559—178no—
570#559—178no—
571#559—174no—
572#559—178no—
573#559C2×D1712yescomplemented
574Q82—178no—
575Q82—178no—
576Q82—172no—
577Q82—178no—
578Q82—174no—
579Q82C2×D1712yescomplemented
580#556—174no—
581#556—1716no—
582#556—178no—
583#556—178no—
584#556—178no—
585#556—174no—
586#556—174no—
587#556—178no—
588#556C2×D1714yescomplemented
589D4×Q8—178no—
590D4×Q8—178no—
591D4×Q8—174no—
592D4×Q8—178no—
593D4×Q8—1716no—
594D4×Q8—174no—
595D4×Q8—178no—
596D4×Q8—174no—
597D4×Q8C2×D1714yescomplemented
598#542—178no—
599#542—1716no—
600#542—1716no—
601#542—178no—
602#542—1716no—
603#542—1716no—
604#542—178no—
605#542—178no—
606#542—178no—
607#542—178no—
608#542—178no—
609#542C2×D1718yescomplemented
610#536—174no—
611#536—174no—
612#536—178no—
613#536—178no—
614#536—178no—
615#536—178no—
616#536—178no—
617#536—178no—
618#536—174no—
619#536C2×D1714yescomplemented
620#533—172no—
621#533—172no—
622#533—174no—
623#533—174no—
624#533—174no—
625#533—174no—
626#533—174no—
627#533—174no—
628#533—172no—
629#533C2×D1712yescomplemented
630#532—172no—
631#532—171no—
632#532—171no—
633#532—172no—
634#532—174no—
635#532—174no—
636#532—171no—
637#532C2×D1711yescharacteristic
638C2×C4⋊Q8—171no—
639C2×C4⋊Q8—172no—
640C2×C4⋊Q8—172no—
641C2×C4⋊Q8—178no—
642C2×C4⋊Q8—178no—
643C2×#127—171no—
644C2×#126—1716no—
645C2×#125—174no—
646C2×#124—172no—
647C2×#124—178no—
648C2×#124—178no—
649C2×#123—178no—
650C2×#123—178no—
651C2×C22⋊Q8—174no—
652C2×C22⋊Q8—174no—
653C2×C22⋊Q8—178no—
654C2×C22⋊Q8—1716no—
655C2×#121—174no—
656C2×C4×Q8—174no—
657C2×C4×Q8—174no—
658C2×C4×Q8—178no—
659C2×C4×D4—174no—
660C2×C4×D4—178no—
661C2×#117—174no—
662C2×#117—174no—
663C22×C42—171no—
664C2×C17—44no—
665C2×C17—41no—
666C2×C17C22×H(5,𝔽2)11yescharacteristic
667C2×C17C22×2−1+412yes—
668D17—44no—
669D17—41no—
670D17#355014yesdirect product factor
671C2×#41—172no—
672C2×#41—174no—
673C2×#41—172no—
674C2×#41—174no—
675C2×#41—172no—
676C2×#41—688no—
677C2×#41C22×D1712yes—
678C22×Q8—174no—
679C22×Q8—174no—
680C22×Q8—178no—
681C22×Q8—172no—
682C22×Q8—178no—
683C22×Q8—178no—
684C22×Q8—178no—
685C22×Q8—174no—
686C22×Q8—6816no—
687C22×Q8C22×D1714yes—
688C22×D4—174no—
689C22×D4—174no—
690C22×D4—172no—
691C23×C4—172no—
692C23×C4—174no—
693C23×C4—171no—
694C23×C4—178no—
695C4⋊Q8—172no—
696C4⋊Q8—174no—
697C4⋊Q8—174no—
698C4⋊Q8—178no—
699C4⋊Q8—178no—
700C4⋊Q8—1716no—
701C4⋊Q8—174no—
702C4⋊Q8—174no—
703C4⋊Q8—174no—
704C4⋊Q8—174no—
705C4⋊Q8—174no—
706C4⋊Q8—1716no—
707C4⋊Q8—1716no—
708C4⋊Q8—1716no—
709C4⋊Q8—178no—
710C4⋊Q8—178no—
711C4⋊Q8—171no—
712C4⋊Q8—172no—
713C4⋊Q8—172no—
714C4⋊Q8—178no—
715C4⋊Q8—178no—
716C4⋊Q8C22×D1711yescharacteristic
717C4⋊Q8C22×D1712yes—
718C4⋊Q8C22×D1712yes—
719C4⋊Q8C22×D1718yes—
720C4⋊Q8C22×D1718yes—
721#127—172no—
722#127—174no—
723#127—171no—
724#127C22×D1711yescharacteristic
725#126—1716no—
726#126—1716no—
727#126—1716no—
728#126—1716no—
729#126—1716no—
730#126—1716no—
731#126—1716no—
732#126C22×D17116yes—
733#125—178no—
734#125—178no—
735#125—174no—
736#125—174no—
737#125—174no—
738#125C22×D1714yes—
739#124—172no—
740#124—178no—
741#124—178no—
742#124—172no—
743#124—178no—
744#124—178no—
745#124—178no—
746#124—1716no—
747#124—1716no—
748#124—1716no—
749#124—1716no—
750#124—172no—
751#124—178no—
752#124—178no—
753#124C22×D1712yes—
754#124C22×D1718yes—
755#124C22×D1718yes—
756#123—178no—
757#123—178no—
758#123—178no—
759#123—178no—
760#123—1716no—
761#123—1716no—
762#123—1716no—
763#123—178no—
764#123—1716no—
765#123—178no—
766#123C22×D1718yes—
767#123C22×D1718yes—
768C22⋊Q8—174no—
769C22⋊Q8—174no—
770C22⋊Q8—178no—
771C22⋊Q8—1716no—
772C22⋊Q8—174no—
773C22⋊Q8—174no—
774C22⋊Q8—178no—
775C22⋊Q8—1716no—
776C22⋊Q8—178no—
777C22⋊Q8—174no—
778C22⋊Q8—178no—
779C22⋊Q8—174no—
780C22⋊Q8—1716no—
781C22⋊Q8—178no—
782C22⋊Q8—1716no—
783C22⋊Q8—1716no—
784C22⋊Q8—1716no—
785C22⋊Q8—178no—
786C22⋊Q8—178no—
787C22⋊Q8—1716no—
788C22⋊Q8—1716no—
789C22⋊Q8—1716no—
790C22⋊Q8C22×D1714yes—
791C22⋊Q8C22×D1714yes—
792C22⋊Q8C22×D1718yes—
793C22⋊Q8C22×D17116yes—
794#121—174no—
795#121—178no—
796#121—174no—
797#121—174no—
798#121—178no—
799#121C22×D1714yes—
800C4×Q8—174no—
801C4×Q8—174no—
802C4×Q8—178no—
803C4×Q8—178no—
804C4×Q8—174no—
805C4×Q8—178no—
806C4×Q8—174no—
807C4×Q8—1716no—
808C4×Q8—178no—
809C4×Q8—178no—
810C4×Q8—174no—
811C4×Q8—178no—
812C4×Q8—174no—
813C4×Q8—1716no—
814C4×Q8—178no—
815C4×Q8C22×D1714yes—
816C4×Q8C22×D1714yes—
817C4×Q8C22×D1718yes—
818C4×D4—174no—
819C4×D4—178no—
820C4×D4—178no—
821C4×D4—1716no—
822C4×D4—174no—
823C4×D4—178no—
824C4×D4—178no—
825C4×D4—1716no—
826C4×D4—174no—
827C4×D4—178no—
828C4×D4C22×D1714yes—
829C4×D4C22×D1718yes—
830#117—174no—
831#117—174no—
832#117—174no—
833#117—174no—
834#117—178no—
835#117—178no—
836#117—178no—
837#117—178no—
838#117—178no—
839#117C22×D1714yes—
840#117C22×D1714yes—
841C2×C4⋊C4—174no—
842C2×C4⋊C4—174no—
843C2×C4⋊C4—174no—
844C2×C4⋊C4—174no—
845C2×C4⋊C4—174no—
846C2×C4⋊C4—178no—
847C2×C4⋊C4—1716no—
848C2×C4⋊C4—178no—
849C2×C22⋊C4—178no—
850C2×C22⋊C4—178no—
851C2×C22⋊C4—178no—
852C2×C22⋊C4—1716no—
853C2×C42—171no—
854C2×C42—172no—
855C2×C42—178no—
856C2×C42—178no—
857C2×C42—172no—
858C2×C42—171no—
859C2×C42—171no—
860C2×C42—171no—
861C2×C42—171no—
862C2×C42—172no—
863C2×C42C22×D1711yescharacteristic
864C17C2×#355011yescharacteristic, complemented, Sylow
865C24—174no—
866C24—171no—
867#41—44no—
868#41—688no—
869#41—684no—
870#41—688no—
871#41—684no—
872#41—684no—
873C2×Q8—48no—
874C2×Q8—178no—
875C2×Q8—174no—
876C2×Q8—178no—
877C2×Q8—174no—
878C2×Q8—1716no—
879C2×Q8—178no—
880C2×Q8—172no—
881C2×Q8—174no—
882C2×Q8—3416no—
883C2×Q8—3416no—
884C2×Q8—688no—
885C2×Q8—6816no—
886C2×Q8—6816no—
887C2×Q8—684no—
888C2×Q8—6816no—
889C2×Q8—6816no—
890C2×Q8C23×D1714yes—
891C2×Q8C23×D1714yes—
892C2×Q8C23×D1718yes—
893C2×Q8C23×D1712yes—
894C2×D4—178no—
895C2×D4—174no—
896C2×D4—174no—
897C2×D4—174no—
898C2×D4—174no—
899C2×D4—174no—
900C2×D4—172no—
901C2×D4—3416no—
902C2×D4—684no—
903C2×D4—688no—
904C2×D4C23×D1714yes—
905C2×D4C23×D1714yes—
906C2×D4C23×D1712yes—
907C22×C4—172no—
908C22×C4—171no—
909C22×C4—172no—
910C22×C4—171no—
911C22×C4—174no—
912C22×C4—178no—
913C22×C4—178no—
914C22×C4—172no—
915C22×C4—174no—
916C22×C4—171no—
917C22×C4—172no—
918C22×C4—172no—
919C22×C4—171no—
920C22×C4—171no—
921C22×C4—178no—
922C22×C4—174no—
923C22×C4—174no—
924C22×C4—1716no—
925C22×C4—348no—
926C22×C4—3416no—
927C22×C4—344no—
928C22×C4—6816no—
929C22×C4C23×D1712yes—
930C22×C4C23×D1711yescharacteristic
931C22×C4C23×D1714yes—
932C22×C4C23×D1718yes—
933C4⋊C4—178no—
934C4⋊C4—174no—
935C4⋊C4—178no—
936C4⋊C4—174no—
937C4⋊C4—178no—
938C4⋊C4—174no—
939C4⋊C4—178no—
940C4⋊C4—174no—
941C4⋊C4—178no—
942C4⋊C4—174no—
943C4⋊C4—178no—
944C4⋊C4—178no—
945C4⋊C4—178no—
946C4⋊C4—1716no—
947C4⋊C4—1716no—
948C4⋊C4—1716no—
949C4⋊C4—178no—
950C4⋊C4—178no—
951C4⋊C4—178no—
952C4⋊C4C23×D1714yes—
953C4⋊C4C23×D1714yes—
954C4⋊C4C23×D1714yes—
955C4⋊C4C23×D1714yes—
956C4⋊C4C23×D1714yes—
957C4⋊C4C23×D1718yes—
958C4⋊C4C23×D17116yes—
959C4⋊C4C23×D1718yes—
960C22⋊C4—178no—
961C22⋊C4—178no—
962C22⋊C4—178no—
963C22⋊C4—1716no—
964C22⋊C4—178no—
965C22⋊C4—178no—
966C22⋊C4—1716no—
967C22⋊C4—178no—
968C22⋊C4—178no—
969C22⋊C4—1716no—
970C22⋊C4—1716no—
971C22⋊C4C23×D1718yes—
972C22⋊C4C23×D1718yes—
973C22⋊C4C23×D1718yes—
974C22⋊C4C23×D17116yes—
975C42—172no—
976C42—172no—
977C42—172no—
978C42—171no—
979C42—172no—
980C42—171no—
981C42—172no—
982C42—178no—
983C42—178no—
984C42—178no—
985C42—178no—
986C42—1716no—
987C42C23×D1712yes—
988C42C23×D1711yescharacteristic
989C42C23×D1711yescharacteristic
990C42C23×D1718yes—
991C42C23×D1718yes—
992C23—171no—
993C23—174no—
994C23—171no—
995C23—348no—
996C23—342no—
997C23—344no—
998C23—3416no—
999C23C24×D1714yes—
1000C23C24×D1711yescharacteristic
1001Q8—28no—
1002Q8—28no—
1003Q8—48no—
1004Q8—42no—
1005Q8—3416no—
1006Q8—3416no—
1007Q8—348no—
1008Q8—348no—
1009Q8—688no—
1010Q8—6816no—
1011Q8—682no—
1012Q8—684no—
1013D4—28no—
1014D4—42no—
1015D4—44no—
1016D4—3416no—
1017D4—348no—
1018D4—682no—
1019D4—684no—
1020D4—684no—
1021D4—684no—
1022D4—684no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—48no—
1027C2×C4—172no—
1028C2×C4—171no—
1029C2×C4—174no—
1030C2×C4—178no—
1031C2×C4—178no—
1032C2×C4—172no—
1033C2×C4—174no—
1034C2×C4—171no—
1035C2×C4—178no—
1036C2×C4—348no—
1037C2×C4—342no—
1038C2×C4—344no—
1039C2×C4—342no—
1040C2×C4—348no—
1041C2×C4—344no—
1042C2×C4—3416no—
1043C2×C4—3416no—
1044C2×C4—348no—
1045C2×C4—342no—
1046C2×C4—344no—
1047C2×C4—348no—
1048C2×C4—342no—
1049C2×C4—344no—
1050C2×C4—6816no—
1051C2×C4—688no—
1052C2×C4C24×D1718yes—
1053C2×C4C24×D1712yes—
1054C2×C4C24×D1714yes—
1055C2×C4C24×D1711yescharacteristic
1056C2×C4C24×D1718yes—
1057C2×C4C24×D1711yescharacteristic
1058C2×C4C24×D1712yes—
1059C22—24no—
1060C22—21no—
1061C22—22no—
1062C22—28no—
1063C22—172no—
1064C22—174no—
1065C22—344no—
1066C22—341no—
1067C22—342no—
1068C22—348no—
1069C22—6816no—
1070C22—684no—
1071C22C25×D1711yescharacteristic
1072C4—21no—
1073C4—24no—
1074C4—28no—
1075C4—22no—
1076C4—28no—
1077C4—172no—
1078C4—174no—
1079C4—341no—
1080C4—344no—
1081C4—348no—
1082C4—342no—
1083C4—348no—
1084C4H(5,𝔽2)×D1712yes—
1085C42−1+4×D1714yes—
1086C2—44no—
1087C2—41no—
1088C2—174no—
1089C2—684no—
1090C2—681no—
1091C2C2×H(5,𝔽2)×D1711yescharacteristic
1092C2C2×2−1+4×D1712yes—
subgroupG/H
center, FrattiniC22C25×D17
commutator, socle, cosocleC22×C17C26
FittingC17×#3550C2
prime radicalD17×#532C2
hypercenter#3550D17
hypocenterC17C2×#3550
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #14543198C2semidirect
2. #14543197C2semidirect
3. #14543196C2semidirect
4. #14543195C2semidirect
5. #14543194C2semidirect
6. #14543193C2semidirect
7. #14543192C2semidirect
8. #14543191C2semidirect
9. #14543190C2semidirect
10. D17×#563C2semidirect
11. D17×#559C2semidirect
12. Q82×D17C2semidirect
13. D17×#556C2semidirect
14. D4×Q8×D17C2semidirect
15. D17×#542C2semidirect
16. D17×#536C2semidirect
17. D17×#533C2semidirect
19. C17×#3550C2semidirect
22. #11763563C22semidirect
23. #11763562C22semidirect
24. #11763561C22semidirect
25. #11763560C22semidirect
26. #11763559C22semidirect
27. #11763558C22semidirect
28. #11763545C22semidirect
29. #11763544C22semidirect
30. #11763543C22semidirect
31. #11763542C22semidirect
32. #11763541C22semidirect
33. Q8×Dic34C22semidirect
34. Q8×Dic34C22semidirect
35. #11763539C22semidirect
36. #11763539C22semidirect
37. #11763539C22semidirect
38. #11763533C22semidirect
39. #11763532C22semidirect
40. #11763531C22semidirect
41. #11763530C22semidirect
42. #11763529C22semidirect
43. #11763528C22semidirect
44. #11763527C22semidirect
45. #11763526C22semidirect
46. Q8×D68C22semidirect
47. D4×Dic34C22semidirect
48. D4×Dic34C22semidirect
49. #11763474C22semidirect
50. #11763474C22semidirect
51. Q8×C22⋊D17C22semidirect
52. #11763472C22semidirect
53. #11763472C22semidirect
54. #11763433C22semidirect
55. #11763432C22semidirect
56. #11763431C22semidirect
57. #11763430C22semidirect
58. #11763429C22semidirect
59. #11763428C22semidirect
60. #11763427C22semidirect
61. #11763426C22semidirect
62. #11763425C22semidirect
63. #11763424C22semidirect
64. #11763423C22semidirect
65. #11763385C22semidirect
66. #11763384C22semidirect
67. #11763383C22semidirect
68. #11763382C22semidirect
69. #11763382C22semidirect
70. #11763381C22semidirect
71. #11763381C22semidirect
72. #11763380C22semidirect
73. #11763379C22semidirect
74. #11763366C22semidirect
75. #11763365C22semidirect
76. #11763364C22semidirect
77. #11763364C22semidirect
78. #11763363C22semidirect
79. #11763363C22semidirect
80. #11763362C22semidirect
81. #11763361C22semidirect
82. #11763361C22semidirect
116. C17×#563C22semidirect
117. C17×#559C22semidirect
118. Q82×C17C22semidirect
119. C17×#556C22semidirect
120. D4×Q8×C17C22semidirect
121. C17×#542C22semidirect
122. C17×#536C22semidirect
123. C17×#533C22semidirect
522. #3550D17direct (N × H)
567. #563C2×D17semidirect
573. #559C2×D17semidirect
579. Q82C2×D17semidirect
588. #556C2×D17semidirect
597. D4×Q8C2×D17semidirect
609. #542C2×D17semidirect
619. #536C2×D17semidirect
629. #533C2×D17semidirect
670. D17#3550direct (N × H)
864. C17C2×#3550semidirect

Maximal subgroups

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

subgroupindex
#145431982
#145431972
#145431962
#145431952
#145431942
#145431932
#145431922
#145431912
#145431902
D17×#5632
D17×#5592
Q82×D172
D17×#5562
D4×Q8×D172
D17×#5422
D17×#5362
D17×#5332
D17×#5322
C17×#35502
C2×#355017