Finite Group Databasebeta

← D17×#1986 #17038803

Subgroups — D17×#1986 #17038803

Order 4352.

1290 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17×#533C211yesmaximal, characteristic
2C4×M16×D17C211yesmaximal, characteristic
3C4×C4⋊C4×D17C211yesmaximal, characteristic
4#14529729C211yesmaximal, characteristic, complemented
5#14529728C211yesmaximal, characteristic, complemented
6#14529727C211yesmaximal, characteristic, complemented
7#14529726C214yesmaximal, complemented
8D17×#339C214yesmaximal
9C17×#1986C211yesmaximal, characteristic, complemented
10C2×M16×D17C2212yes—
11#11763366C2211yescharacteristic
12#11763365C412yescomplemented
13#11763364C411yescharacteristic, complemented
14#11763364C411yescharacteristic, complemented
15#11763363—21no—
16#11763363—21no—
17#11763362C2212yes—
18#11763361—21no—
19#11763361—21no—
20C4⋊Q8×D17C411yescharacteristic, complemented
21C4⋊Q8×D17C411yescharacteristic, complemented
22#125×D17C412yescomplemented
23C22⋊Q8×D17—21no—
24C22⋊Q8×D17—21no—
25C4×Q8×D17—21no—
26C4×Q8×D17—21no—
27#117×D17C2212yes—
28C2×C4⋊C4×D17—21no—
29C2×C42×D17C2212yes—
30C2×C42×D17C2211yescharacteristic
31C4×#63223C2211yescharacteristic
32#11762761—21no—
33M16×Dic17C2212yes—
34C4×#63218—21no—
35#97×D17—21no—
36C4×C8×D17—21no—
37C4⋊C4×Dic17—21no—
38C4×#63225C2212yes—
39C4×C4⋊Dic17C2211yescharacteristic
40#11762660—21no—
41#95×D17—21no—
42#11762570C2214yes—
43#11762569C2214yes—
44#11762568C2214yes—
45C17×#533C2211yescharacteristic
46C4×M16×C17C2211yescharacteristic
47C4×C4⋊C4×C17C2211yescharacteristic
48C17×#339C2214yes—
49C2×Q8×D17—21no—
50C2×Q8×D17—21no—
51C22×C4×D17—22no—
52C22×C4×D17D411yescharacteristic
53C22×C4×D17D411yescharacteristic
54C22×C4×D17C2311yescharacteristic
55C2×M16×C17C2312yes—
56C17×C4⋊Q8C2×C411yescharacteristic, complemented
57C17×C4⋊Q8C2×C411yescharacteristic, complemented
58C17×#125C2×C412yescomplemented
59C17×C22⋊Q8—21no—
60C17×C22⋊Q8—21no—
61C4×Q8×C17—21no—
62C4×Q8×C17—21no—
63C17×#117C2312yes—
64C2×C4⋊C4×C17—21no—
65C2×C42×C17C2312yes—
66C2×C42×C17C2311yescharacteristic
67#10587632—21no—
68#10587632—21no—
69Q8×Dic17—21no—
70Q8×Dic17—21no—
71#10587630—21no—
72#10587630—21no—
73#10587612C2312yes—
74C2×C4⋊Dic17—21no—
75#10587610—21no—
76#10587610—21no—
77C2×#63225—22no—
78C2×C4×Dic17—22no—
79C2×C4×Dic17D411yescharacteristic
80C2×C4×Dic17D411yescharacteristic
81C2×C4×Dic17C2312yes—
82C2×C4×Dic17C2311yescharacteristic
83C2×#63223C2312yes—
84M16×D17—24no—
85M16×D17Q818yescomplemented
86C2×#63218—22no—
87C2×C8×D17—22no—
88#10587583—21no—
89#10587583—21no—
90#10587582—22no—
91#10587582—22no—
92#10587578C2×C412yes—
93#10587578C2×C412yes—
94C4⋊C4×D17—28no—
95C4⋊C4×D17—22no—
96C4⋊C4×D17—22no—
97C4⋊C4×D17—21no—
98C4⋊C4×D17—21no—
99C4⋊C4×D17C2×C412yes—
100C4⋊C4×D17C2×C412yes—
101#10587576C2×C412yescomplemented
102#10587576C2×C412yescomplemented
103#10587575—22no—
104#10587575—22no—
105#10587574—21no—
106#10587574—21no—
107#10587574C2×C412yescomplemented
108#10587574C2×C412yescomplemented
109#10587573—21no—
110#10587573—21no—
111#10587573—22no—
112#10587573—22no—
113C22⋊C4×D17—22no—
114#10587564—22no—
115#10587564—22no—
116#10587563—22no—
117#10587558—22no—
118C42×D17—22no—
119C42×D17—28no—
120C42×D17C2×C411yescharacteristic
121C42×D17C2×C411yescharacteristic
122C42×D17C2×C411yescharacteristic
123C42×D17C2×C411yescharacteristic
124C42×D17D411yescharacteristic
125C42×D17D411yescharacteristic
126C42×D17D411yescharacteristic
127C42×D17D411yescharacteristic
128#10587556C2×C412yescomplemented
129#10587555C2×C411yescharacteristic, complemented
130#10587555C2×C411yescharacteristic, complemented
131C4×Dic34—22no—
132C4×Dic34—22no—
133C4×Dic34—21no—
134C4×Dic34—21no—
135C17×#97—21no—
136C4×C8×C17—21no—
137C17×#95—21no—
138#10587502—21no—
139#10587502—22no—
140#10587486—22no—
141C8×Dic17—22no—
142#10587474—21no—
143C4×#3622—21no—
144C23×D17C2×D411yescharacteristic
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C22×C4×C17—22no—
148C22×C4×C17C2×D411yescharacteristic
149C22×C4×C17C2×D411yescharacteristic
150C22×C4×C17C2411yescharacteristic
151C22×Dic17—22no—
152C22×Dic17C2×D411yescharacteristic
153C22×Dic17C2×D411yescharacteristic
154C22×Dic17C2×D411yescharacteristic
155Q8×D17—44no—
156Q8×D17—44no—
157C2×C4×D17—24no—
158C2×C4×D17—28no—
159C2×C4×D17—22no—
160C2×C4×D17—22no—
161C2×C4×D17—42no—
162C2×C4×D17—44no—
163C2×C4×D17—44no—
164C2×C4×D17C22⋊C411yescharacteristic
165C2×C4×D17C22⋊C411yescharacteristic
166C2×C4×D17C22⋊C411yescharacteristic
167C2×C4×D17C22⋊C411yescharacteristic
168C2×C4×D17C22⋊C411yescharacteristic
169C2×C4×D17C22⋊C411yescharacteristic
170C2×C4×D17C22⋊C411yescharacteristic
171C2×C4×D17C22⋊C411yescharacteristic
172C2×C4×D17C22×C411yescharacteristic
173C2×C4×D17C22×C411yescharacteristic
174C2×C4×D17C2×D411yescharacteristic
175C2×C4×D17C2×D411yescharacteristic
176C2×C4×D17C2×Q814yes—
177C2×C4×D17#4114yes—
178C2×Dic34—21no—
179C2×Dic34—21no—
180C2×Dic34—22no—
181C2×Dic34—22no—
182M16×C17—22no—
183M16×C17C2×Q814yescomplemented
184C2×C8×C17—22no—
185C4⋊C4×C17—24no—
186C4⋊C4×C17—22no—
187C4⋊C4×C17—22no—
188C4⋊C4×C17—21no—
189C4⋊C4×C17—21no—
190C4⋊C4×C17C22×C412yes—
191C4⋊C4×C17C22×C412yes—
192C22⋊C4×C17—22no—
193C42×C17—22no—
194C42×C17—24no—
195C42×C17C22×C411yescharacteristic
196C42×C17C22×C411yescharacteristic
197C42×C17C2×D411yescharacteristic
198C42×C17C2×D411yescharacteristic
199C22⋊Dic17—22no—
200#63227—22no—
201#63227—22no—
202C4⋊Dic17—24no—
203C4⋊Dic17—21no—
204C4⋊Dic17—21no—
205C4⋊Dic17—22no—
206C4⋊Dic17—22no—
207C4⋊Dic17C22×C412yes—
208C4⋊Dic17C22×C412yes—
209#63225—28no—
210#63225—22no—
211#63225—22no—
212#63225—22no—
213#63225—22no—
214#63225—22no—
215#63225—22no—
216#63225—22no—
217#63225—22no—
218C4×Dic17—22no—
219C4×Dic17—22no—
220C4×Dic17—22no—
221C4×Dic17—24no—
222C4×Dic17—44no—
223C4×Dic17C22⋊C411yescharacteristic
224C4×Dic17C22⋊C411yescharacteristic
225C4×Dic17C22⋊C411yescharacteristic
226C4×Dic17C22⋊C411yescharacteristic
227C4×Dic17C22⋊C411yescharacteristic
228C4×Dic17C22⋊C411yescharacteristic
229C4×Dic17C22⋊C411yescharacteristic
230C4×Dic17C22⋊C411yescharacteristic
231C4×Dic17C22×C411yescharacteristic
232C4×Dic17C22×C411yescharacteristic
233C4×Dic17C2×D411yescharacteristic
234C4×Dic17C2×D411yescharacteristic
235#63223—22no—
236#63223C2×Q814yescomplemented
237C2×#3622—22no—
238#63218—28no—
239C8×D17—28no—
240C2×#1986—171nomaximal, Sylow
241C23×C17C22×D411yescharacteristic
242C22×D17—22no—
243C22×D17—22no—
244C22×D17C2×C22⋊C411yescharacteristic
245C22×D17C2×C22⋊C411yescharacteristic
246C22×D17#12412yes—
247C22×D17C4⋊Q812yes—
248Q8×C17—42no—
249Q8×C17—42no—
250C2×C4×C17—22no—
251C2×C4×C17—24no—
252C2×C4×C17—22no—
253C2×C4×C17—22no—
254C2×C4×C17—41no—
255C2×C4×C17—42no—
256C2×C4×C17—42no—
257C2×C4×C17C2×C22⋊C411yescharacteristic
258C2×C4×C17C2×C22⋊C411yescharacteristic
259C2×C4×C17C2×C22⋊C411yescharacteristic
260C2×C4×C17C2×C22⋊C411yescharacteristic
261C2×C4×C17C23×C411yescharacteristic
262C2×C4×C17C22×D411yescharacteristic
263C2×C4×C17C22×Q812yes—
264C2×C4×C17C2×#4112yes—
265C2×Dic17—22no—
266C2×Dic17—24no—
267C2×Dic17—22no—
268C2×Dic17—22no—
269C2×Dic17—41no—
270C2×Dic17—42no—
271C2×Dic17—42no—
272C2×Dic17C2×C22⋊C411yescharacteristic
273C2×Dic17C2×C22⋊C411yescharacteristic
274C2×Dic17C2×C22⋊C411yescharacteristic
275C2×Dic17C2×C22⋊C411yescharacteristic
276C2×Dic17C2×C22⋊C411yescharacteristic
277C2×Dic17C2×C22⋊C411yescharacteristic
278C2×Dic17#12412yes—
279C2×Dic17C4⋊Q812yes—
280C4×D17—22no—
281C4×D17—22no—
282C4×D17—22no—
283C4×D17—22no—
284C4×D17—22no—
285C4×D17—41no—
286C4×D17—41no—
287C4×D17—416no—
288C4×D17—44no—
289C4×D17—44no—
290C4×D17#10414yes—
291C4×D17C4×Q814yes—
292C4×D17C4×Q814yes—
293C4×D17C22⋊Q814yes—
294C4×D17C22⋊Q814yes—
295Dic34—44no—
296Dic34—42no—
297Dic34—42no—
298Dic34—44no—
299C8×C17—24no—
300#3622—24no—
301C2×#533—171no—
302C2×C4×M16—171no—
303C2×C4×C4⋊C4—171no—
304#1986—171no—
305#1986—171no—
306#1986—174no—
307#1986—171no—
308#1986D1711yescharacteristic, direct product factor
309C2×#339—174no—
310C22×C17—21no—
311C22×C17—21no—
312C22×C17C22×C22⋊C411yescharacteristic
313C22×C17C2×#12411yescharacteristic
314C22×C17C2×C4⋊Q811yescharacteristic
315C2×D17—21no—
316C2×D17—21no—
317C2×D17—24no—
318C2×D17—24no—
319C2×D17#39112yes—
320C2×D17#39112yes—
321C2×D17C2×#10412yes—
322C2×D17#42112yes—
323C4×C17—21no—
324C4×C17—21no—
325C4×C17—21no—
326C4×C17—44no—
327C4×C17—42no—
328C4×C17—42no—
329C4×C17C2×#10412yes—
330C4×C17C2×C4×Q812yes—
331C4×C17C2×C22⋊Q812yes—
332Dic17—21no—
333Dic17—21no—
334Dic17—21no—
335Dic17—44no—
336Dic17—42no—
337Dic17—42no—
338Dic17#39112yes—
339Dic17#39112yes—
340Dic17C2×#10412yes—
341C22×M16—172no—
342#533—171no—
343#533—171no—
344#533—172no—
345#533—172no—
346#533—171no—
347#533—341no—
348#533—341no—
349#533—341no—
350#533—341no—
351#533C2×D1711yescharacteristic
352C2×C4⋊Q8—171no—
353C2×C4⋊Q8—171no—
354C2×#125—172no—
355C2×C22⋊Q8—341no—
356C2×C22⋊Q8—341no—
357C2×C4×Q8—341no—
358C2×C4×Q8—341no—
359C2×#117—172no—
360C22×C4⋊C4—341no—
361C22×C42—171no—
362C22×C42—172no—
363C4×M16—172no—
364C4×M16—171no—
365C4×M16—341no—
366C4×M16—341no—
367C4×M16C2×D1711yescharacteristic
368C2×#97—341no—
369C2×C4×C8—341no—
370C4×C4⋊C4—172no—
371C4×C4⋊C4—171no—
372C4×C4⋊C4—341no—
373C4×C4⋊C4—341no—
374C4×C4⋊C4C2×D1711yescharacteristic
375C2×#95—341no—
376#339—174no—
377#339—174no—
378#339—174no—
379#339C2×D1714yes—
380C2×C17—21no—
381C2×C17—21no—
382C2×C17C2×#39111yescharacteristic
383C2×C17C22×#10411yescharacteristic
384C2×C17C2×#42111yescharacteristic
385D17—22no—
386D17#198614yesdirect product factor
387C22×Q8—341no—
388C22×Q8—341no—
389C23×C4—171no—
390C23×C4—171no—
391C23×C4—171no—
392C23×C4—342no—
393C2×M16—172no—
394C2×M16—178no—
395C2×M16—342no—
396C2×M16—344no—
397C2×M16C22×D1712yes—
398C22×C8—342no—
399C4⋊Q8—172no—
400C4⋊Q8—172no—
401C4⋊Q8—171no—
402C4⋊Q8—171no—
403C4⋊Q8—341no—
404C4⋊Q8—341no—
405C4⋊Q8—341no—
406C4⋊Q8—341no—
407C4⋊Q8C4×D1711yescharacteristic, complemented
408C4⋊Q8C4×D1711yescharacteristic, complemented
409#125—172no—
410#125—172no—
411#125—172no—
412#125—342no—
413#125—342no—
414#125C4×D1712yescomplemented
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—342no—
418C22⋊Q8—342no—
419C22⋊Q8—342no—
420C22⋊Q8—342no—
421C22⋊Q8—341no—
422C22⋊Q8—341no—
423C22⋊Q8—341no—
424C22⋊Q8—341no—
425C22⋊Q8—341no—
426C22⋊Q8—341no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—342no—
430C4×Q8—342no—
431C4×Q8—342no—
432C4×Q8—342no—
433C4×Q8—341no—
434C4×Q8—341no—
435C4×Q8—341no—
436C4×Q8—341no—
437C4×Q8—341no—
438C4×Q8—341no—
439#117—172no—
440#117—172no—
441#117—172no—
442#117—342no—
443#117—342no—
444#117C22×D1712yes—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—172no—
447C2×C4⋊C4—172no—
448C2×C4⋊C4—342no—
449C2×C4⋊C4—342no—
450C2×C4⋊C4—341no—
451C2×C4⋊C4—341no—
452C2×C4⋊C4—348no—
453C2×C4⋊C4—342no—
454C2×C4⋊C4—341no—
455C2×C22⋊C4—342no—
456C2×C42—171no—
457C2×C42—171no—
458C2×C42—171no—
459C2×C42—171no—
460C2×C42—171no—
461C2×C42—171no—
462C2×C42—171no—
463C2×C42—171no—
464C2×C42—171no—
465C2×C42—171no—
466C2×C42—171no—
467C2×C42—172no—
468C2×C42—342no—
469C2×C42—348no—
470C2×C42—342no—
471C2×C42C22×D1712yes—
472C2×C42C22×D1711yescharacteristic
473#97—21no—
474#97—342no—
475#97—341no—
476C4×C8—21no—
477C4×C8—342no—
478C4×C8—341no—
479#95—21no—
480#95—342no—
481#95—341no—
482C17C2×#198611yescharacteristic, complemented, Sylow
483C24—171no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—342no—
487C2×Q8—342no—
488C2×Q8—341no—
489C2×Q8—341no—
490C2×Q8—684no—
491C2×Q8—684no—
492C22×C4—22no—
493C22×C4—171no—
494C22×C4—171no—
495C22×C4—171no—
496C22×C4—171no—
497C22×C4—171no—
498C22×C4—174no—
499C22×C4—174no—
500C22×C4—171no—
501C22×C4—171no—
502C22×C4—171no—
503C22×C4—171no—
504C22×C4—171no—
505C22×C4—171no—
506C22×C4—171no—
507C22×C4—171no—
508C22×C4—171no—
509C22×C4—171no—
510C22×C4—344no—
511C22×C4—342no—
512C22×C4—342no—
513C22×C4—348no—
514C22×C4—342no—
515C22×C4—682no—
516C22×C4—684no—
517C22×C4—684no—
518C22×C4D4×D1711yescharacteristic
519C22×C4D4×D1711yescharacteristic
520C22×C4C23×D1711yescharacteristic
521M16—22no—
522M16—174no—
523M16—348no—
524M16—342no—
525M16Q8×D1714yescomplemented
526C2×C8—22no—
527C2×C8—348no—
528C2×C8—342no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—172no—
535C4⋊C4—172no—
536C4⋊C4—342no—
537C4⋊C4—342no—
538C4⋊C4—342no—
539C4⋊C4—342no—
540C4⋊C4—342no—
541C4⋊C4—342no—
542C4⋊C4—342no—
543C4⋊C4—342no—
544C4⋊C4—348no—
545C4⋊C4—344no—
546C4⋊C4—342no—
547C4⋊C4—342no—
548C4⋊C4—341no—
549C4⋊C4—341no—
550C4⋊C4C2×C4×D1712yes—
551C4⋊C4C2×C4×D1712yes—
552C22⋊C4—22no—
553C22⋊C4—342no—
554C22⋊C4—342no—
555C22⋊C4—342no—
556C42—22no—
557C42—24no—
558C42—171no—
559C42—171no—
560C42—171no—
561C42—171no—
562C42—171no—
563C42—171no—
564C42—171no—
565C42—171no—
566C42—171no—
567C42—171no—
568C42—171no—
569C42—171no—
570C42—342no—
571C42—342no—
572C42—342no—
573C42—344no—
574C42—684no—
575C42C2×C4×D1711yescharacteristic
576C42C2×C4×D1711yescharacteristic
577C42D4×D1711yescharacteristic
578C42D4×D1711yescharacteristic
579C23—171no—
580C23—171no—
581C23—172no—
582C23—172no—
583C23—342no—
584C23—342no—
585C23C2×D4×D1711yescharacteristic
586Q8—42no—
587Q8—42no—
588Q8—682no—
589Q8—684no—
590Q8—684no—
591Q8—682no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—171no—
600C2×C4—171no—
601C2×C4—171no—
602C2×C4—172no—
603C2×C4—172no—
604C2×C4—174no—
605C2×C4—174no—
606C2×C4—174no—
607C2×C4—174no—
608C2×C4—174no—
609C2×C4—171no—
610C2×C4—171no—
611C2×C4—171no—
612C2×C4—342no—
613C2×C4—342no—
614C2×C4—342no—
615C2×C4—342no—
616C2×C4—342no—
617C2×C4—342no—
618C2×C4—344no—
619C2×C4—342no—
620C2×C4—342no—
621C2×C4—681no—
622C2×C4—681no—
623C2×C4—684no—
624C2×C4—684no—
625C2×C4—6816no—
626C2×C4—681no—
627C2×C4—682no—
628C2×C4—682no—
629C2×C4C22⋊C4×D1711yescharacteristic
630C2×C4C22⋊C4×D1711yescharacteristic
631C2×C4C22⋊C4×D1711yescharacteristic
632C2×C4C22⋊C4×D1711yescharacteristic
633C2×C4C22×C4×D1711yescharacteristic
634C2×C4C2×D4×D1711yescharacteristic
635C2×C4C2×Q8×D1712yes—
636C2×C4#41×D1712yes—
637C8—24no—
638C8—344no—
639C22—21no—
640C22—21no—
641C22—172no—
642C22—172no—
643C22—172no—
644C22—172no—
645C22—344no—
646C22—344no—
647C22—341no—
648C22—341no—
649C22C2×C22⋊C4×D1711yescharacteristic
650C22#124×D1711yescharacteristic
651C22C4⋊Q8×D1711yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—44no—
656C4—42no—
657C4—42no—
658C4—172no—
659C4—172no—
660C4—172no—
661C4—341no—
662C4—341no—
663C4—341no—
664C4—684no—
665C4—682no—
666C4—682no—
667C4#104×D1712yes—
668C4C4×Q8×D1712yes—
669C4C22⋊Q8×D1712yes—
670C2—21no—
671C2—21no—
672C2—174no—
673C2—342no—
674C2D17×#39111yescharacteristic
675C2C2×#104×D1711yescharacteristic
676C2D17×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1986C2
socleC22×C17C22×C22⋊C4
prime radicalC23×D17C2×D4
cosocleC22×C4×C17C24
hypercenter#1986D17
hypocenterC17C2×#1986
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #14529729C2semidirect
5. #14529728C2semidirect
6. #14529727C2semidirect
7. #14529726C2semidirect
9. C17×#1986C2semidirect
12. #11763365C4semidirect
13. #11763364C4semidirect
14. #11763364C4semidirect
20. C4⋊Q8×D17C4semidirect
21. C4⋊Q8×D17C4semidirect
22. #125×D17C4semidirect
56. C17×C4⋊Q8C2×C4semidirect
57. C17×C4⋊Q8C2×C4semidirect
58. C17×#125C2×C4semidirect
85. M16×D17Q8semidirect
101. #10587576C2×C4semidirect
102. #10587576C2×C4semidirect
107. #10587574C2×C4semidirect
108. #10587574C2×C4semidirect
128. #10587556C2×C4semidirect
129. #10587555C2×C4semidirect
130. #10587555C2×C4semidirect
183. M16×C17C2×Q8semidirect
236. #63223C2×Q8semidirect
308. #1986D17direct (N × H)
386. D17#1986direct (N × H)
407. C4⋊Q8C4×D17semidirect
408. C4⋊Q8C4×D17semidirect
414. #125C4×D17semidirect
482. C17C2×#1986semidirect
525. M16Q8×D17semidirect

Maximal subgroups

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

subgroupindex
D17×#5332
C4×M16×D172
C4×C4⋊C4×D172
#145297292
#145297282
#145297272
#145297262
D17×#3392
C17×#19862
C2×#198617