Finite Group Databasebeta

← D17×#2314 #17192913

Subgroups — D17×#2314 #17192913

Order 4352.

2678 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D17C211yesmaximal, characteristic
2#14531394C211yesmaximal, characteristic, complemented
3#14531393C211yesmaximal, characteristic, complemented
4#14531392C211yesmaximal, characteristic, complemented
5#14531391C212yesmaximal, complemented
6#14531390C214yesmaximal, complemented
7#14531389C212yesmaximal, complemented
8#14531388C214yesmaximal, complemented
9D17×#388C214yesmaximal
10D17×#387C214yesmaximal, complemented
11D17×#384C211yesmaximal, characteristic, complemented
12D17×#382C211yesmaximal, characteristic, complemented
13D17×#380C212yesmaximal
14C4×C4⋊C4×D17C212yesmaximal, complemented
15C17×#2314C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C2×#10587612C2211yescharacteristic
18C2×#10587578C2212yes—
19C2×#10587558C2211yescharacteristic
20C2×#10587558C2211yescharacteristic
21C2×#10587563C2212yes—
22#117×D17C4116yescomplemented
23C2×C4⋊C4×D17C2212yes—
24C2×C4⋊C4×D17C2212yes—
25C2×C4⋊C4×D17C2214yes—
26C2×C4⋊C4×D17C2212yes—
27C2×C22⋊C4×D17C2214yes—
28C2×C22⋊C4×D17C2212yes—
29C2×C42×D17C2214yes—
30C2×C42×D17C2211yescharacteristic
31C2×C42×D17C2211yescharacteristic
32#11762703C2214yes—
33#11762702C2214yes—
34#11762701C2214yes—
35#11762700C2214yes—
36#11762699C2214yes—
37#11762698C2214yes—
38#11762697C2214yes—
39#11762696C2214yescomplemented
40#11762695C2214yescomplemented
41#11762694C2214yescomplemented
42#11762693C2214yescomplemented
43#11762692C2214yescomplemented
44#11762691C2214yescomplemented
45#11762690C2214yescomplemented
46#11762679C2211yescharacteristic, complemented
47#11762678C2214yescomplemented
48#11762678C2212yescomplemented
49#11762675C2211yescharacteristic, complemented
50#11762674C2212yescomplemented
51#11762673C2214yescomplemented
52#11762669C2212yes—
53#11762668C2214yes—
54#11762667C2214yes—
55#11762666C2212yes—
56#11762666C2212yes—
57C4⋊C4×Dic17C2212yescomplemented
58C4⋊C4×Dic17C2212yescomplemented
59C4×#63225C2214yescomplemented
60C4×C4⋊Dic17C2212yescomplemented
61#11762660C2214yescomplemented
62#95×D17C2214yes—
63#95×D17C2214yes—
64#95×D17C2214yes—
65C2×C17×#117C2211yescharacteristic
66C17×#388C2214yes—
67C17×#387C2214yescomplemented
68C17×#384C2211yescharacteristic, complemented
69C17×#382C2211yescharacteristic, complemented
70C17×#380C2212yes—
71C4×C4⋊C4×C17C2212yescomplemented
72C24×D17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C22×C4×D17—24no—
76C22×C4×D17—24no—
77C22×C4×D17C2×C418yes—
78C22×C4×D17C2314yes—
79C22×C4×D17C2314yes—
80C22×C4×D17C2312yes—
81C22×C4×D17C2312yes—
82C22×C4×D17C2311yescharacteristic
83C22×C4×D17C2311yescharacteristic
84C22×C4×D17C2311yescharacteristic
85C22×C4×D17C2311yescharacteristic
86C17×#117C2×C418yescomplemented
87C2×C4⋊C4×C17C2312yes—
88C2×C4⋊C4×C17C2312yes—
89C2×C4⋊C4×C17C2314yes—
90C2×C4⋊C4×C17C2312yes—
91C2×C22⋊C4×C17C2314yes—
92C2×C22⋊C4×C17C2312yes—
93C2×C42×C17C2314yes—
94C2×C42×C17C2311yescharacteristic
95C2×C42×C17C2311yescharacteristic
96C2×C22⋊Dic17C2314yes—
97C2×C22⋊Dic17C2312yes—
98C2×#63227C2314yes—
99C2×#63227C2314yes—
100C2×#63227C2312yes—
101C2×#63227C2312yes—
102#10587612C2×C418yescomplemented
103C2×C4⋊Dic17C2312yes—
104C2×C4⋊Dic17C2312yes—
105C2×C4⋊Dic17C2314yes—
106C2×C4⋊Dic17C2312yes—
107C2×#63225C2314yes—
108C2×#63225C2314yes—
109C2×#63225C2314yes—
110C2×#63225C2314yes—
111C2×#63225C2312yes—
112C2×#63225C2312yes—
113C2×C4×Dic17C2314yes—
114C2×C4×Dic17C2314yes—
115C2×C4×Dic17C2314yes—
116C2×C4×Dic17C2312yes—
117C2×C4×Dic17C2312yes—
118C2×C4×Dic17C2311yescharacteristic
119C2×C4×Dic17C2311yescharacteristic
120#10587578C2×C4116yescomplemented
121C4⋊C4×D17—28no—
122C4⋊C4×D17—28no—
123C4⋊C4×D17—48no—
124C4⋊C4×D17C2×C4116yes—
125C22⋊C4×D17—48no—
126C22⋊C4×D17C2×C4116yes—
127#10587563C2×C4116yescomplemented
128#10587558C2×C418yescomplemented
129#10587558C2×C418yescomplemented
130C42×D17—48no—
131C42×D17C2×C418yes—
132C42×D17C2×C418yes—
133C17×#95C2314yes—
134C17×#95C2314yes—
135C17×#95C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144#10587502C2314yes—
145C24×C17C2411yescharacteristic
146C23×D17—22no—
147C23×D17—22no—
148C23×D17—24no—
149C23×D17—24no—
150C23×D17C22×C414yes—
151C23×D17C2411yescharacteristic
152C23×D17C2411yescharacteristic
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17C22×C414yes—
156C22×C4×C17C2414yes—
157C22×C4×C17C2414yes—
158C22×C4×C17C2411yescharacteristic
159C22×C4×C17C2412yes—
160C22×C4×C17C2412yes—
161C22×C4×C17C2411yescharacteristic
162C22×Dic17—22no—
163C22×Dic17—22no—
164C22×Dic17C22×C414yes—
165C22×Dic17C2414yes—
166C22×Dic17C2414yes—
167C22×Dic17C2411yescharacteristic
168C22×Dic17C2412yes—
169C22×Dic17C2412yes—
170C22×Dic17C2411yescharacteristic
171C2×C4×D17—22no—
172C2×C4×D17—22no—
173C2×C4×D17—24no—
174C2×C4×D17—24no—
175C2×C4×D17—24no—
176C2×C4×D17—24no—
177C2×C4×D17—22no—
178C2×C4×D17—22no—
179C2×C4×D17—22no—
180C2×C4×D17—22no—
181C2×C4×D17—232no—
182C2×C4×D17—28no—
183C2×C4×D17—28no—
184C2×C4×D17—28no—
185C2×C4×D17—28no—
186C2×C4×D17—28no—
187C2×C4×D17—28no—
188C2×C4×D17C22×C414yes—
189C2×C4×D17C22×C414yes—
190C2×C4×D17C22×C414yes—
191C2×C4×D17C22×C418yes—
192C2×C4×D17C22×C418yes—
193C2×C4×D17C22×C414yes—
194C2×C4×D17#4114yes—
195C2×C4×D17#4114yes—
196C4⋊C4×C17—24no—
197C4⋊C4×C17—24no—
198C4⋊C4×C17—44no—
199C4⋊C4×C17C22×C418yes—
200C22⋊C4×C17—44no—
201C22⋊C4×C17C22×C418yes—
202C42×C17—44no—
203C42×C17C22×C414yes—
204C42×C17C22×C414yes—
205C22⋊Dic17—44no—
206C22⋊Dic17C22×C418yes—
207#63227—44no—
208#63227—44no—
209#63227C22×C418yes—
210#63227C22×C418yes—
211C4⋊Dic17—24no—
212C4⋊Dic17—24no—
213C4⋊Dic17—44no—
214C4⋊Dic17C22×C418yes—
215#63225—28no—
216#63225—28no—
217#63225—44no—
218#63225—44no—
219#63225C22×C418yes—
220#63225C22×C418yes—
221C4×Dic17—44no—
222C4×Dic17—44no—
223C4×Dic17—44no—
224C4×Dic17C22×C414yes—
225C4×Dic17C22×C414yes—
226C4×Dic17C22×C418yes—
227C4×Dic17C22×C418yes—
228C2×#2314—171nomaximal, Sylow
229C23×C17—21no—
230C23×C17—21no—
231C23×C17—22no—
232C23×C17—22no—
233C23×C17C23×C412yes—
234C23×C17C2511yescharacteristic
235C22×D17—21no—
236C22×D17—21no—
237C22×D17—22no—
238C22×D17—22no—
239C22×D17—28no—
240C22×D17—216no—
241C22×D17—44no—
242C22×D17—44no—
243C22×D17—48no—
244C22×D17C23×C412yes—
245C22×D17C23×C412yes—
246C22×D17C2×#4112yes—
247C22×D17C2×#4112yes—
248C22×D17H(5,𝔽2)14yes—
249C22×D172−1+414yes—
250C2×C4×C17—21no—
251C2×C4×C17—21no—
252C2×C4×C17—22no—
253C2×C4×C17—22no—
254C2×C4×C17—22no—
255C2×C4×C17—22no—
256C2×C4×C17—28no—
257C2×C4×C17—24no—
258C2×C4×C17—24no—
259C2×C4×C17—24no—
260C2×C4×C17—24no—
261C2×C4×C17—24no—
262C2×C4×C17—24no—
263C2×C4×C17C23×C414yes—
264C2×C4×C17C23×C414yes—
265C2×C4×C17C23×C412yes—
266C2×C4×C17C23×C412yes—
267C2×C4×C17C2×#4112yes—
268C2×C4×C17C2×#4112yes—
269C2×Dic17—21no—
270C2×Dic17—21no—
271C2×Dic17—22no—
272C2×Dic17—22no—
273C2×Dic17—22no—
274C2×Dic17—22no—
275C2×Dic17—28no—
276C2×Dic17—24no—
277C2×Dic17—24no—
278C2×Dic17—24no—
279C2×Dic17—24no—
280C2×Dic17—24no—
281C2×Dic17—24no—
282C2×Dic17C23×C414yes—
283C2×Dic17C23×C414yes—
284C2×Dic17C23×C412yes—
285C2×Dic17C23×C412yes—
286C2×Dic17C2×#4112yes—
287C2×Dic17C2×#4112yes—
288C4×D17—28no—
289C4×D17—216no—
290C4×D17—216no—
291C4×D17—28no—
292C4×D17—28no—
293C4×D17—416no—
294C4×D17—416no—
295C4×D17#117116yes—
296C22×#117—171no—
297#2314—174no—
298#2314—174no—
299#2314—171no—
300#2314—171no—
301#2314—172no—
302#2314—172no—
303#2314—171no—
304#2314D1711yescharacteristic, direct product factor
305C2×#388—174no—
306C2×#387—174no—
307C2×#384—171no—
308C2×#382—171no—
309C2×#380—172no—
310C2×C4×C4⋊C4—172no—
311C22×C17—22no—
312C22×C17—24no—
313C22×C17—41no—
314C22×C17—41no—
315C22×C17—42no—
316C22×C17C24×C411yescharacteristic
317C22×C17C22×#4111yescharacteristic
318C22×C17C22×#4111yescharacteristic
319C22×C17C2×H(5,𝔽2)12yes—
320C22×C17C2×2−1+412yes—
321C2×D17—22no—
322C2×D17—24no—
323C2×D17—41no—
324C2×D17—41no—
325C2×D17—42no—
326C2×D17—416no—
327C2×D17C2×#11714yes—
328C2×D17#52018yes—
329C2×D17#54014yes—
330C2×D17#54114yes—
331C2×D17#54218yes—
332C4×C17—22no—
333C4×C17—24no—
334C4×C17—24no—
335C4×C17—44no—
336C4×C17—44no—
337C4×C17C2×#11714yes—
338Dic17—22no—
339Dic17—24no—
340Dic17—24no—
341Dic17—44no—
342Dic17—44no—
343Dic17C2×#11714yes—
344C24×C4—171no—
345C2×#117—171no—
346C2×#117—1716no—
347C2×#117—172no—
348C2×#117—172no—
349C2×#117—171no—
350C2×#117—171no—
351C2×#117C2×D1711yescharacteristic
352C22×C4⋊C4—172no—
353C22×C4⋊C4—172no—
354C22×C4⋊C4—172no—
355C22×C4⋊C4—174no—
356C22×C22⋊C4—172no—
357C22×C22⋊C4—174no—
358C22×C42—171no—
359C22×C42—171no—
360C22×C42—174no—
361#388—174no—
362#388—174no—
363#388—174no—
364#388—174no—
365#388—174no—
366#388—174no—
367#388—174no—
368#388C2×D1714yes—
369#387—174no—
370#387—174no—
371#387—174no—
372#387—174no—
373#387—174no—
374#387—174no—
375#387—174no—
376#387C2×D1714yescomplemented
377#384—174no—
378#384—172no—
379#384—171no—
380#384C2×D1711yescharacteristic, complemented
381#382—172no—
382#382—171no—
383#382—174no—
384#382C2×D1711yescharacteristic, complemented
385#380—172no—
386#380—172no—
387#380—172no—
388#380—174no—
389#380—174no—
390#380C2×D1712yes—
391C4×C4⋊C4—172no—
392C4×C4⋊C4—172no—
393C4×C4⋊C4—172no—
394C4×C4⋊C4—174no—
395C4×C4⋊C4—174no—
396C4×C4⋊C4C2×D1712yescomplemented
397C2×#95—174no—
398C2×#95—174no—
399C2×#95—174no—
400C2×C17—42no—
401C2×C17C22×#11711yescharacteristic
402C2×C17C2×#52012yes—
403C2×C17C2×#54011yescharacteristic
404C2×C17C2×#54111yescharacteristic
405C2×C17C2×#54212yes—
406D17—42no—
407D17#231418yesdirect product factor
408C25—171no—
409C23×C4—171no—
410C23×C4—171no—
411C23×C4—178no—
412C23×C4—172no—
413C23×C4—172no—
414C23×C4—171no—
415C23×C4—171no—
416C23×C4—171no—
417C23×C4—174no—
418C23×C4—174no—
419C23×C4—344no—
420C23×C4—344no—
421C23×C4C22×D1711yescharacteristic
422#117—178no—
423#117—1716no—
424#117—1716no—
425#117—178no—
426#117—178no—
427#117C4×D1718yescomplemented
428C2×C4⋊C4—172no—
429C2×C4⋊C4—172no—
430C2×C4⋊C4—172no—
431C2×C4⋊C4—1716no—
432C2×C4⋊C4—174no—
433C2×C4⋊C4—172no—
434C2×C4⋊C4—174no—
435C2×C4⋊C4—172no—
436C2×C4⋊C4—174no—
437C2×C4⋊C4—174no—
438C2×C4⋊C4—174no—
439C2×C4⋊C4—348no—
440C2×C4⋊C4—348no—
441C2×C4⋊C4—688no—
442C2×C4⋊C4C22×D1712yes—
443C2×C4⋊C4C22×D1712yes—
444C2×C4⋊C4C22×D1714yes—
445C2×C4⋊C4C22×D1712yes—
446C2×C22⋊C4—172no—
447C2×C22⋊C4—172no—
448C2×C22⋊C4—172no—
449C2×C22⋊C4—1716no—
450C2×C22⋊C4—174no—
451C2×C22⋊C4—174no—
452C2×C22⋊C4—174no—
453C2×C22⋊C4—688no—
454C2×C22⋊C4C22×D1714yes—
455C2×C22⋊C4C22×D1712yes—
456C2×C42—172no—
457C2×C42—171no—
458C2×C42—172no—
459C2×C42—171no—
460C2×C42—178no—
461C2×C42—178no—
462C2×C42—174no—
463C2×C42—174no—
464C2×C42—174no—
465C2×C42—688no—
466C2×C42C22×D1714yes—
467C2×C42C22×D1711yescharacteristic
468C2×C42C22×D1711yescharacteristic
469#95—174no—
470#95—174no—
471#95—174no—
472#95—174no—
473#95—174no—
474#95—174no—
475#95—174no—
476#95—174no—
477#95—174no—
478#95C22×D1714yes—
479#95C22×D1714yes—
480#95C22×D1714yes—
481C17C2×#231411yescharacteristic, complemented, Sylow
482C24—171no—
483C24—174no—
484C24—171no—
485C24—344no—
486C24—342no—
487C24—342no—
488C24—344no—
489C24C23×D1711yescharacteristic
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—171no—
493C22×C4—174no—
494C22×C4—174no—
495C22×C4—174no—
496C22×C4—174no—
497C22×C4—171no—
498C22×C4—172no—
499C22×C4—172no—
500C22×C4—178no—
501C22×C4—178no—
502C22×C4—174no—
503C22×C4—174no—
504C22×C4—174no—
505C22×C4—174no—
506C22×C4—174no—
507C22×C4—342no—
508C22×C4—342no—
509C22×C4—3432no—
510C22×C4—344no—
511C22×C4—344no—
512C22×C4—344no—
513C22×C4—344no—
514C22×C4—342no—
515C22×C4—342no—
516C22×C4—348no—
517C22×C4—348no—
518C22×C4—348no—
519C22×C4—348no—
520C22×C4—348no—
521C22×C4—348no—
522C22×C4—342no—
523C22×C4—342no—
524C22×C4—342no—
525C22×C4—342no—
526C22×C4C2×C4×D1714yes—
527C22×C4C23×D1714yes—
528C22×C4C23×D1714yes—
529C22×C4C23×D1711yescharacteristic
530C22×C4C23×D1712yes—
531C22×C4C23×D1712yes—
532C22×C4C23×D1711yescharacteristic
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—44no—
536C4⋊C4—178no—
537C4⋊C4—178no—
538C4⋊C4—178no—
539C4⋊C4—348no—
540C4⋊C4—348no—
541C4⋊C4—344no—
542C4⋊C4—344no—
543C4⋊C4—684no—
544C4⋊C4—684no—
545C4⋊C4—684no—
546C4⋊C4C2×C4×D1718yes—
547C22⋊C4—44no—
548C22⋊C4—178no—
549C22⋊C4—178no—
550C22⋊C4—178no—
551C22⋊C4—684no—
552C22⋊C4—684no—
553C22⋊C4—684no—
554C22⋊C4C2×C4×D1718yes—
555C42—44no—
556C42—178no—
557C42—178no—
558C42—174no—
559C42—174no—
560C42—684no—
561C42—684no—
562C42—684no—
563C42C2×C4×D1714yes—
564C42C2×C4×D1714yes—
565C23—21no—
566C23—21no—
567C23—22no—
568C23—22no—
569C23—172no—
570C23—172no—
571C23—172no—
572C23—174no—
573C23—174no—
574C23—172no—
575C23—348no—
576C23—3416no—
577C23—341no—
578C23—341no—
579C23—342no—
580C23—342no—
581C23—684no—
582C23—684no—
583C23—688no—
584C23C22×C4×D1712yes—
585C23C24×D1711yescharacteristic
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—28no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—172no—
600C2×C4—172no—
601C2×C4—172no—
602C2×C4—1716no—
603C2×C4—174no—
604C2×C4—174no—
605C2×C4—172no—
606C2×C4—348no—
607C2×C4—348no—
608C2×C4—3416no—
609C2×C4—3416no—
610C2×C4—348no—
611C2×C4—341no—
612C2×C4—341no—
613C2×C4—342no—
614C2×C4—342no—
615C2×C4—342no—
616C2×C4—342no—
617C2×C4—348no—
618C2×C4—344no—
619C2×C4—344no—
620C2×C4—344no—
621C2×C4—344no—
622C2×C4—344no—
623C2×C4—344no—
624C2×C4—6816no—
625C2×C4—6816no—
626C2×C4C22×C4×D1714yes—
627C2×C4C22×C4×D1714yes—
628C2×C4C22×C4×D1712yes—
629C2×C4C22×C4×D1712yes—
630C2×C4#41×D1712yes—
631C2×C4#41×D1712yes—
632C22—22no—
633C22—24no—
634C22—41no—
635C22—41no—
636C22—42no—
637C22—174no—
638C22—174no—
639C22—178no—
640C22—174no—
641C22—178no—
642C22—342no—
643C22—344no—
644C22—6816no—
645C22—681no—
646C22—681no—
647C22—682no—
648C22C23×C4×D1711yescharacteristic
649C22C2×#41×D1711yescharacteristic
650C22C2×#41×D1711yescharacteristic
651C22H(5,𝔽2)×D1712yes—
652C222−1+4×D1712yes—
653C4—22no—
654C4—24no—
655C4—24no—
656C4—44no—
657C4—44no—
658C4—174no—
659C4—342no—
660C4—344no—
661C4—344no—
662C4—684no—
663C4—684no—
664C4#117×D1714yes—
665C2—42no—
666C2—178no—
667C2—682no—
668C2C2×#117×D1711yescharacteristic
669C2D17×#52012yes—
670C2D17×#54011yescharacteristic
671C2D17×#54111yescharacteristic
672C2D17×#54212yes—
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2314C2
socle, cosocleC23×C17C25
prime radicalC24×D17C23
hypercenter#2314D17
hypocenterC17C2×#2314
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #14531394C2semidirect
3. #14531393C2semidirect
4. #14531392C2semidirect
5. #14531391C2semidirect
6. #14531390C2semidirect
7. #14531389C2semidirect
8. #14531388C2semidirect
10. D17×#387C2semidirect
11. D17×#384C2semidirect
12. D17×#382C2semidirect
14. C4×C4⋊C4×D17C2semidirect
15. C17×#2314C2semidirect
22. #117×D17C4semidirect
39. #11762696C22semidirect
40. #11762695C22semidirect
41. #11762694C22semidirect
42. #11762693C22semidirect
43. #11762692C22semidirect
44. #11762691C22semidirect
45. #11762690C22semidirect
46. #11762679C22semidirect
47. #11762678C22semidirect
48. #11762678C22semidirect
49. #11762675C22semidirect
50. #11762674C22semidirect
51. #11762673C22semidirect
57. C4⋊C4×Dic17C22semidirect
58. C4⋊C4×Dic17C22semidirect
59. C4×#63225C22semidirect
60. C4×C4⋊Dic17C22semidirect
61. #11762660C22semidirect
67. C17×#387C22semidirect
68. C17×#384C22semidirect
69. C17×#382C22semidirect
71. C4×C4⋊C4×C17C22semidirect
86. C17×#117C2×C4semidirect
102. #10587612C2×C4semidirect
120. #10587578C2×C4semidirect
127. #10587563C2×C4semidirect
128. #10587558C2×C4semidirect
129. #10587558C2×C4semidirect
304. #2314D17direct (N × H)
376. #387C2×D17semidirect
380. #384C2×D17semidirect
384. #382C2×D17semidirect
396. C4×C4⋊C4C2×D17semidirect
407. D17#2314direct (N × H)
427. #117C4×D17semidirect
481. C17C2×#2314semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D172
#145313942
#145313932
#145313922
#145313912
#145313902
#145313892
#145313882
D17×#3882
D17×#3872
D17×#3842
D17×#3822
D17×#3802
C4×C4⋊C4×D172
C17×#23142
C2×#231417