Finite Group Databasebeta

← D17×#2610 #17205166

Subgroups — D17×#2610 #17205166

Order 4352.

3286 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×D17C211yesmaximal, characteristic, complemented
2C2×#117×D17C211yesmaximal, characteristic, complemented
3#14534474C211yesmaximal, characteristic, complemented
4#14534473C211yesmaximal, characteristic, complemented
5#14534472C211yesmaximal, characteristic, complemented
6#14534471C211yesmaximal, characteristic, complemented
7#14534470C212yesmaximal, complemented
8#14534469C212yesmaximal, complemented
9#14534468C212yesmaximal, complemented
10#14534467C212yesmaximal, complemented
11#14534466C211yesmaximal, characteristic, complemented
12#14534465C211yesmaximal, characteristic, complemented
13#14534464C211yesmaximal, characteristic, complemented
14D17×#395C211yesmaximal, characteristic, complemented
15D17×#394C211yesmaximal, characteristic, complemented
16D17×#393C211yesmaximal, characteristic, complemented
17D17×#392C211yesmaximal, characteristic
18D17×#390C212yesmaximal, complemented
19D17×#388C212yesmaximal, complemented
20D17×#388C212yesmaximal, complemented
21D17×#386C212yesmaximal, complemented
22D17×#376C211yesmaximal, characteristic, complemented
23C17×#2610C211yesmaximal, characteristic, complemented
24C22×Q8×D17C2211yescharacteristic
25C22×D4×D17C2212yes—
26C22×D4×D17C2211yescharacteristic
27C23×C4×D17C2211yescharacteristic
28C2×#10587633C2211yescharacteristic, complemented
29C2×#10587561C2211yescharacteristic, complemented
30C2×#10587622C2211yescharacteristic, complemented
31C2×#10587571C2212yescomplemented
32C2×#10587571C2212yescomplemented
33#124×D17—28no—
34C2×#10587612C2211yescharacteristic, complemented
35C2×#10587578C2211yescharacteristic, complemented
36C2×#10587578C2211yescharacteristic, complemented
37C2×#10587558C2211yescharacteristic, complemented
38C2×#10587558C2211yescharacteristic, complemented
39C2×#10587563C2211yescharacteristic, complemented
40C2×#10587563C2211yescharacteristic, complemented
41#117×D17—28no—
42C2×C4⋊C4×D17C2211yescharacteristic
43C2×C4⋊C4×D17C2211yescharacteristic
44C2×C4⋊C4×D17C2212yes—
45C2×C22⋊C4×D17C2211yescharacteristic
46C2×C22⋊C4×D17C2211yescharacteristic
47C2×C22⋊C4×D17C2212yes—
48C2×C22⋊C4×D17C2212yes—
49C2×C22⋊C4×D17C2212yes—
50C2×C22⋊C4×D17C2212yes—
51C2×C22⋊C4×D17C2212yes—
52C2×C22⋊C4×D17C2212yes—
53C2×C42×D17C2212yes—
54C2×C42×D17C2211yescharacteristic
55C2×C42×D17C2211yescharacteristic
56#11762730C2211yescharacteristic, complemented
57#11762730C2212yescomplemented
58#11762729C2212yescomplemented
59#11762729C2211yescharacteristic, complemented
60#11762728C2211yescharacteristic, complemented
61#11762727C2211yescharacteristic, complemented
62#11762726C2211yescharacteristic, complemented
63#11762725C2212yescomplemented
64#11762724C2212yescomplemented
65#11762723C2211yescharacteristic, complemented
66#11762722C2211yescharacteristic, complemented
67#11762722C2212yescomplemented
68#11762721C2211yescharacteristic, complemented
69#11762721C2212yescomplemented
70#11762720C2211yescharacteristic, complemented
71#11762719C2211yescharacteristic
72#11762718C2212yes—
73#11762718C2211yescharacteristic
74#11762717C2212yes—
75#11762717C2211yescharacteristic
76#11762712C2212yescomplemented
77#11762711C2212yescomplemented
78#11762710C2212yescomplemented
79#11762709C2212yescomplemented
80#11762709C2212yescomplemented
81#11762709C2212yescomplemented
82#11762709C2212yescomplemented
83#11762703C2212yescomplemented
84#11762703C2212yescomplemented
85#11762702C2212yescomplemented
86#11762702C2212yescomplemented
87#11762701C2212yescomplemented
88#11762701C2212yescomplemented
89#11762700C2212yescomplemented
90#11762700C2212yescomplemented
91#11762699C2212yescomplemented
92#11762699C2212yescomplemented
93#11762698C2212yescomplemented
94#11762698C2212yescomplemented
95#11762697C2212yescomplemented
96#11762697C2212yescomplemented
97#11762689C2212yescomplemented
98#11762688C2212yescomplemented
99#11762687C2212yescomplemented
100#11762687C2212yescomplemented
101#11762686C2212yescomplemented
102#11762685C2212yescomplemented
103#11762685C2212yescomplemented
104#11762655C2212yescomplemented
105#11762655C2211yescharacteristic, complemented
106#11762654C2211yescharacteristic, complemented
107#11762654C2212yescomplemented
108#11762654C2211yescharacteristic, complemented
109#95×D17C2212yes—
110#95×D17C2211yescharacteristic
111#95×D17C2211yescharacteristic
112#95×D17C2212yes—
113#95×D17C2212yes—
114C2×C17×#124C2211yescharacteristic, complemented
115C2×C17×#117C2211yescharacteristic, complemented
116C17×#395C2211yescharacteristic, complemented
117C17×#394C2211yescharacteristic, complemented
118C17×#393C2211yescharacteristic, complemented
119C17×#392C2211yescharacteristic
120C17×#390C2212yescomplemented
121C17×#388C2212yescomplemented
122C17×#388C2212yescomplemented
123C17×#386C2212yescomplemented
124C17×#376C2211yescharacteristic, complemented
125C24×D17C2312yes—
126C24×D17C2311yescharacteristic
127C22×Q8×C17C2311yescharacteristic
128C22×D4×C17C2312yes—
129C22×D4×C17C2311yescharacteristic
130C23×C4×C17C2311yescharacteristic
131C22×C22⋊D17C2312yes—
132C22×C22⋊D17C2312yes—
133C22×C22⋊D17C2312yes—
134C23×Dic17C2311yescharacteristic
135C2×Q8×D17—24no—
136C2×Q8×D17—44no—
137C2×D4×D17—28no—
138C2×D4×D17—24no—
139C2×D4×D17—28no—
140C2×D4×D17—44no—
141C2×D4×D17—44no—
142C22×D68C2312yes—
143C22×D68C2311yescharacteristic
144C22×C4×D17—24no—
145C22×C4×D17—24no—
146C22×C4×D17—24no—
147C22×C4×D17C2311yescharacteristic
148C22×C4×D17C2311yescharacteristic
149C22×C4×D17C2312yes—
150C22×C4×D17C2312yes—
151C22×C4×D17C2311yescharacteristic
152C22×C4×D17C2311yescharacteristic
153C22×C4×D17C2311yescharacteristic
154C22×C4×D17C2311yescharacteristic
155C22×C4×D17C2311yescharacteristic
156C22×C4×D17C2312yes—
157C22×C4×D17C2311yescharacteristic
158C22×Dic34C2312yes—
159C22×Dic34C2311yescharacteristic
160C17×#124—24no—
161C17×#117—24no—
162C2×C4⋊C4×C17C2311yescharacteristic
163C2×C4⋊C4×C17C2311yescharacteristic
164C2×C4⋊C4×C17C2312yes—
165C2×C22⋊C4×C17C2312yes—
166C2×C22⋊C4×C17C2312yes—
167C2×C22⋊C4×C17C2312yes—
168C2×C22⋊C4×C17C2312yes—
169C2×C22⋊C4×C17C2311yescharacteristic
170C2×C22⋊C4×C17C2311yescharacteristic
171C2×C22⋊C4×C17C2312yes—
172C2×C22⋊C4×C17C2312yes—
173C2×C42×C17C2311yescharacteristic
174C2×C42×C17C2312yes—
175C2×C42×C17C2311yescharacteristic
176C2×C22⋊Dic17C2312yes—
177C2×C22⋊Dic17C2312yes—
178C2×C22⋊Dic17C2312yes—
179C2×C22⋊Dic17C2312yes—
180C2×C22⋊Dic17C2311yescharacteristic
181C2×C22⋊Dic17C2311yescharacteristic
182C2×C22⋊Dic17C2312yes—
183C2×C22⋊Dic17C2312yes—
184#10587633—24no—
185#10587622—24no—
186C2×#63227C2312yes—
187C2×#63227C2312yes—
188C2×#63227C2312yes—
189C2×#63227C2312yes—
190C2×#63227C2312yes—
191C2×#63227C2312yes—
192C2×#63227C2312yes—
193C2×#63227C2312yes—
194C2×#63227C2311yescharacteristic
195C2×#63227C2311yescharacteristic
196C2×#63227C2311yescharacteristic
197C2×#63227C2311yescharacteristic
198C2×#63227C2312yes—
199C2×#63227C2312yes—
200C2×#63227C2312yes—
201C2×#63227C2312yes—
202#10587612—24no—
203C2×C4⋊Dic17C2311yescharacteristic
204C2×C4⋊Dic17C2311yescharacteristic
205C2×C4⋊Dic17C2312yes—
206C2×#63225C2311yescharacteristic
207C2×#63225C2311yescharacteristic
208C2×#63225C2311yescharacteristic
209C2×#63225C2311yescharacteristic
210C2×#63225C2312yes—
211C2×#63225C2312yes—
212C2×C4×Dic17C2311yescharacteristic
213C2×C4×Dic17C2312yes—
214C2×C4×Dic17C2311yescharacteristic
215C2×C4×Dic17C2312yes—
216C2×C4×Dic17C2311yescharacteristic
217C2×C4×Dic17C2312yes—
218C2×C4×Dic17C2311yescharacteristic
219C2×C4×Dic17C2311yescharacteristic
220C2×C4×Dic17C2311yescharacteristic
221#10587578—24no—
222#10587578—24no—
223C4⋊C4×D17—24no—
224C4⋊C4×D17—24no—
225C4⋊C4×D17—44no—
226#10587571—28no—
227#10587571—28no—
228C22⋊C4×D17—24no—
229C22⋊C4×D17—24no—
230C22⋊C4×D17—28no—
231C22⋊C4×D17—28no—
232C22⋊C4×D17—28no—
233C22⋊C4×D17—28no—
234C22⋊C4×D17—44no—
235C22⋊C4×D17—44no—
236#10587563—24no—
237#10587563—24no—
238#10587561—24no—
239#10587558—24no—
240#10587558—24no—
241C42×D17—24no—
242C42×D17—28no—
243C42×D17D418yescomplemented
244C17×#95C2312yes—
245C17×#95C2312yes—
246C17×#95C2312yes—
247C17×#95C2311yescharacteristic
248C17×#95C2311yescharacteristic
249#10587502C2312yes—
250#10587502C2312yes—
251#10587502C2312yes—
252#10587502C2312yes—
253#10587502C2312yes—
254#10587502C2312yes—
255#10587502C2312yes—
256#10587502C2312yes—
257#10587502C2312yes—
258#10587502C2311yescharacteristic
259#10587502C2312yes—
260#10587502C2311yescharacteristic
261#10587502C2312yes—
262C24×C17C2412yes—
263C24×C17C2411yescharacteristic
264C23×D17—22no—
265C23×D17—22no—
266C23×D17—24no—
267C23×D17—24no—
268C23×D17—24no—
269C23×D17—24no—
270C23×D17—24no—
271C23×D17—24no—
272C23×D17—24no—
273C23×D17—24no—
274C23×D17—24no—
275C23×D17#4114yes—
276C23×D17C2412yes—
277C23×D17C2411yescharacteristic
278C23×D17C2411yescharacteristic
279C2×Q8×C17—22no—
280C2×Q8×C17—42no—
281C2×D4×C17—24no—
282C2×D4×C17—22no—
283C2×D4×C17—24no—
284C2×D4×C17—42no—
285C2×D4×C17—42no—
286C22×C4×C17—22no—
287C22×C4×C17—22no—
288C22×C4×C17—22no—
289C22×C4×C17C2412yes—
290C22×C4×C17C2412yes—
291C22×C4×C17C2411yescharacteristic
292C22×C4×C17C2411yescharacteristic
293C22×C4×C17C2411yescharacteristic
294C22×C4×C17C2411yescharacteristic
295C22×C4×C17C2411yescharacteristic
296C22×C4×C17C2411yescharacteristic
297C22×C4×C17C2412yes—
298C2×C22⋊D17—24no—
299C2×C22⋊D17—24no—
300C2×C22⋊D17—24no—
301C2×C22⋊D17—24no—
302C2×C22⋊D17—24no—
303C2×C22⋊D17—42no—
304C2×C22⋊D17—42no—
305C2×C22⋊D17—42no—
306C2×C22⋊D17—42no—
307C22×Dic17—22no—
308C22×Dic17—22no—
309C22×Dic17—22no—
310C22×Dic17C2412yes—
311C22×Dic17C2412yes—
312C22×Dic17C2411yescharacteristic
313C22×Dic17C2411yescharacteristic
314C22×Dic17C2411yescharacteristic
315C22×Dic17C2411yescharacteristic
316C22×Dic17C2411yescharacteristic
317C22×Dic17C2411yescharacteristic
318C22×Dic17C2412yes—
319Q8×D17—416no—
320D4×D17—432no—
321D4×D17—416no—
322C2×D68—24no—
323C2×D68—22no—
324C2×D68—24no—
325C2×D68—42no—
326C2×D68—42no—
327C2×C4×D17—232no—
328C2×C4×D17—22no—
329C2×C4×D17—22no—
330C2×C4×D17—22no—
331C2×C4×D17—22no—
332C2×C4×D17—22no—
333C2×C4×D17—22no—
334C2×C4×D17—24no—
335C2×C4×D17—24no—
336C2×C4×D17—24no—
337C2×C4×D17—24no—
338C2×C4×D17—22no—
339C2×C4×D17—22no—
340C2×C4×D17—22no—
341C2×C4×D17—22no—
342C2×C4×D17—24no—
343C2×C4×D17—22no—
344C2×C4×D17—22no—
345C2×C4×D17—24no—
346C2×C4×D17—24no—
347C2×C4×D17—24no—
348C2×C4×D17—24no—
349C2×C4×D17—24no—
350C2×C4×D17—24no—
351C2×C4×D17—24no—
352C2×C4×D17C2×D414yes—
353C2×C4×D17C2×D414yes—
354C2×C4×D17C2×D414yes—
355C2×C4×D17#4114yes—
356C2×C4×D17#4118yes—
357C2×Dic34—22no—
358C2×Dic34—24no—
359C2×Dic34—42no—
360C2×Dic34—42no—
361C2×Dic34—42no—
362C4⋊C4×C17—22no—
363C4⋊C4×C17—22no—
364C4⋊C4×C17—42no—
365C22⋊C4×C17—24no—
366C22⋊C4×C17—24no—
367C22⋊C4×C17—22no—
368C22⋊C4×C17—22no—
369C22⋊C4×C17—24no—
370C22⋊C4×C17—24no—
371C22⋊C4×C17—42no—
372C22⋊C4×C17—42no—
373C42×C17—22no—
374C42×C17—24no—
375C42×C17C2×D414yescomplemented
376C22⋊Dic17—22no—
377C22⋊Dic17—22no—
378C22⋊Dic17—24no—
379C22⋊Dic17—24no—
380C22⋊Dic17—24no—
381C22⋊Dic17—24no—
382C22⋊Dic17—42no—
383C22⋊Dic17—42no—
384#63227—22no—
385#63227—22no—
386#63227—24no—
387#63227—24no—
388#63227—24no—
389#63227—24no—
390#63227—22no—
391#63227—22no—
392#63227—24no—
393#63227—24no—
394#63227—24no—
395#63227—24no—
396#63227—42no—
397#63227—42no—
398#63227—42no—
399#63227—42no—
400C4⋊Dic17—22no—
401C4⋊Dic17—22no—
402C4⋊Dic17—42no—
403#63225—22no—
404#63225—22no—
405#63225—22no—
406#63225—22no—
407#63225—42no—
408#63225—42no—
409C4×Dic17—22no—
410C4×Dic17—24no—
411C4×Dic17—22no—
412C4×Dic17—22no—
413C4×Dic17—24no—
414C4×Dic17—24no—
415C4×Dic17C2×D414yescomplemented
416C4×Dic17C2×D414yescomplemented
417C4×Dic17C2×D414yescomplemented
418C2×#2610—171nomaximal, Sylow
419C23×C17—21no—
420C23×C17—21no—
421C23×C17—22no—
422C23×C17—22no—
423C23×C17—22no—
424C23×C17—22no—
425C23×C17—22no—
426C23×C17—22no—
427C23×C17—22no—
428C23×C17—22no—
429C23×C17—22no—
430C23×C17C2×#4112yes—
431C23×C17C2511yescharacteristic
432C22×D17—21no—
433C22×D17—21no—
434C22×D17—22no—
435C22×D17—22no—
436C22×D17—28no—
437C22×D17—216no—
438C22×D17—22no—
439C22×D17—22no—
440C22×D17—22no—
441C22×D17—22no—
442C22×D17—22no—
443C22×D17—22no—
444C22×D17—22no—
445C22×D17—44no—
446C22×D17—44no—
447C22×D17—48no—
448C22×D17—48no—
449C22×D17—48no—
450C22×D17—48no—
451C22×D17—48no—
452C22×D17—48no—
453C22×D17—48no—
454C22×D17—48no—
455C22×D17C22×D412yes—
456C22×D17C2×#4112yes—
457C22×D17C2×#4112yes—
458C22×D17C2×#4112yes—
459C22×D17C2×#4114yes—
460C22×D17H(5,𝔽2)14yes—
461Q8×C17—44no—
462D4×C17—48no—
463D4×C17—44no—
464C2×C4×C17—28no—
465C2×C4×C17—21no—
466C2×C4×C17—22no—
467C2×C4×C17—21no—
468C2×C4×C17—21no—
469C2×C4×C17—21no—
470C2×C4×C17—22no—
471C2×C4×C17—22no—
472C2×C4×C17—22no—
473C2×C4×C17—21no—
474C2×C4×C17—21no—
475C2×C4×C17—22no—
476C2×C4×C17—22no—
477C2×C4×C17—22no—
478C2×C4×C17—22no—
479C2×C4×C17—22no—
480C2×C4×C17—22no—
481C2×C4×C17—22no—
482C2×C4×C17—22no—
483C2×C4×C17C22×D412yes—
484C2×C4×C17C22×D412yes—
485C2×C4×C17C22×D412yes—
486C2×C4×C17C2×#4114yes—
487C2×C4×C17C2×#4112yes—
488C22⋊D17—48no—
489C22⋊D17—48no—
490C22⋊D17—48no—
491C2×Dic17—28no—
492C2×Dic17—21no—
493C2×Dic17—21no—
494C2×Dic17—21no—
495C2×Dic17—21no—
496C2×Dic17—22no—
497C2×Dic17—22no—
498C2×Dic17—22no—
499C2×Dic17—22no—
500C2×Dic17—22no—
501C2×Dic17—21no—
502C2×Dic17—21no—
503C2×Dic17—22no—
504C2×Dic17—22no—
505C2×Dic17—22no—
506C2×Dic17—22no—
507C2×Dic17—22no—
508C2×Dic17—22no—
509C2×Dic17—22no—
510C2×Dic17C22×D412yes—
511C2×Dic17C22×D412yes—
512C2×Dic17C22×D412yes—
513C2×Dic17C2×#4112yes—
514C2×Dic17C2×#4114yes—
515D68—48no—
516D68—44no—
517C4×D17—28no—
518C4×D17—28no—
519C4×D17—28no—
520C4×D17—28no—
521C4×D17—28no—
522C4×D17—28no—
523C4×D17—216no—
524C4×D17—44no—
525C4×D17—44no—
526C4×D17—48no—
527C4×D17—48no—
528Dic34—48no—
529Dic34—44no—
530C22×#124—171no—
531C22×#117—171no—
532#2610—171no—
533#2610—171no—
534#2610—171no—
535#2610—171no—
536#2610—172no—
537#2610—172no—
538#2610—172no—
539#2610—172no—
540#2610—171no—
541#2610—171no—
542#2610—171no—
543#2610D1711yescharacteristic, direct product factor
544C2×#395—171no—
545C2×#394—171no—
546C2×#393—171no—
547C2×#392—171no—
548C2×#390—172no—
549C2×#388—172no—
550C2×#388—172no—
551C2×#386—172no—
552C2×#376—171no—
553C22×C17—22no—
554C22×C17—24no—
555C22×C17—41no—
556C22×C17—41no—
557C22×C17—42no—
558C22×C17—42no—
559C22×C17—42no—
560C22×C17—42no—
561C22×C17—42no—
562C22×C17—42no—
563C22×C17—42no—
564C22×C17—42no—
565C22×C17C23×D411yescharacteristic
566C22×C17C22×#4111yescharacteristic
567C22×C17C22×#4111yescharacteristic
568C22×C17C22×#4112yes—
569C22×C17C2×H(5,𝔽2)12yes—
570C2×D17—22no—
571C2×D17—24no—
572C2×D17—41no—
573C2×D17—41no—
574C2×D17—42no—
575C2×D17—416no—
576C2×D17—42no—
577C2×D17—42no—
578C2×D17—42no—
579C2×D17—42no—
580C2×D17—42no—
581C2×D17—42no—
582C2×D17—42no—
583C2×D17—816no—
584C2×D17#52514yes—
585C2×D17#53214yes—
586C2×D17#53514yes—
587C2×D17#55118yes—
588C2×D17#55518yes—
589C4×C17—22no—
590C4×C17—22no—
591C4×C17—22no—
592C4×C17—22no—
593C4×C17—24no—
594C4×C17—41no—
595C4×C17—42no—
596C4×C17—41no—
597C4×C17—42no—
598Dic17—22no—
599Dic17—22no—
600Dic17—22no—
601Dic17—22no—
602Dic17—24no—
603Dic17—41no—
604Dic17—42no—
605Dic17—41no—
606Dic17—42no—
607C23×Q8—171no—
608C23×D4—172no—
609C23×D4—171no—
610C24×C4—171no—
611C2×#124—171no—
612C2×#124—171no—
613C2×#124—172no—
614C2×#124—172no—
615C2×#124—171no—
616C2×#124—348no—
617C2×#124C2×D1711yescharacteristic, complemented
618C2×#117—171no—
619C2×#117—171no—
620C2×#117—171no—
621C2×#117—171no—
622C2×#117—171no—
623C2×#117—171no—
624C2×#117—171no—
625C2×#117—348no—
626C2×#117C2×D1711yescharacteristic, complemented
627C22×C4⋊C4—171no—
628C22×C4⋊C4—171no—
629C22×C4⋊C4—172no—
630C22×C22⋊C4—171no—
631C22×C22⋊C4—172no—
632C22×C22⋊C4—172no—
633C22×C22⋊C4—171no—
634C22×C22⋊C4—172no—
635C22×C22⋊C4—172no—
636C22×C22⋊C4—172no—
637C22×C22⋊C4—172no—
638C22×C42—171no—
639C22×C42—171no—
640C22×C42—172no—
641#395—171no—
642#395—172no—
643#395—171no—
644#395—172no—
645#395—171no—
646#395C2×D1711yescharacteristic, complemented
647#394—171no—
648#394—171no—
649#394—172no—
650#394—172no—
651#394—171no—
652#394C2×D1711yescharacteristic, complemented
653#393—171no—
654#393—172no—
655#393—171no—
656#393—172no—
657#393—171no—
658#393C2×D1711yescharacteristic, complemented
659#392—172no—
660#392—171no—
661#392—172no—
662#392—171no—
663#392—171no—
664#392C2×D1711yescharacteristic
665#390—172no—
666#390—172no—
667#390—172no—
668#390—172no—
669#390—172no—
670#390—172no—
671#390—172no—
672#390C2×D1712yescomplemented
673#388—172no—
674#388—172no—
675#388—172no—
676#388—172no—
677#388—172no—
678#388—172no—
679#388—172no—
680#388—172no—
681#388—172no—
682#388—172no—
683#388—172no—
684#388—172no—
685#388—172no—
686#388—172no—
687#388C2×D1712yescomplemented
688#388C2×D1712yescomplemented
689#386—172no—
690#386—172no—
691#386—172no—
692#386—172no—
693#386—172no—
694#386—172no—
695#386—172no—
696#386C2×D1712yescomplemented
697#376—172no—
698#376—171no—
699#376—171no—
700#376—171no—
701#376—172no—
702#376C2×D1711yescharacteristic, complemented
703C2×#95—171no—
704C2×#95—171no—
705C2×#95—172no—
706C2×#95—172no—
707C2×#95—172no—
708C2×C17—42no—
709C2×C17—82no—
710C2×C17C2×#52511yescharacteristic
711C2×C17C2×#53211yescharacteristic
712C2×C17C2×#53511yescharacteristic
713C2×C17C2×#55112yes—
714C2×C17C2×#55512yes—
715D17—42no—
716D17—82no—
717D17#261018yesdirect product factor
718C25—171no—
719C25—172no—
720C22×Q8—172no—
721C22×Q8—171no—
722C22×Q8—344no—
723C22×Q8—684no—
724C22×Q8C22×D1711yescharacteristic
725C22×D4—172no—
726C22×D4—172no—
727C22×D4—172no—
728C22×D4—172no—
729C22×D4—171no—
730C22×D4—344no—
731C22×D4—348no—
732C22×D4—348no—
733C22×D4—684no—
734C22×D4—684no—
735C22×D4C22×D1712yes—
736C22×D4C22×D1711yescharacteristic
737C23×C4—171no—
738C23×C4—171no—
739C23×C4—171no—
740C23×C4—171no—
741C23×C4—172no—
742C23×C4—171no—
743C23×C4—171no—
744C23×C4—172no—
745C23×C4—171no—
746C23×C4—172no—
747C23×C4—171no—
748C23×C4—171no—
749C23×C4—344no—
750C23×C4—344no—
751C23×C4—344no—
752C23×C4C22×D1711yescharacteristic
753#124—24no—
754#124—348no—
755#124—348no—
756#124—344no—
757#124—344no—
758#124—344no—
759#117—24no—
760#117—344no—
761#117—344no—
762#117—344no—
763#117—344no—
764#117—344no—
765#117—344no—
766#117—344no—
767C2×C4⋊C4—171no—
768C2×C4⋊C4—171no—
769C2×C4⋊C4—171no—
770C2×C4⋊C4—171no—
771C2×C4⋊C4—171no—
772C2×C4⋊C4—171no—
773C2×C4⋊C4—172no—
774C2×C4⋊C4—172no—
775C2×C4⋊C4—172no—
776C2×C4⋊C4—344no—
777C2×C4⋊C4—344no—
778C2×C4⋊C4—684no—
779C2×C4⋊C4C22×D1711yescharacteristic
780C2×C4⋊C4C22×D1711yescharacteristic
781C2×C4⋊C4C22×D1712yes—
782C2×C22⋊C4—171no—
783C2×C22⋊C4—171no—
784C2×C22⋊C4—172no—
785C2×C22⋊C4—172no—
786C2×C22⋊C4—172no—
787C2×C22⋊C4—172no—
788C2×C22⋊C4—171no—
789C2×C22⋊C4—171no—
790C2×C22⋊C4—171no—
791C2×C22⋊C4—171no—
792C2×C22⋊C4—172no—
793C2×C22⋊C4—172no—
794C2×C22⋊C4—172no—
795C2×C22⋊C4—172no—
796C2×C22⋊C4—172no—
797C2×C22⋊C4—172no—
798C2×C22⋊C4—172no—
799C2×C22⋊C4—172no—
800C2×C22⋊C4—172no—
801C2×C22⋊C4—172no—
802C2×C22⋊C4—172no—
803C2×C22⋊C4—172no—
804C2×C22⋊C4—172no—
805C2×C22⋊C4—172no—
806C2×C22⋊C4—344no—
807C2×C22⋊C4—344no—
808C2×C22⋊C4—348no—
809C2×C22⋊C4—348no—
810C2×C22⋊C4—348no—
811C2×C22⋊C4—348no—
812C2×C22⋊C4—684no—
813C2×C22⋊C4—684no—
814C2×C22⋊C4C22×D1711yescharacteristic
815C2×C22⋊C4C22×D1711yescharacteristic
816C2×C22⋊C4C22×D1712yes—
817C2×C22⋊C4C22×D1712yes—
818C2×C22⋊C4C22×D1712yes—
819C2×C22⋊C4C22×D1712yes—
820C2×C22⋊C4C22×D1712yes—
821C2×C22⋊C4C22×D1712yes—
822C2×C42—171no—
823C2×C42—171no—
824C2×C42—171no—
825C2×C42—178no—
826C2×C42—171no—
827C2×C42—171no—
828C2×C42—171no—
829C2×C42—172no—
830C2×C42—172no—
831C2×C42—172no—
832C2×C42—344no—
833C2×C42—348no—
834C2×C42C22×D1711yescharacteristic
835C2×C42C22×D1712yes—
836C2×C42C22×D1711yescharacteristic
837#95—172no—
838#95—172no—
839#95—172no—
840#95—171no—
841#95—172no—
842#95—172no—
843#95—171no—
844#95—172no—
845#95—172no—
846#95—172no—
847#95—172no—
848#95—172no—
849#95—172no—
850#95C22×D1712yes—
851#95C22×D1711yescharacteristic
852#95C22×D1711yescharacteristic
853#95C22×D1712yes—
854#95C22×D1712yes—
855C17C2×#261011yescharacteristic, complemented, Sylow
856C24—171no—
857C24—174no—
858C24—171no—
859C24—172no—
860C24—342no—
861C24—344no—
862C24—342no—
863C24—344no—
864C24—344no—
865C24—344no—
866C24—344no—
867C24—344no—
868C24—344no—
869C24—344no—
870C24—344no—
871C24C23×D1712yes—
872C24C23×D1711yescharacteristic
873C2×Q8—22no—
874C2×Q8—42no—
875C2×Q8—344no—
876C2×Q8—342no—
877C2×Q8—682no—
878C2×Q8—682no—
879C2×Q8—682no—
880C2×Q8—6816no—
881C2×D4—24no—
882C2×D4—22no—
883C2×D4—24no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—344no—
887C2×D4—344no—
888C2×D4—344no—
889C2×D4—344no—
890C2×D4—344no—
891C2×D4—344no—
892C2×D4—342no—
893C2×D4—344no—
894C2×D4—682no—
895C2×D4—682no—
896C2×D4—6832no—
897C2×D4—6816no—
898C2×D4—682no—
899C2×D4—682no—
900C2×D4—682no—
901C2×D4—682no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—172no—
906C22×C4—171no—
907C22×C4—171no—
908C22×C4—171no—
909C22×C4—171no—
910C22×C4—174no—
911C22×C4—174no—
912C22×C4—174no—
913C22×C4—178no—
914C22×C4—174no—
915C22×C4—172no—
916C22×C4—171no—
917C22×C4—172no—
918C22×C4—171no—
919C22×C4—342no—
920C22×C4—342no—
921C22×C4—344no—
922C22×C4—342no—
923C22×C4—344no—
924C22×C4—342no—
925C22×C4—342no—
926C22×C4—342no—
927C22×C4—342no—
928C22×C4—342no—
929C22×C4—344no—
930C22×C4—344no—
931C22×C4—3432no—
932C22×C4—342no—
933C22×C4—342no—
934C22×C4—344no—
935C22×C4—344no—
936C22×C4—344no—
937C22×C4—344no—
938C22×C4—344no—
939C22×C4—344no—
940C22×C4—344no—
941C22×C4—344no—
942C22×C4—342no—
943C22×C4—342no—
944C22×C4—342no—
945C22×C4—342no—
946C22×C4—342no—
947C22×C4C23×D1712yes—
948C22×C4C23×D1711yescharacteristic
949C22×C4C23×D1712yes—
950C22×C4C23×D1711yescharacteristic
951C22×C4C23×D1711yescharacteristic
952C22×C4C23×D1711yescharacteristic
953C22×C4C23×D1711yescharacteristic
954C22×C4C23×D1712yes—
955C22×C4C23×D1711yescharacteristic
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—42no—
959C4⋊C4—342no—
960C4⋊C4—342no—
961C4⋊C4—342no—
962C4⋊C4—342no—
963C4⋊C4—342no—
964C4⋊C4—342no—
965C4⋊C4—682no—
966C4⋊C4—682no—
967C4⋊C4—682no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—24no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—342no—
977C22⋊C4—342no—
978C22⋊C4—344no—
979C22⋊C4—344no—
980C22⋊C4—344no—
981C22⋊C4—344no—
982C22⋊C4—344no—
983C22⋊C4—344no—
984C22⋊C4—342no—
985C22⋊C4—342no—
986C22⋊C4—344no—
987C22⋊C4—344no—
988C22⋊C4—342no—
989C22⋊C4—342no—
990C22⋊C4—344no—
991C22⋊C4—344no—
992C22⋊C4—344no—
993C22⋊C4—344no—
994C22⋊C4—682no—
995C22⋊C4—682no—
996C22⋊C4—682no—
997C22⋊C4—682no—
998C22⋊C4—682no—
999C22⋊C4—682no—
1000C42—22no—
1001C42—24no—
1002C42—174no—
1003C42—174no—
1004C42—174no—
1005C42—342no—
1006C42—342no—
1007C42—344no—
1008C42—344no—
1009C42—342no—
1010C42—344no—
1011C42D4×D1714yescomplemented
1012C23—21no—
1013C23—21no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—172no—
1024C23—172no—
1025C23—174no—
1026C23—172no—
1027C23—174no—
1028C23—172no—
1029C23—348no—
1030C23—3416no—
1031C23—341no—
1032C23—341no—
1033C23—342no—
1034C23—342no—
1035C23—342no—
1036C23—342no—
1037C23—342no—
1038C23—342no—
1039C23—342no—
1040C23—342no—
1041C23—342no—
1042C23—684no—
1043C23—684no—
1044C23—688no—
1045C23—688no—
1046C23—688no—
1047C23—688no—
1048C23—688no—
1049C23—688no—
1050C23—688no—
1051C23—688no—
1052C23#41×D1712yes—
1053C23C24×D1711yescharacteristic
1054Q8—44no—
1055Q8—684no—
1056Q8—688no—
1057D4—48no—
1058D4—44no—
1059D4—688no—
1060D4—684no—
1061D4—688no—
1062D4—688no—
1063D4—688no—
1064C2×C4—28no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—172no—
1084C2×C4—172no—
1085C2×C4—172no—
1086C2×C4—174no—
1087C2×C4—172no—
1088C2×C4—348no—
1089C2×C4—348no—
1090C2×C4—348no—
1091C2×C4—3416no—
1092C2×C4—348no—
1093C2×C4—348no—
1094C2×C4—348no—
1095C2×C4—348no—
1096C2×C4—341no—
1097C2×C4—342no—
1098C2×C4—341no—
1099C2×C4—341no—
1100C2×C4—341no—
1101C2×C4—342no—
1102C2×C4—342no—
1103C2×C4—342no—
1104C2×C4—341no—
1105C2×C4—341no—
1106C2×C4—342no—
1107C2×C4—342no—
1108C2×C4—342no—
1109C2×C4—342no—
1110C2×C4—342no—
1111C2×C4—342no—
1112C2×C4—342no—
1113C2×C4—342no—
1114C2×C4—688no—
1115C2×C4—684no—
1116C2×C4—684no—
1117C2×C4—688no—
1118C2×C4C2×D4×D1712yes—
1119C2×C4C2×D4×D1712yes—
1120C2×C4C2×D4×D1712yes—
1121C2×C4#41×D1714yes—
1122C2×C4#41×D1712yes—
1123C22—22no—
1124C22—24no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—174no—
1136C22—174no—
1137C22—178no—
1138C22—174no—
1139C22—178no—
1140C22—342no—
1141C22—344no—
1142C22—6816no—
1143C22—681no—
1144C22—681no—
1145C22—682no—
1146C22—682no—
1147C22—682no—
1148C22—682no—
1149C22—682no—
1150C22—682no—
1151C22—682no—
1152C22—682no—
1153C22—13616no—
1154C22C22×D4×D1711yescharacteristic
1155C22C2×#41×D1711yescharacteristic
1156C22C2×#41×D1711yescharacteristic
1157C22C2×#41×D1712yes—
1158C22H(5,𝔽2)×D1712yes—
1159C4—22no—
1160C4—22no—
1161C4—22no—
1162C4—24no—
1163C4—22no—
1164C4—42no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—342no—
1169C4—342no—
1170C4—342no—
1171C4—344no—
1172C4—342no—
1173C4—682no—
1174C4—681no—
1175C4—681no—
1176C4—682no—
1177C2—42no—
1178C2—82no—
1179C2—178no—
1180C2—682no—
1181C2—1362no—
1182C2D17×#52511yescharacteristic
1183C2D17×#53211yescharacteristic
1184C2D17×#53511yescharacteristic
1185C2D17×#55112yes—
1186C2D17×#55512yes—
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2610C2
prime radicalD17×#392C2
hypercenter#2610D17
hypocenterC17C2×#2610
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. C2×#124×D17C2semidirect
2. C2×#117×D17C2semidirect
3. #14534474C2semidirect
4. #14534473C2semidirect
5. #14534472C2semidirect
6. #14534471C2semidirect
7. #14534470C2semidirect
8. #14534469C2semidirect
9. #14534468C2semidirect
10. #14534467C2semidirect
11. #14534466C2semidirect
12. #14534465C2semidirect
13. #14534464C2semidirect
14. D17×#395C2semidirect
15. D17×#394C2semidirect
16. D17×#393C2semidirect
18. D17×#390C2semidirect
19. D17×#388C2semidirect
20. D17×#388C2semidirect
21. D17×#386C2semidirect
22. D17×#376C2semidirect
23. C17×#2610C2semidirect
28. C2×#10587633C22semidirect
29. C2×#10587561C22semidirect
30. C2×#10587622C22semidirect
31. C2×#10587571C22semidirect
32. C2×#10587571C22semidirect
34. C2×#10587612C22semidirect
35. C2×#10587578C22semidirect
36. C2×#10587578C22semidirect
37. C2×#10587558C22semidirect
38. C2×#10587558C22semidirect
39. C2×#10587563C22semidirect
40. C2×#10587563C22semidirect
56. #11762730C22semidirect
57. #11762730C22semidirect
58. #11762729C22semidirect
59. #11762729C22semidirect
60. #11762728C22semidirect
61. #11762727C22semidirect
62. #11762726C22semidirect
63. #11762725C22semidirect
64. #11762724C22semidirect
65. #11762723C22semidirect
66. #11762722C22semidirect
67. #11762722C22semidirect
68. #11762721C22semidirect
69. #11762721C22semidirect
70. #11762720C22semidirect
76. #11762712C22semidirect
77. #11762711C22semidirect
78. #11762710C22semidirect
79. #11762709C22semidirect
80. #11762709C22semidirect
81. #11762709C22semidirect
82. #11762709C22semidirect
83. #11762703C22semidirect
84. #11762703C22semidirect
85. #11762702C22semidirect
86. #11762702C22semidirect
87. #11762701C22semidirect
88. #11762701C22semidirect
89. #11762700C22semidirect
90. #11762700C22semidirect
91. #11762699C22semidirect
92. #11762699C22semidirect
93. #11762698C22semidirect
94. #11762698C22semidirect
95. #11762697C22semidirect
96. #11762697C22semidirect
97. #11762689C22semidirect
98. #11762688C22semidirect
99. #11762687C22semidirect
100. #11762687C22semidirect
101. #11762686C22semidirect
102. #11762685C22semidirect
103. #11762685C22semidirect
104. #11762655C22semidirect
105. #11762655C22semidirect
106. #11762654C22semidirect
107. #11762654C22semidirect
108. #11762654C22semidirect
114. C2×C17×#124C22semidirect
115. C2×C17×#117C22semidirect
116. C17×#395C22semidirect
117. C17×#394C22semidirect
118. C17×#393C22semidirect
120. C17×#390C22semidirect
121. C17×#388C22semidirect
122. C17×#388C22semidirect
123. C17×#386C22semidirect
124. C17×#376C22semidirect
243. C42×D17D4semidirect
375. C42×C17C2×D4semidirect
415. C4×Dic17C2×D4semidirect
416. C4×Dic17C2×D4semidirect
417. C4×Dic17C2×D4semidirect
543. #2610D17direct (N × H)
617. C2×#124C2×D17semidirect
626. C2×#117C2×D17semidirect
646. #395C2×D17semidirect
652. #394C2×D17semidirect
658. #393C2×D17semidirect
672. #390C2×D17semidirect
687. #388C2×D17semidirect
688. #388C2×D17semidirect
696. #386C2×D17semidirect
702. #376C2×D17semidirect
717. D17#2610direct (N × H)
855. C17C2×#2610semidirect
1011. C42D4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D172
C2×#117×D172
#145344742
#145344732
#145344722
#145344712
#145344702
#145344692
#145344682
#145344672
#145344662
#145344652
#145344642
D17×#3952
D17×#3942
D17×#3932
D17×#3922
D17×#3902
D17×#3882
D17×#3862
D17×#3762
C17×#26102
C2×#261017