Finite Group Databasebeta

← D17×#2636 #17201039

Subgroups — D17×#2636 #17201039

Order 4352.

3218 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D17C211yesmaximal, characteristic, complemented
2C2×C4×D4×D17C211yesmaximal, characteristic, complemented
3#14534688C212yesmaximal, complemented
4#14534687C212yesmaximal, complemented
5#14534686C212yesmaximal, complemented
6#14534685C212yesmaximal, complemented
7#14534684C211yesmaximal, characteristic, complemented
8#14534683C211yesmaximal, characteristic, complemented
9#14534682C211yesmaximal, characteristic, complemented
10#14534681C211yesmaximal, characteristic, complemented
11#14534680C211yesmaximal, characteristic, complemented
12#14534679C211yesmaximal, characteristic, complemented
13#14534678C211yesmaximal, characteristic, complemented
14D17×#400C211yesmaximal, characteristic, complemented
15D17×#399C211yesmaximal, characteristic, complemented
16D17×#396C212yesmaximal, complemented
17D17×#394C211yesmaximal, characteristic, complemented
18D17×#394C212yesmaximal, complemented
19D17×#392C211yesmaximal, characteristic
20D17×#386C212yesmaximal, complemented
21D17×#385C212yesmaximal, complemented
22D17×#382C211yesmaximal, characteristic, complemented
23C17×#2636C211yesmaximal, characteristic, complemented
24C22×D4×D17C2211yescharacteristic
25C22×D4×D17C2212yes—
26C23×C4×D17C2212yes—
27C2×#10587584C2211yescharacteristic, complemented
28C2×#10587584C2211yescharacteristic, complemented
29C2×#10587584C2211yescharacteristic, complemented
30C2×#10587562C2211yescharacteristic, complemented
31C2×#10587565C2211yescharacteristic, complemented
32C2×#10587565C2211yescharacteristic, complemented
33C2×#10587565C2211yescharacteristic, complemented
34#126×D17—28no—
35C2×C4×D68C2211yescharacteristic, complemented
36C2×D4×Dic17C2211yescharacteristic, complemented
37C2×#10587579C2211yescharacteristic, complemented
38C2×C4×C22⋊D17C2212yescomplemented
39C2×#10587567C2212yescomplemented
40C4×D4×D17—28no—
41C2×C4⋊C4×D17C2211yescharacteristic
42C2×C4⋊C4×D17C2211yescharacteristic
43C2×C4⋊C4×D17C2211yescharacteristic
44C2×C4⋊C4×D17C2211yescharacteristic
45C2×C4⋊C4×D17C2212yes—
46C2×C4⋊C4×D17C2212yes—
47C2×C22⋊C4×D17C2212yes—
48C2×C22⋊C4×D17C2211yescharacteristic
49C2×C22⋊C4×D17C2212yes—
50C2×C22⋊C4×D17C2211yescharacteristic
51C2×C22⋊C4×D17C2211yescharacteristic
52C2×C22⋊C4×D17C2212yes—
53C2×C22⋊C4×D17C2212yes—
54C2×C22⋊C4×D17C2212yes—
55C2×C42×D17C2211yescharacteristic
56#11762751C2212yescomplemented
57#11762750C2212yescomplemented
58#11762749C2211yescharacteristic, complemented
59#11762748C2211yescharacteristic, complemented
60#11762747C2211yescharacteristic, complemented
61#11762746C2211yescharacteristic, complemented
62#11762745C2211yescharacteristic, complemented
63#11762745C2212yescomplemented
64#11762744C2211yescharacteristic, complemented
65#11762744C2212yescomplemented
66#11762733C2212yescomplemented
67#11762732C2212yescomplemented
68#11762732C2212yescomplemented
69#11762732C2212yescomplemented
70#11762731C2212yescomplemented
71#11762731C2212yescomplemented
72#11762731C2212yescomplemented
73#11762727C2211yescharacteristic, complemented
74#11762727C2212yescomplemented
75#11762726C2211yescharacteristic, complemented
76#11762726C2212yescomplemented
77#11762725C2212yescomplemented
78#11762725C2212yescomplemented
79#11762725C2212yescomplemented
80#11762724C2212yescomplemented
81#11762724C2212yescomplemented
82#11762724C2212yescomplemented
83#11762723C2211yescharacteristic, complemented
84#11762723C2212yescomplemented
85#11762719C2211yescharacteristic
86#11762718C2211yescharacteristic
87#11762718C2212yes—
88#11762717C2211yescharacteristic
89#11762717C2212yes—
90#11762689C2212yescomplemented
91#11762688C2212yescomplemented
92#11762687C2212yescomplemented
93#11762687C2212yescomplemented
94#11762686C2212yescomplemented
95#11762685C2212yescomplemented
96#11762685C2212yescomplemented
97#11762684C2212yescomplemented
98#11762683C2212yescomplemented
99#11762683C2212yescomplemented
100#11762682C2212yescomplemented
101#11762681C2212yescomplemented
102#11762680C2212yescomplemented
103#11762680C2212yescomplemented
104#11762675C2211yescharacteristic, complemented
105#11762674C2212yescomplemented
106#11762673C2211yescharacteristic, complemented
107#11762673C2211yescharacteristic, complemented
108#11762673C2212yescomplemented
109#95×D17C2212yes—
110#95×D17C2211yescharacteristic
111#95×D17C2211yescharacteristic
112#95×D17C2212yes—
113#95×D17C2212yes—
114C2×C17×#126C2211yescharacteristic, complemented
115C2×C4×D4×C17C2211yescharacteristic, complemented
116C17×#400C2211yescharacteristic, complemented
117C17×#399C2211yescharacteristic, complemented
118C17×#396C2212yescomplemented
119C17×#394C2211yescharacteristic, complemented
120C17×#394C2212yescomplemented
121C17×#392C2211yescharacteristic
122C17×#386C2212yescomplemented
123C17×#385C2212yescomplemented
124C17×#382C2211yescharacteristic, complemented
125C24×D17C2311yescharacteristic
126C24×D17C2312yes—
127C22×D4×C17C2311yescharacteristic
128C22×D4×C17C2312yes—
129C23×C4×C17C2312yes—
130C22×C22⋊D17C2312yes—
131C22×C22⋊D17C2312yes—
132C22×C22⋊D17C2312yes—
133C23×Dic17C2312yes—
134C2×D4×D17—28no—
135C2×D4×D17—28no—
136C2×D4×D17—24no—
137C2×D4×D17—44no—
138C2×D4×D17—44no—
139C22×D68C2311yescharacteristic
140C22×D68C2312yes—
141C22×C4×D17—28no—
142C22×C4×D17—44no—
143C22×C4×D17—44no—
144C22×C4×D17C2311yescharacteristic
145C22×C4×D17C2311yescharacteristic
146C22×C4×D17C2311yescharacteristic
147C22×C4×D17C2312yes—
148C22×C4×D17C2312yes—
149C22×C4×D17C2312yes—
150C22×C4×D17C2311yescharacteristic
151C22×C4×D17C2311yescharacteristic
152C22×C4×D17C2311yescharacteristic
153C22×C4×D17C2312yes—
154C22×C4×D17C2312yes—
155C17×#126—24no—
156C4×D4×C17—24no—
157C2×C4⋊C4×C17C2311yescharacteristic
158C2×C4⋊C4×C17C2311yescharacteristic
159C2×C4⋊C4×C17C2311yescharacteristic
160C2×C4⋊C4×C17C2311yescharacteristic
161C2×C4⋊C4×C17C2312yes—
162C2×C4⋊C4×C17C2312yes—
163C2×C22⋊C4×C17C2312yes—
164C2×C22⋊C4×C17C2311yescharacteristic
165C2×C22⋊C4×C17C2312yes—
166C2×C22⋊C4×C17C2311yescharacteristic
167C2×C22⋊C4×C17C2311yescharacteristic
168C2×C22⋊C4×C17C2312yes—
169C2×C22⋊C4×C17C2312yes—
170C2×C22⋊C4×C17C2312yes—
171C2×C42×C17C2311yescharacteristic
172C2×C22⋊Dic17C2311yescharacteristic
173C2×C22⋊Dic17C2311yescharacteristic
174C2×C22⋊Dic17C2311yescharacteristic
175C2×C22⋊Dic17C2312yes—
176C2×C22⋊Dic17C2312yes—
177C2×C22⋊Dic17C2312yes—
178C2×C22⋊Dic17C2312yes—
179C2×C22⋊Dic17C2312yes—
180D4×Dic17—24no—
181C4×C22⋊D17—28no—
182C2×#63227C2311yescharacteristic
183C2×#63227C2311yescharacteristic
184C2×#63227C2311yescharacteristic
185C2×#63227C2311yescharacteristic
186C2×#63227C2312yes—
187C2×#63227C2312yes—
188C2×#63227C2312yes—
189C2×#63227C2311yescharacteristic
190C2×#63227C2312yes—
191C2×#63227C2311yescharacteristic
192C2×#63227C2312yes—
193C2×#63227C2312yes—
194C2×#63227C2312yes—
195C2×#63227C2312yes—
196C2×#63227C2312yes—
197C2×#63227C2312yes—
198C2×C4⋊Dic17C2311yescharacteristic
199C2×C4⋊Dic17C2311yescharacteristic
200C2×C4⋊Dic17C2311yescharacteristic
201C2×C4⋊Dic17C2311yescharacteristic
202C2×C4⋊Dic17C2312yes—
203C2×C4⋊Dic17C2312yes—
204C2×#63225C2311yescharacteristic
205C2×#63225C2311yescharacteristic
206C2×#63225C2311yescharacteristic
207C2×#63225C2311yescharacteristic
208C2×#63225C2312yes—
209C2×#63225C2311yescharacteristic
210C2×#63225C2311yescharacteristic
211C2×#63225C2312yes—
212C2×#63225C2312yes—
213C2×#63225C2312yes—
214C2×#63225C2312yes—
215C2×C4×Dic17C2311yescharacteristic
216C2×C4×Dic17C2311yescharacteristic
217C2×C4×Dic17C2311yescharacteristic
218#10587584—24no—
219#10587584—24no—
220#10587584—24no—
221#10587579—24no—
222C4⋊C4×D17—24no—
223C4⋊C4×D17—24no—
224C4⋊C4×D17—24no—
225C4⋊C4×D17—24no—
226C4⋊C4×D17—44no—
227C4⋊C4×D17—44no—
228#10587567—28no—
229C22⋊C4×D17—28no—
230C22⋊C4×D17—28no—
231C22⋊C4×D17—24no—
232C22⋊C4×D17—24no—
233C22⋊C4×D17—24no—
234C22⋊C4×D17—44no—
235C22⋊C4×D17—44no—
236C22⋊C4×D17—44no—
237#10587565—24no—
238#10587565—24no—
239#10587565—24no—
240#10587562—24no—
241C4×D68—24no—
242C42×D17D418yescomplemented
243C17×#95C2311yescharacteristic
244C17×#95C2311yescharacteristic
245C17×#95C2312yes—
246C17×#95C2312yes—
247C17×#95C2312yes—
248#10587502C2312yes—
249#10587502C2312yes—
250#10587502C2312yes—
251#10587502C2312yes—
252#10587502C2311yescharacteristic
253#10587502C2312yes—
254#10587502C2311yescharacteristic
255#10587502C2312yes—
256#10587502C2312yes—
257#10587502C2312yes—
258#10587502C2312yes—
259#10587502C2312yes—
260#10587502C2312yes—
261C24×C17C2411yescharacteristic
262C24×C17C2412yes—
263C23×D17—24no—
264C23×D17—24no—
265C23×D17—24no—
266C23×D17—24no—
267C23×D17—24no—
268C23×D17—24no—
269C23×D17—22no—
270C23×D17—24no—
271C23×D17—22no—
272C23×D17—24no—
273C23×D17—22no—
274C23×D17#4118yes—
275C23×D17C2411yescharacteristic
276C23×D17C2412yes—
277C23×D17C2411yescharacteristic
278C2×D4×C17—24no—
279C2×D4×C17—24no—
280C2×D4×C17—22no—
281C2×D4×C17—42no—
282C2×D4×C17—42no—
283C22×C4×C17—24no—
284C22×C4×C17—42no—
285C22×C4×C17—42no—
286C22×C4×C17C2412yes—
287C22×C4×C17C2412yes—
288C22×C4×C17C2411yescharacteristic
289C22×C4×C17C2411yescharacteristic
290C22×C4×C17C2412yes—
291C22×C4×C17C2411yescharacteristic
292C22×C4×C17C2411yescharacteristic
293C22×C4×C17C2411yescharacteristic
294C22×C4×C17C2411yescharacteristic
295C2×C22⋊D17—24no—
296C2×C22⋊D17—24no—
297C2×C22⋊D17—24no—
298C2×C22⋊D17—24no—
299C2×C22⋊D17—24no—
300C2×C22⋊D17—42no—
301C2×C22⋊D17—42no—
302C2×C22⋊D17—42no—
303C2×C22⋊D17—42no—
304C22×Dic17—24no—
305C22×Dic17—42no—
306C22×Dic17—42no—
307C22×Dic17C2412yes—
308C22×Dic17C2412yes—
309C22×Dic17C2411yescharacteristic
310C22×Dic17C2411yescharacteristic
311C22×Dic17C2412yes—
312C22×Dic17C2411yescharacteristic
313C22×Dic17C2411yescharacteristic
314C22×Dic17C2411yescharacteristic
315C22×Dic17C2411yescharacteristic
316D4×D17—232no—
317D4×D17—432no—
318C2×D68—24no—
319C2×D68—22no—
320C2×D68—24no—
321C2×D68—42no—
322C2×D68—42no—
323C2×C4×D17—24no—
324C2×C4×D17—24no—
325C2×C4×D17—22no—
326C2×C4×D17—22no—
327C2×C4×D17—24no—
328C2×C4×D17—22no—
329C2×C4×D17—22no—
330C2×C4×D17—22no—
331C2×C4×D17—24no—
332C2×C4×D17—24no—
333C2×C4×D17—24no—
334C2×C4×D17—24no—
335C2×C4×D17—24no—
336C2×C4×D17—24no—
337C2×C4×D17—24no—
338C2×C4×D17—22no—
339C2×C4×D17—24no—
340C2×C4×D17—24no—
341C2×C4×D17—24no—
342C2×C4×D17—22no—
343C2×C4×D17—24no—
344C2×C4×D17—24no—
345C2×C4×D17—432no—
346C2×C4×D17—42no—
347C2×C4×D17—42no—
348C2×C4×D17—42no—
349C2×C4×D17—42no—
350C2×C4×D17C2×D414yes—
351C2×C4×D17C2×D414yes—
352C2×C4×D17C2×D414yes—
353C4⋊C4×C17—22no—
354C4⋊C4×C17—22no—
355C4⋊C4×C17—22no—
356C4⋊C4×C17—22no—
357C4⋊C4×C17—42no—
358C4⋊C4×C17—42no—
359C22⋊C4×C17—24no—
360C22⋊C4×C17—22no—
361C22⋊C4×C17—22no—
362C22⋊C4×C17—22no—
363C22⋊C4×C17—24no—
364C22⋊C4×C17—42no—
365C22⋊C4×C17—42no—
366C22⋊C4×C17—42no—
367C42×C17C2×D414yescomplemented
368C22⋊Dic17—24no—
369C22⋊Dic17—22no—
370C22⋊Dic17—22no—
371C22⋊Dic17—22no—
372C22⋊Dic17—24no—
373C22⋊Dic17—42no—
374C22⋊Dic17—42no—
375C22⋊Dic17—42no—
376#63227—24no—
377#63227—24no—
378#63227—24no—
379#63227—22no—
380#63227—22no—
381#63227—22no—
382#63227—24no—
383#63227—22no—
384#63227—22no—
385#63227—22no—
386#63227—42no—
387#63227—42no—
388#63227—42no—
389#63227—42no—
390#63227—42no—
391#63227—42no—
392C4⋊Dic17—22no—
393C4⋊Dic17—22no—
394C4⋊Dic17—22no—
395C4⋊Dic17—22no—
396C4⋊Dic17—42no—
397C4⋊Dic17—42no—
398#63225—22no—
399#63225—22no—
400#63225—22no—
401#63225—22no—
402#63225—22no—
403#63225—22no—
404#63225—24no—
405#63225—42no—
406#63225—42no—
407#63225—42no—
408#63225—42no—
409C4×Dic17C2×D414yescomplemented
410C4×Dic17C2×D414yescomplemented
411C4×Dic17C2×D414yescomplemented
412C2×#2636—171nomaximal, Sylow
413C23×C17—22no—
414C23×C17—22no—
415C23×C17—22no—
416C23×C17—22no—
417C23×C17—22no—
418C23×C17—22no—
419C23×C17—21no—
420C23×C17—22no—
421C23×C17—22no—
422C23×C17—21no—
423C23×C17—21no—
424C23×C17C2×#4114yes—
425C23×C17C2511yescharacteristic
426C22×D17—22no—
427C22×D17—22no—
428C22×D17—22no—
429C22×D17—22no—
430C22×D17—22no—
431C22×D17—22no—
432C22×D17—216no—
433C22×D17—216no—
434C22×D17—216no—
435C22×D17—21no—
436C22×D17—22no—
437C22×D17—21no—
438C22×D17—22no—
439C22×D17—21no—
440C22×D17—48no—
441C22×D17—48no—
442C22×D17—48no—
443C22×D17—48no—
444C22×D17—44no—
445C22×D17—44no—
446C22×D17—44no—
447C22×D17—48no—
448C22×D17—48no—
449C22×D17C22×D412yes—
450C22×D17C2×#4114yes—
451C22×D17C2×#4114yes—
452C22×D17H(5,𝔽2)14yes—
453C22×D17H(5,𝔽2)12yes—
454C22×D172−1+412yes—
455D4×C17—28no—
456D4×C17—48no—
457C2×C4×C17—22no—
458C2×C4×C17—21no—
459C2×C4×C17—22no—
460C2×C4×C17—21no—
461C2×C4×C17—21no—
462C2×C4×C17—21no—
463C2×C4×C17—21no—
464C2×C4×C17—22no—
465C2×C4×C17—22no—
466C2×C4×C17—22no—
467C2×C4×C17—22no—
468C2×C4×C17—21no—
469C2×C4×C17—22no—
470C2×C4×C17—22no—
471C2×C4×C17—22no—
472C2×C4×C17—22no—
473C2×C4×C17—22no—
474C2×C4×C17—22no—
475C2×C4×C17—22no—
476C2×C4×C17—21no—
477C2×C4×C17—48no—
478C2×C4×C17C22×D412yes—
479C2×C4×C17C22×D412yes—
480C2×C4×C17C22×D412yes—
481C22⋊D17—216no—
482C22⋊D17—48no—
483C22⋊D17—48no—
484C2×Dic17—22no—
485C2×Dic17—22no—
486C2×Dic17—21no—
487C2×Dic17—21no—
488C2×Dic17—22no—
489C2×Dic17—21no—
490C2×Dic17—21no—
491C2×Dic17—21no—
492C2×Dic17—22no—
493C2×Dic17—22no—
494C2×Dic17—22no—
495C2×Dic17—21no—
496C2×Dic17—22no—
497C2×Dic17—22no—
498C2×Dic17—22no—
499C2×Dic17—22no—
500C2×Dic17—22no—
501C2×Dic17—22no—
502C2×Dic17—22no—
503C2×Dic17—21no—
504C2×Dic17—48no—
505C2×Dic17C22×D412yes—
506C2×Dic17C22×D412yes—
507C2×Dic17C22×D412yes—
508D68—28no—
509D68—48no—
510C4×D17—28no—
511C4×D17—28no—
512C4×D17—28no—
513C4×D17—48no—
514C4×D17—48no—
515C4×D17—44no—
516C4×D17—44no—
517C4×D17—48no—
518C4×D17—44no—
519C4×D17—48no—
520C4×D17—48no—
521C22×#126—171no—
522C22×C4×D4—171no—
523#2636—171no—
524#2636—171no—
525#2636—172no—
526#2636—171no—
527#2636—172no—
528#2636—171no—
529#2636—172no—
530#2636—172no—
531#2636—171no—
532#2636—171no—
533#2636—171no—
534#2636D1711yescharacteristic, direct product factor
535C2×#400—171no—
536C2×#399—171no—
537C2×#396—172no—
538C2×#394—172no—
539C2×#394—171no—
540C2×#392—171no—
541C2×#386—172no—
542C2×#385—172no—
543C2×#382—171no—
544C22×C17—24no—
545C22×C17—24no—
546C22×C17—24no—
547C22×C17—42no—
548C22×C17—42no—
549C22×C17—42no—
550C22×C17—42no—
551C22×C17—41no—
552C22×C17—41no—
553C22×C17—41no—
554C22×C17—42no—
555C22×C17—42no—
556C22×C17C23×D411yescharacteristic
557C22×C17C22×#4112yes—
558C22×C17C2×H(5,𝔽2)12yes—
559C22×C17C2×H(5,𝔽2)11yescharacteristic
560C22×C17C2×2−1+411yescharacteristic
561C2×D17—24no—
562C2×D17—24no—
563C2×D17—24no—
564C2×D17—42no—
565C2×D17—42no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—432no—
569C2×D17—41no—
570C2×D17—41no—
571C2×D17—41no—
572C2×D17—42no—
573C2×D17—42no—
574C2×D17—88no—
575C2×D17#52514yes—
576C2×D17#53514yes—
577C2×D17#53714yes—
578C2×D17#53818yes—
579C2×D17#53918yes—
580C4×C17—22no—
581C4×C17—22no—
582C4×C17—22no—
583C4×C17—41no—
584C4×C17—42no—
585C4×C17—41no—
586C4×C17—41no—
587C4×C17—42no—
588C4×C17—42no—
589Dic17—22no—
590Dic17—22no—
591Dic17—22no—
592Dic17—41no—
593Dic17—42no—
594Dic17—41no—
595Dic17—41no—
596Dic17—42no—
597Dic17—42no—
598C23×D4—171no—
599C23×D4—172no—
600C24×C4—172no—
601C2×#126—171no—
602C2×#126—171no—
603C2×#126—171no—
604C2×#126—171no—
605C2×#126—171no—
606C2×#126—171no—
607C2×#126—171no—
608C2×#126—348no—
609C2×#126C2×D1711yescharacteristic, complemented
610C2×C4×D4—171no—
611C2×C4×D4—172no—
612C2×C4×D4—171no—
613C2×C4×D4—172no—
614C2×C4×D4—171no—
615C2×C4×D4—348no—
616C2×C4×D4C2×D1711yescharacteristic, complemented
617C22×C4⋊C4—171no—
618C22×C4⋊C4—171no—
619C22×C4⋊C4—171no—
620C22×C4⋊C4—171no—
621C22×C4⋊C4—172no—
622C22×C4⋊C4—172no—
623C22×C22⋊C4—171no—
624C22×C22⋊C4—171no—
625C22×C22⋊C4—172no—
626C22×C22⋊C4—172no—
627C22×C22⋊C4—171no—
628C22×C22⋊C4—172no—
629C22×C22⋊C4—172no—
630C22×C22⋊C4—172no—
631C22×C42—171no—
632#400—171no—
633#400—171no—
634#400—171no—
635#400—172no—
636#400—172no—
637#400C2×D1711yescharacteristic, complemented
638#399—172no—
639#399—171no—
640#399—172no—
641#399—171no—
642#399—171no—
643#399C2×D1711yescharacteristic, complemented
644#396—172no—
645#396—172no—
646#396—172no—
647#396—172no—
648#396—172no—
649#396—172no—
650#396—172no—
651#396C2×D1712yescomplemented
652#394—171no—
653#394—172no—
654#394—171no—
655#394—172no—
656#394—172no—
657#394—172no—
658#394—172no—
659#394—172no—
660#394—172no—
661#394—172no—
662#394—171no—
663#394—172no—
664#394C2×D1711yescharacteristic, complemented
665#394C2×D1712yescomplemented
666#392—172no—
667#392—171no—
668#392—172no—
669#392—171no—
670#392—171no—
671#392C2×D1711yescharacteristic
672#386—172no—
673#386—172no—
674#386—172no—
675#386—172no—
676#386—172no—
677#386—172no—
678#386—172no—
679#386C2×D1712yescomplemented
680#385—172no—
681#385—172no—
682#385—172no—
683#385—172no—
684#385—172no—
685#385—172no—
686#385—172no—
687#385C2×D1712yescomplemented
688#382—172no—
689#382—171no—
690#382—171no—
691#382—171no—
692#382—172no—
693#382C2×D1711yescharacteristic, complemented
694C2×#95—171no—
695C2×#95—171no—
696C2×#95—172no—
697C2×#95—172no—
698C2×#95—172no—
699C2×C17—44no—
700C2×C17—81no—
701C2×C17C2×#52511yescharacteristic
702C2×C17C2×#53511yescharacteristic
703C2×C17C2×#53711yescharacteristic
704C2×C17C2×#53812yes—
705C2×C17C2×#53912yes—
706D17—44no—
707D17—81no—
708D17#263618yesdirect product factor
709C25—172no—
710C25—171no—
711C22×D4—172no—
712C22×D4—172no—
713C22×D4—172no—
714C22×D4—171no—
715C22×D4—172no—
716C22×D4—344no—
717C22×D4—348no—
718C22×D4—348no—
719C22×D4—684no—
720C22×D4—684no—
721C22×D4C22×D1711yescharacteristic
722C22×D4C22×D1712yes—
723C23×C4—171no—
724C23×C4—171no—
725C23×C4—171no—
726C23×C4—172no—
727C23×C4—171no—
728C23×C4—171no—
729C23×C4—171no—
730C23×C4—172no—
731C23×C4—172no—
732C23×C4—172no—
733C23×C4—172no—
734C23×C4—172no—
735C23×C4—348no—
736C23×C4—684no—
737C23×C4—684no—
738C23×C4C22×D1712yes—
739#126—24no—
740#126—344no—
741#126—344no—
742#126—344no—
743#126—344no—
744#126—344no—
745#126—344no—
746#126—344no—
747C4×D4—24no—
748C4×D4—348no—
749C4×D4—344no—
750C4×D4—348no—
751C4×D4—344no—
752C4×D4—344no—
753C2×C4⋊C4—172no—
754C2×C4⋊C4—171no—
755C2×C4⋊C4—171no—
756C2×C4⋊C4—171no—
757C2×C4⋊C4—171no—
758C2×C4⋊C4—171no—
759C2×C4⋊C4—171no—
760C2×C4⋊C4—171no—
761C2×C4⋊C4—171no—
762C2×C4⋊C4—171no—
763C2×C4⋊C4—171no—
764C2×C4⋊C4—172no—
765C2×C4⋊C4—172no—
766C2×C4⋊C4—172no—
767C2×C4⋊C4—172no—
768C2×C4⋊C4—172no—
769C2×C4⋊C4—172no—
770C2×C4⋊C4—344no—
771C2×C4⋊C4—344no—
772C2×C4⋊C4—344no—
773C2×C4⋊C4—344no—
774C2×C4⋊C4—684no—
775C2×C4⋊C4—684no—
776C2×C4⋊C4C22×D1711yescharacteristic
777C2×C4⋊C4C22×D1711yescharacteristic
778C2×C4⋊C4C22×D1711yescharacteristic
779C2×C4⋊C4C22×D1711yescharacteristic
780C2×C4⋊C4C22×D1712yes—
781C2×C4⋊C4C22×D1712yes—
782C2×C22⋊C4—172no—
783C2×C22⋊C4—171no—
784C2×C22⋊C4—171no—
785C2×C22⋊C4—171no—
786C2×C22⋊C4—172no—
787C2×C22⋊C4—172no—
788C2×C22⋊C4—172no—
789C2×C22⋊C4—171no—
790C2×C22⋊C4—171no—
791C2×C22⋊C4—171no—
792C2×C22⋊C4—171no—
793C2×C22⋊C4—171no—
794C2×C22⋊C4—171no—
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—348no—
807C2×C22⋊C4—344no—
808C2×C22⋊C4—344no—
809C2×C22⋊C4—344no—
810C2×C22⋊C4—348no—
811C2×C22⋊C4—684no—
812C2×C22⋊C4—684no—
813C2×C22⋊C4—684no—
814C2×C22⋊C4C22×D1712yes—
815C2×C22⋊C4C22×D1711yescharacteristic
816C2×C22⋊C4C22×D1711yescharacteristic
817C2×C22⋊C4C22×D1711yescharacteristic
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×C42C22×D1711yescharacteristic
827#95—172no—
828#95—172no—
829#95—172no—
830#95—172no—
831#95—171no—
832#95—172no—
833#95—171no—
834#95—172no—
835#95—172no—
836#95—172no—
837#95—172no—
838#95—172no—
839#95—172no—
840#95C22×D1712yes—
841#95C22×D1711yescharacteristic
842#95C22×D1711yescharacteristic
843#95C22×D1712yes—
844#95C22×D1712yes—
845C17C2×#263611yescharacteristic, complemented, Sylow
846C24—171no—
847C24—178no—
848C24—172no—
849C24—171no—
850C24—344no—
851C24—344no—
852C24—344no—
853C24—344no—
854C24—344no—
855C24—344no—
856C24—342no—
857C24—344no—
858C24—344no—
859C24—342no—
860C24—342no—
861C24C23×D1711yescharacteristic
862C24C23×D1712yes—
863C2×D4—24no—
864C2×D4—24no—
865C2×D4—22no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—344no—
869C2×D4—344no—
870C2×D4—344no—
871C2×D4—3432no—
872C2×D4—344no—
873C2×D4—344no—
874C2×D4—344no—
875C2×D4—344no—
876C2×D4—342no—
877C2×D4—682no—
878C2×D4—682no—
879C2×D4—682no—
880C2×D4—682no—
881C2×D4—682no—
882C2×D4—682no—
883C2×D4—6832no—
884C22×C4—24no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—171no—
888C22×C4—171no—
889C22×C4—171no—
890C22×C4—174no—
891C22×C4—174no—
892C22×C4—174no—
893C22×C4—172no—
894C22×C4—171no—
895C22×C4—171no—
896C22×C4—172no—
897C22×C4—172no—
898C22×C4—171no—
899C22×C4—344no—
900C22×C4—342no—
901C22×C4—342no—
902C22×C4—344no—
903C22×C4—344no—
904C22×C4—342no—
905C22×C4—342no—
906C22×C4—342no—
907C22×C4—344no—
908C22×C4—344no—
909C22×C4—344no—
910C22×C4—342no—
911C22×C4—344no—
912C22×C4—344no—
913C22×C4—344no—
914C22×C4—344no—
915C22×C4—344no—
916C22×C4—344no—
917C22×C4—344no—
918C22×C4—342no—
919C22×C4—344no—
920C22×C4—344no—
921C22×C4—344no—
922C22×C4—682no—
923C22×C4—682no—
924C22×C4—682no—
925C22×C4—682no—
926C22×C4—6832no—
927C22×C4—682no—
928C22×C4—682no—
929C22×C4C23×D1712yes—
930C22×C4C23×D1711yescharacteristic
931C22×C4C23×D1711yescharacteristic
932C22×C4C23×D1712yes—
933C22×C4C23×D1712yes—
934C22×C4C23×D1711yescharacteristic
935C22×C4C23×D1711yescharacteristic
936C22×C4C23×D1711yescharacteristic
937C22×C4C23×D1711yescharacteristic
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—344no—
945C4⋊C4—342no—
946C4⋊C4—342no—
947C4⋊C4—342no—
948C4⋊C4—342no—
949C4⋊C4—342no—
950C4⋊C4—342no—
951C4⋊C4—342no—
952C4⋊C4—342no—
953C4⋊C4—342no—
954C4⋊C4—342no—
955C4⋊C4—682no—
956C4⋊C4—682no—
957C4⋊C4—682no—
958C4⋊C4—682no—
959C4⋊C4—682no—
960C4⋊C4—682no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—344no—
970C22⋊C4—342no—
971C22⋊C4—342no—
972C22⋊C4—342no—
973C22⋊C4—344no—
974C22⋊C4—344no—
975C22⋊C4—344no—
976C22⋊C4—342no—
977C22⋊C4—342no—
978C22⋊C4—342no—
979C22⋊C4—344no—
980C22⋊C4—344no—
981C22⋊C4—342no—
982C22⋊C4—342no—
983C22⋊C4—342no—
984C22⋊C4—682no—
985C22⋊C4—682no—
986C22⋊C4—682no—
987C22⋊C4—682no—
988C22⋊C4—682no—
989C22⋊C4—682no—
990C22⋊C4—682no—
991C22⋊C4—682no—
992C22⋊C4—682no—
993C42—174no—
994C42—174no—
995C42—174no—
996C42D4×D1714yescomplemented
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—21no—
1004C23—22no—
1005C23—22no—
1006C23—21no—
1007C23—21no—
1008C23—172no—
1009C23—174no—
1010C23—174no—
1011C23—172no—
1012C23—172no—
1013C23—174no—
1014C23—3416no—
1015C23—3416no—
1016C23—3416no—
1017C23—342no—
1018C23—342no—
1019C23—342no—
1020C23—342no—
1021C23—342no—
1022C23—342no—
1023C23—341no—
1024C23—342no—
1025C23—342no—
1026C23—341no—
1027C23—341no—
1028C23—688no—
1029C23—688no—
1030C23—688no—
1031C23—688no—
1032C23—688no—
1033C23—684no—
1034C23—684no—
1035C23—688no—
1036C23—684no—
1037C23#41×D1714yes—
1038C23C24×D1711yescharacteristic
1039D4—28no—
1040D4—48no—
1041D4—348no—
1042D4—3416no—
1043D4—688no—
1044D4—688no—
1045D4—688no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—48no—
1067C2×C4—172no—
1068C2×C4—172no—
1069C2×C4—172no—
1070C2×C4—348no—
1071C2×C4—348no—
1072C2×C4—348no—
1073C2×C4—342no—
1074C2×C4—341no—
1075C2×C4—342no—
1076C2×C4—341no—
1077C2×C4—341no—
1078C2×C4—341no—
1079C2×C4—341no—
1080C2×C4—342no—
1081C2×C4—342no—
1082C2×C4—342no—
1083C2×C4—342no—
1084C2×C4—341no—
1085C2×C4—342no—
1086C2×C4—342no—
1087C2×C4—342no—
1088C2×C4—342no—
1089C2×C4—342no—
1090C2×C4—342no—
1091C2×C4—342no—
1092C2×C4—341no—
1093C2×C4—688no—
1094C2×C4—688no—
1095C2×C4—688no—
1096C2×C4—688no—
1097C2×C4—684no—
1098C2×C4—684no—
1099C2×C4—688no—
1100C2×C4—684no—
1101C2×C4—688no—
1102C2×C4C2×D4×D1712yes—
1103C2×C4C2×D4×D1712yes—
1104C2×C4C2×D4×D1712yes—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—41no—
1113C22—41no—
1114C22—42no—
1115C22—42no—
1116C22—41no—
1117C22—174no—
1118C22—174no—
1119C22—178no—
1120C22—178no—
1121C22—174no—
1122C22—344no—
1123C22—344no—
1124C22—344no—
1125C22—6832no—
1126C22—682no—
1127C22—682no—
1128C22—682no—
1129C22—682no—
1130C22—681no—
1131C22—681no—
1132C22—682no—
1133C22—682no—
1134C22—681no—
1135C22—1368no—
1136C22C22×D4×D1711yescharacteristic
1137C22C2×#41×D1712yes—
1138C22H(5,𝔽2)×D1712yes—
1139C22H(5,𝔽2)×D1711yescharacteristic
1140C222−1+4×D1711yescharacteristic
1141C4—22no—
1142C4—22no—
1143C4—22no—
1144C4—42no—
1145C4—41no—
1146C4—41no—
1147C4—42no—
1148C4—42no—
1149C4—41no—
1150C4—342no—
1151C4—342no—
1152C4—342no—
1153C4—682no—
1154C4—681no—
1155C4—681no—
1156C4—682no—
1157C4—682no—
1158C4—681no—
1159C2—44no—
1160C2—81no—
1161C2—178no—
1162C2—684no—
1163C2—1361no—
1164C2D17×#52511yescharacteristic
1165C2D17×#53511yescharacteristic
1166C2D17×#53711yescharacteristic
1167C2D17×#53812yes—
1168C2D17×#53912yes—
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2636C2
prime radicalD17×#392C2
hypercenter#2636D17
hypocenterC17C2×#2636
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2636

Complements

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

NH ≅ G/Ntype
1. C2×#126×D17C2semidirect
2. C2×C4×D4×D17C2semidirect
3. #14534688C2semidirect
4. #14534687C2semidirect
5. #14534686C2semidirect
6. #14534685C2semidirect
7. #14534684C2semidirect
8. #14534683C2semidirect
9. #14534682C2semidirect
10. #14534681C2semidirect
11. #14534680C2semidirect
12. #14534679C2semidirect
13. #14534678C2semidirect
14. D17×#400C2semidirect
15. D17×#399C2semidirect
16. D17×#396C2semidirect
17. D17×#394C2semidirect
18. D17×#394C2semidirect
20. D17×#386C2semidirect
21. D17×#385C2semidirect
22. D17×#382C2semidirect
23. C17×#2636C2semidirect
27. C2×#10587584C22semidirect
28. C2×#10587584C22semidirect
29. C2×#10587584C22semidirect
30. C2×#10587562C22semidirect
31. C2×#10587565C22semidirect
32. C2×#10587565C22semidirect
33. C2×#10587565C22semidirect
35. C2×C4×D68C22semidirect
36. C2×D4×Dic17C22semidirect
37. C2×#10587579C22semidirect
38. C2×C4×C22⋊D17C22semidirect
39. C2×#10587567C22semidirect
56. #11762751C22semidirect
57. #11762750C22semidirect
58. #11762749C22semidirect
59. #11762748C22semidirect
60. #11762747C22semidirect
61. #11762746C22semidirect
62. #11762745C22semidirect
63. #11762745C22semidirect
64. #11762744C22semidirect
65. #11762744C22semidirect
66. #11762733C22semidirect
67. #11762732C22semidirect
68. #11762732C22semidirect
69. #11762732C22semidirect
70. #11762731C22semidirect
71. #11762731C22semidirect
72. #11762731C22semidirect
73. #11762727C22semidirect
74. #11762727C22semidirect
75. #11762726C22semidirect
76. #11762726C22semidirect
77. #11762725C22semidirect
78. #11762725C22semidirect
79. #11762725C22semidirect
80. #11762724C22semidirect
81. #11762724C22semidirect
82. #11762724C22semidirect
83. #11762723C22semidirect
84. #11762723C22semidirect
90. #11762689C22semidirect
91. #11762688C22semidirect
92. #11762687C22semidirect
93. #11762687C22semidirect
94. #11762686C22semidirect
95. #11762685C22semidirect
96. #11762685C22semidirect
97. #11762684C22semidirect
98. #11762683C22semidirect
99. #11762683C22semidirect
100. #11762682C22semidirect
101. #11762681C22semidirect
102. #11762680C22semidirect
103. #11762680C22semidirect
104. #11762675C22semidirect
105. #11762674C22semidirect
106. #11762673C22semidirect
107. #11762673C22semidirect
108. #11762673C22semidirect
114. C2×C17×#126C22semidirect
115. C2×C4×D4×C17C22semidirect
116. C17×#400C22semidirect
117. C17×#399C22semidirect
118. C17×#396C22semidirect
119. C17×#394C22semidirect
120. C17×#394C22semidirect
122. C17×#386C22semidirect
123. C17×#385C22semidirect
124. C17×#382C22semidirect
242. C42×D17D4semidirect
367. C42×C17C2×D4semidirect
409. C4×Dic17C2×D4semidirect
410. C4×Dic17C2×D4semidirect
411. C4×Dic17C2×D4semidirect
534. #2636D17direct (N × H)
609. C2×#126C2×D17semidirect
616. C2×C4×D4C2×D17semidirect
637. #400C2×D17semidirect
643. #399C2×D17semidirect
651. #396C2×D17semidirect
664. #394C2×D17semidirect
665. #394C2×D17semidirect
679. #386C2×D17semidirect
687. #385C2×D17semidirect
693. #382C2×D17semidirect
708. D17#2636direct (N × H)
845. C17C2×#2636semidirect
996. C42D4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D172
C2×C4×D4×D172
#145346882
#145346872
#145346862
#145346852
#145346842
#145346832
#145346822
#145346812
#145346802
#145346792
#145346782
D17×#4002
D17×#3992
D17×#3962
D17×#3942
D17×#3922
D17×#3862
D17×#3852
D17×#3822
C17×#26362
C2×#263617