Finite Group Databasebeta

← C17×#24468 #16882212

Subgroups — C17×#24468 #16882212

Order 4352.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3488C211yesmaximal, characteristic, complemented
2C17×#3055C211yesmaximal, characteristic, complemented
3C2×C17×#453C211yesmaximal, characteristic, complemented
4C17×#3006C211yesmaximal, characteristic, complemented
5C2×C17×#421C211yesmaximal, characteristic, complemented
6C17×#2619C211yesmaximal, characteristic, complemented
7C17×#2040C211yesmaximal, characteristic, complemented
8C17×#2037C211yesmaximal, characteristic, complemented
9C17×#2006C211yesmaximal, characteristic, complemented
10C17×#2002C211yesmaximal, characteristic, complemented
11C17×#1900C211yesmaximal, characteristic, complemented
12C17×#1897C211yesmaximal, characteristic, complemented
13C17×#1883C211yesmaximal, characteristic, complemented
14C17×#1860C211yesmaximal, characteristic, complemented
15C17×#1792C211yesmaximal, characteristic, complemented
16C2×C17×H(5,𝔽2)C2211yescharacteristic
17C22×#41×C17C2211yescharacteristic
18C2×C17×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C17×AGL(1,ℤ/8)C2211yescharacteristic, complemented
20C2×C17×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×M16×C17C2211yescharacteristic, complemented
22C17×#550—21no—
23C17×#548—21no—
24C17×#546—22no—
25C17×#546—21no—
26D42×C17—22no—
27D42×C17—21no—
28C17×#537—21no—
29C17×#537C2211yescharacteristic
30C17×#535—21no—
31C17×#535C2211yescharacteristic
32C2×C17×#127C2211yescharacteristic, complemented
33C17×#525—21no—
34C17×#525C2211yescharacteristic
35C2×C17×#121—21no—
36C2×C17×#121C2211yescharacteristic
37C2×C17×#121C2211yescharacteristic, complemented
38C17×#520C2211yescharacteristic
39C2×C17×#117C2211yescharacteristic, complemented
40C17×#469—21no—
41C17×#468—21no—
42C17×#466—21no—
43C17×#465—21no—
44C17×#453—24no—
45C17×#449—21no—
46C17×#449—21no—
47C17×#448—21no—
48C17×#447—21no—
49C17×#428C2211yescharacteristic, complemented
50C17×#421—24no—
51C2×C17×#104C2211yescharacteristic
52C2×C17×#104C2211yescharacteristic
53C2×C17×#104C2211yescharacteristic, complemented
54C2×C17×#104C2211yescharacteristic, complemented
55C2×C17×#104C2211yescharacteristic, complemented
56C2×C17×#104C2211yescharacteristic, complemented
57C17×#418C2211yescharacteristic, complemented
58C17×#417C2211yescharacteristic
59C17×#417C2211yescharacteristic, complemented
60C17×#417C2211yescharacteristic, complemented
61C2×C17×#100C2211yescharacteristic, complemented
62C2×C17×#100C2211yescharacteristic, complemented
63C17×#407C2211yescharacteristic, complemented
64C17×#394—22no—
65C17×#392—22no—
66C17×#390C2211yescharacteristic, complemented
67C17×#390C2211yescharacteristic, complemented
68C17×#382C2211yescharacteristic, complemented
69C17×#343C2211yescharacteristic, complemented
70C17×#343C2211yescharacteristic, complemented
71C17×#339C2211yescharacteristic, complemented
72C17×#339C2211yescharacteristic, complemented
73C17×H(5,𝔽2)—22no—
74C17×H(5,𝔽2)—22no—
75C17×H(5,𝔽2)—41no—
76C17×H(5,𝔽2)—41no—
77C2×#41×C17—21no—
78C2×#41×C17—21no—
79C2×#41×C17—21no—
80C2×#41×C17—21no—
81C2×#41×C17—22no—
82C2×#41×C17—22no—
83C2×#41×C17—41no—
84C2×#41×C17—41no—
85C2×#41×C17D411yescharacteristic, complemented
86C2×#41×C17D411yescharacteristic, complemented
87C2×#41×C17C2311yescharacteristic
88C2×#41×C17C2311yescharacteristic
89C2×#41×C17C2311yescharacteristic
90C22×Q8×C17D411yescharacteristic, complemented
91C22×D4×C17—21no—
92C22×D4×C17—22no—
93C22×D4×C17—22no—
94C22×D4×C17—21no—
95C22×D4×C17—21no—
96C22×D4×C17—21no—
97C22×D4×C17—22no—
98C22×D4×C17D412yes—
99C22×D4×C17D411yescharacteristic, complemented
100C22×D4×C17C2311yescharacteristic
101C22×D4×C17C2311yescharacteristic
102C23×C4×C17—21no—
103C23×C4×C17C2311yescharacteristic
104C17×AGL(1,ℤ/8)—22no—
105C17×AGL(1,ℤ/8)—22no—
106C17×AGL(1,ℤ/8)—22no—
107C17×AGL(1,ℤ/8)—41no—
108C17×AGL(1,ℤ/8)—41no—
109C17×AGL(1,ℤ/8)—41no—
110C2×SD16×C17—21no—
111C2×SD16×C17—21no—
112C2×SD16×C17—21no—
113C2×D8×C17—21no—
114C2×D8×C17—21no—
115C2×D8×C17—21no—
116C2×M16×C17—21no—
117C2×M16×C17—22no—
118C2×M16×C17—41no—
119C2×M16×C17C2311yescharacteristic
120C2×M16×C17C2311yescharacteristic
121C2×M16×C17C2311yescharacteristic
122C2×M16×C17C2311yescharacteristic
123C22×C8×C17—21no—
124C17×#127—22no—
125C17×#127—21no—
126C17×#127—22no—
127C17×#127—41no—
128C17×#124—22no—
129C17×#124—21no—
130C17×#123—22no—
131C17×#123—21no—
132C17×C22⋊Q8—22no—
133C17×C22⋊Q8—21no—
134C17×C22⋊Q8—21no—
135C17×C22⋊Q8D411yescharacteristic, complemented
136C17×C22⋊Q8D411yescharacteristic, complemented
137C17×#121—22no—
138C17×#121—22no—
139C17×#121—22no—
140C17×#121—22no—
141C17×#121—22no—
142C17×#121—21no—
143C17×#121—21no—
144C17×#121—21no—
145C17×#121—21no—
146C17×#121—21no—
147C17×#121—21no—
148C17×#121—22no—
149C17×#121—21no—
150C17×#121—21no—
151C17×#121—21no—
152C17×#121—21no—
153C17×#121—21no—
154C17×#121—21no—
155C17×#121D411yescharacteristic, complemented
156C17×#121D411yescharacteristic, complemented
157C17×#120—22no—
158C17×#120—22no—
159C17×#120—22no—
160C17×#120—21no—
161C17×#120—22no—
162C4×Q8×C17—21no—
163C4×D4×C17—22no—
164C4×D4×C17—22no—
165C4×D4×C17—21no—
166C4×D4×C17—22no—
167C4×D4×C17—21no—
168C4×D4×C17—21no—
169C17×#117—21no—
170C17×#117—22no—
171C17×#117—41no—
172C17×#117C2311yescharacteristic
173C2×C4⋊C4×C17—21no—
174C2×C4⋊C4×C17—21no—
175C2×C4⋊C4×C17C2311yescharacteristic
176C2×C4⋊C4×C17C2311yescharacteristic
177C2×C22⋊C4×C17—22no—
178C2×C22⋊C4×C17—21no—
179C2×C22⋊C4×C17—21no—
180C2×C22⋊C4×C17—22no—
181C2×C22⋊C4×C17—22no—
182C2×C22⋊C4×C17D412yes—
183C2×C42×C17C2311yescharacteristic
184C2×C42×C17C2311yescharacteristic
185C17×#107—21no—
186C17×#106—21no—
187C17×#104—22no—
188C17×#104—22no—
189C17×#104—22no—
190C17×#104—22no—
191C17×#104—41no—
192C17×#104D414yescomplemented
193C17×#103—21no—
194C17×#103—21no—
195C17×#103—21no—
196C17×#102—21no—
197C17×#102—21no—
198C17×#102—21no—
199C17×#102—21no—
200C17×#102—21no—
201C17×#100—22no—
202C17×#100—41no—
203C17×C22⋊C8—21no—
204C17×C22⋊C8—21no—
205C17×#95—22no—
206C24×C17—22no—
207C24×C17—21no—
208C24×C17—21no—
209C24×C17C2×D412yes—
210C24×C17C2×D411yescharacteristic
211#41×C17—21no—
212#41×C17—21no—
213#41×C17—22no—
214#41×C17—22no—
215#41×C17—21no—
216#41×C17—21no—
217#41×C17—21no—
218#41×C17—21no—
219#41×C17—21no—
220#41×C17—21no—
221#41×C17—21no—
222#41×C17—21no—
223#41×C17—42no—
224#41×C17—42no—
225#41×C17—41no—
226#41×C17—41no—
227#41×C17—42no—
228#41×C17—42no—
229#41×C17—42no—
230#41×C17—42no—
231#41×C17—42no—
232#41×C17—42no—
233#41×C17C2×D412yes—
234#41×C17#4112yes—
235C2×Q8×C17—21no—
236C2×Q8×C17—22no—
237C2×Q8×C17—41no—
238C2×Q8×C17C2×D411yescharacteristic
239C2×Q8×C17C2×D411yescharacteristic
240C2×Q8×C17C2×D411yescharacteristic
241C2×D4×C17—21no—
242C2×D4×C17—22no—
243C2×D4×C17—22no—
244C2×D4×C17—22no—
245C2×D4×C17—21no—
246C2×D4×C17—21no—
247C2×D4×C17—22no—
248C2×D4×C17—21no—
249C2×D4×C17—21no—
250C2×D4×C17—21no—
251C2×D4×C17—22no—
252C2×D4×C17—22no—
253C2×D4×C17—22no—
254C2×D4×C17—21no—
255C2×D4×C17—22no—
256C2×D4×C17—21no—
257C2×D4×C17—21no—
258C2×D4×C17—21no—
259C2×D4×C17—21no—
260C2×D4×C17—21no—
261C2×D4×C17—21no—
262C2×D4×C17—21no—
263C2×D4×C17—21no—
264C2×D4×C17—21no—
265C2×D4×C17—21no—
266C2×D4×C17—21no—
267C2×D4×C17—21no—
268C2×D4×C17—21no—
269C2×D4×C17—41no—
270C2×D4×C17—42no—
271C2×D4×C17—42no—
272C2×D4×C17—44no—
273C2×D4×C17—42no—
274C2×D4×C17—42no—
275C2×D4×C17—44no—
276C2×D4×C17—44no—
277C2×D4×C17—42no—
278C2×D4×C17—42no—
279C2×D4×C17—41no—
280C2×D4×C17—41no—
281C2×D4×C17—82no—
282C2×D4×C17—82no—
283C2×D4×C17—82no—
284C2×D4×C17—82no—
285C2×D4×C17—84no—
286C2×D4×C17C2×D411yescharacteristic
287C2×D4×C17C2×D411yescharacteristic
288C2×D4×C17C2×D411yescharacteristic
289C22×C4×C17—21no—
290C22×C4×C17—21no—
291C22×C4×C17—21no—
292C22×C4×C17—21no—
293C22×C4×C17—21no—
294C22×C4×C17—22no—
295C22×C4×C17—21no—
296C22×C4×C17—21no—
297C22×C4×C17—22no—
298C22×C4×C17—21no—
299C22×C4×C17—21no—
300C22×C4×C17—21no—
301C22×C4×C17—21no—
302C22×C4×C17—21no—
303C22×C4×C17—21no—
304C22×C4×C17—42no—
305C22×C4×C17—42no—
306C22×C4×C17C2×D411yescharacteristic
307C22×C4×C17C2×D411yescharacteristic
308C22×C4×C17C2×D411yescharacteristic
309C22×C4×C17C2×D411yescharacteristic
310C22×C4×C17C2×D411yescharacteristic
311C22×C4×C17C2×D412yes—
312C22×C4×C17C2411yescharacteristic
313SD16×C17—42no—
314SD16×C17—42no—
315SD16×C17—42no—
316D8×C17—42no—
317D8×C17—42no—
318D8×C17—42no—
319M16×C17—21no—
320M16×C17—21no—
321M16×C17—21no—
322M16×C17—21no—
323M16×C17—21no—
324M16×C17—21no—
325M16×C17—21no—
326M16×C17—42no—
327M16×C17C2×D412yescomplemented
328C2×C8×C17—21no—
329C2×C8×C17—21no—
330C2×C8×C17—21no—
331C2×C8×C17—21no—
332C2×C8×C17—42no—
333C4⋊C4×C17—22no—
334C4⋊C4×C17—22no—
335C4⋊C4×C17—21no—
336C4⋊C4×C17—21no—
337C4⋊C4×C17—21no—
338C4⋊C4×C17—21no—
339C4⋊C4×C17—21no—
340C4⋊C4×C17—21no—
341C4⋊C4×C17—42no—
342C4⋊C4×C17C2×D411yescharacteristic
343C4⋊C4×C17C2×D411yescharacteristic
344C22⋊C4×C17—22no—
345C22⋊C4×C17—22no—
346C22⋊C4×C17—22no—
347C22⋊C4×C17—22no—
348C22⋊C4×C17—22no—
349C22⋊C4×C17—21no—
350C22⋊C4×C17—21no—
351C22⋊C4×C17—21no—
352C22⋊C4×C17—22no—
353C22⋊C4×C17—21no—
354C22⋊C4×C17—21no—
355C22⋊C4×C17—22no—
356C22⋊C4×C17—42no—
357C22⋊C4×C17—41no—
358C22⋊C4×C17—41no—
359C22⋊C4×C17—82no—
360C22⋊C4×C17—82no—
361C42×C17—22no—
362C42×C17—21no—
363C42×C17—21no—
364C42×C17—21no—
365C42×C17—21no—
366C42×C17C2×D412yescomplemented
367#24468C1711yesmaximal, characteristic, direct product factor, Sylow
368C23×C17—21no—
369C23×C17—21no—
370C23×C17—21no—
371C23×C17—22no—
372C23×C17—21no—
373C23×C17—21no—
374C23×C17—22no—
375C23×C17—22no—
376C23×C17—41no—
377C23×C17—41no—
378C23×C17—42no—
379C23×C17—42no—
380C23×C17—44no—
381C23×C17—42no—
382C23×C17—42no—
383C23×C17—42no—
384C23×C17—42no—
385C23×C17—41no—
386C23×C17—41no—
387C23×C17—41no—
388C23×C17—81no—
389C23×C17—82no—
390C23×C17—82no—
391C23×C17#12011yescharacteristic
392C23×C17#12011yescharacteristic
393C23×C17C22×D411yescharacteristic
394Q8×C17—21no—
395Q8×C17—21no—
396Q8×C17—21no—
397Q8×C17—21no—
398Q8×C17—21no—
399Q8×C17—42no—
400Q8×C17#12112yes—
401D4×C17—22no—
402D4×C17—22no—
403D4×C17—21no—
404D4×C17—21no—
405D4×C17—21no—
406D4×C17—21no—
407D4×C17—21no—
408D4×C17—42no—
409D4×C17—42no—
410D4×C17—44no—
411D4×C17—42no—
412D4×C17—44no—
413D4×C17—44no—
414D4×C17—42no—
415D4×C17—41no—
416D4×C17—41no—
417D4×C17—41no—
418D4×C17—41no—
419D4×C17—41no—
420D4×C17—41no—
421D4×C17—41no—
422D4×C17—41no—
423D4×C17—41no—
424D4×C17—41no—
425D4×C17—41no—
426D4×C17—41no—
427D4×C17—81no—
428D4×C17—82no—
429D4×C17—82no—
430D4×C17—82no—
431D4×C17—82no—
432D4×C17—88no—
433D4×C17—82no—
434D4×C17—82no—
435D4×C17#12112yes—
436C2×C4×C17—21no—
437C2×C4×C17—21no—
438C2×C4×C17—21no—
439C2×C4×C17—21no—
440C2×C4×C17—21no—
441C2×C4×C17—21no—
442C2×C4×C17—21no—
443C2×C4×C17—21no—
444C2×C4×C17—21no—
445C2×C4×C17—22no—
446C2×C4×C17—21no—
447C2×C4×C17—21no—
448C2×C4×C17—22no—
449C2×C4×C17—21no—
450C2×C4×C17—22no—
451C2×C4×C17—21no—
452C2×C4×C17—21no—
453C2×C4×C17—21no—
454C2×C4×C17—22no—
455C2×C4×C17—42no—
456C2×C4×C17—42no—
457C2×C4×C17—42no—
458C2×C4×C17—44no—
459C2×C4×C17—41no—
460C2×C4×C17—41no—
461C2×C4×C17—41no—
462C2×C4×C17—41no—
463C2×C4×C17—41no—
464C2×C4×C17—41no—
465C2×C4×C17—42no—
466C2×C4×C17—41no—
467C2×C4×C17—41no—
468C2×C4×C17—42no—
469C2×C4×C17—41no—
470C2×C4×C17—41no—
471C2×C4×C17—82no—
472C2×C4×C17#12011yescharacteristic
473C2×C4×C17#12011yescharacteristic
474C2×C4×C17C22×D411yescharacteristic
475C2×C4×C17C22×D411yescharacteristic
476C2×C4×C17C22×D411yescharacteristic
477C2×C4×C17C2×#4111yescharacteristic
478C2×C4×C17H(5,𝔽2)11yescharacteristic
479C2×C4×C17H(5,𝔽2)11yescharacteristic
480C8×C17—22no—
481C8×C17—41no—
482C8×C17—41no—
483C8×C17—41no—
484#3488C2×C1711yescharacteristic, complemented
485#3055C2×C1711yescharacteristic, complemented
486C2×#453C2×C1711yescharacteristic, complemented
487#3006C2×C1711yescharacteristic, complemented
488C2×#421C2×C1711yescharacteristic, complemented
489#2619C2×C1711yescharacteristic, complemented
490#2040C2×C1711yescharacteristic, complemented
491#2037C2×C1711yescharacteristic, complemented
492#2006C2×C1711yescharacteristic, complemented
493#2002C2×C1711yescharacteristic, complemented
494#1900C2×C1711yescharacteristic, complemented
495#1897C2×C1711yescharacteristic, complemented
496#1883C2×C1711yescharacteristic, complemented
497#1860C2×C1711yescharacteristic, complemented
498#1792C2×C1711yescharacteristic, complemented
499C22×C17—21no—
500C22×C17—21no—
501C22×C17—21no—
502C22×C17—21no—
503C22×C17—22no—
504C22×C17—21no—
505C22×C17—21no—
506C22×C17—21no—
507C22×C17—21no—
508C22×C17—41no—
509C22×C17—41no—
510C22×C17—41no—
511C22×C17—41no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—41no—
515C22×C17—41no—
516C22×C17—41no—
517C22×C17—42no—
518C22×C17—41no—
519C22×C17—81no—
520C22×C17—81no—
521C22×C17—82no—
522C22×C17—82no—
523C22×C17—82no—
524C22×C17—82no—
525C22×C17—84no—
526C22×C17—81no—
527C22×C17—81no—
528C22×C17—81no—
529C22×C17—164no—
530C22×C17C2×#12011yescharacteristic
531C22×C17D4211yescharacteristic
532C22×C17#54611yescharacteristic
533C4×C17—21no—
534C4×C17—21no—
535C4×C17—22no—
536C4×C17—42no—
537C4×C17—41no—
538C4×C17—41no—
539C4×C17—42no—
540C4×C17—41no—
541C4×C17—41no—
542C4×C17—81no—
543C4×C17—81no—
544C4×C17C2×#12111yescharacteristic
545C4×C17#53411yescharacteristic
546C4×C17D4211yescharacteristic
547C4×C17#54611yescharacteristic
548C2×H(5,𝔽2)C22×C1711yescharacteristic
549C22×#41C22×C1711yescharacteristic
550C2×AGL(1,ℤ/8)C22×C1711yescharacteristic
551C2×AGL(1,ℤ/8)C22×C1711yescharacteristic, complemented
552C2×AGL(1,ℤ/8)C22×C1711yescharacteristic, complemented
553C22×M16C22×C1711yescharacteristic, complemented
554#550—21no—
555#548—21no—
556#546—21no—
557#546—22no—
558D42—22no—
559D42—21no—
560#537—21no—
561#537C22×C1711yescharacteristic
562#535—21no—
563#535C22×C1711yescharacteristic
564C2×#127C22×C1711yescharacteristic, complemented
565#525—21no—
566#525C22×C1711yescharacteristic
567C2×#121—21no—
568C2×#121C22×C1711yescharacteristic
569C2×#121C22×C1711yescharacteristic, complemented
570#520C22×C1711yescharacteristic
571C2×#117C22×C1711yescharacteristic, complemented
572#469—21no—
573#468—21no—
574#466—21no—
575#465—21no—
576#453—24no—
577#449—21no—
578#449—21no—
579#448—21no—
580#447—21no—
581#428C22×C1711yescharacteristic, complemented
582#421—24no—
583C2×#104C22×C1711yescharacteristic
584C2×#104C22×C1711yescharacteristic
585C2×#104C22×C1711yescharacteristic, complemented
586C2×#104C22×C1711yescharacteristic, complemented
587C2×#104C22×C1711yescharacteristic, complemented
588C2×#104C22×C1711yescharacteristic, complemented
589#418C22×C1711yescharacteristic, complemented
590#417C22×C1711yescharacteristic
591#417C22×C1711yescharacteristic, complemented
592#417C22×C1711yescharacteristic, complemented
593C2×#100C22×C1711yescharacteristic, complemented
594C2×#100C22×C1711yescharacteristic, complemented
595#407C22×C1711yescharacteristic, complemented
596#394—22no—
597#392—22no—
598#390C22×C1711yescharacteristic, complemented
599#390C22×C1711yescharacteristic, complemented
600#382C22×C1711yescharacteristic, complemented
601#343C22×C1711yescharacteristic, complemented
602#343C22×C1711yescharacteristic, complemented
603#339C22×C1711yescharacteristic, complemented
604#339C22×C1711yescharacteristic, complemented
605C2×C17—21no—
606C2×C17—21no—
607C2×C17—41no—
608C2×C17—41no—
609C2×C17—42no—
610C2×C17—81no—
611C2×C17—82no—
612C2×C17—81no—
613C2×C17—161no—
614C2×C17#241011yescharacteristic
615C2×C17#301911yescharacteristic
616C2×C17#302111yescharacteristic
617H(5,𝔽2)—22no—
618H(5,𝔽2)—22no—
619H(5,𝔽2)—41no—
620H(5,𝔽2)—41no—
621C2×#41—21no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—22no—
626C2×#41—22no—
627C2×#41—41no—
628C2×#41—41no—
629C2×#41D4×C1711yescharacteristic, complemented
630C2×#41D4×C1711yescharacteristic, complemented
631C2×#41C23×C1711yescharacteristic
632C2×#41C23×C1711yescharacteristic
633C2×#41C23×C1711yescharacteristic
634C22×Q8D4×C1711yescharacteristic, complemented
635C22×D4—21no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—21no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—22no—
642C22×D4D4×C1712yes—
643C22×D4D4×C1711yescharacteristic, complemented
644C22×D4C23×C1711yescharacteristic
645C22×D4C23×C1711yescharacteristic
646C23×C4—21no—
647C23×C4C23×C1711yescharacteristic
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)—22no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—41no—
652AGL(1,ℤ/8)—41no—
653AGL(1,ℤ/8)—41no—
654C2×SD16—21no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×D8—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×M16—21no—
661C2×M16—22no—
662C2×M16—41no—
663C2×M16C23×C1711yescharacteristic
664C2×M16C23×C1711yescharacteristic
665C2×M16C23×C1711yescharacteristic
666C2×M16C23×C1711yescharacteristic
667C22×C8—21no—
668#127—22no—
669#127—21no—
670#127—22no—
671#127—41no—
672#124—22no—
673#124—21no—
674#123—22no—
675#123—21no—
676C22⋊Q8—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679C22⋊Q8D4×C1711yescharacteristic, complemented
680C22⋊Q8D4×C1711yescharacteristic, complemented
681#121—22no—
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121D4×C1711yescharacteristic, complemented
700#121D4×C1711yescharacteristic, complemented
701#120—22no—
702#120—22no—
703#120—22no—
704#120—21no—
705#120—22no—
706C4×Q8—21no—
707C4×D4—22no—
708C4×D4—22no—
709C4×D4—21no—
710C4×D4—22no—
711C4×D4—21no—
712C4×D4—21no—
713#117—21no—
714#117—22no—
715#117—41no—
716#117C23×C1711yescharacteristic
717C2×C4⋊C4—21no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4C23×C1711yescharacteristic
720C2×C4⋊C4C23×C1711yescharacteristic
721C2×C22⋊C4—22no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4D4×C1712yes—
727C2×C42C23×C1711yescharacteristic
728C2×C42C23×C1711yescharacteristic
729#107—21no—
730#106—21no—
731#104—22no—
732#104—22no—
733#104—22no—
734#104—22no—
735#104—41no—
736#104D4×C1714yescomplemented
737#103—21no—
738#103—21no—
739#103—21no—
740#102—21no—
741#102—21no—
742#102—21no—
743#102—21no—
744#102—21no—
745#100—22no—
746#100—41no—
747C22⋊C8—21no—
748C22⋊C8—21no—
749#95—22no—
750C17#2446811yescharacteristic, direct product factor, Sylow
751C24—22no—
752C24—21no—
753C24—21no—
754C24C2×D4×C1712yes—
755C24C2×D4×C1711yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41C2×D4×C1712yes—
779#41#41×C1712yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×D4×C1711yescharacteristic
784C2×Q8C2×D4×C1711yescharacteristic
785C2×Q8C2×D4×C1711yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—84no—
831C2×D4C2×D4×C1711yescharacteristic
832C2×D4C2×D4×C1711yescharacteristic
833C2×D4C2×D4×C1711yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×D4×C1711yescharacteristic
852C22×C4C2×D4×C1711yescharacteristic
853C22×C4C2×D4×C1711yescharacteristic
854C22×C4C2×D4×C1711yescharacteristic
855C22×C4C2×D4×C1711yescharacteristic
856C22×C4C2×D4×C1712yes—
857C22×C4C24×C1711yescharacteristic
858SD16—42no—
859SD16—42no—
860SD16—42no—
861D8—42no—
862D8—42no—
863D8—42no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—42no—
872M16C2×D4×C1712yescomplemented
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—42no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4C2×D4×C1711yescharacteristic
888C4⋊C4C2×D4×C1711yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—42no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C42—22no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42C2×D4×C1712yescomplemented
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23C17×#12011yescharacteristic
936C23C17×#12011yescharacteristic
937C23C22×D4×C1711yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8C17×#12112yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—82no—
972D4—81no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4C17×#12112yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4C17×#12011yescharacteristic
1017C2×C4C17×#12011yescharacteristic
1018C2×C4C22×D4×C1711yescharacteristic
1019C2×C4C22×D4×C1711yescharacteristic
1020C2×C4C22×D4×C1711yescharacteristic
1021C2×C4C2×#41×C1711yescharacteristic
1022C2×C4C17×H(5,𝔽2)11yescharacteristic
1023C2×C4C17×H(5,𝔽2)11yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—22no—
1037C22—41no—
1038C22—41no—
1039C22—42no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—42no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—42no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×C17×#12011yescharacteristic
1060C22D42×C1711yescharacteristic
1061C22C17×#54611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×C17×#12111yescharacteristic
1074C4C17×#53411yescharacteristic
1075C4D42×C1711yescharacteristic
1076C4C17×#54611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2C17×#241011yescharacteristic
1087C2C17×#301911yescharacteristic
1088C2C17×#302111yescharacteristic
subgroupG/H
center, socleC22×C17C2×#120
commutator, Frattini, cosocleC22×C4C24×C17
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3488C2semidirect
2. C17×#3055C2semidirect
3. C2×C17×#453C2semidirect
4. C17×#3006C2semidirect
5. C2×C17×#421C2semidirect
6. C17×#2619C2semidirect
7. C17×#2040C2semidirect
8. C17×#2037C2semidirect
9. C17×#2006C2semidirect
10. C17×#2002C2semidirect
11. C17×#1900C2semidirect
12. C17×#1897C2semidirect
13. C17×#1883C2semidirect
14. C17×#1860C2semidirect
15. C17×#1792C2semidirect
19. C2×C17×AGL(1,ℤ/8)C22semidirect
20. C2×C17×AGL(1,ℤ/8)C22semidirect
21. C22×M16×C17C22semidirect
32. C2×C17×#127C22semidirect
37. C2×C17×#121C22semidirect
39. C2×C17×#117C22semidirect
49. C17×#428C22semidirect
53. C2×C17×#104C22semidirect
54. C2×C17×#104C22semidirect
55. C2×C17×#104C22semidirect
56. C2×C17×#104C22semidirect
57. C17×#418C22semidirect
59. C17×#417C22semidirect
60. C17×#417C22semidirect
61. C2×C17×#100C22semidirect
62. C2×C17×#100C22semidirect
63. C17×#407C22semidirect
66. C17×#390C22semidirect
67. C17×#390C22semidirect
68. C17×#382C22semidirect
69. C17×#343C22semidirect
70. C17×#343C22semidirect
71. C17×#339C22semidirect
72. C17×#339C22semidirect
85. C2×#41×C17D4semidirect
86. C2×#41×C17D4semidirect
90. C22×Q8×C17D4semidirect
99. C22×D4×C17D4semidirect
135. C17×C22⋊Q8D4semidirect
136. C17×C22⋊Q8D4semidirect
155. C17×#121D4semidirect
156. C17×#121D4semidirect
192. C17×#104D4semidirect
327. M16×C17C2×D4semidirect
366. C42×C17C2×D4semidirect
367. #24468C17direct (N × H)
484. #3488C2×C17semidirect
485. #3055C2×C17semidirect
486. C2×#453C2×C17semidirect
487. #3006C2×C17semidirect
488. C2×#421C2×C17semidirect
489. #2619C2×C17semidirect
490. #2040C2×C17semidirect
491. #2037C2×C17semidirect
492. #2006C2×C17semidirect
493. #2002C2×C17semidirect
494. #1900C2×C17semidirect
495. #1897C2×C17semidirect
496. #1883C2×C17semidirect
497. #1860C2×C17semidirect
498. #1792C2×C17semidirect
551. C2×AGL(1,ℤ/8)C22×C17semidirect
552. C2×AGL(1,ℤ/8)C22×C17semidirect
553. C22×M16C22×C17semidirect
564. C2×#127C22×C17semidirect
569. C2×#121C22×C17semidirect
571. C2×#117C22×C17semidirect
581. #428C22×C17semidirect
585. C2×#104C22×C17semidirect
586. C2×#104C22×C17semidirect
587. C2×#104C22×C17semidirect
588. C2×#104C22×C17semidirect
589. #418C22×C17semidirect
591. #417C22×C17semidirect
592. #417C22×C17semidirect
593. C2×#100C22×C17semidirect
594. C2×#100C22×C17semidirect
595. #407C22×C17semidirect
598. #390C22×C17semidirect
599. #390C22×C17semidirect
600. #382C22×C17semidirect
601. #343C22×C17semidirect
602. #343C22×C17semidirect
603. #339C22×C17semidirect
604. #339C22×C17semidirect
629. C2×#41D4×C17semidirect
630. C2×#41D4×C17semidirect
634. C22×Q8D4×C17semidirect
643. C22×D4D4×C17semidirect
679. C22⋊Q8D4×C17semidirect
680. C22⋊Q8D4×C17semidirect
699. #121D4×C17semidirect
700. #121D4×C17semidirect
736. #104D4×C17semidirect
750. C17#24468direct (N × H)
872. M16C2×D4×C17semidirect
911. C42C2×D4×C17semidirect

Maximal subgroups

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

subgroupindex
C17×#34882
C17×#30552
C2×C17×#4532
C17×#30062
C2×C17×#4212
C17×#26192
C17×#20402
C17×#20372
C17×#20062
C17×#20022
C17×#19002
C17×#18972
C17×#18832
C17×#18602
C17×#17922
#2446817