Finite Group Databasebeta

← C17×#10417 #16868161

Subgroups — C17×#10417 #16868161

Order 4352.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2547C211yesmaximal, characteristic
2C17×#1990C211yesmaximal, characteristic, complemented
3C17×#1948C211yesmaximal, characteristic, complemented
4C17×#1802C211yesmaximal, characteristic
5C2×C17×#332C211yesmaximal, characteristic, complemented
6C2×C17×D4⋊C8C211yesmaximal, characteristic
7C17×#1279C211yesmaximal, characteristic, complemented
8C2×C17×C4⋊Q8C2211yescharacteristic
9C2×C17×#124—21no—
10C2×C4×D4×C17C2211yescharacteristic
11C2×C17×#106—21no—
12C2×C17×C4⋊C8C2211yescharacteristic
13C2×C17×C4⋊C8C2211yescharacteristic
14C2×C17×#102—21no—
15C2×C4×C8×C17C2211yescharacteristic
16C17×#397—22no—
17C17×#391—21no—
18C17×#384C2211yescharacteristic
19C17×#380—21no—
20C17×#380—21no—
21C4×C4⋊C4×C17C2211yescharacteristic
22C17×#340—21no—
23C17×#340—22no—
24C17×#340—21no—
25C17×#332—22no—
26C17×D4⋊C8—22no—
27C22×Q8×C17—21no—
28C22×D4×C17D411yescharacteristic
29C23×C4×C17—21no—
30C22×C8×C17—21no—
31C22×C8×C17—21no—
32C22×C8×C17—21no—
33C17×C4⋊Q8—21no—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8—21no—
36C17×C4⋊Q8—21no—
37C17×#124—42no—
38C17×#124—42no—
39C4×D4×C17—21no—
40C4×D4×C17—21no—
41C4×D4×C17—21no—
42C4×D4×C17—21no—
43C2×C4⋊C4×C17—21no—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17D411yescharacteristic
48C2×C4⋊C4×C17D412yes—
49C2×C4⋊C4×C17D411yescharacteristic
50C2×C4⋊C4×C17D411yescharacteristic
51C2×C22⋊C4×C17—22no—
52C2×C22⋊C4×C17—22no—
53C2×C22⋊C4×C17—21no—
54C2×C42×C17—21no—
55C2×C42×C17C2311yescharacteristic
56C17×#106—42no—
57C17×C4⋊C8—21no—
58C17×C4⋊C8—21no—
59C17×C4⋊C8—21no—
60C17×C4⋊C8D412yes—
61C17×#102—42no—
62C4×C8×C17—21no—
63C4×C8×C17—21no—
64C17×#95—22no—
65C17×#95—22no—
66C17×#95—21no—
67C24×C17—21no—
68C2×Q8×C17—41no—
69C2×Q8×C17—41no—
70C2×Q8×C17—41no—
71C2×Q8×C17—41no—
72C2×Q8×C17—41no—
73C2×Q8×C17—41no—
74C2×D4×C17—21no—
75C2×D4×C17—21no—
76C2×D4×C17—21no—
77C2×D4×C17—21no—
78C2×D4×C17—21no—
79C2×D4×C17SD1612yes—
80C22×C4×C17—21no—
81C22×C4×C17—22no—
82C22×C4×C17—21no—
83C22×C4×C17—21no—
84C22×C4×C17—41no—
85C22×C4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17—41no—
88C22×C4×C17—41no—
89C22×C4×C17—41no—
90C22×C4×C17—41no—
91C22×C4×C17C2×D411yescharacteristic
92C22×C4×C17C2×D411yescharacteristic
93C22×C4×C17C2×D411yescharacteristic
94C2×C8×C17—22no—
95C2×C8×C17—22no—
96C2×C8×C17—41no—
97C2×C8×C17—41no—
98C2×C8×C17—41no—
99C2×C8×C17—41no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C2×C8×C17—41no—
103C4⋊C4×C17—22no—
104C4⋊C4×C17—21no—
105C4⋊C4×C17—22no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—21no—
108C4⋊C4×C17—21no—
109C4⋊C4×C17—21no—
110C4⋊C4×C17—21no—
111C4⋊C4×C17—42no—
112C4⋊C4×C17—41no—
113C4⋊C4×C17—41no—
114C4⋊C4×C17—41no—
115C4⋊C4×C17—41no—
116C4⋊C4×C17—41no—
117C4⋊C4×C17—41no—
118C22⋊C4×C17—44no—
119C22⋊C4×C17—44no—
120C22⋊C4×C17—41no—
121C22⋊C4×C17—41no—
122C42×C17—41no—
123C42×C17—41no—
124C42×C17C2×D411yescharacteristic
125C42×C17#4111yescharacteristic
126C42×C17#4111yescharacteristic
127C42×C17#4111yescharacteristic
128#10417C1711yesmaximal, characteristic, direct product factor, Sylow
129C23×C17—22no—
130C23×C17—41no—
131C23×C17—41no—
132C23×C17—41no—
133C23×C17—41no—
134C23×C17—41no—
135C23×C17—41no—
136C23×C17#12011yescharacteristic
137Q8×C17—81no—
138Q8×C17—81no—
139Q8×C17—81no—
140Q8×C17—81no—
141D4×C17—22no—
142D4×C17—22no—
143D4×C17—41no—
144D4×C17—41no—
145C2×C4×C17—21no—
146C2×C4×C17—21no—
147C2×C4×C17—41no—
148C2×C4×C17—42no—
149C2×C4×C17—41no—
150C2×C4×C17—41no—
151C2×C4×C17—42no—
152C2×C4×C17—41no—
153C2×C4×C17—41no—
154C2×C4×C17—42no—
155C2×C4×C17—41no—
156C2×C4×C17—41no—
157C2×C4×C17—41no—
158C2×C4×C17—41no—
159C2×C4×C17—81no—
160C2×C4×C17—81no—
161C2×C4×C17—81no—
162C2×C4×C17—81no—
163C2×C4×C17—81no—
164C2×C4×C17—81no—
165C2×C4×C17—81no—
166C2×C4×C17#12111yescharacteristic
167C2×C4×C17#12111yescharacteristic
168C2×C4×C17#12111yescharacteristic
169C2×C4×C17#12311yescharacteristic
170C2×C4×C17#12311yescharacteristic
171C2×C4×C17#12411yescharacteristic
172C2×C4×C17C2×SD1611yescharacteristic
173C2×C4×C17#13511yescharacteristic
174C2×C4×C17#13511yescharacteristic
175C2×C4×C17#13511yescharacteristic
176C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C17#13711yescharacteristic
180C8×C17—42no—
181C8×C17—42no—
182C8×C17—81no—
183#2547C2×C1711yescharacteristic
184#1990C2×C1711yescharacteristic, complemented
185#1948C2×C1711yescharacteristic, complemented
186#1802C2×C1711yescharacteristic
187C2×#332C2×C1711yescharacteristic, complemented
188C2×D4⋊C8C2×C1711yescharacteristic
189#1279C2×C1711yescharacteristic, complemented
190C22×C17—42no—
191C22×C17—42no—
192C22×C17—42no—
193C22×C17—81no—
194C22×C17—81no—
195C22×C17—81no—
196C22×C17—81no—
197C22×C17#39411yescharacteristic
198C22×C17#44911yescharacteristic
199C22×C17#44911yescharacteristic
200C22×C17#45011yescharacteristic
201C22×C17#45211yescharacteristic
202C22×C17#45411yescharacteristic
203C22×C17#45611yescharacteristic
204C4×C17—21no—
205C4×C17—21no—
206C4×C17—81no—
207C4×C17—81no—
208C4×C17—82no—
209C4×C17—81no—
210C4×C17—161no—
211C4×C17#46311yescharacteristic
212C4×C17#46411yescharacteristic
213C4×C17#46511yescharacteristic
214C4×C17#46911yescharacteristic
215C4×C17#48111yescharacteristic
216C4×C17#48211yescharacteristic
217C4×C17#48811yescharacteristic
218C4×C17#48911yescharacteristic
219C2×C4⋊Q8C22×C1711yescharacteristic
220C2×#124—21no—
221C2×C4×D4C22×C1711yescharacteristic
222C2×#106—21no—
223C2×C4⋊C8C22×C1711yescharacteristic
224C2×C4⋊C8C22×C1711yescharacteristic
225C2×#102—21no—
226C2×C4×C8C22×C1711yescharacteristic
227#397—22no—
228#391—21no—
229#384C22×C1711yescharacteristic
230#380—21no—
231#380—21no—
232C4×C4⋊C4C22×C1711yescharacteristic
233#340—21no—
234#340—21no—
235#340—22no—
236#332—22no—
237D4⋊C8—22no—
238C2×C17—82no—
239C2×C17#162811yescharacteristic
240C2×C17#163511yescharacteristic
241C2×C17#165011yescharacteristic
242C2×C17#165411yescharacteristic
243C2×C17#203411yescharacteristic
244C2×C17#203811yescharacteristic
245C2×C17#204211yescharacteristic
246C22×Q8—21no—
247C22×D4D4×C1711yescharacteristic
248C23×C4—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256#124—42no—
257#124—42no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4×C1711yescharacteristic
267C2×C4⋊C4D4×C1712yes—
268C2×C4⋊C4D4×C1711yescharacteristic
269C2×C4⋊C4D4×C1711yescharacteristic
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—21no—
273C2×C42—21no—
274C2×C42C23×C1711yescharacteristic
275#106—42no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8D4×C1712yes—
280#102—42no—
281C4×C8—21no—
282C4×C8—21no—
283#95—22no—
284#95—22no—
285#95—21no—
286C17#1041711yescharacteristic, direct product factor, Sylow
287C24—21no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4SD16×C1712yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4C2×D4×C1711yescharacteristic
312C22×C4C2×D4×C1711yescharacteristic
313C22×C4C2×D4×C1711yescharacteristic
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C22⋊C4—44no—
339C22⋊C4—44no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—41no—
343C42—41no—
344C42C2×D4×C1711yescharacteristic
345C42#41×C1711yescharacteristic
346C42#41×C1711yescharacteristic
347C42#41×C1711yescharacteristic
348C23—22no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23C17×#12011yescharacteristic
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360D4—22no—
361D4—22no—
362D4—41no—
363D4—41no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C17×#12111yescharacteristic
386C2×C4C17×#12111yescharacteristic
387C2×C4C17×#12111yescharacteristic
388C2×C4C17×#12311yescharacteristic
389C2×C4C17×#12311yescharacteristic
390C2×C4C17×#12411yescharacteristic
391C2×C4C2×SD16×C1711yescharacteristic
392C2×C4C17×#13511yescharacteristic
393C2×C4C17×#13511yescharacteristic
394C2×C4C17×#13511yescharacteristic
395C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
396C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
397C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
398C2×C4C17×#13711yescharacteristic
399C8—42no—
400C8—42no—
401C8—81no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22C17×#39411yescharacteristic
410C22C17×#44911yescharacteristic
411C22C17×#44911yescharacteristic
412C22C17×#45011yescharacteristic
413C22C17×#45211yescharacteristic
414C22C17×#45411yescharacteristic
415C22C17×#45611yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4—161no—
423C4C17×#46311yescharacteristic
424C4C17×#46411yescharacteristic
425C4C17×#46511yescharacteristic
426C4C17×#46911yescharacteristic
427C4C17×#48111yescharacteristic
428C4C17×#48211yescharacteristic
429C4C17×#48811yescharacteristic
430C4C17×#48911yescharacteristic
431C2—82no—
432C2C17×#162811yescharacteristic
433C2C17×#163511yescharacteristic
434C2C17×#165011yescharacteristic
435C2C17×#165411yescharacteristic
436C2C17×#203411yescharacteristic
437C2C17×#203811yescharacteristic
438C2C17×#204211yescharacteristic
subgroupG/H
center, socleC23×C17#120
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC22×D4×C17D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1990C2semidirect
3. C17×#1948C2semidirect
5. C2×C17×#332C2semidirect
7. C17×#1279C2semidirect
128. #10417C17direct (N × H)
184. #1990C2×C17semidirect
185. #1948C2×C17semidirect
187. C2×#332C2×C17semidirect
189. #1279C2×C17semidirect
286. C17#10417direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#25472
C17×#19902
C17×#19482
C17×#18022
C2×C17×#3322
C2×C17×D4⋊C82
C17×#12792
#1041717