Finite Group Databasebeta

← C17×#10587 #16868331

Subgroups — C17×#10587 #16868331

Order 4352.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#1982C211yesmaximal, characteristic
2C17×#1957C211yesmaximal, characteristic
3C17×#1947C211yesmaximal, characteristic, complemented
4C17×#1939C211yesmaximal, characteristic, complemented
5C2×C17×#334C211yesmaximal, characteristic, complemented
6C2×C17×#331C211yesmaximal, characteristic
7C17×#1296C211yesmaximal, characteristic, complemented
8C2×C17×#127C2211yescharacteristic
9C2×C17×#107—21no—
10C2×C17×C4⋊C8—21no—
11C2×C17×C4⋊C8C2211yescharacteristic
12C2×C17×C4⋊C8C2211yescharacteristic
13C2×C17×C4⋊C8C2211yescharacteristic
14C2×C17×#102—21no—
15C2×C17×#102—21no—
16C2×C17×#102—21no—
17C2×C17×#102—21no—
18C2×C4×C8×C17C2211yescharacteristic
19C17×#384C2211yescharacteristic
20C4×C4⋊C4×C17C2211yescharacteristic
21C17×#340—21no—
22C17×#336—21no—
23C17×#334—22no—
24C17×#331—22no—
25C22×D4×C17—21no—
26C22×D4×C17—21no—
27C22×D4×C17—21no—
28C22×C8×C17—21no—
29C22×C8×C17—21no—
30C22×C8×C17—21no—
31C22×C8×C17D411yescharacteristic
32C22×C8×C17D411yescharacteristic
33C17×#127—21no—
34C17×#127—21no—
35C17×#127—21no—
36C17×#127Q812yes—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17—21no—
40C2×C4⋊C4×C17D411yescharacteristic
41C2×C4⋊C4×C17D411yescharacteristic
42C2×C42×C17—21no—
43C2×C42×C17C2311yescharacteristic
44C17×#107—42no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8—21no—
47C17×C4⋊C8—21no—
48C17×C4⋊C8—21no—
49C17×C4⋊C8—21no—
50C17×C4⋊C8—42no—
51C17×C4⋊C8D412yes—
52C17×#102—42no—
53C17×#102—42no—
54C17×#102—42no—
55C17×#102—42no—
56C4×C8×C17—21no—
57C4×C8×C17—21no—
58C17×#95—21no—
59C24×C17—41no—
60C2×D4×C17—22no—
61C2×D4×C17—22no—
62C2×D4×C17—22no—
63C2×D4×C17—41no—
64C2×D4×C17—41no—
65C2×D4×C17—41no—
66C2×D4×C17—41no—
67C2×D4×C17—41no—
68C2×D4×C17—41no—
69C2×D4×C17—41no—
70C2×D4×C17—41no—
71C2×D4×C17—41no—
72C2×D4×C17—41no—
73C2×D4×C17—41no—
74C2×D4×C17—81no—
75C2×D4×C17—81no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—41no—
79C22×C4×C17C2×D411yescharacteristic
80C22×C4×C17C2×D411yescharacteristic
81C22×C4×C17#4111yescharacteristic
82C2×C8×C17—21no—
83C2×C8×C17—21no—
84C2×C8×C17—22no—
85C2×C8×C17—21no—
86C2×C8×C17—21no—
87C2×C8×C17—21no—
88C2×C8×C17—41no—
89C2×C8×C17—41no—
90C2×C8×C17—41no—
91C2×C8×C17—41no—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C2×C8×C17—41no—
95C2×C8×C17—41no—
96C2×C8×C17D812yes—
97C4⋊C4×C17—21no—
98C4⋊C4×C17—21no—
99C4⋊C4×C17—21no—
100C4⋊C4×C17—41no—
101C4⋊C4×C17—41no—
102C4⋊C4×C17—41no—
103C4⋊C4×C17—41no—
104C4⋊C4×C17—81no—
105C4⋊C4×C17SD1612yes—
106C42×C17—41no—
107C42×C17—41no—
108C42×C17C2×D411yescharacteristic
109C42×C17C2×Q811yescharacteristic
110C42×C17#4111yescharacteristic
111C42×C17#4111yescharacteristic
112#10587C1711yesmaximal, characteristic, direct product factor, Sylow
113C23×C17—42no—
114C23×C17—81no—
115C23×C17—81no—
116C23×C17—81no—
117C23×C17—81no—
118C23×C17—81no—
119C23×C17—81no—
120C23×C17#12111yescharacteristic
121D4×C17—42no—
122D4×C17—42no—
123D4×C17—42no—
124D4×C17—42no—
125D4×C17—82no—
126D4×C17—82no—
127D4×C17—81no—
128D4×C17—81no—
129D4×C17—81no—
130D4×C17—81no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—22no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—81no—
140C2×C4×C17—81no—
141C2×C4×C17—81no—
142C2×C4×C17#12111yescharacteristic
143C2×C4×C17#12111yescharacteristic
144C2×C4×C17C22⋊Q811yescharacteristic
145C2×C4×C17C22⋊Q811yescharacteristic
146C2×C4×C17C22⋊Q811yescharacteristic
147C2×C4×C17#12611yescharacteristic
148C2×C4×C17C2×D811yescharacteristic
149C2×C4×C17C2×SD1611yescharacteristic
150C2×C4×C17#13511yescharacteristic
151C2×C4×C17#13511yescharacteristic
152C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C17#13711yescharacteristic
156C8×C17—22no—
157C8×C17—42no—
158C8×C17—41no—
159C8×C17—81no—
160C8×C17—81no—
161#1982C2×C1711yescharacteristic
162#1957C2×C1711yescharacteristic
163#1947C2×C1711yescharacteristic, complemented
164#1939C2×C1711yescharacteristic, complemented
165C2×#334C2×C1711yescharacteristic, complemented
166C2×#331C2×C1711yescharacteristic
167#1296C2×C1711yescharacteristic, complemented
168C22×C17—82no—
169C22×C17—82no—
170C22×C17—82no—
171C22×C17—161no—
172C22×C17—161no—
173C22×C17—161no—
174C22×C17—161no—
175C22×C17#39611yescharacteristic
176C22×C17#45911yescharacteristic
177C22×C17#46411yescharacteristic
178C22×C17#46511yescharacteristic
179C22×C17#46911yescharacteristic
180C22×C17#47111yescharacteristic
181C22×C17#47211yescharacteristic
182C4×C17—21no—
183C4×C17—21no—
184C4×C17—42no—
185C4×C17—81no—
186C4×C17—161no—
187C4×C17#46011yescharacteristic
188C4×C17#46311yescharacteristic
189C4×C17#46611yescharacteristic
190C4×C17#46811yescharacteristic
191C4×C17#47411yescharacteristic
192C4×C17#47611yescharacteristic
193C4×C17#47811yescharacteristic
194C4×C17#47811yescharacteristic
195C2×#127C22×C1711yescharacteristic
196C2×#107—21no—
197C2×C4⋊C8—21no—
198C2×C4⋊C8C22×C1711yescharacteristic
199C2×C4⋊C8C22×C1711yescharacteristic
200C2×C4⋊C8C22×C1711yescharacteristic
201C2×#102—21no—
202C2×#102—21no—
203C2×#102—21no—
204C2×#102—21no—
205C2×C4×C8C22×C1711yescharacteristic
206#384C22×C1711yescharacteristic
207C4×C4⋊C4C22×C1711yescharacteristic
208#340—21no—
209#336—21no—
210#334—22no—
211#331—22no—
212C2×C17—162no—
213C2×C17#166511yescharacteristic
214C2×C17#167811yescharacteristic
215C2×C17#168711yescharacteristic
216C2×C17#170211yescharacteristic
217C2×C17#206311yescharacteristic
218C2×C17#206511yescharacteristic
219C2×C17#206711yescharacteristic
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8D4×C1711yescharacteristic
227C22×C8D4×C1711yescharacteristic
228#127—21no—
229#127—21no—
230#127—21no—
231#127Q8×C1712yes—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4D4×C1711yescharacteristic
236C2×C4⋊C4D4×C1711yescharacteristic
237C2×C42—21no—
238C2×C42C23×C1711yescharacteristic
239#107—42no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—42no—
246C4⋊C8D4×C1712yes—
247#102—42no—
248#102—42no—
249#102—42no—
250#102—42no—
251C4×C8—21no—
252C4×C8—21no—
253#95—21no—
254C17#1058711yescharacteristic, direct product factor, Sylow
255C24—41no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—81no—
271C2×D4—81no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4C2×D4×C1711yescharacteristic
276C22×C4C2×D4×C1711yescharacteristic
277C22×C4#41×C1711yescharacteristic
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—22no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8D8×C1712yes—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C4⋊C4SD16×C1712yes—
302C42—41no—
303C42—41no—
304C42C2×D4×C1711yescharacteristic
305C42C2×Q8×C1711yescharacteristic
306C42#41×C1711yescharacteristic
307C42#41×C1711yescharacteristic
308C23—42no—
309C23—81no—
310C23—81no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—81no—
315C23C17×#12111yescharacteristic
316D4—42no—
317D4—42no—
318D4—42no—
319D4—42no—
320D4—82no—
321D4—82no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C17×#12111yescharacteristic
338C2×C4C17×#12111yescharacteristic
339C2×C4C17×C22⋊Q811yescharacteristic
340C2×C4C17×C22⋊Q811yescharacteristic
341C2×C4C17×C22⋊Q811yescharacteristic
342C2×C4C17×#12611yescharacteristic
343C2×C4C2×D8×C1711yescharacteristic
344C2×C4C2×SD16×C1711yescharacteristic
345C2×C4C17×#13511yescharacteristic
346C2×C4C17×#13511yescharacteristic
347C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
348C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
349C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
350C2×C4C17×#13711yescharacteristic
351C8—22no—
352C8—42no—
353C8—41no—
354C8—81no—
355C8—81no—
356C22—82no—
357C22—82no—
358C22—82no—
359C22—161no—
360C22—161no—
361C22—161no—
362C22—161no—
363C22C17×#39611yescharacteristic
364C22C17×#45911yescharacteristic
365C22C17×#46411yescharacteristic
366C22C17×#46511yescharacteristic
367C22C17×#46911yescharacteristic
368C22C17×#47111yescharacteristic
369C22C17×#47211yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—161no—
375C4C17×#46011yescharacteristic
376C4C17×#46311yescharacteristic
377C4C17×#46611yescharacteristic
378C4C17×#46811yescharacteristic
379C4C17×#47411yescharacteristic
380C4C17×#47611yescharacteristic
381C4C17×#47811yescharacteristic
382C4C17×#47811yescharacteristic
383C2—162no—
384C2C17×#166511yescharacteristic
385C2C17×#167811yescharacteristic
386C2C17×#168711yescharacteristic
387C2C17×#170211yescharacteristic
388C2C17×#206311yescharacteristic
389C2C17×#206511yescharacteristic
390C2C17×#206711yescharacteristic
subgroupG/H
center, socleC23×C17#121
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC2×C17×#127C22
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
3. C17×#1947C2semidirect
4. C17×#1939C2semidirect
5. C2×C17×#334C2semidirect
7. C17×#1296C2semidirect
112. #10587C17direct (N × H)
163. #1947C2×C17semidirect
164. #1939C2×C17semidirect
165. C2×#334C2×C17semidirect
167. #1296C2×C17semidirect
254. C17#10587direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#19822
C17×#19572
C17×#19472
C17×#19392
C2×C17×#3342
C2×C17×#3312
C17×#12962
#1058717