Finite Group Databasebeta

← C17×#13466 #16871210

Subgroups — C17×#13466 #16871210

Order 4352.

314 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2155C211yesmaximal, characteristic, complemented
2C17×#2150C211yesmaximal, characteristic, complemented
3C17×#2145C211yesmaximal, characteristic
4C17×#2143C211yesmaximal, characteristic
5C17×#1974C211yesmaximal, characteristic
6C17×#1945C211yesmaximal, characteristic, complemented
7C17×#1388C211yesmaximal, characteristic, complemented
8C2×C17×#135C2211yescharacteristic
9C2×C17×M32C2211yescharacteristic
10C2×C17×M32C2211yescharacteristic
11C2×C17×#108C2211yescharacteristic
12C2×C17×#108C2211yescharacteristic
13C17×#427C2211yescharacteristic
14C17×#424—21no—
15C2×C17×#104—21no—
16C17×#408—21no—
17C2×C4×C8×C17C2211yescharacteristic
18C17×#365—22no—
19C17×C4⋊C16—22no—
20C17×#360—22no—
21C17×#359—22no—
22C17×#339—21no—
23C2×#41×C17—21no—
24C17×#135—21no—
25C17×#135—21no—
26C17×#135—21no—
27C17×#135—21no—
28C2×Q16×C17Q811yescharacteristic
29C2×SD16×C17—21no—
30C2×D8×C17Q811yescharacteristic
31C2×M16×C17—21no—
32C2×M16×C17—21no—
33C22×C8×C17D411yescharacteristic
34C22×C8×C17C2311yescharacteristic
35C17×#117—21no—
36C2×C42×C17D411yescharacteristic
37C17×M32—21no—
38C17×M32—21no—
39C17×M32—21no—
40C17×M32—21no—
41C2×C16×C17—21no—
42C2×C16×C17D412yes—
43C17×#108—21no—
44C17×#108—21no—
45C17×#108—21no—
46C17×#108—21no—
47C17×#107—21no—
48C17×#106D412yes—
49C17×C4⋊C8—42no—
50C17×#104—41no—
51C17×#104—41no—
52C17×C22⋊C8—42no—
53C4×C8×C17—21no—
54C4×C8×C17—21no—
55#41×C17—41no—
56#41×C17—41no—
57#41×C17—41no—
58#41×C17—41no—
59C2×Q8×C17—21no—
60C2×D4×C17—21no—
61C2×D4×C17—41no—
62C22×C4×C17—21no—
63C22×C4×C17—41no—
64C22×C4×C17C2×D411yescharacteristic
65Q16×C17—21no—
66Q16×C17—21no—
67SD16×C17—41no—
68SD16×C17—41no—
69D8×C17—21no—
70D8×C17—21no—
71M16×C17—41no—
72M16×C17—41no—
73M16×C17—41no—
74M16×C17—41no—
75C2×C8×C17—21no—
76C2×C8×C17—21no—
77C2×C8×C17—21no—
78C2×C8×C17—41no—
79C2×C8×C17—41no—
80C2×C8×C17C2×D411yescharacteristic
81C2×C8×C17C2×D411yescharacteristic
82C2×C8×C17C2×Q811yescharacteristic
83C2×C8×C17#4111yescharacteristic
84C2×C8×C17#4111yescharacteristic
85C2×C8×C17#4111yescharacteristic
86C4⋊C4×C17—22no—
87C22⋊C4×C17—41no—
88C42×C17—21no—
89C42×C17—41no—
90C42×C17SD1611yescharacteristic
91C42×C17SD1611yescharacteristic
92C16×C17—22no—
93C16×C17—41no—
94#13466C1711yesmaximal, characteristic, direct product factor, Sylow
95C23×C17—41no—
96C23×C17#13511yescharacteristic
97Q8×C17—41no—
98Q8×C17—41no—
99D4×C17—41no—
100D4×C17—41no—
101D4×C17—81no—
102D4×C17—81no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17—41no—
108C2×C4×C17—81no—
109C2×C4×C17—81no—
110C2×C4×C17#12111yescharacteristic
111C2×C4×C17#12111yescharacteristic
112C2×C4×C17C22⋊Q811yescharacteristic
113C2×C4×C17C2×SD1611yescharacteristic
114C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
116C8×C17—41no—
117C8×C17—81no—
118C8×C17—81no—
119C8×C17#12111yescharacteristic
120C8×C17C22⋊Q811yescharacteristic
121C8×C17C22⋊Q811yescharacteristic
122C8×C17#12611yescharacteristic
123#2155C2×C1711yescharacteristic, complemented
124#2150C2×C1711yescharacteristic, complemented
125#2145C2×C1711yescharacteristic
126#2143C2×C1711yescharacteristic
127#1974C2×C1711yescharacteristic
128#1945C2×C1711yescharacteristic, complemented
129#1388C2×C1711yescharacteristic, complemented
130C22×C17—41no—
131C22×C17—82no—
132C22×C17—81no—
133C22×C17#46311yescharacteristic
134C22×C17#46511yescharacteristic
135C22×C17#47811yescharacteristic
136C4×C17—22no—
137C4×C17—41no—
138C4×C17—82no—
139C4×C17—81no—
140C4×C17#39611yescharacteristic
141C4×C17#46011yescharacteristic
142C4×C17#46911yescharacteristic
143C4×C17#47611yescharacteristic
144C2×#135C22×C1711yescharacteristic
145C2×M32C22×C1711yescharacteristic
146C2×M32C22×C1711yescharacteristic
147C2×#108C22×C1711yescharacteristic
148C2×#108C22×C1711yescharacteristic
149#427C22×C1711yescharacteristic
150#424—21no—
151C2×#104—21no—
152#408—21no—
153C2×C4×C8C22×C1711yescharacteristic
154#365—22no—
155C4⋊C16—22no—
156#360—22no—
157#359—22no—
158#339—21no—
159C2×C17—21no—
160C2×C17—21no—
161C2×C17—21no—
162C2×C17—161no—
163C2×C17#206511yescharacteristic
164C2×#41—21no—
165#135—21no—
166#135—21no—
167#135—21no—
168#135—21no—
169C2×Q16Q8×C1711yescharacteristic
170C2×SD16—21no—
171C2×D8Q8×C1711yescharacteristic
172C2×M16—21no—
173C2×M16—21no—
174C22×C8D4×C1711yescharacteristic
175C22×C8C23×C1711yescharacteristic
176#117—21no—
177C2×C42D4×C1711yescharacteristic
178M32—21no—
179M32—21no—
180M32—21no—
181M32—21no—
182C2×C16—21no—
183C2×C16D4×C1712yes—
184#108—21no—
185#108—21no—
186#108—21no—
187#108—21no—
188#107—21no—
189#106D4×C1712yes—
190C4⋊C8—42no—
191#104—41no—
192#104—41no—
193C22⋊C8—42no—
194C4×C8—21no—
195C4×C8—21no—
196C17#1346611yescharacteristic, direct product factor, Sylow
197#41—41no—
198#41—41no—
199#41—41no—
200#41—41no—
201C2×Q8—21no—
202C2×D4—21no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—41no—
206C22×C4C2×D4×C1711yescharacteristic
207Q16—21no—
208Q16—21no—
209SD16—41no—
210SD16—41no—
211D8—21no—
212D8—21no—
213M16—41no—
214M16—41no—
215M16—41no—
216M16—41no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8C2×D4×C1711yescharacteristic
223C2×C8C2×D4×C1711yescharacteristic
224C2×C8C2×Q8×C1711yescharacteristic
225C2×C8#41×C1711yescharacteristic
226C2×C8#41×C1711yescharacteristic
227C2×C8#41×C1711yescharacteristic
228C4⋊C4—22no—
229C22⋊C4—41no—
230C42—21no—
231C42—41no—
232C42SD16×C1711yescharacteristic
233C42SD16×C1711yescharacteristic
234C16—22no—
235C16—41no—
236C23—41no—
237C23C17×#13511yescharacteristic
238Q8—41no—
239Q8—41no—
240D4—41no—
241D4—41no—
242D4—81no—
243D4—81no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4C17×#12111yescharacteristic
252C2×C4C17×#12111yescharacteristic
253C2×C4C17×C22⋊Q811yescharacteristic
254C2×C4C2×SD16×C1711yescharacteristic
255C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
256C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
257C8—41no—
258C8—81no—
259C8—81no—
260C8C17×#12111yescharacteristic
261C8C17×C22⋊Q811yescharacteristic
262C8C17×C22⋊Q811yescharacteristic
263C8C17×#12611yescharacteristic
264C22—41no—
265C22—82no—
266C22—81no—
267C22C17×#46311yescharacteristic
268C22C17×#46511yescharacteristic
269C22C17×#47811yescharacteristic
270C4—22no—
271C4—41no—
272C4—82no—
273C4—81no—
274C4C17×#39611yescharacteristic
275C4C17×#46011yescharacteristic
276C4C17×#46911yescharacteristic
277C4C17×#47611yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—161no—
282C2C17×#206511yescharacteristic
subgroupG/H
centerC4×C17#469
commutator, Frattini, cosocleC22×C8C23×C17
socleC2×C17#2065
prime radicalC2×C17×#135C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#2155C2semidirect
2. C17×#2150C2semidirect
6. C17×#1945C2semidirect
7. C17×#1388C2semidirect
94. #13466C17direct (N × H)
123. #2155C2×C17semidirect
124. #2150C2×C17semidirect
128. #1945C2×C17semidirect
129. #1388C2×C17semidirect
196. C17#13466direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#21552
C17×#21502
C17×#21452
C17×#21432
C17×#19742
C17×#19452
C17×#13882
#1346617