Finite Group Databasebeta

← C17×#13127 #16870871

Subgroups — C17×#13127 #16870871

Order 4352.

300 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2153C211yesmaximal, characteristic, complemented
2C17×#2117C211yesmaximal, characteristic
3C17×#2115C211yesmaximal, characteristic
4C2×C17×#347C211yesmaximal, characteristic, complemented
5C17×#1765C211yesmaximal, characteristic
6C17×#1378C211yesmaximal, characteristic, complemented
7C17×#1377C211yesmaximal, characteristic, complemented
8C2×C17×#131C2211yescharacteristic
9C2×C17×M32C2211yescharacteristic
10C2×C17×M32C2211yescharacteristic
11C2×C17×M32C2211yescharacteristic
12C2×C17×M32C2211yescharacteristic
13C2×C17×#104C411yescharacteristic
14C17×#416C411yescharacteristic
15C17×#405C2211yescharacteristic
16C2×C17×#97C2211yescharacteristic
17C17×#364—22no—
18C17×#350—22no—
19C17×#349—22no—
20C17×#347—22no—
21C17×#341C411yescharacteristic
22C17×#339C411yescharacteristic
23C2×#41×C17C2×C411yescharacteristic
24C17×#131—21no—
25C17×#131—21no—
26C17×#131—21no—
27C17×#131—21no—
28C2×M16×C17—21no—
29C2×M16×C17C2×C411yescharacteristic
30C2×M16×C17C2×C411yescharacteristic
31C22×C8×C17—21no—
32C22×C8×C17C2×C411yescharacteristic
33C22×C8×C17C2311yescharacteristic
34C17×#117C2×C411yescharacteristic
35C2×C42×C17C2×C411yescharacteristic
36C17×M32—21no—
37C17×M32—21no—
38C17×M32—21no—
39C17×M32—21no—
40C17×M32—21no—
41C17×M32—21no—
42C17×M32D412yes—
43C17×M32D412yes—
44C2×C16×C17—21no—
45C2×C16×C17—21no—
46C2×C16×C17—21no—
47C2×C16×C17—21no—
48C17×#104—22no—
49C17×#103—21no—
50C17×#102—21no—
51C17×#97—21no—
52C17×#97—21no—
53C17×#97—21no—
54C4×C8×C17—21no—
55#41×C17—21no—
56#41×C17—21no—
57#41×C17—21no—
58#41×C17—21no—
59C2×Q8×C17M1611yescharacteristic
60C2×D4×C17—21no—
61C2×D4×C17M1611yescharacteristic
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17C22×C411yescharacteristic
65M16×C17—21no—
66M16×C17—21no—
67M16×C17—21no—
68M16×C17—41no—
69M16×C17—41no—
70M16×C17M1612yes—
71C2×C8×C17—21no—
72C2×C8×C17—21no—
73C2×C8×C17—21no—
74C2×C8×C17—21no—
75C2×C8×C17—21no—
76C2×C8×C17—41no—
77C2×C8×C17—41no—
78C2×C8×C17C2×D411yescharacteristic
79C2×C8×C17C2×D411yescharacteristic
80C2×C8×C17#4111yescharacteristic
81C2×C8×C17#4111yescharacteristic
82C2×C8×C17#4111yescharacteristic
83C2×C8×C17#4111yescharacteristic
84C4⋊C4×C17—21no—
85C22⋊C4×C17—21no—
86C42×C17—21no—
87C42×C17—21no—
88C42×C17—21no—
89C16×C17—22no—
90C16×C17—22no—
91C16×C17—41no—
92C16×C17—41no—
93#13127C1711yesmaximal, characteristic, direct product factor, Sylow
94C23×C17—21no—
95C23×C17#13111yescharacteristic
96Q8×C17—21no—
97Q8×C17—21no—
98D4×C17—21no—
99D4×C17—21no—
100D4×C17—41no—
101D4×C17—41no—
102C2×C4×C17—21no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—81no—
108C2×C4×C17#11711yescharacteristic
109C2×C4×C17C4×D411yescharacteristic
110C2×C4×C17C4×D411yescharacteristic
111C2×C4×C17C2×M1611yescharacteristic
112C2×C4×C17C2×M1611yescharacteristic
113C2×C4×C17#13111yescharacteristic
114C8×C17—22no—
115C8×C17—41no—
116C8×C17—41no—
117C8×C17#12111yescharacteristic
118C8×C17#12311yescharacteristic
119C8×C17#12411yescharacteristic
120C8×C17#12611yescharacteristic
121#2153C2×C1711yescharacteristic, complemented
122#2117C2×C1711yescharacteristic
123#2115C2×C1711yescharacteristic
124C2×#347C2×C1711yescharacteristic, complemented
125#1765C2×C1711yescharacteristic
126#1378C2×C1711yescharacteristic, complemented
127#1377C2×C1711yescharacteristic, complemented
128C22×C17—41no—
129C22×C17—41no—
130C22×C17—81no—
131C22×C17#43311yescharacteristic
132C22×C17#43511yescharacteristic
133C22×C17#43611yescharacteristic
134C4×C17—41no—
135C4×C17—81no—
136C4×C17—81no—
137C4×C17#38811yescharacteristic
138C4×C17#43211yescharacteristic
139C4×C17#43511yescharacteristic
140C4×C17#43511yescharacteristic
141C2×#131C22×C1711yescharacteristic
142C2×M32C22×C1711yescharacteristic
143C2×M32C22×C1711yescharacteristic
144C2×M32C22×C1711yescharacteristic
145C2×M32C22×C1711yescharacteristic
146C2×#104C4×C1711yescharacteristic
147#416C4×C1711yescharacteristic
148#405C22×C1711yescharacteristic
149C2×#97C22×C1711yescharacteristic
150#364—22no—
151#350—22no—
152#349—22no—
153#347—22no—
154#341C4×C1711yescharacteristic
155#339C4×C1711yescharacteristic
156C2×C17—21no—
157C2×C17—21no—
158C2×C17—21no—
159C2×C17—81no—
160C2×C17#192411yescharacteristic
161C2×#41C2×C4×C1711yescharacteristic
162#131—21no—
163#131—21no—
164#131—21no—
165#131—21no—
166C2×M16—21no—
167C2×M16C2×C4×C1711yescharacteristic
168C2×M16C2×C4×C1711yescharacteristic
169C22×C8—21no—
170C22×C8C2×C4×C1711yescharacteristic
171C22×C8C23×C1711yescharacteristic
172#117C2×C4×C1711yescharacteristic
173C2×C42C2×C4×C1711yescharacteristic
174M32—21no—
175M32—21no—
176M32—21no—
177M32—21no—
178M32—21no—
179M32—21no—
180M32D4×C1712yes—
181M32D4×C1712yes—
182C2×C16—21no—
183C2×C16—21no—
184C2×C16—21no—
185C2×C16—21no—
186#104—22no—
187#103—21no—
188#102—21no—
189#97—21no—
190#97—21no—
191#97—21no—
192C4×C8—21no—
193C17#1312711yescharacteristic, direct product factor, Sylow
194#41—21no—
195#41—21no—
196#41—21no—
197#41—21no—
198C2×Q8M16×C1711yescharacteristic
199C2×D4—21no—
200C2×D4M16×C1711yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4C22×C4×C1711yescharacteristic
204M16—21no—
205M16—21no—
206M16—21no—
207M16—41no—
208M16—41no—
209M16M16×C1712yes—
210C2×C8—21no—
211C2×C8—21no—
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8C2×D4×C1711yescharacteristic
218C2×C8C2×D4×C1711yescharacteristic
219C2×C8#41×C1711yescharacteristic
220C2×C8#41×C1711yescharacteristic
221C2×C8#41×C1711yescharacteristic
222C2×C8#41×C1711yescharacteristic
223C4⋊C4—21no—
224C22⋊C4—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C16—22no—
229C16—22no—
230C16—41no—
231C16—41no—
232C23—21no—
233C23C17×#13111yescharacteristic
234Q8—21no—
235Q8—21no—
236D4—21no—
237D4—21no—
238D4—41no—
239D4—41no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—81no—
246C2×C4C17×#11711yescharacteristic
247C2×C4C4×D4×C1711yescharacteristic
248C2×C4C4×D4×C1711yescharacteristic
249C2×C4C2×M16×C1711yescharacteristic
250C2×C4C2×M16×C1711yescharacteristic
251C2×C4C17×#13111yescharacteristic
252C8—22no—
253C8—41no—
254C8—41no—
255C8C17×#12111yescharacteristic
256C8C17×#12311yescharacteristic
257C8C17×#12411yescharacteristic
258C8C17×#12611yescharacteristic
259C22—41no—
260C22—41no—
261C22—81no—
262C22C17×#43311yescharacteristic
263C22C17×#43511yescharacteristic
264C22C17×#43611yescharacteristic
265C4—41no—
266C4—81no—
267C4—81no—
268C4C17×#38811yescharacteristic
269C4C17×#43211yescharacteristic
270C4C17×#43511yescharacteristic
271C4C17×#43511yescharacteristic
272C2—21no—
273C2—21no—
274C2—21no—
275C2—81no—
276C2C17×#192411yescharacteristic
subgroupG/H
centerC4×C17#388
commutatorC22×C4C22×C4×C17
Frattini, cosocleC22×C8C23×C17
socleC2×C17#1924
prime radicalC2×#41×C17C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C17 ◁ C22×C8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#2153C2semidirect
4. C2×C17×#347C2semidirect
6. C17×#1378C2semidirect
7. C17×#1377C2semidirect
93. #13127C17direct (N × H)
121. #2153C2×C17semidirect
124. C2×#347C2×C17semidirect
126. #1378C2×C17semidirect
127. #1377C2×C17semidirect
193. C17#13127direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#21532
C17×#21172
C17×#21152
C2×C17×#3472
C17×#17652
C17×#13782
C17×#13772
#1312717