Finite Group Databasebeta

← C17×#13128 #16870872

Subgroups — C17×#13128 #16870872

Order 4352.

328 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#364C211yesmaximal, characteristic, complemented
2C2×C17×#349C211yesmaximal, characteristic
3C2×C17×#349C211yesmaximal, characteristic
4C2×C17×#347C211yesmaximal, characteristic, complemented
5C17×#1753C211yesmaximal, characteristic
6C17×#1376C211yesmaximal, characteristic, complemented
7C17×#1375C211yesmaximal, characteristic, complemented
8C22×M16×C17C2211yescharacteristic
9C2×C17×M32C2211yescharacteristic
10C2×C17×M32C2211yescharacteristic
11C2×C17×M32C2211yescharacteristic
12C2×C17×M32C2211yescharacteristic
13C2×C17×C22⋊C8C411yescharacteristic
14C2×C17×#97C2211yescharacteristic
15C2×C4×C8×C17C2211yescharacteristic
16C4×C22⋊C4×C17C411yescharacteristic
17C17×#364—22no—
18C17×#349—22no—
19C17×#349—22no—
20C17×#347—22no—
21C17×#336C411yescharacteristic
22C17×#336C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C2×M16×C17—21no—
25C2×M16×C17—21no—
26C2×M16×C17—21no—
27C2×M16×C17—21no—
28C2×M16×C17—21no—
29C2×M16×C17—21no—
30C22×C8×C17C2×C411yescharacteristic
31C22×C8×C17C2×C411yescharacteristic
32C22×C8×C17C2×C411yescharacteristic
33C22×C8×C17C2311yescharacteristic
34C2×C22⋊C4×C17—21no—
35C2×C42×C17C2×C411yescharacteristic
36C2×C42×C17C2×C411yescharacteristic
37C17×M32—21no—
38C17×M32—21no—
39C17×M32—21no—
40C17×M32—21no—
41C17×M32—21no—
42C17×M32—21no—
43C17×M32D412yes—
44C17×M32D412yes—
45C2×C16×C17—21no—
46C2×C16×C17—21no—
47C2×C16×C17—21no—
48C2×C16×C17—21no—
49C17×C22⋊C8—22no—
50C17×#97—21no—
51C17×#97—21no—
52C4×C8×C17—21no—
53C4×C8×C17—21no—
54C17×#95—21no—
55C24×C17M1611yescharacteristic
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17M1611yescharacteristic
65C22×C4×C17C22×C411yescharacteristic
66M16×C17—41no—
67M16×C17—41no—
68M16×C17—41no—
69M16×C17—41no—
70C2×C8×C17—21no—
71C2×C8×C17—21no—
72C2×C8×C17—21no—
73C2×C8×C17—21no—
74C2×C8×C17—21no—
75C2×C8×C17—21no—
76C2×C8×C17—21no—
77C2×C8×C17—21no—
78C2×C8×C17M1612yes—
79C2×C8×C17C2×D411yescharacteristic
80C2×C8×C17C2×D411yescharacteristic
81C2×C8×C17#4111yescharacteristic
82C2×C8×C17#4111yescharacteristic
83C2×C8×C17#4111yescharacteristic
84C2×C8×C17#4111yescharacteristic
85C22⋊C4×C17—42no—
86C42×C17—21no—
87C42×C17—21no—
88C42×C17—21no—
89C42×C17—21no—
90C16×C17—22no—
91C16×C17—22no—
92C16×C17—41no—
93C16×C17—41no—
94#13128C1711yesmaximal, characteristic, direct product factor, Sylow
95C23×C17—21no—
96C23×C17—21no—
97C23×C17—21no—
98C23×C17—41no—
99C23×C17—41no—
100C23×C17C2×M1611yescharacteristic
101C2×C4×C17—22no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17#11711yescharacteristic
115C2×C4×C17C4×D411yescharacteristic
116C2×C4×C17C4×D411yescharacteristic
117C2×C4×C17C2×M1611yescharacteristic
118C2×C4×C17#13111yescharacteristic
119C2×C4×C17#13111yescharacteristic
120C8×C17—22no—
121C8×C17—41no—
122C8×C17—41no—
123C8×C17#12111yescharacteristic
124C8×C17#12311yescharacteristic
125C8×C17#12411yescharacteristic
126C8×C17#12611yescharacteristic
127C2×#364C2×C1711yescharacteristic, complemented
128C2×#349C2×C1711yescharacteristic
129C2×#349C2×C1711yescharacteristic
130C2×#347C2×C1711yescharacteristic, complemented
131#1753C2×C1711yescharacteristic
132#1376C2×C1711yescharacteristic, complemented
133#1375C2×C1711yescharacteristic, complemented
134C22×C17—21no—
135C22×C17—21no—
136C22×C17—41no—
137C22×C17—41no—
138C22×C17—41no—
139C22×C17—81no—
140C22×C17—81no—
141C22×C17#43211yescharacteristic
142C22×C17#43511yescharacteristic
143C22×C17#43511yescharacteristic
144C4×C17—42no—
145C4×C17—41no—
146C4×C17—81no—
147C4×C17#38811yescharacteristic
148C4×C17#43311yescharacteristic
149C4×C17#43511yescharacteristic
150C4×C17#43611yescharacteristic
151C22×M16C22×C1711yescharacteristic
152C2×M32C22×C1711yescharacteristic
153C2×M32C22×C1711yescharacteristic
154C2×M32C22×C1711yescharacteristic
155C2×M32C22×C1711yescharacteristic
156C2×C22⋊C8C4×C1711yescharacteristic
157C2×#97C22×C1711yescharacteristic
158C2×C4×C8C22×C1711yescharacteristic
159C4×C22⋊C4C4×C1711yescharacteristic
160#364—22no—
161#349—22no—
162#349—22no—
163#347—22no—
164#336C4×C1711yescharacteristic
165#336C4×C1711yescharacteristic
166C2×C17—21no—
167C2×C17—21no—
168C2×C17—81no—
169C2×C17#192411yescharacteristic
170C2×C17#216511yescharacteristic
171C2×C17#216611yescharacteristic
172C23×C4C2×C4×C1711yescharacteristic
173C2×M16—21no—
174C2×M16—21no—
175C2×M16—21no—
176C2×M16—21no—
177C2×M16—21no—
178C2×M16—21no—
179C22×C8C2×C4×C1711yescharacteristic
180C22×C8C2×C4×C1711yescharacteristic
181C22×C8C2×C4×C1711yescharacteristic
182C22×C8C23×C1711yescharacteristic
183C2×C22⋊C4—21no—
184C2×C42C2×C4×C1711yescharacteristic
185C2×C42C2×C4×C1711yescharacteristic
186M32—21no—
187M32—21no—
188M32—21no—
189M32—21no—
190M32—21no—
191M32—21no—
192M32D4×C1712yes—
193M32D4×C1712yes—
194C2×C16—21no—
195C2×C16—21no—
196C2×C16—21no—
197C2×C16—21no—
198C22⋊C8—22no—
199#97—21no—
200#97—21no—
201C4×C8—21no—
202C4×C8—21no—
203#95—21no—
204C17#1312811yescharacteristic, direct product factor, Sylow
205C24M16×C1711yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4M16×C1711yescharacteristic
215C22×C4C22×C4×C1711yescharacteristic
216M16—41no—
217M16—41no—
218M16—41no—
219M16—41no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8M16×C1712yes—
229C2×C8C2×D4×C1711yescharacteristic
230C2×C8C2×D4×C1711yescharacteristic
231C2×C8#41×C1711yescharacteristic
232C2×C8#41×C1711yescharacteristic
233C2×C8#41×C1711yescharacteristic
234C2×C8#41×C1711yescharacteristic
235C22⋊C4—42no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C16—22no—
241C16—22no—
242C16—41no—
243C16—41no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23C2×M16×C1711yescharacteristic
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4C17×#11711yescharacteristic
264C2×C4C4×D4×C1711yescharacteristic
265C2×C4C4×D4×C1711yescharacteristic
266C2×C4C2×M16×C1711yescharacteristic
267C2×C4C17×#13111yescharacteristic
268C2×C4C17×#13111yescharacteristic
269C8—22no—
270C8—41no—
271C8—41no—
272C8C17×#12111yescharacteristic
273C8C17×#12311yescharacteristic
274C8C17×#12411yescharacteristic
275C8C17×#12611yescharacteristic
276C22—21no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—81no—
282C22—81no—
283C22C17×#43211yescharacteristic
284C22C17×#43511yescharacteristic
285C22C17×#43511yescharacteristic
286C4—42no—
287C4—41no—
288C4—81no—
289C4C17×#38811yescharacteristic
290C4C17×#43311yescharacteristic
291C4C17×#43511yescharacteristic
292C4C17×#43611yescharacteristic
293C2—21no—
294C2—21no—
295C2—81no—
296C2C17×#192411yescharacteristic
297C2C17×#216511yescharacteristic
298C2C17×#216611yescharacteristic
subgroupG/H
centerC2×C4×C17#117
commutatorC22×C4C22×C4×C17
Frattini, cosocleC22×C8C23×C17
socleC22×C17#432
prime radicalC24×C17M16
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C17 ◁ C2×C17×#97 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C17×#364C2semidirect
4. C2×C17×#347C2semidirect
6. C17×#1376C2semidirect
7. C17×#1375C2semidirect
94. #13128C17direct (N × H)
127. C2×#364C2×C17semidirect
130. C2×#347C2×C17semidirect
132. #1376C2×C17semidirect
133. #1375C2×C17semidirect
204. C17#13128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#3642
C2×C17×#3492
C2×C17×#3472
C17×#17532
C17×#13762
C17×#13752
#1312817