Finite Group Databasebeta

← C17×#13122 #16870866

Subgroups — C17×#13122 #16870866

Order 4352.

326 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#364C211yesmaximal, characteristic, complemented
2C2×C17×#350C211yesmaximal, characteristic
3C17×#2113C211yesmaximal, characteristic
4C17×#2108C211yesmaximal, characteristic, complemented
5C17×#1764C211yesmaximal, characteristic
6C17×#1379C211yesmaximal, characteristic, complemented
7C17×#1374C211yesmaximal, characteristic, complemented
8C2×C17×#131C2211yescharacteristic
9C2×C17×M32C2211yescharacteristic
10C2×C17×M32C2211yescharacteristic
11C22×C16×C17C2211yescharacteristic
12C22×C16×C17C2211yescharacteristic
13C2×C17×#104C411yescharacteristic
14C17×#416C411yescharacteristic
15C17×#405C2211yescharacteristic
16C2×C4×C8×C17C2211yescharacteristic
17C17×#364—22no—
18C17×#350—22no—
19C17×C22⋊C16—21no—
20C17×C22⋊C16—21no—
21C17×#346—21no—
22C4×C16×C17—21no—
23C17×#341C411yescharacteristic
24C17×#339C411yescharacteristic
25C2×#41×C17C2×C411yescharacteristic
26C17×#131—21no—
27C17×#131—21no—
28C17×#131—21no—
29C17×#131—21no—
30C2×M16×C17—21no—
31C2×M16×C17C2×C411yescharacteristic
32C2×M16×C17C2×C411yescharacteristic
33C22×C8×C17—21no—
34C22×C8×C17C2×C411yescharacteristic
35C22×C8×C17C2311yescharacteristic
36C17×#117C2×C411yescharacteristic
37C2×C42×C17C2×C411yescharacteristic
38C17×M32—21no—
39C17×M32—21no—
40C17×M32—21no—
41C17×M32D412yes—
42C2×C16×C17—21no—
43C2×C16×C17—21no—
44C2×C16×C17—21no—
45C2×C16×C17—21no—
46C2×C16×C17—21no—
47C2×C16×C17—21no—
48C2×C16×C17—21no—
49C2×C16×C17D411yescharacteristic
50C2×C16×C17D411yescharacteristic
51C17×#104—22no—
52C17×#103C811yescharacteristic
53C17×#103C811yescharacteristic
54C17×#102C811yescharacteristic
55C17×#102C811yescharacteristic
56C17×#97—21no—
57C4×C8×C17—21no—
58C4×C8×C17—21no—
59C4×C8×C17—21no—
60#41×C17—21no—
61#41×C17—21no—
62#41×C17—21no—
63#41×C17—21no—
64C2×Q8×C17C2×C811yescharacteristic
65C2×D4×C17—21no—
66C2×D4×C17C2×C811yescharacteristic
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17C22×C411yescharacteristic
70M16×C17—21no—
71M16×C17—21no—
72M16×C17—21no—
73M16×C17—41no—
74M16×C17—41no—
75M16×C17M1612yes—
76C2×C8×C17—21no—
77C2×C8×C17—21no—
78C2×C8×C17—21no—
79C2×C8×C17—21no—
80C2×C8×C17—41no—
81C2×C8×C17—41no—
82C2×C8×C17C2×C811yescharacteristic
83C2×C8×C17C2×C811yescharacteristic
84C2×C8×C17C2×D411yescharacteristic
85C2×C8×C17C2×D411yescharacteristic
86C2×C8×C17#4111yescharacteristic
87C2×C8×C17#4111yescharacteristic
88C2×C8×C17#4111yescharacteristic
89C2×C8×C17#4111yescharacteristic
90C4⋊C4×C17C2×C811yescharacteristic
91C4⋊C4×C17C2×C811yescharacteristic
92C22⋊C4×C17—21no—
93C42×C17—21no—
94C42×C17—21no—
95C42×C17—21no—
96C16×C17—22no—
97C16×C17—21no—
98C16×C17—21no—
99C16×C17—41no—
100C16×C17—41no—
101#13122C1711yesmaximal, characteristic, direct product factor, Sylow
102C23×C17—21no—
103C23×C17#13111yescharacteristic
104Q8×C17—21no—
105Q8×C17—21no—
106D4×C17—21no—
107D4×C17—21no—
108D4×C17—41no—
109D4×C17—41no—
110C2×C4×C17—22no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17#11711yescharacteristic
119C2×C4×C17C4×D411yescharacteristic
120C2×C4×C17C4×D411yescharacteristic
121C2×C4×C17C22×C811yescharacteristic
122C2×C4×C17C2×M1611yescharacteristic
123C2×C4×C17#13111yescharacteristic
124C8×C17—21no—
125C8×C17—21no—
126C8×C17—22no—
127C8×C17—41no—
128C8×C17#12111yescharacteristic
129C8×C17#12311yescharacteristic
130C8×C17#12411yescharacteristic
131C8×C17#12611yescharacteristic
132C2×#364C2×C1711yescharacteristic, complemented
133C2×#350C2×C1711yescharacteristic
134#2113C2×C1711yescharacteristic
135#2108C2×C1711yescharacteristic, complemented
136#1764C2×C1711yescharacteristic
137#1379C2×C1711yescharacteristic, complemented
138#1374C2×C1711yescharacteristic, complemented
139C22×C17—21no—
140C22×C17—21no—
141C22×C17—41no—
142C22×C17—41no—
143C22×C17—41no—
144C22×C17#43311yescharacteristic
145C22×C17C8×D411yescharacteristic
146C22×C17#43611yescharacteristic
147C4×C17—42no—
148C4×C17—41no—
149C4×C17—41no—
150C4×C17—41no—
151C4×C17#38811yescharacteristic
152C4×C17#43111yescharacteristic
153C4×C17C8×D411yescharacteristic
154C4×C17#43511yescharacteristic
155C2×#131C22×C1711yescharacteristic
156C2×M32C22×C1711yescharacteristic
157C2×M32C22×C1711yescharacteristic
158C22×C16C22×C1711yescharacteristic
159C22×C16C22×C1711yescharacteristic
160C2×#104C4×C1711yescharacteristic
161#416C4×C1711yescharacteristic
162#405C22×C1711yescharacteristic
163C2×C4×C8C22×C1711yescharacteristic
164#364—22no—
165#350—22no—
166C22⋊C16—21no—
167C22⋊C16—21no—
168#346—21no—
169C4×C16—21no—
170#341C4×C1711yescharacteristic
171#339C4×C1711yescharacteristic
172C2×C17—21no—
173C2×C17—21no—
174C2×C17—81no—
175C2×C17#192311yescharacteristic
176C2×C17#217011yescharacteristic
177C2×C17#217111yescharacteristic
178C2×#41C2×C4×C1711yescharacteristic
179#131—21no—
180#131—21no—
181#131—21no—
182#131—21no—
183C2×M16—21no—
184C2×M16C2×C4×C1711yescharacteristic
185C2×M16C2×C4×C1711yescharacteristic
186C22×C8—21no—
187C22×C8C2×C4×C1711yescharacteristic
188C22×C8C23×C1711yescharacteristic
189#117C2×C4×C1711yescharacteristic
190C2×C42C2×C4×C1711yescharacteristic
191M32—21no—
192M32—21no—
193M32—21no—
194M32D4×C1712yes—
195C2×C16—21no—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—21no—
199C2×C16—21no—
200C2×C16—21no—
201C2×C16—21no—
202C2×C16D4×C1711yescharacteristic
203C2×C16D4×C1711yescharacteristic
204#104—22no—
205#103C8×C1711yescharacteristic
206#103C8×C1711yescharacteristic
207#102C8×C1711yescharacteristic
208#102C8×C1711yescharacteristic
209#97—21no—
210C4×C8—21no—
211C4×C8—21no—
212C4×C8—21no—
213C17#1312211yescharacteristic, direct product factor, Sylow
214#41—21no—
215#41—21no—
216#41—21no—
217#41—21no—
218C2×Q8C2×C8×C1711yescharacteristic
219C2×D4—21no—
220C2×D4C2×C8×C1711yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4C22×C4×C1711yescharacteristic
224M16—21no—
225M16—21no—
226M16—21no—
227M16—41no—
228M16—41no—
229M16M16×C1712yes—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8C2×C8×C1711yescharacteristic
237C2×C8C2×C8×C1711yescharacteristic
238C2×C8C2×D4×C1711yescharacteristic
239C2×C8C2×D4×C1711yescharacteristic
240C2×C8#41×C1711yescharacteristic
241C2×C8#41×C1711yescharacteristic
242C2×C8#41×C1711yescharacteristic
243C2×C8#41×C1711yescharacteristic
244C4⋊C4C2×C8×C1711yescharacteristic
245C4⋊C4C2×C8×C1711yescharacteristic
246C22⋊C4—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C16—21no—
251C16—21no—
252C16—22no—
253C16—41no—
254C16—41no—
255C23—21no—
256C23C17×#13111yescharacteristic
257Q8—21no—
258Q8—21no—
259D4—21no—
260D4—21no—
261D4—41no—
262D4—41no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4C17×#11711yescharacteristic
272C2×C4C4×D4×C1711yescharacteristic
273C2×C4C4×D4×C1711yescharacteristic
274C2×C4C22×C8×C1711yescharacteristic
275C2×C4C2×M16×C1711yescharacteristic
276C2×C4C17×#13111yescharacteristic
277C8—21no—
278C8—21no—
279C8—22no—
280C8—41no—
281C8C17×#12111yescharacteristic
282C8C17×#12311yescharacteristic
283C8C17×#12411yescharacteristic
284C8C17×#12611yescharacteristic
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22C17×#43311yescharacteristic
291C22C8×D4×C1711yescharacteristic
292C22C17×#43611yescharacteristic
293C4—42no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4C17×#38811yescharacteristic
298C4C17×#43111yescharacteristic
299C4C8×D4×C1711yescharacteristic
300C4C17×#43511yescharacteristic
301C2—21no—
302C2—21no—
303C2—81no—
304C2C17×#192311yescharacteristic
305C2C17×#217011yescharacteristic
306C2C17×#217111yescharacteristic
subgroupG/H
centerC2×C8×C17C2×D4
commutatorC2×C4C22×C8×C17
Frattini, cosocleC22×C8C23×C17
socleC22×C17C8×D4
prime radicalC2×#41×C17C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8×C17 ◁ C22×C16×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C17×#364C2semidirect
4. C17×#2108C2semidirect
6. C17×#1379C2semidirect
7. C17×#1374C2semidirect
101. #13122C17direct (N × H)
132. C2×#364C2×C17semidirect
135. #2108C2×C17semidirect
137. #1379C2×C17semidirect
138. #1374C2×C17semidirect
213. C17#13122direct (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×#3502
C17×#21132
C17×#21082
C17×#17642
C17×#13792
C17×#13742
#1312217