Finite Group Databasebeta

← C17×#7483 #16865227

Subgroups — C17×#7483 #16865227

Order 4352.

262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#356C211yesmaximal, characteristic
2C17×#1886C211yesmaximal, characteristic
3C17×#1558C211yesmaximal, characteristic
4C2×C17×C4⋊Q8C2211yescharacteristic
5C17×#519C411yescharacteristic
6C17×#432—21no—
7C17×#419—21no—
8C2×C17×#101—21no—
9C2×C17×#101C411yescharacteristic
10C17×#356—21no—
11C17×#356C412yescomplemented
12C17×#339—21no—
13C17×#333—21no—
14C17×#333C412yescomplemented
15C22×Q8×C17C2×C411yescharacteristic
16C22×Q8×C17D411yescharacteristic
17C2×M16×C17—21no—
18C2×M16×C17—41no—
19C17×C4⋊Q8—41no—
20C17×C4⋊Q8C2×C411yescharacteristic
21C17×C4⋊Q8C2×C411yescharacteristic
22C17×C4⋊Q8D411yescharacteristic
23C17×C4⋊Q8Q811yescharacteristic
24C4×Q8×C17—42no—
25C17×#117—21no—
26C17×#117—41no—
27C2×C4⋊C4×C17—41no—
28C2×C42×C17D411yescharacteristic
29C17×C4⋊C8—22no—
30C17×#103—42no—
31C17×#101—22no—
32C17×#101—41no—
33C17×#101—41no—
34C17×C22⋊C8—41no—
35C17×#97—41no—
36C2×Q8×C17—21no—
37C2×Q8×C17—21no—
38C2×Q8×C17—41no—
39C2×Q8×C17—41no—
40C2×Q8×C17—41no—
41C2×Q8×C17—41no—
42C2×Q8×C17C4211yescharacteristic
43C2×Q8×C17C22⋊C411yescharacteristic
44C2×Q8×C17C4⋊C411yescharacteristic
45C2×Q8×C17C4⋊C411yescharacteristic
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17C22⋊C411yescharacteristic
50M16×C17—41no—
51M16×C17—42no—
52M16×C17—41no—
53M16×C17—81no—
54C2×C8×C17—41no—
55C2×C8×C17—42no—
56C2×C8×C17—81no—
57C4⋊C4×C17—22no—
58C4⋊C4×C17—41no—
59C4⋊C4×C17—41no—
60C4⋊C4×C17—41no—
61C4⋊C4×C17—41no—
62C4⋊C4×C17—42no—
63C22⋊C4×C17—41no—
64C42×C17—21no—
65C42×C17—41no—
66C42×C17—42no—
67C42×C17C22⋊C411yescharacteristic
68C42×C17C4⋊C411yescharacteristic
69#7483C1711yesmaximal, characteristic, direct product factor, Sylow
70C23×C17#9911yescharacteristic
71Q8×C17—41no—
72Q8×C17—41no—
73Q8×C17—41no—
74Q8×C17—41no—
75Q8×C17—42no—
76Q8×C17—81no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—42no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—42no—
91C2×C4×C17#9511yescharacteristic
92C2×C4×C17#9911yescharacteristic
93C8×C17—82no—
94C8×C17—81no—
95C8×C17—82no—
96C2×#356C2×C1711yescharacteristic
97#1886C2×C1711yescharacteristic
98#1558C2×C1711yescharacteristic
99C22×C17—41no—
100C22×C17#34211yescharacteristic
101C22×C17AΣL(1,𝔽16)11yescharacteristic
102C22×C17#35211yescharacteristic
103C4×C17—22no—
104C4×C17—21no—
105C4×C17—21no—
106C4×C17—41no—
107C4×C17—41no—
108C4×C17—41no—
109C4×C17—41no—
110C4×C17—41no—
111C4×C17—82no—
112C2×C4⋊Q8C22×C1711yescharacteristic
113#519C4×C1711yescharacteristic
114#432—21no—
115#419—21no—
116C2×#101—21no—
117C2×#101C4×C1711yescharacteristic
118#356—21no—
119#356C4×C1712yescomplemented
120#339—21no—
121#333—21no—
122#333C4×C1712yescomplemented
123C2×C17—21no—
124C2×C17—21no—
125C2×C17—21no—
126C2×C17#139011yescharacteristic
127C22×Q8C2×C4×C1711yescharacteristic
128C22×Q8D4×C1711yescharacteristic
129C2×M16—21no—
130C2×M16—41no—
131C4⋊Q8—41no—
132C4⋊Q8C2×C4×C1711yescharacteristic
133C4⋊Q8C2×C4×C1711yescharacteristic
134C4⋊Q8D4×C1711yescharacteristic
135C4⋊Q8Q8×C1711yescharacteristic
136C4×Q8—42no—
137#117—21no—
138#117—41no—
139C2×C4⋊C4—41no—
140C2×C42D4×C1711yescharacteristic
141C4⋊C8—22no—
142#103—42no—
143#101—22no—
144#101—41no—
145#101—41no—
146C22⋊C8—41no—
147#97—41no—
148C17#748311yescharacteristic, direct product factor, Sylow
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8C42×C1711yescharacteristic
156C2×Q8C22⋊C4×C1711yescharacteristic
157C2×Q8C4⋊C4×C1711yescharacteristic
158C2×Q8C4⋊C4×C1711yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4C22⋊C4×C1711yescharacteristic
163M16—42no—
164M16—41no—
165M16—41no—
166M16—81no—
167C2×C8—42no—
168C2×C8—41no—
169C2×C8—81no—
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C22⋊C4—41no—
177C42—21no—
178C42—41no—
179C42—42no—
180C42C22⋊C4×C1711yescharacteristic
181C42C4⋊C4×C1711yescharacteristic
182C23C17×#9911yescharacteristic
183Q8—41no—
184Q8—41no—
185Q8—41no—
186Q8—41no—
187Q8—42no—
188Q8—81no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4C17×#9511yescharacteristic
204C2×C4C17×#9911yescharacteristic
205C8—81no—
206C8—82no—
207C8—82no—
208C22—41no—
209C22C17×#34211yescharacteristic
210C22C17×AΣL(1,𝔽16)11yescharacteristic
211C22C17×#35211yescharacteristic
212C4—22no—
213C4—21no—
214C4—21no—
215C4—41no—
216C4—41no—
217C4—41no—
218C4—41no—
219C4—41no—
220C4—82no—
221C2—21no—
222C2—21no—
223C2—21no—
224C2C17×#139011yescharacteristic
subgroupG/H
center, socleC2×C17#1390
commutatorC2×Q8C42×C17
Frattini, cosocleC2×C4⋊Q8C22×C17
prime radicalC23×C17#99
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C17 ◁ C23×C17 ◁ C22×C4×C17 ◁ C2×C17×C4⋊Q8 ◁ G

Complements

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

NH ≅ G/Ntype
11. C17×#356C4semidirect
14. C17×#333C4semidirect
69. #7483C17direct (N × H)
119. #356C4×C17semidirect
122. #333C4×C17semidirect
148. C17#7483direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#3562
C17×#18862
C17×#15582
#748317