Finite Group Databasebeta

← C17×#10631 #16868375

Subgroups — C17×#10631 #16868375

Order 4352.

362 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C17×#1961C211yesmaximal, characteristic
2C17×#1849C211yesmaximal, characteristic, complemented
3C17×#1545C212yesmaximal
4C17×#1286C212yesmaximal, complemented
5C17×#1281C211yesmaximal, characteristic, complemented
6C2×C17×#127C2211yescharacteristic
7C17×#431C2212yes—
8C2×C17×#108—21no—
9C2×C17×#108—21no—
10C17×#423C2212yes—
11C2×C17×#102—21no—
12C2×C17×#102—21no—
13C2×C17×#97C2211yescharacteristic
14C17×#382C2211yescharacteristic
15C17×#331—24no—
16C22×D4×C17—21no—
17C22×D4×C17—22no—
18C2×M16×C17—22no—
19C22×C8×C17D411yescharacteristic
20C22×C8×C17D411yescharacteristic
21C17×#127—21no—
22C17×#127—22no—
23C17×#127D412yes—
24C2×C4⋊C4×C17—21no—
25C2×C42×C17C2311yescharacteristic
26C17×#108—42no—
27C17×#108—42no—
28C17×C4⋊C8—22no—
29C17×C4⋊C8—22no—
30C17×C4⋊C8—22no—
31C17×#102—42no—
32C17×#102—42no—
33C17×C22⋊C8—22no—
34C17×#97—22no—
35C4×C8×C17—22no—
36C17×#95—22no—
37C24×C17—41no—
38C2×D4×C17—22no—
39C2×D4×C17—24no—
40C2×D4×C17—41no—
41C2×D4×C17—42no—
42C2×D4×C17—41no—
43C2×D4×C17—41no—
44C2×D4×C17—41no—
45C2×D4×C17—41no—
46C2×D4×C17—84no—
47C22×C4×C17—41no—
48C22×C4×C17C2×D411yescharacteristic
49C22×C4×C17#4112yes—
50M16×C17—42no—
51M16×C17—42no—
52C2×C8×C17—21no—
53C2×C8×C17—21no—
54C2×C8×C17—21no—
55C2×C8×C17—21no—
56C2×C8×C17—42no—
57C2×C8×C17—42no—
58C2×C8×C17D812yes—
59C2×C8×C17SD1612yes—
60C4⋊C4×C17—41no—
61C4⋊C4×C17—41no—
62C42×C17C2×D411yescharacteristic
63C42×C17#4111yescharacteristic
64C42×C17#4112yes—
65#10631C1711yesmaximal, characteristic, direct product factor, Sylow
66C23×C17—42no—
67C23×C17—84no—
68C23×C17—81no—
69C23×C17—81no—
70C23×C17#12411yescharacteristic
71D4×C17—42no—
72D4×C17—42no—
73D4×C17—84no—
74D4×C17—84no—
75D4×C17—81no—
76D4×C17—81no—
77C2×C4×C17—42no—
78C2×C4×C17—82no—
79C2×C4×C17—81no—
80C2×C4×C17#12111yescharacteristic
81C2×C4×C17#12312yes—
82C2×C4×C17#12311yescharacteristic
83C2×C4×C17#12612yes—
84C2×C4×C17C2×D811yescharacteristic
85C2×C4×C17C2×SD1611yescharacteristic
86C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
87C2×C4×C17#13711yescharacteristic
88C8×C17—22no—
89C8×C17—22no—
90C8×C17—82no—
91C8×C17—82no—
92#1961C2×C1711yescharacteristic
93#1849C2×C1711yescharacteristic, complemented
94#1545C2×C1712yes—
95#1286C2×C1712yescomplemented
96#1281C2×C1711yescharacteristic, complemented
97C22×C17—22no—
98C22×C17—82no—
99C22×C17—84no—
100C22×C17—162no—
101C22×C17—162no—
102C22×C17#39711yescharacteristic
103C22×C17#48611yescharacteristic
104C22×C17#48911yescharacteristic
105C4×C17—22no—
106C4×C17—22no—
107C4×C17—161no—
108C4×C17#45911yescharacteristic
109C4×C17#46111yescharacteristic
110C4×C17#48011yescharacteristic
111C4×C17#48111yescharacteristic
112C2×#127C22×C1711yescharacteristic
113#431C22×C1712yes—
114C2×#108—21no—
115C2×#108—21no—
116#423C22×C1712yes—
117C2×#102—21no—
118C2×#102—21no—
119C2×#97C22×C1711yescharacteristic
120#382C22×C1711yescharacteristic
121#331—24no—
122C2×C17—21no—
123C2×C17—21no—
124C2×C17—162no—
125C2×C17#207111yescharacteristic
126C2×C17#208112yes—
127C22×D4—21no—
128C22×D4—22no—
129C2×M16—22no—
130C22×C8D4×C1711yescharacteristic
131C22×C8D4×C1711yescharacteristic
132#127—22no—
133#127—21no—
134#127D4×C1712yes—
135C2×C4⋊C4—21no—
136C2×C42C23×C1711yescharacteristic
137#108—42no—
138#108—42no—
139C4⋊C8—22no—
140C4⋊C8—22no—
141C4⋊C8—22no—
142#102—42no—
143#102—42no—
144C22⋊C8—22no—
145#97—22no—
146C4×C8—22no—
147#95—22no—
148C17#1063111yescharacteristic, direct product factor, Sylow
149C24—41no—
150C2×D4—24no—
151C2×D4—22no—
152C2×D4—41no—
153C2×D4—42no—
154C2×D4—41no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—84no—
159C22×C4—41no—
160C22×C4C2×D4×C1711yescharacteristic
161C22×C4#41×C1712yes—
162M16—42no—
163M16—42no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8D8×C1712yes—
171C2×C8SD16×C1712yes—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C42C2×D4×C1711yescharacteristic
175C42#41×C1712yes—
176C42#41×C1711yescharacteristic
177C23—42no—
178C23—84no—
179C23—81no—
180C23—81no—
181C23C17×#12411yescharacteristic
182D4—42no—
183D4—42no—
184D4—84no—
185D4—84no—
186D4—81no—
187D4—81no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4C17×#12111yescharacteristic
192C2×C4C17×#12312yes—
193C2×C4C17×#12311yescharacteristic
194C2×C4C17×#12612yes—
195C2×C4C2×D8×C1711yescharacteristic
196C2×C4C2×SD16×C1711yescharacteristic
197C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
198C2×C4C17×#13711yescharacteristic
199C8—22no—
200C8—22no—
201C8—82no—
202C8—82no—
203C22—22no—
204C22—82no—
205C22—84no—
206C22—162no—
207C22—162no—
208C22C17×#39711yescharacteristic
209C22C17×#48611yescharacteristic
210C22C17×#48911yescharacteristic
211C4—22no—
212C4—22no—
213C4—161no—
214C4C17×#45911yescharacteristic
215C4C17×#46111yescharacteristic
216C4C17×#48011yescharacteristic
217C4C17×#48111yescharacteristic
218C2—21no—
219C2—21no—
220C2—162no—
221C2C17×#207111yescharacteristic
222C2C17×#208112yes—
subgroupG/H
center, socleC22×C17#397
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC2×C17×#127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1849C2semidirect
4. C17×#1286C2semidirect
5. C17×#1281C2semidirect
65. #10631C17direct (N × H)
93. #1849C2×C17semidirect
95. #1286C2×C17semidirect
96. #1281C2×C17semidirect
148. C17#10631direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#19612
C17×#18492
C17×#15452
C17×#12862
C17×#12812
#1063117