Finite Group Databasebeta

← C17×#1615 #14524621

Subgroups — C17×#1615 #14524621

Order 2176.

208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 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×#539C211yesmaximal, characteristic
2C17×#484C211yesmaximal, characteristic, complemented
3C17×#481C211yesmaximal, characteristic
4C17×#400C211yesmaximal, characteristic, complemented
5C17×#328C211yesmaximal, characteristic, complemented
6C17×#327C211yesmaximal, characteristic
7C17×#324C211yesmaximal, characteristic, complemented
8C17×#126—21no—
9C17×#125—21no—
10C17×#123—21no—
11C17×#123—21no—
12C17×C22⋊Q8—21no—
13C17×C22⋊Q8C2211yescharacteristic
14C17×#121C2211yescharacteristic
15C4×D4×C17—21no—
16C2×C4⋊C4×C17C2211yescharacteristic
17C2×C4⋊C4×C17C2211yescharacteristic
18C17×#107—21no—
19C17×#106—21no—
20C17×#103—21no—
21C17×#102—21no—
22C17×C22⋊C8C2211yescharacteristic
23C17×C22⋊C8C2211yescharacteristic
24C17×#95—21no—
25C17×#95—21no—
26C17×#95C2211yescharacteristic
27C2×Q8×C17D411yescharacteristic
28C2×D4×C17—21no—
29C2×D4×C17D411yescharacteristic
30C22×C4×C17—21no—
31C22×C4×C17—21no—
32C22×C4×C17—21no—
33C22×C4×C17D411yescharacteristic
34C22×C4×C17D411yescharacteristic
35C22×C4×C17C2311yescharacteristic
36C2×C8×C17—21no—
37C2×C8×C17—21no—
38C4⋊C4×C17—21no—
39C4⋊C4×C17—21no—
40C4⋊C4×C17—21no—
41C4⋊C4×C17—21no—
42C4⋊C4×C17—21no—
43C4⋊C4×C17—21no—
44C4⋊C4×C17—21no—
45C4⋊C4×C17—21no—
46C4⋊C4×C17D411yescharacteristic
47C4⋊C4×C17D411yescharacteristic
48C22⋊C4×C17—21no—
49C22⋊C4×C17—21no—
50C22⋊C4×C17—21no—
51C22⋊C4×C17—21no—
52C22⋊C4×C17—21no—
53C42×C17—21no—
54C23×C17—21no—
55C23×C17C2×D411yescharacteristic
56Q8×C17—41no—
57D4×C17—41no—
58D4×C17—41no—
59D4×C17—41no—
60C2×C4×C17—21no—
61C2×C4×C17—21no—
62C2×C4×C17—21no—
63C2×C4×C17—21no—
64C2×C4×C17—21no—
65C2×C4×C17—21no—
66C2×C4×C17—21no—
67C2×C4×C17—41no—
68C2×C4×C17—41no—
69C2×C4×C17—41no—
70C2×C4×C17—41no—
71C2×C4×C17—42no—
72C2×C4×C17—41no—
73C2×C4×C17—41no—
74C2×C4×C17—81no—
75C2×C4×C17C2×D411yescharacteristic
76C2×C4×C17C2×D411yescharacteristic
77C8×C17—41no—
78C8×C17—41no—
79#1615C1711yesmaximal, characteristic, direct product factor, Sylow
80C22×C17—21no—
81C22×C17—21no—
82C22×C17—41no—
83C22×C17—41no—
84C22×C17—41no—
85C22×C17#12011yescharacteristic
86C22×C17#13511yescharacteristic
87C22×C17#13711yescharacteristic
88C4×C17—21no—
89C4×C17—21no—
90C4×C17—41no—
91C4×C17—41no—
92C4×C17—41no—
93C4×C17—41no—
94C4×C17—41no—
95C4×C17—81no—
96C4×C17—81no—
97#539C2×C1711yescharacteristic
98#484C2×C1711yescharacteristic, complemented
99#481C2×C1711yescharacteristic
100#400C2×C1711yescharacteristic, complemented
101#328C2×C1711yescharacteristic, complemented
102#327C2×C1711yescharacteristic
103#324C2×C1711yescharacteristic, complemented
104C2×C17—21no—
105C2×C17—21no—
106C2×C17—81no—
107C2×C17#45211yescharacteristic
108C2×C17#45411yescharacteristic
109C2×C17#45811yescharacteristic
110#126—21no—
111#125—21no—
112#123—21no—
113#123—21no—
114C22⋊Q8—21no—
115C22⋊Q8C22×C1711yescharacteristic
116#121C22×C1711yescharacteristic
117C4×D4—21no—
118C2×C4⋊C4C22×C1711yescharacteristic
119C2×C4⋊C4C22×C1711yescharacteristic
120#107—21no—
121#106—21no—
122#103—21no—
123#102—21no—
124C22⋊C8C22×C1711yescharacteristic
125C22⋊C8C22×C1711yescharacteristic
126#95—21no—
127#95—21no—
128#95C22×C1711yescharacteristic
129C17#161511yescharacteristic, direct product factor, Sylow
130C2×Q8D4×C1711yescharacteristic
131C2×D4—21no—
132C2×D4D4×C1711yescharacteristic
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4D4×C1711yescharacteristic
137C22×C4D4×C1711yescharacteristic
138C22×C4C23×C1711yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4D4×C1711yescharacteristic
150C4⋊C4D4×C1711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—21no—
156C42—21no—
157C23—21no—
158C23C2×D4×C1711yescharacteristic
159Q8—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—42no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—81no—
178C2×C4C2×D4×C1711yescharacteristic
179C2×C4C2×D4×C1711yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22C17×#12011yescharacteristic
188C22C17×#13511yescharacteristic
189C22C17×#13711yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—41no—
195C4—41no—
196C4—41no—
197C4—81no—
198C4—81no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2C17×#45211yescharacteristic
203C2C17×#45411yescharacteristic
204C2C17×#45811yescharacteristic
subgroupG/H
center, socleC22×C17#120
commutator, Frattini, cosocleC22×C4C23×C17
prime radicalC17×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#484C2semidirect
4. C17×#400C2semidirect
5. C17×#328C2semidirect
7. C17×#324C2semidirect
79. #1615C17direct (N × H)
98. #484C2×C17semidirect
100. #400C2×C17semidirect
101. #328C2×C17semidirect
103. #324C2×C17semidirect
129. C17#1615direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#5392
C17×#4842
C17×#4812
C17×#4002
C17×#3282
C17×#3272
C17×#3242
#161517