Finite Group Databasebeta

← C17×#10428 #16868172

Subgroups — C17×#10428 #16868172

Order 4352.

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

normal subgroups only

This group has 386 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×#2822C211yesmaximal, characteristic
2C17×#1992C212yesmaximal
3C17×#1836C211yesmaximal, characteristic
4C2×C17×#330C212yesmaximal
5C17×#1295C211yesmaximal, characteristic
6C2×C17×#125C2212yes—
7C2×C17×#97C2212yes—
8C2×C17×#97C2211yescharacteristic
9C17×#400—22no—
10C17×#398—22no—
11C17×#398—22no—
12C17×#384C2211yescharacteristic
13C17×#382C2211yescharacteristic
14C17×#340—22no—
15C17×#340—22no—
16C17×#340—22no—
17C17×#330—24no—
18C22×C8×C17—22no—
19C22×C8×C17—21no—
20C17×#125—22no—
21C17×#125—22no—
22C17×#125—22no—
23C17×#125—22no—
24C2×C4⋊C4×C17—22no—
25C2×C4⋊C4×C17—22no—
26C2×C4⋊C4×C17—22no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—22no—
29C2×C4⋊C4×C17D412yes—
30C2×C4⋊C4×C17D412yes—
31C2×C4⋊C4×C17D412yes—
32C2×C42×C17C2311yescharacteristic
33C17×#97—22no—
34C17×#97—21no—
35C17×#97—22no—
36C17×#97D412yes—
37C17×#95—24no—
38C17×#95—22no—
39C17×#95—22no—
40C22×C4×C17—22no—
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17—41no—
44C22×C4×C17C2×D412yes—
45C22×C4×C17C2×D411yescharacteristic
46C2×C8×C17—24no—
47C2×C8×C17—22no—
48C2×C8×C17—42no—
49C2×C8×C17—41no—
50C2×C8×C17—41no—
51C2×C8×C17—42no—
52C4⋊C4×C17—22no—
53C4⋊C4×C17—22no—
54C4⋊C4×C17—22no—
55C4⋊C4×C17—22no—
56C4⋊C4×C17—42no—
57C4⋊C4×C17—44no—
58C4⋊C4×C17—42no—
59C4⋊C4×C17—42no—
60C4⋊C4×C17—42no—
61C4⋊C4×C17—42no—
62C4⋊C4×C17—42no—
63C4⋊C4×C17—82no—
64C42×C17C2×D411yescharacteristic
65C42×C17#4111yescharacteristic
66C42×C17#4112yes—
67#10428C1711yesmaximal, characteristic, direct product factor, Sylow
68C23×C17#12011yescharacteristic
69C2×C4×C17—22no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—22no—
73C2×C4×C17—42no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17—42no—
78C2×C4×C17—42no—
79C2×C4×C17—42no—
80C2×C4×C17—42no—
81C2×C4×C17—42no—
82C2×C4×C17—81no—
83C2×C4×C17—82no—
84C2×C4×C17#12112yes—
85C2×C4×C17#12111yescharacteristic
86C2×C4×C17#12312yes—
87C2×C4×C17#12411yescharacteristic
88C8×C17—44no—
89C8×C17—42no—
90#2822C2×C1711yescharacteristic
91#1992C2×C1712yes—
92#1836C2×C1711yescharacteristic
93C2×#330C2×C1712yes—
94#1295C2×C1711yescharacteristic
95C22×C17#39411yescharacteristic
96C22×C17#45411yescharacteristic
97C22×C17#45412yes—
98C22×C17#45511yescharacteristic
99C22×C17#45612yes—
100C4×C17—22no—
101C4×C17—22no—
102C4×C17—21no—
103C4×C17—21no—
104C4×C17—82no—
105C4×C17—82no—
106C4×C17—82no—
107C4×C17—161no—
108C2×#125C22×C1712yes—
109C2×#97C22×C1712yes—
110C2×#97C22×C1711yescharacteristic
111#400—22no—
112#398—22no—
113#398—22no—
114#384C22×C1711yescharacteristic
115#382C22×C1711yescharacteristic
116#340—22no—
117#340—22no—
118#340—22no—
119#330—24no—
120C2×C17#165811yescharacteristic
121C2×C17#166311yescharacteristic
122C2×C17#166412yes—
123C2×C17#203812yes—
124C2×C17#204011yescharacteristic
125C22×C8—22no—
126C22×C8—21no—
127#125—22no—
128#125—22no—
129#125—22no—
130#125—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4D4×C1712yes—
137C2×C4⋊C4D4×C1712yes—
138C2×C4⋊C4D4×C1712yes—
139C2×C42C23×C1711yescharacteristic
140#97—22no—
141#97—21no—
142#97—22no—
143#97D4×C1712yes—
144#95—24no—
145#95—22no—
146#95—22no—
147C17#1042811yescharacteristic, direct product factor, Sylow
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—41no—
152C22×C4C2×D4×C1712yes—
153C22×C4C2×D4×C1711yescharacteristic
154C2×C8—24no—
155C2×C8—22no—
156C2×C8—42no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—42no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—44no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—82no—
172C42C2×D4×C1711yescharacteristic
173C42#41×C1711yescharacteristic
174C42#41×C1712yes—
175C23C17×#12011yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4C17×#12112yes—
192C2×C4C17×#12111yescharacteristic
193C2×C4C17×#12312yes—
194C2×C4C17×#12411yescharacteristic
195C8—44no—
196C8—42no—
197C22C17×#39411yescharacteristic
198C22C17×#45412yes—
199C22C17×#45411yescharacteristic
200C22C17×#45511yescharacteristic
201C22C17×#45612yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—161no—
210C2C17×#165811yescharacteristic
211C2C17×#166311yescharacteristic
212C2C17×#166412yes—
213C2C17×#203812yes—
214C2C17×#204011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C17#120
commutator, Frattini, cosocleC2×C42C23×C17
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
67. #10428C17direct (N × H)
147. C17#10428direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#28222
C17×#19922
C17×#18362
C2×C17×#3302
C17×#12952
#1042817