Finite Group Databasebeta

← C17×#10363 #16868107

Subgroups — C17×#10363 #16868107

Order 4352.

416 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2862C211yesmaximal, characteristic
2C17×#1994C211yesmaximal, characteristic
3C17×#1518C212yesmaximal
4C17×#1286C212yesmaximal
5C17×#1276C211yesmaximal, characteristic
6C17×#533C2211yescharacteristic
7C2×C17×C4⋊Q8—21no—
8C17×#431C2212yes—
9C17×#423C2211yescharacteristic
10C17×#391—24no—
11C17×#382—21no—
12C17×#382C2212yes—
13C43×C17C2211yescharacteristic
14C17×#339—21no—
15C17×#339—21no—
16C17×#328—24no—
17C22×Q8×C17—22no—
18C2×M16×C17—21no—
19C17×C4⋊Q8—42no—
20C17×C4⋊Q8—42no—
21C17×C4⋊Q8Q812yescomplemented
22C17×#125—21no—
23C17×C22⋊Q8—22no—
24C4×Q8×C17—22no—
25C17×#117—21no—
26C2×C4⋊C4×C17—22no—
27C2×C4⋊C4×C17—22no—
28C2×C42×C17—22no—
29C2×C42×C17D411yescharacteristic
30C2×C42×C17D411yescharacteristic
31C2×C42×C17C2311yescharacteristic
32C17×C4⋊C8—22no—
33C17×C4⋊C8—22no—
34C17×C22⋊C8—22no—
35C4×C8×C17—22no—
36C17×#95—24no—
37C17×#95—22no—
38C17×#95D414yes—
39C2×Q8×C17—22no—
40C2×Q8×C17—44no—
41C2×Q8×C17—48no—
42C22×C4×C17—21no—
43C22×C4×C17—21no—
44C22×C4×C17—24no—
45C22×C4×C17C2×D412yes—
46C22×C4×C17C2×D411yescharacteristic
47M16×C17—41no—
48M16×C17—41no—
49C2×C8×C17—41no—
50C2×C8×C17—42no—
51C4⋊C4×C17—22no—
52C4⋊C4×C17—22no—
53C4⋊C4×C17—44no—
54C4⋊C4×C17—42no—
55C4⋊C4×C17—42no—
56C4⋊C4×C17—42no—
57C22⋊C4×C17—41no—
58C42×C17—21no—
59C42×C17—21no—
60C42×C17—44no—
61C42×C17—41no—
62C42×C17SD1612yes—
63C42×C17Q1612yes—
64C42×C17C2×Q811yescharacteristic
65C42×C17#4111yescharacteristic
66C42×C17#4112yes—
67#10363C1711yesmaximal, characteristic, direct product factor, Sylow
68C23×C17#12011yescharacteristic
69Q8×C17—82no—
70Q8×C17—88no—
71C2×C4×C17—24no—
72C2×C4×C17—22no—
73C2×C4×C17—22no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17—48no—
77C2×C4×C17—42no—
78C2×C4×C17—44no—
79C2×C4×C17C22⋊Q812yes—
80C2×C4×C17C22⋊Q811yescharacteristic
81C2×C4×C17#12412yes—
82C2×C4×C17#12411yescharacteristic
83C2×C4×C17C2×SD1611yescharacteristic
84C2×C4×C17C2×Q1611yescharacteristic
85C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
86C2×C4×C17#13711yescharacteristic
87C8×C17—82no—
88C8×C17—81no—
89#2862C2×C1711yescharacteristic
90#1994C2×C1711yescharacteristic
91#1518C2×C1712yes—
92#1286C2×C1712yes—
93#1276C2×C1711yescharacteristic
94C22×C17—22no—
95C22×C17#39311yescharacteristic
96C22×C17#45011yescharacteristic
97C22×C17#45111yescharacteristic
98C4×C17—24no—
99C4×C17—22no—
100C4×C17—22no—
101C4×C17—42no—
102C4×C17—84no—
103C4×C17—82no—
104C4×C17#47511yescharacteristic
105C4×C17#47711yescharacteristic
106C4×C17#48711yescharacteristic
107C4×C17#48911yescharacteristic
108#533C22×C1711yescharacteristic
109C2×C4⋊Q8—21no—
110#431C22×C1712yes—
111#423C22×C1711yescharacteristic
112#391—24no—
113#382—21no—
114#382C22×C1712yes—
115C43C22×C1711yescharacteristic
116#339—21no—
117#339—21no—
118#328—24no—
119C2×C17—21no—
120C2×C17—21no—
121C2×C17#202411yescharacteristic
122C2×C17#203112yes—
123C22×Q8—22no—
124C2×M16—21no—
125C4⋊Q8—42no—
126C4⋊Q8—42no—
127C4⋊Q8Q8×C1712yescomplemented
128#125—21no—
129C22⋊Q8—22no—
130C4×Q8—22no—
131#117—21no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C42—22no—
135C2×C42D4×C1711yescharacteristic
136C2×C42D4×C1711yescharacteristic
137C2×C42C23×C1711yescharacteristic
138C4⋊C8—22no—
139C4⋊C8—22no—
140C22⋊C8—22no—
141C4×C8—22no—
142#95—24no—
143#95—22no—
144#95D4×C1714yes—
145C17#1036311yescharacteristic, direct product factor, Sylow
146C2×Q8—22no—
147C2×Q8—44no—
148C2×Q8—48no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—24no—
152C22×C4C2×D4×C1712yes—
153C22×C4C2×D4×C1711yescharacteristic
154M16—41no—
155M16—41no—
156C2×C8—42no—
157C2×C8—41no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—44no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C22⋊C4—41no—
165C42—21no—
166C42—21no—
167C42—44no—
168C42—41no—
169C42SD16×C1712yes—
170C42Q16×C1712yes—
171C42C2×Q8×C1711yescharacteristic
172C42#41×C1711yescharacteristic
173C42#41×C1712yes—
174C23C17×#12011yescharacteristic
175Q8—82no—
176Q8—88no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—48no—
183C2×C4—42no—
184C2×C4—44no—
185C2×C4C17×C22⋊Q812yes—
186C2×C4C17×C22⋊Q811yescharacteristic
187C2×C4C17×#12412yes—
188C2×C4C17×#12411yescharacteristic
189C2×C4C2×SD16×C1711yescharacteristic
190C2×C4C2×Q16×C1711yescharacteristic
191C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
192C2×C4C17×#13711yescharacteristic
193C8—82no—
194C8—81no—
195C22—22no—
196C22C17×#39311yescharacteristic
197C22C17×#45011yescharacteristic
198C22C17×#45111yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—84no—
204C4—82no—
205C4C17×#47511yescharacteristic
206C4C17×#47711yescharacteristic
207C4C17×#48711yescharacteristic
208C4C17×#48911yescharacteristic
209C2—21no—
210C2—21no—
211C2C17×#202411yescharacteristic
212C2C17×#203112yes—
subgroupG/H
center, socleC22×C17#393
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC23×C17#120
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
21. C17×C4⋊Q8Q8semidirect
67. #10363C17direct (N × H)
127. C4⋊Q8Q8×C17semidirect
145. C17#10363direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#28622
C17×#19942
C17×#15182
C17×#12862
C17×#12762
#1036317