Finite Group Databasebeta

← C17×#10031 #16867775

Subgroups — C17×#10031 #16867775

Order 4352.

468 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3249C211yesmaximal, characteristic
2C17×#3113C212yesmaximal
3C17×#1985C211yesmaximal, characteristic
4C17×#1531C212yesmaximal
5C17×#1290C211yesmaximal, characteristic
6C17×#533C2212yes—
7C2×C4×Q8×C17C2211yescharacteristic
8C17×#483—22no—
9C17×#477—22no—
10C17×#475—22no—
11C17×#467—22no—
12C17×#462—22no—
13C17×#462—22no—
14C17×#451—22no—
15C17×#441—24no—
16C17×#432C2212yes—
17C2×C17×C4⋊C8C2211yescharacteristic
18C2×C17×#97C2211yescharacteristic
19C17×#336—22no—
20C17×#330—24no—
21C22×Q8×C17D411yescharacteristic
22C2×Q16×C17—24no—
23C2×Q16×C17—22no—
24C22×C8×C17—21no—
25C22×C8×C17D412yes—
26C17×C4⋊Q8D412yes—
27C17×C4⋊Q8D412yes—
28C17×#125—22no—
29C17×C22⋊Q8—22no—
30C17×C22⋊Q8—22no—
31C4×Q8×C17—22no—
32C4×Q8×C17—22no—
33C4×Q8×C17—22no—
34C4×Q8×C17—22no—
35C17×#117—22no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17D411yescharacteristic
38C2×C42×C17—21no—
39C2×C42×C17C2311yescharacteristic
40C17×#107—22no—
41C17×#106—24no—
42C17×C4⋊C8—22no—
43C17×C4⋊C8—22no—
44C17×#103—24no—
45C17×#103—24no—
46C17×#103—24no—
47C17×C22⋊C8—22no—
48C17×#97—22no—
49C17×#97D414yes—
50C2×Q8×C17—22no—
51C2×Q8×C17—22no—
52C2×Q8×C17—22no—
53C2×Q8×C17—42no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17C2×D411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17#4111yescharacteristic
59Q16×C17—48no—
60Q16×C17—82no—
61C2×C8×C17—22no—
62C2×C8×C17—22no—
63C2×C8×C17—24no—
64C2×C8×C17—41no—
65C2×C8×C17—41no—
66C2×C8×C17—42no—
67C4⋊C4×C17—22no—
68C4⋊C4×C17—22no—
69C4⋊C4×C17—22no—
70C4⋊C4×C17—22no—
71C4⋊C4×C17—22no—
72C4⋊C4×C17—42no—
73C4⋊C4×C17—42no—
74C4⋊C4×C17—42no—
75C22⋊C4×C17—42no—
76C42×C17—41no—
77C42×C17—42no—
78C42×C17—41no—
79C42×C17C2×D412yes—
80C42×C17C2×D412yes—
81#10031C1711yesmaximal, characteristic, direct product factor, Sylow
82C23×C17#12111yescharacteristic
83Q8×C17—24no—
84Q8×C17—42no—
85Q8×C17—44no—
86Q8×C17—42no—
87Q8×C17—42no—
88C2×C4×C17—22no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—22no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—41no—
96C2×C4×C17—42no—
97C2×C4×C17—42no—
98C2×C4×C17—42no—
99C2×C4×C17#12012yes—
100C2×C4×C17#12011yescharacteristic
101C2×C4×C17#12112yes—
102C2×C4×C17#12711yescharacteristic
103C8×C17—42no—
104C8×C17—44no—
105C8×C17—42no—
106#3249C2×C1711yescharacteristic
107#3113C2×C1712yes—
108#1985C2×C1711yescharacteristic
109#1531C2×C1712yes—
110#1290C2×C1711yescharacteristic
111C22×C17—21no—
112C22×C17—21no—
113C22×C17#39211yescharacteristic
114C22×C17#47312yes—
115C4×C17—21no—
116C4×C17—22no—
117C4×C17—22no—
118C4×C17—42no—
119C4×C17—82no—
120C4×C17—82no—
121C4×C17—81no—
122C4×C17#45511yescharacteristic
123C4×C17#45611yescharacteristic
124#533C22×C1712yes—
125C2×C4×Q8C22×C1711yescharacteristic
126#483—22no—
127#477—22no—
128#475—22no—
129#467—22no—
130#462—22no—
131#462—22no—
132#451—22no—
133#441—24no—
134#432C22×C1712yes—
135C2×C4⋊C8C22×C1711yescharacteristic
136C2×#97C22×C1711yescharacteristic
137#336—22no—
138#330—24no—
139C2×C17—22no—
140C2×C17#200711yescharacteristic
141C2×C17#201011yescharacteristic
142C2×C17#202011yescharacteristic
143C22×Q8D4×C1711yescharacteristic
144C2×Q16—24no—
145C2×Q16—22no—
146C22×C8—21no—
147C22×C8D4×C1712yes—
148C4⋊Q8D4×C1712yes—
149C4⋊Q8D4×C1712yes—
150#125—22no—
151C22⋊Q8—22no—
152C22⋊Q8—22no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157#117—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4D4×C1711yescharacteristic
160C2×C42—21no—
161C2×C42C23×C1711yescharacteristic
162#107—22no—
163#106—24no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166#103—24no—
167#103—24no—
168#103—24no—
169C22⋊C8—22no—
170#97—22no—
171#97D4×C1714yes—
172C17#1003111yescharacteristic, direct product factor, Sylow
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—42no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4C2×D4×C1711yescharacteristic
180C22×C4C2×D4×C1711yescharacteristic
181C22×C4#41×C1711yescharacteristic
182Q16—48no—
183Q16—82no—
184C2×C8—22no—
185C2×C8—24no—
186C2×C8—22no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—42no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C22⋊C4—42no—
199C42—41no—
200C42—41no—
201C42—42no—
202C42C2×D4×C1712yes—
203C42C2×D4×C1712yes—
204C23C17×#12111yescharacteristic
205Q8—24no—
206Q8—42no—
207Q8—44no—
208Q8—42no—
209Q8—42no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4C17×#12012yes—
222C2×C4C17×#12011yescharacteristic
223C2×C4C17×#12112yes—
224C2×C4C17×#12711yescharacteristic
225C8—42no—
226C8—44no—
227C8—42no—
228C22—21no—
229C22—21no—
230C22C17×#39211yescharacteristic
231C22C17×#47312yes—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—82no—
237C4—82no—
238C4—81no—
239C4C17×#45511yescharacteristic
240C4C17×#45611yescharacteristic
241C2—22no—
242C2C17×#200711yescharacteristic
243C2C17×#201011yescharacteristic
244C2C17×#202011yescharacteristic
subgroupG/H
center, socleC22×C17#392
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC23×C17#121
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
81. #10031C17direct (N × H)
172. C17#10031direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#32492
C17×#31132
C17×#19852
C17×#15312
C17×#12902
#1003117