Finite Group Databasebeta

← C17×#10359 #16868103

Subgroups — C17×#10359 #16868103

Order 4352.

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

normal subgroups only

This group has 400 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×#2844C211yesmaximal, characteristic
2C17×#1993C212yesmaximal
3C17×#1960C211yesmaximal, characteristic
4C17×#1295C211yesmaximal, characteristic
5C17×#1295C212yesmaximal
6C2×C17×C4⋊Q8C2211yescharacteristic
7C2×C17×#103—21no—
8C2×C17×#103—21no—
9C2×C17×#97C2211yescharacteristic
10C2×C17×#97C2212yes—
11C17×#400—22no—
12C17×#400—21no—
13C17×#395—22no—
14C17×#395—21no—
15C17×#382C2211yescharacteristic
16C17×#382C2212yes—
17C17×#340—22no—
18C17×#340—22no—
19C22×Q8×C17—21no—
20C22×Q8×C17—21no—
21C22×C8×C17—22no—
22C22×C8×C17—21no—
23C17×C4⋊Q8—22no—
24C17×C4⋊Q8—21no—
25C17×C4⋊Q8Q812yescomplemented
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×C17D411yescharacteristic
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C42×C17C2311yescharacteristic
34C17×#103—42no—
35C17×#103—42no—
36C17×#97—22no—
37C17×#97—22no—
38C17×#97—22no—
39C17×#95—21no—
40C17×#95—22no—
41C17×#95—21no—
42C17×#95—22no—
43C17×#95—22no—
44C17×#95—22no—
45C2×Q8×C17—22no—
46C2×Q8×C17—41no—
47C2×Q8×C17—41no—
48C2×Q8×C17—41no—
49C2×Q8×C17—41no—
50C2×Q8×C17—41no—
51C2×Q8×C17—81no—
52C2×Q8×C17—82no—
53C22×C4×C17—21no—
54C22×C4×C17—22no—
55C22×C4×C17—21no—
56C22×C4×C17—22no—
57C22×C4×C17—41no—
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D412yes—
60C2×C8×C17—24no—
61C2×C8×C17—22no—
62C2×C8×C17—41no—
63C2×C8×C17—42no—
64C2×C8×C17—42no—
65C2×C8×C17—41no—
66C4⋊C4×C17—24no—
67C4⋊C4×C17—41no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—42no—
70C4⋊C4×C17—42no—
71C4⋊C4×C17—42no—
72C4⋊C4×C17—81no—
73C4⋊C4×C17—82no—
74C42×C17C2×Q811yescharacteristic
75C42×C17#4112yes—
76C42×C17#4111yescharacteristic
77#10359C1711yesmaximal, characteristic, direct product factor, Sylow
78C23×C17#12011yescharacteristic
79Q8×C17—42no—
80Q8×C17—42no—
81Q8×C17—81no—
82Q8×C17—81no—
83Q8×C17—84no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—22no—
87C2×C4×C17—22no—
88C2×C4×C17—42no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17—42no—
94C2×C4×C17—42no—
95C2×C4×C17—42no—
96C2×C4×C17—42no—
97C2×C4×C17—42no—
98C2×C4×C17—42no—
99C2×C4×C17—81no—
100C2×C4×C17—81no—
101C2×C4×C17C22⋊Q812yes—
102C2×C4×C17C22⋊Q811yescharacteristic
103C2×C4×C17#12412yes—
104C2×C4×C17#12411yescharacteristic
105C8×C17—42no—
106C8×C17—44no—
107#2844C2×C1711yescharacteristic
108#1993C2×C1712yes—
109#1960C2×C1711yescharacteristic
110#1295C2×C1711yescharacteristic
111#1295C2×C1712yes—
112C22×C17#39311yescharacteristic
113C22×C17#45311yescharacteristic
114C22×C17#45411yescharacteristic
115C22×C17#45512yes—
116C22×C17#45612yes—
117C4×C17—21no—
118C4×C17—21no—
119C4×C17—22no—
120C4×C17—22no—
121C4×C17—81no—
122C4×C17—82no—
123C4×C17—81no—
124C4×C17—82no—
125C4×C17—82no—
126C2×C4⋊Q8C22×C1711yescharacteristic
127C2×#103—21no—
128C2×#103—21no—
129C2×#97C22×C1711yescharacteristic
130C2×#97C22×C1712yes—
131#400—22no—
132#400—21no—
133#395—22no—
134#395—21no—
135#382C22×C1711yescharacteristic
136#382C22×C1712yes—
137#340—22no—
138#340—22no—
139C2×C17#165911yescharacteristic
140C2×C17#166011yescharacteristic
141C2×C17#166412yes—
142C2×C17#202711yescharacteristic
143C2×C17#202812yes—
144C22×Q8—21no—
145C22×Q8—21no—
146C22×C8—22no—
147C22×C8—21no—
148C4⋊Q8—22no—
149C4⋊Q8—21no—
150C4⋊Q8Q8×C1712yescomplemented
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4D4×C1712yes—
155C2×C4⋊C4D4×C1712yes—
156C2×C4⋊C4D4×C1711yescharacteristic
157C2×C4⋊C4D4×C1711yescharacteristic
158C2×C42C23×C1711yescharacteristic
159#103—42no—
160#103—42no—
161#97—22no—
162#97—22no—
163#97—22no—
164#95—22no—
165#95—21no—
166#95—21no—
167#95—22no—
168#95—22no—
169#95—22no—
170C17#1035911yescharacteristic, direct product factor, Sylow
171C2×Q8—22no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—81no—
178C2×Q8—82no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—41no—
184C22×C4C2×D4×C1712yes—
185C22×C4C2×D4×C1711yescharacteristic
186C2×C8—22no—
187C2×C8—24no—
188C2×C8—41no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—41no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—81no—
199C4⋊C4—82no—
200C42C2×Q8×C1711yescharacteristic
201C42#41×C1712yes—
202C42#41×C1711yescharacteristic
203C23C17×#12011yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—81no—
207Q8—81no—
208Q8—84no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4C17×C22⋊Q812yes—
227C2×C4C17×C22⋊Q811yescharacteristic
228C2×C4C17×#12412yes—
229C2×C4C17×#12411yescharacteristic
230C8—42no—
231C8—44no—
232C22C17×#39311yescharacteristic
233C22C17×#45311yescharacteristic
234C22C17×#45411yescharacteristic
235C22C17×#45512yes—
236C22C17×#45612yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—82no—
242C4—81no—
243C4—82no—
244C4—81no—
245C4—82no—
246C2C17×#165911yescharacteristic
247C2C17×#166011yescharacteristic
248C2C17×#166412yes—
249C2C17×#202711yescharacteristic
250C2C17×#202812yes—
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
25. C17×C4⋊Q8Q8semidirect
77. #10359C17direct (N × H)
150. C4⋊Q8Q8×C17semidirect
170. C17#10359direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#28442
C17×#19932
C17×#19602
C17×#12952
#1035917