Finite Group Databasebeta

← C17×#10036 #16867780

Subgroups — C17×#10036 #16867780

Order 4352.

528 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3162C211yesmaximal, characteristic, complemented
2C17×#3101C212yesmaximal
3C17×#1955C211yesmaximal, characteristic
4C17×#1481C212yesmaximal, complemented
5C17×#1275C211yesmaximal, characteristic, complemented
6C17×#533C2212yes—
7C2×C4×D4×C17C2211yescharacteristic
8C17×#501—22no—
9C17×#501—22no—
10C17×#483—22no—
11C17×#476—22no—
12C17×#461—22no—
13C17×#450—22no—
14C4×SD16×C17—24no—
15C17×#431C2212yes—
16C17×#427—22no—
17C2×C17×C4⋊C8C2211yescharacteristic
18C2×C17×C22⋊C8—22no—
19C2×C17×#97C2211yescharacteristic
20C17×Q8⋊C8—24no—
21C22×D4×C17D411yescharacteristic
22C23×C4×C17—21no—
23C2×SD16×C17—24no—
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×D4×C17—22no—
34C4×D4×C17—22no—
35C17×#117—22no—
36C2×C4⋊C4×C17D411yescharacteristic
37C2×C22⋊C4×C17—21no—
38C2×C42×C17C2311yescharacteristic
39C17×#107—22no—
40C17×#107—22no—
41C17×#106—24no—
42C17×#106—24no—
43C17×C4⋊C8—22no—
44C17×C4⋊C8—22no—
45C17×#103—24no—
46C17×#102—24no—
47C17×C22⋊C8—22no—
48C17×C22⋊C8—44no—
49C17×#97—22no—
50C4×C8×C17D414yes—
51C24×C17—21no—
52C2×Q8×C17—22no—
53C2×Q8×C17—22no—
54C2×D4×C17—22no—
55C2×D4×C17—42no—
56C22×C4×C17—21no—
57C22×C4×C17—41no—
58C22×C4×C17—41no—
59C22×C4×C17—42no—
60C22×C4×C17—42no—
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×C4×C17#4111yescharacteristic
64SD16×C17—48no—
65C2×C8×C17—22no—
66C2×C8×C17—22no—
67C2×C8×C17—24no—
68C2×C8×C17—41no—
69C2×C8×C17—42no—
70C2×C8×C17SD1614yescomplemented
71C4⋊C4×C17—22no—
72C4⋊C4×C17—22no—
73C4⋊C4×C17—22no—
74C4⋊C4×C17—22no—
75C4⋊C4×C17—22no—
76C4⋊C4×C17—42no—
77C4⋊C4×C17—42no—
78C22⋊C4×C17—42no—
79C22⋊C4×C17—42no—
80C42×C17—42no—
81C42×C17C2×D412yes—
82C42×C17C2×D412yes—
83#10036C1711yesmaximal, characteristic, direct product factor, Sylow
84C23×C17—22no—
85C23×C17—41no—
86C23×C17—42no—
87C23×C17—41no—
88C23×C17—42no—
89C23×C17#12111yescharacteristic
90Q8×C17—44no—
91Q8×C17—44no—
92D4×C17—24no—
93D4×C17—42no—
94C2×C4×C17—41no—
95C2×C4×C17—41no—
96C2×C4×C17—42no—
97C2×C4×C17—42no—
98C2×C4×C17—41no—
99C2×C4×C17—42no—
100C2×C4×C17—82no—
101C2×C4×C17—81no—
102C2×C4×C17—81no—
103C2×C4×C17#12012yes—
104C2×C4×C17#12011yescharacteristic
105C2×C4×C17#12112yes—
106C2×C4×C17#12711yescharacteristic
107C2×C4×C17C2×SD1612yes—
108C2×C4×C17#13712yes—
109C8×C17—24no—
110C8×C17—44no—
111C8×C17—81no—
112#3162C2×C1711yescharacteristic, complemented
113#3101C2×C1712yes—
114#1955C2×C1711yescharacteristic
115#1481C2×C1712yescomplemented
116#1275C2×C1711yescharacteristic, complemented
117C22×C17—21no—
118C22×C17—21no—
119C22×C17—44no—
120C22×C17—42no—
121C22×C17—82no—
122C22×C17—81no—
123C22×C17—81no—
124C22×C17#39211yescharacteristic
125C22×C17#46112yes—
126C4×C17—22no—
127C4×C17—22no—
128C4×C17—82no—
129C4×C17—81no—
130C4×C17—82no—
131C4×C17#44812yes—
132C4×C17#49211yescharacteristic
133C4×C17#49711yescharacteristic
134#533C22×C1712yes—
135C2×C4×D4C22×C1711yescharacteristic
136#501—22no—
137#501—22no—
138#483—22no—
139#476—22no—
140#461—22no—
141#450—22no—
142C4×SD16—24no—
143#431C22×C1712yes—
144#427—22no—
145C2×C4⋊C8C22×C1711yescharacteristic
146C2×C22⋊C8—22no—
147C2×#97C22×C1711yescharacteristic
148Q8⋊C8—24no—
149C2×C17—22no—
150C2×C17—82no—
151C2×C17#201011yescharacteristic
152C2×C17#201311yescharacteristic
153C2×C17#201711yescharacteristic
154C22×D4D4×C1711yescharacteristic
155C23×C4—21no—
156C2×SD16—24no—
157C22×C8—21no—
158C22×C8D4×C1712yes—
159C4⋊Q8D4×C1712yes—
160C4⋊Q8D4×C1712yes—
161#125—22no—
162C22⋊Q8—22no—
163C22⋊Q8—22no—
164C4×Q8—22no—
165C4×Q8—22no—
166C4×D4—22no—
167C4×D4—22no—
168#117—22no—
169C2×C4⋊C4D4×C1711yescharacteristic
170C2×C22⋊C4—21no—
171C2×C42C23×C1711yescharacteristic
172#107—22no—
173#107—22no—
174#106—24no—
175#106—24no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178#103—24no—
179#102—24no—
180C22⋊C8—22no—
181C22⋊C8—44no—
182#97—22no—
183C4×C8D4×C1714yes—
184C17#1003611yescharacteristic, direct product factor, Sylow
185C24—21no—
186C2×Q8—22no—
187C2×Q8—22no—
188C2×D4—22no—
189C2×D4—42no—
190C22×C4—21no—
191C22×C4—41no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—41no—
195C22×C4C2×D4×C1711yescharacteristic
196C22×C4C2×D4×C1711yescharacteristic
197C22×C4#41×C1711yescharacteristic
198SD16—48no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—24no—
202C2×C8—41no—
203C2×C8—42no—
204C2×C8SD16×C1714yescomplemented
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C42—42no—
215C42C2×D4×C1712yes—
216C42C2×D4×C1712yes—
217C23—22no—
218C23—41no—
219C23—42no—
220C23—41no—
221C23—42no—
222C23C17×#12111yescharacteristic
223Q8—44no—
224Q8—44no—
225D4—24no—
226D4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—82no—
236C2×C4C17×#12012yes—
237C2×C4C17×#12011yescharacteristic
238C2×C4C17×#12112yes—
239C2×C4C17×#12711yescharacteristic
240C2×C4C2×SD16×C1712yes—
241C2×C4C17×#13712yes—
242C8—24no—
243C8—44no—
244C8—81no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—81no—
252C22C17×#39211yescharacteristic
253C22C17×#46112yes—
254C4—22no—
255C4—22no—
256C4—82no—
257C4—81no—
258C4—82no—
259C4C17×#44812yes—
260C4C17×#49211yescharacteristic
261C4C17×#49711yescharacteristic
262C2—22no—
263C2—82no—
264C2C17×#201011yescharacteristic
265C2C17×#201311yescharacteristic
266C2C17×#201711yescharacteristic
subgroupG/H
centerC2×C4×C17#127
commutator, Frattini, cosocleC2×C42C23×C17
socleC22×C17#392
prime radicalC22×D4×C17D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3162C2semidirect
4. C17×#1481C2semidirect
5. C17×#1275C2semidirect
70. C2×C8×C17SD16semidirect
83. #10036C17direct (N × H)
112. #3162C2×C17semidirect
115. #1481C2×C17semidirect
116. #1275C2×C17semidirect
184. C17#10036direct (N × H)
204. C2×C8SD16×C17semidirect

Maximal subgroups

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

subgroupindex
C17×#31622
C17×#31012
C17×#19552
C17×#14812
C17×#12752
#1003617