Finite Group Databasebeta

← C17×#7409 #16865153

Subgroups — C17×#7409 #16865153

Order 4352.

268 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 46 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×#2007C211yesmaximal, characteristic
2C17×#1394C211yesmaximal, characteristic, complemented
3C17×#1272C211yesmaximal, characteristic, complemented
4C2×C17×#137—21no—
5C17×#537C411yescharacteristic
6C2×C17×#104—21no—
7C2×C17×#101—21no—
8C17×#391C2211yescharacteristic
9C17×#343C411yescharacteristic
10C17×#336—21no—
11C2×#41×C17—21no—
12C22×Q8×C17D411yescharacteristic
13C17×#137—42no—
14C17×#137—41no—
15C17×#137—41no—
16C2×Q16×C17—41no—
17C2×SD16×C17—41no—
18C2×M16×C17—21no—
19C2×M16×C17—41no—
20C22×C8×C17—41no—
21C17×C22⋊Q8—41no—
22C17×#121—41no—
23C17×#121—41no—
24C2×C4⋊C4×C17C2×C411yescharacteristic
25C2×C42×C17D411yescharacteristic
26C17×#104—42no—
27C17×#101—22no—
28C17×#101—41no—
29C17×#95—41no—
30#41×C17—41no—
31#41×C17—41no—
32#41×C17—41no—
33#41×C17—41no—
34C2×Q8×C17—21no—
35C2×Q8×C17—21no—
36C2×Q8×C17—41no—
37C2×Q8×C17—41no—
38C2×Q8×C17D811yescharacteristic
39C2×Q8×C17SD1611yescharacteristic
40C2×D4×C17—21no—
41C2×D4×C17—41no—
42C2×D4×C17—41no—
43C22×C4×C17—21no—
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17—41no—
47C22×C4×C17C22⋊C411yescharacteristic
48Q16×C17—42no—
49Q16×C17—42no—
50SD16×C17—42no—
51SD16×C17—42no—
52M16×C17—22no—
53M16×C17—41no—
54M16×C17—42no—
55M16×C17—81no—
56C2×C8×C17—41no—
57C2×C8×C17—42no—
58C2×C8×C17—81no—
59C2×C8×C17—81no—
60C2×C8×C17—81no—
61C4⋊C4×C17—41no—
62C4⋊C4×C17—41no—
63C22⋊C4×C17—42no—
64C42×C17—41no—
65#7409C1711yesmaximal, characteristic, direct product factor, Sylow
66C23×C17—41no—
67C23×C17#9911yescharacteristic
68Q8×C17—41no—
69Q8×C17—41no—
70Q8×C17—41no—
71Q8×C17—41no—
72Q8×C17—81no—
73D4×C17—41no—
74D4×C17—41no—
75D4×C17—81no—
76D4×C17—81no—
77D4×C17—161no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—41no—
85C2×C4×C17—41no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—81no—
91C2×C4×C17—81no—
92C2×C4×C17—81no—
93C2×C4×C17#10211yescharacteristic
94C2×C4×C17#10411yescharacteristic
95C8×C17—42no—
96C8×C17—82no—
97C8×C17—82no—
98#2007C2×C1711yescharacteristic
99#1394C2×C1711yescharacteristic, complemented
100#1272C2×C1711yescharacteristic, complemented
101C22×C17—21no—
102C22×C17—21no—
103C22×C17—81no—
104C22×C17—81no—
105C22×C17—81no—
106C22×C17#32711yescharacteristic
107C22×C17AΣL(1,𝔽16)11yescharacteristic
108C22×C17#35311yescharacteristic
109C4×C17—21no—
110C4×C17—21no—
111C4×C17—41no—
112C4×C17—41no—
113C4×C17—41no—
114C4×C17—41no—
115C4×C17—81no—
116C4×C17—81no—
117C2×#137—21no—
118#537C4×C1711yescharacteristic
119C2×#104—21no—
120C2×#101—21no—
121#391C22×C1711yescharacteristic
122#343C4×C1711yescharacteristic
123#336—21no—
124C2×C17—21no—
125C2×C17—21no—
126C2×C17—161no—
127C2×C17#134311yescharacteristic
128C2×C17#140311yescharacteristic
129C2×C17#140511yescharacteristic
130C2×#41—21no—
131C22×Q8D4×C1711yescharacteristic
132#137—42no—
133#137—41no—
134#137—41no—
135C2×Q16—41no—
136C2×SD16—41no—
137C2×M16—21no—
138C2×M16—41no—
139C22×C8—41no—
140C22⋊Q8—41no—
141#121—41no—
142#121—41no—
143C2×C4⋊C4C2×C4×C1711yescharacteristic
144C2×C42D4×C1711yescharacteristic
145#104—42no—
146#101—22no—
147#101—41no—
148#95—41no—
149C17#740911yescharacteristic, direct product factor, Sylow
150#41—41no—
151#41—41no—
152#41—41no—
153#41—41no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8D8×C1711yescharacteristic
159C2×Q8SD16×C1711yescharacteristic
160C2×D4—21no—
161C2×D4—41no—
162C2×D4—41no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—41no—
167C22×C4C22⋊C4×C1711yescharacteristic
168Q16—42no—
169Q16—42no—
170SD16—42no—
171SD16—42no—
172M16—22no—
173M16—41no—
174M16—42no—
175M16—81no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C22⋊C4—42no—
184C42—41no—
185C23—41no—
186C23C17×#9911yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—81no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196D4—161no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—81no—
212C2×C4C17×#10211yescharacteristic
213C2×C4C17×#10411yescharacteristic
214C8—42no—
215C8—82no—
216C8—82no—
217C22—21no—
218C22—21no—
219C22—81no—
220C22—81no—
221C22—81no—
222C22C17×#32711yescharacteristic
223C22C17×AΣL(1,𝔽16)11yescharacteristic
224C22C17×#35311yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—81no—
233C2—21no—
234C2—21no—
235C2—161no—
236C2C17×#134311yescharacteristic
237C2C17×#140311yescharacteristic
238C2C17×#140511yescharacteristic
subgroupG/H
center, socleC22×C17AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C17
Frattini, cosocle#391C22×C17
prime radicalC17×#537C4
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C23×C17 ◁ C22×C4×C17 ◁ C17×#391 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1394C2semidirect
3. C17×#1272C2semidirect
65. #7409C17direct (N × H)
99. #1394C2×C17semidirect
100. #1272C2×C17semidirect
149. C17#7409direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#20072
C17×#13942
C17×#12722
#740917