Finite Group Databasebeta

← C17×#13428 #16871172

Subgroups — C17×#13428 #16871172

Order 4352.

444 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2734C211yesmaximal, characteristic
2C2×C17×#356C212yesmaximal
3C17×#1886C212yesmaximal
4C17×#1857C211yesmaximal, characteristic
5C17×#1394C211yesmaximal, characteristic
6C2×C17×C4⋊Q8C2212yes—
7C17×#519C2211yescharacteristic
8C17×#428—21no—
9C17×#419—22no—
10C2×C17×#101C2212yes—
11C2×C17×#101C2211yescharacteristic
12C17×#398—21no—
13C17×#395—22no—
14C17×#391C2211yescharacteristic
15C17×#389—21no—
16C17×#387—22no—
17C17×#356—24no—
18C17×#339—21no—
19C17×#339—22no—
20C22×Q8×C17D412yes—
21C22×Q8×C17C2311yescharacteristic
22C2×M16×C17—21no—
23C2×M16×C17—22no—
24C17×C4⋊Q8—22no—
25C17×C4⋊Q8—22no—
26C17×C4⋊Q8—22no—
27C17×C4⋊Q8—22no—
28C4×Q8×C17—41no—
29C4×Q8×C17—41no—
30C17×#117—22no—
31C17×#117—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—22no—
34C2×C4⋊C4×C17—22no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17D411yescharacteristic
38C2×C42×C17D412yes—
39C2×C42×C17D411yescharacteristic
40C17×#107—41no—
41C17×#106—41no—
42C17×#103—42no—
43C17×#103—42no—
44C17×#101—21no—
45C17×#101—22no—
46C17×#101—22no—
47C17×#101D412yes—
48C17×#95—21no—
49C17×#95—22no—
50C17×#95—22no—
51C17×#95—22no—
52C2×Q8×C17—22no—
53C2×Q8×C17—22no—
54C2×Q8×C17—41no—
55C2×Q8×C17—41no—
56C2×Q8×C17—42no—
57C2×Q8×C17—42no—
58C2×Q8×C17C2×D411yescharacteristic
59C2×Q8×C17#4111yescharacteristic
60C2×Q8×C17#4112yes—
61C22×C4×C17—21no—
62C22×C4×C17—22no—
63C22×C4×C17—22no—
64C22×C4×C17—21no—
65C22×C4×C17C2×D412yes—
66C22×C4×C17C2×D411yescharacteristic
67M16×C17—22no—
68M16×C17—41no—
69M16×C17—42no—
70M16×C17—42no—
71C2×C8×C17—41no—
72C2×C8×C17—42no—
73C4⋊C4×C17—24no—
74C4⋊C4×C17—22no—
75C4⋊C4×C17—22no—
76C4⋊C4×C17—21no—
77C4⋊C4×C17—21no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—42no—
80C4⋊C4×C17—42no—
81C4⋊C4×C17—42no—
82C4⋊C4×C17—42no—
83C4⋊C4×C17—81no—
84C4⋊C4×C17—81no—
85C22⋊C4×C17—41no—
86C42×C17—22no—
87C42×C17—22no—
88C42×C17—41no—
89C42×C17—41no—
90C42×C17—42no—
91#13428C1711yesmaximal, characteristic, direct product factor, Sylow
92C23×C17#12011yescharacteristic
93Q8×C17—41no—
94Q8×C17—41no—
95Q8×C17—42no—
96Q8×C17—44no—
97Q8×C17—82no—
98C2×C4×C17—21no—
99C2×C4×C17—22no—
100C2×C4×C17—21no—
101C2×C4×C17—22no—
102C2×C4×C17—22no—
103C2×C4×C17—24no—
104C2×C4×C17—41no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17—41no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—42no—
114C2×C4×C17—42no—
115C2×C4×C17#12112yes—
116C2×C4×C17#12111yescharacteristic
117C2×C4×C17#12312yes—
118C2×C4×C17#12411yescharacteristic
119C8×C17—42no—
120C8×C17—82no—
121#2734C2×C1711yescharacteristic
122C2×#356C2×C1712yes—
123#1886C2×C1712yes—
124#1857C2×C1711yescharacteristic
125#1394C2×C1711yescharacteristic
126C22×C17—21no—
127C22×C17—21no—
128C22×C17#39411yescharacteristic
129C22×C17B(4,𝔽2)11yescharacteristic
130C22×C17#45811yescharacteristic
131C4×C17—21no—
132C4×C17—22no—
133C4×C17—22no—
134C4×C17—21no—
135C4×C17—44no—
136C4×C17—42no—
137C4×C17—81no—
138C4×C17—81no—
139C4×C17—81no—
140C4×C17—82no—
141C2×C4⋊Q8C22×C1712yes—
142#519C22×C1711yescharacteristic
143#428—21no—
144#419—22no—
145C2×#101C22×C1712yes—
146C2×#101C22×C1711yescharacteristic
147#398—21no—
148#395—22no—
149#391C22×C1711yescharacteristic
150#389—21no—
151#387—22no—
152#356—24no—
153#339—21no—
154#339—22no—
155C2×C17—21no—
156C2×C17—21no—
157C2×C17#204411yescharacteristic
158C2×C17#220311yescharacteristic
159C2×C17#220511yescharacteristic
160C22×Q8D4×C1712yes—
161C22×Q8C23×C1711yescharacteristic
162C2×M16—21no—
163C2×M16—22no—
164C4⋊Q8—22no—
165C4⋊Q8—22no—
166C4⋊Q8—22no—
167C4⋊Q8—22no—
168C4×Q8—41no—
169C4×Q8—41no—
170#117—22no—
171#117—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4D4×C1711yescharacteristic
178C2×C42D4×C1712yes—
179C2×C42D4×C1711yescharacteristic
180#107—41no—
181#106—41no—
182#103—42no—
183#103—42no—
184#101—21no—
185#101—22no—
186#101—22no—
187#101D4×C1712yes—
188#95—21no—
189#95—22no—
190#95—22no—
191#95—22no—
192C17#1342811yescharacteristic, direct product factor, Sylow
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8C2×D4×C1711yescharacteristic
200C2×Q8#41×C1711yescharacteristic
201C2×Q8#41×C1712yes—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4C2×D4×C1712yes—
207C22×C4C2×D4×C1711yescharacteristic
208M16—22no—
209M16—41no—
210M16—42no—
211M16—42no—
212C2×C8—41no—
213C2×C8—42no—
214C4⋊C4—24no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C22⋊C4—41no—
227C42—22no—
228C42—22no—
229C42—41no—
230C42—41no—
231C42—42no—
232C23C17×#12011yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—42no—
236Q8—44no—
237Q8—82no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4C17×#12112yes—
256C2×C4C17×#12111yescharacteristic
257C2×C4C17×#12312yes—
258C2×C4C17×#12411yescharacteristic
259C8—42no—
260C8—82no—
261C22—21no—
262C22—21no—
263C22C17×#39411yescharacteristic
264C22C17×B(4,𝔽2)11yescharacteristic
265C22C17×#45811yescharacteristic
266C4—21no—
267C4—22no—
268C4—22no—
269C4—21no—
270C4—44no—
271C4—42no—
272C4—81no—
273C4—81no—
274C4—81no—
275C4—82no—
276C2—21no—
277C2—21no—
278C2C17×#204411yescharacteristic
279C2C17×#220311yescharacteristic
280C2C17×#220511yescharacteristic
subgroupG/H
center, socleC22×C17B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C17
prime radicalC23×C17#120
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C23×C17 ◁ C22×Q8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
91. #13428C17direct (N × H)
192. C17#13428direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#27342
C2×C17×#3562
C17×#18862
C17×#18572
C17×#13942
#1342817