Finite Group Databasebeta

← C17×#13302 #16871046

Subgroups — C17×#13302 #16871046

Order 4352.

420 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2567C211yesmaximal, characteristic
2C17×#1801C211yesmaximal, characteristic
3C4×C17×#101C211yesmaximal, characteristic
4C17×#1394C214yesmaximal
5C2×C17×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C17C2211yescharacteristic
7C17×#423—21no—
8C2×C17×#101C2212yes—
9C2×C17×#101C2212yes—
10C4×M16×C17—21no—
11C17×#395—21no—
12C17×#395—21no—
13C17×#391C2212yes—
14C17×#389—21no—
15C17×#389—21no—
16C17×#384C412yes—
17C4×C4⋊C4×C17C411yescharacteristic
18C17×#343—21no—
19C17×#343—21no—
20C22×Q8×C17—21no—
21C22×Q8×C17C2311yescharacteristic
22C2×M16×C17—22no—
23C2×M16×C17—22no—
24C17×C4⋊Q8—41no—
25C17×C4⋊Q8—41no—
26C4×Q8×C17—41no—
27C4×Q8×C17—41no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—22no—
31C2×C4⋊C4×C17—22no—
32C2×C4⋊C4×C17C2×C412yes—
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C4⋊C4×C17D411yescharacteristic
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C42×C17C2×C411yescharacteristic
37C2×C42×C17C2×C412yes—
38C2×C42×C17D411yescharacteristic
39C2×C42×C17D411yescharacteristic
40C17×C4⋊C8—41no—
41C17×C4⋊C8—41no—
42C17×#101—22no—
43C17×#101—24no—
44C17×#101Q814yescomplemented
45C17×#97—41no—
46C4×C8×C17—41no—
47C17×#95—21no—
48C17×#95—22no—
49C17×#95—22no—
50C2×Q8×C17—41no—
51C2×Q8×C17—41no—
52C2×Q8×C17—42no—
53C2×Q8×C17—82no—
54C2×Q8×C17C2×Q812yes—
55C2×Q8×C17#4112yes—
56C22×C4×C17—22no—
57C22×C4×C17—22no—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22×C411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17C2×D411yescharacteristic
65M16×C17—24no—
66M16×C17—42no—
67M16×C17—42no—
68M16×C17—42no—
69C2×C8×C17—42no—
70C2×C8×C17—42no—
71C4⋊C4×C17—24no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—42no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—82no—
79C4⋊C4×C17—82no—
80C42×C17—21no—
81C42×C17—21no—
82C42×C17—21no—
83C42×C17—21no—
84C42×C17—21no—
85C42×C17—21no—
86C42×C17—42no—
87#13302C1711yesmaximal, characteristic, direct product factor, Sylow
88C23×C17C2×C22⋊C411yescharacteristic
89Q8×C17—42no—
90Q8×C17—42no—
91Q8×C17—84no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—22no—
99C2×C4×C17—24no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—42no—
104C2×C4×C17—42no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—42no—
111C2×C4×C17#9911yescharacteristic
112C2×C4×C17#9911yescharacteristic
113C2×C4×C17C4×Q812yes—
114C2×C4×C17C22⋊Q812yes—
115C2×C4×C17#12411yescharacteristic
116C2×C4×C17C4⋊Q811yescharacteristic
117C8×C17—44no—
118C8×C17—82no—
119#2567C2×C1711yescharacteristic
120#1801C2×C1711yescharacteristic
121C4×#101C2×C1711yescharacteristic
122#1394C2×C1714yes—
123C22×C17—21no—
124C22×C17—21no—
125C22×C17#39111yescharacteristic
126C22×C17C2×#9911yescharacteristic
127C22×C17#41011yescharacteristic
128C4×C17—21no—
129C4×C17—22no—
130C4×C17—21no—
131C4×C17—22no—
132C4×C17—21no—
133C4×C17—44no—
134C4×C17—41no—
135C4×C17—41no—
136C4×C17—41no—
137C4×C17—82no—
138C4×C17#35612yes—
139C2×C4⋊Q8C4×C1711yescharacteristic
140C2×C4×Q8C22×C1711yescharacteristic
141#423—21no—
142C2×#101C22×C1712yes—
143C2×#101C22×C1712yes—
144C4×M16—21no—
145#395—21no—
146#395—21no—
147#391C22×C1712yes—
148#389—21no—
149#389—21no—
150#384C4×C1712yes—
151C4×C4⋊C4C4×C1711yescharacteristic
152#343—21no—
153#343—21no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17#199611yescharacteristic
157C2×C17C2×#35611yescharacteristic
158C2×C17#213411yescharacteristic
159C22×Q8—21no—
160C22×Q8C23×C1711yescharacteristic
161C2×M16—22no—
162C2×M16—22no—
163C4⋊Q8—41no—
164C4⋊Q8—41no—
165C4×Q8—41no—
166C4×Q8—41no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4C2×C4×C1712yes—
172C2×C4⋊C4C2×C4×C1711yescharacteristic
173C2×C4⋊C4D4×C1711yescharacteristic
174C2×C4⋊C4D4×C1711yescharacteristic
175C2×C42C2×C4×C1711yescharacteristic
176C2×C42C2×C4×C1712yes—
177C2×C42D4×C1711yescharacteristic
178C2×C42D4×C1711yescharacteristic
179C4⋊C8—41no—
180C4⋊C8—41no—
181#101—22no—
182#101—24no—
183#101Q8×C1714yescomplemented
184#97—41no—
185C4×C8—41no—
186#95—21no—
187#95—22no—
188#95—22no—
189C17#1330211yescharacteristic, direct product factor, Sylow
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—42no—
193C2×Q8—82no—
194C2×Q8C2×Q8×C1712yes—
195C2×Q8#41×C1712yes—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4C22⋊C4×C1711yescharacteristic
199C22×C4C22⋊C4×C1711yescharacteristic
200C22×C4C22⋊C4×C1711yescharacteristic
201C22×C4C22⋊C4×C1711yescharacteristic
202C22×C4C22×C4×C1711yescharacteristic
203C22×C4C2×D4×C1711yescharacteristic
204C22×C4C2×D4×C1711yescharacteristic
205M16—24no—
206M16—42no—
207M16—42no—
208M16—42no—
209C2×C8—42no—
210C2×C8—42no—
211C4⋊C4—24no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—82no—
219C4⋊C4—82no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—42no—
227C23C2×C22⋊C4×C1711yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—84no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4C17×#9911yescharacteristic
251C2×C4C17×#9911yescharacteristic
252C2×C4C4×Q8×C1712yes—
253C2×C4C17×C22⋊Q812yes—
254C2×C4C17×#12411yescharacteristic
255C2×C4C17×C4⋊Q811yescharacteristic
256C8—44no—
257C8—82no—
258C22—21no—
259C22—21no—
260C22C17×#39111yescharacteristic
261C22C2×C17×#9911yescharacteristic
262C22C17×#41011yescharacteristic
263C4—22no—
264C4—21no—
265C4—21no—
266C4—22no—
267C4—21no—
268C4—44no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4C17×#35612yes—
274C2—21no—
275C2—21no—
276C2C17×#199611yescharacteristic
277C2C2×C17×#35611yescharacteristic
278C2C17×#213411yescharacteristic
subgroupG/H
center, socleC22×C17C2×#99
commutatorC22×C4C22×C4×C17
Frattini, cosocleC22×Q8C23×C17
prime radicalC23×C17C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×Q8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
44. C17×#101Q8semidirect
87. #13302C17direct (N × H)
183. #101Q8×C17semidirect
189. C17#13302direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#25672
C17×#18012
C4×C17×#1012
C17×#13942
#1330217