Finite Group Databasebeta

← #14534752

Subgroups — #14534752

Order 2176.

352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 133 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⋊#401C212yesmaximal
2#11762751C212yesmaximal
3#11762748C212yesmaximal
4#11762747C212yesmaximal
5#11762715C211yesmaximal, characteristic
6#11762714C211yesmaximal, characteristic
7#11762714C211yesmaximal, characteristic
8#11762708C211yesmaximal, characteristic
9#11762705C211yesmaximal, characteristic
10#11762655C211yesmaximal, characteristic
11C17×#389C211yesmaximal, characteristic
12C22×Dic34C2211yescharacteristic
13C2×C4⋊C4×C17C2211yescharacteristic
14C2×C4⋊C4×C17C2211yescharacteristic
15C2×C4⋊C4×C17C2212yes—
16C2×C42×C17C2211yescharacteristic
17C2×C4⋊Dic17C2211yescharacteristic
18C2×C4⋊Dic17C2212yes—
19C2×#63225C2212yes—
20C2×C4×Dic17C2211yescharacteristic
21C2×C4×Dic17C2211yescharacteristic
22C17×#95C2212yes—
23#10587502C2212yes—
24#10587502C2212yes—
25#10587502C2212yes—
26#10587502C2212yes—
27#10587502C2212yes—
28#10587502C2212yes—
29#10587502C2212yes—
30#10587502C2212yes—
31#10587502C2211yescharacteristic
32#10587502C2211yescharacteristic
33#10587502C2211yescharacteristic
34#10587502C2211yescharacteristic
35C22×C4×C17C2311yescharacteristic
36C22×C4×C17C2311yescharacteristic
37C22×C4×C17C2312yes—
38C22×C4×C17C2312yes—
39C22×C4×C17C2311yescharacteristic
40C22×Dic17C2312yes—
41C22×Dic17C2311yescharacteristic
42C22×Dic17C2311yescharacteristic
43C22×Dic17C2311yescharacteristic
44C22×Dic17C2311yescharacteristic
45C22×Dic17C2312yes—
46C2×Dic34—22no—
47C2×Dic34—22no—
48C2×Dic34—22no—
49C4⋊C4×C17—22no—
50C4⋊C4×C17—22no—
51C4⋊C4×C17—42no—
52C42×C17—22no—
53C4⋊Dic17—22no—
54C4⋊Dic17—42no—
55#63225—42no—
56C4×Dic17—22no—
57C4×Dic17—22no—
58C23×C17C2411yescharacteristic
59C2×C4×C17—21no—
60C2×C4×C17—21no—
61C2×C4×C17—22no—
62C2×C4×C17—22no—
63C2×C4×C17—21no—
64C2×C4×C17—22no—
65C2×C4×C17—22no—
66C2×C4×C17—21no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—22no—
70C2×C4×C17—22no—
71C2×C4×C17#4112yes—
72C2×C4×C17#4112yes—
73C2×C4×C17#4112yes—
74C2×Dic17—22no—
75C2×Dic17—22no—
76C2×Dic17—22no—
77C2×Dic17—21no—
78C2×Dic17—21no—
79C2×Dic17—21no—
80C2×Dic17—21no—
81C2×Dic17—22no—
82C2×Dic17—21no—
83C2×Dic17—22no—
84C2×Dic17—21no—
85C2×Dic17—21no—
86C2×Dic17—21no—
87C2×Dic17—22no—
88C2×Dic17—21no—
89C2×Dic17—21no—
90C2×Dic17—21no—
91C2×Dic17—21no—
92Dic34—44no—
93#2645—171nomaximal, Sylow
94C22×C17C2×#4111yescharacteristic
95C22×C17C2×#4111yescharacteristic
96C22×C17C2×#4111yescharacteristic
97C22×C17H(5,𝔽2)11yescharacteristic
98C22×C172−1+411yescharacteristic
99C22×C172−1+411yescharacteristic
100C22×C172−1+411yescharacteristic
101C4×C17—41no—
102C4×C17—42no—
103C4×C17—41no—
104C4×C17—42no—
105C4×C17#12614yes—
106Dic17—42no—
107Dic17—41no—
108Dic17—41no—
109Dic17—41no—
110Dic17—41no—
111Dic17—42no—
112#401—172no—
113#400—172no—
114#400—172no—
115#400—172no—
116#391—171no—
117#391—171no—
118#391—171no—
119#389—171no—
120#389—171no—
121#389D1711yescharacteristic
122#376—171no—
123C2×C17C2×#12611yescharacteristic
124C2×C17#54111yescharacteristic
125C2×C17#54111yescharacteristic
126C2×C17#54111yescharacteristic
127C2×C17#54211yescharacteristic
128C2×C17#54211yescharacteristic
129C2×C17#54211yescharacteristic
130C22×Q8—171no—
131C2×C4⋊C4—171no—
132C2×C4⋊C4—172no—
133C2×C4⋊C4—172no—
134C2×C4⋊C4C2×D1711yescharacteristic
135C2×C4⋊C4C2×D1711yescharacteristic
136C2×C4⋊C4C2×D1712yes—
137C2×C42—171no—
138C2×C42—171no—
139C2×C42C2×D1711yescharacteristic
140#95—171no—
141#95—171no—
142#95—171no—
143#95—171no—
144#95—172no—
145#95—172no—
146#95—172no—
147#95—172no—
148#95—172no—
149#95—172no—
150#95—172no—
151#95—172no—
152#95C2×D1712yes—
153C17#264511yescharacteristic, complemented, Sylow
154C2×Q8—342no—
155C2×Q8—342no—
156C2×Q8—342no—
157C22×C4—171no—
158C22×C4—171no—
159C22×C4—172no—
160C22×C4—171no—
161C22×C4—171no—
162C22×C4—172no—
163C22×C4C22×D1711yescharacteristic
164C22×C4C22×D1711yescharacteristic
165C22×C4C22×D1712yes—
166C22×C4C22×D1712yes—
167C22×C4C22×D1711yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—22no—
170C4⋊C4—42no—
171C4⋊C4—342no—
172C4⋊C4—682no—
173C4⋊C4—682no—
174C42—22no—
175C42—342no—
176C42—342no—
177C23C23×D1711yescharacteristic
178Q8—684no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—341no—
192C2×C4—341no—
193C2×C4—342no—
194C2×C4—342no—
195C2×C4—341no—
196C2×C4—342no—
197C2×C4—341no—
198C2×C4—341no—
199C2×C4—341no—
200C2×C4—342no—
201C2×C4—342no—
202C2×C4—341no—
203C2×C4—341no—
204C2×C4—342no—
205C2×C4—341no—
206C2×C4—341no—
207C2×C4—341no—
208C2×C4—341no—
209C2×C4#6325212yes—
210C2×C4#6325412yes—
211C2×C4#6325612yes—
212C22C2×#6325211yescharacteristic
213C22C2×#6325411yescharacteristic
214C22#1058769111yescharacteristic
215C22C2×#6325611yescharacteristic
216C22#1058769411yescharacteristic
217C22#1058769711yescharacteristic
218C22#1058769711yescharacteristic
219C4—41no—
220C4—42no—
221C4—41no—
222C4—42no—
223C4—682no—
224C4—681no—
225C4—681no—
226C4—681no—
227C4—681no—
228C4—682no—
229C4#1058758414yes—
230C2C2×#1058758411yescharacteristic
231C2#1176341711yescharacteristic
232C2#1176341911yescharacteristic
233C2#1176342211yescharacteristic
234C2#1176342411yescharacteristic
235C2#1176342611yescharacteristic
236C2#1176343311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#389C2
hypercenter#389D17
hypocenterC17#2645
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
153. C17#2645semidirect

Maximal subgroups

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

subgroupindex
C17⋊#4012
#117627512
#117627482
#117627472
#117627152
#117627142
#117627082
#117627052
#117626552
C17×#3892
#264517