Finite Group Databasebeta

← #14534153

Subgroups — #14534153

Order 2176.

484 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 161 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
1C2×#10587573C212yesmaximal
2#11762742C212yesmaximal
3#11762739C211yesmaximal, characteristic
4#11762713C212yesmaximal
5#11762713C212yesmaximal
6#11762706C212yesmaximal
7#11762704C212yesmaximal
8#11762678C211yesmaximal, characteristic
9C17×#398C211yesmaximal, characteristic
10C22×Dic34C2212yes—
11C2×C4⋊C4×C17C2212yes—
12C2×C4⋊C4×C17C2211yescharacteristic
13C2×C4⋊C4×C17C2211yescharacteristic
14C2×C4⋊Dic17C2211yescharacteristic
15C2×C4⋊Dic17C2211yescharacteristic
16C2×#63225C2212yes—
17C2×#63225C2212yes—
18C2×#63225C2212yes—
19C2×#63225C2212yes—
20C2×#63225C2212yes—
21C2×C4×Dic17C2212yes—
22C2×C4×Dic17C2212yes—
23C2×C4×Dic17C2211yescharacteristic
24#10587573—28no—
25C17×#95C2212yes—
26C17×#95C2211yescharacteristic
27#10587502C2212yes—
28#10587502C2212yes—
29#10587502C2212yes—
30#10587502C2211yescharacteristic
31#10587502C2212yes—
32C22×C4×C17C2311yescharacteristic
33C22×C4×C17C2311yescharacteristic
34C22×C4×C17C2312yes—
35C22×C4×C17C2311yescharacteristic
36C22×C4×C17C2312yes—
37C22×Dic17C2312yes—
38C22×Dic17C2312yes—
39C22×Dic17C2312yes—
40C22×Dic17C2312yes—
41C2×Dic34—24no—
42C2×Dic34—24no—
43C2×Dic34Q818yescomplemented
44C4⋊C4×C17—24no—
45C4⋊C4×C17—41no—
46C4⋊C4×C17—41no—
47C4⋊Dic17—41no—
48C4⋊Dic17—41no—
49#63225—24no—
50#63225—24no—
51#63225—24no—
52#63225—24no—
53#63225—42no—
54C4×Dic17—24no—
55C4×Dic17—24no—
56C4×Dic17D414yes—
57C23×C17C2411yescharacteristic
58C2×C4×C17—22no—
59C2×C4×C17—22no—
60C2×C4×C17—21no—
61C2×C4×C17—21no—
62C2×C4×C17—22no—
63C2×C4×C17—22no—
64C2×C4×C17—22no—
65C2×C4×C17—21no—
66C2×C4×C17—22no—
67C2×C4×C17—21no—
68C2×C4×C17—22no—
69C2×C4×C17C2×D412yes—
70C2×C4×C17C2×Q814yes—
71C2×Dic17—22no—
72C2×Dic17—22no—
73C2×Dic17—22no—
74C2×Dic17—22no—
75C2×Dic17—22no—
76C2×Dic17—22no—
77C2×Dic17—22no—
78C2×Dic17—22no—
79C2×Dic17C2×D414yes—
80C2×Dic17C2×Q814yes—
81C2×Dic17C2×Q814yes—
82C2×Dic17#4114yes—
83Dic34—216no—
84#2582—171nomaximal, Sylow
85C22×C17C22×D411yescharacteristic
86C22×C17C22×Q812yes—
87C22×C17C2×#4112yes—
88C22×C17H(5,𝔽2)11yescharacteristic
89C22×C172−1+411yescharacteristic
90C4×C17—24no—
91C4×C17—22no—
92C4×C17—42no—
93C4×C17—41no—
94C4×C17—41no—
95Dic17—24no—
96Dic17—42no—
97Dic17—42no—
98Dic17C22⋊Q818yes—
99C2×C4×Q8—172no—
100#398—171no—
101#398—172no—
102#398D1711yescharacteristic
103#391—172no—
104#391—172no—
105#389—172no—
106#389—172no—
107#384—171no—
108C2×C17C2×C22⋊Q812yes—
109C2×C17#53711yescharacteristic
110C2×C17#55712yes—
111C2×C17Q8211yescharacteristic
112C2×C17#55911yescharacteristic
113C22×Q8—172no—
114C4×Q8—348no—
115C2×C4⋊C4—172no—
116C2×C4⋊C4—172no—
117C2×C4⋊C4—172no—
118C2×C4⋊C4—172no—
119C2×C4⋊C4—171no—
120C2×C4⋊C4—172no—
121C2×C4⋊C4—171no—
122C2×C4⋊C4C2×D1712yes—
123C2×C4⋊C4C2×D1711yescharacteristic
124C2×C4⋊C4C2×D1711yescharacteristic
125C2×C42—171no—
126C2×C42—172no—
127C2×C42—172no—
128#95—172no—
129#95—172no—
130#95—172no—
131#95—171no—
132#95—172no—
133#95C2×D1712yes—
134#95C2×D1711yescharacteristic
135C17#258211yescharacteristic, complemented, Sylow
136C2×Q8—178no—
137C2×Q8—344no—
138C2×Q8—344no—
139C22×C4—172no—
140C22×C4—172no—
141C22×C4—172no—
142C22×C4—172no—
143C22×C4C22×D1711yescharacteristic
144C22×C4C22×D1711yescharacteristic
145C22×C4C22×D1712yes—
146C22×C4C22×D1711yescharacteristic
147C22×C4C22×D1712yes—
148C4⋊C4—24no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—344no—
152C4⋊C4—344no—
153C4⋊C4—344no—
154C4⋊C4—344no—
155C4⋊C4—682no—
156C4⋊C4—681no—
157C4⋊C4—681no—
158C42—174no—
159C42—344no—
160C42—344no—
161C23C23×D1711yescharacteristic
162Q8—3416no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—174no—
175C2×C4—174no—
176C2×C4—174no—
177C2×C4—174no—
178C2×C4—342no—
179C2×C4—342no—
180C2×C4—342no—
181C2×C4—342no—
182C2×C4—342no—
183C2×C4—342no—
184C2×C4—342no—
185C2×C4—342no—
186C2×C4D4×D1712yes—
187C2×C4Q8×D1714yes—
188C22C2×D4×D1711yescharacteristic
189C22#1058769111yescharacteristic
190C22C2×Q8×D1712yes—
191C22#41×D1712yes—
192C22#1058769711yescharacteristic
193C4—24no—
194C4—22no—
195C4—41no—
196C4—41no—
197C4—42no—
198C4—178no—
199C4—344no—
200C4—682no—
201C4—682no—
202C2C22⋊Q8×D1712yes—
203C2#1176338611yescharacteristic
204C2#1176353612yes—
205C2#1176353911yescharacteristic
206C2#1176354311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#398C2
hypercenter#398D17
hypocenterC17#2582
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
43. C2×Dic34Q8semidirect
135. C17#2582semidirect

Maximal subgroups

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

subgroupindex
C2×#105875732
#117627422
#117627392
#117627132
#117627062
#117627042
#117626782
C17×#3982
#258217