Finite Group Databasebeta

← #14535734

Subgroups — #14535734

Order 2176.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10587575C212yesmaximal
2#11762743C212yesmaximal
3#11762742C212yesmaximal
4#11762740C212yesmaximal
5#11762707C211yesmaximal, characteristic
6#11762707C211yesmaximal, characteristic
7#11762704C212yesmaximal
8#11762692C212yesmaximal
9C17×#389C211yesmaximal, characteristic
10C2×C4⋊C4×C17C2211yescharacteristic
11C2×C4⋊C4×C17C2212yes—
12C2×C4⋊C4×C17C2211yescharacteristic
13C2×C42×C17C2211yescharacteristic
14C2×C4⋊Dic17C2211yescharacteristic
15C2×C4⋊Dic17C2211yescharacteristic
16C2×C4⋊Dic17C2211yescharacteristic
17C2×C4⋊Dic17C2211yescharacteristic
18C2×#63225C2212yes—
19C2×#63225C2212yes—
20C2×#63225C2212yes—
21C2×#63225C2212yes—
22C2×#63225C2212yes—
23C2×#63225C2212yes—
24C2×C4×Dic17C2212yes—
25#10587575—28no—
26C17×#95C2212yes—
27#10587502C2212yes—
28#10587502C2212yes—
29#10587502C2212yes—
30#10587502C2212yes—
31#10587502C2212yes—
32C22×C4×C17C2312yes—
33C22×C4×C17C2312yes—
34C22×C4×C17C2311yescharacteristic
35C22×C4×C17C2311yescharacteristic
36C22×C4×C17C2311yescharacteristic
37C22×Dic17C2312yes—
38C22×Dic17C2312yes—
39C22×Dic17C2312yes—
40C22×Dic17C2312yes—
41C4⋊C4×C17—24no—
42C4⋊C4×C17—22no—
43C4⋊C4×C17—41no—
44C42×C17—41no—
45C4⋊Dic17—41no—
46C4⋊Dic17—41no—
47C4⋊Dic17D414yes—
48C4⋊Dic17Q814yes—
49#63225—24no—
50#63225—24no—
51#63225—24no—
52#63225—24no—
53#63225—24no—
54#63225—42no—
55C4×Dic17—24no—
56C23×C17C2411yescharacteristic
57C2×C4×C17—21no—
58C2×C4×C17—21no—
59C2×C4×C17—21no—
60C2×C4×C17—21no—
61C2×C4×C17—21no—
62C2×C4×C17—21no—
63C2×C4×C17—22no—
64C2×C4×C17—22no—
65C2×C4×C17—22no—
66C2×C4×C17—22no—
67C2×C4×C17—22no—
68C2×C4×C17—22no—
69C2×C4×C17C2×D412yes—
70C2×C4×C17C2×Q812yes—
71C2×C4×C17#4112yes—
72C2×Dic17—22no—
73C2×Dic17—22no—
74C2×Dic17—22no—
75C2×Dic17—22no—
76C2×Dic17—22no—
77C2×Dic17—22no—
78C2×Dic17—22no—
79C2×Dic17—22no—
80C2×Dic17—22no—
81C2×Dic17—22no—
82C2×Dic17C2×D414yes—
83C2×Dic17C2×Q814yes—
84#2726—171nomaximal, Sylow
85C22×C17C22×D411yescharacteristic
86C22×C17C22×Q811yescharacteristic
87C22×C17C2×#4111yescharacteristic
88C22×C17H(5,𝔽2)11yescharacteristic
89C22×C172−1+411yescharacteristic
90C22×C172−1+411yescharacteristic
91C22×C172−1+411yescharacteristic
92C4×C17—22no—
93C4×C17—22no—
94C4×C17—22no—
95C4×C17—42no—
96C4×C17—42no—
97Dic17—24no—
98Dic17—24no—
99Dic17—42no—
100Dic17—42no—
101C2×#125—172no—
102#398—172no—
103#398—172no—
104#398—172no—
105#389—172no—
106#389—171no—
107#389—171no—
108#389D1711yescharacteristic
109#387—172no—
110C2×C17#53711yescharacteristic
111C2×C17#53911yescharacteristic
112C2×C17#54411yescharacteristic
113C2×C17#54711yescharacteristic
114C2×C17D4×Q811yescharacteristic
115C2×C17#55711yescharacteristic
116C2×C17#56411yescharacteristic
117#125—348no—
118C2×C4⋊C4—171no—
119C2×C4⋊C4—171no—
120C2×C4⋊C4—172no—
121C2×C4⋊C4—172no—
122C2×C4⋊C4—172no—
123C2×C4⋊C4—172no—
124C2×C4⋊C4—172no—
125C2×C4⋊C4—172no—
126C2×C4⋊C4—171no—
127C2×C4⋊C4—171no—
128C2×C4⋊C4C2×D1712yes—
129C2×C4⋊C4C2×D1711yescharacteristic
130C2×C4⋊C4C2×D1711yescharacteristic
131C2×C42—172no—
132C2×C42C2×D1711yescharacteristic
133#95—172no—
134#95—172no—
135#95—172no—
136#95—172no—
137#95—172no—
138#95C2×D1712yes—
139C17#272611yescharacteristic, complemented, Sylow
140C22×C4—172no—
141C22×C4—172no—
142C22×C4—172no—
143C22×C4—172no—
144C22×C4C22×D1712yes—
145C22×C4C22×D1712yes—
146C22×C4C22×D1711yescharacteristic
147C22×C4C22×D1711yescharacteristic
148C22×C4C22×D1711yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—24no—
151C4⋊C4—41no—
152C4⋊C4—174no—
153C4⋊C4—174no—
154C4⋊C4—344no—
155C4⋊C4—344no—
156C4⋊C4—344no—
157C4⋊C4—344no—
158C4⋊C4—344no—
159C4⋊C4—682no—
160C4⋊C4—681no—
161C4⋊C4—681no—
162C42—41no—
163C42—344no—
164C23C23×D1711yescharacteristic
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—174no—
178C2×C4—174no—
179C2×C4—342no—
180C2×C4—342no—
181C2×C4—342no—
182C2×C4—342no—
183C2×C4—342no—
184C2×C4—342no—
185C2×C4—342no—
186C2×C4—342no—
187C2×C4—342no—
188C2×C4—342no—
189C2×C4#6325212yes—
190C2×C4D4×D1712yes—
191C2×C4Q8×D1712yes—
192C22C2×#6325211yescharacteristic
193C22C2×D4×D1711yescharacteristic
194C22#1058769111yescharacteristic
195C22C2×Q8×D1711yescharacteristic
196C22#1058769411yescharacteristic
197C22#1058769711yescharacteristic
198C22#1058769711yescharacteristic
199C4—22no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—42no—
204C4—344no—
205C4—344no—
206C4—682no—
207C4—682no—
208C2#1176338611yescharacteristic
209C2#1176340611yescharacteristic
210C2#1176343811yescharacteristic
211C2#1176346411yescharacteristic
212C2#1176347411yescharacteristic
213C2#1176353711yescharacteristic
214C2C17⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#389C2
hypercenter#389D17
hypocenterC17#2726
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
139. C17#2726semidirect

Maximal subgroups

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

subgroupindex
C2×#105875752
#117627432
#117627422
#117627402
#117627072
#117627042
#117626922
C17×#3892
#272617