Finite Group Databasebeta

← #14536274

Subgroups — #14536274

Order 2176.

344 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#11762751C212yesmaximal
2#11762748C211yesmaximal, characteristic
3#11762743C212yesmaximal
4#11762739C211yesmaximal, characteristic
5#11762704C212yesmaximal
6#11762693C212yesmaximal
7#11762691C212yesmaximal
8#11762676C212yesmaximal
9C17×#382C211yesmaximal, characteristic
10C2×C4⋊C4×C17C2211yescharacteristic
11C2×C4⋊C4×C17C2211yescharacteristic
12C2×C42×C17C2211yescharacteristic
13C2×C4⋊Dic17C2211yescharacteristic
14C2×C4⋊Dic17C2211yescharacteristic
15C2×#63225C2212yes—
16C2×#63225C2212yes—
17C2×#63225C2212yes—
18C2×#63225C2212yes—
19C2×C4×Dic17C2212yes—
20C17×#95C2212yes—
21C17×#95C2212yes—
22#10587502C2211yescharacteristic
23#10587502C2212yes—
24#10587502C2212yes—
25#10587502C2212yes—
26#10587502C2212yes—
27#10587502C2212yes—
28#10587502C2212yes—
29#10587502C2212yes—
30#10587502C2211yescharacteristic
31C22×C4×C17C2312yes—
32C22×C4×C17C2311yescharacteristic
33C22×C4×C17C2311yescharacteristic
34C22×C4×C17C2312yes—
35C22×C4×C17C2311yescharacteristic
36C22×Dic17C2312yes—
37C22×Dic17C2312yes—
38C22×Dic17C2312yes—
39C22×Dic17C2312yes—
40C4⋊C4×C17—41no—
41C4⋊C4×C17—41no—
42C42×C17—22no—
43C4⋊Dic17—41no—
44C4⋊Dic17—41no—
45#63225—24no—
46#63225—24no—
47#63225—24no—
48#63225—42no—
49C4×Dic17—24no—
50C23×C17C2411yescharacteristic
51C2×C4×C17—21no—
52C2×C4×C17—21no—
53C2×C4×C17—22no—
54C2×C4×C17—22no—
55C2×C4×C17—22no—
56C2×C4×C17—22no—
57C2×C4×C17—22no—
58C2×C4×C17—21no—
59C2×C4×C17—21no—
60C2×C4×C17—22no—
61C2×C4×C17—22no—
62C2×C4×C17—22no—
63C2×C4×C17#4112yes—
64C2×Dic17—22no—
65C2×Dic17—22no—
66C2×Dic17—22no—
67C2×Dic17—22no—
68C2×Dic17—22no—
69C2×Dic17—22no—
70C2×Dic17—22no—
71C2×Dic17—22no—
72C2×Dic17—22no—
73C2×Dic17—22no—
74C2×Dic17—22no—
75C2×Dic17#4114yes—
76#2769—171nomaximal, Sylow
77C22×C17C2×#4111yescharacteristic
78C22×C17C2×#4112yes—
79C22×C17H(5,𝔽2)11yescharacteristic
80C22×C172−1+411yescharacteristic
81C22×C172−1+412yes—
82C4×C17—22no—
83C4×C17—42no—
84C4×C17—42no—
85C4×C17—41no—
86C4×C17—41no—
87Dic17—24no—
88Dic17—42no—
89Dic17—42no—
90Dic17—42no—
91#400—171no—
92#400—172no—
93#398—171no—
94#398—172no—
95#389—172no—
96#387—172no—
97#387—172no—
98#383—172no—
99#382D1711yescharacteristic
100C2×C17#53911yescharacteristic
101C2×C17#54112yes—
102C2×C17#55212yes—
103C2×C17#55511yescharacteristic
104C2×C17#56311yescharacteristic
105C2×C4⋊C4—172no—
106C2×C4⋊C4—172no—
107C2×C4⋊C4—172no—
108C2×C4⋊C4—172no—
109C2×C4⋊C4—171no—
110C2×C4⋊C4—171no—
111C2×C4⋊C4C2×D1711yescharacteristic
112C2×C4⋊C4C2×D1711yescharacteristic
113C2×C42—172no—
114C2×C42C2×D1711yescharacteristic
115#95—171no—
116#95—172no—
117#95—172no—
118#95—172no—
119#95—172no—
120#95—171no—
121#95—172no—
122#95—172no—
123#95—172no—
124#95C2×D1712yes—
125#95C2×D1712yes—
126C17#276911yescharacteristic, complemented, Sylow
127C22×C4—172no—
128C22×C4—172no—
129C22×C4—172no—
130C22×C4—172no—
131C22×C4C22×D1712yes—
132C22×C4C22×D1711yescharacteristic
133C22×C4C22×D1711yescharacteristic
134C22×C4C22×D1712yes—
135C22×C4C22×D1711yescharacteristic
136C4⋊C4—41no—
137C4⋊C4—41no—
138C4⋊C4—344no—
139C4⋊C4—344no—
140C4⋊C4—344no—
141C4⋊C4—682no—
142C4⋊C4—681no—
143C4⋊C4—681no—
144C42—22no—
145C42—344no—
146C23C23×D1711yescharacteristic
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—174no—
160C2×C4—342no—
161C2×C4—342no—
162C2×C4—342no—
163C2×C4—342no—
164C2×C4—342no—
165C2×C4—342no—
166C2×C4—342no—
167C2×C4—342no—
168C2×C4—342no—
169C2×C4—342no—
170C2×C4—342no—
171C2×C4#6325212yes—
172C22C2×#6325211yescharacteristic
173C22#1058769111yescharacteristic
174C22#1058769411yescharacteristic
175C22#41×D1712yes—
176C22#1058769712yes—
177C4—22no—
178C4—42no—
179C4—42no—
180C4—41no—
181C4—41no—
182C4—344no—
183C4—682no—
184C4—682no—
185C4—682no—
186C2#1176340611yescharacteristic
187C2#1176341812yes—
188C2#1176349812yes—
189C2#1176352111yescharacteristic
190C2#1176355911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#382C2
hypercenter#382D17
hypocenterC17#2769
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
126. C17#2769semidirect

Maximal subgroups

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

subgroupindex
#117627512
#117627482
#117627432
#117627392
#117627042
#117626932
#117626912
#117626762
C17×#3822
#276917