Finite Group Databasebeta

← #14533974

Subgroups — #14533974

Order 2176.

452 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 153 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×#10587576C211yesmaximal, characteristic
2C2×#10587573C211yesmaximal, characteristic
3#11762743C214yesmaximal
4#11762715C211yesmaximal, characteristic
5#11762714C211yesmaximal, characteristic
6#11762691C214yesmaximal
7#11762678C211yesmaximal, characteristic
8C4×#63225C211yesmaximal, characteristic
9C17×#382C211yesmaximal, characteristic
10C22×Dic34C2211yescharacteristic
11C2×C4⋊C4×C17C2211yescharacteristic
12C2×C4⋊C4×C17C2211yescharacteristic
13C2×C42×C17C2211yescharacteristic
14C2×C4⋊Dic17C2211yescharacteristic
15C2×C4⋊Dic17C2212yes—
16C2×#63225C2212yes—
17C2×#63225C2214yes—
18C2×#63225C2212yes—
19C2×#63225C2212yes—
20C2×C4×Dic17C2212yes—
21C2×C4×Dic17C2211yescharacteristic
22C2×C4×Dic17C2211yescharacteristic
23#10587576—24no—
24#10587573—24no—
25C17×#95C2214yes—
26#10587502C2212yes—
27#10587502C2214yes—
28#10587502C2214yes—
29C22×C4×C17C2312yes—
30C22×C4×C17C2312yes—
31C22×C4×C17C2312yes—
32C22×C4×C17C2311yescharacteristic
33C22×Dic17C2312yes—
34C22×Dic17C2311yescharacteristic
35C22×Dic17C2311yescharacteristic
36C22×Dic17C2312yes—
37C22×Dic17C2312yes—
38C2×Dic34—22no—
39C2×Dic34—22no—
40C2×Dic34Q814yes—
41C4⋊C4×C17—22no—
42C4⋊C4×C17—22no—
43C42×C17—22no—
44C4⋊Dic17—22no—
45C4⋊Dic17—24no—
46#63225—24no—
47#63225—24no—
48#63225—24no—
49#63225—28no—
50C4×Dic17—22no—
51C4×Dic17—24no—
52C4×Dic17D414yes—
53C23×C17C2411yescharacteristic
54C2×C4×C17—22no—
55C2×C4×C17—22no—
56C2×C4×C17—22no—
57C2×C4×C17—24no—
58C2×C4×C17—22no—
59C2×C4×C17—24no—
60C2×C4×C17—22no—
61C2×C4×C17C2×D412yes—
62C2×C4×C17C2×Q812yes—
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—24no—
72C2×Dic17C2×D412yes—
73C2×Dic17C2×D412yes—
74C2×Dic17C2×Q814yes—
75C2×Dic17#4114yes—
76Dic34—28no—
77#2565—171nomaximal, Sylow
78C22×C17C22×D411yescharacteristic
79C22×C17C22×Q811yescharacteristic
80C22×C17C2×#4111yescharacteristic
81C22×C17C2×#4112yes—
82C22×C172−1+412yes—
83C4×C17—42no—
84C4×C17—42no—
85C4×C17—42no—
86C4×C17C22⋊Q814yes—
87Dic17—24no—
88Dic17—22no—
89Dic17—22no—
90Dic17—24no—
91Dic17—42no—
92C2×#125—171no—
93C2×C4×Q8—171no—
94#398—174no—
95#391—171no—
96#391—171no—
97#387—174no—
98#384—171no—
99#382D1711yescharacteristic
100C4×C4⋊C4—171no—
101C2×C17C2×C22⋊Q811yescharacteristic
102C2×C17#53211yescharacteristic
103C2×C17#53611yescharacteristic
104C2×C17#55212yes—
105C2×C17#55712yes—
106C22×Q8—171no—
107#125—344no—
108C4×Q8—344no—
109C2×C4⋊C4—172no—
110C2×C4⋊C4—171no—
111C2×C4⋊C4—172no—
112C2×C4⋊C4—172no—
113C2×C4⋊C4—172no—
114C2×C4⋊C4—174no—
115C2×C4⋊C4C2×D1711yescharacteristic
116C2×C4⋊C4C2×D1711yescharacteristic
117C2×C42—171no—
118C2×C42—172no—
119C2×C42—171no—
120C2×C42C2×D1711yescharacteristic
121#95—172no—
122#95—174no—
123#95—174no—
124#95C2×D1714yes—
125C17#256511yescharacteristic, complemented, Sylow
126C2×Q8—174no—
127C2×Q8—342no—
128C2×Q8—342no—
129C22×C4—172no—
130C22×C4—172no—
131C22×C4—171no—
132C22×C4—171no—
133C22×C4—172no—
134C22×C4C22×D1712yes—
135C22×C4C22×D1712yes—
136C22×C4C22×D1712yes—
137C22×C4C22×D1711yescharacteristic
138C4⋊C4—22no—
139C4⋊C4—22no—
140C4⋊C4—344no—
141C4⋊C4—344no—
142C4⋊C4—344no—
143C4⋊C4—344no—
144C4⋊C4—348no—
145C4⋊C4—342no—
146C42—22no—
147C42—174no—
148C42—344no—
149C42—342no—
150C23C23×D1711yescharacteristic
151Q8—348no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—172no—
160C2×C4—172no—
161C2×C4—174no—
162C2×C4—174no—
163C2×C4—342no—
164C2×C4—342no—
165C2×C4—342no—
166C2×C4—342no—
167C2×C4—342no—
168C2×C4—342no—
169C2×C4—342no—
170C2×C4—344no—
171C2×C4#6325212yes—
172C2×C4D4×D1712yes—
173C2×C4Q8×D1712yes—
174C22C2×#6325211yescharacteristic
175C22C2×D4×D1711yescharacteristic
176C22C2×Q8×D1711yescharacteristic
177C22#41×D1712yes—
178C22#1058769712yes—
179C4—42no—
180C4—42no—
181C4—42no—
182C4—344no—
183C4—344no—
184C4—342no—
185C4—342no—
186C4—682no—
187C4#1058758214yes—
188C2C2×#1058758211yescharacteristic
189C2#1176335811yescharacteristic
190C2#1176337911yescharacteristic
191C2#1176349812yes—
192C2#1176353612yes—
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#382C2
hypercenter#382D17
hypocenterC17#2565
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
125. C17#2565semidirect

Maximal subgroups

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

subgroupindex
C2×#105875762
C2×#105875732
#117627432
#117627152
#117627142
#117626912
#117626782
C4×#632252
C17×#3822
#256517