Finite Group Databasebeta

← #17953629

Subgroups — #17953629

Order 4352.

418 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 88 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×#11763655C212yesmaximal
2#14543627C214yesmaximal
3#14531386C211yesmaximal, characteristic
4C2×C22⋊#3624C2214yes—
5#11763655—22no—
6#11763655—22no—
7C22×#63225C2211yescharacteristic
8#11762696—22no—
9#11762690—22no—
10#11762670C412yes—
11#11762669C411yescharacteristic
12C22⋊C4×Dic17C2212yes—
13C17×#380C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×Dic17C2×C411yescharacteristic
16C23×Dic17C2311yescharacteristic
17C22×#3624—24no—
18C2×C4⋊C4×C17—21no—
19C2×C22⋊C4×C17C2×C412yes—
20C2×C22⋊Dic17C2×C412yes—
21C2×C4⋊Dic17—21no—
22C2×#63225—24no—
23C2×#63225D412yes—
24C2×#63225D412yes—
25C2×C4×Dic17—22no—
26C22⋊#3624—24no—
27C22⋊#3624—24no—
28C17×#95—21no—
29#10587502—21no—
30#10587502—24no—
31#10587502—22no—
32C24×C17C22×C411yescharacteristic
33C22×C4×C17—22no—
34C22×C4×C17—22no—
35C22×C4×C17—81no—
36C22×C4×C17C22⋊C411yescharacteristic
37C22×C4×C17C22⋊C411yescharacteristic
38C22×Dic17—22no—
39C22×Dic17—22no—
40C22×Dic17—22no—
41C22×Dic17—22no—
42C22×Dic17—81no—
43C22×Dic17C22⋊C412yes—
44C22×Dic17C2×D412yes—
45C22×Dic17#4114yes—
46C2×#3624—44no—
47C2×#3624—84no—
48C4⋊C4×C17—81no—
49C22⋊C4×C17—24no—
50C22⋊Dic17—24no—
51C4⋊Dic17—81no—
52#63225—24no—
53#63225—24no—
54C4×Dic17—82no—
55#8737—171nomaximal, Sylow
56C23×C17—41no—
57C23×C17—41no—
58C23×C17C2×C22⋊C411yescharacteristic
59C23×C17#11712yes—
60C23×C17#13112yes—
61C23×C17#13112yes—
62C2×C4×C17—21no—
63C2×C4×C17—21no—
64C2×C4×C17—41no—
65C2×C4×C17—41no—
66C2×C4×C17—42no—
67C2×C4×C17—42no—
68C2×C4×C17—42no—
69C2×C4×C17—82no—
70C2×Dic17—22no—
71C2×Dic17—22no—
72C2×Dic17—22no—
73C2×Dic17—44no—
74C2×Dic17—42no—
75C2×Dic17—44no—
76C2×Dic17—42no—
77C2×Dic17—42no—
78C2×Dic17—42no—
79C2×Dic17#12314yes—
80#3624—84no—
81#2313—171no—
82C2×#324—172no—
83#1282—174no—
84C22×C17—21no—
85C22×C17—22no—
86C22×C17—21no—
87C22×C17—22no—
88C22×C17—42no—
89C22×C17—42no—
90C22×C17#38111yescharacteristic
91C22×C17#40811yescharacteristic
92C22×C17#40811yescharacteristic
93C22×C17#43314yes—
94C4×C17—41no—
95C4×C17—41no—
96C4×C17—82no—
97Dic17—24no—
98Dic17—42no—
99Dic17—82no—
100C22×C4⋊C4—171no—
101C2×C22⋊C8—174no—
102#387—342no—
103#387—342no—
104#381—172no—
105#380—171no—
106#380#59511yescharacteristic
107C4×C22⋊C4—172no—
108#324—342no—
109#324—342no—
110C2×C17—21no—
111C2×C17—21no—
112C2×C17—24no—
113C2×C17#181811yescharacteristic
114C2×C17#182811yescharacteristic
115C2×C17#183011yescharacteristic
116C23×C4—171no—
117C23×C4—171no—
118C23×C4C2×#59511yescharacteristic
119C22×C8—344no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—172no—
122C2×C4⋊C4—172no—
123C2×C4⋊C4—344no—
124C2×C4⋊C4—341no—
125C2×C22⋊C4—172no—
126C2×C22⋊C4C2×#59512yes—
127C2×C42—342no—
128C22⋊C8—344no—
129C22⋊C8—344no—
130#95—21no—
131#95—342no—
132#95—344no—
133#95—341no—
134C17#873711yescharacteristic, complemented, Sylow
135C24C22×#59511yescharacteristic
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—81no—
139C22×C4—174no—
140C22×C4—172no—
141C22×C4—172no—
142C22×C4—342no—
143C22×C4—342no—
144C22×C4—342no—
145C22×C4—342no—
146C22×C4—1361no—
147C22×C4C22⋊#59511yescharacteristic
148C22×C4C22⋊#59511yescharacteristic
149C2×C8—684no—
150C2×C8—1364no—
151C4⋊C4—81no—
152C4⋊C4—344no—
153C4⋊C4—344no—
154C4⋊C4—1361no—
155C22⋊C4—24no—
156C22⋊C4—344no—
157C42—1362no—
158C23—41no—
159C23—41no—
160C23#1058767712yes—
161C23#1058767812yes—
162C23#1058768012yes—
163C23C2×C22⋊#59511yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—82no—
172C2×C4—174no—
173C2×C4—342no—
174C2×C4—342no—
175C2×C4—342no—
176C2×C4—682no—
177C2×C4—684no—
178C2×C4—684no—
179C2×C4—682no—
180C2×C4—682no—
181C2×C4—682no—
182C8—1364no—
183C22—21no—
184C22—22no—
185C22—21no—
186C22—22no—
187C22—42no—
188C22—42no—
189C22#1176375211yescharacteristic
190C22#1176378311yescharacteristic
191C22#1176378411yescharacteristic
192C22#1176383414yes—
193C4—41no—
194C4—41no—
195C4—82no—
196C4—344no—
197C4—682no—
198C4—1362no—
199C2—21no—
200C2—21no—
201C2—24no—
202C2#1454467811yescharacteristic
203C2#1454469511yescharacteristic
204C2#1454469811yescharacteristic
subgroupG/H
centerC22#11763752
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC17×#380C4
socleC22×C17#381
cosocleC23×Dic17C23
hypercenter#380#595
hypocenterC17#8737
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ #380

Complements

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

NH ≅ G/Ntype
134. C17#8737semidirect

Maximal subgroups

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

subgroupindex
C2×#117636552
#145436272
#145313862
#873717