Finite Group Databasebeta

← #17953589

Subgroups — #17953589

Order 4352.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#14544511C212yesmaximal
2#14543660C214yesmaximal, complemented
3#14531189C211yesmaximal, characteristic
4C2×#10587543—22no—
5C2×#10587542C2214yes—
6#11763675—22no—
7C2×#10587578C412yes—
8C2×C42×D17C2211yescharacteristic
9#11762679C411yescharacteristic
10#11762674C2212yes—
11#11762666—22no—
12C4⋊C4×Dic17—22no—
13C17×#384C411yescharacteristic
14C22×C4×D17C2×C411yescharacteristic
15C22×C4×D17D412yes—
16C22×#3624—24no—
17C2×C4⋊C4×C17—22no—
18C2×C4⋊C4×C17C2×C412yes—
19C2×C42×C17C2×C411yescharacteristic
20C2×#63227—22no—
21C2×C4⋊Dic17—22no—
22C2×C4⋊Dic17C2×C412yes—
23C2×C4×Dic17—22no—
24C2×C4×Dic17D412yes—
25C2×C4×Dic17C2311yescharacteristic
26#10587578—44no—
27C42×D17—24no—
28#10587543—28no—
29#10587542—28no—
30#10587502—24no—
31C23×D17C22⋊C411yescharacteristic
32C22×C4×C17—22no—
33C22×C4×C17C22⋊C412yes—
34C22×C4×C17C22×C411yescharacteristic
35C22×Dic17—22no—
36C22×Dic17C22⋊C411yescharacteristic
37C22×Dic17C2×D412yes—
38C2×C4×D17—22no—
39C2×C4×D17—22no—
40C2×C4×D17—22no—
41C2×C4×D17—24no—
42C2×C4×D17—24no—
43C2×C4×D17—42no—
44C2×#3624—28no—
45C2×#3624—44no—
46C2×#3624—44no—
47C4⋊C4×C17—42no—
48C4⋊C4×C17—44no—
49C42×C17—22no—
50#63227—44no—
51C4⋊Dic17—44no—
52C4⋊Dic17—42no—
53C4×Dic17—24no—
54C4×Dic17—44no—
55C4×Dic17#4114yes—
56#8721—171nomaximal, Sylow
57C23×C17C2×C22⋊C411yescharacteristic
58C22×D17—21no—
59C22×D17—21no—
60C22×D17—22no—
61C22×D17—22no—
62C22×D17#10112yes—
63C2×C4×C17—22no—
64C2×C4×C17—21no—
65C2×C4×C17—21no—
66C2×C4×C17—22no—
67C2×C4×C17—42no—
68C2×C4×C17—44no—
69C2×C4×C17#10414yes—
70C2×C4×C17#11712yes—
71C2×Dic17—21no—
72C2×Dic17—21no—
73C2×Dic17—22no—
74C2×Dic17—22no—
75C2×Dic17—42no—
76C2×Dic17—44no—
77C2×Dic17#10012yes—
78C2×Dic17#12314yes—
79C4×D17—28no—
80C4×D17—48no—
81#3624—48no—
82#2285—171no—
83#1749—172no—
84#1295—174no—
85C22×C17#38111yescharacteristic
86C22×C17C2×#10011yescharacteristic
87C22×C17C2×#10111yescharacteristic
88C22×C17C2×#10412yes—
89C22×C17#42112yes—
90C2×D17—22no—
91C2×D17—24no—
92C2×D17—41no—
93C2×D17—42no—
94C2×D17—41no—
95C4×C17—22no—
96C4×C17—24no—
97C4×C17—82no—
98Dic17—22no—
99Dic17—24no—
100Dic17—82no—
101C2×#117—172no—
102C22×C42—171no—
103C2×C22⋊C8—342no—
104C2×#97—174no—
105#384—171no—
106#384#59511yescharacteristic
107#382—172no—
108#380—342no—
109C4×C4⋊C4—342no—
110#336—342no—
111C2×C17#152511yescharacteristic
112C2×C17#153112yes—
113C2×C17#153611yescharacteristic
114C2×C17#182111yescharacteristic
115C2×C17#182612yes—
116D17—42no—
117C23×C4—171no—
118C23×C4—172no—
119C22×C8—344no—
120#117—684no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—172no—
123C2×C4⋊C4—342no—
124C2×C4⋊C4C2×#59512yes—
125C2×C22⋊C4—342no—
126C2×C42—171no—
127C2×C42—172no—
128C2×C42—344no—
129C2×C42—342no—
130C2×C42C2×#59511yescharacteristic
131C22⋊C8—348no—
132#97—348no—
133#95—344no—
134C17#872111yescharacteristic, complemented, Sylow
135C24—171no—
136C22×C4—22no—
137C22×C4—171no—
138C22×C4—172no—
139C22×C4—342no—
140C22×C4—344no—
141C22×C4—342no—
142C22×C4—342no—
143C22×C4—344no—
144C22×C4—342no—
145C22×C4—682no—
146C22×C4C22⋊#59512yes—
147C22×C4C22×#59511yescharacteristic
148C2×C8—348no—
149C2×C8—684no—
150C2×C8—684no—
151C4⋊C4—42no—
152C4⋊C4—44no—
153C4⋊C4—682no—
154C4⋊C4—684no—
155C22⋊C4—684no—
156C42—22no—
157C42—174no—
158C42—344no—
159C42—684no—
160C23—172no—
161C23—341no—
162C23—341no—
163C23—342no—
164C23—342no—
165C23C2×C22⋊#59511yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—44no—
172C2×C4—174no—
173C2×C4—172no—
174C2×C4—348no—
175C2×C4—341no—
176C2×C4—341no—
177C2×C4—342no—
178C2×C4—342no—
179C2×C4—688no—
180C2×C4—682no—
181C2×C4—684no—
182C2×C4#1058755014yes—
183C2×C4#1058767712yes—
184C8—688no—
185C22—342no—
186C22—344no—
187C22—682no—
188C22—681no—
189C22—681no—
190C22#1176375211yescharacteristic
191C22D17⋊#10011yescharacteristic
192C22D17⋊#10111yescharacteristic
193C22C2×#1058755012yes—
194C22#1176380712yes—
195C4—22no—
196C4—24no—
197C4—82no—
198C4—342no—
199C4—344no—
200C4—1362no—
201C2—682no—
202C2#1454424011yescharacteristic
203C2#1454425812yes—
204C2#1454427311yescharacteristic
205C2#1454468411yescharacteristic
206C2#1454469112yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#384C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#384#595
hypocenterC17#8721
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #14543660C2semidirect
134. C17#8721semidirect

Maximal subgroups

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

subgroupindex
#145445112
#145436602
#145311892
#872117