Finite Group Databasebeta

← #17953582

Subgroups — #17953582

Order 4352.

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

normal subgroups only

This group has 554 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
3D17×#382C211yesmaximal, characteristic
4C2×#10587543—22no—
5C2×#10587542C2214yes—
6#11763675—22no—
7C2×C4⋊C4×D17C412yes—
8C2×C42×D17C2211yescharacteristic
9#11762675C411yescharacteristic
10#11762674C2212yes—
11#11762673—22no—
12#95×D17—22no—
13C17×#382C411yescharacteristic
14C22×C4×D17—22no—
15C22×C4×D17C2×C411yescharacteristic
16C22×C4×D17D412yes—
17C22×#3624—24no—
18C2×C4⋊C4×C17C2×C412yes—
19C2×C42×C17C2×C411yescharacteristic
20C2×C4⋊Dic17C2×C412yes—
21C2×#63225—22no—
22C2×C4×Dic17D412yes—
23C2×C4×Dic17C2311yescharacteristic
24C4⋊C4×D17—44no—
25C42×D17—24no—
26#10587543—28no—
27#10587542—28no—
28C17×#95—22no—
29#10587502—22no—
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×C4×D17—44no—
45C2×C4×D17—44no—
46C2×C4×D17—44no—
47C2×#3624—28no—
48C2×#3624—44no—
49C2×#3624—44no—
50C4⋊C4×C17—42no—
51C42×C17—22no—
52C4⋊Dic17—42no—
53#63225—44no—
54C4×Dic17—24no—
55C4×Dic17#4114yes—
56#8719—171nomaximal, Sylow
57C23×C17C2×C22⋊C411yescharacteristic
58C22×D17—21no—
59C22×D17—21no—
60C22×D17—22no—
61C22×D17#10112yes—
62C22×D17#10414yes—
63C2×C4×C17—21no—
64C2×C4×C17—21no—
65C2×C4×C17—22no—
66C2×C4×C17—22no—
67C2×C4×C17—22no—
68C2×C4×C17—42no—
69C2×C4×C17—42no—
70C2×C4×C17—42no—
71C2×C4×C17#11712yes—
72C2×Dic17—21no—
73C2×Dic17—21no—
74C2×Dic17—22no—
75C2×Dic17—22no—
76C2×Dic17—42no—
77C2×Dic17—42no—
78C2×Dic17—42no—
79C2×Dic17#10012yes—
80C2×Dic17#12314yes—
81C4×D17—28no—
82C4×D17—48no—
83C4×D17—88no—
84#3624—48no—
85C2×#382—171no—
86#1749—172no—
87#1295—174no—
88C22×C17#38111yescharacteristic
89C22×C17C2×#10011yescharacteristic
90C22×C17C2×#10111yescharacteristic
91C22×C17C2×#10412yes—
92C22×C17#42112yes—
93C2×D17—22no—
94C2×D17—24no—
95C2×D17—24no—
96C2×D17—22no—
97C2×D17#33014yes—
98C4×C17—22no—
99C4×C17—42no—
100C4×C17—82no—
101Dic17—22no—
102Dic17—24no—
103Dic17—82no—
104C22×C4⋊C4—172no—
105C22×C42—171no—
106C2×C22⋊C8—342no—
107C2×#97—174no—
108#382—172no—
109#382—171no—
110#382—342no—
111#382#59511yescharacteristic
112C2×#95—342no—
113#336—342no—
114C2×C17C2×#33011yescharacteristic
115C2×C17#152712yes—
116C2×C17#153411yescharacteristic
117C2×C17#182111yescharacteristic
118C2×C17#182612yes—
119D17—24no—
120C23×C4—171no—
121C23×C4—172no—
122C23×C4—342no—
123C22×C8—344no—
124C2×C4⋊C4—172no—
125C2×C4⋊C4—342no—
126C2×C4⋊C4—684no—
127C2×C4⋊C4C2×#59512yes—
128C2×C42—171no—
129C2×C42—172no—
130C2×C42—344no—
131C2×C42C2×#59511yescharacteristic
132C22⋊C8—348no—
133#97—348no—
134#95—22no—
135#95—344no—
136#95—342no—
137C17#871911yescharacteristic, complemented, Sylow
138C24—171no—
139C22×C4—22no—
140C22×C4—171no—
141C22×C4—172no—
142C22×C4—342no—
143C22×C4—344no—
144C22×C4—342no—
145C22×C4—344no—
146C22×C4—342no—
147C22×C4—342no—
148C22×C4—682no—
149C22×C4—684no—
150C22×C4—684no—
151C22×C4—684no—
152C22×C4C22⋊#59512yes—
153C22×C4C22×#59511yescharacteristic
154C2×C8—348no—
155C2×C8—684no—
156C2×C8—684no—
157C4⋊C4—42no—
158C4⋊C4—682no—
159C4⋊C4—684no—
160C42—22no—
161C42—174no—
162C42—344no—
163C23—172no—
164C23—174no—
165C23—341no—
166C23—341no—
167C23—342no—
168C23C2×C22⋊#59511yescharacteristic
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—174no—
178C2×C4—172no—
179C2×C4—348no—
180C2×C4—341no—
181C2×C4—341no—
182C2×C4—342no—
183C2×C4—342no—
184C2×C4—688no—
185C2×C4—682no—
186C2×C4—682no—
187C2×C4—682no—
188C2×C4—1368no—
189C2×C4#1058767712yes—
190C8—688no—
191C22—174no—
192C22—342no—
193C22—344no—
194C22—344no—
195C22—342no—
196C22#1176375211yescharacteristic
197C22D17⋊#10011yescharacteristic
198C22D17⋊#10111yescharacteristic
199C22D17⋊#10412yes—
200C22#1176380612yes—
201C4—22no—
202C4—42no—
203C4—82no—
204C4—342no—
205C4—344no—
206C4—1362no—
207C2—344no—
208C2D17⋊#33011yescharacteristic
209C2#1454424412yes—
210C2#1454426711yescharacteristic
211C2#1454468411yescharacteristic
212C2#1454469212yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#382#595
hypocenterC17#8719
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #14543660C2semidirect
137. C17#8719semidirect

Maximal subgroups

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

subgroupindex
#145445112
#145436602
D17×#3822
#871917