Finite Group Databasebeta

← #16935614

Subgroups — #16935614

Order 4352.

552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11763173C212yesmaximal
2#14536852C211yesmaximal, characteristic, complemented
3C2×#11762550C212yesmaximal, complemented
4#14526665C211yesmaximal, characteristic, complemented
5C17×#1961C211yesmaximal, characteristic
6C2×#10587556C2212yes—
7#11763173—24no—
8#11763173—24no—
9C2×#10587503—22no—
10C2×#10587503—22no—
11C2×#10587474C2212yes—
12#11762749—22no—
13#11762741—22no—
14#11762739—22no—
15#11762550—24no—
16C2×C17×#127C2211yescharacteristic
17C2×C17×#102—22no—
18C2×C17×#97C2211yescharacteristic
19C17×#382C2211yescharacteristic
20C22×D4×C17—22no—
21C22×D4×C17—21no—
22C22×C8×C17—21no—
23C17×#127—22no—
24C17×#127—21no—
25C17×#127D412yes—
26C2×C4⋊C4×C17D412yes—
27C2×C42×C17C2311yescharacteristic
28C2×C4⋊Dic17—22no—
29C2×C4⋊Dic17D412yes—
30C2×C4⋊Dic17D412yes—
31C2×#63225—22no—
32C2×#63225—22no—
33C22×#3622—22no—
34#10587556—22no—
35#10587556—22no—
36#10587556—22no—
37#10587556—22no—
38C17×#102—44no—
39C17×#97—22no—
40C17×#95—22no—
41#10587503—28no—
42#10587503—28no—
43#10587502—24no—
44#10587502—22no—
45#10587474—22no—
46#10587474D414yes—
47C24×C17—41no—
48C2×D4×C17—24no—
49C2×D4×C17—22no—
50C2×D4×C17—42no—
51C2×D4×C17—48no—
52C2×D4×C17—42no—
53C2×D4×C17—42no—
54C2×D4×C17—41no—
55C22×C4×C17—22no—
56C22×C4×C17C2×D412yes—
57C22×C4×C17C2×D411yescharacteristic
58C22×Dic17—22no—
59C22×Dic17—22no—
60C2×C8×C17—22no—
61C2×C8×C17—41no—
62C2×C8×C17—41no—
63C4⋊C4×C17—42no—
64C42×C17C2×D411yescharacteristic
65C42×C17C2×D412yes—
66C42×C17#4111yescharacteristic
67C4⋊Dic17—22no—
68C4⋊Dic17—22no—
69C4⋊Dic17—22no—
70C4⋊Dic17—22no—
71C4⋊Dic17—82no—
72#63225—42no—
73#63225—42no—
74#63225—42no—
75#63225—42no—
76C2×#3622—24no—
77C2×#3622—44no—
78#10080—171nomaximal, Sylow
79C23×C17—42no—
80C23×C17—81no—
81C23×C17—84no—
82C23×C17—81no—
83C23×C17#12011yescharacteristic
84D4×C17—48no—
85D4×C17—44no—
86D4×C17—84no—
87D4×C17—82no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—24no—
91C2×C4×C17—42no—
92C2×C4×C17—44no—
93C2×C4×C17#12012yes—
94C2×C4×C17#12112yes—
95C2×C4×C17#12111yescharacteristic
96C2×C4×C17#12711yescharacteristic
97C2×Dic17—42no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—44no—
101C2×Dic17—42no—
102C8×C17—42no—
103#3622—44no—
104C2×#490—172no—
105#2822—171no—
106#1961D1711yescharacteristic
107C2×#330—172no—
108#1295—171no—
109C22×C17—84no—
110C22×C17—82no—
111C22×C17—162no—
112C22×C17—162no—
113C22×C17#39211yescharacteristic
114C22×C17#45311yescharacteristic
115C22×C17#45414yes—
116C22×C17#45411yescharacteristic
117C4×C17—22no—
118C4×C17—22no—
119C4×C17—21no—
120C4×C17—21no—
121C4×C17—82no—
122Dic17—82no—
123Dic17—82no—
124C2×#127C2×D1711yescharacteristic
125C2×#125—172no—
126#490—344no—
127#490—344no—
128C2×#102—22no—
129C2×#102—342no—
130C2×#102—342no—
131C2×#97—172no—
132C2×#97C2×D1711yescharacteristic
133#400—342no—
134#398—342no—
135#398—342no—
136#382C2×D1711yescharacteristic
137#330—344no—
138C2×C17—162no—
139C2×C17#165712yes—
140C2×C17#165812yes—
141C2×C17#200312yes—
142C2×C17#200611yescharacteristic
143C22×D4—22no—
144C22×D4—21no—
145C22×C8—21no—
146C22×C8—342no—
147#127—21no—
148#127—22no—
149#127D6812yes—
150#125—342no—
151#125—342no—
152#125—342no—
153#125—342no—
154C2×C4⋊C4—172no—
155C2×C4⋊C4—172no—
156C2×C4⋊C4—342no—
157C2×C4⋊C4—342no—
158C2×C4⋊C4—342no—
159C2×C4⋊C4C22⋊D1712yes—
160C2×C42C22×D1711yescharacteristic
161#102—44no—
162#102—348no—
163#102—348no—
164#97—22no—
165#97—174no—
166#97—342no—
167#95—22no—
168#95—344no—
169#95—342no—
170C17#1008011yescharacteristic, complemented, Sylow
171C24—41no—
172C2×D4—24no—
173C2×D4—22no—
174C2×D4—42no—
175C2×D4—48no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—41no—
179C22×C4—22no—
180C22×C4—342no—
181C22×C4—342no—
182C22×C4D4×D1712yes—
183C22×C4C2×C22⋊D1711yescharacteristic
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—344no—
188C2×C8—684no—
189C4⋊C4—42no—
190C4⋊C4—342no—
191C4⋊C4—342no—
192C4⋊C4—342no—
193C4⋊C4—342no—
194C4⋊C4—682no—
195C4⋊C4—682no—
196C4⋊C4—682no—
197C4⋊C4—682no—
198C4⋊C4—1362no—
199C42C2×D6811yescharacteristic
200C42#6325211yescharacteristic
201C42D4×D1712yes—
202C23—42no—
203C23—81no—
204C23—84no—
205C23—81no—
206C23#1058762311yescharacteristic
207D4—48no—
208D4—44no—
209D4—84no—
210D4—82no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—21no—
214C2×C4—42no—
215C2×C4—44no—
216C2×C4—682no—
217C2×C4—682no—
218C2×C4—682no—
219C2×C4—684no—
220C2×C4—682no—
221C2×C4#1058756812yes—
222C2×C4#1058757012yes—
223C2×C4#1058761611yescharacteristic
224C2×C4#1058762611yescharacteristic
225C8—42no—
226C8—684no—
227C22—84no—
228C22—82no—
229C22—162no—
230C22—162no—
231C22#1176271811yescharacteristic
232C22#1176297611yescharacteristic
233C22#1176298014yes—
234C22#1176298111yescharacteristic
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—82no—
240C4—1362no—
241C4—1362no—
242C2—162no—
243C2#1452808012yes—
244C2#1452808512yes—
245C2#1452980712yes—
246C2#1452982511yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1961C2
socleC23×C17#120
prime radicalC2×C17×#127C22
hypercenter#1961D17
hypocenterC17#10080
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. #14536852C2semidirect
3. C2×#11762550C2semidirect
4. #14526665C2semidirect
170. C17#10080semidirect

Maximal subgroups

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

subgroupindex
C2×#117631732
#145368522
C2×#117625502
#145266652
C17×#19612
#1008017