Finite Group Databasebeta

← #16935617

Subgroups — #16935617

Order 4352.

552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11763174C212yesmaximal
2#14536852C211yesmaximal, characteristic, complemented
3#14529607C211yesmaximal, characteristic
4C2×#11762550C212yesmaximal, complemented
5C17×#1295C211yesmaximal, characteristic, complemented
6C2×#10587560C2211yescharacteristic
7C2×#10587556C2212yes—
8#11763174—24no—
9#11763174—24no—
10C2×#10587492—22no—
11C2×#10587492—22no—
12C2×#10587480—22no—
13C2×#10587474C2211yescharacteristic
14#11762749—22no—
15#11762741—22no—
16#11762739—22no—
17#11762550—24no—
18C2×C17×#97C2212yes—
19C17×#382C2211yescharacteristic
20C22×D68—21no—
21C22×D68—22no—
22C22×C8×C17—22no—
23C2×C4⋊C4×C17D412yes—
24C2×C42×C17C2311yescharacteristic
25C2×C4⋊Dic17—22no—
26C2×C4⋊Dic17D412yes—
27C2×C4⋊Dic17D412yes—
28C2×#63225—22no—
29C2×#63225—22no—
30C22×#3622—21no—
31#10587560—22no—
32#10587560—21no—
33#10587560D412yes—
34#10587556—22no—
35#10587556—22no—
36#10587556—22no—
37#10587556—22no—
38C17×#97—22no—
39C17×#97D414yes—
40C17×#95—22no—
41#10587502—24no—
42#10587502—22no—
43#10587492—28no—
44#10587492—28no—
45#10587480—44no—
46#10587474—22no—
47C23×D17—41no—
48C22×C4×C17—22no—
49C22×C4×C17C2×D411yescharacteristic
50C22×C4×C17C2×D412yes—
51C22×Dic17—22no—
52C22×Dic17—22no—
53C2×D68—24no—
54C2×D68—22no—
55C2×D68—48no—
56C2×D68—42no—
57C2×D68—42no—
58C2×D68—42no—
59C2×D68—41no—
60C2×C8×C17—24no—
61C2×C8×C17—44no—
62C4⋊C4×C17—42no—
63C42×C17C2×D412yes—
64C42×C17C2×D411yescharacteristic
65C42×C17#4111yescharacteristic
66C4⋊Dic17—22no—
67C4⋊Dic17—22no—
68C4⋊Dic17—22no—
69C4⋊Dic17—22no—
70C4⋊Dic17—82no—
71#63225—42no—
72#63225—42no—
73#63225—42no—
74#63225—42no—
75C2×#3622—22no—
76C2×#3622—41no—
77C2×#3622—41no—
78#10080—171nomaximal, Sylow
79C23×C17#12011yescharacteristic
80C22×D17—42no—
81C22×D17—81no—
82C22×D17—84no—
83C22×D17—81no—
84C2×C4×C17—21no—
85C2×C4×C17—24no—
86C2×C4×C17—21no—
87C2×C4×C17—42no—
88C2×C4×C17—44no—
89C2×C4×C17#12012yes—
90C2×C4×C17#12111yescharacteristic
91C2×C4×C17#12112yes—
92C2×C4×C17#12711yescharacteristic
93C2×Dic17—42no—
94C2×Dic17—42no—
95C2×Dic17—42no—
96C2×Dic17—44no—
97C2×Dic17—42no—
98D68—48no—
99D68—44no—
100D68—84no—
101D68—82no—
102C8×C17—44no—
103#3622—42no—
104C2×#490—172no—
105#2822—171no—
106#1961—171no—
107C2×#330—172no—
108#1295D1711yescharacteristic, complemented
109C22×C17#39211yescharacteristic
110C22×C17#45311yescharacteristic
111C22×C17#45414yes—
112C22×C17#45411yescharacteristic
113C2×D17—84no—
114C2×D17—82no—
115C2×D17—162no—
116C2×D17—162no—
117C4×C17—22no—
118C4×C17—22no—
119C4×C17—21no—
120C4×C17—21no—
121C4×C17—82no—
122Dic17—82no—
123Dic17—82no—
124C2×#127—171no—
125C2×#125—172no—
126#490—344no—
127#490—344no—
128C2×#102—342no—
129C2×#102—342no—
130C2×#102—342no—
131C2×#97—171no—
132C2×#97C2×D1712yes—
133#400—342no—
134#398—342no—
135#398—342no—
136#382C2×D1711yescharacteristic
137#330—344no—
138C2×C17#165712yes—
139C2×C17#165812yes—
140C2×C17#200312yes—
141C2×C17#200611yescharacteristic
142D17—162no—
143C22×D4—341no—
144C22×D4—342no—
145C22×C8—22no—
146C22×C8—341no—
147#127—172no—
148#127—342no—
149#127—341no—
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⋊C4D6812yes—
160C2×C42C22×D1711yescharacteristic
161#102—348no—
162#102—348no—
163#102—684no—
164#97—22no—
165#97—342no—
166#97D6814yes—
167#95—22no—
168#95—344no—
169#95—342no—
170C17#1008011yescharacteristic, complemented, Sylow
171C24—681no—
172C2×D4—344no—
173C2×D4—342no—
174C2×D4—682no—
175C2×D4—688no—
176C2×D4—682no—
177C2×D4—681no—
178C2×D4—682no—
179C22×C4—22no—
180C22×C4—342no—
181C22×C4—342no—
182C22×C4C2×D6811yescharacteristic
183C22×C4D4×D1712yes—
184C2×C8—24no—
185C2×C8—44no—
186C2×C8—342no—
187C2×C8—681no—
188C2×C8—681no—
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×D6812yes—
200C42D4×D1711yescharacteristic
201C42#6325611yescharacteristic
202C23—682no—
203C23—1361no—
204C23—1364no—
205C23—1361no—
206C23#1058756811yescharacteristic
207D4—688no—
208D4—684no—
209D4—1364no—
210D4—1362no—
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#1058756011yescharacteristic
222C2×C4#1058756812yes—
223C2×C4#1058758112yes—
224C2×C4#1058758111yescharacteristic
225C8—44no—
226C8—682no—
227C22—2722no—
228C22—2722no—
229C22—1364no—
230C22—1362no—
231C22#1176271911yescharacteristic
232C22#1176297911yescharacteristic
233C22#1176298314yes—
234C22#1176298411yescharacteristic
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—82no—
240C4—1362no—
241C4—1362no—
242C2—2722no—
243C2#1452808312yes—
244C2#1452808712yes—
245C2#1452980912yes—
246C2#1452982811yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1295C2
socleC23×C17#120
prime radicalC2×#10587560C22
hypercenter#1295D17
hypocenterC17#10080
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #14536852C2semidirect
4. C2×#11762550C2semidirect
5. C17×#1295C2semidirect
108. #1295D17semidirect
170. C17#10080semidirect

Maximal subgroups

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

subgroupindex
C2×#117631742
#145368522
#145296072
C2×#117625502
C17×#12952
#1008017