Finite Group Databasebeta

← #16935320

Subgroups — #16935320

Order 4352.

476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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#14539308C211yesmaximal, characteristic
2#14538824C212yesmaximal
3#14529724C211yesmaximal, characteristic
4#14527188C212yesmaximal
5C17×#1275C211yesmaximal, characteristic
6#11763366C2212yes—
7C2×C4×Dic34C2211yescharacteristic
8#11763218—22no—
9#11763218—22no—
10#11763145—22no—
11#11763105—22no—
12#11763020—22no—
13#11762967—22no—
14C4×Dic68—24no—
15#11762847—22no—
16C2×C4⋊#3622C2211yescharacteristic
17#11762563—22no—
18#11762541—24no—
19C17×#431C2212yes—
20C2×C17×#97C2211yescharacteristic
21C22×Dic34D411yescharacteristic
22C22×C8×C17D412yes—
23C2×C42×C17C2311yescharacteristic
24#10587612—22no—
25C2×C4⋊Dic17D411yescharacteristic
26#10587610—22no—
27#10587610—22no—
28C2×#63225—21no—
29C2×C4×Dic17—21no—
30C22×#3622—21no—
31C2×Dic68—24no—
32#10587556—22no—
33#10587555D412yes—
34#10587555D412yes—
35C4×Dic34—22no—
36C4×Dic34—22no—
37C4×Dic34—22no—
38C4×Dic34—22no—
39C17×C4⋊C8—22no—
40C17×C22⋊C8—22no—
41C17×#97—22no—
42C4×C8×C17D414yes—
43#10587489—22no—
44#10587489—22no—
45#10587489—24no—
46#10587488—24no—
47#10587487—24no—
48#10587487—24no—
49C4⋊#3622—22no—
50C22×C4×C17C2×D411yescharacteristic
51C22×C4×C17C2×D411yescharacteristic
52C22×C4×C17#4111yescharacteristic
53C22×Dic17—21no—
54C22×Dic17—21no—
55C2×Dic34—22no—
56C2×Dic34—22no—
57C2×Dic34—22no—
58C2×Dic34—42no—
59C2×C8×C17—22no—
60C2×C8×C17—22no—
61C2×C8×C17—24no—
62C2×C8×C17Q1614yescomplemented
63C42×C17C2×D412yes—
64C42×C17C2×D412yes—
65C22⋊Dic17—42no—
66C4⋊Dic17—22no—
67C4⋊Dic17—22no—
68C4⋊Dic17—22no—
69C4⋊Dic17—22no—
70C4⋊Dic17—22no—
71#63225—42no—
72#63225—42no—
73#63225—42no—
74C4×Dic17—41no—
75C4×Dic17—41no—
76C4×Dic17—42no—
77C2×#3622—41no—
78C2×#3622—42no—
79Dic68—48no—
80#10037—171nomaximal, Sylow
81C23×C17#12111yescharacteristic
82C2×C4×C17—41no—
83C2×C4×C17—41no—
84C2×C4×C17#12012yes—
85C2×C4×C17#12011yescharacteristic
86C2×C4×C17#12112yes—
87C2×C4×C17#12711yescharacteristic
88C2×C4×C17C2×Q1612yes—
89C2×C4×C17#13712yes—
90C2×Dic17—22no—
91C2×Dic17—41no—
92C2×Dic17—41no—
93C2×Dic17—42no—
94C2×Dic17—42no—
95C2×Dic17—42no—
96C2×Dic17—41no—
97Dic34—24no—
98Dic34—42no—
99Dic34—44no—
100Dic34—44no—
101C8×C17—24no—
102C8×C17—44no—
103#3622—81no—
104#3162—171no—
105#3104—172no—
106#1985—171no—
107#1481—172no—
108#1275D1711yescharacteristic
109C22×C17—21no—
110C22×C17—21no—
111C22×C17#39211yescharacteristic
112C22×C17#46212yes—
113C4×C17—22no—
114C4×C17—22no—
115C4×C17#45112yes—
116C4×C17#49411yescharacteristic
117C4×C17#49711yescharacteristic
118Dic17—42no—
119Dic17—82no—
120Dic17—82no—
121Dic17—81no—
122#533—172no—
123C2×C4×Q8—171no—
124#501—342no—
125#501—342no—
126#484—342no—
127#477—342no—
128#462—342no—
129#451—342no—
130C4×Q16—344no—
131#431C2×D1712yes—
132#427—342no—
133C2×C4⋊C8—171no—
134C2×#97C2×D1711yescharacteristic
135#336—342no—
136Q8⋊C8—344no—
137C2×C17—22no—
138C2×C17#201011yescharacteristic
139C2×C17#201611yescharacteristic
140C2×C17#201711yescharacteristic
141C22×Q8—171no—
142C2×Q16—344no—
143C22×C8—341no—
144C22×C8D6812yes—
145C4⋊Q8—172no—
146C4⋊Q8—172no—
147#125—342no—
148C22⋊Q8—342no—
149C22⋊Q8—342no—
150C4×Q8—342no—
151C4×Q8—342no—
152C4×Q8—342no—
153C4×Q8—342no—
154#117—342no—
155C2×C4⋊C4—171no—
156C2×C4⋊C4—341no—
157C2×C42—341no—
158C2×C42C22×D1711yescharacteristic
159#107—342no—
160#107—342no—
161#107—344no—
162#106—344no—
163C4⋊C8—22no—
164C4⋊C8—342no—
165#103—344no—
166#103—344no—
167C22⋊C8—22no—
168#97—22no—
169C4×C8D6814yes—
170C17#1003711yescharacteristic, complemented, Sylow
171C2×Q8—342no—
172C2×Q8—342no—
173C2×Q8—342no—
174C2×Q8—682no—
175C22×C4—341no—
176C22×C4—341no—
177C22×C4C2×D6811yescharacteristic
178C22×C4D4×D1711yescharacteristic
179C22×C4#6325611yescharacteristic
180Q16—688no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—24no—
184C2×C8—681no—
185C2×C8—682no—
186C2×C8Dic6814yescomplemented
187C4⋊C4—342no—
188C4⋊C4—342no—
189C4⋊C4—342no—
190C4⋊C4—342no—
191C4⋊C4—342no—
192C4⋊C4—682no—
193C4⋊C4—682no—
194C4⋊C4—682no—
195C22⋊C4—682no—
196C42—681no—
197C42—682no—
198C42—681no—
199C42C2×D6812yes—
200C42D4×D1712yes—
201C23#1058758111yescharacteristic
202Q8—344no—
203Q8—682no—
204Q8—684no—
205Q8—684no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—342no—
209C2×C4—681no—
210C2×C4—681no—
211C2×C4—682no—
212C2×C4—681no—
213C2×C4—682no—
214C2×C4—682no—
215C2×C4#1058756011yescharacteristic
216C2×C4#1058756812yes—
217C2×C4#1058756811yescharacteristic
218C2×C4#1058758112yes—
219C2×C4C2×Dic6812yes—
220C2×C4#1058759512yes—
221C8—24no—
222C8—44no—
223C8—1361no—
224C22—21no—
225C22—21no—
226C22#1176271911yescharacteristic
227C22#1176302012yes—
228C4—22no—
229C4—22no—
230C4—682no—
231C4—1362no—
232C4—1361no—
233C4—1362no—
234C4#1176296712yes—
235C4#1176318911yescharacteristic
236C4#1176320311yescharacteristic
237C2—22no—
238C2#1452985211yescharacteristic
239C2#1452988611yescharacteristic
240C2#1452988911yescharacteristic
subgroupG/H
centerC2×C4#10587560
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1275C2
socleC22×C17#392
prime radicalC23×C17#121
hypercenter#1275D17
hypocenterC17#10037
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
62. C2×C8×C17Q16semidirect
170. C17#10037semidirect
186. C2×C8Dic68semidirect

Maximal subgroups

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

subgroupindex
#145393082
#145388242
#145297242
#145271882
C17×#12752
#1003717