Finite Group Databasebeta

← #16935285

Subgroups — #16935285

Order 4352.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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#14540129C211yesmaximal, characteristic
2#14538914C212yesmaximal
3#14527398C212yesmaximal
4#14526654C211yesmaximal, characteristic
5C17×#1985C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763139—22no—
8#11763105—22no—
9#11763094—22no—
10#11763050—22no—
11#11763020—22no—
12#11763019—22no—
13#11762965—22no—
14#11762914—24no—
15#11762866C2212yes—
16#11762550—24no—
17C2×C4×Q8×C17C2211yescharacteristic
18C2×C17×C4⋊C8C2211yescharacteristic
19C2×C17×#97C2211yescharacteristic
20C17×#336—22no—
21C22×Q8×C17D411yescharacteristic
22C22×C8×C17—21no—
23C22×C8×C17D412yes—
24C4×Q8×C17—22no—
25C4×Q8×C17—22no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17D411yescharacteristic
28C2×C42×C17—21no—
29C2×C42×C17C2311yescharacteristic
30C2×#63231—24no—
31#10587612—22no—
32#10587610—22no—
33#10587610—22no—
34C2×Dic68—22no—
35#10587556—22no—
36#10587555D412yes—
37#10587555D412yes—
38C4×Dic34—22no—
39C4×Dic34—22no—
40C17×C4⋊C8—22no—
41C17×#97—22no—
42#10587506—24no—
43C22⋊#3622—22no—
44#10587489—22no—
45#10587487—24no—
46#10587481—24no—
47#10587479—24no—
48C4⋊#3622—22no—
49#10587474D414yes—
50C2×Q8×C17—22no—
51C2×Q8×C17—42no—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17C2×D411yescharacteristic
55C22×C4×C17C2×D411yescharacteristic
56C22×C4×C17#4111yescharacteristic
57C2×Dic34—22no—
58C2×Dic34—22no—
59C2×C8×C17—22no—
60C2×C8×C17—22no—
61C2×C8×C17—41no—
62C2×C8×C17—41no—
63C2×C8×C17—42no—
64C4⋊C4×C17—22no—
65C4⋊C4×C17—42no—
66C42×C17—41no—
67C42×C17—41no—
68C42×C17C2×D412yes—
69C42×C17C2×D412yes—
70C22⋊Dic17—42no—
71#63231—48no—
72C4⋊Dic17—22no—
73C4⋊Dic17—22no—
74C4⋊Dic17—22no—
75C4⋊Dic17—22no—
76#63225—42no—
77#63225—42no—
78C4×Dic17—42no—
79C2×#3622—24no—
80Dic68—82no—
81#10031—171nomaximal, Sylow
82C23×C17#12111yescharacteristic
83Q8×C17—24no—
84Q8×C17—42no—
85C2×C4×C17—22no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—22no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17—41no—
92C2×C4×C17—41no—
93C2×C4×C17—42no—
94C2×C4×C17#12012yes—
95C2×C4×C17#12011yescharacteristic
96C2×C4×C17#12112yes—
97C2×C4×C17#12711yescharacteristic
98C2×Dic17—42no—
99C2×Dic17—42no—
100Dic34—44no—
101Dic34—42no—
102Dic34—42no—
103C8×C17—42no—
104C8×C17—42no—
105#3622—44no—
106#3249—171no—
107#3113—172no—
108#1985D1711yescharacteristic
109#1531—172no—
110#1290—171no—
111C22×C17—21no—
112C22×C17—21no—
113C22×C17#39211yescharacteristic
114C22×C17#47312yes—
115C4×C17—21no—
116C4×C17—22no—
117C4×C17—22no—
118C4×C17—42no—
119C4×C17—81no—
120C4×C17#45511yescharacteristic
121C4×C17#45611yescharacteristic
122Dic17—82no—
123Dic17—82no—
124#533—172no—
125C2×C4×Q8C2×D1711yescharacteristic
126#483—342no—
127#477—342no—
128#475—342no—
129#467—342no—
130#462—342no—
131#462—342no—
132#451—342no—
133#441—344no—
134#432—172no—
135C2×C4⋊C8C2×D1711yescharacteristic
136C2×#97C2×D1711yescharacteristic
137#336—22no—
138#330—344no—
139C2×C17—22no—
140C2×C17#200711yescharacteristic
141C2×C17#201011yescharacteristic
142C2×C17#202011yescharacteristic
143C22×Q8D6811yescharacteristic
144C2×Q16—342no—
145C2×Q16—344no—
146C22×C8—21no—
147C22×C8C22⋊D1712yes—
148C4⋊Q8—172no—
149C4⋊Q8—172no—
150#125—342no—
151C22⋊Q8—342no—
152C22⋊Q8—342no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—342no—
156C4×Q8—342no—
157#117—342no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4D6811yescharacteristic
160C2×C42—21no—
161C2×C42C22×D1711yescharacteristic
162#107—342no—
163#106—344no—
164C4⋊C8—22no—
165C4⋊C8—342no—
166#103—344no—
167#103—344no—
168#103—344no—
169C22⋊C8—342no—
170#97—22no—
171#97—174no—
172C17#1003111yescharacteristic, complemented, Sylow
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—342no—
176C2×Q8—342no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4C2×D6811yescharacteristic
180C22×C4#6325211yescharacteristic
181C22×C4C2×C22⋊D1711yescharacteristic
182Q16—688no—
183Q16—1362no—
184C2×C8—22no—
185C2×C8—22no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—42no—
189C2×C8—344no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—342no—
193C4⋊C4—342no—
194C4⋊C4—342no—
195C4⋊C4—342no—
196C4⋊C4—682no—
197C4⋊C4—682no—
198C22⋊C4—682no—
199C42—41no—
200C42—41no—
201C42—682no—
202C42D4×D1712yes—
203C42D4×D1712yes—
204C23#1058761611yescharacteristic
205Q8—24no—
206Q8—42no—
207Q8—684no—
208Q8—682no—
209Q8—682no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—682no—
220C2×C4—682no—
221C2×C4#1058756812yes—
222C2×C4#1058757012yes—
223C2×C4#1058762311yescharacteristic
224C2×C4#1058762611yescharacteristic
225C8—42no—
226C8—42no—
227C8—684no—
228C22—21no—
229C22—21no—
230C22#1176271811yescharacteristic
231C22#1176308412yes—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—81no—
237C4—1362no—
238C4—1362no—
239C4#1176298611yescharacteristic
240C4#1176299111yescharacteristic
241C2—22no—
242C2#1452983011yescharacteristic
243C2#1452985111yescharacteristic
244C2#1452990511yescharacteristic
subgroupG/H
centerC22#11762718
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1985C2
socleC22×C17#392
prime radicalC23×C17#121
hypercenter#1985D17
hypocenterC17#10031
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
172. C17#10031semidirect

Maximal subgroups

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

subgroupindex
#145401292
#145389142
#145273982
#145266542
C17×#19852
#1003117