Finite Group Databasebeta

← #17949262

Subgroups — #17949262

Order 4352.

252 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 36 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#14543881C211yesmaximal, characteristic
2#14543715C211yesmaximal, characteristic
3#14529886C211yesmaximal, characteristic
4C2×#10587545—21no—
5#11763654—21no—
6C22×Dic68—21no—
7C2×#10587555C411yescharacteristic
8C2×#10587487—21no—
9#11762715C2211yescharacteristic
10C17×#336C411yescharacteristic
11C22×Dic34—21no—
12C22×Dic34D411yescharacteristic
13C2×#63247—41no—
14C22×C8×C17—21no—
15C2×C42×C17C2×C411yescharacteristic
16C2×C4⋊Dic17—41no—
17C2×C4⋊Dic17D411yescharacteristic
18C2×Dic68—42no—
19C2×Dic68—42no—
20C2×Dic68—41no—
21C2×Dic68—41no—
22#10587555—42no—
23C22⋊#3624—41no—
24#10587545—22no—
25#10587545—41no—
26#10587502—41no—
27#10587487—42no—
28C22×C4×C17—21no—
29C22×C4×C17C22⋊C411yescharacteristic
30C22×Dic17—21no—
31C22×Dic17—21no—
32C22×Dic17—41no—
33C2×Dic34—22no—
34C2×Dic34—21no—
35C2×Dic34—41no—
36C2×Dic34—41no—
37C2×Dic34—41no—
38C2×Dic34—41no—
39C2×Dic34—41no—
40C2×Dic34—41no—
41C2×Dic34—41no—
42C2×Dic34D811yescharacteristic
43C2×Dic34SD1611yescharacteristic
44#63247—42no—
45#63247—81no—
46C2×#3624—81no—
47C2×#3624—81no—
48C2×C8×C17—22no—
49C2×C8×C17—41no—
50C2×C8×C17—41no—
51C42×C17—41no—
52C4⋊Dic17—42no—
53C4⋊Dic17—41no—
54C4⋊Dic17—42no—
55Dic68—44no—
56Dic68—44no—
57#7405—171nomaximal, Sylow
58C23×C17#9911yescharacteristic
59C2×C4×C17—21no—
60C2×C4×C17—21no—
61C2×C4×C17—22no—
62C2×C4×C17—41no—
63C2×C4×C17—41no—
64C2×C4×C17#10211yescharacteristic
65C2×C4×C17#10411yescharacteristic
66C2×Dic17—21no—
67C2×Dic17—21no—
68C2×Dic17—41no—
69C2×Dic17—41no—
70C2×Dic17—42no—
71C2×Dic17—41no—
72C2×Dic17—81no—
73C2×Dic17—81no—
74C2×Dic17—81no—
75Dic34—41no—
76Dic34—41no—
77Dic34—42no—
78Dic34—42no—
79Dic34—81no—
80Dic34—81no—
81Dic34—81no—
82#3624—82no—
83#3624—161no—
84C8×C17—42no—
85#2016—171no—
86#1394—171no—
87#1319—171no—
88C22×C17—21no—
89C22×C17—21no—
90C22×C17#32711yescharacteristic
91C22×C17AΣL(1,𝔽16)11yescharacteristic
92C22×C17#35311yescharacteristic
93C4×C17—21no—
94C4×C17—21no—
95C4×C17—42no—
96Dic17—41no—
97Dic17—41no—
98Dic17—82no—
99Dic17—81no—
100C22×Q16—341no—
101C2×C4⋊Q8—171no—
102C2×#103—341no—
103C2×#101—341no—
104#391—171no—
105#336#59511yescharacteristic
106#324—341no—
107C2×C17—21no—
108C2×C17—21no—
109C2×C17#134311yescharacteristic
110C2×C17#140711yescharacteristic
111C2×C17#141111yescharacteristic
112C22×Q8—171no—
113C22×Q8—341no—
114C2×Q16—682no—
115C2×Q16—681no—
116C2×Q16—681no—
117C2×Q16—682no—
118C2×M16—681no—
119C22×C8—21no—
120C4⋊Q8—682no—
121C2×C4⋊C4—171no—
122C2×C4⋊C4—681no—
123C2×C42C2×#59511yescharacteristic
124#103—682no—
125#101—342no—
126#101—681no—
127C22⋊C8—681no—
128#95—681no—
129C17#740511yescharacteristic, complemented, Sylow
130C2×Q8—171no—
131C2×Q8—171no—
132C2×Q8—342no—
133C2×Q8—341no—
134C2×Q8—681no—
135C2×Q8—681no—
136C2×Q8—681no—
137C2×Q8—681no—
138C2×Q8—681no—
139C2×Q8—681no—
140C2×Q8—681no—
141C22×C4—21no—
142C22×C4—341no—
143C22×C4—341no—
144C22×C4—681no—
145C22×C4C22⋊#59511yescharacteristic
146Q16—684no—
147Q16—684no—
148M16—682no—
149M16—1361no—
150C2×C8—22no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8—1361no—
154C2×C8—1361no—
155C4⋊C4—681no—
156C4⋊C4—682no—
157C4⋊C4—682no—
158C42—41no—
159C23#1058753911yescharacteristic
160Q8—681no—
161Q8—681no—
162Q8—682no—
163Q8—682no—
164Q8—1361no—
165Q8—1361no—
166Q8—1361no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—341no—
173C2×C4—341no—
174C2×C4—681no—
175C2×C4—681no—
176C2×C4—681no—
177C2×C4—682no—
178C2×C4—1361no—
179C2×C4—1361no—
180C2×C4—1361no—
181C2×C4#1058754711yescharacteristic
182C2×C4#1058755011yescharacteristic
183C8—42no—
184C8—2721no—
185C8—1362no—
186C22—21no—
187C22—21no—
188C22#1176366111yescharacteristic
189C22#1176371011yescharacteristic
190C22#1176371411yescharacteristic
191C4—21no—
192C4—21no—
193C4—42no—
194C4—681no—
195C4—681no—
196C4—1361no—
197C4—1362no—
198C2—21no—
199C2—21no—
200C2#1454376311yescharacteristic
201C2#1454391411yescharacteristic
202C2#1454392211yescharacteristic
subgroupG/H
centerC22#11763714
commutatorC2×C42×C17C2×C4
FrattiniC2×C42C2×#595
FittingC17×#336C4
socleC22×C17#353
prime radicalC23×C17#99
cosocle#11762715C22
hypercenter#336#595
hypocenterC17#7405
LCSG ▷ C2×C42×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
129. C17#7405semidirect

Maximal subgroups

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

subgroupindex
#145438812
#145437152
#145298862
#740517