Finite Group Databasebeta

← C2×#14534749 #17201446

Subgroups — C2×#14534749 #17201446

Order 4352.

1830 conjugacy classes of subgroups; only the 667 normal subgroups are shown.

normal subgroups only

This group has 1830 conjugacy classes of subgroups — too many to draw. Only its 667 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#14534749C2116yesmaximal, direct product factor
2C2×C17⋊#401C212yesmaximal
3C2×#11762750C216yesmaximal
4C2×#11762715C213yesmaximal
5C2×#11762707C213yesmaximal
6C2×C17×#376C211yesmaximal, characteristic
7C23×Dic34C2211yescharacteristic
8C22×C4⋊Dic17C2213yes—
9C22×#63225C2216yes—
10C17⋊#401C22116yes—
11#11762750C22148yes—
12#11762715C22124yes—
13#11762707C22124yes—
14C2×#10587502C2216yes—
15C2×#10587502C2216yes—
16C2×#10587502C2216yes—
17C22×C42×C17C2213yes—
18C17×#376C2218yes—
19C2×C17×#95C2213yes—
20C2×C17×#95C2211yescharacteristic
21C23×C4×C17C2313yes—
22C23×C4×C17C2313yes—
23C23×C4×C17C2311yescharacteristic
24C23×Dic17C2316yes—
25C23×Dic17C2312yes—
26C22×Dic34—212no—
27C22×Dic34C2314yes—
28C2×C42×C17—212no—
29C2×C42×C17C23112yes—
30C2×C4⋊Dic17—212no—
31C2×C4⋊Dic17C23112yes—
32C2×#63225—412no—
33C2×#63225C23124yes—
34C17×#95C23112yes—
35C17×#95C2314yes—
36#10587502C23124yes—
37#10587502C23124yes—
38#10587502C23124yes—
39C24×C17C2411yescharacteristic
40C22×C4×C17—26no—
41C22×C4×C17—26no—
42C22×C4×C17—26no—
43C22×C4×C17—212no—
44C22×C4×C17—26no—
45C22×C4×C17#41112yes—
46C22×C4×C17C2416yes—
47C22×C4×C17C2416yes—
48C22×C4×C17C2412yes—
49C22×Dic17—212no—
50C22×Dic17—212no—
51C22×Dic17—212no—
52C22×Dic17—212no—
53C22×Dic17C2414yes—
54C22×Dic17C24112yes—
55C2×Dic34—224no—
56C2×Dic34—416no—
57C42×C17—224no—
58C4⋊Dic17—224no—
59#63225—424no—
60C2×#2645—171nomaximal, Sylow
61C23×C17C2×#4116yes—
62C23×C17H(5,𝔽2)12yes—
63C23×C172−1+416yes—
64C23×C17C2511yescharacteristic
65C2×C4×C17—26no—
66C2×C4×C17—26no—
67C2×C4×C17—26no—
68C2×C4×C17—212no—
69C2×C4×C17—26no—
70C2×C4×C17—412no—
71C2×C4×C17—412no—
72C2×C4×C17#126116yes—
73C2×C4×C17C2×#41112yes—
74C2×Dic17—212no—
75C2×Dic17—212no—
76C2×Dic17—212no—
77C2×Dic17—212no—
78C2×Dic17—48no—
79C2×Dic17—424no—
80Dic34—416no—
81#2645—1716no—
82C2×#401—172no—
83C2×#400—176no—
84C2×#391—173no—
85C2×#389—173no—
86C2×#376D1711yescharacteristic
87C22×C17C2×#12614yes—
88C22×C17#541112yes—
89C22×C17#542112yes—
90C22×C17C22×#4113yes—
91C22×C17C2×H(5,𝔽2)11yescharacteristic
92C22×C17C2×2−1+413yes—
93C4×C17—46no—
94C4×C17—46no—
95C4×C17C2×#12618yes—
96Dic17—44no—
97Dic17—412no—
98C23×Q8—171no—
99C22×C4⋊C4—173no—
100C22×C4⋊C4—176no—
101C22×C42C2×D1713yes—
102#401—1716no—
103#400—1748no—
104#391—1724no—
105#389—1724no—
106#376C2×D1718yes—
107C2×#95—176no—
108C2×#95—176no—
109C2×#95—176no—
110C2×#95C2×D1713yes—
111C2×#95C2×D1711yescharacteristic
112C2×C17#264518yescomplemented
113C2×C17C22×#12611yescharacteristic
114C2×C17C2×#54113yes—
115C2×C17C2×#54213yes—
116C22×Q8—174no—
117C22×Q8—3412no—
118C23×C4—176no—
119C23×C4—172no—
120C23×C4C22×D1713yes—
121C23×C4C22×D1713yes—
122C23×C4C22×D1711yescharacteristic
123C2×C4⋊C4—1712no—
124C2×C4⋊C4—1724no—
125C2×C4⋊C4—3412no—
126C2×C4⋊C4—6812no—
127C2×C42—212no—
128C2×C42C22×D17112yes—
129#95—1724no—
130#95—1724no—
131#95—1724no—
132#95C22×D17112yes—
133#95C22×D1714yes—
134C17C2×#264511yescharacteristic, complemented, Sylow
135C24C23×D1711yescharacteristic
136C2×Q8—3424no—
137C2×Q8—6816no—
138C22×C4—26no—
139C22×C4—26no—
140C22×C4—26no—
141C22×C4—212no—
142C22×C4—26no—
143C22×C4—174no—
144C22×C4—1712no—
145C22×C4—3412no—
146C22×C4—3412no—
147C22×C4—3412no—
148C22×C4—3412no—
149C22×C4#63252112yes—
150C22×C4C23×D1716yes—
151C22×C4C23×D1716yes—
152C22×C4C23×D1712yes—
153C4⋊C4—3424no—
154C4⋊C4—6824no—
155C42—224no—
156C23C2×#6325216yes—
157C23#1058769612yes—
158C23#1058769716yes—
159C23C24×D1711yescharacteristic
160Q8—6816no—
161C2×C4—26no—
162C2×C4—26no—
163C2×C4—26no—
164C2×C4—212no—
165C2×C4—26no—
166C2×C4—412no—
167C2×C4—412no—
168C2×C4—3412no—
169C2×C4—3412no—
170C2×C4—3412no—
171C2×C4—3412no—
172C2×C4—688no—
173C2×C4—6824no—
174C2×C4#10587562116yes—
175C2×C4C2×#63252112yes—
176C22C2×#1058756214yes—
177C22#11763421112yes—
178C22#11763430112yes—
179C22C22×#6325213yes—
180C22C2×#1058769611yescharacteristic
181C22C2×#1058769713yes—
182C4—46no—
183C4—46no—
184C4—6812no—
185C4—684no—
186C4C2×#1058756218yes—
187C2#1453474918yesdirect product factor
188C2C22×#1058756211yescharacteristic
189C2C2×#1176342113yes—
190C2C2×#1176343013yes—
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#376C2
socle, prime radicalC24×C17C24
hypercenterC2×#376D17
hypocenterC17C2×#2645
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
1. #14534749C2direct (N × H)
112. C2×C17#2645semidirect
134. C17C2×#2645semidirect
187. C2#14534749direct (N × H)

Maximal subgroups

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

subgroupindex
#145347492
C2×C17⋊#4012
C2×#117627502
C2×#117627152
C2×#117627072
C2×C17×#3762
C2×#264517