Finite Group Databasebeta

← #17949287

Subgroups — #17949287

Order 4352.

198 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 32 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#14543731C211yesmaximal, characteristic, complemented
2#14543692C211yesmaximal, characteristic, complemented
3#14530068C211yesmaximal, characteristic
4#11763812—21no—
5#11763705—21no—
6#11762832C2211yescharacteristic
7C2×#10587508—21no—
8#11762793—21no—
9#11762567C411yescharacteristic
10C17×#575C411yescharacteristic
11C2×#41×C17—21no—
12C2×#63247—22no—
13C17×#137—41no—
14C17×AGL(1,ℤ/8)—41no—
15C17×#135—41no—
16C2×M16×C17C2×C411yescharacteristic
17C2×C4×Dic17D411yescharacteristic
18C2×#63223—21no—
19C2×#63223D411yescharacteristic
20#10587544—41no—
21C4⋊#3624—41no—
22#10587538—41no—
23#10587508—41no—
24#10587508—41no—
25#10587507—41no—
26#10587504—41no—
27#10587485—41no—
28#41×C17—41no—
29#41×C17—41no—
30#41×C17—41no—
31#41×C17—41no—
32C2×Q8×C17—21no—
33C2×D4×C17—21no—
34C2×D4×C17—41no—
35C22×C4×C17—41no—
36C22×C4×C17C22⋊C411yescharacteristic
37C22×Dic17—21no—
38#63247—82no—
39C2×#3624—42no—
40Q16×C17—41no—
41SD16×C17—42no—
42D8×C17—41no—
43M16×C17—41no—
44C2×C8×C17—21no—
45C4×Dic17—21no—
46C4×Dic17D811yescharacteristic
47C4×Dic17SD1611yescharacteristic
48#63223—41no—
49#63223—41no—
50#63223—41no—
51C2×#3622—21no—
52C2×#3622—41no—
53#63216—81no—
54#7414—171nomaximal, Sylow
55C23×C17—41no—
56C23×C17#10411yescharacteristic
57Q8×C17—41no—
58Q8×C17—41no—
59D4×C17—41no—
60D4×C17—41no—
61D4×C17—81no—
62D4×C17—81no—
63C2×C4×C17—21no—
64C2×C4×C17—21no—
65C2×C4×C17—41no—
66C2×C4×C17—81no—
67C2×C4×C17—81no—
68C2×C4×C17#9911yescharacteristic
69C2×C4×C17#10211yescharacteristic
70C2×Dic17—21no—
71C2×Dic17—21no—
72C2×Dic17—41no—
73C2×Dic17—41no—
74#3624—82no—
75C8×C17—41no—
76#3622—41no—
77#3622—81no—
78#2050—171no—
79#1327—171no—
80#1309—171no—
81C22×C17—21no—
82C22×C17—41no—
83C22×C17—81no—
84C22×C17—161no—
85C22×C17#32711yescharacteristic
86C4×C17—21no—
87C4×C17—81no—
88C4×C17AΣL(1,𝔽16)11yescharacteristic
89C4×C17#35511yescharacteristic
90Dic17—21no—
91Dic17—21no—
92Dic17—41no—
93#575#59511yescharacteristic
94#423—171no—
95#423—341no—
96C2×#104—341no—
97#413—341no—
98#349—341no—
99#338—171no—
100C2×C17—21no—
101C2×C17—41no—
102C2×C17—161no—
103C2×C17#134511yescharacteristic
104C2×#41—21no—
105#137—41no—
106AGL(1,ℤ/8)—41no—
107#135—41no—
108C2×M16—171no—
109C2×M16—341no—
110C2×M16—342no—
111C2×M16C2×#59511yescharacteristic
112C2×C42—171no—
113M32—681no—
114C4⋊C8—681no—
115C4⋊C8—681no—
116C4⋊C8—681no—
117#104—681no—
118#104—681no—
119#101—681no—
120#100—681no—
121C17#741411yescharacteristic, complemented, Sylow
122#41—41no—
123#41—41no—
124#41—41no—
125#41—41no—
126C2×Q8—21no—
127C2×D4—21no—
128C2×D4—41no—
129C22×C4—41no—
130C22×C4—341no—
131C22×C4C22⋊#59511yescharacteristic
132Q16—41no—
133SD16—42no—
134D8—41no—
135M16—41no—
136M16—681no—
137M16—681no—
138M16—681no—
139M16—1362no—
140C2×C8—21no—
141C2×C8—341no—
142C2×C8—681no—
143C2×C8—682no—
144C42—171no—
145C42—171no—
146C42—341no—
147C16—1361no—
148C23—41no—
149C23#1058754811yescharacteristic
150Q8—41no—
151Q8—41no—
152D4—41no—
153D4—41no—
154D4—81no—
155D4—81no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—341no—
162C2×C4—341no—
163C2×C4—681no—
164C2×C4—681no—
165C2×C4#1058754711yescharacteristic
166C2×C4#1058755111yescharacteristic
167C8—41no—
168C8—681no—
169C8—1361no—
170C8—1362no—
171C22—21no—
172C22—41no—
173C22—81no—
174C22—161no—
175C22#1176366011yescharacteristic
176C4—21no—
177C4—81no—
178C4—341no—
179C4—341no—
180C4—681no—
181C4#1176370911yescharacteristic
182C4#1176371711yescharacteristic
183C2—21no—
184C2—41no—
185C2—161no—
186C2#1454376611yescharacteristic
subgroupG/H
centerC2#14543766
commutatorC2×M16×C17C2×C4
FrattiniC2×M16C2×#595
Fitting, prime radicalC17×#575C4
socleC2×C17#1345
cosocle#11762832C22
hypercenter#575#595
hypocenterC17#7414
LCSG ▷ C2×M16×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14543731C2semidirect
2. #14543692C2semidirect
121. C17#7414semidirect

Maximal subgroups

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

subgroupindex
#145437312
#145436922
#145300682
#741417