Finite Group Databasebeta

← #17949253

Subgroups — #17949253

Order 4352.

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

normal subgroups only

This group has 234 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#14543875C211yesmaximal, characteristic
2#14543719C211yesmaximal, characteristic
3#14529903C211yesmaximal, characteristic
4#11763795—21no—
5#11763705—21no—
6C2×#10587628—21no—
7C2×#10587507—21no—
8#11762775C2211yescharacteristic
9#11762574C411yescharacteristic
10C22×Q16×C17C411yescharacteristic
11C22×Q8×C17—21no—
12C2×#63252D411yescharacteristic
13D17⋊M16—41no—
14C2×Q16×C17—41no—
15C2×Q16×C17—42no—
16C22×C8×C17C2×C411yescharacteristic
17C2×#63231—41no—
18#10587628—42no—
19#10587628—42no—
20C2×#63230—41no—
21C2×#63223—21no—
22C2×#63223D411yescharacteristic
23#10587553—22no—
24#10587545—41no—
25#10587538—41no—
26#10587507—42no—
27#10587491—41no—
28C2×Q8×C17—22no—
29C2×Q8×C17—41no—
30C2×Q8×C17—41no—
31C2×Q8×C17—41no—
32C2×Q8×C17—41no—
33C2×Q8×C17—41no—
34C22×C4×C17—41no—
35C22×C4×C17C22⋊C411yescharacteristic
36C2×C22⋊D17—21no—
37#63252—41no—
38#63252—41no—
39C2×D68SD1611yescharacteristic
40C2×C4×D17—21no—
41C2×Dic34D811yescharacteristic
42#63247—42no—
43#63243—81no—
44#63242—81no—
45Q16×C17—42no—
46Q16×C17—42no—
47C2×C8×C17—21no—
48C2×C8×C17—41no—
49#63231—44no—
50#63230—44no—
51#63223—22no—
52#63223—41no—
53#63223—41no—
54C2×#3622—21no—
55C2×#3622—41no—
56#63216—81no—
57#7401—171nomaximal, Sylow
58C23×C17#10411yescharacteristic
59C22×D17—21no—
60Q8×C17—42no—
61Q8×C17—42no—
62Q8×C17—81no—
63Q8×C17—81no—
64C2×C4×C17—21no—
65C2×C4×C17—21no—
66C2×C4×C17—42no—
67C2×C4×C17—81no—
68C2×C4×C17—81no—
69C2×C4×C17#9911yescharacteristic
70C2×C4×C17#10211yescharacteristic
71C22⋊D17—81no—
72C2×Dic17—21no—
73D68—41no—
74C4×D17—41no—
75C4×D17—41no—
76Dic34—41no—
77#3624—82no—
78C8×C17—41no—
79#3622—42no—
80#3622—41no—
81#2020—171no—
82#1392—171no—
83#1321—171no—
84C22×C17—21no—
85C22×C17—41no—
86C22×C17#32711yescharacteristic
87C2×D17—41no—
88C2×D17—81no—
89C4×C17—21no—
90C4×C17—82no—
91C4×C17AΣL(1,𝔽16)11yescharacteristic
92C4×C17#35311yescharacteristic
93Dic17—41no—
94C2×#137—341no—
95C22×Q16#59511yescharacteristic
96#413—341no—
97C2×#101—341no—
98#408—171no—
99#349—341no—
100#341—171no—
101C2×C17—21no—
102C2×C17—41no—
103C2×C17#134311yescharacteristic
104D17—81no—
105C2×#41—171no—
106C22×Q8—21no—
107#137—682no—
108#137—682no—
109C2×Q16—41no—
110C2×Q16—42no—
111C2×Q16—681no—
112C2×SD16—681no—
113C2×M16—171no—
114C2×M16—341no—
115C2×M16—681no—
116C22×C8C2×#59511yescharacteristic
117M32—681no—
118#101—682no—
119#101—681no—
120#100—342no—
121C22⋊C8—681no—
122C17#740111yescharacteristic, complemented, Sylow
123#41—681no—
124#41—681no—
125C2×Q8—22no—
126C2×Q8—41no—
127C2×Q8—41no—
128C2×Q8—41no—
129C2×Q8—41no—
130C2×Q8—41no—
131C2×Q8—171no—
132C2×D4—171no—
133C2×D4—341no—
134C22×C4—41no—
135C22×C4—341no—
136C22×C4C22⋊#59511yescharacteristic
137Q16—42no—
138Q16—42no—
139Q16—684no—
140SD16—684no—
141M16—342no—
142M16—681no—
143M16—681no—
144M16—682no—
145M16—1361no—
146C2×C8—21no—
147C2×C8—41no—
148C2×C8—341no—
149C2×C8—681no—
150C2×C8—1361no—
151C16—1361no—
152C23—341no—
153C23#1058754811yescharacteristic
154Q8—42no—
155Q8—42no—
156Q8—81no—
157Q8—81no—
158Q8—681no—
159D4—681no—
160D4—1361no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4—341no—
167C2×C4—681no—
168C2×C4—681no—
169C2×C4#1058754711yescharacteristic
170C2×C4#1058755111yescharacteristic
171C8—41no—
172C8—682no—
173C8—681no—
174C8—1362no—
175C22—21no—
176C22—41no—
177C22—681no—
178C22—1361no—
179C22#1176366011yescharacteristic
180C4—21no—
181C4—82no—
182C4—681no—
183C4#1176370911yescharacteristic
184C4#1176371311yescharacteristic
185C2—21no—
186C2—41no—
187C2—1361no—
188C2#1454376211yescharacteristic
subgroupG/H
centerC2#14543762
commutatorC22×C8×C17C2×C4
FrattiniC22×C8C2×#595
FittingC22×Q16×C17C4
socleC2×C17#1343
prime radicalC2×#63252D4
cosocle#11762775C22
hypercenterC22×Q16#595
hypocenterC17#7401
LCSG ▷ C22×C8×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
122. C17#7401semidirect

Maximal subgroups

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

subgroupindex
#145438752
#145437192
#145299032
#740117