Finite Group Databasebeta

← #17949247

Subgroups — #17949247

Order 4352.

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

normal subgroups only

This group has 258 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#14543872C211yesmaximal, characteristic, complemented
2#14543719C211yesmaximal, characteristic, complemented
3#14529891C211yesmaximal, characteristic
4#11763788—21no—
5#11763705—21no—
6C2×#10587618—21no—
7C2×#10587504—21no—
8#11762775C2211yescharacteristic
9#11762574C411yescharacteristic, complemented
10C22×D8×C17C411yescharacteristic, complemented
11C22×D4×C17—21no—
12C2×#63252D411yescharacteristic
13#10587677—41no—
14C2×D8×C17—41no—
15C2×D8×C17—42no—
16C22×C8×C17C2×C411yescharacteristic
17C2×#63229—41no—
18#10587618—42no—
19#10587618—42no—
20C2×#63228—41no—
21C2×#63223—21no—
22C2×#63223D411yescharacteristic
23#10587551—22no—
24#10587539—41no—
25#10587538—41no—
26#10587504—42no—
27#10587491—41no—
28C24×C17—41no—
29C2×D4×C17—22no—
30C2×D4×C17—41no—
31C2×D4×C17—41no—
32C2×D4×C17—41no—
33C2×D4×C17—41no—
34C2×D4×C17—41no—
35C22×C4×C17C22⋊C411yescharacteristic
36C2×C22⋊D17—21no—
37#63252—41no—
38#63252—41no—
39C2×D68D811yescharacteristic
40C2×C4×D17—21no—
41C2×Dic34SD1611yescharacteristic
42C22⋊#595—42no—
43C4⋊#595—81no—
44C4×#595—81no—
45D8×C17—42no—
46D8×C17—42no—
47C2×C8×C17—21no—
48C2×C8×C17—41no—
49#63229—44no—
50#63228—44no—
51#63223—22no—
52#63223—41no—
53#63223—41no—
54C2×#3622—21no—
55C2×#3622—41no—
56#63216—81no—
57#7398—171nomaximal, Sylow
58C23×C17—42no—
59C23×C17—81no—
60C23×C17—81no—
61C23×C17—162no—
62C23×C17#10411yescharacteristic
63C22×D17—21no—
64C2×#595—82no—
65D4×C17—42no—
66D4×C17—42no—
67D4×C17—81no—
68D4×C17—81no—
69C2×C4×C17—21no—
70C2×C4×C17—21no—
71C2×C4×C17#9911yescharacteristic
72C2×C4×C17#10211yescharacteristic
73C22⋊D17—81no—
74C2×Dic17—21no—
75D68—41no—
76C4×D17—41no—
77C4×D17—41no—
78Dic34—41no—
79C8×C17—41no—
80#3622—42no—
81#3622—41no—
82#2018—171no—
83#1391—171no—
84#1321—171no—
85C22×C17—21no—
86C22×C17—41no—
87C22×C17—82no—
88C22×C17—162no—
89C22×C17—162no—
90C22×C17—162no—
91C22×C17#32711yescharacteristic
92C2×D17—41no—
93C2×D17—81no—
94#595—162no—
95C4×C17—21no—
96C4×C17AΣL(1,𝔽16)11yescharacteristic
97C4×C17#35311yescharacteristic
98Dic17—41no—
99C2×AGL(1,ℤ/8)—341no—
100C22×D8#59511yescharacteristic, complemented
101C2×#100—341no—
102#410—341no—
103#408—171no—
104#349—341no—
105#341—171no—
106C2×C17—21no—
107C2×C17—41no—
108C2×C17—162no—
109C2×C17#134311yescharacteristic
110D17—81no—
111C2×#41—171no—
112C22×D4—21no—
113AGL(1,ℤ/8)—682no—
114AGL(1,ℤ/8)—682no—
115C2×SD16—681no—
116C2×D8—41no—
117C2×D8—42no—
118C2×D8—681no—
119C2×M16—171no—
120C2×M16—341no—
121C22×C8C2×#59511yescharacteristic
122#117—681no—
123M32—681no—
124#100—682no—
125#99—342no—
126#99—681no—
127C22⋊C8—681no—
128C17#739811yescharacteristic, complemented, Sylow
129C24—41no—
130#41—681no—
131#41—681no—
132C2×Q8—171no—
133C2×D4—22no—
134C2×D4—41no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4—41no—
138C2×D4—41no—
139C2×D4—171no—
140C2×D4—341no—
141C22×C4—341no—
142C22×C4C22⋊#59511yescharacteristic
143SD16—684no—
144D8—42no—
145D8—42no—
146D8—684no—
147M16—342no—
148M16—681no—
149M16—681no—
150C2×C8—21no—
151C2×C8—41no—
152C2×C8—341no—
153C2×C8—681no—
154C4⋊C4—1361no—
155C22⋊C4—682no—
156C42—1361no—
157C16—1361no—
158C23—42no—
159C23—81no—
160C23—81no—
161C23—162no—
162C23—341no—
163C23#1058754811yescharacteristic
164Q8—681no—
165D4—42no—
166D4—42no—
167D4—81no—
168D4—81no—
169D4—681no—
170D4—1361no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—341no—
174C2×C4—681no—
175C2×C4—681no—
176C2×C4—1362no—
177C2×C4#1058754711yescharacteristic
178C2×C4#1058755111yescharacteristic
179C8—41no—
180C8—682no—
181C8—681no—
182C22—21no—
183C22—41no—
184C22—82no—
185C22—162no—
186C22—162no—
187C22—162no—
188C22—681no—
189C22—1361no—
190C22#1176366011yescharacteristic
191C4—21no—
192C4—2722no—
193C4—681no—
194C4#1176370911yescharacteristic
195C4#1176371311yescharacteristic
196C2—21no—
197C2—41no—
198C2—162no—
199C2—1361no—
200C2#1454376211yescharacteristic
subgroupG/H
centerC2#14543762
commutatorC22×C8×C17C2×C4
FrattiniC22×C8C2×#595
FittingC22×D8×C17C4
socleC2×C17#1343
prime radical#14529891C2
cosocle#11762775C22
hypercenterC22×D8#595
hypocenterC17#7398
LCSG ▷ C22×C8×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. #14543872C2semidirect
2. #14543719C2semidirect
9. #11762574C4semidirect
10. C22×D8×C17C4semidirect
100. C22×D8#595semidirect
128. C17#7398semidirect

Maximal subgroups

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

subgroupindex
#145438722
#145437192
#145298912
#739817