Finite Group Databasebeta

← #17948372

Subgroups — #17948372

Order 4352.

286 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 42 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#14543705C211yesmaximal, characteristic
2#14543647C211yesmaximal, characteristic
3#14529791C211yesmaximal, characteristic
4#11763751—21no—
5C22⋊#63216—21no—
6C2×#10587632—21no—
7C2×#10587506—21no—
8C2×#10587491C2211yescharacteristic
9#11762572C411yescharacteristic, complemented
10C22×Q16×C17C411yescharacteristic, complemented
11C22×Q8×C17—21no—
12C22×C4×D17D411yescharacteristic
13C2×C22⋊#595—41no—
14C2×C4⋊#595—41no—
15C2×Q16×C17—41no—
16C2×Q16×C17—42no—
17C22×C8×C17C2×C411yescharacteristic
18#10587632—42no—
19#10587632—42no—
20C2×#63227—41no—
21C2×C4⋊Dic17—21no—
22C2×#63225—41no—
23C22×#3622D411yescharacteristic
24(C2×#595)⋊C4—22no—
25C2×#63216—41no—
26#10587506—42no—
27#10587491—41no—
28C23×D17D811yescharacteristic
29C22×#595—42no—
30C2×Q8×C17—22no—
31C2×Q8×C17—41no—
32C2×Q8×C17—41no—
33C2×Q8×C17—41no—
34C2×Q8×C17—41no—
35C2×Q8×C17—41no—
36C22×C4×C17—41no—
37C22×C4×C17C22⋊C411yescharacteristic
38C22×Dic17—41no—
39C22×Dic17SD1611yescharacteristic
40C2×C4×D17—21no—
41C2×C4×D17—21no—
42C2×C4×D17—41no—
43C2×C4×D17—41no—
44C22⋊#595—81no—
45C22⋊#595—81no—
46C4⋊#595—81no—
47C4⋊#595—81no—
48Q16×C17—42no—
49Q16×C17—42no—
50C2×C8×C17—21no—
51C2×C8×C17—41no—
52#63227—44no—
53C4⋊Dic17—22no—
54C4⋊Dic17—41no—
55#63225—44no—
56C2×#3622—21no—
57C2×#3622—41no—
58#63216—81no—
59#7078—171nomaximal, Sylow
60C23×C17#10211yescharacteristic
61C22×D17—21no—
62C22×D17—21no—
63C22×D17—41no—
64C22×D17—41no—
65C22×D17SD3211yescharacteristic
66C22×D17Q3211yescharacteristic
67C2×#595—82no—
68C2×#595—82no—
69C2×#595—82no—
70Q8×C17—42no—
71Q8×C17—42no—
72Q8×C17—81no—
73Q8×C17—81no—
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17—42no—
77C2×C4×C17—81no—
78C2×C4×C17—81no—
79C2×C4×C17#9911yescharacteristic
80C2×C4×C17#10411yescharacteristic
81C2×Dic17—21no—
82C2×Dic17—41no—
83C2×Dic17—42no—
84C2×Dic17—81no—
85C2×Dic17—81no—
86C4×D17—41no—
87C4×D17—41no—
88C4×D17—81no—
89C8×C17—41no—
90#3622—41no—
91#2001—171no—
92#1314—171no—
93#1289—171no—
94C22×C17—21no—
95C22×C17—21no—
96C22×C17#32711yescharacteristic
97C22×C17#35811yescharacteristic
98C22×C17#36011yescharacteristic
99C2×D17—21no—
100C2×D17—21no—
101C2×D17—41no—
102C2×D17—41no—
103C2×D17—41no—
104C2×D17—41no—
105C2×D17—81no—
106#595—162no—
107C4×C17—21no—
108C4×C17—82no—
109C4×C17AΣL(1,𝔽16)11yescharacteristic
110C4×C17#35311yescharacteristic
111Dic17—41no—
112Dic17—82no—
113C22×Q16#59511yescharacteristic, complemented
114C2×C22⋊Q8—341no—
115C2×#103—341no—
116C2×C22⋊C8—171no—
117#380—341no—
118C22⋊C16—341no—
119#340—171no—
120C2×C17—21no—
121C2×C17—21no—
122C2×C17#134011yescharacteristic
123C2×C17#134311yescharacteristic
124C2×C17#134811yescharacteristic
125D17—41no—
126D17—41no—
127C22×Q8—21no—
128C23×C4—171no—
129C2×Q16—41no—
130C2×Q16—42no—
131C22×C8—171no—
132C22×C8C2×#59511yescharacteristic
133C22⋊Q8—682no—
134C22⋊Q8—682no—
135C2×C4⋊C4—341no—
136C2×C4⋊C4—681no—
137C2×C4⋊C4—681no—
138C2×C22⋊C4—681no—
139C2×C22⋊C4—681no—
140C2×C16—681no—
141#103—682no—
142C22⋊C8—681no—
143#95—342no—
144C17#707811yescharacteristic, complemented, Sylow
145C24—171no—
146C2×Q8—22no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C22×C4—41no—
153C22×C4—171no—
154C22×C4—341no—
155C22×C4—341no—
156C22×C4—681no—
157C22×C4—681no—
158C22×C4—681no—
159C22×C4—682no—
160C22×C4C22⋊#59511yescharacteristic
161Q16—42no—
162Q16—42no—
163C2×C8—21no—
164C2×C8—41no—
165C2×C8—341no—
166C2×C8—681no—
167C4⋊C4—342no—
168C4⋊C4—681no—
169C4⋊C4—684no—
170C4⋊C4—1361no—
171C4⋊C4—1361no—
172C22⋊C4—684no—
173C22⋊C4—1361no—
174C22⋊C4—1361no—
175C16—1361no—
176C23—171no—
177C23—171no—
178C23—341no—
179C23—341no—
180C23—681no—
181C23—681no—
182C23#1058754711yescharacteristic
183Q8—42no—
184Q8—42no—
185Q8—81no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—341no—
193C2×C4—681no—
194C2×C4—681no—
195C2×C4—681no—
196C2×C4—682no—
197C2×C4—1361no—
198C2×C4—1362no—
199C2×C4—1362no—
200C2×C4—1362no—
201C2×C4—1361no—
202C2×C4—1361no—
203C2×C4#1058754811yescharacteristic
204C2×C4#1058755111yescharacteristic
205C8—41no—
206C8—681no—
207C22—21no—
208C22—21no—
209C22—341no—
210C22—341no—
211C22—681no—
212C22—681no—
213C22—681no—
214C22—681no—
215C22—1361no—
216C22#1176366011yescharacteristic
217C22#1176372211yescharacteristic
218C22#1176372611yescharacteristic
219C4—21no—
220C4—82no—
221C4—2722no—
222C4—681no—
223C4—1362no—
224C4#1176370911yescharacteristic
225C4#1176371311yescharacteristic
226C2—21no—
227C2—21no—
228C2—681no—
229C2—681no—
230C2#1454375611yescharacteristic
231C2#1454376211yescharacteristic
232C2#1454377211yescharacteristic
subgroupG/H
centerC22#11763660
commutatorC22×C8×C17C2×C4
FrattiniC22×C8C2×#595
FittingC22×Q16×C17C4
socleC22×C17#327
prime radicalC23×D17D8
cosocleC2×#10587491C22
hypercenterC22×Q16#595
hypocenterC17#7078
LCSG ▷ C22×C8×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
9. #11762572C4semidirect
10. C22×Q16×C17C4semidirect
113. C22×Q16#595semidirect
144. C17#7078semidirect

Maximal subgroups

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

subgroupindex
#145437052
#145436472
#145297912
#707817