Finite Group Databasebeta

← #17949117

Subgroups — #17949117

Order 4352.

356 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 38 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#14543710C212yesmaximal, complemented
2#14528702C211yesmaximal, characteristic
3#11763652—22no—
4C2×#10587505—22no—
5#11762672C411yescharacteristic
6#11762672C2211yescharacteristic
7C22×#41×C17C411yescharacteristic
8C2×#41×C17—41no—
9C2×#41×C17—41no—
10C2×#41×C17—44no—
11C22×Q8×C17C811yescharacteristic, complemented
12C22×D4×C17—21no—
13C22×D4×C17C811yescharacteristic, complemented
14C23×C4×C17—21no—
15C23×C4×C17C2×C411yescharacteristic
16C2×C22⋊Dic17—21no—
17C2×C22⋊Dic17D412yes—
18C22⋊#3624—42no—
19#10587505—44no—
20#10587502—41no—
21#10587502—41no—
22C24×C17—21no—
23C24×C17C22⋊C411yescharacteristic
24#41×C17—44no—
25#41×C17—44no—
26#41×C17—44no—
27#41×C17—44no—
28C2×Q8×C17—42no—
29C2×Q8×C17—41no—
30C2×D4×C17—24no—
31C2×D4×C17—41no—
32C2×D4×C17—42no—
33C2×D4×C17—41no—
34C2×D4×C17—41no—
35C2×D4×C17—42no—
36C22×C4×C17—21no—
37C22×C4×C17—21no—
38C22×C4×C17—21no—
39C22×C4×C17—42no—
40C22×C4×C17—42no—
41C22×C4×C17—42no—
42C22×C4×C17—42no—
43C22×C4×C17C2×C811yescharacteristic
44C22×C4×C17M1611yescharacteristic
45C22×Dic17—22no—
46C22×Dic17—41no—
47C2×#3624—82no—
48C22⋊Dic17—42no—
49C22⋊Dic17—42no—
50#7339—171nomaximal, Sylow
51C23×C17—22no—
52C23×C17—22no—
53C23×C17—41no—
54C23×C17—41no—
55C23×C17—81no—
56C23×C17—82no—
57C23×C17C22⋊C811yescharacteristic
58C23×C17#9911yescharacteristic
59C23×C17#10011yescharacteristic
60Q8×C17—42no—
61Q8×C17—42no—
62D4×C17—44no—
63D4×C17—42no—
64D4×C17—42no—
65D4×C17—44no—
66C2×C4×C17—22no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—41no—
70C2×C4×C17—42no—
71C2×C4×C17—48no—
72C2×C4×C17—41no—
73C2×C4×C17—42no—
74C2×C4×C17—41no—
75C2×C4×C17—41no—
76C2×Dic17—42no—
77C2×Dic17—82no—
78C2×Dic17—81no—
79C2×Dic17—82no—
80#3624—162no—
81#1782—171no—
82#1317—172no—
83C22×C17—21no—
84C22×C17—21no—
85C22×C17—41no—
86C22×C17—41no—
87C22×C17—41no—
88C22×C17—42no—
89C22×C17—82no—
90C22×C17—82no—
91C22×C17—82no—
92C22×C17—82no—
93C22×C17#32311yescharacteristic
94C22×C17AΣL(1,𝔽16)12yes—
95C4×C17—41no—
96C4×C17—42no—
97C4×C17—41no—
98Dic17—82no—
99Dic17—161no—
100C22×#41#59511yescharacteristic
101C2×#99—342no—
102#381—171no—
103#381—171no—
104#323—342no—
105C2×C17—22no—
106C2×C17—21no—
107C2×C17—41no—
108C2×C17—41no—
109C2×C17—82no—
110C2×C17#131611yescharacteristic
111C2×#41—41no—
112C2×#41—41no—
113C2×#41—44no—
114C22×Q8#362411yescharacteristic, complemented
115C22×D4—21no—
116C22×D4#362411yescharacteristic, complemented
117C23×C4—21no—
118C23×C4C2×#59511yescharacteristic
119C2×C22⋊C4—172no—
120C2×C22⋊C4—341no—
121#99—684no—
122C22⋊C8—682no—
123#95—681no—
124#95—681no—
125C17#733911yescharacteristic, complemented, Sylow
126C24—21no—
127C24C22⋊#59511yescharacteristic
128#41—44no—
129#41—44no—
130#41—44no—
131#41—44no—
132C2×Q8—42no—
133C2×Q8—41no—
134C2×D4—24no—
135C2×D4—41no—
136C2×D4—42no—
137C2×D4—41no—
138C2×D4—41no—
139C2×D4—42no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—342no—
148C22×C4—681no—
149C22×C4C2×#362411yescharacteristic
150C22×C4#6324711yescharacteristic
151C2×C8—1362no—
152C22⋊C4—682no—
153C22⋊C4—682no—
154C23—22no—
155C23—22no—
156C23—41no—
157C23—41no—
158C23—81no—
159C23—82no—
160C23#1058755111yescharacteristic
161C23C22⋊#362411yescharacteristic
162C23#1058755311yescharacteristic
163Q8—42no—
164Q8—42no—
165D4—44no—
166D4—42no—
167D4—42no—
168D4—44no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—48no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—682no—
180C2×C4—1361no—
181C2×C4—1362no—
182C2×C4—1362no—
183C8—2722no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—42no—
190C22—82no—
191C22—82no—
192C22—82no—
193C22—82no—
194C22#1176365211yescharacteristic
195C22#1176370912yes—
196C4—41no—
197C4—42no—
198C4—41no—
199C4—2721no—
200C4—1362no—
201C2—22no—
202C2—21no—
203C2—41no—
204C2—41no—
205C2—82no—
206C2#1454370811yescharacteristic
subgroupG/H
centerC2#14543708
commutatorC22×C4×C17C2×C8
FrattiniC23×C4C2×#595
Fitting, prime radicalC22×#41×C17C4
socleC2×C17#1316
cosocle#11762672C22
hypercenterC22×#41#595
hypocenterC17#7339
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #14543710C2semidirect
11. C22×Q8×C17C8semidirect
13. C22×D4×C17C8semidirect
114. C22×Q8#3624semidirect
116. C22×D4#3624semidirect
125. C17#7339semidirect

Maximal subgroups

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

subgroupindex
#145437102
#145287022
#733917