Finite Group Databasebeta

← #17949029

Subgroups — #17949029

Order 4352.

484 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 54 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#14544613C212yesmaximal
2#14528695C211yesmaximal, characteristic
3C2×#10587539—22no—
4C2×#10587551C414yescomplemented
5#11763752—22no—
6C22×#63252C2211yescharacteristic
7C2×C22⋊#3622C411yescharacteristic, complemented
8C2×#10587491—22no—
9C2×C17×C22⋊C8C411yescharacteristic, complemented
10C23×C4×C17C2×C411yescharacteristic
11C22×C22⋊D17C2×C412yes—
12C2×#63252—41no—
13C2×#63252—41no—
14C2×#63252—44no—
15C22×D68D411yescharacteristic
16C22×C4×D17D412yes—
17C22×Dic34Q811yescharacteristic
18C2×C22⋊#595—24no—
19C22×C8×C17—21no—
20C22×#3622—21no—
21#10587551—44no—
22(C2×#595)⋊C4—42no—
23(C2×#595)⋊C4—42no—
24#10587539—44no—
25C17×C22⋊C8—41no—
26C22⋊#3622—41no—
27#10587491—44no—
28C24×C17C4211yescharacteristic
29C23×D17C22⋊C412yes—
30C22×#595—44no—
31C22×C4×C17—21no—
32C22×C4×C17—21no—
33C22×C4×C17—42no—
34C22×C4×C17C22⋊C411yescharacteristic
35C22×C4×C17C4⋊C411yescharacteristic
36C2×C22⋊D17—24no—
37C2×C22⋊D17—42no—
38C2×C22⋊D17—42no—
39C22×Dic17C4⋊C412yes—
40#63252—48no—
41#63252—48no—
42C2×D68—24no—
43C2×D68—41no—
44C2×C4×D17—24no—
45C2×C4×D17—22no—
46C2×C4×D17—22no—
47C2×C4×D17—42no—
48C2×Dic34—41no—
49C2×Dic34—42no—
50C22⋊#595—44no—
51C22⋊#595—44no—
52C2×C8×C17—42no—
53C2×C8×C17—41no—
54C2×#3622—42no—
55C2×#3622—41no—
56#7305—171nomaximal, Sylow
57C23×C17—21no—
58C23×C17—22no—
59C23×C17—41no—
60C23×C17—41no—
61C23×C17#9511yescharacteristic
62C22×D17—22no—
63C22×D17—22no—
64C22×D17—42no—
65C22×D17—42no—
66C22×D17#9914yes—
67C2×#595—84no—
68C2×#595—84no—
69C2×#595—84no—
70C2×C4×C17—22no—
71C2×C4×C17—22no—
72C2×C4×C17—21no—
73C2×C4×C17—42no—
74C2×C4×C17—42no—
75C2×C4×C17#9911yescharacteristic
76C2×C4×C17#9911yescharacteristic
77C22⋊D17—48no—
78C2×Dic17—22no—
79C2×Dic17—22no—
80C2×Dic17—22no—
81D68—44no—
82C4×D17—44no—
83C4×D17—44no—
84Dic34—44no—
85C8×C17—81no—
86#3622—81no—
87#1782—172no—
88#1780—171no—
89C22×C17—21no—
90C22×C17—21no—
91C22×C17—41no—
92C22×C17—41no—
93C22×C17—41no—
94C22×C17—82no—
95C22×C17#34212yes—
96C22×C17#34211yescharacteristic
97C2×D17—24no—
98C2×D17—42no—
99C2×D17—42no—
100C2×D17—44no—
101C2×D17—82no—
102#595—164no—
103C4×C17—21no—
104C4×C17—21no—
105C4×C17—41no—
106Dic17—42no—
107C22×#41—171no—
108C2×#99—174no—
109C2×#99—342no—
110C2×C22⋊C8—171no—
111C2×C22⋊C8—342no—
112C2×C22⋊C8#59511yescharacteristic, complemented
113#381—342no—
114C2×C17—22no—
115C2×C17—81no—
116C2×C17#130411yescharacteristic
117C2×C17#139111yescharacteristic
118C2×C17#139111yescharacteristic
119D17—44no—
120C2×#41—681no—
121C2×#41—681no—
122C2×#41—684no—
123C22×Q8—171no—
124C22×D4—172no—
125C22×D4—171no—
126C23×C4—172no—
127C23×C4C2×#59511yescharacteristic
128C22×C8—21no—
129C22×C8—341no—
130C2×C22⋊C4—344no—
131#99—684no—
132#99—684no—
133C22⋊C8—41no—
134C22⋊C8—684no—
135C22⋊C8—681no—
136#95—682no—
137#95—682no—
138C17#730511yescharacteristic, complemented, Sylow
139C24—172no—
140C24C4×#59511yescharacteristic
141#41—688no—
142#41—688no—
143C2×Q8—682no—
144C2×Q8—681no—
145C2×D4—344no—
146C2×D4—344no—
147C2×D4—681no—
148C2×D4—682no—
149C2×D4—682no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—42no—
153C22×C4—172no—
154C22×C4—344no—
155C22×C4—342no—
156C22×C4—342no—
157C22×C4—682no—
158C22×C4—684no—
159C22×C4C4⋊#59511yescharacteristic
160C22×C4C22⋊#59511yescharacteristic
161C2×C8—42no—
162C2×C8—41no—
163C2×C8—682no—
164C2×C8—681no—
165C22⋊C4—684no—
166C22⋊C4—684no—
167C23—21no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—174no—
172C23—342no—
173C23—342no—
174C23—682no—
175C23—682no—
176C23(C2×#595)⋊C411yescharacteristic
177Q8—684no—
178D4—684no—
179D4—688no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—342no—
186C2×C4—342no—
187C2×C4—342no—
188C2×C4—684no—
189C2×C4—684no—
190C2×C4—1364no—
191C2×C4—1364no—
192C2×C4—1364no—
193C2×C4#1058753911yescharacteristic
194C2×C4#1058755111yescharacteristic
195C8—81no—
196C8—1361no—
197C22—21no—
198C22—21no—
199C22—41no—
200C22—41no—
201C22—41no—
202C22—82no—
203C22—344no—
204C22—684no—
205C22—682no—
206C22—682no—
207C22—1362no—
208C22#1176368612yes—
209C22#1176368711yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—2724no—
214C4—682no—
215C2—22no—
216C2—81no—
217C2—684no—
218C2#1454368311yescharacteristic
219C2#1454387211yescharacteristic
220C2#1454387311yescharacteristic
subgroupG/H
centerC22#11763687
commutatorC24×C17C42
FrattiniC23×C4C2×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17#342
prime radical, cosocleC22×#63252C22
hypercenterC2×C22⋊C8#595
hypocenterC17#7305
LCSG ▷ C24×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#10587551C4semidirect
7. C2×C22⋊#3622C4semidirect
9. C2×C17×C22⋊C8C4semidirect
112. C2×C22⋊C8#595semidirect
138. C17#7305semidirect

Maximal subgroups

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

subgroupindex
#145446132
#145286952
#730517