Finite Group Databasebeta

← #17962669

Subgroups — #17962669

Order 4352.

458 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 60 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#14545057C212yesmaximal, complemented
2#14543915C214yesmaximal, complemented
3#14539234C211yesmaximal, characteristic
4#11763788—22no—
5#11763716—22no—
6#11763714C2214yescomplemented
7C2×#10587618—22no—
8#11763359C2211yescharacteristic
9#11763196—22no—
10#11763185C2212yes—
11#11763181C412yescomplemented
12C4×#63223C411yescharacteristic, complemented
13C2×C17×#127C411yescharacteristic, complemented
14C22×D4×C17—21no—
15C22×D4×C17—41no—
16C2×#63252D412yes—
17#10587677—42no—
18C17×#127—21no—
19C17×#127—41no—
20C17×#127C2×C412yes—
21C2×C42×C17C2×C411yescharacteristic
22C2×#63229—24no—
23#10587618—44no—
24#10587618—44no—
25C2×#63228—24no—
26#10587616—41no—
27C2×#63223—21no—
28#10587561D412yes—
29#10587560C2311yescharacteristic
30C4×D68—41no—
31#10587555C2×C411yescharacteristic
32#10587551—42no—
33#10587539—24no—
34#10587474—21no—
35C4×#3622C2×C412yes—
36C24×C17—41no—
37C2×D4×C17—22no—
38C2×D4×C17—42no—
39C2×D4×C17—42no—
40C2×D4×C17—42no—
41C2×D4×C17—42no—
42C2×D4×C17—41no—
43C2×D4×C17—84no—
44C22×C4×C17—21no—
45C22×C4×C17C22⋊C411yescharacteristic
46C2×C22⋊D17—22no—
47#63252—42no—
48#63252—42no—
49C2×D68—41no—
50C2×D68C2×D412yes—
51C2×C4×D17—22no—
52C2×Dic34C22⋊C412yes—
53C22⋊#595—44no—
54C4⋊#595—82no—
55C4×#595—82no—
56C42×C17—21no—
57C42×C17C22⋊C411yescharacteristic
58C42×C17C22×C411yescharacteristic
59#63229—48no—
60#63228—48no—
61#63227—42no—
62C4⋊Dic17—41no—
63#63223—24no—
64C2×#3622—22no—
65#13585—171nomaximal, Sylow
66C23×C17—42no—
67C23×C17—81no—
68C23×C17—81no—
69C23×C17—84no—
70C23×C17#9911yescharacteristic
71C22×D17—22no—
72C2×#595—84no—
73D4×C17—44no—
74D4×C17—84no—
75D4×C17—84no—
76D4×C17—82no—
77C2×C4×C17—21no—
78C2×C4×C17—22no—
79C2×C4×C17—21no—
80C2×C4×C17—42no—
81C2×C4×C17#9911yescharacteristic
82C2×C4×C17C2×C22⋊C411yescharacteristic
83C22⋊D17—82no—
84C2×Dic17—22no—
85D68—42no—
86D68—82no—
87C4×D17—42no—
88C4×D17—42no—
89Dic34—42no—
90#3622—24no—
91#3151—171no—
92#2126—172no—
93#1408—174no—
94C22×C17—21no—
95C22×C17—41no—
96C22×C17—84no—
97C22×C17—82no—
98C22×C17—162no—
99C22×C17—162no—
100C22×C17C2×#9911yescharacteristic
101C2×D17—42no—
102C2×D17—82no—
103#595—164no—
104C4×C17—22no—
105C4×C17—21no—
106C4×C17—41no—
107C4×C17#35312yes—
108Dic17—42no—
109C2×AGL(1,ℤ/8)—342no—
110#532—171no—
111C2×#127#59511yescharacteristic, complemented
112#496—342no—
113#493—172no—
114#492—172no—
115#410—342no—
116C4×M16—171no—
117#354—342no—
118#353—174no—
119C2×C17—21no—
120C2×C17—41no—
121C2×C17—162no—
122C2×C17C2×#35311yescharacteristic
123D17—82no—
124C2×#41—172no—
125C22×D4—21no—
126C22×D4—41no—
127AGL(1,ℤ/8)—684no—
128AGL(1,ℤ/8)—684no—
129C2×SD16—344no—
130C2×D8—344no—
131C2×M16—341no—
132C4⋊Q8—171no—
133#127—21no—
134#127—41no—
135#127—171no—
136#127C2×#59512yes—
137#124—172no—
138#121—681no—
139C4×D4—681no—
140#117—682no—
141C2×C42C2×#59511yescharacteristic
142#99—344no—
143#99—682no—
144#97—341no—
145C4×C8—172no—
146C17#1358511yescharacteristic, complemented, Sylow
147C24—41no—
148#41—682no—
149#41—682no—
150C2×Q8—172no—
151C2×D4—22no—
152C2×D4—42no—
153C2×D4—42no—
154C2×D4—42no—
155C2×D4—42no—
156C2×D4—41no—
157C2×D4—84no—
158C2×D4—172no—
159C2×D4—342no—
160C2×D4—681no—
161C22×C4—21no—
162C22×C4—342no—
163C22×C4C22⋊#59511yescharacteristic
164SD16—688no—
165D8—688no—
166M16—344no—
167C2×C8—342no—
168C4⋊C4—681no—
169C4⋊C4—1362no—
170C22⋊C4—682no—
171C22⋊C4—684no—
172C42—21no—
173C42—1362no—
174C42C22⋊#59511yescharacteristic
175C42C22×#59511yescharacteristic
176C23—42no—
177C23—81no—
178C23—81no—
179C23—84no—
180C23—342no—
181C23#1058755111yescharacteristic
182Q8—682no—
183D4—44no—
184D4—84no—
185D4—84no—
186D4—82no—
187D4—682no—
188D4—1362no—
189D4—1362no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—342no—
195C2×C4—682no—
196C2×C4—682no—
197C2×C4—1364no—
198C2×C4#1058755111yescharacteristic
199C2×C4C2×C22⋊#59511yescharacteristic
200C8—344no—
201C22—21no—
202C22—41no—
203C22—84no—
204C22—82no—
205C22—162no—
206C22—162no—
207C22—682no—
208C22—1362no—
209C22C2×#1058755111yescharacteristic
210C4—22no—
211C4—21no—
212C4—41no—
213C4—2724no—
214C4—682no—
215C4#1176371312yes—
216C2—21no—
217C2—41no—
218C2—162no—
219C2—1362no—
220C2C2×#1176371311yescharacteristic
subgroupG/H
centerC2C2×#11763713
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C17×#127C4
socleC2×C17C2×#353
prime radical#14539234C2
cosocle#10587560C23
hypercenterC2×#127#595
hypocenterC17#13585
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #14545057C2semidirect
2. #14543915C2semidirect
6. #11763714C22semidirect
11. #11763181C4semidirect
12. C4×#63223C4semidirect
13. C2×C17×#127C4semidirect
111. C2×#127#595semidirect
146. C17#13585semidirect

Maximal subgroups

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

subgroupindex
#145450572
#145439152
#145392342
#1358517