Finite Group Databasebeta

← #17959849

Subgroups — #17959849

Order 4352.

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

normal subgroups only

This group has 280 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#14545153C212yesmaximal, complemented
2#14543790C212yesmaximal, complemented
3#14543788C212yesmaximal, complemented
4#14539187C211yesmaximal, characteristic
5#11763732—22no—
6#11763705—22no—
7#11763701C2214yes—
8#11763359C411yescharacteristic
9#11763179C411yescharacteristic
10#11763179C2211yescharacteristic
11#11763175C411yescharacteristic
12#11763175C2211yescharacteristic
13#11763166—22no—
14#11762808—22no—
15C4×#63223C2211yescharacteristic
16C2×C17×#125C411yescharacteristic
17C2×#63252—21no—
18C17×#125—21no—
19C17×#125—41no—
20C17×#125C2×C411yescharacteristic
21C17×#125C2×C411yescharacteristic
22C2×C4⋊C4×C17—21no—
23C2×C4⋊C4×C17—41no—
24C2×C42×C17C2×C411yescharacteristic
25#10587616—41no—
26C2×#63223D412yes—
27#10587561—21no—
28#10587560C2×C411yescharacteristic
29C4×D68—41no—
30#10587555C2×C411yescharacteristic
31#10587538—24no—
32#10587481—22no—
33#10587481—22no—
34#10587480—22no—
35#10587480—22no—
36#10587474C2×C411yescharacteristic
37#10587474C2311yescharacteristic
38C4×#3622D412yes—
39C22×C4×C17—21no—
40C22×C4×C17—41no—
41C22×C4×C17C22⋊C411yescharacteristic
42C2×C22⋊D17—41no—
43#63252—44no—
44C2×D68—21no—
45C2×D68—41no—
46C2×C4×D17—41no—
47C2×Dic34—21no—
48C4⋊C4×C17—21no—
49C4⋊C4×C17—21no—
50C4⋊C4×C17—41no—
51C4⋊C4×C17—41no—
52C4⋊C4×C17—42no—
53C4⋊C4×C17—41no—
54C42×C17—21no—
55C42×C17C22⋊C411yescharacteristic
56C42×C17C22×C411yescharacteristic
57#63227—42no—
58C4⋊Dic17—41no—
59#63223—42no—
60C2×#3622C22⋊C412yes—
61C2×#3622C2×D412yes—
62#63216—44no—
63#11917—171nomaximal, Sylow
64C23×C17#10011yescharacteristic
65C22×D17—41no—
66C2×C4×C17—22no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—41no—
70C2×C4×C17—41no—
71C2×C4×C17—81no—
72C2×C4×C17—82no—
73C2×C4×C17#10011yescharacteristic
74C2×C4×C17C2×C22⋊C411yescharacteristic
75C22⋊D17—82no—
76C2×Dic17—41no—
77D68—42no—
78D68—82no—
79C4×D17—82no—
80Dic34—42no—
81#3622—22no—
82#3622—22no—
83#3142—171no—
84#2165—172no—
85#1356—172no—
86#1355—172no—
87C22×C17—21no—
88C22×C17—41no—
89C22×C17C2×#10011yescharacteristic
90C2×D17—82no—
91C2×D17—81no—
92C4×C17—21no—
93C4×C17—41no—
94C4×C17—41no—
95C4×C17—81no—
96C4×C17—81no—
97C4×C17#42112yes—
98Dic17—81no—
99#532—171no—
100C2×#125#59511yescharacteristic
101#491—171no—
102#491—171no—
103#490—171no—
104#490—171no—
105#488—342no—
106#417—342no—
107C4×M16—171no—
108#364—342no—
109#349—342no—
110#347—174no—
111C2×C17—21no—
112C2×C17—41no—
113C2×C17#153311yescharacteristic
114D17—161no—
115C2×#41—341no—
116C2×M16—172no—
117C4⋊Q8—171no—
118#127—171no—
119#125—21no—
120#125—41no—
121#125C2×#59511yescharacteristic
122#125C2×#59511yescharacteristic
123#124—341no—
124#121—681no—
125C4×D4—681no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—41no—
128C2×C42C2×#59511yescharacteristic
129M32—344no—
130#103—342no—
131#103—342no—
132#102—342no—
133#102—342no—
134#97—171no—
135#97—171no—
136C4×C8—172no—
137C17#1191711yescharacteristic, complemented, Sylow
138#41—684no—
139C2×Q8—341no—
140C2×D4—341no—
141C2×D4—681no—
142C2×D4—681no—
143C22×C4—21no—
144C22×C4—41no—
145C22×C4—681no—
146C22×C4C22⋊#59511yescharacteristic
147M16—682no—
148C2×C8—172no—
149C2×C8—172no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—42no—
155C4⋊C4—41no—
156C4⋊C4—681no—
157C22⋊C4—682no—
158C42—21no—
159C42C22⋊#59511yescharacteristic
160C42C22×#59511yescharacteristic
161C16—684no—
162C23—681no—
163C23#1058755311yescharacteristic
164Q8—682no—
165D4—682no—
166D4—1362no—
167D4—1362no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—81no—
174C2×C4—82no—
175C2×C4—681no—
176C2×C4—1362no—
177C2×C4#1058755311yescharacteristic
178C2×C4C2×C22⋊#59511yescharacteristic
179C8—342no—
180C8—342no—
181C22—21no—
182C22—41no—
183C22—1362no—
184C22—1361no—
185C22C2×#1058755311yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—81no—
190C4—81no—
191C4—1361no—
192C4#1176380812yes—
193C2—21no—
194C2—41no—
195C2—2721no—
196C2#1454426511yescharacteristic
subgroupG/H
centerC2#14544265
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C17×#125C4
socleC2×C17#1533
prime radical#11763359C4
cosocle#10587474C23
hypercenterC2×#125#595
hypocenterC17#11917
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #14545153C2semidirect
2. #14543790C2semidirect
3. #14543788C2semidirect
137. C17#11917semidirect

Maximal subgroups

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

subgroupindex
#145451532
#145437902
#145437882
#145391872
#1191717