Finite Group Databasebeta

← #17958469

Subgroups — #17958469

Order 4352.

288 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 64 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#14543733C212yesmaximal, complemented
3#14543719C212yesmaximal
4#14537426C211yesmaximal, characteristic
5#11763732—22no—
6#11763705C2214yes—
7#11763701—22no—
8C4×#63252C411yescharacteristic
9#11762868—22no—
10#11762860—22no—
11#11762835C411yescharacteristic
12#11762835C2211yescharacteristic
13#11762775C411yescharacteristic
14#11762775C2211yescharacteristic
15C4×#63223C2211yescharacteristic
16C2×C4×C8×C17C411yescharacteristic
17C2×#63252C2×C411yescharacteristic
18C22×C8×C17C2×C411yescharacteristic
19C22×C8×C17C2×C411yescharacteristic
20C2×C42×C17C2×C411yescharacteristic
21C4×C22⋊D17—22no—
22#10587612C2×C411yescharacteristic
23C2×#63223C2×C411yescharacteristic
24C2×#63223C2311yescharacteristic
25C4×D68—21no—
26#10587558—21no—
27C42×D17—21no—
28C4×Dic34—21no—
29#10587538—24no—
30C4×C8×C17—21no—
31C4×C8×C17—21no—
32#10587491—22no—
33#10587491—22no—
34#10587485—22no—
35#10587485—22no—
36#10587474D412yes—
37C4×#3622D412yes—
38C22×C4×C17—21no—
39C22×C4×C17C22×C411yescharacteristic
40C2×C22⋊D17—21no—
41#63252—41no—
42#63252—41no—
43C2×D68M1611yescharacteristic
44C2×C4×D17—22no—
45C2×C4×D17—21no—
46C2×Dic34M1611yescharacteristic
47C2×C8×C17—21no—
48C2×C8×C17—21no—
49C2×C8×C17—41no—
50C2×C8×C17—41no—
51C42×C17—21no—
52C42×C17C22⋊C411yescharacteristic
53C42×C17C22⋊C411yescharacteristic
54C22⋊Dic17M1612yes—
55#63227—22no—
56C4⋊Dic17—21no—
57#63225—22no—
58C4×Dic17—22no—
59C4×Dic17—21no—
60#63223—41no—
61#63223—41no—
62C2×#3622C22⋊C412yes—
63C2×#3622C2×D412yes—
64#63216—44no—
65#11524—171nomaximal, Sylow
66C23×C17C2×M1611yescharacteristic
67C22×D17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—42no—
73C2×C4×C17C2×C22⋊C411yescharacteristic
74C2×C4×C17C2×M1611yescharacteristic
75C22⋊D17—42no—
76C2×Dic17—22no—
77C2×Dic17—21no—
78D68—41no—
79C4×D17—44no—
80C4×D17—41no—
81C4×D17—41no—
82Dic34—41no—
83C8×C17—41no—
84C8×C17—41no—
85#3622—22no—
86#3622—22no—
87#2922—171no—
88#2165—172no—
89#1328—172no—
90#1321—172no—
91C22×C17—21no—
92C22×C17—41no—
93C22×C17#40711yescharacteristic
94C2×D17—42no—
95C2×D17—41no—
96C4×C17—22no—
97C4×C17—21no—
98C4×C17—41no—
99C4×C17#41011yescharacteristic
100C4×C17#41311yescharacteristic
101Dic17—42no—
102Dic17—41no—
103C4×#41—171no—
104#433—342no—
105#431—342no—
106#424—171no—
107#424—171no—
108#408—171no—
109#408—171no—
110C4×M16—171no—
111C2×C4×C8#59511yescharacteristic
112#364—342no—
113#349—174no—
114#347—342no—
115C2×C17—21no—
116C2×C17—41no—
117C2×C17#146411yescharacteristic
118D17—81no—
119C2×#41—171no—
120C2×M16—171no—
121C2×M16—171no—
122C22×C8C2×#59511yescharacteristic
123C22×C8C2×#59511yescharacteristic
124C4×Q8—341no—
125C4×D4—341no—
126C4×D4—342no—
127#117—171no—
128#117—341no—
129C2×C42—341no—
130C2×C42C2×#59511yescharacteristic
131M32—344no—
132C4⋊C8—342no—
133C4⋊C8—342no—
134C22⋊C8—342no—
135C22⋊C8—342no—
136#97—172no—
137C4×C8—21no—
138C4×C8—21no—
139C4×C8—172no—
140C17#1152411yescharacteristic, complemented, Sylow
141#41—681no—
142#41—681no—
143C2×Q8—171no—
144C2×D4—171no—
145C2×D4—341no—
146C22×C4—21no—
147C22×C4—342no—
148C22×C4—341no—
149C22×C4C22×#59511yescharacteristic
150M16—681no—
151M16—681no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8—172no—
157C2×C8—172no—
158C4⋊C4—342no—
159C4⋊C4—341no—
160C22⋊C4—172no—
161C22⋊C4—342no—
162C42—21no—
163C42—342no—
164C42—341no—
165C42C22⋊#59511yescharacteristic
166C42C22⋊#59511yescharacteristic
167C16—684no—
168C23—341no—
169C23D17⋊M1611yescharacteristic
170Q8—681no—
171D4—681no—
172D4—682no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—342no—
179C2×C4—341no—
180C2×C4—684no—
181C2×C4—681no—
182C2×C4—681no—
183C2×C4D17⋊M1611yescharacteristic
184C2×C4C2×C22⋊#59511yescharacteristic
185C8—41no—
186C8—41no—
187C8—342no—
188C8—342no—
189C22—21no—
190C22—41no—
191C22—682no—
192C22—681no—
193C22#1176378111yescharacteristic
194C4—22no—
195C4—21no—
196C4—41no—
197C4—682no—
198C4—681no—
199C4#1176378811yescharacteristic
200C4#1176379511yescharacteristic
201C2—21no—
202C2—41no—
203C2—1361no—
204C2#1454403711yescharacteristic
subgroupG/H
centerC4#11763788
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×C8×C17C4
socleC2×C17#1464
prime radicalC2×#63252C2×C4
cosocleC2×#63223C23
hypercenterC2×C4×C8#595
hypocenterC17#11524
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
1. #14545153C2semidirect
2. #14543733C2semidirect
140. C17#11524semidirect

Maximal subgroups

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

subgroupindex
#145451532
#145437332
#145437192
#145374262
#1152417