Finite Group Databasebeta

← #17958461

Subgroups — #17958461

Order 4352.

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

normal subgroups only

This group has 284 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#14543731C212yesmaximal, complemented
3#14543717C212yesmaximal
4#14537420C211yesmaximal, characteristic
5#11763732—22no—
6#11763705C2214yes—
7#11763701—22no—
8C2×#10587558C411yescharacteristic
9#11762871—22no—
10#11762868—22no—
11#11762832C411yescharacteristic
12#11762832C2211yescharacteristic
13#11762772C411yescharacteristic
14#11762772C2211yescharacteristic
15C4×#63223C2211yescharacteristic
16C4×M16×C17C411yescharacteristic
17C22×C4×D17C2×C411yescharacteristic
18C2×M16×C17C2×C411yescharacteristic
19C2×M16×C17C2×C411yescharacteristic
20C2×C42×C17C2×C411yescharacteristic
21C2×#63227—21no—
22C2×#63225—21no—
23C2×C4×Dic17C2×C411yescharacteristic
24C2×#63223C2×C411yescharacteristic
25C2×#63223C2311yescharacteristic
26#10587558—22no—
27#10587558—21no—
28#10587558—21no—
29#10587538—24no—
30C17×#97—21no—
31C4×C8×C17—21no—
32#10587491—22no—
33#10587491—22no—
34#10587485—22no—
35#10587485—22no—
36#10587474D412yes—
37C4×#3622D412yes—
38C23×D17M1611yescharacteristic
39C22×C4×C17—21no—
40C22×C4×C17C22×C411yescharacteristic
41C22×Dic17—21no—
42C22×Dic17M1611yescharacteristic
43C2×C4×D17—21no—
44C2×C4×D17—21no—
45C2×C4×D17—41no—
46C2×C4×D17—41no—
47M16×C17—41no—
48M16×C17—41no—
49C2×C8×C17—21no—
50C2×C8×C17—21no—
51C42×C17—21no—
52C42×C17C22⋊C411yescharacteristic
53C42×C17C22⋊C411yescharacteristic
54#63227—22no—
55#63227—22no—
56#63225—22no—
57#63225—22no—
58C4×Dic17—21no—
59C4×Dic17M1612yes—
60#63223—41no—
61#63223—41no—
62C2×#3622C22⋊C412yes—
63C2×#3622C2×D412yes—
64#63216—44no—
65#11522—171nomaximal, Sylow
66C23×C17C2×M1611yescharacteristic
67C22×D17—21no—
68C22×D17—41no—
69C22×D17—81no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—81no—
75C2×C4×C17C2×C22⋊C411yescharacteristic
76C2×C4×C17C2×M1611yescharacteristic
77C2×Dic17—21no—
78C2×Dic17—22no—
79C2×Dic17—41no—
80C2×Dic17—81no—
81C4×D17—42no—
82C4×D17—41no—
83C4×D17—41no—
84C8×C17—41no—
85C8×C17—41no—
86#3622—22no—
87#3622—22no—
88#2921—171no—
89#2165—172no—
90#1327—172no—
91#1320—172no—
92C22×C17—21no—
93C22×C17—41no—
94C22×C17#40711yescharacteristic
95C2×D17—42no—
96C2×D17—41no—
97C2×D17—82no—
98C4×C17—21no—
99C4×C17—41no—
100C4×C17—41no—
101C4×C17#41011yescharacteristic
102C4×C17#41311yescharacteristic
103Dic17—42no—
104Dic17—41no—
105C2×#117—171no—
106#433—342no—
107#433—342no—
108#423—171no—
109#423—171no—
110#407—171no—
111#407—171no—
112C4×M16—171no—
113C4×M16#59511yescharacteristic
114#364—342no—
115#349—174no—
116#347—342no—
117C2×C17—21no—
118C2×C17—41no—
119C2×C17#146411yescharacteristic
120D17—81no—
121C23×C4—171no—
122C2×M16—171no—
123C2×M16—171no—
124C2×M16C2×#59511yescharacteristic
125C2×M16C2×#59511yescharacteristic
126#117—342no—
127#117—341no—
128#117—341no—
129C2×C4⋊C4—341no—
130C2×C22⋊C4—341no—
131C2×C42—171no—
132C2×C42C2×#59511yescharacteristic
133M32—344no—
134C4⋊C8—342no—
135C4⋊C8—342no—
136C22⋊C8—342no—
137C22⋊C8—342no—
138#97—21no—
139#97—172no—
140C4×C8—21no—
141C4×C8—172no—
142C17#1152211yescharacteristic, complemented, Sylow
143C24—171no—
144C22×C4—21no—
145C22×C4—171no—
146C22×C4—341no—
147C22×C4—341no—
148C22×C4—341no—
149C22×C4—681no—
150C22×C4—681no—
151C22×C4C22×#59511yescharacteristic
152M16—41no—
153M16—41no—
154M16—681no—
155M16—681no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—172no—
159C2×C8—172no—
160C4⋊C4—342no—
161C4⋊C4—342no—
162C22⋊C4—342no—
163C22⋊C4—342no—
164C42—21no—
165C42—172no—
166C42—341no—
167C42C22⋊#59511yescharacteristic
168C42C22⋊#59511yescharacteristic
169C16—684no—
170C23—341no—
171C23—681no—
172C23—1361no—
173C23D17⋊M1611yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—81no—
179C2×C4—342no—
180C2×C4—341no—
181C2×C4—682no—
182C2×C4—681no—
183C2×C4—681no—
184C2×C4—681no—
185C2×C4—1361no—
186C2×C4D17⋊M1611yescharacteristic
187C2×C4C2×C22⋊#59511yescharacteristic
188C8—41no—
189C8—41no—
190C8—342no—
191C8—342no—
192C22—21no—
193C22—41no—
194C22—682no—
195C22—681no—
196C22—1362no—
197C22#1176378111yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—682no—
202C4—681no—
203C4#1176378811yescharacteristic
204C4#1176379511yescharacteristic
205C2—21no—
206C2—41no—
207C2—1361no—
208C2#1454403711yescharacteristic
subgroupG/H
centerC4#11763788
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×M16×C17C4
socleC2×C17#1464
prime radicalC23×D17M16
cosocleC2×#63223C23
hypercenterC4×M16#595
hypocenterC17#11522
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. #14545153C2semidirect
2. #14543731C2semidirect
142. C17#11522semidirect

Maximal subgroups

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

subgroupindex
#145451532
#145437312
#145437172
#145374202
#1152217