Finite Group Databasebeta

← #17958459

Subgroups — #17958459

Order 4352.

284 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 68 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#14543730C212yesmaximal, complemented
3#14543716C212yesmaximal
4#14537422C211yesmaximal, characteristic
5#11763732—22no—
6#11763705C2214yes—
7#11763701—22no—
8#11762870—22no—
9#11762870—22no—
10#11762833C411yescharacteristic
11#11762833C2211yescharacteristic
12#11762773C411yescharacteristic
13#11762773C2211yescharacteristic
14C4×#63223C411yescharacteristic
15C4×#63223C2211yescharacteristic
16C2×C17×#117C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C17×#117—21no—
19C17×#117—21no—
20C17×#117—22no—
21C2×C4⋊C4×C17—21no—
22C2×C22⋊C4×C17—21no—
23C2×C42×C17C2×C411yescharacteristic
24C2×C42×C17C2×C411yescharacteristic
25C2×#63223C2×C411yescharacteristic
26C2×#63223C2×C411yescharacteristic
27C2×#63223C2×C411yescharacteristic
28C2×#63223C2311yescharacteristic
29#10587538—24no—
30C22⋊#3622—22no—
31C22⋊#3622—22no—
32C4⋊#3622—22no—
33C4⋊#3622—22no—
34#10587474—21no—
35#10587474D412yes—
36C4×#3622—21no—
37C4×#3622D412yes—
38C24×C17M1611yescharacteristic
39C22×C4×C17—21no—
40C22×C4×C17—21no—
41C22×C4×C17—21no—
42C22×C4×C17—21no—
43C22×C4×C17—41no—
44C22×C4×C17—41no—
45C22×C4×C17M1611yescharacteristic
46C22×C4×C17C22×C411yescharacteristic
47C4⋊C4×C17—22no—
48C4⋊C4×C17—22no—
49C22⋊C4×C17—22no—
50C22⋊C4×C17—22no—
51C42×C17—21no—
52C42×C17—21no—
53C42×C17C22⋊C411yescharacteristic
54C42×C17C22⋊C411yescharacteristic
55C42×C17M1612yes—
56#63223—41no—
57#63223—41no—
58#63223—41no—
59#63223—41no—
60C2×#3622—21no—
61C2×#3622—21no—
62C2×#3622C22⋊C412yes—
63C2×#3622C2×D412yes—
64#63216—44no—
65#11522—171nomaximal, Sylow
66C23×C17—21no—
67C23×C17—41no—
68C23×C17—81no—
69C23×C17C2×M1611yescharacteristic
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—22no—
75C2×C4×C17—21no—
76C2×C4×C17—42no—
77C2×C4×C17—41no—
78C2×C4×C17—41no—
79C2×C4×C17—41no—
80C2×C4×C17—81no—
81C2×C4×C17—81no—
82C2×C4×C17C2×C22⋊C411yescharacteristic
83C2×C4×C17C2×M1611yescharacteristic
84#3622—22no—
85#3622—22no—
86#3622—41no—
87#3622—41no—
88#2921—171no—
89#2165—172no—
90#1327—172no—
91#1320—172no—
92C22×C17—21no—
93C22×C17—41no—
94C22×C17—42no—
95C22×C17—41no—
96C22×C17—82no—
97C22×C17#40711yescharacteristic
98C4×C17—21no—
99C4×C17—41no—
100C4×C17—41no—
101C4×C17—42no—
102C4×C17—41no—
103C4×C17#41011yescharacteristic
104C4×C17#41311yescharacteristic
105C2×#117#59511yescharacteristic
106#433—342no—
107#433—342no—
108#423—171no—
109#423—171no—
110#407—171no—
111#407—171no—
112C4×M16—171no—
113C4×M16—171no—
114#364—342no—
115#349—174no—
116#347—342no—
117C2×C17—21no—
118C2×C17—41no—
119C2×C17—81no—
120C2×C17#146411yescharacteristic
121C23×C4C2×#59511yescharacteristic
122C2×M16—171no—
123C2×M16—171no—
124C2×M16—171no—
125C2×M16—171no—
126#117—22no—
127#117—21no—
128#117—21no—
129C2×C4⋊C4—21no—
130C2×C22⋊C4—21no—
131C2×C42C2×#59511yescharacteristic
132C2×C42C2×#59511yescharacteristic
133M32—344no—
134C4⋊C8—342no—
135C4⋊C8—342no—
136C22⋊C8—342no—
137C22⋊C8—342no—
138#97—172no—
139#97—341no—
140C4×C8—172no—
141C4×C8—341no—
142C17#1152211yescharacteristic, complemented, Sylow
143C24#6324711yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4#6324711yescharacteristic
151C22×C4C22×#59511yescharacteristic
152M16—681no—
153M16—681no—
154M16—681no—
155M16—681no—
156C2×C8—172no—
157C2×C8—172no—
158C2×C8—341no—
159C2×C8—341no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C42—21no—
165C42—21no—
166C42#6324712yes—
167C42C22⋊#59511yescharacteristic
168C42C22⋊#59511yescharacteristic
169C16—684no—
170C23—21no—
171C23—41no—
172C23—81no—
173C23C2×#6324711yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4C2×#6324711yescharacteristic
187C2×C4C2×C22⋊#59511yescharacteristic
188C8—342no—
189C8—342no—
190C8—681no—
191C8—681no—
192C22—21no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—82no—
197C22#1176377911yescharacteristic
198C4—21no—
199C4—42no—
200C4—41no—
201C4—41no—
202C4—41no—
203C4#1176378811yescharacteristic
204C4#1176379511yescharacteristic
205C2—21no—
206C2—41no—
207C2—81no—
208C2#1454403511yescharacteristic
subgroupG/H
centerC4#11763788
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC2×C17#1464
prime radicalC24×C17M16
cosocleC2×#63223C23
hypercenterC2×#117#595
hypocenterC17#11522
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #14545153C2semidirect
2. #14543730C2semidirect
142. C17#11522semidirect

Maximal subgroups

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

subgroupindex
#145451532
#145437302
#145437162
#145374222
#1152217