Finite Group Databasebeta

← #49122952

Subgroups — #49122952

Order 36224.

262 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 65 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#31827029C211yesmaximal, characteristic
2#31826449C211yesmaximal, characteristic, complemented
3#31826261C214yesmaximal, complemented
4#413×C283C211yesmaximal, characteristic, complemented
5C22×D1132C411yescharacteristic
6C2×#17985376—21no—
7#22583606C412yes—
8#22583599C2212yes—
9#22583584—21no—
10#22583584—21no—
11#22583578—21no—
12#22583578—21no—
13#22583569C411yescharacteristic
14#22583529C2212yescomplemented
15#22583527—21no—
16C2×#41×C283C2211yescharacteristic
17C2×M16×C283—21no—
18#101×C283C2212yescomplemented
19#100×C283—21no—
20C23×D283—21no—
21C2×D1132—21no—
22C2×D1132—41no—
23C2×D1132—41no—
24C2×D1132C2×C412yes—
25C2×C22⋊D283—22no—
26C2×C22⋊D283—22no—
27#17985376—22no—
28#17985376—41no—
29C2×C283⋊C8—41no—
30C4⋊Dic283—21no—
31C22⋊Dic283—21no—
32(C2×D283)⋊C4—22no—
33(C2×D283)⋊C4—22no—
34C4×Dic283C2×C412yes—
35#41×C283—41no—
36#41×C283—41no—
37C2×Q8×C283C2311yescharacteristic
38C2×D4×C283C2×C411yescharacteristic
39C2×D4×C283D411yescharacteristic
40C2×D4×C283D411yescharacteristic
41C22×C4×C283C2×C411yescharacteristic
42C22×C4×C283D411yescharacteristic
43C22×C4×C283D411yescharacteristic
44M16×C283—22no—
45M16×C283—41no—
46C2×C8×C283—41no—
47C22×D283—22no—
48C22×D283—42no—
49C22×D283—82no—
50D1132—42no—
51D1132—41no—
52D1132—41no—
53C22⋊D283—82no—
54C22⋊D283—82no—
55C2×Dic283—22no—
56C283⋊C8—42no—
57C23×C283C22⋊C411yescharacteristic
58C23×C283C22⋊C411yescharacteristic
59C23×C283C22⋊C411yescharacteristic
60Q8×C283—41no—
61D4×C283—41no—
62D4×C283—41no—
63D4×C283—41no—
64C2×C4×C283—21no—
65C2×C4×C283—21no—
66C2×C4×C283—21no—
67C2×C4×C283—21no—
68C2×C4×C283—21no—
69C2×C4×C283—21no—
70C2×C4×C283C22⋊C411yescharacteristic
71C2×C4×C283C22×C411yescharacteristic
72C2×C4×C283C2×D411yescharacteristic
73C2×C4×C283C2×D411yescharacteristic
74C8×C283—42no—
75C22×C283—21no—
76C22×C283—21no—
77C22×C283—21no—
78C22×C283—41no—
79C22×C283—41no—
80C22×C283—41no—
81C22×C283C2×C22⋊C411yescharacteristic
82C2×D283—42no—
83C2×D283—42no—
84C2×D283—42no—
85C2×D283—84no—
86C4×C283—21no—
87C4×C283—21no—
88C4×C283—21no—
89C4×C283#9911yescharacteristic
90C4×C283#9911yescharacteristic
91Dic283—42no—
92C2×C283—21no—
93C2×C283—41no—
94C2×C283—41no—
95C2×C283—41no—
96C2×C283C2×#9911yescharacteristic
97D283—82no—
98C283#213411yescharacteristic, complemented, Sylow
99#2134—2831nomaximal, Sylow
100#535—2831no—
101#413—2831no—
102#413D28311yescharacteristic, complemented
103#355—2834no—
104C2×#41C2×D28311yescharacteristic
105C22×D4—2831no—
106C2×M16—21no—
107C2×M16—5661no—
108#127—2832no—
109#124—2832no—
110#121—5661no—
111#121—5661no—
112#120—5661no—
113#120—5661no—
114#117—2831no—
115#101—2832no—
116#101C2×D28312yescomplemented
117#100—21no—
118#100—5661no—
119C24—5661no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D28311yescharacteristic
123C2×D4—2832no—
124C2×D4—5662no—
125C2×D4—5662no—
126C2×D4—5661no—
127C2×D4—11321no—
128C2×D4—11321no—
129C2×D4C4×D28311yescharacteristic
130C2×D4C22⋊D28311yescharacteristic
131C2×D4D113211yescharacteristic
132C22×C4C4×D28311yescharacteristic
133C22×C4C22⋊D28311yescharacteristic
134C22×C4D113211yescharacteristic
135M16—22no—
136M16—41no—
137M16—5662no—
138M16—11321no—
139C2×C8—41no—
140C2×C8—11321no—
141C4⋊C4—5661no—
142C22⋊C4—5661no—
143C22⋊C4—5662no—
144C22⋊C4—5662no—
145C42—2832no—
146C23—5662no—
147C23—11322no—
148C23—22642no—
149C23(C2×D283)⋊C411yescharacteristic
150C23(C2×D283)⋊C411yescharacteristic
151C23(C2×D283)⋊C411yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—11322no—
157D4—11321no—
158D4—11321no—
159D4—22642no—
160D4—22642no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—5662no—
168C2×C4(C2×D283)⋊C411yescharacteristic
169C2×C4C2×C4×D28311yescharacteristic
170C2×C4C2×C22⋊D28311yescharacteristic
171C2×C4C2×D113211yescharacteristic
172C8—42no—
173C8—11322no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—11322no—
181C22—11322no—
182C22—11322no—
183C22—22644no—
184C22C2×(C2×D283)⋊C411yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—11322no—
189C4#2258352411yescharacteristic
190C4#2258352411yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—22642no—
196C2C2×#2258352411yescharacteristic
subgroupG/H
centerC2C2×#22583524
commutatorC2×C4×C283C22×C4
FrattiniC2×Q8C22×D283
Fitting#413×C283C2
socleC2×C283C2×#99
prime radical#31827029C2
cosocleC2×Q8×C283C23
hypercenter#413D283
hypocenterC283#2134
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #31826449C2semidirect
3. #31826261C2semidirect
4. #413×C283C2semidirect
14. #22583529C22semidirect
18. #101×C283C22semidirect
98. C283#2134semidirect
102. #413D283semidirect
116. #101C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270292
#318264492
#318262612
#413×C2832
#2134283