Finite Group Databasebeta

← #49132731

Subgroups — #49132731

Order 36224.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#31827082C212yesmaximal, complemented
2#31826753C212yesmaximal, complemented
3#31826749C212yesmaximal, complemented
4#31826723C211yesmaximal, characteristic, complemented
5#31826692C212yesmaximal, complemented
6#31826686C212yesmaximal, complemented
7#31826678C212yesmaximal, complemented
8#31826493C211yesmaximal, characteristic, complemented
9#469×C283C211yesmaximal, characteristic
10C2×Dic1132C2211yescharacteristic
11C2×#17985380C2212yes—
12C22×C283⋊C8C2211yescharacteristic
13#22583609C2212yes—
14#22583603—22no—
15#22583597—22no—
16#22583597C2212yes—
17#22583591—22no—
18#22583589C2212yes—
19#22583587—22no—
20#22583575C2212yes—
21D4×Dic283C2212yes—
22#22583569C2211yescharacteristic
23#22583542C2211yescharacteristic
24#22583541C2212yes—
25Dic283⋊C8C2212yes—
26Dic283⋊C8C2212yes—
27#22583535C2212yes—
28#22583533C2212yes—
29#22583531C2212yes—
30C2×D8×C283C2211yescharacteristic
31C2×M16×C283C2211yescharacteristic
32#121×C283C2212yes—
33#106×C283C2211yescharacteristic
34#102×C283C2212yes—
35C2×Dic566—22no—
36C2×Dic566C2312yes—
37C22×Dic283—22no—
38Dic1132—41no—
39#17985380—42no—
40C2×C283⋊C8—41no—
41C2×C283⋊C8C2312yes—
42C4⋊Dic283D412yes—
43C4⋊Dic283C2312yes—
44Dic283⋊C4—22no—
45Dic283⋊C4—22no—
46Dic283⋊C4—22no—
47C22⋊Dic283—22no—
48C22⋊Dic283—22no—
49C22⋊Dic283—22no—
50C22⋊Dic283—22no—
51C22⋊Dic283D411yescharacteristic
52C22⋊Dic283D411yescharacteristic
53C4×Dic283—22no—
54C4×Dic283C2312yes—
55C2×D4×C283—22no—
56C2×D4×C283C2312yes—
57C22×C4×C283C2311yescharacteristic
58D8×C283—41no—
59M16×C283—41no—
60C2×C8×C283C2311yescharacteristic
61C2×C8×C283C2311yescharacteristic
62C4⋊C4×C283C2312yes—
63C22⋊C4×C283—22no—
64Dic566—22no—
65Dic566—22no—
66Dic566—82no—
67C2×Dic283—22no—
68C2×Dic283—22no—
69C2×Dic283—82no—
70C2×Dic283C2×D412yes—
71C2×Dic283C2×D412yes—
72C283⋊C8—22no—
73C23×C283—22no—
74C23×C283C2×D411yescharacteristic
75D4×C283—22no—
76D4×C283—22no—
77D4×C283—82no—
78C2×C4×C283—21no—
79C2×C4×C283—21no—
80C2×C4×C283—22no—
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2411yescharacteristic
83C8×C283—21no—
84C8×C283—21no—
85C22×C283—21no—
86C22×C283—22no—
87C22×C283—42no—
88C22×C283—42no—
89C22×C283—42no—
90C22×C283C22×D411yescharacteristic
91C4×C283—21no—
92C4×C283—42no—
93C4×C283H(5,𝔽2)11yescharacteristic
94C4×C2832−1+411yescharacteristic
95Dic283—22no—
96Dic283—22no—
97Dic283—42no—
98Dic283—42no—
99C2×C283—41no—
100C2×C283—82no—
101C2×C283#53711yescharacteristic
102C2×C283#57712yes—
103C283#326311yescharacteristic, complemented, Sylow
104#3263—2831nomaximal, Sylow
105#542—2832no—
106#476—2832no—
107#475—2832no—
108#470—2831no—
109#469D28311yescharacteristic
110#465—2832no—
111#464—2832no—
112#463—2832no—
113#424—2831no—
114C2×Q16—2831no—
115C2×SD16—2832no—
116C2×D8C2×D28311yescharacteristic
117C2×M16C2×D28311yescharacteristic
118C22×C8—2831no—
119C4⋊Q8—2832no—
120#126—5662no—
121#124—2832no—
122#124—5662no—
123#123—5662no—
124C22⋊Q8—2832no—
125C22⋊Q8—5662no—
126#121C2×D28312yes—
127C4×Q8—2832no—
128C4×D4—2832no—
129#117—2831no—
130#106—2831no—
131#106—2832no—
132#106C2×D28311yescharacteristic
133C4⋊C8—2832no—
134C4⋊C8—2832no—
135#103—2832no—
136#103—2832no—
137#102—2832no—
138#102C2×D28312yes—
139C2×Q8—2832no—
140C2×Q8—5662no—
141C2×D4—22no—
142C2×D4C22×D28312yes—
143C22×C4—5662no—
144C22×C4C22×D28311yescharacteristic
145Q16—11321no—
146SD16—11322no—
147D8—41no—
148M16—41no—
149C2×C8—2832no—
150C2×C8—11321no—
151C2×C8C22×D28311yescharacteristic
152C2×C8C22×D28311yescharacteristic
153C4⋊C4—2832no—
154C4⋊C4—2832no—
155C4⋊C4—5662no—
156C4⋊C4—5662no—
157C4⋊C4—5662no—
158C4⋊C4C22×D28312yes—
159C22⋊C4—22no—
160C22⋊C4—2831no—
161C22⋊C4—2831no—
162C22⋊C4—5662no—
163C22⋊C4—5662no—
164C22⋊C4—5662no—
165C22⋊C4—5662no—
166C42—2832no—
167C42—5662no—
168C23—22no—
169C23D4×D28311yescharacteristic
170Q8—5662no—
171Q8—5662no—
172Q8—22642no—
173D4—22no—
174D4—22no—
175D4—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—2832no—
180C2×C4—2832no—
181C2×C4—5662no—
182C2×C4—5662no—
183C2×C4—22642no—
184C2×C4D4×D28311yescharacteristic
185C2×C4C23×D28311yescharacteristic
186C8—21no—
187C8—21no—
188C8—5662no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D28311yescharacteristic
195C4—21no—
196C4—42no—
197C4—5662no—
198C4—5662no—
199C4—11322no—
200C4—11322no—
201C4#2258365511yescharacteristic
202C4#2258365711yescharacteristic
203C2—41no—
204C2—82no—
205C2#3182704211yescharacteristic
206C2#3182727512yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting, prime radical#469×C283C2
socleC22×C283C22×D4
hypercenter#469D283
hypocenterC283#3263
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #31827082C2semidirect
2. #31826753C2semidirect
3. #31826749C2semidirect
4. #31826723C2semidirect
5. #31826692C2semidirect
6. #31826686C2semidirect
7. #31826678C2semidirect
8. #31826493C2semidirect
103. C283#3263semidirect

Maximal subgroups

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

subgroupindex
#318270822
#318267532
#318267492
#318267232
#318266922
#318266862
#318266782
#318264932
#469×C2832
#3263283