Finite Group Databasebeta

← #49131547

Subgroups — #49131547

Order 36224.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#31826942C211yesmaximal, characteristic, complemented
2#31826786C212yesmaximal, complemented
3#31826769C212yesmaximal, complemented
4#31826662C212yesmaximal, complemented
5#31826603C212yesmaximal, complemented
6#31826565C212yesmaximal, complemented
7C4×#17985380C212yesmaximal, complemented
8#31826526C211yesmaximal, characteristic, complemented
9#540×C283C211yesmaximal, characteristic
10C22×Dic566C2211yescharacteristic
11C2×#17985380C2212yes—
12C2×#17985380C2212yes—
13C4×Dic566C2212yes—
14C4×Dic566C2212yes—
15#22583575—22no—
16#22583569C2211yescharacteristic
17#22583566—22no—
18#22583543C2212yes—
19#22583541C2212yes—
20C4⋊(C283⋊C8)C2212yes—
21#22583533C2212yes—
22#22583533C2212yes—
23#22583531C2212yes—
24#22583531C2212yes—
25C22⋊(C283⋊C8)C2212yes—
26#22583521C2211yescharacteristic
27C4×C283⋊C8C2211yescharacteristic
28#127×C283C2211yescharacteristic
29#125×C283C2211yescharacteristic
30#123×C283—22no—
31#121×C283—22no—
32#121×C283C2212yes—
33C4×D4×C283C2212yes—
34#117×C283C2211yescharacteristic
35C2×Dic566—24no—
36C2×Dic566—21no—
37C2×Dic566C2312yes—
38C22×Dic283—21no—
39#17985380—24no—
40#17985380—24no—
41C2×C283⋊C8C2312yes—
42C2×C283⋊C8C2312yes—
43C4⋊Dic283C2312yes—
44Dic283⋊C4—22no—
45Dic283⋊C4—22no—
46C22⋊Dic283—21no—
47C4×Dic283—22no—
48C4×Dic283—22no—
49C4×Dic283—21no—
50C2×D4×C283—22no—
51C2×D4×C283—22no—
52C2×D4×C283C2312yes—
53C22×C4×C283—22no—
54C22×C4×C283C2311yescharacteristic
55C4⋊C4×C283—22no—
56C4⋊C4×C283D412yes—
57C4⋊C4×C283C2312yes—
58C22⋊C4×C283—22no—
59C22⋊C4×C283—22no—
60C22⋊C4×C283D412yes—
61C42×C283C2311yescharacteristic
62C42×C283C2311yescharacteristic
63Dic566—24no—
64Dic566—22no—
65Dic566#4114yes—
66C2×Dic283—24no—
67C2×Dic283—22no—
68C2×Dic283—22no—
69C283⋊C8—22no—
70C283⋊C8—22no—
71C23×C283—22no—
72C23×C283C2×D411yescharacteristic
73D4×C283—22no—
74D4×C283—22no—
75D4×C283—82no—
76D4×C283—82no—
77C2×C4×C283—22no—
78C2×C4×C283—22no—
79C2×C4×C283—82no—
80C2×C4×C283C2×D412yes—
81C2×C4×C283C2×D412yes—
82C2×C4×C283C2×D411yescharacteristic
83C2×C4×C283C2411yescharacteristic
84C22×C283—21no—
85C22×C283—22no—
86C22×C283—42no—
87C22×C283—42no—
88C22×C283—42no—
89C22×C283C22×D411yescharacteristic
90C4×C283—21no—
91C4×C283—22no—
92C4×C283—22no—
93C4×C283—42no—
94C4×C283C2×#4112yes—
95Dic283—24no—
96Dic283—42no—
97C2×C283—41no—
98C2×C283—82no—
99C2×C283#52511yescharacteristic
100C2×C283#57712yes—
101C283#312611yescharacteristic, complemented, Sylow
102#3126—2831nomaximal, Sylow
103#540D28311yescharacteristic
104#519—2831no—
105#482—2832no—
106#479—2832no—
107#460—2832no—
108#448—2832no—
109#440—2832no—
110C4×SD16—2832no—
111#433—2831no—
112C22×Q8—2831no—
113C2×SD16—2832no—
114C2×SD16—2832no—
115#127C2×D28311yescharacteristic
116#125C2×D28311yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D28312yes—
120C4×Q8—2832no—
121C4×Q8—2832no—
122C4×Q8—5662no—
123C4×D4C2×D28312yes—
124#117—2831no—
125#117—5662no—
126#117C2×D28311yescharacteristic
127#107—2832no—
128#106—2832no—
129C4⋊C8—2832no—
130#103—2832no—
131#103—2832no—
132#102—2832no—
133#102—2832no—
134C22⋊C8—2832no—
135#97—2831no—
136C4×C8—2831no—
137C2×Q8—2832no—
138C2×Q8—5664no—
139C2×Q8—5661no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D28312yes—
143C22×C4—22no—
144C22×C4—5661no—
145C22×C4C22×D28311yescharacteristic
146SD16—5664no—
147SD16—5664no—
148C2×C8—2832no—
149C2×C8—2832no—
150C4⋊C4—22no—
151C4⋊C4—2832no—
152C4⋊C4—5662no—
153C4⋊C4—5662no—
154C4⋊C4C22⋊D28312yes—
155C4⋊C4C22×D28312yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—5661no—
159C22⋊C4C22⋊D28312yes—
160C42—5661no—
161C42—5662no—
162C42—5662no—
163C42C22×D28311yescharacteristic
164C42C22×D28311yescharacteristic
165C23—22no—
166C23C2×C22⋊D28311yescharacteristic
167Q8—2834no—
168Q8—5664no—
169Q8—5662no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—5664no—
178C2×C4—5662no—
179C2×C4—5662no—
180C2×C4C2×C22⋊D28312yes—
181C2×C4C2×C22⋊D28312yes—
182C2×C4C2×C22⋊D28311yescharacteristic
183C2×C4C23×D28311yescharacteristic
184C8—5662no—
185C8—5662no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D28311yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—5664no—
197C4—11322no—
198C4#41×D28312yes—
199C2—41no—
200C2—82no—
201C2#3182697211yescharacteristic
202C2#3182727612yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting, prime radical#540×C283C2
socleC22×C283C22×D4
hypercenter#540D283
hypocenterC283#3126
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #31826942C2semidirect
2. #31826786C2semidirect
3. #31826769C2semidirect
4. #31826662C2semidirect
5. #31826603C2semidirect
6. #31826565C2semidirect
7. C4×#17985380C2semidirect
8. #31826526C2semidirect
101. C283#3126semidirect

Maximal subgroups

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

subgroupindex
#318269422
#318267862
#318267692
#318266622
#318266032
#318265652
C4×#179853802
#318265262
#540×C2832
#3126283