Finite Group Databasebeta

← #49131553

Subgroups — #49131553

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#31827070C211yesmaximal, characteristic
2#31826942C211yesmaximal, characteristic, complemented
3#31826790C212yesmaximal, complemented
4#31826773C212yesmaximal, complemented
5#31826666C212yesmaximal, complemented
6#31826606C212yesmaximal, complemented
7#31826567C212yesmaximal, complemented
8C4×#17985381C212yesmaximal, complemented
9#433×C283C211yesmaximal, characteristic, complemented
10C22×Dic566C2211yescharacteristic
11C2×#17985381C2212yes—
12C2×#17985381C2212yes—
13#22583607C2211yescharacteristic
14#22583602C2211yescharacteristic
15#22583595—22no—
16#22583584C2212yes—
17#22583583—22no—
18C4×Dic566C2212yes—
19C4×Dic566C2212yes—
20#22583575—22no—
21C4×D1132C2212yes—
22#22583569C2211yescharacteristic
23#22583566—22no—
24#22583544C2212yes—
25#22583542C2212yes—
26#22583535C2212yes—
27#22583535C2212yes—
28#22583532C2212yes—
29#22583532C2212yes—
30#117×C283C2211yescharacteristic
31C4⋊C8×C283C2212yes—
32C22⋊C8×C283C2212yes—
33#97×C283C2211yescharacteristic
34C4×C8×C283C2211yescharacteristic
35C2×Dic566—24no—
36C2×Dic566—21no—
37C2×Dic566C2312yes—
38C2×D1132—22no—
39C2×D1132C2312yes—
40C2×C22⋊D283—22no—
41C22×Dic283—21no—
42C2×C4×D283—22no—
43#17985381—24no—
44#17985381—24no—
45C4⋊Dic283C2312yes—
46C4⋊Dic283C2312yes—
47Dic283⋊C4—22no—
48Dic283⋊C4—22no—
49Dic283⋊C4—22no—
50C22⋊Dic283—21no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53C4×Dic283—22no—
54C4×Dic283—22no—
55C4×Dic283—21no—
56C22×C4×C283C2311yescharacteristic
57C2×C8×C283C2312yes—
58C2×C8×C283C2312yes—
59C4⋊C4×C283D412yes—
60C22⋊C4×C283D412yes—
61C42×C283C2311yescharacteristic
62C42×C283C2311yescharacteristic
63C22×D283—22no—
64Dic566—24no—
65Dic566—22no—
66Dic566#4114yes—
67D1132—22no—
68D1132—22no—
69D1132—82no—
70C22⋊D283—82no—
71C2×Dic283—24no—
72C2×Dic283—22no—
73C2×Dic283—22no—
74C2×Dic283—22no—
75C4×D283—82no—
76C23×C283C2×D411yescharacteristic
77C2×C4×C283—22no—
78C2×C4×C283C2×D412yes—
79C2×C4×C283C2×D412yes—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2411yescharacteristic
82C8×C283—22no—
83C8×C283—22no—
84C22×C283—21no—
85C22×C283—22no—
86C22×C283C22×D411yescharacteristic
87C2×D283—42no—
88C2×D283—42no—
89C2×D283—42no—
90C4×C283—21no—
91C4×C283—22no—
92C4×C283—22no—
93C4×C283C2×#4112yes—
94Dic283—24no—
95Dic283—42no—
96Dic283—42no—
97C2×C283—41no—
98C2×C283#52511yescharacteristic
99C2×C283#57712yes—
100D283—82no—
101C283#312611yescharacteristic, complemented, Sylow
102#3126—2831nomaximal, Sylow
103#540—2831no—
104#519—2831no—
105#482—2832no—
106#479—2832no—
107#460—2832no—
108#448—2832no—
109#440—2832no—
110C4×SD16—2832no—
111#433D28311yescharacteristic, complemented
112C22×Q8—2831no—
113C2×SD16—2832no—
114C2×SD16—2832no—
115#127—2831no—
116#125—2831no—
117#123—5662no—
118#121—2832no—
119#121—5662no—
120C4×Q8—2832no—
121C4×Q8—2832no—
122C4×Q8—5662no—
123C4×D4—2832no—
124#117—2831no—
125#117—5662no—
126#117C2×D28311yescharacteristic
127#107—2832no—
128#106—2832no—
129C4⋊C8C2×D28312yes—
130#103—2832no—
131#103—2832no—
132#102—2832no—
133#102—2832no—
134C22⋊C8C2×D28312yes—
135#97C2×D28311yescharacteristic
136C4×C8C2×D28311yescharacteristic
137C2×Q8—2832no—
138C2×Q8—5664no—
139C2×Q8—5661no—
140C2×D4—2832no—
141C2×D4—5662no—
142C2×D4—5662no—
143C22×C4—5661no—
144C22×C4—5662no—
145C22×C4C22×D28311yescharacteristic
146SD16—5664no—
147SD16—5664no—
148C2×C8C22×D28312yes—
149C2×C8C22×D28312yes—
150C4⋊C4—2832no—
151C4⋊C4—2832no—
152C4⋊C4—5662no—
153C4⋊C4—5662no—
154C4⋊C4—5662no—
155C4⋊C4D113212yes—
156C22⋊C4—5661no—
157C22⋊C4—5662no—
158C22⋊C4—5662no—
159C22⋊C4D113212yes—
160C42—5661no—
161C42—5662no—
162C42—5662no—
163C42C22×D28311yescharacteristic
164C42C22×D28311yescharacteristic
165C23—5662no—
166C23C2×D113211yescharacteristic
167Q8—2834no—
168Q8—5664no—
169Q8—5662no—
170D4—5662no—
171D4—5662no—
172D4—22642no—
173D4—22642no—
174C2×C4—22no—
175C2×C4—5664no—
176C2×C4—5662no—
177C2×C4—5662no—
178C2×C4—5662no—
179C2×C4—22642no—
180C2×C4C2×D113212yes—
181C2×C4C2×D113212yes—
182C2×C4C2×D113211yescharacteristic
183C2×C4C23×D28311yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—11322no—
189C22—11322no—
190C22—11322no—
191C22C22×D113211yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—5664no—
196C4—11322no—
197C4—11322no—
198C4#41×D28312yes—
199C2—41no—
200C2—22642no—
201C2#3182697711yescharacteristic
202C2#3182727712yes—
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#433×C283C2
socleC22×C283C22×D4
prime radical#31827070C2
hypercenter#433D283
hypocenterC283#3126
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #31826942C2semidirect
3. #31826790C2semidirect
4. #31826773C2semidirect
5. #31826666C2semidirect
6. #31826606C2semidirect
7. #31826567C2semidirect
8. C4×#17985381C2semidirect
9. #433×C283C2semidirect
101. C283#3126semidirect
111. #433D283semidirect

Maximal subgroups

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

subgroupindex
#318270702
#318269422
#318267902
#318267732
#318266662
#318266062
#318265672
C4×#179853812
#433×C2832
#3126283