Finite Group Databasebeta

← #49131391

Subgroups — #49131391

Order 36224.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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#31827022C211yesmaximal, characteristic
2#31826795C212yesmaximal
3#31826750C212yesmaximal, complemented
4#31826675C212yesmaximal, complemented
5#31826621C212yesmaximal
6#31826570C214yesmaximal, complemented
7#31826522C211yesmaximal, characteristic
8C2×C4×Q8×C283C211yesmaximal, characteristic
9C2×#17985382C2214yes—
10#22583610C2211yescharacteristic
11#22583610C2211yescharacteristic
12#22583602—21no—
13#22583589—21no—
14#22583589C2212yes—
15C4×Dic566—21no—
16C4×Dic566C2212yes—
17#22583569—21no—
18#22583541C2214yes—
19C4⋊(C283⋊C8)C2212yes—
20#22583534C2214yes—
21#22583533C2214yes—
22C22⋊(C283⋊C8)C2212yes—
23#22583521C2212yes—
24C22×Q8×C283C2211yescharacteristic
25C4×Q8×C283—21no—
26C4×Q8×C283—21no—
27C4×Q8×C283C2212yes—
28C4×Q8×C283C2212yes—
29C2×C4⋊C4×C283—21no—
30C2×C4⋊C4×C283C2211yescharacteristic
31C2×C42×C283—21no—
32C2×C42×C283C2211yescharacteristic
33C2×Dic566—21no—
34C2×Dic566C2312yes—
35#17985382—28no—
36C2×C283⋊C8C2314yes—
37C4⋊Dic283—21no—
38C4⋊Dic283—21no—
39C4⋊Dic283—21no—
40C4⋊Dic283C2312yes—
41Dic283⋊C4—22no—
42Dic283⋊C4—22no—
43C22⋊Dic283—22no—
44C4×Dic283—22no—
45C2×Q8×C283—24no—
46C2×Q8×C283—21no—
47C2×Q8×C283C2312yes—
48C22×C4×C283—21no—
49C22×C4×C283—21no—
50C22×C4×C283D411yescharacteristic
51C22×C4×C283D411yescharacteristic
52C22×C4×C283C2311yescharacteristic
53C4⋊C4×C283—22no—
54C4⋊C4×C283—22no—
55C4⋊C4×C283—21no—
56C4⋊C4×C283C2312yes—
57C42×C283—22no—
58C42×C283—22no—
59C42×C283D411yescharacteristic
60C42×C283D411yescharacteristic
61C42×C283C2311yescharacteristic
62C42×C283C2311yescharacteristic
63Dic566—24no—
64Dic566—42no—
65C2×Dic283—22no—
66C2×Dic283—22no—
67C283⋊C8—24no—
68C23×C283C2×D411yescharacteristic
69Q8×C283—24no—
70Q8×C283—22no—
71Q8×C283#4114yes—
72C2×C4×C283—24no—
73C2×C4×C283—22no—
74C2×C4×C283—22no—
75C2×C4×C283—22no—
76C2×C4×C283—22no—
77C2×C4×C283—22no—
78C2×C4×C283—42no—
79C2×C4×C283C2×D411yescharacteristic
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2×D411yescharacteristic
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2411yescharacteristic
85C22×C283—21no—
86C22×C283—21no—
87C22×C283#13712yes—
88C22×C283C22×D411yescharacteristic
89C4×C283—24no—
90C4×C283—21no—
91C4×C283—21no—
92C4×C283—21no—
93C4×C283—21no—
94C4×C283—42no—
95C4×C283#13712yes—
96C4×C283C2×#4112yes—
97Dic283—42no—
98Dic283—42no—
99C2×C283—22no—
100C2×C283#52511yescharacteristic
101C2×C283C2×#13711yescharacteristic
102C2×C283C2×#13711yescharacteristic
103C283#311311yescharacteristic, complemented, Sylow
104#3113—2831nomaximal, Sylow
105#533—2831no—
106C2×C4×Q8D28311yescharacteristic
107#483—2832no—
108#475—2832no—
109#462—2832no—
110#451—2832no—
111#441—2834no—
112#432—2831no—
113C22×Q8C2×D28311yescharacteristic
114C2×Q16—2834no—
115C4⋊Q8—2831no—
116C4⋊Q8—2831no—
117#125—5661no—
118C22⋊Q8—2832no—
119C22⋊Q8—5661no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—2832no—
123C4×Q8—5661no—
124C4×Q8C2×D28312yes—
125C4×Q8C2×D28312yes—
126#117—5661no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D28311yescharacteristic
129C2×C42—21no—
130C2×C42C2×D28311yescharacteristic
131#106—2834no—
132C4⋊C8—2832no—
133#103—2834no—
134#103—2834no—
135C22⋊C8—2832no—
136#97—2832no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—2832no—
140C2×Q8—5661no—
141C2×Q8C22×D28312yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D28311yescharacteristic
145C22×C4C22⋊D28311yescharacteristic
146C22×C4C22×D28311yescharacteristic
147Q16—5668no—
148C2×C8—2834no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—2832no—
153C4⋊C4—5662no—
154C4⋊C4—5662no—
155C4⋊C4—5661no—
156C4⋊C4—5661no—
157C4⋊C4—5661no—
158C4⋊C4C22×D28312yes—
159C22⋊C4—5662no—
160C42—22no—
161C42—22no—
162C42—5662no—
163C42C22⋊D28311yescharacteristic
164C42C22⋊D28311yescharacteristic
165C42C22×D28311yescharacteristic
166C42C22×D28311yescharacteristic
167C23C2×C22⋊D28311yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—5664no—
171Q8—11322no—
172Q8#1798539214yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—5662no—
181C2×C4—5662no—
182C2×C4C2×C22⋊D28311yescharacteristic
183C2×C4C2×C22⋊D28311yescharacteristic
184C2×C4C2×C22⋊D28311yescharacteristic
185C2×C4C2×C22⋊D28311yescharacteristic
186C2×C4C2×C22⋊D28311yescharacteristic
187C2×C4C23×D28311yescharacteristic
188C8—5664no—
189C22—21no—
190C22—21no—
191C22#2258364012yes—
192C22C22×C22⋊D28311yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—11322no—
200C4—11322no—
201C4#2258364112yes—
202C4C2×#1798539212yes—
203C2—22no—
204C2#3182697611yescharacteristic
205C2C2×#2258364011yescharacteristic
206C2C2×#2258364111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×C4×Q8×C283C2
socleC22×C283C22×D4
prime radicalC23×C283C2×D4
hypercenterC2×C4×Q8D283
hypocenterC283#3113
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #31826750C2semidirect
4. #31826675C2semidirect
6. #31826570C2semidirect
103. C283#3113semidirect

Maximal subgroups

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

subgroupindex
#318270222
#318267952
#318267502
#318266752
#318266212
#318265702
#318265222
C2×C4×Q8×C2832
#3113283