Finite Group Databasebeta

← #49120451

Subgroups — #49120451

Order 36224.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#31827135C211yesmaximal, characteristic
2#31826742C211yesmaximal, characteristic, complemented
3#31826672C211yesmaximal, characteristic, complemented
4#31826209C211yesmaximal, characteristic, complemented
5#31826197C211yesmaximal, characteristic, complemented
6#31826194C211yesmaximal, characteristic, complemented
7#486×C283C211yesmaximal, characteristic, complemented
8C2×#17985391—21no—
9C2×#17985382—21no—
10#22583606—21no—
11#22583582—22no—
12#22583581—21no—
13C4×Dic566C2211yescharacteristic
14C4×D1132C2211yescharacteristic
15D4×Dic283—21no—
16#22583543—21no—
17C4⋊(C283⋊C8)C2211yescharacteristic
18C4⋊(C283⋊C8)C2211yescharacteristic
19#22583534—21no—
20#22583530—21no—
21C4⋊Q8×C283C2211yescharacteristic
22#127×C283C2211yescharacteristic
23#102×C283—22no—
24C4×C8×C283C2211yescharacteristic
25#17985391—42no—
26#17985391—42no—
27C2×Dic566D411yescharacteristic
28C2×D1132D411yescharacteristic
29C2×C22⋊D283—22no—
30C2×C22⋊D283—22no—
31C22×Dic283—22no—
32C2×C4×D283—21no—
33#17985382—42no—
34C2×C283⋊C8—21no—
35C2×C283⋊C8—21no—
36C4⋊Dic283D411yescharacteristic
37C4⋊Dic283D411yescharacteristic
38Dic283⋊C4—21no—
39C22⋊Dic283—22no—
40(C2×D283)⋊C4—21no—
41C4×Dic283—21no—
42C2×Q8×C283—21no—
43C2×D4×C283—21no—
44C2×D4×C283—21no—
45C2×D4×C283D412yes—
46C2×C8×C283—21no—
47C4⋊C4×C283—21no—
48C4⋊C4×C283—21no—
49C42×C283C2311yescharacteristic
50C22×D283—21no—
51Dic566—21no—
52Dic566D812yes—
53D1132—21no—
54D1132—21no—
55C22⋊D283—44no—
56C22⋊D283—82no—
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—21no—
60C2×Dic283—44no—
61C4×D283—41no—
62C4×D283—41no—
63C283⋊C8—41no—
64C283⋊C8—41no—
65C23×C283—22no—
66Q8×C283—41no—
67Q8×C283—41no—
68D4×C283—42no—
69D4×C283—41no—
70D4×C283—41no—
71D4×C283—41no—
72D4×C283—41no—
73C2×C4×C283—41no—
74C2×C4×C283C2×D411yescharacteristic
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283C2×D411yescharacteristic
77C8×C283—41no—
78C22×C283—42no—
79C22×C283—42no—
80C22×C283—42no—
81C22×C283#12011yescharacteristic
82C2×D283—41no—
83C2×D283—41no—
84C2×D283—41no—
85C4×C283—21no—
86C4×C283—81no—
87C4×C283C2×D811yescharacteristic
88C4×C283#13511yescharacteristic
89C4×C283AGL(1,ℤ/8)11yescharacteristic
90C4×C283#13711yescharacteristic
91Dic283—22no—
92Dic283—41no—
93Dic283—41no—
94C2×C283—82no—
95C2×C283#44711yescharacteristic
96C2×C283#45211yescharacteristic
97C2×C283#45511yescharacteristic
98D283—81no—
99C283#164111yescharacteristic, complemented, Sylow
100#1641—2831nomaximal, Sylow
101#550—2831no—
102#486D28311yescharacteristic, complemented
103#474—2831no—
104#462—2831no—
105#331—2831no—
106Q8⋊C8—2831no—
107D4⋊C8—2831no—
108C2×#41—5661no—
109C2×Q16—5661no—
110C4⋊Q8C2×D28311yescharacteristic
111#127—5661no—
112#127C2×D28311yescharacteristic
113#121—5661no—
114#121—5662no—
115C4×Q8—2831no—
116C4×D4—2831no—
117C4×D4—5661no—
118#107—5661no—
119C4⋊C8—2831no—
120C4⋊C8—2831no—
121#103—5661no—
122#102—22no—
123#102—5661no—
124C4×C8C2×D28311yescharacteristic
125#41—11322no—
126#41—11322no—
127C2×Q8—21no—
128C2×Q8—2831no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—2831no—
132C2×D4—5662no—
133C2×D4—5662no—
134C2×D4C22⋊D28312yes—
135C22×C4—5662no—
136C22×C4—5661no—
137Q16—11322no—
138C2×C8—21no—
139C2×C8—5661no—
140C2×C8—5661no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2831no—
144C4⋊C4—2831no—
145C4⋊C4—5661no—
146C22⋊C4—5662no—
147C22⋊C4—5661no—
148C42—5661no—
149C42C22×D28311yescharacteristic
150C23—22no—
151C23—5661no—
152Q8—41no—
153Q8—41no—
154Q8—2832no—
155Q8—5661no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—5661no—
162D4—5661no—
163D4—11324no—
164D4—22642no—
165C2×C4—41no—
166C2×C4—5661no—
167C2×C4—5661no—
168C2×C4—5661no—
169C2×C4—11324no—
170C2×C4—11321no—
171C2×C4—11321no—
172C2×C4D4×D28311yescharacteristic
173C2×C4D4×D28311yescharacteristic
174C2×C4C2×C22⋊D28311yescharacteristic
175C8—41no—
176C8—11321no—
177C8—11321no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—11321no—
182C22—11321no—
183C22—11321no—
184C22#2258357811yescharacteristic
185C4—21no—
186C4—81no—
187C4—5662no—
188C4—11321no—
189C4—11321no—
190C4D8×D28311yescharacteristic
191C4#2258363111yescharacteristic
192C4#2258363411yescharacteristic
193C4#2258363911yescharacteristic
194C2—82no—
195C2—22641no—
196C2#3182659711yescharacteristic
197C2#3182662411yescharacteristic
198C2#3182664211yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#486×C283C2
socleC22×C283#120
prime radical#31827135C2
hypercenter#486D283
hypocenterC283#1641
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #31826742C2semidirect
3. #31826672C2semidirect
4. #31826209C2semidirect
5. #31826197C2semidirect
6. #31826194C2semidirect
7. #486×C283C2semidirect
99. C283#1641semidirect
102. #486D283semidirect

Maximal subgroups

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

subgroupindex
#318271352
#318267422
#318266722
#318262092
#318261972
#318261942
#486×C2832
#1641283