Finite Group Databasebeta

← #49122432

Subgroups — #49122432

Order 36224.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#31827018C211yesmaximal, characteristic, complemented
2#31826483C211yesmaximal, characteristic
3C2×#22583536C211yesmaximal, characteristic
4#31826438C211yesmaximal, characteristic
5#31826237C211yesmaximal, characteristic, complemented
6#31826224C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C2×#17985376C2211yescharacteristic
10#22583609—21no—
11#22583601—21no—
12#22583587—22no—
13C4×Dic566—22no—
14#22583569C2211yescharacteristic
15C2×C4×Dic283C2211yescharacteristic
16#22583538—22no—
17#22583536—21no—
18#22583536—21no—
19#22583524—22no—
20C2×M16×C283C2211yescharacteristic
21#117×C283C2211yescharacteristic
22#117×C283C2211yescharacteristic
23#17985392—21no—
24#17985392—21no—
25#17985392—21no—
26#17985392—21no—
27C2×Dic566—22no—
28C2×Dic566Q811yescharacteristic, complemented
29C2×D1132Q811yescharacteristic, complemented
30C2×C22⋊D283—21no—
31C22×Dic283—21no—
32C2×C4×D283—21no—
33#17985376—21no—
34#17985376—21no—
35C2×C283⋊C8—21no—
36C4⋊Dic283—22no—
37C4⋊Dic283—21no—
38Dic283⋊C4—22no—
39Dic283⋊C4—22no—
40C22⋊Dic283D412yes—
41C4×Dic283—21no—
42C4×Dic283—21no—
43C4×Dic283D411yescharacteristic
44C4×Dic283D411yescharacteristic
45C22×C4×C283C2311yescharacteristic
46M16×C283—21no—
47M16×C283—21no—
48C2×C8×C283—21no—
49C4⋊C4×C283—21no—
50C4⋊C4×C283—21no—
51C22⋊C4×C283—21no—
52C22⋊C4×C283—21no—
53C42×C283—21no—
54C42×C283D412yes—
55C22×D283—21no—
56Dic566—21no—
57Dic566—21no—
58Dic566—44no—
59D1132—21no—
60D1132—21no—
61C22⋊D283—41no—
62C22⋊D283—41no—
63C2×Dic283—21no—
64C2×Dic283—21no—
65C2×Dic283—22no—
66C2×Dic283—21no—
67C2×Dic283—42no—
68C4×D283—41no—
69C4×D283—41no—
70C283⋊C8—41no—
71C23×C283C2×D411yescharacteristic
72C2×C4×C283—22no—
73C2×C4×C283—41no—
74C2×C4×C283C2×D411yescharacteristic
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283C2×Q811yescharacteristic
77C2×C4×C283#4111yescharacteristic
78C2×C4×C283#4111yescharacteristic
79C2×C4×C283#4111yescharacteristic
80C8×C283—41no—
81C22×C283—41no—
82C22×C283#12011yescharacteristic
83C22×C283C22⋊Q811yescharacteristic
84C22×C283#12411yescharacteristic
85C2×D283—41no—
86C2×D283—81no—
87C4×C283—42no—
88C4×C283—81no—
89C4×C283C22⋊Q811yescharacteristic
90C4×C283C22⋊Q811yescharacteristic
91C4×C283#12411yescharacteristic
92C4×C283#12411yescharacteristic
93Dic283—22no—
94Dic283—41no—
95Dic283—42no—
96Dic283—41no—
97C2×C283—21no—
98C2×C283—21no—
99C2×C283—21no—
100C2×C283#39311yescharacteristic
101D283—81no—
102C283#203111yescharacteristic, complemented, Sylow
103#2031—2831nomaximal, Sylow
104#533—2831no—
105#421—2831no—
106C2×#104—2831no—
107#410—2831no—
108#344—2831no—
109#339—2831no—
110H(3,ℤ/4)D28311yescharacteristic, complemented
111C2×#41—2831no—
112C2×M16—2831no—
113C2×M16C2×D28311yescharacteristic
114C4⋊Q8—5661no—
115#125—5661no—
116C22⋊Q8—5662no—
117C4×Q8—5662no—
118#117—2831no—
119#117C2×D28311yescharacteristic
120#117C2×D28311yescharacteristic
121C2×C42—2831no—
122#104—5661no—
123#104—5661no—
124#104—5662no—
125#99—5662no—
126#41—5661no—
127#41—5661no—
128#41—5661no—
129#41—5661no—
130C2×Q8—2831no—
131C2×Q8—5662no—
132C2×D4—2831no—
133C2×D4—5661no—
134C22×C4—5661no—
135C22×C4—5661no—
136C22×C4C22×D28311yescharacteristic
137M16—21no—
138M16—21no—
139M16—5661no—
140M16—5661no—
141C2×C8—21no—
142C2×C8—5661no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—5662no—
146C4⋊C4—5662no—
147C4⋊C4—5662no—
148C4⋊C4—5661no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—2832no—
152C42—21no—
153C42—2831no—
154C42—2831no—
155C42—5661no—
156C42—5661no—
157C42D113212yes—
158C23—5661no—
159C23D4×D28311yescharacteristic
160Q8—5661no—
161Q8—5661no—
162Q8—11324no—
163D4—5661no—
164D4—5661no—
165D4—11321no—
166D4—11321no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—5661no—
170C2×C4—5661no—
171C2×C4—5662no—
172C2×C4—5661no—
173C2×C4—11322no—
174C2×C4—11321no—
175C2×C4—11321no—
176C2×C4D4×D28311yescharacteristic
177C2×C4C2×D113211yescharacteristic
178C2×C4Q8×D28311yescharacteristic
179C2×C4#1798539111yescharacteristic
180C2×C4#1798539211yescharacteristic
181C2×C4#1798539211yescharacteristic
182C8—41no—
183C8—11321no—
184C22—41no—
185C22—11321no—
186C22—22641no—
187C22#2258358011yescharacteristic
188C22#2258358811yescharacteristic
189C22#2258359611yescharacteristic
190C4—42no—
191C4—81no—
192C4—5662no—
193C4—11321no—
194C4—11322no—
195C4—11321no—
196C4#2258358811yescharacteristic
197C4#2258359011yescharacteristic
198C4#2258359611yescharacteristic
199C4#2258359811yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—22641no—
204C2#3182637811yescharacteristic
subgroupG/H
centerC4#22583598
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingH(3,ℤ/4)×C283C2
socleC2×C283#393
prime radicalC2×#17985392C22
hypercenterH(3,ℤ/4)D283
hypocenterC283#2031
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #31827018C2semidirect
5. #31826237C2semidirect
6. #31826224C2semidirect
7. H(3,ℤ/4)×C283C2semidirect
28. C2×Dic566Q8semidirect
29. C2×D1132Q8semidirect
102. C283#2031semidirect
110. H(3,ℤ/4)D283semidirect

Maximal subgroups

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

subgroupindex
#318270182
#318264832
C2×#225835362
#318264382
#318262372
#318262242
H(3,ℤ/4)×C2832
#2031283