Finite Group Databasebeta

← #49120348

Subgroups — #49120348

Order 36224.

256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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#31827119C211yesmaximal, characteristic, complemented
2#31826811C211yesmaximal, characteristic, complemented
3#31826657C211yesmaximal, characteristic, complemented
4#31826212C211yesmaximal, characteristic, complemented
5D4⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#459×C283C211yesmaximal, characteristic, complemented
8C2×#17985391—21no—
9C2×#17985377—21no—
10#22583610C2211yescharacteristic
11#22583594—22no—
12#22583590—21no—
13#22583584—21no—
14C4×D1132C2211yescharacteristic
15C2×C4⋊Dic283—21no—
16C4⋊(C283⋊C8)C2211yescharacteristic
17#22583531—22no—
18#22583531—21no—
19C4×C283⋊C8C2211yescharacteristic
20C2×D8×C283—21no—
21#127×C283C2211yescharacteristic
22C4×D4×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24#102×C283—21no—
25#17985391—42no—
26#17985391—42no—
27C2×Dic566—21no—
28C2×D1132D411yescharacteristic
29C2×C22⋊D283—22no—
30C22×Dic283—22no—
31C2×C4×D283—21no—
32#17985377—42no—
33C2×C283⋊C8—21no—
34C2×C283⋊C8—21no—
35C4⋊Dic283—22no—
36C4⋊Dic283—21no—
37C4⋊Dic283D411yescharacteristic
38C4⋊Dic283D412yes—
39(C2×D283)⋊C4—22no—
40(C2×D283)⋊C4—21no—
41C2×D4×C283—21no—
42C2×D4×C283—21no—
43C2×D4×C283—21no—
44C2×D4×C283D411yescharacteristic
45C22×C4×C283—21no—
46D8×C283—42no—
47C2×C8×C283—21no—
48C4⋊C4×C283D411yescharacteristic
49C22⋊C4×C283—21no—
50C42×C283C2311yescharacteristic
51C22×D283—21no—
52Dic566—41no—
53Dic566—41no—
54D1132—21no—
55D1132—21no—
56C22⋊D283—44no—
57C2×Dic283—21no—
58C2×Dic283—22no—
59C2×Dic283—44no—
60C4×D283—41no—
61C4×D283—41no—
62C283⋊C8—41no—
63C283⋊C8—41no—
64C23×C283—21no—
65C23×C283—41no—
66D4×C283—21no—
67D4×C283—42no—
68D4×C283—41no—
69D4×C283—41no—
70D4×C283—41no—
71D4×C283—41no—
72D4×C283D812yescomplemented
73C2×C4×C283—21no—
74C2×C4×C283—41no—
75C2×C4×C283—41no—
76C2×C4×C283C2×D411yescharacteristic
77C2×C4×C283C2×D411yescharacteristic
78C2×C4×C283C2×D411yescharacteristic
79C8×C283—41no—
80C22×C283—22no—
81C22×C283—41no—
82C22×C283—41no—
83C22×C283—81no—
84C22×C283—81no—
85C22×C283—81no—
86C22×C283#12011yescharacteristic
87C2×D283—41no—
88C2×D283—41no—
89C2×D283—41no—
90C4×C283—21no—
91C4×C283—41no—
92C4×C283C2×D811yescharacteristic
93C4×C283#13511yescharacteristic
94C4×C283AGL(1,ℤ/8)11yescharacteristic
95C4×C283AGL(1,ℤ/8)11yescharacteristic
96Dic283—41no—
97Dic283—42no—
98C2×C283—42no—
99C2×C283—161no—
100C2×C283#44711yescharacteristic
101C2×C283#44911yescharacteristic
102C2×C283#45411yescharacteristic
103D283—81no—
104C283#162511yescharacteristic, complemented, Sylow
105#1625—2831nomaximal, Sylow
106#547—2831no—
107#486—2831no—
108#459—2831no—
109#459D28311yescharacteristic, complemented
110#332—2831no—
111D4⋊C8—2831no—
112D4⋊C8—2831no—
113C2×#41—5661no—
114C2×D8—21no—
115C2×D8—5661no—
116C4⋊Q8—2831no—
117#127C2×D28311yescharacteristic
118#123—5662no—
119C22⋊Q8—5661no—
120#121—5661no—
121C4×D4—2831no—
122C4×D4C2×D28311yescharacteristic
123C2×C4⋊C4—5661no—
124C4⋊C8—2831no—
125C4⋊C8C2×D28311yescharacteristic
126#102—21no—
127#102—5661no—
128#102—5662no—
129C4×C8—2831no—
130#41—11322no—
131#41—11322no—
132C2×Q8—5661no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—2831no—
137C2×D4—5662no—
138C2×D4C22⋊D28311yescharacteristic
139C22×C4—21no—
140C22×C4—5662no—
141C22×C4—5661no—
142D8—42no—
143D8—11322no—
144C2×C8—21no—
145C2×C8—5661no—
146C2×C8—5661no—
147C4⋊C4—2831no—
148C4⋊C4—2832no—
149C4⋊C4—5662no—
150C4⋊C4—5661no—
151C4⋊C4C22⋊D28311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5662no—
154C22⋊C4—5661no—
155C42C22×D28311yescharacteristic
156C23—21no—
157C23—41no—
158C23—5661no—
159Q8—11321no—
160Q8—11321no—
161D4—21no—
162D4—42no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—5661no—
168D4—5661no—
169D4—11324no—
170D4#1798537712yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5661no—
175C2×C4—5662no—
176C2×C4—11324no—
177C2×C4—11321no—
178C2×C4—11321no—
179C2×C4D4×D28311yescharacteristic
180C2×C4D4×D28311yescharacteristic
181C2×C4C2×C22⋊D28311yescharacteristic
182C8—41no—
183C8—11321no—
184C8—11321no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—11321no—
192C22—11321no—
193C22—11321no—
194C22#2258357811yescharacteristic
195C4—21no—
196C4—41no—
197C4—11321no—
198C4—11322no—
199C4C2×#1798537711yescharacteristic
200C4#2258362911yescharacteristic
201C4#2258363411yescharacteristic
202C4#2258363511yescharacteristic
203C2—42no—
204C2—161no—
205C2—22641no—
206C2#3182659811yescharacteristic
207C2#3182660711yescharacteristic
208C2#3182663611yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#459×C283C2
socleC22×C283#120
hypercenter#459D283
hypocenterC283#1625
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #31827119C2semidirect
2. #31826811C2semidirect
3. #31826657C2semidirect
4. #31826212C2semidirect
5. D4⋊(C283⋊C8)C2semidirect
6. #31826192C2semidirect
7. #459×C283C2semidirect
72. D4×C283D8semidirect
104. C283#1625semidirect
109. #459D283semidirect
170. D4#17985377semidirect

Maximal subgroups

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

subgroupindex
#318271192
#318268112
#318266572
#318262122
D4⋊(C283⋊C8)2
#318261922
#459×C2832
#1625283