Finite Group Databasebeta

← #49120352

Subgroups — #49120352

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#31826812C211yesmaximal, characteristic, complemented
3#31826661C211yesmaximal, characteristic, complemented
4#31826660C211yesmaximal, characteristic, complemented
5#31826210C211yesmaximal, characteristic, complemented
6#31826194C211yesmaximal, characteristic, complemented
7D4⋊C8×C283C211yesmaximal, characteristic, complemented
8C2×#17985391—21no—
9C2×D2264—21no—
10C2×#17985377—21no—
11#22583610C2211yescharacteristic
12#22583607C2211yescharacteristic
13#22583594—22no—
14#22583590—21no—
15#22583584—21no—
16C4×D1132C2211yescharacteristic
17C2×C4⋊Dic283—21no—
18C4⋊(C283⋊C8)C2211yescharacteristic
19#22583532—22no—
20#22583532—21no—
21#22583530—21no—
22C4×D4×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4×C8×C283C2211yescharacteristic
25#17985391—42no—
26#17985391—42no—
27C2×Dic566—21no—
28C2×D1132—21no—
29C2×D1132—21no—
30C2×D1132—21no—
31C2×D1132D411yescharacteristic
32C2×C22⋊D283—22no—
33C22×Dic283—22no—
34C2×C4×D283—21no—
35D2264—42no—
36#17985377—42no—
37C2×C283⋊C8—21no—
38C4⋊Dic283—22no—
39C4⋊Dic283—21no—
40C4⋊Dic283D411yescharacteristic
41C4⋊Dic283D412yes—
42(C2×D283)⋊C4—22no—
43(C2×D283)⋊C4—21no—
44C2×D4×C283D411yescharacteristic
45C22×C4×C283—21no—
46C2×C8×C283—21no—
47C2×C8×C283—21no—
48C4⋊C4×C283D411yescharacteristic
49C22⋊C4×C283—21no—
50C42×C283C2311yescharacteristic
51C22×D283—21no—
52C22×D283—41no—
53Dic566—41no—
54Dic566—41no—
55D1132—21no—
56D1132—21no—
57D1132—42no—
58D1132—41no—
59D1132—41no—
60D1132—41no—
61D1132—41no—
62C22⋊D283—44no—
63C2×Dic283—21no—
64C2×Dic283—22no—
65C2×Dic283—44no—
66C4×D283—41no—
67C4×D283—41no—
68C283⋊C8—41no—
69C23×C283—21no—
70D4×C283—21no—
71D4×C283D812yescomplemented
72C2×C4×C283—21no—
73C2×C4×C283—41no—
74C2×C4×C283—41no—
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283C2×D411yescharacteristic
77C2×C4×C283C2×D411yescharacteristic
78C8×C283—41no—
79C8×C283—41no—
80C22×C283—22no—
81C22×C283—41no—
82C22×C283—41no—
83C22×C283#12011yescharacteristic
84C2×D283—41no—
85C2×D283—41no—
86C2×D283—41no—
87C2×D283—81no—
88C2×D283—81no—
89C2×D283—81no—
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#44711yescharacteristic
100C2×C283#44911yescharacteristic
101C2×C283#45411yescharacteristic
102D283—81no—
103D283—161no—
104C283#162511yescharacteristic, complemented, Sylow
105#1625—2831nomaximal, Sylow
106#547—2831no—
107#486—2831no—
108#459—2831no—
109#459—2831no—
110#332—2831no—
111D4⋊C8—2831no—
112D4⋊C8D28311yescharacteristic, complemented
113C2×#41—5661no—
114C2×D8—5661no—
115C2×D8—5661no—
116C4⋊Q8—2831no—
117#127—2831no—
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—5661no—
127#102—5662no—
128#102—5661no—
129C4×C8C2×D28311yescharacteristic
130#41—11322no—
131#41—11322no—
132C2×Q8—5661no—
133C2×D4—2831no—
134C2×D4—5662no—
135C2×D4—5661no—
136C2×D4—5661no—
137C2×D4—5661no—
138C2×D4D113211yescharacteristic
139C22×C4—21no—
140C22×C4—5662no—
141C22×C4—5661no—
142D8—11322no—
143D8—11322no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—5661no—
147C4⋊C4—2831no—
148C4⋊C4—2832no—
149C4⋊C4—5662no—
150C4⋊C4—5661no—
151C4⋊C4D113211yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5662no—
154C22⋊C4—5661no—
155C42C22×D28311yescharacteristic
156C23—21no—
157C23—5661no—
158C23—11321no—
159Q8—11321no—
160Q8—11321no—
161D4—21no—
162D4—5661no—
163D4—5661no—
164D4—11322no—
165D4—11324no—
166D4—11321no—
167D4—11321no—
168D4—11321no—
169D4—11321no—
170D4D226412yescomplemented
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×D113211yescharacteristic
182C8—41no—
183C8—41no—
184C8—11321no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—11321no—
189C22—11321no—
190C22—11321no—
191C22—22641no—
192C22—22641no—
193C22—22641no—
194C22#2258358011yescharacteristic
195C4—21no—
196C4—41no—
197C4—11321no—
198C4—11322no—
199C4C2×D226411yescharacteristic
200C4#2258363111yescharacteristic
201C4#2258363411yescharacteristic
202C4#2258363811yescharacteristic
203C2—42no—
204C2—45281no—
205C2—22641no—
206C2#3182660111yescharacteristic
207C2#3182661111yescharacteristic
208C2#3182663911yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
FittingD4⋊C8×C283C2
socleC22×C283#120
hypercenterD4⋊C8D283
hypocenterC283#1625
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #31827119C2semidirect
2. #31826812C2semidirect
3. #31826661C2semidirect
4. #31826660C2semidirect
5. #31826210C2semidirect
6. #31826194C2semidirect
7. D4⋊C8×C283C2semidirect
71. D4×C283D8semidirect
104. C283#1625semidirect
112. D4⋊C8D283semidirect
170. D4D2264semidirect

Maximal subgroups

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

subgroupindex
#318271192
#318268122
#318266612
#318266602
#318262102
#318261942
D4⋊C8×C2832
#1625283