Finite Group Databasebeta

← #49120379

Subgroups — #49120379

Order 36224.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D1132C211yesmaximal, characteristic
2#31826838C211yesmaximal, characteristic, complemented
3#31826756C211yesmaximal, characteristic, complemented
4#31826755C211yesmaximal, characteristic, complemented
5#31826208C211yesmaximal, characteristic, complemented
6#31826194C211yesmaximal, characteristic, complemented
7D4⋊C8×C283C211yesmaximal, characteristic, complemented
8C22×D1132—21no—
9C2×D4×D283—21no—
10C2×#17985381—22no—
11#22583610C2211yescharacteristic, complemented
12#22583607C2211yescharacteristic
13#22583585—21no—
14#22583584—21no—
15#22583580—22no—
16C4×D1132C2211yescharacteristic
17#22583542—21no—
18#22583541—21no—
19C4⋊(C283⋊C8)C2211yescharacteristic, complemented
20#22583532—21no—
21#22583531—21no—
22C4×D4×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic, complemented
24C4×C8×C283C2211yescharacteristic, complemented
25C23×D283—22no—
26C2×Dic566—21no—
27C2×D1132—22no—
28C2×D1132—21no—
29C2×D1132—21no—
30C2×D1132—42no—
31C2×D1132—42no—
32C2×D1132D411yescharacteristic
33C2×D1132D412yes—
34C2×C22⋊D283—22no—
35D4×D283—42no—
36D4×D283—42no—
37C2×C4×D283—21no—
38#17985381—44no—
39C2×C283⋊C8—21no—
40C4⋊Dic283—21no—
41C4⋊Dic283—21no—
42C4⋊Dic283D411yescharacteristic
43(C2×D283)⋊C4—22no—
44(C2×D283)⋊C4—21no—
45C2×D4×C283D411yescharacteristic
46C22×C4×C283—21no—
47C2×C8×C283—21no—
48C2×C8×C283—21no—
49C4⋊C4×C283D411yescharacteristic
50C22⋊C4×C283—21no—
51C42×C283C2311yescharacteristic
52C22×D283—21no—
53C22×D283—22no—
54C22×D283—44no—
55C22×D283—44no—
56C22×D283—82no—
57Dic566—42no—
58D1132—21no—
59D1132—42no—
60D1132—44no—
61D1132—41no—
62D1132—41no—
63D1132—41no—
64D1132—41no—
65D1132SD1612yescomplemented
66C22⋊D283—44no—
67C2×Dic283—21no—
68C2×Dic283—41no—
69C4×D283—41no—
70C4×D283—41no—
71C283⋊C8—41no—
72C23×C283—21no—
73D4×C283—21no—
74D4×C283SD1612yescomplemented
75C2×C4×C283—21no—
76C2×C4×C283—41no—
77C2×C4×C283—41no—
78C2×C4×C283C2×D411yescharacteristic
79C2×C4×C283C2×D411yescharacteristic
80C2×C4×C283C2×D411yescharacteristic
81C8×C283—22no—
82C8×C283—41no—
83C22×C283—22no—
84C22×C283—41no—
85C22×C283—41no—
86C22×C283#12011yescharacteristic
87C2×D283—22no—
88C2×D283—41no—
89C2×D283—41no—
90C2×D283—42no—
91C2×D283—42no—
92C2×D283—42no—
93C2×D283—88no—
94C4×C283—21no—
95C4×C283—41no—
96C4×C283C2×SD1611yescharacteristic
97C4×C283C2×SD1611yescharacteristic
98C4×C283AGL(1,ℤ/8)11yescharacteristic
99C4×C283AGL(1,ℤ/8)11yescharacteristic
100Dic283—41no—
101Dic283—81no—
102C2×C283—42no—
103C2×C283#45011yescharacteristic
104C2×C283#45011yescharacteristic
105C2×C283#45311yescharacteristic
106D283—42no—
107D283—82no—
108C283#162911yescharacteristic, complemented, Sylow
109#1629—2831nomaximal, Sylow
110D42—2831no—
111#492—2831no—
112#476—2831no—
113#476—2831no—
114#331—2831no—
115D4⋊C8—2831no—
116D4⋊C8D28311yescharacteristic, complemented
117C22×D4—5661no—
118C22×D4—5661no—
119C2×SD16—5662no—
120C4⋊Q8—2831no—
121#127—2831no—
122#121—5661no—
123#121—5661no—
124#120—5662no—
125C4×D4—2831no—
126C4×D4C2×D28311yescharacteristic
127#106—5661no—
128#106—5661no—
129C4⋊C8—2831no—
130C4⋊C8C2×D28311yescharacteristic, complemented
131#102—5661no—
132#102—5661no—
133C4×C8C2×D28311yescharacteristic, complemented
134C24—5662no—
135C2×Q8—5661no—
136C2×D4—2831no—
137C2×D4—2832no—
138C2×D4—5662no—
139C2×D4—5662no—
140C2×D4—5661no—
141C2×D4—5661no—
142C2×D4—11322no—
143C2×D4—11322no—
144C2×D4—11322no—
145C2×D4—11322no—
146C2×D4D113211yescharacteristic
147C22×C4—21no—
148C22×C4—5661no—
149SD16—11324no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—5661no—
153C4⋊C4—2831no—
154C4⋊C4—5661no—
155C4⋊C4—5661no—
156C4⋊C4D113211yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—5662no—
159C22⋊C4—5661no—
160C42C22×D28311yescharacteristic
161C23—21no—
162C23—5661no—
163C23—5662no—
164C23—11324no—
165C23—11324no—
166C23—22642no—
167Q8—11322no—
168D4—21no—
169D4—2832no—
170D4—5661no—
171D4—11322no—
172D4—11324no—
173D4—11324no—
174D4—11321no—
175D4—11321no—
176D4—11321no—
177D4—11321no—
178D4#1798538112yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—5661no—
183C2×C4—11321no—
184C2×C4—11321no—
185C2×C4—11321no—
186C2×C4D4×D28311yescharacteristic
187C2×C4D4×D28311yescharacteristic
188C2×C4C2×D113211yescharacteristic
189C8—22no—
190C8—41no—
191C8—11321no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—5662no—
196C22—11321no—
197C22—11321no—
198C22—11322no—
199C22—11322no—
200C22—11322no—
201C22—22648no—
202C22#2258358011yescharacteristic
203C4—21no—
204C4—41no—
205C4—11321no—
206C4—22641no—
207C4SD16×D28311yescharacteristic
208C4C2×#1798538111yescharacteristic
209C4#2258363411yescharacteristic
210C4#2258363811yescharacteristic
211C2—42no—
212C2—11322no—
213C2—22642no—
214C2#3182661711yescharacteristic
215C2#3182661811yescharacteristic
216C2#3182663411yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
FittingD4⋊C8×C283C2
socleC22×C283#120
prime radicalD4×D1132C2
hypercenterD4⋊C8D283
hypocenterC283#1629
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
2. #31826838C2semidirect
3. #31826756C2semidirect
4. #31826755C2semidirect
5. #31826208C2semidirect
6. #31826194C2semidirect
7. D4⋊C8×C283C2semidirect
11. #22583610C22semidirect
19. C4⋊(C283⋊C8)C22semidirect
23. C4⋊C8×C283C22semidirect
24. C4×C8×C283C22semidirect
65. D1132SD16semidirect
74. D4×C283SD16semidirect
108. C283#1629semidirect
116. D4⋊C8D283semidirect
130. C4⋊C8C2×D283semidirect
133. C4×C8C2×D283semidirect
178. D4#17985381semidirect

Maximal subgroups

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

subgroupindex
D4×D11322
#318268382
#318267562
#318267552
#318262082
#318261942
D4⋊C8×C2832
#1629283