Finite Group Databasebeta

← #49120415

Subgroups — #49120415

Order 36224.

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

normal subgroups only

This group has 234 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#31827120C211yesmaximal, characteristic
2#31826816C211yesmaximal, characteristic, complemented
3#31826756C211yesmaximal, characteristic, complemented
4#31826755C211yesmaximal, characteristic, complemented
5#31826212C211yesmaximal, characteristic, complemented
6#31826194C211yesmaximal, characteristic, complemented
7D4⋊C8×C283C211yesmaximal, characteristic, complemented
8C2×#17985392—21no—
9#22583610C2211yescharacteristic
10#22583610C2211yescharacteristic
11#22583592—22no—
12#22583589—21no—
13#22583581—21no—
14C4×D1132C2211yescharacteristic
15C4⋊C4×D283—21no—
16#22583542—21no—
17#22583541—21no—
18C4⋊(C283⋊C8)C2211yescharacteristic
19#22583535—22no—
20#22583532—21no—
21#22583531—21no—
22C4×D4×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4×C8×C283C2211yescharacteristic
25#17985392—42no—
26#17985392—42no—
27C2×Dic566—21no—
28C2×Dic566—21no—
29C2×D1132D411yescharacteristic
30C2×C22⋊D283—22no—
31C2×C4×D283—22no—
32C2×C4×D283—21no—
33C2×C283⋊C8—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283D411yescharacteristic
38C4⋊Dic283D412yes—
39Dic283⋊C4—22no—
40C22⋊Dic283—22no—
41(C2×D283)⋊C4—21no—
42C2×D4×C283D411yescharacteristic
43C22×C4×C283—21no—
44C2×C8×C283—21no—
45C2×C8×C283—21no—
46C4⋊C4×C283D411yescharacteristic
47C22⋊C4×C283—21no—
48C42×C283C2311yescharacteristic
49C22×D283—21no—
50Dic566—41no—
51Dic566—41no—
52Dic566—42no—
53D1132—21no—
54D1132SD1612yes—
55C22⋊D283—44no—
56C2×Dic283—21no—
57C2×Dic283—22no—
58C2×Dic283—41no—
59C4×D283—44no—
60C4×D283—41no—
61C4×D283—41no—
62C283⋊C8—41no—
63C23×C283—21no—
64D4×C283—21no—
65D4×C283—21no—
66C2×C4×C283—21no—
67C2×C4×C283—41no—
68C2×C4×C283—41no—
69C2×C4×C283C2×D411yescharacteristic
70C2×C4×C283C2×D411yescharacteristic
71C2×C4×C283C2×D411yescharacteristic
72C8×C283—41no—
73C8×C283—41no—
74C22×C283—41no—
75C22×C283—41no—
76C22×C283—41no—
77C22×C283#12011yescharacteristic
78C2×D283—22no—
79C2×D283—41no—
80C2×D283—41no—
81C4×C283—21no—
82C4×C283—41no—
83C4×C283C2×SD1611yescharacteristic
84C4×C283#13511yescharacteristic
85C4×C283AGL(1,ℤ/8)11yescharacteristic
86C4×C283#13711yescharacteristic
87Dic283—42no—
88Dic283—41no—
89Dic283—81no—
90C2×C283—81no—
91C2×C283#45011yescharacteristic
92C2×C283#45211yescharacteristic
93C2×C283#45411yescharacteristic
94D283—42no—
95C283#163511yescharacteristic, complemented, Sylow
96#1635—2831nomaximal, Sylow
97#547—2831no—
98#487—2831no—
99#476—2831no—
100#476—2831no—
101#332—2831no—
102D4⋊C8—2831no—
103D4⋊C8D28311yescharacteristic, complemented
104C2×#41—5661no—
105C4⋊Q8—2831no—
106C4⋊Q8—2831no—
107#123—5662no—
108C22⋊Q8—5661no—
109#121—5661no—
110C4×D4—2831no—
111C4×D4C2×D28311yescharacteristic
112C2×C4⋊C4—5661no—
113#106—5661no—
114#106—5661no—
115C4⋊C8—2831no—
116C4⋊C8C2×D28311yescharacteristic
117#103—5662no—
118#102—5661no—
119#102—5661no—
120C4×C8C2×D28311yescharacteristic
121#41—11322no—
122#41—11322no—
123C2×Q8—5661no—
124C2×Q8—5661no—
125C2×D4—2831no—
126C2×D4—5662no—
127C2×D4D113211yescharacteristic
128C22×C4—21no—
129C22×C4—5662no—
130C22×C4—5661no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5661no—
134C4⋊C4—2832no—
135C4⋊C4—2831no—
136C4⋊C4—5662no—
137C4⋊C4—5661no—
138C4⋊C4—5661no—
139C4⋊C4—5661no—
140C4⋊C4D113211yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—5662no—
143C22⋊C4—5661no—
144C42C22×D28311yescharacteristic
145C23—21no—
146C23—5661no—
147Q8—11322no—
148Q8—11321no—
149Q8—11321no—
150D4—21no—
151D4—21no—
152D4—2832no—
153D4—5661no—
154D4—11324no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—5661no—
159C2×C4—5662no—
160C2×C4—11324no—
161C2×C4—11321no—
162C2×C4—11321no—
163C2×C4—11321no—
164C2×C4D4×D28311yescharacteristic
165C2×C4D4×D28311yescharacteristic
166C2×C4C2×D113211yescharacteristic
167C8—41no—
168C8—41no—
169C8—11321no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—5662no—
174C22—11321no—
175C22—11321no—
176C22#2258358011yescharacteristic
177C4—21no—
178C4—41no—
179C4—11322no—
180C4—11321no—
181C4—22641no—
182C4SD16×D28311yescharacteristic
183C4#2258363211yescharacteristic
184C4#2258363411yescharacteristic
185C4#2258364311yescharacteristic
186C2—81no—
187C2—11322no—
188C2#3182661711yescharacteristic
189C2#3182662911yescharacteristic
190C2#3182663911yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
FittingD4⋊C8×C283C2
socleC22×C283#120
prime radical#31827120C2
hypercenterD4⋊C8D283
hypocenterC283#1635
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. #31826816C2semidirect
3. #31826756C2semidirect
4. #31826755C2semidirect
5. #31826212C2semidirect
6. #31826194C2semidirect
7. D4⋊C8×C283C2semidirect
95. C283#1635semidirect
103. D4⋊C8D283semidirect

Maximal subgroups

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

subgroupindex
#318271202
#318268162
#318267562
#318267552
#318262122
#318261942
D4⋊C8×C2832
#1635283