Finite Group Databasebeta

← #49120413

Subgroups — #49120413

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#31827118C211yesmaximal, characteristic
2#31826817C211yesmaximal, characteristic, complemented
3#31826756C211yesmaximal, characteristic, complemented
4#31826756C211yesmaximal, characteristic, complemented
5#31826192C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#332×C283C211yesmaximal, characteristic, complemented
8C2×#17985393—21no—
9#22583610C2211yescharacteristic
10#22583595—22no—
11#22583586—21no—
12#22583585—21no—
13C4×D1132C2211yescharacteristic
14C4×D1132C2211yescharacteristic
15C4⋊C4×D283—21no—
16#22583542—21no—
17#22583542—21no—
18#22583533—22no—
19#22583532—21no—
20#22583532—21no—
21C4×C283⋊C8C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25#17985393—42no—
26#17985393—42no—
27C2×Dic566—21no—
28C2×D1132—22no—
29C2×D1132D411yescharacteristic
30C2×D1132D411yescharacteristic
31C2×C4×D283—22no—
32C2×C4×D283—21no—
33C2×C4×D283—21no—
34C2×C283⋊C8—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283D411yescharacteristic
38C4⋊Dic283D411yescharacteristic
39Dic283⋊C4—22no—
40(C2×D283)⋊C4—22no—
41(C2×D283)⋊C4—21no—
42(C2×D283)⋊C4—21no—
43C2×Q8×C283—21no—
44C2×C8×C283—21no—
45C2×C8×C283—21no—
46C4⋊C4×C283—21no—
47C4⋊C4×C283D412yes—
48C42×C283C2311yescharacteristic
49C22×D283—21no—
50C22×D283—21no—
51Dic566—42no—
52D1132—21no—
53D1132—21no—
54D1132—21no—
55D1132—44no—
56D1132SD1612yes—
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—41no—
60C4×D283—44no—
61C4×D283—41no—
62C4×D283—41no—
63C4×D283—41no—
64C4×D283—41no—
65C283⋊C8—41no—
66Q8×C283—41no—
67Q8×C283—41no—
68C2×C4×C283—22no—
69C2×C4×C283C2×D411yescharacteristic
70C2×C4×C283C2×D411yescharacteristic
71C2×C4×C283C2×D411yescharacteristic
72C8×C283—41no—
73C8×C283—41no—
74C22×C283#12011yescharacteristic
75C2×D283—22no—
76C2×D283—41no—
77C2×D283—41no—
78C2×D283—41no—
79C2×D283—41no—
80C2×D283—41no—
81C4×C283—21no—
82C4×C283—42no—
83C4×C283C2×SD1611yescharacteristic
84C4×C283#13511yescharacteristic
85C4×C283AGL(1,ℤ/8)11yescharacteristic
86C4×C283#13711yescharacteristic
87Dic283—41no—
88Dic283—41no—
89Dic283—81no—
90C2×C283#45011yescharacteristic
91C2×C283#45211yescharacteristic
92C2×C283#45411yescharacteristic
93D283—42no—
94D283—81no—
95C283#163511yescharacteristic, complemented, Sylow
96#1635—2831nomaximal, Sylow
97#547—2831no—
98#487—2831no—
99#476—2831no—
100#476—2831no—
101#332D28311yescharacteristic, complemented
102D4⋊C8—2831no—
103D4⋊C8—2831no—
104C2×#41—5661no—
105C4⋊Q8—2831no—
106C4⋊Q8C2×D28311yescharacteristic
107#123—5662no—
108C22⋊Q8—5661no—
109#121—5661no—
110C4×D4—2831no—
111C4×D4—2831no—
112C2×C4⋊C4—5661no—
113#106—5661no—
114#106—5661no—
115C4⋊C8C2×D28311yescharacteristic
116C4⋊C8C2×D28311yescharacteristic
117#103—5662no—
118#102—5661no—
119#102—5661no—
120C4×C8—2831no—
121#41—11322no—
122#41—11322no—
123C2×Q8—21no—
124C2×Q8—5661no—
125C2×D4—2831no—
126C2×D4—2831no—
127C2×D4—5662no—
128C22×C4—5662no—
129C22×C4—5661no—
130C22×C4—5661no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5661no—
134C4⋊C4—21no—
135C4⋊C4—2831no—
136C4⋊C4—2831no—
137C4⋊C4—5662no—
138C4⋊C4—5661no—
139C4⋊C4—5661no—
140C4⋊C4D113212yes—
141C22⋊C4—5662no—
142C22⋊C4—5661no—
143C22⋊C4—5661no—
144C42C22×D28311yescharacteristic
145C23—5661no—
146C23—5661no—
147Q8—41no—
148Q8—41no—
149Q8—11322no—
150D4—2832no—
151D4—5661no—
152D4—5661no—
153D4—5661no—
154D4—11324no—
155C2×C4—22no—
156C2×C4—5661no—
157C2×C4—5661no—
158C2×C4—11324no—
159C2×C4—11321no—
160C2×C4—11321no—
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—5662no—
171C22—11321no—
172C22—11321no—
173C22—11321no—
174C22—11321no—
175C22—11321no—
176C22#2258358011yescharacteristic
177C4—21no—
178C4—42no—
179C4—11321no—
180C4—11321no—
181C4—22641no—
182C4SD16×D28311yescharacteristic
183C4#2258363111yescharacteristic
184C4#2258363411yescharacteristic
185C4#2258364211yescharacteristic
186C2—11322no—
187C2—22641no—
188C2#3182661711yescharacteristic
189C2#3182663011yescharacteristic
190C2#3182664011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#332×C283C2
socleC22×C283#120
prime radical#31827118C2
hypercenter#332D283
hypocenterC283#1635
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31826817C2semidirect
3. #31826756C2semidirect
4. #31826756C2semidirect
5. #31826192C2semidirect
6. #31826192C2semidirect
7. #332×C283C2semidirect
95. C283#1635semidirect
101. #332D283semidirect

Maximal subgroups

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

subgroupindex
#318271182
#318268172
#318267562
#318261922
#332×C2832
#1635283