Finite Group Databasebeta

← #49120525

Subgroups — #49120525

Order 36224.

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

normal subgroups only

This group has 234 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#31827130C211yesmaximal, characteristic
2#31826861C211yesmaximal, characteristic, complemented
3#31826751C211yesmaximal, characteristic, complemented
4#31826671C211yesmaximal, characteristic
5#31826195C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic
7#332×C283C211yesmaximal, characteristic, complemented
8C2×Q8×D283—21no—
9C2×#17985381—21no—
10#22583610C2211yescharacteristic
11#22583609—21no—
12#22583588—22no—
13#22583586—21no—
14C4×Dic566C2211yescharacteristic
15C4×D1132C2211yescharacteristic
16#22583572—21no—
17#22583542—21no—
18#22583541—22no—
19#22583535—21no—
20#22583535—21no—
21C4×C283⋊C8C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25C2×Dic566—22no—
26C2×Dic566—21no—
27C2×Dic566D411yescharacteristic
28Q8×D283—42no—
29Q8×D283—42no—
30C2×D1132D411yescharacteristic
31C2×C4×D283—22no—
32C2×C4×D283—21no—
33#17985381—42no—
34C2×C283⋊C8—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283D411yescharacteristic
38C4⋊Dic283D411yescharacteristic
39Dic283⋊C4—22no—
40Dic283⋊C4—21no—
41(C2×D283)⋊C4—22no—
42(C2×D283)⋊C4—21no—
43C4×Dic283—21no—
44C2×Q8×C283—21no—
45C2×C8×C283—21no—
46C2×C8×C283—21no—
47C4⋊C4×C283—21no—
48C4⋊C4×C283D412yes—
49C42×C283C2311yescharacteristic
50C22×D283—21no—
51Dic566—21no—
52Dic566—44no—
53Dic566—41no—
54Dic566—41no—
55Dic566SD1612yescomplemented
56D1132—21no—
57D1132SD1612yes—
58C2×Dic283—21no—
59C2×Dic283—21no—
60C2×Dic283—21no—
61C2×Dic283—41no—
62C4×D283—44no—
63C4×D283—41no—
64C4×D283—41no—
65C283⋊C8—22no—
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—
78C4×C283—21no—
79C4×C283—42no—
80C4×C283C2×SD1611yescharacteristic
81C4×C283C2×SD1611yescharacteristic
82C4×C283AGL(1,ℤ/8)11yescharacteristic
83C4×C283#13711yescharacteristic
84Dic283—22no—
85Dic283—41no—
86Dic283—41no—
87Dic283—81no—
88C2×C283#44811yescharacteristic
89C2×C283#45011yescharacteristic
90C2×C283#45611yescharacteristic
91D283—42no—
92C283#165111yescharacteristic, complemented, Sylow
93#1651—2831nomaximal, Sylow
94D4×Q8—2831no—
95#498—2831no—
96#475—2831no—
97#461—2831no—
98#332D28311yescharacteristic, complemented
99Q8⋊C8—2831no—
100D4⋊C8—2831no—
101C22×Q8—5661no—
102C2×SD16—5661no—
103C4⋊Q8—2831no—
104C4⋊Q8—5661no—
105C4⋊Q8C2×D28311yescharacteristic
106C22⋊Q8—5661no—
107C22⋊Q8—5662no—
108C4×Q8—2831no—
109C4×D4—2831no—
110C4×D4—5661no—
111#106—5661no—
112#106—5662no—
113C4⋊C8C2×D28311yescharacteristic
114C4⋊C8C2×D28311yescharacteristic
115#103—5661no—
116#103—5661no—
117C4×C8—2831no—
118C2×Q8—21no—
119C2×Q8—2831no—
120C2×Q8—5662no—
121C2×Q8—5661no—
122C2×Q8—11322no—
123C2×Q8—11322no—
124C2×D4—2831no—
125C22×C4—5662no—
126C22×C4—5661no—
127SD16—11322no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5661no—
131C4⋊C4—21no—
132C4⋊C4—2831no—
133C4⋊C4—2831no—
134C4⋊C4—5662no—
135C4⋊C4—5661no—
136C4⋊C4—5661no—
137C4⋊C4—5661no—
138C4⋊C4D113212yes—
139C22⋊C4—5662no—
140C22⋊C4—5661no—
141C42—5661no—
142C42C22×D28311yescharacteristic
143C23—5661no—
144Q8—41no—
145Q8—41no—
146Q8—2832no—
147Q8—5661no—
148Q8—11324no—
149Q8—11321no—
150Q8—11321no—
151D4—2832no—
152D4—5661no—
153C2×C4—22no—
154C2×C4—5661no—
155C2×C4—5661no—
156C2×C4—5661no—
157C2×C4—11324no—
158C2×C4—11321no—
159C2×C4—11321no—
160C2×C4—11321no—
161C2×C4D4×D28311yescharacteristic
162C2×C4D4×D28311yescharacteristic
163C2×C4C2×D113211yescharacteristic
164C8—41no—
165C8—41no—
166C8—5662no—
167C22—5662no—
168C22—11321no—
169C22—11321no—
170C22#2258358011yescharacteristic
171C4—21no—
172C4—42no—
173C4—5662no—
174C4—11321no—
175C4—11321no—
176C4—22641no—
177C4SD16×D28311yescharacteristic
178C4SD16×D28311yescharacteristic
179C4#2258363411yescharacteristic
180C4#2258364211yescharacteristic
181C2—11322no—
182C2#3182660511yescharacteristic
183C2#3182661711yescharacteristic
184C2#3182665011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#332×C283C2
socleC22×C283#120
prime radicalC2×D1132D4
hypercenter#332D283
hypocenterC283#1651
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. #31826861C2semidirect
3. #31826751C2semidirect
5. #31826195C2semidirect
7. #332×C283C2semidirect
55. Dic566SD16semidirect
92. C283#1651semidirect
98. #332D283semidirect

Maximal subgroups

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

subgroupindex
#318271302
#318268612
#318267512
#318266712
#318261952
#318261922
#332×C2832
#1651283