Finite Group Databasebeta

← #49120427

Subgroups — #49120427

Order 36224.

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

normal subgroups only

This group has 228 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#31826817C211yesmaximal, characteristic, complemented
3#31826761C211yesmaximal, characteristic, complemented
4#31826756C211yesmaximal, characteristic
5#31826195C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic
7#332×C283C211yesmaximal, characteristic, complemented
8C2×Q8×D283—21no—
9#22583610C2211yescharacteristic
10#22583609—21no—
11#22583588—22no—
12#22583586—21no—
13C4×Dic566C2211yescharacteristic
14C4×D1132C2211yescharacteristic
15#22583572—21no—
16#22583544—21no—
17#22583542—21no—
18#22583535—21no—
19#22583533—22no—
20#22583532—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—
33C2×C283⋊C8—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283D411yescharacteristic
37C4⋊Dic283D411yescharacteristic
38Dic283⋊C4—22no—
39Dic283⋊C4—21no—
40(C2×D283)⋊C4—22no—
41(C2×D283)⋊C4—21no—
42C4×Dic283—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—
50Dic566—21no—
51Dic566—44no—
52Dic566—42no—
53Dic566SD1612yes—
54D1132—21no—
55D1132Q1612yes—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—41no—
60C4×D283—44no—
61C4×D283—41no—
62C4×D283—41no—
63C283⋊C8—41no—
64Q8×C283—41no—
65Q8×C283—41no—
66C2×C4×C283—22no—
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C2×C4×C283C2×D411yescharacteristic
70C8×C283—41no—
71C8×C283—41no—
72C22×C283#12011yescharacteristic
73C2×D283—22no—
74C2×D283—41no—
75C2×D283—41no—
76C4×C283—21no—
77C4×C283—42no—
78C4×C283C2×SD1611yescharacteristic
79C4×C283C2×Q1611yescharacteristic
80C4×C283AGL(1,ℤ/8)11yescharacteristic
81C4×C283#13711yescharacteristic
82Dic283—22no—
83Dic283—41no—
84Dic283—41no—
85Dic283—81no—
86C2×C283#45011yescharacteristic
87C2×C283#45111yescharacteristic
88C2×C283#45411yescharacteristic
89D283—42no—
90C283#163711yescharacteristic, complemented, Sylow
91#1637—2831nomaximal, Sylow
92D4×Q8—2831no—
93#487—2831no—
94#477—2831no—
95#476—2831no—
96#332D28311yescharacteristic, complemented
97Q8⋊C8—2831no—
98D4⋊C8—2831no—
99C22×Q8—5661no—
100C4⋊Q8—2831no—
101C4⋊Q8—5661no—
102C4⋊Q8C2×D28311yescharacteristic
103C22⋊Q8—5661no—
104C22⋊Q8—5662no—
105C4×Q8—2831no—
106C4×D4—2831no—
107C4×D4—5661no—
108#107—5661no—
109#106—5661no—
110C4⋊C8C2×D28311yescharacteristic
111C4⋊C8C2×D28311yescharacteristic
112#103—5661no—
113#103—5662no—
114#102—5661no—
115C4×C8—2831no—
116C2×Q8—21no—
117C2×Q8—2831no—
118C2×Q8—5662no—
119C2×Q8—5661no—
120C2×Q8—11322no—
121C2×Q8—11322no—
122C2×D4—2831no—
123C22×C4—5662no—
124C22×C4—5661no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5661no—
128C4⋊C4—21no—
129C4⋊C4—2831no—
130C4⋊C4—2831no—
131C4⋊C4—5662no—
132C4⋊C4—5661no—
133C4⋊C4—5661no—
134C4⋊C4—5661no—
135C4⋊C4D113212yes—
136C22⋊C4—5662no—
137C22⋊C4—5661no—
138C42—5661no—
139C42C22×D28311yescharacteristic
140C23—5661no—
141Q8—41no—
142Q8—41no—
143Q8—2832no—
144Q8—5661no—
145Q8—11322no—
146Q8—11324no—
147D4—2832no—
148D4—5661no—
149C2×C4—22no—
150C2×C4—5661no—
151C2×C4—5661no—
152C2×C4—5661no—
153C2×C4—11324no—
154C2×C4—11321no—
155C2×C4—11321no—
156C2×C4—11321no—
157C2×C4D4×D28311yescharacteristic
158C2×C4D4×D28311yescharacteristic
159C2×C4C2×D113211yescharacteristic
160C8—41no—
161C8—41no—
162C8—11321no—
163C22—5662no—
164C22—11321no—
165C22—11321no—
166C22#2258358011yescharacteristic
167C4—21no—
168C4—42no—
169C4—5662no—
170C4—11321no—
171C4—11321no—
172C4—22641no—
173C4SD16×D28311yescharacteristic
174C4Q16×D28311yescharacteristic
175C4#2258363411yescharacteristic
176C4#2258363911yescharacteristic
177C2—11322no—
178C2#3182661711yescharacteristic
179C2#3182662211yescharacteristic
180C2#3182664011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#332×C283C2
socleC22×C283#120
prime radicalC2×D1132D4
hypercenter#332D283
hypocenterC283#1637
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. #31826761C2semidirect
5. #31826195C2semidirect
7. #332×C283C2semidirect
90. C283#1637semidirect
96. #332D283semidirect

Maximal subgroups

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

subgroupindex
#318271302
#318268172
#318267612
#318267562
#318261952
#318261922
#332×C2832
#1637283