Finite Group Databasebeta

← #49120448

Subgroups — #49120448

Order 36224.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#31827201C211yesmaximal, characteristic
2#31826811C211yesmaximal, characteristic
3#31826751C211yesmaximal, characteristic, complemented
4#31826676C211yesmaximal, characteristic, complemented
5#31826195C211yesmaximal, characteristic, complemented
6#31826195C211yesmaximal, characteristic, complemented
7#331×C283C211yesmaximal, characteristic
8C2×Dic1132—21no—
9#22583610C2211yescharacteristic
10#22583597—21no—
11#22583597—21no—
12#22583591—22no—
13C4×Dic566C2211yescharacteristic
14C4×Dic566C2211yescharacteristic
15D4×Dic283—21no—
16D4×Dic283—21no—
17#22583542—21no—
18#22583535—21no—
19#22583535—21no—
20#22583531—22no—
21C4×C283⋊C8C2211yescharacteristic
22#127×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25C2×Dic566—21no—
26C2×Dic566D411yescharacteristic
27C2×Dic566D411yescharacteristic
28C22×Dic283—22no—
29Dic1132—42no—
30C2×C283⋊C8—21no—
31C4⋊Dic283—21no—
32C4⋊Dic283—21no—
33C4⋊Dic283D411yescharacteristic
34C4⋊Dic283D411yescharacteristic
35Dic283⋊C4—21no—
36Dic283⋊C4—21no—
37C22⋊Dic283—22no—
38C22⋊Dic283—22no—
39C22⋊Dic283—22no—
40C4×Dic283—21no—
41C4×Dic283—21no—
42C2×D4×C283—21no—
43C2×D4×C283—21no—
44C2×D4×C283D412yes—
45C2×C8×C283—21no—
46C2×C8×C283—21no—
47C42×C283C2311yescharacteristic
48Dic566—21no—
49Dic566—21no—
50Dic566—21no—
51Dic566—21no—
52Dic566—41no—
53Dic566—41no—
54C2×Dic283—21no—
55C2×Dic283—21no—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C2×Dic283—41no—
59C2×Dic283—82no—
60C283⋊C8—41no—
61C23×C283—22no—
62D4×C283—42no—
63D4×C283—41no—
64D4×C283—41no—
65D4×C283—41no—
66D4×C283—41no—
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C2×C4×C283C2×D411yescharacteristic
70C8×C283—41no—
71C8×C283—41no—
72C22×C283—42no—
73C22×C283—42no—
74C22×C283—42no—
75C22×C283#12011yescharacteristic
76C4×C283—21no—
77C4×C283#13511yescharacteristic
78C4×C283#13511yescharacteristic
79C4×C283AGL(1,ℤ/8)11yescharacteristic
80C4×C283#13711yescharacteristic
81Dic283—41no—
82Dic283—41no—
83Dic283—41no—
84Dic283—41no—
85Dic283—81no—
86C2×C283—82no—
87C2×C283#44911yescharacteristic
88C2×C283#45211yescharacteristic
89C2×C283#45511yescharacteristic
90C283#164011yescharacteristic, complemented, Sylow
91#1640—2831nomaximal, Sylow
92#559—2831no—
93#486—2831no—
94#475—2831no—
95#462—2831no—
96#331D28311yescharacteristic
97Q8⋊C8—2831no—
98Q8⋊C8—2831no—
99C2×Q16—5661no—
100C4⋊Q8—2831no—
101#127C2×D28311yescharacteristic
102#124—5661no—
103#124—5661no—
104#123—5662no—
105C4×Q8—2831no—
106C4×Q8—2831no—
107C4×D4—5661no—
108C4×D4—5661no—
109#106—5661no—
110C4⋊C8C2×D28311yescharacteristic
111C4⋊C8C2×D28311yescharacteristic
112#103—5661no—
113#103—5661no—
114#102—5662no—
115C4×C8—2831no—
116C2×Q8—2831no—
117C2×Q8—2831no—
118C2×Q8—5661no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4D113212yes—
122C22×C4—5662no—
123Q16—11322no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—5661no—
127C4⋊C4—2831no—
128C4⋊C4—2831no—
129C4⋊C4—5661no—
130C4⋊C4—5661no—
131C4⋊C4—5661no—
132C4⋊C4—5661no—
133C22⋊C4—5662no—
134C22⋊C4—5662no—
135C22⋊C4—5662no—
136C42—5661no—
137C42—5661no—
138C42C22×D28311yescharacteristic
139C23—22no—
140Q8—5661no—
141Q8—5661no—
142Q8—5661no—
143Q8—5661no—
144Q8—11321no—
145Q8—11321no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—5661no—
152C2×C4—5661no—
153C2×C4—5661no—
154C2×C4—5661no—
155C2×C4—11321no—
156C2×C4—22642no—
157C2×C4D4×D28311yescharacteristic
158C2×C4D4×D28311yescharacteristic
159C2×C4C2×D113211yescharacteristic
160C8—41no—
161C8—41no—
162C8—11321no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#2258358011yescharacteristic
167C4—21no—
168C4—11321no—
169C4—11321no—
170C4—11321no—
171C4—11321no—
172C4—22641no—
173C4#2258362911yescharacteristic
174C4#2258363111yescharacteristic
175C4#2258363411yescharacteristic
176C4#2258363911yescharacteristic
177C2—82no—
178C2#3182661111yescharacteristic
179C2#3182662811yescharacteristic
180C2#3182664511yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#331×C283C2
socleC22×C283#120
prime radical#127×C283C22
hypercenter#331D283
hypocenterC283#1640
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #31826751C2semidirect
4. #31826676C2semidirect
5. #31826195C2semidirect
6. #31826195C2semidirect
90. C283#1640semidirect

Maximal subgroups

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

subgroupindex
#318272012
#318268112
#318267512
#318266762
#318261952
#331×C2832
#1640283