Finite Group Databasebeta

← #49120598

Subgroups — #49120598

Order 36224.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#31827215C211yesmaximal, characteristic
2#31826874C211yesmaximal, characteristic, complemented
3#31826834C211yesmaximal, characteristic, complemented
4#31826824C211yesmaximal, characteristic
5#31826206C211yesmaximal, characteristic, complemented
6#31826206C211yesmaximal, characteristic, complemented
7#329×C283C211yesmaximal, characteristic
8#22583610C2211yescharacteristic
9#22583608—21no—
10#22583603—21no—
11#22583603—21no—
12#22583602C2211yescharacteristic
13#22583602C2211yescharacteristic
14#22583591—21no—
15#22583587—21no—
16#22583587—21no—
17#22583544—21no—
18#22583542—21no—
19#22583535—21no—
20#22583535—21no—
21#22583534—21no—
22#22583531—21no—
23#22583521C2211yescharacteristic
24#124×C283C2211yescharacteristic
25#97×C283C2211yescharacteristic
26#97×C283C2211yescharacteristic
27C2×Dic566—21no—
28C2×Dic566—21no—
29C22×Dic283—21no—
30C2×C283⋊C8—21no—
31C4⋊Dic283—21no—
32C4⋊Dic283—21no—
33C4⋊Dic283D411yescharacteristic
34C4⋊Dic283D411yescharacteristic
35C4⋊Dic283D411yescharacteristic
36C4⋊Dic283D411yescharacteristic
37Dic283⋊C4—21no—
38Dic283⋊C4—21no—
39Dic283⋊C4—21no—
40Dic283⋊C4—21no—
41Dic283⋊C4—21no—
42Dic283⋊C4—21no—
43C22⋊Dic283—21no—
44C22⋊Dic283—21no—
45C22⋊Dic283—21no—
46C4×Dic283—21no—
47C2×Q8×C283D411yescharacteristic
48C2×D4×C283D411yescharacteristic
49C2×C8×C283—21no—
50C2×C8×C283—21no—
51C22⋊C4×C283—21no—
52C22⋊C4×C283—21no—
53C42×C283C2311yescharacteristic
54Dic566—42no—
55Dic566—81no—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—21no—
60C2×Dic283—41no—
61C2×Dic283—81no—
62C283⋊C8—41no—
63C23×C283—21no—
64Q8×C283—41no—
65D4×C283—41no—
66C2×C4×C283—21no—
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C2×C4×C283C2×D411yescharacteristic
70C8×C283—22no—
71C8×C283—41no—
72C22×C283—41no—
73C22×C283—41no—
74C22×C283—41no—
75C22×C283#12011yescharacteristic
76C4×C283—21no—
77C4×C283—21no—
78C4×C283—21no—
79C4×C283—41no—
80Dic283—41no—
81Dic283—41no—
82Dic283—41no—
83Dic283—41no—
84Dic283—81no—
85C2×C283—81no—
86C2×C283#45411yescharacteristic
87C2×C283#45511yescharacteristic
88C2×C283#45611yescharacteristic
89C283#166411yescharacteristic, complemented, Sylow
90#1664—2831nomaximal, Sylow
91#563—2831no—
92#501—2831no—
93#491—2831no—
94#489—2831no—
95#330—2831no—
96#330—2831no—
97#329D28311yescharacteristic
98C4⋊Q8—2831no—
99C4⋊Q8—5661no—
100#126—5661no—
101#126—5661no—
102#125—2831no—
103#125—2831no—
104#124C2×D28311yescharacteristic
105#123—5661no—
106C22⋊Q8—5661no—
107C22⋊Q8—5661no—
108#107—5661no—
109#106—5661no—
110#103—5661no—
111#103—5661no—
112#103—5661no—
113#102—5661no—
114#97—2831no—
115#97C2×D28311yescharacteristic
116#97C2×D28311yescharacteristic
117C2×Q8—5661no—
118C2×Q8—5661no—
119C2×Q8D113211yescharacteristic
120C2×D4D113211yescharacteristic
121C22×C4—5661no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—5661no—
125C4⋊C4—2831no—
126C4⋊C4—2831no—
127C4⋊C4—2831no—
128C4⋊C4—2831no—
129C4⋊C4—5661no—
130C4⋊C4—5661no—
131C4⋊C4—5661no—
132C4⋊C4—5661no—
133C4⋊C4—5661no—
134C4⋊C4—5661no—
135C4⋊C4—5661no—
136C4⋊C4—5661no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—5661no—
140C22⋊C4—5661no—
141C22⋊C4—5661no—
142C42—5661no—
143C42C22×D28311yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—11322no—
147Q8—22641no—
148D4—41no—
149C2×C4—21no—
150C2×C4—5661no—
151C2×C4—5661no—
152C2×C4—5661no—
153C2×C4—5661no—
154C2×C4—11321no—
155C2×C4—22641no—
156C2×C4D4×D28311yescharacteristic
157C2×C4D4×D28311yescharacteristic
158C2×C4C2×D113211yescharacteristic
159C8—22no—
160C8—41no—
161C8—11321no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#2258358011yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—11321no—
171C4—11321no—
172C4—11321no—
173C4—11321no—
174C4—22641no—
175C2—81no—
176C2#3182663911yescharacteristic
177C2#3182664511yescharacteristic
178C2#3182664911yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#329×C283C2
socleC22×C283#120
prime radicalC2×D4×C283D4
hypercenter#329D283
hypocenterC283#1664
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31826874C2semidirect
3. #31826834C2semidirect
5. #31826206C2semidirect
6. #31826206C2semidirect
89. C283#1664semidirect

Maximal subgroups

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

subgroupindex
#318272152
#318268742
#318268342
#318268242
#318262062
#329×C2832
#1664283