Finite Group Databasebeta

← #49120575

Subgroups — #49120575

Order 36224.

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

normal subgroups only

This group has 208 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#31827209C211yesmaximal, characteristic
2#31826871C211yesmaximal, characteristic, complemented
3#31826827C211yesmaximal, characteristic, complemented
4#31826206C211yesmaximal, characteristic, complemented
5#31826205C211yesmaximal, characteristic, complemented
6#31826204C211yesmaximal, characteristic, complemented
7#497×C283C211yesmaximal, characteristic, complemented
8#22583602C2211yescharacteristic
9#22583598C2211yescharacteristic
10#22583594—21no—
11#22583592—21no—
12#22583587—21no—
13#22583586—21no—
14#22583583—21no—
15#22583582—21no—
16#22583543—21no—
17#22583541—21no—
18#22583533—21no—
19#22583530—21no—
20#22583521C2211yescharacteristic
21#22583521C2211yescharacteristic
22C2×Q16×C283—21no—
23C2×SD16×C283—21no—
24C4⋊Q8×C283C2211yescharacteristic
25#124×C283C2211yescharacteristic
26#97×C283C2211yescharacteristic
27C2×Dic566D411yescharacteristic
28C2×D1132D411yescharacteristic
29C2×C22⋊D283—21no—
30C2×C22⋊D283—21no—
31C22×Dic283—21no—
32C2×C4×D283—21no—
33C2×C283⋊C8—21no—
34C2×C283⋊C8—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283D411yescharacteristic
37C4⋊Dic283D411yescharacteristic
38Dic283⋊C4—21no—
39Dic283⋊C4—21no—
40Dic283⋊C4—21no—
41C22⋊Dic283—21no—
42(C2×D283)⋊C4—21no—
43(C2×D283)⋊C4—21no—
44(C2×D283)⋊C4—21no—
45C2×Q8×C283—21no—
46C2×Q8×C283D411yescharacteristic
47C2×D4×C283D411yescharacteristic
48Q16×C283—42no—
49SD16×C283—42no—
50C2×C8×C283—21no—
51C4⋊C4×C283—21no—
52C4⋊C4×C283—21no—
53C22⋊C4×C283—21no—
54C22⋊C4×C283—21no—
55C42×C283C2311yescharacteristic
56C22×D283—21no—
57Dic566—41no—
58D1132—41no—
59C22⋊D283—81no—
60C22⋊D283—81no—
61C2×Dic283—21no—
62C2×Dic283—21no—
63C2×Dic283—21no—
64C2×Dic283—81no—
65C4×D283—81no—
66C283⋊C8—22no—
67C283⋊C8—41no—
68C23×C283—21no—
69Q8×C283—41no—
70Q8×C283—41no—
71Q8×C283—41no—
72D4×C283—41no—
73C2×C4×C283—21no—
74C2×C4×C283—41no—
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283C2×D411yescharacteristic
77C2×C4×C283C2×D411yescharacteristic
78C8×C283—22no—
79C22×C283—41no—
80C22×C283—41no—
81C22×C283—41no—
82C22×C283#12011yescharacteristic
83C2×D283—41no—
84C2×D283—41no—
85C2×D283—41no—
86C4×C283—21no—
87C4×C283—21no—
88C4×C283—21no—
89C4×C283—41no—
90C4×C283—81no—
91Dic283—41no—
92Dic283—41no—
93Dic283—41no—
94C2×C283—81no—
95C2×C283#45311yescharacteristic
96C2×C283#45511yescharacteristic
97C2×C283#45611yescharacteristic
98D283—81no—
99C283#166111yescharacteristic, complemented, Sylow
100#1661—2831nomaximal, Sylow
101#562—2831no—
102#501—2831no—
103#497D28311yescharacteristic, complemented
104#489—2831no—
105#330—2831no—
106#329—2831no—
107#329—2831no—
108C2×Q16—21no—
109C2×SD16—21no—
110C4⋊Q8C2×D28311yescharacteristic
111#125—2831no—
112#124—2831no—
113#124C2×D28311yescharacteristic
114#123—5661no—
115#123—5661no—
116C22⋊Q8—5661no—
117C22⋊Q8—5661no—
118#121—5661no—
119#121—5661no—
120#107—5661no—
121#106—5661no—
122#103—5661no—
123#102—5661no—
124#97—2831no—
125#97—2831no—
126#97C2×D28311yescharacteristic
127C2×Q8—21no—
128C2×Q8—2831no—
129C2×Q8C22⋊D28311yescharacteristic
130C2×D4—2831no—
131C2×D4—5661no—
132C2×D4—5661no—
133C2×D4C22⋊D28311yescharacteristic
134C22×C4—5661no—
135C22×C4—5661no—
136Q16—42no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—5661no—
140C2×C8—5661no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2831no—
144C4⋊C4—2831no—
145C4⋊C4—5661no—
146C4⋊C4—5661no—
147C4⋊C4—5661no—
148C4⋊C4—5661no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—5661no—
152C22⋊C4—5661no—
153C22⋊C4—5661no—
154C22⋊C4—5661no—
155C42C22×D28311yescharacteristic
156C23—21no—
157C23—5661no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—11321no—
162D4—41no—
163D4—11321no—
164D4—22641no—
165D4—22641no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—5661no—
169C2×C4—5661no—
170C2×C4—5661no—
171C2×C4—22641no—
172C2×C4—22641no—
173C2×C4D4×D28311yescharacteristic
174C2×C4D4×D28311yescharacteristic
175C2×C4C2×C22⋊D28311yescharacteristic
176C8—22no—
177C8—5662no—
178C8—11321no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—11321no—
183C22—11321no—
184C22—11321no—
185C22#2258357811yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—11321no—
192C4—11321no—
193C4—11321no—
194C2—81no—
195C2—22641no—
196C2#3182663211yescharacteristic
197C2#3182664111yescharacteristic
198C2#3182664611yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#497×C283C2
socleC22×C283#120
prime radical#31827209C2
hypercenter#497D283
hypocenterC283#1661
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #31826871C2semidirect
3. #31826827C2semidirect
4. #31826206C2semidirect
5. #31826205C2semidirect
6. #31826204C2semidirect
7. #497×C283C2semidirect
99. C283#1661semidirect
103. #497D283semidirect

Maximal subgroups

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

subgroupindex
#318272092
#318268712
#318268272
#318262062
#318262052
#318262042
#497×C2832
#1661283