Finite Group Databasebeta

← #49120212

Subgroups — #49120212

Order 36224.

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

normal subgroups only

This group has 308 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#31827027C211yesmaximal, characteristic
2#31826604C212yesmaximal, complemented
3#31826198C212yesmaximal, complemented
4#31826189C211yesmaximal, characteristic, complemented
5#393×C283C211yesmaximal, characteristic, complemented
6C22×C22⋊D283—21no—
7C2×#17985379—22no—
8#22583594—22no—
9#22583584—21no—
10#22583584C2212yes—
11#22583580—22no—
12#22583534—22no—
13C22⋊(C283⋊C8)C2212yescomplemented
14C22×Q8×C283C2211yescharacteristic, complemented
15C2×C22⋊C4×C283—21no—
16C2×C22⋊C4×C283C2211yescharacteristic
17#95×C283—21no—
18#95×C283C2211yescharacteristic, complemented
19C23×D283—21no—
20C2×D1132—21no—
21C2×D1132D412yes—
22C2×C22⋊D283—22no—
23C2×C22⋊D283—22no—
24C2×C22⋊D283—42no—
25C2×C22⋊D283—42no—
26C22×Dic283—21no—
27#17985379—44no—
28C2×C283⋊C8—22no—
29C4⋊Dic283—21no—
30C4⋊Dic283D412yes—
31(C2×D283)⋊C4—22no—
32(C2×D283)⋊C4—22no—
33C24×C283D411yescharacteristic
34C2×Q8×C283—22no—
35C2×Q8×C283—42no—
36C22×C4×C283—21no—
37C22×C4×C283—21no—
38C22×C4×C283D411yescharacteristic
39C22×C4×C283C2311yescharacteristic
40C22⋊C4×C283—22no—
41C22⋊C4×C283—42no—
42C22×D283—22no—
43C22×D283—42no—
44C22×D283—81no—
45C22×D283—81no—
46D1132—42no—
47D1132—81no—
48C22⋊D283—44no—
49C22⋊D283—42no—
50C22⋊D283—42no—
51C2×Dic283—22no—
52C2×Dic283—42no—
53C283⋊C8—42no—
54C23×C283—21no—
55C23×C283—21no—
56C23×C283—41no—
57C23×C283—41no—
58C23×C283SD1612yescomplemented
59C23×C283C2×D411yescharacteristic
60Q8×C283—24no—
61Q8×C283—42no—
62C2×C4×C283—22no—
63C2×C4×C283—21no—
64C2×C4×C283—41no—
65C2×C4×C283—41no—
66C2×C4×C283—41no—
67C2×C4×C283—41no—
68C2×C4×C283—41no—
69C2×C4×C283—41no—
70C2×C4×C283—41no—
71C2×C4×C283C2×D412yes—
72C22×C283—21no—
73C22×C283—21no—
74C22×C283—22no—
75C22×C283—42no—
76C22×C283—41no—
77C22×C283—41no—
78C22×C283—81no—
79C22×C283#12011yescharacteristic
80C22×C283C2×SD1611yescharacteristic
81C22×C283AGL(1,ℤ/8)11yescharacteristic
82C2×D283—42no—
83C2×D283—42no—
84C2×D283—42no—
85C2×D283—84no—
86C4×C283—22no—
87C4×C283—41no—
88C4×C283—42no—
89C4×C283—81no—
90Dic283—42no—
91C2×C283—21no—
92C2×C283—21no—
93C2×C283—42no—
94C2×C283#45011yescharacteristic
95C2×C283#45511yescharacteristic
96C2×C283B(4,𝔽2)11yescharacteristic
97D283—82no—
98C283#160111yescharacteristic, complemented, Sylow
99#1601—2831nomaximal, Sylow
100#534—2831no—
101#448—2832no—
102#393D28311yescharacteristic, complemented
103#327—2832no—
104#323—2831no—
105C22×Q8C2×D28311yescharacteristic, complemented
106C22×D4—5661no—
107C2×SD16—5662no—
108#123—5662no—
109#121—2832no—
110#121—5661no—
111#120—5662no—
112C2×C22⋊C4—21no—
113C2×C22⋊C4C2×D28311yescharacteristic
114#103—5662no—
115C22⋊C8—2832no—
116#95—21no—
117#95C2×D28311yescharacteristic, complemented
118C24—5661no—
119C24C22⋊D28311yescharacteristic
120C2×Q8—22no—
121C2×Q8—42no—
122C2×D4—2832no—
123C2×D4—5661no—
124C2×D4—5662no—
125C2×D4—5662no—
126C2×D4—11322no—
127C2×D4—11322no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—5661no—
131C22×C4C22⋊D28311yescharacteristic
132C22×C4C22×D28311yescharacteristic
133SD16—11324no—
134C2×C8—5662no—
135C4⋊C4—2832no—
136C4⋊C4—5661no—
137C22⋊C4—22no—
138C22⋊C4—42no—
139C22⋊C4—5662no—
140C22⋊C4—5662no—
141C23—21no—
142C23—21no—
143C23—41no—
144C23—41no—
145C23—5662no—
146C23—11322no—
147C23—22641no—
148C23—22641no—
149C23#1798537912yescomplemented
150C23C2×C22⋊D28311yescharacteristic
151Q8—24no—
152Q8—42no—
153D4—11322no—
154D4—11324no—
155D4—11322no—
156D4—11322no—
157D4—22641no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—5662no—
168C2×C4—11322no—
169C2×C4D4×D28312yes—
170C8—11322no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—81no—
178C22—11322no—
179C22—11322no—
180C22—11322no—
181C22—22644no—
182C22#2258357811yescharacteristic
183C22C2×#1798537911yescharacteristic
184C22#2258363511yescharacteristic
185C4—22no—
186C4—41no—
187C4—42no—
188C4—81no—
189C4—11322no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—22642no—
194C2#3182661511yescharacteristic
195C2#3182664211yescharacteristic
196C2#3182665111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#393×C283C2
socleC22×C283#120
prime radical#31827027C2
hypercenter#393D283
hypocenterC283#1601
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #31826604C2semidirect
3. #31826198C2semidirect
4. #31826189C2semidirect
5. #393×C283C2semidirect
13. C22⋊(C283⋊C8)C22semidirect
14. C22×Q8×C283C22semidirect
18. #95×C283C22semidirect
58. C23×C283SD16semidirect
98. C283#1601semidirect
102. #393D283semidirect
105. C22×Q8C2×D283semidirect
117. #95C2×D283semidirect
149. C23#17985379semidirect

Maximal subgroups

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

subgroupindex
#318270272
#318266042
#318261982
#318261892
#393×C2832
#1601283