Finite Group Databasebeta

← #49120249

Subgroups — #49120249

Order 36224.

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

normal subgroups only

This group has 280 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#31826779C212yesmaximal, complemented
3#31826390C211yesmaximal, characteristic, complemented
4#31826200C212yesmaximal, complemented
5#323×C283C211yesmaximal, characteristic, complemented
6C22×C22⋊D283—21no—
7#22583594—22no—
8#22583584—21no—
9#22583584C2212yes—
10#22583580—22no—
11C2×C4⋊Dic283C2211yescharacteristic, complemented
12C2×C22⋊Dic283—21no—
13#22583544—22no—
14#22583532—22no—
15C283⋊#95—21no—
16C283⋊#95C2211yescharacteristic, complemented
17C2×C22⋊C4×C283C2211yescharacteristic
18C22⋊C8×C283C2212yescomplemented
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—
27C22×Dic283—21no—
28C22×Dic283—21no—
29C4⋊Dic283—21no—
30C4⋊Dic283—22no—
31C4⋊Dic283D412yes—
32C22⋊Dic283—42no—
33(C2×D283)⋊C4—22no—
34(C2×D283)⋊C4—22no—
35C24×C283D411yescharacteristic
36C22×C4×C283D411yescharacteristic
37C22×C4×C283C2311yescharacteristic
38C2×C8×C283—22no—
39C22⋊C4×C283—22no—
40C22×D283—22no—
41C22×D283—42no—
42C22×D283—81no—
43C22×D283—81no—
44D1132—42no—
45D1132—81no—
46C22⋊D283—44no—
47C22⋊D283—42no—
48C22⋊D283—42no—
49C2×Dic283—22no—
50C2×Dic283—42no—
51C2×Dic283—41no—
52C2×Dic283—41no—
53C2×Dic283—41no—
54C2×Dic283—41no—
55C2×Dic283—41no—
56C2×Dic283—41no—
57C23×C283—21no—
58C23×C283—21no—
59C23×C283—41no—
60C23×C283—41no—
61C23×C283D812yes—
62C23×C283C2×D411yescharacteristic
63C2×C4×C283—21no—
64C2×C4×C283—41no—
65C2×C4×C283—41no—
66C2×C4×C283C2×D412yes—
67C8×C283—42no—
68C22×C283—21no—
69C22×C283—21no—
70C22×C283—22no—
71C22×C283—42no—
72C22×C283—41no—
73C22×C283—41no—
74C22×C283—81no—
75C22×C283#12011yescharacteristic
76C22×C283C2×D811yescharacteristic
77C22×C283AGL(1,ℤ/8)11yescharacteristic
78C2×D283—42no—
79C2×D283—42no—
80C2×D283—42no—
81C2×D283—84no—
82C4×C283—22no—
83C4×C283—41no—
84Dic283—42no—
85Dic283—81no—
86Dic283—81no—
87C2×C283—21no—
88C2×C283—21no—
89C2×C283—42no—
90C2×C283#44711yescharacteristic
91C2×C283#45511yescharacteristic
92C2×C283#45811yescharacteristic
93D283—82no—
94C283#160711yescharacteristic, complemented, Sylow
95#1607—2831nomaximal, Sylow
96#534—2831no—
97#480—2832no—
98#397—2831no—
99#327—2832no—
100#323D28311yescharacteristic, complemented
101C22×D4—5661no—
102#123—5662no—
103#121—2832no—
104#121—5661no—
105#120—5662no—
106C2×C4⋊C4—2831no—
107C2×C22⋊C4—5661no—
108C2×C22⋊C4C2×D28311yescharacteristic
109#107—5662no—
110#102—5662no—
111C22⋊C8C2×D28312yescomplemented
112#95—2831no—
113#95—5661no—
114C24—5661no—
115C24D113211yescharacteristic
116C2×D4—2832no—
117C2×D4—5661no—
118C2×D4—5662no—
119C2×D4—5662no—
120C2×D4—11322no—
121C2×D4—11322no—
122C22×C4—5661no—
123C22×C4—5661no—
124C22×C4—5661no—
125C22×C4D113211yescharacteristic
126C22×C4C22×D28311yescharacteristic
127C2×C8—22no—
128C4⋊C4—2832no—
129C4⋊C4—5661no—
130C4⋊C4—5662no—
131C22⋊C4—22no—
132C22⋊C4—5662no—
133C22⋊C4—5662no—
134C22⋊C4—11322no—
135C23—21no—
136C23—21no—
137C23—41no—
138C23—41no—
139C23—5662no—
140C23—11322no—
141C23—22641no—
142C23—22641no—
143C23D226412yes—
144C23C2×D113211yescharacteristic
145D4—11322no—
146D4—11324no—
147D4—11322no—
148D4—11322no—
149D4—22641no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—5662no—
154C2×C4—11322no—
155C2×C4—11321no—
156C2×C4—11321no—
157C2×C4—11321no—
158C2×C4—11321no—
159C2×C4—11321no—
160C2×C4—11321no—
161C2×C4D4×D28312yes—
162C8—42no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—81no—
170C22—11322no—
171C22—11322no—
172C22—11322no—
173C22—22644no—
174C22#2258358011yescharacteristic
175C22C2×D226411yescharacteristic
176C22#2258363811yescharacteristic
177C4—22no—
178C4—41no—
179C4—11322no—
180C4—22641no—
181C4—22641no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—22642no—
186C2#3182660111yescharacteristic
187C2#3182664511yescharacteristic
188C2#3182665611yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#323×C283C2
socleC22×C283#120
prime radical#31827027C2
hypercenter#323D283
hypocenterC283#1607
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #31826779C2semidirect
3. #31826390C2semidirect
4. #31826200C2semidirect
5. #323×C283C2semidirect
11. C2×C4⋊Dic283C22semidirect
16. C283⋊#95C22semidirect
18. C22⋊C8×C283C22semidirect
94. C283#1607semidirect
100. #323D283semidirect
111. C22⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270272
#318267792
#318263902
#318262002
#323×C2832
#1607283