Finite Group Databasebeta

← #49120277

Subgroups — #49120277

Order 36224.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#31827053C211yesmaximal, characteristic
2#31826796C211yesmaximal, characteristic, complemented
3#31826779C211yesmaximal, characteristic, complemented
4#31826390C211yesmaximal, characteristic, complemented
5#31826203C211yesmaximal, characteristic, complemented
6#31826200C211yesmaximal, characteristic, complemented
7#323×C283C211yesmaximal, characteristic, complemented
8#22583603—21no—
9#22583596—21no—
10#22583592—21no—
11#22583589C2211yescharacteristic
12#22583584C2211yescharacteristic
13#22583583—21no—
14#22583579—21no—
15C4×C22⋊D283—21no—
16C2×C4⋊Dic283C2211yescharacteristic
17C2×C22⋊Dic283—21no—
18#22583544—21no—
19#22583542—21no—
20#22583535—21no—
21#22583532—21no—
22C283⋊#95—21no—
23C283⋊#95C2211yescharacteristic
24C2×C22⋊C4×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic
26C22⋊C8×C283C2211yescharacteristic
27C2×Dic566D411yescharacteristic
28C2×D1132D411yescharacteristic
29C2×C22⋊D283—21no—
30C2×C22⋊D283—21no—
31C2×C22⋊D283—21no—
32C22×Dic283—21no—
33C22×Dic283—21no—
34C2×C4×D283—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283D411yescharacteristic
38C4⋊Dic283D411yescharacteristic
39Dic283⋊C4—21no—
40Dic283⋊C4—21no—
41C22⋊Dic283—21no—
42C22⋊Dic283—21no—
43C22⋊Dic283—21no—
44C22⋊Dic283—42no—
45(C2×D283)⋊C4—21no—
46(C2×D283)⋊C4—21no—
47C4×Dic283—21no—
48C24×C283D411yescharacteristic
49C22×C4×C283D411yescharacteristic
50C22×C4×C283C2311yescharacteristic
51C2×C8×C283—21no—
52C2×C8×C283—21no—
53C22⋊C4×C283—21no—
54C22⋊C4×C283—21no—
55C22×D283—21no—
56Dic566—41no—
57D1132—41no—
58C22⋊D283—41no—
59C22⋊D283—41no—
60C22⋊D283—81no—
61C22⋊D283—81no—
62C2×Dic283—21no—
63C2×Dic283—21no—
64C2×Dic283—21no—
65C2×Dic283—41no—
66C2×Dic283—41no—
67C2×Dic283—41no—
68C2×Dic283—41no—
69C2×Dic283—41no—
70C2×Dic283—41no—
71C4×D283—81no—
72C23×C283—21no—
73C23×C283—21no—
74C23×C283—21no—
75C23×C283—41no—
76C23×C283—41no—
77C23×C283C2×D411yescharacteristic
78C2×C4×C283—21no—
79C2×C4×C283—41no—
80C2×C4×C283—41no—
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2×D411yescharacteristic
83C8×C283—41no—
84C8×C283—41no—
85C22×C283—21no—
86C22×C283—21no—
87C22×C283—42no—
88C22×C283—41no—
89C22×C283—41no—
90C22×C283—41no—
91C22×C283—81no—
92C22×C283#12011yescharacteristic
93C22×C283#13511yescharacteristic
94C22×C283AGL(1,ℤ/8)11yescharacteristic
95C2×D283—41no—
96C2×D283—41no—
97C2×D283—41no—
98C4×C283—21no—
99C4×C283—21no—
100C4×C283—41no—
101Dic283—41no—
102Dic283—41no—
103Dic283—41no—
104Dic283—81no—
105Dic283—81no—
106C2×C283—21no—
107C2×C283—21no—
108C2×C283—81no—
109C2×C283#44911yescharacteristic
110C2×C283#45511yescharacteristic
111C2×C283#45811yescharacteristic
112D283—81no—
113C283#161211yescharacteristic, complemented, Sylow
114#1612—2831nomaximal, Sylow
115#538—2831no—
116#483—2831no—
117#480—2831no—
118#397—2831no—
119#328—2831no—
120#327—2831no—
121#323D28311yescharacteristic, complemented
122#126—5661no—
123#124—5661no—
124#123—5661no—
125C22⋊Q8—2831no—
126#121—2831no—
127#121—5661no—
128#120—5661no—
129C4×D4—5661no—
130C2×C4⋊C4—2831no—
131C2×C22⋊C4—5661no—
132C2×C22⋊C4C2×D28311yescharacteristic
133#107—5661no—
134#106—5661no—
135#103—5661no—
136#102—5661no—
137C22⋊C8C2×D28311yescharacteristic
138C22⋊C8C2×D28311yescharacteristic
139#95—2831no—
140#95—5661no—
141C24D113211yescharacteristic
142C2×Q8—2831no—
143C2×D4—2831no—
144C2×D4—5661no—
145C2×D4—5661no—
146C2×D4—5661no—
147C22×C4—5661no—
148C22×C4—5661no—
149C22×C4—5661no—
150C22×C4D113211yescharacteristic
151C22×C4C22×D28311yescharacteristic
152C2×C8—21no—
153C2×C8—21no—
154C4⋊C4—2831no—
155C4⋊C4—2831no—
156C4⋊C4—5661no—
157C4⋊C4—5661no—
158C4⋊C4—5661no—
159C4⋊C4—5661no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—5661no—
163C22⋊C4—5661no—
164C22⋊C4—5661no—
165C22⋊C4—5661no—
166C22⋊C4—5661no—
167C22⋊C4—11322no—
168C42—5661no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—5661no—
175C23C2×D113211yescharacteristic
176Q8—11321no—
177D4—11321no—
178D4—11321no—
179D4—11321no—
180D4—22641no—
181D4—22641no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—5661no—
186C2×C4—5661no—
187C2×C4—5661no—
188C2×C4—11321no—
189C2×C4—11321no—
190C2×C4—11321no—
191C2×C4—11321no—
192C2×C4—11321no—
193C2×C4—11321no—
194C2×C4—22641no—
195C2×C4D4×D28311yescharacteristic
196C2×C4D4×D28311yescharacteristic
197C8—41no—
198C8—41no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—11321no—
207C22—11321no—
208C22—11321no—
209C22#2258358011yescharacteristic
210C22#2258363211yescharacteristic
211C22#2258363811yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—11321no—
216C4—11321no—
217C4—11321no—
218C4—22641no—
219C4—22641no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—22641no—
224C2#3182661211yescharacteristic
225C2#3182664511yescharacteristic
226C2#3182665611yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#323×C283C2
socleC22×C283#120
prime radical#31827053C2
hypercenter#323D283
hypocenterC283#1612
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. #31826796C2semidirect
3. #31826779C2semidirect
4. #31826390C2semidirect
5. #31826203C2semidirect
6. #31826200C2semidirect
7. #323×C283C2semidirect
113. C283#1612semidirect
121. #323D283semidirect

Maximal subgroups

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

subgroupindex
#318270532
#318267962
#318267792
#318263902
#318262032
#318262002
#323×C2832
#1612283