Finite Group Databasebeta

← #49120308

Subgroups — #49120308

Order 36224.

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

normal subgroups only

This group has 240 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#31827055C211yesmaximal, characteristic
2#31826783C211yesmaximal, characteristic, complemented
3#31826400C211yesmaximal, characteristic, complemented
4#31826202C211yesmaximal, characteristic, complemented
5#31826200C211yesmaximal, characteristic, complemented
6#31826188C211yesmaximal, characteristic, complemented
7#484×C283C211yesmaximal, characteristic, complemented
8#22583605—21no—
9#22583599—21no—
10#22583595—21no—
11#22583585—21no—
12#22583584C2211yescharacteristic
13#22583580—21no—
14(C22⋊D283)⋊C4—21no—
15C2×Dic283⋊C4—21no—
16C2×(C2×D283)⋊C4—21no—
17C2×(C2×D283)⋊C4C2211yescharacteristic
18#22583541—21no—
19#22583530—21no—
20C22⋊(C283⋊C8)C2211yescharacteristic
21C283⋊#95C2211yescharacteristic
22C22⋊Q8×C283C2211yescharacteristic
23C2×C4⋊C4×C283C2211yescharacteristic
24#107×C283—21no—
25#103×C283—21no—
26C22⋊C8×C283C2211yescharacteristic
27C23×D283D411yescharacteristic
28C2×D1132—21no—
29C2×D1132—21no—
30C2×D1132D411yescharacteristic
31C2×C22⋊D283—21no—
32C22×Dic283—21no—
33C22×Dic283D411yescharacteristic
34C2×C4×D283—21no—
35C2×C283⋊C8—21no—
36C4⋊Dic283D411yescharacteristic
37Dic283⋊C4—21no—
38Dic283⋊C4—42no—
39(C2×D283)⋊C4—21no—
40(C2×D283)⋊C4—21no—
41(C2×D283)⋊C4—21no—
42(C2×D283)⋊C4—21no—
43(C2×D283)⋊C4—21no—
44(C2×D283)⋊C4—21no—
45(C2×D283)⋊C4—42no—
46C4×Dic283—21no—
47C2×Q8×C283D411yescharacteristic
48C22×C4×C283—21no—
49C22×C4×C283C2311yescharacteristic
50C2×C8×C283—21no—
51C4⋊C4×C283—21no—
52C4⋊C4×C283—21no—
53C4⋊C4×C283—21no—
54C4⋊C4×C283D411yescharacteristic
55C22⋊C4×C283—21no—
56C22×D283—21no—
57C22×D283—21no—
58C22×D283—21no—
59C22×D283—21no—
60C22×D283—41no—
61C22×D283—41no—
62D1132—41no—
63D1132—81no—
64D1132—81no—
65C22⋊D283—41no—
66C22⋊D283—41no—
67C2×Dic283—22no—
68C2×Dic283—21no—
69C2×Dic283—21no—
70C2×Dic283—41no—
71C2×Dic283—41no—
72C2×Dic283—41no—
73C4×D283—81no—
74C283⋊C8—41no—
75C23×C283C2×D411yescharacteristic
76Q8×C283—41no—
77C2×C4×C283—21no—
78C2×C4×C283—21no—
79C2×C4×C283—41no—
80C2×C4×C283—41no—
81C2×C4×C283—41no—
82C2×C4×C283—41no—
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2×D411yescharacteristic
85C8×C283—41no—
86C22×C283—21no—
87C22×C283—21no—
88C22×C283#12011yescharacteristic
89C22×C283#13511yescharacteristic
90C22×C283#13711yescharacteristic
91C2×D283—42no—
92C2×D283—41no—
93C2×D283—41no—
94C2×D283—41no—
95C2×D283—41no—
96C2×D283—41no—
97C2×D283—41no—
98C2×D283—81no—
99C4×C283—21no—
100C4×C283—21no—
101C4×C283—41no—
102C4×C283—41no—
103C4×C283—81no—
104Dic283—42no—
105Dic283—41no—
106Dic283—41no—
107C2×C283—21no—
108C2×C283—21no—
109C2×C283#45211yescharacteristic
110C2×C283#45311yescharacteristic
111C2×C283#45811yescharacteristic
112D283—81no—
113D283—81no—
114C283#161811yescharacteristic, complemented, Sylow
115#1618—2831nomaximal, Sylow
116#538—2831no—
117#484D28311yescharacteristic, complemented
118#481—2831no—
119#399—2831no—
120#328—2831no—
121#327—2831no—
122#323—2831no—
123#126—5661no—
124#124—5661no—
125#123—5661no—
126C22⋊Q8C2×D28311yescharacteristic
127#121—2831no—
128#121—5661no—
129#120—5661no—
130C4×D4—5661no—
131C2×C4⋊C4—5661no—
132C2×C4⋊C4C2×D28311yescharacteristic
133C2×C22⋊C4—2831no—
134C2×C22⋊C4—5661no—
135#107—21no—
136#106—5661no—
137#103—21no—
138#102—5661no—
139C22⋊C8—2831no—
140C22⋊C8C2×D28311yescharacteristic
141#95—2831no—
142C24—2831no—
143C2×Q8C22⋊D28311yescharacteristic
144C2×D4—2831no—
145C2×D4—5661no—
146C2×D4—5661no—
147C2×D4—5661no—
148C22×C4—21no—
149C22×C4—2831no—
150C22×C4—5661no—
151C22×C4—5661no—
152C22×C4C22×D28311yescharacteristic
153C2×C8—21no—
154C2×C8—5661no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—2831no—
159C4⋊C4—5661no—
160C4⋊C4—11322no—
161C4⋊C4C22⋊D28311yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—5661no—
164C22⋊C4—5661no—
165C22⋊C4—5661no—
166C22⋊C4—5661no—
167C22⋊C4—5661no—
168C22⋊C4—5661no—
169C22⋊C4—11322no—
170C42—5661no—
171C23—5661no—
172C23—5661no—
173C23—5661no—
174C23—5661no—
175C23—11321no—
176C23—11321no—
177C23D4×D28311yescharacteristic
178Q8—41no—
179D4—11321no—
180D4—11321no—
181D4—11321no—
182D4—22641no—
183D4—22641no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—5662no—
191C2×C4—5661no—
192C2×C4—5661no—
193C2×C4—11321no—
194C2×C4—11321no—
195C2×C4—11321no—
196C2×C4—22641no—
197C2×C4D4×D28311yescharacteristic
198C2×C4C2×C22⋊D28311yescharacteristic
199C8—41no—
200C8—11321no—
201C22—21no—
202C22—21no—
203C22—11322no—
204C22—11321no—
205C22—11321no—
206C22—11321no—
207C22—11321no—
208C22—11321no—
209C22—11321no—
210C22—22641no—
211C22#2258357811yescharacteristic
212C22#2258363311yescharacteristic
213C22#2258364211yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—11322no—
220C4—11321no—
221C4—11321no—
222C2—21no—
223C2—21no—
224C2—22641no—
225C2—22641no—
226C2#3182662611yescharacteristic
227C2#3182663111yescharacteristic
228C2#3182665411yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#484×C283C2
socleC22×C283#120
prime radical#31827055C2
hypercenter#484D283
hypocenterC283#1618
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #31826783C2semidirect
3. #31826400C2semidirect
4. #31826202C2semidirect
5. #31826200C2semidirect
6. #31826188C2semidirect
7. #484×C283C2semidirect
114. C283#1618semidirect
117. #484D283semidirect

Maximal subgroups

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

subgroupindex
#318270552
#318267832
#318264002
#318262022
#318262002
#318261882
#484×C2832
#1618283