Finite Group Databasebeta

← #44450855

Subgroups — #44450855

Order 29824.

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#28417022C211yesmaximal, characteristic
2#28416770C211yesmaximal, characteristic, complemented
3#28416370C211yesmaximal, characteristic, complemented
4#28416173C211yesmaximal, characteristic, complemented
5#28416169C211yesmaximal, characteristic, complemented
6#28416158C211yesmaximal, characteristic, complemented
7#481×C233C211yesmaximal, characteristic, complemented
8#21418530—21no—
9#21418521—21no—
10#21418519—21no—
11#21418514C2211yescharacteristic
12#21418507—21no—
13#21418503—21no—
14D4×Dic233—21no—
15C2×#16836573—21no—
16C2×#16836571—21no—
17C2×#16836571C2211yescharacteristic
18#21418468—21no—
19#21418458—21no—
20C22⋊#14272338C2211yescharacteristic
21#21418442C2211yescharacteristic
22#121×C233C2211yescharacteristic
23C2×C4⋊C4×C233C2211yescharacteristic
24#106×C233—21no—
25#102×C233—21no—
26C22⋊C8×C233C2211yescharacteristic
27C23×D233D411yescharacteristic
28C2×Dic466D411yescharacteristic
29C2×C22⋊D233—21no—
30C2×C22⋊D233—21no—
31C22×Dic233—21no—
32C22×Dic233—21no—
33C22×Dic233D411yescharacteristic
34C2×#14272338—21no—
35C4⋊Dic233—21no—
36C4⋊Dic233D411yescharacteristic
37#16836573—21no—
38#16836573—42no—
39C22⋊Dic233—21no—
40C22⋊Dic233—21no—
41#16836571—21no—
42#16836571—21no—
43#16836571—21no—
44#16836571—21no—
45#16836571—42no—
46C4×Dic233—21no—
47C2×D4×C233—21no—
48C2×D4×C233D411yescharacteristic
49C22×C4×C233—21no—
50C22×C4×C233C2311yescharacteristic
51C2×C8×C233—21no—
52C4⋊C4×C233—21no—
53C4⋊C4×C233—21no—
54C4⋊C4×C233D411yescharacteristic
55C22⋊C4×C233—21no—
56C22×D233—21no—
57C22×D233—21no—
58C22×D233—21no—
59C22×D233—41no—
60C22×D233—41no—
61Dic466—41no—
62C22⋊D233—81no—
63C22⋊D233—81no—
64C2×Dic233—22no—
65C2×Dic233—21no—
66C2×Dic233—21no—
67C2×Dic233—21no—
68C2×Dic233—41no—
69C2×Dic233—41no—
70C2×Dic233—41no—
71C2×Dic233—81no—
72#14272338—41no—
73C23×C233—21no—
74C23×C233C2×D411yescharacteristic
75D4×C233—41no—
76D4×C233—41no—
77D4×C233—41no—
78C2×C4×C233—21no—
79C2×C4×C233—41no—
80C2×C4×C233—41no—
81C2×C4×C233—41no—
82C2×C4×C233—41no—
83C2×C4×C233C2×D411yescharacteristic
84C2×C4×C233C2×D411yescharacteristic
85C8×C233—41no—
86C22×C233—21no—
87C22×C233—21no—
88C22×C233—41no—
89C22×C233—41no—
90C22×C233—41no—
91C22×C233#12011yescharacteristic
92C22×C233#13511yescharacteristic
93C22×C233#13711yescharacteristic
94C2×D233—42no—
95C2×D233—41no—
96C2×D233—41no—
97C2×D233—41no—
98C2×D233—81no—
99C4×C233—21no—
100C4×C233—21no—
101C4×C233—41no—
102C4×C233—81no—
103Dic233—42no—
104Dic233—41no—
105Dic233—41no—
106Dic233—41no—
107C2×C233—21no—
108C2×C233—21no—
109C2×C233—81no—
110C2×C233#45211yescharacteristic
111C2×C233#45311yescharacteristic
112C2×C233#45811yescharacteristic
113D233—81no—
114C233#161811yescharacteristic, complemented, Sylow
115#1618—2331nomaximal, Sylow
116#538—2331no—
117#484—2331no—
118#481D23311yescharacteristic, complemented
119#399—2331no—
120#328—2331no—
121#327—2331no—
122#323—2331no—
123#126—4661no—
124#124—4661no—
125#123—4661no—
126C22⋊Q8—2331no—
127#121—4661no—
128#121C2×D23311yescharacteristic
129#120—4661no—
130C4×D4—4661no—
131C2×C4⋊C4—4661no—
132C2×C4⋊C4C2×D23311yescharacteristic
133C2×C22⋊C4—4661no—
134C2×C22⋊C4—2331no—
135#107—4661no—
136#106—21no—
137#103—4661no—
138#102—21no—
139C22⋊C8—2331no—
140C22⋊C8C2×D23311yescharacteristic
141#95—2331no—
142C24—2331no—
143C2×Q8—2331no—
144C2×D4—21no—
145C2×D4—4661no—
146C2×D4—4661no—
147C2×D4C22⋊D23311yescharacteristic
148C22×C4—21no—
149C22×C4—4661no—
150C22×C4—4661no—
151C22×C4—2331no—
152C22×C4C22×D23311yescharacteristic
153C2×C8—21no—
154C2×C8—4661no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—9322no—
158C4⋊C4—4661no—
159C4⋊C4—4661no—
160C4⋊C4—2331no—
161C4⋊C4C22⋊D23311yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—9322no—
164C22⋊C4—4661no—
165C22⋊C4—4661no—
166C22⋊C4—4661no—
167C22⋊C4—4661no—
168C22⋊C4—4661no—
169C22⋊C4—4661no—
170C42—4661no—
171C23—21no—
172C23—9321no—
173C23—9321no—
174C23—4661no—
175C23—4661no—
176C23—4661no—
177C23D4×D23311yescharacteristic
178Q8—9321no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—18641no—
183D4—18641no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—18641no—
190C2×C4—9321no—
191C2×C4—9321no—
192C2×C4—9321no—
193C2×C4—4662no—
194C2×C4—4661no—
195C2×C4—4661no—
196C2×C4—4661no—
197C2×C4D4×D23311yescharacteristic
198C2×C4C2×C22⋊D23311yescharacteristic
199C8—41no—
200C8—9321no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—18641no—
207C22—9322no—
208C22—9321no—
209C22—9321no—
210C22—9321no—
211C22#2141850311yescharacteristic
212C22#2141855611yescharacteristic
213C22#2141856411yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—81no—
218C4—9322no—
219C4—9321no—
220C4—9321no—
221C4—9321no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—18641no—
226C2#2841659411yescharacteristic
227C2#2841660111yescharacteristic
228C2#2841662411yescharacteristic
subgroupG/H
centerC22#21418503
commutator, cosocleC22×C4×C233C23
FrattiniC22×C4C22×D233
Fitting#481×C233C2
socleC22×C233#120
prime radical#28417022C2
hypercenter#481D233
hypocenterC233#1618
LCSG ▷ C22×C4×C233 ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #28416770C2semidirect
3. #28416370C2semidirect
4. #28416173C2semidirect
5. #28416169C2semidirect
6. #28416158C2semidirect
7. #481×C233C2semidirect
114. C233#1618semidirect
118. #481D233semidirect

Maximal subgroups

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

subgroupindex
#284170222
#284167702
#284163702
#284161732
#284161692
#284161582
#481×C2332
#1618233