Finite Group Databasebeta

← #29594296

Subgroups — #29594296

Order 15616.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#21448074C211yesmaximal, characteristic
2#21447724C211yesmaximal, characteristic, complemented
3#21445190C211yesmaximal, characteristic, complemented
4#21445176C211yesmaximal, characteristic
5#21443890C211yesmaximal, characteristic, complemented
6#21443869C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic
8C2×#14519721—21no—
9C2×#14519721—21no—
10#16840142C2211yescharacteristic
11#16840048—21no—
12#16839959—21no—
13C8×Dic122C2211yescharacteristic
14#16839580—21no—
15#16839537—21no—
16C4×#11758185C2211yescharacteristic
17#16839515C2211yescharacteristic
18#16839507—21no—
19#16839506—21no—
20C61×#493C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×#11758200—41no—
26#14519777—21no—
27C4×Dic122D411yescharacteristic
28#14519721—42no—
29#14519721—42no—
30C2×#11758185D411yescharacteristic
31C2×#11758185D411yescharacteristic
32#14519709—41no—
33C4⋊#92418—21no—
34C4⋊#92418D411yescharacteristic
35#14519706—21no—
36#14519702—41no—
37#14519698—41no—
38C8×Dic61—21no—
39C2×D8×C61—21no—
40C2×D8×C61—21no—
41#127×C61—21no—
42C2×C16×C61—21no—
43C4⋊C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×D4×C61—41no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×Dic122—41no—
49C2×Dic122D811yescharacteristic
50D8×C61—41no—
51D8×C61—41no—
52D8×C61—81no—
53C2×C8×C61—41no—
54C2×C8×C61C2×D411yescharacteristic
55C2×C8×C61#4111yescharacteristic
56C42×C61C2×D411yescharacteristic
57#11758200—82no—
58C4⋊Dic61—41no—
59C4⋊Dic61—41no—
60C4⋊Dic61D811yescharacteristic
61#11758196—21no—
62C4×Dic61—21no—
63C2×#92418—21no—
64C2×#92418—41no—
65Dic244—41no—
66Dic244—41no—
67Dic244—81no—
68C16×C61—41no—
69#11758185—21no—
70#11758185SD1612yescomplemented
71C23×C61—81no—
72D4×C61—81no—
73D4×C61—81no—
74D4×C61—81no—
75D4×C61—81no—
76D4×C61—161no—
77C2×C4×C61#12111yescharacteristic
78C2×C4×C61C2×D811yescharacteristic
79C2×C4×C61#13511yescharacteristic
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—81no—
83Dic122—21no—
84Dic122—21no—
85Dic122—81no—
86Dic122—81no—
87C8×C61—21no—
88C8×C61—81no—
89C8×C61C2×SD1611yescharacteristic
90C8×C61AGL(1,ℤ/8)11yescharacteristic
91#92418—41no—
92#92418—81no—
93#12444—611nomaximal, Sylow
94C22×C61—161no—
95C22×C61—161no—
96C22×C61—161no—
97C22×C61#46611yescharacteristic
98C4×C61—21no—
99C4×C61#46011yescharacteristic
100C4×C61#47211yescharacteristic
101C4×C61#50911yescharacteristic
102C4×C61#51011yescharacteristic
103Dic61—41no—
104Dic61—41no—
105Dic61—161no—
106#2248—611no—
107#2183—611no—
108#1670—611no—
109#1668—611no—
110#1371—611no—
111#1362—611no—
112#1361D6111yescharacteristic
113C2×C61—321no—
114C2×C61#166811yescharacteristic
115C2×C61#222011yescharacteristic
116C2×C61#222311yescharacteristic
117C2×SD32—1221no—
118C2×SD32—1221no—
119#494—611no—
120#493C2×D6111yescharacteristic
121#475—1221no—
122#460—1221no—
123C8×Q8—611no—
124C4⋊C16—1221no—
125C4⋊C16C2×D6111yescharacteristic
126#346—1221no—
127C4×C16—611no—
128#335—611no—
129#335C2×D6111yescharacteristic
130#332—1221no—
131#331—1221no—
132C61#1244411yescharacteristic, complemented, Sylow
133C2×Q16—1221no—
134C2×Q16—1221no—
135C2×SD16—2441no—
136C2×D8—21no—
137C2×D8—21no—
138C4⋊Q8—1221no—
139#127—21no—
140C4×Q8—611no—
141SD32—2442no—
142SD32—2442no—
143C2×C16—21no—
144C2×C16—611no—
145C2×C16—611no—
146#106—2441no—
147C4⋊C8—21no—
148C4⋊C8—611no—
149C4⋊C8—1221no—
150C4⋊C8—1221no—
151#103—2441no—
152#102—2441no—
153C4×C8—1221no—
154C4×C8C22×D6111yescharacteristic
155C2×Q8—611no—
156C2×Q8—2441no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160Q16—4881no—
161Q16—2441no—
162Q16—2441no—
163SD16—4882no—
164D8—41no—
165D8—41no—
166D8—81no—
167C2×C8—41no—
168C2×C8—1221no—
169C2×C8—2441no—
170C2×C8#1175822211yescharacteristic
171C2×C8D4×D6111yescharacteristic
172C4⋊C4—611no—
173C4⋊C4—1221no—
174C4⋊C4—2441no—
175C4⋊C4—2441no—
176C42—1221no—
177C42D4×D6111yescharacteristic
178C16—41no—
179C16—612no—
180C16—1221no—
181C23—81no—
182Q8—1221no—
183Q8—1221no—
184Q8—4881no—
185Q8—4881no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—4881no—
194C2×C4#1451975011yescharacteristic
195C2×C4D8×D6111yescharacteristic
196C2×C4#1451979811yescharacteristic
197C8—21no—
198C8—81no—
199C8—4881no—
200C8—2441no—
201C8SD16×D6111yescharacteristic
202C8#1451980111yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1683999711yescharacteristic
207C4—21no—
208C4—9761no—
209C4—2441no—
210C4—2441no—
211C4#1683996111yescharacteristic
212C4#1684003111yescharacteristic
213C4#1684019611yescharacteristic
214C4#1684020111yescharacteristic
215C2—321no—
216C2#2144517811yescharacteristic
217C2#2144793111yescharacteristic
218C2#2144794811yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61#466
prime radicalC61×#493C22
hypercenter#1361D61
hypocenterC61#12444
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #21447724C2semidirect
3. #21445190C2semidirect
5. #21443890C2semidirect
6. #21443869C2semidirect
70. #11758185SD16semidirect
132. C61#12444semidirect

Maximal subgroups

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

subgroupindex
#214480742
#214477242
#214451902
#214451762
#214438902
#214438692
C61×#13612
#1244461