Finite Group Databasebeta

← #30606042

Subgroups — #30606042

Order 15616.

234 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 60 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#21461468C211yesmaximal, characteristic, complemented
2#21461417C211yesmaximal, characteristic, complemented
3#21460845C211yesmaximal, characteristic, complemented
4#21460778C211yesmaximal, characteristic, complemented
5#21460778C211yesmaximal, characteristic, complemented
6#21460738C211yesmaximal, characteristic, complemented
7#21447694C211yesmaximal, characteristic
8#16840796—21no—
9#16840790—21no—
10#16840651C2211yescharacteristic
11#16840623C2211yescharacteristic
12#16840623C2211yescharacteristic
13#16840610—21no—
14#16840610—21no—
15#16840603C2211yescharacteristic
16C2×D976C411yescharacteristic
17#16839844C2211yescharacteristic
18#16839844C2211yescharacteristic
19#16839562C411yescharacteristic
20#16839562C411yescharacteristic
21#16839537C2211yescharacteristic
22C61×#367C411yescharacteristic
23C2×#11758213—41no—
24C2×D61⋊C8—41no—
25C2×#11758187—21no—
26C4⋊#92420—21no—
27C4⋊#92420—21no—
28#14519834—41no—
29#14519834—41no—
30C4×#92420D411yescharacteristic
31C4×#92420D411yescharacteristic
32C2×D488C2×C411yescharacteristic
33C2×D488C2×C411yescharacteristic
34#14519739—21no—
35#14519739—21no—
36D976—22no—
37C2×#11758185C2×C411yescharacteristic
38#14519697—21no—
39#14519697—21no—
40C8×Dic61C2311yescharacteristic
41C2×C16×C61C2×C411yescharacteristic
42#107×C61C2×C411yescharacteristic
43#107×C61C2×C411yescharacteristic
44C2×D244—21no—
45C2×D244—21no—
46C2×C4×D61—41no—
47C2×C4×D61—41no—
48C2×#92420—21no—
49C2×#92420—21no—
50C2×#92420—41no—
51C2×#92420—41no—
52#11758213—82no—
53D61⋊C8—82no—
54C2×C8×C61C22×C411yescharacteristic
55C4⋊C4×C61—21no—
56C4⋊C4×C61—21no—
57#11758198—41no—
58#11758198—41no—
59C4×Dic61C2×D411yescharacteristic
60C2×#92418#4111yescharacteristic
61D488—21no—
62D488—21no—
63D488—21no—
64D488M1612yescomplemented
65#11758187—22no—
66C16×C61—21no—
67#11758185—21no—
68C22×D61—41no—
69C22×D61—41no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61C4×D411yescharacteristic
73C2×Dic61AGL(1,ℤ/8)11yescharacteristic
74C2×Dic61AGL(1,ℤ/8)11yescharacteristic
75D244—22no—
76D244—41no—
77D244—41no—
78D244—41no—
79C4×D61—81no—
80C4×D61—81no—
81C4×D61—81no—
82C4×D61—81no—
83#92420—41no—
84#92420—41no—
85#92420—81no—
86#92420—81no—
87C8×C61C2×M1611yescharacteristic
88C8×C61#13111yescharacteristic
89#92418—21no—
90#12078—611nomaximal, Sylow
91C22×C61#44211yescharacteristic
92C2×D61—42no—
93C2×D61—81no—
94C2×D61—81no—
95C2×D61—81no—
96C2×D61—81no—
97C2×D61—81no—
98C4×C61—81no—
99C4×C61—81no—
100C4×C61#43511yescharacteristic
101C4×C61#44311yescharacteristic
102Dic61—21no—
103Dic61—21no—
104#2177—611no—
105#1594—611no—
106#1580—611no—
107#1368—611no—
108#1333—611no—
109#1333—611no—
110#1313—611no—
111C2×C61#158611yescharacteristic
112C2×C61AGL(1,ℤ/16)11yescharacteristic
113C2×C61AGL(1,ℤ/16)11yescharacteristic
114D61—82no—
115D61—161no—
116C2×D16—611no—
117C4×D8—611no—
118C4×D8—611no—
119#436—1221no—
120C8×D4—1221no—
121#367#692311yescharacteristic
122#357—611no—
123#357—611no—
124#346—611no—
125#346—611no—
126#334—611no—
127#334—611no—
128D4⋊C8—1221no—
129D4⋊C8—1221no—
130#322—611no—
131C61#1207811yescharacteristic, complemented, Sylow
132C2×D8—611no—
133C2×D8—611no—
134C2×M16—2441no—
135C22×C8—2441no—
136C4×D4—1221no—
137C4×D4—1221no—
138D16—1222no—
139C2×C16—611no—
140C2×C16—1221no—
141C2×C16C2×#692311yescharacteristic
142#107C2×#692311yescharacteristic
143#107C2×#692311yescharacteristic
144C4⋊C8—1221no—
145C4⋊C8—1221no—
146#102—1221no—
147#102—1221no—
148C22⋊C8—2441no—
149C22⋊C8—2441no—
150C4×C8—611no—
151C4×C8—611no—
152C4×C8—611no—
153C2×D4—1221no—
154C2×D4—1221no—
155C22×C4—2441no—
156C22×C4—2441no—
157D8—612no—
158D8—1221no—
159D8—1221no—
160D8—1221no—
161M16—4882no—
162C2×C8—611no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8—4882no—
166C2×C8—2441no—
167C2×C8—2441no—
168C2×C8C22×#692311yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—21no—
171C22⋊C4—2441no—
172C22⋊C4—2441no—
173C42—611no—
174C16—21no—
175C16—1222no—
176C16—1221no—
177C23—2441no—
178C23—2441no—
179D4—1222no—
180D4—2441no—
181D4—2441no—
182D4—2441no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—611no—
186C2×C4—611no—
187C2×C4—4881no—
188C2×C4—4881no—
189C2×C4—4881no—
190C2×C4—4881no—
191C2×C4D4×#692311yescharacteristic
192C8—1221no—
193C8—4881no—
194C8—4881no—
195C8—2441no—
196C8—2441no—
197C8D61⋊M1611yescharacteristic
198C8#1451986511yescharacteristic
199C22—4881no—
200C22—4881no—
201C22—4881no—
202C22—4881no—
203C22—4881no—
204C22—2442no—
205C22#1684080311yescharacteristic
206C4—81no—
207C4—81no—
208C4—1221no—
209C4—1221no—
210C4#1684079211yescharacteristic
211C4#1684080611yescharacteristic
212C2—9761no—
213C2—4882no—
214C2#2146143911yescharacteristic
215C2#2146223011yescharacteristic
216C2#2146223111yescharacteristic
subgroupG/H
centerC22#16840803
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#367C4
socleC22×C61#442
prime radicalC2×D976C4
cosocleC8×Dic61C23
hypercenter#367#6923
hypocenterC61#12078
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
1. #21461468C2semidirect
2. #21461417C2semidirect
3. #21460845C2semidirect
4. #21460778C2semidirect
5. #21460778C2semidirect
6. #21460738C2semidirect
64. D488M16semidirect
131. C61#12078semidirect

Maximal subgroups

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

subgroupindex
#214614682
#214614172
#214608452
#214607782
#214607382
#214476942
#1207861