Finite Group Databasebeta

← #29591969

Subgroups — #29591969

Order 15616.

234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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#21447693C211yesmaximal, characteristic
2#21444644C211yesmaximal, characteristic, complemented
3#21443884C211yesmaximal, characteristic, complemented
4#21443786C211yesmaximal, characteristic, complemented
5#21443785C211yesmaximal, characteristic, complemented
6#21443740C211yesmaximal, characteristic, complemented
7C61×#1594C211yesmaximal, characteristic, complemented
8C2×#14519718C411yescharacteristic
9C4×D488C2211yescharacteristic
10C8×D244—21no—
11#16839589C411yescharacteristic
12#16839563C411yescharacteristic
13#16839562C411yescharacteristic
14#16839538C2211yescharacteristic
15#16839538C2211yescharacteristic
16#16839513C2211yescharacteristic
17#16839491—21no—
18C4×D8×C61C2211yescharacteristic
19C61×#436—21no—
20C61×#334C2211yescharacteristic
21C61×D4⋊C8—21no—
22C61×#322C2211yescharacteristic
23C2×D488C2×C411yescharacteristic
24C2×C8×D61—41no—
25C4×D244—21no—
26#14519718—22no—
27C2×#11758185—21no—
28C2×#11758185C2×C411yescharacteristic
29C2×#11758185C2×C411yescharacteristic
30#14519711C2×C411yescharacteristic
31C4⋊#92418—21no—
32#14519699—21no—
33#14519689—41no—
34C2×D8×C61C2×C411yescharacteristic
35C2×M16×C61—41no—
36C4×D4×C61—21no—
37#107×C61C2×C411yescharacteristic
38C4⋊C8×C61—21no—
39#102×C61—21no—
40C22⋊C8×C61—41no—
41C4×C8×C61D411yescharacteristic
42C4×C8×C61D411yescharacteristic
43C4×C8×C61C2311yescharacteristic
44C2×D4×C61—21no—
45C22×C4×C61—41no—
46C2×D244—21no—
47C2×C4×D61—41no—
48D8×C61—21no—
49D8×C61—21no—
50M16×C61—82no—
51C2×C8×C61—21no—
52C2×C8×C61—21no—
53C2×C8×C61—41no—
54C2×C8×C61C22×C411yescharacteristic
55C2×C8×C61#4111yescharacteristic
56C4⋊C4×C61—21no—
57C22⋊C4×C61—41no—
58C42×C61C2×D411yescharacteristic
59#11758198—41no—
60C4⋊Dic61—21no—
61C2×#92418—41no—
62D488—21no—
63D488M1612yescomplemented
64C8×D61—82no—
65#11758185—22no—
66#11758185—21no—
67#11758185—21no—
68C23×C61—41no—
69C22×D61—41no—
70D4×C61—41no—
71D4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61—81no—
74C2×C4×C61—81no—
75C2×C4×C61C4×D411yescharacteristic
76C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
77C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
78C2×Dic61—41no—
79D244—22no—
80D244—41no—
81C4×D61—81no—
82C4×D61—81no—
83C8×C61—21no—
84C8×C61—41no—
85C8×C61—41no—
86C8×C61—81no—
87C8×C61C2×M1611yescharacteristic
88C8×C61#13111yescharacteristic
89#92418—81no—
90#12078—611nomaximal, Sylow
91C22×C61—81no—
92C22×C61—81no—
93C22×C61—81no—
94C22×C61#44211yescharacteristic
95C2×D61—42no—
96C2×D61—81no—
97C2×D61—81no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—81no—
101C4×C61#43511yescharacteristic
102C4×C61#44311yescharacteristic
103Dic61—81no—
104#2177—611no—
105#1594D6111yescharacteristic, complemented
106#1580—611no—
107#1368—611no—
108#1333—611no—
109#1333—611no—
110#1313—611no—
111C2×C61—161no—
112C2×C61#158611yescharacteristic
113C2×C61AGL(1,ℤ/16)11yescharacteristic
114C2×C61AGL(1,ℤ/16)11yescharacteristic
115D61—82no—
116C2×D16—611no—
117C4×D8—611no—
118C4×D8C2×D6111yescharacteristic
119#436—21no—
120C8×D4—1221no—
121#367—611no—
122#357—611no—
123#357—611no—
124#346—611no—
125#346—611no—
126#334—611no—
127#334C2×D6111yescharacteristic
128D4⋊C8—21no—
129D4⋊C8—1221no—
130#322C2×D6111yescharacteristic
131C61#1207811yescharacteristic, complemented, Sylow
132C2×D8—611no—
133C2×D8C4×D6111yescharacteristic
134C2×M16—41no—
135C22×C8—2441no—
136C4×D4—21no—
137C4×D4—1221no—
138D16—1222no—
139C2×C16—611no—
140C2×C16—611no—
141C2×C16—1221no—
142#107—611no—
143#107C4×D6111yescharacteristic
144C4⋊C8—21no—
145C4⋊C8—1221no—
146#102—21no—
147#102—1221no—
148C22⋊C8—41no—
149C22⋊C8—2441no—
150C4×C8C22⋊D6111yescharacteristic
151C4×C8C22⋊D6111yescharacteristic
152C4×C8C22×D6111yescharacteristic
153C2×D4—21no—
154C2×D4—1221no—
155C22×C4—41no—
156C22×C4—2441no—
157D8—21no—
158D8—21no—
159D8—612no—
160D8—1221no—
161M16—82no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—41no—
165C2×C8—4882no—
166C2×C8—2441no—
167C2×C8C2×C4×D6111yescharacteristic
168C2×C8#1175822211yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—1221no—
171C22⋊C4—41no—
172C22⋊C4—2441no—
173C42C2×C22⋊D6111yescharacteristic
174C16—1222no—
175C16—1221no—
176C16—1221no—
177C23—41no—
178C23—2441no—
179D4—41no—
180D4—41no—
181D4—1222no—
182D4—2441no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4—4881no—
187C2×C4—4881no—
188C2×C4—2441no—
189C2×C4C4×C22⋊D6111yescharacteristic
190C2×C4#1451980211yescharacteristic
191C2×C4#1451980311yescharacteristic
192C8—21no—
193C8—41no—
194C8—41no—
195C8—81no—
196C8—4881no—
197C8M16×D6111yescharacteristic
198C8#1451978511yescharacteristic
199C22—81no—
200C22—81no—
201C22—81no—
202C22—4881no—
203C22—4881no—
204C22—2442no—
205C22#1683987211yescharacteristic
206C4—21no—
207C4—21no—
208C4—81no—
209C4—4881no—
210C4#1683983111yescharacteristic
211C4#1683987711yescharacteristic
212C2—161no—
213C2—4882no—
214C2#2144468111yescharacteristic
215C2#2144771511yescharacteristic
216C2#2144771711yescharacteristic
subgroupG/H
centerC22#16839872
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1594C2
socleC22×C61#442
prime radicalC2×#14519718C4
cosocleC4×C8×C61C23
hypercenter#1594D61
hypocenterC61#12078
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #1594

Complements

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

NH ≅ G/Ntype
2. #21444644C2semidirect
3. #21443884C2semidirect
4. #21443786C2semidirect
5. #21443785C2semidirect
6. #21443740C2semidirect
7. C61×#1594C2semidirect
63. D488M16semidirect
105. #1594D61semidirect
131. C61#12078semidirect

Maximal subgroups

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

subgroupindex
#214476932
#214446442
#214438842
#214437862
#214437852
#214437402
C61×#15942
#1207861