Finite Group Databasebeta

← #29591970

Subgroups — #29591970

Order 15616.

234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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#21447696C211yesmaximal, characteristic
2#21444732C211yesmaximal, characteristic, complemented
3#21444642C211yesmaximal, characteristic, complemented
4#21443785C211yesmaximal, characteristic, complemented
5#21443785C211yesmaximal, characteristic, complemented
6#21443741C211yesmaximal, characteristic, complemented
7C61×#1368C211yesmaximal, characteristic, complemented
8C2×D976C411yescharacteristic
9C4×D488C2211yescharacteristic
10C4×D488C2211yescharacteristic
11#16839839—21no—
12#16839827—21no—
13#16839590C411yescharacteristic
14#16839564C411yescharacteristic
15#16839564C411yescharacteristic
16#16839538C2211yescharacteristic
17#16839489—21no—
18#16839489—21no—
19#16839483C2211yescharacteristic
20C61×#346C2211yescharacteristic
21C61×#334C2211yescharacteristic
22C61×#334C2211yescharacteristic
23C2×D488C2×C411yescharacteristic
24C2×D488C2×C411yescharacteristic
25C2×#11758189—41no—
26C2×C8×D61—41no—
27C4×D244—21no—
28C4×D244—21no—
29D976—22no—
30C2×#11758185—21no—
31#14519711C2×C411yescharacteristic
32#14519711C2×C411yescharacteristic
33#14519699—21no—
34#14519699—21no—
35#14519689—41no—
36#14519689—41no—
37C4×#92418D411yescharacteristic
38C4×#92418D411yescharacteristic
39C2×C16×C61C2×C411yescharacteristic
40C2×C16×C61C2×C411yescharacteristic
41C4⋊C8×C61—21no—
42C4⋊C8×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×D244—21no—
45C2×D244—21no—
46C2×C4×D61—41no—
47C2×C4×D61—41no—
48C2×C8×C61—41no—
49C2×C8×C61—41no—
50C2×C8×C61C22×C411yescharacteristic
51C2×C8×C61#4111yescharacteristic
52C42×C61C2×D411yescharacteristic
53#11758198—41no—
54#11758198—41no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57C2×#92418—21no—
58C2×#92418—21no—
59D488—21no—
60D488—21no—
61D488—21no—
62D488M1612yescomplemented
63#11758189—82no—
64C8×D61—82no—
65C16×C61—21no—
66C16×C61—21no—
67#11758185—22no—
68C22×D61—41no—
69C22×D61—41no—
70C2×C4×C61C4×D411yescharacteristic
71C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
72C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
73C2×Dic61—41no—
74C2×Dic61—41no—
75D244—22no—
76D244—41no—
77D244—41no—
78D244—41no—
79C4×D61—81no—
80C4×D61—81no—
81C4×D61—81no—
82C4×D61—81no—
83C8×C61—21no—
84C8×C61—81no—
85C8×C61—81no—
86C8×C61C2×M1611yescharacteristic
87C8×C61#13111yescharacteristic
88#92418—41no—
89#92418—41no—
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—21no—
99C4×C61—21no—
100C4×C61#43511yescharacteristic
101C4×C61#44311yescharacteristic
102Dic61—81no—
103Dic61—81no—
104#2177—611no—
105#1594—611no—
106#1580—611no—
107#1368D6111yescharacteristic, complemented
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—611no—
122#357—611no—
123#357—611no—
124#346—611no—
125#346C2×D6111yescharacteristic
126#334C2×D6111yescharacteristic
127#334C2×D6111yescharacteristic
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—1221no—
140C2×C16C4×D6111yescharacteristic
141C2×C16C4×D6111yescharacteristic
142#107—611no—
143#107—611no—
144C4⋊C8—21no—
145C4⋊C8—21no—
146#102—1221no—
147#102—1221no—
148C22⋊C8—2441no—
149C22⋊C8—2441no—
150C4×C8—611no—
151C4×C8—611no—
152C4×C8C22×D6111yescharacteristic
153C2×D4—1221no—
154C2×D4—1221no—
155C22×C4—2441no—
156C22×C4—2441no—
157D8—612no—
158D8—1221no—
159D8—1221no—
160D8—1221no—
161M16—4882no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—1221no—
165C2×C8—1221no—
166C2×C8—4882no—
167C2×C8C2×C4×D6111yescharacteristic
168C2×C8#1175822611yescharacteristic
169C4⋊C4—1221no—
170C4⋊C4—1221no—
171C22⋊C4—2441no—
172C22⋊C4—2441no—
173C42D4×D6111yescharacteristic
174C16—21no—
175C16—21no—
176C16—1222no—
177C23—2441no—
178C23—2441no—
179D4—1222no—
180D4—2441no—
181D4—2441no—
182D4—2441no—
183C2×C4—4881no—
184C2×C4—4881no—
185C2×C4—4881no—
186C2×C4—4881no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4#1451973911yescharacteristic
190C2×C4#1451980411yescharacteristic
191C2×C4#1451980411yescharacteristic
192C8—21no—
193C8—81no—
194C8—81no—
195C8—2441no—
196C8—2441no—
197C8M16×D6111yescharacteristic
198C8#1451978311yescharacteristic
199C22—4881no—
200C22—4881no—
201C22—4881no—
202C22—4881no—
203C22—4881no—
204C22—2442no—
205C22#1683987311yescharacteristic
206C4—21no—
207C4—21no—
208C4—4881no—
209C4—4881no—
210C4#1683983211yescharacteristic
211C4#1683987811yescharacteristic
212C2—9761no—
213C2—4882no—
214C2#2144468211yescharacteristic
215C2#2144771611yescharacteristic
216C2#2144771611yescharacteristic
subgroupG/H
centerC22#16839873
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1368C2
socleC22×C61#442
prime radicalC2×D976C4
cosocleC4×C8×C61C23
hypercenter#1368D61
hypocenterC61#12078
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1368

Complements

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

NH ≅ G/Ntype
2. #21444732C2semidirect
3. #21444642C2semidirect
4. #21443785C2semidirect
5. #21443785C2semidirect
6. #21443741C2semidirect
7. C61×#1368C2semidirect
62. D488M16semidirect
107. #1368D61semidirect
131. C61#12078semidirect

Maximal subgroups

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

subgroupindex
#214476962
#214447322
#214446422
#214437852
#214437412
C61×#13682
#1207861