Finite Group Databasebeta

← #29594264

Subgroups — #29594264

Order 15616.

224 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 59 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#21448075C211yesmaximal, characteristic, complemented
2#21447901C211yesmaximal, characteristic, complemented
3#21447896C211yesmaximal, characteristic
4#21447657C211yesmaximal, characteristic, complemented
5#21443857C211yesmaximal, characteristic, complemented
6#21443855C211yesmaximal, characteristic, complemented
7C61×#1373C211yesmaximal, characteristic, complemented
8#16840205—21no—
9#16840200—21no—
10C2×#14519722—21no—
11C2×#14519722—21no—
12#16840178—21no—
13#16840142C2211yescharacteristic
14#16840139C2211yescharacteristic
15#16839880C2211yescharacteristic
16#16839583C2211yescharacteristic
17#16839579—21no—
18#16839576—21no—
19#16839545—21no—
20C61×#364C2211yescharacteristic
21C61×#364C2211yescharacteristic
22C4×C16×C61C2211yescharacteristic
23#14519799D411yescharacteristic
24C2×Dic244—21no—
25C2×Dic244—21no—
26C2×D488—21no—
27C2×D488—21no—
28#14519783—21no—
29#14519777—21no—
30#14519774—21no—
31Dic488—41no—
32#14519722—42no—
33#14519722—41no—
34#14519722—41no—
35#14519722—41no—
36#14519722—41no—
37D976—41no—
38#14519717—21no—
39#14519716—41no—
40C16×D61—41no—
41#14519713D411yescharacteristic
42#14519705—21no—
43M32×C61—21no—
44M32×C61—21no—
45C2×C16×C61D411yescharacteristic
46C2×C16×C61D411yescharacteristic
47C4×C8×C61C2311yescharacteristic
48#11758222—21no—
49C2×D244—41no—
50C2×D244—81no—
51C2×Dic122—41no—
52C2×C8×C61C2×D411yescharacteristic
53C2×C8×C61C2×D411yescharacteristic
54C42×C61#4111yescharacteristic
55C4⋊Dic61—81no—
56#11758194—21no—
57Dic244—41no—
58Dic244—41no—
59Dic244—41no—
60Dic244—41no—
61Dic244D811yescharacteristic
62D488—41no—
63D488—41no—
64D488—41no—
65D488—41no—
66D488D811yescharacteristic
67#11758190—21no—
68#11758189—41no—
69C8×D61—41no—
70C16×C61—21no—
71C16×C61—41no—
72C16×C61—41no—
73C16×C61D811yescharacteristic
74C16×C61D811yescharacteristic
75#11758185—41no—
76C22×D61—81no—
77C2×C4×C61—21no—
78C2×C4×C61#12111yescharacteristic
79C22⋊D61—41no—
80C2×Dic61—81no—
81D244—21no—
82D244—81no—
83D244—81no—
84D244—162no—
85C4×D61—41no—
86Dic122—21no—
87Dic122—81no—
88Dic122—81no—
89C8×C61C2×D811yescharacteristic
90C8×C61C2×D811yescharacteristic
91C8×C61#13511yescharacteristic
92C8×C61AGL(1,ℤ/8)11yescharacteristic
93#92418—41no—
94#12438—611nomaximal, Sylow
95C22×C61#47211yescharacteristic
96C2×D61—41no—
97C2×D61—162no—
98C2×D61—161no—
99C4×C61—22no—
100C4×C61#45911yescharacteristic
101C4×C61#46611yescharacteristic
102Dic61—41no—
103Dic61—161no—
104#2248—611no—
105#2214—611no—
106#2213—611no—
107#2170—611no—
108#1373D6111yescharacteristic, complemented
109#1358—611no—
110#1357—611no—
111C2×C61—21no—
112C2×C61#166711yescharacteristic
113D61—81no—
114D61—321no—
115#510—1221no—
116#509—1221no—
117C2×SD32—1221no—
118C2×SD32—1221no—
119#504—1221no—
120#494—611no—
121#493—611no—
122#443—611no—
123#364—611no—
124#364C2×D6111yescharacteristic
125#364C2×D6111yescharacteristic
126#362—1221no—
127#361—1221no—
128#350—1221no—
129C4×C16C2×D6111yescharacteristic
130C61#1243811yescharacteristic, complemented, Sylow
131#135—611no—
132C2×Q16—1221no—
133C2×Q16—1221no—
134C2×D8—1221no—
135C2×D8—1221no—
136#131—1221no—
137C4⋊Q8—1221no—
138#127—1221no—
139Q32—2441no—
140SD32—2442no—
141SD32—2441no—
142SD32—2441no—
143SD32—2441no—
144SD32—2441no—
145D16—2441no—
146M32—21no—
147M32—21no—
148M32—1221no—
149M32—2441no—
150C2×C16—2441no—
151C2×C16D24411yescharacteristic
152C2×C16D24411yescharacteristic
153#108—611no—
154#104—1221no—
155C4×C8C22×D6111yescharacteristic
156#41—1221no—
157C2×Q8—2441no—
158C2×D4—4881no—
159C2×D4—2441no—
160Q16—611no—
161Q16—2441no—
162Q16—2441no—
163Q16—2441no—
164Q16—2441no—
165SD16—1221no—
166D8—611no—
167D8—2441no—
168D8—2441no—
169D8—2441no—
170D8—2441no—
171M16—1221no—
172M16—2441no—
173C2×C8—2441no—
174C2×C8C2×D24411yescharacteristic
175C2×C8D4×D6111yescharacteristic
176C4⋊C4—4881no—
177C42#1175822611yescharacteristic
178C16—21no—
179C16—41no—
180C16—41no—
181C16—2441no—
182C16D48811yescharacteristic
183C16D48811yescharacteristic
184C23—4881no—
185Q8—1221no—
186Q8—4881no—
187Q8—4881no—
188D4—1221no—
189D4—9762no—
190D4—4881no—
191D4—4881no—
192D4—2441no—
193C2×C4—21no—
194C2×C4—4881no—
195C2×C4—2441no—
196C2×C4#1451975211yescharacteristic
197C8—2441no—
198C8D8×D6111yescharacteristic
199C8C2×D48811yescharacteristic
200C8#1451980011yescharacteristic
201C8#1451980511yescharacteristic
202C22—9762no—
203C22—9761no—
204C22—2441no—
205C22#1684003311yescharacteristic
206C4—22no—
207C4—9761no—
208C4—2441no—
209C4#1683995811yescharacteristic
210C4#1683999911yescharacteristic
211C2—21no—
212C2—19521no—
213C2—4881no—
214C2#2144517511yescharacteristic
subgroupG/H
centerC2#21445175
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1373C2
socleC2×C61#1667
prime radical#21447896C2
hypercenter#1373D61
hypocenterC61#12438
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1373

Complements

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

NH ≅ G/Ntype
1. #21448075C2semidirect
2. #21447901C2semidirect
4. #21447657C2semidirect
5. #21443857C2semidirect
6. #21443855C2semidirect
7. C61×#1373C2semidirect
108. #1373D61semidirect
130. C61#12438semidirect

Maximal subgroups

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

subgroupindex
#214480752
#214479012
#214478962
#214476572
#214438572
#214438552
C61×#13732
#1243861