Finite Group Databasebeta

← #29594260

Subgroups — #29594260

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#21447897C211yesmaximal, characteristic, complemented
2#21447892C211yesmaximal, characteristic
3#21447657C211yesmaximal, characteristic, complemented
4#21443895C211yesmaximal, characteristic, complemented
5#21443858C211yesmaximal, characteristic, complemented
6#21443856C211yesmaximal, characteristic, complemented
7C61×#2248C211yesmaximal, characteristic, complemented
8#16840203—21no—
9#16840198—21no—
10#16840178—21no—
11#16839880C2211yescharacteristic
12#16839583C2211yescharacteristic
13#16839583C2211yescharacteristic
14#16839583C2211yescharacteristic
15#16839578—21no—
16#16839575—21no—
17#16839545—21no—
18C2×SD32×C61—21no—
19C2×SD32×C61—21no—
20C61×#494C2211yescharacteristic
21C61×#493C2211yescharacteristic
22C4×C16×C61C2211yescharacteristic
23#14519799D411yescharacteristic
24#14519783—21no—
25#14519723—41no—
26#14519721—41no—
27#14519720—41no—
28#14519718—41no—
29#14519717—21no—
30#14519717—21no—
31#14519717—21no—
32#14519716—41no—
33C16×D61—41no—
34#14519713D411yescharacteristic
35#14519705—21no—
36C2×Q16×C61—21no—
37C2×Q16×C61—21no—
38C2×D8×C61—21no—
39C2×D8×C61—21no—
40C4⋊Q8×C61—21no—
41#127×C61—21no—
42SD32×C61—42no—
43SD32×C61—41no—
44SD32×C61—41no—
45C2×C16×C61D411yescharacteristic
46C2×C16×C61D411yescharacteristic
47C4×C8×C61C2311yescharacteristic
48C2×Q8×C61—41no—
49C2×D4×C61—41no—
50C2×D4×C61—81no—
51#11758222—21no—
52Q16×C61—41no—
53Q16×C61—41no—
54Q16×C61—41no—
55Q16×C61—41no—
56D8×C61—41no—
57D8×C61—41no—
58D8×C61—41no—
59D8×C61—41no—
60C2×C8×C61C2×D411yescharacteristic
61C2×C8×C61C2×D411yescharacteristic
62C4⋊C4×C61—81no—
63C42×C61#4111yescharacteristic
64#11758194—21no—
65Dic244D811yescharacteristic
66D488D811yescharacteristic
67#11758190—21no—
68#11758189—41no—
69C8×D61—41no—
70C16×C61—21no—
71C16×C61D811yescharacteristic
72C16×C61D811yescharacteristic
73#11758185—41no—
74#11758185—41no—
75#11758185—41no—
76C23×C61—81no—
77Q8×C61—81no—
78Q8×C61—81no—
79D4×C61—81no—
80D4×C61—81no—
81D4×C61—162no—
82C2×C4×C61—21no—
83C2×C4×C61—81no—
84C2×C4×C61#12111yescharacteristic
85C22⋊D61—41no—
86D244—21no—
87C4×D61—41no—
88Dic122—21no—
89C8×C61C2×D811yescharacteristic
90C8×C61C2×D811yescharacteristic
91C8×C61#13511yescharacteristic
92C8×C61AGL(1,ℤ/8)11yescharacteristic
93#92418—41no—
94#12438—611nomaximal, Sylow
95C22×C61—162no—
96C22×C61—161no—
97C22×C61#47211yescharacteristic
98C2×D61—41no—
99C4×C61—22no—
100C4×C61—161no—
101C4×C61#45911yescharacteristic
102C4×C61#46611yescharacteristic
103Dic61—41no—
104#2248D6111yescharacteristic, complemented
105#2214—611no—
106#2213—611no—
107#2170—611no—
108#1373—611no—
109#1358—611no—
110#1357—611no—
111C2×C61—21no—
112C2×C61—321no—
113C2×C61#166711yescharacteristic
114D61—81no—
115#510—1221no—
116#509—1221no—
117C2×SD32—21no—
118C2×SD32—21no—
119#504—1221no—
120#494C2×D6111yescharacteristic
121#493C2×D6111yescharacteristic
122#443—611no—
123#364—611no—
124#364—611no—
125#364—611no—
126#362—1221no—
127#361—1221no—
128#350—1221no—
129C4×C16C2×D6111yescharacteristic
130C61#1243811yescharacteristic, complemented, Sylow
131#135—611no—
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—21no—
135C2×D8—21no—
136#131—1221no—
137C4⋊Q8—21no—
138#127—21no—
139Q32—2441no—
140SD32—42no—
141SD32—41no—
142SD32—41no—
143SD32—2441no—
144SD32—2441no—
145D16—2441no—
146M32—1221no—
147M32—1221no—
148M32—1221no—
149M32—2441no—
150C2×C16—2441no—
151C2×C16C22⋊D6111yescharacteristic
152C2×C16C22⋊D6111yescharacteristic
153#108—611no—
154#104—1221no—
155C4×C8C22×D6111yescharacteristic
156#41—1221no—
157C2×Q8—41no—
158C2×D4—41no—
159C2×D4—81no—
160Q16—41no—
161Q16—41no—
162Q16—41no—
163Q16—41no—
164Q16—611no—
165SD16—1221no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8—611no—
171M16—1221no—
172M16—2441no—
173C2×C8—2441no—
174C2×C8D4×D6111yescharacteristic
175C2×C8C2×C22⋊D6111yescharacteristic
176C4⋊C4—81no—
177C42#1175822411yescharacteristic
178C16—21no—
179C16—2441no—
180C16—2441no—
181C16—2441no—
182C16#1175819911yescharacteristic
183C16#1175819911yescharacteristic
184C23—81no—
185Q8—81no—
186Q8—81no—
187Q8—1221no—
188D4—81no—
189D4—81no—
190D4—162no—
191D4—1221no—
192D4—2441no—
193C2×C4—21no—
194C2×C4—81no—
195C2×C4—2441no—
196C2×C4#1451974811yescharacteristic
197C8—2441no—
198C8D8×D6111yescharacteristic
199C8C2×#1175819911yescharacteristic
200C8#1451979611yescharacteristic
201C8#1451980311yescharacteristic
202C22—162no—
203C22—161no—
204C22—2441no—
205C22#1684002911yescharacteristic
206C4—22no—
207C4—161no—
208C4—2441no—
209C4#1683995411yescharacteristic
210C4#1683999511yescharacteristic
211C2—21no—
212C2—321no—
213C2—4881no—
214C2#2144517111yescharacteristic
subgroupG/H
centerC2#21445171
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2248C2
socleC2×C61#1667
prime radical#21447892C2
hypercenter#2248D61
hypocenterC61#12438
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #21447897C2semidirect
3. #21447657C2semidirect
4. #21443895C2semidirect
5. #21443858C2semidirect
6. #21443856C2semidirect
7. C61×#2248C2semidirect
104. #2248D61semidirect
130. C61#12438semidirect

Maximal subgroups

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

subgroupindex
#214478972
#214478922
#214476572
#214438952
#214438582
#214438562
C61×#22482
#1243861