Finite Group Databasebeta

← #29594263

Subgroups — #29594263

Order 15616.

224 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 63 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#21447900C211yesmaximal, characteristic, complemented
3#21447895C211yesmaximal, characteristic
4#21443895C211yesmaximal, characteristic, complemented
5#21443857C211yesmaximal, characteristic, complemented
6#21443855C211yesmaximal, characteristic, complemented
7C61×#2170C211yesmaximal, characteristic, complemented
8#16840202—21no—
9#16840197—21no—
10C2×#14519722—21no—
11C2×#14519722—21no—
12#16840142C2211yescharacteristic
13#16840139C2211yescharacteristic
14#16839583C2211yescharacteristic
15#16839583C2211yescharacteristic
16#16839577—21no—
17#16839574—21no—
18C61×#504—21no—
19C61×#443C2211yescharacteristic
20C61×#364C2211yescharacteristic
21C61×#350—21no—
22C4×C16×C61C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×D488—21no—
26C2×D488—21no—
27#14519777—21no—
28#14519774—21no—
29#14519723—41no—
30#14519722—42no—
31#14519722—41no—
32#14519722—41no—
33#14519721—41no—
34#14519720—41no—
35#14519718—41no—
36#14519717—21no—
37#14519717—21no—
38#135×C61D411yescharacteristic
39#131×C61—21no—
40M32×C61—21no—
41M32×C61—41no—
42C2×C16×C61—41no—
43C2×C16×C61D411yescharacteristic
44C2×C16×C61D411yescharacteristic
45#108×C61D411yescharacteristic
46#104×C61—21no—
47C4×C8×C61C2311yescharacteristic
48#41×C61—21no—
49C2×D244—41no—
50C2×D244—81no—
51C2×Dic122—41no—
52Q16×C61D811yescharacteristic
53SD16×C61—21no—
54D8×C61D811yescharacteristic
55M16×C61—21no—
56M16×C61—41no—
57C2×C8×C61—41no—
58C2×C8×C61C2×D411yescharacteristic
59C2×C8×C61C2×D411yescharacteristic
60C42×C61#4111yescharacteristic
61C4⋊Dic61—81no—
62Dic244—41no—
63Dic244—41no—
64Dic244—41no—
65Dic244—41no—
66D488—41no—
67D488—41no—
68D488—41no—
69D488—41no—
70C16×C61—21no—
71C16×C61—41no—
72C16×C61D811yescharacteristic
73C16×C61D811yescharacteristic
74#11758185—41no—
75#11758185—41no—
76C22×D61—81no—
77Q8×C61—21no—
78D4×C61—21no—
79D4×C61—41no—
80C2×C4×C61—21no—
81C2×C4×C61—41no—
82C2×C4×C61#12111yescharacteristic
83C2×Dic61—81no—
84D244—81no—
85D244—81no—
86D244—162no—
87Dic122—81no—
88Dic122—81no—
89C8×C61—41no—
90C8×C61C2×D811yescharacteristic
91C8×C61C2×D811yescharacteristic
92C8×C61#13511yescharacteristic
93C8×C61AGL(1,ℤ/8)11yescharacteristic
94#12438—611nomaximal, Sylow
95C22×C61—41no—
96C22×C61#47211yescharacteristic
97C2×D61—162no—
98C2×D61—161no—
99C4×C61—22no—
100C4×C61—41no—
101C4×C61#45911yescharacteristic
102C4×C61#46611yescharacteristic
103Dic61—161no—
104#2248—611no—
105#2214—611no—
106#2213—611no—
107#2170D6111yescharacteristic, complemented
108#1373—611no—
109#1358—611no—
110#1357—611no—
111C2×C61—21no—
112C2×C61—81no—
113C2×C61#166711yescharacteristic
114D61—321no—
115#510—1221no—
116#509—1221no—
117C2×SD32—1221no—
118C2×SD32—1221no—
119#504—21no—
120#494—611no—
121#493—611no—
122#443C2×D6111yescharacteristic
123#364—611no—
124#364—611no—
125#364C2×D6111yescharacteristic
126#362—1221no—
127#361—1221no—
128#350—21no—
129C4×C16C2×D6111yescharacteristic
130C61#1243811yescharacteristic, complemented, Sylow
131#135D24411yescharacteristic
132C2×Q16—1221no—
133C2×Q16—1221no—
134C2×D8—1221no—
135C2×D8—1221no—
136#131—21no—
137C4⋊Q8—1221no—
138#127—1221no—
139Q32—2441no—
140SD32—2442no—
141SD32—2441no—
142SD32—2441no—
143SD32—2441no—
144SD32—2441no—
145D16—2441no—
146M32—21no—
147M32—41no—
148M32—1221no—
149M32—1221no—
150C2×C16—41no—
151C2×C16C22⋊D6111yescharacteristic
152C2×C16C22⋊D6111yescharacteristic
153#108D24411yescharacteristic
154#104—21no—
155C4×C8C22×D6111yescharacteristic
156#41—21no—
157C2×Q8—2441no—
158C2×D4—4881no—
159C2×D4—2441no—
160Q16—2441no—
161Q16—2441no—
162Q16—2441no—
163Q16—2441no—
164Q16D48811yescharacteristic
165SD16—21no—
166D8—2441no—
167D8—2441no—
168D8—2441no—
169D8—2441no—
170D8D48811yescharacteristic
171M16—21no—
172M16—41no—
173C2×C8—41no—
174C2×C8C2×D24411yescharacteristic
175C2×C8C2×C22⋊D6111yescharacteristic
176C4⋊C4—4881no—
177C42#1175822211yescharacteristic
178C16—21no—
179C16—41no—
180C16—2441no—
181C16—2441no—
182C16#1175819911yescharacteristic
183C16#1175819911yescharacteristic
184C23—4881no—
185Q8—21no—
186Q8—4881no—
187Q8—4881no—
188D4—21no—
189D4—41no—
190D4—9762no—
191D4—4881no—
192D4—4881no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—4881no—
196C2×C4#1451975111yescharacteristic
197C8—41no—
198C8C2×#1175819911yescharacteristic
199C8C2×D48811yescharacteristic
200C8#1451979911yescharacteristic
201C8#1451980211yescharacteristic
202C22—41no—
203C22—9762no—
204C22—9761no—
205C22#1684003211yescharacteristic
206C4—22no—
207C4—41no—
208C4—9761no—
209C4#1683995711yescharacteristic
210C4#1683999811yescharacteristic
211C2—21no—
212C2—81no—
213C2—19521no—
214C2#2144517411yescharacteristic
subgroupG/H
centerC2#21445174
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2170C2
socleC2×C61#1667
prime radical#21447895C2
hypercenter#2170D61
hypocenterC61#12438
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2170

Complements

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

NH ≅ G/Ntype
1. #21448075C2semidirect
2. #21447900C2semidirect
4. #21443895C2semidirect
5. #21443857C2semidirect
6. #21443855C2semidirect
7. C61×#2170C2semidirect
107. #2170D61semidirect
130. C61#12438semidirect

Maximal subgroups

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

subgroupindex
#214480752
#214479002
#214478952
#214438952
#214438572
#214438552
C61×#21702
#1243861