Finite Group Databasebeta

← #29594261

Subgroups — #29594261

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#21448074C211yesmaximal, characteristic, complemented
2#21447900C211yesmaximal, characteristic, complemented
3#21447656C211yesmaximal, characteristic, complemented
4#21443894C211yesmaximal, characteristic, complemented
5#21443857C211yesmaximal, characteristic, complemented
6#21443856C211yesmaximal, characteristic, complemented
7C61×#2213C211yesmaximal, characteristic
8#16840202—21no—
9C2×#14519721—21no—
10C2×#14519721—21no—
11#16840179—21no—
12#16840142C2211yescharacteristic
13#16839583C2211yescharacteristic
14#16839583C2211yescharacteristic
15#16839577—21no—
16#16839546—21no—
17C4×#11758185C2211yescharacteristic
18C61×#509—21no—
19C61×#493C2211yescharacteristic
20C61×#443C2211yescharacteristic
21C61×#364C2211yescharacteristic
22C61×#361—21no—
23C2×Dic244—21no—
24C2×Dic244—21no—
25#14519777—21no—
26#14519723—41no—
27#14519721—42no—
28#14519721—41no—
29#14519721—41no—
30#14519721—41no—
31#14519717—21no—
32#14519717—21no—
33#14519717—41no—
34C2×#11758185—41no—
35C2×#11758185D411yescharacteristic
36C2×#11758185D411yescharacteristic
37#135×C61D411yescharacteristic
38C2×D8×C61—21no—
39C2×D8×C61—21no—
40#131×C61—21no—
41#127×C61—21no—
42SD32×C61—41no—
43D16×C61—41no—
44M32×C61—21no—
45#108×C61D411yescharacteristic
46#104×C61—21no—
47C4×C8×C61C2311yescharacteristic
48#41×C61—21no—
49C2×D4×C61—41no—
50C2×D4×C61—81no—
51C2×Dic122—41no—
52Q16×C61D811yescharacteristic
53SD16×C61—21no—
54D8×C61—41no—
55D8×C61—41no—
56D8×C61—41no—
57D8×C61—41no—
58D8×C61D811yescharacteristic
59M16×C61—21no—
60M16×C61—41no—
61C2×C8×C61—41no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C42×C61#4111yescharacteristic
65C4⋊Dic61—81no—
66Dic244—41no—
67Dic244—41no—
68Dic244—41no—
69Dic244—41no—
70C16×C61—41no—
71#11758185—21no—
72#11758185—41no—
73#11758185—41no—
74#11758185D811yescharacteristic
75#11758185D811yescharacteristic
76C23×C61—81no—
77Q8×C61—21no—
78D4×C61—21no—
79D4×C61—41no—
80D4×C61—81no—
81D4×C61—81no—
82D4×C61—162no—
83C2×C4×C61—21no—
84C2×C4×C61—41no—
85C2×C4×C61#12111yescharacteristic
86C2×Dic61—81no—
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—162no—
97C22×C61—161no—
98C22×C61#47211yescharacteristic
99C4×C61—22no—
100C4×C61—41no—
101C4×C61#45911yescharacteristic
102C4×C61#46611yescharacteristic
103Dic61—161no—
104#2248—611no—
105#2214—611no—
106#2213D6111yescharacteristic
107#2170—611no—
108#1373—611no—
109#1358—611no—
110#1357—611no—
111C2×C61—21no—
112C2×C61—81no—
113C2×C61—321no—
114C2×C61#166711yescharacteristic
115#510—1221no—
116#509—21no—
117C2×SD32—1221no—
118C2×SD32—1221no—
119#504—1221no—
120#494—611no—
121#493C2×D6111yescharacteristic
122#443C2×D6111yescharacteristic
123#364—611no—
124#364—611no—
125#364C2×D6111yescharacteristic
126#362—1221no—
127#361—21no—
128#350—1221no—
129C4×C16—611no—
130C61#1243811yescharacteristic, complemented, Sylow
131#135C22⋊D6111yescharacteristic
132C2×Q16—1221no—
133C2×Q16—1221no—
134C2×D8—21no—
135C2×D8—21no—
136#131—21no—
137C4⋊Q8—1221no—
138#127—21no—
139Q32—2441no—
140SD32—41no—
141SD32—2441no—
142SD32—2441no—
143SD32—2442no—
144SD32—2441no—
145D16—41no—
146M32—21no—
147M32—1221no—
148M32—1221no—
149M32—2441no—
150C2×C16—611no—
151C2×C16—611no—
152C2×C16—2441no—
153#108C22⋊D6111yescharacteristic
154#104—21no—
155C4×C8C22×D6111yescharacteristic
156#41—21no—
157C2×Q8—2441no—
158C2×D4—41no—
159C2×D4—81no—
160Q16—2441no—
161Q16—2441no—
162Q16—2441no—
163Q16—2441no—
164Q16#1175819911yescharacteristic
165SD16—21no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8#1175819911yescharacteristic
171M16—21no—
172M16—41no—
173C2×C8—41no—
174C2×C8D4×D6111yescharacteristic
175C2×C8C2×C22⋊D6111yescharacteristic
176C4⋊C4—4881no—
177C42#1175822411yescharacteristic
178C16—41no—
179C16—611no—
180C16—611no—
181C16—1221no—
182C16—2441no—
183C16—2441no—
184C23—81no—
185Q8—21no—
186Q8—4881no—
187Q8—4881no—
188D4—21no—
189D4—41no—
190D4—81no—
191D4—81no—
192D4—162no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—4881no—
196C2×C4#1451974911yescharacteristic
197C8—41no—
198C8D8×D6111yescharacteristic
199C8C2×#1175819911yescharacteristic
200C8#1451979711yescharacteristic
201C8#1451980111yescharacteristic
202C22—41no—
203C22—162no—
204C22—161no—
205C22#1684003011yescharacteristic
206C4—22no—
207C4—41no—
208C4—9761no—
209C4#1683995511yescharacteristic
210C4#1683999611yescharacteristic
211C2—21no—
212C2—81no—
213C2—321no—
214C2#2144517211yescharacteristic
subgroupG/H
centerC2#21445172
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
Fitting, prime radicalC61×#2213C2
socleC2×C61#1667
hypercenter#2213D61
hypocenterC61#12438
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #21448074C2semidirect
2. #21447900C2semidirect
3. #21447656C2semidirect
4. #21443894C2semidirect
5. #21443857C2semidirect
6. #21443856C2semidirect
130. C61#12438semidirect

Maximal subgroups

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

subgroupindex
#214480742
#214479002
#214476562
#214438942
#214438572
#214438562
C61×#22132
#1243861