Finite Group Databasebeta

← #29593388

Subgroups — #29593388

Order 15616.

318 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 55 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#21457200C211yesmaximal, characteristic
2#21448033C212yesmaximal, complemented
3#21443803C212yesmaximal, complemented
4#21443770C211yesmaximal, characteristic, complemented
5C61×#2102C211yesmaximal, characteristic, complemented
6#16840312—21no—
7#16840053—22no—
8#16840015—21no—
9#16840015C2212yes—
10#16839958—22no—
11#16839586—22no—
12#16839574—22no—
13#16839544C2212yes—
14C61×#430C2211yescharacteristic
15C61×#423C2211yescharacteristic
16C61×#344—21no—
17C61×#339—21no—
18C61×H(3,ℤ/4)C2211yescharacteristic
19C2×#11758222—41no—
20C2×D488—21no—
21C2×D488D412yes—
22#14519777—21no—
23#14519774—21no—
24#14519765—41no—
25#14519751—22no—
26#14519751—41no—
27C4×D244—22no—
28C4×D244—41no—
29#14519717—22no—
30#14519709—21no—
31#14519709D412yes—
32#14519699—22no—
33#14519699—22no—
34C2×M16×C61—21no—
35C2×M16×C61D411yescharacteristic
36C2×M16×C61C2311yescharacteristic
37#117×C61—21no—
38C2×C42×C61D411yescharacteristic
39#108×C61—22no—
40C4⋊C8×C61—22no—
41C22×C4×C61—21no—
42C22×C4×C61C2×D411yescharacteristic
43C2×C22⋊D61—42no—
44#11758222—84no—
45C2×D244—22no—
46C2×D244—41no—
47C2×D244—41no—
48C2×C4×D61—42no—
49C2×Dic122—41no—
50M16×C61—41no—
51M16×C61—41no—
52M16×C61—41no—
53M16×C61—41no—
54C2×C8×C61—21no—
55C2×C8×C61—41no—
56C2×C8×C61C2×D412yes—
57C4⋊C4×C61—41no—
58C22⋊C4×C61—41no—
59C42×C61—21no—
60C42×C61—41no—
61C42×C61SD1611yescharacteristic
62C42×C61SD1611yescharacteristic
63#11758198—42no—
64#11758198—42no—
65C4⋊Dic61—22no—
66C4⋊Dic61—41no—
67D488—42no—
68D488—81no—
69#11758185—42no—
70C23×C61AGL(1,ℤ/8)11yescharacteristic
71C22×D61—42no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—42no—
77C2×C4×C61—81no—
78C2×C4×C61#12011yescharacteristic
79C2×C4×C61C2×SD1611yescharacteristic
80C22⋊D61—84no—
81C2×Dic61—42no—
82D244—42no—
83D244—42no—
84D244—82no—
85D244—82no—
86C4×D61—84no—
87Dic122—82no—
88C8×C61—22no—
89C8×C61—41no—
90C8×C61—81no—
91#12307—611nomaximal, Sylow
92C22×C61—21no—
93C22×C61—41no—
94C22×C61#45011yescharacteristic
95C2×D61—82no—
96C2×D61—82no—
97C2×D61—82no—
98C4×C61—22no—
99C4×C61—21no—
100C4×C61—41no—
101C4×C61—161no—
102C4×C61#45411yescharacteristic
103C4×C61#45811yescharacteristic
104Dic61—82no—
105#3253—611no—
106#2238—612no—
107#2102D6111yescharacteristic, complemented
108#1339—612no—
109#1327—611no—
110C2×C61—21no—
111C2×C61—41no—
112C2×C61#161611yescharacteristic
113D61—162no—
114#532—1221no—
115#476—1222no—
116#469—612no—
117#469—1221no—
118#459—1222no—
119#430C2×D6111yescharacteristic
120#423C2×D6111yescharacteristic
121#365—1222no—
122#361—1222no—
123#349—612no—
124#344—21no—
125#339—21no—
126H(3,ℤ/4)C2×D6111yescharacteristic
127C61#1230711yescharacteristic, complemented, Sylow
128C2×#41—2441no—
129C2×D8—612no—
130C2×D8—1221no—
131C2×M16—21no—
132C2×M16C22⋊D6111yescharacteristic
133C2×M16C22×D6111yescharacteristic
134C4⋊Q8—1221no—
135#127—1221no—
136#124—2441no—
137#121—1222no—
138#121—2441no—
139C4×D4—1222no—
140C4×D4—2441no—
141#117—21no—
142C2×C42C22⋊D6111yescharacteristic
143M32—1222no—
144#108—22no—
145#106—612no—
146#106—1221no—
147C4⋊C8—22no—
148#102—1222no—
149#102—1222no—
150#41—4884no—
151C2×Q8—2441no—
152C2×D4—1222no—
153C2×D4—2441no—
154C2×D4—2441no—
155C2×D4—2442no—
156C22×C4—21no—
157C22×C4—2442no—
158C22×C4C2×C22⋊D6111yescharacteristic
159D8—4881no—
160D8—2442no—
161M16—41no—
162M16—41no—
163M16—41no—
164M16—41no—
165C2×C8—21no—
166C2×C8—41no—
167C2×C8D4×D6112yes—
168C4⋊C4—41no—
169C4⋊C4—1222no—
170C4⋊C4—2441no—
171C22⋊C4—41no—
172C22⋊C4—2442no—
173C22⋊C4—2442no—
174C42—21no—
175C42—41no—
176C42#1175820111yescharacteristic
177C42#1175820111yescharacteristic
178C16—2442no—
179C23—2442no—
180C23#1451980211yescharacteristic
181Q8—4882no—
182D4—4882no—
183D4—4882no—
184D4—4884no—
185D4—2442no—
186D4—2442no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—81no—
193C2×C4—4884no—
194C2×C4—2442no—
195C2×C4#1451974511yescharacteristic
196C2×C4C2×#1175820111yescharacteristic
197C8—22no—
198C8—41no—
199C8—81no—
200C22—21no—
201C22—41no—
202C22—4882no—
203C22—4882no—
204C22—4882no—
205C22#1683991211yescharacteristic
206C4—22no—
207C4—21no—
208C4—41no—
209C4—161no—
210C4—4882no—
211C4#1683993411yescharacteristic
212C4#1683995111yescharacteristic
213C2—21no—
214C2—41no—
215C2—9762no—
216C2#2144485511yescharacteristic
subgroupG/H
centerC2#21444855
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#2102C2
socleC2×C61#1616
prime radical#21457200C2
hypercenter#2102D61
hypocenterC61#12307
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2102

Complements

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

NH ≅ G/Ntype
2. #21448033C2semidirect
3. #21443803C2semidirect
4. #21443770C2semidirect
5. C61×#2102C2semidirect
107. #2102D61semidirect
127. C61#12307semidirect

Maximal subgroups

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

subgroupindex
#214572002
#214480332
#214438032
#214437702
C61×#21022
#1230761