Finite Group Databasebeta

← #29593391

Subgroups — #29593391

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#21448034C212yesmaximal, complemented
3#21447394C211yesmaximal, characteristic, complemented
4#21443805C212yesmaximal, complemented
5C61×#1327C211yesmaximal, characteristic, complemented
6#16840312—21no—
7#16840053—22no—
8#16840015—21no—
9#16840015C2212yes—
10#16839958—22no—
11#16839811C2211yescharacteristic
12#16839585—22no—
13#16839576—22no—
14#16839534—21no—
15#16839522—21no—
16#16839519C2211yescharacteristic
17C61×#423C2211yescharacteristic
18C61×#349C2212yes—
19C2×#11758222—41no—
20C2×D488—21no—
21C2×D488D412yes—
22C2×#11758194—21no—
23#14519777—21no—
24#14519774—21no—
25#14519765—41no—
26#14519751—22no—
27#14519751—41no—
28C4×D244—22no—
29C4×D244—41no—
30#14519736—21no—
31#14519713—22no—
32#14519709—21no—
33#14519709D412yes—
34#14519699—22no—
35#14519699—22no—
36C2×M16×C61D411yescharacteristic
37C2×M16×C61C2311yescharacteristic
38C2×C42×C61D411yescharacteristic
39M32×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—
52C2×C8×C61—21no—
53C2×C8×C61C2×D412yes—
54C42×C61—21no—
55C42×C61SD1611yescharacteristic
56C42×C61SD1611yescharacteristic
57C22⋊Dic61—41no—
58#11758198—42no—
59#11758198—42no—
60C4⋊Dic61—22no—
61C4⋊Dic61—41no—
62C4⋊Dic61—41no—
63C4×Dic61—41no—
64#11758194—41no—
65#11758194—41no—
66C2×#92418—41no—
67D488—42no—
68D488—81no—
69C16×C61—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#12011yescharacteristic
78C2×C4×C61C2×SD1611yescharacteristic
79C22⋊D61—84no—
80C2×Dic61—42no—
81C2×Dic61—81no—
82D244—42no—
83D244—42no—
84D244—82no—
85D244—82no—
86C4×D61—84no—
87Dic122—82no—
88C8×C61—22no—
89C8×C61—41no—
90#92418—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#45411yescharacteristic
102C4×C61#45811yescharacteristic
103Dic61—82no—
104Dic61—161no—
105#3253—611no—
106#2238—612no—
107#2102—611no—
108#1339—612no—
109#1327D6111yescharacteristic, complemented
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#430—611no—
120#423C2×D6111yescharacteristic
121#365—1222no—
122#361—1222no—
123#349C2×D6112yes—
124#344—1221no—
125#339—1221no—
126H(3,ℤ/4)—611no—
127C61#1230711yescharacteristic, complemented, Sylow
128C2×#41—2441no—
129C2×D8—612no—
130C2×D8—1221no—
131C2×M16—1221no—
132C2×M16D24411yescharacteristic
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—1221no—
142C2×C42D24411yescharacteristic
143M32—22no—
144#108—1222no—
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×D24411yescharacteristic
159D8—4881no—
160D8—2442no—
161M16—41no—
162M16—41no—
163M16—2441no—
164M16—2441no—
165C2×C8—21no—
166C2×C8—2441no—
167C2×C8D4×D6112yes—
168C4⋊C4—1222no—
169C4⋊C4—2441no—
170C4⋊C4—2441no—
171C22⋊C4—2442no—
172C22⋊C4—2441no—
173C22⋊C4—2442no—
174C42—21no—
175C42—2441no—
176C42#1175819011yescharacteristic
177C42#1175819011yescharacteristic
178C16—42no—
179C23—2442no—
180C23#1451980511yescharacteristic
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—4884no—
193C2×C4—4881no—
194C2×C4—2442no—
195C2×C4#1451974711yescharacteristic
196C2×C4C2×#1175819011yescharacteristic
197C8—22no—
198C8—41no—
199C8—4881no—
200C22—21no—
201C22—41no—
202C22—4882no—
203C22—4882no—
204C22—4882no—
205C22#1683991511yescharacteristic
206C4—22no—
207C4—21no—
208C4—41no—
209C4—9761no—
210C4—4882no—
211C4#1683993711yescharacteristic
212C4#1683995311yescharacteristic
213C2—21no—
214C2—41no—
215C2—9762no—
216C2#2144485811yescharacteristic
subgroupG/H
centerC2#21444858
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#1327C2
socleC2×C61#1616
prime radical#21457200C2
hypercenter#1327D61
hypocenterC61#12307
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #21448034C2semidirect
3. #21447394C2semidirect
4. #21443805C2semidirect
5. C61×#1327C2semidirect
109. #1327D61semidirect
127. C61#12307semidirect

Maximal subgroups

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

subgroupindex
#214572002
#214480342
#214473942
#214438052
C61×#13272
#1230761