Finite Group Databasebeta

← #29593389

Subgroups — #29593389

Order 15616.

318 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 318 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#21448031C212yesmaximal, complemented
2#21447394C211yesmaximal, characteristic, complemented
3#21443804C212yesmaximal, complemented
4#21443770C211yesmaximal, characteristic, complemented
5C61×#3253C211yesmaximal, characteristic
6#16839811C2211yescharacteristic
7#16839584—22no—
8#16839575—22no—
9#16839544C2212yes—
10#16839534—21no—
11#16839522—21no—
12#16839519C2211yescharacteristic
13C61×#532—21no—
14C61×#476—22no—
15C61×#469—21no—
16C61×#469C2212yes—
17C61×#459—22no—
18C61×#423C2211yescharacteristic
19C2×#11758194—21no—
20#14519736—21no—
21#14519717—22no—
22#14519713—22no—
23C2×#41×C61—41no—
24C2×D8×C61—21no—
25C2×D8×C61D412yes—
26C2×M16×C61D411yescharacteristic
27C2×M16×C61C2311yescharacteristic
28C4⋊Q8×C61—21no—
29#127×C61—21no—
30#124×C61—41no—
31#121×C61—22no—
32#121×C61—41no—
33C4×D4×C61—22no—
34C4×D4×C61—41no—
35C2×C42×C61D411yescharacteristic
36#106×C61—21no—
37#106×C61D412yes—
38C4⋊C8×C61—22no—
39#102×C61—22no—
40#102×C61—22no—
41#41×C61—84no—
42C2×Q8×C61—41no—
43C2×D4×C61—22no—
44C2×D4×C61—41no—
45C2×D4×C61—41no—
46C2×D4×C61—42no—
47C22×C4×C61—21no—
48C22×C4×C61—42no—
49C22×C4×C61C2×D411yescharacteristic
50D8×C61—42no—
51D8×C61—81no—
52M16×C61—41no—
53M16×C61—41no—
54C2×C8×C61—21no—
55C2×C8×C61C2×D412yes—
56C4⋊C4×C61—22no—
57C4⋊C4×C61—41no—
58C22⋊C4×C61—42no—
59C22⋊C4×C61—42no—
60C42×C61—21no—
61C42×C61SD1611yescharacteristic
62C42×C61SD1611yescharacteristic
63C22⋊Dic61—41no—
64C4⋊Dic61—41no—
65C4×Dic61—41no—
66#11758194—41no—
67#11758194—41no—
68C2×#92418—41no—
69#11758185—42no—
70C23×C61—42no—
71C23×C61AGL(1,ℤ/8)11yescharacteristic
72Q8×C61—82no—
73D4×C61—42no—
74D4×C61—42no—
75D4×C61—82no—
76D4×C61—82no—
77D4×C61—84no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61—84no—
85C2×C4×C61#12011yescharacteristic
86C2×C4×C61C2×SD1611yescharacteristic
87C2×Dic61—81no—
88C8×C61—22no—
89C8×C61—41no—
90#92418—81no—
91#12307—611nomaximal, Sylow
92C22×C61—21no—
93C22×C61—41no—
94C22×C61—82no—
95C22×C61—82no—
96C22×C61—82no—
97C22×C61#45011yescharacteristic
98C4×C61—22no—
99C4×C61—21no—
100C4×C61—41no—
101C4×C61—82no—
102C4×C61#45411yescharacteristic
103C4×C61#45811yescharacteristic
104Dic61—161no—
105#3253D6111yescharacteristic
106#2238—612no—
107#2102—611no—
108#1339—612no—
109#1327—611no—
110C2×C61—21no—
111C2×C61—41no—
112C2×C61—162no—
113C2×C61#161611yescharacteristic
114#532—21no—
115#476—22no—
116#469—21no—
117#469C2×D6112yes—
118#459—22no—
119#430—611no—
120#423C2×D6111yescharacteristic
121#365—1222no—
122#361—1222no—
123#349—612no—
124#344—1221no—
125#339—1221no—
126H(3,ℤ/4)—611no—
127C61#1230711yescharacteristic, complemented, Sylow
128C2×#41—41no—
129C2×D8—21no—
130C2×D8C22⋊D6112yes—
131C2×M16—1221no—
132C2×M16C22⋊D6111yescharacteristic
133C2×M16C22×D6111yescharacteristic
134C4⋊Q8—21no—
135#127—21no—
136#124—41no—
137#121—22no—
138#121—41no—
139C4×D4—22no—
140C4×D4—41no—
141#117—1221no—
142C2×C42C22⋊D6111yescharacteristic
143M32—1222no—
144#108—1222no—
145#106—21no—
146#106C22⋊D6112yes—
147C4⋊C8—22no—
148#102—22no—
149#102—22no—
150#41—84no—
151C2×Q8—41no—
152C2×D4—22no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—42no—
156C22×C4—21no—
157C22×C4—42no—
158C22×C4C2×C22⋊D6111yescharacteristic
159D8—42no—
160D8—81no—
161M16—41no—
162M16—41no—
163M16—2441no—
164M16—2441no—
165C2×C8—21no—
166C2×C8—2441no—
167C2×C8C2×C22⋊D6112yes—
168C4⋊C4—22no—
169C4⋊C4—41no—
170C4⋊C4—2441no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C22⋊C4—2441no—
174C42—21no—
175C42—2441no—
176C42#1175820011yescharacteristic
177C42#1175820011yescharacteristic
178C16—2442no—
179C23—42no—
180C23#1451980311yescharacteristic
181Q8—82no—
182D4—42no—
183D4—42no—
184D4—82no—
185D4—82no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—84no—
194C2×C4—4881no—
195C2×C4#1451974611yescharacteristic
196C2×C4C2×#1175820011yescharacteristic
197C8—22no—
198C8—41no—
199C8—4881no—
200C22—21no—
201C22—41no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#1683991311yescharacteristic
206C4—22no—
207C4—21no—
208C4—41no—
209C4—82no—
210C4—9761no—
211C4#1683993511yescharacteristic
212C4#1683995211yescharacteristic
213C2—21no—
214C2—41no—
215C2—162no—
216C2#2144485611yescharacteristic
subgroupG/H
centerC2#21444856
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
Fitting, prime radicalC61×#3253C2
socleC2×C61#1616
hypercenter#3253D61
hypocenterC61#12307
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #21448031C2semidirect
2. #21447394C2semidirect
3. #21443804C2semidirect
4. #21443770C2semidirect
127. C61#12307semidirect

Maximal subgroups

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

subgroupindex
#214480312
#214473942
#214438042
#214437702
C61×#32532
#1230761