Finite Group Databasebeta

← #29593359

Subgroups — #29593359

Order 15616.

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

normal subgroups only

This group has 310 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#21456714C211yesmaximal, characteristic
2#21448038C212yesmaximal, complemented
3#21443806C212yesmaximal, complemented
4#21443757C211yesmaximal, characteristic
5C61×#2098C211yesmaximal, characteristic
6#16840333—21no—
7#16840104—22no—
8#16840020C2212yes—
9#16840003—21no—
10#16839920—22no—
11#16839586—22no—
12#16839577—22no—
13#16839544C2212yes—
14C61×#430C2211yescharacteristic
15C61×#424—21no—
16C61×#421—21no—
17C61×#408C2211yescharacteristic
18C61×H(3,ℤ/4)C2211yescharacteristic
19C22×Dic122—21no—
20C2×Dic244—21no—
21C2×Dic244D412yes—
22#14519775—41no—
23#14519764—41no—
24#14519758—41no—
25#14519758—41no—
26#14519756—22no—
27#14519756—22no—
28#14519736—21no—
29#14519717—22no—
30#14519711—21no—
31#14519709D412yes—
32#14519702—22no—
33#14519702—22no—
34C2×#41×C61D411yescharacteristic
35C2×M16×C61—21no—
36C2×M16×C61C2311yescharacteristic
37C22×C8×C61D411yescharacteristic
38#117×C61—21no—
39#108×C61—22no—
40C4⋊C8×C61—42no—
41#104×C61—42no—
42C22⋊C8×C61—22no—
43#41×C61—41no—
44#41×C61—41no—
45C2×Q8×C61SD1611yescharacteristic
46C2×D4×C61—21no—
47C2×D4×C61SD1611yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61C2×D411yescharacteristic
50C22×Dic61—41no—
51C2×Dic122—22no—
52C2×Dic122—41no—
53C2×Dic122—81no—
54C2×Dic122—81no—
55M16×C61—41no—
56M16×C61—41no—
57M16×C61—41no—
58C2×C8×C61—21no—
59C2×C8×C61—41no—
60C2×C8×C61—41no—
61C2×C8×C61C2×D412yes—
62C4⋊C4×C61—41no—
63C22⋊C4×C61—41no—
64C42×C61—22no—
65C22⋊Dic61—41no—
66C22⋊Dic61—42no—
67C22⋊Dic61—42no—
68C4⋊Dic61—22no—
69#11758196—42no—
70#11758196—42no—
71C4×Dic61—41no—
72Dic244—42no—
73Dic244—81no—
74#11758185—42no—
75C23×C61—21no—
76C23×C61AGL(1,ℤ/8)11yescharacteristic
77Q8×C61—41no—
78D4×C61—41no—
79D4×C61—81no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61—42no—
86C2×C4×C61#12011yescharacteristic
87C2×C4×C61C2×SD1611yescharacteristic
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—82no—
91Dic122—42no—
92Dic122—42no—
93Dic122—82no—
94C8×C61—22no—
95C8×C61—41no—
96C8×C61—81no—
97#12302—611nomaximal, Sylow
98C22×C61—21no—
99C22×C61—41no—
100C22×C61—42no—
101C22×C61—41no—
102C22×C61#45011yescharacteristic
103C4×C61—21no—
104C4×C61—41no—
105C4×C61—82no—
106C4×C61#45311yescharacteristic
107C4×C61#45811yescharacteristic
108Dic61—82no—
109Dic61—82no—
110#3202—611no—
111#2239—612no—
112#2098D6111yescharacteristic
113#1340—612no—
114#1321—611no—
115C2×C61—21no—
116C2×C61—41no—
117C2×C61—81no—
118C2×C61#161311yescharacteristic
119#536—1221no—
120#485—1222no—
121#470—612no—
122#467—1221no—
123#451—1222no—
124#430C2×D6111yescharacteristic
125#424—21no—
126#421—21no—
127#408C2×D6111yescharacteristic
128#365—1222no—
129#362—1222no—
130#349—612no—
131H(3,ℤ/4)C2×D6111yescharacteristic
132C61#1230211yescharacteristic, complemented, Sylow
133C2×#41C22⋊D6111yescharacteristic
134C22×Q8—1221no—
135C2×Q16—612no—
136C2×Q16—1221no—
137C2×M16—21no—
138C2×M16C22×D6111yescharacteristic
139C22×C8C22⋊D6111yescharacteristic
140C4⋊Q8—2441no—
141#124—2441no—
142#123—2441no—
143#123—2441no—
144C22⋊Q8—1222no—
145C22⋊Q8—1222no—
146#117—21no—
147#117—1221no—
148M32—1222no—
149#108—22no—
150#107—1221no—
151#106—612no—
152C4⋊C8—42no—
153#104—42no—
154#103—1222no—
155#103—1222no—
156C22⋊C8—22no—
157#41—41no—
158#41—41no—
159C2×Q8—1222no—
160C2×Q8—4881no—
161C2×Q8—4881no—
162C2×Q8—2441no—
163C2×Q8#1175820111yescharacteristic
164C2×D4—21no—
165C2×D4#1175820111yescharacteristic
166C22×C4—21no—
167C22×C4—2441no—
168C22×C4C2×C22⋊D6111yescharacteristic
169Q16—4881no—
170Q16—2442no—
171M16—41no—
172M16—41no—
173M16—41no—
174C2×C8—21no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8D4×D6112yes—
178C4⋊C4—41no—
179C4⋊C4—1222no—
180C4⋊C4—2442no—
181C4⋊C4—2442no—
182C22⋊C4—41no—
183C22⋊C4—2441no—
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C42—22no—
187C42—2441no—
188C16—2442no—
189C23—21no—
190C23#1451980211yescharacteristic
191Q8—41no—
192Q8—4882no—
193Q8—2442no—
194Q8—2442no—
195D4—41no—
196D4—81no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—4882no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4#1451974511yescharacteristic
207C2×C4C2×#1175820111yescharacteristic
208C8—22no—
209C8—41no—
210C8—81no—
211C22—21no—
212C22—41no—
213C22—42no—
214C22—41no—
215C22#1683991211yescharacteristic
216C4—21no—
217C4—41no—
218C4—82no—
219C4—4882no—
220C4—4882no—
221C4#1683992911yescharacteristic
222C4#1683995111yescharacteristic
223C2—21no—
224C2—41no—
225C2—81no—
226C2#2144483811yescharacteristic
subgroupG/H
centerC2#21444838
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#2098C2
socleC2×C61#1613
prime radicalC2×#41×C61D4
hypercenter#2098D61
hypocenterC61#12302
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2098

Complements

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

NH ≅ G/Ntype
2. #21448038C2semidirect
3. #21443806C2semidirect
132. C61#12302semidirect

Maximal subgroups

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

subgroupindex
#214567142
#214480382
#214438062
#214437572
C61×#20982
#1230261