Finite Group Databasebeta

← #29599678

Subgroups — #29599678

Order 15616.

310 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 95 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#21456347C211yesmaximal, characteristic
2#21447593C211yesmaximal, characteristic
3#21446607C211yesmaximal, characteristic
4#21443934C211yesmaximal, characteristic
5#21443917C211yesmaximal, characteristic
6#21443906C211yesmaximal, characteristic
7C2×C61×#365C211yesmaximal, characteristic
8#16840393—21no—
9C2×#14519717C2211yescharacteristic
10#16840169—22no—
11#16840162—21no—
12#16840159—21no—
13#16839810—21no—
14C2×#14519713C2211yescharacteristic
15#16839802—21no—
16#16839800C2211yescharacteristic
17#16839717C2211yescharacteristic
18#16839586—21no—
19#16839586—21no—
20#16839533—21no—
21C2×M32×C61C2211yescharacteristic
22C2×#108×C61C2211yescharacteristic
23C2×#106×C61C2211yescharacteristic
24C61×#365—22no—
25C2×#11758194—21no—
26C2×#11758194D411yescharacteristic
27#14519776—22no—
28#14519776—41no—
29#14519768—22no—
30#14519768—41no—
31#14519756—42no—
32#14519736—21no—
33#14519736D411yescharacteristic
34#14519717—21no—
35#14519717—21no—
36C2×#11758185Q812yescomplemented
37#14519713—21no—
38#14519713Q812yescomplemented
39#14519712—42no—
40#14519711—21no—
41#14519710—22no—
42#14519709D411yescharacteristic
43#14519709D411yescharacteristic
44#14519708—22no—
45#14519687—21no—
46C8×Dic61—21no—
47C2×M16×C61—21no—
48C22×C8×C61C2311yescharacteristic
49C2×C4⋊C4×C61—21no—
50M32×C61—21no—
51M32×C61Q812yescomplemented
52C2×C16×C61—21no—
53#108×C61—21no—
54#108×C61—21no—
55#106×C61—21no—
56#106×C61D412yes—
57C22×C4×C61—41no—
58C22×C4×C61C2×D411yescharacteristic
59C2×Dic122—42no—
60M16×C61—41no—
61M16×C61—41no—
62C2×C8×C61—41no—
63C2×C8×C61C2×D411yescharacteristic
64C2×C8×C61C2×D411yescharacteristic
65C2×C8×C61C2×Q811yescharacteristic
66C2×C8×C61C2×Q811yescharacteristic
67C2×C8×C61C2×Q811yescharacteristic
68C2×C8×C61#4111yescharacteristic
69C4⋊C4×C61—22no—
70C4⋊C4×C61—41no—
71C22⋊Dic61—41no—
72C22⋊Dic61SD1612yes—
73C4⋊Dic61—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61—42no—
77#11758196—42no—
78#11758196—42no—
79C4×Dic61—21no—
80C4×Dic61—41no—
81#11758194—21no—
82#11758194—22no—
83#11758194—41no—
84#11758194SD1612yes—
85C2×#92418—21no—
86C2×#92418—41no—
87C16×C61—22no—
88#11758185—22no—
89C23×C61C2×SD1611yescharacteristic
90C2×C4×C61—42no—
91C2×C4×C61—161no—
92C2×C4×C61#12011yescharacteristic
93C2×C4×C61C22⋊Q811yescharacteristic
94C2×C4×C61C4⋊Q811yescharacteristic
95C2×C4×C61C2×SD1611yescharacteristic
96C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C61#13711yescharacteristic
98C2×Dic61—22no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101Dic122—162no—
102C8×C61—81no—
103C8×C61C22⋊Q811yescharacteristic
104C8×C61C22⋊Q811yescharacteristic
105C8×C61C4⋊Q811yescharacteristic
106C8×C61C4⋊Q811yescharacteristic
107#92418—22no—
108#92418—42no—
109#13460—611nomaximal, Sylow
110C22×C61—41no—
111C22×C61#45011yescharacteristic
112C22×C61#47511yescharacteristic
113C22×C61#49811yescharacteristic
114C4×C61—82no—
115C4×C61#39511yescharacteristic
116C4×C61#44811yescharacteristic
117C4×C61#47611yescharacteristic
118C4×C61#50111yescharacteristic
119Dic61—42no—
120Dic61—81no—
121Dic61—81no—
122#3163—611no—
123#2155—611no—
124C2×#365D6111yescharacteristic
125#1953—611no—
126#1389—611no—
127#1383—611no—
128#1378—611no—
129C2×C61—21no—
130C2×C61—21no—
131C2×C61—21no—
132C2×C61#205811yescharacteristic
133#544—1221no—
134C2×M32—611no—
135C2×M32C2×D6111yescharacteristic
136#501—1222no—
137#499—1221no—
138#498—1221no—
139#430—1221no—
140C2×#108—611no—
141C2×#108C2×D6111yescharacteristic
142#428—1221no—
143#427—611no—
144C2×#106C2×D6111yescharacteristic
145#405—611no—
146#365—22no—
147#365—1221no—
148#365—1221no—
149#344—1221no—
150C61#1346011yescharacteristic, complemented, Sylow
151C2×M16—21no—
152C2×M16—611no—
153C2×M16—1221no—
154C22×C8C22×D6111yescharacteristic
155C4⋊Q8—1222no—
156C4⋊Q8—2441no—
157#125—1222no—
158#125—2441no—
159C22⋊Q8—2442no—
160#117—611no—
161#117—1221no—
162C2×C4⋊C4—21no—
163M32—21no—
164M32—1221no—
165M32—1221no—
166M32Dic12212yescomplemented
167C2×C16—21no—
168C2×C16—612no—
169#108—21no—
170#108—21no—
171#108—612no—
172#108—1221no—
173#108—2442no—
174#107—1222no—
175#107—1221no—
176#106—21no—
177#106—611no—
178#106—611no—
179#106—1222no—
180#106C22⋊D6112yes—
181#97—1221no—
182C4×C8—1221no—
183C2×Q8—2442no—
184C22×C4—41no—
185C22×C4D4×D6111yescharacteristic
186M16—41no—
187M16—41no—
188M16—612no—
189M16—1221no—
190M16—1222no—
191M16—2441no—
192C2×C8—41no—
193C2×C8—1221no—
194C2×C8—2441no—
195C2×C8C2×Dic12211yescharacteristic
196C2×C8#1175822211yescharacteristic
197C2×C8D4×D6111yescharacteristic
198C2×C8Q8×D6111yescharacteristic
199C2×C8Q8×D6111yescharacteristic
200C2×C8C2×C22⋊D6111yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—41no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—2442no—
207C4⋊C4—2442no—
208C4⋊C4—2442no—
209C22⋊C4—612no—
210C22⋊C4—2441no—
211C42—1221no—
212C42—2441no—
213C16—22no—
214C16—1222no—
215C23SD16×D6111yescharacteristic
216Q8—9762no—
217C2×C4—42no—
218C2×C4—161no—
219C2×C4—1222no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4#1451974511yescharacteristic
223C2×C4#1451975511yescharacteristic
224C2×C4#1451977611yescharacteristic
225C2×C4SD16×D6111yescharacteristic
226C2×C4#1451980411yescharacteristic
227C2×C4#1451980611yescharacteristic
228C8—81no—
229C8—1222no—
230C8—2442no—
231C8#1451975511yescharacteristic
232C8#1451975611yescharacteristic
233C8#1451977511yescharacteristic
234C8#1451977611yescharacteristic
235C22—41no—
236C22#1683991111yescharacteristic
237C22#1684004611yescharacteristic
238C22#1684015911yescharacteristic
239C4—82no—
240C4—4881no—
241C4—4881no—
242C4—2442no—
243C4#1683968211yescharacteristic
244C4#1683989911yescharacteristic
245C4#1684005111yescharacteristic
246C4#1684016911yescharacteristic
247C2—21no—
248C2—21no—
249C2—21no—
250C2#2144715011yescharacteristic
subgroupG/H
centerC2#21447150
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#365C2
socleC2×C61#2058
prime radicalC23×C61C2×SD16
hypercenterC2×#365D61
hypocenterC61#13460
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
36. C2×#11758185Q8semidirect
38. #14519713Q8semidirect
51. M32×C61Q8semidirect
150. C61#13460semidirect
166. M32Dic122semidirect

Maximal subgroups

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

subgroupindex
#214563472
#214475932
#214466072
#214439342
#214439172
#214439062
C2×C61×#3652
#1346061