Finite Group Databasebeta

← #29591541

Subgroups — #29591541

Order 15616.

280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 79 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#21456447C211yesmaximal, characteristic
2#21447585C211yesmaximal, characteristic, complemented
3#21443881C212yesmaximal, complemented
4#21443859C212yesmaximal, complemented
5C61×#2166C211yesmaximal, characteristic, complemented
6#16840374C411yescharacteristic
7#16840367C411yescharacteristic
8C2×#14519717—21no—
9#16840164C2211yescharacteristic
10#16840135C2211yescharacteristic
11#16840131C411yescharacteristic
12#16840127C411yescharacteristic
13#16840008—21no—
14#16839991—21no—
15#16839864—21no—
16C4×#11758190—21no—
17#16839583—21no—
18#16839583C2212yes—
19C61×#405C2211yescharacteristic
20C61×#364C2212yes—
21C61×#349—21no—
22C61×#347—21no—
23C2×#11758190—21no—
24C2×#11758190—21no—
25#14519777C2×C411yescharacteristic
26#14519774C2×C411yescharacteristic
27#14519770—41no—
28#14519769C2×C411yescharacteristic
29#14519769C2×C411yescharacteristic
30#14519767—41no—
31#14519762—41no—
32#14519756—21no—
33#14519751—21no—
34#14519750—41no—
35C4×Dic122—21no—
36C4×D244—21no—
37#14519717—22no—
38#14519717—41no—
39C2×#11758185—41no—
40#14519711—21no—
41#14519709—21no—
42#14519702—21no—
43#14519702—21no—
44#14519699—21no—
45#14519699—21no—
46C2×M16×C61D411yescharacteristic
47C22×C8×C61D411yescharacteristic
48#117×C61C2×C411yescharacteristic
49M32×C61—22no—
50#97×C61C2×C411yescharacteristic
51#97×C61D411yescharacteristic
52C4×C8×C61D411yescharacteristic
53C4×C8×C61C2311yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C2×C22⋊D61—41no—
56C2×D244—21no—
57C2×D244—41no—
58C2×C4×D61—41no—
59C2×Dic122—21no—
60M16×C61—22no—
61C2×C8×C61—21no—
62C2×C8×C61—21no—
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22⋊C411yescharacteristic
65C2×C8×C61C2×D411yescharacteristic
66C2×C8×C61C2×D411yescharacteristic
67C4⋊C4×C61—21no—
68C22⋊C4×C61—21no—
69C42×C61C22⋊C411yescharacteristic
70C42×C61C22×C411yescharacteristic
71C22⋊Dic61—41no—
72#11758198—41no—
73#11758198—41no—
74C4⋊Dic61—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61—41no—
77#11758196—41no—
78#11758196—41no—
79#11758196—41no—
80#11758196—41no—
81C4×Dic61—41no—
82#11758190—42no—
83#11758190—41no—
84#11758190—41no—
85C16×C61—42no—
86#11758185—42no—
87C23×C61#10011yescharacteristic
88C22×D61—41no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61#10011yescharacteristic
94C2×C4×C61C2×C22⋊C411yescharacteristic
95C22⋊D61—161no—
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99D244—41no—
100D244—41no—
101D244—161no—
102C4×D61—161no—
103Dic122—41no—
104Dic122—41no—
105C8×C61—21no—
106C8×C61—21no—
107C8×C61#13512yes—
108C8×C61AGL(1,ℤ/8)11yescharacteristic
109C8×C61#13711yescharacteristic
110#11991—611nomaximal, Sylow
111C22×C61—21no—
112C22×C61—41no—
113C22×C61C2×#10011yescharacteristic
114C2×D61—81no—
115C2×D61—81no—
116C2×D61—81no—
117C4×C61—21no—
118C4×C61—41no—
119C4×C61—41no—
120C4×C61#41611yescharacteristic
121C4×C61#41711yescharacteristic
122Dic61—81no—
123Dic61—81no—
124Dic61—81no—
125#3174—611no—
126#2166D6111yescharacteristic, complemented
127#2153—611no—
128#1366—612no—
129#1359—612no—
130C2×C61—21no—
131C2×C61—41no—
132C2×C61#155111yescharacteristic
133D61—161no—
134#541—611no—
135#540—611no—
136C2×M32—1221no—
137#499—611no—
138#492—611no—
139#491—611no—
140#490—611no—
141#468—1221no—
142#465—1221no—
143#440—1221no—
144C4×SD16—1221no—
145#405C2×D6111yescharacteristic
146#364—612no—
147#364—1221no—
148#364C2×D6112yes—
149#349—21no—
150#347—21no—
151C61#1199111yescharacteristic, complemented, Sylow
152C2×SD16—1221no—
153C2×SD16—1221no—
154C2×M16C22⋊D6111yescharacteristic
155C22×C8D24411yescharacteristic
156C4⋊Q8—611no—
157#127—611no—
158#126—2441no—
159#125—611no—
160#125—611no—
161#125—2441no—
162#123—2441no—
163C22⋊Q8—1221no—
164#121—1221no—
165#121—2441no—
166C4×Q8—1221no—
167C4×D4—1221no—
168#117C4×D6111yescharacteristic
169M32—22no—
170M32—1222no—
171M32—2441no—
172C2×C16—2441no—
173#107—1221no—
174#106—1221no—
175#103—1221no—
176#103—1221no—
177#102—1221no—
178#102—1221no—
179#97C4×D6111yescharacteristic
180#97C22⋊D6111yescharacteristic
181C4×C8D24411yescharacteristic
182C4×C8C22×D6111yescharacteristic
183C2×Q8—1221no—
184C2×D4—1221no—
185C2×D4—2441no—
186C2×D4—2441no—
187C22×C4—2441no—
188C22×C4#1175819811yescharacteristic
189SD16—2441no—
190SD16—2442no—
191SD16—2441no—
192M16—22no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8#1175819811yescharacteristic
196C2×C8#1175819811yescharacteristic
197C2×C8C2×D24411yescharacteristic
198C2×C8C2×C22⋊D6111yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—1221no—
201C4⋊C4—1221no—
202C4⋊C4—2441no—
203C4⋊C4—2441no—
204C4⋊C4—2441no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C22⋊C4—21no—
208C22⋊C4—2441no—
209C22⋊C4—2441no—
210C22⋊C4—2441no—
211C42—2441no—
212C42#1175819811yescharacteristic
213C42C2×C4×D6111yescharacteristic
214C16—42no—
215C16—2442no—
216C23—2441no—
217C23#1451969311yescharacteristic
218Q8—2441no—
219Q8—2441no—
220D4—9761no—
221D4—9761no—
222D4—2441no—
223D4—2441no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—9761no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4#1451969311yescharacteristic
233C2×C4C2×#1175819811yescharacteristic
234C8—21no—
235C8—21no—
236C8#1451979712yes—
237C8#1451980511yescharacteristic
238C8#1451981011yescharacteristic
239C22—21no—
240C22—41no—
241C22—4881no—
242C22—4881no—
243C22—4881no—
244C22C2×#1451969311yescharacteristic
245C4—21no—
246C4—41no—
247C4—41no—
248C4—4881no—
249C4—4881no—
250C4—4881no—
251C4#1683975611yescharacteristic
252C4#1683976411yescharacteristic
253C2—21no—
254C2—41no—
255C2—9761no—
256C2#2144451511yescharacteristic
subgroupG/H
centerC2#21444515
commutatorC42×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#2166C2
socleC2×C61#1551
prime radical#16840367C4
cosocleC4×C8×C61C23
hypercenter#2166D61
hypocenterC61#11991
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #21447585C2semidirect
3. #21443881C2semidirect
4. #21443859C2semidirect
5. C61×#2166C2semidirect
126. #2166D61semidirect
151. C61#11991semidirect

Maximal subgroups

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

subgroupindex
#214564472
#214475852
#214438812
#214438592
C61×#21662
#1199161