Finite Group Databasebeta

← #29567785

Subgroups — #29567785

Order 15616.

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

normal subgroups only

This group has 274 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#21447504C211yesmaximal, characteristic
2#21444554C211yesmaximal, characteristic
3C61×#1884C211yesmaximal, characteristic
4#16839786—21no—
5#16839746—21no—
6#16839561—21no—
7#16839559C412yescomplemented
8#16839511—21no—
9#16839506C412yescomplemented
10C61×#568C411yescharacteristic
11C61×#532C2211yescharacteristic
12C61×#421—21no—
13C61×#410C411yescharacteristic
14C61×#339—21no—
15C2×#11758194—41no—
16C2×#11758194—41no—
17C4⋊#92418—22no—
18C4⋊#92418—41no—
19#14519696—22no—
20#14519694—41no—
21C2×#41×C61C2×C411yescharacteristic
22C2×#41×C61D411yescharacteristic
23#131×C61—42no—
24C2×M16×C61—21no—
25C2×M16×C61—41no—
26C4⋊Q8×C61D411yescharacteristic
27#127×C61C2×C411yescharacteristic
28#124×C61C2×C411yescharacteristic
29#124×C61Q811yescharacteristic
30#121×C61—41no—
31C4×D4×C61—41no—
32#117×C61—21no—
33C2×C42×C61D411yescharacteristic
34#104×C61—42no—
35#99×C61—41no—
36#41×C61—41no—
37#41×C61—41no—
38#41×C61—41no—
39#41×C61—41no—
40C2×Q8×C61C22⋊C411yescharacteristic
41C2×Q8×C61C4⋊C411yescharacteristic
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61—41no—
45C2×D4×C61C4211yescharacteristic
46C2×D4×C61C4⋊C411yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C22⋊C411yescharacteristic
51M16×C61—22no—
52M16×C61—41no—
53M16×C61—42no—
54C2×C8×C61—41no—
55C2×C8×C61—42no—
56C4⋊C4×C61—41no—
57C4⋊C4×C61—41no—
58C22⋊C4×C61—41no—
59C22⋊C4×C61—41no—
60C22⋊C4×C61—41no—
61C42×C61—21no—
62C42×C61—41no—
63C42×C61C22⋊C411yescharacteristic
64C42×C61C4⋊C411yescharacteristic
65#11758194—42no—
66#11758194—82no—
67#11758194—81no—
68C2×#92418—42no—
69C2×#92418—81no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61#9911yescharacteristic
73Q8×C61—41no—
74Q8×C61—41no—
75D4×C61—41no—
76D4×C61—41no—
77D4×C61—42no—
78D4×C61—81no—
79D4×C61—81no—
80D4×C61—81no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—81no—
94C2×C4×C61#9511yescharacteristic
95C2×C4×C61#9911yescharacteristic
96C8×C61—42no—
97#92418—82no—
98#92418—82no—
99#7496—611nomaximal, Sylow
100C22×C61—21no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—81no—
105C22×C61—81no—
106C22×C61#34211yescharacteristic
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61—41no—
111C4×C61—41no—
112C4×C61—41no—
113C4×C61—161no—
114C4×C61AΣL(1,𝔽16)11yescharacteristic
115C4×C61#35211yescharacteristic
116#2132—611no—
117#1884D6111yescharacteristic
118#1560—611no—
119C2×C61—21no—
120C2×C61—41no—
121C2×C61—81no—
122C2×C61—81no—
123C2×C61#139011yescharacteristic
124#568Dic6111yescharacteristic
125#532C2×D6111yescharacteristic
126#423—1221no—
127#421—21no—
128#413—1221no—
129#410Dic6111yescharacteristic
130#356—1221no—
131#355—612no—
132#339—21no—
133#333—1221no—
134#331—612no—
135C61#749611yescharacteristic, complemented, Sylow
136C2×#41C2×Dic6111yescharacteristic
137C2×#41C22⋊D6111yescharacteristic
138#131—42no—
139C2×M16—21no—
140C2×M16—41no—
141C2×M16—2441no—
142C2×M16—2441no—
143C4⋊Q8D24411yescharacteristic
144#127C4×D6111yescharacteristic
145#124Dic12211yescharacteristic
146#124C4×D6111yescharacteristic
147#121—41no—
148C4×D4—41no—
149#117—21no—
150C2×C42C22⋊D6111yescharacteristic
151C4⋊C8—1222no—
152C4⋊C8—2441no—
153#104—42no—
154#101—1222no—
155#100—2441no—
156#99—41no—
157#41—41no—
158#41—41no—
159#41—41no—
160#41—41no—
161C2×Q8C4⋊Dic6111yescharacteristic
162C2×Q8#1175819811yescharacteristic
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—41no—
166C2×D4C4×Dic6111yescharacteristic
167C2×D4#1175819611yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4C22⋊Dic6111yescharacteristic
172M16—22no—
173M16—41no—
174M16—42no—
175M16—4882no—
176M16—4881no—
177M16—2442no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—4881no—
181C2×C8—2442no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C42—21no—
188C42—41no—
189C42#1175819611yescharacteristic
190C42#1175819811yescharacteristic
191C23—21no—
192C23—21no—
193C23#1451969211yescharacteristic
194Q8—41no—
195Q8—41no—
196D4—41no—
197D4—41no—
198D4—42no—
199D4—81no—
200D4—81no—
201D4—81no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4#1451968411yescharacteristic
216C2×C4#1451969211yescharacteristic
217C8—42no—
218C8—4882no—
219C8—4882no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22#1683952911yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—161no—
234C4#1683954911yescharacteristic
235C4#1683955211yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—81no—
240C2#2144393711yescharacteristic
subgroupG/H
centerC2#21443937
commutatorC2×D4×C61C42
Frattini#532C2×D61
FittingC61×#1884C2
socleC2×C61#1390
prime radical, cosocleC61×#532C22
hypercenter#1884D61
hypocenterC61#7496
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1884

Complements

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

NH ≅ G/Ntype
7. #16839559C4semidirect
9. #16839506C4semidirect
135. C61#7496semidirect

Maximal subgroups

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

subgroupindex
#214475042
#214445542
C61×#18842
#749661