Finite Group Databasebeta

← #29567382

Subgroups — #29567382

Order 15616.

318 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 39 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#21445782C211yesmaximal, characteristic
2#21443757C211yesmaximal, characteristic, complemented
3C61×#1315C211yesmaximal, characteristic, complemented
4#16840598C411yescharacteristic
5#16839778—21no—
6#16839759—21no—
7#16839736C411yescharacteristic
8#16839544—21no—
9C61×#408C2211yescharacteristic
10C61×C22⋊C16—21no—
11#14519825C812yes—
12#14519824—41no—
13#14519823—41no—
14#14519822—21no—
15#14519822—41no—
16C2×#11758222—21no—
17C2×#11758222—41no—
18#41×D61—42no—
19#14519736—21no—
20#14519717—41no—
21#14519703—42no—
22#14519702—41no—
23#14519699—41no—
24#14519692—41no—
25C2×#41×C61C2×C411yescharacteristic
26C2×M16×C61D411yescharacteristic
27C22×C8×C61D411yescharacteristic
28C2×C16×C61—41no—
29C22⋊C8×C61—41no—
30#41×C61—41no—
31#41×C61—41no—
32C2×Q8×C61C2×C811yescharacteristic
33C2×D4×C61—21no—
34C2×D4×C61M1611yescharacteristic
35C22×C4×C61—21no—
36C22×C4×C61C22⋊C411yescharacteristic
37C2×C22⋊D61—42no—
38C2×C22⋊D61—41no—
39#11758226—42no—
40Q8×D61—42no—
41#11758224—42no—
42#11758224—44no—
43D4×D61—42no—
44D4×D61—44no—
45#11758222—22no—
46#11758222—22no—
47#11758222—41no—
48#11758222—42no—
49#11758222—41no—
50#11758222—42no—
51#11758222—42no—
52C2×D244—21no—
53C2×D244—41no—
54C2×C4×D61—41no—
55C2×C4×D61—42no—
56C2×Dic122—21no—
57C2×Dic122—41no—
58M16×C61—41no—
59C2×C8×C61—21no—
60C2×C8×C61—21no—
61C2×C8×C61—41no—
62C22⋊Dic61—41no—
63C4⋊Dic61—41no—
64C4×Dic61—41no—
65C16×C61—81no—
66#11758185—81no—
67C23×C61—21no—
68C23×C61#10011yescharacteristic
69C22×D61—41no—
70C22×D61—42no—
71Q8×C61—41no—
72D4×C61—41no—
73D4×C61—42no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61C22⋊C811yescharacteristic
80C2×C4×C61#9911yescharacteristic
81C22⋊D61—42no—
82C22⋊D61—44no—
83C22⋊D61—42no—
84C2×Dic61—41no—
85C2×Dic61—42no—
86C2×Dic61—81no—
87D244—22no—
88D244—42no—
89D244—41no—
90C4×D61—42no—
91C4×D61—44no—
92C4×D61—42no—
93Dic122—22no—
94Dic122—41no—
95Dic122—42no—
96C8×C61—41no—
97C8×C61—41no—
98#7347—611nomaximal, Sylow
99C22×C61—21no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—81no—
103C22×C61#32311yescharacteristic
104C2×D61—42no—
105C2×D61—161no—
106C2×D61—162no—
107C4×C61—21no—
108C4×C61—41no—
109C4×C61AΣL(1,𝔽16)11yescharacteristic
110C4×C61AΣL(1,𝔽16)11yescharacteristic
111Dic61—42no—
112Dic61—161no—
113#1794—611no—
114#1321—611no—
115#1315D6111yescharacteristic, complemented
116C2×C61—21no—
117C2×C61—41no—
118C2×C61—81no—
119C2×C61#131611yescharacteristic
120D61—82no—
121#585—611no—
122#421—1221no—
123#416—1221no—
124#410—611no—
125#408C2×D6111yescharacteristic
126#349—1221no—
127C22⋊C16—21no—
128C61#734711yescharacteristic, complemented, Sylow
1292−1+4—612no—
1302−1+4—2441no—
131H(5,𝔽2)—1221no—
132H(5,𝔽2)—2441no—
133H(5,𝔽2)—2441no—
134C2×#41—1221no—
135C2×#41—2441no—
136C2×#41—2442no—
137C2×#41C4×D6111yescharacteristic
138C2×M16D24411yescharacteristic
139C22×C8C22⋊D6111yescharacteristic
140#117—1221no—
141M32—2441no—
142C2×C16—41no—
143#104—2442no—
144#103—2441no—
145#102—2441no—
146#99—2441no—
147C22⋊C8—41no—
148#41—41no—
149#41—41no—
150#41—1222no—
151#41—1222no—
152#41—2441no—
153#41—2442no—
154#41—2442no—
155#41—2442no—
156#41—2442no—
157#41—2444no—
158#41—2442no—
159#41—2441no—
160C2×Q8—1221no—
161C2×Q8—2441no—
162C2×Q8—2442no—
163C2×Q8C8×D6111yescharacteristic
164C2×D4—21no—
165C2×D4—1221no—
166C2×D4—2441no—
167C2×D4—2442no—
168C2×D4—2444no—
169C2×D4—2442no—
170C2×D4—2441no—
171C2×D4#1175818911yescharacteristic
172C22×C4—21no—
173C22×C4—2441no—
174C22×C4—2442no—
175C22×C4#1175819811yescharacteristic
176M16—41no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—41no—
180C4⋊C4—2441no—
181C22⋊C4—2441no—
182C42—2441no—
183C16—81no—
184C16—4881no—
185C23—21no—
186C23—2441no—
187C23—2442no—
188C23#1451969311yescharacteristic
189Q8—41no—
190Q8—1222no—
191Q8—2442no—
192Q8—2441no—
193D4—41no—
194D4—42no—
195D4—1222no—
196D4—2442no—
197D4—2442no—
198D4—2444no—
199D4—2442no—
200D4—2441no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—4881no—
207C2×C4—2442no—
208C2×C4—2444no—
209C2×C4—2441no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4#1451968911yescharacteristic
213C2×C4#1451969111yescharacteristic
214C8—41no—
215C8—41no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—9761no—
221C22—9762no—
222C22—2442no—
223C22#1683948511yescharacteristic
224C4—21no—
225C4—41no—
226C4—9761no—
227C4—2442no—
228C4#1683954811yescharacteristic
229C4#1683955011yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—4882no—
234C2#2144374611yescharacteristic
subgroupG/H
centerC4#16839550
commutatorC2×Q8×C61C2×C8
Frattini#408C2×D61
FittingC61×#1315C2
socleC2×C61#1316
prime radical#16840598C4
cosocleC61×#408C22
hypercenter#1315D61
hypocenterC61#7347
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #21443757C2semidirect
3. C61×#1315C2semidirect
115. #1315D61semidirect
128. C61#7347semidirect

Maximal subgroups

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

subgroupindex
#214457822
#214437572
C61×#13152
#734761