Finite Group Databasebeta

← #30594823

Subgroups — #30594823

Order 15616.

318 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460753C211yesmaximal, characteristic, complemented
2#21460741C211yesmaximal, characteristic, complemented
3#21445785C211yesmaximal, characteristic
4#16840658—21no—
5C22⋊#11758187—21no—
6#16840598C411yescharacteristic
7#16839780—21no—
8#16839756—21no—
9#16839729C2211yescharacteristic
10C61×#410C411yescharacteristic
11#14519851—41no—
12C2×#11758187—41no—
13#14519825C812yes—
14#14519824—41no—
15#14519823—41no—
16#14519822—21no—
17#14519822—41no—
18C2×#11758222—21no—
19C2×#11758222—41no—
20#41×D61—42no—
21C2×#11758194D411yescharacteristic
22C22×#92418D411yescharacteristic
23#14519705—42no—
24#14519700—41no—
25#14519697—41no—
26C22⋊#92418—41no—
27C2×#41×C61C2×C411yescharacteristic
28#117×C61—21no—
29#99×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—
58C4⋊C4×C61—41no—
59C22⋊C4×C61—41no—
60C42×C61—41no—
61#11758194—41no—
62C2×#92418—21no—
63C2×#92418—21no—
64C2×#92418—41no—
65#11758187—81no—
66#11758187—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×C61—81no—
80C2×C4×C61C22⋊C811yescharacteristic
81C2×C4×C61#9911yescharacteristic
82C22⋊D61—42no—
83C22⋊D61—44no—
84C22⋊D61—42no—
85C2×Dic61—41no—
86C2×Dic61—42no—
87D244—22no—
88D244—42no—
89D244—41no—
90C4×D61—42no—
91C4×D61—44no—
92C4×D61—42no—
93Dic122—22no—
94Dic122—41no—
95Dic122—42no—
96#92418—41no—
97#92418—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×C61—161no—
110C4×C61AΣL(1,𝔽16)11yescharacteristic
111C4×C61AΣL(1,𝔽16)11yescharacteristic
112Dic61—42no—
113#1794—611no—
114#1321—611no—
115#1315—611no—
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#692311yescharacteristic
125#408—611no—
126#349—1221no—
127C22⋊C16—1221no—
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×#41C2×#692311yescharacteristic
138C2×M16—611no—
139C22×C8—611no—
140#117—21no—
141M32—2441no—
142C2×C16—2441no—
143#104—2442no—
144#103—2441no—
145#102—2441no—
146#99—41no—
147C22⋊C8—2441no—
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×Q8D61⋊C811yescharacteristic
164C2×D4—21no—
165C2×D4—1221no—
166C2×D4—2441no—
167C2×D4—2442no—
168C2×D4—2444no—
169C2×D4—2442no—
170C2×D4—2441no—
171C2×D4#1175821311yescharacteristic
172C22×C4—21no—
173C22×C4—2441no—
174C22×C4—2442no—
175C22×C4C22⋊#692311yescharacteristic
176M16—2441no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—2441no—
180C4⋊C4—41no—
181C22⋊C4—41no—
182C42—41no—
183C16—4881no—
184C16—4881no—
185C23—21no—
186C23—2441no—
187C23—2442no—
188C23#1451983711yescharacteristic
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—81no—
207C2×C4—2442no—
208C2×C4—2444no—
209C2×C4—2441no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4#1451983411yescharacteristic
213C2×C4#1451983611yescharacteristic
214C8—2441no—
215C8—2441no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—9761no—
221C22—9762no—
222C22—2442no—
223C22#1684060611yescharacteristic
224C4—21no—
225C4—41no—
226C4—161no—
227C4—2442no—
228C4#1684066311yescharacteristic
229C4#1684066311yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—4882no—
234C2#2146074411yescharacteristic
subgroupG/H
centerC4#16840663
commutatorC2×Q8×C61C2×C8
FrattiniC2×#41C2×#6923
FittingC61×#410C4
socleC2×C61#1316
prime radical#16840598C4
cosocle#16839729C22
hypercenter#410#6923
hypocenterC61#7347
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #21460753C2semidirect
2. #21460741C2semidirect
128. C61#7347semidirect

Maximal subgroups

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

subgroupindex
#214607532
#214607412
#214457852
#734761