Finite Group Databasebeta

← #30594820

Subgroups — #30594820

Order 15616.

318 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 38 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#21445783C211yesmaximal, characteristic
4#16840658—21no—
5C22⋊#11758187—21no—
6#16839779—21no—
7#16839758—21no—
8#16839736C411yescharacteristic
9#16839729C2211yescharacteristic
10C61×#585C411yescharacteristic
11#14519851—41no—
12C2×#11758187—41no—
13C2×#11758194D411yescharacteristic
14C22×#92418D411yescharacteristic
15#14519736—21no—
16#14519704—42no—
17#14519701—41no—
18#14519698—41no—
19#14519692—41no—
20C22⋊#92418—41no—
212−1+4×C61—21no—
222−1+4×C61—41no—
23H(5,𝔽2)×C61—41no—
24H(5,𝔽2)×C61—41no—
25H(5,𝔽2)×C61C812yes—
26C2×#41×C61—21no—
27C2×#41×C61—41no—
28C2×#41×C61—42no—
29C2×#41×C61C2×C411yescharacteristic
30#41×C61—22no—
31#41×C61—22no—
32#41×C61—41no—
33#41×C61—42no—
34#41×C61—41no—
35#41×C61—41no—
36#41×C61—42no—
37#41×C61—42no—
38#41×C61—44no—
39#41×C61—42no—
40#41×C61—41no—
41#41×C61—42no—
42C2×Q8×C61—21no—
43C2×Q8×C61—42no—
44C2×Q8×C61—41no—
45C2×Q8×C61M1611yescharacteristic
46C2×D4×C61—21no—
47C2×D4×C61—21no—
48C2×D4×C61—42no—
49C2×D4×C61—44no—
50C2×D4×C61—41no—
51C2×D4×C61—42no—
52C2×D4×C61—41no—
53C2×D4×C61C2×C811yescharacteristic
54C22×C4×C61—21no—
55C22×C4×C61—41no—
56C22×C4×C61—42no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22⋊Dic61—41no—
59C4⋊Dic61—41no—
60C4×Dic61—41no—
61#11758194—41no—
62C2×#92418—21no—
63C2×#92418—21no—
64C2×#92418—41no—
65#11758187—81no—
66#11758187—81no—
67C23×C61—21no—
68C23×C61—41no—
69C23×C61—42no—
70C23×C61#10011yescharacteristic
71Q8×C61—22no—
72Q8×C61—41no—
73Q8×C61—42no—
74Q8×C61—41no—
75D4×C61—22no—
76D4×C61—41no—
77D4×C61—42no—
78D4×C61—42no—
79D4×C61—42no—
80D4×C61—44no—
81D4×C61—42no—
82D4×C61—41no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—42no—
87C2×C4×C61—41no—
88C2×C4×C61—44no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61C22⋊C811yescharacteristic
94C2×C4×C61#9911yescharacteristic
95C2×Dic61—81no—
96#92418—41no—
97#92418—41no—
98#7346—611nomaximal, Sylow
99C22×C61—21no—
100C22×C61—41no—
101C22×C61—42no—
102C22×C61—41no—
103C22×C61—81no—
104C22×C61—161no—
105C22×C61—162no—
106C22×C61#32311yescharacteristic
107C4×C61—21no—
108C4×C61—41no—
109C4×C61—42no—
110C4×C61AΣL(1,𝔽16)11yescharacteristic
111C4×C61AΣL(1,𝔽16)11yescharacteristic
112Dic61—161no—
113#1794—611no—
114#1321—611no—
115#1315—611no—
116C2×C61—21no—
117C2×C61—41no—
118C2×C61—81no—
119C2×C61—82no—
120C2×C61#131611yescharacteristic
121#585#692311yescharacteristic
122#421—1221no—
123#416—1221no—
124#410—611no—
125#408—611no—
126#349—1221no—
127C22⋊C16—1221no—
128C61#734611yescharacteristic, complemented, Sylow
1292−1+4—21no—
1302−1+4—41no—
131H(5,𝔽2)—41no—
132H(5,𝔽2)—41no—
133H(5,𝔽2)#9242012yes—
134C2×#41—21no—
135C2×#41—41no—
136C2×#41—42no—
137C2×#41C2×#692311yescharacteristic
138C2×M16—611no—
139C22×C8—611no—
140#117—1221no—
141M32—2441no—
142C2×C16—2441no—
143#104—2442no—
144#103—2441no—
145#102—2441no—
146#99—2441no—
147C22⋊C8—2441no—
148#41—22no—
149#41—22no—
150#41—41no—
151#41—42no—
152#41—41no—
153#41—41no—
154#41—42no—
155#41—42no—
156#41—44no—
157#41—42no—
158#41—41no—
159#41—42no—
160C2×Q8—21no—
161C2×Q8—42no—
162C2×Q8—41no—
163C2×Q8#1175821711yescharacteristic
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—42no—
167C2×D4—44no—
168C2×D4—41no—
169C2×D4—42no—
170C2×D4—41no—
171C2×D4C2×#9242011yescharacteristic
172C22×C4—21no—
173C22×C4—41no—
174C22×C4—42no—
175C22×C4C22⋊#692311yescharacteristic
176M16—2441no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—2441no—
180C4⋊C4—2441no—
181C22⋊C4—2441no—
182C42—2441no—
183C16—4881no—
184C16—4881no—
185C23—21no—
186C23—41no—
187C23—42no—
188C23#1451983711yescharacteristic
189Q8—22no—
190Q8—41no—
191Q8—42no—
192Q8—41no—
193D4—22no—
194D4—41no—
195D4—42no—
196D4—42no—
197D4—42no—
198D4—44no—
199D4—42no—
200D4—41no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—44no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—4881no—
212C2×C4C22⋊#9242011yescharacteristic
213C2×C4#1451983511yescharacteristic
214C8—2441no—
215C8—2441no—
216C22—21no—
217C22—41no—
218C22—42no—
219C22—41no—
220C22—81no—
221C22—161no—
222C22—162no—
223C22#1684060511yescharacteristic
224C4—21no—
225C4—41no—
226C4—42no—
227C4—9761no—
228C4#1684066211yescharacteristic
229C4#1684066211yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—82no—
234C2#2146074311yescharacteristic
subgroupG/H
centerC4#16840662
commutatorC2×D4×C61C2×C8
FrattiniC2×#41C2×#6923
Fitting, prime radicalC61×#585C4
socleC2×C61#1316
cosocle#16839729C22
hypercenter#585#6923
hypocenterC61#7346
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #21460753C2semidirect
2. #21460741C2semidirect
128. C61#7346semidirect

Maximal subgroups

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

subgroupindex
#214607532
#214607412
#214457832
#734661