Finite Group Databasebeta

← C59×#36584 #28448693

Subgroups — C59×#36584 #28448693

Order 15104.

1590 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2859C213yesmaximal
2C59×#2571C216yesmaximal
3C59×#2509C2112yesmaximal
4C59×#2351C214yesmaximal
5Q8×C4⋊C4×C59C212yesmaximal
6C4×#125×C59C213yesmaximal
7C42×Q8×C59C211yesmaximal, characteristic
8C2×#125×C59C2213yes—
9C2×C4×Q8×C59C2212yes—
10C2×C4×Q8×C59C2214yes—
11C2×C4×Q8×C59C2211yescharacteristic
12C59×#400C22124yes—
13C59×#389C22112yes—
14C59×#389C22112yes—
15C59×#389C22112yes—
16C59×#389C22112yes—
17C59×#389C2216yes—
18C59×#387C22112yes—
19C59×#384C2216yes—
20C59×#382C22112yes—
21C59×#382C2211yescharacteristic
22C59×#382C2216yes—
23C4×C4⋊C4×C59C2216yes—
24C4×C4⋊C4×C59C22112yes—
25C4×C4⋊C4×C59C2213yes—
26C4×C4⋊C4×C59C2216yes—
27C43×C59C2213yes—
28C22×Q8×C59C2311yescharacteristic
29#125×C59—212no—
30C4×Q8×C59—28no—
31C4×Q8×C59—216no—
32C4×Q8×C59Q818yes—
33C2×C4⋊C4×C59C2312yes—
34C2×C4⋊C4×C59C2316yes—
35C2×C4⋊C4×C59C2316yes—
36C2×C4⋊C4×C59C23112yes—
37C2×C4⋊C4×C59C23112yes—
38C2×C4⋊C4×C59C23112yes—
39C2×C4⋊C4×C59C23112yes—
40C2×C4⋊C4×C59C2313yes—
41C2×C42×C59C2316yes—
42C2×C42×C59C2313yes—
43C2×C42×C59C23112yes—
44C2×C42×C59C2316yes—
45C2×C42×C59C2313yes—
46C2×C42×C59C2311yescharacteristic
47#95×C59C2314yes—
48#95×C59C2316yes—
49#95×C59C23112yes—
50#95×C59C23112yes—
51#95×C59C23124yes—
52C2×Q8×C59C2×Q814yes—
53C2×Q8×C59#4118yes—
54C22×C4×C59C2414yes—
55C22×C4×C59C2416yes—
56C22×C4×C59C24112yes—
57C22×C4×C59C2413yes—
58C22×C4×C59C2412yes—
59C22×C4×C59C2413yes—
60C22×C4×C59C2411yescharacteristic
61C4⋊C4×C59—212no—
62C4⋊C4×C59—224no—
63C4⋊C4×C59—224no—
64C4⋊C4×C59—212no—
65C4⋊C4×C59—24no—
66C4⋊C4×C59—412no—
67C4⋊C4×C59—412no—
68C4⋊C4×C59C2×Q8112yes—
69C42×C59—212no—
70C42×C59—224no—
71C42×C59—26no—
72C42×C59—46no—
73C42×C59C2×Q8112yes—
74C42×C59#4114yes—
75C23×C59C2511yescharacteristic
76Q8×C59#125116yescomplemented
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—26no—
80C2×C4×C59—24no—
81C2×C4×C59—212no—
82C2×C4×C59—26no—
83C2×C4×C59—212no—
84C2×C4×C59—26no—
85C2×C4×C59—24no—
86C2×C4×C59—26no—
87C2×C4×C59—212no—
88C2×C4×C59—24no—
89C2×C4×C59C22×Q816yes—
90C2×C4×C59C22×Q816yes—
91C2×C4×C59C22×Q812yes—
92C2×C4×C59C2×#4114yes—
93C2×C4×C59C2×#41112yes—
94C2×C4×C59C2×#4112yes—
95C2×C4×C592−1+412yes—
96#36584C5911yesmaximal, characteristic, direct product factor, Sylow
97C22×C59C23×Q811yescharacteristic
98C22×C59C22×#4112yes—
99C22×C59C22×#4111yescharacteristic
100C22×C59C2×2−1+411yescharacteristic
101C22×C59#58512yes—
102C4×C59—24no—
103C4×C59—26no—
104C4×C59—412no—
105C4×C59—44no—
106C4×C59—46no—
107C4×C59C2×#125112yes—
108C4×C59#55714yes—
109#2859C2×C5913yes—
110#2571C2×C5916yes—
111#2509C2×C59112yes—
112#2351C2×C5914yes—
113Q8×C4⋊C4C2×C5912yes—
114C4×#125C2×C5913yes—
115C42×Q8C2×C5911yescharacteristic
116C2×C59C22×#12511yescharacteristic
117C2×C59C2×#55711yescharacteristic
118C2×C59#348012yes—
119C2×C59#350411yescharacteristic
120C2×C59#351812yes—
121C2×#125C22×C5913yes—
122C2×C4×Q8C22×C5914yes—
123C2×C4×Q8C22×C5912yes—
124C2×C4×Q8C22×C5911yescharacteristic
125#400C22×C59124yes—
126#389C22×C5916yes—
127#389C22×C59112yes—
128#389C22×C59112yes—
129#389C22×C59112yes—
130#389C22×C59112yes—
131#387C22×C59112yes—
132#384C22×C5916yes—
133#382C22×C5911yescharacteristic
134#382C22×C5916yes—
135#382C22×C59112yes—
136C4×C4⋊C4C22×C5916yes—
137C4×C4⋊C4C22×C59112yes—
138C4×C4⋊C4C22×C5913yes—
139C4×C4⋊C4C22×C5916yes—
140C43C22×C5913yes—
141C59#3658411yescharacteristic, direct product factor, Sylow
142C22×Q8C23×C5911yescharacteristic
143#125—212no—
144C4×Q8—216no—
145C4×Q8—28no—
146C4×Q8Q8×C5918yes—
147C2×C4⋊C4C23×C5916yes—
148C2×C4⋊C4C23×C59112yes—
149C2×C4⋊C4C23×C5916yes—
150C2×C4⋊C4C23×C59112yes—
151C2×C4⋊C4C23×C5912yes—
152C2×C4⋊C4C23×C59112yes—
153C2×C4⋊C4C23×C59112yes—
154C2×C4⋊C4C23×C5913yes—
155C2×C42C23×C5916yes—
156C2×C42C23×C59112yes—
157C2×C42C23×C5913yes—
158C2×C42C23×C5916yes—
159C2×C42C23×C5913yes—
160C2×C42C23×C5911yescharacteristic
161#95C23×C5914yes—
162#95C23×C5916yes—
163#95C23×C59112yes—
164#95C23×C59112yes—
165#95C23×C59124yes—
166C2×Q8C2×Q8×C5914yes—
167C2×Q8#41×C5918yes—
168C22×C4C24×C5914yes—
169C22×C4C24×C5916yes—
170C22×C4C24×C59112yes—
171C22×C4C24×C5913yes—
172C22×C4C24×C5912yes—
173C22×C4C24×C5913yes—
174C22×C4C24×C5911yescharacteristic
175C4⋊C4—212no—
176C4⋊C4—224no—
177C4⋊C4—224no—
178C4⋊C4—212no—
179C4⋊C4—24no—
180C4⋊C4—412no—
181C4⋊C4—412no—
182C4⋊C4C2×Q8×C59112yes—
183C42—212no—
184C42—224no—
185C42—26no—
186C42—46no—
187C42C2×Q8×C59112yes—
188C42#41×C5914yes—
189C23C25×C5911yescharacteristic
190Q8#125×C59116yescomplemented
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—26no—
194C2×C4—24no—
195C2×C4—26no—
196C2×C4—212no—
197C2×C4—212no—
198C2×C4—26no—
199C2×C4—24no—
200C2×C4—26no—
201C2×C4—24no—
202C2×C4—212no—
203C2×C4C22×Q8×C5916yes—
204C2×C4C22×Q8×C5916yes—
205C2×C4C22×Q8×C5912yes—
206C2×C4C2×#41×C5914yes—
207C2×C4C2×#41×C59112yes—
208C2×C4C2×#41×C5912yes—
209C2×C42−1+4×C5912yes—
210C22C23×Q8×C5911yescharacteristic
211C22C22×#41×C5912yes—
212C22C22×#41×C5911yescharacteristic
213C22C2×2−1+4×C5911yescharacteristic
214C22C59×#58512yes—
215C4—24no—
216C4—26no—
217C4—44no—
218C4—46no—
219C4—412no—
220C4C2×#125×C59112yes—
221C4C59×#55714yes—
222C2C22×#125×C5911yescharacteristic
223C2C2×C59×#55711yescharacteristic
224C2C59×#348012yes—
225C2C59×#350411yescharacteristic
226C2C59×#351812yes—
subgroupG/H
center, socle, prime radicalC23×C59C25
commutator, Frattini, cosocleC23C25×C59
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C59 ◁ G

Complements

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

NH ≅ G/Ntype
76. Q8×C59#125semidirect
96. #36584C59direct (N × H)
141. C59#36584direct (N × H)
190. Q8#125×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#28592
C59×#25712
C59×#25092
C59×#23512
Q8×C4⋊C4×C592
C4×#125×C592
C42×Q8×C592
#3658459