Finite Group Databasebeta

← C59×#7826 #28419935

Subgroups — C59×#7826 #28419935

Order 15104.

462 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C59×#2683C211yesmaximal, characteristic
2C59×#2100C212yesmaximal, complemented
3C59×#2094C211yesmaximal, characteristic
4C59×#1271C212yesmaximal, complemented
5C59×#1270C211yesmaximal, characteristic
6C2×C22⋊Q8×C59—22no—
7C2×#106×C59—21no—
8C2×#102×C59—21no—
9C59×#396—22no—
10C59×#395—21no—
11C59×#390C2211yescharacteristic
12C59×#389C2212yes—
13C59×#386—21no—
14C59×#384C2211yescharacteristic
15C59×#340—22no—
16C59×#340—22no—
17C59×#336C2212yes—
18C59×#336C2211yescharacteristic
19C22×Q8×C59—21no—
20C22×D4×C59D411yescharacteristic
21C23×C4×C59—21no—
22C22×C8×C59—21no—
23C22×C8×C59—22no—
24C22⋊Q8×C59—44no—
25C22⋊Q8×C59—44no—
26C2×C4⋊C4×C59—22no—
27C2×C4⋊C4×C59—22no—
28C2×C4⋊C4×C59—22no—
29C2×C4⋊C4×C59—21no—
30C2×C4⋊C4×C59D412yes—
31C2×C4⋊C4×C59D412yes—
32C2×C4⋊C4×C59D411yescharacteristic
33C2×C22⋊C4×C59—22no—
34C2×C22⋊C4×C59—22no—
35C2×C22⋊C4×C59—21no—
36C2×C42×C59C2311yescharacteristic
37#106×C59—42no—
38#102×C59—42no—
39#95×C59—21no—
40#95×C59—22no—
41C24×C59—21no—
42C2×Q8×C59—44no—
43C2×Q8×C59—81no—
44C2×D4×C59—21no—
45C2×D4×C59—41no—
46C2×D4×C59—41no—
47C2×D4×C59Q1612yes—
48C22×C4×C59—22no—
49C22×C4×C59—22no—
50C22×C4×C59—21no—
51C22×C4×C59—44no—
52C22×C4×C59—41no—
53C22×C4×C59—81no—
54C22×C4×C59C2×D412yes—
55C22×C4×C59C2×D411yescharacteristic
56C2×C8×C59—22no—
57C2×C8×C59—41no—
58C2×C8×C59—41no—
59C2×C8×C59—42no—
60C2×C8×C59—42no—
61C2×C8×C59—42no—
62C4⋊C4×C59—22no—
63C4⋊C4×C59—44no—
64C4⋊C4×C59—41no—
65C4⋊C4×C59—42no—
66C4⋊C4×C59—41no—
67C4⋊C4×C59—41no—
68C4⋊C4×C59—44no—
69C4⋊C4×C59—42no—
70C4⋊C4×C59—42no—
71C4⋊C4×C59SD1614yes—
72C22⋊C4×C59—44no—
73C22⋊C4×C59—42no—
74C22⋊C4×C59—42no—
75C22⋊C4×C59—81no—
76C42×C59—41no—
77C23×C59—22no—
78C23×C59—42no—
79C23×C59—41no—
80C23×C59—42no—
81C23×C59—41no—
82C23×C59#12011yescharacteristic
83Q8×C59—84no—
84D4×C59—42no—
85D4×C59—81no—
86C2×C4×C59—21no—
87C2×C4×C59—22no—
88C2×C4×C59—22no—
89C2×C4×C59—21no—
90C2×C4×C59—24no—
91C2×C4×C59—42no—
92C2×C4×C59—42no—
93C2×C4×C59—42no—
94C2×C4×C59—42no—
95C2×C4×C59—41no—
96C2×C4×C59—42no—
97C2×C4×C59—42no—
98C2×C4×C59—84no—
99C2×C4×C59—81no—
100C2×C4×C59—82no—
101C2×C4×C59C2×SD1612yes—
102C2×C4×C59C2×Q1611yescharacteristic
103C2×C4×C59AGL(1,ℤ/8)12yes—
104C2×C4×C59#13711yescharacteristic
105C8×C59—42no—
106C8×C59—82no—
107#7826C5911yesmaximal, characteristic, direct product factor, Sylow
108C22×C59—42no—
109C22×C59—44no—
110C22×C59—82no—
111C22×C59—81no—
112C22×C59—81no—
113C22×C59#45012yes—
114C22×C59#45111yescharacteristic
115C22×C59#45311yescharacteristic
116C22×C59#45412yes—
117C22×C59#45811yescharacteristic
118C4×C59—21no—
119C4×C59—21no—
120C4×C59—22no—
121C4×C59—22no—
122C4×C59—44no—
123C4×C59—82no—
124C4×C59—81no—
125C4×C59—161no—
126#2683C2×C5911yescharacteristic
127#2100C2×C5912yescomplemented
128#2094C2×C5911yescharacteristic
129#1271C2×C5912yescomplemented
130#1270C2×C5911yescharacteristic
131C2×C59—82no—
132C2×C59#161411yescharacteristic
133C2×C59#161612yes—
134C2×C59#162911yescharacteristic
135C2×C59#163712yes—
136C2×C59#165711yescharacteristic
137C2×C22⋊Q8—22no—
138C2×#106—21no—
139C2×#102—21no—
140#396—22no—
141#395—21no—
142#390C22×C5911yescharacteristic
143#389C22×C5912yes—
144#386—21no—
145#384C22×C5911yescharacteristic
146#340—22no—
147#340—22no—
148#336C22×C5911yescharacteristic
149#336C22×C5912yes—
150C59#782611yescharacteristic, direct product factor, Sylow
151C22×Q8—21no—
152C22×D4D4×C5911yescharacteristic
153C23×C4—21no—
154C22×C8—21no—
155C22×C8—22no—
156C22⋊Q8—44no—
157C22⋊Q8—44no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4D4×C5912yes—
163C2×C4⋊C4D4×C5912yes—
164C2×C4⋊C4D4×C5911yescharacteristic
165C2×C22⋊C4—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—21no—
168C2×C42C23×C5911yescharacteristic
169#106—42no—
170#102—42no—
171#95—21no—
172#95—22no—
173C24—21no—
174C2×Q8—44no—
175C2×Q8—81no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4Q16×C5912yes—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—44no—
184C22×C4—41no—
185C22×C4—81no—
186C22×C4C2×D4×C5912yes—
187C22×C4C2×D4×C5911yescharacteristic
188C2×C8—22no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—42no—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—44no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—44no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4SD16×C5914yes—
204C22⋊C4—44no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—81no—
208C42—41no—
209C23—22no—
210C23—42no—
211C23—41no—
212C23—42no—
213C23—41no—
214C23#120×C5911yescharacteristic
215Q8—84no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—24no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4C2×SD16×C5912yes—
234C2×C4C2×Q16×C5911yescharacteristic
235C2×C4AGL(1,ℤ/8)×C5912yes—
236C2×C4#137×C5911yescharacteristic
237C8—42no—
238C8—82no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22C59×#45012yes—
245C22C59×#45111yescharacteristic
246C22C59×#45311yescharacteristic
247C22C59×#45412yes—
248C22C59×#45811yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—44no—
254C4—82no—
255C4—81no—
256C4—161no—
257C2—82no—
258C2C59×#161411yescharacteristic
259C2C59×#161612yes—
260C2C59×#162911yescharacteristic
261C2C59×#163712yes—
262C2C59×#165711yescharacteristic
subgroupG/H
center, socleC23×C59#120
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC22×D4×C59D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#2100C2semidirect
4. C59×#1271C2semidirect
107. #7826C59direct (N × H)
127. #2100C2×C59semidirect
129. #1271C2×C59semidirect
150. C59#7826direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#26832
C59×#21002
C59×#20942
C59×#12712
C59×#12702
#782659