Finite Group Databasebeta

← C59×#7829 #28419938

Subgroups — C59×#7829 #28419938

Order 15104.

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

normal subgroups only

This group has 394 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×#2734C211yesmaximal, characteristic
2C59×#2100C212yesmaximal
3C59×#2095C211yesmaximal, characteristic
4C59×#1272C211yesmaximal, characteristic
5C59×#1271C212yesmaximal
6C2×C4⋊Q8×C59—21no—
7C2×#107×C59—21no—
8C2×#103×C59—21no—
9C59×#398—21no—
10C59×#395—22no—
11C59×#391C2211yescharacteristic
12C59×#389C2212yes—
13C59×#387—22no—
14C59×#384C2211yescharacteristic
15C59×#340—22no—
16C59×#340—22no—
17C59×#336C2211yescharacteristic
18C59×#336C2212yes—
19C22×Q8×C59—21no—
20C22×Q8×C59D411yescharacteristic
21C22×C8×C59—21no—
22C22×C8×C59—22no—
23C4⋊Q8×C59—42no—
24C4⋊Q8×C59—42no—
25C2×C4⋊C4×C59—22no—
26C2×C4⋊C4×C59—22no—
27C2×C4⋊C4×C59—22no—
28C2×C4⋊C4×C59—21no—
29C2×C4⋊C4×C59—21no—
30C2×C4⋊C4×C59D412yes—
31C2×C4⋊C4×C59D412yes—
32C2×C4⋊C4×C59D411yescharacteristic
33C2×C42×C59—21no—
34C2×C42×C59C2311yescharacteristic
35#107×C59—42no—
36#103×C59—42no—
37#95×C59—21no—
38#95×C59—22no—
39#95×C59—22no—
40#95×C59—22no—
41C2×Q8×C59—21no—
42C2×Q8×C59—42no—
43C2×Q8×C59—41no—
44C2×Q8×C59—41no—
45C2×Q8×C59—81no—
46C2×Q8×C59—81no—
47C2×Q8×C59SD1612yes—
48C22×C4×C59—22no—
49C22×C4×C59—21no—
50C22×C4×C59—21no—
51C22×C4×C59—22no—
52C22×C4×C59—41no—
53C22×C4×C59C2×D411yescharacteristic
54C22×C4×C59C2×D412yes—
55C2×C8×C59—22no—
56C2×C8×C59—41no—
57C2×C8×C59—41no—
58C2×C8×C59—42no—
59C2×C8×C59—42no—
60C2×C8×C59—42no—
61C4⋊C4×C59—22no—
62C4⋊C4×C59—44no—
63C4⋊C4×C59—41no—
64C4⋊C4×C59—42no—
65C4⋊C4×C59—41no—
66C4⋊C4×C59—41no—
67C4⋊C4×C59—44no—
68C4⋊C4×C59—42no—
69C4⋊C4×C59—42no—
70C4⋊C4×C59—81no—
71C4⋊C4×C59Q1614yes—
72C42×C59—41no—
73C42×C59—42no—
74C23×C59#12011yescharacteristic
75Q8×C59—42no—
76Q8×C59—81no—
77Q8×C59—84no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—21no—
82C2×C4×C59—22no—
83C2×C4×C59—24no—
84C2×C4×C59—42no—
85C2×C4×C59—41no—
86C2×C4×C59—42no—
87C2×C4×C59—41no—
88C2×C4×C59—42no—
89C2×C4×C59—41no—
90C2×C4×C59—42no—
91C2×C4×C59—42no—
92C2×C4×C59—42no—
93C2×C4×C59—81no—
94C2×C4×C59—82no—
95C2×C4×C59C2×SD1611yescharacteristic
96C2×C4×C59C2×Q1612yes—
97C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
98C2×C4×C59#13712yes—
99C8×C59—42no—
100C8×C59—82no—
101#7829C5911yesmaximal, characteristic, direct product factor, Sylow
102C22×C59#45011yescharacteristic
103C22×C59#45112yes—
104C22×C59#45311yescharacteristic
105C22×C59#45412yes—
106C22×C59#45811yescharacteristic
107C4×C59—21no—
108C4×C59—21no—
109C4×C59—22no—
110C4×C59—22no—
111C4×C59—42no—
112C4×C59—44no—
113C4×C59—82no—
114C4×C59—81no—
115C4×C59—161no—
116#2734C2×C5911yescharacteristic
117#2100C2×C5912yes—
118#2095C2×C5911yescharacteristic
119#1272C2×C5911yescharacteristic
120#1271C2×C5912yes—
121C2×C59#161311yescharacteristic
122C2×C59#161712yes—
123C2×C59#163311yescharacteristic
124C2×C59#163712yes—
125C2×C59#165711yescharacteristic
126C2×C4⋊Q8—21no—
127C2×#107—21no—
128C2×#103—21no—
129#398—21no—
130#395—22no—
131#391C22×C5911yescharacteristic
132#389C22×C5912yes—
133#387—22no—
134#384C22×C5911yescharacteristic
135#340—22no—
136#340—22no—
137#336C22×C5911yescharacteristic
138#336C22×C5912yes—
139C59#782911yescharacteristic, direct product factor, Sylow
140C22×Q8—21no—
141C22×Q8D4×C5911yescharacteristic
142C22×C8—21no—
143C22×C8—22no—
144C4⋊Q8—42no—
145C4⋊Q8—42no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4D4×C5912yes—
152C2×C4⋊C4D4×C5912yes—
153C2×C4⋊C4D4×C5911yescharacteristic
154C2×C42—21no—
155C2×C42C23×C5911yescharacteristic
156#107—42no—
157#103—42no—
158#95—21no—
159#95—22no—
160#95—22no—
161#95—22no—
162C2×Q8—21no—
163C2×Q8—42no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—81no—
167C2×Q8—81no—
168C2×Q8SD16×C5912yes—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4C2×D4×C5911yescharacteristic
175C22×C4C2×D4×C5912yes—
176C2×C8—22no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C4⋊C4—22no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—44no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—44no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4Q16×C5914yes—
193C42—41no—
194C42—42no—
195C23#120×C5911yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—84no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—81no—
215C2×C4—82no—
216C2×C4C2×SD16×C5911yescharacteristic
217C2×C4C2×Q16×C5912yes—
218C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
219C2×C4#137×C5912yes—
220C8—42no—
221C8—82no—
222C22C59×#45011yescharacteristic
223C22C59×#45112yes—
224C22C59×#45311yescharacteristic
225C22C59×#45412yes—
226C22C59×#45811yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—44no—
233C4—82no—
234C4—81no—
235C4—161no—
236C2C59×#161311yescharacteristic
237C2C59×#161712yes—
238C2C59×#163311yescharacteristic
239C2C59×#163712yes—
240C2C59×#165711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C59#120
commutator, Frattini, cosocleC2×C42C23×C59
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
101. #7829C59direct (N × H)
139. C59#7829direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#27342
C59×#21002
C59×#20952
C59×#12722
C59×#12712
#782959