Finite Group Databasebeta

← #28489648

Subgroups — #28489648

Order 15104.

468 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 85 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#21434222C212yesmaximal
2#21425035C211yesmaximal, characteristic
3#21422711C212yesmaximal
4#21421966C211yesmaximal, characteristic
5C59×#3249C211yesmaximal, characteristic
6C2×C4×Dic118C2211yescharacteristic
7#16837730—22no—
8#16837684—22no—
9#16837609—22no—
10#16837557—22no—
11#16837507—24no—
12#16837459C2212yes—
13C2×#14273638C2211yescharacteristic
14#16837156—22no—
15#16837144—24no—
16C59×#533C2212yes—
17C59×#477—22no—
18C59×#467—22no—
19C59×#462—22no—
20C2×C4⋊C8×C59C2211yescharacteristic
21C22×Dic118D411yescharacteristic
22C2×#11745672—24no—
23C22×C59⋊C8—21no—
24C4×Dic118—22no—
25C4×Dic118—22no—
26C2×C4⋊Dic59D411yescharacteristic
27C2×Dic59⋊C4—21no—
28C2×C4×Dic59—21no—
29#14273658—24no—
30C4⋊(C59⋊C8)—22no—
31#14273651—24no—
32#14273650—24no—
33C22⋊(C59⋊C8)—22no—
34#14273638—22no—
35#14273638D414yes—
36C2×Q16×C59—22no—
37C22×C8×C59D412yes—
38C4⋊Q8×C59D412yes—
39C4⋊Q8×C59D412yes—
40#125×C59—22no—
41C22⋊Q8×C59—22no—
42C22⋊Q8×C59—22no—
43C4×Q8×C59—22no—
44C4×Q8×C59—22no—
45#117×C59—22no—
46C2×C42×C59C2311yescharacteristic
47#107×C59—22no—
48C4⋊C8×C59—22no—
49#103×C59—24no—
50C2×Q8×C59—22no—
51C2×Q8×C59—22no—
52C22×C4×C59C2×D411yescharacteristic
53C22×C4×C59C2×D411yescharacteristic
54C22×C4×C59#4111yescharacteristic
55C22×Dic59—21no—
56C22×Dic59—21no—
57C2×Dic118—22no—
58C2×Dic118—42no—
59Q16×C59—82no—
60C2×C8×C59—22no—
61C2×C8×C59—42no—
62C4⋊C4×C59—22no—
63C4⋊C4×C59—22no—
64C4⋊C4×C59—22no—
65C4⋊C4×C59—22no—
66C4⋊C4×C59—42no—
67C4⋊C4×C59—42no—
68C22⋊C4×C59—42no—
69C42×C59—42no—
70C42×C59C2×D412yes—
71C42×C59C2×D412yes—
72#11745672—48no—
73C4⋊Dic59—22no—
74Dic59⋊C4—42no—
75C4×Dic59—41no—
76C4×Dic59—41no—
77C2×C59⋊C8—22no—
78C2×C59⋊C8—24no—
79C2×C59⋊C8—41no—
80C2×C59⋊C8—41no—
81C23×C59#12111yescharacteristic
82Q8×C59—44no—
83Q8×C59—42no—
84Q8×C59—42no—
85C2×C4×C59—22no—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59—41no—
89C2×C4×C59—42no—
90C2×C4×C59—42no—
91C2×C4×C59#12012yes—
92C2×C4×C59#12011yescharacteristic
93C2×C4×C59#12112yes—
94C2×C4×C59#12711yescharacteristic
95C2×Dic59—22no—
96C2×Dic59—41no—
97C2×Dic59—41no—
98C2×Dic59—41no—
99C2×Dic59—42no—
100Dic118—24no—
101Dic118—42no—
102C8×C59—42no—
103C59⋊C8—42no—
104C59⋊C8—44no—
105#10031—591nomaximal, Sylow
106C22×C59—21no—
107C22×C59—21no—
108C22×C59#39211yescharacteristic
109C22×C59#47312yes—
110C4×C59—21no—
111C4×C59—22no—
112C4×C59—22no—
113C4×C59—82no—
114C4×C59—82no—
115C4×C59#45511yescharacteristic
116C4×C59#45611yescharacteristic
117Dic59—42no—
118Dic59—81no—
119#3249D5911yescharacteristic
120#3113—592no—
121#1985—591no—
122#1531—592no—
123#1290—591no—
124C2×C59—22no—
125C2×C59#200711yescharacteristic
126C2×C59#201011yescharacteristic
127C2×C59#202011yescharacteristic
128#533C2×D5912yes—
129C2×C4×Q8—591no—
130#483—1182no—
131#477—22no—
132#475—1182no—
133#467—22no—
134#462—22no—
135#462—1182no—
136#451—1182no—
137#441—1184no—
138#432—592no—
139C2×C4⋊C8C2×D5911yescharacteristic
140C2×#97—591no—
141#336—1182no—
142#330—1184no—
143C59#1003111yescharacteristic, complemented, Sylow
144C22×Q8—591no—
145C2×Q16—22no—
146C2×Q16—1184no—
147C22×C8—1181no—
148C22×C8C22⋊D5912yes—
149C4⋊Q8C22⋊D5912yes—
150C4⋊Q8C22⋊D5912yes—
151#125—22no—
152C22⋊Q8—22no—
153C22⋊Q8—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—1182no—
157C4×Q8—1182no—
158#117—22no—
159C2×C4⋊C4—591no—
160C2×C4⋊C4—1181no—
161C2×C42—1181no—
162C2×C42C22×D5911yescharacteristic
163#107—22no—
164#106—1184no—
165C4⋊C8—22no—
166C4⋊C8—1182no—
167#103—24no—
168#103—1184no—
169#103—1184no—
170C22⋊C8—1182no—
171#97—594no—
172#97—1182no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—1182no—
176C2×Q8—2362no—
177C22×C4—1181no—
178C22×C4—1181no—
179C22×C4D4×D5911yescharacteristic
180C22×C4#1174568711yescharacteristic
181C22×C4C2×C22⋊D5911yescharacteristic
182Q16—82no—
183Q16—2368no—
184C2×C8—22no—
185C2×C8—42no—
186C2×C8—1182no—
187C2×C8—1184no—
188C2×C8—2361no—
189C2×C8—2361no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—1182no—
197C4⋊C4—2362no—
198C22⋊C4—42no—
199C42—42no—
200C42—2361no—
201C42—2361no—
202C42D4×D5912yes—
203C42C2×C22⋊D5912yes—
204C23#1427369811yescharacteristic
205Q8—44no—
206Q8—42no—
207Q8—42no—
208Q8—1184no—
209Q8—2362no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—1182no—
217C2×C4—2362no—
218C2×C4—2361no—
219C2×C4—2361no—
220C2×C4—2361no—
221C2×C4#1427369512yes—
222C2×C4#1427369611yescharacteristic
223C2×C4#1427369912yes—
224C2×C4#1427372311yescharacteristic
225C8—42no—
226C8—2362no—
227C8—2364no—
228C22—21no—
229C22—21no—
230C22#1683731011yescharacteristic
231C22#1683767412yes—
232C4—22no—
233C4—22no—
234C4—21no—
235C4—82no—
236C4—82no—
237C4—4721no—
238C4—2362no—
239C4#1683758011yescharacteristic
240C4#1683758511yescharacteristic
241C2—22no—
242C2#2142514311yescharacteristic
243C2#2142516011yescharacteristic
244C2#2142521511yescharacteristic
subgroupG/H
centerC22#16837310
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#3249C2
socleC22×C59#392
prime radicalC23×C59#121
hypercenter#3249D59
hypocenterC59#10031
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
143. C59#10031semidirect

Maximal subgroups

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

subgroupindex
#214342222
#214250352
#214227112
#214219662
C59×#32492
#1003159