Finite Group Databasebeta

← #28489645

Subgroups — #28489645

Order 15104.

520 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 83 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#21435441C211yesmaximal, characteristic, complemented
2#21434195C212yesmaximal
3#21422710C212yesmaximal, complemented
4#21421966C211yesmaximal, characteristic, complemented
5C59×#1955C211yesmaximal, characteristic
6#16837959C2212yes—
7#16837737—22no—
8#16837698—22no—
9#16837682—22no—
10#16837643—22no—
11#16837613—22no—
12#16837607—22no—
13#16837553—22no—
14#16837502—24no—
15#16837459C2212yes—
16#16837143—24no—
17C2×C4×D4×C59C2211yescharacteristic
18C2×C4⋊C8×C59C2211yescharacteristic
19C2×C22⋊C8×C59—22no—
20C2×#97×C59C2211yescharacteristic
21C2×Dic236—22no—
22C2×#11745670—24no—
23#14273727D412yes—
24#14273727D412yes—
25#14273719—22no—
26#14273706—22no—
27#14273706—22no—
28C4×Dic118—22no—
29C4×Dic118—22no—
30#14273686—22no—
31#14273661—22no—
32#14273660—24no—
33C4⋊(C59⋊C8)—22no—
34#14273652—24no—
35#14273650—24no—
36#14273648—24no—
37C22⋊(C59⋊C8)—22no—
38#14273638D414yes—
39C22×D4×C59D411yescharacteristic
40C23×C4×C59—21no—
41C22×C8×C59—21no—
42C22×C8×C59D412yes—
43C4×D4×C59—22no—
44C4×D4×C59—22no—
45C2×C4⋊C4×C59D411yescharacteristic
46C2×C22⋊C4×C59—21no—
47C2×C42×C59C2311yescharacteristic
48C4⋊C8×C59—22no—
49C22⋊C8×C59—44no—
50#97×C59—22no—
51C24×C59—21no—
52C2×D4×C59—22no—
53C2×D4×C59—42no—
54C22×C4×C59—21no—
55C22×C4×C59—42no—
56C22×C4×C59—42no—
57C22×C4×C59—41no—
58C22×C4×C59—41no—
59C22×C4×C59C2×D411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59#4111yescharacteristic
62C2×Dic118—22no—
63C2×Dic118—22no—
64C2×C8×C59—22no—
65C2×C8×C59—22no—
66C2×C8×C59—41no—
67C2×C8×C59—41no—
68C2×C8×C59—42no—
69C4⋊C4×C59—22no—
70C22⋊C4×C59—42no—
71C42×C59C2×D412yes—
72C42×C59C2×D412yes—
73C22⋊Dic59—42no—
74#11745670—48no—
75C4⋊Dic59—22no—
76C4⋊Dic59—22no—
77C4⋊Dic59—22no—
78C4⋊Dic59—22no—
79Dic59⋊C4—42no—
80Dic59⋊C4—42no—
81C4×Dic59—42no—
82C2×C59⋊C8—24no—
83Dic236—82no—
84C23×C59—22no—
85C23×C59—42no—
86C23×C59—41no—
87C23×C59—41no—
88C23×C59—42no—
89C23×C59#12111yescharacteristic
90D4×C59—24no—
91D4×C59—42no—
92C2×C4×C59—22no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—41no—
96C2×C4×C59—42no—
97C2×C4×C59—41no—
98C2×C4×C59—82no—
99C2×C4×C59—81no—
100C2×C4×C59—81no—
101C2×C4×C59#12011yescharacteristic
102C2×C4×C59#12012yes—
103C2×C4×C59#12112yes—
104C2×C4×C59#12711yescharacteristic
105C2×Dic59—42no—
106C2×Dic59—42no—
107Dic118—44no—
108Dic118—42no—
109Dic118—42no—
110C8×C59—42no—
111C8×C59—42no—
112C59⋊C8—44no—
113#10030—591nomaximal, Sylow
114C22×C59—21no—
115C22×C59—21no—
116C22×C59—44no—
117C22×C59—42no—
118C22×C59—82no—
119C22×C59—81no—
120C22×C59—81no—
121C22×C59#39211yescharacteristic
122C22×C59#47312yes—
123C4×C59—21no—
124C4×C59—22no—
125C4×C59—22no—
126C4×C59—81no—
127C4×C59#45311yescharacteristic
128C4×C59#45411yescharacteristic
129Dic59—82no—
130Dic59—82no—
131#3249—591no—
132#3110—592no—
133#1955D5911yescharacteristic
134#1531—592no—
135#1290—591no—
136C2×C59—22no—
137C2×C59—82no—
138C2×C59#200611yescharacteristic
139C2×C59#201011yescharacteristic
140C2×C59#202011yescharacteristic
141#533—592no—
142C2×C4×D4C2×D5911yescharacteristic
143#484—1182no—
144#477—1182no—
145#474—1182no—
146#467—1182no—
147#462—1182no—
148#461—1182no—
149#450—1182no—
150#440—1184no—
151#432—592no—
152C2×C4⋊C8C2×D5911yescharacteristic
153C2×C22⋊C8—22no—
154C2×#97C2×D5911yescharacteristic
155#330—1184no—
156C59#1003011yescharacteristic, complemented, Sylow
157C22×D4D23611yescharacteristic
158C23×C4—21no—
159C2×Q16—1182no—
160C2×SD16—1184no—
161C22×C8—21no—
162C22×C8C22⋊D5912yes—
163C4⋊Q8—592no—
164C4⋊Q8—592no—
165#125—1182no—
166C22⋊Q8—1182no—
167C22⋊Q8—1182no—
168C4×Q8—1182no—
169C4×Q8—1182no—
170C4×D4—22no—
171C4×D4—22no—
172#117—1182no—
173C2×C4⋊C4D23611yescharacteristic
174C2×C22⋊C4—21no—
175C2×C42C22×D5911yescharacteristic
176#107—1184no—
177#107—1182no—
178C4⋊C8—22no—
179C4⋊C8—1182no—
180#103—1184no—
181#103—1184no—
182#102—1184no—
183C22⋊C8—44no—
184C22⋊C8—1182no—
185#97—22no—
186#97—594no—
187C24—21no—
188C2×Q8—1182no—
189C2×Q8—1182no—
190C2×D4—22no—
191C2×D4—42no—
192C22×C4—21no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4C2×D23611yescharacteristic
198C22×C4#1174568511yescharacteristic
199C22×C4C2×C22⋊D5911yescharacteristic
200Q16—4722no—
201SD16—2368no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—42no—
207C2×C8—1184no—
208C4⋊C4—22no—
209C4⋊C4—1182no—
210C4⋊C4—1182no—
211C4⋊C4—1182no—
212C4⋊C4—1182no—
213C4⋊C4—2362no—
214C4⋊C4—2362no—
215C22⋊C4—42no—
216C22⋊C4—2362no—
217C42—2362no—
218C42D4×D5912yes—
219C42D4×D5912yes—
220C23—22no—
221C23—42no—
222C23—41no—
223C23—42no—
224C23—41no—
225C23#1427370111yescharacteristic
226Q8—2364no—
227Q8—2362no—
228Q8—2362no—
229D4—24no—
230D4—42no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—82no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—2362no—
241C2×C4—2362no—
242C2×C4#1427369511yescharacteristic
243C2×C4#1427369712yes—
244C2×C4#1427370012yes—
245C2×C4#1427372311yescharacteristic
246C8—42no—
247C8—42no—
248C8—2364no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22#1683731111yescharacteristic
257C22#1683767712yes—
258C4—22no—
259C4—22no—
260C4—21no—
261C4—81no—
262C4—4722no—
263C4—4722no—
264C4#1683756911yescharacteristic
265C4#1683757411yescharacteristic
266C2—22no—
267C2—82no—
268C2#2142513711yescharacteristic
269C2#2142516311yescharacteristic
270C2#2142521711yescharacteristic
subgroupG/H
centerC22#16837311
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1955C2
socleC22×C59#392
prime radicalC22×D4×C59D4
hypercenter#1955D59
hypocenterC59#10030
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #21435441C2semidirect
3. #21422710C2semidirect
4. #21421966C2semidirect
156. C59#10030semidirect

Maximal subgroups

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

subgroupindex
#214354412
#214341952
#214227102
#214219662
C59×#19552
#1003059