Finite Group Databasebeta

← #28489682

Subgroups — #28489682

Order 15104.

476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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#21434131C212yesmaximal
2#21425036C211yesmaximal, characteristic
3#21422499C212yesmaximal
4#21421927C211yesmaximal, characteristic
5C59×#3162C211yesmaximal, characteristic
6C2×C4×Dic118C2211yescharacteristic
7#16837735—22no—
8#16837694—22no—
9#16837609—22no—
10#16837557—22no—
11C4×#11745672—24no—
12#16837455C2212yes—
13C2×C4⋊(C59⋊C8)C2211yescharacteristic
14#16837156—22no—
15Q8⋊(C59⋊C8)—24no—
16C59×#533C2212yes—
17C59×#501—22no—
18C59×#501—22no—
19C59×#427—22no—
20C2×#97×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#14273660—24no—
30C4⋊(C59⋊C8)—22no—
31C4⋊(C59⋊C8)—22no—
32#14273651—24no—
33#14273650—24no—
34C22⋊(C59⋊C8)—22no—
35C4×C59⋊C8D414yes—
36C22×C8×C59D412yes—
37C4⋊Q8×C59D412yes—
38C4⋊Q8×C59D412yes—
39#125×C59—22no—
40C22⋊Q8×C59—22no—
41C22⋊Q8×C59—22no—
42C4×Q8×C59—22no—
43C4×Q8×C59—22no—
44#117×C59—22no—
45C2×C42×C59C2311yescharacteristic
46#107×C59—22no—
47#107×C59—22no—
48#106×C59—24no—
49#97×C59—22no—
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—
59C2×C8×C59—22no—
60C2×C8×C59—22no—
61C2×C8×C59Q1614yescomplemented
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—24no—
78C2×C59⋊C8—41no—
79C2×C59⋊C8—42no—
80C23×C59#12111yescharacteristic
81Q8×C59—44no—
82Q8×C59—44no—
83C2×C4×C59—41no—
84C2×C4×C59—41no—
85C2×C4×C59—42no—
86C2×C4×C59—42no—
87C2×C4×C59#12012yes—
88C2×C4×C59#12011yescharacteristic
89C2×C4×C59#12112yes—
90C2×C4×C59#12711yescharacteristic
91C2×C4×C59C2×Q1612yes—
92C2×C4×C59#13712yes—
93C2×Dic59—22no—
94C2×Dic59—41no—
95C2×Dic59—41no—
96C2×Dic59—42no—
97C2×Dic59—41no—
98Dic118—24no—
99Dic118—42no—
100C8×C59—24no—
101C59⋊C8—44no—
102C59⋊C8—81no—
103#10037—591nomaximal, Sylow
104C22×C59—21no—
105C22×C59—21no—
106C22×C59#39211yescharacteristic
107C22×C59#46212yes—
108C4×C59—22no—
109C4×C59—22no—
110C4×C59—82no—
111C4×C59—82no—
112C4×C59#45112yes—
113C4×C59#49411yescharacteristic
114C4×C59#49711yescharacteristic
115Dic59—42no—
116Dic59—81no—
117#3162D5911yescharacteristic
118#3104—592no—
119#1985—591no—
120#1481—592no—
121#1275—591no—
122C2×C59—22no—
123C2×C59#201011yescharacteristic
124C2×C59#201611yescharacteristic
125C2×C59#201711yescharacteristic
126#533C2×D5912yes—
127C2×C4×Q8—591no—
128#501—22no—
129#501—22no—
130#484—1182no—
131#477—1182no—
132#462—1182no—
133#451—1182no—
134C4×Q16—1184no—
135#431—592no—
136#427—22no—
137C2×C4⋊C8—591no—
138C2×#97C2×D5911yescharacteristic
139#336—1182no—
140Q8⋊C8—1184no—
141C59#1003711yescharacteristic, complemented, Sylow
142C22×Q8—591no—
143C2×Q16—1184no—
144C22×C8—1181no—
145C22×C8C22⋊D5912yes—
146C4⋊Q8C22⋊D5912yes—
147C4⋊Q8C22⋊D5912yes—
148#125—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—1182no—
154C4×Q8—1182no—
155#117—22no—
156C2×C4⋊C4—591no—
157C2×C4⋊C4—1181no—
158C2×C42—1181no—
159C2×C42C22×D5911yescharacteristic
160#107—22no—
161#107—22no—
162#107—1184no—
163#106—24no—
164C4⋊C8—1182no—
165C4⋊C8—1182no—
166#103—1184no—
167#103—1184no—
168C22⋊C8—1182no—
169#97—22no—
170C4×C8—594no—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—1182no—
174C2×Q8—2362no—
175C22×C4—1181no—
176C22×C4—1181no—
177C22×C4D4×D5911yescharacteristic
178C22×C4#1174568711yescharacteristic
179C22×C4C2×C22⋊D5911yescharacteristic
180Q16—2368no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—1184no—
184C2×C8—2361no—
185C2×C8—2362no—
186C2×C8#1174567214yescomplemented
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—1182no—
194C4⋊C4—2362no—
195C22⋊C4—42no—
196C42—42no—
197C42—2361no—
198C42—2361no—
199C42D4×D5912yes—
200C42C2×C22⋊D5912yes—
201C23#1427369811yescharacteristic
202Q8—44no—
203Q8—44no—
204Q8—1184no—
205Q8—2362no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—1182no—
211C2×C4—2362no—
212C2×C4—2361no—
213C2×C4—2361no—
214C2×C4—2361no—
215C2×C4#1427369512yes—
216C2×C4#1427369611yescharacteristic
217C2×C4#1427369912yes—
218C2×C4#1427372311yescharacteristic
219C2×C4C2×#1174567212yes—
220C2×C4#1427375812yes—
221C8—24no—
222C8—4721no—
223C8—2364no—
224C22—21no—
225C22—21no—
226C22#1683731011yescharacteristic
227C22#1683760912yes—
228C4—22no—
229C4—22no—
230C4—82no—
231C4—82no—
232C4—4721no—
233C4—2362no—
234C4#1683755812yes—
235C4#1683778111yescharacteristic
236C4#1683779411yescharacteristic
237C2—22no—
238C2#2142516011yescharacteristic
239C2#2142519611yescharacteristic
240C2#2142519911yescharacteristic
subgroupG/H
centerC2×C4#14273723
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#3162C2
socleC22×C59#392
prime radicalC23×C59#121
hypercenter#3162D59
hypocenterC59#10037
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
61. C2×C8×C59Q16semidirect
141. C59#10037semidirect
186. C2×C8#11745672semidirect

Maximal subgroups

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

subgroupindex
#214341312
#214250362
#214224992
#214219272
C59×#31622
#1003759