Finite Group Databasebeta

← #28492780

Subgroups — #28492780

Order 15104.

364 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 81 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#21424249C211yesmaximal, characteristic
2#21422796C212yesmaximal
3#21422608C212yesmaximal
4#21421966C211yesmaximal, characteristic
5C59×#3249C211yesmaximal, characteristic
6#16837459C2212yes—
7C2×C4⋊(C59⋊C8)C2211yescharacteristic
8C2×Dic59⋊C8—22no—
9#16837248C2211yescharacteristic
10#16837148—22no—
11#16837148—22no—
12#16837139—24no—
13C59×#533C2212yes—
14C59×#477—22no—
15C59×#467—22no—
16C59×#462—22no—
17C2×C4⋊C8×C59C2211yescharacteristic
18C22×C59⋊C8—21no—
19C2×C4×Dic59—21no—
20C4⋊(C59⋊C8)—22no—
21C4⋊(C59⋊C8)—22no—
22Dic59⋊C8—44no—
23C22⋊(C59⋊C8)—22no—
24#14273638—22no—
25C59⋊#95—21no—
26C59⋊#95D412yes—
27C2×Q16×C59—22no—
28C22×C8×C59D412yes—
29C4⋊Q8×C59D412yes—
30C4⋊Q8×C59D412yes—
31#125×C59—22no—
32C22⋊Q8×C59—22no—
33C22⋊Q8×C59—22no—
34C4×Q8×C59—22no—
35C4×Q8×C59—22no—
36#117×C59—22no—
37C2×C42×C59C2311yescharacteristic
38#107×C59—22no—
39C4⋊C8×C59—22no—
40#103×C59—24no—
41C2×Q8×C59—22no—
42C2×Q8×C59—22no—
43C22×C4×C59C2×D411yescharacteristic
44C22×C4×C59C2×D411yescharacteristic
45C22×C4×C59#4111yescharacteristic
46C22×Dic59—22no—
47Q16×C59—82no—
48C2×C8×C59—22no—
49C2×C8×C59—42no—
50C4⋊C4×C59—22no—
51C4⋊C4×C59—22no—
52C4⋊C4×C59—22no—
53C4⋊C4×C59—22no—
54C4⋊C4×C59—42no—
55C4⋊C4×C59—42no—
56C22⋊C4×C59—42no—
57C42×C59—42no—
58C42×C59C2×D412yes—
59C42×C59#4112yes—
60C4×Dic59—22no—
61C4×Dic59—22no—
62C2×C59⋊C8—42no—
63C2×C59⋊C8—41no—
64C2×C59⋊C8—42no—
65C23×C59#12111yescharacteristic
66Q8×C59—42no—
67Q8×C59—42no—
68Q8×C59—82no—
69C2×C4×C59—22no—
70C2×C4×C59—21no—
71C2×C4×C59—21no—
72C2×C4×C59—41no—
73C2×C4×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59#12011yescharacteristic
76C2×C4×C59#12112yes—
77C2×C4×C59#12312yes—
78C2×C4×C59#12411yescharacteristic
79C2×Dic59—24no—
80C2×Dic59—42no—
81C2×Dic59—42no—
82C8×C59—42no—
83C59⋊C8—82no—
84C59⋊C8—81no—
85#10516—591nomaximal, Sylow
86C22×C59—21no—
87C22×C59—21no—
88C22×C59#39411yescharacteristic
89C22×C59#47312yes—
90C4×C59—22no—
91C4×C59—21no—
92C4×C59—22no—
93C4×C59—82no—
94C4×C59—82no—
95C4×C59#45311yescharacteristic
96C4×C59#45611yescharacteristic
97Dic59—44no—
98#3249D5911yescharacteristic
99#1843—591no—
100#1552—592no—
101#1506—592no—
102#1290—591no—
103C2×C59—22no—
104C2×C59#203911yescharacteristic
105C2×C59#204711yescharacteristic
106C2×C59#205311yescharacteristic
107#533C2×D5912yes—
108#477—22no—
109#467—22no—
110#462—22no—
111#432—592no—
112C2×C4⋊C8—591no—
113C2×C4⋊C8—1182no—
114C2×C4⋊C8C2×D5911yescharacteristic
115#376—591no—
116#332—1182no—
117#332—1182no—
118#328—1184no—
119C59#1051611yescharacteristic, complemented, Sylow
120C2×Q16—22no—
121C22×C8—1181no—
122C22×C8C22⋊D5912yes—
123C4⋊Q8C22⋊D5912yes—
124C4⋊Q8C22⋊D5912yes—
125#125—22no—
126C22⋊Q8—22no—
127C22⋊Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130#117—22no—
131C2×C42—1181no—
132C2×C42C22×D5911yescharacteristic
133#107—22no—
134C4⋊C8—22no—
135C4⋊C8—1182no—
136C4⋊C8—1182no—
137C4⋊C8—2364no—
138#103—24no—
139C22⋊C8—1182no—
140#97—1182no—
141#95—592no—
142#95—1181no—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—1182no—
146C22×C4D4×D5911yescharacteristic
147C22×C4#1174568711yescharacteristic
148C22×C4C2×C22⋊D5911yescharacteristic
149Q16—82no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—2362no—
153C2×C8—2361no—
154C2×C8—2362no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C42—42no—
163C42—1182no—
164C42—1182no—
165C42#1174568712yes—
166C42C2×C22⋊D5912yes—
167C23#1427369811yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—82no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—1184no—
178C2×C4—2362no—
179C2×C4—2362no—
180C2×C4#1427369611yescharacteristic
181C2×C4#1427369912yes—
182C2×C4#1427370812yes—
183C2×C4#1427371411yescharacteristic
184C8—42no—
185C8—4722no—
186C8—4721no—
187C22—21no—
188C22—21no—
189C22#1683731611yescharacteristic
190C22#1683767412yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—82no—
195C4—82no—
196C4—2364no—
197C4#1683757011yescharacteristic
198C4#1683758511yescharacteristic
199C2—22no—
200C2#2142531711yescharacteristic
201C2#2142536111yescharacteristic
202C2#2142539911yescharacteristic
subgroupG/H
centerC22#16837316
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#3249C2
socleC22×C59#394
prime radicalC23×C59#121
hypercenter#3249D59
hypocenterC59#10516
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
119. C59#10516semidirect

Maximal subgroups

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

subgroupindex
#214242492
#214227962
#214226082
#214219662
C59×#32492
#1051659