Finite Group Databasebeta

← #28483065

Subgroups — #28483065

Order 15104.

428 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 119 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#21427282C211yesmaximal, characteristic
2#21425066C211yesmaximal, characteristic
3#21424264C212yesmaximal
4#21421978C212yesmaximal
5C2×C59×#330C211yesmaximal, characteristic
6C2×#14273661—22no—
7C2×#14273659—22no—
8C2×#14273638C2211yescharacteristic
9#16837301—22no—
10#16837288—22no—
11#16837288—22no—
12#16837272C2211yescharacteristic
13#16837268C2212yes—
14#16837164—22no—
15C2×#125×C59C2211yescharacteristic
16C2×#97×C59C2212yes—
17C59×#330C414yescomplemented
18C22×C59⋊C8—21no—
19C2×C4⋊Dic59—21no—
20C2×C4⋊Dic59—22no—
21C2×C4⋊Dic59—22no—
22C2×C4⋊Dic59D412yes—
23C2×C4⋊Dic59D412yes—
24C2×C4×Dic59—22no—
25#14273661—44no—
26#14273659—44no—
27#14273638—22no—
28C59⋊#95—22no—
29C59⋊#95—22no—
30C59⋊#95—22no—
31C59⋊#95—22no—
32C22×C8×C59—22no—
33#125×C59—22no—
34#125×C59C2×C412yes—
35#125×C59Q812yes—
36C2×C4⋊C4×C59—22no—
37C2×C4⋊C4×C59D412yes—
38C2×C42×C59C2311yescharacteristic
39#97×C59—22no—
40#97×C59C2×C414yes—
41C22×C4×C59—22no—
42C22×C4×C59C2×D411yescharacteristic
43C22×C4×C59C2×D412yes—
44C22×Dic59—22no—
45C22×Dic59—22no—
46C22×Dic59—41no—
47C2×C8×C59—24no—
48C2×C8×C59—24no—
49C2×C8×C59—24no—
50C4⋊C4×C59—24no—
51C4⋊C4×C59—24no—
52C4⋊C4×C59—22no—
53C4⋊C4×C59C4⋊C414yes—
54C42×C59C22×C411yescharacteristic
55C42×C59C2×Q811yescharacteristic
56C42×C59#4112yes—
57C4⋊Dic59—42no—
58C4⋊Dic59—42no—
59C4⋊Dic59—42no—
60C4⋊Dic59—42no—
61C4⋊Dic59—42no—
62C4⋊Dic59—82no—
63C4×Dic59—82no—
64C2×C59⋊C8—22no—
65C2×C59⋊C8—41no—
66C2×C59⋊C8—41no—
67C23×C59#12011yescharacteristic
68C2×C4×C59—22no—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—22no—
72C2×C4×C59—24no—
73C2×C4×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59C2×C4⋊C411yescharacteristic
76C2×C4×C59C4×D412yes—
77C2×C4×C59C22⋊Q812yes—
78C2×C4×C59#12311yescharacteristic
79C2×Dic59—42no—
80C2×Dic59—42no—
81C2×Dic59—42no—
82C2×Dic59—42no—
83C2×Dic59—42no—
84C2×Dic59—42no—
85C2×Dic59—82no—
86C2×Dic59—81no—
87C8×C59—28no—
88C59⋊C8—42no—
89#8913—591nomaximal, Sylow
90C22×C59#38511yescharacteristic
91C22×C59#45312yes—
92C22×C59#45411yescharacteristic
93C22×C59#45612yes—
94C22×C59#45611yescharacteristic
95C4×C59—21no—
96C4×C59—21no—
97C4×C59—22no—
98C4×C59—22no—
99C4×C59—44no—
100Dic59—82no—
101Dic59—82no—
102Dic59—161no—
103#2382—591no—
104#1992—591no—
105#1847—592no—
106C2×#330D5911yescharacteristic
107#1295—592no—
108C2×C59#165611yescharacteristic
109C2×C59#166012yes—
110C2×C59#166311yescharacteristic
111C2×C59#185711yescharacteristic
112C2×C59#185912yes—
113C2×#125C2×D5911yescharacteristic
114C2×#107—1182no—
115C2×#106—1182no—
116C2×#97—591no—
117C2×#97C2×D5912yes—
118#389—1182no—
119#387—1182no—
120#387—1182no—
121#384—591no—
122#382—592no—
123#340—1182no—
124#330Dic5914yescomplemented
125C59#891311yescharacteristic, complemented, Sylow
126C22×C8—22no—
127C22×C8—1181no—
128#125—22no—
129#125Dic11812yes—
130#125C2×Dic5912yes—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—592no—
134C2×C4⋊C4—1182no—
135C2×C4⋊C4—1181no—
136C2×C4⋊C4—1182no—
137C2×C4⋊C4D23612yes—
138C2×C42—1182no—
139C2×C42C22×D5911yescharacteristic
140#107—2364no—
141#106—2364no—
142#97—22no—
143#97—1182no—
144#97C2×Dic5914yes—
145#95—1182no—
146#95—1182no—
147#95—1182no—
148#95—1182no—
149C22×C4—22no—
150C22×C4—1182no—
151C22×C4—1182no—
152C22×C4—2361no—
153C22×C4C2×D23611yescharacteristic
154C22×C4D4×D5912yes—
155C2×C8—24no—
156C2×C8—24no—
157C2×C8—24no—
158C2×C8—1182no—
159C2×C8—2361no—
160C2×C8—2361no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—4722no—
165C4⋊C4—2362no—
166C4⋊C4—2362no—
167C4⋊C4—2362no—
168C4⋊C4—2362no—
169C4⋊C4—2362no—
170C4⋊C4C4⋊Dic5914yes—
171C42—4722no—
172C42C2×Dic11811yescharacteristic
173C42#1174568712yes—
174C42C22×Dic5911yescharacteristic
175C23#1427369711yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—4722no—
184C2×C4—4721no—
185C2×C4—2362no—
186C2×C4—2362no—
187C2×C4—2362no—
188C2×C4—2362no—
189C2×C4—2362no—
190C2×C4—2362no—
191C2×C4C2×C4⋊Dic5911yescharacteristic
192C2×C4D4×Dic5912yes—
193C2×C4#1427370412yes—
194C2×C4#1427371111yescharacteristic
195C8—28no—
196C8—2362no—
197C22#1683727711yescharacteristic
198C22#1683757112yes—
199C22#1683757711yescharacteristic
200C22#1683758612yes—
201C22#1683758711yescharacteristic
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—9441no—
208C4—4722no—
209C4—4722no—
210C2#2142339111yescharacteristic
211C2#2142340912yes—
212C2#2142342511yescharacteristic
213C2#2142431311yescharacteristic
214C2#2142432412yes—
subgroupG/H
centerC23#14273697
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC2×C59×#330C2
socle, prime radicalC23×C59#120
cosocleC2×C42×C59C23
hypercenterC2×#330D59
hypocenterC59#8913
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
17. C59×#330C4semidirect
124. #330Dic59semidirect
125. C59#8913semidirect

Maximal subgroups

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

subgroupindex
#214272822
#214250662
#214242642
#214219782
C2×C59×#3302
#891359