Finite Group Databasebeta

← #28499889

Subgroups — #28499889

Order 15104.

280 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 61 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#21434498C211yesmaximal, characteristic
2#21425906C212yesmaximal, complemented
3#21422131C211yesmaximal, characteristic, complemented
4#21422128C212yesmaximal, complemented
5C59×#1356C211yesmaximal, characteristic, complemented
6#16837953C411yescharacteristic
7#125×D59C411yescharacteristic
8#16837770C411yescharacteristic
9#16837768C411yescharacteristic
10#16837767C2211yescharacteristic
11#16837758—22no—
12#16837402—22no—
13#16837354C2211yescharacteristic
14#16837222—22no—
15#16837183—22no—
16#16837180C2212yes—
17C59×#491C2211yescharacteristic
18C59×#347C2212yes—
19C2×#11745689—21no—
20C2×#11745659D412yes—
21#14273724C2×C411yescharacteristic
22#14273719C2×C411yescharacteristic
23#14273718—21no—
24#14273717—41no—
25#14273716—21no—
26#14273702—41no—
27#14273689—41no—
28C4⋊C4×D59—21no—
29C4⋊C4×D59—41no—
30C42×D59C2×C411yescharacteristic
31#14273667—22no—
32#14273651—22no—
33#14273649—22no—
34#14273647—22no—
35#14273638C2×C411yescharacteristic
36C8×Dic59D412yes—
37C4⋊Q8×C59C2×C411yescharacteristic
38#125×C59C2×C411yescharacteristic
39M32×C59—22no—
40#103×C59—22no—
41#97×C59C2311yescharacteristic
42C2×Q8×C59—21no—
43#11745689—44no—
44C2×D236—21no—
45C2×D236—41no—
46C2×D236—41no—
47C2×C4×D59—21no—
48C2×C4×D59—41no—
49C2×C4×D59—41no—
50C2×C4×D59C22⋊C411yescharacteristic
51C2×C8×C59C2×D412yes—
52C4⋊C4×C59—21no—
53C4⋊C4×C59—41no—
54C4⋊C4×C59—41no—
55C42×C59C22×C411yescharacteristic
56(C2×D59)⋊C4—42no—
57C4⋊Dic59—21no—
58C4⋊Dic59—41no—
59Dic59⋊C4—41no—
60Dic59⋊C4—41no—
61Dic59⋊C4—41no—
62C4×Dic59—21no—
63C4×Dic59C22⋊C411yescharacteristic
64C2×C59⋊C8C22⋊C412yes—
65#11745659—42no—
66C16×C59—42no—
67C59⋊C16—42no—
68C22×D59—41no—
69C22×D59#10011yescharacteristic
70Q8×C59—42no—
71C2×C4×C59—21no—
72C2×C4×C59—41no—
73C2×C4×C59—41no—
74C2×C4×C59C2×C22⋊C411yescharacteristic
75C2×Dic59—21no—
76C2×Dic59—41no—
77C2×Dic59#10011yescharacteristic
78D236—42no—
79D236—82no—
80D236—82no—
81C4×D59—22no—
82C4×D59—82no—
83C4×D59—81no—
84C4×D59—82no—
85C8×C59—22no—
86C59⋊C8—22no—
87#11917—591nomaximal, Sylow
88C22×C59C2×#10011yescharacteristic
89C2×D59—21no—
90C2×D59—41no—
91C2×D59—82no—
92C2×D59—81no—
93C4×C59—41no—
94C4×C59—81no—
95C4×C59—81no—
96C4×C59#42112yes—
97Dic59—21no—
98Dic59—41no—
99Dic59—81no—
100#3142—591no—
101#2165—592no—
102#1356—591no—
103#1356D5911yescharacteristic, complemented
104#1355—592no—
105C2×C59—21no—
106C2×C59#153311yescharacteristic
107D59—41no—
108D59—161no—
109#532—591no—
110C2×#125—591no—
111#491—591no—
112#491C2×D5911yescharacteristic
113#490—591no—
114#490—591no—
115#488—1182no—
116#417—1182no—
117C4×M16—591no—
118#364—1182no—
119#349—1182no—
120#347—592no—
121#347C2×D5912yes—
122C59#1191711yescharacteristic, complemented, Sylow
123C2×#41—1181no—
124C2×M16—592no—
125C4⋊Q8C4×D5911yescharacteristic
126#127—591no—
127#125—591no—
128#125—1181no—
129#125—2361no—
130#125C4×D5911yescharacteristic
131#124—1181no—
132#121—2361no—
133C4×D4—2361no—
134C2×C4⋊C4—1181no—
135C2×C4⋊C4—2361no—
136C2×C42—591no—
137M32—22no—
138M32—1182no—
139#103—22no—
140#103—1182no—
141#102—1182no—
142#102—1182no—
143#97—591no—
144#97C22×D5911yescharacteristic
145C4×C8—592no—
146#41—2364no—
147C2×Q8—21no—
148C2×D4—1181no—
149C2×D4—2361no—
150C2×D4—2361no—
151C22×C4—591no—
152C22×C4—1181no—
153C22×C4—2361no—
154C22×C4—2361no—
155M16—2362no—
156C2×C8—592no—
157C2×C8D4×D5912yes—
158C4⋊C4—21no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—1181no—
162C4⋊C4—2361no—
163C4⋊C4—2361no—
164C4⋊C4—2361no—
165C4⋊C4—2361no—
166C22⋊C4—2362no—
167C42—591no—
168C42—1181no—
169C42C2×C4×D5911yescharacteristic
170C16—42no—
171C16—2362no—
172C23—591no—
173C23—2361no—
174Q8—42no—
175D4—4722no—
176D4—4722no—
177D4—2362no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—591no—
182C2×C4—1182no—
183C2×C4—1181no—
184C2×C4—4721no—
185C2×C4—4722no—
186C2×C4—4722no—
187C2×C4—2361no—
188C2×C4C22⋊C4×D5911yescharacteristic
189C8—22no—
190C8—1182no—
191C22—1181no—
192C22—4722no—
193C22—4721no—
194C22—2361no—
195C22#100×D5911yescharacteristic
196C4—41no—
197C4—81no—
198C4—81no—
199C4—1181no—
200C4—4721no—
201C4—2361no—
202C4#1683741712yes—
203C2—21no—
204C2—9441no—
205C2—2361no—
206C2#2142271811yescharacteristic
subgroupG/H
centerC2#21422718
commutatorC42×C59C22×C4
Frattini#97C22×D59
FittingC59×#1356C2
socleC2×C59#1533
prime radical#16837953C4
cosocle#97×C59C23
hypercenter#1356D59
hypocenterC59#11917
LCSG ▷ C42×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
2. #21425906C2semidirect
3. #21422131C2semidirect
4. #21422128C2semidirect
5. C59×#1356C2semidirect
103. #1356D59semidirect
122. C59#11917semidirect

Maximal subgroups

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

subgroupindex
#214344982
#214259062
#214221312
#214221282
C59×#13562
#1191759