Finite Group Databasebeta

← #28499884

Subgroups — #28499884

Order 15104.

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

normal subgroups only

This group has 274 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#21434475C211yesmaximal, characteristic
2#21425906C212yesmaximal
3#21422131C211yesmaximal, characteristic, complemented
4#21422130C212yesmaximal, complemented
5C59×#1356C211yesmaximal, characteristic, complemented
6#16837958C411yescharacteristic
7C4⋊Q8×D59C411yescharacteristic
8#16837772C411yescharacteristic
9#16837771C2211yescharacteristic
10#16837770C411yescharacteristic
11#16837751—22no—
12#16837409—22no—
13#16837354C2211yescharacteristic
14#16837222—22no—
15#16837183—22no—
16#16837180C2212yes—
17C59×#491C2211yescharacteristic
18C59×#347C2212yes—
19C2×Q8×D59—21no—
20C2×#11745659D412yes—
21#14273727C2×C411yescharacteristic
22#14273726—21no—
23#14273726—41no—
24#14273725—21no—
25#14273719C2×C411yescharacteristic
26#14273705—41no—
27#14273692—41no—
28#14273685—21no—
29C4⋊C4×D59—41no—
30C42×D59C2×C411yescharacteristic
31#14273667—22no—
32#14273652—22no—
33#14273651—22no—
34#14273650—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—
43Q8×D59—44no—
44C2×C4×D59—21no—
45C2×C4×D59—41no—
46C2×C4×D59C22⋊C411yescharacteristic
47C2×Dic118—21no—
48C2×Dic118—41no—
49C2×Dic118—41no—
50C2×C8×C59C2×D412yes—
51C4⋊C4×C59—21no—
52C4⋊C4×C59—41no—
53C4⋊C4×C59—41no—
54C42×C59C22×C411yescharacteristic
55(C2×D59)⋊C4—41no—
56C4⋊Dic59—21no—
57C4⋊Dic59—41no—
58Dic59⋊C4—42no—
59Dic59⋊C4—41no—
60Dic59⋊C4—41no—
61C4×Dic59—21no—
62C4×Dic59—41no—
63C4×Dic59C22⋊C411yescharacteristic
64C2×C59⋊C8C22⋊C412yes—
65#11745659—42no—
66C16×C59—42no—
67C59⋊C16—42no—
68C22×D59#10011yescharacteristic
69Q8×C59—42no—
70C2×C4×C59—21no—
71C2×C4×C59—41no—
72C2×C4×C59—41no—
73C2×C4×C59C2×C22⋊C411yescharacteristic
74C2×Dic59—21no—
75C2×Dic59—41no—
76C2×Dic59—41no—
77C2×Dic59#10011yescharacteristic
78C4×D59—22no—
79C4×D59—42no—
80C4×D59—82no—
81Dic118—42no—
82Dic118—82no—
83Dic118—82no—
84C8×C59—22no—
85C59⋊C8—22no—
86#11916—591nomaximal, Sylow
87C22×C59C2×#10011yescharacteristic
88C2×D59—21no—
89C2×D59—41no—
90C4×C59—41no—
91C4×C59—81no—
92C4×C59—81no—
93C4×C59#42112yes—
94Dic59—22no—
95Dic59—21no—
96Dic59—81no—
97Dic59—81no—
98#3139—591no—
99#2165—592no—
100#1356—591no—
101#1356—592no—
102#1356D5911yescharacteristic, complemented
103C2×C59—21no—
104C2×C59#153311yescharacteristic
105D59—41no—
106#533—591no—
107C2×C4⋊Q8—591no—
108#491—591no—
109#491—591no—
110#491—591no—
111#491C2×D5911yescharacteristic
112#487—1182no—
113#419—1182no—
114C4×M16—591no—
115#364—1182no—
116#349—1182no—
117#347—592no—
118#347C2×D5912yes—
119C59#1191611yescharacteristic, complemented, Sylow
120C22×Q8—1181no—
121C2×M16—592no—
122C4⋊Q8—591no—
123C4⋊Q8—1181no—
124C4⋊Q8—1181no—
125C4⋊Q8—2361no—
126C4⋊Q8C4×D5911yescharacteristic
127#125—591no—
128#125C4×D5911yescharacteristic
129C22⋊Q8—2361no—
130C4×Q8—2361no—
131#117—1181no—
132C2×C4⋊C4—2361no—
133C2×C42—591no—
134M32—22no—
135M32—1182no—
136#103—22no—
137#103—1182no—
138#103—1182no—
139#103—1182no—
140#97—591no—
141#97C22×D5911yescharacteristic
142C4×C8—592no—
143C2×Q8—21no—
144C2×Q8—1181no—
145C2×Q8—2361no—
146C2×Q8—2361no—
147C2×Q8—2364no—
148C22×C4—591no—
149C22×C4—1181no—
150C22×C4—2361no—
151M16—2362no—
152C2×C8—592no—
153C2×C8D4×D5912yes—
154C4⋊C4—21no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—1181no—
158C4⋊C4—2361no—
159C4⋊C4—2361no—
160C4⋊C4—2362no—
161C4⋊C4—2361no—
162C22⋊C4—2361no—
163C42—591no—
164C42—1181no—
165C42—2361no—
166C42C2×C4×D5911yescharacteristic
167C16—42no—
168C16—2362no—
169C23—591no—
170Q8—42no—
171Q8—4722no—
172Q8—4722no—
173Q8—2362no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—591no—
178C2×C4—1181no—
179C2×C4—1182no—
180C2×C4—4722no—
181C2×C4—2362no—
182C2×C4—2361no—
183C2×C4—2361no—
184C2×C4C22⋊C4×D5911yescharacteristic
185C8—22no—
186C8—1182no—
187C22—1181no—
188C22—2361no—
189C22#100×D5911yescharacteristic
190C4—41no—
191C4—81no—
192C4—81no—
193C4—1182no—
194C4—1181no—
195C4—4721no—
196C4—4721no—
197C4#1683741712yes—
198C2—21no—
199C2—2361no—
200C2#2142271811yescharacteristic
subgroupG/H
centerC2#21422718
commutatorC42×C59C22×C4
Frattini#97C22×D59
FittingC59×#1356C2
socleC2×C59#1533
prime radicalC22×D59#100
cosocle#97×C59C23
hypercenter#1356D59
hypocenterC59#11916
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
3. #21422131C2semidirect
4. #21422130C2semidirect
5. C59×#1356C2semidirect
102. #1356D59semidirect
119. C59#11916semidirect

Maximal subgroups

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

subgroupindex
#214344752
#214259062
#214221312
#214221302
C59×#13562
#1191659