Finite Group Databasebeta

← #28509546

Subgroups — #28509546

Order 15104.

200 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C2×#16837240C211yesmaximal, characteristic, complemented
2C2×#16837235C211yesmaximal, characteristic, complemented
3#21426188C211yesmaximal, characteristic, complemented
4#21426179C211yesmaximal, characteristic
5#21422295C211yesmaximal, characteristic, complemented
6#21422278C211yesmaximal, characteristic, complemented
7C59×#1415C211yesmaximal, characteristic, complemented
8C2×Dic472C2211yescharacteristic
9C2×C16×D59C2211yescharacteristic
10#16837644—21no—
11#16837635—21no—
12#16837240—22no—
13#16837235—22no—
14C2×C59⋊C32C2211yescharacteristic
15#16837228C2211yescharacteristic
16#16837205—21no—
17#16837203—21no—
18C2×D16×C59C2211yescharacteristic
19C2×C32×C59C2211yescharacteristic
20C59×#366C2211yescharacteristic
21C2×Dic236—21no—
22C2×C8×D59D411yescharacteristic
23#14273707—41no—
24#14273698—41no—
25Dic472—21no—
26Dic472—21no—
27C2×C59⋊C16D411yescharacteristic
28C16×D59—21no—
29C16×D59—21no—
30#14273661—21no—
31#14273650—41no—
32#14273648—41no—
33C59⋊C32D412yescomplemented
34C2×D8×C59—21no—
35D16×C59—21no—
36D16×C59—21no—
37C2×C16×C59C2311yescharacteristic
38#107×C59—21no—
39C32×C59—21no—
40C2×D4×C59—41no—
41C2×C22⋊D59—81no—
42C2×C4×D59D811yescharacteristic
43C2×Dic118—41no—
44D8×C59—41no—
45D8×C59—41no—
46C2×C8×C59C2×D411yescharacteristic
47C4⋊C4×C59—41no—
48C22⋊Dic59—81no—
49(C2×D59)⋊C4—81no—
50C4⋊Dic59—41no—
51C4⋊Dic59—81no—
52C2×C59⋊C8D811yescharacteristic
53Dic236—41no—
54Dic236—41no—
55C8×D59—21no—
56C8×D59—21no—
57C16×C59C2×D411yescharacteristic
58C16×C59#4111yescharacteristic
59C59⋊C16—21no—
60C23×C59—81no—
61C22×D59D1611yescharacteristic
62D4×C59—81no—
63D4×C59—81no—
64C2×C4×C59—81no—
65C2×C4×C59C2×D811yescharacteristic
66C22⋊D59—162no—
67C2×Dic59—81no—
68C2×Dic59—81no—
69C2×Dic59D1611yescharacteristic
70C4×D59—21no—
71C4×D59—21no—
72Dic118—81no—
73Dic118—81no—
74C8×C59#12111yescharacteristic
75C8×C59#13511yescharacteristic
76C59⋊C8—21no—
77#13699—591nomaximal, Sylow
78C22×C59—161no—
79C22×C59—161no—
80C22×C59—161no—
81C22×C59C2×D1611yescharacteristic
82C2×D59—21no—
83C2×D59—21no—
84C2×D59—21no—
85C4×C59—161no—
86C4×C59#46611yescharacteristic
87C4×C59#50811yescharacteristic
88Dic59—21no—
89Dic59—161no—
90Dic59—161no—
91C2×SD64—591no—
92C2×M64—591no—
93#2216—591no—
94#2215—591no—
95#1423—591no—
96#1416—591no—
97#1415D5911yescharacteristic, complemented
98C2×C59—321no—
99C2×C59#221511yescharacteristic
100C2×C59#226311yescharacteristic
101C2×C59#226411yescharacteristic
102D59—41no—
103C2×Q32—591no—
104C2×D16C2×D5911yescharacteristic
105C22×C16—591no—
106#467—1181no—
107#466—1181no—
108SD64—1182no—
109M64—1182no—
110C2×C32—591no—
111C2×C32C2×D5911yescharacteristic
112#366—591no—
113#366C2×D5911yescharacteristic
114#358—1181no—
115#357—1181no—
116C59#1369911yescharacteristic, complemented, Sylow
117C2×Q16—1181no—
118C2×D8—21no—
119C22×C8—591no—
120C22⋊Q8—2361no—
121#121—2361no—
122Q32—1181no—
123Q32—1181no—
124D16—21no—
125D16—21no—
126C2×C16—591no—
127C2×C16—1181no—
128C2×C16—1181no—
129C2×C16C22×D5911yescharacteristic
130#107—21no—
131#107—1181no—
132#103—2361no—
133#102—2361no—
134C32—21no—
135C32—592no—
136C2×Q8—2361no—
137C2×D4—41no—
138C2×D4—4721no—
139C22×C4—591no—
140Q16—2361no—
141Q16—2361no—
142D8—41no—
143D8—41no—
144C2×C8—591no—
145C2×C8—1181no—
146C2×C8—1181no—
147C2×C8D4×D5911yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—4721no—
150C4⋊C4—2361no—
151C22⋊C4—4721no—
152C22⋊C4—4721no—
153C16—1181no—
154C16#1174568511yescharacteristic
155C16D4×D5911yescharacteristic
156C23—81no—
157C23—591no—
158Q8—4721no—
159Q8—4721no—
160D4—81no—
161D4—81no—
162D4—9442no—
163C2×C4—81no—
164C2×C4—591no—
165C2×C4—1181no—
166C2×C4—1181no—
167C2×C4—4721no—
168C2×C4—4721no—
169C2×C4D8×D5911yescharacteristic
170C8—1181no—
171C8#1427370011yescharacteristic
172C8#1427374811yescharacteristic
173C22—161no—
174C22—161no—
175C22—161no—
176C22—1181no—
177C22—1181no—
178C22—1181no—
179C22D16×D5911yescharacteristic
180C4—161no—
181C4—1181no—
182C4—9441no—
183C4—9441no—
184C4#1683763711yescharacteristic
185C4#1683783311yescharacteristic
186C2—321no—
187C2—2361no—
188C2#2142618111yescharacteristic
189C2#2142640711yescharacteristic
190C2#2142641211yescharacteristic
subgroupG/H
centerC22D16×D59
commutator, cosocleC2×C16×C59C23
FrattiniC2×C16C22×D59
FittingC59×#1415C2
socleC22×C59C2×D16
prime radical#21426179C2
hypercenter#1415D59
hypocenterC59#13699
LCSG ▷ C2×C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#16837240C2semidirect
2. C2×#16837235C2semidirect
3. #21426188C2semidirect
5. #21422295C2semidirect
6. #21422278C2semidirect
7. C59×#1415C2semidirect
33. C59⋊C32D4semidirect
97. #1415D59semidirect
116. C59#13699semidirect

Maximal subgroups

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

subgroupindex
C2×#168372402
C2×#168372352
#214261882
#214261792
#214222952
#214222782
C59×#14152
#1369959