Finite Group Databasebeta

← #28509536

Subgroups — #28509536

Order 15104.

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

normal subgroups only

This group has 210 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×#16837237C211yesmaximal, characteristic, complemented
2C2×#16837235C211yesmaximal, characteristic, complemented
3#21426183C211yesmaximal, characteristic, complemented
4#21426179C211yesmaximal, characteristic, complemented
5#21422297C211yesmaximal, characteristic, complemented
6#21422275C211yesmaximal, characteristic, complemented
7C59×#1415C211yesmaximal, characteristic, complemented
8C2×D944C2211yescharacteristic
9C2×C16×D59C2211yescharacteristic
10#16837639—21no—
11#16837635—21no—
12#16837237—22no—
13#16837235—22no—
14C2×C59⋊C32C2211yescharacteristic
15#16837228C2211yescharacteristic
16#16837203—21no—
17#16837202—21no—
18C2×D16×C59C2211yescharacteristic
19C2×C32×C59C2211yescharacteristic
20C59×#366C2211yescharacteristic
21C2×D472—21no—
22C2×C8×D59D411yescharacteristic
23#14273702—41no—
24#14273698—41no—
25D944—21no—
26D944—21no—
27C2×C59⋊C16D411yescharacteristic
28C16×D59—21no—
29C16×D59—21no—
30#14273661—21no—
31#14273648—41no—
32#14273647—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×D236—41no—
43C2×D236—81no—
44C2×C4×D59D811yescharacteristic
45D8×C59—41no—
46D8×C59—41no—
47C2×C8×C59C2×D411yescharacteristic
48C4⋊C4×C59—41no—
49C22⋊Dic59—81no—
50(C2×D59)⋊C4—81no—
51C4⋊Dic59—41no—
52C2×C59⋊C8D811yescharacteristic
53D472—41no—
54D472—41no—
55C8×D59—21no—
56C8×D59—21no—
57C16×C59C2×D411yescharacteristic
58C16×C59#4111yescharacteristic
59C59⋊C16—21no—
60C23×C59—81no—
61C22×D59—81no—
62C22×D59D1611yescharacteristic
63D4×C59—81no—
64D4×C59—81no—
65C2×C4×C59—81no—
66C2×C4×C59C2×D811yescharacteristic
67C22⋊D59—162no—
68C2×Dic59—81no—
69C2×Dic59D1611yescharacteristic
70D236—81no—
71D236—81no—
72D236—162no—
73C4×D59—21no—
74C4×D59—21no—
75C8×C59#12111yescharacteristic
76C8×C59#13511yescharacteristic
77C59⋊C8—21no—
78#13697—591nomaximal, Sylow
79C22×C59—161no—
80C22×C59—161no—
81C22×C59—161no—
82C22×C59C2×D1611yescharacteristic
83C2×D59—21no—
84C2×D59—21no—
85C2×D59—21no—
86C2×D59—161no—
87C2×D59—161no—
88C2×D59—161no—
89C4×C59—161no—
90C4×C59#46611yescharacteristic
91C4×C59#50811yescharacteristic
92Dic59—21no—
93Dic59—161no—
94C2×D32—591no—
95C2×M64—591no—
96#2215—591no—
97#2215—591no—
98#1424—591no—
99#1415—591no—
100#1415D5911yescharacteristic, complemented
101C2×C59—321no—
102C2×C59#221511yescharacteristic
103C2×C59#226311yescharacteristic
104C2×C59#226311yescharacteristic
105D59—41no—
106D59—321no—
107C2×D16—591no—
108C2×D16C2×D5911yescharacteristic
109C22×C16—591no—
110#466—1181no—
111#466—1181no—
112D32—1182no—
113M64—1182no—
114C2×C32—591no—
115C2×C32C2×D5911yescharacteristic
116#366—591no—
117#366C2×D5911yescharacteristic
118#357—1181no—
119#357—1181no—
120C59#1369711yescharacteristic, complemented, Sylow
121C2×D8—21no—
122C2×D8—1181no—
123C22×C8—591no—
124#121—2361no—
125#121—2361no—
126D16—21no—
127D16—21no—
128D16—1181no—
129D16—1181no—
130C2×C16—591no—
131C2×C16—1181no—
132C2×C16—1181no—
133C2×C16C22×D5911yescharacteristic
134#107—21no—
135#107—1181no—
136#102—2361no—
137#102—2361no—
138C32—21no—
139C32—592no—
140C2×D4—41no—
141C2×D4—4721no—
142C2×D4—4721no—
143C2×D4—2361no—
144C22×C4—591no—
145D8—41no—
146D8—41no—
147D8—2361no—
148D8—2361no—
149C2×C8—591no—
150C2×C8—1181no—
151C2×C8—1181no—
152C2×C8D4×D5911yescharacteristic
153C4⋊C4—41no—
154C4⋊C4—2361no—
155C22⋊C4—4721no—
156C22⋊C4—4721no—
157C16—1181no—
158C16#1174568511yescharacteristic
159C16D4×D5911yescharacteristic
160C23—81no—
161C23—591no—
162C23—4721no—
163D4—81no—
164D4—81no—
165D4—9442no—
166D4—9442no—
167D4—4721no—
168D4—4721no—
169C2×C4—81no—
170C2×C4—591no—
171C2×C4—1181no—
172C2×C4—1181no—
173C2×C4—4721no—
174C2×C4D8×D5911yescharacteristic
175C8—1181no—
176C8#1427370011yescharacteristic
177C8#1427374811yescharacteristic
178C22—161no—
179C22—161no—
180C22—161no—
181C22—1181no—
182C22—1181no—
183C22—1181no—
184C22—9441no—
185C22—9441no—
186C22—9441no—
187C22D16×D5911yescharacteristic
188C4—161no—
189C4—1181no—
190C4—9441no—
191C4#1683763711yescharacteristic
192C4#1683783311yescharacteristic
193C2—321no—
194C2—18881no—
195C2—2361no—
196C2#2142618111yescharacteristic
197C2#2142640711yescharacteristic
198C2#2142641011yescharacteristic
subgroupG/H
centerC22D16×D59
commutator, cosocleC2×C16×C59C23
FrattiniC2×C16C22×D59
FittingC59×#1415C2
socleC22×C59C2×D16
hypercenter#1415D59
hypocenterC59#13697
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×#16837237C2semidirect
2. C2×#16837235C2semidirect
3. #21426183C2semidirect
4. #21426179C2semidirect
5. #21422297C2semidirect
6. #21422275C2semidirect
7. C59×#1415C2semidirect
33. C59⋊C32D4semidirect
100. #1415D59semidirect
120. C59#13697semidirect

Maximal subgroups

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

subgroupindex
C2×#168372372
C2×#168372352
#214261832
#214261792
#214222972
#214222752
C59×#14152
#1369759