Finite Group Databasebeta

← D59×#1705 #28576324

Subgroups — D59×#1705 #28576324

Order 15104.

994 conjugacy classes of subgroups; only the 239 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 239 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#498×D59C213yesmaximal, complemented
2#492×D59C213yesmaximal
3#21423684C213yesmaximal, complemented
4#21423683C211yesmaximal, characteristic, complemented
5#21423682C213yesmaximal, complemented
6C82×D59C211yesmaximal, characteristic, complemented
7C59×#1705C211yesmaximal, characteristic, complemented
8C2×SD16×D59—26no—
9C4⋊Q8×D59C2213yes—
10#127×D59C2211yescharacteristic
11#16837800C2213yescomplemented
12#16837799—26no—
13#16837798C2216yescomplemented
14#16837776C2213yes—
15#16837775C2213yes—
16#16837774C2213yes—
17#16837773—26no—
18#106×D59—26no—
19C4×C8×D59C2213yes—
20C8×C59⋊C8C2213yescomplemented
21C59×#498C2213yescomplemented
22C59×#492C2213yes—
23C82×C59C2211yescharacteristic, complemented
24C2×Q8×D59—23no—
25C2×D4×D59—23no—
26C2×#11745660—26no—
27C2×#11745670—26no—
28C2×#11745671—26no—
29SD16×D59—424no—
30C2×C8×D59D416yes—
31#14273727C2313yes—
32#14273726—26no—
33#14273725—23no—
34#14273724C2311yescharacteristic
35#14273723—23no—
36C4⋊C4×D59—26no—
37C42×D59C2311yescharacteristic
38#14273659—26no—
39#14273658—212no—
40C4×C59⋊C8C2313yes—
41C8×Dic59D416yes—
42C2×SD16×C59—26no—
43C4⋊Q8×C59C2313yes—
44#127×C59C2311yescharacteristic
45#106×C59—26no—
46C4×C8×C59C2313yes—
47C23×D59—41no—
48C2×Q8×C59—23no—
49C2×D4×C59—23no—
50C2×C22⋊D59—43no—
51Q8×D59—412no—
52D4×D59—412no—
53C2×D236—23no—
54C2×C4×D59—43no—
55C2×C4×D59C2×D413yes—
56C2×Dic118—23no—
57C2×Dic118—43no—
58SD16×C59—412no—
59C2×C8×C59C2×D416yes—
60C4⋊C4×C59—26no—
61C42×C59C2411yescharacteristic
62#11745671—412no—
63#11745670—412no—
64C4⋊Dic59—26no—
65Dic59⋊C4—46no—
66C4×Dic59C2×D413yes—
67C2×C59⋊C8C2×D416yes—
68#11745660—412no—
69C8×D59SD16124yescomplemented
70C23×C59—41no—
71C22×D59—41no—
72C22×D59—86no—
73C22×D59#12711yescharacteristic
74Q8×C59—46no—
75D4×C59—46no—
76C2×C4×C59—43no—
77C2×C4×C59C22×D413yes—
78C22⋊D59—86no—
79C2×Dic59—43no—
80C2×Dic59#12713yes—
81D236—46no—
82C4×D59—86no—
83C4×D59C2×SD16112yes—
84Dic118—46no—
85Dic118—86no—
86C8×C59C2×SD16112yescomplemented
87C59⋊C8C2×SD16112yescomplemented
88C2×#1705—591nomaximal, Sylow
89C22×C59—83no—
90C22×C59C2×#12711yescharacteristic
91C2×D59—83no—
92C2×D59—164no—
93C2×D59#49216yes—
94C4×C59—83no—
95C4×C59C22×SD1616yes—
96Dic59—83no—
97Dic59#49216yes—
98C2×#498—593no—
99C2×#492—593no—
100#1705—593no—
101#1705—593no—
102#1705—591no—
103#1705D5911yescharacteristic, direct product factor
104C2×C82—591no—
105C2×C59—161no—
106C2×C59C2×#49213yes—
107D59—161no—
108D59#170514yesdirect product factor
109C22×SD16—1186no—
110C2×C4⋊Q8—593no—
111C2×#127—591no—
112#498—596no—
113#498—593no—
114#498—1186no—
115#498C2×D5913yescomplemented
116#492—593no—
117#492—593no—
118#492—593no—
119#492—1186no—
120#492C2×D5913yes—
121C2×#106—1186no—
122C2×C4×C8—593no—
123C82—593no—
124C82C2×D5911yescharacteristic, complemented
125C59C2×#170511yescharacteristic, complemented, Sylow
126C22×Q8—1183no—
127C22×D4—1183no—
128C2×SD16—26no—
129C2×SD16—1186no—
130C2×SD16—1186no—
131C2×SD16—1186no—
132C2×SD16—23624no—
133C22×C8—596no—
134C4⋊Q8—593no—
135C4⋊Q8—1186no—
136C4⋊Q8—1183no—
137C4⋊Q8C22×D5913yes—
138#127—591no—
139#127—1183no—
140#127C22×D5911yescharacteristic
141C2×C4⋊C4—1186no—
142C2×C42—591no—
143#106—26no—
144#106—11812no—
145#106—1186no—
146C4×C8—596no—
147C4×C8—593no—
148C4×C8C22×D5913yes—
149C24—2361no—
150C2×Q8—23no—
151C2×Q8—1183no—
152C2×Q8—2363no—
153C2×Q8—23612no—
154C2×D4—23no—
155C2×D4—1183no—
156C2×D4—23612no—
157C2×D4—2363no—
158C22×C4—593no—
159C22×C4—2363no—
160SD16—412no—
161SD16—23612no—
162SD16—23612no—
163SD16—23612no—
164C2×C8—596no—
165C2×C8—5924no—
166C2×C8D4×D5916yes—
167C4⋊C4—26no—
168C4⋊C4—1186no—
169C4⋊C4—2366no—
170C42—593no—
171C42C23×D5911yescharacteristic
172C23—41no—
173C23—591no—
174C23—4726no—
175C23—2361no—
176Q8—46no—
177Q8—4726no—
178Q8—2366no—
179D4—46no—
180D4—4726no—
181D4—2366no—
182C2×C4—43no—
183C2×C4—593no—
184C2×C4—5912no—
185C2×C4—4726no—
186C2×C4—2363no—
187C2×C4C2×D4×D5913yes—
188C8—5912no—
189C8SD16×D59112yescomplemented
190C22—83no—
191C22—596no—
192C22—9444no—
193C22—4723no—
194C22#127×D5911yescharacteristic
195C4—83no—
196C4—596no—
197C4—4723no—
198C4C2×SD16×D5916yes—
199C2—161no—
200C2—594no—
201C2—9441no—
202C2#492×D5913yes—
subgroupG/H
centerC22#127×D59
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC59×#1705C2
socleC22×C59C2×#127
prime radical#127×D59C22
hypercenter#1705D59
hypocenterC59C2×#1705
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #1705

Complements

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

NH ≅ G/Ntype
1. #498×D59C2semidirect
3. #21423684C2semidirect
4. #21423683C2semidirect
5. #21423682C2semidirect
6. C82×D59C2semidirect
7. C59×#1705C2semidirect
11. #16837800C22semidirect
13. #16837798C22semidirect
20. C8×C59⋊C8C22semidirect
21. C59×#498C22semidirect
23. C82×C59C22semidirect
69. C8×D59SD16semidirect
86. C8×C59C2×SD16semidirect
87. C59⋊C8C2×SD16semidirect
103. #1705D59direct (N × H)
108. D59#1705direct (N × H)
115. #498C2×D59semidirect
124. C82C2×D59semidirect
125. C59C2×#1705semidirect
189. C8SD16×D59semidirect

Maximal subgroups

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

subgroupindex
#498×D592
#492×D592
#214236842
#214236832
#214236822
C82×D592
C59×#17052
C2×#170559