Finite Group Databasebeta

← #21425199

Subgroups — #21425199

Order 7552.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#16838200C212yesmaximal, complemented
2#16837370C211yesmaximal, characteristic, complemented
3#16837369C212yesmaximal, complemented
4C59⋊#338C211yesmaximal, characteristic, complemented
5C59×#575C211yesmaximal, characteristic, complemented
6C2×#11745685C2211yescharacteristic
7#14273758—22no—
8#14273757—22no—
9#14273753—22no—
10#14273752—22no—
11#14273747—24no—
12C2×#11745664C2212yes—
13C22×C59⋊C8C2211yescharacteristic
14C22⋊(C59⋊C8)—24no—
15(C2×D59)⋊C8—22no—
16C2×#41×C59C2212yes—
17#137×C59—22no—
18AGL(1,ℤ/8)×C59—22no—
19#135×C59—22no—
20C2×M16×C59C2211yescharacteristic
21#41×C59—22no—
22#41×C59—22no—
23#41×C59—22no—
24#41×C59—22no—
25C2×Q8×C59D412yes—
26C2×D4×C59—22no—
27C2×D4×C59D412yes—
28C22×C4×C59—22no—
29C22×C4×C59C2311yescharacteristic
30C2×C22⋊D59—21no—
31#11745685—22no—
32#11745685—22no—
33C2×D236D411yescharacteristic
34C2×C4×D59—21no—
35C2×Dic118D411yescharacteristic
36Q16×C59—22no—
37SD16×C59—24no—
38D8×C59—22no—
39M16×C59—22no—
40C2×C8×C59D412yes—
41#11745672—24no—
42#11745671—24no—
43#11745670—24no—
44#11745669—24no—
45#11745664—22no—
46#11745664—22no—
47C2×C59⋊C8—21no—
48C2×C59⋊C8—22no—
49C2×C59⋊C8D414yes—
50C23×C59—22no—
51C23×C59#4111yescharacteristic
52C22×D59—21no—
53Q8×C59—22no—
54Q8×C59—22no—
55D4×C59—22no—
56D4×C59—22no—
57D4×C59—42no—
58D4×C59—42no—
59C2×C4×C59—22no—
60C2×C4×C59—42no—
61C2×C4×C59—42no—
62C2×C4×C59C2×D411yescharacteristic
63C2×C4×C59C2×D412yes—
64C2×C4×C59C2×D412yes—
65C2×C4×C59C2×D411yescharacteristic
66C22⋊D59—42no—
67C2×Dic59—21no—
68D236—22no—
69C4×D59—41no—
70C4×D59—41no—
71Dic118—22no—
72C8×C59—22no—
73C59⋊C8—24no—
74C59⋊C8—41no—
75C22×C59—41no—
76C22×C59—44no—
77C22×C59—42no—
78C22×C59#12111yescharacteristic
79C22×C59#12112yes—
80C2×D59—42no—
81C2×D59—41no—
82C4×C59—42no—
83C4×C59#12012yes—
84C4×C59#12011yescharacteristic
85C4×C59#12711yescharacteristic
86Dic59—41no—
87#2017—591nomaximal, Sylow
88C2×C59—21no—
89C2×C59—22no—
90C2×C59—82no—
91C2×C59#39211yescharacteristic
92D59—81no—
93#575—592no—
94#575D5911yescharacteristic, complemented
95#408—592no—
96#408—591no—
97#338—591no—
98C59#201711yescharacteristic, complemented, Sylow
99C2×#41—591no—
100C2×#41C2×D5912yes—
101#137—22no—
102#137—1182no—
103#137—1182no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—1182no—
106AGL(1,ℤ/8)—1182no—
107#135—22no—
108#135—1184no—
109C2×M16—592no—
110C2×M16C2×D5911yescharacteristic
111C22×C8—591no—
112C22⋊C8—1184no—
113C22⋊C8—1182no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—1182no—
119#41—1182no—
120C2×Q8—591no—
121C2×Q8C22⋊D5912yes—
122C2×D4—22no—
123C2×D4—591no—
124C2×D4—1181no—
125C2×D4C22⋊D5912yes—
126C22×C4—22no—
127C22×C4—1181no—
128C22×C4C22×D5911yescharacteristic
129Q16—22no—
130Q16—1184no—
131SD16—24no—
132SD16—1184no—
133SD16—1184no—
134D8—22no—
135D8—1184no—
136M16—22no—
137M16—1182no—
138M16—1182no—
139C2×C8—594no—
140C2×C8—1182no—
141C2×C8—1181no—
142C2×C8C22⋊D5912yes—
143C23—22no—
144C23—1181no—
145C23#1174568711yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—1182no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—1182no—
154D4—2362no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—1181no—
159C2×C4—2361no—
160C2×C4—2361no—
161C2×C4D4×D5911yescharacteristic
162C2×C4D4×D5912yes—
163C2×C4C2×C22⋊D5912yes—
164C2×C4C2×C22⋊D5911yescharacteristic
165C8—22no—
166C8—1184no—
167C8—2361no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—2362no—
172C22—2361no—
173C22#1427369811yescharacteristic
174C22#1427369912yes—
175C4—42no—
176C4—2361no—
177C4#1427369512yes—
178C4#1427369611yescharacteristic
179C4#1427372311yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—4721no—
184C2#1683731011yescharacteristic
subgroupG/H
centerC4#14273723
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#575C2
socleC2×C59#392
hypercenter#575D59
hypocenterC59#2017
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #16838200C2semidirect
2. #16837370C2semidirect
3. #16837369C2semidirect
4. C59⋊#338C2semidirect
5. C59×#575C2semidirect
94. #575D59semidirect
98. C59#2017semidirect