Finite Group Databasebeta

← #21424512

Subgroups — #21424512

Order 7552.

342 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 85 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#16838169C211yesmaximal, characteristic, complemented
2#16837909C211yesmaximal, characteristic
3#16837365C212yesmaximal, complemented
4#16837174C212yesmaximal, complemented
5C59×#413C211yesmaximal, characteristic, complemented
6C22×C4×D59C2211yescharacteristic
7#14273734—24no—
8C2×#11745664—22no—
9C2×#11745664C2212yes—
10#14273708C412yes—
11#14273703—21no—
12#14273698—21no—
13#14273695C412yes—
14C4×C22⋊D59—22no—
15#14273686C2211yescharacteristic
16(C2×D59)⋊C8—24no—
17C2×#41×C59C2211yescharacteristic
18C2×M16×C59C2212yes—
19#101×C59—21no—
20#100×C59—21no—
21C23×D59C2×C411yescharacteristic
22#41×C59—22no—
23#41×C59—22no—
24C2×Q8×C59D411yescharacteristic
25C2×D4×C59C2×C412yes—
26C2×D4×C59D411yescharacteristic
27C22×C4×C59D412yes—
28C22×C4×C59C2311yescharacteristic
29C2×C22⋊D59—22no—
30C22×Dic59C2×C411yescharacteristic
31C2×C4×D59—22no—
32C2×C4×D59—21no—
33C2×C4×D59—21no—
34C2×C4×D59—22no—
35M16×C59—22no—
36M16×C59—22no—
37C2×C8×C59—22no—
38C22⋊Dic59—22no—
39C22⋊Dic59C2×C412yes—
40(C2×D59)⋊C4—22no—
41C4⋊Dic59—21no—
42Dic59⋊C4—22no—
43C4×Dic59—21no—
44#11745664—24no—
45#11745664—22no—
46#11745664—22no—
47C2×C59⋊C8—24no—
48C2×C59⋊C8D414yescomplemented
49C23×C59C22⋊C412yes—
50C23×C59C22×C411yescharacteristic
51C22×D59—21no—
52C22×D59—22no—
53C22×D59—42no—
54Q8×C59—22no—
55D4×C59—24no—
56D4×C59—22no—
57C2×C4×C59—22no—
58C2×C4×C59—22no—
59C2×C4×C59C22⋊C412yes—
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D412yes—
62C2×C4×C59C2×D411yescharacteristic
63C2×C4×C59#4112yes—
64C22⋊D59—44no—
65C2×Dic59—22no—
66C2×Dic59—21no—
67C2×Dic59—22no—
68C4×D59—41no—
69C4×D59—42no—
70C4×D59—41no—
71C8×C59—42no—
72C59⋊C8—24no—
73C22×C59—22no—
74C22×C59—41no—
75C22×C59—42no—
76C22×C59C2×C22⋊C411yescharacteristic
77C22×C59C4×D412yes—
78C2×D59—22no—
79C2×D59—24no—
80C2×D59—41no—
81C2×D59—42no—
82C2×D59—41no—
83C4×C59—22no—
84C4×C59#12011yescharacteristic
85C4×C59#12112yes—
86C4×C59#12311yescharacteristic
87Dic59—42no—
88Dic59—41no—
89#1891—591nomaximal, Sylow
90C2×C59—21no—
91C2×C59—22no—
92C2×C59—42no—
93C2×C59#38611yescharacteristic
94D59—42no—
95#568—591no—
96#525—591no—
97#413D5911yescharacteristic, complemented
98#407—592no—
99#344—592no—
100C59#189111yescharacteristic, complemented, Sylow
101C2×#41C2×D5911yescharacteristic
102C23×C4—591no—
103#131—1184no—
104C2×M16—592no—
105C2×M16—1182no—
106C2×M16C2×D5912yes—
107#123—592no—
108C22⋊Q8—1181no—
109#121—1181no—
110#120—592no—
111C4×D4—1182no—
112#117—591no—
113#101—21no—
114#100—21no—
115C22⋊C8—1184no—
116C24—591no—
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D5911yescharacteristic
120C2×D4—1182no—
121C2×D4C4×D5912yes—
122C2×D4C22⋊D5911yescharacteristic
123C22×C4—591no—
124C22×C4—1181no—
125C22×C4—1182no—
126C22×C4—1182no—
127C22×C4—1181no—
128C22×C4D23612yes—
129C22×C4C22×D5911yescharacteristic
130M16—22no—
131M16—22no—
132M16—1184no—
133M16—1182no—
134M16—1182no—
135C2×C8—22no—
136C2×C8—594no—
137C2×C8—1184no—
138C4⋊C4—1182no—
139C4⋊C4—1181no—
140C22⋊C4—592no—
141C22⋊C4—1182no—
142C22⋊C4—1182no—
143C42—1181no—
144C23—1181no—
145C23—1182no—
146C23—2362no—
147C23(C2×D59)⋊C412yes—
148C23C2×C4×D5911yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—2364no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—1182no—
156C2×C4—1181no—
157C2×C4—1182no—
158C2×C4—2361no—
159C2×C4—2362no—
160C2×C4—2361no—
161C2×C4(C2×D59)⋊C412yes—
162C2×C4C2×D23611yescharacteristic
163C2×C4D4×D5912yes—
164C2×C4#1174568712yes—
165C2×C4C2×C22⋊D5911yescharacteristic
166C8—42no—
167C8—1184no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—1182no—
172C22—1184no—
173C22—2361no—
174C22—2362no—
175C22—2361no—
176C22C2×(C2×D59)⋊C411yescharacteristic
177C22(C22⋊D59)⋊C412yes—
178C4—22no—
179C4—2362no—
180C4—2361no—
181C4#1427369711yescharacteristic
182C4#1427369912yes—
183C4#1427371111yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—2362no—
188C2#1683727911yescharacteristic
subgroupG/H
centerC4#14273697
commutatorC23×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#413C2
socleC2×C59#386
hypercenter#413D59
hypocenterC59#1891
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #16838169C2semidirect
3. #16837365C2semidirect
4. #16837174C2semidirect
5. C59×#413C2semidirect
48. C2×C59⋊C8D4semidirect
97. #413D59semidirect
100. C59#1891semidirect