Finite Group Databasebeta

← #21422685

Subgroups — #21422685

Order 7552.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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#16837936C211yesmaximal, characteristic
2C2×#14273638C211yesmaximal, characteristic, complemented
3#16837143C212yesmaximal, complemented
4#16837141C212yesmaximal, complemented
5C4×M16×C59C211yesmaximal, characteristic, complemented
6C22×C59⋊C8—21no—
7#14273721—21no—
8#14273719C2211yescharacteristic
9#14273715C2211yescharacteristic
10#14273710—21no—
11#14273706C411yescharacteristic
12#14273701C411yescharacteristic
13C4×Dic118C411yescharacteristic
14C4×D236C411yescharacteristic
15C4×C22⋊D59—21no—
16#14273684—21no—
17#14273638—21no—
18#14273638C2212yes—
19C2×M16×C59—21no—
20C2×C42×C59C2211yescharacteristic
21#97×C59C2212yes—
22C4×C8×C59—21no—
23C22×C4×C59C2×C411yescharacteristic
24C22×C4×C59D411yescharacteristic
25C22×C4×C59D411yescharacteristic
26C2×C22⋊D59—21no—
27C2×D236C2×C411yescharacteristic
28C2×C4×D59—21no—
29C2×Dic118C2×C411yescharacteristic
30M16×C59—24no—
31C2×C8×C59—22no—
32C42×C59C2×C411yescharacteristic
33C42×C59D411yescharacteristic
34C42×C59D411yescharacteristic
35C42×C59C2311yescharacteristic
36C22⋊Dic59—21no—
37(C2×D59)⋊C4—21no—
38(C2×D59)⋊C4—21no—
39(C2×D59)⋊C4—21no—
40(C2×D59)⋊C4—21no—
41C4⋊Dic59C2×C411yescharacteristic
42C4⋊Dic59C2×C411yescharacteristic
43Dic59⋊C4—21no—
44Dic59⋊C4—21no—
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47C4×Dic59—21no—
48C2×C59⋊C8—24no—
49C2×C59⋊C8—22no—
50C23×C59C22⋊C411yescharacteristic
51C22×D59—21no—
52C2×C4×C59—22no—
53C2×C4×C59—22no—
54C2×C4×C59—41no—
55C2×C4×C59C22⋊C411yescharacteristic
56C2×C4×C59C22⋊C411yescharacteristic
57C2×C4×C59C22⋊C411yescharacteristic
58C2×C4×C59C22×C411yescharacteristic
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C22⋊D59—42no—
62C2×Dic59—21no—
63C2×Dic59—21no—
64C2×Dic59—21no—
65D236—41no—
66C4×D59—42no—
67Dic118—41no—
68C8×C59—24no—
69C59⋊C8—24no—
70C22×C59—21no—
71C22×C59—21no—
72C22×C59#10412yes—
73C22×C59C2×C22⋊C411yescharacteristic
74C2×D59—41no—
75C2×D59—41no—
76C2×D59—41no—
77C4×C59—21no—
78C4×C59—21no—
79C4×C59—21no—
80C4×C59—21no—
81C4×C59—21no—
82C4×C59#10412yes—
83Dic59—41no—
84Dic59—41no—
85Dic59—41no—
86#1524—591nomaximal, Sylow
87C2×C59—22no—
88C2×C59#41311yescharacteristic
89C2×C59C2×#10411yescharacteristic
90C2×C59C2×#10411yescharacteristic
91D59—81no—
92#529—591no—
93C4×M16D5911yescharacteristic, complemented
94C2×#97—591no—
95#330—592no—
96#329—592no—
97C59#152411yescharacteristic, complemented, Sylow
98C2×M16—21no—
99C22×C8—1181no—
100#126—1181no—
101#125—591no—
102#124—591no—
103#123—1181no—
104C22⋊Q8—591no—
105#121—591no—
106C4×Q8—591no—
107C4×D4—591no—
108C4×D4—1181no—
109#117—1181no—
110C2×C42C2×D5911yescharacteristic
111#97—592no—
112#97—1181no—
113#97C2×D5912yes—
114C4×C8—21no—
115C2×Q8—591no—
116C2×D4—591no—
117C2×D4—1181no—
118C22×C4—1181no—
119C22×C4C4×D5911yescharacteristic
120C22×C4D23611yescharacteristic
121C22×C4C22⋊D5911yescharacteristic
122M16—24no—
123C2×C8—22no—
124C2×C8—1184no—
125C2×C8—1182no—
126C4⋊C4—591no—
127C4⋊C4—591no—
128C4⋊C4—1181no—
129C4⋊C4—1181no—
130C4⋊C4—1181no—
131C4⋊C4—1181no—
132C22⋊C4—1181no—
133C22⋊C4—1181no—
134C22⋊C4—1181no—
135C22⋊C4—1181no—
136C22⋊C4—1181no—
137C42—1181no—
138C42C4×D5911yescharacteristic
139C42D23611yescharacteristic
140C42C22⋊D5911yescharacteristic
141C42C22×D5911yescharacteristic
142C23—1181no—
143C23(C2×D59)⋊C411yescharacteristic
144Q8—2361no—
145D4—2361no—
146D4—2362no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—1181no—
151C2×C4—1181no—
152C2×C4—1181no—
153C2×C4—2362no—
154C2×C4(C2×D59)⋊C411yescharacteristic
155C2×C4(C2×D59)⋊C411yescharacteristic
156C2×C4(C2×D59)⋊C411yescharacteristic
157C2×C4C2×C4×D5911yescharacteristic
158C2×C4C2×D23611yescharacteristic
159C2×C4C2×C22⋊D5911yescharacteristic
160C8—24no—
161C8—1184no—
162C22—21no—
163C22—21no—
164C22—2361no—
165C22—2361no—
166C22—2361no—
167C22#1427365512yes—
168C22C2×(C2×D59)⋊C411yescharacteristic
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—2361no—
175C4—2361no—
176C4—2361no—
177C4#1427365312yes—
178C2—22no—
179C2—4721no—
180C2#1683738411yescharacteristic
181C2C2×#1427365311yescharacteristic
182C2C2×#1427365511yescharacteristic
subgroupG/H
centerC2×C4(C2×D59)⋊C4
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC4×M16×C59C2
socleC22×C59C2×C22⋊C4
hypercenterC4×M16D59
hypocenterC59#1524
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×#14273638C2semidirect
3. #16837143C2semidirect
4. #16837141C2semidirect
5. C4×M16×C59C2semidirect
93. C4×M16D59semidirect
97. C59#1524semidirect