Finite Group Databasebeta

← #21422717

Subgroups — #21422717

Order 7552.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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
5C59×#432C211yesmaximal, 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×C42×C59C2211yescharacteristic
20C4⋊C8×C59—21no—
21C22⋊C8×C59—21no—
22#97×C59C2212yes—
23C22×C4×C59C2×C411yescharacteristic
24C22×C4×C59D411yescharacteristic
25C22×C4×C59D411yescharacteristic
26C2×C22⋊D59—21no—
27C2×D236C2×C411yescharacteristic
28C2×C4×D59—21no—
29C2×Dic118C2×C411yescharacteristic
30C2×C8×C59—22no—
31C42×C59C2×C411yescharacteristic
32C42×C59D411yescharacteristic
33C42×C59D411yescharacteristic
34C42×C59C2311yescharacteristic
35C22⋊Dic59—21no—
36(C2×D59)⋊C4—21no—
37(C2×D59)⋊C4—21no—
38(C2×D59)⋊C4—21no—
39(C2×D59)⋊C4—21no—
40C4⋊Dic59C2×C411yescharacteristic
41C4⋊Dic59C2×C411yescharacteristic
42Dic59⋊C4—21no—
43Dic59⋊C4—21no—
44Dic59⋊C4—21no—
45Dic59⋊C4—21no—
46C4×Dic59—21no—
47C2×C59⋊C8—24no—
48C2×C59⋊C8—22no—
49C23×C59C22⋊C411yescharacteristic
50C22×D59—21no—
51C2×C4×C59—22no—
52C2×C4×C59—41no—
53C2×C4×C59—41no—
54C2×C4×C59C22⋊C411yescharacteristic
55C2×C4×C59C22⋊C411yescharacteristic
56C2×C4×C59C22⋊C411yescharacteristic
57C2×C4×C59C22×C411yescharacteristic
58C2×C4×C59C2×D411yescharacteristic
59C2×C4×C59C2×D411yescharacteristic
60C22⋊D59—42no—
61C2×Dic59—21no—
62C2×Dic59—21no—
63C2×Dic59—21no—
64D236—41no—
65C4×D59—42no—
66Dic118—41no—
67C8×C59—42no—
68C59⋊C8—24no—
69C22×C59—21no—
70C22×C59—21no—
71C22×C59#10412yes—
72C22×C59C2×C22⋊C411yescharacteristic
73C2×D59—41no—
74C2×D59—41no—
75C2×D59—41no—
76C4×C59—21no—
77C4×C59—21no—
78C4×C59—21no—
79C4×C59—21no—
80C4×C59—21no—
81C4×C59—21no—
82Dic59—41no—
83Dic59—41no—
84Dic59—41no—
85#1532—591nomaximal, Sylow
86C2×C59—22no—
87C2×C59#41311yescharacteristic
88C2×C59C2×#10411yescharacteristic
89C2×C59#42111yescharacteristic
90D59—81no—
91#529—591no—
92#432D5911yescharacteristic, complemented
93C2×#97—591no—
94#330—592no—
95#329—592no—
96C59#153211yescharacteristic, complemented, Sylow
97C22×C8—1181no—
98#126—1181no—
99#125—591no—
100#124—591no—
101#123—1181no—
102C22⋊Q8—591no—
103#121—591no—
104C4×Q8—591no—
105C4×D4—591no—
106C4×D4—1181no—
107#117—1181no—
108C2×C42C2×D5911yescharacteristic
109C4⋊C8—21no—
110C22⋊C8—21no—
111#97—592no—
112#97—1181no—
113#97C2×D5912yes—
114C2×Q8—591no—
115C2×D4—591no—
116C2×D4—1181no—
117C22×C4—1181no—
118C22×C4C4×D5911yescharacteristic
119C22×C4D23611yescharacteristic
120C22×C4C22⋊D5911yescharacteristic
121C2×C8—22no—
122C2×C8—1184no—
123C2×C8—1182no—
124C4⋊C4—591no—
125C4⋊C4—591no—
126C4⋊C4—1181no—
127C4⋊C4—1181no—
128C4⋊C4—1181no—
129C4⋊C4—1181no—
130C22⋊C4—1181no—
131C22⋊C4—1181no—
132C22⋊C4—1181no—
133C22⋊C4—1181no—
134C22⋊C4—1181no—
135C42—1181no—
136C42C4×D5911yescharacteristic
137C42D23611yescharacteristic
138C42C22⋊D5911yescharacteristic
139C42C22×D5911yescharacteristic
140C23—1181no—
141C23(C2×D59)⋊C411yescharacteristic
142Q8—2361no—
143D4—2361no—
144D4—2362no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—1181no—
149C2×C4—1181no—
150C2×C4—1181no—
151C2×C4—2362no—
152C2×C4(C2×D59)⋊C411yescharacteristic
153C2×C4(C2×D59)⋊C411yescharacteristic
154C2×C4(C2×D59)⋊C411yescharacteristic
155C2×C4C2×C4×D5911yescharacteristic
156C2×C4C2×D23611yescharacteristic
157C2×C4C2×C22⋊D5911yescharacteristic
158C8—42no—
159C8—1184no—
160C22—21no—
161C22—21no—
162C22—2361no—
163C22—2361no—
164C22—2361no—
165C22#1427365312yes—
166C22C2×(C2×D59)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—2361no—
174C4—2361no—
175C4—2361no—
176C2—22no—
177C2—4721no—
178C2#1683738411yescharacteristic
179C2C2×#1427365311yescharacteristic
180C2#1683742011yescharacteristic
subgroupG/H
centerC22C2×(C2×D59)⋊C4
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×#432C2
socleC22×C59C2×C22⋊C4
hypercenter#432D59
hypocenterC59#1532
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×#14273638C2semidirect
3. #16837143C2semidirect
4. #16837141C2semidirect
5. C59×#432C2semidirect
92. #432D59semidirect
96. C59#1532semidirect