Finite Group Databasebeta

← #21425769

Subgroups — #21425769

Order 7552.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#16837972C211yesmaximal, characteristic
2#16837374C212yesmaximal
3#16837197C211yesmaximal, characteristic, complemented
4#16837196C212yesmaximal, complemented
5C59×#354C211yesmaximal, characteristic, complemented
6C2×#11745687C2211yescharacteristic
7C2×Q8×D59C411yescharacteristic, complemented
8#14273727C411yescharacteristic, complemented
9#14273725C411yescharacteristic, complemented
10#14273714C2211yescharacteristic
11#14273709—22no—
12#14273704—22no—
13#14273684C411yescharacteristic, complemented
14#14273683—22no—
15#14273642C2212yes—
16#14273641—22no—
17#124×C59C2211yescharacteristic
18#99×C59C2212yes—
19C2×Q8×C59C2×C411yescharacteristic
20C2×D4×C59C2311yescharacteristic
21C2×C22⋊D59D412yes—
22C22×Dic59D412yes—
23Q8×D59—42no—
24#11745687—42no—
25C2×C4×D59—21no—
26C2×C4×D59C2×C411yescharacteristic
27C2×Dic118—21no—
28C2×Dic118C2×C411yescharacteristic
29C2×Dic118C2×C411yescharacteristic
30C22⋊C4×C59—22no—
31C22⋊C4×C59—22no—
32C42×C59C2×C411yescharacteristic
33C22⋊Dic59—22no—
34C22⋊Dic59—22no—
35(C2×D59)⋊C4—21no—
36C4⋊Dic59—22no—
37Dic59⋊C4—21no—
38Dic59⋊C4—22no—
39Dic59⋊C4—42no—
40C4×Dic59—42no—
41C4×Dic59C2×C411yescharacteristic
42C23×C59C2×D412yes—
43C22×D59C22⋊C411yescharacteristic
44Q8×C59—41no—
45D4×C59—41no—
46C2×C4×C59—21no—
47C2×C4×C59—21no—
48C2×C4×C59—42no—
49C2×C4×C59C22×C411yescharacteristic
50C22⋊D59—42no—
51C2×Dic59—22no—
52C2×Dic59—22no—
53C2×Dic59—21no—
54C2×Dic59—21no—
55C2×Dic59—42no—
56C2×Dic59C22⋊C412yes—
57C2×Dic59C22⋊C411yescharacteristic
58C4×D59—22no—
59C4×D59—42no—
60Dic118—41no—
61Dic118—42no—
62Dic118—41no—
63C22×C59—22no—
64C22×C59—42no—
65C22×C59C2×C22⋊C411yescharacteristic
66C2×D59—21no—
67C2×D59—41no—
68C4×C59—21no—
69C4×C59—41no—
70C4×C59—41no—
71C4×C59—82no—
72Dic59—22no—
73Dic59—41no—
74Dic59—41no—
75Dic59—82no—
76Dic59#9912yes—
77#2129—591nomaximal, Sylow
78C2×C59—21no—
79C2×C59—42no—
80C2×C59C2×#9911yescharacteristic
81D59—41no—
82#536—591no—
83#410—592no—
84#354—591no—
85#354—592no—
86#354D5911yescharacteristic, complemented
87C59#212911yescharacteristic, complemented, Sylow
88C2×#41—591no—
89C22×Q8—591no—
90C4⋊Q8—591no—
91C4⋊Q8—591no—
92#124—591no—
93#124C2×D5911yescharacteristic
94#123—1182no—
95C22⋊Q8—1182no—
96#117—591no—
97#117—1182no—
98#99—592no—
99#99—1182no—
100#99C2×D5912yes—
101#41—2362no—
102C2×Q8—591no—
103C2×Q8—591no—
104C2×Q8—1181no—
105C2×Q8—2362no—
106C2×Q8C4×D5911yescharacteristic
107C2×D4—592no—
108C2×D4C22×D5911yescharacteristic
109C22×C4—592no—
110C22×C4—591no—
111C22×C4—1181no—
112C4⋊C4—1181no—
113C4⋊C4—1182no—
114C4⋊C4—1182no—
115C4⋊C4—2362no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—1181no—
119C22⋊C4—1182no—
120C22⋊C4—1182no—
121C42—591no—
122C42—2362no—
123C42C4×D5911yescharacteristic
124C23—591no—
125C23D4×D5912yes—
126Q8—41no—
127Q8—2361no—
128Q8—2361no—
129Q8—2362no—
130D4—41no—
131D4—2362no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—591no—
136C2×C4—592no—
137C2×C4—1182no—
138C2×C4—1182no—
139C2×C4—1182no—
140C2×C4—1181no—
141C2×C4—1181no—
142C2×C4—2362no—
143C2×C4—2362no—
144C2×C4C2×C4×D5911yescharacteristic
145C22—22no—
146C22—42no—
147C22—1181no—
148C22—2361no—
149C22C22⋊C4×D5911yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—592no—
155C4—1182no—
156C4—4722no—
157C4—2361no—
158C4—2361no—
159C2—21no—
160C2—42no—
161C2—2361no—
162C2#99×D5911yescharacteristic
subgroupG/H
centerC2#99×D59
commutatorC2×C4×C59C22×C4
FrattiniC2×D4C22×D59
FittingC59×#354C2
socleC2×C59C2×#99
hypercenter#354D59
hypocenterC59#2129
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #16837197C2semidirect
4. #16837196C2semidirect
5. C59×#354C2semidirect
7. C2×Q8×D59C4semidirect
8. #14273727C4semidirect
9. #14273725C4semidirect
13. #14273684C4semidirect
86. #354D59semidirect
87. C59#2129semidirect