Finite Group Databasebeta

← #21425778

Subgroups — #21425778

Order 7552.

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

normal subgroups only

This group has 250 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#16837951C211yesmaximal, characteristic
2#16837385C212yesmaximal, complemented
3#16837200C212yesmaximal, complemented
4#16837199C211yesmaximal, characteristic, complemented
5C59×#355C211yesmaximal, characteristic, complemented
6C2×#11745689C2211yescharacteristic
7C2×#11745687C411yescharacteristic
8M16×D59—22no—
9#14273725C2211yescharacteristic
10#14273723C411yescharacteristic
11#14273715C411yescharacteristic
12#14273700—22no—
13(C22⋊D59)⋊C4—22no—
14C42×D59C411yescharacteristic
15#14273646C2212yes—
16#14273643—22no—
17#124×C59C2211yescharacteristic
18#101×C59C2212yes—
19C2×Q8×C59C2311yescharacteristic
20C2×D4×C59C2×C411yescharacteristic
21C2×C22⋊D59—22no—
22C2×C22⋊D59—21no—
23C22×Dic59—21no—
24#11745689—41no—
25#11745689—41no—
26#11745687—41no—
27#11745687—41no—
28C2×D236C2×C411yescharacteristic
29C2×D236D412yes—
30C2×C4×D59—21no—
31C2×C4×D59C2×C411yescharacteristic
32C2×C4×D59D412yes—
33C2×Dic118C2×C411yescharacteristic
34M16×C59—22no—
35C22⋊C4×C59—22no—
36C42×C59C2×C411yescharacteristic
37(C2×D59)⋊C4—22no—
38Dic59⋊C4—22no—
39C4×Dic59—21no—
40C4×Dic59C2×C411yescharacteristic
41#11745664—22no—
42#11745659—42no—
43C8×D59—42no—
44C23×C59—21no—
45C22×D59C22⋊C412yes—
46C22×D59C22⋊C411yescharacteristic
47Q8×C59—41no—
48D4×C59—41no—
49C2×C4×C59—21no—
50C2×C4×C59C22×C411yescharacteristic
51C2×C4×C59C2×D412yes—
52C22⋊D59—44no—
53C22⋊D59—42no—
54C2×Dic59—21no—
55C2×Dic59—21no—
56C2×Dic59—41no—
57C2×Dic59—41no—
58C2×Dic59C22⋊C411yescharacteristic
59D236—41no—
60D236—42no—
61C4×D59—22no—
62C4×D59—22no—
63C4×D59—21no—
64C4×D59—21no—
65C4×D59—42no—
66Dic118—41no—
67C8×C59—42no—
68C59⋊C8—42no—
69C22×C59—42no—
70C22×C59—41no—
71C22×C59C2×C22⋊C411yescharacteristic
72C2×D59—21no—
73C2×D59—22no—
74C2×D59—41no—
75C2×D59—42no—
76C4×C59—22no—
77C4×C59—21no—
78C4×C59—41no—
79Dic59—22no—
80Dic59—41no—
81Dic59#9911yescharacteristic
82Dic59#9911yescharacteristic
83#2132—591nomaximal, Sylow
84C2×C59—21no—
85C2×C59—81no—
86C2×C59C2×#9911yescharacteristic
87D59—41no—
88D59—42no—
89#532—591no—
90#413—592no—
91#356—592no—
92#355—591no—
93#355D5911yescharacteristic, complemented
94C59#213211yescharacteristic, complemented, Sylow
95C2×#41—591no—
96C2×#41—591no—
97C2×M16—1182no—
98C4⋊Q8—591no—
99#127—591no—
100#124—591no—
101#124C2×D5911yescharacteristic
102#121—1182no—
103C4×D4—1182no—
104C2×C42—591no—
105#101—592no—
106#101C2×D5912yes—
107#100—1182no—
108#41—2361no—
109#41—2361no—
110#41—2361no—
111#41—2361no—
112C2×Q8—591no—
113C2×Q8C22×D5911yescharacteristic
114C2×D4—591no—
115C2×D4—592no—
116C2×D4—1182no—
117C2×D4—1181no—
118C2×D4C4×D5911yescharacteristic
119C22×C4—591no—
120C22×C4—592no—
121C22×C4—1181no—
122C22×C4—1181no—
123M16—22no—
124M16—1182no—
125M16—2362no—
126C2×C8—2362no—
127C4⋊C4—1182no—
128C22⋊C4—22no—
129C22⋊C4—1182no—
130C42—591no—
131C42—1181no—
132C42C4×D5911yescharacteristic
133C23—21no—
134C23—592no—
135C23—591no—
136Q8—41no—
137Q8—2361no—
138D4—41no—
139D4—2362no—
140D4—2361no—
141D4—2364no—
142D4—2362no—
143C2×C4—21no—
144C2×C4—591no—
145C2×C4—1182no—
146C2×C4—1182no—
147C2×C4—1181no—
148C2×C4—1181no—
149C2×C4—1181no—
150C2×C4—1181no—
151C2×C4—2362no—
152C2×C4—2361no—
153C2×C4—2361no—
154C2×C4C2×C4×D5911yescharacteristic
155C2×C4D4×D5912yes—
156C8—42no—
157C8—2362no—
158C22—42no—
159C22—41no—
160C22—1181no—
161C22—1182no—
162C22—2361no—
163C22—2362no—
164C22C22⋊C4×D5911yescharacteristic
165C4—22no—
166C4—21no—
167C4—41no—
168C4—591no—
169C4—591no—
170C4—1182no—
171C4—2361no—
172C2—21no—
173C2—81no—
174C2—2361no—
175C2—2362no—
176C2#99×D5911yescharacteristic
subgroupG/H
centerC2#99×D59
commutatorC2×C4×C59C22×C4
FrattiniC2×Q8C22×D59
FittingC59×#355C2
socleC2×C59C2×#99
hypercenter#355D59
hypocenterC59#2132
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #16837385C2semidirect
3. #16837200C2semidirect
4. #16837199C2semidirect
5. C59×#355C2semidirect
93. #355D59semidirect
94. C59#2132semidirect