Finite Group Databasebeta

← #21425786

Subgroups — #21425786

Order 7552.

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

normal subgroups only

This group has 262 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#16837970C211yesmaximal, characteristic
2#16837385C212yesmaximal, complemented
3#16837199C211yesmaximal, characteristic, complemented
4#16837198C212yesmaximal, complemented
5C59×#355C211yesmaximal, characteristic, complemented
6C2×#11745689C2211yescharacteristic
7C2×D4×D59C411yescharacteristic
8M16×D59—22no—
9#14273724C411yescharacteristic
10#14273723C411yescharacteristic
11#14273716C2211yescharacteristic
12#14273700—22no—
13#14273697—22no—
14#14273684C411yescharacteristic
15#14273646C2212yescomplemented
16#14273643—22no—
17#124×C59C2211yescharacteristic
18#101×C59C2212yescomplemented
19C23×D59—21no—
20C2×Q8×C59C2311yescharacteristic
21C2×D4×C59C2×C411yescharacteristic
22C2×C22⋊D59—22no—
23C2×C22⋊D59—21no—
24#11745689—42no—
25D4×D59—42no—
26C2×D236—22no—
27C2×D236C2×C411yescharacteristic
28C2×D236C2×C411yescharacteristic
29C2×D236D412yes—
30C2×C4×D59C2×C411yescharacteristic
31C2×C4×D59D412yes—
32M16×C59—22no—
33C22⋊C4×C59—22no—
34C42×C59C2×C411yescharacteristic
35(C2×D59)⋊C4—21no—
36(C2×D59)⋊C4—22no—
37Dic59⋊C4—21no—
38C4×Dic59C2×C411yescharacteristic
39#11745664—22no—
40#11745659—42no—
41C8×D59—42no—
42C23×C59—21no—
43C22×D59—21no—
44C22×D59—42no—
45C22×D59—82no—
46C22×D59C22⋊C411yescharacteristic
47C22×D59C22⋊C412yes—
48Q8×C59—41no—
49D4×C59—41no—
50C2×C4×C59—21no—
51C2×C4×C59C22×C411yescharacteristic
52C2×C4×C59C2×D412yes—
53C22⋊D59—42no—
54C22⋊D59—82no—
55C2×Dic59—21no—
56C2×Dic59C22⋊C411yescharacteristic
57D236—41no—
58D236—42no—
59D236—41no—
60D236—82no—
61C4×D59—22no—
62C4×D59—22no—
63C4×D59—22no—
64C8×C59—42no—
65C59⋊C8—42no—
66C22×C59—42no—
67C22×C59—41no—
68C22×C59C2×C22⋊C411yescharacteristic
69C2×D59—21no—
70C2×D59—22no—
71C2×D59—42no—
72C2×D59—41no—
73C2×D59—42no—
74C2×D59—41no—
75C2×D59—84no—
76C4×C59—22no—
77C4×C59—21no—
78C4×C59—41no—
79Dic59—41no—
80Dic59#9912yes—
81#2134—591nomaximal, Sylow
82C2×C59—21no—
83C2×C59—81no—
84C2×C59C2×#9911yescharacteristic
85D59—42no—
86D59—41no—
87D59—81no—
88#535—591no—
89#413—592no—
90#355—591no—
91#355—592no—
92#355D5911yescharacteristic, complemented
93C59#213411yescharacteristic, complemented, Sylow
94C2×#41—591no—
95C22×D4—591no—
96C2×M16—1182no—
97#127—591no—
98#127—591no—
99#124—591no—
100#124C2×D5911yescharacteristic
101#121—1182no—
102#120—1182no—
103#117—591no—
104#101—592no—
105#101C2×D5912yescomplemented
106#100—1182no—
107C24—1181no—
108#41—2362no—
109C2×Q8C22×D5911yescharacteristic
110C2×D4—591no—
111C2×D4—591no—
112C2×D4—592no—
113C2×D4—1182no—
114C2×D4—1181no—
115C2×D4—1182no—
116C2×D4—2362no—
117C2×D4C4×D5911yescharacteristic
118C22×C4—591no—
119C22×C4—592no—
120M16—22no—
121M16—1182no—
122M16—2362no—
123C2×C8—2362no—
124C4⋊C4—1181no—
125C22⋊C4—22no—
126C22⋊C4—1181no—
127C22⋊C4—1182no—
128C42—591no—
129C42C4×D5911yescharacteristic
130C23—21no—
131C23—591no—
132C23—592no—
133C23—1181no—
134C23—4722no—
135C23—2362no—
136Q8—41no—
137D4—41no—
138D4—4722no—
139D4—4722no—
140D4—2362no—
141D4—2361no—
142D4—2361no—
143D4—2362no—
144C2×C4—21no—
145C2×C4—591no—
146C2×C4—1182no—
147C2×C4—1182no—
148C2×C4—1182no—
149C2×C4—1181no—
150C2×C4C2×C4×D5911yescharacteristic
151C2×C4D4×D5912yes—
152C8—42no—
153C8—2362no—
154C22—42no—
155C22—41no—
156C22—1181no—
157C22—1182no—
158C22—4724no—
159C22—2362no—
160C22—2362no—
161C22—2361no—
162C22—2361no—
163C22C22⋊C4×D5911yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—592no—
168C4—2361no—
169C2—21no—
170C2—81no—
171C2—4721no—
172C2—2361no—
173C2—2362no—
174C2#99×D5911yescharacteristic
subgroupG/H
centerC2#99×D59
commutatorC2×C4×C59C22×C4
FrattiniC2×Q8C22×D59
FittingC59×#355C2
socleC2×C59C2×#99
hypercenter#355D59
hypocenterC59#2134
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. #16837199C2semidirect
4. #16837198C2semidirect
5. C59×#355C2semidirect
15. #14273646C22semidirect
18. #101×C59C22semidirect
92. #355D59semidirect
93. C59#2134semidirect
105. #101C2×D59semidirect