Finite Group Databasebeta

← #21432155

Subgroups — #21432155

Order 7552.

430 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#14273721C211yesmaximal, characteristic
2#16837340C212yesmaximal, complemented
3#16837337C212yesmaximal
4#16837333C212yesmaximal, complemented
5#16837328C212yesmaximal
6#16837321C212yesmaximal, complemented
7#16837313C212yesmaximal
8#16837270C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C59C211yesmaximal, characteristic, complemented
10#14273721—24no—
11C2×Dic59⋊C4C2211yescharacteristic
12C2×Dic59⋊C4C2211yescharacteristic
13C2×Dic59⋊C4C2211yescharacteristic
14C2×Dic59⋊C4C2214yes—
15C2×(C2×D59)⋊C4C2211yescharacteristic
16C2×(C2×D59)⋊C4C2211yescharacteristic
17C2×(C2×D59)⋊C4C2211yescharacteristic
18C2×(C2×D59)⋊C4C2214yes—
19C59⋊#95C2212yes—
20C59⋊#95C2212yes—
21C59⋊#95C2212yes—
22C59⋊#95C2214yes—
23C59⋊#95C2214yes—
24C22×Q8×C59C2212yes—
25C4⋊Q8×C59—24no—
26C2×C4⋊C4×C59C2212yes—
27C2×C4⋊C4×C59C2212yes—
28C2×C42×C59C2211yescharacteristic
29C23×D59C2311yescharacteristic
30C2×Q8×C59—24no—
31C2×Q8×C59—44no—
32C22×C4×C59C2314yes—
33C22×C4×C59C2311yescharacteristic
34C22×C4×C59C2311yescharacteristic
35C22×C4×C59C2311yescharacteristic
36C22×Dic59C2314yes—
37C22×Dic59C2311yescharacteristic
38C22×Dic59C2311yescharacteristic
39C22×Dic59C2311yescharacteristic
40C4⋊C4×C59—24no—
41C4⋊C4×C59—24no—
42C42×C59D414yes—
43(C2×D59)⋊C4—22no—
44(C2×D59)⋊C4—22no—
45(C2×D59)⋊C4—22no—
46(C2×D59)⋊C4—44no—
47Dic59⋊C4—22no—
48Dic59⋊C4—22no—
49Dic59⋊C4—22no—
50Dic59⋊C4—44no—
51C23×C59C2411yescharacteristic
52C22×D59—21no—
53C22×D59—22no—
54C22×D59—22no—
55C22×D59—22no—
56Q8×C59—48no—
57C2×C4×C59—22no—
58C2×C4×C59—22no—
59C2×C4×C59—22no—
60C2×C4×C59—24no—
61C2×C4×C59—24no—
62C2×C4×C59—24no—
63C2×C4×C59C2×D412yes—
64C2×C4×C59C2×D412yes—
65C2×C4×C59C2×D412yes—
66C2×Dic59—21no—
67C2×Dic59—21no—
68C2×Dic59—21no—
69C2×Dic59—22no—
70C2×Dic59—24no—
71C2×Dic59—22no—
72C2×Dic59—22no—
73C2×Dic59—24no—
74C2×Dic59—24no—
75C22×C59C22×D411yescharacteristic
76C22×C59H(5,𝔽2)12yes—
77C22×C592−1+412yes—
78C22×C592−1+412yes—
79C2×D59—41no—
80C2×D59—41no—
81C2×D59—41no—
82C2×D59—44no—
83C4×C59—22no—
84C4×C59—22no—
85C4×C59—22no—
86C4×C59—44no—
87Dic59—41no—
88Dic59—41no—
89Dic59—41no—
90Dic59—44no—
91#2821—591nomaximal, Sylow
92C2×C59#53511yescharacteristic
93C2×C59#53611yescharacteristic
94C2×C59#53611yescharacteristic
95C2×C59#56314yes—
96D59—81no—
97C2×C4⋊Q8D5911yescharacteristic, complemented
98C2×#126—591no—
99#400—592no—
100#399—592no—
101#398—592no—
102#397—592no—
103#395—592no—
104#393—592no—
105#383—591no—
106C59#282111yescharacteristic, complemented, Sylow
107C22×Q8C2×D5912yes—
108C4⋊Q8—24no—
109#126—1184no—
110C2×C4⋊C4—591no—
111C2×C4⋊C4—591no—
112C2×C4⋊C4—591no—
113C2×C4⋊C4—594no—
114C2×C4⋊C4C2×D5912yes—
115C2×C4⋊C4C2×D5912yes—
116C2×C22⋊C4—591no—
117C2×C22⋊C4—591no—
118C2×C22⋊C4—591no—
119C2×C22⋊C4—594no—
120C2×C42C2×D5911yescharacteristic
121#95—592no—
122#95—592no—
123#95—592no—
124#95—594no—
125#95—594no—
126C24—591no—
127C2×Q8—24no—
128C2×Q8—44no—
129C22×C4—594no—
130C22×C4—591no—
131C22×C4—591no—
132C22×C4—591no—
133C22×C4C22×D5914yes—
134C22×C4C22×D5911yescharacteristic
135C22×C4C22×D5911yescharacteristic
136C22×C4C22×D5911yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—24no—
139C4⋊C4—1182no—
140C4⋊C4—1182no—
141C4⋊C4—1182no—
142C4⋊C4—2364no—
143C22⋊C4—1182no—
144C22⋊C4—1182no—
145C22⋊C4—1182no—
146C22⋊C4—2364no—
147C42C22⋊D5914yes—
148C23—1181no—
149C23—1182no—
150C23—1182no—
151C23—1182no—
152C23C23×D5911yescharacteristic
153Q8—48no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—1181no—
161C2×C4—1181no—
162C2×C4—1181no—
163C2×C4—1184no—
164C2×C4—1182no—
165C2×C4—1184no—
166C2×C4—1184no—
167C2×C4—1182no—
168C2×C4—1182no—
169C2×C4C2×C22⋊D5912yes—
170C2×C4C2×C22⋊D5912yes—
171C2×C4C2×C22⋊D5912yes—
172C22—2364no—
173C22—2361no—
174C22—2361no—
175C22—2361no—
176C22C22×C22⋊D5911yescharacteristic
177C22#1427377212yes—
178C22#1427377512yes—
179C22#1427377512yes—
180C4—22no—
181C4—22no—
182C4—22no—
183C4—44no—
184C4—2364no—
185C4—2361no—
186C4—2361no—
187C4—2361no—
188C2—4721no—
189C2#1683796911yescharacteristic
190C2#1683797611yescharacteristic
191C2#1683797611yescharacteristic
192C2#1683815114yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC2×C4⋊Q8×C59C2
hypercenterC2×C4⋊Q8D59
hypocenterC59#2821
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16837340C2semidirect
4. #16837333C2semidirect
6. #16837321C2semidirect
8. #16837270C2semidirect
9. C2×C4⋊Q8×C59C2semidirect
97. C2×C4⋊Q8D59semidirect
106. C59#2821semidirect