Finite Group Databasebeta

← #21435288

Subgroups — #21435288

Order 7552.

368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837952C211yesmaximal, characteristic
2C2×#14273719C211yesmaximal, characteristic, complemented
3#16837811C212yesmaximal, complemented
4#16837767C212yesmaximal, complemented
5#16837721C212yesmaximal, complemented
6#16837716C212yesmaximal, complemented
7#16837703C214yesmaximal, complemented
8C59×#432C211yesmaximal, characteristic, complemented
9C2×#11745685—21no—
10#14273727C2211yescharacteristic
11#14273724C2211yescharacteristic
12#14273719—21no—
13#14273719—21no—
14#14273719C2212yes—
15#14273719C2212yes—
16#14273715—21no—
17#14273701—21no—
18#14273701C2212yes—
19C4×D236—21no—
20C4×D236C2212yes—
21C2×C4⋊Dic59C2211yescharacteristic
22C2×C4⋊Dic59C2211yescharacteristic
23C2×Dic59⋊C4—21no—
24C2×Dic59⋊C4—21no—
25#14273661C2214yes—
26#14273659C2214yes—
27#14273649C2214yes—
28#14273649C2214yes—
29C2×C42×C59C2211yescharacteristic
30C4⋊C8×C59C2212yes—
31C22⋊C8×C59C2212yes—
32#97×C59C2212yes—
33C22×C4×C59D411yescharacteristic
34C22×C4×C59D411yescharacteristic
35C22×C4×C59C2311yescharacteristic
36C2×C22⋊D59—22no—
37C22×Dic59—21no—
38C22×Dic59—21no—
39#11745685—44no—
40C2×D236—21no—
41C2×D236—21no—
42C2×D236C2312yes—
43C2×C4×D59—22no—
44C2×Dic118—21no—
45C2×C8×C59C2314yes—
46C42×C59D411yescharacteristic
47C42×C59D411yescharacteristic
48C42×C59C2311yescharacteristic
49C42×C59C2311yescharacteristic
50(C2×D59)⋊C4—22no—
51(C2×D59)⋊C4—22no—
52C4⋊Dic59—21no—
53C4⋊Dic59—21no—
54C4⋊Dic59—21no—
55C4⋊Dic59C2312yes—
56C4⋊Dic59C2312yes—
57C4⋊Dic59C2312yes—
58Dic59⋊C4—22no—
59Dic59⋊C4—22no—
60Dic59⋊C4—22no—
61Dic59⋊C4—22no—
62C23×C59C2×D411yescharacteristic
63C22×D59—22no—
64C2×C4×C59—22no—
65C2×C4×C59—22no—
66C2×C4×C59—41no—
67C2×C4×C59C2×D411yescharacteristic
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2411yescharacteristic
73C22⋊D59—44no—
74C2×Dic59—22no—
75C2×Dic59—22no—
76C2×Dic59—22no—
77C2×Dic59—42no—
78C2×Dic59—42no—
79D236—24no—
80D236—42no—
81D236—42no—
82C4×D59—44no—
83Dic118—42no—
84C8×C59—24no—
85C22×C59—21no—
86C22×C59—21no—
87C22×C59AGL(1,ℤ/8)12yes—
88C22×C59C22×D411yescharacteristic
89C2×D59—42no—
90C2×D59—42no—
91C2×D59—42no—
92C4×C59—21no—
93C4×C59—21no—
94C4×C59—21no—
95C4×C59—21no—
96C4×C59—21no—
97C4×C592−1+412yes—
98Dic59—42no—
99Dic59—42no—
100Dic59—42no—
101#3234—591nomaximal, Sylow
102C2×C59—22no—
103C2×C59#53611yescharacteristic
104C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
105C2×C59#57511yescharacteristic
106D59—82no—
107#532—591no—
108C2×#125—591no—
109#501—592no—
110#490—592no—
111#481—592no—
112#480—592no—
113#478—594no—
114#432D5911yescharacteristic, complemented
115C59#323411yescharacteristic, complemented, Sylow
116C2×#41—1181no—
117C4⋊Q8—591no—
118#127—591no—
119#125—592no—
120#125—592no—
121#125—1181no—
122#125—1181no—
123#124—1181no—
124#121—592no—
125#121—1181no—
126C4×D4—592no—
127C4×D4—1181no—
128C2×C4⋊C4—591no—
129C2×C4⋊C4—591no—
130C2×C4⋊C4—1181no—
131C2×C4⋊C4—1181no—
132C2×C42C2×D5911yescharacteristic
133#107—594no—
134#106—594no—
135C4⋊C8C2×D5912yes—
136#102—594no—
137#102—594no—
138C22⋊C8C2×D5912yes—
139#97C2×D5912yes—
140#41—2364no—
141C2×Q8—1181no—
142C2×D4—592no—
143C2×D4—1182no—
144C2×D4—1181no—
145C2×D4—1181no—
146C22×C4—1181no—
147C22×C4—1181no—
148C22×C4—1182no—
149C22×C4D23611yescharacteristic
150C22×C4D23611yescharacteristic
151C22×C4C22×D5911yescharacteristic
152C2×C8C22×D5914yes—
153C4⋊C4—592no—
154C4⋊C4—592no—
155C4⋊C4—592no—
156C4⋊C4—1181no—
157C4⋊C4—1181no—
158C4⋊C4—1182no—
159C4⋊C4—1182no—
160C4⋊C4—1182no—
161C4⋊C4—1182no—
162C4⋊C4—1181no—
163C22⋊C4—1182no—
164C22⋊C4—1182no—
165C42D23611yescharacteristic
166C42D23611yescharacteristic
167C42C22×D5911yescharacteristic
168C42C22×D5911yescharacteristic
169C23—1182no—
170C23C2×D23611yescharacteristic
171Q8—2362no—
172D4—1184no—
173D4—2362no—
174D4—2362no—
175D4—2364no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—1182no—
180C2×C4—1182no—
181C2×C4—1182no—
182C2×C4—2364no—
183C2×C4—2362no—
184C2×C4—2362no—
185C2×C4C2×D23611yescharacteristic
186C2×C4C2×D23611yescharacteristic
187C2×C4C2×D23611yescharacteristic
188C2×C4C2×D23611yescharacteristic
189C2×C4C2×D23611yescharacteristic
190C2×C4C23×D5911yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—2362no—
195C22—2362no—
196C22—2362no—
197C22#1427375512yes—
198C22C22×D23611yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—21no—
204C4—2362no—
205C4—2362no—
206C4—2362no—
207C4#1427377412yes—
208C2—22no—
209C2—4722no—
210C2#1683797811yescharacteristic
211C2C2×#1427375511yescharacteristic
212C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#432C2
socleC22×C59C22×D4
hypercenter#432D59
hypocenterC59#3234
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×#14273719C2semidirect
3. #16837811C2semidirect
4. #16837767C2semidirect
5. #16837721C2semidirect
6. #16837716C2semidirect
7. #16837703C2semidirect
8. C59×#432C2semidirect
114. #432D59semidirect
115. C59#3234semidirect