Finite Group Databasebeta

← #21423131

Subgroups — #21423131

Order 7552.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#16837979C211yesmaximal, characteristic
2#16837720C211yesmaximal, characteristic, complemented
3#16837340C211yesmaximal, characteristic, complemented
4#16837137C211yesmaximal, characteristic, complemented
5#16837136C211yesmaximal, characteristic, complemented
6#16837127C211yesmaximal, characteristic, complemented
7C59×#481C211yesmaximal, characteristic, complemented
8C2×#11745687—21no—
9#14273705—21no—
10#14273704—21no—
11#14273701C2211yescharacteristic
12#14273700—21no—
13#14273699—21no—
14#14273699—21no—
15C2×Dic59⋊C4C2211yescharacteristic
16#14273658—21no—
17#14273647—21no—
18C22⋊(C59⋊C8)C2211yescharacteristic
19C59⋊#95—21no—
20C59⋊#95—21no—
21C59⋊#95C2211yescharacteristic
22#121×C59C2211yescharacteristic
23C2×C4⋊C4×C59C2211yescharacteristic
24#106×C59—21no—
25#102×C59—21no—
26C22⋊C8×C59C2211yescharacteristic
27C2×D4×C59—21no—
28C2×D4×C59D411yescharacteristic
29C22×C4×C59—21no—
30C22×C4×C59C2311yescharacteristic
31C2×C22⋊D59—21no—
32C2×C22⋊D59—21no—
33C2×C22⋊D59—21no—
34C22×Dic59—21no—
35C22×Dic59—21no—
36C22×Dic59D411yescharacteristic
37C22×Dic59D411yescharacteristic
38#11745687—42no—
39#11745687—42no—
40C2×D236D411yescharacteristic
41C2×C4×D59—21no—
42C2×Dic118—21no—
43C2×C8×C59—21no—
44C4⋊C4×C59—21no—
45C4⋊C4×C59—21no—
46C4⋊C4×C59D411yescharacteristic
47C22⋊C4×C59—21no—
48C22⋊Dic59—21no—
49(C2×D59)⋊C4—21no—
50(C2×D59)⋊C4—21no—
51C4⋊Dic59D411yescharacteristic
52Dic59⋊C4—21no—
53Dic59⋊C4—21no—
54Dic59⋊C4—21no—
55C2×C59⋊C8—21no—
56C23×C59—21no—
57C23×C59C2×D411yescharacteristic
58C22×D59—21no—
59D4×C59—41no—
60D4×C59—41no—
61D4×C59—41no—
62C2×C4×C59—21no—
63C2×C4×C59—41no—
64C2×C4×C59—42no—
65C2×C4×C59—41no—
66C2×C4×C59C2×D411yescharacteristic
67C2×C4×C59C2×D411yescharacteristic
68C22⋊D59—42no—
69C22⋊D59—41no—
70C22⋊D59—41no—
71C22⋊D59—81no—
72C2×Dic59—21no—
73C2×Dic59—21no—
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—42no—
77C2×Dic59—41no—
78C2×Dic59—41no—
79C2×Dic59—41no—
80C2×Dic59—41no—
81C2×Dic59SD1612yes—
82D236—41no—
83C4×D59—42no—
84Dic118—42no—
85C8×C59—41no—
86C59⋊C8—41no—
87C22×C59—21no—
88C22×C59—21no—
89C22×C59—41no—
90C22×C59—41no—
91C22×C59—41no—
92C22×C59#12011yescharacteristic
93C22×C59C2×SD1611yescharacteristic
94C22×C59AGL(1,ℤ/8)11yescharacteristic
95C2×D59—41no—
96C2×D59—41no—
97C2×D59—41no—
98C4×C59—21no—
99C4×C59—21no—
100C4×C59—41no—
101C4×C59—81no—
102Dic59—22no—
103Dic59—41no—
104Dic59—41no—
105Dic59—81no—
106#1616—591nomaximal, Sylow
107C2×C59—21no—
108C2×C59—21no—
109C2×C59—81no—
110C2×C59#45011yescharacteristic
111C2×C59#45411yescharacteristic
112C2×C59#45811yescharacteristic
113D59—81no—
114#537—591no—
115#481—591no—
116#481D5911yescharacteristic, complemented
117#400—591no—
118#327—591no—
119#327—591no—
120#324—591no—
121C59#161611yescharacteristic, complemented, Sylow
122C2×#41—1181no—
123C22⋊Q8—1181no—
124C22⋊Q8—1181no—
125#121—591no—
126#121—1181no—
127#121—1181no—
128#121—1181no—
129#121C2×D5911yescharacteristic
130C2×C4⋊C4—591no—
131C2×C4⋊C4C2×D5911yescharacteristic
132#106—21no—
133#106—1181no—
134#102—21no—
135#102—1181no—
136C22⋊C8—591no—
137C22⋊C8C2×D5911yescharacteristic
138#95—591no—
139#95—1181no—
140#95—1181no—
141#41—2362no—
142#41—2362no—
143C2×Q8—1181no—
144C2×D4—21no—
145C2×D4—591no—
146C2×D4—1181no—
147C2×D4—1181no—
148C2×D4—1181no—
149C2×D4C22⋊D5911yescharacteristic
150C22×C4—21no—
151C22×C4—591no—
152C22×C4—591no—
153C22×C4—1181no—
154C22×C4—1181no—
155C22×C4—1181no—
156C22×C4C22×D5911yescharacteristic
157C2×C8—21no—
158C2×C8—1181no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—591no—
162C4⋊C4—1181no—
163C4⋊C4—1181no—
164C4⋊C4—1181no—
165C4⋊C4C22⋊D5911yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—1181no—
168C22⋊C4—1181no—
169C22⋊C4—1181no—
170C23—21no—
171C23—1181no—
172C23D4×D5911yescharacteristic
173Q8—2362no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—4721no—
178D4—2361no—
179D4—2362no—
180D4—2361no—
181D4—2361no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—41no—
186C2×C4—592no—
187C2×C4—1181no—
188C2×C4—1181no—
189C2×C4—1181no—
190C2×C4—1181no—
191C2×C4—2362no—
192C2×C4—2362no—
193C2×C4—2361no—
194C2×C4—2361no—
195C2×C4—2361no—
196C2×C4—2361no—
197C2×C4D4×D5911yescharacteristic
198C2×C4C2×C22⋊D5911yescharacteristic
199C8—41no—
200C8—2361no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—2361no—
207C22—2361no—
208C22—2361no—
209C22#1427369511yescharacteristic
210C22SD16×D5911yescharacteristic
211C22#1427375411yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—1182no—
217C4—4721no—
218C4—2361no—
219C4—2361no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—4721no—
224C2#1683755111yescharacteristic
225C2#1683757311yescharacteristic
226C2#1683759111yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#481C2
socleC22×C59#120
hypercenter#481D59
hypocenterC59#1616
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #16837720C2semidirect
3. #16837340C2semidirect
4. #16837137C2semidirect
5. #16837136C2semidirect
6. #16837127C2semidirect
7. C59×#481C2semidirect
116. #481D59semidirect
121. C59#1616semidirect