Finite Group Databasebeta

← #21425513

Subgroups — #21425513

Order 7552.

258 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 77 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×#14273649C211yesmaximal, characteristic
2C2×#14273647C211yesmaximal, characteristic
3#16837303C211yesmaximal, characteristic
4#16837267C211yesmaximal, characteristic, complemented
5#16837164C211yesmaximal, characteristic, complemented
6#16837156C211yesmaximal, characteristic, complemented
7C59×#340C211yesmaximal, characteristic, complemented
8C22×D236C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×(C2×D59)⋊C4—21no—
12C2×(C2×D59)⋊C4—21no—
13C2×C4×Dic59C2211yescharacteristic
14#14273649—22no—
15#14273647—22no—
16C59⋊#95—21no—
17C59⋊#95—21no—
18C22×C8×C59C2211yescharacteristic
19C2×C4⋊C4×C59C2211yescharacteristic
20C2×C4⋊C4×C59C2211yescharacteristic
21C23×D59—21no—
22C22×C4×C59—21no—
23C22×C4×C59—21no—
24C22×C4×C59C2311yescharacteristic
25C22×Dic59—21no—
26C22×Dic59D411yescharacteristic
27C22×Dic59D411yescharacteristic
28C2×D236—21no—
29C2×D236—21no—
30C2×D236—21no—
31C2×D236—21no—
32C2×D236—21no—
33C2×D236D412yes—
34C2×C8×C59—21no—
35C2×C8×C59—21no—
36C2×C8×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59—21no—
41(C2×D59)⋊C4—42no—
42(C2×D59)⋊C4—42no—
43C4⋊Dic59—21no—
44C4⋊Dic59—21no—
45C4×Dic59—21no—
46C4×Dic59—21no—
47C2×C59⋊C8—21no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C23×C59C2×D411yescharacteristic
51C22×D59—22no—
52C22×D59—41no—
53C22×D59—41no—
54C22×D59—41no—
55C22×D59—41no—
56C22×D59—41no—
57C22×D59—41no—
58C2×C4×C59—41no—
59C2×C4×C59—41no—
60C2×C4×C59—41no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59C2×D411yescharacteristic
65C2×C4×C59#4111yescharacteristic
66C2×C4×C59#4111yescharacteristic
67C2×C4×C59#4111yescharacteristic
68C2×C4×C59#4111yescharacteristic
69C2×C4×C59#4111yescharacteristic
70C2×Dic59—21no—
71C2×Dic59—21no—
72C2×Dic59—21no—
73C2×Dic59—21no—
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—41no—
77C2×Dic59—41no—
78C2×Dic59—41no—
79D236—22no—
80D236—22no—
81D236—41no—
82D236—41no—
83C8×C59—41no—
84C59⋊C8—41no—
85C22×C59#12111yescharacteristic
86C22×C59#12311yescharacteristic
87C22×C59#12411yescharacteristic
88C22×C59#13511yescharacteristic
89C22×C59#13511yescharacteristic
90C22×C59AGL(1,ℤ/8)11yescharacteristic
91C22×C59AGL(1,ℤ/8)11yescharacteristic
92C2×D59—42no—
93C2×D59—42no—
94C2×D59—42no—
95C2×D59—81no—
96C2×D59—81no—
97C2×D59—81no—
98C2×D59—81no—
99C4×C59—81no—
100C4×C59—81no—
101C4×C59#12311yescharacteristic
102C4×C59#12311yescharacteristic
103C4×C59#12611yescharacteristic
104C4×C59#12611yescharacteristic
105Dic59—41no—
106Dic59—41no—
107Dic59—81no—
108#2073—591nomaximal, Sylow
109C2×C59#39711yescharacteristic
110C2×C59#46311yescharacteristic
111C2×C59#46311yescharacteristic
112C2×C59#48211yescharacteristic
113C2×C59#48211yescharacteristic
114C2×C59#48811yescharacteristic
115C2×C59#49011yescharacteristic
116D59—82no—
117C2×#102—591no—
118C2×#102—591no—
119#390—591no—
120#382—591no—
121#340—591no—
122#340D5911yescharacteristic, complemented
123#336—591no—
124C59#207311yescharacteristic, complemented, Sylow
125C22×D4—591no—
126C22×C8—591no—
127C22×C8C2×D5911yescharacteristic
128C2×C4⋊C4—591no—
129C2×C4⋊C4C2×D5911yescharacteristic
130C2×C4⋊C4C2×D5911yescharacteristic
131C2×C22⋊C4—1181no—
132C2×C22⋊C4—1181no—
133C2×C42—591no—
134#102—1182no—
135#102—1182no—
136#95—1181no—
137#95—1181no—
138C24—1181no—
139C2×D4—592no—
140C2×D4—1181no—
141C2×D4—1181no—
142C2×D4—1181no—
143C2×D4—1181no—
144C2×D4—1181no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—591no—
148C22×C4—591no—
149C22×C4—1181no—
150C22×C4C22×D5911yescharacteristic
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—1181no—
155C2×C8—1181no—
156C2×C8—1181no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1181no—
162C4⋊C4—1181no—
163C22⋊C4—2362no—
164C22⋊C4—2362no—
165C42—1181no—
166C42—1181no—
167C23—1182no—
168C23—2361no—
169C23—2361no—
170C23—2361no—
171C23—2361no—
172C23—2361no—
173C23—2361no—
174C23D4×D5911yescharacteristic
175D4—1182no—
176D4—1182no—
177D4—2361no—
178D4—2361no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—1181no—
186C2×C4—1181no—
187C2×C4—1181no—
188C2×C4—1181no—
189C2×C4—1181no—
190C2×C4—1181no—
191C2×C4—2361no—
192C2×C4—2361no—
193C2×C4—2361no—
194C2×C4#1174568511yescharacteristic
195C2×C4#1174568511yescharacteristic
196C2×C4#1174568511yescharacteristic
197C2×C4D4×D5911yescharacteristic
198C2×C4#1174568711yescharacteristic
199C2×C4#1174568911yescharacteristic
200C8—41no—
201C8—2361no—
202C22—4721no—
203C22—4721no—
204C22—4721no—
205C22—4721no—
206C22—2362no—
207C22—2362no—
208C22—2362no—
209C22#1427370011yescharacteristic
210C22#1427371211yescharacteristic
211C22#1427371311yescharacteristic
212C22#1427374811yescharacteristic
213C22#1427375011yescharacteristic
214C22#1427375111yescharacteristic
215C22#1427375411yescharacteristic
216C4—81no—
217C4—81no—
218C4—4721no—
219C4—2361no—
220C4—2361no—
221C4#1427370911yescharacteristic
222C4#1427371211yescharacteristic
223C4#1427372111yescharacteristic
224C4#1427372211yescharacteristic
225C2—4722no—
226C2#1683733111yescharacteristic
227C2#1683761611yescharacteristic
228C2#1683762011yescharacteristic
229C2#1683772811yescharacteristic
230C2#1683772911yescharacteristic
231C2#1683775811yescharacteristic
232C2#1683776511yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#340C2
socleC23×C59C2×D4
hypercenter#340D59
hypocenterC59#2073
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
4. #16837267C2semidirect
5. #16837164C2semidirect
6. #16837156C2semidirect
7. C59×#340C2semidirect
122. #340D59semidirect
124. C59#2073semidirect