Finite Group Databasebeta

← #21423145

Subgroups — #21423145

Order 7552.

240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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#16837989C211yesmaximal, characteristic
2#16837738C211yesmaximal, characteristic, complemented
3#16837718C211yesmaximal, characteristic, complemented
4#16837339C211yesmaximal, characteristic, complemented
5#16837138C211yesmaximal, characteristic, complemented
6#16837125C211yesmaximal, characteristic, complemented
7C59×#327C211yesmaximal, characteristic, complemented
8#14273722—21no—
9#14273713—21no—
10#14273711—21no—
11#14273706C2211yescharacteristic
12#14273699—21no—
13#14273695—21no—
14D4×Dic59—21no—
15C2×C4⋊Dic59—21no—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×(C2×D59)⋊C4—21no—
18C2×(C2×D59)⋊C4C2211yescharacteristic
19#14273661—21no—
20#14273658—21no—
21#14273652—21no—
22#14273648—21no—
23C22⋊(C59⋊C8)C2211yescharacteristic
24#121×C59C2211yescharacteristic
25C22⋊C8×C59C2211yescharacteristic
26#95×C59C2211yescharacteristic
27C23×D59D411yescharacteristic
28C2×D4×C59—21no—
29C2×D4×C59D411yescharacteristic
30C22×C4×C59—21no—
31C22×C4×C59C2311yescharacteristic
32C2×C22⋊D59—21no—
33C2×C22⋊D59—21no—
34C22×Dic59—21no—
35C22×Dic59—21no—
36C22×Dic59D411yescharacteristic
37C2×Dic118D411yescharacteristic
38C2×C8×C59—21no—
39C4⋊C4×C59D411yescharacteristic
40C22⋊C4×C59—21no—
41C22⋊Dic59—21no—
42C22⋊Dic59—21no—
43(C2×D59)⋊C4—21no—
44(C2×D59)⋊C4—21no—
45(C2×D59)⋊C4—21no—
46(C2×D59)⋊C4—21no—
47(C2×D59)⋊C4—42no—
48C4⋊Dic59—21no—
49C4⋊Dic59—21no—
50C4⋊Dic59—21no—
51C4⋊Dic59—42no—
52C4⋊Dic59D411yescharacteristic
53Dic59⋊C4—21no—
54C4×Dic59—21no—
55C2×C59⋊C8—21no—
56C23×C59—21no—
57C23×C59C2×D411yescharacteristic
58C22×D59—21no—
59C22×D59—21no—
60C22×D59—21no—
61C22×D59—41no—
62C22×D59—41no—
63D4×C59—41no—
64D4×C59—41no—
65D4×C59—41no—
66C2×C4×C59—22no—
67C2×C4×C59—21no—
68C2×C4×C59—41no—
69C2×C4×C59—41no—
70C2×C4×C59—41no—
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C22⋊D59—81no—
74C22⋊D59—81no—
75C2×Dic59—21no—
76C2×Dic59—21no—
77C2×Dic59—21no—
78C2×Dic59—41no—
79C2×Dic59—41no—
80C2×Dic59—41no—
81C2×Dic59—41no—
82C2×Dic59—81no—
83Dic118—41no—
84C8×C59—41no—
85C59⋊C8—41no—
86C22×C59—21no—
87C22×C59—21no—
88C22×C59—41no—
89C22×C59—41no—
90C22×C59—41no—
91C22×C59#12011yescharacteristic
92C22×C59#13511yescharacteristic
93C22×C59#13711yescharacteristic
94C2×D59—42no—
95C2×D59—41no—
96C2×D59—41no—
97C2×D59—41no—
98C2×D59—81no—
99C4×C59—21no—
100C4×C59—21no—
101C4×C59—42no—
102C4×C59—41no—
103Dic59—41no—
104Dic59—41no—
105Dic59—41no—
106Dic59—81no—
107#1618—591nomaximal, Sylow
108C2×C59—21no—
109C2×C59—21no—
110C2×C59—81no—
111C2×C59#45211yescharacteristic
112C2×C59#45311yescharacteristic
113C2×C59#45811yescharacteristic
114D59—81no—
115#538—591no—
116#484—591no—
117#481—591no—
118#399—591no—
119#328—591no—
120#327D5911yescharacteristic, complemented
121#323—591no—
122C59#161811yescharacteristic, complemented, Sylow
123#126—1181no—
124#124—1181no—
125#123—1181no—
126C22⋊Q8—591no—
127#121—1181no—
128#121C2×D5911yescharacteristic
129#120—1181no—
130C4×D4—1181no—
131C2×C4⋊C4—591no—
132C2×C4⋊C4—1181no—
133C2×C22⋊C4—591no—
134C2×C22⋊C4—1181no—
135#107—1181no—
136#106—1181no—
137#103—1181no—
138#102—1181no—
139C22⋊C8—591no—
140C22⋊C8C2×D5911yescharacteristic
141#95C2×D5911yescharacteristic
142C24—591no—
143C2×Q8—591no—
144C2×D4—21no—
145C2×D4—1181no—
146C2×D4—1181no—
147C2×D4D23611yescharacteristic
148C22×C4—21no—
149C22×C4—591no—
150C22×C4—1181no—
151C22×C4—1181no—
152C22×C4C22×D5911yescharacteristic
153C2×C8—21no—
154C2×C8—1181no—
155C4⋊C4—591no—
156C4⋊C4—1181no—
157C4⋊C4—1181no—
158C4⋊C4—1181no—
159C4⋊C4—1181no—
160C4⋊C4—2362no—
161C4⋊C4D23611yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—1181no—
164C22⋊C4—1181no—
165C22⋊C4—1181no—
166C22⋊C4—1181no—
167C22⋊C4—1181no—
168C22⋊C4—1181no—
169C22⋊C4—2362no—
170C42—1181no—
171C23—21no—
172C23—1181no—
173C23—1181no—
174C23—1181no—
175C23—2361no—
176C23—2361no—
177C23D4×D5911yescharacteristic
178Q8—2361no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—4721no—
183D4—4721no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—1181no—
190C2×C4—1181no—
191C2×C4—1181no—
192C2×C4—4721no—
193C2×C4—2361no—
194C2×C4—2361no—
195C2×C4—2361no—
196C2×C4—2361no—
197C2×C4C2×D23611yescharacteristic
198C2×C4D4×D5911yescharacteristic
199C8—41no—
200C8—2361no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—4721no—
207C22—2362no—
208C22—2361no—
209C22—2361no—
210C22—2361no—
211C22#1427369711yescharacteristic
212C22#1427374611yescharacteristic
213C22#1427375611yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—4721no—
219C4—2361no—
220C4—2361no—
221C4—2361no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—4721no—
226C2#1683756511yescharacteristic
227C2#1683757111yescharacteristic
228C2#1683759311yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#327C2
socleC22×C59#120
hypercenter#327D59
hypocenterC59#1618
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #16837738C2semidirect
3. #16837718C2semidirect
4. #16837339C2semidirect
5. #16837138C2semidirect
6. #16837125C2semidirect
7. C59×#327C2semidirect
120. #327D59semidirect
122. C59#1618semidirect