Finite Group Databasebeta

← #21423113

Subgroups — #21423113

Order 7552.

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

normal subgroups only

This group has 232 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#16837992C211yesmaximal, characteristic
2#16837730C211yesmaximal, characteristic, complemented
3#16837716C211yesmaximal, characteristic, complemented
4#16837329C211yesmaximal, characteristic, complemented
5#16837135C211yesmaximal, characteristic, complemented
6#16837125C211yesmaximal, characteristic, complemented
7C59×#328C211yesmaximal, characteristic, complemented
8#14273722—21no—
9#14273716—21no—
10#14273712—21no—
11#14273702—21no—
12#14273701C2211yescharacteristic
13#14273697—21no—
14(C22⋊D59)⋊C4—21no—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×(C2×D59)⋊C4—21no—
17C2×(C2×D59)⋊C4C2211yescharacteristic
18#14273661—21no—
19#14273658—21no—
20#14273651—21no—
21#14273649—21no—
22C22⋊(C59⋊C8)C2211yescharacteristic
23C59⋊#95—21no—
24C22⋊Q8×C59C2211yescharacteristic
25C22⋊C8×C59C2211yescharacteristic
26#95×C59C2211yescharacteristic
27C23×D59D411yescharacteristic
28C2×Q8×C59D411yescharacteristic
29C22×C4×C59—21no—
30C22×C4×C59C2311yescharacteristic
31C2×C22⋊D59—21no—
32C22×Dic59—21no—
33C22×Dic59D411yescharacteristic
34C2×D236—21no—
35C2×D236—21no—
36C2×D236D411yescharacteristic
37C2×C4×D59—21no—
38C2×C8×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59D411yescharacteristic
41C22⋊C4×C59—21no—
42(C2×D59)⋊C4—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—21no—
48(C2×D59)⋊C4—42no—
49C4⋊Dic59—21no—
50C4⋊Dic59—21no—
51C4⋊Dic59D411yescharacteristic
52Dic59⋊C4—21no—
53C4×Dic59—21no—
54C2×C59⋊C8—21no—
55C23×C59C2×D411yescharacteristic
56C22×D59—21no—
57C22×D59—21no—
58C22×D59—21no—
59C22×D59—21no—
60C22×D59—41no—
61C22×D59—41no—
62Q8×C59—41no—
63C2×C4×C59—21no—
64C2×C4×C59—21no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59—41no—
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C22⋊D59—41no—
72C22⋊D59—41no—
73C2×Dic59—21no—
74C2×Dic59—21no—
75C2×Dic59—41no—
76C2×Dic59—41no—
77C2×Dic59—41no—
78C2×Dic59—41no—
79D236—41no—
80D236—81no—
81D236—81no—
82C4×D59—81no—
83C8×C59—41no—
84C59⋊C8—41no—
85C22×C59—21no—
86C22×C59—21no—
87C22×C59#12011yescharacteristic
88C22×C59#13511yescharacteristic
89C22×C59AGL(1,ℤ/8)11yescharacteristic
90C2×D59—42no—
91C2×D59—41no—
92C2×D59—41no—
93C2×D59—41no—
94C2×D59—41no—
95C2×D59—41no—
96C2×D59—41no—
97C2×D59—81no—
98C4×C59—21no—
99C4×C59—21no—
100C4×C59—41no—
101C4×C59—41no—
102C4×C59—81no—
103Dic59—41no—
104Dic59—41no—
105Dic59—81no—
106#1612—591nomaximal, Sylow
107C2×C59—21no—
108C2×C59—21no—
109C2×C59#44911yescharacteristic
110C2×C59#45511yescharacteristic
111C2×C59#45811yescharacteristic
112D59—81no—
113D59—81no—
114#538—591no—
115#483—591no—
116#480—591no—
117#397—591no—
118#328D5911yescharacteristic, complemented
119#327—591no—
120#323—591no—
121C59#161211yescharacteristic, complemented, Sylow
122#126—1181no—
123#124—1181no—
124#123—1181no—
125C22⋊Q8C2×D5911yescharacteristic
126#121—591no—
127#121—1181no—
128#120—1181no—
129C4×D4—1181no—
130C2×C4⋊C4—591no—
131C2×C22⋊C4—591no—
132C2×C22⋊C4—1181no—
133#107—1181no—
134#106—1181no—
135#103—1181no—
136#102—1181no—
137C22⋊C8—591no—
138C22⋊C8C2×D5911yescharacteristic
139#95—1181no—
140#95C2×D5911yescharacteristic
141C24—591no—
142C2×Q8D23611yescharacteristic
143C2×D4—591no—
144C2×D4—1181no—
145C2×D4—1181no—
146C2×D4—1181no—
147C22×C4—21no—
148C22×C4—591no—
149C22×C4—1181no—
150C22×C4—1181no—
151C22×C4C22×D5911yescharacteristic
152C2×C8—21no—
153C2×C8—1181no—
154C4⋊C4—21no—
155C4⋊C4—591no—
156C4⋊C4—1181no—
157C4⋊C4—1181no—
158C4⋊C4—1181no—
159C4⋊C4D23611yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—1181no—
162C22⋊C4—1181no—
163C22⋊C4—1181no—
164C22⋊C4—1181no—
165C22⋊C4—1181no—
166C22⋊C4—1181no—
167C22⋊C4—2362no—
168C42—1181no—
169C23—1181no—
170C23—1181no—
171C23—1181no—
172C23—1181no—
173C23—2361no—
174C23—2361no—
175C23D4×D5911yescharacteristic
176Q8—41no—
177D4—4721no—
178D4—4721no—
179D4—2361no—
180D4—2361no—
181D4—2361no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—1181no—
189C2×C4—1181no—
190C2×C4—4721no—
191C2×C4—2361no—
192C2×C4—2361no—
193C2×C4—2361no—
194C2×C4—2361no—
195C2×C4C2×D23611yescharacteristic
196C2×C4D4×D5911yescharacteristic
197C8—41no—
198C8—2361no—
199C22—21no—
200C22—21no—
201C22—4721no—
202C22—2362no—
203C22—2361no—
204C22—2361no—
205C22—2361no—
206C22—2361no—
207C22—2361no—
208C22—2361no—
209C22#1427369711yescharacteristic
210C22#1427375011yescharacteristic
211C22#1427375411yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—4721no—
218C4—2361no—
219C4—2361no—
220C2—21no—
221C2—21no—
222C2—4721no—
223C2—4721no—
224C2#1683755011yescharacteristic
225C2#1683758111yescharacteristic
226C2#1683759311yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#328C2
socleC22×C59#120
hypercenter#328D59
hypocenterC59#1612
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #16837730C2semidirect
3. #16837716C2semidirect
4. #16837329C2semidirect
5. #16837135C2semidirect
6. #16837125C2semidirect
7. C59×#328C2semidirect
118. #328D59semidirect
121. C59#1612semidirect