Finite Group Databasebeta

← #21423085

Subgroups — #21423085

Order 7552.

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

normal subgroups only

This group has 228 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#16838027C211yesmaximal, characteristic
2#16837732C211yesmaximal, characteristic, complemented
3#16837328C211yesmaximal, characteristic
4#16837140C211yesmaximal, characteristic, complemented
5#16837139C211yesmaximal, characteristic, complemented
6#16837125C211yesmaximal, characteristic
7C59×#483C211yesmaximal, characteristic, complemented
8#14273707—21no—
9#14273706C2211yescharacteristic
10#14273705—21no—
11#14273705—21no—
12#14273704—21no—
13#14273703—21no—
14C2×(C2×D59)⋊C4—21no—
15C2×(C2×D59)⋊C4C2211yescharacteristic
16C22⋊C4×D59—21no—
17#14273658—21no—
18#14273650—21no—
19C22⋊(C59⋊C8)C2211yescharacteristic
20C59⋊#95—21no—
21C59⋊#95C2211yescharacteristic
22C22⋊Q8×C59C2211yescharacteristic
23C2×C4⋊C4×C59C2211yescharacteristic
24#106×C59—21no—
25#103×C59—21no—
26C22⋊C8×C59C2211yescharacteristic
27C23×D59D411yescharacteristic
28C2×Q8×C59D411yescharacteristic
29C22×C4×C59—21no—
30C22×C4×C59C2311yescharacteristic
31C22×Dic59—21no—
32C22×Dic59D411yescharacteristic
33C2×C4×D59—21no—
34C2×C4×D59—21no—
35C2×Dic118—21no—
36C2×Dic118D411yescharacteristic
37C2×C8×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59—21no—
41C4⋊C4×C59D411yescharacteristic
42C22⋊C4×C59—21no—
43C22⋊Dic59—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⋊Dic59D411yescharacteristic
51Dic59⋊C4—21no—
52Dic59⋊C4—21no—
53Dic59⋊C4—21no—
54C2×C59⋊C8—21no—
55C23×C59C2×D411yescharacteristic
56C22×D59—21no—
57C22×D59—21no—
58C22×D59—41no—
59C22×D59—41no—
60C22×D59SD1612yes—
61Q8×C59—41no—
62C2×C4×C59—21no—
63C2×C4×C59—21no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×Dic59—21no—
71C2×Dic59—21no—
72C2×Dic59—21no—
73C2×Dic59—41no—
74C2×Dic59—41no—
75C2×Dic59—41no—
76C2×Dic59—41no—
77C4×D59—81no—
78C4×D59—81no—
79Dic118—41no—
80Dic118—81no—
81C8×C59—41no—
82C59⋊C8—41no—
83C22×C59—21no—
84C22×C59—21no—
85C22×C59#12011yescharacteristic
86C22×C59C2×SD1611yescharacteristic
87C22×C59#13711yescharacteristic
88C2×D59—22no—
89C2×D59—41no—
90C2×D59—41no—
91C2×D59—42no—
92C2×D59—81no—
93C4×C59—21no—
94C4×C59—21no—
95C4×C59—41no—
96C4×C59—41no—
97C4×C59—81no—
98Dic59—41no—
99Dic59—41no—
100Dic59—41no—
101Dic59—81no—
102#1608—591nomaximal, Sylow
103C2×C59—21no—
104C2×C59—21no—
105C2×C59#44811yescharacteristic
106C2×C59#45511yescharacteristic
107C2×C59#45811yescharacteristic
108D59—42no—
109#543—591no—
110#483—591no—
111#483D5911yescharacteristic, complemented
112#397—591no—
113#328—591no—
114#328—591no—
115#323—591no—
116C59#160811yescharacteristic, complemented, Sylow
117C22⋊Q8—591no—
118C22⋊Q8—1181no—
119C22⋊Q8—1181no—
120C22⋊Q8—1181no—
121C22⋊Q8—1181no—
122C22⋊Q8—1181no—
123C22⋊Q8C2×D5911yescharacteristic
124C2×C4⋊C4C2×D5911yescharacteristic
125C2×C22⋊C4—591no—
126C2×C22⋊C4—1181no—
127C2×C22⋊C4—1181no—
128#106—21no—
129#106—1181no—
130#103—21no—
131#103—1181no—
132C22⋊C8—591no—
133C22⋊C8C2×D5911yescharacteristic
134#95—591no—
135#95—1181no—
136C24—591no—
137C2×Q8—591no—
138C2×Q8—1181no—
139C2×Q8C22⋊D5911yescharacteristic
140C22×C4—21no—
141C22×C4—591no—
142C22×C4—1181no—
143C22×C4—1181no—
144C22×C4—1181no—
145C22×C4C22×D5911yescharacteristic
146C2×C8—21no—
147C2×C8—1181no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—591no—
152C4⋊C4—1181no—
153C4⋊C4—1181no—
154C4⋊C4—1181no—
155C4⋊C4—1181no—
156C4⋊C4C22⋊D5911yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—1181no—
159C22⋊C4—1181no—
160C22⋊C4—1181no—
161C22⋊C4—1181no—
162C22⋊C4—1181no—
163C22⋊C4—2362no—
164C23—592no—
165C23—1181no—
166C23—1181no—
167C23—2361no—
168C23—2361no—
169C23D4×D5911yescharacteristic
170Q8—41no—
171Q8—4721no—
172Q8—2361no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—1181no—
180C2×C4—1181no—
181C2×C4—1181no—
182C2×C4—4721no—
183C2×C4—4721no—
184C2×C4—2361no—
185C2×C4—2361no—
186C2×C4—2361no—
187C2×C4—2361no—
188C2×C4D4×D5911yescharacteristic
189C2×C4C2×C22⋊D5911yescharacteristic
190C8—41no—
191C8—2361no—
192C22—21no—
193C22—21no—
194C22—1182no—
195C22—4721no—
196C22—2362no—
197C22—2361no—
198C22—2361no—
199C22#1427369511yescharacteristic
200C22SD16×D5911yescharacteristic
201C22#1427375611yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—4721no—
208C4—2361no—
209C4—2361no—
210C4—2361no—
211C2—21no—
212C2—21no—
213C2—2362no—
214C2#1683753911yescharacteristic
215C2#1683757811yescharacteristic
216C2#1683759111yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#483C2
socleC22×C59#120
hypercenter#483D59
hypocenterC59#1608
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #16837732C2semidirect
4. #16837140C2semidirect
5. #16837139C2semidirect
7. C59×#483C2semidirect
111. #483D59semidirect
116. C59#1608semidirect