Finite Group Databasebeta

← #21423401

Subgroups — #21423401

Order 7552.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#16838144C211yesmaximal, characteristic
2#16837794C211yesmaximal, characteristic, complemented
3#16837764C211yesmaximal, characteristic, complemented
4#16837142C211yesmaximal, characteristic, complemented
5#16837141C211yesmaximal, characteristic, complemented
6#16837141C211yesmaximal, characteristic, complemented
7C59×#489C211yesmaximal, characteristic, complemented
8C2×#11745672—21no—
9C2×#11745671—21no—
10#14273716—21no—
11#14273715C2211yescharacteristic
12#14273715C2211yescharacteristic
13#14273713—21no—
14#14273713—21no—
15#14273697—21no—
16#14273697—21no—
17#14273695—21no—
18#14273650—21no—
19#14273647—21no—
20#14273638C2211yescharacteristic, complemented
21#14273638C2211yescharacteristic, complemented
22C4⋊Q8×C59C2211yescharacteristic, complemented
23#124×C59C2211yescharacteristic
24#103×C59—21no—
25#102×C59—21no—
26#97×C59C2211yescharacteristic, complemented
27C23×D59—21no—
28C2×Q8×C59—21no—
29C2×Q8×C59D411yescharacteristic
30C2×D4×C59D411yescharacteristic
31C2×C22⋊D59—21no—
32C2×C22⋊D59—21no—
33C2×D236—21no—
34C2×D236D411yescharacteristic
35C2×D236D411yescharacteristic
36C2×Dic118D411yescharacteristic
37C2×Dic118D411yescharacteristic
38C2×C8×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59—21no—
41C22⋊C4×C59—21no—
42C22⋊C4×C59—21no—
43C42×C59C2311yescharacteristic
44C22⋊Dic59—21no—
45#11745672—42no—
46#11745671—42no—
47(C2×D59)⋊C4—21no—
48(C2×D59)⋊C4—21no—
49(C2×D59)⋊C4—21no—
50(C2×D59)⋊C4—21no—
51(C2×D59)⋊C4—21no—
52(C2×D59)⋊C4—21no—
53C4×Dic59—21no—
54C2×C59⋊C8—21no—
55C2×C59⋊C8—21no—
56C23×C59—21no—
57C22×D59—21no—
58C22×D59—21no—
59C22×D59—81no—
60C22×D59—81no—
61C22×D59—81no—
62Q8×C59—41no—
63Q8×C59—41no—
64Q8×C59—41no—
65D4×C59—41no—
66C2×C4×C59—21no—
67C2×C4×C59—41no—
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C22⋊D59—81no—
72C22⋊D59—81no—
73C2×Dic59—21no—
74C2×Dic59—21no—
75D236—41no—
76D236—41no—
77D236—81no—
78Dic118—41no—
79Dic118—41no—
80C8×C59—41no—
81C59⋊C8—22no—
82C59⋊C8—41no—
83C22×C59—41no—
84C22×C59—41no—
85C22×C59—41no—
86C22×C59#12011yescharacteristic
87C2×D59—41no—
88C2×D59—41no—
89C2×D59—41no—
90C2×D59—41no—
91C2×D59—41no—
92C2×D59—41no—
93C2×D59—84no—
94C4×C59—21no—
95C4×C59—21no—
96C4×C59—21no—
97C4×C59—41no—
98C4×C59—81no—
99Dic59—41no—
100Dic59—41no—
101#1659—591nomaximal, Sylow
102C2×C59—81no—
103C2×C59#45311yescharacteristic
104C2×C59#45511yescharacteristic
105C2×C59#45511yescharacteristic
106D59—81no—
107D59—81no—
108H(3,𝔽4)—591no—
109#497—591no—
110#489—591no—
111#489D5911yescharacteristic, complemented
112#329—591no—
113#329—591no—
114#329—591no—
115C59#165911yescharacteristic, complemented, Sylow
116C2×Q16—1181no—
117C2×SD16—1181no—
118C4⋊Q8C2×D5911yescharacteristic, complemented
119#124—591no—
120#124—591no—
121#124—1181no—
122#124—1181no—
123#124—1181no—
124#124C2×D5911yescharacteristic
125#120—1181no—
126#120—1181no—
127#120—1181no—
128#103—21no—
129#103—1181no—
130#102—21no—
131#102—1181no—
132#97—591no—
133#97—591no—
134#97C2×D5911yescharacteristic, complemented
135C24—1181no—
136C2×Q8—21no—
137C2×Q8—591no—
138C2×Q8—591no—
139C2×Q8C22⋊D5911yescharacteristic
140C2×D4—591no—
141C2×D4—591no—
142C2×D4—1181no—
143C2×D4—1181no—
144C2×D4—1181no—
145C2×D4C22⋊D5911yescharacteristic
146Q16—2362no—
147SD16—2362no—
148C2×C8—21no—
149C2×C8—1181no—
150C2×C8—1181no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—1181no—
156C22⋊C4—1181no—
157C22⋊C4—1181no—
158C22⋊C4—1181no—
159C22⋊C4—1181no—
160C22⋊C4—1181no—
161C22⋊C4—1181no—
162C42—1181no—
163C42C22×D5911yescharacteristic
164C23—21no—
165C23—1181no—
166C23—1181no—
167C23—4721no—
168C23—4721no—
169C23—4721no—
170Q8—41no—
171Q8—41no—
172Q8—41no—
173Q8—2361no—
174Q8—2361no—
175D4—41no—
176D4—4721no—
177D4—4721no—
178D4—4721no—
179D4—2361no—
180D4—2361no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—1181no—
184C2×C4—1181no—
185C2×C4D4×D5911yescharacteristic
186C2×C4D4×D5911yescharacteristic
187C2×C4C2×C22⋊D5911yescharacteristic
188C8—41no—
189C8—1182no—
190C8—2361no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—4724no—
195C22—2361no—
196C22—2361no—
197C22—2361no—
198C22—2361no—
199C22—2361no—
200C22—2361no—
201C22#1427369511yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—81no—
207C4—2361no—
208C4—2361no—
209C2—81no—
210C2—4721no—
211C2—4721no—
212C2#1683756811yescharacteristic
213C2#1683757811yescharacteristic
214C2#1683757911yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#489C2
socleC22×C59#120
hypercenter#489D59
hypocenterC59#1659
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #16837794C2semidirect
3. #16837764C2semidirect
4. #16837142C2semidirect
5. #16837141C2semidirect
6. #16837141C2semidirect
7. C59×#489C2semidirect
20. #14273638C22semidirect
21. #14273638C22semidirect
22. C4⋊Q8×C59C22semidirect
26. #97×C59C22semidirect
111. #489D59semidirect
115. C59#1659semidirect
118. C4⋊Q8C2×D59semidirect
134. #97C2×D59semidirect