Finite Group Databasebeta

← #21423418

Subgroups — #21423418

Order 7552.

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

normal subgroups only

This group has 196 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#16838146C211yesmaximal, characteristic
2#16837770C211yesmaximal, characteristic, complemented
3#16837764C211yesmaximal, characteristic, complemented
4#16837143C211yesmaximal, characteristic, complemented
5#16837142C211yesmaximal, characteristic, complemented
6#16837141C211yesmaximal, characteristic, complemented
7C59×#489C211yesmaximal, characteristic, complemented
8#14273719C2211yescharacteristic
9#14273715C2211yescharacteristic
10#14273711—21no—
11#14273709—21no—
12#14273704—21no—
13#14273703—21no—
14#14273700—21no—
15#14273699—21no—
16#14273651—21no—
17#14273651—21no—
18#14273650—21no—
19#14273647—21no—
20#14273638C2211yescharacteristic
21#14273638C2211yescharacteristic
22C4⋊Q8×C59C2211yescharacteristic
23#124×C59C2211yescharacteristic
24#103×C59—21no—
25#102×C59—21no—
26#97×C59C2211yescharacteristic
27C2×Q8×C59—21no—
28C2×Q8×C59D411yescharacteristic
29C2×D4×C59D411yescharacteristic
30C2×C22⋊D59—21no—
31C2×C22⋊D59—21no—
32C22×Dic59—21no—
33C2×D236D411yescharacteristic
34C2×C4×D59—21no—
35C2×Dic118D411yescharacteristic
36C2×C8×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—21no—
39C22⋊C4×C59—21no—
40C22⋊C4×C59—21no—
41C42×C59C2311yescharacteristic
42C22⋊Dic59—21no—
43(C2×D59)⋊C4—21no—
44(C2×D59)⋊C4—21no—
45(C2×D59)⋊C4—21no—
46C4⋊Dic59—21no—
47C4⋊Dic59D411yescharacteristic
48C4⋊Dic59D411yescharacteristic
49Dic59⋊C4—21no—
50Dic59⋊C4—21no—
51Dic59⋊C4—21no—
52C2×C59⋊C8—21no—
53C2×C59⋊C8—21no—
54C23×C59—21no—
55C22×D59—21no—
56Q8×C59—41no—
57Q8×C59—42no—
58D4×C59—41no—
59C2×C4×C59—21no—
60C2×C4×C59—41no—
61C2×C4×C59C2×D411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C2×C4×C59C2×D411yescharacteristic
64C22⋊D59—81no—
65C22⋊D59—81no—
66C2×Dic59—21no—
67C2×Dic59—21no—
68C2×Dic59—21no—
69C2×Dic59—81no—
70D236—41no—
71C4×D59—81no—
72Dic118—41no—
73C8×C59—41no—
74C59⋊C8—41no—
75C59⋊C8—41no—
76C22×C59—41no—
77C22×C59—41no—
78C22×C59—41no—
79C22×C59#12011yescharacteristic
80C2×D59—41no—
81C2×D59—41no—
82C2×D59—41no—
83C4×C59—21no—
84C4×C59—21no—
85C4×C59—21no—
86C4×C59—41no—
87C4×C59—81no—
88Dic59—41no—
89Dic59—41no—
90Dic59—41no—
91#1662—591nomaximal, Sylow
92C2×C59—81no—
93C2×C59#45411yescharacteristic
94C2×C59#45511yescharacteristic
95C2×C59#45511yescharacteristic
96D59—81no—
97#562—591no—
98#491—591no—
99#489—591no—
100#489D5911yescharacteristic, complemented
101#330—591no—
102#329—591no—
103#329—591no—
104C59#166211yescharacteristic, complemented, Sylow
105C4⋊Q8C2×D5911yescharacteristic
106#125—591no—
107#124—591no—
108#124C2×D5911yescharacteristic
109#123—1181no—
110#123—1181no—
111C22⋊Q8—1181no—
112C22⋊Q8—1181no—
113#121—1181no—
114#121—1181no—
115#103—21no—
116#103—1181no—
117#103—1181no—
118#103—1181no—
119#102—21no—
120#102—1181no—
121#97—591no—
122#97—591no—
123#97C2×D5911yescharacteristic
124C2×Q8—21no—
125C2×Q8—591no—
126C2×Q8C22⋊D5911yescharacteristic
127C2×D4—591no—
128C2×D4—1181no—
129C2×D4—1181no—
130C2×D4C22⋊D5911yescharacteristic
131C22×C4—1181no—
132C22×C4—1181no—
133C2×C8—21no—
134C2×C8—1181no—
135C2×C8—1181no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—591no—
139C4⋊C4—591no—
140C4⋊C4—1181no—
141C4⋊C4—1181no—
142C4⋊C4—1181no—
143C4⋊C4—1181no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—1181no—
147C22⋊C4—1181no—
148C22⋊C4—1181no—
149C22⋊C4—1181no—
150C42C22×D5911yescharacteristic
151C23—21no—
152C23—1181no—
153Q8—41no—
154Q8—42no—
155Q8—2361no—
156D4—41no—
157D4—4721no—
158D4—4721no—
159D4—2361no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—1181no—
163C2×C4—1181no—
164C2×C4—1181no—
165C2×C4—4721no—
166C2×C4—4721no—
167C2×C4D4×D5911yescharacteristic
168C2×C4D4×D5911yescharacteristic
169C2×C4C2×C22⋊D5911yescharacteristic
170C8—41no—
171C8—2361no—
172C8—2361no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—2361no—
177C22—2361no—
178C22—2361no—
179C22#1427369511yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—81no—
185C4—2361no—
186C4—2361no—
187C4—2361no—
188C2—81no—
189C2—4721no—
190C2#1683757311yescharacteristic
191C2#1683757811yescharacteristic
192C2#1683757911yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#489C2
socleC22×C59#120
hypercenter#489D59
hypocenterC59#1662
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. #16837770C2semidirect
3. #16837764C2semidirect
4. #16837143C2semidirect
5. #16837142C2semidirect
6. #16837141C2semidirect
7. C59×#489C2semidirect
100. #489D59semidirect
104. C59#1662semidirect