Finite Group Databasebeta

← #21423429

Subgroups — #21423429

Order 7552.

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

normal subgroups only

This group has 184 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#16838152C211yesmaximal, characteristic
2#16837808C211yesmaximal, characteristic, complemented
3#16837770C211yesmaximal, characteristic, complemented
4#16837143C211yesmaximal, characteristic, complemented
5#16837143C211yesmaximal, characteristic, complemented
6#16837142C211yesmaximal, characteristic
7C59×#489C211yesmaximal, characteristic
8#14273725—21no—
9#14273720—21no—
10#14273720—21no—
11#14273719C2211yescharacteristic
12#14273719C2211yescharacteristic
13#14273708—21no—
14#14273704—21no—
15#14273704—21no—
16#14273660—21no—
17#14273658—21no—
18#14273651—21no—
19#14273651—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
30C22×Dic59—21no—
31C2×Dic118—21no—
32C2×C8×C59—21no—
33C4⋊C4×C59—21no—
34C4⋊C4×C59—21no—
35C22⋊C4×C59—21no—
36C22⋊C4×C59—21no—
37C42×C59C2311yescharacteristic
38C22⋊Dic59—21no—
39C22⋊Dic59—21no—
40C22⋊Dic59—21no—
41C4⋊Dic59D411yescharacteristic
42C4⋊Dic59D411yescharacteristic
43C4⋊Dic59D411yescharacteristic
44C4⋊Dic59D411yescharacteristic
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47Dic59⋊C4—21no—
48Dic59⋊C4—21no—
49Dic59⋊C4—21no—
50Dic59⋊C4—21no—
51C4×Dic59—21no—
52C2×C59⋊C8—21no—
53C2×C59⋊C8—21no—
54C23×C59—21no—
55Q8×C59—41no—
56Q8×C59—42no—
57D4×C59—41no—
58C2×C4×C59—21no—
59C2×C4×C59—41no—
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C2×Dic59—21no—
64C2×Dic59—21no—
65C2×Dic59—21no—
66C2×Dic59—21no—
67C2×Dic59—81no—
68Dic118—81no—
69C8×C59—41no—
70C59⋊C8—22no—
71C59⋊C8—41no—
72C22×C59—41no—
73C22×C59—41no—
74C22×C59—41no—
75C22×C59#12011yescharacteristic
76C4×C59—21no—
77C4×C59—21no—
78C4×C59—21no—
79C4×C59—41no—
80C4×C59—81no—
81Dic59—41no—
82Dic59—41no—
83Dic59—41no—
84Dic59—41no—
85#1664—591nomaximal, Sylow
86C2×C59—81no—
87C2×C59#45411yescharacteristic
88C2×C59#45511yescharacteristic
89C2×C59#45611yescharacteristic
90#563—591no—
91#501—591no—
92#491—591no—
93#489D5911yescharacteristic
94#330—591no—
95#330—591no—
96#329—591no—
97C59#166411yescharacteristic, complemented, Sylow
98C4⋊Q8—1181no—
99C4⋊Q8C2×D5911yescharacteristic
100#126—1181no—
101#126—1181no—
102#125—591no—
103#125—591no—
104#124C2×D5911yescharacteristic
105#123—1181no—
106C22⋊Q8—1181no—
107C22⋊Q8—1181no—
108#107—1181no—
109#106—1181no—
110#103—21no—
111#103—1181no—
112#103—1181no—
113#102—21no—
114#97—591no—
115#97—591no—
116#97C2×D5911yescharacteristic
117C2×Q8—21no—
118C2×Q8—1181no—
119C2×Q8C22⋊D5911yescharacteristic
120C2×D4C22⋊D5911yescharacteristic
121C22×C4—1181no—
122C2×C8—21no—
123C2×C8—1181no—
124C2×C8—1181no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—591no—
128C4⋊C4—591no—
129C4⋊C4—591no—
130C4⋊C4—591no—
131C4⋊C4—1181no—
132C4⋊C4—1181no—
133C4⋊C4—1181no—
134C4⋊C4—1181no—
135C4⋊C4—1181no—
136C4⋊C4—1181no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—1181no—
140C22⋊C4—1181no—
141C22⋊C4—1181no—
142C42—1181no—
143C42C22×D5911yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—42no—
147Q8—4721no—
148D4—41no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—1181no—
152C2×C4—1181no—
153C2×C4—1181no—
154C2×C4—1181no—
155C2×C4—4721no—
156C2×C4D4×D5911yescharacteristic
157C2×C4D4×D5911yescharacteristic
158C2×C4C2×C22⋊D5911yescharacteristic
159C8—41no—
160C8—1182no—
161C8—2361no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1427369511yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—81no—
171C4—2361no—
172C4—2361no—
173C4—2361no—
174C4—2361no—
175C2—81no—
176C2#1683757311yescharacteristic
177C2#1683757911yescharacteristic
178C2#1683758311yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#489C2
socleC22×C59#120
hypercenter#489D59
hypocenterC59#1664
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. #16837808C2semidirect
3. #16837770C2semidirect
4. #16837143C2semidirect
5. #16837143C2semidirect
97. C59#1664semidirect