Finite Group Databasebeta

← #21423323

Subgroups — #21423323

Order 7552.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#16838117C211yesmaximal, characteristic
2#16837754C211yesmaximal, characteristic, complemented
3#16837604C211yesmaximal, characteristic, complemented
4#16837150C211yesmaximal, characteristic, complemented
5D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic, complemented
7C59×#474C211yesmaximal, characteristic, complemented
8C2×#11745671—21no—
9#14273727C2211yescharacteristic
10#14273713—22no—
11#14273701—21no—
12#14273698—21no—
13C4×D236C2211yescharacteristic
14#14273686—21no—
15#14273685—21no—
16C4⋊(C59⋊C8)C2211yescharacteristic
17#14273651—21no—
18#14273650—22no—
19C4×C59⋊C8C2211yescharacteristic
20C4⋊Q8×C59C2211yescharacteristic
21C4×D4×C59C2211yescharacteristic
22#107×C59—21no—
23C4⋊C8×C59C2211yescharacteristic
24#102×C59—21no—
25C2×Q8×C59—21no—
26C2×D4×C59D411yescharacteristic
27C22×C4×C59—21no—
28C2×C22⋊D59—22no—
29C2×D236D411yescharacteristic
30C2×C4×D59—21no—
31C2×Dic118D412yes—
32C2×C8×C59—21no—
33C4⋊C4×C59—21no—
34C4⋊C4×C59—21no—
35C4⋊C4×C59D411yescharacteristic
36C22⋊C4×C59—21no—
37C42×C59C2311yescharacteristic
38C22⋊Dic59—22no—
39#11745671—42no—
40(C2×D59)⋊C4—22no—
41(C2×D59)⋊C4—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59—21no—
44C4⋊Dic59D411yescharacteristic
45C4×Dic59—22no—
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48C23×C59—21no—
49C22×D59—21no—
50Q8×C59—41no—
51Q8×C59—41no—
52D4×C59—21no—
53D4×C59—21no—
54C2×C4×C59—21no—
55C2×C4×C59—41no—
56C2×C4×C59—41no—
57C2×C4×C59—41no—
58C2×C4×C59C2×D411yescharacteristic
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C22⋊D59—82no—
62C2×Dic59—21no—
63C2×Dic59—22no—
64D236—21no—
65D236—21no—
66C4×D59—41no—
67C4×D59—41no—
68Dic118—42no—
69C8×C59—41no—
70C59⋊C8—41no—
71C59⋊C8—41no—
72C22×C59—41no—
73C22×C59—41no—
74C22×C59—41no—
75C22×C59#12011yescharacteristic
76C2×D59—41no—
77C2×D59—41no—
78C2×D59—41no—
79C4×C59—21no—
80C4×C59—41no—
81C4×C59—81no—
82C4×C59#13511yescharacteristic
83C4×C59#13511yescharacteristic
84C4×C59AGL(1,ℤ/8)11yescharacteristic
85C4×C59#13711yescharacteristic
86Dic59—41no—
87Dic59—42no—
88#1646—591nomaximal, Sylow
89C2×C59—81no—
90C2×C59#44911yescharacteristic
91C2×C59#45211yescharacteristic
92C2×C59#45511yescharacteristic
93D59—81no—
94#555—591no—
95#487—591no—
96#474D5911yescharacteristic, complemented
97#461—591no—
98#333—591no—
99D4⋊C8—591no—
100D4⋊C8—591no—
101C59#164611yescharacteristic, complemented, Sylow
102C2×SD16—1181no—
103C4⋊Q8—591no—
104C4⋊Q8C2×D5911yescharacteristic
105#124—1182no—
106#121—1181no—
107#121—1181no—
108C4×D4—591no—
109C4×D4C2×D5911yescharacteristic
110#117—1181no—
111#117—1181no—
112#107—21no—
113C4⋊C8—591no—
114C4⋊C8C2×D5911yescharacteristic
115#103—1182no—
116#103—1181no—
117#102—21no—
118C4×C8—591no—
119C2×Q8—21no—
120C2×Q8—592no—
121C2×D4—591no—
122C2×D4—1182no—
123C2×D4C22⋊D5911yescharacteristic
124C22×C4—21no—
125C22×C4—1181no—
126SD16—2362no—
127C2×C8—21no—
128C2×C8—1181no—
129C2×C8—1181no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—591no—
133C4⋊C4—1181no—
134C4⋊C4—1181no—
135C4⋊C4C22⋊D5911yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—1182no—
138C22⋊C4—1182no—
139C22⋊C4—1181no—
140C42—1182no—
141C42C22×D5911yescharacteristic
142C23—21no—
143C23—1181no—
144Q8—41no—
145Q8—41no—
146Q8—2362no—
147D4—21no—
148D4—21no—
149D4—1181no—
150D4—1181no—
151D4—4722no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—1181no—
157C2×C4—1182no—
158C2×C4—2361no—
159C2×C4—2361no—
160C2×C4D4×D5911yescharacteristic
161C2×C4D4×D5911yescharacteristic
162C2×C4C2×C22⋊D5911yescharacteristic
163C8—41no—
164C8—2361no—
165C8—2361no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—2361no—
170C22—2361no—
171C22—2361no—
172C22#1427369511yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—2361no—
177C4—2362no—
178C4#1427374611yescharacteristic
179C4#1427374711yescharacteristic
180C4#1427375111yescharacteristic
181C4#1427375811yescharacteristic
182C2—81no—
183C2—4721no—
184C2#1683754411yescharacteristic
185C2#1683756211yescharacteristic
186C2#1683757811yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#474C2
socleC22×C59#120
hypercenter#474D59
hypocenterC59#1646
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #16837754C2semidirect
3. #16837604C2semidirect
4. #16837150C2semidirect
5. D4⋊(C59⋊C8)C2semidirect
6. #16837129C2semidirect
7. C59×#474C2semidirect
96. #474D59semidirect
101. C59#1646semidirect