Finite Group Databasebeta

← #21423327

Subgroups — #21423327

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#16837753C211yesmaximal, characteristic, complemented
3#16837682C211yesmaximal, characteristic, complemented
4#16837608C211yesmaximal, characteristic, complemented
5#16837150C211yesmaximal, characteristic, complemented
6#16837131C211yesmaximal, characteristic, complemented
7C59×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11745660—21no—
9#14273727C2211yescharacteristic
10#14273727C2211yescharacteristic
11#14273713—22no—
12#14273701—21no—
13#14273698—21no—
14C4×D236C2211yescharacteristic
15#14273686—21no—
16#14273685—21no—
17#14273660—21no—
18C4⋊(C59⋊C8)C2211yescharacteristic
19#14273652—22no—
20#14273652—21no—
21#14273648—21no—
22C4×D4×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24C4×C8×C59C2211yescharacteristic
25C2×D4×C59D411yescharacteristic
26C22×C4×C59—21no—
27C2×C22⋊D59—22no—
28C2×D236D411yescharacteristic
29C2×C4×D59—21no—
30C2×Dic118—21no—
31C2×Dic118D412yes—
32C2×C8×C59—21no—
33C2×C8×C59—21no—
34C4⋊C4×C59D411yescharacteristic
35C22⋊C4×C59—21no—
36C42×C59C2311yescharacteristic
37C22⋊Dic59—22no—
38(C2×D59)⋊C4—22no—
39(C2×D59)⋊C4—21no—
40C4⋊Dic59—21no—
41C4⋊Dic59—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59—21no—
44C4⋊Dic59D411yescharacteristic
45C4×Dic59—22no—
46C2×C59⋊C8—21no—
47#11745660—42no—
48C23×C59—21no—
49C22×D59—21no—
50D4×C59—21no—
51D4×C59—21no—
52C2×C4×C59—21no—
53C2×C4×C59—41no—
54C2×C4×C59—41no—
55C2×C4×C59C2×D411yescharacteristic
56C2×C4×C59C2×D411yescharacteristic
57C2×C4×C59C2×D411yescharacteristic
58C22⋊D59—82no—
59C2×Dic59—21no—
60C2×Dic59—22no—
61C2×Dic59—41no—
62D236—21no—
63D236—21no—
64C4×D59—41no—
65C4×D59—41no—
66Dic118—42no—
67Dic118—41no—
68Dic118—41no—
69C8×C59—41no—
70C8×C59—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#13511yescharacteristic
82C4×C59#13511yescharacteristic
83C4×C59AGL(1,ℤ/8)11yescharacteristic
84C4×C59#13711yescharacteristic
85Dic59—41no—
86Dic59—42no—
87Dic59—81no—
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#474—591no—
97#461—591no—
98#333—591no—
99D4⋊C8—591no—
100D4⋊C8D5911yescharacteristic, complemented
101C59#164611yescharacteristic, complemented, Sylow
102C2×SD16—1181no—
103C4⋊Q8—591no—
104C4⋊Q8—591no—
105#124—1182no—
106#121—1181no—
107#121—1181no—
108C4×D4—591no—
109C4×D4C2×D5911yescharacteristic
110#117—1181no—
111#117—1181no—
112#107—1181no—
113C4⋊C8—591no—
114C4⋊C8C2×D5911yescharacteristic
115#103—1181no—
116#103—1182no—
117#102—1181no—
118C4×C8C2×D5911yescharacteristic
119C2×Q8—592no—
120C2×Q8—1181no—
121C2×D4—591no—
122C2×D4—1182no—
123C2×D4D23611yescharacteristic
124C22×C4—21no—
125C22×C4—1181no—
126SD16—2362no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—1181no—
130C4⋊C4—591no—
131C4⋊C4—1181no—
132C4⋊C4—1181no—
133C4⋊C4—1181no—
134C4⋊C4—1181no—
135C4⋊C4D23611yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—1182no—
138C22⋊C4—1182no—
139C22⋊C4—1181no—
140C42—1182no—
141C42C22×D5911yescharacteristic
142C23—21no—
143C23—1181no—
144Q8—2362no—
145Q8—2361no—
146Q8—2361no—
147D4—21no—
148D4—21no—
149D4—1181no—
150D4—1181no—
151D4—4722no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—1181no—
156C2×C4—1182no—
157C2×C4—2361no—
158C2×C4—2361no—
159C2×C4—2361no—
160C2×C4C2×D23611yescharacteristic
161C2×C4D4×D5911yescharacteristic
162C2×C4D4×D5911yescharacteristic
163C8—41no—
164C8—41no—
165C8—2361no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—2361no—
170C22—2361no—
171C22—2361no—
172C22#1427369711yescharacteristic
173C4—21no—
174C4—41no—
175C4—4721no—
176C4—2361no—
177C4—2362no—
178C4#1427374811yescharacteristic
179C4#1427374911yescharacteristic
180C4#1427375111yescharacteristic
181C4#1427376011yescharacteristic
182C2—81no—
183C2—4721no—
184C2#1683754811yescharacteristic
185C2#1683756611yescharacteristic
186C2#1683758111yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×D4⋊C8C2
socleC22×C59#120
hypercenterD4⋊C8D59
hypocenterC59#1646
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16837753C2semidirect
3. #16837682C2semidirect
4. #16837608C2semidirect
5. #16837150C2semidirect
6. #16837131C2semidirect
7. C59×D4⋊C8C2semidirect
100. D4⋊C8D59semidirect
101. C59#1646semidirect