Finite Group Databasebeta

← #21423262

Subgroups — #21423262

Order 7552.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#16838067C211yesmaximal, characteristic
2#16837754C211yesmaximal, characteristic, complemented
3#16837698C211yesmaximal, characteristic, complemented
4#16837693C211yesmaximal, characteristic
5#16837132C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic
7C59×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D59—21no—
9#14273727C2211yescharacteristic
10#14273726—21no—
11#14273705—22no—
12#14273703—21no—
13C4×Dic118C2211yescharacteristic
14C4×D236C2211yescharacteristic
15#14273689—21no—
16#14273661—21no—
17#14273659—21no—
18#14273652—21no—
19#14273650—22no—
20#14273649—21no—
21C4×C59⋊C8C2211yescharacteristic
22C4⋊Q8×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24C4⋊C8×C59C2211yescharacteristic
25C2×Q8×C59—21no—
26Q8×D59—42no—
27Q8×D59—42no—
28C2×D236D411yescharacteristic
29C2×C4×D59—22no—
30C2×C4×D59—21no—
31C2×Dic118—22no—
32C2×Dic118—21no—
33C2×Dic118D411yescharacteristic
34C2×C8×C59—21no—
35C2×C8×C59—21no—
36C4⋊C4×C59—21no—
37C4⋊C4×C59D412yes—
38C42×C59C2311yescharacteristic
39(C2×D59)⋊C4—22no—
40(C2×D59)⋊C4—21no—
41C4⋊Dic59—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59D411yescharacteristic
44C4⋊Dic59D411yescharacteristic
45Dic59⋊C4—22no—
46Dic59⋊C4—21no—
47C4×Dic59—21no—
48C2×C59⋊C8—21no—
49C22×D59—21no—
50Q8×C59—41no—
51Q8×C59—41no—
52C2×C4×C59—22no—
53C2×C4×C59C2×D411yescharacteristic
54C2×C4×C59C2×D411yescharacteristic
55C2×C4×C59C2×D411yescharacteristic
56C2×Dic59—21no—
57C2×Dic59—21no—
58C2×Dic59—21no—
59C2×Dic59—41no—
60D236—21no—
61D236Q1612yes—
62C4×D59—44no—
63C4×D59—41no—
64C4×D59—41no—
65Dic118—21no—
66Dic118—44no—
67Dic118—42no—
68Dic118SD1612yes—
69C8×C59—41no—
70C8×C59—41no—
71C59⋊C8—41no—
72C22×C59#12011yescharacteristic
73C2×D59—22no—
74C2×D59—41no—
75C2×D59—41no—
76C4×C59—21no—
77C4×C59—42no—
78C4×C59C2×SD1611yescharacteristic
79C4×C59C2×Q1611yescharacteristic
80C4×C59AGL(1,ℤ/8)11yescharacteristic
81C4×C59#13711yescharacteristic
82Dic59—22no—
83Dic59—41no—
84Dic59—41no—
85Dic59—81no—
86#1637—591nomaximal, Sylow
87C2×C59#45011yescharacteristic
88C2×C59#45111yescharacteristic
89C2×C59#45411yescharacteristic
90D59—42no—
91D4×Q8—591no—
92#487—591no—
93#477—591no—
94#476—591no—
95#332D5911yescharacteristic, complemented
96Q8⋊C8—591no—
97D4⋊C8—591no—
98C59#163711yescharacteristic, complemented, Sylow
99C22×Q8—1181no—
100C4⋊Q8—591no—
101C4⋊Q8—1181no—
102C4⋊Q8C2×D5911yescharacteristic
103C22⋊Q8—1181no—
104C22⋊Q8—1182no—
105C4×Q8—591no—
106C4×D4—591no—
107C4×D4—1181no—
108#107—1181no—
109#106—1181no—
110C4⋊C8C2×D5911yescharacteristic
111C4⋊C8C2×D5911yescharacteristic
112#103—1181no—
113#103—1182no—
114#102—1181no—
115C4×C8—591no—
116C2×Q8—21no—
117C2×Q8—591no—
118C2×Q8—1182no—
119C2×Q8—1181no—
120C2×Q8—2362no—
121C2×Q8—2362no—
122C2×D4—591no—
123C22×C4—1182no—
124C22×C4—1181no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—1181no—
128C4⋊C4—21no—
129C4⋊C4—591no—
130C4⋊C4—591no—
131C4⋊C4—1182no—
132C4⋊C4—1181no—
133C4⋊C4—1181no—
134C4⋊C4—1181no—
135C4⋊C4D23612yes—
136C22⋊C4—1182no—
137C22⋊C4—1181no—
138C42—1181no—
139C42C22×D5911yescharacteristic
140C23—1181no—
141Q8—41no—
142Q8—41no—
143Q8—592no—
144Q8—1181no—
145Q8—2362no—
146Q8—2364no—
147D4—592no—
148D4—1181no—
149C2×C4—22no—
150C2×C4—1181no—
151C2×C4—1181no—
152C2×C4—1181no—
153C2×C4—2364no—
154C2×C4—2361no—
155C2×C4—2361no—
156C2×C4—2361no—
157C2×C4C2×D23611yescharacteristic
158C2×C4D4×D5911yescharacteristic
159C2×C4D4×D5911yescharacteristic
160C8—41no—
161C8—41no—
162C8—2361no—
163C22—1182no—
164C22—2361no—
165C22—2361no—
166C22#1427369711yescharacteristic
167C4—21no—
168C4—42no—
169C4—1182no—
170C4—4721no—
171C4—2361no—
172C4—2361no—
173C4SD16×D5911yescharacteristic
174C4Q16×D5911yescharacteristic
175C4#1427375111yescharacteristic
176C4#1427375611yescharacteristic
177C2—2362no—
178C2#1683755411yescharacteristic
179C2#1683755911yescharacteristic
180C2#1683757711yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#332C2
socleC22×C59#120
hypercenter#332D59
hypocenterC59#1637
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #16837754C2semidirect
3. #16837698C2semidirect
5. #16837132C2semidirect
7. C59×#332C2semidirect
95. #332D59semidirect
98. C59#1637semidirect