Finite Group Databasebeta

← #21425665

Subgroups — #21425665

Order 7552.

198 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 79 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#16837300C211yesmaximal, characteristic
2#16837268C211yesmaximal, characteristic
3#16837165C211yesmaximal, characteristic
4#16837165C211yesmaximal, characteristic
5#16837165C211yesmaximal, characteristic
6#16837165C211yesmaximal, characteristic
7C59×#336C211yesmaximal, characteristic
8C2×C4⋊Dic59C2211yescharacteristic
9C2×C4⋊Dic59C2211yescharacteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C2×Dic59⋊C4—21no—
13C59⋊#95—21no—
14C59⋊#95—21no—
15C59⋊#95—21no—
16C22×C8×C59C2211yescharacteristic
17C22×C8×C59C2211yescharacteristic
18C2×C42×C59C2211yescharacteristic
19C22×C4×C59D411yescharacteristic
20C22×C4×C59D411yescharacteristic
21C22×C4×C59C2311yescharacteristic
22C22×Dic59—21no—
23C22×Dic59—21no—
24C22×Dic59—21no—
25C22×Dic59—21no—
26C2×C8×C59—21no—
27C2×C8×C59—21no—
28C2×C8×C59—21no—
29C2×C8×C59—21no—
30C2×C8×C59—21no—
31C2×C8×C59—21no—
32C42×C59—21no—
33C42×C59—21no—
34C4⋊Dic59—21no—
35C4⋊Dic59—21no—
36C4⋊Dic59—21no—
37C4⋊Dic59—21no—
38C4⋊Dic59—21no—
39C4⋊Dic59—21no—
40C4⋊Dic59—21no—
41C4⋊Dic59Q812yes—
42Dic59⋊C4—42no—
43C23×C59C2×D411yescharacteristic
44C2×C4×C59—21no—
45C2×C4×C59—21no—
46C2×C4×C59—21no—
47C2×C4×C59—21no—
48C2×C4×C59—21no—
49C2×C4×C59—21no—
50C2×C4×C59C2×Q811yescharacteristic
51C2×C4×C59#4111yescharacteristic
52C2×C4×C59#4111yescharacteristic
53C2×C4×C59#4111yescharacteristic
54C2×C4×C59#4111yescharacteristic
55C2×C4×C59#4111yescharacteristic
56C2×Dic59—22no—
57C2×Dic59—41no—
58C2×Dic59—41no—
59C2×Dic59—41no—
60C2×Dic59—41no—
61C2×Dic59—41no—
62C2×Dic59—41no—
63C2×Dic59—41no—
64C2×Dic59—41no—
65C2×Dic59—41no—
66C2×Dic59—41no—
67C2×Dic59—41no—
68C8×C59—41no—
69C8×C59—41no—
70C22×C59C22⋊Q811yescharacteristic
71C22×C59#12311yescharacteristic
72C22×C59#12411yescharacteristic
73C22×C59#13511yescharacteristic
74C22×C59#13511yescharacteristic
75C22×C59AGL(1,ℤ/8)11yescharacteristic
76C22×C59#13711yescharacteristic
77C4×C59—41no—
78C4×C59—41no—
79C4×C59#12511yescharacteristic
80C4×C59#12511yescharacteristic
81C4×C59#12611yescharacteristic
82C4×C59#12611yescharacteristic
83Dic59—42no—
84Dic59—81no—
85Dic59—81no—
86Dic59—81no—
87#2101—591nomaximal, Sylow
88C2×C59#40011yescharacteristic
89C2×C59#47811yescharacteristic
90C2×C59#47911yescharacteristic
91C2×C59#48211yescharacteristic
92C2×C59#48511yescharacteristic
93C2×C59#48811yescharacteristic
94C2×C59#48911yescharacteristic
95#389—591no—
96#382—591no—
97#340—591no—
98#340—591no—
99#340—591no—
100#340—591no—
101#336D5911yescharacteristic
102C59#210111yescharacteristic, complemented, Sylow
103C22×C8C2×D5911yescharacteristic
104C22×C8C2×D5911yescharacteristic
105C2×C4⋊C4—591no—
106C2×C4⋊C4—591no—
107C2×C4⋊C4—591no—
108C2×C4⋊C4—591no—
109C2×C4⋊C4—1181no—
110C2×C42C2×D5911yescharacteristic
111#95—1181no—
112#95—1181no—
113#95—1181no—
114C22×C4—1181no—
115C22×C4—1181no—
116C22×C4—1181no—
117C22×C4—1181no—
118C22×C4D23611yescharacteristic
119C22×C4D23611yescharacteristic
120C22×C4C22×D5911yescharacteristic
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—21no—
127C4⋊C4—592no—
128C4⋊C4—1181no—
129C4⋊C4—1181no—
130C4⋊C4—1181no—
131C4⋊C4—1181no—
132C4⋊C4—1181no—
133C4⋊C4—1181no—
134C4⋊C4—1181no—
135C4⋊C4—2362no—
136C42—21no—
137C42—21no—
138C23C2×D23611yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—1182no—
146C2×C4—2361no—
147C2×C4—2361no—
148C2×C4—2361no—
149C2×C4—2361no—
150C2×C4—2361no—
151C2×C4—2361no—
152C2×C4—2361no—
153C2×C4—2361no—
154C2×C4—2361no—
155C2×C4—2361no—
156C2×C4—2361no—
157C2×C4#1174568511yescharacteristic
158C2×C4#1174568511yescharacteristic
159C2×C4#1174568711yescharacteristic
160C2×C4#1174568711yescharacteristic
161C2×C4#1174568711yescharacteristic
162C2×C4Q8×D5911yescharacteristic
163C8—41no—
164C8—41no—
165C22#1427370711yescharacteristic
166C22#1427371111yescharacteristic
167C22#1427371511yescharacteristic
168C22#1427374911yescharacteristic
169C22#1427374911yescharacteristic
170C22#1427375511yescharacteristic
171C22#1427376011yescharacteristic
172C4—41no—
173C4—41no—
174C4—4721no—
175C4—4721no—
176C4—4721no—
177C4—2362no—
178C4#1427371711yescharacteristic
179C4#1427371711yescharacteristic
180C4#1427372011yescharacteristic
181C4#1427372011yescharacteristic
182C2#1683734211yescharacteristic
183C2#1683770311yescharacteristic
184C2#1683771011yescharacteristic
185C2#1683772711yescharacteristic
186C2#1683774411yescharacteristic
187C2#1683775711yescharacteristic
188C2#1683776211yescharacteristic
subgroupG/H
centerC23C2×D236
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#336C2
socleC23×C59C2×D4
hypercenter#336D59
hypocenterC59#2101
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
102. C59#2101semidirect