Finite Group Databasebeta

← #21425664

Subgroups — #21425664

Order 7552.

198 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 81 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#16837268C211yesmaximal, characteristic
2#16837164C211yesmaximal, characteristic
3#16837164C211yesmaximal, characteristic
4#16837164C211yesmaximal, characteristic
5#16837164C211yesmaximal, characteristic
6#16837157C211yesmaximal, characteristic
7C59×#389C211yesmaximal, characteristic
8C22×C59⋊C8C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C59⋊#95—21no—
13C59⋊#95—21no—
14C2×C4⋊C4×C59—21no—
15C2×C4⋊C4×C59C2211yescharacteristic
16C2×C4⋊C4×C59C2211yescharacteristic
17C2×C42×C59C2211yescharacteristic
18#95×C59—21no—
19C22×C4×C59—21no—
20C22×C4×C59—21no—
21C22×C4×C59D411yescharacteristic
22C22×C4×C59D411yescharacteristic
23C22×C4×C59C2311yescharacteristic
24C22×Dic59—21no—
25C22×Dic59—21no—
26C4⋊C4×C59—21no—
27C4⋊C4×C59—21no—
28C4⋊C4×C59—21no—
29C4⋊C4×C59—42no—
30C4⋊C4×C59Q812yes—
31C42×C59—21no—
32C42×C59—21no—
33C4⋊Dic59—21no—
34C4⋊Dic59—21no—
35C4⋊Dic59—21no—
36C4⋊Dic59—21no—
37C2×C59⋊C8—21no—
38C2×C59⋊C8—21no—
39C2×C59⋊C8—21no—
40C2×C59⋊C8—21no—
41C2×C59⋊C8—21no—
42C2×C59⋊C8—21no—
43C23×C59C2×D411yescharacteristic
44C2×C4×C59—22no—
45C2×C4×C59—21no—
46C2×C4×C59—21no—
47C2×C4×C59—21no—
48C2×C4×C59—21no—
49C2×C4×C59—21no—
50C2×C4×C59—21no—
51C2×C4×C59—41no—
52C2×C4×C59—41no—
53C2×C4×C59—41no—
54C2×C4×C59—41no—
55C2×C4×C59—41no—
56C2×C4×C59C2×Q811yescharacteristic
57C2×C4×C59#4111yescharacteristic
58C2×C4×C59#4111yescharacteristic
59C2×C4×C59#4111yescharacteristic
60C2×C4×C59#4111yescharacteristic
61C2×C4×C59#4111yescharacteristic
62C2×Dic59—41no—
63C2×Dic59—41no—
64C2×Dic59—41no—
65C2×Dic59—41no—
66C2×Dic59—41no—
67C2×Dic59—41no—
68C59⋊C8—41no—
69C59⋊C8—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—42no—
78C4×C59—41no—
79C4×C59—41no—
80C4×C59—81no—
81C4×C59#12511yescharacteristic
82C4×C59#12511yescharacteristic
83C4×C59#12611yescharacteristic
84C4×C59#12611yescharacteristic
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#389D5911yescharacteristic
96#382—591no—
97#340—591no—
98#340—591no—
99#340—591no—
100#340—591no—
101#336—591no—
102C59#210111yescharacteristic, complemented, Sylow
103C22×C8—591no—
104C22×C8—591no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—591no—
107C2×C4⋊C4—591no—
108C2×C4⋊C4C2×D5911yescharacteristic
109C2×C4⋊C4C2×D5911yescharacteristic
110C2×C42C2×D5911yescharacteristic
111#95—21no—
112#95—1181no—
113#95—1181no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—1181no—
117C22×C4—1181no—
118C22×C4C22⋊D5911yescharacteristic
119C22×C4C22⋊D5911yescharacteristic
120C22×C4C22×D5911yescharacteristic
121C2×C8—1181no—
122C2×C8—1181no—
123C2×C8—1181no—
124C2×C8—1181no—
125C2×C8—1181no—
126C2×C8—1181no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—42no—
131C4⋊C4—1181no—
132C4⋊C4—1181no—
133C4⋊C4—1181no—
134C4⋊C4—1181no—
135C4⋊C4Dic11812yes—
136C42—21no—
137C42—21no—
138C23C2×C22⋊D5911yescharacteristic
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—2361no—
152C2×C4—2361no—
153C2×C4—2361no—
154C2×C4—2361no—
155C2×C4—2361no—
156C2×C4—2361no—
157C2×C4C2×Dic11811yescharacteristic
158C2×C4#1174568511yescharacteristic
159C2×C4#1174568711yescharacteristic
160C2×C4#1174568711yescharacteristic
161C2×C4#1174568911yescharacteristic
162C2×C4#1174568911yescharacteristic
163C8—2361no—
164C8—2361no—
165C22#1427370611yescharacteristic
166C22#1427370811yescharacteristic
167C22#1427371611yescharacteristic
168C22#1427374711yescharacteristic
169C22#1427374711yescharacteristic
170C22#1427375311yescharacteristic
171C22#1427375811yescharacteristic
172C4—42no—
173C4—41no—
174C4—41no—
175C4—81no—
176C4—4721no—
177C4—4721no—
178C4#1427371811yescharacteristic
179C4#1427371811yescharacteristic
180C4#1427372211yescharacteristic
181C4#1427372211yescharacteristic
182C2#1683734111yescharacteristic
183C2#1683770211yescharacteristic
184C2#1683770911yescharacteristic
185C2#1683772311yescharacteristic
186C2#1683774011yescharacteristic
187C2#1683775911yescharacteristic
188C2#1683776411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#389C2
socleC23×C59C2×D4
hypercenter#389D59
hypocenterC59#2101
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
102. C59#2101semidirect