Finite Group Databasebeta

← #21425597

Subgroups — #21425597

Order 7552.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#14273658C211yesmaximal, characteristic
2C2×C4⋊(C59⋊C8)C211yesmaximal, characteristic
3#16837300C211yesmaximal, characteristic
4#16837164C211yesmaximal, characteristic
5#16837164C211yesmaximal, characteristic
6#16837164C211yesmaximal, characteristic
7C59×#389C211yesmaximal, characteristic
8C22×C59⋊C8C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C2×Dic59⋊C4—21no—
13#14273658—22no—
14C4⋊(C59⋊C8)—22no—
15C59⋊#95—21no—
16C2×C4⋊C4×C59—21no—
17C2×C4⋊C4×C59C2211yescharacteristic
18C2×C4⋊C4×C59C2211yescharacteristic
19C2×C42×C59C2211yescharacteristic
20#95×C59—21no—
21C22×C4×C59—21no—
22C22×C4×C59—21no—
23C22×C4×C59D411yescharacteristic
24C22×C4×C59D411yescharacteristic
25C22×C4×C59C2311yescharacteristic
26C22×Dic59—21no—
27C22×Dic59—21no—
28C4⋊C4×C59—21no—
29C4⋊C4×C59—21no—
30C4⋊C4×C59—21no—
31C4⋊C4×C59—42no—
32C4⋊C4×C59Q812yes—
33C42×C59—21no—
34C42×C59—21no—
35C4⋊Dic59—21no—
36C4⋊Dic59—21no—
37C4⋊Dic59—21no—
38C4⋊Dic59Q812yes—
39Dic59⋊C4—42no—
40C2×C59⋊C8—21no—
41C2×C59⋊C8—21no—
42C2×C59⋊C8—21no—
43C2×C59⋊C8—21no—
44C2×C59⋊C8—21no—
45C2×C59⋊C8D412yes—
46C23×C59C2×D411yescharacteristic
47C2×C4×C59—21no—
48C2×C4×C59—21no—
49C2×C4×C59—21no—
50C2×C4×C59—22no—
51C2×C4×C59—21no—
52C2×C4×C59—21no—
53C2×C4×C59—41no—
54C2×C4×C59—41no—
55C2×C4×C59—41no—
56C2×C4×C59—41no—
57C2×C4×C59—41no—
58C2×C4×C59SD1612yes—
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59C2×Q811yescharacteristic
61C2×C4×C59C2×Q811yescharacteristic
62C2×C4×C59#4111yescharacteristic
63C2×C4×C59#4111yescharacteristic
64C2×C4×C59#4111yescharacteristic
65C2×Dic59—22no—
66C2×Dic59—41no—
67C2×Dic59—41no—
68C2×Dic59—41no—
69C2×Dic59—41no—
70C2×Dic59—41no—
71C59⋊C8—22no—
72C59⋊C8—41no—
73C22×C59#12111yescharacteristic
74C22×C59C22⋊Q811yescharacteristic
75C22×C59C22⋊Q811yescharacteristic
76C22×C59C2×SD1611yescharacteristic
77C22×C59#13511yescharacteristic
78C22×C59AGL(1,ℤ/8)11yescharacteristic
79C22×C59#13711yescharacteristic
80C4×C59—22no—
81C4×C59—41no—
82C4×C59—42no—
83C4×C59—81no—
84C4×C59#12311yescharacteristic
85C4×C59#12511yescharacteristic
86C4×C59#12511yescharacteristic
87C4×C59C4⋊Q811yescharacteristic
88Dic59—42no—
89Dic59—81no—
90#2088—591nomaximal, Sylow
91C2×C59#39811yescharacteristic
92C2×C59#46511yescharacteristic
93C2×C59#46811yescharacteristic
94C2×C59#47511yescharacteristic
95C2×C59#47611yescharacteristic
96C2×C59#47811yescharacteristic
97C2×C59#47911yescharacteristic
98C2×#106—591no—
99C2×C4⋊C8—591no—
100#389—591no—
101#389D5911yescharacteristic
102#340—591no—
103#340—591no—
104#340—591no—
105C59#208811yescharacteristic, complemented, Sylow
106C22×C8—591no—
107C22×C8—591no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—591no—
110C2×C4⋊C4—591no—
111C2×C4⋊C4—1181no—
112C2×C4⋊C4C2×D5911yescharacteristic
113C2×C4⋊C4C2×D5911yescharacteristic
114C2×C42C2×D5911yescharacteristic
115#106—1182no—
116C4⋊C8—1182no—
117#95—21no—
118#95—1181no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—1181no—
122C22×C4—1181no—
123C22×C4C22⋊D5911yescharacteristic
124C22×C4C22⋊D5911yescharacteristic
125C22×C4C22×D5911yescharacteristic
126C2×C8—592no—
127C2×C8—1181no—
128C2×C8—1181no—
129C2×C8—1181no—
130C2×C8—1181no—
131C2×C8—1181no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—42no—
136C4⋊C4—592no—
137C4⋊C4—1181no—
138C4⋊C4—1181no—
139C4⋊C4—1181no—
140C4⋊C4—2362no—
141C4⋊C4Dic11812yes—
142C42—21no—
143C42—21no—
144C23C2×C22⋊D5911yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—1182no—
157C2×C4—2361no—
158C2×C4—2361no—
159C2×C4—2361no—
160C2×C4—2361no—
161C2×C4—2361no—
162C2×C4#1174567012yes—
163C2×C4C2×Dic11811yescharacteristic
164C2×C4#1174568511yescharacteristic
165C2×C4D4×D5911yescharacteristic
166C2×C4#1174568711yescharacteristic
167C2×C4Q8×D5911yescharacteristic
168C2×C4#1174568911yescharacteristic
169C8—1182no—
170C8—2361no—
171C22#1427369911yescharacteristic
172C22#1427370311yescharacteristic
173C22#1427370611yescharacteristic
174C22C2×#1174567011yescharacteristic
175C22#1427374711yescharacteristic
176C22#1427375211yescharacteristic
177C22#1427375811yescharacteristic
178C4—22no—
179C4—41no—
180C4—42no—
181C4—81no—
182C4—4721no—
183C4—2362no—
184C4#1427371211yescharacteristic
185C4#1427371711yescharacteristic
186C4#1427371811yescharacteristic
187C4#1427372611yescharacteristic
188C2#1683733511yescharacteristic
189C2#1683762911yescharacteristic
190C2#1683765011yescharacteristic
191C2#1683768411yescharacteristic
192C2#1683769211yescharacteristic
193C2#1683769911yescharacteristic
194C2#1683770911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#389C2
socleC23×C59C2×D4
hypercenter#389D59
hypocenterC59#2088
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
105. C59#2088semidirect