Finite Group Databasebeta

← #21423331

Subgroups — #21423331

Order 7552.

240 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 61 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#16837805C211yesmaximal, characteristic, complemented
2#16837682C211yesmaximal, characteristic, complemented
3#16837607C211yesmaximal, characteristic, complemented
4#16837148C211yesmaximal, characteristic, complemented
5D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
7C59×#547C211yesmaximal, characteristic
8C2×#11745670—21no—
9#14273727C2211yescharacteristic
10#14273660—21no—
11#14273660—22no—
12C4⋊(C59⋊C8)C2211yescharacteristic
13C4⋊(C59⋊C8)C2211yescharacteristic
14#14273650—21no—
15#14273648—21no—
16C4×C59⋊C8C2211yescharacteristic
17C2×#41×C59—21no—
18C4⋊Q8×C59C2211yescharacteristic
19#123×C59—22no—
20C22⋊Q8×C59—21no—
21#121×C59—21no—
22C4×D4×C59C2211yescharacteristic
23C4×D4×C59C2211yescharacteristic
24C2×C4⋊C4×C59—21no—
25#41×C59—42no—
26#41×C59—42no—
27C2×Q8×C59—21no—
28C2×D4×C59—22no—
29C2×D4×C59D411yescharacteristic
30C2×D4×C59D411yescharacteristic
31C22×C4×C59—22no—
32C22×C4×C59—21no—
33C22×C4×C59—21no—
34C2×Dic118—21no—
35C4⋊C4×C59—22no—
36C4⋊C4×C59—21no—
37C4⋊C4×C59D411yescharacteristic
38C4⋊C4×C59D411yescharacteristic
39C4⋊C4×C59D412yes—
40C22⋊C4×C59—22no—
41C22⋊C4×C59—21no—
42C22⋊C4×C59—21no—
43C42×C59C2311yescharacteristic
44#11745670—42no—
45C4⋊Dic59—21no—
46C4⋊Dic59—21no—
47C2×C59⋊C8—21no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C23×C59—21no—
51C23×C59—21no—
52Q8×C59—41no—
53Q8×C59—41no—
54D4×C59—21no—
55D4×C59—21no—
56D4×C59—21no—
57D4×C59—44no—
58D4×C59D812yes—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—22no—
62C2×C4×C59—44no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59C2×D411yescharacteristic
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×Dic59—41no—
71Dic118—41no—
72Dic118—41no—
73C59⋊C8—22no—
74C59⋊C8—41no—
75C59⋊C8—41no—
76C22×C59—22no—
77C22×C59—41no—
78C22×C59—41no—
79C22×C59—41no—
80C22×C59—41no—
81C22×C59—41no—
82C22×C59#12011yescharacteristic
83C4×C59—21no—
84C4×C59—41no—
85C4×C59—42no—
86C4×C59—41no—
87C4×C59C2×D811yescharacteristic
88C4×C59#13511yescharacteristic
89C4×C59AGL(1,ℤ/8)11yescharacteristic
90C4×C59#13711yescharacteristic
91Dic59—81no—
92#1647—591nomaximal, Sylow
93C2×C59—42no—
94C2×C59—81no—
95C2×C59#44711yescharacteristic
96C2×C59#45211yescharacteristic
97C2×C59#45611yescharacteristic
98#547D5911yescharacteristic
99#500—591no—
100#474—591no—
101#461—591no—
102#332—591no—
103D4⋊C8—591no—
104D4⋊C8—591no—
105C59#164711yescharacteristic, complemented, Sylow
106C2×#41—21no—
107C2×SD16—1181no—
108C4⋊Q8—591no—
109C4⋊Q8C2×D5911yescharacteristic
110#123—22no—
111C22⋊Q8—21no—
112#121—21no—
113C4×D4C2×D5911yescharacteristic
114C4×D4C2×D5911yescharacteristic
115C2×C4⋊C4—21no—
116#107—1181no—
117#107—1182no—
118C4⋊C8—591no—
119C4⋊C8—591no—
120#103—1181no—
121#102—1181no—
122C4×C8—591no—
123#41—42no—
124#41—42no—
125C2×Q8—21no—
126C2×Q8—1181no—
127C2×D4—22no—
128C2×D4C22⋊D5911yescharacteristic
129C2×D4C22⋊D5911yescharacteristic
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133SD16—2362no—
134C2×C8—1181no—
135C2×C8—1181no—
136C2×C8—1181no—
137C4⋊C4—22no—
138C4⋊C4—21no—
139C4⋊C4—1181no—
140C4⋊C4—1181no—
141C4⋊C4C22⋊D5911yescharacteristic
142C4⋊C4C22⋊D5911yescharacteristic
143C4⋊C4C22⋊D5912yes—
144C22⋊C4—22no—
145C22⋊C4—21no—
146C22⋊C4—21no—
147C42C22×D5911yescharacteristic
148C23—21no—
149C23—21no—
150Q8—41no—
151Q8—41no—
152Q8—2361no—
153Q8—2361no—
154D4—21no—
155D4—21no—
156D4—21no—
157D4—44no—
158D4#1174566912yes—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—44no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—2361no—
168C2×C4C2×C22⋊D5911yescharacteristic
169C2×C4C2×C22⋊D5911yescharacteristic
170C2×C4C2×C22⋊D5911yescharacteristic
171C8—1182no—
172C8—2361no—
173C8—2361no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22#1427369611yescharacteristic
181C4—21no—
182C4—41no—
183C4—42no—
184C4—41no—
185C4—4721no—
186C4C2×#1174566911yescharacteristic
187C4#1427374711yescharacteristic
188C4#1427375311yescharacteristic
189C4#1427375711yescharacteristic
190C2—42no—
191C2—81no—
192C2#1683753611yescharacteristic
193C2#1683756411yescharacteristic
194C2#1683758511yescharacteristic
subgroupG/H
centerC22#14273696
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#547C2
socleC22×C59#120
hypercenter#547D59
hypocenterC59#1647
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #16837805C2semidirect
2. #16837682C2semidirect
3. #16837607C2semidirect
4. #16837148C2semidirect
5. D4⋊(C59⋊C8)C2semidirect
6. D4⋊(C59⋊C8)C2semidirect
105. C59#1647semidirect