Finite Group Databasebeta

← #21423329

Subgroups — #21423329

Order 7552.

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

normal subgroups only

This group has 240 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#16838056C211yesmaximal, characteristic
2#16837805C211yesmaximal, characteristic, complemented
3#16837679C211yesmaximal, characteristic, complemented
4#16837149C211yesmaximal, characteristic, complemented
5D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic, complemented
7C59×#461C211yesmaximal, characteristic, complemented
8C2×#11745687—21no—
9#14273727C2211yescharacteristic
10#14273711—22no—
11#14273707—21no—
12#14273701—21no—
13C4×D236C2211yescharacteristic
14C2×C4⋊Dic59—21no—
15#14273660—21no—
16#14273660—22no—
17C4⋊(C59⋊C8)C2211yescharacteristic
18#14273647—21no—
19C4×C59⋊C8C2211yescharacteristic
20C2×SD16×C59—21no—
21C4⋊Q8×C59C2211yescharacteristic
22C4×D4×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24#103×C59—21no—
25C2×Q8×C59—21no—
26C2×D4×C59D411yescharacteristic
27C22×C4×C59—21no—
28C2×C22⋊D59—22no—
29C22×Dic59—22no—
30#11745687—42no—
31#11745687—42no—
32C2×D236D411yescharacteristic
33C2×C4×D59—21no—
34C2×Dic118—21no—
35SD16×C59—42no—
36C2×C8×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59D411yescharacteristic
40C22⋊C4×C59—21no—
41C42×C59C2311yescharacteristic
42(C2×D59)⋊C4—22no—
43(C2×D59)⋊C4—21no—
44C4⋊Dic59—22no—
45C4⋊Dic59—21no—
46C4⋊Dic59D411yescharacteristic
47C4⋊Dic59D412yes—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C23×C59—21no—
51C22×D59—21no—
52Q8×C59—41no—
53Q8×C59—41no—
54D4×C59—21no—
55D4×C59D812yes—
56C2×C4×C59—21no—
57C2×C4×C59—41no—
58C2×C4×C59—41no—
59C2×C4×C59—41no—
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C22⋊D59—44no—
64C2×Dic59—22no—
65C2×Dic59—21no—
66C2×Dic59—44no—
67D236—21no—
68D236—21no—
69C4×D59—41no—
70C4×D59—41no—
71Dic118—41no—
72Dic118—41no—
73C8×C59—41no—
74C59⋊C8—22no—
75C59⋊C8—41no—
76C22×C59—22no—
77C22×C59—41no—
78C22×C59—41no—
79C22×C59#12011yescharacteristic
80C2×D59—41no—
81C2×D59—41no—
82C2×D59—41no—
83C4×C59—21no—
84C4×C59—41no—
85C4×C59—81no—
86C4×C59C2×D811yescharacteristic
87C4×C59#13511yescharacteristic
88C4×C59AGL(1,ℤ/8)11yescharacteristic
89C4×C59#13711yescharacteristic
90Dic59—42no—
91Dic59—41no—
92#1647—591nomaximal, Sylow
93C2×C59—42no—
94C2×C59#44711yescharacteristic
95C2×C59#45211yescharacteristic
96C2×C59#45611yescharacteristic
97D59—81no—
98#547—591no—
99#500—591no—
100#474—591no—
101#461D5911yescharacteristic, complemented
102#332—591no—
103D4⋊C8—591no—
104D4⋊C8—591no—
105C59#164711yescharacteristic, complemented, Sylow
106C2×#41—1181no—
107C2×SD16—21no—
108C4⋊Q8—591no—
109C4⋊Q8C2×D5911yescharacteristic
110#123—1182no—
111C22⋊Q8—1181no—
112#121—1181no—
113C4×D4—591no—
114C4×D4C2×D5911yescharacteristic
115C2×C4⋊C4—1181no—
116#107—1181no—
117#107—1182no—
118C4⋊C8—591no—
119C4⋊C8C2×D5911yescharacteristic
120#103—21no—
121#102—1181no—
122C4×C8—591no—
123#41—2362no—
124#41—2362no—
125C2×Q8—21no—
126C2×Q8—1181no—
127C2×D4—591no—
128C2×D4—1182no—
129C2×D4C22⋊D5911yescharacteristic
130C22×C4—21no—
131C22×C4—1182no—
132C22×C4—1181no—
133SD16—42no—
134C2×C8—21no—
135C2×C8—1181no—
136C2×C8—1181no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—591no—
140C4⋊C4—592no—
141C4⋊C4—1182no—
142C4⋊C4—1181no—
143C4⋊C4C22⋊D5911yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—1182no—
146C22⋊C4—1181no—
147C42C22×D5911yescharacteristic
148C23—21no—
149C23—1181no—
150Q8—41no—
151Q8—41no—
152Q8—2361no—
153Q8—2361no—
154D4—21no—
155D4—1181no—
156D4—1181no—
157D4—2364no—
158D4#1174566912yes—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—1181no—
164C2×C4—1182no—
165C2×C4—2364no—
166C2×C4—2361no—
167C2×C4—2361no—
168C2×C4D4×D5911yescharacteristic
169C2×C4D4×D5911yescharacteristic
170C2×C4C2×C22⋊D5911yescharacteristic
171C8—41no—
172C8—1182no—
173C8—2361no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—2361no—
178C22—2361no—
179C22—2361no—
180C22#1427369511yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—2361no—
185C4—2362no—
186C4C2×#1174566911yescharacteristic
187C4#1427374811yescharacteristic
188C4#1427375211yescharacteristic
189C4#1427375611yescharacteristic
190C2—42no—
191C2—4721no—
192C2#1683753511yescharacteristic
193C2#1683756111yescharacteristic
194C2#1683758311yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#461C2
socleC22×C59#120
hypercenter#461D59
hypocenterC59#1647
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #16837805C2semidirect
3. #16837679C2semidirect
4. #16837149C2semidirect
5. D4⋊(C59⋊C8)C2semidirect
6. #16837129C2semidirect
7. C59×#461C2semidirect
101. #461D59semidirect
105. C59#1647semidirect