Finite Group Databasebeta

← #21426064

Subgroups — #21426064

Order 7552.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#16838204C211yesmaximal, characteristic
2C2×#14273670C211yesmaximal, characteristic, complemented
3#16837674C211yesmaximal, characteristic, complemented
4#16837216C211yesmaximal, characteristic, complemented
5#16837209C211yesmaximal, characteristic, complemented
6#16837187C211yesmaximal, characteristic, complemented
7C59×#510C211yesmaximal, characteristic, complemented
8#14273773—21no—
9#14273758—21no—
10#14273754—22no—
11#14273752—21no—
12#14273750—21no—
13C2×D472C2211yescharacteristic
14D8×D59—21no—
15#14273733C2211yescharacteristic
16#14273670—22no—
17C2×C59⋊C16C2211yescharacteristic, complemented
18#14273663C2211yescharacteristic, complemented
19#14273646—21no—
20#135×C59C2211yescharacteristic
21C2×Q16×C59C2211yescharacteristic, complemented
22Q32×C59—21no—
23SD32×C59—21no—
24M32×C59C2211yescharacteristic, complemented
25#41×C59—21no—
26C2×Q8×C59—21no—
27#11745689—22no—
28D4×D59—22no—
29D4×D59—42no—
30#11745685—41no—
31#11745685D411yescharacteristic
32C2×D236—21no—
33C2×D236—41no—
34Q16×C59—21no—
35Q16×C59—21no—
36Q16×C59D411yescharacteristic
37SD16×C59—21no—
38D8×C59D411yescharacteristic
39C2×C8×C59C2311yescharacteristic
40#11745672—41no—
41#11745671—22no—
42#11745671—41no—
43#11745669—22no—
44#11745664—21no—
45#11745664D411yescharacteristic
46D472—21no—
47D472D412yes—
48#11745659—21no—
49C8×D59—21no—
50C16×C59—21no—
51C59⋊C16—21no—
52C22×D59—42no—
53C22×D59—41no—
54Q8×C59—21no—
55Q8×C59—41no—
56Q8×C59—41no—
57D4×C59—21no—
58D4×C59—41no—
59C2×C4×C59—41no—
60C2×C4×C59—41no—
61C2×C4×C59C2×D411yescharacteristic
62C22⋊D59—21no—
63C22⋊D59—42no—
64D236—22no—
65D236—42no—
66D236—41no—
67D236D811yescharacteristic
68C4×D59—21no—
69C4×D59—42no—
70Dic118D811yescharacteristic
71C8×C59C2×D411yescharacteristic
72C8×C59C2×D411yescharacteristic
73C59⋊C8—21no—
74C59⋊C8—41no—
75C22×C59—41no—
76C22×C59AGL(1,ℤ/8)11yescharacteristic
77C2×D59—21no—
78C2×D59—42no—
79C2×D59—162no—
80C2×D59—161no—
81C4×C59—41no—
82C4×C59—81no—
83C4×C59#12011yescharacteristic
84C4×C59C2×D811yescharacteristic
85Dic59—21no—
86#2194—591nomaximal, Sylow
87C2×C59—21no—
88C2×C59—81no—
89C2×C59#44711yescharacteristic
90D59—41no—
91D59—82no—
92#576—591no—
93#510D5911yescharacteristic, complemented
94C2×SD32—591no—
95#473—591no—
96#361—591no—
97#359—591no—
98#350—591no—
99C59#219411yescharacteristic, complemented, Sylow
100H(5,𝔽2)—1181no—
101#137—1181no—
102AGL(1,ℤ/8)—1181no—
103AGL(1,ℤ/8)—1182no—
104#135—1181no—
105#135C2×D5911yescharacteristic
106C2×Q16C2×D5911yescharacteristic, complemented
107C2×D8—591no—
108C2×D8—1181no—
109#131—591no—
110Q32—21no—
111SD32—21no—
112SD32—1182no—
113M32C2×D5911yescharacteristic, complemented
114C2×C16—591no—
115#108—591no—
116#101—1181no—
117#41—21no—
118#41—591no—
119#41—1182no—
120#41—2361no—
121C2×Q8—21no—
122C2×D4—1182no—
123C2×D4—1181no—
124C2×D4—2361no—
125C2×D4—2362no—
126Q16—21no—
127Q16—21no—
128Q16—2361no—
129Q16C22⋊D5911yescharacteristic
130SD16—21no—
131SD16—1182no—
132SD16—2361no—
133D8—592no—
134D8—1182no—
135D8—1181no—
136D8C22⋊D5911yescharacteristic
137M16—591no—
138M16—1181no—
139M16—1181no—
140C2×C8—1181no—
141C2×C8C22×D5911yescharacteristic
142C16—21no—
143C16—1181no—
144C23—2362no—
145C23—2361no—
146Q8—21no—
147Q8—41no—
148Q8—41no—
149Q8—591no—
150D4—21no—
151D4—41no—
152D4—591no—
153D4—1181no—
154D4—1182no—
155D4—2362no—
156D4—2362no—
157D4—2361no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—1181no—
161C2×C4—2362no—
162C2×C4D4×D5911yescharacteristic
163C8—1181no—
164C8—2361no—
165C8D4×D5911yescharacteristic
166C8C2×C22⋊D5911yescharacteristic
167C22—41no—
168C22—1181no—
169C22—9441no—
170C22—9442no—
171C22—2362no—
172C22#1427375111yescharacteristic
173C4—41no—
174C4—81no—
175C4—1181no—
176C4#1427369511yescharacteristic
177C4D8×D5911yescharacteristic
178C2—21no—
179C2—81no—
180C2—4722no—
181C2—2361no—
182C2#1683753411yescharacteristic
subgroupG/H
centerC2#16837534
commutatorC2×C8×C59C23
FrattiniC2×C8C22×D59
FittingC59×#510C2
socleC2×C59#447
hypercenter#510D59
hypocenterC59#2194
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C2×#14273670C2semidirect
3. #16837674C2semidirect
4. #16837216C2semidirect
5. #16837209C2semidirect
6. #16837187C2semidirect
7. C59×#510C2semidirect
17. C2×C59⋊C16C22semidirect
18. #14273663C22semidirect
21. C2×Q16×C59C22semidirect
24. M32×C59C22semidirect
93. #510D59semidirect
99. C59#2194semidirect
106. C2×Q16C2×D59semidirect
113. M32C2×D59semidirect