Finite Group Databasebeta

← #21426065

Subgroups — #21426065

Order 7552.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#16838207C211yesmaximal, characteristic
2#16837843C211yesmaximal, characteristic, complemented
3C2×#14273670C211yesmaximal, characteristic, complemented
4#16837214C211yesmaximal, characteristic, complemented
5#16837208C211yesmaximal, characteristic, complemented
6#16837186C211yesmaximal, characteristic, complemented
7C59×#473C211yesmaximal, characteristic, complemented
8#14273773—21no—
9#14273755—21no—
10#14273755—22no—
11#14273749—21no—
12#14273749C2211yescharacteristic
13C2×D472—21no—
14C2×D472C2211yescharacteristic
15#14273673—21no—
16#14273670—22no—
17#14273670—21no—
18#14273667C2211yescharacteristic, complemented
19C2×C59⋊C16C2211yescharacteristic, complemented
20#137×C59—21no—
21C2×Q16×C59C2211yescharacteristic, complemented
22#131×C59C2211yescharacteristic
23#108×C59C2211yescharacteristic, complemented
24#101×C59—21no—
25#41×C59D411yescharacteristic
26C2×Q8×C59—21no—
27#11745689—41no—
28D4×D59—42no—
29D4×D59—41no—
30#11745685—22no—
31#11745685—21no—
32C2×D236—22no—
33C2×D236—21no—
34Q16×C59—21no—
35Q16×C59—21no—
36Q16×C59—41no—
37SD16×C59—41no—
38M16×C59—21no—
39M16×C59—21no—
40M16×C59D411yescharacteristic
41C2×C8×C59—21no—
42C2×C8×C59C2311yescharacteristic
43Dic236D411yescharacteristic
44D472—22no—
45D472—21no—
46D472D411yescharacteristic
47D472D412yes—
48#11745660—22no—
49#11745660—21no—
50C59⋊C16—21no—
51C59⋊C16—21no—
52C22×D59—42no—
53C22×D59—41no—
54Q8×C59—41no—
55Q8×C59—41no—
56Q8×C59D811yescharacteristic
57D4×C59—21no—
58D4×C59D811yescharacteristic
59C2×C4×C59—21no—
60C2×C4×C59—41no—
61C2×C4×C59C2×D411yescharacteristic
62C22⋊D59—42no—
63C22⋊D59—41no—
64D236—22no—
65D236—21no—
66D236—42no—
67D236—41no—
68C4×D59—42no—
69C4×D59—41no—
70Dic118—21no—
71C8×C59—21no—
72C8×C59—41no—
73C8×C59C2×D411yescharacteristic
74C8×C59C2×D411yescharacteristic
75C22×C59—21no—
76C22×C59AGL(1,ℤ/8)11yescharacteristic
77C2×D59—42no—
78C2×D59—41no—
79C2×D59—161no—
80C2×D59—162no—
81C4×C59—21no—
82C4×C59—81no—
83C4×C59#12011yescharacteristic
84C4×C59C2×D811yescharacteristic
85Dic59—41no—
86#2194—591nomaximal, Sylow
87C2×C59—21no—
88C2×C59—41no—
89C2×C59#44711yescharacteristic
90D59—82no—
91D59—81no—
92#576—591no—
93#510—591no—
94C2×SD32—591no—
95#473D5911yescharacteristic, complemented
96#361—591no—
97#359—591no—
98#350—591no—
99C59#219411yescharacteristic, complemented, Sylow
100H(5,𝔽2)—1181no—
101#137—21no—
102AGL(1,ℤ/8)—1182no—
103AGL(1,ℤ/8)—1181no—
104#135—591no—
105#135—1181no—
106C2×Q16C2×D5911yescharacteristic, complemented
107C2×D8—591no—
108C2×D8—1181no—
109#131C2×D5911yescharacteristic
110Q32—1181no—
111SD32—1182no—
112SD32—1181no—
113M32—591no—
114C2×C16—591no—
115#108C2×D5911yescharacteristic, complemented
116#101—21no—
117#41—1182no—
118#41—1181no—
119#41—2361no—
120#41C22⋊D5911yescharacteristic
121C2×Q8—21no—
122C2×D4—1182no—
123C2×D4—1181no—
124C2×D4—2362no—
125C2×D4—2361no—
126Q16—21no—
127Q16—21no—
128Q16—41no—
129Q16—591no—
130SD16—41no—
131SD16—1182no—
132SD16—1181no—
133D8—592no—
134D8—591no—
135D8—1182no—
136D8—1181no—
137M16—21no—
138M16—21no—
139M16C22⋊D5911yescharacteristic
140C2×C8—21no—
141C2×C8C22×D5911yescharacteristic
142C16—1181no—
143C16—1181no—
144C23—2362no—
145C23—2361no—
146Q8—41no—
147Q8—41no—
148Q8—1181no—
149Q8#1174566911yescharacteristic
150D4—21no—
151D4—1182no—
152D4—1181no—
153D4—2362no—
154D4—2362no—
155D4—2361no—
156D4—2361no—
157D4#1174566911yescharacteristic
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—2362no—
161C2×C4—2361no—
162C2×C4C2×C22⋊D5911yescharacteristic
163C8—21no—
164C8—41no—
165C8D4×D5911yescharacteristic
166C8D4×D5911yescharacteristic
167C22—21no—
168C22—9441no—
169C22—9442no—
170C22—2362no—
171C22—2361no—
172C22#1427375211yescharacteristic
173C4—21no—
174C4—81no—
175C4—2361no—
176C4#1427369511yescharacteristic
177C4C2×#1174566911yescharacteristic
178C2—21no—
179C2—41no—
180C2—4722no—
181C2—4721no—
182C2#1683753511yescharacteristic
subgroupG/H
centerC2#16837535
commutatorC2×C8×C59C23
FrattiniC2×C8C22×D59
FittingC59×#473C2
socleC2×C59#447
hypercenter#473D59
hypocenterC59#2194
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #473

Complements

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

NH ≅ G/Ntype
2. #16837843C2semidirect
3. C2×#14273670C2semidirect
4. #16837214C2semidirect
5. #16837208C2semidirect
6. #16837186C2semidirect
7. C59×#473C2semidirect
18. #14273667C22semidirect
19. C2×C59⋊C16C22semidirect
21. C2×Q16×C59C22semidirect
23. #108×C59C22semidirect
95. #473D59semidirect
99. C59#2194semidirect
106. C2×Q16C2×D59semidirect
115. #108C2×D59semidirect