Finite Group Databasebeta

← #21426066

Subgroups — #21426066

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#16838203C211yesmaximal, characteristic
2#16837843C211yesmaximal, characteristic, complemented
3#16837674C211yesmaximal, characteristic, complemented
4#16837215C211yesmaximal, characteristic, complemented
5#16837210C211yesmaximal, characteristic, complemented
6#16837185C211yesmaximal, characteristic, complemented
7C2×SD32×C59C211yesmaximal, characteristic, complemented
8#14273772—21no—
9#14273758—21no—
10#14273753—21no—
11#14273751—22no—
12#14273749C2211yescharacteristic
13#14273746—21no—
14D8×D59—21no—
15#14273733C2211yescharacteristic
16#14273673—21no—
17#14273670—21no—
18#14273667C2211yescharacteristic, complemented
19#14273663C2211yescharacteristic, complemented
20#14273646—21no—
21C2×Q16×C59C2211yescharacteristic, complemented
22C2×D8×C59C2211yescharacteristic
23SD32×C59—22no—
24C2×C16×C59C2211yescharacteristic, complemented
25C2×Q8×C59—21no—
26C2×D4×C59—21no—
27C2×C22⋊D59—42no—
28#11745687—22no—
29#11745687—41no—
30D4×D59—22no—
31D4×D59—41no—
32#11745685—21no—
33#11745685D411yescharacteristic
34Q16×C59—21no—
35Q16×C59—21no—
36D8×C59—21no—
37D8×C59D412yes—
38C2×C8×C59C2311yescharacteristic
39#11745672—41no—
40#11745671—41no—
41#11745670—22no—
42#11745669—22no—
43#11745664—21no—
44#11745664D411yescharacteristic
45Dic236D411yescharacteristic
46D472D411yescharacteristic
47#11745660—21no—
48#11745659—21no—
49C8×D59—21no—
50C16×C59—21no—
51C59⋊C16—21no—
52C23×C59—41no—
53C22×D59—42no—
54Q8×C59—41no—
55Q8×C59—41no—
56D4×C59—22no—
57D4×C59—41no—
58C2×C4×C59—41no—
59C2×C4×C59C2×D411yescharacteristic
60C22⋊D59—21no—
61C22⋊D59—42no—
62C22⋊D59—42no—
63C22⋊D59—41no—
64C2×Dic59—42no—
65D236—21no—
66D236D811yescharacteristic
67C4×D59—21no—
68C4×D59—41no—
69Dic118—21no—
70Dic118D811yescharacteristic
71C8×C59C2×D411yescharacteristic
72C8×C59C2×D411yescharacteristic
73C59⋊C8—21no—
74C59⋊C8—41no—
75C22×C59—42no—
76C22×C59—161no—
77C22×C59AGL(1,ℤ/8)11yescharacteristic
78C2×D59—21no—
79C2×D59—41no—
80C2×D59—162no—
81C4×C59—81no—
82C4×C59#12011yescharacteristic
83C4×C59C2×D811yescharacteristic
84Dic59—21no—
85Dic59—41no—
86#2194—591nomaximal, Sylow
87C2×C59—21no—
88C2×C59—82no—
89C2×C59#44711yescharacteristic
90D59—41no—
91D59—81no—
92#576—591no—
93#510—591no—
94C2×SD32D5911yescharacteristic, complemented
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—591no—
105#135—1181no—
106C2×Q16C2×D5911yescharacteristic, complemented
107C2×D8—1181no—
108C2×D8C2×D5911yescharacteristic
109#131—591no—
110Q32—1181no—
111SD32—22no—
112SD32—1181no—
113M32—591no—
114C2×C16C2×D5911yescharacteristic, complemented
115#108—591no—
116#101—1181no—
117#41—591no—
118#41—1182no—
119#41—1181no—
120#41—2361no—
121C2×Q8—21no—
122C2×D4—21no—
123C2×D4—1182no—
124C2×D4—2361no—
125C2×D4—2362no—
126Q16—21no—
127Q16—21no—
128Q16—591no—
129Q16—2361no—
130SD16—1182no—
131SD16—1181no—
132SD16—2361no—
133D8—21no—
134D8—591no—
135D8—1182no—
136D8C22⋊D5912yes—
137M16—591no—
138M16—1181no—
139M16—1181no—
140C2×C8—1181no—
141C2×C8C22×D5911yescharacteristic
142C16—21no—
143C16—1181no—
144C23—41no—
145C23—2362no—
146Q8—41no—
147Q8—41no—
148Q8—591no—
149Q8—1181no—
150D4—22no—
151D4—41no—
152D4—591no—
153D4—1181no—
154D4—1181no—
155D4—2362no—
156D4—2362no—
157D4—2361no—
158C2×C4—41no—
159C2×C4—1181no—
160C2×C4—2362no—
161C2×C4—2361no—
162C2×C4D4×D5911yescharacteristic
163C8—1181no—
164C8—2361no—
165C8D4×D5911yescharacteristic
166C8C2×C22⋊D5911yescharacteristic
167C22—42no—
168C22—161no—
169C22—1181no—
170C22—9442no—
171C22—2361no—
172C22#1427375111yescharacteristic
173C4—81no—
174C4—1181no—
175C4—2361no—
176C4#1427369511yescharacteristic
177C4D8×D5911yescharacteristic
178C2—21no—
179C2—82no—
180C2—4721no—
181C2—2361no—
182C2#1683753411yescharacteristic
subgroupG/H
centerC2#16837534
commutatorC2×C8×C59C23
FrattiniC2×C8C22×D59
FittingC2×SD32×C59C2
socleC2×C59#447
hypercenterC2×SD32D59
hypocenterC59#2194
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. #16837843C2semidirect
3. #16837674C2semidirect
4. #16837215C2semidirect
5. #16837210C2semidirect
6. #16837185C2semidirect
7. C2×SD32×C59C2semidirect
18. #14273667C22semidirect
19. #14273663C22semidirect
21. C2×Q16×C59C22semidirect
24. C2×C16×C59C22semidirect
94. C2×SD32D59semidirect
99. C59#2194semidirect
106. C2×Q16C2×D59semidirect
114. C2×C16C2×D59semidirect