Finite Group Databasebeta

← #29600668

Subgroups — #29600668

Order 15616.

324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C22×D976C211yesmaximal, characteristic
2C2×#16839599C212yesmaximal, complemented
3#21443996C212yesmaximal, complemented
4C22⋊#14519683C211yesmaximal, characteristic, complemented
5C61×#2216C211yesmaximal, characteristic, complemented
6C22×D488—21no—
7C2×D976—24no—
8C2×D976—21no—
9C2×D976C2212yes—
10#16839599—24no—
11C2×#14519683C2212yescomplemented
12C2×Q32×C61C2211yescharacteristic, complemented
13C22×C16×C61C2211yescharacteristic
14C61×#467—21no—
15C61×#366C2211yescharacteristic, complemented
16C61×#358—21no—
17C22×D244—41no—
18C2×D488—24no—
19C2×D488—22no—
20C2×D488—42no—
21C2×D488—41no—
22D976—24no—
23D976—22no—
24D976D414yes—
25#14519683—22no—
26C2×Q16×C61—21no—
27C22×C8×C61D411yescharacteristic
28C22⋊Q8×C61—41no—
29Q32×C61—22no—
30C2×C16×C61—22no—
31C2×C16×C61D411yescharacteristic
32C2×C16×C61C2311yescharacteristic
33#107×C61—21no—
34#103×C61—41no—
35C23×D61—81no—
36C2×Q8×C61—41no—
37C22×C4×C61D811yescharacteristic
38C2×D244—44no—
39C2×D244—42no—
40C2×D244—82no—
41C2×D244—81no—
42Q16×C61—41no—
43Q16×C61—41no—
44C2×C8×C61—21no—
45C2×C8×C61—21no—
46C2×C8×C61D811yescharacteristic
47C2×C8×C61C2×D411yescharacteristic
48C4⋊C4×C61—41no—
49C4⋊C4×C61—81no—
50C22⋊C4×C61—81no—
51D488—24no—
52D488—44no—
53D488—42no—
54C16×C61—21no—
55C16×C61C2×D412yes—
56C23×C61D1611yescharacteristic
57C22×D61—84no—
58C22×D61—82no—
59C22×D61—162no—
60C22×D61—162no—
61Q8×C61—81no—
62Q8×C61—81no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—81no—
66C2×C4×C61—81no—
67C2×C4×C61D1611yescharacteristic
68C2×C4×C61C2×D811yescharacteristic
69D244—44no—
70D244—84no—
71D244—82no—
72C8×C61—21no—
73C8×C61#12011yescharacteristic
74C8×C61AGL(1,ℤ/8)11yescharacteristic
75#13664—611nomaximal, Sylow
76C22×C61—21no—
77C22×C61—21no—
78C22×C61SD6412yescomplemented
79C22×C61C2×D1611yescharacteristic
80C2×D61—84no—
81C2×D61—168no—
82C2×D61—162no—
83C2×D61—162no—
84C4×C61—21no—
85C4×C61—161no—
86C4×C61—161no—
87C4×C61#44711yescharacteristic
88C4×C61#50911yescharacteristic
89C22×D16—611no—
90C2×SD64—612no—
91#2216D6111yescharacteristic, complemented
92#1415—612no—
93C22⋊C32—611no—
94C2×C61—22no—
95C2×C61#218411yescharacteristic
96C2×C61C2×SD6411yescharacteristic
97C2×C61#226311yescharacteristic
98D61—164no—
99C22×D8—1221no—
100C2×Q32C2×D6111yescharacteristic, complemented
101C2×D16—612no—
102C2×D16—1224no—
103C2×D16—1221no—
104C22×C16C2×D6111yescharacteristic
105#467—21no—
106SD64—1224no—
107C2×C32—612no—
108#366C2×D6111yescharacteristic, complemented
109#358—21no—
110C61#1366411yescharacteristic, complemented, Sylow
111C22×D4—2441no—
112C2×Q16—21no—
113C2×D8—1224no—
114C2×D8—1222no—
115C2×D8—2442no—
116C2×D8—2441no—
117C22×C8C22⋊D6111yescharacteristic
118C22⋊Q8—41no—
119Q32—22no—
120D16—614no—
121D16—1224no—
122D16—1222no—
123C2×C16—22no—
124C2×C16C22⋊D6111yescharacteristic
125C2×C16C22×D6111yescharacteristic
126#107—21no—
127#103—41no—
128C32—1222no—
129C24—4881no—
130C2×Q8—41no—
131C2×D4—4882no—
132C2×D4—4881no—
133C2×D4—2444no—
134C2×D4—2442no—
135C22×C4#1175819911yescharacteristic
136Q16—41no—
137Q16—41no—
138D8—1224no—
139D8—2444no—
140D8—2442no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8#1175819911yescharacteristic
144C2×C8C2×C22⋊D6111yescharacteristic
145C4⋊C4—41no—
146C4⋊C4—81no—
147C22⋊C4—81no—
148C16—21no—
149C16D4×D6112yes—
150C23—9762no—
151C23—9762no—
152C23—4884no—
153C23—4882no—
154C23#1451971811yescharacteristic
155Q8—81no—
156Q8—81no—
157D4—4884no—
158D4—4882no—
159D4—2444no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4#1451971811yescharacteristic
165C2×C4C2×#1175819911yescharacteristic
166C8—21no—
167C8#1451974511yescharacteristic
168C8#1451980211yescharacteristic
169C22—21no—
170C22—21no—
171C22—9768no—
172C22—9762no—
173C22—9762no—
174C22—4884no—
175C22#1683959912yescomplemented
176C22C2×#1451971811yescharacteristic
177C4—21no—
178C4—161no—
179C4—161no—
180C4#1683989511yescharacteristic
181C4#1684019711yescharacteristic
182C2—22no—
183C2—9764no—
184C2#2144773011yescharacteristic
185C2C2×#1683959911yescharacteristic
186C2#2144813111yescharacteristic
subgroupG/H
centerC22C2×#14519718
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#2216C2
socleC22×C61C2×D16
prime radicalC22×D976C2
hypercenter#2216D61
hypocenterC61#13664
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ #2216

Complements

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

NH ≅ G/Ntype
2. C2×#16839599C2semidirect
3. #21443996C2semidirect
4. C22⋊#14519683C2semidirect
5. C61×#2216C2semidirect
11. C2×#14519683C22semidirect
12. C2×Q32×C61C22semidirect
15. C61×#366C22semidirect
78. C22×C61SD64semidirect
91. #2216D61semidirect
100. C2×Q32C2×D61semidirect
108. #366C2×D61semidirect
110. C61#13664semidirect
175. C22#16839599semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D9762
C2×#168395992
#214439962
C22⋊#145196832
C61×#22162
#1366461