Finite Group Databasebeta

← #44398423

Subgroups — #44398423

Order 29056.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#28409587C211yesmaximal, characteristic
2#28409054C211yesmaximal, characteristic
3C4⋊C8×D227C211yesmaximal, characteristic
4#28408780C211yesmaximal, characteristic, complemented
5#28408780C211yesmaximal, characteristic, complemented
6#28408778C211yesmaximal, characteristic, complemented
7#332×C227C211yesmaximal, characteristic, complemented
8C2×#16813867—21no—
9C2×C8×D227—21no—
10#20300288C2211yescharacteristic
11#20300279—21no—
12#20300268C412yes—
13#20300264—21no—
14Q8×Dic227—21no—
15#20300253C412yes—
16#20300246—21no—
17C42×D227C2211yescharacteristic
18C4⋊(C227⋊C8)C2211yescharacteristic
19C4⋊(C227⋊C8)C2211yescharacteristic
20Dic227⋊C8—21no—
21Dic227⋊C8—21no—
22C4⋊Q8×C227C2211yescharacteristic
23C4⋊C8×C227C2211yescharacteristic
24C4⋊C8×C227C2211yescharacteristic
25C2×Dic454C2×C412yes—
26C2×C4×D227C2×C411yescharacteristic
27C2×C4×D227D411yescharacteristic
28C2×C4×D227D411yescharacteristic
29#16813867—42no—
30C2×C227⋊C8—21no—
31C2×C227⋊C8—21no—
32C8×D227—42no—
33C4⋊Dic227—22no—
34C4⋊Dic227—21no—
35C4⋊Dic227—21no—
36Dic227⋊C4—22no—
37(C2×D227)⋊C4—22no—
38C4×Dic227—22no—
39C4×Dic227C2×C411yescharacteristic
40C4×Dic227D411yescharacteristic
41C4×Dic227D411yescharacteristic
42C2×Q8×C227—21no—
43C2×C8×C227—21no—
44C2×C8×C227—21no—
45C4⋊C4×C227—21no—
46C4⋊C4×C227C2×C412yes—
47C42×C227C2311yescharacteristic
48C22×D227C22⋊C411yescharacteristic
49Dic454—42no—
50C2×Dic227—22no—
51C2×Dic227C22⋊C411yescharacteristic
52C2×Dic227C22⋊C411yescharacteristic
53C2×Dic227C22⋊C411yescharacteristic
54C4×D227—21no—
55C4×D227—21no—
56C4×D227—41no—
57C4×D227SD1612yes—
58C4×D227Q1612yes—
59C227⋊C8—41no—
60C227⋊C8—41no—
61Q8×C227—41no—
62Q8×C227—41no—
63C2×C4×C227—22no—
64C2×C4×C227C22×C411yescharacteristic
65C2×C4×C227C2×D411yescharacteristic
66C2×C4×C227C2×D411yescharacteristic
67C8×C227—41no—
68C8×C227—41no—
69C22×C227C2×C22⋊C411yescharacteristic
70C2×D227—21no—
71C2×D227—21no—
72C2×D227#10312yes—
73C4×C227—21no—
74C4×C227—42no—
75C4×C227C2×SD1611yescharacteristic
76C4×C227C2×Q1611yescharacteristic
77C4×C227AGL(1,ℤ/8)11yescharacteristic
78C4×C227#13711yescharacteristic
79Dic227—21no—
80Dic227—21no—
81Dic227—42no—
82Dic227#10312yes—
83C2×C227#41311yescharacteristic
84C2×C227C2×#10311yescharacteristic
85C2×C227#41711yescharacteristic
86D227—22no—
87C227#155011yescharacteristic, complemented, Sylow
88#1550—2271nomaximal, Sylow
89#533—2271no—
90#423—2271no—
91C2×C4⋊C8—2271no—
92#333—2271no—
93#333—2271no—
94#332—2271no—
95#332D22711yescharacteristic, complemented
96C2×M16—4541no—
97C22×C8—4541no—
98C4⋊Q8—2271no—
99C4⋊Q8C2×D22711yescharacteristic
100#125—4541no—
101C22⋊Q8—4541no—
102C22⋊Q8—2272no—
103C4×Q8—4541no—
104C4×Q8—2272no—
105#117—4541no—
106C2×C42—2271no—
107C4⋊C8—4541no—
108C4⋊C8—4541no—
109C4⋊C8—2271no—
110C4⋊C8—2271no—
111C4⋊C8C2×D22711yescharacteristic
112C4⋊C8C2×D22711yescharacteristic
113C2×Q8—21no—
114C2×Q8—2272no—
115C22×C4—2271no—
116C22×C4—2271no—
117C22×C4—2271no—
118M16—9082no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—9082no—
122C2×C8—4541no—
123C2×C8—4541no—
124C4⋊C4—21no—
125C4⋊C4—4542no—
126C4⋊C4—4542no—
127C4⋊C4—4541no—
128C4⋊C4—4541no—
129C4⋊C4C4×D22712yes—
130C22⋊C4—4542no—
131C42—4542no—
132C42—2271no—
133C42—2271no—
134C42—2271no—
135C42C22×D22711yescharacteristic
136C23—2271no—
137Q8—41no—
138Q8—41no—
139Q8—9082no—
140C2×C4—22no—
141C2×C4—9081no—
142C2×C4—4542no—
143C2×C4—4541no—
144C2×C4—4541no—
145C2×C4—2271no—
146C2×C4—2271no—
147C2×C4—2271no—
148C2×C4—2272no—
149C2×C4—2272no—
150C2×C4C2×C4×D22711yescharacteristic
151C2×C4D4×D22711yescharacteristic
152C2×C4D4×D22711yescharacteristic
153C8—41no—
154C8—41no—
155C8—9081no—
156C8—9081no—
157C22—4541no—
158C22—4541no—
159C22—2272no—
160C22C22⋊C4×D22711yescharacteristic
161C4—21no—
162C4—42no—
163C4—9082no—
164C4—4541no—
165C4—4541no—
166C4—2272no—
167C4SD16×D22711yescharacteristic
168C4Q16×D22711yescharacteristic
169C4#2030031211yescharacteristic
170C4#2030031711yescharacteristic
171C2—4542no—
172C2#2840901511yescharacteristic
173C2#103×D22711yescharacteristic
174C2#2840903011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D227
commutatorC2×C4×C227C22×C4
FrattiniC42C22×D227
Fitting#332×C227C2
socleC22×C227C2×C22⋊C4
prime radicalC22×D227C22⋊C4
cosocleC42×C227C23
hypercenter#332D227
hypocenterC227#1550
LCSG ▷ C2×C4×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #28408780C2semidirect
5. #28408780C2semidirect
6. #28408778C2semidirect
7. #332×C227C2semidirect
87. C227#1550semidirect
95. #332D227semidirect

Maximal subgroups

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

subgroupindex
#284095872
#284090542
C4⋊C8×D2272
#284087802
#284087782
#332×C2272
#1550227