Finite Group Databasebeta

← #44401686

Subgroups — #44401686

Order 29056.

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#28409829C211yesmaximal, characteristic
2#28409475C211yesmaximal, characteristic, complemented
3#28409472C211yesmaximal, characteristic, complemented
4#28409291C211yesmaximal, characteristic, complemented
5#28408841C211yesmaximal, characteristic, complemented
6#28408813C211yesmaximal, characteristic, complemented
7#360×C227C211yesmaximal, characteristic, complemented
8#41×D227—21no—
9#20300320—21no—
10#20300317—21no—
11#20300315—21no—
12#20300312—21no—
13#20300310C2211yescharacteristic
14#20300308—21no—
15C2×Dic908C2211yescharacteristic, complemented
16C2×#16813867C2211yescharacteristic
17#20300268—21no—
18Dic1816—21no—
19#20300234—21no—
20#20300233—21no—
21#20300232—21no—
22#20300228C2211yescharacteristic, complemented
23#20300211—21no—
24#135×C227C2211yescharacteristic
25M32×C227C2211yescharacteristic, complemented
26#106×C227C2211yescharacteristic, complemented
27#16813885—21no—
28#16813884—21no—
29#16813884—41no—
30#16813883—21no—
31#16813883—41no—
32C2×Dic454—21no—
33Q8×D227—21no—
34D4×D227—21no—
35D4×D227—41no—
36C2×C4×D227—41no—
37C2×C4×D227D411yescharacteristic
38Dic908—21no—
39Dic908—21no—
40Dic908D411yescharacteristic
41#16813874—21no—
42#16813873—21no—
43#16813872—21no—
44#16813871—21no—
45D1816D411yescharacteristic
46#16813869—21no—
47#16813867—21no—
48#16813867—21no—
49C2×C227⋊C8D411yescharacteristic
50C4⋊Dic227—41no—
51(C2×D227)⋊C4—41no—
52C227⋊C16—21no—
53#41×C227—21no—
54Q16×C227D411yescharacteristic
55SD16×C227—21no—
56D8×C227D411yescharacteristic
57C2×C8×C227C2311yescharacteristic
58C4⋊C4×C227—21no—
59C16×C227—21no—
60C22×D227—41no—
61C22×D227D811yescharacteristic
62Dic454—21no—
63Dic454—41no—
64Dic454—41no—
65Dic454—41no—
66D908—21no—
67D908—41no—
68C22⋊D227—41no—
69C22⋊D227—41no—
70C22⋊D227—41no—
71C2×Dic227—41no—
72C2×Dic227—41no—
73C2×Dic227D811yescharacteristic
74C4×D227—21no—
75C4×D227—21no—
76C4×D227—41no—
77C4×D227—41no—
78C4×D227—41no—
79C227⋊C8—21no—
80Q8×C227—21no—
81D4×C227—21no—
82D4×C227—41no—
83C2×C4×C227—41no—
84C2×C4×C227—41no—
85C2×C4×C227C2×D411yescharacteristic
86C8×C227C2×D411yescharacteristic
87C8×C227C2×D411yescharacteristic
88C22×C227—41no—
89C22×C227C2×D811yescharacteristic
90C2×D227—21no—
91C2×D227—41no—
92C2×D227—41no—
93C2×D227—82no—
94C4×C227—41no—
95C4×C227—81no—
96C4×C227#12011yescharacteristic
97C4×C227AGL(1,ℤ/8)11yescharacteristic
98Dic227—21no—
99Dic227—41no—
100Dic227—81no—
101C2×C227—21no—
102C2×C227—81no—
103C2×C227#44711yescharacteristic
104D227—41no—
105D227—81no—
106C227#219111yescharacteristic, complemented, Sylow
107#2191—2271nomaximal, Sylow
108#575—2271no—
109#510—2271no—
110#510—2271no—
111#470—2271no—
112#360—2271no—
113#360D22711yescharacteristic, complemented
114#349—2271no—
115C2×#41—4541no—
116#137—4541no—
117#137—4541no—
118AGL(1,ℤ/8)—4541no—
119AGL(1,ℤ/8)—4541no—
120#135—4541no—
121#135—2271no—
122#135C2×D22711yescharacteristic
123C2×Q16—2271no—
124C2×M16—2271no—
125C22⋊Q8—4541no—
126Q32—4541no—
127Q32—4541no—
128SD32—4541no—
129SD32—4541no—
130M32—2271no—
131M32C2×D22711yescharacteristic, complemented
132#106C2×D22711yescharacteristic, complemented
133#103—4541no—
134#41—21no—
135#41—9081no—
136#41—9081no—
137#41—4541no—
138#41—4541no—
139#41—4541no—
140C2×Q8—4541no—
141C2×Q8—4541no—
142C2×D4—9081no—
143C2×D4—4541no—
144C22×C4—9081no—
145C22×C4—2271no—
146Q16—4541no—
147Q16—4541no—
148Q16—4541no—
149Q16—2271no—
150Q16D90811yescharacteristic
151SD16—21no—
152SD16—4541no—
153SD16—4541no—
154SD16—4541no—
155D8—4541no—
156D8—2271no—
157D8D90811yescharacteristic
158M16—4541no—
159M16—4541no—
160C2×C8—2271no—
161C2×C8C22×D22711yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—9081no—
164C22⋊C4—9081no—
165C16—21no—
166C16—4541no—
167C23—9081no—
168C23—2271no—
169Q8—21no—
170Q8—9081no—
171Q8—9081no—
172Q8—9081no—
173Q8—4541no—
174D4—21no—
175D4—41no—
176D4—9081no—
177D4—9081no—
178D4—9081no—
179D4—9081no—
180D4—4541no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—9081no—
184C2×C4—9081no—
185C2×C4—9081no—
186C2×C4—9081no—
187C2×C4—9081no—
188C2×C4—4541no—
189C2×C4—4541no—
190C2×C4—2271no—
191C2×C4D4×D22711yescharacteristic
192C8—4541no—
193C8D4×D22711yescharacteristic
194C8C2×D90811yescharacteristic
195C22—41no—
196C22—18162no—
197C22—9081no—
198C22—9081no—
199C22—4541no—
200C22D8×D22711yescharacteristic
201C4—41no—
202C4—81no—
203C4—18161no—
204C4—9081no—
205C4—4541no—
206C4#2030025811yescharacteristic
207C4#2030031511yescharacteristic
208C2—21no—
209C2—81no—
210C2—18161no—
211C2—9081no—
212C2#2840916711yescharacteristic
subgroupG/H
centerC2#28409167
commutator, cosocleC2×C8×C227C23
FrattiniC2×C8C22×D227
Fitting#360×C227C2
socleC2×C227#447
prime radical#28409829C2
hypercenter#360D227
hypocenterC227#2191
LCSG ▷ C2×C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #28409475C2semidirect
3. #28409472C2semidirect
4. #28409291C2semidirect
5. #28408841C2semidirect
6. #28408813C2semidirect
7. #360×C227C2semidirect
15. C2×Dic908C22semidirect
22. #20300228C22semidirect
25. M32×C227C22semidirect
26. #106×C227C22semidirect
106. C227#2191semidirect
113. #360D227semidirect
131. M32C2×D227semidirect
132. #106C2×D227semidirect

Maximal subgroups

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

subgroupindex
#284098292
#284094752
#284094722
#284092912
#284088412
#284088132
#360×C2272
#2191227