Finite Group Databasebeta

← #44398838

Subgroups — #44398838

Order 29056.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#28409697C211yesmaximal, characteristic, complemented
2#28409380C211yesmaximal, characteristic, complemented
3#28409233C211yesmaximal, characteristic, complemented
4#28409228C211yesmaximal, characteristic
5#28408762C211yesmaximal, characteristic, complemented
6#28408759C211yesmaximal, characteristic, complemented
7#332×C227C211yesmaximal, characteristic, complemented
8C2×Q8×D227—21no—
9C2×#16813873—21no—
10C2×D1816—21no—
11#20300287—21no—
12#20300285C2211yescharacteristic
13#20300266—22no—
14#20300264—21no—
15C4×Dic454C2211yescharacteristic
16C4×D908C2211yescharacteristic
17#20300250—21no—
18#20300210—21no—
19#20300210—21no—
20#20300208—22no—
21C4×C227⋊C8C2211yescharacteristic
22C4⋊Q8×C227C2211yescharacteristic
23C4⋊C8×C227C2211yescharacteristic
24C4⋊C8×C227C2211yescharacteristic
25C2×Dic454—22no—
26C2×Dic454D411yescharacteristic
27Q8×D227—42no—
28Q8×D227—42no—
29C2×D908—21no—
30C2×D908—21no—
31C2×D908—21no—
32C2×D908D411yescharacteristic
33C2×C4×D227—22no—
34C2×C4×D227—21no—
35#16813873—42no—
36D1816—42no—
37C2×C227⋊C8—21no—
38C4⋊Dic227D411yescharacteristic
39C4⋊Dic227D411yescharacteristic
40Dic227⋊C4—22no—
41Dic227⋊C4—21no—
42(C2×D227)⋊C4—22no—
43(C2×D227)⋊C4—21no—
44C4×Dic227—21no—
45C2×Q8×C227—21no—
46C2×C8×C227—21no—
47C2×C8×C227—21no—
48C4⋊C4×C227—21no—
49C4⋊C4×C227D412yes—
50C42×C227C2311yescharacteristic
51C22×D227—21no—
52C22×D227—41no—
53Dic454—21no—
54Dic454—44no—
55Dic454D812yescomplemented
56D908—21no—
57D908—42no—
58D908—41no—
59D908—41no—
60D908—41no—
61D908—41no—
62D908SD1612yescomplemented
63C2×Dic227—21no—
64C2×Dic227—21no—
65C2×Dic227—21no—
66C4×D227—44no—
67C4×D227—41no—
68C4×D227—41no—
69C227⋊C8—41no—
70Q8×C227—41no—
71Q8×C227—41no—
72C2×C4×C227—22no—
73C2×C4×C227C2×D411yescharacteristic
74C2×C4×C227C2×D411yescharacteristic
75C2×C4×C227C2×D411yescharacteristic
76C8×C227—41no—
77C8×C227—41no—
78C22×C227#12011yescharacteristic
79C2×D227—22no—
80C2×D227—41no—
81C2×D227—41no—
82C2×D227—81no—
83C2×D227—81no—
84C2×D227—81no—
85C4×C227—21no—
86C4×C227—42no—
87C4×C227C2×D811yescharacteristic
88C4×C227C2×SD1611yescharacteristic
89C4×C227AGL(1,ℤ/8)11yescharacteristic
90C4×C227#13711yescharacteristic
91Dic227—22no—
92Dic227—41no—
93Dic227—41no—
94C2×C227#44711yescharacteristic
95C2×C227#44811yescharacteristic
96C2×C227#45411yescharacteristic
97D227—42no—
98D227—161no—
99C227#162711yescharacteristic, complemented, Sylow
100#1627—2271nomaximal, Sylow
101D4×Q8—2271no—
102#486—2271no—
103#460—2271no—
104#459—2271no—
105#332D22711yescharacteristic, complemented
106Q8⋊C8—2271no—
107D4⋊C8—2271no—
108C22×Q8—4541no—
109C2×SD16—4541no—
110C2×D8—4541no—
111C4⋊Q8—4541no—
112C4⋊Q8C2×D22711yescharacteristic
113#127—2271no—
114C22⋊Q8—4541no—
115C22⋊Q8—4542no—
116C4×Q8—2271no—
117C4×D4—4541no—
118C4×D4—2271no—
119C4⋊C8C2×D22711yescharacteristic
120C4⋊C8C2×D22711yescharacteristic
121#102—4541no—
122#102—4541no—
123#102—4542no—
124C4×C8—2271no—
125C2×Q8—21no—
126C2×Q8—9082no—
127C2×Q8—9082no—
128C2×Q8—4542no—
129C2×Q8—2271no—
130C2×D4—4541no—
131C2×D4—4541no—
132C2×D4—4541no—
133C2×D4—2271no—
134C22×C4—4542no—
135C22×C4—4541no—
136SD16—9082no—
137D8—9082no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—4541no—
141C4⋊C4—21no—
142C4⋊C4—4542no—
143C4⋊C4—4541no—
144C4⋊C4—2271no—
145C4⋊C4—2271no—
146C4⋊C4D90812yes—
147C22⋊C4—4542no—
148C22⋊C4—4541no—
149C42—4541no—
150C42C22×D22711yescharacteristic
151C23—9081no—
152C23—4541no—
153Q8—41no—
154Q8—41no—
155Q8—9084no—
156Q8—4541no—
157Q8—2272no—
158D4—9082no—
159D4—9081no—
160D4—9081no—
161D4—9081no—
162D4—9081no—
163D4—4541no—
164D4—2272no—
165C2×C4—22no—
166C2×C4—9084no—
167C2×C4—9081no—
168C2×C4—9081no—
169C2×C4—4541no—
170C2×C4—4541no—
171C2×C4—4541no—
172C2×C4D4×D22711yescharacteristic
173C2×C4D4×D22711yescharacteristic
174C2×C4C2×D90811yescharacteristic
175C8—41no—
176C8—41no—
177C8—9081no—
178C22—18161no—
179C22—18161no—
180C22—18161no—
181C22—9081no—
182C22—9081no—
183C22—4542no—
184C22#2030025811yescharacteristic
185C4—21no—
186C4—42no—
187C4—9081no—
188C4—9081no—
189C4—4542no—
190C4D8×D22711yescharacteristic
191C4SD16×D22711yescharacteristic
192C4#2030031511yescharacteristic
193C4#2030032011yescharacteristic
194C2—36321no—
195C2—9082no—
196C2#2840916711yescharacteristic
197C2#2840917211yescharacteristic
198C2#2840920711yescharacteristic
subgroupG/H
centerC22#20300258
commutator, cosocleC42×C227C23
FrattiniC42C22×D227
Fitting#332×C227C2
socleC22×C227#120
prime radical#28409228C2
hypercenter#332D227
hypocenterC227#1627
LCSG ▷ C42×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #28409697C2semidirect
2. #28409380C2semidirect
3. #28409233C2semidirect
5. #28408762C2semidirect
6. #28408759C2semidirect
7. #332×C227C2semidirect
55. Dic454D8semidirect
62. D908SD16semidirect
99. C227#1627semidirect
105. #332D227semidirect

Maximal subgroups

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

subgroupindex
#284096972
#284093802
#284092332
#284092282
#284087622
#284087592
#332×C2272
#1627227