Finite Group Databasebeta

← #44398802

Subgroups — #44398802

Order 29056.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#28409703C211yesmaximal, characteristic, complemented
2#28409409C211yesmaximal, characteristic, complemented
3#28409233C211yesmaximal, characteristic, complemented
4#28409227C211yesmaximal, characteristic, complemented
5#28408775C211yesmaximal, characteristic, complemented
6#28408764C211yesmaximal, characteristic, complemented
7D4⋊C8×C227C211yesmaximal, characteristic, complemented
8C2×#16813884—21no—
9C2×#16813873—21no—
10C2×D1816—22no—
11C2×#16813869—21no—
12#20300285C2211yescharacteristic
13#20300285C2211yescharacteristic
14#20300284—21no—
15#20300262—21no—
16#20300261—22no—
17C4×Dic454C2211yescharacteristic
18#20300250—21no—
19C4⋊(C227⋊C8)C2211yescharacteristic
20#20300210—21no—
21#20300208—21no—
22C4×D4×C227C2211yescharacteristic
23C4⋊C8×C227C2211yescharacteristic
24C4×C8×C227C2211yescharacteristic
25#16813884—42no—
26#16813884—42no—
27C2×Dic454D411yescharacteristic
28C2×D908—21no—
29C2×D908—21no—
30C2×D908—21no—
31C2×D908—21no—
32C2×D908—21no—
33C2×D908D412yes—
34C2×C22⋊D227—22no—
35C2×C22⋊D227—22no—
36C2×C4×D227—22no—
37#16813873—42no—
38D1816—44no—
39#16813869—42no—
40C2×C227⋊C8—21no—
41C4⋊Dic227D411yescharacteristic
42Dic227⋊C4—21no—
43(C2×D227)⋊C4—22no—
44C4×Dic227—21no—
45C2×D4×C227D411yescharacteristic
46C22×C4×C227—21no—
47C2×C8×C227—21no—
48C2×C8×C227—21no—
49C4⋊C4×C227D411yescharacteristic
50C22⋊C4×C227—21no—
51C42×C227C2311yescharacteristic
52C22×D227—22no—
53C22×D227—41no—
54Dic454—21no—
55Dic454D812yescomplemented
56D908—42no—
57D908—42no—
58D908—41no—
59D908—41no—
60D908—41no—
61D908—41no—
62D908—41no—
63D908—41no—
64D908—41no—
65D908—41no—
66C22⋊D227—44no—
67C22⋊D227—82no—
68C2×Dic227—21no—
69C2×Dic227—21no—
70C4×D227—44no—
71C227⋊C8—41no—
72C23×C227—21no—
73D4×C227—21no—
74D4×C227—21no—
75C2×C4×C227—21no—
76C2×C4×C227—41no—
77C2×C4×C227—41no—
78C2×C4×C227C2×D411yescharacteristic
79C2×C4×C227C2×D411yescharacteristic
80C2×C4×C227C2×D411yescharacteristic
81C8×C227—22no—
82C8×C227—41no—
83C22×C227—41no—
84C22×C227—41no—
85C22×C227—41no—
86C22×C227#12011yescharacteristic
87C2×D227—42no—
88C2×D227—42no—
89C2×D227—42no—
90C2×D227—81no—
91C2×D227—81no—
92C2×D227—81no—
93C4×C227—21no—
94C4×C227—41no—
95C4×C227C2×D811yescharacteristic
96C4×C227#13511yescharacteristic
97C4×C227AGL(1,ℤ/8)11yescharacteristic
98C4×C227AGL(1,ℤ/8)11yescharacteristic
99Dic227—22no—
100Dic227—41no—
101C2×C227—81no—
102C2×C227#44711yescharacteristic
103C2×C227#44911yescharacteristic
104C2×C227#45311yescharacteristic
105D227—82no—
106D227—161no—
107C227#162111yescharacteristic, complemented, Sylow
108#1621—2271nomaximal, Sylow
109#550—2271no—
110#493—2271no—
111#460—2271no—
112#459—2271no—
113#331—2271no—
114Q8⋊C8—2271no—
115D4⋊C8D22711yescharacteristic, complemented
116C2×#41—4541no—
117C2×SD16—4541no—
118C2×D8—4542no—
119C2×D8—4541no—
120#127—4541no—
121#127—2271no—
122#127—2271no—
123#121—4542no—
124#121—4541no—
125C4×Q8—2271no—
126C4×D4—4541no—
127C4×D4C2×D22711yescharacteristic
128C4⋊C8—2271no—
129C4⋊C8C2×D22711yescharacteristic
130#102—4541no—
131#102—4541no—
132C4×C8C2×D22711yescharacteristic
133#41—9082no—
134#41—9082no—
135C2×Q8—2271no—
136C2×D4—4542no—
137C2×D4—4542no—
138C2×D4—4541no—
139C2×D4—4541no—
140C2×D4—4541no—
141C2×D4—4541no—
142C2×D4—4541no—
143C2×D4—2272no—
144C2×D4D90811yescharacteristic
145C22×C4—21no—
146C22×C4—4542no—
147SD16—9082no—
148D8—9084no—
149D8—9082no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—4541no—
153C4⋊C4—4541no—
154C4⋊C4—2271no—
155C4⋊C4D90811yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—4542no—
158C42—4541no—
159C42C22×D22711yescharacteristic
160C23—21no—
161C23—9081no—
162C23—4542no—
163Q8—4541no—
164Q8—2272no—
165D4—21no—
166D4—21no—
167D4—18162no—
168D4—9082no—
169D4—9082no—
170D4—9084no—
171D4—9081no—
172D4—9081no—
173D4—9081no—
174D4—9081no—
175D4—9081no—
176D4—9081no—
177D4—9081no—
178D4—9081no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—9084no—
183C2×C4—4541no—
184C2×C4—4541no—
185C2×C4D4×D22711yescharacteristic
186C2×C4D4×D22711yescharacteristic
187C2×C4C2×D90811yescharacteristic
188C8—22no—
189C8—41no—
190C8—9081no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—18161no—
195C22—18161no—
196C22—18161no—
197C22—9082no—
198C22—9082no—
199C22—9082no—
200C22#2030025811yescharacteristic
201C4—21no—
202C4—41no—
203C4—9081no—
204C4—4542no—
205C4D8×D22711yescharacteristic
206C4#2030031011yescharacteristic
207C4#2030031511yescharacteristic
208C4#2030031611yescharacteristic
209C2—81no—
210C2—18162no—
211C2—36321no—
212C2#2840916711yescharacteristic
213C2#2840917911yescharacteristic
214C2#2840920111yescharacteristic
subgroupG/H
centerC22#20300258
commutator, cosocleC42×C227C23
FrattiniC42C22×D227
FittingD4⋊C8×C227C2
socleC22×C227#120
hypercenterD4⋊C8D227
hypocenterC227#1621
LCSG ▷ C42×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #28409703C2semidirect
2. #28409409C2semidirect
3. #28409233C2semidirect
4. #28409227C2semidirect
5. #28408775C2semidirect
6. #28408764C2semidirect
7. D4⋊C8×C227C2semidirect
55. Dic454D8semidirect
107. C227#1621semidirect
115. D4⋊C8D227semidirect

Maximal subgroups

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

subgroupindex
#284097032
#284094092
#284092332
#284092272
#284087752
#284087642
D4⋊C8×C2272
#1621227