Finite Group Databasebeta

← #44401756

Subgroups — #44401756

Order 29056.

216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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#28409781C211yesmaximal, characteristic, complemented
2#28409217C211yesmaximal, characteristic, complemented
3#28409214C211yesmaximal, characteristic, complemented
4#28409207C211yesmaximal, characteristic
5#28408830C211yesmaximal, characteristic, complemented
6#28408828C211yesmaximal, characteristic, complemented
7#356×C227C211yesmaximal, characteristic, complemented
8#20300336C2211yescharacteristic
9#20300321—21no—
10#20300319—21no—
11#20300316—21no—
12#20300286C2211yescharacteristic
13#20300283—21no—
14#20300282—21no—
15#20300278—21no—
16#20300277C2211yescharacteristic
17#20300273—21no—
18#20300266—21no—
19#20300264—21no—
20#20300216—21no—
21#20300214—21no—
22#20300214—21no—
23#20300207C2211yescharacteristic
24C4⋊Q8×C227C2211yescharacteristic
25#101×C227C2211yescharacteristic
26#101×C227C2211yescharacteristic
27#16813885—41no—
28#16813884—21no—
29#16813884—21no—
30#16813884—21no—
31C2×Dic454D411yescharacteristic
32Q8×D227—41no—
33C2×D908D411yescharacteristic
34C2×C4×D227—21no—
35Dic908—41no—
36#16813874—41no—
37#16813873—41no—
38#16813873—41no—
39#16813871—41no—
40D1816—41no—
41#16813868—21no—
42C4⋊Dic227—21no—
43Dic227⋊C4—21no—
44Dic227⋊C4—21no—
45Dic227⋊C4—21no—
46Dic227⋊C4—21no—
47Dic227⋊C4—21no—
48(C2×D227)⋊C4—21no—
49(C2×D227)⋊C4—21no—
50(C2×D227)⋊C4—21no—
51(C2×D227)⋊C4—21no—
52(C2×D227)⋊C4—21no—
53C4×Dic227D411yescharacteristic
54C4×Dic227D411yescharacteristic
55C2×Q8×C227D411yescharacteristic
56C2×Q8×C227C2311yescharacteristic
57M16×C227—21no—
58M16×C227—21no—
59C4⋊C4×C227—21no—
60C4⋊C4×C227—21no—
61C42×C227D411yescharacteristic
62C22×D227—21no—
63Dic454—21no—
64Dic454—21no—
65Dic454—21no—
66Dic454—41no—
67D908—21no—
68D908—21no—
69D908—21no—
70D908—41no—
71C22⋊D227—41no—
72C2×Dic227—21no—
73C2×Dic227—21no—
74C2×Dic227—21no—
75C4×D227—41no—
76C4×D227—41no—
77C4×D227—41no—
78C4×D227—81no—
79C227⋊C8—41no—
80Q8×C227—41no—
81Q8×C227—41no—
82C2×C4×C227—21no—
83C2×C4×C227—21no—
84C2×C4×C227C2×D411yescharacteristic
85C2×C4×C227C2×D411yescharacteristic
86C2×C4×C227C2×D411yescharacteristic
87C8×C227—41no—
88C8×C227—41no—
89C22×C227#12011yescharacteristic
90C2×D227—42no—
91C2×D227—41no—
92C2×D227—41no—
93C4×C227—21no—
94C4×C227—21no—
95C4×C227—21no—
96C4×C227—41no—
97C4×C227—41no—
98Dic227—41no—
99Dic227—41no—
100Dic227—41no—
101Dic227—41no—
102C2×C227—21no—
103C2×C227B(4,𝔽2)11yescharacteristic
104D227—81no—
105D227—81no—
106C227#220311yescharacteristic, complemented, Sylow
107#2203—2271nomaximal, Sylow
108#563—2271no—
109#456—2271no—
110#456—2271no—
111#454—2271no—
112#356—2271no—
113#356D22711yescharacteristic, complemented
114#355—2271no—
1152−1+4—2271no—
116#137—4541no—
117#137—4541no—
118AGL(1,ℤ/8)—4541no—
119C4⋊Q8—2271no—
120C4⋊Q8C2×D22711yescharacteristic
121#126—4541no—
122#126—4541no—
123#125—4541no—
124#124—2271no—
125#123—4541no—
126C22⋊Q8—4541no—
127C22⋊Q8—4541no—
128#104—4541no—
129#104—4541no—
130#104—4541no—
131#101—2271no—
132#101C2×D22711yescharacteristic
133#101C2×D22711yescharacteristic
134#41—9081no—
135#41—4541no—
136#41—4541no—
137#41—4541no—
138C2×Q8—9081no—
139C2×Q8—2271no—
140C2×Q8D90811yescharacteristic
141C2×Q8C22×D22711yescharacteristic
142C2×D4—2271no—
143C22×C4—4541no—
144Q16—9081no—
145Q16—9081no—
146SD16—9081no—
147SD16—9081no—
148SD16—9081no—
149D8—9081no—
150M16—21no—
151M16—21no—
152M16—4541no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—4541no—
156C4⋊C4—4541no—
157C4⋊C4—4541no—
158C4⋊C4—4541no—
159C4⋊C4—4541no—
160C4⋊C4—4541no—
161C22⋊C4—4541no—
162C22⋊C4—4541no—
163C22⋊C4—4541no—
164C22⋊C4—4541no—
165C22⋊C4—4541no—
166C42—2271no—
167C42—2271no—
168C42D90811yescharacteristic
169C23—4541no—
170Q8—41no—
171Q8—41no—
172Q8—9081no—
173Q8—4541no—
174Q8—4541no—
175Q8—4541no—
176D4—9081no—
177D4—9081no—
178D4—4541no—
179D4—4541no—
180D4—4541no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—18161no—
184C2×C4—9081no—
185C2×C4—9081no—
186C2×C4—9081no—
187C2×C4—4541no—
188C2×C4—4541no—
189C2×C4—4541no—
190C2×C4D4×D22711yescharacteristic
191C2×C4D4×D22711yescharacteristic
192C2×C4C2×D90811yescharacteristic
193C8—41no—
194C8—41no—
195C8—9081no—
196C22—9082no—
197C22—9081no—
198C22—9081no—
199C22#2030025811yescharacteristic
200C4—21no—
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—9081no—
206C4—9081no—
207C4—9081no—
208C4—9081no—
209C2—21no—
210C2—18161no—
211C2—18161no—
212C2#2840922011yescharacteristic
subgroupG/H
centerC2#28409220
commutator, cosocleC2×Q8×C227C23
FrattiniC2×Q8C22×D227
Fitting#356×C227C2
socleC2×C227B(4,𝔽2)
prime radical#28409207C2
hypercenter#356D227
hypocenterC227#2203
LCSG ▷ C2×Q8×C227 ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
1. #28409781C2semidirect
2. #28409217C2semidirect
3. #28409214C2semidirect
5. #28408830C2semidirect
6. #28408828C2semidirect
7. #356×C227C2semidirect
106. C227#2203semidirect
113. #356D227semidirect

Maximal subgroups

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

subgroupindex
#284097812
#284092172
#284092142
#284092072
#284088302
#284088282
#356×C2272
#2203227