Finite Group Databasebeta

← #44401745

Subgroups — #44401745

Order 29056.

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

normal subgroups only

This group has 226 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#28409785C211yesmaximal, characteristic, complemented
2#28409222C211yesmaximal, characteristic
3#28409210C211yesmaximal, characteristic
4#28408826C211yesmaximal, characteristic, complemented
5#28408822C211yesmaximal, characteristic, complemented
6#28408821C211yesmaximal, characteristic, complemented
7#458×C227C211yesmaximal, characteristic
8#20300318—21no—
9#20300287—21no—
10#20300281—21no—
11#20300281—21no—
12#20300278—21no—
13#20300275C2211yescharacteristic
14#20300269—21no—
15#20300269C2211yescharacteristic
16#20300267—21no—
17#20300265—21no—
18#20300215—21no—
19#20300205C2211yescharacteristic
20#20300203—21no—
21#20300203C2211yescharacteristic
22H(5,𝔽2)×C227C2211yescharacteristic
23#123×C227—21no—
24#123×C227C2211yescharacteristic
25#99×C227—21no—
26#99×C227C2211yescharacteristic
27C2×Dic454—21no—
28C2×Dic454D411yescharacteristic
29C22×Dic227D411yescharacteristic
30#16813874—41no—
31#16813872—41no—
32#16813868—21no—
33C4⋊Dic227—21no—
34C4⋊Dic227—21no—
35Dic227⋊C4—21no—
36Dic227⋊C4—21no—
37Dic227⋊C4—21no—
38Dic227⋊C4—21no—
39Dic227⋊C4—21no—
40Dic227⋊C4—41no—
41C22⋊Dic227—21no—
42C22⋊Dic227—21no—
43C22⋊Dic227—21no—
44C22⋊Dic227—21no—
45C22⋊Dic227—41no—
46C22⋊Dic227D411yescharacteristic
47C4×Dic227—21no—
48C4×Dic227D411yescharacteristic
49#41×C227—21no—
50#41×C227—41no—
51C2×D4×C227—21no—
52C2×D4×C227—21no—
53C2×D4×C227—41no—
54C2×D4×C227C2311yescharacteristic
55C22×C4×C227D411yescharacteristic
56C4⋊C4×C227—21no—
57C4⋊C4×C227—41no—
58C22⋊C4×C227—21no—
59C22⋊C4×C227—21no—
60C22⋊C4×C227—41no—
61C22⋊C4×C227D411yescharacteristic
62Dic454—41no—
63Dic454—81no—
64C2×Dic227—21no—
65C2×Dic227—21no—
66C2×Dic227—21no—
67C2×Dic227—21no—
68C2×Dic227—41no—
69C2×Dic227—41no—
70C227⋊C8—41no—
71C23×C227—21no—
72C23×C227—21no—
73C23×C227C2×D411yescharacteristic
74C23×C227C2×D411yescharacteristic
75Q8×C227—21no—
76D4×C227—21no—
77D4×C227—41no—
78D4×C227—41no—
79D4×C227—41no—
80D4×C227—41no—
81C2×C4×C227—21no—
82C2×C4×C227—21no—
83C2×C4×C227—21no—
84C2×C4×C227—21no—
85C2×C4×C227—41no—
86C2×C4×C227—41no—
87C2×C4×C227—41no—
88C2×C4×C227C2×D411yescharacteristic
89C22×C227—21no—
90C22×C227—21no—
91C22×C227—41no—
92C22×C227—41no—
93C22×C227—41no—
94C22×C227—81no—
95C22×C227—81no—
96C22×C227#12011yescharacteristic
97C4×C227—21no—
98C4×C227—41no—
99C4×C227—41no—
100C4×C227—41no—
101C4×C227—81no—
102Dic227—41no—
103Dic227—41no—
104Dic227—41no—
105Dic227—41no—
106Dic227—81no—
107C2×C227—21no—
108C2×C227—41no—
109C2×C227—41no—
110C2×C227—81no—
111C2×C227B(4,𝔽2)11yescharacteristic
112C227#220111yescharacteristic, complemented, Sylow
113#2201—2271nomaximal, Sylow
114#563—2271no—
115#458—2271no—
116#458D22711yescharacteristic
117#455—2271no—
118#354—2271no—
119#352—2271no—
120#352—2271no—
121H(5,𝔽2)C2×D22711yescharacteristic
122#137—4541no—
123C4⋊Q8—4541no—
124#126—4541no—
125#126—4541no—
126#125—4541no—
127#124—2271no—
128#123—21no—
129#123—4541no—
130#123—2271no—
131#123C2×D22711yescharacteristic
132C22⋊Q8—4541no—
133C22⋊Q8—4541no—
134#104—4541no—
135#100—2271no—
136#99—21no—
137#99—4541no—
138#99—2271no—
139#99C2×D22711yescharacteristic
140#41—21no—
141#41—41no—
142C2×Q8—4541no—
143C2×Q8—2271no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—41no—
147C2×D4C22×D22711yescharacteristic
148C22×C4—2271no—
149C22×C4C22⋊D22711yescharacteristic
150Q16—9081no—
151SD16—9081no—
152M16—4541no—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—9081no—
156C4⋊C4—4541no—
157C4⋊C4—4541no—
158C4⋊C4—4541no—
159C4⋊C4—4541no—
160C4⋊C4—4541no—
161C4⋊C4—4541no—
162C4⋊C4—4541no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—41no—
166C22⋊C4—9081no—
167C22⋊C4—4541no—
168C22⋊C4—4541no—
169C22⋊C4—4541no—
170C22⋊C4—4541no—
171C22⋊C4—2271no—
172C22⋊C4C22⋊D22711yescharacteristic
173C42—4541no—
174C42—2271no—
175C23—21no—
176C23—21no—
177C23D4×D22711yescharacteristic
178C23C2×C22⋊D22711yescharacteristic
179Q8—21no—
180Q8—18161no—
181Q8—9081no—
182D4—21no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—9081no—
195C2×C4—9081no—
196C2×C4—4541no—
197C2×C4—4541no—
198C2×C4—4541no—
199C2×C4—4541no—
200C2×C4D4×D22711yescharacteristic
201C8—9081no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—81no—
209C22#2030025611yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—81no—
215C4—18161no—
216C4—9081no—
217C4—9081no—
218C4—9081no—
219C4—9081no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—81no—
224C2#2840921811yescharacteristic
subgroupG/H
centerC2#28409218
commutator, cosocleC2×D4×C227C23
FrattiniC2×D4C22×D227
Fitting#458×C227C2
socleC2×C227B(4,𝔽2)
prime radicalH(5,𝔽2)×C227C22
hypercenter#458D227
hypocenterC227#2201
LCSG ▷ C2×D4×C227 ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #28409785C2semidirect
4. #28408826C2semidirect
5. #28408822C2semidirect
6. #28408821C2semidirect
112. C227#2201semidirect

Maximal subgroups

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

subgroupindex
#284097852
#284092222
#284092102
#284088262
#284088222
#284088212
#458×C2272
#2201227