Finite Group Databasebeta

← #15675396

Subgroups — #15675396

Order 2944.

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

normal subgroups only

This group has 270 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#13093160C211yesmaximal, characteristic, complemented
2#13092604C211yesmaximal, characteristic, complemented
3#13092595C211yesmaximal, characteristic, complemented
4#13092211C211yesmaximal, characteristic, complemented
5#13092204C211yesmaximal, characteristic, complemented
6#13092203C211yesmaximal, characteristic, complemented
7C23×B(4,𝔽2)C211yesmaximal, characteristic, complemented
8C23×H(5,𝔽2)C2211yescharacteristic
9C23×#120—21no—
10C23×#120C2211yescharacteristic
11#10625124—21no—
12#10625122—21no—
13#10625108—21no—
14#10625108—21no—
15#10625108C2211yescharacteristic
16#10625107—21no—
17#10625107C2211yescharacteristic
18#10625056—21no—
19#10625056—21no—
20#10625056—21no—
21C23×#99—21no—
22C23×#99C2211yescharacteristic
23#10625019—21no—
24#10625016—21no—
25#10625016C2211yescharacteristic
26#10625015C2211yescharacteristic
27C24×C23D411yescharacteristic, complemented
28C23×D23D411yescharacteristic, complemented
29#41×C23—21no—
30#41×C23—41no—
31C2×D4×C23—21no—
32C2×D4×C23—21no—
33C2×D4×C23—21no—
34C2×D4×C23—41no—
35C2×D4×C23—41no—
36C2×D4×C23C2311yescharacteristic
37C2×C22⋊D23—21no—
38C2×C22⋊D23—21no—
39C2×C22⋊D23—21no—
40C2×C22⋊D23—41no—
41C2×Dic46—21no—
42C2×Dic46D411yescharacteristic, complemented
43C22⋊C4×C23—21no—
44C22⋊C4×C23—21no—
45C22⋊C4×C23—41no—
46C22⋊C4×C23D411yescharacteristic, complemented
47C22⋊Dic23—21no—
48C22⋊Dic23—21no—
49C22⋊Dic23—21no—
50C22⋊Dic23—21no—
51C22⋊Dic23—21no—
52C22⋊Dic23D411yescharacteristic, complemented
53#67275—41no—
54#67273—41no—
55(C2×D23)⋊C4—21no—
56(C2×D23)⋊C4—21no—
57(C2×D23)⋊C4—21no—
58(C2×D23)⋊C4—41no—
59C4×Dic23—21no—
60C4×Dic23D411yescharacteristic, complemented
61#67267—21no—
62C23×C23—21no—
63C23×C23—21no—
64C23×C23—21no—
65C23×C23—41no—
66C23×C23—81no—
67C23×C23C2×D411yescharacteristic
68C23×C23C2×D411yescharacteristic
69C22×D23—21no—
70C22×D23—41no—
71C22×D23—81no—
72Q8×C23—21no—
73D4×C23—21no—
74D4×C23—41no—
75D4×C23—41no—
76D4×C23—41no—
77D4×C23—41no—
78D4×C23—81no—
79D4×C23—82no—
80C2×C4×C23—21no—
81C2×C4×C23—21no—
82C2×C4×C23—21no—
83C2×C4×C23—41no—
84C2×C4×C23—41no—
85C2×C4×C23C2×D411yescharacteristic
86C22⋊D23—81no—
87C22⋊D23—81no—
88C22⋊D23—81no—
89C22⋊D23—82no—
90C2×Dic23—21no—
91C2×Dic23—21no—
92C2×Dic23—21no—
93C2×Dic23—41no—
94Dic46—41no—
95Dic46—81no—
96C23⋊C8—41no—
97#2199—231nomaximal, Sylow
98C22×C23—21no—
99C22×C23—21no—
100C22×C23—41no—
101C22×C23—41no—
102C22×C23—41no—
103C22×C23—41no—
104C22×C23—42no—
105C22×C23—41no—
106C22×C23—41no—
107C22×C23—81no—
108C22×C23—81no—
109C22×C23—81no—
110C22×C23#12011yescharacteristic
111C2×D23—41no—
112C2×D23—41no—
113C2×D23—42no—
114C2×D23—41no—
115C2×D23—81no—
116C4×C23—21no—
117C4×C23—41no—
118C4×C23—41no—
119C4×C23—81no—
120Dic23—41no—
121Dic23—41no—
122Dic23—41no—
123Dic23—81no—
124H(3,𝔽4)—231no—
125B(4,𝔽2)—231no—
126B(4,𝔽2)D2311yescharacteristic, complemented
127#455—231no—
128#354—231no—
129AΣL(1,𝔽16)—231no—
130AΣL(1,𝔽16)—231no—
131C2×C23—21no—
132C2×C23—41no—
133C2×C23—41no—
134C2×C23—81no—
135C2×C23—81no—
136C2×C23B(4,𝔽2)11yescharacteristic
137D23—81no—
138H(5,𝔽2)C2×D2311yescharacteristic
139#137—461no—
140#124—231no—
141#124—461no—
142#124—461no—
143#124—461no—
144#124—461no—
145#120—21no—
146#120—231no—
147#120—461no—
148#120—461no—
149#120—461no—
150#120C2×D2311yescharacteristic
151#104—461no—
152#100—231no—
153#99—21no—
154#99—231no—
155#99—461no—
156#99C2×D2311yescharacteristic
157C23#219911yescharacteristic, complemented, Sylow
158C24—231no—
159C24C22⋊D2311yescharacteristic, complemented
160#41—21no—
161#41—41no—
162C2×Q8—231no—
163C2×Q8—461no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4—461no—
170C2×D4—461no—
171C2×D4—461no—
172C2×D4—921no—
173C2×D4C22×D2311yescharacteristic
174Q16—921no—
175SD16—921no—
176M16—461no—
177C22⋊C4—21no—
178C22⋊C4—21no—
179C22⋊C4—41no—
180C22⋊C4—231no—
181C22⋊C4—461no—
182C22⋊C4—461no—
183C22⋊C4—461no—
184C22⋊C4—461no—
185C22⋊C4—461no—
186C22⋊C4—461no—
187C22⋊C4—461no—
188C22⋊C4—461no—
189C22⋊C4—921no—
190C22⋊C4C22⋊D2311yescharacteristic, complemented
191C42—231no—
192C42—461no—
193C23—21no—
194C23—21no—
195C23—21no—
196C23—41no—
197C23—81no—
198C23—461no—
199C23—921no—
200C23—1841no—
201C23D4×D2311yescharacteristic
202C23C2×C22⋊D2311yescharacteristic
203Q8—21no—
204Q8—921no—
205Q8—1841no—
206D4—21no—
207D4—41no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—81no—
212D4—82no—
213D4—1841no—
214D4—1841no—
215D4—1841no—
216D4—1842no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—461no—
223C2×C4—461no—
224C2×C4—461no—
225C2×C4—921no—
226C2×C4D4×D2311yescharacteristic
227C8—921no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—42no—
235C22—41no—
236C22—41no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—921no—
241C22—921no—
242C22—922no—
243C22—921no—
244C22—1841no—
245C22#1062510811yescharacteristic
246C4—21no—
247C4—41no—
248C4—41no—
249C4—81no—
250C4—921no—
251C4—921no—
252C4—921no—
253C4—1841no—
254C2—21no—
255C2—41no—
256C2—41no—
257C2—81no—
258C2—81no—
259C2—1841no—
260C2#1309260311yescharacteristic
subgroupG/H
centerC2#13092603
commutator, cosocleC2×D4×C23C23
FrattiniC2×D4C22×D23
FittingC23×B(4,𝔽2)C2
socleC2×C23B(4,𝔽2)
hypercenterB(4,𝔽2)D23
hypocenterC23#2199
LCSG ▷ C2×D4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ B(4,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #13093160C2semidirect
2. #13092604C2semidirect
3. #13092595C2semidirect
4. #13092211C2semidirect
5. #13092204C2semidirect
6. #13092203C2semidirect
7. C23×B(4,𝔽2)C2semidirect
27. C24×C23D4semidirect
28. C23×D23D4semidirect
42. C2×Dic46D4semidirect
46. C22⋊C4×C23D4semidirect
52. C22⋊Dic23D4semidirect
60. C4×Dic23D4semidirect
126. B(4,𝔽2)D23semidirect
157. C23#2199semidirect
159. C24C22⋊D23semidirect
190. C22⋊C4C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130931602
#130926042
#130925952
#130922112
#130922042
#130922032
C23×B(4,𝔽2)2
#219923