Finite Group Databasebeta

← #37574527

Subgroups — #37574527

Order 24448.

260 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 45 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#27132852C211yesmaximal, characteristic, complemented
2#27132849C211yesmaximal, characteristic, complemented
3#27132830C211yesmaximal, characteristic, complemented
4#27132456C211yesmaximal, characteristic, complemented
5#27132453C211yesmaximal, characteristic, complemented
6#27132450C211yesmaximal, characteristic, complemented
7#560×C191C211yesmaximal, characteristic, complemented
8#20259367C2211yescharacteristic
9#20259348—21no—
10#20259305—21no—
11#20259291—21no—
12#20259250—21no—
13#20259239C2211yescharacteristic
14#20259237C2211yescharacteristic
15#20259237C2211yescharacteristic
16#20259236—21no—
17#20259236—21no—
18#127×C191C2211yescharacteristic
19#126×C191—21no—
20#123×C191—21no—
21#123×C191C2211yescharacteristic
22#121×C191—21no—
23#121×C191—21no—
24#121×C191—21no—
25#120×C191—21no—
26#120×C191C2211yescharacteristic
27#15690287—21no—
28#15690286—41no—
29C2×C22⋊D191—21no—
30C2×C22⋊D191—21no—
31C2×C22⋊D191—41no—
32D4×D191—41no—
33#15690275—41no—
34#15690272—41no—
35#15690271—21no—
36Dic191⋊C4—41no—
37C22⋊Dic191—21no—
38C22⋊Dic191—21no—
39C22⋊Dic191—41no—
40(C2×D191)⋊C4—41no—
41C24×C191D411yescharacteristic
42C2×D4×C191—21no—
43C2×D4×C191—21no—
44C2×D4×C191—21no—
45C2×D4×C191—21no—
46C2×D4×C191—21no—
47C2×D4×C191D411yescharacteristic, complemented
48C2×D4×C191C2311yescharacteristic
49C22×C4×C191—21no—
50C22×C4×C191D411yescharacteristic, complemented
51C4⋊C4×C191—21no—
52C4⋊C4×C191—21no—
53C4⋊C4×C191—21no—
54C22⋊C4×C191—21no—
55C22⋊C4×C191—21no—
56C22⋊C4×C191—21no—
57C22⋊C4×C191—21no—
58C22⋊C4×C191—21no—
59C22⋊C4×C191D411yescharacteristic
60C22⋊C4×C191D411yescharacteristic, complemented
61C42×C191D411yescharacteristic, complemented
62C22×D191—21no—
63C22×D191—21no—
64Dic382—21no—
65D764—21no—
66C22⋊D191—41no—
67C22⋊D191—41no—
68C22⋊D191—41no—
69C22⋊D191—82no—
70C2×Dic191—21no—
71C2×Dic191—21no—
72C2×Dic191—41no—
73C2×Dic191—41no—
74C4×D191—41no—
75C191⋊C8—41no—
76C23×C191—21no—
77C23×C191—21no—
78C23×C191—41no—
79C23×C191—81no—
80C23×C191C2×D411yescharacteristic
81C23×C191C2×D411yescharacteristic
82D4×C191—41no—
83D4×C191—41no—
84D4×C191—81no—
85D4×C191—81no—
86D4×C191—81no—
87D4×C191—81no—
88D4×C191—81no—
89C2×C4×C191—21no—
90C2×C4×C191—21no—
91C2×C4×C191—21no—
92C2×C4×C191—21no—
93C2×C4×C191—41no—
94C2×C4×C191—81no—
95C2×C4×C191C2×D411yescharacteristic
96C22×C191—21no—
97C22×C191—21no—
98C22×C191—41no—
99C22×C191—41no—
100C22×C191—41no—
101C22×C191—41no—
102C22×C191—41no—
103C22×C191—41no—
104C22×C191—42no—
105C22×C191—41no—
106C22×C191—41no—
107C22×C191—81no—
108C22×C191#12011yescharacteristic
109C2×D191—41no—
110C2×D191—81no—
111C2×D191—81no—
112C4×C191—21no—
113C4×C191—41no—
114C4×C191—41no—
115C4×C191—41no—
116C4×C191—41no—
117Dic191—41no—
118Dic191—81no—
119Dic191—81no—
120C2×C191—21no—
121C2×C191—41no—
122C2×C191—41no—
123C2×C191—81no—
124C2×C191—81no—
125C2×C191B(4,𝔽2)11yescharacteristic
126D191—81no—
127C191#220011yescharacteristic, complemented, Sylow
128#2200—1911nomaximal, Sylow
129#560D19111yescharacteristic, complemented
130#458—1911no—
131B(4,𝔽2)—1911no—
132#453—1911no—
133#353—1911no—
134#352—1911no—
135AΣL(1,𝔽16)—1911no—
136H(5,𝔽2)—1911no—
137AGL(1,ℤ/8)—3821no—
138#127C2×D19111yescharacteristic
139#126—21no—
140#123—21no—
141#123—3821no—
142#123C2×D19111yescharacteristic
143#121—21no—
144#121—21no—
145#121—21no—
146#120—21no—
147#120—3821no—
148#120C2×D19111yescharacteristic
149#104—3821no—
150#100—1911no—
151#99—3821no—
152#99—3821no—
153#99—1911no—
154#99—1911no—
155C24C22⋊D19111yescharacteristic
156#41—3821no—
157#41—7641no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—3821no—
164C2×D4—3821no—
165C2×D4—7641no—
166C2×D4—7641no—
167C2×D4C22⋊D19111yescharacteristic, complemented
168C2×D4C22×D19111yescharacteristic
169C22×C4—21no—
170C22×C4C22⋊D19111yescharacteristic, complemented
171SD16—7641no—
172D8—7641no—
173M16—3821no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—7641no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—21no—
181C22⋊C4—21no—
182C22⋊C4—21no—
183C22⋊C4—3821no—
184C22⋊C4—3821no—
185C22⋊C4—7641no—
186C22⋊C4—7641no—
187C22⋊C4C22⋊D19111yescharacteristic
188C22⋊C4C22⋊D19111yescharacteristic, complemented
189C42C22⋊D19111yescharacteristic, complemented
190C23—21no—
191C23—21no—
192C23—41no—
193C23—81no—
194C23—3821no—
195C23—3821no—
196C23C2×C22⋊D19111yescharacteristic
197C23C2×C22⋊D19111yescharacteristic
198Q8—3821no—
199D4—41no—
200D4—41no—
201D4—81no—
202D4—81no—
203D4—81no—
204D4—81no—
205D4—81no—
206D4—3821no—
207D4—15282no—
208D4—7641no—
209D4—7641no—
210D4—7641no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—81no—
217C2×C4—3821no—
218C2×C4—3821no—
219C2×C4—7641no—
220C2×C4—7641no—
221C2×C4—7641no—
222C2×C4C2×C22⋊D19111yescharacteristic
223C8—7641no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22—81no—
236C22—15281no—
237C22—15281no—
238C22—7641no—
239C22#2025929111yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—15281no—
246C4—15281no—
247C4—7641no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—15281no—
254C2#2713285011yescharacteristic
subgroupG/H
centerC2#27132850
commutator, cosocleC2×D4×C191C23
FrattiniC2×D4C22×D191
Fitting#560×C191C2
socleC2×C191B(4,𝔽2)
hypercenter#560D191
hypocenterC191#2200
LCSG ▷ C2×D4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #560

Complements

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

NH ≅ G/Ntype
1. #27132852C2semidirect
2. #27132849C2semidirect
3. #27132830C2semidirect
4. #27132456C2semidirect
5. #27132453C2semidirect
6. #27132450C2semidirect
7. #560×C191C2semidirect
47. C2×D4×C191D4semidirect
50. C22×C4×C191D4semidirect
60. C22⋊C4×C191D4semidirect
61. C42×C191D4semidirect
127. C191#2200semidirect
129. #560D191semidirect
167. C2×D4C22⋊D191semidirect
170. C22×C4C22⋊D191semidirect
188. C22⋊C4C22⋊D191semidirect
189. C42C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
#271328522
#271328492
#271328302
#271324562
#271324532
#271324502
#560×C1912
#2200191