Finite Group Databasebeta

← #25009348

Subgroups — #25009348

Order 11008.

664 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135751C211yesmaximal, characteristic, complemented
2#19133534C212yesmaximal, complemented
3#19132598C212yesmaximal, complemented
4#19132527C211yesmaximal, characteristic, complemented
5C43×#2679C211yesmaximal, characteristic
6#14583530C2211yescharacteristic, complemented
7#14583050—22no—
8#14582904—21no—
9#14582668C2211yescharacteristic, complemented
10#14582659—21no—
11#14582635—22no—
12#14582625C2212yescomplemented
13C2×#120×C43—22no—
14C2×#120×C43—21no—
15C43×#394—22no—
16C43×#394C2212yes—
17C43×#390—21no—
18C43×#390C2211yescharacteristic
19C2×#10621883—42no—
20C2×#10621877—21no—
21#13063324—41no—
22#13063316—41no—
23#13063304—22no—
24#13063284—21no—
25#13063246—42no—
26#13063246—41no—
27#13063246—41no—
28C22⋊(C43⋊C8)—22no—
29C25×C43—21no—
30C22×D4×C43—21no—
31C22×D4×C43—22no—
32C22×D4×C43D411yescharacteristic
33C22×D4×C43D412yes—
34#120×C43—48no—
35#120×C43—42no—
36#120×C43—42no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43C2311yescharacteristic
39C2×C22⋊C4×C43—22no—
40C2×C22⋊C4×C43—21no—
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—22no—
43C2×C22⋊C4×C43—22no—
44C2×C42×C43D411yescharacteristic
45#95×C43D412yes—
46C24×C43—22no—
47C24×C43—21no—
48C24×C43—44no—
49C24×C43—42no—
50C24×C43—82no—
51C24×C43—81no—
52C24×C43—81no—
53C2×D4×C43—24no—
54C2×D4×C43—21no—
55C2×D4×C43—44no—
56C2×D4×C43—44no—
57C2×D4×C43—44no—
58C2×D4×C43—41no—
59C2×D4×C43—41no—
60C2×D4×C43—42no—
61C2×D4×C43—81no—
62C2×D4×C43—82no—
63C2×D4×C43—81no—
64C2×D4×C43SD1612yescomplemented
65C22×C4×C43—21no—
66C22×C4×C43—22no—
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D412yes—
69C2×Dic86—22no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—81no—
72C22⋊C4×C43—44no—
73C22⋊C4×C43—42no—
74C22⋊C4×C43—44no—
75C22⋊C4×C43—44no—
76C22⋊C4×C43—42no—
77C22⋊C4×C43—42no—
78C42×C43—41no—
79C22⋊Dic43—41no—
80#10621883—84no—
81C4⋊Dic43—21no—
82C4⋊Dic43—21no—
83C4⋊Dic43—22no—
84Dic43⋊C4—42no—
85C4×Dic43—41no—
86#10621877—41no—
87#10621877—41no—
88C2×C43⋊C8—42no—
89C2×C43⋊C8—41no—
90C23×C43—24no—
91C23×C43—22no—
92C23×C43—42no—
93C23×C43—42no—
94C23×C43—42no—
95C23×C43—42no—
96C23×C43—42no—
97C23×C43—42no—
98C23×C43—41no—
99C23×C43—42no—
100C23×C43—41no—
101C23×C43—42no—
102C23×C43—88no—
103C23×C43—84no—
104C23×C43—88no—
105C23×C43—84no—
106C23×C43—84no—
107C23×C43#12011yescharacteristic
108D4×C43—42no—
109D4×C43—44no—
110D4×C43—81no—
111D4×C43—84no—
112D4×C43—82no—
113D4×C43—88no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43C2×SD1611yescharacteristic
125C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
126C2×Dic43—41no—
127C2×Dic43—41no—
128Dic86—82no—
129C43⋊C8—81no—
130C43⋊C8—82no—
131#12208—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—44no—
135C22×C43—44no—
136C22×C43—44no—
137C22×C43—42no—
138C22×C43—44no—
139C22×C43—82no—
140C22×C43—82no—
141C22×C43—82no—
142C22×C43—816no—
143C22×C43—82no—
144C22×C43—81no—
145C22×C43—81no—
146C22×C43—82no—
147C22×C43#45011yescharacteristic
148C22×C43#45511yescharacteristic
149C22×C43B(4,𝔽2)11yescharacteristic
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—42no—
153C4×C43—42no—
154C4×C43—82no—
155Dic43—81no—
156Dic43—81no—
157#2679D4311yescharacteristic
158#2027—431no—
159#1599—432no—
160#1345—432no—
161#1318—431no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43—82no—
165C2×C43—84no—
166C2×C43#160111yescharacteristic
167C2×C43#219611yescharacteristic
168C2×C43#220211yescharacteristic
169#544—431no—
170C2×#120—22no—
171C2×#120—21no—
172#450—862no—
173#418—861no—
174#394—22no—
175#394C2×D4312yes—
176#390—21no—
177#390C2×D4311yescharacteristic
178#343—431no—
179#339—861no—
180#328—862no—
181#324—432no—
182C43#1220811yescharacteristic, complemented, Sylow
183C25—21no—
184C22×D4—21no—
185C22×D4—22no—
186C22×D4C22⋊D4311yescharacteristic
187C22×D4C22⋊D4312yes—
188C2×SD16—1722no—
189C2×M16—861no—
190C4⋊Q8—1721no—
191#125—1721no—
192C22⋊Q8—862no—
193#120—48no—
194#120—42no—
195#120—42no—
196#117—861no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C22×D4311yescharacteristic
199C2×C22⋊C4—22no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C42C22⋊D4311yescharacteristic
205#102—1721no—
206#102—1721no—
207#102—1722no—
208C22⋊C8—862no—
209#95C22⋊D4312yes—
210C24—22no—
211C24—21no—
212C24—44no—
213C24—42no—
214C24—82no—
215C24—81no—
216C24—81no—
217C2×Q8—862no—
218C2×D4—24no—
219C2×D4—21no—
220C2×D4—41no—
221C2×D4—42no—
222C2×D4—41no—
223C2×D4—44no—
224C2×D4—44no—
225C2×D4—44no—
226C2×D4—81no—
227C2×D4—81no—
228C2×D4—82no—
229C2×D4#1062188312yescomplemented
230C22×C4—21no—
231C22×C4—22no—
232C22×C4C2×C22⋊D4311yescharacteristic
233C22×C4C2×C22⋊D4312yes—
234SD16—3444no—
235M16—1721no—
236M16—1721no—
237C2×C8—1722no—
238C2×C8—1721no—
239C4⋊C4—41no—
240C4⋊C4—81no—
241C4⋊C4—861no—
242C4⋊C4—861no—
243C4⋊C4—862no—
244C4⋊C4—1722no—
245C22⋊C4—44no—
246C22⋊C4—44no—
247C22⋊C4—44no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—1721no—
252C42—41no—
253C42—1721no—
254C23—24no—
255C23—22no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—41no—
263C23—42no—
264C23—42no—
265C23—41no—
266C23—88no—
267C23—84no—
268C23—88no—
269C23—84no—
270C23—84no—
271C23#1306329411yescharacteristic
272Q8—3442no—
273D4—42no—
274D4—44no—
275D4—81no—
276D4—84no—
277D4—82no—
278D4—88no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4C2×#1062188311yescharacteristic
292C2×C4#1306335111yescharacteristic
293C8—3441no—
294C8—3442no—
295C22—21no—
296C22—21no—
297C22—44no—
298C22—44no—
299C22—44no—
300C22—44no—
301C22—42no—
302C22—82no—
303C22—82no—
304C22—82no—
305C22—816no—
306C22—81no—
307C22—82no—
308C22—81no—
309C22—82no—
310C22#1458305011yescharacteristic
311C22#1458307711yescharacteristic
312C22#1458308611yescharacteristic
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—82no—
318C4—3441no—
319C4—3441no—
320C2—21no—
321C2—21no—
322C2—84no—
323C2—82no—
324C2#1913354711yescharacteristic
325C2#1913657911yescharacteristic
326C2#1913661211yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
Fitting, prime radicalC43×#2679C2
socleC22×C43B(4,𝔽2)
hypercenter#2679D43
hypocenterC43#12208
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2679

Complements

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

NH ≅ G/Ntype
1. #19135751C2semidirect
2. #19133534C2semidirect
3. #19132598C2semidirect
4. #19132527C2semidirect
6. #14583530C22semidirect
9. #14582668C22semidirect
12. #14582625C22semidirect
64. C2×D4×C43SD16semidirect
182. C43#12208semidirect
229. C2×D4#10621883semidirect

Maximal subgroups

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

subgroupindex
#191357512
#191335342
#191325982
#191325272
C43×#26792
#1220843