Finite Group Databasebeta

← #24985620

Subgroups — #24985620

Order 11008.

682 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 95 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#19136123C211yesmaximal, characteristic, complemented
2#19135998C212yesmaximal, complemented
3#19132416C212yesmaximal, complemented
4#19132416C211yesmaximal, characteristic, complemented
5C43×#2679C211yesmaximal, characteristic
6C2×#13063258—21no—
7C2×#13063246—21no—
8C2×#13063246—22no—
9#14582769C2211yescharacteristic, complemented
10#14582661—22no—
11#14582654C2211yescharacteristic, complemented
12#14582654C2212yescomplemented
13C2×#120×C43—22no—
14C2×#120×C43—21no—
15C43×#394—22no—
16C43×#394—21no—
17C43×#390C2211yescharacteristic
18C43×#390C2212yes—
19C22×C43⋊C8—21no—
20C22×C43⋊C8—22no—
21C2×C4⋊Dic43—22no—
22C2×C4⋊Dic43—21no—
23#13063258—42no—
24#13063246—42no—
25#13063246—44no—
26C25×C43—21no—
27C22×D4×C43—21no—
28C22×D4×C43—22no—
29C22×D4×C43D412yes—
30C22×D4×C43D411yescharacteristic
31#120×C43—44no—
32#120×C43—42no—
33#120×C43—44no—
34#120×C43—42no—
35C2×C4⋊C4×C43D412yes—
36C2×C4⋊C4×C43D411yescharacteristic
37C2×C22⋊C4×C43—22no—
38C2×C22⋊C4×C43—21no—
39C2×C22⋊C4×C43—22no—
40C2×C22⋊C4×C43—22no—
41C2×C22⋊C4×C43—22no—
42C2×C42×C43C2311yescharacteristic
43#95×C43—21no—
44C24×C43—22no—
45C24×C43—21no—
46C24×C43—44no—
47C24×C43—42no—
48C24×C43—81no—
49C24×C43—82no—
50C24×C43—81no—
51C2×D4×C43—22no—
52C2×D4×C43—21no—
53C2×D4×C43—44no—
54C2×D4×C43—44no—
55C2×D4×C43—44no—
56C2×D4×C43—42no—
57C2×D4×C43—42no—
58C2×D4×C43—41no—
59C2×D4×C43—41no—
60C2×D4×C43—81no—
61C2×D4×C43—82no—
62C2×D4×C43D814yes—
63C2×D4×C43SD1612yes—
64C22×C4×C43—21no—
65C22×C4×C43—22no—
66C22×C4×C43C2×D412yes—
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—41no—
69C4⋊C4×C43—42no—
70C4⋊C4×C43—41no—
71C22⋊C4×C43—44no—
72C22⋊C4×C43—42no—
73C22⋊C4×C43—42no—
74C22⋊C4×C43—42no—
75C22⋊C4×C43—42no—
76C22⋊C4×C43—42no—
77C22⋊C4×C43—42no—
78C22⋊C4×C43—42no—
79C42×C43—41no—
80C4⋊Dic43—41no—
81C4⋊Dic43—41no—
82C4⋊Dic43—42no—
83C4⋊Dic43—42no—
84C2×C43⋊C8—22no—
85C2×C43⋊C8—41no—
86C2×C43⋊C8—41no—
87C2×C43⋊C8—42no—
88C2×C43⋊C8—42no—
89C2×C43⋊C8—42no—
90C23×C43—24no—
91C23×C43—22no—
92C23×C43—42no—
93C23×C43—42no—
94C23×C43—42no—
95C23×C43—41no—
96C23×C43—42no—
97C23×C43—42no—
98C23×C43—42no—
99C23×C43—42no—
100C23×C43—42no—
101C23×C43—41no—
102C23×C43—84no—
103C23×C43—88no—
104C23×C43—88no—
105C23×C43—84no—
106C23×C43—84no—
107C23×C43#12011yescharacteristic
108D4×C43—44no—
109D4×C43—42no—
110D4×C43—82no—
111D4×C43—81no—
112D4×C43—84no—
113D4×C43—88no—
114C2×C4×C43—21no—
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—21no—
118C2×C4×C43—42no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43C2×D812yes—
124C2×C4×C43C2×SD1611yescharacteristic
125C2×C4×C43AGL(1,ℤ/8)12yes—
126C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
127C2×Dic43—82no—
128C2×Dic43—81no—
129C43⋊C8—42no—
130C43⋊C8—82no—
131#7786—431nomaximal, Sylow
132C22×C43—44no—
133C22×C43—42no—
134C22×C43—44no—
135C22×C43—44no—
136C22×C43—44no—
137C22×C43—816no—
138C22×C43—82no—
139C22×C43—82no—
140C22×C43—82no—
141C22×C43—81no—
142C22×C43—82no—
143C22×C43—81no—
144C22×C43—82no—
145C22×C43#44712yes—
146C22×C43#45011yescharacteristic
147C22×C43#45311yescharacteristic
148C22×C43#45512yes—
149C22×C43#45811yescharacteristic
150C4×C43—22no—
151C4×C43—22no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—81no—
155C4×C43—82no—
156Dic43—161no—
157#2679D4311yescharacteristic
158#2093—431no—
159#2071—432no—
160#1270—431no—
161#1270—432no—
162C2×C43—84no—
163C2×C43—82no—
164C2×C43#160712yes—
165C2×C43#161311yescharacteristic
166C2×C43#161911yescharacteristic
167C2×C43#163912yes—
168C2×C43#165911yescharacteristic
169C2×#120—22no—
170C2×#120—21no—
171C2×#107—861no—
172C2×#102—862no—
173C2×#102—861no—
174#394—22no—
175#394—21no—
176#390C2×D4312yes—
177#390C2×D4311yescharacteristic
178#384—431no—
179#340—862no—
180#336—432no—
181#336—431no—
182C43#778611yescharacteristic, complemented, Sylow
183C25—21no—
184C22×D4—22no—
185C22×D4—21no—
186C22×D4C22⋊D4312yes—
187C22×D4C22⋊D4311yescharacteristic
188C22×C8—861no—
189C22×C8—862no—
190#120—42no—
191#120—44no—
192#120—44no—
193#120—42no—
194C2×C4⋊C4—862no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4C22⋊D4312yes—
197C2×C4⋊C4C22⋊D4311yescharacteristic
198C2×C22⋊C4—21no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C42C22×D4311yescharacteristic
204#107—1722no—
205#102—1722no—
206#102—1724no—
207#95—21no—
208C24—21no—
209C24—22no—
210C24—42no—
211C24—44no—
212C24—81no—
213C24—82no—
214C24—81no—
215C2×D4—21no—
216C2×D4—22no—
217C2×D4—41no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—41no—
221C2×D4—44no—
222C2×D4—44no—
223C2×D4—44no—
224C2×D4—81no—
225C2×D4—82no—
226C2×D4#1062188214yes—
227C2×D4#1062188312yes—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—1721no—
231C22×C4C2×C22⋊D4312yes—
232C22×C4C2×C22⋊D4311yescharacteristic
233C2×C8—862no—
234C2×C8—1722no—
235C2×C8—1722no—
236C2×C8—1722no—
237C2×C8—1721no—
238C2×C8—1721no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—1721no—
242C4⋊C4—1721no—
243C4⋊C4—1722no—
244C4⋊C4—1722no—
245C22⋊C4—42no—
246C22⋊C4—44no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C42—41no—
254C23—22no—
255C23—24no—
256C23—42no—
257C23—41no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—41no—
264C23—42no—
265C23—42no—
266C23—88no—
267C23—84no—
268C23—88no—
269C23—84no—
270C23—84no—
271C23#1306329411yescharacteristic
272D4—44no—
273D4—42no—
274D4—82no—
275D4—81no—
276D4—88no—
277D4—84no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—3441no—
288C2×C4—3442no—
289C2×C4C2×#1062188212yes—
290C2×C4C2×#1062188311yescharacteristic
291C2×C4#1306335111yescharacteristic
292C2×C4#1306335112yes—
293C8—3442no—
294C8—1722no—
295C22—44no—
296C22—44no—
297C22—44no—
298C22—42no—
299C22—44no—
300C22—816no—
301C22—82no—
302C22—82no—
303C22—82no—
304C22—82no—
305C22—81no—
306C22—82no—
307C22—81no—
308C22#1458303312yes—
309C22#1458305011yescharacteristic
310C22#1458306711yescharacteristic
311C22#1458307712yes—
312C22#1458308911yescharacteristic
313C4—22no—
314C4—22no—
315C4—21no—
316C4—21no—
317C4—82no—
318C4—81no—
319C4—6881no—
320C2—82no—
321C2—84no—
322C2#1913358112yes—
323C2#1913361511yescharacteristic
324C2#1913364911yescharacteristic
325C2#1913377412yes—
326C2#1913390111yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2679C2
socleC23×C43#120
hypercenter#2679D43
hypocenterC43#7786
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2679

Complements

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

NH ≅ G/Ntype
1. #19136123C2semidirect
2. #19135998C2semidirect
3. #19132416C2semidirect
4. #19132416C2semidirect
9. #14582769C22semidirect
11. #14582654C22semidirect
12. #14582654C22semidirect
182. C43#7786semidirect

Maximal subgroups

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

subgroupindex
#191361232
#191359982
#191324162
C43×#26792
#778643