Finite Group Databasebeta

← #24985317

Subgroups — #24985317

Order 11008.

604 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 87 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#19140967C211yesmaximal, characteristic, complemented
2#19135826C212yesmaximal, complemented
3#19132417C212yesmaximal, complemented
4#19132416C211yesmaximal, characteristic, complemented
5C43×#2011C211yesmaximal, characteristic
6C2×#13063302—22no—
7C2×#13063246—22no—
8C2×#13063246—22no—
9#14582822—22no—
10#14582819—21no—
11#14582797C2212yes—
12#14582779—21no—
13#14582654C2212yes—
14C22×D8×C43—21no—
15C2×#127×C43C2211yescharacteristic
16C2×#102×C43—21no—
17C43×#390C2211yescharacteristic
18C43×#336C2211yescharacteristic
19C22×Dic86—21no—
20C23×Dic43—21no—
21C22×C43⋊C8—22no—
22#13063302—44no—
23#13063302—44no—
24C2×C4⋊Dic43D412yes—
25C2×C4⋊Dic43D412yes—
26C2×Dic43⋊C4—22no—
27C2×Dic43⋊C4—22no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—21no—
30#13063246—44no—
31#13063246—44no—
32C43⋊#95—21no—
33C43⋊#95—22no—
34C22×D4×C43—21no—
35C22×D4×C43—22no—
36C22×D4×C43D411yescharacteristic
37C2×D8×C43—42no—
38C2×D8×C43—42no—
39C2×D8×C43—42no—
40C22×C8×C43—21no—
41#127×C43—42no—
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C22⋊C4×C43—22no—
44C2×C42×C43C2311yescharacteristic
45#102×C43—42no—
46C24×C43—21no—
47C24×C43—41no—
48C2×D4×C43—21no—
49C2×D4×C43—22no—
50C2×D4×C43—24no—
51C2×D4×C43—42no—
52C2×D4×C43—41no—
53C2×D4×C43—41no—
54C2×D4×C43—41no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43—42no—
58C2×D4×C43—42no—
59C2×D4×C43—42no—
60C2×D4×C43—41no—
61C2×D4×C43—42no—
62C2×D4×C43—41no—
63C2×D4×C43SD1612yes—
64C22×C4×C43—21no—
65C22×C4×C43C2×D412yes—
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—22no—
68C22×Dic43—22no—
69C22×Dic43—44no—
70C22×Dic43—81no—
71C2×Dic86—44no—
72C2×Dic86—81no—
73D8×C43—48no—
74C2×C8×C43—22no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C4⋊C4×C43—41no—
78C22⋊C4×C43—42no—
79C22⋊C4×C43—42no—
80C42×C43—41no—
81C22⋊Dic43—44no—
82C22⋊Dic43—81no—
83C4⋊Dic43—22no—
84C4⋊Dic43—42no—
85C4⋊Dic43D814yescomplemented
86Dic43⋊C4—44no—
87Dic43⋊C4—42no—
88Dic43⋊C4—42no—
89C2×C43⋊C8—42no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8—42no—
92C23×C43—22no—
93C23×C43—42no—
94C23×C43—41no—
95C23×C43—42no—
96C23×C43—41no—
97C23×C43—42no—
98C23×C43—82no—
99C23×C43—81no—
100C23×C43—81no—
101C23×C43—82no—
102C23×C43#12011yescharacteristic
103D4×C43—42no—
104D4×C43—42no—
105D4×C43—42no—
106D4×C43—44no—
107D4×C43—44no—
108D4×C43—81no—
109D4×C43—81no—
110D4×C43—81no—
111D4×C43—82no—
112D4×C43—82no—
113C2×C4×C43—21no—
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—21no—
117C2×C4×C43—42no—
118C2×C4×C43—41no—
119C2×C4×C43C2×D812yes—
120C2×C4×C43C2×SD1611yescharacteristic
121C2×C4×C43AGL(1,ℤ/8)12yes—
122C2×C4×C43#13711yescharacteristic
123C2×Dic43—24no—
124C2×Dic43—42no—
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—42no—
128C2×Dic43—42no—
129C2×Dic43—84no—
130Dic86—84no—
131C8×C43—42no—
132C43⋊C8—82no—
133#7738—431nomaximal, Sylow
134C22×C43—42no—
135C22×C43—44no—
136C22×C43—82no—
137C22×C43—81no—
138C22×C43—81no—
139C22×C43—82no—
140C22×C43—84no—
141C22×C43—161no—
142C22×C43—162no—
143C22×C43—161no—
144C22×C43#44712yes—
145C22×C43#44811yescharacteristic
146C22×C43#45311yescharacteristic
147C22×C43#45412yes—
148C22×C43B(4,𝔽2)11yescharacteristic
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—22no—
152C4×C43—22no—
153C4×C43—81no—
154Dic43—44no—
155Dic43—82no—
156#2683—431no—
157#2041—432no—
158#2011D4311yescharacteristic
159#1271—432no—
160#1270—431no—
161C2×C43—82no—
162C2×C43—162no—
163C2×C43#159611yescharacteristic
164C2×C43#159812yes—
165C2×C43#161911yescharacteristic
166C2×C43#162712yes—
167C2×C43#165711yescharacteristic
168C22×D8—21no—
169C2×#127C2×D4311yescharacteristic
170C2×C22⋊Q8—862no—
171C2×#102—21no—
172C2×#102—862no—
173C2×#102—862no—
174#396—862no—
175#395—861no—
176#390C2×D4311yescharacteristic
177#389—432no—
178#386—861no—
179#336—432no—
180#336C2×D4311yescharacteristic
181C43#773811yescharacteristic, complemented, Sylow
182C22×Q8—861no—
183C22×D4—22no—
184C22×D4—21no—
185C22×D4C22⋊D4311yescharacteristic
186C23×C4—861no—
187C2×D8—42no—
188C2×D8—42no—
189C2×D8—42no—
190C22×C8—21no—
191C22×C8—862no—
192#127—42no—
193C22⋊Q8—1724no—
194C22⋊Q8—1724no—
195C2×C4⋊C4—432no—
196C2×C4⋊C4—432no—
197C2×C4⋊C4—862no—
198C2×C4⋊C4—862no—
199C2×C4⋊C4C22⋊D4311yescharacteristic
200C2×C22⋊C4—22no—
201C2×C22⋊C4—861no—
202C2×C22⋊C4—862no—
203C2×C42C22×D4311yescharacteristic
204#102—42no—
205#102—1724no—
206#102—1724no—
207#95—861no—
208#95—862no—
209C24—21no—
210C24—41no—
211C2×Q8—3441no—
212C2×Q8—1724no—
213C2×D4—24no—
214C2×D4—22no—
215C2×D4—21no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4—42no—
221C2×D4—42no—
222C2×D4—42no—
223C2×D4—41no—
224C2×D4—42no—
225C2×D4—41no—
226C2×D4—42no—
227C2×D4—41no—
228C2×D4#1062188312yes—
229C22×C4—21no—
230C22×C4—862no—
231C22×C4—862no—
232C22×C4—3441no—
233C22×C4—1724no—
234C22×C4D4×D4312yes—
235C22×C4C2×C22⋊D4311yescharacteristic
236D8—48no—
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—1722no—
241C2×C8—1722no—
242C2×C8—1722no—
243C4⋊C4—41no—
244C4⋊C4—434no—
245C4⋊C4—862no—
246C4⋊C4—1722no—
247C4⋊C4—1724no—
248C4⋊C4—1722no—
249C4⋊C4—1722no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—3441no—
253C22⋊C4—1724no—
254C42—41no—
255C23—22no—
256C23—41no—
257C23—42no—
258C23—41no—
259C23—42no—
260C23—42no—
261C23—81no—
262C23—82no—
263C23—82no—
264C23—81no—
265C23#1306329311yescharacteristic
266Q8—3444no—
267D4—42no—
268D4—42no—
269D4—42no—
270D4—44no—
271D4—44no—
272D4—81no—
273D4—81no—
274D4—81no—
275D4—82no—
276D4—82no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—864no—
284C2×C4—3444no—
285C2×C4—1722no—
286C2×C4—1722no—
287C2×C4—1722no—
288C2×C4—1722no—
289C2×C4—1722no—
290C2×C4D8×D4312yes—
291C2×C4C2×#1062188311yescharacteristic
292C2×C4#1306334912yes—
293C2×C4#1306335511yescharacteristic
294C8—42no—
295C8—3442no—
296C22—44no—
297C22—42no—
298C22—82no—
299C22—81no—
300C22—81no—
301C22—82no—
302C22—84no—
303C22—162no—
304C22—161no—
305C22—161no—
306C22#1458303112yes—
307C22#1458303711yescharacteristic
308C22#1458306611yescharacteristic
309C22#1458307012yes—
310C22#1458308511yescharacteristic
311C4—21no—
312C4—21no—
313C4—22no—
314C4—22no—
315C4—81no—
316C4—3442no—
317C4—1724no—
318C2—82no—
319C2—162no—
320C2#1913351711yescharacteristic
321C2#1913352812yes—
322C2#1913364711yescharacteristic
323C2#1913369712yes—
324C2#1913389111yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2011C2
socleC23×C43#120
hypercenter#2011D43
hypocenterC43#7738
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2011

Complements

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

NH ≅ G/Ntype
1. #19140967C2semidirect
2. #19135826C2semidirect
3. #19132417C2semidirect
4. #19132416C2semidirect
85. C4⋊Dic43D8semidirect
181. C43#7738semidirect

Maximal subgroups

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

subgroupindex
#191409672
#191358262
#191324172
#191324162
C43×#20112
#773843