Finite Group Databasebeta

← #25071505

Subgroups — #25071505

Order 11008.

870 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 191 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#19148405C211yesmaximal, characteristic
2#19145748C212yesmaximal
3#19139807C211yesmaximal, characteristic
4#19133639C218yesmaximal
5#19133095C212yesmaximal
6C43×#1461C211yesmaximal, characteristic
7Q8×Dic86—22no—
8#14583628—22no—
9#14583625—24no—
10#14583530—21no—
11#14583530C2214yes—
12#14583456—22no—
13#14583456C2212yes—
14C2×#13063325C2211yescharacteristic
15#14583377—21no—
16#14583304—22no—
17#14583250—22no—
18#14583235C2218yes—
19#14583195—24no—
20#14582838C2214yes—
21#14582806—21no—
22#14582805—22no—
23#14582764—21no—
24C4×C4⋊Dic43C2211yescharacteristic
25#14582637C2218yes—
26C2×C4×Q8×C43C2211yescharacteristic
27C43×#431C2212yes—
28C43×#324C2214yes—
29C22×Dic86—21no—
30#13063325—22no—
31#13063325—22no—
32#13063325—22no—
33#13063325—22no—
34#13063325D412yes—
35#13063325D412yes—
36#13063324—24no—
37#13063324—28no—
38#13063317—24no—
39#13063317—22no—
40#13063316—24no—
41#13063316—28no—
42#13063304—22no—
43#13063304—24no—
44#13063304C2314yes—
45Q8×Dic43—24no—
46Q8×Dic43—24no—
47C4×Dic86—24no—
48C4×Dic86—24no—
49C4×Dic86—22no—
50C4×Dic86D414yes—
51#13063284—24no—
52#13063284—22no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43C2312yes—
56C2×C4×Dic43—21no—
57#13063259—28no—
58#13063250—28no—
59C43⋊#95—24no—
60C43⋊#95—24no—
61C43⋊#95C2312yes—
62C22×Q8×C43D411yescharacteristic
63C4×Q8×C43—22no—
64C4×Q8×C43—22no—
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C4⋊C4×C43C2312yes—
67C2×C42×C43D412yes—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—22no—
70C22⋊C8×C43C2314yes—
71C4×C8×C43—22no—
72C2×Q8×C43—22no—
73C2×Q8×C43—22no—
74C2×Q8×C43Q1614yes—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D412yes—
77C22×C4×C43C2×D412yes—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2411yescharacteristic
80C22×Dic43—22no—
81C22×Dic43—22no—
82C2×Dic86—22no—
83C2×Dic86—24no—
84C2×Dic86—44no—
85C2×Dic86—41no—
86C2×Dic86—41no—
87C2×Dic86C2×D414yes—
88C2×C8×C43—24no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—24no—
91C42×C43—22no—
92C42×C43—22no—
93C42×C43C2×D412yes—
94C42×C43C2×D412yes—
95C22⋊Dic43—24no—
96C4⋊Dic43—24no—
97C4⋊Dic43—24no—
98C4⋊Dic43—24no—
99C4⋊Dic43—22no—
100C4⋊Dic43—22no—
101C4⋊Dic43—22no—
102C4⋊Dic43—24no—
103C4⋊Dic43—42no—
104C4⋊Dic43—42no—
105C4⋊Dic43C2×D414yes—
106Dic43⋊C4—28no—
107Dic43⋊C4—24no—
108Dic43⋊C4—24no—
109C4×Dic43—28no—
110C4×Dic43—24no—
111C4×Dic43—42no—
112C23×C43C22×D411yescharacteristic
113Q8×C43—28no—
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—41no—
119C2×C4×C43—42no—
120C2×C4×C43#12011yescharacteristic
121C2×C4×C43#12012yes—
122C2×C4×C43#12011yescharacteristic
123C2×C4×C43C2×Q1614yes—
124C2×C4×C43C2×Q1612yes—
125C2×C4×C43#13712yes—
126C2×C4×C43C22×D412yes—
127C2×Dic43—24no—
128C2×Dic43—24no—
129C2×Dic43—42no—
130C2×Dic43—44no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43—42no—
134Dic86—44no—
135Dic86—44no—
136Dic86—84no—
137Dic86—82no—
138Dic86—82no—
139C8×C43—44no—
140#18411—431nomaximal, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43C2×#12011yescharacteristic
144C22×C43C22×Q1611yescharacteristic
145C22×C43C2×#13711yescharacteristic
146C4×C43—24no—
147C4×C43—21no—
148C4×C43—22no—
149C4×C43—42no—
150C4×C43#45114yes—
151C4×C43#45412yes—
152Dic43—44no—
153Dic43—44no—
154Dic43—82no—
155Dic43—82no—
156#3502—431no—
157#3230—432no—
158#2568—431no—
159#1617—438no—
160#1503—432no—
161#1461D4311yescharacteristic
162C2×C43—21no—
163C2×C43—21no—
164C2×C43C2×#45111yescharacteristic
165C2×C43C2×#45411yescharacteristic
166C2×C43#302811yescharacteristic
167Q82—862no—
168#557—864no—
169#557—862no—
170#544—434no—
171#544—861no—
172#533—432no—
173#533—862no—
174C2×C4⋊Q8—431no—
175#519—861no—
176C2×C4×Q8C2×D4311yescharacteristic
177#500—862no—
178#487—862no—
179#484—438no—
180#477—864no—
181#431C2×D4312yes—
182#400—434no—
183#391—861no—
184#391—862no—
185#382—861no—
186C4×C4⋊C4—431no—
187#328—438no—
188#324C2×D4314yes—
189C43#1841111yescharacteristic, complemented, Sylow
190C22×Q8—861no—
191C22×Q8D17211yescharacteristic
192C4⋊Q8—432no—
193C4⋊Q8—432no—
194C4⋊Q8—862no—
195C4⋊Q8—862no—
196C4⋊Q8—868no—
197C4⋊Q8—864no—
198C4⋊Q8—862no—
199C4⋊Q8—862no—
200#125—864no—
201#125—868no—
202#125—864no—
203#125—862no—
204C22⋊Q8—434no—
205C22⋊Q8—862no—
206C22⋊Q8—864no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×Q8—434no—
210C4×Q8—864no—
211C4×Q8—864no—
212C4×Q8—864no—
213C4×Q8—864no—
214C4×Q8—862no—
215#117—862no—
216#117—864no—
217C2×C4⋊C4—432no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4D17211yescharacteristic
221C2×C4⋊C4C22×D4312yes—
222C2×C42—861no—
223C2×C42D17212yes—
224C2×C42C22×D4311yescharacteristic
225#107—868no—
226C4⋊C8—22no—
227#103—868no—
228C22⋊C8C22×D4314yes—
229C4×C8—22no—
230#95—432no—
231#95—864no—
232#95—864no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—434no—
236C2×Q8—864no—
237C2×Q8—862no—
238C2×Q8—1724no—
239C2×Q8—1721no—
240C2×Q8—1721no—
241C2×Q8Dic17214yes—
242C22×C4—862no—
243C22×C4—862no—
244C22×C4C2×D17211yescharacteristic
245C22×C4C2×D17212yes—
246C22×C4C2×D17212yes—
247C22×C4C2×D17211yescharacteristic
248C22×C4C23×D4311yescharacteristic
249C2×C8—24no—
250C4⋊C4—22no—
251C4⋊C4—24no—
252C4⋊C4—434no—
253C4⋊C4—864no—
254C4⋊C4—864no—
255C4⋊C4—864no—
256C4⋊C4—868no—
257C4⋊C4—862no—
258C4⋊C4—862no—
259C4⋊C4—864no—
260C4⋊C4—862no—
261C4⋊C4—864no—
262C4⋊C4—864no—
263C4⋊C4—1722no—
264C4⋊C4—1722no—
265C22⋊C4—864no—
266C42—22no—
267C42—22no—
268C42—868no—
269C42—864no—
270C42—1722no—
271C42D4×D4312yes—
272C42D4×D4312yes—
273C23C22×D17211yescharacteristic
274Q8—28no—
275Q8—3442no—
276Q8—3444no—
277Q8—3442no—
278Q8—1724no—
279Q8—1724no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—864no—
287C2×C4—864no—
288C2×C4—1722no—
289C2×C4—1724no—
290C2×C4—1722no—
291C2×C4—1722no—
292C2×C4—1722no—
293C2×C4#1306329511yescharacteristic
294C2×C4#1306329512yes—
295C2×C4#1306329511yescharacteristic
296C2×C4C2×Dic17214yes—
297C2×C4C2×Dic17212yes—
298C2×C4#1306335812yes—
299C2×C4C2×D4×D4312yes—
300C8—44no—
301C22—21no—
302C22—21no—
303C22C2×#1306329511yescharacteristic
304C22C22×Dic17211yescharacteristic
305C22C2×#1306335811yescharacteristic
306C4—22no—
307C4—24no—
308C4—21no—
309C4—42no—
310C4—3442no—
311C4—3442no—
312C4—1724no—
313C4—1724no—
314C4#1458305714yes—
315C4#1458307412yes—
316C2—21no—
317C2—21no—
318C2C2×#1458305711yescharacteristic
319C2C2×#1458307411yescharacteristic
320C2#1914400211yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1461C2
socleC22×C43C2×#120
prime radicalC23×C43C22×D4
hypercenter#1461D43
hypocenterC43#18411
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
189. C43#18411semidirect

Maximal subgroups

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

subgroupindex
#191484052
#191457482
#191398072
#191336392
#191330952
C43×#14612
#1841143