Finite Group Databasebeta

← #25071499

Subgroups — #25071499

Order 11008.

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

normal subgroups only

This group has 906 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#19145741C212yesmaximal
3#19139580C211yesmaximal, characteristic
4#19133605C218yesmaximal
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
15C2×#13063323—21no—
16#14583377—21no—
17#14583297—22no—
18#14583250—22no—
19#14583230C2218yes—
20#14583185—24no—
21#14582829C2214yes—
22#14582804—21no—
23#14582797—22no—
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#13063323—44no—
39#13063317—24no—
40#13063317—22no—
41#13063316—24no—
42#13063316—28no—
43#13063304—22no—
44#13063304—24no—
45#13063304C2314yes—
46Q8×Dic43—24no—
47Q8×Dic43—24no—
48C4×Dic86—24no—
49C4×Dic86—24no—
50C4×Dic86—22no—
51C4×Dic86D414yes—
52#13063284—24no—
53#13063284—22no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43C2312yes—
57C2×Dic43⋊C4—24no—
58C2×C4×Dic43—21no—
59#13063257—28no—
60#13063250—28no—
61C43⋊#95—24no—
62C43⋊#95C2312yes—
63C22×Q8×C43D411yescharacteristic
64C4×Q8×C43—22no—
65C4×Q8×C43—22no—
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C4⋊C4×C43C2312yes—
68C2×C42×C43D412yes—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—22no—
71C22⋊C8×C43C2314yes—
72C4×C8×C43—22no—
73C2×Q8×C43—22no—
74C2×Q8×C43—22no—
75C2×Q8×C43SD1614yes—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D412yes—
78C22×C4×C43C2×D412yes—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2411yescharacteristic
81C22×Dic43—22no—
82C22×Dic43—22no—
83C2×Dic86—22no—
84C2×Dic86—24no—
85C2×Dic86—42no—
86C2×Dic86—42no—
87C2×Dic86—42no—
88C2×Dic86C2×D414yes—
89C2×C8×C43—24no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—24no—
92C42×C43—22no—
93C42×C43—22no—
94C42×C43C2×D412yes—
95C42×C43C2×D412yes—
96C22⋊Dic43—24no—
97C4⋊Dic43—24no—
98C4⋊Dic43—24no—
99C4⋊Dic43—24no—
100C4⋊Dic43—24no—
101C4⋊Dic43—22no—
102C4⋊Dic43—22no—
103C4⋊Dic43—22no—
104C4⋊Dic43—24no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107C4⋊Dic43C2×D414yes—
108Dic43⋊C4—28no—
109Dic43⋊C4—24no—
110Dic43⋊C4—24no—
111Dic43⋊C4—48no—
112C4×Dic43—28no—
113C4×Dic43—24no—
114C4×Dic43—42no—
115C23×C43C22×D411yescharacteristic
116Q8×C43—28no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43#12011yescharacteristic
124C2×C4×C43#12012yes—
125C2×C4×C43#12011yescharacteristic
126C2×C4×C43C2×SD1614yes—
127C2×C4×C43C2×SD1612yes—
128C2×C4×C43#13712yes—
129C2×C4×C43C22×D412yes—
130C2×Dic43—24no—
131C2×Dic43—24no—
132C2×Dic43—24no—
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C2×Dic43—42no—
138Dic86—44no—
139Dic86—44no—
140Dic86—84no—
141Dic86—84no—
142C8×C43—44no—
143#18410—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43C2×#12011yescharacteristic
147C22×C43C22×SD1611yescharacteristic
148C22×C43C2×#13711yescharacteristic
149C4×C43—24no—
150C4×C43—21no—
151C4×C43—22no—
152C4×C43—42no—
153C4×C43#44814yes—
154C4×C43#45612yes—
155Dic43—44no—
156Dic43—44no—
157Dic43—44no—
158Dic43—82no—
159#3502—431no—
160#3229—432no—
161#2546—431no—
162#1611—438no—
163#1503—432no—
164#1461D4311yescharacteristic
165C2×C43—21no—
166C2×C43—21no—
167C2×C43C2×#44811yescharacteristic
168C2×C43C2×#45611yescharacteristic
169C2×C43#302811yescharacteristic
170Q82—862no—
171#557—864no—
172#557—862no—
173#544—434no—
174#544—861no—
175#533—432no—
176#533—862no—
177C2×C4⋊Q8—431no—
178C2×C4⋊Q8—861no—
179#519—861no—
180C2×C4×Q8C2×D4311yescharacteristic
181#498—862no—
182#487—862no—
183#483—438no—
184#475—864no—
185#431C2×D4312yes—
186#398—434no—
187#391—861no—
188#389—862no—
189C4×C4⋊C4—431no—
190#328—438no—
191#324C2×D4314yes—
192C43#1841011yescharacteristic, complemented, Sylow
193C22×Q8—861no—
194C22×Q8D17211yescharacteristic
195C4⋊Q8—432no—
196C4⋊Q8—432no—
197C4⋊Q8—862no—
198C4⋊Q8—862no—
199C4⋊Q8—868no—
200C4⋊Q8—864no—
201C4⋊Q8—862no—
202C4⋊Q8—862no—
203C4⋊Q8—1724no—
204#125—864no—
205#125—868no—
206#125—864no—
207#125—862no—
208C22⋊Q8—434no—
209C22⋊Q8—862no—
210C22⋊Q8—864no—
211C4×Q8—22no—
212C4×Q8—22no—
213C4×Q8—434no—
214C4×Q8—864no—
215C4×Q8—864no—
216C4×Q8—864no—
217C4×Q8—864no—
218C4×Q8—862no—
219#117—862no—
220#117—864no—
221C2×C4⋊C4—432no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—864no—
225C2×C4⋊C4D17211yescharacteristic
226C2×C4⋊C4C22×D4312yes—
227C2×C42—861no—
228C2×C42D17212yes—
229C2×C42C22×D4311yescharacteristic
230#106—868no—
231C4⋊C8—22no—
232#103—868no—
233C22⋊C8C22×D4314yes—
234C4×C8—22no—
235#95—432no—
236#95—864no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—434no—
240C2×Q8—864no—
241C2×Q8—862no—
242C2×Q8—1722no—
243C2×Q8—1722no—
244C2×Q8—1722no—
245C2×Q8#1062187314yes—
246C22×C4—862no—
247C22×C4—862no—
248C22×C4C2×D17211yescharacteristic
249C22×C4C2×D17212yes—
250C22×C4C2×D17212yes—
251C22×C4C2×D17211yescharacteristic
252C22×C4C23×D4311yescharacteristic
253C2×C8—24no—
254C4⋊C4—22no—
255C4⋊C4—24no—
256C4⋊C4—434no—
257C4⋊C4—864no—
258C4⋊C4—864no—
259C4⋊C4—864no—
260C4⋊C4—864no—
261C4⋊C4—868no—
262C4⋊C4—862no—
263C4⋊C4—862no—
264C4⋊C4—864no—
265C4⋊C4—862no—
266C4⋊C4—864no—
267C4⋊C4—864no—
268C4⋊C4—1721no—
269C4⋊C4—1721no—
270C4⋊C4—1728no—
271C22⋊C4—864no—
272C42—22no—
273C42—22no—
274C42—868no—
275C42—864no—
276C42—1722no—
277C42D4×D4312yes—
278C42D4×D4312yes—
279C23C22×D17211yescharacteristic
280Q8—28no—
281Q8—3444no—
282Q8—3444no—
283Q8—1724no—
284Q8—1724no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—864no—
292C2×C4—864no—
293C2×C4—864no—
294C2×C4—1722no—
295C2×C4—1722no—
296C2×C4—1722no—
297C2×C4—1722no—
298C2×C4—1722no—
299C2×C4#1306329511yescharacteristic
300C2×C4#1306329512yes—
301C2×C4#1306329511yescharacteristic
302C2×C4C2×#1062187314yes—
303C2×C4C2×#1062187312yes—
304C2×C4#1306335812yes—
305C2×C4C2×D4×D4312yes—
306C8—44no—
307C22—21no—
308C22—21no—
309C22C2×#1306329511yescharacteristic
310C22C22×#1062187311yescharacteristic
311C22C2×#1306335811yescharacteristic
312C4—21no—
313C4—22no—
314C4—24no—
315C4—42no—
316C4—3442no—
317C4—1724no—
318C4—1724no—
319C4—1724no—
320C4#1458304014yes—
321C4#1458308412yes—
322C2—21no—
323C2—21no—
324C2C2×#1458304011yescharacteristic
325C2C2×#1458308411yescharacteristic
326C2#1914400211yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1461C2
socleC22×C43C2×#120
prime radicalC23×C43C22×D4
hypercenter#1461D43
hypocenterC43#18410
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
192. C43#18410semidirect

Maximal subgroups

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

subgroupindex
#191484052
#191457412
#191395802
#191336052
#191330952
C43×#14612
#1841043