Finite Group Databasebeta

← #14734989

Subgroups — #14734989

Order 2816.

1152 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 171 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#13079603C212yesmaximal, complemented
2#13079080C211yesmaximal, characteristic, complemented
3#13067922C214yesmaximal, complemented
4#13067905C214yesmaximal, complemented
5#13067240C211yesmaximal, characteristic, complemented
6#13067214C212yesmaximal, complemented
7C2×C11×H(3,𝔽4)C211yesmaximal, characteristic, complemented
8C11×H(3,𝔽4)—24no—
9C11×H(3,𝔽4)—22no—
10C11×H(3,𝔽4)C2214yes—
11C2×C11×#124—21no—
12C2×C11×#124—22no—
13C2×C11×#124C2211yescharacteristic
14C2×C11×#124C2212yes—
15C2×C11×#120—21no—
16C2×C11×#120—22no—
17C2×#66995—21no—
18C2×#66985—21no—
19#10623008C2211yescharacteristic, complemented
20#10622840—22no—
21#10622830—22no—
22#10622673C2212yescomplemented
23#10622672—22no—
24#10622671C2212yescomplemented
25#10622671C2214yescomplemented
26#10622670—24no—
27#10622668C2214yescomplemented
28#10622539C2212yescomplemented
29C4×#4318C2211yescharacteristic, complemented
30#10622178C2218yescomplemented
31#10622178C2214yescomplemented
32C25×C11—21no—
33C22×Q8×C11D411yescharacteristic
34C22×Q8×C11D412yes—
35C22×D4×C11—22no—
36C22×D4×C11—21no—
37C22×D4×C11D411yescharacteristic
38C22×D4×C11D412yes—
39C2×#4339—21no—
40C11×#124—28no—
41C11×#124—24no—
42C11×#124—28no—
43C11×#124—24no—
44C11×#124—22no—
45C11×#124—22no—
46C11×#124—22no—
47C11×#124D414yes—
48C11×#124D412yes—
49C11×#124C2314yes—
50C11×#124C2312yes—
51C11×#120—28no—
52C11×#120—24no—
53C11×#120—28no—
54C11×#120—24no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63#66995—44no—
64C2×#4325—22no—
65C2×#4325—24no—
66C2×#4324—22no—
67#66985—44no—
68C2×#4323—22no—
69C2×#4323—24no—
70#66983—22no—
71C2×#4318—21no—
72#66928—21no—
73#66927C2311yescharacteristic, complemented
74C4×D44—22no—
75#66922C2311yescharacteristic, complemented
76#66899—24no—
77#66896—24no—
78C22⋊(C11⋊C8)—22no—
79C4⋊(C11⋊C8)—22no—
80#66867C2312yescomplemented
81#66867C2314yescomplemented
82C4×C11⋊C8—21no—
83#18992—111nomaximal, Sylow
84C24×C11—24no—
85C24×C11—21no—
86C24×C11—22no—
87C24×C11—84no—
88C24×C11—82no—
89C2×Q8×C11—22no—
90C2×Q8×C11—21no—
91C2×Q8×C11—42no—
92C2×Q8×C11—82no—
93C2×Q8×C11C2×D414yes—
94C2×Q8×C11C2×D412yes—
95C2×D4×C11—24no—
96C2×D4×C11—28no—
97C2×D4×C11—22no—
98C2×D4×C11—21no—
99C2×D4×C11—42no—
100C2×D4×C11—82no—
101C2×D4×C11—84no—
102C2×D4×C11—82no—
103C2×D4×C11C2×D414yes—
104C2×D4×C11C2×D412yes—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C2×C22⋊D11—41no—
110#4339—42no—
111#4339—42no—
112C2×D44—22no—
113C2×D44—21no—
114C2×C4×D11—41no—
115C2×Dic22—21no—
116C11×C22⋊C4—28no—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C42×C11—24no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D412yes—
127C42×C11C2411yescharacteristic
128#4326—44no—
129#4325—44no—
130#4325—84no—
131#4324—44no—
132#4323—44no—
133#4323—84no—
134(C2×D11)⋊C4—42no—
135C4⋊Dic11—22no—
136#4318—24no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—24no—
139C2×H(3,𝔽4)D1111yescharacteristic, complemented
140#3213—112no—
141#3153—111no—
142#1659—114no—
143#1655—114no—
144#1533—111no—
145#1527—112no—
146C23×C11—22no—
147C23×C11—24no—
148C23×C11—44no—
149C23×C11—44no—
150C23×C11—44no—
151C23×C11—42no—
152C23×C11—44no—
153C23×C11—84no—
154C23×C11—88no—
155C23×C11—816no—
156C23×C11#12011yescharacteristic
157C22×D11—41no—
158Q8×C11—42no—
159Q8×C11—44no—
160Q8×C11—81no—
161Q8×C11—82no—
162D4×C11—42no—
163D4×C11—44no—
164D4×C11—81no—
165D4×C11—82no—
166D4×C11—84no—
167D4×C11—88no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—42no—
172C2×C4×C11—44no—
173C2×C4×C11—42no—
174C2×C4×C11#12012yes—
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11C22×D412yes—
177C2×C4×C11C22×D411yescharacteristic
178C22⋊D11—82no—
179C2×Dic11—41no—
180D44—41no—
181D44—44no—
182D44—41no—
183C4×D11—82no—
184Dic22—41no—
185Dic22—41no—
186C11⋊C8—24no—
187C11⋊C8—44no—
188C2×#137—221no—
189C2×AGL(1,ℤ/8)—221no—
190H(3,𝔽4)—24no—
191H(3,𝔽4)—22no—
192H(3,𝔽4)C2×D1114yes—
193#532—111no—
194C2×#124—21no—
195C2×#124—22no—
196C2×#124C2×D1111yescharacteristic
197C2×#124C2×D1112yes—
198C2×#120—21no—
199C2×#120—22no—
200#497—112no—
201#496—112no—
202#496—114no—
203#495—222no—
204#489—114no—
205#463—224no—
206#448—222no—
207#447—222no—
208#432—112no—
209C4×M16—111no—
210#329—118no—
211#329—114no—
212C22×C11—22no—
213C22×C11—42no—
214C22×C11—44no—
215C22×C11—44no—
216C22×C11—44no—
217C22×C11—44no—
218C22×C11—84no—
219C22×C11—88no—
220C22×C11—816no—
221C22×C11#45312yes—
222C22×C11C2×#12011yescharacteristic
223C2×D11—81no—
224C2×D11—82no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—22no—
228C4×C11—22no—
229C4×C11—42no—
230C4×C11—44no—
231Dic11—81no—
232C25—21no—
233C2×#41—221no—
234C22×Q8C22⋊D1111yescharacteristic
235C22×Q8C22⋊D1112yes—
236C22×D4—22no—
237C22×D4—21no—
238C22×D4C22⋊D1111yescharacteristic
239C22×D4C22⋊D1112yes—
240#137—444no—
241AGL(1,ℤ/8)—444no—
242C2×Q16—222no—
243C2×SD16—222no—
244C2×SD16—222no—
245C2×SD16—224no—
246C2×D8—222no—
247C2×D8—224no—
248C2×M16—221no—
249C4⋊Q8—111no—
250#127—111no—
251#124—28no—
252#124—24no—
253#124—28no—
254#124—24no—
255#124—22no—
256#124—22no—
257#124—22no—
258#124—221no—
259#124C22⋊D1114yes—
260#124C22⋊D1112yes—
261#124C22×D1114yes—
262#124C22×D1112yes—
263#121—222no—
264#120—28no—
265#120—24no—
266#120—28no—
267#120—24no—
268C4×D4—222no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C42—21no—
275C2×C42C22×D1111yescharacteristic
276C4⋊C8—222no—
277#103—224no—
278#102—224no—
279C22⋊C8—222no—
280#97—112no—
281#97—114no—
282C4×C8—221no—
283C2×C11—22no—
284C2×C11—82no—
285C2×C11—84no—
286C2×C11C2×#45311yescharacteristic
287C2×C11#301912yes—
288D11—161no—
289C24—24no—
290C24—21no—
291C24—22no—
292C24—84no—
293C24—82no—
294#41—442no—
295#41—442no—
296C2×Q8—22no—
297C2×Q8—21no—
298C2×Q8—42no—
299C2×Q8—82no—
300C2×Q8—221no—
301C2×Q8C2×C22⋊D1114yes—
302C2×Q8C2×C22⋊D1112yes—
303C2×D4—24no—
304C2×D4—28no—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4—42no—
308C2×D4—82no—
309C2×D4—84no—
310C2×D4—82no—
311C2×D4—222no—
312C2×D4—221no—
313C2×D4—441no—
314C2×D4C2×C22⋊D1114yes—
315C2×D4C2×C22⋊D1112yes—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—441no—
319C22×C4C2×C22⋊D1111yescharacteristic
320C22×C4C2×C22⋊D1112yes—
321Q16—444no—
322SD16—444no—
323SD16—444no—
324SD16—884no—
325D8—444no—
326D8—884no—
327M16—224no—
328C2×C8—222no—
329C2×C8—224no—
330C4⋊C4—222no—
331C22⋊C4—28no—
332C22⋊C4—24no—
333C22⋊C4—24no—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—442no—
340C42—24no—
341C42C2×C22⋊D1111yescharacteristic
342C42C2×C22⋊D1112yes—
343C42C23×D1111yescharacteristic
344C11#1899211yescharacteristic, complemented, Sylow
345C23—22no—
346C23—24no—
347C23—44no—
348C23—44no—
349C23—44no—
350C23—42no—
351C23—44no—
352C23—84no—
353C23—88no—
354C23—816no—
355C23—441no—
356C23#6700611yescharacteristic
357Q8—42no—
358Q8—44no—
359Q8—81no—
360Q8—82no—
361Q8—441no—
362Q8—441no—
363D4—42no—
364D4—44no—
365D4—81no—
366D4—82no—
367D4—84no—
368D4—88no—
369D4—441no—
370D4—444no—
371D4—441no—
372D4—882no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—42no—
377C2×C4—44no—
378C2×C4—42no—
379C2×C4—441no—
380C2×C4—882no—
381C2×C4#6700612yes—
382C2×C4#6700611yescharacteristic
383C2×C4C22×C22⋊D1112yes—
384C2×C4C22×C22⋊D1111yescharacteristic
385C8—224no—
386C8—444no—
387C22—22no—
388C22—42no—
389C22—44no—
390C22—44no—
391C22—44no—
392C22—44no—
393C22—84no—
394C22—88no—
395C22—816no—
396C22—881no—
397C22—882no—
398C22#1062285412yes—
399C22C2×#6700611yescharacteristic
400C4—21no—
401C4—21no—
402C4—22no—
403C4—22no—
404C4—42no—
405C4—44no—
406C4—881no—
407C2—22no—
408C2—82no—
409C2—84no—
410C2—1761no—
411C2C2×#1062285411yescharacteristic
412C2#1307797312yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×H(3,𝔽4)C2
socleC22×C11C2×#120
hypercenterC2×H(3,𝔽4)D11
hypocenterC11#18992
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #13079603C2semidirect
2. #13079080C2semidirect
3. #13067922C2semidirect
4. #13067905C2semidirect
5. #13067240C2semidirect
6. #13067214C2semidirect
7. C2×C11×H(3,𝔽4)C2semidirect
19. #10623008C22semidirect
22. #10622673C22semidirect
24. #10622671C22semidirect
25. #10622671C22semidirect
27. #10622668C22semidirect
28. #10622539C22semidirect
29. C4×#4318C22semidirect
30. #10622178C22semidirect
31. #10622178C22semidirect
73. #66927C23semidirect
75. #66922C23semidirect
80. #66867C23semidirect
81. #66867C23semidirect
139. C2×H(3,𝔽4)D11semidirect
344. C11#18992semidirect

Maximal subgroups

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

subgroupindex
#130796032
#130790802
#130679222
#130679052
#130672402
#130672142
C2×C11×H(3,𝔽4)2
#1899211