Finite Group Databasebeta

← #14664258

Subgroups — #14664258

Order 2816.

586 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 73 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#13073770C211yesmaximal, characteristic
2D11×#342C211yesmaximal, characteristic
3#13066941C211yesmaximal, characteristic
4#13066637C211yesmaximal, characteristic, complemented
5#13066617C211yesmaximal, characteristic, complemented
6#13066615C211yesmaximal, characteristic, complemented
7C11×#1351C211yesmaximal, characteristic, complemented
8C2×#66999C411yescharacteristic, complemented
9C2×C22⋊C4×D11—21no—
10C2×C22⋊C4×D11C2211yescharacteristic
11C11×#393C2211yescharacteristic
12#10622844C411yescharacteristic, complemented
13#10622568—21no—
14#10622566C2211yescharacteristic
15#10622557—21no—
16#10622339—21no—
17#10622287C411yescharacteristic, complemented
18#10622282—21no—
19#10622279C411yescharacteristic, complemented
20#10622277—21no—
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C24×D11D411yescharacteristic
28C22×Q8×C11C2×C411yescharacteristic, complemented
29C22×C4×D11—41no—
30C22×C4×D11C2×C411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11D411yescharacteristic
38#66999—41no—
39#66999—41no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—41no—
45C2×(C2×D11)⋊C4C2×C411yescharacteristic
46C2×(C2×D11)⋊C4D411yescharacteristic
47C2×C4⋊Dic11C2×C411yescharacteristic, complemented
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C2×#4313—41no—
51C22⋊C4×D11—24no—
52C22⋊C4×D11—41no—
53C22⋊C4×D11—41no—
54C22⋊C4×D11—42no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic, complemented
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95C2×C411yescharacteristic, complemented
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11759—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C23×D11—21no—
67C23×D11—21no—
68C23×D11—21no—
69C23×D11—21no—
70C23×D11—22no—
71C23×D11—42no—
72C23×D11—81no—
73C23×D11C22⋊C411yescharacteristic
74C23×D11C22⋊C411yescharacteristic
75C2×Q8×C11—41no—
76C2×Q8×C11—81no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—41no—
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—42no—
92C2×C4×D11—44no—
93C2×C4×D11—81no—
94C2×C4×D11—82no—
95C2×C4×D11—82no—
96C2×C8×C11—41no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—81no—
101C22⋊Dic11—22no—
102C22⋊Dic11—41no—
103C22⋊Dic11—41no—
104C22⋊Dic11—41no—
105C22⋊Dic11—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—44no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—81no—
114C4⋊Dic11—41no—
115Dic11⋊C4—42no—
116C4×Dic11—81no—
117C2×C11⋊C8—41no—
118#4313—82no—
119#2561—111no—
120C2×#342—111no—
121#1462—111no—
122#1351—111no—
123#1351D1111yescharacteristic, complemented
124#1344—111no—
125#1344—111no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11AGL(1,ℤ/8)11yescharacteristic
132C23×C11#13711yescharacteristic
133C22×D11—22no—
134C22×D11—22no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—22no—
139C22×D11—22no—
140C22×D11—21no—
141C22×D11—22no—
142C22×D11—41no—
143C22×D11—42no—
144C22×D11—42no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—81no—
148C22×D11—81no—
149C22×D11—84no—
150C22×D11—82no—
151C22×D11—82no—
152C22×D11#9911yescharacteristic
153C22×D11#9911yescharacteristic
154C22×D11#10412yes—
155Q8×C11—82no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—81no—
181C2×Dic11—81no—
182C4×D11—42no—
183C4×D11—81no—
184C4×D11—81no—
185C4×D11—81no—
186C4×D11—88no—
187C8×C11—81no—
188C11⋊C8—81no—
189C2×C22⋊Q8—111no—
190C22×C22⋊C4—111no—
191C22×C22⋊C4—221no—
192#407—221no—
193#397—111no—
194#397—111no—
195#393—111no—
196#393C2×D1111yescharacteristic
197#388—221no—
198#388—221no—
199#381—221no—
200#379—221no—
201C4×C22⋊C4—111no—
202#342—111no—
203#342—221no—
204#342C2×D1111yescharacteristic
205#323—111no—
206#323—221no—
207#323C2×D1111yescharacteristic
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—81no—
217C22×C11C2×#9911yescharacteristic
218C22×C11#41711yescharacteristic
219C22×C11C2×#10411yescharacteristic
220C2×D11—21no—
221C2×D11—21no—
222C2×D11—21no—
223C2×D11—21no—
224C2×D11—21no—
225C2×D11—22no—
226C2×D11—42no—
227C2×D11—42no—
228C2×D11—44no—
229C2×D11—44no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—42no—
233C2×D11—81no—
234C2×D11—82no—
235C2×D11—82no—
236C2×D11#35412yes—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11—81no—
240C4×C11—82no—
241C4×C11—81no—
242Dic11—41no—
243Dic11—41no—
244Dic11—81no—
245Dic11—82no—
246Dic11—81no—
247C25—111no—
248C22×Q8C4×D1111yescharacteristic, complemented
249C23×C4—111no—
250C23×C4—111no—
251C23×C4—441no—
252C2×M16—441no—
253C22⋊Q8—441no—
254C22⋊Q8—441no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—221no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—224no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—441no—
270C2×C22⋊C4—441no—
271C2×C22⋊C4—442no—
272C2×C22⋊C4—441no—
273C2×C22⋊C4C22×D1111yescharacteristic
274C2×C42—221no—
275C22⋊C8—21no—
276C22⋊C8—221no—
277C22⋊C8—441no—
278#95—21no—
279#95—111no—
280#95—221no—
281#95—221no—
282#95—221no—
283#95C4×D1111yescharacteristic, complemented
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—41no—
287C2×C11—41no—
288C2×C11#150411yescharacteristic
289C2×C11#212111yescharacteristic
290C2×C11C2×#35411yescharacteristic
291D11—22no—
292D11—41no—
293D11—42no—
294C24—111no—
295C24—111no—
296C24—221no—
297C24—222no—
298C24—221no—
299C24—221no—
300C24—221no—
301C24—442no—
302C24—881no—
303C24D4×D1111yescharacteristic
304C2×Q8—41no—
305C2×Q8—81no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—442no—
318C22×C4—444no—
319C22×C4—441no—
320C22×C4—881no—
321C22×C4—882no—
322C22×C4—882no—
323C22×C4C2×C4×D1111yescharacteristic
324C22×C4D4×D1111yescharacteristic
325M16—882no—
326C2×C8—41no—
327C2×C8—441no—
328C4⋊C4—441no—
329C4⋊C4—442no—
330C22⋊C4—22no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—81no—
334C22⋊C4—222no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—442no—
340C22⋊C4—444no—
341C22⋊C4—442no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—881no—
347C42—881no—
348C11#1175911yescharacteristic, complemented, Sylow
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—111no—
354C23—111no—
355C23—112no—
356C23—222no—
357C23—222no—
358C23—222no—
359C23—222no—
360C23—222no—
361C23—221no—
362C23—221no—
363C23—221no—
364C23—221no—
365C23—441no—
366C23—441no—
367C23—441no—
368C23—442no—
369C23—442no—
370C23—881no—
371C23—881no—
372C23—882no—
373C23—882no—
374C23—884no—
375C23C22⋊C4×D1111yescharacteristic
376C23#6696711yescharacteristic
377C23#6697111yescharacteristic
378Q8—82no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—442no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—442no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—881no—
405C2×C4—881no—
406C2×C4—881no—
407C2×C4—888no—
408C2×C4—881no—
409C2×C4—881no—
410C8—81no—
411C8—881no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—81no—
421C22—112no—
422C22—221no—
423C22—221no—
424C22—221no—
425C22—222no—
426C22—221no—
427C22—221no—
428C22—442no—
429C22—442no—
430C22—442no—
431C22—444no—
432C22—444no—
433C22—441no—
434C22—441no—
435C22—881no—
436C22—882no—
437C22—882no—
438C22D11×#9911yescharacteristic
439C22#1062241611yescharacteristic
440C22D11×#10411yescharacteristic
441C4—41no—
442C4—41no—
443C4—81no—
444C4—82no—
445C4—81no—
446C4—441no—
447C4—441no—
448C4—881no—
449C4—882no—
450C4—881no—
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—222no—
456C2—441no—
457C2—442no—
458C2#1306711911yescharacteristic
459C2#1307025911yescharacteristic
460C2D11×#35411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radicalC24×D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11759
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
4. #13066637C2semidirect
5. #13066617C2semidirect
6. #13066615C2semidirect
7. C11×#1351C2semidirect
8. C2×#66999C4semidirect
12. #10622844C4semidirect
17. #10622287C4semidirect
19. #10622279C4semidirect
28. C22×Q8×C11C2×C4semidirect
47. C2×C4⋊Dic11C2×C4semidirect
57. C11×#95C2×C4semidirect
61. C11⋊#95C2×C4semidirect
123. #1351D11semidirect
248. C22×Q8C4×D11semidirect
283. #95C4×D11semidirect
348. C11#11759semidirect

Maximal subgroups

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

subgroupindex
#130737702
D11×#3422
#130669412
#130666372
#130666172
#130666152
C11×#13512
#1175911