Finite Group Databasebeta

← #14664230

Subgroups — #14664230

Order 2816.

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

normal subgroups only

This group has 778 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#13071935C211yesmaximal, characteristic
2C2×#10622164C211yesmaximal, characteristic, complemented
3#13066638C212yesmaximal, complemented
4#13066614C212yesmaximal, complemented
5C11×#1462C211yesmaximal, characteristic, complemented
6C22×#4339C411yescharacteristic, complemented
7C22×C11×C22⋊C4C2211yescharacteristic
8C2×#67006—21no—
9C22×C22⋊Dic11—21no—
10C11×#407—21no—
11#10622826—21no—
12#10622824C411yescharacteristic, complemented
13#10622573C411yescharacteristic, complemented
14#10622573C2211yescharacteristic
15#10622569—21no—
16#10622569—21no—
17#10622560C411yescharacteristic, complemented
18#10622560C2211yescharacteristic
19C11×#323—21no—
20C11×#323C2212yes—
21#10622164—21no—
22#10622164C2212yes—
23C25×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×C22⋊D11—21no—
29C23×Dic11—41no—
30C2×#4339—41no—
31C2×#4339—41no—
32C2×#4339—44no—
33C22×D44C2×C411yescharacteristic, complemented
34C22×C4×D11—21no—
35C22×Dic22C2×C411yescharacteristic, complemented
36C2×C11×M16—41no—
37C2×C11×C22⋊C4—41no—
38C2×C11×C22⋊C4—41no—
39C2×C11×C22⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4D411yescharacteristic
41C2×C11×C22⋊C4D411yescharacteristic
42C2×C11×C22⋊C4C2311yescharacteristic
43#67006—44no—
44C2×C22⋊Dic11—24no—
45C2×C22⋊Dic11—22no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—41no—
50C2×C22⋊Dic11—42no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8—41no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95C2×C411yescharacteristic, complemented
59C11⋊#95C2×C411yescharacteristic, complemented
60#11753—111nomaximal, Sylow
61C24×C11—21no—
62C24×C11—21no—
63C24×C11—22no—
64C24×C11—21no—
65C24×C11—21no—
66C24×C11—42no—
67C24×C11—81no—
68C24×C11C22⋊C411yescharacteristic
69C24×C11C22⋊C411yescharacteristic
70C24×C11C2×D411yescharacteristic
71C23×D11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—42no—
77C22×C4×C11—81no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—24no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—42no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—81no—
92C2×C22⋊D11—81no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—44no—
97C22×Dic11—42no—
98C22×Dic11—82no—
99C22×Dic11—82no—
100#4339—44no—
101#4339—44no—
102#4339—44no—
103#4339—44no—
104C2×D44—41no—
105C2×D44—42no—
106C2×C4×D11—42no—
107C2×C4×D11—42no—
108C2×C4×D11—42no—
109C2×Dic22—41no—
110C2×Dic22—42no—
111C11×M16—82no—
112C2×C8×C11—42no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C22⋊Dic11—24no—
118C22⋊Dic11—44no—
119C22⋊Dic11—42no—
120C22⋊Dic11—42no—
121C22⋊Dic11—42no—
122C22⋊Dic11—42no—
123(C2×D11)⋊C4—81no—
124(C2×D11)⋊C4—81no—
125#2404—111no—
126C2×#342—111no—
127#1462D1111yescharacteristic, complemented
128#1351—112no—
129#1343—112no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—41no—
142C23×C11—42no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11—84no—
151C23×C11—82no—
152C23×C11—82no—
153C23×C11#9911yescharacteristic
154C23×C11#9911yescharacteristic
155C23×C11#10412yes—
156C23×C11C2×C22⋊C411yescharacteristic
157C23×C11AGL(1,ℤ/8)11yescharacteristic
158C23×C11#13711yescharacteristic
159C22×D11—22no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—81no—
178C22⋊D11—44no—
179C22⋊D11—44no—
180C22⋊D11—84no—
181C22⋊D11—82no—
182C22⋊D11—82no—
183C2×Dic11—22no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—44no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—88no—
194C2×Dic11—82no—
195C2×Dic11—82no—
196D44—42no—
197D44—42no—
198C4×D11—48no—
199Dic22—42no—
200Dic22—42no—
201C8×C11—82no—
202C22×#41—111no—
203C2×#120—221no—
204C22×C22⋊C4—221no—
205C22×C22⋊C4C2×D1111yescharacteristic
206#407—21no—
207#393—111no—
208#393—111no—
209#392—111no—
210#392—111no—
211#386—221no—
212#386—221no—
213#386—221no—
214#381—111no—
215#342—112no—
216#342—221no—
217#323—21no—
218#323C2×D1112yes—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—22no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11AΣL(1,𝔽16)12yes—
245C22×C11C2×#9911yescharacteristic
246C22×C11#41711yescharacteristic
247C22×C11C2×#10411yescharacteristic
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C4×C11—41no—
256C4×C11—41no—
257C4×C11—41no—
258C4×C11—41no—
259Dic11—42no—
260Dic11—81no—
261Dic11—81no—
262Dic11—84no—
263C25D4411yescharacteristic
264C2×#41—441no—
265C2×#41—441no—
266C2×#41—444no—
267C22×Q8—111no—
268C22×D4—111no—
269C22×D4—221no—
270C22×D4—221no—
271C22×D4—221no—
272C23×C4—221no—
273C23×C4—441no—
274C23×C4C4×D1111yescharacteristic
275C23×C4C22⋊D1111yescharacteristic
276C2×M16—41no—
277#120—444no—
278C2×C22⋊C4—41no—
279C2×C22⋊C4—41no—
280C2×C22⋊C4—224no—
281C2×C22⋊C4—222no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—221no—
284C2×C22⋊C4—221no—
285C2×C22⋊C4—221no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—441no—
288C2×C22⋊C4—442no—
289C2×C22⋊C4C4×D1111yescharacteristic
290C2×C22⋊C4D4411yescharacteristic
291C2×C22⋊C4C22⋊D1111yescharacteristic
292C2×C22⋊C4C22×D1111yescharacteristic
293C22⋊C8—22no—
294C22⋊C8—41no—
295#95—111no—
296#95—111no—
297#95—221no—
298#95—221no—
299#95—221no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—22no—
303C2×C11—41no—
304C2×C11—41no—
305C2×C11—42no—
306C2×C11—41no—
307C2×C11#150411yescharacteristic
308C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
309C2×C11#212711yescharacteristic
310D11—82no—
311C24—21no—
312C24—21no—
313C24—22no—
314C24—21no—
315C24—21no—
316C24—42no—
317C24—81no—
318C24—221no—
319C24(C2×D11)⋊C411yescharacteristic
320C24(C2×D11)⋊C411yescharacteristic
321C24C2×D4411yescharacteristic
322#41—444no—
323#41—444no—
324#41—444no—
325#41—444no—
326C2×Q8—441no—
327C2×Q8—442no—
328C2×D4—224no—
329C2×D4—441no—
330C2×D4—442no—
331C2×D4—442no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—442no—
335C2×D4—442no—
336C2×D4—442no—
337C2×D4—441no—
338C2×D4—441no—
339C2×D4—881no—
340C2×D4—881no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—42no—
346C22×C4—81no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—442no—
351C22×C4—442no—
352C22×C4—442no—
353C22×C4—444no—
354C22×C4—442no—
355C22×C4—882no—
356C22×C4—882no—
357C22×C4(C2×D11)⋊C411yescharacteristic
358C22×C4(C2×D11)⋊C411yescharacteristic
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361M16—82no—
362C2×C8—42no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—224no—
368C22⋊C4—442no—
369C22⋊C4—442no—
370C22⋊C4—444no—
371C22⋊C4—442no—
372C22⋊C4—442no—
373C22⋊C4—881no—
374C22⋊C4—881no—
375C11#1175311yescharacteristic, complemented, Sylow
376C23—22no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—22no—
385C23—21no—
386C23—21no—
387C23—41no—
388C23—42no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—42no—
394C23—81no—
395C23—81no—
396C23—84no—
397C23—82no—
398C23—82no—
399C23—222no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23#6687011yescharacteristic
407C23#6687011yescharacteristic
408C23#6688912yes—
409C23#6696111yescharacteristic
410C23#6696211yescharacteristic
411C23C2×(C2×D11)⋊C411yescharacteristic
412Q8—442no—
413Q8—442no—
414D4—442no—
415D4—442no—
416D4—444no—
417D4—444no—
418D4—884no—
419D4—882no—
420D4—882no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—81no—
433C2×C4—222no—
434C2×C4—448no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—444no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—888no—
445C2×C4—882no—
446C2×C4—882no—
447C8—82no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—22no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—41no—
462C22—41no—
463C22—44no—
464C22—44no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—81no—
470C22—81no—
471C22—82no—
472C22—82no—
473C22—442no—
474C22—442no—
475C22—442no—
476C22—881no—
477C22—881no—
478C22—881no—
479C22—881no—
480C22#1062211312yes—
481C22C2×#6687011yescharacteristic
482C22#1062274611yescharacteristic
483C22C2×#6688911yescharacteristic
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—442no—
489C4—881no—
490C4—881no—
491C4—884no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—41no—
496C2—41no—
497C2—42no—
498C2—41no—
499C2—882no—
500C2#1306712111yescharacteristic
501C2C2×#1062211311yescharacteristic
502C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1462C2
socleC22×C11C2×#99
prime radical#13071935C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1462D11
hypocenterC11#11753
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. C2×#10622164C2semidirect
3. #13066638C2semidirect
4. #13066614C2semidirect
5. C11×#1462C2semidirect
6. C22×#4339C4semidirect
12. #10622824C4semidirect
13. #10622573C4semidirect
17. #10622560C4semidirect
33. C22×D44C2×C4semidirect
35. C22×Dic22C2×C4semidirect
58. C11⋊#95C2×C4semidirect
59. C11⋊#95C2×C4semidirect
127. #1462D11semidirect
375. C11#11753semidirect

Maximal subgroups

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

subgroupindex
#130719352
C2×#106221642
#130666382
#130666142
C11×#14622
#1175311