Finite Group Databasebeta

← #14656242

Subgroups — #14656242

Order 2816.

634 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079923C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic, complemented
3#13069411C211yesmaximal, characteristic, complemented
4#13067067C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66985—21no—
12#10623008C2211yescharacteristic
13C11×#463—22no—
14C11×#461—21no—
15C11×#459—21no—
16C11×#423C2211yescharacteristic
17C11×#417—21no—
18C2×C22⋊(C11⋊C8)—22no—
19#10622700—21no—
20#10622685—21no—
21#10622651—22no—
22#10622632—21no—
23#10622629—22no—
24#10622628—21no—
25#10622628—21no—
26#10622620—21no—
27#10622579—21no—
28#10622537C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31D4⋊(C11⋊C8)—22no—
32#10622121—22no—
33C2×C11×#41—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C2×#4339—21no—
37C11×AGL(1,ℤ/8)—42no—
38C11×AGL(1,ℤ/8)—42no—
39C2×C11×SD16—22no—
40C2×C11×D8—22no—
41C2×C11×M16—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×#127D411yescharacteristic
44C11×#124—21no—
45C11×#121—21no—
46C11×#121—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4324—22no—
57#66985—42no—
58#66985—42no—
59C2×#4323—22no—
60C2×#4323—22no—
61#66983—21no—
62#66983—21no—
63C2×#4318—21no—
64C22×C11⋊C8—21no—
65C22×C11⋊C8D412yes—
66#66928—21no—
67#66927D411yescharacteristic
68C4×D44—21no—
69C4×D44—21no—
70#66922D411yescharacteristic
71C11×C4⋊C8—21no—
72C11×C4⋊C8D412yes—
73C11×#103—22no—
74C11×#102—22no—
75#66896—22no—
76C22⋊(C11⋊C8)—44no—
77#66874—22no—
78#66873—22no—
79#66873—22no—
80#66871—22no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)—21no—
84C4⋊(C11⋊C8)D412yes—
85C4×C11⋊C8—21no—
86C4×C11⋊C8—21no—
87#10254—111nomaximal, Sylow
88C24×C11—21no—
89C11×#41—41no—
90C11×#41—41no—
91C11×#41—41no—
92C11×#41—41no—
93C2×Q8×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—41no—
103C2×D4×C11D812yescomplemented
104C22×C4×C11—21no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—41no—
114#4339—41no—
115#4339—41no—
116#4339—41no—
117#4339—41no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×C4×D11—41no—
122C2×Dic22—21no—
123C11×SD16—44no—
124C11×D8—44no—
125C11×M16—41no—
126C11×M16—41no—
127C2×C8×C11—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140#4324—44no—
141#4323—44no—
142#4323—82no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147#4318—41no—
148#4318—41no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—42no—
153C2×C11⋊C8—41no—
154C2×C11⋊C8—41no—
155#3245—111no—
156#3036—111no—
157#3036D1111yescharacteristic, complemented
158#1954—111no—
159#1492—111no—
160#1492—111no—
161#1292—111no—
162C23×C11—22no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11#12111yescharacteristic
169C22×D11—41no—
170Q8×C11—41no—
171Q8×C11—41no—
172D4×C11—22no—
173D4×C11—22no—
174D4×C11—42no—
175D4×C11—41no—
176D4×C11—41no—
177D4×C11—41no—
178D4×C11—41no—
179D4×C11—41no—
180D4×C11—41no—
181D4×C11—81no—
182D4×C11—81no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—82no—
190C2×C4×C11—81no—
191C2×C4×C11—81no—
192C2×C4×C11—81no—
193C2×C4×C11—81no—
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12711yescharacteristic
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11#13511yescharacteristic
202C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
203C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
204C22⋊D11—81no—
205C22⋊D11—81no—
206C2×Dic11—41no—
207D44—42no—
208D44—41no—
209D44—41no—
210D44—41no—
211D44—41no—
212C4×D11—81no—
213C4×D11—81no—
214Dic22—41no—
215Dic22—41no—
216C8×C11—42no—
217C11⋊C8—42no—
218C11⋊C8—42no—
219C11⋊C8—42no—
220C2×AGL(1,ℤ/8)—21no—
221C2×AGL(1,ℤ/8)—221no—
222#532—111no—
223#532C2×D1111yescharacteristic
224C2×C4×D4C2×D1111yescharacteristic
225#474—221no—
226#474—221no—
227#466—222no—
228#463—22no—
229#463—222no—
230#461—21no—
231#461—221no—
232#459—21no—
233#459—221no—
234#459—221no—
235#459—221no—
236#423—111no—
237#423C2×D1111yescharacteristic
238C2×C4⋊C8—111no—
239#417—21no—
240#417—221no—
241C2×C22⋊C8—222no—
242C2×C4×C8—111no—
243D4⋊C8—222no—
244D4⋊C8—222no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—44no—
248C22×C11—42no—
249C22×C11—82no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11#39211yescharacteristic
256C22×C11#46611yescharacteristic
257C22×C11#46911yescharacteristic
258C2×D11—81no—
259C2×D11—81no—
260C2×D11—81no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—81no—
265C4×C11—81no—
266C4×C11#44711yescharacteristic
267C4×C11#44711yescharacteristic
268C4×C11#44911yescharacteristic
269C4×C11#44911yescharacteristic
270C4×C11#45311yescharacteristic
271C4×C11#45411yescharacteristic
272Dic11—81no—
273C2×#41—21no—
274C2×#41—221no—
275C22×D4C22⋊D1111yescharacteristic
276C23×C4—21no—
277AGL(1,ℤ/8)—42no—
278AGL(1,ℤ/8)—42no—
279AGL(1,ℤ/8)—442no—
280AGL(1,ℤ/8)—442no—
281C2×SD16—22no—
282C2×SD16—222no—
283C2×D8—22no—
284C2×D8—222no—
285C2×D8—222no—
286C2×M16—21no—
287C2×M16—221no—
288C22×C8—112no—
289C22×C8—221no—
290C4⋊Q8—111no—
291C4⋊Q8C22⋊D1111yescharacteristic
292#127—111no—
293#127C22⋊D1111yescharacteristic
294#124—21no—
295#124—221no—
296#121—21no—
297#121—21no—
298#121—221no—
299#121—221no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—221no—
307C4×D4—221no—
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C42C22×D1111yescharacteristic
311#107—222no—
312C4⋊C8—21no—
313C4⋊C8—112no—
314C4⋊C8—221no—
315C4⋊C8—221no—
316C4⋊C8—221no—
317C4⋊C8C22⋊D1112yes—
318#103—22no—
319#103—222no—
320#102—22no—
321#102—222no—
322#102—222no—
323#102—222no—
324C22⋊C8—444no—
325C4×C8—221no—
326C4×C8—221no—
327C2×C11—21no—
328C2×C11—21no—
329C2×C11—82no—
330C2×C11—161no—
331C2×C11#199911yescharacteristic
332C2×C11#200611yescharacteristic
333C2×C11#201711yescharacteristic
334D11—161no—
335C24—21no—
336#41—41no—
337#41—41no—
338#41—41no—
339#41—41no—
340#41—441no—
341#41—441no—
342#41—441no—
343#41—441no—
344C2×Q8—21no—
345C2×Q8—221no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—41no—
355C2×D4—221no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—441no—
359C2×D4#432312yescomplemented
360C22×C4—21no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—441no—
367C22×C4D4×D1111yescharacteristic
368C22×C4#434111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370SD16—44no—
371SD16—444no—
372D8—44no—
373D8—444no—
374D8—882no—
375M16—41no—
376M16—41no—
377M16—441no—
378M16—441no—
379C2×C8—22no—
380C2×C8—222no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—441no—
384C2×C8—441no—
385C2×C8—442no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C42D4×D1111yescharacteristic
399C42D4×D1111yescharacteristic
400C42C2×C22⋊D1111yescharacteristic
401C42C2×C22⋊D1111yescharacteristic
402C11#1025411yescharacteristic, complemented, Sylow
403C23—22no—
404C23—42no—
405C23—42no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—441no—
410C23#6699211yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—441no—
414Q8—441no—
415D4—22no—
416D4—22no—
417D4—42no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—41no—
422D4—41no—
423D4—41no—
424D4—81no—
425D4—81no—
426D4—442no—
427D4—441no—
428D4—441no—
429D4—441no—
430D4—441no—
431D4—881no—
432D4—881no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—82no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—441no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4C2×#432311yescharacteristic
448C2×C4#6698511yescharacteristic
449C2×C4#6699011yescharacteristic
450C2×C4#6699011yescharacteristic
451C2×C4#6699111yescharacteristic
452C2×C4#6699211yescharacteristic
453C2×C4#6699311yescharacteristic
454C2×C4#6700211yescharacteristic
455C2×C4#6700311yescharacteristic
456C2×C4#6700611yescharacteristic
457C8—42no—
458C8—442no—
459C8—442no—
460C8—442no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—42no—
465C22—82no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22#1062265111yescharacteristic
475C22#1062265211yescharacteristic
476C22#1062283611yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—81no—
481C4—81no—
482C4—881no—
483C4#1062264911yescharacteristic
484C4#1062265011yescharacteristic
485C4#1062281111yescharacteristic
486C4#1062281411yescharacteristic
487C4#1062283011yescharacteristic
488C4#1062285111yescharacteristic
489C2—21no—
490C2—21no—
491C2—82no—
492C2—161no—
493C2—1761no—
494C2#1306961211yescharacteristic
495C2#1306965611yescharacteristic
496C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#10254
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079923C2semidirect
2. #13078080C2semidirect
3. #13069411C2semidirect
4. #13067067C2semidirect
5. #13067066C2semidirect
6. #13066490C2semidirect
7. C11×#3036C2semidirect
103. C2×D4×C11D8semidirect
157. #3036D11semidirect
359. C2×D4#4323semidirect
402. C11#10254semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130780802
#130694112
#130670672
#130670662
#130664902
C11×#30362
#1025411