Finite Group Databasebeta

← #14788835

Subgroups — #14788835

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66927C211yesmaximal, characteristic
2C2×#10622640C212yesmaximal, complemented
3C2×#10622659C212yesmaximal, complemented
4#13069850C212yesmaximal, complemented
5#13069703C212yesmaximal, complemented
6#13069543C212yesmaximal, complemented
7#13068596C211yesmaximal, characteristic, complemented
8#13068546C212yesmaximal, complemented
9C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
10C23×D44—21no—
11C23×D44—21no—
12C23×D44C2212yes—
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic, complemented
15C22×C42×C11C2211yescharacteristic
16C22×#4325C2214yescomplemented
17C2×#66927—21no—
18C2×#66927—21no—
19C2×#66927—28no—
20C2×#66927C2212yes—
21C2×#66927C2212yes—
22C11×#391C2211yescharacteristic, complemented
23C11×#389C2211yescharacteristic, complemented
24C11×#387—21no—
25C11×#385—21no—
26C11×#380C2211yescharacteristic
27C4×C11×C4⋊C4—21no—
28C4×C11×C4⋊C4C2211yescharacteristic, complemented
29C4×C11×C22⋊C4—21no—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622659—28no—
32#10622640—28no—
33C2×#66873C2214yescomplemented
34C2×#66873C2214yescomplemented
35C2×#66873C2214yescomplemented
36C2×C4⋊(C11⋊C8)C2212yescomplemented
37#10622162C2212yescomplemented
38C24×D11—22no—
39C22×Q8×C11C2311yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C22×D44—28no—
44C22×D44—28no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—22no—
49C22×D44—22no—
50C22×D44—28no—
51C22×D44—24no—
52C22×D44—24no—
53C22×D44—44no—
54C22×D44—44no—
55C22×D44—44no—
56C22×D44—44no—
57C22×D44—44no—
58C22×D44C2314yes—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8D414yescomplemented
61C4×Q8×C11—24no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—24no—
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×#4325—28no—
78C2×#4325—28no—
79C2×#4325—44no—
80C22×C11⋊C8C2314yes—
81#66927—28no—
82#66927—28no—
83#66927—28no—
84#66927—24no—
85#66927D418yes—
86C11×#95—21no—
87C11×#95—21no—
88C11×#95—21no—
89C11×#95—21no—
90C11×#95—21no—
91C22⋊(C11⋊C8)—24no—
92#66873—28no—
93#66873—28no—
94#66873—44no—
95C4⋊(C11⋊C8)—24no—
96#24211—111nomaximal, Sylow
97C24×C11C2×D411yescharacteristic
98C23×D11—28no—
99C23×D11—24no—
100C23×D11—44no—
101C23×D11—44no—
102C23×D11—44no—
103C23×D11—44no—
104C23×D11—44no—
105C23×D11—44no—
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C2×D412yescomplemented
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11SD1614yescomplemented
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C2×D44—28no—
131C2×D44—28no—
132C2×D44—28no—
133C2×D44—28no—
134C2×D44—28no—
135C2×D44—24no—
136C2×D44—24no—
137C2×D44—24no—
138C2×D44—24no—
139C2×D44—24no—
140C2×D44—416no—
141C2×D44—416no—
142C2×D44—432no—
143C2×D44—44no—
144C2×D44—44no—
145C2×D44—44no—
146C2×D44—44no—
147C2×D44—44no—
148C2×D44—432no—
149C2×D44—44no—
150C2×D44—44no—
151C2×D44—44no—
152C2×D44—44no—
153C2×D44—44no—
154C2×D44C2×D418yes—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4C2×D412yescomplemented
162C11×C22⋊C4—24no—
163C11×C22⋊C4—42no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—42no—
168C42×C11—42no—
169C42×C11C2×D414yes—
170#4325—416no—
171C2×C11⋊C8—24no—
172C2×C11⋊C8—24no—
173C2×C11⋊C8—24no—
174C22×#127—111no—
175C2×#460—112no—
176C2×#450—112no—
177C4×C22⋊Q8D1111yescharacteristic, complemented
178#2041—112no—
179#2014—112no—
180#1982—112no—
181#1797—111no—
182#1786—112no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11#12112yes—
188C23×C11C2×SD1612yes—
189C23×C11AGL(1,ℤ/8)12yes—
190C23×C11C22×D411yescharacteristic
191C22×D11—28no—
192C22×D11—416no—
193C22×D11—416no—
194C22×D11—416no—
195C22×D11—44no—
196C22×D11—44no—
197C22×D11—44no—
198C22×D11—44no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—88no—
202C22×D11—88no—
203C22×D11—88no—
204C22×D11—88no—
205Q8×C11—24no—
206Q8×C11—42no—
207C2×C4×C11—28no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—28no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11#12012yes—
232C2×C4×C11#12012yes—
233C2×C4×C11#12112yes—
234C2×C4×C11C2×SD1612yes—
235C2×C4×C11C2×SD1612yes—
236C2×C4×C11AGL(1,ℤ/8)12yes—
237C2×C4×C11AGL(1,ℤ/8)12yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)12yes—
242D44—28no—
243D44—28no—
244D44—416no—
245D44—416no—
246D44—416no—
247D44—416no—
248D44—44no—
249D44—44no—
250D44—416no—
251C11⋊C8—44no—
252C23×D4—112no—
253C23×D4—221no—
254C23×D4—221no—
255C22×SD16—114no—
256C2×#127—112no—
257C2×#127—112no—
258C2×#127—228no—
259C2×#127—221no—
260C2×#127—221no—
261C2×C22⋊Q8C2×D1111yescharacteristic
262C2×C4×Q8C2×D1111yescharacteristic, complemented
263C22×C42C2×D1111yescharacteristic
264#460—228no—
265#450—228no—
266C2×C4⋊C8—112no—
267C2×#102—114no—
268C2×#102—114no—
269C2×#102—114no—
270C2×C22⋊C8—112no—
271#391C2×D1111yescharacteristic, complemented
272#389C2×D1111yescharacteristic, complemented
273#387—21no—
274#385—21no—
275#380C2×D1111yescharacteristic
276C4×C4⋊C4—21no—
277C4×C4⋊C4C2×D1111yescharacteristic, complemented
278C4×C22⋊C4—21no—
279#336—112no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11#46014yescomplemented
287C22×C11C2×#12011yescharacteristic
288C22×C11C2×#12111yescharacteristic
289C22×C11#53511yescharacteristic
290C22×C11C22×SD1611yescharacteristic
291C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C2×D11—48no—
295C2×D11—48no—
296C2×D11—48no—
297C2×D11—832no—
298C2×D11—84no—
299C2×D11—84no—
300C2×D11—84no—
301C2×D11—84no—
302C4×C11—22no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—81no—
309C4×C11—81no—
310C4×C11#45014yescomplemented
311C4×C11D4212yes—
312C4×C11#54612yes—
313C25—222no—
314C22×Q8C22×D1111yescharacteristic
315C22×D4—114no—
316C22×D4—228no—
317C22×D4—228no—
318C22×D4—228no—
319C22×D4—224no—
320C22×D4—224no—
321C22×D4—222no—
322C22×D4—222no—
323C22×D4—222no—
324C22×D4—222no—
325C22×D4—222no—
326C22×D4—444no—
327C22×D4—444no—
328C22×D4—444no—
329C22×D4—444no—
330C22×D4—444no—
331C23×C4C22⋊D1111yescharacteristic
332C23×C4C22⋊D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334C2×SD16—228no—
335C2×SD16—228no—
336C2×SD16—444no—
337C22×C8—114no—
338#127—118no—
339#127—228no—
340#127—228no—
341#127—228no—
342#127—224no—
343C22⋊Q8—22no—
344C22⋊Q8D4414yescomplemented
345C4×Q8—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C22×D1111yescharacteristic
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C42—24no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42C22⋊D1111yescharacteristic
358C2×C42C22⋊D1111yescharacteristic
359C2×C42C22×D1111yescharacteristic
360C2×C42C22×D1111yescharacteristic
361C4⋊C8—224no—
362#102—228no—
363#102—228no—
364#102—444no—
365C22⋊C8—224no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371C2×C11—24no—
372C2×C11#240811yescharacteristic
373C2×C11C2×#45011yescharacteristic
374C2×C11#300311yescharacteristic
375C2×C11C2×#46011yescharacteristic
376C2×C11#303811yescharacteristic
377C2×C11#320811yescharacteristic
378C2×C11#321711yescharacteristic
379D11—88no—
380C24—228no—
381C24—224no—
382C24—444no—
383C24—444no—
384C24—444no—
385C24—444no—
386C24—444no—
387C24—444no—
388C24C2×C22⋊D1111yescharacteristic
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8C2×D4412yescomplemented
393C2×D4—118no—
394C2×D4—228no—
395C2×D4—228no—
396C2×D4—228no—
397C2×D4—228no—
398C2×D4—228no—
399C2×D4—224no—
400C2×D4—224no—
401C2×D4—224no—
402C2×D4—224no—
403C2×D4—224no—
404C2×D4—4416no—
405C2×D4—4416no—
406C2×D4—4432no—
407C2×D4—444no—
408C2×D4—444no—
409C2×D4—444no—
410C2×D4—444no—
411C2×D4—444no—
412C2×D4—4432no—
413C2×D4—444no—
414C2×D4—444no—
415C2×D4—444no—
416C2×D4—444no—
417C2×D4—444no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4#432514yescomplemented
430C22×C4C2×D4412yes—
431C22×C4#433912yes—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438SD16—4416no—
439C2×C8—224no—
440C2×C8—224no—
441C2×C8—224no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—42no—
447C4⋊C4—42no—
448C4⋊C4C2×D4412yescomplemented
449C22⋊C4—24no—
450C22⋊C4—42no—
451C42—22no—
452C42—22no—
453C42—22no—
454C42—42no—
455C42—42no—
456C42D4×D1114yes—
457C11#2421111yescharacteristic, complemented, Sylow
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—228no—
463C23—4416no—
464C23—4416no—
465C23—4416no—
466C23—444no—
467C23—444no—
468C23—444no—
469C23—444no—
470C23—444no—
471C23—444no—
472C23—888no—
473C23—888no—
474C23—888no—
475C23—888no—
476C23#6698312yes—
477C23C2×#432512yes—
478C23#6700212yes—
479C23C22×C22⋊D1111yescharacteristic
480Q8—24no—
481Q8—42no—
482D4—228no—
483D4—228no—
484D4—4416no—
485D4—4416no—
486D4—4416no—
487D4—4416no—
488D4—444no—
489D4—444no—
490D4—4416no—
491C2×C4—28no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4#6698312yes—
516C2×C4#6699012yes—
517C2×C4#6699012yes—
518C2×C4C2×#432512yes—
519C2×C4C2×#432512yes—
520C2×C4#6700212yes—
521C2×C4#6700212yes—
522C2×C4C22×D4411yescharacteristic
523C2×C4C2×#433911yescharacteristic
524C2×C4C2×D4×D1112yes—
525C2×C4#6704212yes—
526C8—444no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—448no—
534C22—448no—
535C22—448no—
536C22—8832no—
537C22—884no—
538C22—884no—
539C22—884no—
540C22—884no—
541C22#1062264014yescomplemented
542C22C2×#6698311yescharacteristic
543C22C2×#6699011yescharacteristic
544C22C22×#432511yescharacteristic
545C22C2×#6700211yescharacteristic
546C22C2×#6700211yescharacteristic
547C22C2×#6700211yescharacteristic
548C22#1062336111yescharacteristic
549C4—22no—
550C4—22no—
551C4—22no—
552C4—22no—
553C4—42no—
554C4—42no—
555C4—81no—
556C4—81no—
557C4#1062265914yescomplemented
558C4D4×D4412yes—
559C4#1062308112yes—
560C2—24no—
561C2—888no—
562C2#1307197211yescharacteristic
563C2C2×#1062265911yescharacteristic
564C2#1307784211yescharacteristic
565C2C2×#1062264011yescharacteristic
566C2#1307809611yescharacteristic
567C2#1307955411yescharacteristic
568C2#1307963111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC22×#66927C2
hypercenterC4×C22⋊Q8D11
hypocenterC11#24211
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622640C2semidirect
3. C2×#10622659C2semidirect
4. #13069850C2semidirect
5. #13069703C2semidirect
6. #13069543C2semidirect
7. #13068596C2semidirect
8. #13068546C2semidirect
9. C4×C11×C22⋊Q8C2semidirect
14. C2×C4×Q8×C11C22semidirect
16. C22×#4325C22semidirect
22. C11×#391C22semidirect
23. C11×#389C22semidirect
28. C4×C11×C4⋊C4C22semidirect
33. C2×#66873C22semidirect
34. C2×#66873C22semidirect
35. C2×#66873C22semidirect
36. C2×C4⋊(C11⋊C8)C22semidirect
37. #10622162C22semidirect
60. C11×C22⋊Q8D4semidirect
109. C2×Q8×C11C2×D4semidirect
121. C22×C4×C11SD16semidirect
161. C11×C4⋊C4C2×D4semidirect
177. C4×C22⋊Q8D11semidirect
262. C2×C4×Q8C2×D11semidirect
271. #391C2×D11semidirect
272. #389C2×D11semidirect
277. C4×C4⋊C4C2×D11semidirect
286. C22×C11#460semidirect
310. C4×C11#450semidirect
344. C22⋊Q8D44semidirect
392. C2×Q8C2×D44semidirect
429. C22×C4#4325semidirect
448. C4⋊C4C2×D44semidirect
457. C11#24211semidirect
541. C22#10622640semidirect
557. C4#10622659semidirect

Maximal subgroups

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

subgroupindex
C22×#669272
C2×#106226402
C2×#106226592
#130698502
#130697032
#130695432
#130685962
#130685462
C4×C11×C22⋊Q82
#2421111