Finite Group Databasebeta

← #14810380

Subgroups — #14810380

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic
2C2×#10622405C212yesmaximal, complemented
3#13076964C211yesmaximal, characteristic
4#13069756C212yesmaximal, complemented
5#13069755C212yesmaximal, complemented
6#13069575C212yesmaximal, complemented
7#13068924C211yesmaximal, characteristic
8#13068923C211yesmaximal, characteristic
9#13068921C211yesmaximal, characteristic
10C22⋊C8×Dic11C211yesmaximal, characteristic
11C11×#1872C211yesmaximal, characteristic
12C23×Dic22—21no—
13C2×C11×C22⋊Q8C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66997C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C22×Dic11⋊C4—21no—
19C22×C4×Dic11C2211yescharacteristic
20C2×#66941—21no—
21C2×#66941—21no—
22C2×#66941—28no—
23C2×#66941C2212yes—
24C2×#66941C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2212yes—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66880C2212yes—
31C2×C8×Dic11C2212yes—
32#10622589C2211yescharacteristic
33#10622587C2211yescharacteristic
34#10622585—21no—
35#10622585—21no—
36C2×#66874C2212yes—
37#10622555—21no—
38#10622555—21no—
39#10622405—28no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11D411yescharacteristic
50C23×Dic11D411yescharacteristic
51C22×Dic22—28no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—44no—
55C22×Dic22—44no—
56C22×Dic22C2311yescharacteristic
57C22×C8×C11C2312yes—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66C2×C22⋊Dic11—21no—
67#66997—24no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2312yes—
72#66977—22no—
73#66977—22no—
74C2×Dic11⋊C4—28no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88#66941—28no—
89#66941—28no—
90#66941—24no—
91#66941—24no—
92#66941—24no—
93#66941D418yes—
94C11×#103—24no—
95C11×C22⋊C8—22no—
96#66899—24no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C22⋊(C11⋊C8)—22no—
102#66880—24no—
103C8×Dic11—24no—
104#66874—24no—
105#25902—111nomaximal, Sylow
106C24×C11C2×D411yescharacteristic
107C2×Q8×C11—22no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—24no—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11SD1614yes—
134C22×Dic11Q1614yes—
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C2×Dic22—28no—
140C2×Dic22—28no—
141C2×Dic22—22no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—22no—
145C2×Dic22—432no—
146C2×Dic22—44no—
147C2×Dic22—44no—
148C2×Dic22—44no—
149C2×Dic22—44no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4C2×D414yes—
159C11×C22⋊C4—42no—
160C22⋊Dic11—42no—
161C4⋊Dic11—24no—
162C4⋊Dic11—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11C2×D414yes—
166Dic11⋊C4—28no—
167Dic11⋊C4—28no—
168Dic11⋊C4—42no—
169Dic11⋊C4—42no—
170Dic11⋊C4—42no—
171Dic11⋊C4—42no—
172Dic11⋊C4—42no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11—22no—
176C4×Dic11C2×D414yes—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C22×C4⋊Q8—111no—
181C2×#487—112no—
182#2857—111no—
183#2024—112no—
184#2024—112no—
185#1990—112no—
186#1872—111no—
187#1872—111no—
188#1872—111no—
189#1872D1111yescharacteristic
190C4×C22⋊C8—111no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11#12412yes—
196C23×C11C2×SD1612yes—
197C23×C11C2×Q1612yes—
198C23×C11C22×D411yescharacteristic
199Q8×C11—42no—
200Q8×C11—42no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—48no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11#12412yes—
216C2×C4×C11C22×D412yes—
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C112−1+412yes—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—28no—
225C2×Dic11—28no—
226C2×Dic11—24no—
227C2×Dic11—48no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11#12012yes—
237C2×Dic11#12012yes—
238C2×Dic11C2×SD1612yes—
239C2×Dic11C2×SD1612yes—
240C2×Dic11C2×Q1612yes—
241C2×Dic11C2×Q1612yes—
242C2×Dic11AGL(1,ℤ/8)12yes—
243C2×Dic11#13712yes—
244Dic22—416no—
245Dic22—416no—
246Dic22—42no—
247Dic22—42no—
248C8×C11—42no—
249C11⋊C8—42no—
250C23×Q8—221no—
251C2×C4⋊Q8—112no—
252C2×C4⋊Q8—112no—
253C2×C4⋊Q8—111no—
254C2×C4⋊Q8—221no—
255C2×C4⋊Q8—221no—
256C2×C4⋊Q8—228no—
257C2×C22⋊Q8—111no—
258C2×C22⋊Q8C2×D1111yescharacteristic
259C22×C4⋊C4—111no—
260C22×C4⋊C4—221no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C42—111no—
263#487—228no—
264C2×#103—112no—
265C2×#103—112no—
266C2×#103—112no—
267C2×#103C2×D1112yes—
268C2×C22⋊C8—111no—
269C2×C22⋊C8C2×D1111yescharacteristic
270C2×C4×C8—112no—
271#391—111no—
272#391—111no—
273#389—221no—
274#389—221no—
275#384—111no—
276#380—221no—
277#380—221no—
278#340—112no—
279#340—112no—
280#340—112no—
281#340C2×D1112yes—
282#336—112no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11#48714yescomplemented
290C22×C11C2×#12011yescharacteristic
291C22×C11C2×#12411yescharacteristic
292C22×C11#53611yescharacteristic
293C22×C11C22×SD1611yescharacteristic
294C22×C11C22×Q1611yescharacteristic
295C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C11C2×#13711yescharacteristic
297C4×C11—22no—
298C4×C11—44no—
299C4×C11—81no—
300C4×C11—81no—
301C4×C11#54812yes—
302C4×C11#54812yes—
303Dic11—22no—
304Dic11—22no—
305Dic11—44no—
306Dic11—81no—
307Dic11—81no—
308Dic11#45014yes—
309Dic11#45114yes—
310C22×Q8—111no—
311C22×Q8—222no—
312C22×Q8—222no—
313C22×Q8—228no—
314C22×Q8—444no—
315C22×Q8—444no—
316C22×Q8C22×D1111yescharacteristic
317C23×C4—21no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—221no—
321C23×C4C22×D1111yescharacteristic
322C22×C8—112no—
323C22×C8C22×D1112yes—
324C4⋊Q8—118no—
325C4⋊Q8—224no—
326C4⋊Q8—224no—
327C4⋊Q8—224no—
328C4⋊Q8—228no—
329C4⋊Q8—228no—
330C4⋊Q8—224no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—222no—
334C22⋊Q8—222no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—228no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—221no—
354C2×C42—111no—
355C2×C42—111no—
356C2×C42—111no—
357C2×C42—111no—
358C2×C42—224no—
359#103—24no—
360#103—224no—
361#103—224no—
362#103—224no—
363C22⋊C8—22no—
364C22⋊C8—222no—
365C4×C8—224no—
366#95—221no—
367#95—221no—
368#95—221no—
369#95—221no—
370C2×C11—24no—
371C2×C11#243611yescharacteristic
372C2×C11C2×#45011yescharacteristic
373C2×C11C2×#45111yescharacteristic
374C2×C11C2×#48711yescharacteristic
375C2×C11#314111yescharacteristic
376C2×C11#322911yescharacteristic
377C2×C11#323011yescharacteristic
378C24D4×D1111yescharacteristic
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—228no—
384C2×Q8—228no—
385C2×Q8—221no—
386C2×Q8—222no—
387C2×Q8—221no—
388C2×Q8—222no—
389C2×Q8—444no—
390C2×Q8—444no—
391C2×Q8—444no—
392C2×Q8—4432no—
393C2×Q8—444no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—114no—
405C22×C4—114no—
406C22×C4—111no—
407C22×C4—111no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—224no—
413C22×C4—222no—
414C22×C4—221no—
415C22×C4—221no—
416C22×C4—442no—
417C22×C4—442no—
418C22×C4#433912yes—
419C22×C4D4×D1111yescharacteristic
420C22×C4#434112yes—
421C22×C4C23×D1111yescharacteristic
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8—222no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—42no—
433C4⋊C4—114no—
434C4⋊C4—228no—
435C4⋊C4—228no—
436C4⋊C4—224no—
437C4⋊C4—222no—
438C4⋊C4—221no—
439C4⋊C4—221no—
440C4⋊C4—442no—
441C4⋊C4—442no—
442C4⋊C4—442no—
443C4⋊C4—442no—
444C4⋊C4—442no—
445C4⋊C4D4×D1114yes—
446C22⋊C4—42no—
447C22⋊C4—442no—
448C42—114no—
449C42—222no—
450C42—222no—
451C42—222no—
452C11#2590211yescharacteristic, complemented, Sylow
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23#6693812yes—
458C23SD16×D1112yes—
459C23Q16×D1112yes—
460C23C2×D4×D1111yescharacteristic
461Q8—42no—
462Q8—42no—
463Q8—4416no—
464Q8—4416no—
465Q8—442no—
466Q8—442no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—48no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—112no—
482C2×C4—112no—
483C2×C4—112no—
484C2×C4—112no—
485C2×C4—112no—
486C2×C4—112no—
487C2×C4—112no—
488C2×C4—112no—
489C2×C4—228no—
490C2×C4—228no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—224no—
496C2×C4—448no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4#6693812yes—
506C2×C4C2×#433911yescharacteristic
507C2×C4C2×D4×D1112yes—
508C2×C4C2×#434111yescharacteristic
509C2×C4#6704312yes—
510C8—42no—
511C8—442no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22#1062240514yescomplemented
519C22C2×#6693811yescharacteristic
520C22D11×#12011yescharacteristic
521C22#1062317911yescharacteristic
522C22C2×SD16×D1111yescharacteristic
523C22C2×Q16×D1111yescharacteristic
524C22D11×AGL(1,ℤ/8)11yescharacteristic
525C22D11×#13711yescharacteristic
526C4—22no—
527C4—44no—
528C4—81no—
529C4—81no—
530C4—114no—
531C4—114no—
532C4—222no—
533C4—222no—
534C4—444no—
535C4—881no—
536C4—881no—
537C4#1062308312yes—
538C4#1062312912yes—
539C2—24no—
540C2#1307227211yescharacteristic
541C2D11×#45011yescharacteristic
542C2D11×#45111yescharacteristic
543C2C2×#1062240511yescharacteristic
544C2#1307900711yescharacteristic
545C2#1307975811yescharacteristic
546C2#1307976511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1872D11
hypocenterC11#25902
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#10622405C2semidirect
4. #13069756C2semidirect
5. #13069755C2semidirect
6. #13069575C2semidirect
289. C22×C11#487semidirect
452. C11#25902semidirect
518. C22#10622405semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106224052
#130769642
#130697562
#130697552
#130695752
#130689242
#130689232
#130689212
C22⋊C8×Dic112
C11×#18722
#2590211