Finite Group Databasebeta

← #14788515

Subgroups — #14788515

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622696C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13073534C211yesmaximal, characteristic, complemented
4#13069852C212yesmaximal, complemented
5#13069693C212yesmaximal
6#13069553C211yesmaximal, characteristic, complemented
7#13069419C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal, complemented
9#13068870C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C2×C11×#556C211yesmaximal, characteristic, complemented
12C11×#556—24no—
13C11×#556—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C2×#66999—21no—
23C22×#4325C2212yes—
24C22×#4323C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66896C2211yescharacteristic
30C2×#66896C2212yes—
31#10622696—24no—
32C4×#4323—24no—
33#10622607—22no—
34#10622600—21no—
35C2×#66873C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622552C2212yes—
38#10622548C2211yescharacteristic
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C11×#126—216no—
54C11×#124—24no—
55C11×#124—24no—
56C11×C22⋊Q8—28no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11D414yes—
63C11×#117—28no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C42×C11—22no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76#66999—44no—
77C2×#4325—24no—
78C2×#4325—24no—
79C2×#4325—42no—
80C2×#4323—22no—
81C2×#4323—22no—
82C2×#4323—22no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2312yes—
90C2×Dic11⋊C4—22no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2311yescharacteristic
94C4×D44—22no—
95C4×D44—22no—
96#66899—24no—
97#66899—24no—
98#66899—42no—
99#66896—22no—
100#66896—42no—
101C11⋊#95—22no—
102#66873—22no—
103#66871—22no—
104C4⋊(C11⋊C8)—22no—
105C4×C11⋊C8—22no—
106#24185—111nomaximal, Sylow
107C24×C11—21no—
108C23×D11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11C2×D414yes—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11C2×D412yes—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—22no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44#4112yes—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—28no—
154C11×C22⋊C4—24no—
155C42×C11—28no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11C2×D412yes—
159C42×C11C2×D412yes—
160#4325—48no—
161#4323—28no—
162(C2×D11)⋊C4—44no—
163(C2×D11)⋊C4—42no—
164(C2×D11)⋊C4—82no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—42no—
170C4⋊Dic11—81no—
171Dic11⋊C4—44no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8#4112yes—
181C2×#556D1111yescharacteristic, complemented
182C2×#461—111no—
183C2×C4×D8—111no—
184#2538—111no—
185#2042—112no—
186#2012—112no—
187#1984—111no—
188#1956—111no—
189#1880—112no—
190#1863—112no—
191#1802—111no—
192C23×C11—22no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11C22×D411yescharacteristic
200C22×D11—22no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207Q8×C11—24no—
208Q8×C11—24no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—44no—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—41no—
215D4×C11—41no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—48no—
231C2×C4×C11#12012yes—
232C2×C4×C11#12012yes—
233C2×C4×C11#13512yes—
234C2×C4×C11AGL(1,ℤ/8)12yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247D44—22no—
248D44—22no—
249D44—41no—
250D44—41no—
251C4×D11—84no—
252C11⋊C8—22no—
253C11⋊C8—41no—
254C11⋊C8—42no—
255C22×SD16—112no—
256C22×D8—111no—
257#556—24no—
258#556—24no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×#126—22no—
261C2×#124C2×D1112yes—
262C2×C22⋊Q8—21no—
263C2×C22⋊Q8—221no—
264C2×C4×Q8C2×D1112yes—
265C2×C4×Q8C2×D1111yescharacteristic
266C2×C4×D4—111no—
267C2×C4×D4C2×D1111yescharacteristic
268C2×#117—21no—
269#461—224no—
270C4×D8—224no—
271C2×#107—111no—
272C2×C4⋊C8—111no—
273C2×#103—112no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#102—111no—
277C2×#102—111no—
278C2×#102—112no—
279C2×C4×C8—111no—
280#396—222no—
281#390—112no—
282#389—112no—
283#384—111no—
284#380—221no—
285#340—112no—
286#336—112no—
287#336—112no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11C2×#12011yescharacteristic
296C22×C11#54811yescharacteristic
297C22×C11#55011yescharacteristic
298C22×C11C2×#13511yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C11#57711yescharacteristic
301C22×C11#57811yescharacteristic
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C4×C11—22no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11#44914yes—
315C4×C11#52511yescharacteristic
316C4×C11#53711yescharacteristic
317C4×C11#54611yescharacteristic
318C4×C11#54711yescharacteristic
319Dic11—82no—
320Dic11—81no—
321C22×Q8C22⋊D1111yescharacteristic
322C22×Q8C22×D1112yes—
323C22×D4—111no—
324C22×D4C22×D1111yescharacteristic
325C23×C4—21no—
326C23×C4—221no—
327C2×SD16—224no—
328C2×SD16—224no—
329C2×SD16—442no—
330C2×D8—222no—
331C2×D8—222no—
332C2×D8—222no—
333C22×C8—111no—
334C22×C8—112no—
335C22×C8—111no—
336C4⋊Q8—22no—
337C4⋊Q8C22⋊D1114yes—
338#126—216no—
339#124—24no—
340#124—24no—
341C22⋊Q8—28no—
342C22⋊Q8—444no—
343C4×Q8—24no—
344C4×Q8—24no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×D4—22no—
348C4×D4—222no—
349C4×D4—222no—
350C4×D4C22⋊D1114yes—
351#117—28no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—112no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4C22⋊D1111yescharacteristic
361C2×C4⋊C4C22⋊D1112yes—
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C42—22no—
370C2×C42C22×D1112yes—
371C2×C42C22×D1111yescharacteristic
372#107—222no—
373C4⋊C8—222no—
374#103—224no—
375#103—224no—
376#103—442no—
377#102—222no—
378#102—222no—
379#102—442no—
380C4×C8—222no—
381#95—222no—
382C2×C11—82no—
383C2×C11#240711yescharacteristic
384C2×C11C2×#44911yescharacteristic
385C2×C11#301311yescharacteristic
386C2×C11#336011yescharacteristic
387C2×C11#336711yescharacteristic
388C2×C11#339311yescharacteristic
389C2×C11#339711yescharacteristic
390D11—82no—
391C24—21no—
392C24—221no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8C2×C22⋊D1114yes—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—112no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4C2×C22⋊D1112yes—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4C2×C22⋊D1112yes—
425C22×C4C2×C22⋊D1112yes—
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429SD16—448no—
430D8—228no—
431C2×C8—112no—
432C2×C8—221no—
433C2×C8—221no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—222no—
440C4⋊C4—28no—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—24no—
445C4⋊C4—21no—
446C4⋊C4—222no—
447C4⋊C4—222no—
448C4⋊C4—221no—
449C4⋊C4—221no—
450C4⋊C4—444no—
451C4⋊C4—442no—
452C4⋊C4—881no—
453C4⋊C4C2×C22⋊D1112yes—
454C22⋊C4—28no—
455C22⋊C4—28no—
456C22⋊C4—24no—
457C22⋊C4—444no—
458C22⋊C4—442no—
459C22⋊C4—882no—
460C42—28no—
461C42—22no—
462C42—22no—
463C42C2×C22⋊D1112yes—
464C42C2×C22⋊D1112yes—
465C11#2418511yescharacteristic, complemented, Sylow
466C23—22no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—222no—
474C23—441no—
475C23—441no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23C22×C22⋊D1111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—44no—
485Q8—42no—
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490D4—222no—
491D4—222no—
492D4—441no—
493D4—441no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—48no—
509C2×C4—442no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—441no—
515C2×C4—884no—
516C2×C4#6700212yes—
517C2×C4#6700312yes—
518C2×C4#6700612yes—
519C2×C4#6700612yes—
520C2×C4#41×D1111yescharacteristic
521C2×C4#41×D1111yescharacteristic
522C2×C4#6704211yescharacteristic
523C2×C4#6704311yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—222no—
527C8—442no—
528C8—441no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—442no—
537C22—442no—
538C22—442no—
539C22—881no—
540C22—881no—
541C22—881no—
542C22—881no—
543C22C2×#6700211yescharacteristic
544C22C2×#6700311yescharacteristic
545C22#1062336211yescharacteristic
546C22#1062336511yescharacteristic
547C22#1062336811yescharacteristic
548C22#1062336911yescharacteristic
549C22C2×#6700611yescharacteristic
550C4—22no—
551C4—42no—
552C4—42no—
553C4—44no—
554C4—42no—
555C4—882no—
556C4—881no—
557C4#1062285114yes—
558C4#1062335511yescharacteristic
559C4#1062335911yescharacteristic
560C4#1062336011yescharacteristic
561C4#1062336411yescharacteristic
562C2—82no—
563C2—882no—
564C2#1307195511yescharacteristic
565C2C2×#1062285111yescharacteristic
566C2#1307793111yescharacteristic
567C2#1308126111yescharacteristic
568C2#1308133011yescharacteristic
569C2#1308160011yescharacteristic
570C2#1308163611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#556D11
hypocenterC11#24185
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10622696C2semidirect
3. #13073534C2semidirect
4. #13069852C2semidirect
6. #13069553C2semidirect
7. #13069419C2semidirect
8. #13068971C2semidirect
9. #13068870C2semidirect
10. #13068616C2semidirect
11. C2×C11×#556C2semidirect
181. C2×#556D11semidirect
465. C11#24185semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
C2×C4×#43232
#130735342
#130698522
#130696932
#130695532
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