Finite Group Databasebeta

← #14790149

Subgroups — #14790149

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13073534C211yesmaximal, characteristic, complemented
4#13069951C212yesmaximal, complemented
5#13069759C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069553C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal
9#13068877C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C2×C11×#554C211yesmaximal, characteristic, complemented
12C11×#554—24no—
13C11×#554—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2212yes—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22C2×#66999—21no—
23C22×#4323C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C2×#66896C2212yes—
26C2×#66896C2211yescharacteristic
27#10622697—24no—
28C4×#4323—24no—
29#10622607—22no—
30#10622600—21no—
31C2×#66873C2212yes—
32C2×#66873C2211yescharacteristic
33C2×#66872C2212yes—
34C2×#66871C2211yescharacteristic
35#10622552C2212yes—
36#10622548C2211yescharacteristic
37#10622541C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11—22no—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8D414yes—
54C11×#125—24no—
55C11×#125—24no—
56C11×C22⋊Q8—28no—
57C11×C22⋊Q8—216no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×D4×C11—24no—
61C4×D4×C11—24no—
62C4×D4×C11—22no—
63C4×D4×C11D414yes—
64C2×C11×C4⋊C4—28no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D412yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76#66999—44no—
77C2×#4323—22no—
78C2×#4323—22no—
79C2×#4323Q814yescomplemented
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—22no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C4×D44—22no—
92C4×D44—22no—
93#66896—22no—
94#66896—24no—
95C11⋊#95—22no—
96#66873—22no—
97#66873—24no—
98#66872—24no—
99#66871—22no—
100C4⋊(C11⋊C8)—22no—
101C4×C11⋊C8—22no—
102#24327—111nomaximal, Sylow
103C24×C11—21no—
104C23×D11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—24no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—81no—
110C2×Q8×C11—81no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11C2×D412yes—
115C2×D4×C11C2×Q812yes—
116C2×D4×C11#4112yes—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—28no—
120C22×C4×C11—24no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—82no—
124C22×C4×C11—82no—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—21no—
131C22×Dic11—22no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44C2×Q812yes—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4C2×D412yes—
149C11×C4⋊C4C2×D414yes—
150C11×C22⋊C4—28no—
151C11×C22⋊C4—24no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156#4323—28no—
157(C2×D11)⋊C4—44no—
158(C2×D11)⋊C4—42no—
159(C2×D11)⋊C4—82no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—42no—
165C4⋊Dic11—81no—
166Dic11⋊C4—44no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8C2×Q812yes—
176C2×#554D1111yescharacteristic, complemented
177C2×#476—111no—
178C2×C4×D8—111no—
179#2538—111no—
180#2059—112no—
181#2025—112no—
182#1990—111no—
183#1984—111no—
184#1879—112no—
185#1864—112no—
186#1802—111no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202Q8×C11—44no—
203Q8×C11—84no—
204D4×C11—22no—
205D4×C11—22no—
206D4×C11—22no—
207D4×C11C22⋊Q814yescomplemented
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—48no—
223C2×C4×C11—88no—
224C2×C4×C11#12012yes—
225C2×C4×C11#12012yes—
226C2×C4×C11#13512yes—
227C2×C4×C11AGL(1,ℤ/8)12yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×Q811yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C112−1+411yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C2×Dic11—41no—
235C2×Dic11—42no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240D44—22no—
241D44—22no—
242D44—41no—
243D44—41no—
244C4×D11—84no—
245C11⋊C8—22no—
246C11⋊C8—41no—
247C11⋊C8—42no—
248C22×D8—111no—
249#554—24no—
250#554—24no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C2×#125C2×D1112yes—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—22no—
255C2×C22⋊Q8—221no—
256C2×C4×Q8C2×D1111yescharacteristic
257C2×C4×D4—111no—
258C2×C4×D4C2×D1112yes—
259C2×C4×D4C2×D1111yescharacteristic
260C22×C4⋊C4—21no—
261#476—224no—
262C4×D8—224no—
263C2×#107—111no—
264C2×#106—112no—
265C2×C4⋊C8—111no—
266C2×#102—112no—
267C2×#102—111no—
268C2×#102—112no—
269C2×#102—111no—
270C2×C4×C8—111no—
271#396—222no—
272#390—112no—
273#389—112no—
274#384—111no—
275#380—221no—
276#340—112no—
277#340—112no—
278#340—112no—
279#336—112no—
280#336—112no—
281C22×C11—24no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11C2×#12011yescharacteristic
289C22×C11#54811yescharacteristic
290C22×C11D4×Q811yescharacteristic
291C22×C11C2×#13511yescharacteristic
292C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C11#57611yescharacteristic
294C22×C11#57711yescharacteristic
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—44no—
307C4×C11#44914yes—
308C4×C11C2×C22⋊Q811yescharacteristic
309C4×C11#53611yescharacteristic
310C4×C11#54811yescharacteristic
311C4×C11D4×Q811yescharacteristic
312Dic11—82no—
313Dic11—81no—
314C22×Q8—21no—
315C22×Q8C22⋊D1111yescharacteristic
316C22×D4—111no—
317C22×D4C22×D1111yescharacteristic
318C23×C4—21no—
319C23×C4—22no—
320C23×C4—221no—
321C2×D8—114no—
322C2×D8—222no—
323C2×D8—222no—
324C22×C8—111no—
325C22×C8—111no—
326C22×C8—112no—
327C4⋊Q8—22no—
328C4⋊Q8C22⋊D1114yes—
329#125—24no—
330#125—24no—
331C22⋊Q8—28no—
332C22⋊Q8—216no—
333C22⋊Q8—444no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×D4—24no—
337C4×D4—24no—
338C4×D4—22no—
339C4×D4—222no—
340C4×D4—222no—
341C4×D4C22⋊D1114yes—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C22⋊D1111yescharacteristic
352C2×C4⋊C4C22⋊D1112yes—
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C4⋊C4C22×D1112yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42C22×D1112yes—
361C2×C42C22×D1111yescharacteristic
362#107—222no—
363#106—224no—
364C4⋊C8—222no—
365#102—224no—
366#102—222no—
367#102—222no—
368#102—224no—
369C4×C8—222no—
370#95—222no—
371C2×C11—44no—
372C2×C11#240911yescharacteristic
373C2×C11C2×#44911yescharacteristic
374C2×C11#301211yescharacteristic
375C2×C11#336011yescharacteristic
376C2×C11#336611yescharacteristic
377C2×C11#338011yescharacteristic
378C2×C11#338411yescharacteristic
379D11—82no—
380C24—21no—
381C24—221no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—24no—
386C2×Q8—81no—
387C2×Q8—81no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—112no—
392C2×D4—221no—
393C2×D4—221no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4Q8×D1112yes—
398C2×D4#434312yes—
399C2×D4C2×C22⋊D1112yes—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—28no—
403C22×C4—24no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—82no—
407C22×C4—82no—
408C22×C4—221no—
409C22×C4—222no—
410C22×C4—442no—
411C22×C4—442no—
412C22×C4—442no—
413C22×C4C2×C22⋊D1112yes—
414C22×C4C2×C22⋊D1112yes—
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C23×D1111yescharacteristic
418D8—228no—
419C2×C8—112no—
420C2×C8—221no—
421C2×C8—221no—
422C2×C8—222no—
423C2×C8—221no—
424C2×C8—221no—
425C2×C8—222no—
426C2×C8—221no—
427C2×C8—222no—
428C4⋊C4—28no—
429C4⋊C4—28no—
430C4⋊C4—22no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—221no—
438C4⋊C4—221no—
439C4⋊C4—444no—
440C4⋊C4—442no—
441C4⋊C4—881no—
442C4⋊C4C2×C22⋊D1114yes—
443C4⋊C4C2×C22⋊D1112yes—
444C22⋊C4—28no—
445C22⋊C4—24no—
446C22⋊C4—444no—
447C22⋊C4—442no—
448C22⋊C4—882no—
449C42—22no—
450C42—22no—
451C42C2×C22⋊D1112yes—
452C42C2×C22⋊D1112yes—
453C11#2432711yescharacteristic, complemented, Sylow
454C23—22no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—222no—
462C23—441no—
463C23—441no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23C22×C22⋊D1111yescharacteristic
469Q8—44no—
470Q8—84no—
471D4—22no—
472D4—22no—
473D4—22no—
474D4—222no—
475D4—222no—
476D4—441no—
477D4—441no—
478D4#6699914yescomplemented
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—48no—
494C2×C4—88no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—442no—
500C2×C4—441no—
501C2×C4—884no—
502C2×C4#6700212yes—
503C2×C4#6700312yes—
504C2×C4#6700612yes—
505C2×C4#6700612yes—
506C2×C4C2×Q8×D1111yescharacteristic
507C2×C4C2×#434311yescharacteristic
508C2×C4#6704011yescharacteristic
509C2×C4#6704011yescharacteristic
510C2×C4C22×C22⋊D1111yescharacteristic
511C2×C4C22×C22⋊D1111yescharacteristic
512C8—222no—
513C8—441no—
514C8—442no—
515C22—24no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—442no—
523C22—442no—
524C22—442no—
525C22—881no—
526C22—881no—
527C22—881no—
528C22—881no—
529C22Q8×C22⋊D1111yescharacteristic
530C22#1062334811yescharacteristic
531C22C2×#6700211yescharacteristic
532C22C2×#6700311yescharacteristic
533C22#1062336611yescharacteristic
534C22#1062336711yescharacteristic
535C22C2×#6700611yescharacteristic
536C4—22no—
537C4—42no—
538C4—42no—
539C4—42no—
540C4—44no—
541C4—881no—
542C4—882no—
543C4#1062285114yes—
544C4C2×#6699911yescharacteristic
545C4Q8×C22⋊D1111yescharacteristic
546C4#1062334711yescharacteristic
547C4#1062334811yescharacteristic
548C2—44no—
549C2—882no—
550C2#1307197511yescharacteristic
551C2C2×#1062285111yescharacteristic
552C2#1307792011yescharacteristic
553C2#1308126511yescharacteristic
554C2#1308132311yescharacteristic
555C2#1308147911yescharacteristic
556C2#1308151511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#554D11
hypocenterC11#24327
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
3. #13073534C2semidirect
4. #13069951C2semidirect
5. #13069759C2semidirect
6. #13069578C2semidirect
7. #13069553C2semidirect
9. #13068877C2semidirect
10. #13068616C2semidirect
11. C2×C11×#554C2semidirect
79. C2×#4323Q8semidirect
176. C2×#554D11semidirect
207. D4×C11C22⋊Q8semidirect
453. C11#24327semidirect
478. D4#66999semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×C4×#43232
#130735342
#130699512
#130697592
#130695782
#130695532
#130689642
#130688772
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