Finite Group Databasebeta

← #14790153

Subgroups — #14790153

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×#10623261C211yesmaximal, characteristic, complemented
2C2×#10622697C211yesmaximal, characteristic, complemented
3C2×C4×D88C211yesmaximal, characteristic
4#13073539C211yesmaximal, characteristic, complemented
5#13069957C212yesmaximal, complemented
6#13069761C212yesmaximal, complemented
7#13069552C211yesmaximal, characteristic, complemented
8#13068965C212yesmaximal
9#13068878C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—22no—
14C22×D88C2211yescharacteristic
15#10623261—24no—
16#10623261—24no—
17C2×#66950—21no—
18C2×#66950—21no—
19C2×#66946C2212yes—
20C2×C4⋊C4×D11—21no—
21C2×#66943C2212yes—
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30#10622697—24no—
31#10622607—22no—
32#10622601C2212yes—
33#10622600—21no—
34#10622598C2212yes—
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37C2×#66872C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C4×D88—24no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×D44C2311yescharacteristic
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C4×D11—22no—
50C22×C4×D11—21no—
51C22×Dic22D411yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8D414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C42×C11C2311yescharacteristic
62#66999—216no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4D412yes—
75C2×C4×Dic11C2312yes—
76C22×C11⋊C8C2312yes—
77C2×D88—22no—
78C2×D88—22no—
79C2×D88Q814yescomplemented
80#66950—28no—
81#66950—44no—
82#66946—24no—
83#66946—24no—
84C4⋊C4×D11—28no—
85#66943—24no—
86#66943—24no—
87C4×D44—22no—
88C4×D44—22no—
89C4×D44—22no—
90C4×D44D414yes—
91C4×Dic22—22no—
92C4×Dic22—22no—
93C4×C8×C11—22no—
94C11⋊#95—22no—
95#66885—22no—
96#66885—22no—
97#66882—22no—
98#66873—24no—
99#66873—24no—
100#66872—24no—
101C4⋊(C11⋊C8)—22no—
102#24327—111nomaximal, Sylow
103C23×D11—21no—
104C23×D11—21no—
105C2×Q8×C11—24no—
106C2×Q8×C11—81no—
107C2×Q8×C11—81no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44C2×D412yes—
126C2×D44C2×Q812yes—
127C2×D44C2×Q812yes—
128C2×D44#4112yes—
129C2×C4×D11—28no—
130C2×C4×D11—24no—
131C2×C4×D11—42no—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C2×C4×D11—42no—
136C2×C4×D11—82no—
137C2×C4×D11—82no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11C2×Q812yes—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—81no—
153C11×C4⋊C4C2×D414yes—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—42no—
160(C2×D11)⋊C4—82no—
161C4⋊Dic11—28no—
162C4⋊Dic11—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—44no—
167C4⋊Dic11C2×D412yes—
168Dic11⋊C4—28no—
169Dic11⋊C4—24no—
170C4×Dic11—22no—
171C4×Dic11—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175D88—28no—
176C2×#554—111no—
177C2×#476—111no—
178C2×C4×D8—111no—
179#2538—111no—
180#2059—112no—
181#2025—112no—
182#1990D1111yescharacteristic, complemented
183#1984—111no—
184#1879—112no—
185#1864—112no—
186#1802—111no—
187C23×C11C22×D411yescharacteristic
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202Q8×C11—84no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—24no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11#12012yes—
212C2×C4×C11#12012yes—
213C2×C4×C11#13512yes—
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×Q811yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233D44—22no—
234D44—22no—
235D44—22no—
236D44—22no—
237D44—22no—
238D44—41no—
239D44—41no—
240D44C22⋊Q814yescomplemented
241C4×D11—48no—
242C4×D11—88no—
243C4×D11—84no—
244Dic22—44no—
245C8×C11—22no—
246C8×C11—41no—
247C11⋊C8—42no—
248C22×D8—111no—
249#554—224no—
250#554—224no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C2×#125—112no—
253C2×C22⋊Q8—221no—
254C2×C22⋊Q8—221no—
255C2×C22⋊Q8—222no—
256C2×C4×Q8—111no—
257C2×C4×D4—112no—
258C2×C4×D4—111no—
259C2×C4×D4—111no—
260C22×C4⋊C4—221no—
261#476—224no—
262C4×D8—224no—
263C2×#107—111no—
264C2×#106—112no—
265C2×C4⋊C8—111no—
266C2×#102—111no—
267C2×#102—111no—
268C2×#102—112no—
269C2×#102—112no—
270C2×C4×C8C2×D1111yescharacteristic
271#396—222no—
272#390—112no—
273#389—112no—
274#384C2×D1111yescharacteristic
275#380—221no—
276#340—112no—
277#340C2×D1112yes—
278#340C2×D1112yes—
279#336—112no—
280#336—112no—
281C22×C11C2×#12011yescharacteristic
282C22×C11#54811yescharacteristic
283C22×C11D4×Q811yescharacteristic
284C22×C11C2×#13511yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C11#57611yescharacteristic
287C22×C11#57711yescharacteristic
288C2×D11—24no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—42no—
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—44no—
304C4×C11—82no—
305C4×C11#44914yes—
306C4×C11C2×C22⋊Q811yescharacteristic
307C4×C11#53611yescharacteristic
308C4×C11#54811yescharacteristic
309C4×C11D4×Q811yescharacteristic
310Dic11—42no—
311Dic11—42no—
312Dic11—42no—
313Dic11—81no—
314C22×Q8—21no—
315C22×Q8—111no—
316C22×D4—111no—
317C22×D4—111no—
318C23×C4—222no—
319C23×C4—221no—
320C23×C4—221no—
321C2×D8—114no—
322C2×D8—222no—
323C2×D8—222no—
324C22×C8—112no—
325C22×C8C22×D1111yescharacteristic
326C22×C8C22×D1111yescharacteristic
327C4⋊Q8—22no—
328C4⋊Q8D4414yes—
329#125—224no—
330#125—224no—
331C22⋊Q8—228no—
332C22⋊Q8—2216no—
333C22⋊Q8—444no—
334C4×Q8—222no—
335C4×Q8—222no—
336C4×D4—114no—
337C4×D4—224no—
338C4×D4—224no—
339C4×D4—222no—
340C4×D4—222no—
341C4×D4—222no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—228no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4C22×D1112yes—
354C2×C4⋊C4C22×D1112yes—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—221no—
359C2×C22⋊C4—222no—
360C2×C42—112no—
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—22no—
370#95—222no—
371C2×C11#240911yescharacteristic
372C2×C11C2×#44911yescharacteristic
373C2×C11#301211yescharacteristic
374C2×C11#336011yescharacteristic
375C2×C11#336611yescharacteristic
376C2×C11#338011yescharacteristic
377C2×C11#338411yescharacteristic
378D11—44no—
379D11—82no—
380C24—221no—
381C24—221no—
382C2×Q8—24no—
383C2×Q8—81no—
384C2×Q8—81no—
385C2×Q8—222no—
386C2×Q8—222no—
387C2×Q8—222no—
388C2×D4—112no—
389C2×D4—112no—
390C2×D4—112no—
391C2×D4—112no—
392C2×D4—221no—
393C2×D4—221no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—221no—
399C2×D4—221no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—228no—
405C22×C4—221no—
406C22×C4—224no—
407C22×C4—221no—
408C22×C4—442no—
409C22×C4—442no—
410C22×C4—442no—
411C22×C4—442no—
412C22×C4—442no—
413C22×C4—882no—
414C22×C4—882no—
415C22×C4D4×D1111yescharacteristic
416C22×C4D4×D1111yescharacteristic
417C22×C4C23×D1111yescharacteristic
418D8—228no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8Q8×D1112yes—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—42no—
433C4⋊C4—81no—
434C4⋊C4—112no—
435C4⋊C4—228no—
436C4⋊C4—228no—
437C4⋊C4—222no—
438C4⋊C4—224no—
439C4⋊C4—221no—
440C4⋊C4—221no—
441C4⋊C4—221no—
442C4⋊C4—444no—
443C4⋊C4C2×D4414yes—
444C22⋊C4—228no—
445C22⋊C4—224no—
446C22⋊C4—444no—
447C22⋊C4—442no—
448C22⋊C4—882no—
449C42—222no—
450C42—222no—
451C42C2×D4412yes—
452C42D4×D1112yes—
453C11#2432711yescharacteristic, complemented, Sylow
454C23—222no—
455C23—222no—
456C23—222no—
457C23—222no—
458C23—441no—
459C23—441no—
460C23—441no—
461C23—441no—
462C23—441no—
463C23—441no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23C2×D4×D1111yescharacteristic
469Q8—84no—
470Q8—444no—
471D4—114no—
472D4—222no—
473D4—222no—
474D4—222no—
475D4—222no—
476D4—222no—
477D4—441no—
478D4—441no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—448no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—888no—
501C2×C4—884no—
502C2×C4#6693512yes—
503C2×C4#6693512yes—
504C2×C4#6696712yes—
505C2×C4#6697212yes—
506C2×C4C22×D4411yescharacteristic
507C2×C4C2×D4×D1111yescharacteristic
508C2×C4C2×Q8×D1111yescharacteristic
509C2×C4#6704011yescharacteristic
510C2×C4#41×D1111yescharacteristic
511C2×C4#6704311yescharacteristic
512C8—22no—
513C8—41no—
514C8—442no—
515C22—224no—
516C22—442no—
517C22—442no—
518C22—442no—
519C22—442no—
520C22—442no—
521C22—442no—
522C22—442no—
523C22—442no—
524C22—442no—
525C22—881no—
526C22—881no—
527C22—881no—
528C22—881no—
529C22C2×#6693511yescharacteristic
530C22#1062320811yescharacteristic
531C22#1062325811yescharacteristic
532C22#1062328811yescharacteristic
533C22C2×#6696711yescharacteristic
534C22#1062329311yescharacteristic
535C22C2×#6697211yescharacteristic
536C4—22no—
537C4—44no—
538C4—82no—
539C4—442no—
540C4—442no—
541C4—442no—
542C4—881no—
543C4#1062242414yes—
544C4Q8×D4411yescharacteristic
545C4#1062310711yescharacteristic
546C4D11×C22⋊Q811yescharacteristic
547C4#1062315911yescharacteristic
548C2—444no—
549C2—882no—
550C2#1307197911yescharacteristic
551C2C2×#1062242411yescharacteristic
552C2#1307792511yescharacteristic
553C2#1308127011yescharacteristic
554C2#1308132811yescharacteristic
555C2#1308148511yescharacteristic
556C2#1308152011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenter#1990D11
hypocenterC11#24327
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
1. C2×#10623261C2semidirect
2. C2×#10622697C2semidirect
4. #13073539C2semidirect
5. #13069957C2semidirect
6. #13069761C2semidirect
7. #13069552C2semidirect
9. #13068878C2semidirect
10. #13068613C2semidirect
11. C11×#1990C2semidirect
79. C2×D88Q8semidirect
182. #1990D11semidirect
240. D44C22⋊Q8semidirect
453. C11#24327semidirect

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106226972
C2×C4×D882
#130735392
#130699572
#130697612
#130695522
#130689652
#130688782
#130686132
C11×#19902
#2432711