Finite Group Databasebeta

← #14796412

Subgroups — #14796412

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622467C211yesmaximal, characteristic, complemented
2C2×#10622465C211yesmaximal, characteristic
3#13073568C211yesmaximal, characteristic
4#13071530C211yesmaximal, characteristic, complemented
5#13070095C211yesmaximal, characteristic, complemented
6#13069987C211yesmaximal, characteristic
7#13069985C211yesmaximal, characteristic
8#13069575C211yesmaximal, characteristic, complemented
9#13069333C211yesmaximal, characteristic, complemented
10#13068972C211yesmaximal, characteristic
11#13068970C211yesmaximal, characteristic
12#13068620C211yesmaximal, characteristic, complemented
13#13068618C211yesmaximal, characteristic, complemented
14#13068615C211yesmaximal, characteristic
15C11×#2084C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×#66949—21no—
18C2×#66949—21no—
19C2×#66946C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#384C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622605—21no—
34#10622605—21no—
35#10622601C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622589—21no—
38#10622589C2211yescharacteristic
39#10622589C2211yescharacteristic
40#10622585—21no—
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46#10622552C2211yescharacteristic
47C4×Dic11⋊C4C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622467—24no—
50#10622465—24no—
51#10622262—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22—21no—
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4D411yescharacteristic
92C2×Dic11⋊C4D411yescharacteristic
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C2×#4314—22no—
101C2×#4314—22no—
102C2×#4314Q814yescomplemented
103#66949—44no—
104#66949—44no—
105#66946—22no—
106#66946—22no—
107#66941—22no—
108#66941—22no—
109#66940—22no—
110#66940—22no—
111#66940—41no—
112#66940D414yes—
113C4×Dic22—22no—
114C4×Dic22—41no—
115C11×#106—22no—
116C11×#106—22no—
117C11×#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66885—41no—
122#66880—22no—
123Dic11⋊C8—22no—
124Dic11⋊C8—41no—
125C8×Dic11—22no—
126#66874—22no—
127#66874—22no—
128#66873—22no—
129#66873—41no—
130#66872—22no—
131C4⋊(C11⋊C8)—41no—
132#24813—111nomaximal, Sylow
133C23×D11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44C2×Q812yes—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—42no—
161C2×Dic22—42no—
162C2×Dic22—42no—
163C2×Dic22C2×D412yes—
164C2×Dic22C2×Q812yes—
165C2×Dic22#4112yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C2×Q812yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—81no—
182C11×C4⋊C4C2×D412yes—
183C42×C11—21no—
184C42×C11—21no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—81no—
195Dic11⋊C4—24no—
196Dic11⋊C4—22no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—81no—
204Dic11⋊C4SD1614yescomplemented
205C4×Dic11—24no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11C2×D412yes—
211C4×Dic11#4112yes—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218#4314—28no—
219C2×#475—111no—
220C2×C4×SD16—111no—
221#2542—111no—
222Q8×C4⋊C4—111no—
223#2084—111no—
224#2084D1111yescharacteristic, complemented
225#2065—111no—
226#2065—111no—
227#1990—111no—
228#1939—111no—
229#1880—111no—
230#1880—111no—
231#1803—111no—
232#1803—111no—
233#1802—111no—
234C23×C11C22×D411yescharacteristic
235C22×D11—22no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11C2×SD1612yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×Q811yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11#12112yes—
283C2×Dic11#12112yes—
284C2×Dic11C2×SD1612yes—
285C2×Dic11C2×SD1612yes—
286C2×Dic11AGL(1,ℤ/8)12yes—
287D44—22no—
288D44—22no—
289D44—41no—
290D44—41no—
291C4×D11—84no—
292Dic22—22no—
293Dic22—22no—
294Dic22—22no—
295Dic22—84no—
296Dic22C22⋊Q814yescomplemented
297C8×C11—22no—
298C8×C11—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C22×SD16—111no—
302C2×C4⋊Q8—111no—
303C2×C22⋊Q8—221no—
304C2×C22⋊Q8—221no—
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×Q8—111no—
308C2×C4×D4—111no—
309#475—224no—
310C4×SD16—224no—
311C2×#106—111no—
312C2×#106C2×D1111yescharacteristic
313C2×#106C2×D1111yescharacteristic
314C2×C4⋊C8—111no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×C4×C8—111no—
324#399—221no—
325#399—221no—
326#390—111no—
327#390—111no—
328#389—111no—
329#389—221no—
330#389—221no—
331#389C2×D1111yescharacteristic
332#384—111no—
333#384—111no—
334#384—221no—
335#384C2×D1111yescharacteristic
336C4×C4⋊C4—111no—
337C4×C4⋊C4—221no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344#336—111no—
345#336C2×D1111yescharacteristic
346C22×C11C2×#12111yescharacteristic
347C22×C11#54611yescharacteristic
348C22×C11D4×Q811yescharacteristic
349C22×C11C22×SD1611yescharacteristic
350C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C11#57711yescharacteristic
352C22×C11#57811yescharacteristic
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C4×C11—22no—
361C4×C11—41no—
362C4×C11—42no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11C2×C22⋊Q811yescharacteristic
367C4×C11#53711yescharacteristic
368C4×C11#55211yescharacteristic
369C4×C11#55411yescharacteristic
370Dic11—24no—
371Dic11—22no—
372Dic11—22no—
373Dic11—41no—
374Dic11—81no—
375Dic11—81no—
376Dic11#46014yes—
377C22×Q8—111no—
378C22×Q8—221no—
379C22×D4—111no—
380C23×C4—221no—
381C2×SD16—114no—
382C2×SD16—222no—
383C2×SD16—222no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8C22×D1111yescharacteristic
387C22×C8C22×D1111yescharacteristic
388C4⋊Q8—222no—
389C4⋊Q8—222no—
390C22⋊Q8—444no—
391C22⋊Q8—444no—
392C4×Q8—114no—
393C4×Q8—222no—
394C4×Q8—222no—
395C4×Q8—222no—
396C4×Q8—441no—
397C4×Q8—441no—
398C4×D4—222no—
399C4×D4—222no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42C22×D1111yescharacteristic
431#106—22no—
432#106—22no—
433#106—222no—
434C4⋊C8—222no—
435C4⋊C8—441no—
436C4⋊C8—441no—
437#103—222no—
438#103—222no—
439#103—222no—
440#102—222no—
441#102—441no—
442#102—441no—
443C4×C8—222no—
444#95—21no—
445#95—111no—
446#95—111no—
447#95—221no—
448C2×C11#241711yescharacteristic
449C2×C11C2×#46011yescharacteristic
450C2×C11#304611yescharacteristic
451C2×C11#329811yescharacteristic
452C2×C11#333211yescharacteristic
453C2×C11Q8×SD1611yescharacteristic
454C2×C11#338611yescharacteristic
455D11—82no—
456C24—221no—
457C2×Q8—112no—
458C2×Q8—112no—
459C2×Q8—112no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—442no—
464C2×Q8—442no—
465C2×Q8—442no—
466C2×D4—112no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—442no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489SD16—228no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8Q8×D1112yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—81no—
512C4⋊C4—114no—
513C4⋊C4—222no—
514C4⋊C4—224no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—442no—
520C4⋊C4—442no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—881no—
526C4⋊C4—881no—
527C4⋊C4D4×D1112yes—
528C22⋊C4—442no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C42—21no—
534C42—21no—
535C42—112no—
536C42—112no—
537C42—224no—
538C42—221no—
539C42—221no—
540C42—442no—
541C42—442no—
542C11#2481311yescharacteristic, complemented, Sylow
543C23—222no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23C2×D4×D1111yescharacteristic
551Q8—114no—
552Q8—222no—
553Q8—222no—
554Q8—222no—
555Q8—884no—
556D4—222no—
557D4—222no—
558D4—441no—
559D4—441no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—112no—
578C2×C4—112no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—222no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—222no—
587C2×C4—221no—
588C2×C4—222no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—884no—
599C2×C4SD16×D1112yes—
600C2×C4C2×D4×D1111yescharacteristic
601C2×C4C2×Q8×D1111yescharacteristic
602C2×C4#6704011yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C2×C4#41×D1111yescharacteristic
605C2×C4#6704211yescharacteristic
606C8—22no—
607C8—41no—
608C8—441no—
609C8—441no—
610C22—442no—
611C22—442no—
612C22—442no—
613C22—881no—
614C22—881no—
615C22—881no—
616C22—881no—
617C22D11×#12111yescharacteristic
618C22#1062318511yescharacteristic
619C22#1062325811yescharacteristic
620C22C2×SD16×D1111yescharacteristic
621C22#1062329311yescharacteristic
622C22D11×AGL(1,ℤ/8)11yescharacteristic
623C22#1062331011yescharacteristic
624C4—22no—
625C4—41no—
626C4—42no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4—114no—
631C4—222no—
632C4—222no—
633C4—224no—
634C4—441no—
635C4—881no—
636C4—881no—
637C4D11×C22⋊Q811yescharacteristic
638C4#1062316011yescharacteristic
639C4#1062322111yescharacteristic
640C4#1062322411yescharacteristic
641C2—882no—
642C2#1307206211yescharacteristic
643C2D11×#46011yescharacteristic
644C2#1307816111yescharacteristic
645C2#1308047911yescharacteristic
646C2#1308094111yescharacteristic
647C2#1308147311yescharacteristic
648C2#1308153411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2084C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2084D11
hypocenterC11#24813
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
1. C2×#10622467C2semidirect
4. #13071530C2semidirect
5. #13070095C2semidirect
8. #13069575C2semidirect
9. #13069333C2semidirect
12. #13068620C2semidirect
13. #13068618C2semidirect
15. C11×#2084C2semidirect
102. C2×#4314Q8semidirect
204. Dic11⋊C4SD16semidirect
224. #2084D11semidirect
296. Dic22C22⋊Q8semidirect
542. C11#24813semidirect

Maximal subgroups

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

subgroupindex
C2×#106224672
C2×#106224652
#130735682
#130715302
#130700952
#130699872
#130699852
#130695752
#130693332
#130689722
#130689702
#130686202
#130686182
#130686152
C11×#20842
#2481311