Finite Group Databasebeta

← #14785931

Subgroups — #14785931

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622653C211yesmaximal, characteristic, complemented
2C22×#66874C211yesmaximal, characteristic, complemented
3#13071981C211yesmaximal, characteristic, complemented
4#13069754C212yesmaximal, complemented
5#13069619C212yesmaximal, complemented
6#13069045C211yesmaximal, characteristic, complemented
7#13068950C212yesmaximal, complemented
8#13068923C212yesmaximal, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068702C211yesmaximal, characteristic, complemented
11C2×C11×#547C211yesmaximal, characteristic
12C22×C11×#41—21no—
13C23×Dic22C2211yescharacteristic
14C11×#547—24no—
15C11×#547—24no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×#4324C2212yes—
27C2×#66977C2212yes—
28C23×C11⋊C8C2211yescharacteristic
29#10622833—21no—
30C2×#66896C2212yes—
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622653—24no—
35#10622592—21no—
36C2×#66874—24no—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39C2×#66874C2212yes—
40#10622560—21no—
41#10622559—21no—
42#10622542C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C2×C11×#41—28no—
48C2×C11×#41—44no—
49C2×C11×#41—44no—
50C22×Q8×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11D411yescharacteristic
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C22×Dic22—22no—
62C22×Dic22—24no—
63C22×Dic22—22no—
64C22×Dic22—21no—
65C22×Dic22—42no—
66C22×Dic22C2312yes—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—22no—
69C11×#123—28no—
70C11×#123—28no—
71C11×C22⋊Q8—28no—
72C11×#121—22no—
73C11×#121—22no—
74C11×#121—22no—
75C11×#121D414yes—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4D414yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—21no—
99C2×#4324—24no—
100C2×#4324—24no—
101C2×#4324—42no—
102C2×C4⋊Dic11C2312yes—
103#66977—24no—
104#66977—42no—
105C2×Dic11⋊C4—22no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—42no—
108C22×C11⋊C8C2312yes—
109C22×C11⋊C8C2312yes—
110#66896—42no—
111C11⋊#95—22no—
112C11⋊#95—22no—
113C11⋊#95—21no—
114C22⋊(C11⋊C8)—22no—
115C22⋊(C11⋊C8)—42no—
116#66874—24no—
117#66874—24no—
118#66874—24no—
119#23961—111nomaximal, Sylow
120C24×C11—21no—
121C24×C11C2×D411yescharacteristic
122C24×C11C2×D411yescharacteristic
123C11×#41—432no—
124C2×Q8×C11—24no—
125C2×Q8×C11—42no—
126C2×Q8×C11—42no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—24no—
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11SD1614yescomplemented
139C2×D4×C11C2×D412yes—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—44no—
168C22×Dic11—42no—
169C2×Dic22—28no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—22no—
173C2×Dic22—22no—
174C2×Dic22—22no—
175C2×Dic22—48no—
176C2×Dic22—44no—
177C2×Dic22—44no—
178C2×Dic22—42no—
179C2×Dic22#4114yescomplemented
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4C2×D412yes—
188C11×C4⋊C4C2×D412yes—
189C11×C4⋊C4C2×D412yes—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—22no—
195C42×C11—21no—
196C42×C11—21no—
197C22⋊Dic11—44no—
198C22⋊Dic11—42no—
199#4324—48no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202Dic11⋊C4—44no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—44no—
210C2×#547D1111yescharacteristic
211C2×#448—111no—
212C22×#103—111no—
213#2409—111no—
214#2024—112no—
215#2000—112no—
216#1893—111no—
217#1877—112no—
218#1872—112no—
219#1869—111no—
220#1823—111no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—21no—
224C23×C11—22no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—42no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—42no—
232C23×C11#12012yes—
233C23×C11C2×SD1612yes—
234C23×C11C2×SD1612yes—
235C23×C11AGL(1,ℤ/8)12yes—
236C23×C11C22×D411yescharacteristic
237Q8×C11—48no—
238D4×C11—28no—
239D4×C11—24no—
240D4×C11—48no—
241D4×C11—48no—
242D4×C11—41no—
243D4×C11—41no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—48no—
258C2×C4×C11—48no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—48no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11#12012yes—
270C2×C4×C11C2×SD1612yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4112yes—
274C2×C4×C11H(5,𝔽2)12yes—
275C2×Dic11—24no—
276C2×Dic11—48no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282Dic22—24no—
283Dic22—24no—
284Dic22—48no—
285Dic22—42no—
286Dic22—42no—
287C11⋊C8—42no—
288C11⋊C8—42no—
289C22×#41—21no—
290C23×Q8—111no—
291C22×SD16—112no—
292C23×C8—111no—
293#547—24no—
294#547—24no—
295C2×C4⋊Q8C2×D1111yescharacteristic
296C2×#123—21no—
297C2×#123—21no—
298C2×C22⋊Q8—21no—
299C2×C22⋊Q8—112no—
300C2×#121C2×D1111yescharacteristic
301C2×#121C2×D1111yescharacteristic
302C2×C4×D4C2×D1111yescharacteristic
303C2×C4×D4C2×D1111yescharacteristic
304C22×C4⋊C4C2×D1111yescharacteristic
305C22×C4⋊C4C2×D1111yescharacteristic
306#448—224no—
307C2×#103—112no—
308C2×#103—112no—
309C2×#103—112no—
310C2×#103—224no—
311C2×#102—112no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—112no—
314#395—221no—
315#393—221no—
316#391—112no—
317#386—221no—
318#385—221no—
319#380—111no—
320#340—112no—
321#340—112no—
322#340—112no—
323#336—112no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—22no—
329C22×C11—24no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—82no—
337C22×C11—82no—
338C22×C11#45014yes—
339C22×C11C2×#12011yescharacteristic
340C22×C11#54612yes—
341C22×C11C22×SD1611yescharacteristic
342C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C11#57812yes—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—41no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11#52511yescharacteristic
352C4×C11#53511yescharacteristic
353C4×C11#54612yes—
354Dic11—44no—
355Dic11—82no—
356C2×#41—28no—
357C2×#41—44no—
358C2×#41—44no—
359C22×Q8—21no—
360C22×Q8—112no—
361C22×Q8—224no—
362C22×Q8—221no—
363C22×Q8—222no—
364C22×Q8—222no—
365C22×Q8—442no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4C22⋊D1111yescharacteristic
369C22×D4C22×D1111yescharacteristic
370C23×C4—21no—
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—221no—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C2×SD16—224no—
377C2×SD16—224no—
378C2×SD16—442no—
379C22×C8—112no—
380C22×C8—112no—
381C22×C8—222no—
382C22×C8—442no—
383C4⋊Q8—22no—
384C4⋊Q8—22no—
385#123—28no—
386#123—28no—
387C22⋊Q8—28no—
388C22⋊Q8—224no—
389C22⋊Q8—442no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121C22⋊D1114yes—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4C22⋊D1111yescharacteristic
407C2×C4⋊C4C22⋊D1114yes—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4C22⋊D1111yescharacteristic
417C2×C22⋊C4C22⋊D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419#103—224no—
420#103—224no—
421#103—224no—
422#102—442no—
423C22⋊C8—222no—
424C22⋊C8—442no—
425#95—221no—
426#95—222no—
427#95—222no—
428C2×C11—24no—
429C2×C11—42no—
430C2×C11—82no—
431C2×C11#240411yescharacteristic
432C2×C11C2×#45011yescharacteristic
433C2×C11#301111yescharacteristic
434C2×C11#329812yes—
435C2×C11#330812yes—
436C24—21no—
437C24C2×C22⋊D1111yescharacteristic
438C24C2×C22⋊D1111yescharacteristic
439#41—432no—
440C2×Q8—24no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×Q8—114no—
444C2×Q8—228no—
445C2×Q8—222no—
446C2×Q8—222no—
447C2×Q8—222no—
448C2×Q8—222no—
449C2×Q8—222no—
450C2×Q8—444no—
451C2×Q8—448no—
452C2×Q8—444no—
453C2×Q8—442no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4#432414yescomplemented
466C2×D4C2×C22⋊D1112yes—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—444no—
488C22×C4—442no—
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1112yes—
494C22×C4C2×C22⋊D1112yes—
495C22×C4C23×D1111yescharacteristic
496SD16—448no—
497C2×C8—222no—
498C2×C8—222no—
499C2×C8—222no—
500C2×C8—222no—
501C2×C8—222no—
502C2×C8—222no—
503C2×C8—444no—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—444no—
514C4⋊C4C2×C22⋊D1112yes—
515C4⋊C4C2×C22⋊D1112yes—
516C4⋊C4C2×C22⋊D1112yes—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—22no—
520C22⋊C4—24no—
521C22⋊C4—22no—
522C22⋊C4—444no—
523C22⋊C4—442no—
524C42—21no—
525C42—21no—
526C11#2396111yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—21no—
530C23—22no—
531C23—22no—
532C23—21no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—42no—
537C23—42no—
538C23#6698512yes—
539C23C2×#432412yes—
540C23C2×#432412yes—
541C23#6700612yes—
542C23C22×C22⋊D1111yescharacteristic
543Q8—48no—
544Q8—224no—
545Q8—224no—
546Q8—448no—
547Q8—442no—
548Q8—442no—
549D4—28no—
550D4—24no—
551D4—48no—
552D4—48no—
553D4—41no—
554D4—41no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—48no—
569C2×C4—48no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—48no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—224no—
581C2×C4—448no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4C2×#432412yes—
588C2×C4#6700612yes—
589C2×C4#41×D1112yes—
590C2×C4#6704212yes—
591C2×C4C22×C22⋊D1111yescharacteristic
592C2×C4C22×C22⋊D1111yescharacteristic
593C8—442no—
594C8—442no—
595C22—24no—
596C22—22no—
597C22—22no—
598C22—24no—
599C22—22no—
600C22—24no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—82no—
608C22—82no—
609C22#1062283114yes—
610C22C2×#6698511yescharacteristic
611C22C22×#432411yescharacteristic
612C22#1062336012yes—
613C22#1062336912yes—
614C22C2×#6700611yescharacteristic
615C4—22no—
616C4—22no—
617C4—42no—
618C4—42no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—444no—
623C4—882no—
624C4#1062335911yescharacteristic
625C4#1062336012yes—
626C4#1062336111yescharacteristic
627C2—24no—
628C2—42no—
629C2—82no—
630C2#1307193111yescharacteristic
631C2C2×#1062283111yescharacteristic
632C2#1307791111yescharacteristic
633C2#1308047512yes—
634C2#1308060112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11#23961
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10622653C2semidirect
2. C22×#66874C2semidirect
3. #13071981C2semidirect
4. #13069754C2semidirect
5. #13069619C2semidirect
6. #13069045C2semidirect
7. #13068950C2semidirect
8. #13068923C2semidirect
9. #13068909C2semidirect
10. #13068702C2semidirect
138. C2×D4×C11SD16semidirect
179. C2×Dic22#41semidirect
465. C2×D4#4324semidirect
526. C11#23961semidirect

Maximal subgroups

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

subgroupindex
C2×#106226532
C22×#668742
#130719812
#130697542
#130696192
#130690452
#130689502
#130689232
#130689092
#130687022
C2×C11×#5472
#2396111