Finite Group Databasebeta

← #14760698

Subgroups — #14760698

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#137×Dic11C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×Dic11C211yesmaximal, characteristic
3C2×#10622777C211yesmaximal, characteristic, complemented
4#13077042C211yesmaximal, characteristic, complemented
5#13069521C211yesmaximal, characteristic, complemented
6#13069402C211yesmaximal, characteristic, complemented
7#13069280C211yesmaximal, characteristic, complemented
8#13069273C211yesmaximal, characteristic, complemented
9#13069133C211yesmaximal, characteristic, complemented
10#13069126C211yesmaximal, characteristic
11#13068680C211yesmaximal, characteristic, complemented
12#13068524C211yesmaximal, characteristic, complemented
13#101×Dic11C211yesmaximal, characteristic, complemented
14#100×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#471C211yesmaximal, characteristic
16C2×C11×#137C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×#131C2211yescharacteristic
20#41×Dic11C2211yescharacteristic
21C2×#67001C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C11×#471C418yescomplemented
25C2×C11×#108C2211yescharacteristic
26C2×C11×#101C2211yescharacteristic
27C2×C11×#100C2211yescharacteristic
28#10622845C2211yescharacteristic
29#10622845C2211yescharacteristic
30C2×#66900C2211yescharacteristic
31#10622838C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66897C2211yescharacteristic
34#10622828C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622797—21no—
37Q16×Dic11—21no—
38#10622777—21no—
39#10622777—21no—
40#10622777—21no—
41#10622777—21no—
42#10622777—21no—
43#10622777—21no—
44SD16×Dic11—21no—
45SD16×Dic11—21no—
46#10622765—21no—
47D8×Dic11—21no—
48#10622735—21no—
49#10622735C2211yescharacteristic
50#10622734C2211yescharacteristic
51#10622734C2211yescharacteristic
52M16×Dic11—21no—
53M16×Dic11C2211yescharacteristic
54M16×Dic11C2211yescharacteristic
55M16×Dic11C2211yescharacteristic
56C2×#66883C2211yescharacteristic
57C2×#66882C2211yescharacteristic
58#10622714—21no—
59#10622714C2211yescharacteristic
60C2×#66879—21no—
61C2×#66879C2211yescharacteristic
62#10622196C2211yescharacteristic
63#10622196C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622192C2211yescharacteristic
66#10622192C2211yescharacteristic
67#10622192C2211yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×Dic11—21no—
72C11×#137—22no—
73C11×#137C2×C414yescomplemented
74C11×AGL(1,ℤ/8)—22no—
75C11×AGL(1,ℤ/8)C2×C414yes—
76C2×C11×Q16—21no—
77C2×C11×SD16—21no—
78C2×C11×SD16—21no—
79C2×C11×SD16—21no—
80C2×C11×SD16—21no—
81C2×C11×SD16—22no—
82C2×C11×SD16C2×C414yescomplemented
83C2×C11×D8—21no—
84C11×#131—22no—
85C11×#131C2×C414yescomplemented
86C2×C11×M16—21no—
87C2×C11×M16C2311yescharacteristic
88C2×C11×M16C2311yescharacteristic
89C2×C11×M16C2311yescharacteristic
90C22×C8×C11—21no—
91C22×C8×C11C2311yescharacteristic
92C2×C22⋊Dic11—21no—
93#67001—22no—
94#67001—22no—
95Q8×Dic11—21no—
96Q8×Dic11—21no—
97Q8×Dic11—21no—
98Q8×Dic11—21no—
99Q8×Dic11D411yescharacteristic
100Q8×Dic11D411yescharacteristic
101D4×Dic11—21no—
102D4×Dic11—21no—
103D4×Dic11—21no—
104D4×Dic11—21no—
105D4×Dic11—21no—
106D4×Dic11—21no—
107D4×Dic11D411yescharacteristic
108D4×Dic11D411yescharacteristic
109#66979—21no—
110#66979C2311yescharacteristic
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4×Dic11—21no—
115C2×C4×Dic11—21no—
116C2×C4×Dic11C2311yescharacteristic
117C2×#4318—21no—
118C2×#4318C2311yescharacteristic
119C2×#4318C2311yescharacteristic
120C2×#4318C2311yescharacteristic
121C22×C11⋊C8—21no—
122C22×C11⋊C8C2311yescharacteristic
123C11×#108C2×C414yescomplemented
124C11×#101C2×C414yescomplemented
125C11×#100C2×C414yescomplemented
126#66900—22no—
127#66899—21no—
128#66899—21no—
129#66899—21no—
130#66899—21no—
131#66899—21no—
132#66899—21no—
133#66897—22no—
134#66896—21no—
135#66896—21no—
136#66896—21no—
137#66896—21no—
138#66896—21no—
139#66896—21no—
140#66883—22no—
141#66882—21no—
142#66882—21no—
143#66882—21no—
144#66882—21no—
145#66881—21no—
146#66881—21no—
147#66879—21no—
148#66879—21no—
149#66879—21no—
150#66879—21no—
151#66879—21no—
152#66879D411yescharacteristic
153#66879D411yescharacteristic
154#66879D411yescharacteristic
155#66879D411yescharacteristic
156C8×Dic11—21no—
157C8×Dic11—21no—
158C8×Dic11—21no—
159C8×Dic11—21no—
160C8×Dic11—21no—
161#21557—111nomaximal, Sylow
162C24×C11—21no—
163C11×#41—21no—
164C11×#41—21no—
165C11×#41C22×C412yes—
166C11×#41#4112yes—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11C22×C412yes—
173C2×Q8×C11C2×D411yescharacteristic
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11C22×C412yes—
181C2×D4×C11C2×D411yescharacteristic
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11C2411yescharacteristic
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—41no—
190C22×Dic11—41no—
191C22×Dic11—82no—
192C22×Dic11#4111yescharacteristic
193C22×Dic11#4111yescharacteristic
194C11×Q16—24no—
195C11×SD16—24no—
196C11×SD16—24no—
197C11×SD16—24no—
198C11×SD16—24no—
199C11×D8—24no—
200C11×M16—24no—
201C11×M16—21no—
202C11×M16—21no—
203C11×M16—21no—
204C11×M16C22×C412yes—
205C11×M16C22×C412yes—
206C11×M16C22×C412yes—
207C2×C8×C11—24no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11C22×C412yes—
212C2×C8×C11C2×D411yescharacteristic
213C2×C8×C11C2×D411yescharacteristic
214C2×C8×C11#4112yes—
215C22⋊Dic11—21no—
216C22⋊Dic11—21no—
217C22⋊Dic11—21no—
218C22⋊Dic11—41no—
219C22⋊Dic11—41no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—41no—
227C4⋊Dic11—41no—
228C4⋊Dic11C2×D411yescharacteristic
229C4⋊Dic11C2×D411yescharacteristic
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233C4×Dic11—41no—
234C4×Dic11—41no—
235C4×Dic11C2×D411yescharacteristic
236C4×Dic11C2×D411yescharacteristic
237C4×Dic11C2×D411yescharacteristic
238C4×Dic11C2×D411yescharacteristic
239#4318—24no—
240#4318—21no—
241#4318—21no—
242#4318—21no—
243#4318—21no—
244#4318—21no—
245#4318#4112yes—
246C2×C11⋊C8—24no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8C2×D411yescharacteristic
253C2×C11⋊C8C2×D411yescharacteristic
254C2×#471D1111yescharacteristic
255C4×#137—111no—
256C4×AGL(1,ℤ/8)—111no—
257C2×#440—111no—
258#2875—111no—
259#1977—111no—
260#1952—111no—
261#1931—111no—
262#1930—111no—
263#1908—111no—
264#1907—111no—
265#1816—111no—
266#1778—111no—
267C4×#101—111no—
268C4×#100—111no—
269C23×C11—21no—
270C23×C11—22no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—81no—
274C23×C11—81no—
275C23×C11C2×#4111yescharacteristic
276Q8×C11—21no—
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—41no—
280Q8×C11—41no—
281Q8×C11C4×D412yes—
282D4×C11—22no—
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—21no—
287D4×C11—41no—
288D4×C11—41no—
289D4×C11C4×D412yes—
290C2×C4×C11—21no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11C23×C411yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C2×#4111yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—81no—
309C2×Dic11—81no—
310C2×Dic11—82no—
311C2×Dic11—82no—
312C2×Dic11—81no—
313C2×Dic11—81no—
314C2×Dic11#12111yescharacteristic
315C2×Dic11#12111yescharacteristic
316C2×Dic11#12111yescharacteristic
317C2×Dic11#12111yescharacteristic
318C8×C11—22no—
319C8×C11—22no—
320C8×C11—22no—
321C8×C11C4×D412yes—
322C8×C11C4×D412yes—
323C11⋊C8—21no—
324C11⋊C8—22no—
325C11⋊C8—21no—
326C11⋊C8—41no—
327C11⋊C8—41no—
328C2×#137C2×D1111yescharacteristic
329C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
330C22×SD16C2×D1111yescharacteristic
331C2×#131—111no—
332C2×#131C2×D1111yescharacteristic
333C4×#41—111no—
334C2×C4×Q8—111no—
335C2×C4×D4—111no—
336#471Dic1118yescomplemented
337#442—221no—
338#441—221no—
339#440—221no—
340#440—221no—
341#440—221no—
342#440—221no—
343#440—221no—
344#440—221no—
345C4×Q16—221no—
346C4×SD16—221no—
347C4×SD16—221no—
348C4×D8—221no—
349C2×#108—111no—
350C2×#108C2×D1111yescharacteristic
351#428—111no—
352#428—111no—
353C2×#107—111no—
354#419—111no—
355#418—111no—
356#417—111no—
357#417—111no—
358C2×#103—111no—
359C2×#102—111no—
360C2×#101—111no—
361C2×#101C2×D1111yescharacteristic
362C2×#100—111no—
363C2×#100C2×D1111yescharacteristic
364#405—111no—
365#405—111no—
366#405—221no—
367#405—221no—
368C4×M16—111no—
369C4×M16—111no—
370C4×M16—111no—
371C4×M16—221no—
372C2×#97—111no—
373C2×#97—221no—
374#343—111no—
375#343—111no—
376#343—111no—
377#343—111no—
378#341—111no—
379#341—111no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—22no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—42no—
386C22×C11—82no—
387C22×C11—82no—
388C22×C11—81no—
389C22×C11—81no—
390C22×C11C4×#4111yescharacteristic
391C22×C11C2×#12111yescharacteristic
392C22×C11#52911yescharacteristic
393C4×C11—22no—
394C4×C11—42no—
395C4×C11C2×C4×D411yescharacteristic
396C4×C11C2×C4×D411yescharacteristic
397C4×C11#52511yescharacteristic
398C4×C11#53211yescharacteristic
399Dic11—21no—
400Dic11—21no—
401Dic11—21no—
402Dic11—21no—
403Dic11—41no—
404Dic11—41no—
405Dic11—81no—
406Dic11—81no—
407C2×#41C22×D1111yescharacteristic
408C22×Q8C22×D1111yescharacteristic
409C22×D4C22×D1111yescharacteristic
410C23×C4—221no—
411#137—22no—
412#137C2×Dic1114yescomplemented
413AGL(1,ℤ/8)—22no—
414AGL(1,ℤ/8)C2×Dic1114yes—
415C2×Q16—21no—
416C2×SD16—21no—
417C2×SD16—21no—
418C2×SD16—21no—
419C2×SD16—21no—
420C2×SD16—22no—
421C2×SD16C2×Dic1114yescomplemented
422C2×D8—21no—
423#131—22no—
424#131—222no—
425#131—222no—
426#131C2×Dic1114yescomplemented
427C2×M16—21no—
428C2×M16—111no—
429C2×M16—111no—
430C2×M16—111no—
431C2×M16—221no—
432C2×M16C22×D1111yescharacteristic
433C2×M16C22×D1111yescharacteristic
434C2×M16C22×D1111yescharacteristic
435C22×C8—21no—
436C22×C8—111no—
437C22×C8—221no—
438C22×C8C22×D1111yescharacteristic
439C4×Q8—111no—
440C4×Q8—111no—
441C4×Q8—221no—
442C4×Q8—221no—
443C4×Q8—221no—
444C4×Q8—221no—
445C4×D4—111no—
446C4×D4—111no—
447C4×D4—221no—
448C4×D4—221no—
449C4×D4—221no—
450C4×D4—221no—
451C4×D4—221no—
452C4×D4—221no—
453#117—111no—
454#117—221no—
455C2×C4⋊C4—111no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—221no—
458C2×C22⋊C4—221no—
459C2×C42—111no—
460C2×C42—221no—
461C2×C42—221no—
462#108—222no—
463#108C2×Dic1114yescomplemented
464#107—221no—
465#107—221no—
466#107—221no—
467#107—221no—
468#106—221no—
469#106—221no—
470#103—221no—
471#103—221no—
472#103—221no—
473#103—221no—
474#103—221no—
475#103—221no—
476#102—221no—
477#102—221no—
478#102—221no—
479#102—221no—
480#102—221no—
481#102—221no—
482#101—222no—
483#101C2×Dic1114yescomplemented
484#100—222no—
485#100C2×Dic1114yescomplemented
486#97—111no—
487#97—111no—
488#97—111no—
489#97—111no—
490#97—221no—
491#97—221no—
492#97—221no—
493#97—221no—
494#97—221no—
495C4×C8—221no—
496C4×C8—221no—
497C4×C8—221no—
498C4×C8—221no—
499C4×C8—221no—
500C2×C11—21no—
501C2×C11—21no—
502C2×C11—42no—
503C2×C11—82no—
504C2×C11C4×#12111yescharacteristic
505C2×C11#306811yescharacteristic
506C2×C11#306911yescharacteristic
507C24—21no—
508#41—21no—
509#41—21no—
510#41#434112yes—
511#41C22×Dic1112yes—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8D4×D1111yescharacteristic
518C2×Q8C22×Dic1112yes—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4D4×D1111yescharacteristic
526C2×D4C22×Dic1112yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—111no—
530C22×C4—111no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—221no—
534C22×C4—221no—
535C22×C4—441no—
536C22×C4—441no—
537C22×C4—882no—
538C22×C4C23×D1111yescharacteristic
539Q16—24no—
540SD16—24no—
541SD16—24no—
542SD16—24no—
543SD16—24no—
544D8—24no—
545M16—21no—
546M16—21no—
547M16—21no—
548M16—24no—
549M16—112no—
550M16—224no—
551M16—221no—
552M16—221no—
553M16—221no—
554M16—221no—
555M16—221no—
556M16C22×Dic1112yes—
557M16C22×Dic1112yes—
558M16C22×Dic1112yes—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—24no—
563C2×C8—111no—
564C2×C8—111no—
565C2×C8—224no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8D4×D1111yescharacteristic
572C2×C8D4×D1111yescharacteristic
573C2×C8#434112yes—
574C2×C8C22×Dic1112yes—
575C4⋊C4—111no—
576C4⋊C4—111no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—221no—
581C4⋊C4—221no—
582C4⋊C4—221no—
583C4⋊C4—441no—
584C4⋊C4—441no—
585C22⋊C4—221no—
586C22⋊C4—221no—
587C22⋊C4—221no—
588C22⋊C4—441no—
589C22⋊C4—441no—
590C42—111no—
591C42—111no—
592C42—111no—
593C42—111no—
594C42—221no—
595C42—221no—
596C42—221no—
597C42—441no—
598C42—441no—
599C11#2155711yescharacteristic, complemented, Sylow
600C23—21no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—81no—
605C23—81no—
606C23#41×D1111yescharacteristic
607Q8—21no—
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8D4×Dic1112yes—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—22no—
617D4—21no—
618D4—41no—
619D4—41no—
620D4D4×Dic1112yes—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—111no—
628C2×C4—111no—
629C2×C4—111no—
630C2×C4—111no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—881no—
638C2×C4—881no—
639C2×C4—882no—
640C2×C4—882no—
641C2×C4—881no—
642C2×C4—881no—
643C2×C4C2×D4×D1111yescharacteristic
644C2×C4C2×D4×D1111yescharacteristic
645C2×C4C2×#434111yescharacteristic
646C2×C4C2×#434111yescharacteristic
647C2×C4#41×D1111yescharacteristic
648C2×C4C23×Dic1111yescharacteristic
649C8—22no—
650C8—22no—
651C8—22no—
652C8—221no—
653C8—221no—
654C8—222no—
655C8—441no—
656C8—441no—
657C8D4×Dic1112yes—
658C8D4×Dic1112yes—
659C22—21no—
660C22—21no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—82no—
666C22—82no—
667C22—81no—
668C22—81no—
669C22#1062313111yescharacteristic
670C22D11×#12111yescharacteristic
671C22#41×Dic1111yescharacteristic
672C4—22no—
673C4—42no—
674C4—221no—
675C4—221no—
676C4—221no—
677C4—221no—
678C4—441no—
679C4—441no—
680C4—881no—
681C4—881no—
682C4#1062312711yescharacteristic
683C4#1062313711yescharacteristic
684C4C2×D4×Dic1111yescharacteristic
685C4C2×D4×Dic1111yescharacteristic
686C2—21no—
687C2—21no—
688C2—42no—
689C2—82no—
690C2#121×Dic1111yescharacteristic
691C2#1307833911yescharacteristic
692C2#1307834811yescharacteristic
subgroupG/H
centerC22D11×#121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#471C2
socleC22×C11C2×#121
prime radicalC2×C11×AGL(1,ℤ/8)C22
cosocleC22×C4×C11C24
hypercenterC2×#471D11
hypocenterC11#21557
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#471

Complements

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

NH ≅ G/Ntype
1. #137×Dic11C2semidirect
3. C2×#10622777C2semidirect
4. #13077042C2semidirect
5. #13069521C2semidirect
6. #13069402C2semidirect
7. #13069280C2semidirect
8. #13069273C2semidirect
9. #13069133C2semidirect
11. #13068680C2semidirect
12. #13068524C2semidirect
13. #101×Dic11C2semidirect
14. #100×Dic11C2semidirect
24. C11×#471C4semidirect
73. C11×#137C2×C4semidirect
82. C2×C11×SD16C2×C4semidirect
85. C11×#131C2×C4semidirect
123. C11×#108C2×C4semidirect
124. C11×#101C2×C4semidirect
125. C11×#100C2×C4semidirect
336. #471Dic11semidirect
412. #137C2×Dic11semidirect
421. C2×SD16C2×Dic11semidirect
426. #131C2×Dic11semidirect
463. #108C2×Dic11semidirect
483. #101C2×Dic11semidirect
485. #100C2×Dic11semidirect
599. C11#21557semidirect

Maximal subgroups

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

subgroupindex
#137×Dic112
AGL(1,ℤ/8)×Dic112
C2×#106227772
#130770422
#130695212
#130694022
#130692802
#130692732
#130691332
#130691262
#130686802
#130685242
#101×Dic112
#100×Dic112
C2×C11×#4712
#2155711