Finite Group Databasebeta

← #14760693

Subgroups — #14760693

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
1C2×#10622813C211yesmaximal, characteristic
2C4×#67004C211yesmaximal, characteristic, complemented
3C2×#10622631C211yesmaximal, characteristic, complemented
4#13077044C211yesmaximal, characteristic, complemented
5#13069522C211yesmaximal, characteristic, complemented
6#13069398C211yesmaximal, characteristic, complemented
7#13069281C211yesmaximal, characteristic, complemented
8#13069270C211yesmaximal, characteristic, complemented
9#13069129C211yesmaximal, characteristic, complemented
10#13069126C211yesmaximal, characteristic
11#13068678C211yesmaximal, characteristic, complemented
12#13068523C211yesmaximal, characteristic, complemented
13C4×#66888C211yesmaximal, characteristic, complemented
14C4×#66897C211yesmaximal, characteristic, complemented
15C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
16C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#67004C2211yescharacteristic
20C2×#67001C2211yescharacteristic
21C2×#67001C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#442—21no—
25C11×#440—21no—
26C4×C11×SD16—21no—
27C4×C11×D8—21no—
28C11×#428C2211yescharacteristic
29C11×#418C2211yescharacteristic
30C11×#417C2211yescharacteristic
31C4×C11×M16C2211yescharacteristic
32#10622845C2211yescharacteristic
33C2×#66897C2211yescharacteristic
34C2×#66897C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622813C418yescomplemented
37C2×#66888C2211yescharacteristic
38C2×#66888C2211yescharacteristic
39C2×#66886C2211yescharacteristic
40C2×#66886C2211yescharacteristic
41#10622643—21no—
42C4×#4326—21no—
43#10622631—21no—
44#10622631—21no—
45#10622631—21no—
46#10622631—21no—
47#10622631—21no—
48C4×#4324—21no—
49#10622617C2211yescharacteristic
50#10622610—21no—
51#10622610—21no—
52#10622610C2211yescharacteristic
53#10622610C2211yescharacteristic
54#10622608C2211yescharacteristic
55C2×#66874C2211yescharacteristic
56C2×#66871C2211yescharacteristic
57C4×#4318—21no—
58C4×#4318C2211yescharacteristic
59C4×#4318C2211yescharacteristic
60C2×#66867—21no—
61C2×#66867C2211yescharacteristic
62#10622196C2211yescharacteristic
63#10622196C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622192C2211yescharacteristic
66#10622168C2211yescharacteristic
67#10622168C2211yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C22×Dic22C2311yescharacteristic
72C11×AGL(1,ℤ/8)—22no—
73C11×AGL(1,ℤ/8)C2×C414yes—
74C2×C11×SD16—21no—
75C2×C11×D8—21no—
76C2×C11×M16C2311yescharacteristic
77C2×C11×M16C2311yescharacteristic
78C4×Q8×C11D411yescharacteristic
79C4×Q8×C11D411yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D411yescharacteristic
87C4×D4×C11D411yescharacteristic
88C11×#117—21no—
89C11×#117C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94#67004—22no—
95#67004C2×C414yescomplemented
96#67001—22no—
97#67001—22no—
98#67001—22no—
99#67001C2×C414yescomplemented
100C2×#4326—21no—
101C2×#4324—21no—
102C2×#4324—21no—
103C2×#4324—21no—
104C2×#4324—22no—
105C2×#4324C2×C414yescomplemented
106C2×C4⋊Dic11C2311yescharacteristic
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11—21no—
109C2×#4318—21no—
110C2×#4318—21no—
111C2×#4318C2311yescharacteristic
112C2×#4318C2311yescharacteristic
113C2×#4318C2311yescharacteristic
114C2×#4318C2311yescharacteristic
115C22×C11⋊C8—21no—
116C22×C11⋊C8—21no—
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C4×Dic22—21no—
120C4×Dic22—21no—
121C4×Dic22—21no—
122C4×Dic22—21no—
123C11×#107—21no—
124C11×#106—21no—
125C11×#103—21no—
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#97—21no—
130C4×C8×C11—21no—
131#66899—21no—
132#66897—22no—
133#66897C2×C414yescomplemented
134#66896—21no—
135#66896—21no—
136#66896—21no—
137#66888—22no—
138#66888C2×C414yescomplemented
139#66886—22no—
140#66886C2×C414yescomplemented
141#66874—21no—
142#66874—21no—
143#66874—21no—
144#66874—21no—
145#66872—21no—
146#66871—21no—
147#66871—21no—
148#66871—21no—
149#66867—21no—
150#66867—21no—
151#66867—21no—
152#66867—21no—
153#66867D411yescharacteristic
154#66867D411yescharacteristic
155#66867D411yescharacteristic
156#66867D411yescharacteristic
157C4×C11⋊C8—21no—
158C4×C11⋊C8—21no—
159C4×C11⋊C8—21no—
160C4×C11⋊C8—21no—
161#21557—111nomaximal, Sylow
162C24×C11—21no—
163C11×#41—21no—
164C11×#41—21no—
165C11×#41C22×C412yes—
166C11×#41#4112yes—
167C2×Q8×C11C2×D411yescharacteristic
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11C22×C412yes—
175C2×D4×C11C2×D411yescharacteristic
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—41no—
181C22×C4×C11—41no—
182C22×C4×C11—82no—
183C22×C4×C11#4111yescharacteristic
184C22×C4×C11#4111yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×Dic11—21no—
187C22×Dic11—21no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22C22×C412yes—
194C11×SD16—24no—
195C11×D8—24no—
196C11×M16—21no—
197C11×M16—21no—
198C11×M16—21no—
199C11×M16C22×C412yes—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—41no—
212C11×C22⋊C4—41no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D411yescharacteristic
219C42×C11C2×D411yescharacteristic
220#4326—24no—
221#4324—24no—
222#4324—24no—
223#4324—24no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226Dic11⋊C4—41no—
227Dic11⋊C4—41no—
228C4×Dic11—41no—
229C4×Dic11—41no—
230#4318—24no—
231#4318—24no—
232#4318—21no—
233#4318—21no—
234#4318—21no—
235#4318—21no—
236#4318—21no—
237#4318C22×C412yes—
238#4318C22×C412yes—
239#4318#4112yes—
240C2×C11⋊C8—24no—
241C2×C11⋊C8—24no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8C22×C412yes—
249C2×C11⋊C8C2×D411yescharacteristic
250C2×C11⋊C8C2×D411yescharacteristic
251C2×C11⋊C8C2×D411yescharacteristic
252C2×C11⋊C8C2×D411yescharacteristic
253C2×C11⋊C8#4112yes—
254C2×#471—111no—
255C4×#137—111no—
256C4×AGL(1,ℤ/8)D1111yescharacteristic
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×C11C4×D412yes—
278D4×C11—22no—
279D4×C11—22no—
280D4×C11—22no—
281D4×C11—22no—
282D4×C11—21no—
283D4×C11—41no—
284D4×C11—41no—
285D4×C11C4×D412yes—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—81no—
295C2×C4×C11—81no—
296C2×C4×C11—82no—
297C2×C4×C11—82no—
298C2×C4×C11—81no—
299C2×C4×C11#12111yescharacteristic
300C2×C4×C11#12111yescharacteristic
301C2×C4×C11#12111yescharacteristic
302C2×C4×C11#12111yescharacteristic
303C2×C4×C11C23×C411yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×Dic11—22no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—81no—
314Dic22—22no—
315Dic22—22no—
316Dic22—41no—
317Dic22—41no—
318C8×C11—22no—
319C8×C11—41no—
320C11⋊C8—22no—
321C11⋊C8—22no—
322C11⋊C8—21no—
323C11⋊C8—22no—
324C11⋊C8—21no—
325C11⋊C8—41no—
326C11⋊C8C4×D412yes—
327C11⋊C8C4×D412yes—
328C2×#137—111no—
329C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
330C22×SD16—111no—
331C2×#131—111no—
332C2×#131—111no—
333C4×#41C2×D1111yescharacteristic
334C2×C4×Q8—111no—
335C2×C4×D4C2×D1111yescharacteristic
336#471—118no—
337#442—21no—
338#441—221no—
339#440—21no—
340#440—221no—
341#440—221no—
342#440—221no—
343#440—221no—
344#440—221no—
345C4×Q16—221no—
346C4×SD16—21no—
347C4×SD16—221no—
348C4×D8—21no—
349C2×#108—111no—
350C2×#108—111no—
351#428—111no—
352#428C2×D1111yescharacteristic
353C2×#107—111no—
354#419—111no—
355#418C2×D1111yescharacteristic
356#417—111no—
357#417C2×D1111yescharacteristic
358C2×#103—111no—
359C2×#102—111no—
360C2×#101—111no—
361C2×#101—111no—
362C2×#100—111no—
363C2×#100—111no—
364#405—111no—
365#405—111no—
366#405—221no—
367#405—221no—
368C4×M16—111no—
369C4×M16—111no—
370C4×M16—221no—
371C4×M16C2×D1111yescharacteristic
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—21no—
395C4×C11—21no—
396C4×C11—21no—
397C4×C11—21no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—81no—
401C4×C11C2×C4×D411yescharacteristic
402C4×C11C2×C4×D411yescharacteristic
403C4×C11#52511yescharacteristic
404C4×C11#53211yescharacteristic
405Dic11—42no—
406Dic11—81no—
407C2×#41C22×D1111yescharacteristic
408C22×Q8—111no—
409C22×D4C22×D1111yescharacteristic
410C23×C4—21no—
411#137—114no—
412#137—222no—
413AGL(1,ℤ/8)—22no—
414AGL(1,ℤ/8)C4×D1114yes—
415C2×Q16—221no—
416C2×SD16—21no—
417C2×SD16—114no—
418C2×SD16—222no—
419C2×SD16—221no—
420C2×SD16—221no—
421C2×SD16—221no—
422C2×D8—21no—
423#131—114no—
424#131—222no—
425#131—222no—
426#131—222no—
427C2×M16—111no—
428C2×M16—111no—
429C2×M16—111no—
430C2×M16—111no—
431C2×M16—221no—
432C2×M16—221no—
433C2×M16C22×D1111yescharacteristic
434C2×M16C22×D1111yescharacteristic
435C22×C8—111no—
436C22×C8—111no—
437C22×C8—221no—
438C22×C8—221no—
439C4×Q8—221no—
440C4×Q8—221no—
441C4×Q8—221no—
442C4×Q8—221no—
443C4×Q8C22⋊D1111yescharacteristic
444C4×Q8C22⋊D1111yescharacteristic
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4C22⋊D1111yescharacteristic
452C4×D4C22⋊D1111yescharacteristic
453#117—21no—
454#117C22×D1111yescharacteristic
455C2×C4⋊C4—111no—
456C2×C4⋊C4—221no—
457C2×C4⋊C4C22×D1111yescharacteristic
458C2×C22⋊C4—21no—
459C2×C42—21no—
460C2×C42—221no—
461C2×C42C22×D1111yescharacteristic
462#108—114no—
463#108—222no—
464#107—21no—
465#107—221no—
466#107—221no—
467#107—221no—
468#106—21no—
469#106—221no—
470#103—21no—
471#103—221no—
472#103—221no—
473#103—221no—
474#103—221no—
475#103—221no—
476#102—21no—
477#102—21no—
478#102—21no—
479#102—221no—
480#102—221no—
481#102—221no—
482#101—114no—
483#101—222no—
484#100—114no—
485#100—222no—
486#97—21no—
487#97—111no—
488#97—111no—
489#97—111no—
490#97—111no—
491#97—221no—
492#97—221no—
493#97—221no—
494#97—221no—
495C4×C8—21no—
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#41C2×C4×D1112yes—
511#41#433912yes—
512C2×Q8—112no—
513C2×Q8—221no—
514C2×Q8—221no—
515C2×Q8—221no—
516C2×Q8—221no—
517C2×Q8—221no—
518C2×Q8C2×C22⋊D1111yescharacteristic
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4C2×C4×D1112yes—
526C2×D4C2×C22⋊D1111yescharacteristic
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—82no—
534C22×C4—221no—
535C22×C4—221no—
536C22×C4#434111yescharacteristic
537C22×C4#434111yescharacteristic
538C22×C4C23×D1111yescharacteristic
539Q16—224no—
540SD16—24no—
541SD16—224no—
542SD16—224no—
543SD16—224no—
544D8—24no—
545M16—21no—
546M16—21no—
547M16—21no—
548M16—112no—
549M16—112no—
550M16—112no—
551M16—224no—
552M16—224no—
553M16—221no—
554M16—221no—
555M16—221no—
556M16—221no—
557M16—221no—
558M16C2×C4×D1112yes—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—112no—
562C2×C8—111no—
563C2×C8—111no—
564C2×C8—112no—
565C2×C8—111no—
566C2×C8—111no—
567C2×C8—224no—
568C2×C8—224no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—221no—
580C4⋊C4—221no—
581C4⋊C4—441no—
582C4⋊C4—441no—
583C4⋊C4C2×C22⋊D1111yescharacteristic
584C4⋊C4C2×C22⋊D1111yescharacteristic
585C22⋊C4—21no—
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—441no—
594C42—441no—
595C42D4×D1111yescharacteristic
596C42D4×D1111yescharacteristic
597C42C2×C22⋊D1111yescharacteristic
598C42C2×C22⋊D1111yescharacteristic
599C11#2155711yescharacteristic, complemented, Sylow
600C23—21no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—81no—
605C23—81no—
606C23C2×#434111yescharacteristic
607Q8—21no—
608Q8—222no—
609Q8—222no—
610Q8—441no—
611Q8—441no—
612Q8C4×C22⋊D1112yes—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—22no—
617D4—21no—
618D4—41no—
619D4—41no—
620D4C4×C22⋊D1112yes—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—81no—
630C2×C4—81no—
631C2×C4—82no—
632C2×C4—82no—
633C2×C4—81no—
634C2×C4—222no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—881no—
639C2×C4#6699211yescharacteristic
640C2×C4#6699211yescharacteristic
641C2×C4#6699211yescharacteristic
642C2×C4#6699211yescharacteristic
643C2×C4C22×C4×D1111yescharacteristic
644C2×C4C2×#433911yescharacteristic
645C2×C4C2×D4×D1111yescharacteristic
646C2×C4#41×D1111yescharacteristic
647C2×C4#41×D1111yescharacteristic
648C2×C4C22×C22⋊D1111yescharacteristic
649C8—22no—
650C8—41no—
651C8—112no—
652C8—112no—
653C8—222no—
654C8—222no—
655C8—221no—
656C8—221no—
657C8—222no—
658C8—441no—
659C22—21no—
660C22—21no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—82no—
666C22—82no—
667C22—81no—
668C22—81no—
669C22C4×#434111yescharacteristic
670C22#1062306911yescharacteristic
671C22C2×#6699211yescharacteristic
672C4—22no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—41no—
678C4—41no—
679C4—81no—
680C4—442no—
681C4—881no—
682C4C4×D4×D1111yescharacteristic
683C4#1062307811yescharacteristic
684C4C2×C4×C22⋊D1111yescharacteristic
685C4#1062336311yescharacteristic
686C2—21no—
687C2—21no—
688C2—42no—
689C2—82no—
690C2C4×#6699211yescharacteristic
691C2#1307834111yescharacteristic
692C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C2×#121
prime radicalC2×C11×AGL(1,ℤ/8)C22
cosocleC22×C4×C11C24
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11#21557
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
2. C4×#67004C2semidirect
3. C2×#10622631C2semidirect
4. #13077044C2semidirect
5. #13069522C2semidirect
6. #13069398C2semidirect
7. #13069281C2semidirect
8. #13069270C2semidirect
9. #13069129C2semidirect
11. #13068678C2semidirect
12. #13068523C2semidirect
13. C4×#66888C2semidirect
14. C4×#66897C2semidirect
36. #10622813C4semidirect
95. #67004C2×C4semidirect
99. #67001C2×C4semidirect
105. C2×#4324C2×C4semidirect
133. #66897C2×C4semidirect
138. #66888C2×C4semidirect
140. #66886C2×C4semidirect
599. C11#21557semidirect

Maximal subgroups

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

subgroupindex
C2×#106228132
C4×#670042
C2×#106226312
#130770442
#130695222
#130693982
#130692812
#130692702
#130691292
#130691262
#130686782
#130685232
C4×#668882
C4×#668972
C4×C11×AGL(1,ℤ/8)2
#2155711