Finite Group Databasebeta

← #14760709

Subgroups — #14760709

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078333C211yesmaximal, characteristic
2#13077519C211yesmaximal, characteristic, complemented
3#13077515C211yesmaximal, characteristic, complemented
4C2×#10622437C211yesmaximal, characteristic, complemented
5C4×#67001C211yesmaximal, characteristic, complemented
6#13069511C211yesmaximal, characteristic, complemented
7#13069405C211yesmaximal, characteristic, complemented
8#13069286C211yesmaximal, characteristic, complemented
9#13069282C211yesmaximal, characteristic, complemented
10#13069117C211yesmaximal, characteristic, complemented
11#13068668C211yesmaximal, characteristic, complemented
12#13068494C211yesmaximal, characteristic, complemented
13#13068418C211yesmaximal, characteristic, complemented
14#13068415C211yesmaximal, characteristic, complemented
15C11×#1906C211yesmaximal, characteristic, complemented
16C11×#575C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623353C2211yescharacteristic
19C2×#67003C2211yescharacteristic
20C2×#67001C2211yescharacteristic
21C2×#67001C2211yescharacteristic
22C2×#67001C2211yescharacteristic
23C2×#66960C2211yescharacteristic
24C11×#421C2211yescharacteristic
25C2×C11×#104C2211yescharacteristic
26C11×#410C2211yescharacteristic
27#10622850C2211yescharacteristic
28#10622849C2211yescharacteristic
29#10622849C2211yescharacteristic
30#10622817C412yescomplemented
31#10622816C412yescomplemented
32#10622813C412yescomplemented
33#10622812C412yescomplemented
34#10622810—22no—
35#10622809—22no—
36#10622745C2211yescharacteristic
37#10622738C2211yescharacteristic
38#10622737C2211yescharacteristic
39C2×#66886C2211yescharacteristic
40C2×#66886C2211yescharacteristic
41#10622735C2211yescharacteristic
42#10622619C2211yescharacteristic
43#10622618C2211yescharacteristic
44#10622611C2211yescharacteristic
45#10622610—21no—
46#10622610—21no—
47#10622610C2211yescharacteristic
48#10622610C2211yescharacteristic
49#10622610C2211yescharacteristic
50C2×#66869C2211yescharacteristic
51C4×#4318—21no—
52C4×#4318C2211yescharacteristic
53C2×C4×C11⋊C8—21no—
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622437—22no—
56#10622437—21no—
57#10622437—21no—
58#10622437—21no—
59#10622437—21no—
60#10622436—22no—
61C11×#344C2211yescharacteristic
62C11×#339C2211yescharacteristic
63#10622194C2211yescharacteristic
64#10622171C2211yescharacteristic
65#10622171C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C2×#4339C2311yescharacteristic
70C11×#137—21no—
71C11×#137C2×C412yes—
72C11×AGL(1,ℤ/8)—21no—
73C11×AGL(1,ℤ/8)C2×C412yes—
74C11×#135—22no—
75C2×C11×M16C2311yescharacteristic
76C2×C11×M16C2311yescharacteristic
77C4×Q8×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11—22no—
80C11×#117—21no—
81C11×#117C2311yescharacteristic
82C11×#117C2311yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85#67004C2×C412yes—
86#67003—22no—
87#67003—21no—
88#67003—21no—
89#67003—21no—
90#67003—21no—
91#67002C2×C412yes—
92#67001—21no—
93#67001—21no—
94#67001—21no—
95#67001—21no—
96#67001—21no—
97#67001—21no—
98#67001—21no—
99#67001—21no—
100#67001C2×C412yes—
101#67001C2×C412yes—
102#67001D412yes—
103#67001D412yes—
104C2×#4326C2×C411yescharacteristic, complemented
105#66995—21no—
106C2×#4325C2×C411yescharacteristic, complemented
107C2×#4324C2×C411yescharacteristic, complemented
108#66985—21no—
109C2×#4323C2×C411yescharacteristic, complemented
110#66979C2311yescharacteristic
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318—21no—
114C2×#4318C2311yescharacteristic
115C2×#4318C2311yescharacteristic
116C2×#4318C2311yescharacteristic
117C2×#4318C2311yescharacteristic
118C22×C11⋊C8—21no—
119C22×C11⋊C8—21no—
120C22×C11⋊C8—21no—
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123#66960—21no—
124#66960—21no—
125#66960—21no—
126#66960—21no—
127C2×#4313—21no—
128C2×C8×D11—21no—
129C11×#104—22no—
130C11×#104—21no—
131C11×#104—21no—
132C11×#99—22no—
133#66901—22no—
134#66901—22no—
135#66900C2×C412yescomplemented
136#66897C2×C412yescomplemented
137#66888C2×C412yescomplemented
138#66887C2×C412yescomplemented
139#66886—22no—
140#66886—21no—
141#66886—21no—
142#66886C2×C412yescomplemented
143#66886C2×C412yescomplemented
144#66883—22no—
145#66879—21no—
146C8×Dic11—21no—
147#66872—21no—
148#66871—21no—
149#66870—22no—
150#66869—21no—
151#66869—21no—
152#66869—22no—
153#66867—21no—
154#66867—21no—
155#66867—21no—
156#66867—21no—
157C4×C11⋊C8—21no—
158C4×C11⋊C8—21no—
159C4×C11⋊C8—21no—
160C4×C11⋊C8—21no—
161C4×C11⋊C8D411yescharacteristic
162C4×C11⋊C8D411yescharacteristic
163C4×C11⋊C8D411yescharacteristic
164C4×C11⋊C8D411yescharacteristic
165#21558—111nomaximal, Sylow
166C11×#41—21no—
167C11×#41—21no—
168C11×#41—21no—
169C11×#41—21no—
170C11×#41—21no—
171C11×#41—21no—
172C11×#41C22×C412yes—
173C11×#41C2×D412yes—
174C2×Q8×C11C22×C411yescharacteristic
175C2×Q8×C11#4111yescharacteristic
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11C22×C411yescharacteristic
179C2×D4×C11#4111yescharacteristic
180C22×C4×C11—21no—
181C22×C4×C11—22no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11C2411yescharacteristic
185C2×C22⋊D11—21no—
186#4339—21no—
187#4339—21no—
188#4339—21no—
189#4339—21no—
190C2×D44C22×C411yescharacteristic
191C2×C4×D11—21no—
192C2×Dic22C22×C411yescharacteristic
193C11×Q16—22no—
194C11×SD16—22no—
195C11×SD16—22no—
196C11×D8—22no—
197C11×M16—21no—
198C11×M16—21no—
199C11×M16—21no—
200C11×M16C22×C412yes—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—21no—
208C11×C22⋊C4#4112yes—
209C42×C11—22no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11C2×D411yescharacteristic
214C42×C11C2×D411yescharacteristic
215C22⋊Dic11—21no—
216#4326—21no—
217#4326—21no—
218#4326—22no—
219#4325—21no—
220#4325—21no—
221#4325—22no—
222#4324—21no—
223#4324—21no—
224#4324—22no—
225#4323—21no—
226#4323—21no—
227#4323—22no—
228C4⋊Dic11—21no—
229C4×Dic11—21no—
230#4318—22no—
231#4318—22no—
232#4318—22no—
233#4318—22no—
234#4318—21no—
235#4318—21no—
236#4318—21no—
237#4318—21no—
238#4318—21no—
239#4318—41no—
240#4318—41no—
241#4318C22×C412yes—
242#4318C22×C412yes—
243#4318C2×D412yes—
244C2×C11⋊C8—22no—
245C2×C11⋊C8—22no—
246C2×C11⋊C8—22no—
247C2×C11⋊C8—22no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—41no—
253C2×C11⋊C8—41no—
254C2×C11⋊C8C22×C411yescharacteristic
255C2×C11⋊C8C22×C411yescharacteristic
256C2×C11⋊C8C2×D411yescharacteristic
257C2×C11⋊C8C2×D411yescharacteristic
258C2×C11⋊C8C2×D411yescharacteristic
259C2×C11⋊C8C2×D411yescharacteristic
260C2×C11⋊C8C2×D411yescharacteristic
261C2×C11⋊C8C2×D411yescharacteristic
262C2×C11⋊C8#4111yescharacteristic
263C2×C11⋊C8#4111yescharacteristic
264C2×C11⋊C8#4111yescharacteristic
265C2×C11⋊C8#4111yescharacteristic
266#4313—41no—
267#4313—41no—
268C8×D11—41no—
269C8×D11—41no—
270#3067—111no—
271#2955—111no—
272#2955—111no—
273C2×#443—111no—
274C4×#131—111no—
275#1976—111no—
276#1953—111no—
277#1932—111no—
278#1932—111no—
279#1906—111no—
280#1906D1111yescharacteristic, complemented
281#1814—111no—
282#1772—111no—
283#1757—111no—
284#1757—111no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11C2×#4111yescharacteristic
288C22×D11—21no—
289Q8×C11—21no—
290Q8×C11—21no—
291Q8×C11—21no—
292Q8×C11C4×D412yes—
293D4×C11—22no—
294D4×C11—22no—
295D4×C11—21no—
296D4×C11—21no—
297D4×C11—21no—
298D4×C11—41no—
299D4×C11—41no—
300D4×C11C4×D412yes—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—21no—
306C2×C4×C11—22no—
307C2×C4×C11—21no—
308C2×C4×C11—42no—
309C2×C4×C11—44no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11C23×C411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C22⋊D11—41no—
320C22⋊D11—41no—
321C2×Dic11—21no—
322C2×Dic11—41no—
323D44—21no—
324D44—21no—
325C4×D11—41no—
326C4×D11—41no—
327Dic22—21no—
328Dic22—21no—
329C8×C11—22no—
330C8×C11—41no—
331C11⋊C8—22no—
332C11⋊C8—22no—
333C11⋊C8—22no—
334C11⋊C8—41no—
335C11⋊C8C4×D411yescharacteristic
336C11⋊C8C4×D411yescharacteristic
337C11⋊C8C4×D411yescharacteristic
338C11⋊C8C4×D411yescharacteristic
339C11⋊C8#12111yescharacteristic
340C11⋊C8#12111yescharacteristic
341C11⋊C8#12111yescharacteristic
342C11⋊C8#12111yescharacteristic
343#575—111no—
344#575C2×D1111yescharacteristic
345C2×#135—111no—
346C2×#131—111no—
347C2×#131—111no—
348C2×#131—111no—
349C2×#131—111no—
350C4×#41C2×D1111yescharacteristic
351#473—112no—
352#472—112no—
353#471—112no—
354#471—112no—
355#444—222no—
356#444—222no—
357#443—221no—
358#443—221no—
359#443—221no—
360#443—221no—
361#443—222no—
362#443—222no—
363#430—111no—
364#430—111no—
365C2×#108—111no—
366C2×#108—111no—
367#427—111no—
368#421—111no—
369#421—111no—
370#421—111no—
371#421C2×D1111yescharacteristic
372C2×#104—111no—
373C2×#104C2×D1111yescharacteristic
374#413—111no—
375#413—111no—
376#410—111no—
377#410C2×D1111yescharacteristic
378#405—111no—
379#405—111no—
380#405—111no—
381#405—111no—
382#405—221no—
383#405—221no—
384C4×M16—111no—
385C4×M16—221no—
386C2×C4×C8—111no—
387C2×C4×C8—221no—
388#344—111no—
389#344—111no—
390#344—111no—
391#344C2×D1111yescharacteristic
392#339—111no—
393#339C2×D1111yescharacteristic
394C22×C11—22no—
395C22×C11—41no—
396C22×C11—42no—
397C22×C11—41no—
398C22×C11—81no—
399C22×C11C4×#4111yescharacteristic
400C22×C11#52511yescharacteristic
401C22×C11#53211yescharacteristic
402C2×D11—41no—
403C2×D11—81no—
404C4×C11—22no—
405C4×C11—22no—
406C4×C11—42no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11—81no—
410C4×C11C2×C4×D411yescharacteristic
411C4×C11C2×C4×D411yescharacteristic
412C4×C11C2×#12111yescharacteristic
413C4×C11#52911yescharacteristic
414Dic11—41no—
415Dic11—81no—
416C2×#41—111no—
417C2×#41C22×D1111yescharacteristic
418C2×#41C22×D1111yescharacteristic
419#137—21no—
420#137—112no—
421#137—221no—
422#137C4×D1112yes—
423AGL(1,ℤ/8)—21no—
424AGL(1,ℤ/8)—112no—
425AGL(1,ℤ/8)—221no—
426AGL(1,ℤ/8)C4×D1112yes—
427#135—22no—
428#135—221no—
429#135—221no—
430#135—221no—
431#135—221no—
432#135—222no—
433C2×Q16—111no—
434C2×SD16—111no—
435C2×SD16—111no—
436C2×D8—111no—
437#131—112no—
438#131—112no—
439#131—112no—
440#131—112no—
441#131—221no—
442#131—221no—
443#131—221no—
444#131—221no—
445#131—221no—
446#131—221no—
447#131—221no—
448#131—221no—
449#131—221no—
450#131—221no—
451#131—221no—
452#131—221no—
453C2×M16—111no—
454C2×M16—111no—
455C2×M16—111no—
456C2×M16—111no—
457C2×M16—221no—
458C2×M16—221no—
459C2×M16—221no—
460C2×M16—221no—
461C2×M16C22×D1111yescharacteristic
462C2×M16C22×D1111yescharacteristic
463C22×C8—111no—
464C22×C8—111no—
465C22×C8—221no—
466C22×C8—221no—
467C22×C8—221no—
468C22×C8—221no—
469C4×Q8—21no—
470C4×D4—21no—
471C4×D4—22no—
472#117—21no—
473#117—111no—
474#117C22×D1111yescharacteristic
475#117C22×D1111yescharacteristic
476C2×C42—21no—
477C2×C42C22×D1111yescharacteristic
478#108—112no—
479#108—112no—
480#108—222no—
481#108—221no—
482#108—221no—
483#108—222no—
484#107—221no—
485#106—221no—
486#104—22no—
487#104—21no—
488#104—21no—
489#104—222no—
490#104—222no—
491#104—222no—
492#104—221no—
493#104—221no—
494#101—112no—
495#101—112no—
496#100—112no—
497#100—112no—
498#99—22no—
499#99—222no—
500#97—221no—
501#97—221no—
502#97—221no—
503#97—221no—
504#97—221no—
505C4×C8—111no—
506C4×C8—111no—
507C4×C8—111no—
508C4×C8—111no—
509C4×C8—221no—
510C4×C8—221no—
511C4×C8—221no—
512C4×C8—221no—
513C4×C8—221no—
514C2×C11—21no—
515C2×C11—21no—
516C2×C11—21no—
517C2×C11—42no—
518C2×C11—81no—
519C2×C11C4×#12111yescharacteristic
520D11—81no—
521#41—21no—
522#41—21no—
523#41—21no—
524#41—21no—
525#41—21no—
526#41—21no—
527#41—221no—
528#41—221no—
529#41—221no—
530#41—221no—
531#41C2×C4×D1112yes—
532#41D4×D1112yes—
533C2×Q8—111no—
534C2×Q8C2×C4×D1111yescharacteristic
535C2×Q8#434111yescharacteristic
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—111no—
539C2×D4—221no—
540C2×D4C2×C4×D1111yescharacteristic
541C2×D4#434111yescharacteristic
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—221no—
547C22×C4C23×D1111yescharacteristic
548Q16—22no—
549Q16—221no—
550Q16—221no—
551Q16—222no—
552SD16—22no—
553SD16—22no—
554SD16—221no—
555SD16—221no—
556SD16—221no—
557SD16—221no—
558SD16—222no—
559SD16—222no—
560D8—22no—
561D8—221no—
562D8—221no—
563D8—222no—
564M16—21no—
565M16—21no—
566M16—21no—
567M16—112no—
568M16—112no—
569M16—112no—
570M16—222no—
571M16—222no—
572M16—222no—
573M16—222no—
574M16—221no—
575M16—221no—
576M16—221no—
577M16—221no—
578M16—221no—
579M16—441no—
580M16—441no—
581M16—441no—
582M16—441no—
583M16C2×C4×D1112yes—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—111no—
587C2×C8—111no—
588C2×C8—111no—
589C2×C8—111no—
590C2×C8—111no—
591C2×C8—111no—
592C2×C8—111no—
593C2×C8—111no—
594C2×C8—111no—
595C2×C8—111no—
596C2×C8—111no—
597C2×C8—111no—
598C2×C8—222no—
599C2×C8—222no—
600C2×C8—222no—
601C2×C8—222no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—441no—
607C2×C8—441no—
608C2×C8—441no—
609C2×C8—441no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—221no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—221no—
617C22⋊C4#434112yes—
618C42—22no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—221no—
623C42D4×D1111yescharacteristic
624C42D4×D1111yescharacteristic
625C11#2155811yescharacteristic, complemented, Sylow
626C23—21no—
627C23—21no—
628C23—221no—
629C23C2×#434111yescharacteristic
630Q8—21no—
631Q8—21no—
632Q8—21no—
633Q8—221no—
634Q8—221no—
635Q8(C22⋊D11)⋊C412yes—
636D4—22no—
637D4—22no—
638D4—21no—
639D4—21no—
640D4—21no—
641D4—41no—
642D4—41no—
643D4—221no—
644D4—221no—
645D4—441no—
646D4—441no—
647D4(C22⋊D11)⋊C412yes—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—42no—
656C2×C4—44no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—221no—
661C2×C4—441no—
662C2×C4—441no—
663C2×C4—441no—
664C2×C4C22×C4×D1111yescharacteristic
665C2×C4C2×D4×D1111yescharacteristic
666C2×C4C2×D4×D1111yescharacteristic
667C2×C4C2×#434111yescharacteristic
668C2×C4#41×D1111yescharacteristic
669C2×C4#41×D1111yescharacteristic
670C8—22no—
671C8—41no—
672C8—111no—
673C8—111no—
674C8—111no—
675C8—111no—
676C8—111no—
677C8—111no—
678C8—111no—
679C8—111no—
680C8—222no—
681C8—222no—
682C8—222no—
683C8—441no—
684C22—22no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—81no—
689C22—441no—
690C22—881no—
691C22C4×#434111yescharacteristic
692C22#1062311711yescharacteristic
693C22#1062312711yescharacteristic
694C4—22no—
695C4—22no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—441no—
701C4—881no—
702C4C2×(C22⋊D11)⋊C411yescharacteristic
703C4C4×D4×D1111yescharacteristic
704C4D11×#12111yescharacteristic
705C4#1062318011yescharacteristic
706C2—21no—
707C2—21no—
708C2—21no—
709C2—42no—
710C2—81no—
711C2—881no—
712C2#1307112611yescharacteristic
subgroupG/H
centerC4D11×#121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1906C2
socleC2×C11C4×#121
prime radical#13078333C2
cosocleC22×C4×C11C24
hypercenter#1906D11
hypocenterC11#21558
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1906

Complements

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

NH ≅ G/Ntype
2. #13077519C2semidirect
3. #13077515C2semidirect
4. C2×#10622437C2semidirect
5. C4×#67001C2semidirect
6. #13069511C2semidirect
7. #13069405C2semidirect
8. #13069286C2semidirect
9. #13069282C2semidirect
10. #13069117C2semidirect
11. #13068668C2semidirect
12. #13068494C2semidirect
13. #13068418C2semidirect
14. #13068415C2semidirect
15. C11×#1906C2semidirect
30. #10622817C4semidirect
31. #10622816C4semidirect
32. #10622813C4semidirect
33. #10622812C4semidirect
104. C2×#4326C2×C4semidirect
106. C2×#4325C2×C4semidirect
107. C2×#4324C2×C4semidirect
109. C2×#4323C2×C4semidirect
135. #66900C2×C4semidirect
136. #66897C2×C4semidirect
137. #66888C2×C4semidirect
138. #66887C2×C4semidirect
142. #66886C2×C4semidirect
143. #66886C2×C4semidirect
280. #1906D11semidirect
625. C11#21558semidirect

Maximal subgroups

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

subgroupindex
#130783332
#130775192
#130775152
C2×#106224372
C4×#670012
#130695112
#130694052
#130692862
#130692822
#130691172
#130686682
#130684942
#130684182
#130684152
C11×#19062
#2155811