Finite Group Databasebeta

← #14780994

Subgroups — #14780994

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2C22×#66995C211yesmaximal, characteristic, complemented
3C2×#10622850C211yesmaximal, characteristic, complemented
4C22×#66900C211yesmaximal, characteristic, complemented
5#13077060C211yesmaximal, characteristic, complemented
6#13069735C214yesmaximal, complemented
7#13069728C214yesmaximal, complemented
8#13068343C211yesmaximal, characteristic, complemented
9C22×C11×#137C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C22×#4339C2211yescharacteristic
13C2×C11×#137—24no—
14C2×C11×#137—24no—
15C2×C11×#137—22no—
16C2×C11×#137—22no—
17C22×C11×Q16C2212yescomplemented
18C22×C11×SD16C2212yescomplemented
19C22×C11×M16C2211yescharacteristic
20C2×#67004—21no—
21#10623353—24no—
22#10623353—24no—
23C2×#67003—22no—
24C2×#67002—21no—
25C22×#4326—21no—
26C2×#66995—24no—
27C2×#66995—22no—
28C2×#66995—24no—
29C2×#66995C2214yes—
30C2×#66995C2212yes—
31C22×#4325—21no—
32C2×#66985C2212yes—
33C22×#4318C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35C22×#4318C2211yescharacteristic
36#10622850—24no—
37C2×#66900—24no—
38C2×#66900C2214yescomplemented
39C2×#66900C2212yescomplemented
40C2×#66897C2212yescomplemented
41#10622742—22no—
42#10622739—22no—
43#10622723C2214yes—
44#10622190C2214yescomplemented
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41D414yes—
53C22×Q8×C11—22no—
54C22×Q8×C11—21no—
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×Q8×C11—22no—
58C22×Q8×C11—22no—
59C22×Q8×C11—21no—
60C22×Q8×C11—21no—
61C22×Q8×C11D414yes—
62C22×Q8×C11C2312yes—
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C2×#4339—21no—
71C2×#4339—21no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—22no—
76C2×#4339D412yes—
77C2×#4339C2312yes—
78C22×D44D411yescharacteristic
79C22×C4×D11—21no—
80C22×Dic22D411yescharacteristic
81C11×#137—216no—
82C11×#137—216no—
83C2×C11×Q16—24no—
84C2×C11×Q16—24no—
85C2×C11×Q16—24no—
86C2×C11×SD16—24no—
87C2×C11×SD16—24no—
88C2×C11×SD16—24no—
89C2×C11×M16—22no—
90C2×C11×M16—22no—
91C2×C11×M16D412yes—
92C2×C11×M16D412yes—
93C22×C8×C11C2312yes—
94#67004—28no—
95#67003—216no—
96#67002—28no—
97C2×#4326—28no—
98C2×#4326—24no—
99C2×#4326—22no—
100#66995—216no—
101#66995—28no—
102#66995—24no—
103#66995—28no—
104#66995—24no—
105C2×#4325—28no—
106C2×#4325—24no—
107C2×#4325—22no—
108C2×#4324—22no—
109#66985—24no—
110#66985—24no—
111C2×#4323—22no—
112C2×#4318—21no—
113C2×#4318—22no—
114C2×#4318—21no—
115C2×#4318—22no—
116C2×#4318—21no—
117C2×#4318—22no—
118C2×#4318—22no—
119C2×#4318D414yes—
120C2×#4318D414yes—
121C2×#4318C2312yes—
122C2×#4318C2312yes—
123C2×#4318C2312yes—
124C22×C11⋊C8—21no—
125C22×C11⋊C8—21no—
126C22×C11⋊C8—21no—
127#66900—28no—
128#66900—24no—
129#66897—24no—
130(C2×D11)⋊C8—28no—
131#23440—111nomaximal, Sylow
132C24×C11—21no—
133C24×C11#4111yescharacteristic
134C23×D11—21no—
135C11×#41—24no—
136C11×#41—24no—
137C11×#41—24no—
138C11×#41—24no—
139C11×#41—42no—
140C11×#41—42no—
141C11×#41—42no—
142C11×#41—42no—
143C2×Q8×C11—24no—
144C2×Q8×C11—22no—
145C2×Q8×C11—21no—
146C2×Q8×C11—24no—
147C2×Q8×C11—24no—
148C2×Q8×C11—24no—
149C2×Q8×C11—24no—
150C2×Q8×C11—22no—
151C2×Q8×C11—21no—
152C2×Q8×C11—22no—
153C2×Q8×C11—21no—
154C2×Q8×C11—22no—
155C2×Q8×C11—22no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—42no—
159C2×Q8×C11—42no—
160C2×Q8×C11—41no—
161C2×Q8×C11—41no—
162C2×Q8×C11—42no—
163C2×Q8×C11—42no—
164C2×Q8×C11—42no—
165C2×Q8×C11C2×D414yes—
166C2×Q8×C11C2×D412yes—
167C2×D4×C11—24no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—41no—
174C2×D4×C11—41no—
175C2×D4×C11—42no—
176C2×D4×C11C2×D412yes—
177C22×C4×C11—24no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—24no—
181C22×C4×C11—41no—
182C22×C4×C11—41no—
183C22×C4×C11—42no—
184C22×C4×C11—41no—
185C22×C4×C11—41no—
186C22×C4×C11—42no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11#4111yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—22no—
198C2×C22⋊D11—22no—
199C2×C22⋊D11—42no—
200C2×C22⋊D11—42no—
201C22×Dic11—21no—
202#4339—24no—
203#4339—24no—
204#4339—22no—
205#4339—22no—
206#4339—22no—
207#4339—22no—
208#4339—42no—
209#4339—42no—
210#4339—42no—
211#4339—42no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44—21no—
215C2×D44C2×D412yes—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—42no—
219C2×C4×D11—42no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×Dic22—21no—
223C2×Dic22C2×D412yes—
224C11×Q16—216no—
225C11×SD16—216no—
226C11×M16—24no—
227C11×M16—24no—
228C2×C8×C11—22no—
229C2×C8×C11—22no—
230C2×C8×C11C2×D414yes—
231#4326—216no—
232#4326—28no—
233#4325—216no—
234#4325—28no—
235#4324—28no—
236#4323—28no—
237#4318—24no—
238#4318—24no—
239#4318—22no—
240#4318—22no—
241#4318—22no—
242#4318—22no—
243#4318—42no—
244#4318C2×D414yes—
245#4318C2×D414yes—
246C2×C11⋊C8—24no—
247C2×C11⋊C8—24no—
248C2×C11⋊C8—22no—
249C2×C11⋊C8—22no—
250C2×C11⋊C8—22no—
251C2×C11⋊C8—42no—
252C2×#575—111no—
253C22×#137—111no—
254C22×#137D1111yescharacteristic, complemented
255C2×#413—111no—
256C22×#101—111no—
257#2879—111no—
258#2020—114no—
259#2019—114no—
260#1738—111no—
261C23×C11—22no—
262C23×C11—42no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—82no—
266C23×C11#12111yescharacteristic
267C23×C11#12111yescharacteristic
268C23×C11#12112yes—
269C23×C11#12112yes—
270C23×C11C2×#4111yescharacteristic
271C22×D11—22no—
272C22×D11—42no—
273C22×D11—82no—
274Q8×C11—24no—
275Q8×C11—22no—
276Q8×C11—24no—
277Q8×C11—22no—
278Q8×C11—42no—
279Q8×C11—41no—
280Q8×C11—42no—
281Q8×C11—41no—
282Q8×C11—44no—
283Q8×C11—44no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—44no—
287D4×C11—44no—
288D4×C11—41no—
289D4×C11—41no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11—44no—
299C2×C4×C11—44no—
300C2×C4×C11#12012yes—
301C2×C4×C11#12012yes—
302C2×C4×C11#12012yes—
303C2×C4×C11#12012yes—
304C2×C4×C11#12012yes—
305C2×C4×C11#12012yes—
306C2×C4×C11#12111yescharacteristic
307C2×C4×C11#12111yescharacteristic
308C2×C4×C11#12112yes—
309C2×C4×C11#12112yes—
310C2×C4×C11#12712yes—
311C2×C4×C11#12712yes—
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C22×D411yescharacteristic
318C22⋊D11—42no—
319C22⋊D11—42no—
320C22⋊D11—44no—
321C2×Dic11—22no—
322C2×Dic11—42no—
323D44—22no—
324D44—22no—
325D44—42no—
326C4×D11—42no—
327C4×D11—42no—
328C4×D11—44no—
329Dic22—22no—
330Dic22—22no—
331Dic22—42no—
332C8×C11—24no—
333C11⋊C8—24no—
334C11⋊C8—24no—
335C11⋊C8—42no—
336C22×#41—111no—
337C22×#41C2×D1111yescharacteristic
338C23×Q8C2×D1111yescharacteristic
339#575—224no—
340#575—224no—
341C2×#137—24no—
342C2×#137—24no—
343C2×#137—22no—
344C2×#137—22no—
345C2×#137—114no—
346C2×#137—112no—
347C2×#137—224no—
348C2×#137—222no—
349C2×#137—221no—
350C2×#137—224no—
351C2×AGL(1,ℤ/8)—112no—
352C2×AGL(1,ℤ/8)—221no—
353C2×#135—222no—
354C22×Q16—221no—
355C22×Q16C2×D1112yescomplemented
356C22×SD16—221no—
357C22×SD16C2×D1112yescomplemented
358C22×M16—111no—
359C22×M16—111no—
360C22×M16—111no—
361C22×M16C2×D1111yescharacteristic
362#413—224no—
363C2×#101—114no—
364C2×#101—112no—
365C2×#101—224no—
366C2×#100—112no—
367#408—114no—
368#408—222no—
369#407—222no—
370#341—114no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—82no—
378C22×C11—82no—
379C22×C11—82no—
380C22×C11#39212yes—
381C22×C11#39212yes—
382C22×C11C2×#12111yescharacteristic
383C22×C11C2×#12111yescharacteristic
384C22×C11C2×#12111yescharacteristic
385C2×D11—42no—
386C2×D11—44no—
387C2×D11—84no—
388C4×C11—42no—
389C4×C11—44no—
390C4×C11#39212yes—
391C4×C11#39212yes—
392C4×C11C2×#12011yescharacteristic
393C4×C11C2×#12011yescharacteristic
394C4×C11C2×#12011yescharacteristic
395C4×C11C2×#12711yescharacteristic
396Dic11—42no—
397C2×#41—22no—
398C2×#41—21no—
399C2×#41—21no—
400C2×#41—22no—
401C2×#41—21no—
402C2×#41—21no—
403C2×#41—22no—
404C2×#41—112no—
405C2×#41—112no—
406C2×#41—221no—
407C2×#41—221no—
408C2×#41—222no—
409C2×#41—222no—
410C2×#41—222no—
411C2×#41—222no—
412C2×#41C22⋊D1114yes—
413C22×Q8—22no—
414C22×Q8—21no—
415C22×Q8—21no—
416C22×Q8—21no—
417C22×Q8—22no—
418C22×Q8—21no—
419C22×Q8—21no—
420C22×Q8—22no—
421C22×Q8—111no—
422C22×Q8C22⋊D1114yes—
423C22×Q8C22×D1112yes—
424C22×Q8C22×D1111yescharacteristic
425C22×D4—21no—
426C22×D4—111no—
427C22×D4—221no—
428C22×D4C22×D1111yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4—221no—
432C23×C4C22×D1111yescharacteristic
433#137—216no—
434#137—216no—
435#137—228no—
436#137—224no—
437#137—2216no—
438#137—228no—
439#137—228no—
440#137—224no—
441AGL(1,ℤ/8)—224no—
442AGL(1,ℤ/8)—228no—
443AGL(1,ℤ/8)—224no—
444#135—2216no—
445C2×Q16—24no—
446C2×Q16—24no—
447C2×Q16—24no—
448C2×Q16—224no—
449C2×Q16—222no—
450C2×Q16—228no—
451C2×SD16—24no—
452C2×SD16—24no—
453C2×SD16—24no—
454C2×SD16—222no—
455C2×SD16—224no—
456C2×SD16—222no—
457C2×SD16—228no—
458C2×D8—222no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16—114no—
462C2×M16—114no—
463C2×M16—112no—
464C2×M16—112no—
465C2×M16—112no—
466C2×M16—221no—
467C2×M16—221no—
468C2×M16—222no—
469C2×M16—222no—
470C2×M16—221no—
471C2×M16—222no—
472C2×M16—222no—
473C2×M16C22⋊D1112yes—
474C2×M16C22⋊D1112yes—
475C22×C8—221no—
476C22×C8—221no—
477C22×C8—221no—
478C22×C8C22×D1112yes—
479#101—228no—
480#101—224no—
481#100—224no—
482C22⋊C8—228no—
483C2×C11—22no—
484C2×C11—21no—
485C2×C11—21no—
486C2×C11—22no—
487C2×C11—82no—
488C2×C11C2×#39211yescharacteristic
489C2×C11#306912yes—
490D11—82no—
491C24—21no—
492C24—221no—
493C24#434111yescharacteristic
494#41—24no—
495#41—24no—
496#41—24no—
497#41—24no—
498#41—42no—
499#41—42no—
500#41—42no—
501#41—42no—
502#41—224no—
503#41—224no—
504#41—222no—
505#41—222no—
506#41—222no—
507#41—222no—
508#41—442no—
509#41—442no—
510#41—442no—
511#41—442no—
512C2×Q8—24no—
513C2×Q8—22no—
514C2×Q8—21no—
515C2×Q8—24no—
516C2×Q8—24no—
517C2×Q8—24no—
518C2×Q8—24no—
519C2×Q8—22no—
520C2×Q8—21no—
521C2×Q8—22no—
522C2×Q8—21no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—42no—
528C2×Q8—42no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—112no—
535C2×Q8—221no—
536C2×Q8—222no—
537C2×Q8—222no—
538C2×Q8C2×C22⋊D1114yes—
539C2×Q8C2×C22⋊D1112yes—
540C2×D4—24no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—42no—
549C2×D4—112no—
550C2×D4—222no—
551C2×D4—222no—
552C2×D4—222no—
553C2×D4—222no—
554C2×D4—221no—
555C2×D4—442no—
556C2×D4—442no—
557C2×D4C2×C22⋊D1112yes—
558C22×C4—24no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—42no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—42no—
568C22×C4—221no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—442no—
572C22×C4—442no—
573C22×C4D4×D1111yescharacteristic
574C22×C4D4×D1111yescharacteristic
575C22×C4D4×D1112yes—
576C22×C4D4×D1112yes—
577C22×C4#434111yescharacteristic
578C22×C4C2×C22⋊D1112yes—
579C22×C4C2×C22⋊D1112yes—
580C22×C4C2×C22⋊D1111yescharacteristic
581C22×C4C2×C22⋊D1111yescharacteristic
582C22×C4C23×D1111yescharacteristic
583Q16—216no—
584Q16—2216no—
585Q16—228no—
586SD16—216no—
587SD16—228no—
588SD16—2216no—
589SD16—228no—
590D8—228no—
591M16—24no—
592M16—24no—
593M16—114no—
594M16—114no—
595M16—224no—
596M16—224no—
597M16—222no—
598M16—222no—
599M16—222no—
600M16—222no—
601M16—442no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—224no—
605C2×C8—224no—
606C2×C8—222no—
607C2×C8—222no—
608C2×C8—222no—
609C2×C8—442no—
610C2×C8C2×C22⋊D1114yes—
611C11#2344011yescharacteristic, complemented, Sylow
612C23—22no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—82no—
617C23—222no—
618C23—442no—
619C23—882no—
620C23#6699111yescharacteristic
621C23#6699111yescharacteristic
622C23#6699212yes—
623C23#6699212yes—
624C23C2×#434111yescharacteristic
625Q8—24no—
626Q8—22no—
627Q8—24no—
628Q8—22no—
629Q8—42no—
630Q8—41no—
631Q8—42no—
632Q8—41no—
633Q8—44no—
634Q8—44no—
635Q8—222no—
636Q8—222no—
637Q8—442no—
638D4—22no—
639D4—22no—
640D4—44no—
641D4—44no—
642D4—41no—
643D4—41no—
644D4—222no—
645D4—222no—
646D4—442no—
647D4—442no—
648D4—444no—
649D4—442no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—222no—
661C2×C4—442no—
662C2×C4—442no—
663C2×C4—444no—
664C2×C4—442no—
665C2×C4#6699012yes—
666C2×C4#6699012yes—
667C2×C4#6699012yes—
668C2×C4#6699012yes—
669C2×C4#6699111yescharacteristic
670C2×C4#6699111yescharacteristic
671C2×C4#6699212yes—
672C2×C4#6699212yes—
673C2×C4#6699312yes—
674C2×C4#6699312yes—
675C2×C4#6700612yes—
676C2×C4#6700612yes—
677C2×C4C2×D4×D1111yescharacteristic
678C2×C4C2×D4×D1111yescharacteristic
679C2×C4C2×D4×D1111yescharacteristic
680C2×C4C22×C22⋊D1111yescharacteristic
681C2×C4C22×C22⋊D1111yescharacteristic
682C2×C4C22×C22⋊D1111yescharacteristic
683C8—24no—
684C8—224no—
685C8—224no—
686C8—442no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—82no—
694C22—82no—
695C22—82no—
696C22—444no—
697C22—442no—
698C22—884no—
699C22#1062283612yes—
700C22#1062283612yes—
701C22C2×#6699111yescharacteristic
702C22C2×#6699211yescharacteristic
703C22C2×#6699211yescharacteristic
704C4—42no—
705C4—44no—
706C4—442no—
707C4#1062283612yes—
708C4#1062283612yes—
709C4C2×#6699011yescharacteristic
710C4C2×#6699011yescharacteristic
711C4C2×#6699311yescharacteristic
712C4C2×#6700611yescharacteristic
713C2—21no—
714C2—21no—
715C2—22no—
716C2—22no—
717C2—82no—
718C2—882no—
719C2C2×#1062283611yescharacteristic
720C2#1307834912yes—
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC22×C11C2×#121
prime radicalC2×#10623353C2
hypercenterC22×#137D11
hypocenterC11#23440
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C22×#66995C2semidirect
3. C2×#10622850C2semidirect
4. C22×#66900C2semidirect
5. #13077060C2semidirect
6. #13069735C2semidirect
7. #13069728C2semidirect
8. #13068343C2semidirect
9. C22×C11×#137C2semidirect
17. C22×C11×Q16C22semidirect
18. C22×C11×SD16C22semidirect
38. C2×#66900C22semidirect
39. C2×#66900C22semidirect
40. C2×#66897C22semidirect
44. #10622190C22semidirect
254. C22×#137D11semidirect
355. C22×Q16C2×D11semidirect
357. C22×SD16C2×D11semidirect
611. C11#23440semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C22×#669952
C2×#106228502
C22×#669002
#130770602
#130697352
#130697282
#130683432
C22×C11×#1372
#2344011