Finite Group Databasebeta

← C4×#10622790 #14760632

Subgroups — C4×#10622790 #14760632

Order 2816.

914 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×#10622790C211yesmaximal, characteristic
2C4×#66995C211yesmaximal, characteristic, complemented
3C4×#66985C211yesmaximal, characteristic
4C4×#66954C211yesmaximal, characteristic, complemented
5#13069521C211yesmaximal, characteristic, complemented
6#13069394C211yesmaximal, characteristic, complemented
7#13069275C211yesmaximal, characteristic, complemented
8#13069268C211yesmaximal, characteristic, complemented
9#13069134C211yesmaximal, characteristic, complemented
10#13069127C211yesmaximal, characteristic
11#13068676C211yesmaximal, characteristic, complemented
12C4×#66883C211yesmaximal, characteristic, complemented
13C4×#66900C211yesmaximal, characteristic, complemented
14C4×#66897C211yesmaximal, characteristic, complemented
15C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66995C2211yescharacteristic
20C2×#66985C2211yescharacteristic
21C2×#66954C2211yescharacteristic
22C2×#66954C2211yescharacteristic
23C4×#4339C2211yescharacteristic
24C4×C11×SD16—21no—
25C4×C11×SD16—21no—
26C4×C11×SD16—21no—
27C4×C11×SD16—21no—
28C2×C11×#106C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C4×C8×C11C2211yescharacteristic
32C2×#66900C2211yescharacteristic
33C2×#66900C2211yescharacteristic
34#10622838C2211yescharacteristic
35C2×#66897C2211yescharacteristic
36C2×#66897C2211yescharacteristic
37#10622828C2211yescharacteristic
38#10622790C418yesdirect product factor
39C2×#66883C2211yescharacteristic
40C2×#66883C2211yescharacteristic
41#10622714C2211yescharacteristic
42#10622714C2211yescharacteristic
43#10622643—21no—
44C4×#4326—21no—
45#10622639—21no—
46C4×#4325—21no—
47#10622631—21no—
48C4×#4324—21no—
49#10622627—21no—
50C4×#4323—21no—
51#10622579C2211yescharacteristic
52#10622579C2211yescharacteristic
53#10622577C2211yescharacteristic
54#10622577C2211yescharacteristic
55C4×#4318C2211yescharacteristic
56C4×#4318C2211yescharacteristic
57C4×#4318C2211yescharacteristic
58#10622302—21no—
59#10622302—21no—
60C4×#4313—21no—
61C4×C8×D11—21no—
62#10622190C2211yescharacteristic
63#10622190C2211yescharacteristic
64#10622168C2211yescharacteristic
65#10622168C2211yescharacteristic
66#10622168C2211yescharacteristic
67#10622168C2211yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C2×#4339C2311yescharacteristic
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—22no—
75C2×C11×SD16C2×C414yescomplemented
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×#4326—21no—
93#66995—22no—
94#66995C2×C414yescomplemented
95C2×#4325—21no—
96C2×#4324—21no—
97#66985—22no—
98#66985C2×C414yes—
99C2×#4323—21no—
100C4×C22⋊D11—21no—
101C4×C22⋊D11—21no—
102#66979C2311yescharacteristic
103C2×#4318C2311yescharacteristic
104C2×#4318C2311yescharacteristic
105C2×#4318C2311yescharacteristic
106C2×#4318C2311yescharacteristic
107C2×#4318C2311yescharacteristic
108C2×#4318C2311yescharacteristic
109#66954—22no—
110#66954—22no—
111#66954—22no—
112#66954C2×C414yescomplemented
113C2×#4313—21no—
114C2×#4313—21no—
115C2×C8×D11—21no—
116C2×C8×D11—21no—
117C4×D44D411yescharacteristic
118C4×D44D411yescharacteristic
119#66925—21no—
120C42×D11—21no—
121C4×Dic22D411yescharacteristic
122C4×Dic22D411yescharacteristic
123C11×#106—21no—
124C11×#106—21no—
125C11×#103—21no—
126C11×#103—21no—
127C11×#102—21no—
128C11×#102—21no—
129C4×C8×C11D411yescharacteristic
130C4×C8×C11D411yescharacteristic
131C4×C8×C11D411yescharacteristic
132C4×C8×C11D411yescharacteristic
133#66900—22no—
134#66900C2×C414yescomplemented
135#66899—21no—
136#66899—21no—
137#66897—22no—
138#66897C2×C414yescomplemented
139#66896—21no—
140#66896—21no—
141#66883—22no—
142#66883C2×C414yescomplemented
143#66879—21no—
144#66879—21no—
145C8×Dic11—21no—
146C8×Dic11—21no—
147#66874—21no—
148#66874—21no—
149#66873—21no—
150#66873—21no—
151#66872—21no—
152#66872—21no—
153#66871—21no—
154#66871—21no—
155#66867—21no—
156#66867—21no—
157#66867—21no—
158C4×C11⋊C8—21no—
159C4×C11⋊C8—21no—
160C4×C11⋊C8—21no—
161C4×#471—111nomaximal, Sylow
162C24×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11C22×C412yes—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11C22×C412yes—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—41no—
179C22×C4×C11—41no—
180C22×C4×C11—82no—
181C22×C4×C11#4111yescharacteristic
182C22×C4×C11#4111yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C2×C22⋊D11—21no—
185#4339—21no—
186#4339—21no—
187#4339C22×C412yes—
188#4339#4112yes—
189C2×D44C2×D411yescharacteristic
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×Dic22C2×D411yescharacteristic
194C11×SD16—24no—
195C11×SD16—24no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11C22×C412yes—
199C2×C8×C11C2×D411yescharacteristic
200C2×C8×C11C2×D411yescharacteristic
201C2×C8×C11C2×D411yescharacteristic
202C2×C8×C11C2×D411yescharacteristic
203C2×C8×C11#4112yes—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—41no—
209C11×C4⋊C4—41no—
210C11×C22⋊C4—41no—
211C11×C22⋊C4—41no—
212C42×C11—41no—
213C42×C11—41no—
214C42×C11C2×D411yescharacteristic
215C42×C11C2×D411yescharacteristic
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C22⋊Dic11—21no—
219#4326—24no—
220#4325—24no—
221#4324—24no—
222#4323—24no—
223(C2×D11)⋊C4—21no—
224(C2×D11)⋊C4—21no—
225C4⋊Dic11C2×D411yescharacteristic
226C4⋊Dic11C2×D411yescharacteristic
227Dic11⋊C4—21no—
228Dic11⋊C4—21no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232#4318—21no—
233#4318—21no—
234#4318—21no—
235#4318—21no—
236#4318—21no—
237#4318—21no—
238#4318—21no—
239#4318—21no—
240#4318C22×C412yes—
241#4318C22×C412yes—
242#4318C22×C412yes—
243#4318#4112yes—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250#4313—24no—
251#4313—24no—
252C8×D11—24no—
253C8×D11—24no—
254C2×#471—111no—
255C4×#137—111no—
256C4×AGL(1,ℤ/8)—111no—
257C2×C4×SD16D1111yescharacteristic, complemented
258C4×#131—111no—
259#1977—111no—
260#1951—111no—
261#1931—111no—
262#1930—111no—
263#1908—111no—
264#1907—111no—
265#1815—111no—
266C4×#108—111no—
267C4×#101—111no—
268C4×#100—111no—
269C23×C11—22no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—81no—
273C23×C11—81no—
274C23×C11C2×#4111yescharacteristic
275C22×D11—21no—
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—41no—
279Q8×C11—41no—
280D4×C11—22no—
281D4×C11—22no—
282D4×C11—41no—
283D4×C11—41no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—82no—
292C2×C4×C11—82no—
293C2×C4×C11—81no—
294C2×C4×C11—81no—
295C2×C4×C11#12111yescharacteristic
296C2×C4×C11#12111yescharacteristic
297C2×C4×C11#12111yescharacteristic
298C2×C4×C11#12111yescharacteristic
299C2×C4×C11C23×C411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C22⋊D11—22no—
306C22⋊D11—22no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310D44—21no—
311D44C4×D412yes—
312C4×D11—22no—
313C4×D11—22no—
314C4×D11—42no—
315C4×D11—42no—
316Dic22—21no—
317Dic22C4×D412yes—
318C8×C11—21no—
319C8×C11—21no—
320C8×C11C4×D412yes—
321C8×C11C4×D412yes—
322C11⋊C8—22no—
323C11⋊C8—22no—
324C11⋊C8—22no—
325C11⋊C8—22no—
326C11⋊C8—41no—
327C11⋊C8—41no—
328C2×#137—111no—
329C2×AGL(1,ℤ/8)—111no—
330C22×SD16C2×D1111yescharacteristic
331C2×#131—111no—
332C2×#131—111no—
333C4×#41—111no—
334C2×C4×Q8C2×D1111yescharacteristic
335C2×C4×D4C2×D1111yescharacteristic
336#471—118no—
337#442—221no—
338#441—221no—
339#440—221no—
340#440—221no—
341C4×Q16—221no—
342C4×SD16—21no—
343C4×SD16—21no—
344C4×SD16—21no—
345C4×SD16—21no—
346C4×SD16—221no—
347C4×SD16—221no—
348C4×D8—221no—
349C2×#108—111no—
350C2×#108—111no—
351#428—111no—
352#428—111no—
353C2×#106C2×D1111yescharacteristic
354#419—111no—
355#418—111no—
356#417—111no—
357#417—111no—
358C2×#103C2×D1111yescharacteristic
359C2×#102C2×D1111yescharacteristic
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—111no—
371C4×M16—221no—
372C2×C4×C8—221no—
373C2×C4×C8C2×D1111yescharacteristic
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—42no—
383C22×C11—82no—
384C22×C11—82no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11C4×#4111yescharacteristic
388C22×C11C2×#12111yescharacteristic
389C22×C11#52911yescharacteristic
390C2×D11—22no—
391C2×D11—41no—
392C2×D11—41no—
393C4×C11—21no—
394C4×C11—21no—
395C4×C11—21no—
396C4×C11—42no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11#47112yescomplemented
400C4×C11C2×C4×D411yescharacteristic
401C4×C11C2×C4×D411yescharacteristic
402C4×C11#52511yescharacteristic
403C4×C11#53211yescharacteristic
404Dic11—22no—
405Dic11—41no—
406Dic11—41no—
407C2×#41—111no—
408C22×Q8C22×D1111yescharacteristic
409C22×D4C22×D1111yescharacteristic
410C23×C4—21no—
411#137—114no—
412#137—222no—
413AGL(1,ℤ/8)—114no—
414AGL(1,ℤ/8)—222no—
415C2×Q16—221no—
416C2×SD16—22no—
417C2×SD16—21no—
418C2×SD16—21no—
419C2×SD16—221no—
420C2×SD16—221no—
421C2×SD16C4×D1114yescomplemented
422C2×D8—221no—
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—111no—
432C2×M16—111no—
433C2×M16—221no—
434C2×M16—221no—
435C22×C8—221no—
436C22×C8—221no—
437C22×C8C22×D1111yescharacteristic
438C22×C8C22×D1111yescharacteristic
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8—111no—
444C4×Q8—111no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—111no—
450C4×D4—111no—
451C4×D4—221no—
452C4×D4—221no—
453#117—111no—
454#117—221no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4C22×D1111yescharacteristic
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—221no—
465#107—221no—
466#106—21no—
467#106—21no—
468#106—221no—
469#106—221no—
470#103—21no—
471#103—21no—
472#103—221no—
473#103—221no—
474#103—221no—
475#103—221no—
476#102—21no—
477#102—21no—
478#102—221no—
479#102—221no—
480#102—221no—
481#102—221no—
482#101—114no—
483#101—222no—
484#100—114no—
485#100—222no—
486#97—221no—
487#97—221no—
488#97—221no—
489#97—221no—
490#97—221no—
491C4×C8—221no—
492C4×C8—221no—
493C4×C8—221no—
494C4×C8—221no—
495C4×C8—221no—
496C4×C8C22⋊D1111yescharacteristic
497C4×C8C22⋊D1111yescharacteristic
498C4×C8C22⋊D1111yescharacteristic
499C4×C8C22⋊D1111yescharacteristic
500C2×C11—21no—
501C2×C11—21no—
502C2×C11—82no—
503C2×C11C4×#12111yescharacteristic
504C2×C11C2×#47111yescharacteristic
505C2×C11#306711yescharacteristic
506D11—42no—
507C24—21no—
508#41—112no—
509#41—112no—
510#41—221no—
511#41—221no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—111no—
518C2×Q8C2×C4×D1112yes—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—111no—
525C2×D4—221no—
526C2×D4C2×C4×D1112yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—82no—
533C22×C4—221no—
534C22×C4—221no—
535C22×C4—221no—
536C22×C4#434111yescharacteristic
537C22×C4#434111yescharacteristic
538C22×C4C23×D1111yescharacteristic
539Q16—224no—
540SD16—24no—
541SD16—24no—
542SD16—224no—
543SD16—224no—
544D8—224no—
545M16—112no—
546M16—112no—
547M16—112no—
548M16—112no—
549M16—224no—
550M16—221no—
551M16—221no—
552M16—221no—
553M16—221no—
554M16—224no—
555M16—221no—
556M16—221no—
557M16—221no—
558M16—221no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—224no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C2×C8—224no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8C2×C4×D1112yes—
570C2×C8#433912yes—
571C2×C8C2×C22⋊D1111yescharacteristic
572C2×C8C2×C22⋊D1111yescharacteristic
573C2×C8C2×C22⋊D1111yescharacteristic
574C2×C8C2×C22⋊D1111yescharacteristic
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—111no—
582C4⋊C4—111no—
583C4⋊C4—221no—
584C4⋊C4—221no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—221no—
588C22⋊C4—221no—
589C22⋊C4—221no—
590C42—41no—
591C42—41no—
592C42—221no—
593C42—221no—
594C42—221no—
595C42D4×D1111yescharacteristic
596C42D4×D1111yescharacteristic
597C42C2×C22⋊D1111yescharacteristic
598C42C2×C22⋊D1111yescharacteristic
599C11C4×#47111yescharacteristic, complemented, Sylow
600C23—22no—
601C23—41no—
602C23—41no—
603C23—81no—
604C23—81no—
605C23—221no—
606C23C2×#434111yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—112no—
612Q8—221no—
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—112no—
618D4—222no—
619D4—222no—
620D4—221no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—82no—
629C2×C4—82no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—221no—
633C2×C4—222no—
634C2×C4—222no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—442no—
638C2×C4—442no—
639C2×C4#6699111yescharacteristic
640C2×C4#6699111yescharacteristic
641C2×C4#6699111yescharacteristic
642C2×C4#6699111yescharacteristic
643C2×C4C22×C4×D1111yescharacteristic
644C2×C4C2×#433911yescharacteristic
645C2×C4C2×D4×D1111yescharacteristic
646C2×C4#41×D1111yescharacteristic
647C2×C4#41×D1111yescharacteristic
648C2×C4C22×C22⋊D1111yescharacteristic
649C8—21no—
650C8—21no—
651C8—222no—
652C8—222no—
653C8—222no—
654C8—222no—
655C8—441no—
656C8—441no—
657C8C4×C22⋊D1112yes—
658C8C4×C22⋊D1112yes—
659C22—21no—
660C22—21no—
661C22—42no—
662C22—82no—
663C22—82no—
664C22—81no—
665C22—81no—
666C22—222no—
667C22—441no—
668C22—441no—
669C22C4×#434111yescharacteristic
670C22#1062308811yescharacteristic
671C22C2×#6699111yescharacteristic
672C4—21no—
673C4—21no—
674C4—21no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4—222no—
679C4—441no—
680C4—441no—
681C4#1062279012yesdirect product factor
682C4C4×D4×D1111yescharacteristic
683C4#1062307911yescharacteristic
684C4C2×C4×C22⋊D1111yescharacteristic
685C4#1062335911yescharacteristic
686C2—21no—
687C2—21no—
688C2—82no—
689C2—442no—
690C2C4×#6699111yescharacteristic
691C2C2×#1062279011yescharacteristic
692C2#1307833211yescharacteristic
subgroupG/H
centerC2×C4#66991
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC22×C11C2×#121
prime radicalC2×#66985C22
cosocleC22×C4×C11C24
hypercenterC2×C4×SD16D11
hypocenterC11C4×#471
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#66995C2semidirect
4. C4×#66954C2semidirect
5. #13069521C2semidirect
6. #13069394C2semidirect
7. #13069275C2semidirect
8. #13069268C2semidirect
9. #13069134C2semidirect
11. #13068676C2semidirect
12. C4×#66883C2semidirect
13. C4×#66900C2semidirect
14. C4×#66897C2semidirect
15. C2×C4×C11×SD16C2semidirect
38. #10622790C4direct (N × H)
75. C2×C11×SD16C2×C4semidirect
94. #66995C2×C4semidirect
112. #66954C2×C4semidirect
134. #66900C2×C4semidirect
138. #66897C2×C4semidirect
142. #66883C2×C4semidirect
257. C2×C4×SD16D11semidirect
399. C4×C11#471semidirect
421. C2×SD16C4×D11semidirect
599. C11C4×#471semidirect
681. C4#10622790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227902
C4×#669952
C4×#669852
C4×#669542
#130695212
#130693942
#130692752
#130692682
#130691342
#130691272
#130686762
C4×#668832
C4×#669002
C4×#668972
C2×C4×C11×SD162
C4×#47111