Finite Group Databasebeta

← C4×#10622816 #14760642

Subgroups — C4×#10622816 #14760642

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×#10622816C211yesmaximal, characteristic
2C4×#67002C211yesmaximal, characteristic
3C2×C4×#4325C211yesmaximal, characteristic, complemented
4C4×#67001C211yesmaximal, characteristic, complemented
5#13069518C211yesmaximal, characteristic, complemented
6#13069393C211yesmaximal, characteristic, complemented
7#13069277C211yesmaximal, characteristic, complemented
8#13069274C211yesmaximal, characteristic, complemented
9#13069133C211yesmaximal, characteristic, complemented
10#13069122C211yesmaximal, characteristic
11#13068673C211yesmaximal, characteristic, complemented
12C4×#66886C211yesmaximal, characteristic, complemented
13C4×#66900C211yesmaximal, characteristic, complemented
14C4×#66887C211yesmaximal, characteristic, complemented
15C4×C11×#137C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67002C2211yescharacteristic
20C2×#67001C2211yescharacteristic
21C2×#67001C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C11×#441—21no—
25C11×#440—21no—
26C4×C11×Q16—21no—
27C4×C11×SD16—21no—
28C11×#428C2211yescharacteristic
29C11×#419C2211yescharacteristic
30C11×#417C2211yescharacteristic
31C4×C11×M16C2211yescharacteristic
32#10622845C2211yescharacteristic
33C2×#66900C2211yescharacteristic
34C2×#66900C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622816C418yesdirect product factor
37C2×#66887C2211yescharacteristic
38C2×#66887C2211yescharacteristic
39C2×#66886C2211yescharacteristic
40C2×#66886C2211yescharacteristic
41#10622639—21no—
42C4×#4325—21no—
43C4×#4325—21no—
44C4×#4325—21no—
45C4×#4325—21no—
46C4×#4325—21no—
47#10622627—21no—
48C4×#4323—21no—
49#10622614C2211yescharacteristic
50#10622610—21no—
51#10622610—21no—
52#10622610C2211yescharacteristic
53#10622610C2211yescharacteristic
54#10622608C2211yescharacteristic
55C2×#66873C2211yescharacteristic
56C2×#66872C2211yescharacteristic
57C4×#4318—21no—
58C4×#4318C2211yescharacteristic
59C4×#4318C2211yescharacteristic
60C2×C4×C11⋊C8—21no—
61C2×C4×C11⋊C8C2211yescharacteristic
62#10622196C2211yescharacteristic
63#10622196C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622192C2211yescharacteristic
66#10622168C2211yescharacteristic
67#10622168C2211yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C11×#137—22no—
73C11×#137C2×C414yescomplemented
74C2×C11×Q16—21no—
75C2×C11×SD16—21no—
76C2×C11×M16C2311yescharacteristic
77C2×C11×M16C2311yescharacteristic
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11D411yescharacteristic
83C4×Q8×C11D411yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D411yescharacteristic
87C4×D4×C11D411yescharacteristic
88C11×#117—21no—
89C11×#117C2311yescharacteristic
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95#67002—22no—
96#67002C2×C414yes—
97#67001—22no—
98#67001—22no—
99#67001—22no—
100#67001C2×C414yescomplemented
101C2×#4325—21no—
102C2×#4325—21no—
103C2×#4325—21no—
104C2×#4325—22no—
105C2×#4325C2×C414yescomplemented
106C2×#4323—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×C4⋊Dic11C2311yescharacteristic
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×D44—21no—
120C4×D44—21no—
121C4×D44—21no—
122C4×D44—21no—
123C11×#107—21no—
124C11×#106—21no—
125C11×#103—21no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#102—21no—
129C11×#97—21no—
130C4×C8×C11—21no—
131#66900—22no—
132#66900C2×C414yescomplemented
133#66899—21no—
134#66899—21no—
135#66899—21no—
136#66896—21no—
137#66887—22no—
138#66887C2×C414yescomplemented
139#66886—22no—
140#66886C2×C414yescomplemented
141#66873—21no—
142#66873—21no—
143#66873—21no—
144#66873—21no—
145#66872—21no—
146#66872—21no—
147#66872—21no—
148#66871—21no—
149#66867—21no—
150#66867—21no—
151#66867—21no—
152#66867—21no—
153C4×C11⋊C8—21no—
154C4×C11⋊C8—21no—
155C4×C11⋊C8—21no—
156C4×C11⋊C8—21no—
157C4×C11⋊C8D411yescharacteristic
158C4×C11⋊C8D411yescharacteristic
159C4×C11⋊C8D411yescharacteristic
160C4×C11⋊C8D411yescharacteristic
161C4×#471—111nomaximal, Sylow
162C23×D11—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×C11C2×D411yescharacteristic
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11#4111yescharacteristic
182C22×C4×C11#4111yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×Dic11—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44C22×C412yes—
191C2×C4×D11—41no—
192C2×C4×D11—41no—
193C2×C4×D11—82no—
194C11×Q16—24no—
195C11×SD16—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⋊C4—41no—
207C11×C4⋊C4—41no—
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C4⋊C4C2×D411yescharacteristic
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—41no—
217C42×C11—41no—
218C42×C11C2×D411yescharacteristic
219C42×C11C2×D411yescharacteristic
220C42×C11C2×D411yescharacteristic
221C42×C11C2×D411yescharacteristic
222#4325—24no—
223#4325—24no—
224#4325—24no—
225#4323—24no—
226(C2×D11)⋊C4—41no—
227(C2×D11)⋊C4—41no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
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×#137D1111yescharacteristic, complemented
256C4×AGL(1,ℤ/8)—111no—
257C2×C4×SD16—111no—
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—21no—
270C23×C11C2×#4111yescharacteristic
271C22×D11—22no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—81no—
275C22×D11—81no—
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—21no—
285D4×C11C4×D412yes—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—41no—
294C2×C4×C11—42no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—42no—
298C2×C4×C11—41no—
299C2×C4×C11—81no—
300C2×C4×C11#12111yescharacteristic
301C2×C4×C11#12111yescharacteristic
302C2×C4×C11#12111yescharacteristic
303C2×C4×C11#12111yescharacteristic
304C2×C4×C11C23×C411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×Dic11—41no—
311C2×Dic11—81no—
312D44—22no—
313D44—22no—
314D44—41no—
315D44—41no—
316C4×D11—82no—
317C4×D11—82no—
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×#137C2×D1111yescharacteristic
329C2×AGL(1,ℤ/8)—111no—
330C22×SD16—111no—
331C2×#131—111no—
332C2×#131—111no—
333C4×#41C2×D1111yescharacteristic
334C2×C4×Q8C2×D1111yescharacteristic
335C2×C4×D4—111no—
336#471—118no—
337#442—221no—
338#441—21no—
339#440—21no—
340#440—221no—
341C4×Q16—21no—
342C4×SD16—21no—
343C4×SD16—221no—
344C4×SD16—221no—
345C4×SD16—221no—
346C4×SD16—221no—
347C4×SD16—221no—
348C4×D8—221no—
349C2×#108—111no—
350C2×#108—111no—
351#428—111no—
352#428C2×D1111yescharacteristic
353C2×#106—111no—
354#419C2×D1111yescharacteristic
355#418—111no—
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×C4×C8—111no—
373C2×C4×C8—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×C11C4×#4111yescharacteristic
386C22×C11C2×#12111yescharacteristic
387C22×C11#52911yescharacteristic
388C2×D11—42no—
389C2×D11—82no—
390C2×D11—81no—
391C2×D11—81no—
392C2×D11—82no—
393C4×C11—21no—
394C4×C11—21no—
395C4×C11—21no—
396C4×C11—22no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—42no—
400C4×C11—81no—
401C4×C11#47112yescomplemented
402C4×C11C2×C4×D411yescharacteristic
403C4×C11C2×C4×D411yescharacteristic
404C4×C11#52511yescharacteristic
405C4×C11#53211yescharacteristic
406Dic11—81no—
407C2×#41C22×D1111yescharacteristic
408C22×Q8C22×D1111yescharacteristic
409C22×D4—111no—
410C23×C4—221no—
411#137—22no—
412#137C4×D1114yescomplemented
413AGL(1,ℤ/8)—114no—
414AGL(1,ℤ/8)—222no—
415C2×Q16—21no—
416C2×SD16—21no—
417C2×SD16—114no—
418C2×SD16—222no—
419C2×SD16—221no—
420C2×SD16—221no—
421C2×SD16—221no—
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—221no—
432C2×M16—221no—
433C2×M16C22×D1111yescharacteristic
434C2×M16C22×D1111yescharacteristic
435C22×C8—111no—
436C22×C8—111no—
437C22×C8—221no—
438C22×C8—221no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8C22⋊D1111yescharacteristic
444C4×Q8C22⋊D1111yescharacteristic
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—221no—
448C4×D4—221no—
449C4×D4—221no—
450C4×D4—221no—
451C4×D4C22⋊D1111yescharacteristic
452C4×D4C22⋊D1111yescharacteristic
453#117—21no—
454#117C22×D1111yescharacteristic
455C2×C4⋊C4—21no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4C22×D1111yescharacteristic
458C2×C22⋊C4—221no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42C22×D1111yescharacteristic
462#108—114no—
463#108—222no—
464#107—21no—
465#107—221no—
466#106—21no—
467#106—221no—
468#106—221no—
469#106—221no—
470#103—21no—
471#103—21no—
472#103—21no—
473#103—221no—
474#103—221no—
475#103—221no—
476#102—21no—
477#102—221no—
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—21no—
487#97—221no—
488#97—221no—
489#97—221no—
490#97—221no—
491C4×C8—21no—
492C4×C8—111no—
493C4×C8—111no—
494C4×C8—111no—
495C4×C8—111no—
496C4×C8—221no—
497C4×C8—221no—
498C4×C8—221no—
499C4×C8—221no—
500C2×C11—21no—
501C2×C11—21no—
502C2×C11—42no—
503C2×C11C4×#12111yescharacteristic
504C2×C11C2×#47111yescharacteristic
505C2×C11#306711yescharacteristic
506D11—82no—
507C24—221no—
508#41—21no—
509#41—21no—
510#41C2×C4×D1112yes—
511#41#433912yes—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8C2×C4×D1112yes—
518C2×Q8C2×C22⋊D1111yescharacteristic
519C2×D4—21no—
520C2×D4—112no—
521C2×D4—221no—
522C2×D4—221no—
523C2×D4—221no—
524C2×D4—221no—
525C2×D4—221no—
526C2×D4C2×C22⋊D1111yescharacteristic
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—221no—
533C22×C4—441no—
534C22×C4—441no—
535C22×C4—882no—
536C22×C4#434111yescharacteristic
537C22×C4#434111yescharacteristic
538C22×C4C23×D1111yescharacteristic
539Q16—24no—
540SD16—24no—
541SD16—224no—
542SD16—224no—
543SD16—224no—
544D8—224no—
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—41no—
580C4⋊C4—41no—
581C4⋊C4—221no—
582C4⋊C4—221no—
583C4⋊C4C2×C22⋊D1111yescharacteristic
584C4⋊C4C2×C22⋊D1111yescharacteristic
585C22⋊C4—21no—
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—441no—
589C22⋊C4—441no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—41no—
594C42—41no—
595C42D4×D1111yescharacteristic
596C42D4×D1111yescharacteristic
597C42C2×C22⋊D1111yescharacteristic
598C42C2×C22⋊D1111yescharacteristic
599C11C4×#47111yescharacteristic, complemented, Sylow
600C23—21no—
601C23—222no—
602C23—441no—
603C23—441no—
604C23—881no—
605C23—881no—
606C23C2×#434111yescharacteristic
607Q8—21no—
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8C4×C22⋊D1112yes—
613D4—22no—
614D4—22no—
615D4—21no—
616D4—222no—
617D4—222no—
618D4—441no—
619D4—441no—
620D4C4×C22⋊D1112yes—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—81no—
635C2×C4—441no—
636C2×C4—882no—
637C2×C4—882no—
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—442no—
665C22—882no—
666C22—882no—
667C22—881no—
668C22—881no—
669C22C4×#434111yescharacteristic
670C22#1062306911yescharacteristic
671C22C2×#6699211yescharacteristic
672C4—22no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—81no—
680C4—881no—
681C4#1062281612yesdirect product factor
682C4C4×D4×D1111yescharacteristic
683C4#1062307811yescharacteristic
684C4C2×C4×C22⋊D1111yescharacteristic
685C4#1062336311yescharacteristic
686C2—21no—
687C2—21no—
688C2—42no—
689C2—882no—
690C2C4×#6699211yescharacteristic
691C2C2×#1062281611yescharacteristic
692C2#1307833311yescharacteristic
subgroupG/H
centerC2×C4#66992
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#137C2
socleC22×C11C2×#121
prime radicalC2×#67002C22
cosocleC22×C4×C11C24
hypercenterC4×#137D11
hypocenterC11C4×#471
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
3. C2×C4×#4325C2semidirect
4. C4×#67001C2semidirect
5. #13069518C2semidirect
6. #13069393C2semidirect
7. #13069277C2semidirect
8. #13069274C2semidirect
9. #13069133C2semidirect
11. #13068673C2semidirect
12. C4×#66886C2semidirect
13. C4×#66900C2semidirect
14. C4×#66887C2semidirect
15. C4×C11×#137C2semidirect
36. #10622816C4direct (N × H)
73. C11×#137C2×C4semidirect
100. #67001C2×C4semidirect
105. C2×#4325C2×C4semidirect
132. #66900C2×C4semidirect
138. #66887C2×C4semidirect
140. #66886C2×C4semidirect
255. C4×#137D11semidirect
401. C4×C11#471semidirect
412. #137C4×D11semidirect
599. C11C4×#471semidirect
681. C4#10622816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228162
C4×#670022
C2×C4×#43252
C4×#670012
#130695182
#130693932
#130692772
#130692742
#130691332
#130691222
#130686732
C4×#668862
C4×#669002
C4×#668872
C4×C11×#1372
C4×#47111