Finite Group Databasebeta

← C2×#21446850 #29706899

Subgroups — C2×#21446850 #29706899

Order 15616.

2190 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519810C211yesmaximal, characteristic, complemented
2C2×#16840329C211yesmaximal, characteristic
3C22×#14519764C211yesmaximal, characteristic, complemented
4C22×#14519703C211yesmaximal, characteristic, complemented
5C2×#16839772C211yesmaximal, characteristic, complemented
6#21446850C218yesmaximal, direct product factor
7C2×#16839523C211yesmaximal, characteristic, complemented
8C22×#100×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×Dic122C2211yescharacteristic
11C2×#14519810—24no—
12C2×#14519810—22no—
13C2×#14519810—24no—
14C2×#14519810C2214yescomplemented
15C22×Dic244—21no—
16C22×#11758190—21no—
17#16840329—22no—
18#16840329—22no—
19#16840329—22no—
20#16840329C2214yes—
21C2×#14519773—21no—
22C2×#14519764—24no—
23C2×#14519764—22no—
24C2×#14519764—21no—
25C2×#14519764—24no—
26C2×#14519764C2214yescomplemented
27C2×#14519748—22no—
28C2×#14519746—22no—
29C2×#14519736C2211yescharacteristic
30C22×C22⋊Dic61—22no—
31C22×C4×Dic61C2211yescharacteristic
32C2×#14519703—24no—
33C2×#14519703C2214yescomplemented
34#16839772—22no—
35#16839772C2214yescomplemented
36C2×#14519702—22no—
37#16839523C2214yescomplemented
38C23×D4×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C22×M16×C61C2211yescharacteristic
41C2×#100×C61—24no—
42C2×#100×C61C2214yescomplemented
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—22no—
46C2×#11758222—22no—
47C2×#11758222—22no—
48C2×#11758222—22no—
49C2×#11758222D412yes—
50C2×#11758222C2312yes—
51C22×Dic122—21no—
52C22×Dic122—21no—
53C22×Dic122—21no—
54C22×Dic122—21no—
55C22×Dic122—22no—
56C22×Dic122—22no—
57C22×Dic122—21no—
58C22×Dic122—22no—
59C22×Dic122D411yescharacteristic
60C22×Dic122D414yescomplemented
61C22×Dic122C2312yes—
62C22×D244D411yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—24no—
65C23×Dic61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68#14519810—216no—
69#14519810—28no—
70#14519810—28no—
71C2×Dic244—28no—
72C2×Dic244—24no—
73C2×#11758190—28no—
74C2×#11758190—24no—
75#14519773—24no—
76#14519773—24no—
77#14519764—216no—
78#14519764—24no—
79#14519764—24no—
80#14519764—28no—
81#14519764—28no—
82#14519748—28no—
83#14519748—28no—
84#14519746—28no—
85#14519746—28no—
86#14519736—21no—
87#14519736—21no—
88#14519736D412yes—
89#14519736C2312yes—
90C2×C4⋊Dic61D412yes—
91C2×C22⋊Dic61—216no—
92C2×C22⋊Dic61—24no—
93C2×C22⋊Dic61—28no—
94C2×C22⋊Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61D414yescomplemented
99C2×C4×Dic61C2312yes—
100#14519703—28no—
101#14519702—28no—
102C25×C61D412yes—
103C22×D4×C61—21no—
104C22×D4×C61—22no—
105C22×D4×C61—22no—
106C22×D4×C61—21no—
107C22×D4×C61—22no—
108C22×D4×C61—21no—
109C22×D4×C61—21no—
110C22×D4×C61—22no—
111C22×D4×C61D412yes—
112C22×D4×C61C2312yes—
113C23×C4×C61C2311yescharacteristic
114C2×M16×C61—22no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—22no—
118C2×M16×C61—22no—
119C2×M16×C61D414yescomplemented
120C2×M16×C61C2312yes—
121C2×M16×C61C2312yes—
122C22×C8×C61—21no—
123C22×C8×C61—21no—
124#100×C61—28no—
125C24×C61—22no—
126C24×C61—24no—
127C24×C61—22no—
128C24×C61—24no—
129C24×C61—48no—
130C24×C61C2×D411yescharacteristic
131C24×C61C2×D414yes—
132C23×D61—21no—
133C2×D4×C61—22no—
134C2×D4×C61—24no—
135C2×D4×C61—22no—
136C2×D4×C61—24no—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61—42no—
144C2×D4×C61—42no—
145C2×D4×C61—42no—
146C2×D4×C61—42no—
147C2×D4×C61—42no—
148C2×D4×C61—42no—
149C2×D4×C61—42no—
150C2×D4×C61—42no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61#4112yes—
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—216no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—88no—
167C22×Dic61—21no—
168C22×Dic61—24no—
169C22×Dic61—24no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—44no—
174C22×Dic61—41no—
175C22×Dic61—41no—
176C22×Dic61—42no—
177#11758222—24no—
178#11758222—24no—
179#11758222—22no—
180#11758222—22no—
181#11758222—22no—
182#11758222—22no—
183#11758222—42no—
184#11758222—42no—
185#11758222—42no—
186#11758222—42no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—21no—
190C2×D244C2×D412yes—
191C2×C4×D61—22no—
192C2×C4×D61—22no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×Dic122—24no—
196C2×Dic122—24no—
197C2×Dic122—22no—
198C2×Dic122—24no—
199C2×Dic122—24no—
200C2×Dic122—22no—
201C2×Dic122—22no—
202C2×Dic122—22no—
203C2×Dic122—22no—
204C2×Dic122—22no—
205C2×Dic122—24no—
206C2×Dic122—21no—
207C2×Dic122—22no—
208C2×Dic122—41no—
209C2×Dic122—41no—
210C2×Dic122—42no—
211C2×Dic122—42no—
212C2×Dic122—42no—
213C2×Dic122—42no—
214C2×Dic122—42no—
215C2×Dic122C2×D412yes—
216C2×Dic122C2×D414yescomplemented
217M16×C61—24no—
218M16×C61—22no—
219M16×C61—22no—
220M16×C61—22no—
221M16×C61—42no—
222M16×C61C2×D414yescomplemented
223C2×C8×C61—24no—
224C2×C8×C61—22no—
225C2×C8×C61—22no—
226C2×C8×C61—42no—
227C22⋊Dic61—232no—
228C22⋊Dic61—216no—
229C22⋊Dic61—22no—
230C22⋊Dic61—22no—
231C4⋊Dic61—22no—
232C4⋊Dic61C2×D414yes—
233C4×Dic61—24no—
234C4×Dic61—22no—
235C4×Dic61—22no—
236C4×Dic61—22no—
237C4×Dic61C2×D414yescomplemented
238Dic244—216no—
239#11758190—216no—
240C23×C61—24no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—48no—
245C23×C61—416no—
246C23×C61—44no—
247C23×C61—44no—
248C23×C61—48no—
249C23×C61—84no—
250C23×C61—88no—
251C23×C61#12011yescharacteristic
252C23×C61#12012yes—
253C23×C61#12011yescharacteristic
254C23×C61#12112yes—
255C23×C61C22×D411yescharacteristic
256C22×D61—22no—
257C22×D61—42no—
258C22×D61—44no—
259D4×C61—42no—
260D4×C61—42no—
261D4×C61—42no—
262D4×C61—42no—
263D4×C61—44no—
264D4×C61—44no—
265C2×C4×C61#12012yes—
266C2×C4×C61#12012yes—
267C2×C4×C61#12012yes—
268C2×C4×C61#12011yescharacteristic
269C2×C4×C61#12011yescharacteristic
270C2×C4×C61#12112yes—
271C2×C4×C61#12112yes—
272C2×C4×C61#12112yes—
273C2×C4×C61#12112yes—
274C2×C4×C61#12112yes—
275C2×C4×C61#12712yes—
276C2×C4×C61#12712yes—
277C2×C4×C61C22×D411yescharacteristic
278C2×C4×C61C22×D411yescharacteristic
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C22×D411yescharacteristic
281C2×C4×C61C22×D411yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C22⋊D61—42no—
284C22⋊D61—42no—
285C22⋊D61—44no—
286C22⋊D61—816no—
287C2×Dic61—24no—
288C2×Dic61—24no—
289C2×Dic61—24no—
290C2×Dic61—22no—
291C2×Dic61—44no—
292C2×Dic61—48no—
293C2×Dic61—42no—
294C2×Dic61—42no—
295C2×Dic61—44no—
296C2×Dic61—44no—
297C2×Dic61—42no—
298C2×Dic61—44no—
299D244—22no—
300D244—22no—
301D244—42no—
302C4×D61—42no—
303C4×D61—42no—
304C4×D61—44no—
305Dic122—24no—
306Dic122—22no—
307Dic122—24no—
308Dic122—22no—
309Dic122—42no—
310Dic122—42no—
311Dic122—44no—
312Dic122—44no—
313Dic122—42no—
314C8×C61—24no—
315C8×C61—42no—
316C2×#2004—611nomaximal, Sylow
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—24no—
320C22×C61—24no—
321C22×C61—48no—
322C22×C61—44no—
323C22×C61—48no—
324C22×C61—84no—
325C22×C61—88no—
326C22×C61—88no—
327C22×C61#39212yes—
328C22×C61#39212yes—
329C22×C61#45514yes—
330C22×C61C2×#12011yescharacteristic
331C22×C61C2×#12011yescharacteristic
332C22×C61C2×#12111yescharacteristic
333C2×D61—42no—
334C2×D61—44no—
335C2×D61—84no—
336C4×C61#39212yes—
337C4×C61#39212yes—
338C4×C61C2×#12011yescharacteristic
339C4×C61C2×#12111yescharacteristic
340C4×C61C2×#12111yescharacteristic
341C4×C61C2×#12711yescharacteristic
342Dic61—44no—
343Dic61—44no—
344Dic61—42no—
345Dic61—44no—
346C22×#137—611no—
347C2×#535—611no—
348C22×#124—611no—
349C22×#104—611no—
350C2×#419—611no—
351C22×#100D6111yescharacteristic, complemented
352#2004—618no—
353C2×#339—611no—
354C2×C61—21no—
355C2×C61—21no—
356C2×C61—22no—
357C2×C61—84no—
358C2×C61#200414yescomplemented
359C2×C61C2×#39211yescharacteristic
360C2×C61C2×#45512yes—
361D61—82no—
362C22×#41—611no—
363C23×Q8—611no—
364C23×D4C2×D6111yescharacteristic
365C2×#137—614no—
366C2×#137—1224no—
367C2×#137—1222no—
368C2×#137—1224no—
369C22×Q16—1221no—
370C22×SD16—1221no—
371C22×M16C2×D6111yescharacteristic
372C22×M16C2×D6111yescharacteristic
373#535—614no—
374#535—1222no—
375#535—1222no—
376#535—1222no—
377C2×#127—1221no—
378C2×#124—614no—
379C2×#124—1224no—
380C2×#124—1224no—
381C2×#124—1221no—
382C2×#124—1222no—
383C2×#121—1222no—
384C2×#120—1222no—
385C2×#117—611no—
386C22×C22⋊C4—1222no—
387C22×C42—611no—
388C2×#104—614no—
389C2×#104—1224no—
390#419—614no—
391#419—1222no—
392C2×#103—1222no—
393C2×#100—24no—
394C2×#100C2×D6114yescomplemented
395#339—614no—
396C61C2×#200411yescharacteristic, complemented, Sylow
397C25D24412yes—
398C2×#41—612no—
399C2×#41—612no—
400C2×#41—1221no—
401C2×#41—1221no—
402C2×#41—1222no—
403C2×#41—1222no—
404C2×#41—1222no—
405C2×#41—1222no—
406C22×Q8—611no—
407C22×Q8—614no—
408C22×Q8—612no—
409C22×Q8—1221no—
410C22×Q8—1222no—
411C22×Q8—1222no—
412C22×Q8—1221no—
413C22×Q8—1221no—
414C22×Q8—1221no—
415C22×Q8—1221no—
416C22×Q8—1222no—
417C22×D4—22no—
418C22×D4—21no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—22no—
425C22×D4—611no—
426C22×D4—1224no—
427C22×D4—1221no—
428C22×D4D24412yes—
429C22×D4C22×D6112yes—
430C23×C4—1221no—
431C23×C4—1221no—
432C23×C4—1221no—
433C23×C4C22×D6111yescharacteristic
434#137—1228no—
435#137—12216no—
436#137—1228no—
437C2×Q16—1224no—
438C2×Q16—1228no—
439C2×SD16—1224no—
440C2×SD16—1228no—
441C2×M16—21no—
442C2×M16—22no—
443C2×M16—21no—
444C2×M16—22no—
445C2×M16—22no—
446C2×M16C22⋊D6114yescomplemented
447C2×M16C22×D6112yes—
448C2×M16C22×D6112yes—
449C22×C8—21no—
450C22×C8—21no—
451#127—1224no—
452#127—1224no—
453#124—1228no—
454#124—1228no—
455#124—1224no—
456#124—12216no—
457#124—1224no—
458#121—1228no—
459#121—1228no—
460#120—1228no—
461#120—1228no—
462#117—612no—
463#117—612no—
464#117—1221no—
465#117—1221no—
466C2×C4⋊C4—612no—
467C2×C22⋊C4—12216no—
468C2×C22⋊C4—1224no—
469C2×C22⋊C4—1228no—
470C2×C22⋊C4—1221no—
471C2×C42—614no—
472C2×C42—612no—
473C2×C42—1221no—
474C2×C42—1221no—
475C2×C42—1222no—
476#104—1228no—
477#103—1228no—
478#100—28no—
479C24—24no—
480C24—22no—
481C24—22no—
482C24—24no—
483C24—48no—
484C24—1221no—
485C24C2×D24411yescharacteristic
486C24C2×D24414yes—
487#41—1222no—
488#41—1222no—
489#41—1222no—
490#41—1222no—
491#41—1224no—
492#41—1224no—
493#41—2442no—
494#41—2442no—
495#41—2442no—
496#41—2442no—
497C2×Q8—612no—
498C2×Q8—614no—
499C2×Q8—1222no—
500C2×Q8—1224no—
501C2×Q8—1221no—
502C2×Q8—1222no—
503C2×Q8—1222no—
504C2×Q8—1222no—
505C2×Q8—1222no—
506C2×Q8—1224no—
507C2×Q8—1222no—
508C2×Q8—1224no—
509C2×Q8—1224no—
510C2×Q8—1224no—
511C2×Q8—1222no—
512C2×Q8—2441no—
513C2×Q8—2441no—
514C2×Q8—2442no—
515C2×Q8—2442no—
516C2×Q8—2442no—
517C2×Q8—2442no—
518C2×Q8—2442no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—24no—
527C2×D4—22no—
528C2×D4—24no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—612no—
538C2×D4—12216no—
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1221no—
543C2×D4—1222no—
544C2×D4—4888no—
545C2×D4—2442no—
546C2×D4—2442no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1224no—
550C22×C4—1224no—
551C22×C4—1222no—
552C22×C4—1221no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—2444no—
556C22×C4—2441no—
557C22×C4—2441no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4—2442no—
561C22×C4C2×D24411yescharacteristic
562C22×C4#1175822212yes—
563C22×C4D4×D6112yes—
564C22×C4D4×D6111yescharacteristic
565C22×C4D4×D6111yescharacteristic
566C22×C4D4×D6112yes—
567C22×C4D4×D6111yescharacteristic
568C22×C4D4×D6111yescharacteristic
569C22×C4C2×C22⋊D6112yes—
570C22×C4C23×D6111yescharacteristic
571Q16—12216no—
572SD16—12216no—
573M16—22no—
574M16—24no—
575M16—22no—
576M16—22no—
577M16—42no—
578M16C2×C22⋊D6114yescomplemented
579C2×C8—22no—
580C2×C8—24no—
581C2×C8—22no—
582C2×C8—42no—
583C4⋊C4—614no—
584C4⋊C4—1222no—
585C22⋊C4—12232no—
586C22⋊C4—12216no—
587C22⋊C4—1222no—
588C22⋊C4—1222no—
589C42—614no—
590C42—1222no—
591C42—1222no—
592C42—1224no—
593C42—1222no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—48no—
599C23—416no—
600C23—48no—
601C23—44no—
602C23—44no—
603C23—84no—
604C23—88no—
605C23—1222no—
606C23—2444no—
607C23—2442no—
608C23#1451974711yescharacteristic
609C23#1451974712yes—
610C23#1451974711yescharacteristic
611C23#1451975112yes—
612C23C22×D24411yescharacteristic
613Q8—1224no—
614Q8—1222no—
615Q8—1224no—
616Q8—1222no—
617Q8—2442no—
618Q8—2442no—
619Q8—2444no—
620Q8—2444no—
621Q8—2442no—
622D4—42no—
623D4—42no—
624D4—42no—
625D4—42no—
626D4—44no—
627D4—44no—
628D4—1222no—
629D4—1222no—
630D4—48816no—
631D4—2442no—
632D4—2442no—
633D4—2444no—
634D4—2442no—
635C2×C4—1224no—
636C2×C4—1224no—
637C2×C4—1222no—
638C2×C4—1224no—
639C2×C4—2444no—
640C2×C4—2448no—
641C2×C4—2444no—
642C2×C4—2442no—
643C2×C4—2442no—
644C2×C4—2442no—
645C2×C4—2444no—
646C2×C4—2444no—
647C2×C4—2442no—
648C2×C4—2442no—
649C2×C4—2444no—
650C2×C4#1451974512yes—
651C2×C4#1451974512yes—
652C2×C4#1451974711yescharacteristic
653C2×C4#1451974712yes—
654C2×C4#1451974711yescharacteristic
655C2×C4#1451975012yes—
656C2×C4#1451975012yes—
657C2×C4#1451975012yes—
658C2×C4#1451975012yes—
659C2×C4#1451975112yes—
660C2×C4#1451977312yes—
661C2×C4#1451977312yes—
662C2×C4C2×D4×D6111yescharacteristic
663C2×C4C2×D4×D6111yescharacteristic
664C2×C4C2×D4×D6111yescharacteristic
665C2×C4C2×D4×D6111yescharacteristic
666C2×C4C22×C22⋊D6111yescharacteristic
667C2×C4C2×#1175822211yescharacteristic
668C8—24no—
669C8—42no—
670C22—22no—
671C22—22no—
672C22—24no—
673C22—24no—
674C22—48no—
675C22—48no—
676C22—44no—
677C22—84no—
678C22—88no—
679C22—88no—
680C22—4884no—
681C22—2444no—
682C22—2442no—
683C22#1683967112yes—
684C22#1683967112yes—
685C22#1683994214yes—
686C22C2×#1451974711yescharacteristic
687C22C2×#1451974711yescharacteristic
688C22C2×#1451975111yescharacteristic
689C4—2444no—
690C4—2444no—
691C4—2442no—
692C4—2444no—
693C4#1683967112yes—
694C4#1683967112yes—
695C4C2×#1451974511yescharacteristic
696C4C2×#1451975011yescharacteristic
697C4C2×#1451975011yescharacteristic
698C4C2×#1451977311yescharacteristic
699C2—21no—
700C2—21no—
701C2—22no—
702C2—84no—
703C2—4882no—
704C2#2144685014yesdirect product factor
705C2C2×#1683967111yescharacteristic
706C2C2×#1683994212yes—
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#100×C61C2
socleC23×C61#120
prime radicalC2×#16840329C2
hypercenterC22×#100D61
hypocenterC61C2×#2004
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#100

Complements

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

NH ≅ G/Ntype
1. C22×#14519810C2semidirect
3. C22×#14519764C2semidirect
4. C22×#14519703C2semidirect
5. C2×#16839772C2semidirect
6. #21446850C2direct (N × H)
7. C2×#16839523C2semidirect
8. C22×#100×C61C2semidirect
14. C2×#14519810C22semidirect
26. C2×#14519764C22semidirect
33. C2×#14519703C22semidirect
35. #16839772C22semidirect
37. #16839523C22semidirect
42. C2×#100×C61C22semidirect
60. C22×Dic122D4semidirect
98. C2×C4×Dic61D4semidirect
119. C2×M16×C61D4semidirect
216. C2×Dic122C2×D4semidirect
222. M16×C61C2×D4semidirect
237. C4×Dic61C2×D4semidirect
351. C22×#100D61semidirect
358. C2×C61#2004semidirect
394. C2×#100C2×D61semidirect
396. C61C2×#2004semidirect
446. C2×M16C22⋊D61semidirect
578. M16C2×C22⋊D61semidirect
704. C2#21446850direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198102
C2×#168403292
C22×#145197642
C22×#145197032
C2×#168397722
#214468502
C2×#168395232
C22×#100×C612
C2×#200461