Finite Group Databasebeta

← C2×#21446839 #29706903

Subgroups — C2×#21446839 #29706903

Order 15616.

2126 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519802C211yesmaximal, characteristic
2C22×#14519766C211yesmaximal, characteristic, complemented
3C22×#14519704C211yesmaximal, characteristic, complemented
4C2×#16839766C211yesmaximal, characteristic, complemented
5C22×#14519696C211yesmaximal, characteristic, complemented
6#21446839C218yesmaximal, direct product factor
7C2×#16839521C211yesmaximal, characteristic, complemented
8C2×C61×#536C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C2×#14519802—24no—
11C2×#14519802—22no—
12C2×#14519802—24no—
13C2×#14519802C2214yes—
14C22×#11758201—21no—
15C22×#11758199—21no—
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×#14519766—24no—
19C2×#14519766—22no—
20C2×#14519766—24no—
21C2×#14519766C2214yescomplemented
22C22×#11758198—22no—
23C22×C4×Dic61C2211yescharacteristic
24C2×#14519704—24no—
25C2×#14519704C2214yescomplemented
26#16839766—22no—
27#16839766C2214yescomplemented
28C2×#14519697—22no—
29C2×#14519696—24no—
30C2×#14519696C2214yescomplemented
31#16839521C2214yescomplemented
32C22×#41×C61C2211yescharacteristic
33C23×Q8×C61C2211yescharacteristic
34C61×#536—22no—
35C61×#536—22no—
36C61×#536—22no—
37C61×#536C2214yescomplemented
38C2×C4⋊Q8×C61—21no—
39C2×#124×C61—21no—
40C2×#123×C61—22no—
41C2×C22⋊Q8×C61—22no—
42C2×#117×C61C2211yescharacteristic
43C24×D61—21no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244—22no—
48C22×D244—21no—
49C22×D244—22no—
50C22×D244—22no—
51C22×D244—21no—
52C22×D244D414yes—
53C22×D244C2312yes—
54C23×Dic61—21no—
55#14519802—216no—
56#14519802—28no—
57#14519802—28no—
58C2×#11758201—28no—
59C2×#11758201—24no—
60C2×#11758199—28no—
61C2×#11758199—24no—
62C2×#11758194—22no—
63C2×#11758194—21no—
64C2×#11758194—21no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194D414yes—
68C2×#11758194C2312yes—
69C2×#11758194C2312yes—
70C22×#92418—21no—
71C22×#92418—21no—
72#14519766—216no—
73#14519766—28no—
74#14519766—28no—
75C2×#11758198—216no—
76C2×#11758198—28no—
77C2×C4×Dic61—22no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61D414yes—
80C2×C4×Dic61C2312yes—
81#14519704—28no—
82#14519697—28no—
83#14519696—28no—
84C2×#41×C61—21no—
85C2×#41×C61—21no—
86C2×#41×C61—22no—
87C2×#41×C61—22no—
88C2×#41×C61—22no—
89C2×#41×C61—22no—
90C2×#41×C61D412yes—
91C2×#41×C61C2312yes—
92C22×Q8×C61—21no—
93C22×Q8×C61—21no—
94C22×Q8×C61—21no—
95C22×Q8×C61—22no—
96C22×Q8×C61—22no—
97C22×Q8×C61—22no—
98C22×Q8×C61—21no—
99C22×Q8×C61—22no—
100C22×Q8×C61D411yescharacteristic
101C22×Q8×C61D412yes—
102C22×Q8×C61C2312yes—
103C22×D4×C61—21no—
104C22×D4×C61D411yescharacteristic
105C23×C4×C61—21no—
106C23×C4×C61D412yes—
107C23×C4×C61C2311yescharacteristic
108C4⋊Q8×C61—24no—
109C4⋊Q8×C61—24no—
110#124×C61—24no—
111#124×C61—24no—
112#123×C61—28no—
113#123×C61—28no—
114C22⋊Q8×C61—28no—
115C22⋊Q8×C61—28no—
116#117×C61—21no—
117#117×C61—21no—
118#117×C61D412yes—
119#117×C61C2312yes—
120C2×C4⋊C4×C61—24no—
121C2×C4⋊C4×C61D412yes—
122C2×C22⋊C4×C61—24no—
123C2×C22⋊C4×C61—21no—
124C2×C42×C61—21no—
125C24×C61—21no—
126C24×C61C2×D411yescharacteristic
127C23×D61—24no—
128C23×D61—22no—
129C23×D61—48no—
130C23×D61—41no—
131C23×D61—41no—
132C23×D61—42no—
133#41×C61—24no—
134#41×C61—24no—
135#41×C61—22no—
136#41×C61—22no—
137#41×C61—22no—
138#41×C61—22no—
139#41×C61—42no—
140#41×C61—42no—
141#41×C61—42no—
142#41×C61—42no—
143C2×Q8×C61—22no—
144C2×Q8×C61—22no—
145C2×Q8×C61—21no—
146C2×Q8×C61—24no—
147C2×Q8×C61—24no—
148C2×Q8×C61—22no—
149C2×Q8×C61—22no—
150C2×Q8×C61—22no—
151C2×Q8×C61—22no—
152C2×Q8×C61—22no—
153C2×Q8×C61—22no—
154C2×Q8×C61—22no—
155C2×Q8×C61—22no—
156C2×Q8×C61—42no—
157C2×Q8×C61—42no—
158C2×Q8×C61—42no—
159C2×Q8×C61—42no—
160C2×Q8×C61—42no—
161C2×Q8×C61—42no—
162C2×Q8×C61—42no—
163C2×Q8×C61—42no—
164C2×Q8×C61C2×D412yes—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—21no—
169C2×D4×C61—22no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61C2×D412yes—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—21no—
176C22×C4×C61—22no—
177C22×C4×C61—24no—
178C22×C4×C61—24no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—42no—
182C22×C4×C61—42no—
183C22×C4×C61C2×D414yes—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D412yes—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61#4112yes—
193C22×C4×C61C2411yescharacteristic
194C22×Dic61—24no—
195C22×Dic61—22no—
196C22×Dic61—44no—
197C2×D244—24no—
198C2×D244—24no—
199C2×D244—24no—
200C2×D244—24no—
201C2×D244—22no—
202C2×D244—22no—
203C2×D244—22no—
204C2×D244—22no—
205C2×D244—24no—
206C2×D244—22no—
207C2×D244—41no—
208C2×D244—41no—
209C2×D244—42no—
210C2×D244—42no—
211C2×D244—42no—
212C2×D244—42no—
213C2×D244—42no—
214C2×D244C2×D414yes—
215C4⋊C4×C61—216no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61C2×D414yes—
218C22⋊C4×C61—216no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C42×C61—22no—
222C42×C61—22no—
223#11758201—216no—
224#11758199—216no—
225#11758198—232no—
226C4×Dic61—24no—
227C4×Dic61—22no—
228C4×Dic61C2×D414yes—
229#11758194—24no—
230#11758194—22no—
231#11758194—22no—
232#11758194—22no—
233#11758194—42no—
234#11758194C2×D414yes—
235C2×#92418—24no—
236C2×#92418—22no—
237C2×#92418—22no—
238C2×#92418—42no—
239C23×C61—24no—
240C23×C61—22no—
241C23×C61—42no—
242C23×C61—44no—
243C23×C61#12012yes—
244C23×C61#12011yescharacteristic
245C23×C61#12011yescharacteristic
246C23×C61#12112yes—
247C23×C61C22×D411yescharacteristic
248C22×D61—24no—
249C22×D61—48no—
250C22×D61—416no—
251C22×D61—42no—
252C22×D61—42no—
253C22×D61—44no—
254C22×D61—44no—
255C22×D61—84no—
256C22×D61—88no—
257C22×D61—84no—
258Q8×C61—22no—
259Q8×C61—22no—
260Q8×C61—42no—
261Q8×C61—42no—
262Q8×C61—42no—
263Q8×C61—42no—
264Q8×C61—44no—
265Q8×C61—44no—
266Q8×C61—42no—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—42no—
270D4×C61—42no—
271D4×C61—44no—
272D4×C61—42no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—24no—
276C2×C4×C61—22no—
277C2×C4×C61—24no—
278C2×C4×C61—44no—
279C2×C4×C61—44no—
280C2×C4×C61—42no—
281C2×C4×C61—44no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—44no—
285C2×C4×C61#12012yes—
286C2×C4×C61#12012yes—
287C2×C4×C61#12012yes—
288C2×C4×C61#12011yescharacteristic
289C2×C4×C61#12011yescharacteristic
290C2×C4×C61#12112yes—
291C2×C4×C61#12112yes—
292C2×C4×C61#12112yes—
293C2×C4×C61#12112yes—
294C2×C4×C61#12112yes—
295C2×C4×C61#12712yes—
296C2×C4×C61#12712yes—
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×Dic61—24no—
304C2×Dic61—44no—
305C2×Dic61—48no—
306D244—24no—
307D244—24no—
308D244—42no—
309D244—42no—
310D244—44no—
311D244—44no—
312#92418—24no—
313#92418—42no—
314C2×#2003—611nomaximal, Sylow
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—24no—
318C22×C61—24no—
319C22×C61—42no—
320C22×C61—44no—
321C22×C61—84no—
322C22×C61#39212yes—
323C22×C61#39212yes—
324C22×C61#45414yes—
325C22×C61C2×#12011yescharacteristic
326C22×C61C2×#12011yescharacteristic
327C22×C61C2×#12111yescharacteristic
328C2×D61—48no—
329C2×D61—44no—
330C2×D61—84no—
331C2×D61—88no—
332C2×D61—84no—
333C2×D61—88no—
334C4×C61—44no—
335C4×C61—42no—
336C4×C61—44no—
337C4×C61#39212yes—
338C4×C61#39212yes—
339C4×C61C2×#12011yescharacteristic
340C4×C61C2×#12111yescharacteristic
341C4×C61C2×#12111yescharacteristic
342C4×C61C2×#12711yescharacteristic
343Dic61—44no—
344C22×AGL(1,ℤ/8)—611no—
345C2×#536D6111yescharacteristic, complemented
346C22×#124—611no—
347C22×#104—611no—
348C2×#418—611no—
349C22×#101—611no—
350#2003—618no—
351C2×#339—611no—
352C2×C61—21no—
353C2×C61—21no—
354C2×C61—22no—
355C2×C61—82no—
356C2×C61#200314yescomplemented
357C2×C61C2×#39211yescharacteristic
358C2×C61C2×#45412yes—
359D61—84no—
360C22×#41C2×D6111yescharacteristic
361C23×Q8C2×D6111yescharacteristic
362C23×D4—611no—
363C2×AGL(1,ℤ/8)—614no—
364C2×AGL(1,ℤ/8)—1224no—
365C2×AGL(1,ℤ/8)—1224no—
366C2×AGL(1,ℤ/8)—1222no—
367C22×SD16—1221no—
368C22×D8—1221no—
369C22×M16—611no—
370C22×M16—611no—
371#536—22no—
372#536—22no—
373#536—22no—
374#536C2×D6114yescomplemented
375C2×C4⋊Q8—21no—
376C2×#124—21no—
377C2×#124—614no—
378C2×#124—1224no—
379C2×#124—1224no—
380C2×#124—1222no—
381C2×#123—22no—
382C2×C22⋊Q8—22no—
383C2×#117C2×D6111yescharacteristic
384C22×C22⋊C4—1222no—
385C22×C42—611no—
386C2×#104—614no—
387C2×#104—1224no—
388#418—614no—
389#418—1222no—
390C2×#102—1222no—
391C2×#101—614no—
392C2×#101—1224no—
393#339—614no—
394C61C2×#200311yescharacteristic, complemented, Sylow
395C25—1221no—
396C2×#41—21no—
397C2×#41—21no—
398C2×#41—22no—
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41C22⋊D6112yes—
403C2×#41C22×D6112yes—
404C22×Q8—22no—
405C22×Q8—22no—
406C22×Q8—22no—
407C22×Q8—22no—
408C22×Q8—21no—
409C22×Q8—21no—
410C22×Q8—21no—
411C22×Q8—21no—
412C22×Q8C22⋊D6111yescharacteristic
413C22×Q8C22⋊D6112yes—
414C22×Q8C22×D6112yes—
415C22×D4—21no—
416C22×D4—614no—
417C22×D4—612no—
418C22×D4—1222no—
419C22×D4—1222no—
420C22×D4—1222no—
421C22×D4—1221no—
422C22×D4—1221no—
423C22×D4—1221no—
424C22×D4—1221no—
425C22×D4—1221no—
426C22×D4C22⋊D6111yescharacteristic
427C23×C4—21no—
428C23×C4—1221no—
429C23×C4C22⋊D6112yes—
430C23×C4C22×D6111yescharacteristic
431AGL(1,ℤ/8)—1228no—
432AGL(1,ℤ/8)—1228no—
433AGL(1,ℤ/8)—12216no—
434C2×SD16—1228no—
435C2×SD16—1224no—
436C2×D8—1228no—
437C2×D8—1224no—
438C2×M16—614no—
439C2×M16—612no—
440C2×M16—612no—
441C2×M16—1222no—
442C2×M16—1221no—
443C2×M16—1221no—
444C2×M16—1222no—
445C2×M16—1222no—
446C22×C8—1221no—
447C22×C8—1221no—
448C4⋊Q8—24no—
449C4⋊Q8—24no—
450#124—24no—
451#124—24no—
452#124—1228no—
453#124—1228no—
454#124—12216no—
455#123—28no—
456#123—28no—
457C22⋊Q8—28no—
458C22⋊Q8—28no—
459#117—21no—
460#117—21no—
461#117C22⋊D6112yes—
462#117C22×D6112yes—
463C2×C4⋊C4—24no—
464C2×C4⋊C4C22⋊D6112yes—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—12216no—
468C2×C22⋊C4—1228no—
469C2×C42—21no—
470C2×C42—614no—
471C2×C42—612no—
472C2×C42—1222no—
473C2×C42—1221no—
474#104—1228no—
475#102—1228no—
476#101—1228no—
477C24—21no—
478C24—1222no—
479C24—1224no—
480C24—2448no—
481C24—2441no—
482C24—2441no—
483C24—2442no—
484C24C2×C22⋊D6111yescharacteristic
485#41—22no—
486#41—22no—
487#41—22no—
488#41—22no—
489#41—24no—
490#41—24no—
491#41—42no—
492#41—42no—
493#41—42no—
494#41—42no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—24no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—21no—
505C2×Q8—24no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8C2×C22⋊D6112yes—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—22no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—614no—
525C2×D4—1222no—
526C2×D4—1222no—
527C2×D4—1222no—
528C2×D4—1222no—
529C2×D4—1222no—
530C2×D4—1224no—
531C2×D4—1224no—
532C2×D4—1224no—
533C2×D4—1224no—
534C2×D4—1224no—
535C2×D4—2441no—
536C2×D4—2441no—
537C2×D4—2442no—
538C2×D4—2442no—
539C2×D4—2442no—
540C2×D4—2442no—
541C2×D4—2442no—
542C2×D4C2×C22⋊D6112yes—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—1222no—
554C22×C4—1224no—
555C22×C4—2444no—
556C22×C4D4×D6112yes—
557C22×C4D4×D6112yes—
558C22×C4D4×D6112yes—
559C22×C4#1175822412yes—
560C22×C4C2×C22⋊D6114yes—
561C22×C4C2×C22⋊D6111yescharacteristic
562C22×C4C2×C22⋊D6111yescharacteristic
563C22×C4C2×C22⋊D6111yescharacteristic
564C22×C4C2×C22⋊D6111yescharacteristic
565C22×C4C2×C22⋊D6111yescharacteristic
566C22×C4C23×D6111yescharacteristic
567SD16—12216no—
568D8—12216no—
569M16—614no—
570M16—1222no—
571M16—1224no—
572M16—1222no—
573M16—1222no—
574M16—2442no—
575C2×C8—1222no—
576C2×C8—1224no—
577C2×C8—1222no—
578C2×C8—2442no—
579C4⋊C4—216no—
580C4⋊C4—22no—
581C4⋊C4C2×C22⋊D6114yes—
582C22⋊C4—216no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—12232no—
586C42—22no—
587C42—22no—
588C42—614no—
589C42—1222no—
590C42—1224no—
591C23—24no—
592C23—22no—
593C23—42no—
594C23—44no—
595C23—1224no—
596C23—4884no—
597C23—4888no—
598C23—4884no—
599C23—2448no—
600C23—24416no—
601C23—2442no—
602C23—2442no—
603C23—2444no—
604C23—2444no—
605C23#1451974512yes—
606C23#1451974611yescharacteristic
607C23#1451974611yescharacteristic
608C23#1451974912yes—
609C23C22×C22⋊D6111yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—42no—
613Q8—42no—
614Q8—42no—
615Q8—42no—
616Q8—44no—
617Q8—44no—
618Q8—42no—
619D4—22no—
620D4—22no—
621D4—42no—
622D4—42no—
623D4—44no—
624D4—42no—
625D4—1224no—
626D4—1224no—
627D4—2442no—
628D4—2442no—
629D4—2444no—
630D4—2444no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—44no—
643C2×C4—1224no—
644C2×C4—2444no—
645C2×C4—2448no—
646C2×C4#1451974512yes—
647C2×C4#1451974512yes—
648C2×C4#1451974512yes—
649C2×C4#1451974611yescharacteristic
650C2×C4#1451974611yescharacteristic
651C2×C4#1451974812yes—
652C2×C4#1451974812yes—
653C2×C4#1451974912yes—
654C2×C4#1451974912yes—
655C2×C4#1451974912yes—
656C2×C4#1451977312yes—
657C2×C4#1451977312yes—
658C2×C4C2×D4×D6111yescharacteristic
659C2×C4C2×D4×D6111yescharacteristic
660C2×C4C2×D4×D6111yescharacteristic
661C2×C4C22×C22⋊D6111yescharacteristic
662C2×C4C22×C22⋊D6111yescharacteristic
663C2×C4C2×#1175822411yescharacteristic
664C8—1224no—
665C8—2442no—
666C22—22no—
667C22—22no—
668C22—24no—
669C22—24no—
670C22—44no—
671C22—42no—
672C22—84no—
673C22—4884no—
674C22—4888no—
675C22—4884no—
676C22—4888no—
677C22—2448no—
678C22—2444no—
679C22#1683967012yes—
680C22#1683967012yes—
681C22#1683993514yes—
682C22C2×#1451974511yescharacteristic
683C22C2×#1451974611yescharacteristic
684C22C2×#1451974911yescharacteristic
685C4—44no—
686C4—44no—
687C4—42no—
688C4—2444no—
689C4#1683967012yes—
690C4#1683967012yes—
691C4C2×#1451974511yescharacteristic
692C4C2×#1451974811yescharacteristic
693C4C2×#1451974911yescharacteristic
694C4C2×#1451977311yescharacteristic
695C2—21no—
696C2—21no—
697C2—22no—
698C2—82no—
699C2—4884no—
700C2#2144683914yesdirect product factor
701C2C2×#1683967011yescharacteristic
702C2C2×#1683993512yes—
subgroupG/H
centerC23#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#536C2
socleC23×C61#120
prime radicalC22×#14519802C2
hypercenterC2×#536D61
hypocenterC61C2×#2003
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. C22×#14519766C2semidirect
3. C22×#14519704C2semidirect
4. C2×#16839766C2semidirect
5. C22×#14519696C2semidirect
6. #21446839C2direct (N × H)
7. C2×#16839521C2semidirect
8. C2×C61×#536C2semidirect
21. C2×#14519766C22semidirect
25. C2×#14519704C22semidirect
27. #16839766C22semidirect
30. C2×#14519696C22semidirect
31. #16839521C22semidirect
37. C61×#536C22semidirect
345. C2×#536D61semidirect
356. C2×C61#2003semidirect
374. #536C2×D61semidirect
394. C61C2×#2003semidirect
700. C2#21446839direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198022
C22×#145197662
C22×#145197042
C2×#168397662
C22×#145196962
#214468392
C2×#168395212
C2×C61×#5362
C2×#200361