Finite Group Databasebeta

← C2×#21446886 #29707031

Subgroups — C2×#21446886 #29707031

Order 15616.

2190 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840562C211yesmaximal, characteristic, complemented
2C2×#16840273C212yesmaximal, complemented
3C2×#16839778C212yesmaximal, complemented
4#21446886C218yesmaximal, direct product factor
5C2×#16839519C211yesmaximal, characteristic, complemented
6C2×C61×#407C211yesmaximal, characteristic, complemented
7C22×#11758222C2212yes—
8#16840562—22no—
9#16840562—24no—
10#16840562C2214yescomplemented
11C2×#14519810—22no—
12C2×#14519805—22no—
13C2×#14519799—22no—
14#16840273—24no—
15#16840273—24no—
16#16840273—24no—
17#16840273C2218yescomplemented
18C2×#14519760—22no—
19C2×#14519756—22no—
20C2×#14519751—22no—
21C2×#14519746—22no—
22C2×C4×C22⋊D61—24no—
23C2×#14519736C2212yes—
24#16839778—24no—
25#16839778C2218yescomplemented
26C2×#14519703—24no—
27#16839519C2214yescomplemented
28C24×C4×C61C2211yescharacteristic
29C22×M16×C61C2211yescharacteristic
30C22×M16×C61C2211yescharacteristic
31C61×#407—22no—
32C61×#407C2214yescomplemented
33C2×C22⋊C8×C61—22no—
34C2×#11758222—22no—
35C2×#11758222—22no—
36C2×#11758222—22no—
37C2×#11758222—22no—
38C2×#11758222—22no—
39C2×#11758222—22no—
40C2×#11758222—22no—
41C2×#11758222—22no—
42C2×#11758222—22no—
43C2×#11758222—22no—
44C2×#11758222D414yescomplemented
45C2×#11758222C2314yes—
46C22×Dic122D412yescomplemented
47C22×D244D412yescomplemented
48C22×C22⋊D61—24no—
49C22×C22⋊D61—22no—
50C22×C4×D61—22no—
51#14519810—28no—
52#14519810—28no—
53#14519805—28no—
54#14519805—28no—
55#14519799—28no—
56#14519799—28no—
57C2×Dic244—22no—
58C2×#11758190—24no—
59C2×D488—22no—
60#14519760—28no—
61#14519760—28no—
62#14519756—28no—
63#14519756—28no—
64#14519751—28no—
65#14519751—28no—
66#14519746—28no—
67#14519746—28no—
68C4×C22⋊D61—216no—
69C4×C22⋊D61—216no—
70#14519736—22no—
71#14519736—22no—
72#14519736D414yescomplemented
73#14519736C2314yes—
74C2×C4⋊Dic61—22no—
75C2×#11758196—24no—
76C2×C22⋊Dic61—24no—
77C2×C22⋊Dic61—22no—
78C2×#11758198—24no—
79C2×C4×Dic61D414yescomplemented
80#14519703—216no—
81C25×C61D411yescharacteristic
82C23×C4×C61—22no—
83C23×C4×C61—22no—
84C23×C4×C61—22no—
85C23×C4×C61—22no—
86C23×C4×C61—21no—
87C23×C4×C61—21no—
88C23×C4×C61—21no—
89C23×C4×C61—21no—
90C23×C4×C61D411yescharacteristic
91C23×C4×C61D412yes—
92C23×C4×C61C2312yes—
93C23×C4×C61C2311yescharacteristic
94C2×M16×C61—22no—
95C2×M16×C61—22no—
96C2×M16×C61—21no—
97C2×M16×C61—22no—
98C2×M16×C61—22no—
99C2×M16×C61D412yescomplemented
100C2×M16×C61C2312yes—
101C2×M16×C61C2312yes—
102C22×C8×C61—21no—
103C22×C8×C61D412yescomplemented
104C22⋊C8×C61—28no—
105C24×C61—22no—
106C24×C61—21no—
107C24×C61—22no—
108C24×C61—21no—
109C24×C61—44no—
110C24×C61C2×D412yes—
111C24×C61C2×D411yescharacteristic
112C23×D61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—24no—
118C22×C4×C61—24no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—24no—
123C22×C4×C61—24no—
124C22×C4×C61—22no—
125C22×C4×C61—41no—
126C22×C4×C61—41no—
127C22×C4×C61—42no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61—42no—
132C22×C4×C61—41no—
133C22×C4×C61—42no—
134C22×C4×C61—41no—
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D412yes—
138C22×C4×C61C2×D412yes—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D412yes—
142C22×C4×C61C2×D412yes—
143C22×C4×C61#4111yescharacteristic
144C22×C4×C61#4111yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C2×C22⋊D61—216no—
147C2×C22⋊D61—24no—
148C2×C22⋊D61—24no—
149C2×C22⋊D61—416no—
150C2×C22⋊D61—42no—
151C2×C22⋊D61—42no—
152C2×C22⋊D61—42no—
153C2×C22⋊D61—42no—
154C22×Dic61—22no—
155C22×Dic61—24no—
156#11758222—24no—
157#11758222—24no—
158#11758222—24no—
159#11758222—24no—
160#11758222—24no—
161#11758222—24no—
162#11758222—24no—
163#11758222—24no—
164#11758222—42no—
165#11758222—42no—
166#11758222—42no—
167#11758222—42no—
168#11758222—42no—
169#11758222—42no—
170#11758222—42no—
171#11758222—42no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244C2×D414yescomplemented
178C2×C4×D61—24no—
179C2×C4×D61—24no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×Dic122—22no—
185C2×Dic122—22no—
186C2×Dic122—22no—
187C2×Dic122—22no—
188C2×Dic122—22no—
189C2×Dic122C2×D414yescomplemented
190M16×C61—24no—
191M16×C61—24no—
192M16×C61—24no—
193M16×C61—42no—
194C2×C8×C61—22no—
195C2×C8×C61—22no—
196C2×C8×C61—22no—
197C2×C8×C61—41no—
198C2×C8×C61—41no—
199C2×C8×C61C2×D414yescomplemented
200C22⋊Dic61—216no—
201C22⋊Dic61—24no—
202C22⋊Dic61—24no—
203#11758198—216no—
204C4⋊Dic61—24no—
205C4⋊Dic61—24no—
206#11758196—216no—
207C4×Dic61—24no—
208C4×Dic61C2×D418yescomplemented
209Dic244—28no—
210D488—28no—
211#11758190—216no—
212C23×C61—28no—
213C23×C61—24no—
214C23×C61—24no—
215C23×C61—22no—
216C23×C61—42no—
217C23×C61—44no—
218C23×C61—44no—
219C23×C61—42no—
220C23×C61—48no—
221C23×C61—44no—
222C23×C61—42no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61#12012yes—
226C23×C61#12012yes—
227C23×C61#12111yescharacteristic
228C23×C61#12111yescharacteristic
229C23×C61C22×D411yescharacteristic
230C22×D61—24no—
231C22×D61—48no—
232C22×D61—42no—
233C22×D61—42no—
234C2×C4×C61—24no—
235C2×C4×C61—22no—
236C2×C4×C61—42no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—42no—
240C2×C4×C61—44no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—44no—
244C2×C4×C61—42no—
245C2×C4×C61#12011yescharacteristic
246C2×C4×C61#12011yescharacteristic
247C2×C4×C61#12012yes—
248C2×C4×C61#12012yes—
249C2×C4×C61#12012yes—
250C2×C4×C61#12112yes—
251C2×C4×C61#12112yes—
252C2×C4×C61#12112yes—
253C2×C4×C61#12112yes—
254C2×C4×C61#12111yescharacteristic
255C2×C4×C61#12111yescharacteristic
256C2×C4×C61#12711yescharacteristic
257C2×C4×C61#12712yes—
258C2×C4×C61#12711yescharacteristic
259C2×C4×C61C22×D412yes—
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C22×D412yes—
262C2×C4×C61C2×#4111yescharacteristic
263C22⋊D61—432no—
264C22⋊D61—44no—
265C22⋊D61—44no—
266C22⋊D61—44no—
267C22⋊D61—44no—
268C2×Dic61—28no—
269C2×Dic61—24no—
270C2×Dic61—48no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273D244—24no—
274D244—24no—
275D244—42no—
276D244—42no—
277C4×D61—44no—
278C4×D61—44no—
279C4×D61—44no—
280C4×D61—44no—
281Dic122—24no—
282Dic122—24no—
283Dic122—42no—
284Dic122—42no—
285C8×C61—24no—
286C8×C61—42no—
287C2×#2010—611nomaximal, Sylow
288C22×C61—24no—
289C22×C61—22no—
290C22×C61—28no—
291C22×C61—24no—
292C22×C61—42no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—44no—
296C22×C61—48no—
297C22×C61—42no—
298C22×C61—44no—
299C22×C61—42no—
300C22×C61—44no—
301C22×C61#39212yes—
302C22×C61#39211yescharacteristic
303C22×C61#39211yescharacteristic
304C22×C61C2×#12012yes—
305C22×C61C2×#12111yescharacteristic
306C2×D61—48no—
307C2×D61—44no—
308C2×D61—84no—
309C2×D61—84no—
310C4×C61—42no—
311C4×C61#39211yescharacteristic
312C4×C61#39212yes—
313C4×C61#39211yescharacteristic
314C4×C61C2×#12011yescharacteristic
315C4×C61C2×#12112yes—
316C4×C61C2×#12711yescharacteristic
317Dic61—48no—
318Dic61—44no—
319C2×#575—611no—
320C2×#525—612no—
321C2×#421—612no—
322C2×#407D6111yescharacteristic, complemented
323#2010—618no—
324C2×H(3,ℤ/4)—611no—
325C2×C61—22no—
326C2×C61—22no—
327C2×C61—21no—
328C2×C61—21no—
329C2×C61—44no—
330C2×C61#201012yescomplemented
331C2×C61C2×#39211yescharacteristic
332D61—84no—
333C22×#41—612no—
334C24×C4C2×D6111yescharacteristic
335#575—614no—
336#575—1224no—
337#575—1222no—
338C2×#137—1222no—
339C2×AGL(1,ℤ/8)—1222no—
340C2×#135—1222no—
341C22×M16C2×D6111yescharacteristic
342C22×M16C2×D6111yescharacteristic
343#525—618no—
344#525—1224no—
345#525—1224no—
346#525—1224no—
347C2×#123—1222no—
348C2×C22⋊Q8—1222no—
349C2×#121—1222no—
350C2×#120—1222no—
351C2×C4×D4—1224no—
352C2×#117—612no—
353#421—618no—
354#421—1224no—
355C2×#104—1224no—
356#407—22no—
357#407C2×D6114yescomplemented
358C2×C22⋊C8—22no—
359H(3,ℤ/4)—614no—
360C61C2×#201011yescharacteristic, complemented, Sylow
361C25D24411yescharacteristic
362C2×#41—614no—
363C2×#41—614no—
364C2×#41—1222no—
365C2×#41—1222no—
366C2×#41—1222no—
367C2×#41—1222no—
368C2×#41—1222no—
369C2×#41—1222no—
370C2×#41—1222no—
371C2×#41—1222no—
372C2×#41—1222no—
373C2×#41—1222no—
374C22×Q8—612no—
375C22×D4—612no—
376C22×D4—1224no—
377C22×D4—1222no—
378C23×C4—21no—
379C23×C4—21no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—1222no—
387C23×C4D24411yescharacteristic
388C23×C4D24412yes—
389C23×C4C22×D6112yes—
390C23×C4C22×D6111yescharacteristic
391#137—1228no—
392#137—1228no—
393AGL(1,ℤ/8)—1228no—
394AGL(1,ℤ/8)—1228no—
395#135—1228no—
396#135—1228no—
397C2×Q16—1222no—
398C2×SD16—1224no—
399C2×D8—1222no—
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—21no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16C22⋊D6112yescomplemented
406C2×M16C22×D6112yes—
407C2×M16C22×D6112yes—
408C22×C8—21no—
409C22×C8C22⋊D6112yescomplemented
410#123—1228no—
411#123—1228no—
412C22⋊Q8—1228no—
413C22⋊Q8—1228no—
414#121—1228no—
415#121—1228no—
416#120—1228no—
417#120—1228no—
418C4×D4—12216no—
419C4×D4—12216no—
420#117—614no—
421#117—614no—
422#117—1222no—
423#117—1222no—
424C2×C4⋊C4—1224no—
425C2×C4⋊C4—1222no—
426C2×C22⋊C4—1224no—
427C2×C22⋊C4—1224no—
428C2×C22⋊C4—1222no—
429C2×C42—614no—
430#104—12216no—
431C22⋊C8—28no—
432C24—22no—
433C24—21no—
434C24—22no—
435C24—21no—
436C24—44no—
437C24—1222no—
438C24C2×D24412yes—
439C24C2×D24411yescharacteristic
440#41—1224no—
441#41—1224no—
442#41—1224no—
443#41—1224no—
444#41—1224no—
445#41—1224no—
446#41—1224no—
447#41—1224no—
448#41—2442no—
449#41—2442no—
450#41—2442no—
451#41—2442no—
452#41—2442no—
453#41—2442no—
454#41—2442no—
455#41—2442no—
456C2×Q8—614no—
457C2×Q8—1222no—
458C2×Q8—1222no—
459C2×Q8—1222no—
460C2×Q8—1222no—
461C2×Q8—1222no—
462C2×D4—614no—
463C2×D4—12216no—
464C2×D4—1224no—
465C2×D4—1224no—
466C2×D4—1222no—
467C2×D4—1222no—
468C2×D4—1222no—
469C2×D4—1222no—
470C2×D4—1222no—
471C2×D4—24416no—
472C2×D4—2442no—
473C2×D4—2442no—
474C2×D4—2442no—
475C2×D4—2442no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—41no—
498C22×C4—1224no—
499C22×C4—1222no—
500C22×C4—1224no—
501C22×C4—1224no—
502C22×C4—2442no—
503C22×C4—2442no—
504C22×C4—2442no—
505C22×C4—2442no—
506C22×C4C2×D24412yes—
507C22×C4C2×D24411yescharacteristic
508C22×C4#1175822211yescharacteristic
509C22×C4#1175822211yescharacteristic
510C22×C4D4×D6112yes—
511C22×C4D4×D6112yes—
512C22×C4D4×D6112yes—
513C22×C4D4×D6112yes—
514C22×C4C2×C22⋊D6111yescharacteristic
515C22×C4C2×C22⋊D6111yescharacteristic
516C22×C4C23×D6111yescharacteristic
517Q16—1228no—
518SD16—12216no—
519D8—1228no—
520M16—24no—
521M16—24no—
522M16—24no—
523M16—42no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8C2×C22⋊D6114yescomplemented
530C4⋊C4—12216no—
531C4⋊C4—1224no—
532C4⋊C4—1224no—
533C22⋊C4—12216no—
534C22⋊C4—12216no—
535C22⋊C4—1224no—
536C22⋊C4—1224no—
537C42—618no—
538C42—1224no—
539C23—28no—
540C23—24no—
541C23—24no—
542C23—22no—
543C23—42no—
544C23—44no—
545C23—44no—
546C23—42no—
547C23—48no—
548C23—44no—
549C23—42no—
550C23—41no—
551C23—41no—
552C23—1224no—
553C23—2448no—
554C23—2442no—
555C23—2442no—
556C23#1451974712yes—
557C23#1451974712yes—
558C23#1451975111yescharacteristic
559C23#1451975111yescharacteristic
560C23C22×D24411yescharacteristic
561Q8—1224no—
562Q8—1224no—
563Q8—2442no—
564Q8—2442no—
565D4—1224no—
566D4—1224no—
567D4—24432no—
568D4—2444no—
569D4—2444no—
570D4—2444no—
571D4—2444no—
572D4—2442no—
573D4—2442no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—1228no—
586C2×C4—1224no—
587C2×C4—2448no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2444no—
591C2×C4—2444no—
592C2×C4—2444no—
593C2×C4—2444no—
594C2×C4#1451974511yescharacteristic
595C2×C4#1451974511yescharacteristic
596C2×C4#1451974512yes—
597C2×C4#1451974712yes—
598C2×C4#1451974712yes—
599C2×C4#1451975012yes—
600C2×C4#1451975012yes—
601C2×C4#1451975012yes—
602C2×C4#1451975012yes—
603C2×C4#1451975111yescharacteristic
604C2×C4#1451975111yescharacteristic
605C2×C4#1451977311yescharacteristic
606C2×C4#1451977312yes—
607C2×C4#1451977311yescharacteristic
608C2×C4C2×D4×D6112yes—
609C2×C4C2×D4×D6112yes—
610C2×C4C22×C22⋊D6111yescharacteristic
611C2×C4C2×#1175822211yescharacteristic
612C8—24no—
613C8—42no—
614C22—24no—
615C22—22no—
616C22—28no—
617C22—24no—
618C22—41no—
619C22—42no—
620C22—41no—
621C22—44no—
622C22—42no—
623C22—48no—
624C22—44no—
625C22—42no—
626C22—44no—
627C22—4884no—
628C22—4884no—
629C22—2448no—
630C22—2444no—
631C22#1683967112yes—
632C22#1683967111yescharacteristic
633C22#1683967111yescharacteristic
634C22C2×#1451974712yes—
635C22C2×#1451975111yescharacteristic
636C4—42no—
637C4—2448no—
638C4—2444no—
639C4#1683967111yescharacteristic
640C4#1683967112yes—
641C4#1683967111yescharacteristic
642C4C2×#1451974511yescharacteristic
643C4C2×#1451975012yes—
644C4C2×#1451977311yescharacteristic
645C2—22no—
646C2—21no—
647C2—22no—
648C2—21no—
649C2—44no—
650C2—4884no—
651C2#2144688612yesdirect product factor
652C2C2×#1683967111yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#407C2
socleC22×C61#392
hypercenterC2×#407D61
hypocenterC61C2×#2010
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#16840562C2semidirect
2. C2×#16840273C2semidirect
3. C2×#16839778C2semidirect
4. #21446886C2direct (N × H)
5. C2×#16839519C2semidirect
6. C2×C61×#407C2semidirect
10. #16840562C22semidirect
17. #16840273C22semidirect
25. #16839778C22semidirect
27. #16839519C22semidirect
32. C61×#407C22semidirect
44. C2×#11758222D4semidirect
46. C22×Dic122D4semidirect
47. C22×D244D4semidirect
72. #14519736D4semidirect
79. C2×C4×Dic61D4semidirect
99. C2×M16×C61D4semidirect
103. C22×C8×C61D4semidirect
177. C2×D244C2×D4semidirect
189. C2×Dic122C2×D4semidirect
199. C2×C8×C61C2×D4semidirect
208. C4×Dic61C2×D4semidirect
322. C2×#407D61semidirect
330. C2×C61#2010semidirect
357. #407C2×D61semidirect
360. C61C2×#2010semidirect
405. C2×M16C22⋊D61semidirect
409. C22×C8C22⋊D61semidirect
529. C2×C8C2×C22⋊D61semidirect
651. C2#21446886direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405622
C2×#168402732
C2×#168397782
#214468862
C2×#168395192
C2×C61×#4072
C2×#201061