Finite Group Databasebeta

← C2×#21447037 #29707607

Subgroups — C2×#21447037 #29707607

Order 15616.

1434 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840336C211yesmaximal, characteristic
2C2×#16839804C211yesmaximal, characteristic, complemented
3C22×#14519703C211yesmaximal, characteristic
4C2×#16839764C211yesmaximal, characteristic
5C2×#16839669C211yesmaximal, characteristic, complemented
6#21447037C218yesmaximal, direct product factor
7C2×#16839523C211yesmaximal, characteristic, complemented
8C22×#101×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840336—22no—
11#16840336—22no—
12#16840336—22no—
13#16840336C2214yes—
14C2×#14519775—21no—
15C2×#14519766—21no—
16C2×#14519760—22no—
17C2×#14519753—21no—
18C2×#14519753—21no—
19C2×#14519736C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22#16839804—22no—
23#16839804C2214yescomplemented
24C2×#14519711—21no—
25C2×#14519709—21no—
26C2×#14519703—24no—
27C2×#14519703C2214yes—
28#16839764—22no—
29#16839764C2214yes—
30C2×#14519702—21no—
31C2×#14519699—21no—
32#16839669—22no—
33#16839669C2214yescomplemented
34C2×#14519684—22no—
35#16839523C2214yescomplemented
36C23×Q8×C61C2211yescharacteristic
37C22×M16×C61C2211yescharacteristic
38C22×M16×C61C2211yescharacteristic
39C2×#101×C61—24no—
40C2×#101×C61C2214yescomplemented
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—22no—
44C2×#11758222—22no—
45C2×#11758222—22no—
46C2×#11758222—22no—
47C2×#11758222D412yes—
48C2×#11758222C2312yes—
49C22×Dic122D411yescharacteristic
50C22×D244D411yescharacteristic
51C22×C22⋊D61—21no—
52C23×Dic61—21no—
53C23×Dic61—21no—
54C22×C4×D61—21no—
55#14519775—24no—
56#14519775—24no—
57#14519766—24no—
58#14519766—24no—
59#14519760—28no—
60#14519760—28no—
61#14519753—24no—
62#14519753—24no—
63#14519753—24no—
64#14519753—24no—
65#14519736—21no—
66#14519736—21no—
67#14519736D412yes—
68#14519736C2312yes—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61D411yescharacteristic
75C2×C4⋊Dic61D411yescharacteristic
76C2×C4⋊Dic61C2312yes—
77C2×#11758196—22no—
78C2×#11758196—22no—
79C2×C22⋊Dic61—21no—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—22no—
84C2×C4×Dic61—22no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61C2312yes—
87#14519711—24no—
88#14519709—24no—
89#14519703—28no—
90#14519702—24no—
91#14519699—24no—
92#14519684—28no—
93C22×Q8×C61—21no—
94C22×Q8×C61—21no—
95C22×Q8×C61—22no—
96C22×Q8×C61—21no—
97C22×Q8×C61—21no—
98C22×Q8×C61—22no—
99C22×Q8×C61—22no—
100C22×Q8×C61—22no—
101C22×Q8×C61D412yes—
102C22×Q8×C61C2312yes—
103C23×C4×C61D412yes—
104C23×C4×C61C2311yescharacteristic
105C2×M16×C61—21no—
106C2×M16×C61—22no—
107C2×M16×C61—21no—
108C2×M16×C61—22no—
109C2×M16×C61—22no—
110C2×M16×C61D414yes—
111C2×M16×C61C2312yes—
112C2×M16×C61C2312yes—
113C22×C8×C61—21no—
114C22×C8×C61—21no—
115#101×C61—28no—
116C24×C61C2×D411yescharacteristic
117C23×D61—21no—
118C2×Q8×C61—22no—
119C2×Q8×C61—22no—
120C2×Q8×C61—24no—
121C2×Q8×C61—24no—
122C2×Q8×C61—22no—
123C2×Q8×C61—22no—
124C2×Q8×C61—22no—
125C2×Q8×C61—22no—
126C2×Q8×C61—22no—
127C2×Q8×C61—22no—
128C2×Q8×C61—42no—
129C2×Q8×C61—42no—
130C2×Q8×C61—42no—
131C2×Q8×C61—42no—
132C2×Q8×C61—42no—
133C2×Q8×C61—42no—
134C2×Q8×C61—42no—
135C2×Q8×C61—42no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—24no—
139C22×C4×C61—24no—
140C22×C4×C61C2×D414yes—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D412yes—
147C22×C4×C61#4112yes—
148C22×C4×C61#4112yes—
149C22×C4×C61#4112yes—
150C22×C4×C61C2411yescharacteristic
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—42no—
154C2×C22⋊D61—42no—
155C22×Dic61—24no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—42no—
162C22×Dic61—42no—
163C22×Dic61—44no—
164C22×Dic61—41no—
165C22×Dic61—41no—
166#11758222—24no—
167#11758222—24no—
168#11758222—22no—
169#11758222—22no—
170#11758222—22no—
171#11758222—22no—
172#11758222—42no—
173#11758222—42no—
174#11758222—42no—
175#11758222—42no—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—21no—
179C2×D244C2×D412yes—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×Dic122—22no—
185C2×Dic122—22no—
186C2×Dic122—21no—
187C2×Dic122C2×D412yes—
188M16×C61—24no—
189M16×C61—22no—
190M16×C61—22no—
191M16×C61—22no—
192M16×C61—42no—
193M16×C61C2×D414yes—
194C2×C8×C61—24no—
195C2×C8×C61—22no—
196C2×C8×C61—22no—
197C2×C8×C61—42no—
198C22⋊Dic61—22no—
199C22⋊Dic61—22no—
200#11758198—28no—
201#11758198—28no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—22no—
205C4⋊Dic61—22no—
206C4⋊Dic61—41no—
207C4⋊Dic61—41no—
208C4⋊Dic61C2×D412yes—
209C4⋊Dic61C2×D412yes—
210#11758196—28no—
211#11758196—28no—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61—42no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61#12011yescharacteristic
220C23×C61#12011yescharacteristic
221C23×C61#12112yes—
222C23×C61#12312yes—
223C23×C61C22×D411yescharacteristic
224C22×D61—22no—
225C22×D61—42no—
226C22×D61—42no—
227C22×D61—42no—
228Q8×C61—42no—
229Q8×C61—42no—
230Q8×C61—42no—
231Q8×C61—42no—
232Q8×C61—44no—
233Q8×C61—44no—
234C2×C4×C61—24no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61—44no—
238C2×C4×C61—44no—
239C2×C4×C61#12011yescharacteristic
240C2×C4×C61#12011yescharacteristic
241C2×C4×C61#12112yes—
242C2×C4×C61#12112yes—
243C2×C4×C61#12112yes—
244C2×C4×C61#12112yes—
245C2×C4×C61#12112yes—
246C2×C4×C61#12312yes—
247C2×C4×C61#12312yes—
248C2×C4×C61#12312yes—
249C2×C4×C61#12412yes—
250C2×C4×C61#12412yes—
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C22⋊D61—42no—
258C22⋊D61—42no—
259C22⋊D61—44no—
260C2×Dic61—24no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—42no—
265C2×Dic61—48no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61—42no—
270C2×Dic61—44no—
271C2×Dic61—42no—
272C2×Dic61—82no—
273C2×Dic61—82no—
274D244—22no—
275D244—22no—
276D244—42no—
277C4×D61—42no—
278C4×D61—42no—
279C4×D61—44no—
280Dic122—22no—
281Dic122—22no—
282Dic122—42no—
283C8×C61—24no—
284C8×C61—42no—
285C2×#2038—611nomaximal, Sylow
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—24no—
291C22×C61—24no—
292C22×C61#39412yes—
293C22×C61#39412yes—
294C22×C61#45412yes—
295C22×C61#45612yes—
296C22×C61C2×#12011yescharacteristic
297C22×C61C2×#12111yescharacteristic
298C22×C61C2×#12311yescharacteristic
299C2×D61—42no—
300C2×D61—42no—
301C2×D61—42no—
302C2×D61—84no—
303C4×C61—44no—
304C4×C61#39412yes—
305C4×C61#39412yes—
306C4×C61C2×#12111yescharacteristic
307C4×C61C2×#12111yescharacteristic
308C4×C61C2×#12311yescharacteristic
309C4×C61C2×#12411yescharacteristic
310Dic61—44no—
311Dic61—42no—
312Dic61—42no—
313Dic61—42no—
314Dic61—82no—
315C2×#536—611no—
316C2×#428—611no—
317C22×#104—611no—
318C2×#417—611no—
319C22×#101D6111yescharacteristic, complemented
320C2×#391—611no—
321#2038—618no—
322C2×#339—611no—
323C2×C61—21no—
324C2×C61—21no—
325C2×C61—22no—
326C2×C61#203814yescomplemented
327C2×C61C2×#39411yescharacteristic
328C2×C61C2×#45411yescharacteristic
329C2×C61C2×#45611yescharacteristic
330D61—82no—
331C22×#41—611no—
332C23×Q8C2×D6111yescharacteristic
333C22×M16C2×D6111yescharacteristic
334C22×M16C2×D6111yescharacteristic
335#536—614no—
336#536—1222no—
337#536—1222no—
338#536—1222no—
339C2×C4⋊Q8—1221no—
340C2×#124—1221no—
341C2×#123—1222no—
342C2×C22⋊Q8—1221no—
343C2×C22⋊Q8—1221no—
344C2×#117—611no—
345C22×C4⋊C4—611no—
346C22×C42—611no—
347#428—614no—
348#428—1222no—
349C2×#107—1221no—
350C2×#106—1221no—
351C2×#104—614no—
352C2×#104—1224no—
353#417—614no—
354#417—1222no—
355C2×#103—1221no—
356C2×#102—1221no—
357C2×#101—24no—
358C2×#101C2×D6114yescomplemented
359#391—614no—
360#391—1222no—
361C2×#95—1222no—
362#339—614no—
363C61C2×#203811yescharacteristic, complemented, Sylow
364C2×#41—612no—
365C2×#41—612no—
366C2×#41—1221no—
367C2×#41—1221no—
368C2×#41—1222no—
369C2×#41—1222no—
370C2×#41—1222no—
371C2×#41—1222no—
372C22×Q8—22no—
373C22×Q8—21no—
374C22×Q8—21no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—22no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—611no—
381C22×Q8D24412yes—
382C22×Q8C22×D6112yes—
383C22×D4—611no—
384C22×D4—1221no—
385C23×C4—1221no—
386C23×C4—1221no—
387C23×C4—1221no—
388C23×C4D24412yes—
389C23×C4C22×D6111yescharacteristic
390C2×M16—21no—
391C2×M16—22no—
392C2×M16—21no—
393C2×M16—22no—
394C2×M16—22no—
395C2×M16C22⋊D6114yes—
396C2×M16C22×D6112yes—
397C2×M16C22×D6112yes—
398C22×C8—21no—
399C22×C8—21no—
400C4⋊Q8—1224no—
401C4⋊Q8—1224no—
402#124—1224no—
403#124—1224no—
404#123—1228no—
405#123—1228no—
406C22⋊Q8—1224no—
407C22⋊Q8—1224no—
408C22⋊Q8—1224no—
409C22⋊Q8—1224no—
410#117—612no—
411#117—612no—
412#117—1221no—
413#117—1221no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—612no—
417C2×C4⋊C4—1222no—
418C2×C4⋊C4—1222no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C22⋊C4—1222no—
425C2×C22⋊C4—1222no—
426C2×C22⋊C4—1221no—
427C2×C42—612no—
428C2×C42—1221no—
429C2×C42—1222no—
430C2×C42—1222no—
431C2×C42—1221no—
432#107—1224no—
433#106—1224no—
434#104—1228no—
435#103—1224no—
436#102—1224no—
437#101—28no—
438#95—1228no—
439C24—1221no—
440C24C2×D24411yescharacteristic
441#41—1222no—
442#41—1222no—
443#41—1222no—
444#41—1222no—
445#41—1224no—
446#41—1224no—
447#41—2442no—
448#41—2442no—
449#41—2442no—
450#41—2442no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—24no—
460C2×Q8—24no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—612no—
470C2×Q8—1221no—
471C2×Q8—1222no—
472C2×Q8—1222no—
473C2×D4—612no—
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—1221no—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4—2442no—
480C2×D4—2442no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—1224no—
486C22×C4—1222no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—2444no—
494C22×C4—2441no—
495C22×C4—2441no—
496C22×C4—2442no—
497C22×C4—2442no—
498C22×C4—2442no—
499C22×C4—2442no—
500C22×C4C2×D24414yes—
501C22×C4C2×D24411yescharacteristic
502C22×C4#1175822212yes—
503C22×C4D4×D6111yescharacteristic
504C22×C4D4×D6111yescharacteristic
505C22×C4D4×D6111yescharacteristic
506C22×C4D4×D6111yescharacteristic
507C22×C4#1175822412yes—
508C22×C4#1175822412yes—
509C22×C4C2×C22⋊D6112yes—
510C22×C4C23×D6111yescharacteristic
511M16—22no—
512M16—24no—
513M16—22no—
514M16—22no—
515M16—42no—
516M16C2×C22⋊D6114yes—
517C2×C8—22no—
518C2×C8—24no—
519C2×C8—22no—
520C2×C8—42no—
521C4⋊C4—612no—
522C4⋊C4—612no—
523C4⋊C4—1228no—
524C4⋊C4—1228no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1222no—
528C4⋊C4—1222no—
529C4⋊C4—2441no—
530C4⋊C4—2441no—
531C22⋊C4—1228no—
532C22⋊C4—1228no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C42—1222no—
536C42—1222no—
537C42—1222no—
538C42—1222no—
539C42—2442no—
540C23—22no—
541C23—22no—
542C23—1222no—
543C23—2442no—
544C23—2442no—
545C23—2442no—
546C23#1451974711yescharacteristic
547C23#1451974711yescharacteristic
548C23#1451975112yes—
549C23#1451976112yes—
550C23C22×D24411yescharacteristic
551Q8—42no—
552Q8—42no—
553Q8—42no—
554Q8—42no—
555Q8—44no—
556Q8—44no—
557Q8—1222no—
558Q8—1222no—
559Q8—2442no—
560D4—1222no—
561D4—1222no—
562D4—2442no—
563D4—2442no—
564D4—2444no—
565D4—2442no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—1224no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—4882no—
576C2×C4—4882no—
577C2×C4—2444no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2448no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4—2444no—
588C2×C4#1451974711yescharacteristic
589C2×C4#1451974711yescharacteristic
590C2×C4#1451974812yes—
591C2×C4#1451974812yes—
592C2×C4#1451974912yes—
593C2×C4#1451974912yes—
594C2×C4#1451975112yes—
595C2×C4#1451975912yes—
596C2×C4#1451975912yes—
597C2×C4#1451976112yes—
598C2×C4#1451976312yes—
599C2×C4#1451976312yes—
600C2×C4C2×D4×D6111yescharacteristic
601C2×C4C2×D4×D6111yescharacteristic
602C2×C4C22×C22⋊D6111yescharacteristic
603C2×C4C2×#1175822411yescharacteristic
604C2×C4C2×#1175822411yescharacteristic
605C2×C4C2×#1175822211yescharacteristic
606C8—24no—
607C8—42no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—24no—
613C22—24no—
614C22—4884no—
615C22—2442no—
616C22—2442no—
617C22—2442no—
618C22#1683967812yes—
619C22#1683967812yes—
620C22#1683993712yes—
621C22#1683994712yes—
622C22C2×#1451974711yescharacteristic
623C22C2×#1451975111yescharacteristic
624C22C2×#1451976111yescharacteristic
625C4—44no—
626C4—4882no—
627C4—2444no—
628C4—2442no—
629C4—2442no—
630C4—2442no—
631C4#1683967812yes—
632C4#1683967812yes—
633C4C2×#1451974811yescharacteristic
634C4C2×#1451974911yescharacteristic
635C4C2×#1451975911yescharacteristic
636C4C2×#1451976311yescharacteristic
637C2—21no—
638C2—21no—
639C2—22no—
640C2—4882no—
641C2#2144703714yesdirect product factor
642C2C2×#1683967811yescharacteristic
643C2C2×#1683993711yescharacteristic
644C2C2×#1683994711yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#101×C61C2
socleC23×C61#120
prime radicalC22×#11758222C22
hypercenterC22×#101D61
hypocenterC61C2×#2038
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
2. C2×#16839804C2semidirect
5. C2×#16839669C2semidirect
6. #21447037C2direct (N × H)
7. C2×#16839523C2semidirect
8. C22×#101×C61C2semidirect
23. #16839804C22semidirect
33. #16839669C22semidirect
35. #16839523C22semidirect
40. C2×#101×C61C22semidirect
319. C22×#101D61semidirect
326. C2×C61#2038semidirect
358. C2×#101C2×D61semidirect
363. C61C2×#2038semidirect
641. C2#21447037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403362
C2×#168398042
C22×#145197032
C2×#168397642
C2×#168396692
#214470372
C2×#168395232
C22×#101×C612
C2×#203861