Finite Group Databasebeta

← C2×#21447047 #29707653

Subgroups — C2×#21447047 #29707653

Order 15616.

1498 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840340C211yesmaximal, characteristic
2C22×#14519705C211yesmaximal, characteristic, complemented
3C2×#16839764C211yesmaximal, characteristic, complemented
4C2×#16839763C211yesmaximal, characteristic, complemented
5C2×#16839628C211yesmaximal, characteristic, complemented
6#21447047C218yesmaximal, direct product factor
7C2×#16839530C211yesmaximal, characteristic, complemented
8C22×#104×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11#16840340—22no—
12#16840340—22no—
13#16840340—22no—
14#16840340C2214yes—
15C2×#14519756—21no—
16C2×#14519753—21no—
17C2×#14519751—21no—
18C2×#14519749—22no—
19C2×#14519748—21no—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C2×#14519705—24no—
23C2×#14519705C2214yescomplemented
24#16839764—22no—
25#16839764C2214yescomplemented
26#16839763—22no—
27#16839763C2214yescomplemented
28C2×#14519702—21no—
29C2×#14519701—21no—
30C2×#14519699—21no—
31C2×#14519698—21no—
32#16839628—22no—
33#16839628C2214yescomplemented
34C2×#14519684—22no—
35#16839530C2214yescomplemented
36C22×#41×C61C2211yescharacteristic
37C22×M16×C61C2211yescharacteristic
38C22×C42×C61C2211yescharacteristic
39C2×#104×C61—24no—
40C2×#104×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—
52C22×C22⋊D61—22no—
53C23×Dic61—21no—
54C23×Dic61D412yes—
55C22×C4×D61—21no—
56C2×#11758194—21no—
57C2×#11758194—22no—
58C2×#11758194—22no—
59C2×#11758194C2312yes—
60C22×#92418—21no—
61#14519756—24no—
62#14519756—24no—
63#14519753—24no—
64#14519753—24no—
65#14519751—24no—
66#14519751—24no—
67#14519749—28no—
68#14519749—28no—
69#14519748—24no—
70#14519748—24no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61D412yes—
81C2×C4⋊Dic61C2312yes—
82C2×C4⋊Dic61C2312yes—
83C2×#11758196—22no—
84C2×C22⋊Dic61—22no—
85C2×#11758198—22no—
86#14519705—28no—
87#14519702—24no—
88#14519701—24no—
89#14519699—24no—
90#14519698—24no—
91#14519684—28no—
92C2×#41×C61—21no—
93C2×#41×C61—21no—
94C2×#41×C61—22no—
95C2×#41×C61—22no—
96C2×#41×C61—22no—
97C2×#41×C61—22no—
98C2×#41×C61D412yes—
99C2×#41×C61C2312yes—
100C22×Q8×C61D411yescharacteristic
101C22×D4×C61—21no—
102C22×D4×C61D411yescharacteristic
103C23×C4×C61—21no—
104C23×C4×C61—21no—
105C23×C4×C61C2311yescharacteristic
106C2×M16×C61—21no—
107C2×M16×C61—22no—
108C2×M16×C61—22no—
109C2×M16×C61C2312yes—
110C22×C8×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61—22no—
113C2×C42×C61D414yescomplemented
114C2×C42×C61C2312yes—
115#104×C61—28no—
116C24×C61—21no—
117C24×C61C2×D411yescharacteristic
118C23×D61—21no—
119#41×C61—24no—
120#41×C61—24no—
121#41×C61—22no—
122#41×C61—22no—
123#41×C61—22no—
124#41×C61—22no—
125#41×C61—42no—
126#41×C61—42no—
127#41×C61—42no—
128#41×C61—42no—
129C2×Q8×C61—21no—
130C2×Q8×C61—22no—
131C2×Q8×C61—22no—
132C2×Q8×C61C2×D412yes—
133C2×D4×C61—22no—
134C2×D4×C61—22no—
135C2×D4×C61—21no—
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—42no—
139C2×D4×C61—42no—
140C2×D4×C61C2×D412yes—
141C22×C4×C61—21no—
142C22×C4×C61—24no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—42no—
147C22×C4×C61—42no—
148C22×C4×C61—42no—
149C22×C4×C61—42no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D412yes—
156C22×C4×C61#4112yes—
157C22×C4×C61#4112yes—
158C22×C4×C61#4112yes—
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—28no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61—84no—
166C22×Dic61—21no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—44no—
171C22×Dic61—44no—
172C22×Dic61—41no—
173C22×Dic61—41no—
174C22×Dic61C2×D414yes—
175#11758222—24no—
176#11758222—24no—
177#11758222—22no—
178#11758222—22no—
179#11758222—22no—
180#11758222—22no—
181#11758222—42no—
182#11758222—42no—
183#11758222—42no—
184#11758222—42no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—21no—
188C2×D244C2×D412yes—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×Dic122—22no—
194C2×Dic122—22no—
195C2×Dic122—21no—
196C2×Dic122C2×D412yes—
197M16×C61—22no—
198M16×C61—22no—
199M16×C61—42no—
200C2×C8×C61—22no—
201C2×C8×C61—42no—
202C42×C61—24no—
203C42×C61—22no—
204C42×C61C2×D414yescomplemented
205C22⋊Dic61—28no—
206#11758198—28no—
207C4⋊Dic61—22no—
208C4⋊Dic61—22no—
209C4⋊Dic61—22no—
210C4⋊Dic61—22no—
211C4⋊Dic61—22no—
212C4⋊Dic61—22no—
213C4⋊Dic61—41no—
214C4⋊Dic61—41no—
215#11758196—28no—
216#11758194—22no—
217#11758194—22no—
218#11758194—42no—
219C2×#92418—22no—
220C2×#92418—42no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61#12011yescharacteristic
228C23×C61#12011yescharacteristic
229C23×C61#12112yes—
230C23×C61#12412yes—
231C23×C61C22×D411yescharacteristic
232C22×D61—22no—
233C22×D61—42no—
234C22×D61—42no—
235C22×D61—42no—
236Q8×C61—22no—
237Q8×C61—22no—
238Q8×C61—42no—
239D4×C61—22no—
240D4×C61—22no—
241D4×C61—42no—
242D4×C61—42no—
243D4×C61—44no—
244D4×C61—42no—
245C2×C4×C61—22no—
246C2×C4×C61—24no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—48no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—44no—
254C2×C4×C61#12011yescharacteristic
255C2×C4×C61#12011yescharacteristic
256C2×C4×C61#12112yes—
257C2×C4×C61#12112yes—
258C2×C4×C61#12112yes—
259C2×C4×C61#12112yes—
260C2×C4×C61#12112yes—
261C2×C4×C61#12312yes—
262C2×C4×C61#12312yes—
263C2×C4×C61#12312yes—
264C2×C4×C61#12312yes—
265C2×C4×C61#12412yes—
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C22⋊D61—42no—
273C22⋊D61—42no—
274C22⋊D61—44no—
275C22⋊D61—88no—
276C2×Dic61—22no—
277C2×Dic61—24no—
278C2×Dic61—42no—
279C2×Dic61—44no—
280C2×Dic61—44no—
281C2×Dic61—44no—
282C2×Dic61—42no—
283C2×Dic61—82no—
284C2×Dic61—82no—
285C2×Dic61—82no—
286D244—22no—
287D244—22no—
288D244—42no—
289C4×D61—42no—
290C4×D61—42no—
291C4×D61—44no—
292Dic122—22no—
293Dic122—22no—
294Dic122—42no—
295C8×C61—42no—
296#92418—42no—
297C2×#2040—611nomaximal, Sylow
298C22×C61—21no—
299C22×C61—21no—
300C22×C61—21no—
301C22×C61—21no—
302C22×C61—24no—
303C22×C61—24no—
304C22×C61—42no—
305C22×C61—42no—
306C22×C61—42no—
307C22×C61—84no—
308C22×C61#39412yes—
309C22×C61#39412yes—
310C22×C61#45412yes—
311C22×C61#45512yes—
312C22×C61C2×#12011yescharacteristic
313C22×C61C2×#12111yescharacteristic
314C22×C61C2×#12411yescharacteristic
315C2×D61—42no—
316C2×D61—42no—
317C2×D61—42no—
318C2×D61—84no—
319C4×C61—44no—
320C4×C61—42no—
321C4×C61#39412yes—
322C4×C61#39412yes—
323C4×C61C2×#12111yescharacteristic
324C4×C61C2×#12111yescharacteristic
325C4×C61C2×#12311yescharacteristic
326C4×C61C2×#12311yescharacteristic
327Dic61—42no—
328Dic61—44no—
329Dic61—82no—
330C2×#537—611no—
331C22×#104—611no—
332C22×#104D6111yescharacteristic, complemented
333C2×#417—611no—
334C2×#417—611no—
335C2×#382—611no—
336#2040—618no—
337C2×#343—611no—
338C2×C61—21no—
339C2×C61—21no—
340C2×C61—22no—
341C2×C61—82no—
342C2×C61#204014yescomplemented
343C2×C61C2×#39411yescharacteristic
344C2×C61C2×#45511yescharacteristic
345C2×C61C2×#45411yescharacteristic
346D61—82no—
347C22×#41—611no—
348C22×#41C2×D6111yescharacteristic
349C22×M16—611no—
350C22×M16C2×D6111yescharacteristic
351#537—614no—
352#537—1222no—
353#537—1222no—
354#537—1222no—
355C2×C22⋊Q8—1221no—
356C2×C22⋊Q8—1221no—
357C2×#121—1221no—
358C2×#121—1222no—
359C2×#121—1221no—
360C22×C4⋊C4—611no—
361C22×C4⋊C4—611no—
362C22×C42C2×D6111yescharacteristic
363C2×#104—24no—
364C2×#104—614no—
365C2×#104—1224no—
366C2×#104C2×D6114yescomplemented
367#417—614no—
368#417—614no—
369#417—1222no—
370#417—1222no—
371C2×#103—1221no—
372C2×#103—1221no—
373C2×#102—1221no—
374C2×#102—1221no—
375#382—614no—
376#382—1222no—
377C2×#95—1222no—
378#343—614no—
379C61C2×#204011yescharacteristic, complemented, Sylow
380C2×#41—21no—
381C2×#41—21no—
382C2×#41—22no—
383C2×#41—22no—
384C2×#41—22no—
385C2×#41—22no—
386C2×#41—612no—
387C2×#41—612no—
388C2×#41—1221no—
389C2×#41—1221no—
390C2×#41—1222no—
391C2×#41—1222no—
392C2×#41—1222no—
393C2×#41—1222no—
394C2×#41D24412yes—
395C2×#41C22×D6112yes—
396C22×Q8—611no—
397C22×Q8D24411yescharacteristic
398C22×D4—21no—
399C22×D4—611no—
400C22×D4—1222no—
401C22×D4—1221no—
402C22×D4D24411yescharacteristic
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—612no—
406C23×C4—1221no—
407C23×C4—1221no—
408C23×C4C22×D6111yescharacteristic
409C2×M16—21no—
410C2×M16—22no—
411C2×M16—22no—
412C2×M16—612no—
413C2×M16—1221no—
414C2×M16—1222no—
415C2×M16—1222no—
416C2×M16C22×D6112yes—
417C22×C8—21no—
418C22×C8—1221no—
419C22⋊Q8—1224no—
420C22⋊Q8—1224no—
421C22⋊Q8—1224no—
422C22⋊Q8—1224no—
423#121—1224no—
424#121—1224no—
425#121—1228no—
426#121—1224no—
427#121—1228no—
428#121—1224no—
429C2×C4⋊C4—612no—
430C2×C4⋊C4—612no—
431C2×C4⋊C4—612no—
432C2×C4⋊C4—1222no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C22⋊C4—1222no—
443C2×C22⋊C4—1222no—
444C2×C42—21no—
445C2×C42—22no—
446C2×C42C22⋊D6114yescomplemented
447C2×C42C22×D6112yes—
448#104—28no—
449#104—1228no—
450#103—1224no—
451#103—1224no—
452#102—1224no—
453#102—1224no—
454#95—1228no—
455C24—21no—
456C24—1221no—
457C24D4×D6111yescharacteristic
458#41—22no—
459#41—22no—
460#41—22no—
461#41—22no—
462#41—24no—
463#41—24no—
464#41—42no—
465#41—42no—
466#41—42no—
467#41—42no—
468#41—1222no—
469#41—1222no—
470#41—1222no—
471#41—1222no—
472#41—1224no—
473#41—1224no—
474#41—2442no—
475#41—2442no—
476#41—2442no—
477#41—2442no—
478C2×Q8—21no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—612no—
482C2×Q8—1221no—
483C2×Q8—1222no—
484C2×Q8—1222no—
485C2×Q8C2×D24412yes—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—612no—
494C2×D4—1228no—
495C2×D4—1222no—
496C2×D4—1222no—
497C2×D4—1221no—
498C2×D4—1222no—
499C2×D4—1222no—
500C2×D4—4884no—
501C2×D4—2442no—
502C2×D4—2442no—
503C2×D4C2×D24412yes—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—614no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1221no—
517C22×C4—1222no—
518C22×C4—1222no—
519C22×C4—1222no—
520C22×C4—2444no—
521C22×C4—2441no—
522C22×C4—2441no—
523C22×C4—2444no—
524C22×C4—2442no—
525C22×C4—2442no—
526C22×C4C2×D24411yescharacteristic
527C22×C4C2×D24411yescharacteristic
528C22×C4#1175822212yes—
529C22×C4D4×D6111yescharacteristic
530C22×C4D4×D6111yescharacteristic
531C22×C4D4×D6111yescharacteristic
532C22×C4#1175822412yes—
533C22×C4#1175822412yes—
534C22×C4C2×C22⋊D6112yes—
535C22×C4C23×D6111yescharacteristic
536M16—22no—
537M16—22no—
538M16—42no—
539M16—1222no—
540M16—1222no—
541M16—2442no—
542C2×C8—22no—
543C2×C8—42no—
544C2×C8—1222no—
545C2×C8—2442no—
546C4⋊C4—1228no—
547C4⋊C4—1222no—
548C4⋊C4—1222no—
549C4⋊C4—1222no—
550C4⋊C4—1222no—
551C4⋊C4—1222no—
552C4⋊C4—1222no—
553C4⋊C4—2441no—
554C4⋊C4—2441no—
555C22⋊C4—1228no—
556C22⋊C4—1228no—
557C42—22no—
558C42—24no—
559C42C2×C22⋊D6114yescomplemented
560C23—22no—
561C23—22no—
562C23—22no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—1222no—
567C23—2442no—
568C23—2442no—
569C23—2442no—
570C23#1451974711yescharacteristic
571C23#1451974711yescharacteristic
572C23#1451974912yes—
573C23#1451976312yes—
574C23C2×D4×D6111yescharacteristic
575Q8—22no—
576Q8—22no—
577Q8—42no—
578Q8—1222no—
579Q8—1222no—
580Q8—2442no—
581D4—22no—
582D4—22no—
583D4—42no—
584D4—42no—
585D4—44no—
586D4—42no—
587D4—1222no—
588D4—1222no—
589D4—4888no—
590D4—2442no—
591D4—2442no—
592D4—2444no—
593D4—2442no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—48no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—44no—
603C2×C4—1224no—
604C2×C4—1222no—
605C2×C4—4882no—
606C2×C4—4882no—
607C2×C4—4882no—
608C2×C4—2444no—
609C2×C4—2442no—
610C2×C4—2444no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2444no—
615C2×C4—2444no—
616C2×C4#1451974711yescharacteristic
617C2×C4#1451974711yescharacteristic
618C2×C4#1451974812yes—
619C2×C4#1451974812yes—
620C2×C4#1451974912yes—
621C2×C4#1451975112yes—
622C2×C4#1451975112yes—
623C2×C4#1451975912yes—
624C2×C4#1451975912yes—
625C2×C4#1451976112yes—
626C2×C4#1451976112yes—
627C2×C4#1451976312yes—
628C2×C4C2×D4×D6111yescharacteristic
629C2×C4C22×C22⋊D6111yescharacteristic
630C2×C4C22×D24411yescharacteristic
631C2×C4C2×#1175822411yescharacteristic
632C2×C4C2×#1175822411yescharacteristic
633C2×C4C2×#1175822211yescharacteristic
634C8—42no—
635C8—2442no—
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—24no—
641C22—24no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—84no—
646C22—4884no—
647C22—2442no—
648C22—2442no—
649C22—2442no—
650C22#1683967812yes—
651C22#1683967812yes—
652C22#1683993612yes—
653C22#1683994112yes—
654C22C2×#1451974711yescharacteristic
655C22C2×#1451974911yescharacteristic
656C22C2×#1451976311yescharacteristic
657C4—44no—
658C4—42no—
659C4—4882no—
660C4—2444no—
661C4—2442no—
662C4#1683967812yes—
663C4#1683967812yes—
664C4C2×#1451974811yescharacteristic
665C4C2×#1451975111yescharacteristic
666C4C2×#1451975911yescharacteristic
667C4C2×#1451976111yescharacteristic
668C2—21no—
669C2—21no—
670C2—22no—
671C2—82no—
672C2—4882no—
673C2#2144704714yesdirect product factor
674C2C2×#1683967811yescharacteristic
675C2C2×#1683994111yescharacteristic
676C2C2×#1683993611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#104×C61C2
socleC23×C61#120
prime radicalC2×#16840340C2
hypercenterC22×#104D61
hypocenterC61C2×#2040
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#14519705C2semidirect
3. C2×#16839764C2semidirect
4. C2×#16839763C2semidirect
5. C2×#16839628C2semidirect
6. #21447047C2direct (N × H)
7. C2×#16839530C2semidirect
8. C22×#104×C61C2semidirect
23. C2×#14519705C22semidirect
25. #16839764C22semidirect
27. #16839763C22semidirect
33. #16839628C22semidirect
35. #16839530C22semidirect
40. C2×#104×C61C22semidirect
113. C2×C42×C61D4semidirect
204. C42×C61C2×D4semidirect
332. C22×#104D61semidirect
342. C2×C61#2040semidirect
366. C2×#104C2×D61semidirect
379. C61C2×#2040semidirect
446. C2×C42C22⋊D61semidirect
559. C42C2×C22⋊D61semidirect
673. C2#21447047direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403402
C22×#145197052
C2×#168397642
C2×#168397632
C2×#168396282
#214470472
C2×#168395302
C22×#104×C612
C2×#204061