Finite Group Databasebeta

← C2×#21447070 #29707773

Subgroups — C2×#21447070 #29707773

Order 15616.

2046 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840324C211yesmaximal, characteristic
2C22×#14519691C212yesmaximal, complemented
3C2×#16839641C212yesmaximal, complemented
4#21447070C218yesmaximal, direct product factor
5C2×#16839529C211yesmaximal, characteristic, complemented
6C2×C61×#385C211yesmaximal, characteristic, complemented
7C23×C22⋊D61C2212yes—
8#16840324—22no—
9#16840324—24no—
10#16840324C2214yes—
11C2×#14519761—22no—
12C2×#14519751—21no—
13C2×#14519751—21no—
14C2×#14519747—22no—
15C22×C22⋊Dic61C2212yes—
16C22×#11758198—22no—
17C2×#14519691—28no—
18C2×#14519691C2218yescomplemented
19#16839641—24no—
20#16839641C2218yescomplemented
21C2×#14519684—22no—
22#16839529C2214yescomplemented
23C24×C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61—21no—
25C22×C22⋊C4×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2211yescharacteristic
27C61×#385—22no—
28C61×#385C2214yescomplemented
29C2×#95×C61—21no—
30C24×D61D412yes—
31C22×D244—21no—
32C22×D244—21no—
33C22×C22⋊D61—24no—
34C22×C22⋊D61—22no—
35C22×C22⋊D61—22no—
36C22×C22⋊D61—22no—
37C22×C22⋊D61—22no—
38C22×C22⋊D61—24no—
39C22×C22⋊D61—24no—
40C22×C22⋊D61—24no—
41C22×C22⋊D61D414yes—
42C22×C22⋊D61C2314yes—
43C23×Dic61—22no—
44C23×Dic61D412yes—
45#14519761—28no—
46#14519761—28no—
47#14519751—24no—
48#14519751—24no—
49#14519751—24no—
50#14519751—24no—
51#14519747—28no—
52#14519747—28no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—21no—
55C2×C22⋊Dic61—24no—
56C2×C22⋊Dic61—24no—
57C2×C22⋊Dic61—22no—
58C2×C22⋊Dic61C2314yes—
59C2×#11758198—22no—
60C2×#11758198—22no—
61C2×#11758198—28no—
62C2×#11758198—48no—
63#14519691—216no—
64#14519684—28no—
65C25×C61C2311yescharacteristic
66C23×C4×C61—22no—
67C23×C4×C61—21no—
68C23×C4×C61—21no—
69C23×C4×C61—21no—
70C23×C4×C61—22no—
71C23×C4×C61—44no—
72C23×C4×C61D411yescharacteristic
73C23×C4×C61D411yescharacteristic
74C23×C4×C61C2312yes—
75C2×C4⋊C4×C61—24no—
76C2×C4⋊C4×C61—44no—
77C2×C22⋊C4×C61—22no—
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61—22no—
80C2×C22⋊C4×C61—22no—
81C2×C22⋊C4×C61D412yes—
82C2×C22⋊C4×C61D414yescomplemented
83C2×C22⋊C4×C61C2312yes—
84C2×C22⋊C4×C61C2312yes—
85#95×C61—24no—
86C24×C61—42no—
87C24×C61—42no—
88C24×C61C2×D412yes—
89C24×C61C2×D411yescharacteristic
90C24×C61C2×D412yes—
91C24×C61C2×D411yescharacteristic
92C24×C61C2×D412yes—
93C24×C61#4112yes—
94C24×C61#4114yes—
95C24×C61C2411yescharacteristic
96C23×D61—22no—
97C23×D61—24no—
98C23×D61—22no—
99C23×D61—24no—
100C23×D61—44no—
101C23×D61—44no—
102C23×D61C2×D414yes—
103C22×C4×C61—24no—
104C22×C4×C61—28no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—24no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—24no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—44no—
114C22×C4×C61—48no—
115C22×C4×C61—44no—
116C22×C4×C61—42no—
117C22×C4×C61—42no—
118C22×C4×C61—44no—
119C22×C4×C61—42no—
120C22×C4×C61—42no—
121C22×C4×C61—41no—
122C22×C4×C61—41no—
123C22×C4×C61—42no—
124C22×C4×C61—42no—
125C22×C4×C61C2×D412yes—
126C22×C4×C61C2×D412yes—
127C2×C22⋊D61—24no—
128C2×C22⋊D61—24no—
129C2×C22⋊D61—28no—
130C2×C22⋊D61—28no—
131C2×C22⋊D61—24no—
132C2×C22⋊D61—24no—
133C2×C22⋊D61—24no—
134C2×C22⋊D61—24no—
135C2×C22⋊D61—24no—
136C2×C22⋊D61—24no—
137C2×C22⋊D61—44no—
138C2×C22⋊D61—44no—
139C2×C22⋊D61—44no—
140C2×C22⋊D61—44no—
141C2×C22⋊D61—44no—
142C2×C22⋊D61—44no—
143C2×C22⋊D61—44no—
144C2×C22⋊D61—44no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—24no—
148C22×Dic61—24no—
149C22×Dic61—24no—
150C22×Dic61—44no—
151C22×Dic61—44no—
152C22×Dic61—44no—
153C22×Dic61C2×D414yes—
154C2×D244—24no—
155C2×D244—24no—
156C2×D244—82no—
157C2×D244—82no—
158C4⋊C4×C61—48no—
159C22⋊C4×C61—24no—
160C22⋊C4×C61—24no—
161C22⋊C4×C61—24no—
162C22⋊C4×C61—22no—
163C22⋊C4×C61C2×D414yescomplemented
164C22⋊Dic61—24no—
165C22⋊Dic61—24no—
166C22⋊Dic61—44no—
167#11758198—28no—
168#11758198—28no—
169#11758198—416no—
170C4⋊Dic61—24no—
171C4⋊Dic61—24no—
172C23×C61—24no—
173C23×C61—22no—
174C23×C61—24no—
175C23×C61—22no—
176C23×C61—42no—
177C23×C61—41no—
178C23×C61—41no—
179C23×C61—42no—
180C23×C61—41no—
181C23×C61—44no—
182C23×C61—48no—
183C23×C61—44no—
184C23×C61—41no—
185C23×C61#12012yes—
186C23×C61#12011yescharacteristic
187C23×C61#12011yescharacteristic
188C23×C61#12112yes—
189C23×C61#12114yes—
190C23×C61#12112yes—
191C23×C61#12114yes—
192C23×C61#12314yes—
193C23×C61#12314yes—
194C23×C61#12412yes—
195C23×C61#12412yes—
196C23×C61C22×D412yes—
197C23×C61C22×D411yescharacteristic
198C23×C61C22×D411yescharacteristic
199C23×C61C2×#4111yescharacteristic
200C23×C61C2×#4112yes—
201C22×D61—24no—
202C22×D61—24no—
203C22×D61—24no—
204C22×D61—44no—
205C22×D61—44no—
206C22×D61—416no—
207C22×D61—44no—
208C22×D61—44no—
209C22×D61—44no—
210C22×D61—44no—
211C22×D61—82no—
212C22×D61—82no—
213C22×D61—88no—
214C2×C4×C61—28no—
215C2×C4×C61—24no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—24no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—48no—
222C2×C4×C61—44no—
223C2×C4×C61—42no—
224C2×C4×C61—44no—
225C2×C4×C61—48no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—44no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—81no—
233C2×C4×C61—81no—
234C22⋊D61—44no—
235C22⋊D61—44no—
236C22⋊D61—44no—
237C22⋊D61—44no—
238C22⋊D61—48no—
239C22⋊D61—48no—
240C2×Dic61—24no—
241C2×Dic61—24no—
242C2×Dic61—24no—
243C2×Dic61—44no—
244C2×Dic61—44no—
245C2×Dic61—44no—
246C2×Dic61—44no—
247C2×Dic61—44no—
248C2×Dic61—88no—
249D244—84no—
250D244—84no—
251C2×#2044—611nomaximal, Sylow
252C22×C61—22no—
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—22no—
256C22×C61—22no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—22no—
260C22×C61—28no—
261C22×C61—24no—
262C22×C61—28no—
263C22×C61—24no—
264C22×C61—42no—
265C22×C61—44no—
266C22×C61—44no—
267C22×C61—42no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—42no—
271C22×C61#39414yes—
272C22×C61#39412yes—
273C22×C61#39412yes—
274C22×C61B(4,𝔽2)12yes—
275C22×C61#45812yes—
276C22×C61C2×#12011yescharacteristic
277C22×C61C2×#12111yescharacteristic
278C22×C61C2×#12112yes—
279C22×C61C2×#12312yes—
280C22×C61C2×#12411yescharacteristic
281C2×D61—48no—
282C2×D61—44no—
283C2×D61—44no—
284C2×D61—44no—
285C2×D61—88no—
286C2×D61—88no—
287C2×D61—84no—
288C4×C61—44no—
289C4×C61—42no—
290C4×C61—44no—
291C4×C61—42no—
292Dic61—44no—
293Dic61—84no—
294C2×#534—611no—
295C22×#99—612no—
296C2×#386—612no—
297C2×#385D6111yescharacteristic, complemented
298#2044—618no—
299C2×#342—611no—
300C2×C61—22no—
301C2×C61—21no—
302C2×C61—22no—
303C2×C61—24no—
304C2×C61—21no—
305C2×C61—22no—
306C2×C61#204414yescomplemented
307C2×C61C2×#39411yescharacteristic
308C2×C61C2×B(4,𝔽2)11yescharacteristic
309C2×C61C2×#45811yescharacteristic
310D61—84no—
311C23×D4—612no—
312C24×C4C2×D6111yescharacteristic
313#534—614no—
314#534—1224no—
315#534—1222no—
316C2×#123—1222no—
317C2×#121—1221no—
318C2×#121—1221no—
319C2×#120—1222no—
320C22×C4⋊C4—21no—
321C22×C22⋊C4—612no—
322C22×C22⋊C4—1222no—
323C22×C22⋊C4C2×D6111yescharacteristic
324C22×C22⋊C4C2×D6111yescharacteristic
325C2×#99—618no—
326C2×#99—1228no—
327#386—618no—
328#386—1224no—
329#385—22no—
330#385C2×D6114yescomplemented
331C2×#95—21no—
332C2×#95—1222no—
333#342—614no—
334C61C2×#204411yescharacteristic, complemented, Sylow
335C25—612no—
336C25C22×D6111yescharacteristic
337C22×D4—614no—
338C22×D4—614no—
339C22×D4—1221no—
340C22×D4—1221no—
341C22×D4—1224no—
342C22×D4—1224no—
343C22×D4—1222no—
344C22×D4—1222no—
345C22×D4—1224no—
346C22×D4—1224no—
347C22×D4—1222no—
348C22×D4—1222no—
349C23×C4—22no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—22no—
353C23×C4—21no—
354C23×C4—44no—
355C23×C4—612no—
356C23×C4—1222no—
357C23×C4C22⋊D6111yescharacteristic
358C23×C4C22⋊D6111yescharacteristic
359C23×C4C22×D6112yes—
360#123—1228no—
361#123—1228no—
362#121—1224no—
363#121—1224no—
364#121—1224no—
365#121—1224no—
366#120—1228no—
367#120—1228no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—1221no—
371C2×C4⋊C4—1221no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—614no—
377C2×C22⋊C4—1222no—
378C2×C22⋊C4—1222no—
379C2×C22⋊C4—1224no—
380C2×C22⋊C4—1224no—
381C2×C22⋊C4—1228no—
382C2×C22⋊C4—1222no—
383C2×C22⋊C4—2448no—
384C2×C22⋊C4D24414yescomplemented
385C2×C22⋊C4C22⋊D6112yes—
386C2×C22⋊C4C22×D6112yes—
387C2×C22⋊C4C22×D6112yes—
388#99—12216no—
389#95—24no—
390#95—1228no—
391C24—42no—
392C24—42no—
393C24—614no—
394C24—1222no—
395C24—1224no—
396C24—1222no—
397C24—1224no—
398C24—2444no—
399C24—2444no—
400C24C2×D24412yes—
401C24#1175822212yes—
402C24D4×D6112yes—
403C24D4×D6112yes—
404C24#1175822614yes—
405C24C2×C22⋊D6111yescharacteristic
406C24C2×C22⋊D6111yescharacteristic
407C24C23×D6111yescharacteristic
408C2×D4—1224no—
409C2×D4—1224no—
410C2×D4—1224no—
411C2×D4—1224no—
412C2×D4—1224no—
413C2×D4—1224no—
414C2×D4—1224no—
415C2×D4—1224no—
416C2×D4—1224no—
417C2×D4—1224no—
418C2×D4—1228no—
419C2×D4—1228no—
420C2×D4—4882no—
421C2×D4—4882no—
422C2×D4—2444no—
423C2×D4—2444no—
424C2×D4—2444no—
425C2×D4—2444no—
426C2×D4—2444no—
427C2×D4—2444no—
428C2×D4—2444no—
429C2×D4—2444no—
430C22×C4—28no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—44no—
441C22×C4—48no—
442C22×C4—44no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—44no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—614no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1224no—
456C22×C4—1224no—
457C22×C4—1224no—
458C22×C4—2444no—
459C22×C4—2444no—
460C22×C4—2444no—
461C22×C4C2×C22⋊D6112yes—
462C22×C4C2×C22⋊D6112yes—
463C4⋊C4—48no—
464C4⋊C4—1224no—
465C4⋊C4—1224no—
466C22⋊C4—24no—
467C22⋊C4—22no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—1228no—
471C22⋊C4—1228no—
472C22⋊C4—1224no—
473C22⋊C4—1224no—
474C22⋊C4—24416no—
475C22⋊C4—2444no—
476C22⋊C4C2×D24414yescomplemented
477C23—22no—
478C23—24no—
479C23—22no—
480C23—24no—
481C23—42no—
482C23—41no—
483C23—41no—
484C23—44no—
485C23—44no—
486C23—42no—
487C23—48no—
488C23—41no—
489C23—41no—
490C23—1224no—
491C23—1224no—
492C23—1224no—
493C23—4888no—
494C23—4882no—
495C23—4882no—
496C23—24416no—
497C23—2444no—
498C23—2444no—
499C23—2444no—
500C23—2444no—
501C23—2444no—
502C23—2444no—
503C23#1451974512yes—
504C23#1451974511yescharacteristic
505C23#1451974511yescharacteristic
506C23#1451975112yes—
507C23#1451975112yes—
508C23#1451975214yes—
509C23#1451975214yes—
510C23#1451976214yes—
511C23#1451976214yes—
512C23#1451976612yes—
513C23#1451976612yes—
514C23C2×D4×D6112yes—
515C23C22×C22⋊D6111yescharacteristic
516C23C22×D24411yescharacteristic
517C23C2×#1175822211yescharacteristic
518C23C2×#1175822612yes—
519D4—4884no—
520D4—4884no—
521D4—2444no—
522D4—2444no—
523D4—2444no—
524D4—2444no—
525D4—2448no—
526D4—2448no—
527C2×C4—28no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—48no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—48no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—1224no—
548C2×C4—1224no—
549C2×C4—1224no—
550C2×C4—4888no—
551C2×C4—2444no—
552C2×C4—2444no—
553C2×C4—2444no—
554C2×C4—2444no—
555C2×C4—2444no—
556C22—21no—
557C22—22no—
558C22—21no—
559C22—22no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—22no—
564C22—24no—
565C22—28no—
566C22—28no—
567C22—24no—
568C22—41no—
569C22—41no—
570C22—42no—
571C22—42no—
572C22—44no—
573C22—44no—
574C22—42no—
575C22—4884no—
576C22—4888no—
577C22—4888no—
578C22—2448no—
579C22—2444no—
580C22—2444no—
581C22—2444no—
582C22#1683967914yes—
583C22#1683967912yes—
584C22#1683967912yes—
585C22#1683994812yes—
586C22#1683995112yes—
587C22C2×#1451974511yescharacteristic
588C22C2×#1451975111yescharacteristic
589C22C2×#1451975212yes—
590C22C2×#1451976212yes—
591C22C2×#1451976611yescharacteristic
592C4—44no—
593C4—44no—
594C4—42no—
595C4—42no—
596C4—4884no—
597C4—2444no—
598C2—21no—
599C2—22no—
600C2—24no—
601C2—22no—
602C2—21no—
603C2—22no—
604C2—4884no—
605C2#2144707014yesdirect product factor
606C2C2×#1683967911yescharacteristic
607C2C2×#1683994811yescharacteristic
608C2C2×#1683995111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC24×C61C24
FrattiniC24C23×D61
FittingC2×C61×#385C2
socleC23×C61#120
prime radicalC2×#16840324C2
hypercenterC2×#385D61
hypocenterC61C2×#2044
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#14519691C2semidirect
3. C2×#16839641C2semidirect
4. #21447070C2direct (N × H)
5. C2×#16839529C2semidirect
6. C2×C61×#385C2semidirect
18. C2×#14519691C22semidirect
20. #16839641C22semidirect
22. #16839529C22semidirect
28. C61×#385C22semidirect
82. C2×C22⋊C4×C61D4semidirect
163. C22⋊C4×C61C2×D4semidirect
297. C2×#385D61semidirect
306. C2×C61#2044semidirect
330. #385C2×D61semidirect
334. C61C2×#2044semidirect
384. C2×C22⋊C4D244semidirect
476. C22⋊C4C2×D244semidirect
605. C2#21447070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403242
C22×#145196912
C2×#168396412
#214470702
C2×#168395292
C2×C61×#3852
C2×#204461