Finite Group Databasebeta

← C2×#21446335 #29681945

Subgroups — C2×#21446335 #29681945

Order 15616.

1698 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
1C22×#14519810C211yesmaximal, characteristic
2C22×#14519785C211yesmaximal, characteristic
3C2×#16839761C211yesmaximal, characteristic
4C22×#14519700C211yesmaximal, characteristic, complemented
5C22×#14519695C211yesmaximal, characteristic, complemented
6#21446335C218yesmaximal, direct product factor
7C2×#16839526C211yesmaximal, characteristic, complemented
8C2×C61×#343C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×Dic122C2211yescharacteristic
11C2×#14519810—22no—
12C2×#14519810—24no—
13C2×#14519810C418yescomplemented
14C2×#14519810C2214yes—
15C22×Dic244—21no—
16C22×#11758190—21no—
17C2×#14519785—22no—
18C2×#14519785—24no—
19C2×#14519785—24no—
20C2×#14519785C2214yes—
21C22×#11758194C2211yescharacteristic
22C22×#11758189—21no—
23C23×#92418C2211yescharacteristic
24C22×C8×D61—21no—
25#16839761—22no—
26#16839761C2214yes—
27C2×#14519700—21no—
28C2×#14519700—21no—
29C2×#14519700—22no—
30C2×#14519700—21no—
31C2×#14519700C2214yescomplemented
32C2×#14519697—21no—
33C2×#14519695—24no—
34C2×#14519695C2214yescomplemented
35#16839526C2214yescomplemented
36C22×M16×C61C2211yescharacteristic
37C22×M16×C61C2211yescharacteristic
38C22×C4⋊C4×C61C2211yescharacteristic
39C61×#343C2214yescomplemented
40C2×#11758222—22no—
41C2×#11758222—21no—
42C2×#11758222—22no—
43C2×#11758222—21no—
44C2×#11758222C2×C414yes—
45C2×#11758222D414yes—
46C2×#11758222D412yes—
47C2×#11758222C2312yes—
48C22×Dic122—21no—
49C22×Dic122—21no—
50C22×Dic122—21no—
51C22×Dic122—21no—
52C22×Dic122—22no—
53C22×Dic122—22no—
54C22×Dic122—22no—
55C22×Dic122—21no—
56C22×Dic122C2×C414yes—
57C22×Dic122D411yescharacteristic
58C22×Dic122C2312yes—
59C22×D244D411yescharacteristic
60C22×C22⋊D61—21no—
61C23×Dic61—21no—
62C22×C4×D61—21no—
63#14519810—216no—
64#14519810—28no—
65#14519810C2×C4116yescomplemented
66C2×Dic244—28no—
67C2×Dic244—24no—
68C2×#11758190—28no—
69C2×#11758190—24no—
70#14519785—216no—
71#14519785—28no—
72#14519785—28no—
73C2×#11758194—21no—
74C2×#11758194—22no—
75C2×#11758194—22no—
76C2×#11758194C2312yes—
77C2×#11758189—28no—
78C2×#11758189—24no—
79C22×#92418—22no—
80C22×#92418—22no—
81C22×#92418—21no—
82C22×#92418D411yescharacteristic
83C22×#92418D411yescharacteristic
84C22×#92418D412yes—
85C22×#92418C2312yes—
86C2×C8×D61—28no—
87C2×C8×D61—24no—
88#14519700—24no—
89#14519700—24no—
90#14519700—24no—
91#14519697—24no—
92#14519695—28no—
93C23×C4×C61—21no—
94C23×C4×C61C2311yescharacteristic
95C2×M16×C61—22no—
96C2×M16×C61—21no—
97C2×M16×C61—22no—
98C2×M16×C61—21no—
99C2×M16×C61C2×C414yes—
100C2×M16×C61D414yes—
101C2×M16×C61C2312yes—
102C2×M16×C61C2312yes—
103C22×C8×C61—21no—
104C22×C8×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2312yes—
111C24×C61#4111yescharacteristic
112C23×D61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61—82no—
117C22×C4×C61C22×C412yes—
118C22×C4×C61C2×D412yes—
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D412yes—
124C22×C4×C61#4111yescharacteristic
125C22×C4×C61#4112yes—
126C22×C4×C61C2411yescharacteristic
127C2×C22⋊D61—24no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—24no—
130C2×C22⋊D61—22no—
131C22×Dic61—21no—
132C22×Dic61—24no—
133C22×Dic61—22no—
134C22×Dic61—41no—
135C22×Dic61—41no—
136C22×Dic61—42no—
137#11758222—24no—
138#11758222—24no—
139#11758222—24no—
140#11758222—24no—
141#11758222—24no—
142#11758222—22no—
143#11758222—22no—
144#11758222C22⋊C418yes—
145#11758222C22×C414yes—
146#11758222C2×D414yes—
147C2×D244—22no—
148C2×D244—21no—
149C2×D244C22⋊C414yes—
150C2×D244C2×D412yes—
151C2×C4×D61—24no—
152C2×C4×D61—24no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×Dic122—22no—
156C2×Dic122—21no—
157C2×Dic122—24no—
158C2×Dic122—24no—
159C2×Dic122—24no—
160C2×Dic122—24no—
161C2×Dic122—22no—
162C2×Dic122—22no—
163C2×Dic122—22no—
164C2×Dic122—22no—
165C2×Dic122—24no—
166C2×Dic122—22no—
167C2×Dic122—42no—
168C2×Dic122—42no—
169C2×Dic122—42no—
170C2×Dic122—42no—
171C2×Dic122—41no—
172C2×Dic122—41no—
173C2×Dic122—42no—
174C2×Dic122C22⋊C414yes—
175C2×Dic122C22×C414yes—
176C2×Dic122C2×D412yes—
177M16×C61—24no—
178M16×C61—24no—
179M16×C61—22no—
180M16×C61—22no—
181M16×C61C22×C414yes—
182M16×C61C2×D414yes—
183C2×C8×C61—24no—
184C2×C8×C61—24no—
185C2×C8×C61—22no—
186C2×C8×C61—22no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61—41no—
191#11758194—22no—
192#11758194—22no—
193#11758194—42no—
194C2×#92418—22no—
195C2×#92418—22no—
196C2×#92418—24no—
197C2×#92418—22no—
198C2×#92418—22no—
199C2×#92418—22no—
200C2×#92418—42no—
201C2×#92418C2×D412yes—
202C2×#92418C2×D412yes—
203Dic244—216no—
204#11758190—216no—
205#11758189—216no—
206C8×D61—216no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61C4×D412yes—
210C23×C61#12111yescharacteristic
211C23×C61#12111yescharacteristic
212C23×C61#12312yes—
213C23×C61C2×#4111yescharacteristic
214C22×D61—22no—
215C22×D61—24no—
216C22×D61—42no—
217C22×D61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—82no—
220C2×C4×C61—82no—
221C2×C4×C61—82no—
222C2×C4×C61C2×C22⋊C412yes—
223C2×C4×C61C2×C22⋊C412yes—
224C2×C4×C61C4×D412yes—
225C2×C4×C61C4×D412yes—
226C2×C4×C61C4×D412yes—
227C2×C4×C61#12012yes—
228C2×C4×C61#12012yes—
229C2×C4×C61#12112yes—
230C2×C4×C61#12112yes—
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61#12312yes—
234C2×C4×C61C23×C411yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C22⋊D61—24no—
241C22⋊D61—24no—
242C22⋊D61—28no—
243C2×Dic61—22no—
244C2×Dic61—24no—
245C2×Dic61—24no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—44no—
249C2×Dic61—44no—
250D244—22no—
251D244—24no—
252D244C2×C22⋊C414yes—
253C4×D61—24no—
254C4×D61—24no—
255C4×D61—28no—
256Dic122—22no—
257Dic122—24no—
258Dic122—24no—
259Dic122—24no—
260Dic122—42no—
261Dic122—42no—
262Dic122—44no—
263Dic122—44no—
264Dic122C2×C22⋊C414yes—
265C8×C61—24no—
266C8×C61—24no—
267#92418—22no—
268#92418—22no—
269#92418—42no—
270C2×#1908—611nomaximal, Sylow
271C22×C61—24no—
272C22×C61—24no—
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61#38612yes—
278C22×C61#38612yes—
279C22×C61#47112yes—
280C22×C61#47312yes—
281C22×C61C2×C4×D411yescharacteristic
282C22×C61C2×#12111yescharacteristic
283C22×C61C2×#12311yescharacteristic
284C2×D61—24no—
285C2×D61—48no—
286C2×D61—42no—
287C2×D61—42no—
288C4×C61—82no—
289C4×C61#38612yes—
290C4×C61#38612yes—
291C4×C61C22×C22⋊C411yescharacteristic
292C4×C61C2×C4×D411yescharacteristic
293C4×C61C2×#12011yescharacteristic
294C4×C61C2×#12111yescharacteristic
295Dic61—24no—
296Dic61—44no—
297C22×#137—611no—
298C22×#131—611no—
299C2×#417—611no—
300C22×#103—611no—
301C22×#101—611no—
302#1908—618no—
303C2×#343D6111yescharacteristic, complemented
304C2×#341—611no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—22no—
308C2×C61#190814yescomplemented
309C2×C61C2×#38611yescharacteristic
310C2×C61C2×#47111yescharacteristic
311C2×C61C2×#47311yescharacteristic
312D61—44no—
313C22×#41—611no—
314C23×Q8—611no—
315C2×#137—618no—
316C2×#137—614no—
317C2×#137—1224no—
318C2×#137—1222no—
319C22×Q16—1221no—
320C22×SD16—1221no—
321C2×#131—614no—
322C2×#131—1222no—
323C2×#131—1224no—
324C2×#131—1224no—
325C22×M16—611no—
326C22×M16—1221no—
327C22×M16C2×D6111yescharacteristic
328C22×M16C2×D6111yescharacteristic
329C23×C8—611no—
330C23×C8—1221no—
331C22×C4⋊C4C2×D6111yescharacteristic
332#417—614no—
333#417—1222no—
334C2×#103—614no—
335C2×#103—1221no—
336C2×#103—1221no—
337C2×#103—1222no—
338C2×#103—1221no—
339C2×#102—1221no—
340C2×#101—614no—
341C2×#101—1224no—
342#343C2×D6114yescomplemented
343#341—614no—
344C61C2×#190811yescharacteristic, complemented, Sylow
345C2×#41—614no—
346C2×#41—614no—
347C2×#41—612no—
348C2×#41—612no—
349C2×#41—1222no—
350C2×#41—1221no—
351C2×#41—1221no—
352C2×#41—1222no—
353C22×Q8—614no—
354C22×Q8—611no—
355C22×Q8—612no—
356C22×Q8—1222no—
357C22×Q8—1221no—
358C22×Q8—1221no—
359C22×Q8—1221no—
360C22×Q8—1222no—
361C22×Q8—1221no—
362C22×Q8—1221no—
363C22×Q8—1222no—
364C22×D4—611no—
365C22×D4—1221no—
366C23×C4—21no—
367C23×C4—1221no—
368C23×C4—1221no—
369C23×C4C22×D6111yescharacteristic
370#137—6116no—
371#137—1228no—
372#137—12216no—
373C2×Q16—1224no—
374C2×Q16—1228no—
375C2×SD16—1224no—
376C2×SD16—1228no—
377#131—1228no—
378#131—12216no—
379#131—1228no—
380C2×M16—21no—
381C2×M16—22no—
382C2×M16—21no—
383C2×M16—22no—
384C2×M16—612no—
385C2×M16—1224no—
386C2×M16—1228no—
387C2×M16—1221no—
388C2×M16—1222no—
389C2×M16—1222no—
390C2×M16C4×D6114yes—
391C2×M16D24414yes—
392C2×M16C22×D6112yes—
393C2×M16C22×D6112yes—
394C22×C8—21no—
395C22×C8—21no—
396C22×C8—611no—
397C22×C8—611no—
398C22×C8—612no—
399C22×C8—612no—
400C22×C8—1224no—
401C22×C8—1228no—
402C22×C8—1222no—
403C22×C8—1222no—
404C22×C8—1221no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C22×D6112yes—
411#103—1224no—
412#103—1224no—
413#103—1224no—
414#102—1224no—
415#101—1228no—
416C24—1221no—
417C24#1175822211yescharacteristic
418#41—614no—
419#41—614no—
420#41—618no—
421#41—1222no—
422#41—1222no—
423#41—1224no—
424#41—1224no—
425#41—1224no—
426#41—1224no—
427#41—1224no—
428C2×Q8—614no—
429C2×Q8—612no—
430C2×Q8—614no—
431C2×Q8—1222no—
432C2×Q8—1224no—
433C2×Q8—1221no—
434C2×Q8—1222no—
435C2×Q8—1222no—
436C2×Q8—1222no—
437C2×Q8—1222no—
438C2×Q8—1222no—
439C2×Q8—1224no—
440C2×Q8—1224no—
441C2×Q8—1224no—
442C2×Q8—1224no—
443C2×Q8—2442no—
444C2×Q8—2442no—
445C2×Q8—2441no—
446C2×Q8—2441no—
447C2×Q8—2442no—
448C2×Q8—2442no—
449C2×Q8—2442no—
450C2×D4—612no—
451C2×D4—614no—
452C2×D4—1222no—
453C2×D4—1224no—
454C2×D4—1222no—
455C2×D4—1224no—
456C2×D4—1221no—
457C2×D4—1222no—
458C22×C4—22no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—82no—
462C22×C4—1221no—
463C22×C4—1222no—
464C22×C4—1224no—
465C22×C4—1224no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1224no—
469C22×C4—2441no—
470C22×C4—2441no—
471C22×C4—2442no—
472C22×C4C2×C4×D6112yes—
473C22×C4C2×D24412yes—
474C22×C4#1175822211yescharacteristic
475C22×C4D4×D6112yes—
476C22×C4D4×D6111yescharacteristic
477C22×C4D4×D6111yescharacteristic
478C22×C4D4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4#1175822612yes—
481C22×C4C23×D6111yescharacteristic
482Q16—12216no—
483SD16—12216no—
484M16—22no—
485M16—22no—
486M16—24no—
487M16—24no—
488M16—12216no—
489M16—1222no—
490M16—1222no—
491M16—2442no—
492M16C2×C4×D6114yes—
493M16C2×D24414yes—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—24no—
497C2×C8—24no—
498C2×C8—612no—
499C2×C8—612no—
500C2×C8—12216no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—1222no—
504C2×C8—1222no—
505C2×C8—1224no—
506C2×C8—1222no—
507C2×C8—2442no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C23—22no—
513C23—22no—
514C23—1222no—
515C23—1224no—
516C23—2442no—
517C23—2442no—
518C23C4×D24412yes—
519C23#1451975011yescharacteristic
520C23#1451975011yescharacteristic
521C23#1451976212yes—
522C23C2×#1175822211yescharacteristic
523Q8—614no—
524Q8—1222no—
525Q8—1224no—
526Q8—1224no—
527Q8—1224no—
528Q8—2442no—
529Q8—2442no—
530Q8—2444no—
531Q8—2444no—
532D4—614no—
533D4—1224no—
534D4—1224no—
535D4—1228no—
536D4—1222no—
537D4—1224no—
538C2×C4—42no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—1222no—
543C2×C4—1224no—
544C2×C4—1224no—
545C2×C4—1224no—
546C2×C4—1228no—
547C2×C4—1224no—
548C2×C4—2442no—
549C2×C4—2442no—
550C2×C4—2444no—
551C2×C4—2444no—
552C2×C4C22⋊C4×D6112yes—
553C2×C4C22⋊C4×D6112yes—
554C2×C4#1451973912yes—
555C2×C4#1451973912yes—
556C2×C4C4×D24412yes—
557C2×C4#1451974712yes—
558C2×C4#1451974712yes—
559C2×C4#1451975011yescharacteristic
560C2×C4#1451975011yescharacteristic
561C2×C4#1451975212yes—
562C2×C4#1451975212yes—
563C2×C4#1451976212yes—
564C2×C4C22×C4×D6111yescharacteristic
565C2×C4C2×D4×D6111yescharacteristic
566C2×C4C2×D4×D6111yescharacteristic
567C2×C4C2×D4×D6111yescharacteristic
568C2×C4C22×D24411yescharacteristic
569C2×C4C2×#1175822611yescharacteristic
570C8—24no—
571C8—24no—
572C8—1222no—
573C8—1222no—
574C8—2442no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—24no—
580C22—24no—
581C22—1224no—
582C22—2442no—
583C22—2442no—
584C22—2448no—
585C22#1683964012yes—
586C22#1683964012yes—
587C22#1684002412yes—
588C22#1684003612yes—
589C22C2×C4×D24411yescharacteristic
590C22C2×#1451975011yescharacteristic
591C22C2×#1451976211yescharacteristic
592C4—82no—
593C4—1224no—
594C4—2444no—
595C4#1683964012yes—
596C4#1683964012yes—
597C4C2×C22⋊C4×D6111yescharacteristic
598C4C2×#1451973911yescharacteristic
599C4C2×#1451974711yescharacteristic
600C4C2×#1451975211yescharacteristic
601C2—21no—
602C2—21no—
603C2—22no—
604C2—2444no—
605C2#2144633514yesdirect product factor
606C2C2×#1683964011yescharacteristic
607C2C2×#1684002411yescharacteristic
608C2C2×#1684003611yescharacteristic
subgroupG/H
centerC23#14519750
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#343C2
socleC23×C61#121
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×#343D61
hypocenterC61C2×#1908
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. C22×#14519700C2semidirect
5. C22×#14519695C2semidirect
6. #21446335C2direct (N × H)
7. C2×#16839526C2semidirect
8. C2×C61×#343C2semidirect
13. C2×#14519810C4semidirect
31. C2×#14519700C22semidirect
34. C2×#14519695C22semidirect
35. #16839526C22semidirect
39. C61×#343C22semidirect
65. #14519810C2×C4semidirect
303. C2×#343D61semidirect
308. C2×C61#1908semidirect
342. #343C2×D61semidirect
344. C61C2×#1908semidirect
605. C2#21446335direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198102
C22×#145197852
C2×#168397612
C22×#145197002
C22×#145196952
#214463352
C2×#168395262
C2×C61×#3432
C2×#190861