Finite Group Databasebeta

← C2×#21461963 #30616264

Subgroups — C2×#21461963 #30616264

Order 15616.

1646 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840765C211yesmaximal, characteristic, complemented
2C22×#14519838C212yesmaximal, complemented
3C22×#14519837C212yesmaximal
4C2×C4×#11758217C211yesmaximal, characteristic, complemented
5#21461963C218yesmaximal, direct product factor
6C22×#14519763C211yesmaximal, characteristic
7C22×#11758217C2212yes—
8C22×#11758217C2212yes—
9#16840765—22no—
10#16840765C2214yescomplemented
11C2×#14519844—21no—
12C2×C4⋊#92420—21no—
13C2×#14519838—28no—
14C2×#14519838C2218yescomplemented
15C2×#14519837—28no—
16C2×#14519837C2218yes—
17C4×#11758217—22no—
18C4×#11758217C2214yescomplemented
19C2×#14519832—21no—
20C2×C4×#92420—21no—
21C23×Dic122C2211yescharacteristic
22C23×C22⋊D61C2211yescharacteristic
23C2×#14519763—21no—
24C2×#14519763—21no—
25C2×#14519763—22no—
26C2×#14519763—21no—
27C2×#14519763—21no—
28C2×#14519763—22no—
29C2×#14519763C414yes—
30C2×#14519763C2214yes—
31C22×C22⋊Dic61C411yescharacteristic
32C22×#11758198C411yescharacteristic
33C22×#11758198C411yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C22⋊C4×C61C411yescharacteristic
36C2×#11758217—22no—
37C2×#11758217—24no—
38C2×#11758217—22no—
39C2×#11758217—24no—
40C2×#11758217—24no—
41C2×#11758217D418yes—
42C2×#11758217C2314yes—
43C2×#11758217C2314yes—
44C22×#92420—22no—
45C22×#92420—22no—
46#14519844—24no—
47C4⋊#92420—24no—
48#14519838—216no—
49#14519837—216no—
50#14519832—24no—
51C4×#92420—24no—
52C24×D61C2×C411yescharacteristic
53C22×Dic122—24no—
54C22×Dic122—21no—
55C22×Dic122—21no—
56C22×Dic122—21no—
57C22×Dic122—21no—
58C22×Dic122—24no—
59C22×Dic122C2×C412yes—
60C22×Dic122C2312yes—
61C22×C22⋊D61—24no—
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C22×C22⋊D61—24no—
67C22×C22⋊D61C2×C412yes—
68C22×C22⋊D61C2312yes—
69C23×Dic61C2×C411yescharacteristic
70C23×Dic61C2×C411yescharacteristic
71C23×Dic61C2311yescharacteristic
72#14519763—24no—
73#14519763—24no—
74#14519763—24no—
75#14519763—24no—
76#14519763—24no—
77#14519763—24no—
78#14519763—24no—
79#14519763—24no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61C2×C414yes—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—22no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—22no—
90C2×#11758198C2×C414yes—
91C2×#11758198C2×C414yes—
92C2×C4×Dic61C2×C412yes—
93C2×C4×Dic61D411yescharacteristic
94C2×C4×Dic61D411yescharacteristic
95C2×C4×Dic61D412yes—
96C2×C4×Dic61D411yescharacteristic
97C2×C4×Dic61D411yescharacteristic
98C2×C4×Dic61D412yes—
99C2×C4×Dic61C2312yes—
100C25×C61C2×C411yescharacteristic
101C23×C4×C61C2×C411yescharacteristic
102C23×C4×C61C2×C411yescharacteristic
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—22no—
106C2×C22⋊C4×C61C2×C414yes—
107C24×C61—21no—
108C24×C61—21no—
109C24×C61—24no—
110C24×C61—42no—
111C24×C61—42no—
112C24×C61C22×C411yescharacteristic
113C24×C61C22×C412yes—
114C23×D61—21no—
115C23×D61—21no—
116C23×D61—24no—
117C23×D61—42no—
118C23×D61—42no—
119C23×D61C22×C412yes—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—24no—
123C22×C4×C61—42no—
124C22×C4×C61C22⋊C411yescharacteristic
125C22×C4×C61C22⋊C411yescharacteristic
126C22×C4×C61C22⋊C412yes—
127C22×C4×C61C22×C412yes—
128C22×C4×C61C22×C412yes—
129C2×C22⋊D61—22no—
130C2×C22⋊D61—22no—
131C2×C22⋊D61—28no—
132C2×C22⋊D61—24no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—22no—
135C2×C22⋊D61—24no—
136C2×C22⋊D61—44no—
137C2×C22⋊D61—44no—
138C2×C22⋊D61—42no—
139C2×C22⋊D61—42no—
140C2×C22⋊D61—42no—
141C2×C22⋊D61—42no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—24no—
145C22×Dic61—42no—
146C22×Dic61C22⋊C411yescharacteristic
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C412yes—
149C22×Dic61C22×C412yes—
150C22×Dic61C22×C412yes—
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D414yes—
157C22×Dic61#4114yes—
158C22×Dic61C2411yescharacteristic
159C2×Dic122—22no—
160C2×Dic122—22no—
161C2×Dic122—28no—
162C2×Dic122—24no—
163C2×Dic122—22no—
164C2×Dic122—22no—
165C2×Dic122—24no—
166C2×Dic122—44no—
167C2×Dic122—44no—
168C2×Dic122—42no—
169C2×Dic122—42no—
170C2×Dic122—42no—
171C2×Dic122—42no—
172#11758217—28no—
173#11758217—24no—
174#11758217—24no—
175#11758217—24no—
176#11758217—44no—
177#11758217C2×D418yes—
178C2×#92420—28no—
179C2×#92420—24no—
180C2×#92420—24no—
181C2×#92420—44no—
182C22⋊C4×C61—24no—
183C22⋊C4×C61—24no—
184C22⋊Dic61—24no—
185C22⋊Dic61—24no—
186#11758198—24no—
187#11758198—24no—
188#11758198—24no—
189#11758198—24no—
190C4×Dic61C22⋊C412yes—
191C4×Dic61C22⋊C412yes—
192C4×Dic61C22⋊C412yes—
193C4×Dic61C22⋊C412yes—
194C4×Dic61C2×D412yes—
195C4×Dic61C2×D412yes—
196C4×Dic61C2×D412yes—
197C4×Dic61C2×D412yes—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—24no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—42no—
210C23×C61—88no—
211C23×C61C2×C22⋊C411yescharacteristic
212C23×C61C2×C22⋊C411yescharacteristic
213C23×C61C4×D414yes—
214C23×C61C23×C411yescharacteristic
215C22×D61—22no—
216C22×D61—24no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61—88no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—24no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61C2×C22⋊C412yes—
235C2×C4×C61C2×C22⋊C412yes—
236C22⋊D61—44no—
237C22⋊D61—42no—
238C22⋊D61—42no—
239C22⋊D61—44no—
240C22⋊D61—44no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—24no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61C2×C22⋊C412yes—
250C2×Dic61C2×C22⋊C412yes—
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C4×D414yes—
254C2×Dic61#12114yes—
255C2×Dic61#12114yes—
256C2×Dic61#12412yes—
257C2×Dic61#12412yes—
258C2×Dic61#12712yes—
259C2×Dic61#12712yes—
260C2×Dic61C22×D411yescharacteristic
261C2×Dic61C22×D412yes—
262C2×Dic61C22×D411yescharacteristic
263C2×Dic61C2×#4112yes—
264Dic122—44no—
265Dic122—42no—
266Dic122—42no—
267Dic122—44no—
268Dic122—44no—
269#92420—28no—
270#92420—44no—
271C2×#1967—611nomaximal, Sylow
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—28no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—84no—
281C22×C61—84no—
282C22×C61—84no—
283C22×C61#39012yes—
284C22×C61#39012yes—
285C22×C61#41312yes—
286C22×C61#41312yes—
287C22×C61C22×C22⋊C411yescharacteristic
288C22×C61C2×C4×D412yes—
289C2×D61—42no—
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—84no—
293C2×D61—84no—
294C2×D61—84no—
295C4×C61—22no—
296C4×C61—22no—
297C4×C61—42no—
298Dic61—22no—
299Dic61—22no—
300Dic61—42no—
301Dic61#39012yes—
302Dic61#39012yes—
303Dic61C2×#12112yes—
304Dic61C2×#12411yescharacteristic
305Dic61C2×#12711yescharacteristic
306C22×#124—611no—
307C2×#423—611no—
308C22×#101—612no—
309C22×#100—612no—
310C2×C4×M16—611no—
311#1967—618no—
312C2×C61—22no—
313C2×C61—22no—
314C2×C61—82no—
315C2×C61#196714yescomplemented
316C2×C61C2×#39011yescharacteristic
317C2×C61C2×#41311yescharacteristic
318C2×C61C2×#41311yescharacteristic
319D61—82no—
320C23×Q8—611no—
321C23×D4—611no—
322C22×M16—612no—
323C22×M16—612no—
324C2×#124—614no—
325C2×#124—614no—
326C2×#124—1221no—
327C2×#124—1221no—
328C2×#124—1222no—
329C2×#124—1221no—
330C2×#124—1221no—
331C2×#124—1222no—
332C22×C22⋊C4—611no—
333C22×C22⋊C4—611no—
334C22×C22⋊C4—611no—
335C22×C22⋊C4#692311yescharacteristic
336C22×C42—611no—
337#423—614no—
338#423—1222no—
339C2×C4⋊C8—1221no—
340C2×C4⋊C8—1221no—
341C2×#101—618no—
342C2×#101—1228no—
343C2×#100—618no—
344C2×#100—1228no—
345C4×M16—614no—
346C4×M16—1222no—
347C2×#97—1221no—
348C2×C4×C8—1221no—
349C61C2×#196711yescharacteristic, complemented, Sylow
350C25—611no—
351C25C2×#692311yescharacteristic
352C22×Q8—612no—
353C22×Q8—612no—
354C22×Q8—1221no—
355C22×Q8—1221no—
356C22×Q8—1221no—
357C22×Q8—1221no—
358C22×Q8—1224no—
359C22×Q8—1224no—
360C22×D4—612no—
361C22×D4—612no—
362C22×D4—1221no—
363C22×D4—1221no—
364C22×D4—1221no—
365C22×D4—1221no—
366C22×D4—1224no—
367C22×D4—1224no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4C2×#692311yescharacteristic
372C23×C4C2×#692311yescharacteristic
373C2×M16—618no—
374C2×M16—614no—
375C2×M16—614no—
376C2×M16—1224no—
377C2×M16—1222no—
378C2×M16—1222no—
379C2×M16—1224no—
380C2×M16—1224no—
381C22×C8—1222no—
382C22×C8—1222no—
383#124—1224no—
384#124—1224no—
385#124—1224no—
386#124—1224no—
387#124—1224no—
388#124—1224no—
389#124—1224no—
390#124—1224no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—614no—
395C2×C22⋊C4—614no—
396C2×C22⋊C4—614no—
397C2×C22⋊C4—1222no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1222no—
403C2×C22⋊C4—1222no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4C2×#692314yes—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—612no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—612no—
413C2×C42—612no—
414C2×C42—612no—
415C4⋊C8—1224no—
416C4⋊C8—1224no—
417#101—12216no—
418#100—12216no—
419#97—1224no—
420C4×C8—1224no—
421C24—21no—
422C24—21no—
423C24—24no—
424C24—42no—
425C24—42no—
426C24—612no—
427C24—1224no—
428C24—1221no—
429C24—1221no—
430C24—2442no—
431C24—2442no—
432C24C22×#692311yescharacteristic
433C24C22×#692312yes—
434C2×Q8—1224no—
435C2×Q8—1222no—
436C2×Q8—1222no—
437C2×Q8—1222no—
438C2×Q8—1222no—
439C2×Q8—1228no—
440C2×Q8—1224no—
441C2×Q8—2444no—
442C2×Q8—2444no—
443C2×Q8—2442no—
444C2×Q8—2442no—
445C2×Q8—2442no—
446C2×Q8—2442no—
447C2×D4—1224no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4—1222no—
451C2×D4—1222no—
452C2×D4—1228no—
453C2×D4—1224no—
454C2×D4—2444no—
455C2×D4—2444no—
456C2×D4—2442no—
457C2×D4—2442no—
458C2×D4—2442no—
459C2×D4—2442no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—24no—
463C22×C4—42no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—614no—
469C22×C4—614no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—612no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1224no—
480C22×C4—2442no—
481C22×C4C22⋊#692311yescharacteristic
482C22×C4C22⋊#692311yescharacteristic
483C22×C4C22⋊#692312yes—
484C22×C4C22×#692312yes—
485C22×C4C22×#692312yes—
486M16—618no—
487M16—1228no—
488M16—1224no—
489M16—1224no—
490M16—1224no—
491M16—2444no—
492C2×C8—1224no—
493C2×C8—1228no—
494C2×C8—1224no—
495C2×C8—2444no—
496C22⋊C4—24no—
497C22⋊C4—24no—
498C22⋊C4—1224no—
499C22⋊C4—1224no—
500C22⋊C4—1224no—
501C22⋊C4—1224no—
502C22⋊C4—1224no—
503C22⋊C4—1224no—
504C42—612no—
505C42—612no—
506C42—612no—
507C42—612no—
508C42—612no—
509C42—612no—
510C42—612no—
511C42—612no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—24no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—88no—
525C23—1224no—
526C23—1222no—
527C23—4888no—
528C23—2442no—
529C23—2442no—
530C23—2442no—
531C23—2442no—
532C23—2442no—
533C23—2442no—
534C23—2442no—
535C23—2442no—
536C23C2×C22⋊#692311yescharacteristic
537C23C2×C22⋊#692311yescharacteristic
538C23D4×#692314yes—
539C23C23×#692311yescharacteristic
540Q8—2444no—
541Q8—2442no—
542Q8—2442no—
543Q8—2444no—
544Q8—2444no—
545D4—2444no—
546D4—2442no—
547D4—2442no—
548D4—2444no—
549D4—2444no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—614no—
559C2×C4—614no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—612no—
563C2×C4—612no—
564C2×C4—611no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—611no—
568C2×C4—614no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—612no—
572C2×C4—612no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1224no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4C2×C22⋊#692312yes—
582C2×C4C2×C22⋊#692312yes—
583C8—1228no—
584C8—2444no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—28no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—84no—
594C22—84no—
595C22—84no—
596C22—4884no—
597C22—4884no—
598C22—4884no—
599C22—2442no—
600C22—2442no—
601C22—2442no—
602C22#1684071412yes—
603C22#1684071412yes—
604C22#1684074812yes—
605C22#1684074912yes—
606C22C22×C22⋊#692311yescharacteristic
607C22C2×D4×#692312yes—
608C4—22no—
609C4—22no—
610C4—42no—
611C4—612no—
612C4—611no—
613C4—611no—
614C4—612no—
615C4—612no—
616C4—1222no—
617C4—1222no—
618C4—2442no—
619C2—22no—
620C2—22no—
621C2—82no—
622C2—4882no—
623C2#2146196314yesdirect product factor
624C2C2×#1684071411yescharacteristic
625C2C2×#1684074811yescharacteristic
626C2C2×#1684074911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61C2×#1967
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840765C2semidirect
2. C22×#14519838C2semidirect
4. C2×C4×#11758217C2semidirect
5. #21461963C2direct (N × H)
10. #16840765C22semidirect
14. C2×#14519838C22semidirect
18. C4×#11758217C22semidirect
315. C2×C61#1967semidirect
349. C61C2×#1967semidirect
623. C2#21461963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407652
C22×#145198382
C22×#145198372
C2×C4×#117582172
#214619632
C22×#145197632
C2×#196761