Finite Group Databasebeta

← C2×#21461206 #30610946

Subgroups — C2×#21461206 #30610946

Order 15616.

1834 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C211yesmaximal, characteristic, complemented
2C22×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
3#21461206C218yesmaximal, direct product factor
4C2×#16840616C212yesmaximal, complemented
5C2×#16840614C212yesmaximal, complemented
6C2×#16840275C211yesmaximal, characteristic
7C24×#6923—21no—
8C22×#11758213—21no—
9#16840733—22no—
10#16840733C2214yescomplemented
11C2×#14519834C2212yes—
12C2×C22⋊#92420—21no—
13C2×(C2×#6923)⋊C4—21no—
14C2×(C2×#6923)⋊C4—22no—
15C2×(C2×#6923)⋊C4C2212yes—
16C2×(C2×#6923)⋊C4C2214yescomplemented
17#16840616C2218yescomplemented
18#16840614C2218yescomplemented
19C22×#11758226C411yescharacteristic, complemented
20C23×C4×D61C2211yescharacteristic
21#16840275—22no—
22#16840275—22no—
23#16840275C414yescomplemented
24#16840275C2214yes—
25C2×#14519762—21no—
26C2×#14519753C2211yescharacteristic
27C2×#14519752C2211yescharacteristic
28C2×#14519751C411yescharacteristic, complemented
29C2×#14519747—21no—
30C2×#14519739—21no—
31C2×#14519737—21no—
32C2×#14519735C411yescharacteristic, complemented
33C2×C22⋊Q8×C61C411yescharacteristic, complemented
34C23×#6923—28no—
35C23×#6923—22no—
36C23×#6923—24no—
37C23×#6923—44no—
38C23×#6923—44no—
39C2×#11758213—24no—
40C2×#11758213—44no—
41C22×#92420—22no—
42#14519834—22no—
43#14519834C2314yes—
44C22⋊#92420—24no—
45(C2×#6923)⋊C4—22no—
46(C2×#6923)⋊C4—24no—
47(C2×#6923)⋊C4C2314yes—
48C24×D61D411yescharacteristic
49C2×#11758226—22no—
50C2×#11758226—44no—
51C2×#11758226C2×C414yescomplemented
52C22×D244—21no—
53C22×D244—21no—
54C22×D244C2×C411yescharacteristic, complemented
55C22×C22⋊D61—21no—
56C23×Dic61D411yescharacteristic
57C22×C4×D61—21no—
58C22×C4×D61—44no—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C412yes—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D412yes—
64C22×C4×D61D412yes—
65C22×C4×D61C2311yescharacteristic
66C22×C4×D61C2312yes—
67#14519762—24no—
68#14519762—24no—
69#14519753—21no—
70#14519753—21no—
71#14519753C2×C412yescomplemented
72#14519753C2312yes—
73#14519752—21no—
74#14519752—21no—
75#14519752C2×C412yescomplemented
76#14519752C2312yes—
77#14519751—22no—
78#14519751C2×C414yescomplemented
79#14519747—24no—
80#14519747—24no—
81#14519739—24no—
82#14519739—24no—
83#14519737—24no—
84#14519737—24no—
85#14519735—22no—
86#14519735C2×C414yescomplemented
87C2×C4⋊Dic61C2×C411yescharacteristic, complemented
88C2×#11758196—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×C4×Dic61—21no—
94C22×Q8×C61C2×C411yescharacteristic, complemented
95C23×C4×C61C2×C411yescharacteristic
96C22⋊Q8×C61—22no—
97C22⋊Q8×C61C2×C414yescomplemented
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
100C2×C22⋊C4×C61—21no—
101C24×C61C22⋊C411yescharacteristic
102C23×D61—24no—
103C23×D61—24no—
104C23×D61—22no—
105C23×D61—22no—
106C23×D61—21no—
107C23×D61C22⋊C412yes—
108C23×D61C22⋊C411yescharacteristic
109C23×D61C2×D412yes—
110C23×D61C2×D411yescharacteristic
111C22×#6923—28no—
112C22×#6923—216no—
113C22×#6923—24no—
114C22×#6923—432no—
115C22×#6923—44no—
116C22×#6923—48no—
117C22×#6923—48no—
118C22×#6923—44no—
119C2×Q8×C61—21no—
120C2×Q8×C61—42no—
121C2×Q8×C61C22×C412yescomplemented
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—42no—
125C22×C4×C61C22⋊C411yescharacteristic
126C22×C4×C61C22⋊C412yes—
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C412yes—
129C2×C22⋊D61—24no—
130C2×C22⋊D61—44no—
131C22×Dic61—21no—
132C22×Dic61—42no—
133C22×Dic61C22⋊C411yescharacteristic
134C22×Dic61C22⋊C412yes—
135C22×Dic61C2×D411yescharacteristic
136C22×Dic61C2×D412yes—
137#11758226—48no—
138#11758226—48no—
139C2×D244—24no—
140C2×D244—22no—
141C2×D244—22no—
142C2×D244—21no—
143C2×D244—42no—
144C2×D244—44no—
145C2×D244—42no—
146C2×D244—42no—
147C2×D244C22×C412yescomplemented
148C2×C4×D61—24no—
149C2×C4×D61—24no—
150C2×C4×D61—24no—
151C2×C4×D61—44no—
152C2×C4×D61—44no—
153C2×C4×D61—44no—
154C2×C4×D61—44no—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61—44no—
158C2×C4×D61C22⋊C412yes—
159C2×C4×D61C22⋊C412yes—
160C2×C4×D61C22⋊C412yes—
161C2×C4×D61C22×C412yes—
162C2×C4×D61C22×C411yescharacteristic
163C2×C4×D61C2×D412yes—
164C2×C4×D61C2×D412yes—
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2411yescharacteristic
168C2×#92420—24no—
169C2×#92420—44no—
170#11758213—48no—
171C4⋊C4×C61—24no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C412yescomplemented
174C22⋊C4×C61—24no—
175#11758198—24no—
176#11758198—22no—
177#11758198—22no—
178#11758198—24no—
179#11758198—22no—
180#11758198—22no—
181C4⋊Dic61—21no—
182C4⋊Dic61C22×C412yescomplemented
183#11758196—22no—
184#11758196—22no—
185C4×Dic61—24no—
186C23×C61—22no—
187C23×C61—22no—
188C23×C61#10414yes—
189C23×C61C2×C22⋊C412yes—
190C23×C61C2×C22⋊C411yescharacteristic
191C22×D61—216no—
192C22×D61—216no—
193C22×D61—22no—
194C22×D61—22no—
195C22×D61—24no—
196C22×D61—22no—
197C22×D61—24no—
198C22×D61—22no—
199C22×D61—22no—
200C22×D61—22no—
201C22×D61—24no—
202C22×D61—24no—
203C22×D61—24no—
204C22×D61—22no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61#9914yes—
209C22×D61C2×C22⋊C412yes—
210C22×D61C2×C22⋊C411yescharacteristic
211C22×D61AGL(1,ℤ/8)12yes—
212C22×D61#13712yes—
213C22×D61C22×D411yescharacteristic
214C2×#6923—28no—
215C2×#6923—432no—
216C2×#6923—44no—
217C2×#6923—416no—
218C2×#6923—44no—
219Q8×C61—42no—
220Q8×C61—42no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C2×C22⋊C412yes—
231C2×C4×C61C23×C411yescharacteristic
232C22⋊D61—48no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—42no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61C2×C22⋊C412yes—
240C2×Dic61C2×C22⋊C411yescharacteristic
241C2×Dic61C22×D411yescharacteristic
242D244—42no—
243D244—42no—
244D244—42no—
245D244—42no—
246D244—48no—
247D244—44no—
248C4×D61—24no—
249C4×D61—24no—
250C4×D61—24no—
251C4×D61—24no—
252C4×D61—42no—
253C4×D61—41no—
254C4×D61—41no—
255C4×D61—42no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—48no—
259#92420—44no—
260C2×#1504—611nomaximal, Sylow
261C22×C61—22no—
262C22×C61—22no—
263C22×C61—28no—
264C22×C61C2×#9912yes—
265C22×C61#41712yes—
266C22×C61C2×#10414yes—
267C22×C61C2×#10412yes—
268C22×C61C22×C22⋊C411yescharacteristic
269C2×D61—28no—
270C2×D61—28no—
271C2×D61—216no—
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—22no—
275C2×D61—21no—
276C2×D61—22no—
277C2×D61—21no—
278C2×D61—24no—
279C2×D61—28no—
280C2×D61—24no—
281C2×D61—42no—
282C2×D61—42no—
283C2×D61—42no—
284C2×D61—84no—
285C2×D61C2×#9914yes—
286C2×D61#41712yes—
287C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
288C2×D61C2×#13711yescharacteristic
289#6923—48no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—22no—
293C4×C61—42no—
294C4×C61—42no—
295Dic61—21no—
296Dic61—22no—
297Dic61—21no—
298Dic61—42no—
299C2×#525—611no—
300C2×#407—611no—
301C22×#95—611no—
302#1504—618no—
303C2×#328—612no—
304C2×#327—612no—
305C2×C61—24no—
306C2×C61#150414yescomplemented
307C2×C61C22×#9911yescharacteristic
308C2×C61C2×#41711yescharacteristic
309C2×C61C22×#10411yescharacteristic
310D61—21no—
311D61—21no—
312D61—24no—
313D61—22no—
314D61—82no—
315C22×#41—611no—
316C24×C4—611no—
317C24×C4—1221no—
318C22×M16—1221no—
319#525—614no—
320#525—614no—
321#525—1222no—
322#525—1222no—
323C2×#123—1221no—
324C2×C22⋊Q8—611no—
325C2×C22⋊Q8#692311yescharacteristic, complemented
326C2×#121—611no—
327C2×#121—611no—
328C2×#120—1221no—
329C2×C4×D4—1221no—
330C2×C4×D4—1221no—
331C2×#117—611no—
332#407—614no—
333#407—1222no—
334C2×C22⋊C8—612no—
335C2×C22⋊C8—1221no—
336C2×#95—612no—
337C2×#95—614no—
338C2×#95—1221no—
339C2×#95—1222no—
340#328—618no—
341#327—618no—
342C61C2×#150411yescharacteristic, complemented, Sylow
343C25—611no—
344C2×#41—614no—
345C2×#41—1222no—
346C2×#41—2444no—
347C22×Q8C2×#692311yescharacteristic, complemented
348C22×D4—611no—
349C22×D4—1221no—
350C22×D4—1221no—
351C22×D4—1221no—
352C23×C4—611no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4—611no—
356C23×C4—612no—
357C23×C4—612no—
358C23×C4—612no—
359C23×C4—611no—
360C23×C4—612no—
361C23×C4—1221no—
362C23×C4—1222no—
363C23×C4—1224no—
364C23×C4—1228no—
365C23×C4—2444no—
366C23×C4—2444no—
367C23×C4—2444no—
368C23×C4C2×#692311yescharacteristic
369C2×M16—1224no—
370C2×M16—2444no—
371C22×C8—1222no—
372#123—1224no—
373#123—1224no—
374C22⋊Q8—22no—
375C22⋊Q8—612no—
376C22⋊Q8—612no—
377C22⋊Q8—1221no—
378C22⋊Q8—1221no—
379C22⋊Q8C2×#692314yescomplemented
380#121—614no—
381#121—612no—
382#121—612no—
383#121—1221no—
384#121—1221no—
385#121—1222no—
386#120—1224no—
387#120—1224no—
388C4×D4—1224no—
389C4×D4—1224no—
390C4×D4—1224no—
391C4×D4—1224no—
392#117—614no—
393#117—1222no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4C2×#692311yescharacteristic, complemented
398C2×C22⋊C4—21no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C42—1221no—
404C22⋊C8—614no—
405C22⋊C8—1224no—
406C22⋊C8—1222no—
407#95—614no—
408#95—1224no—
409#95—1222no—
410C24—611no—
411C24—611no—
412C24—612no—
413C24—612no—
414C24—1224no—
415C24—1222no—
416C24—1222no—
417C24—1224no—
418C24—1221no—
419C24C22⋊#692311yescharacteristic
420#41—2448no—
421#41—2448no—
422C2×Q8—21no—
423C2×Q8—42no—
424C2×Q8C22×#692312yescomplemented
425C2×D4—612no—
426C2×D4—1222no—
427C2×D4—1222no—
428C2×D4—1224no—
429C2×D4—1224no—
430C2×D4—1221no—
431C2×D4—2442no—
432C2×D4—2444no—
433C2×D4—2442no—
434C2×D4—2442no—
435C2×D4—2444no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—612no—
442C22×C4—612no—
443C22×C4—612no—
444C22×C4—612no—
445C22×C4—612no—
446C22×C4—612no—
447C22×C4—612no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—612no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—1224no—
454C22×C4—1224no—
455C22×C4—1224no—
456C22×C4—1224no—
457C22×C4—12216no—
458C22×C4—1228no—
459C22×C4—1221no—
460C22×C4—2442no—
461C22×C4—2442no—
462C22×C4—2444no—
463C22×C4—2444no—
464C22×C4—2444no—
465C22×C4—2444no—
466C22×C4—2444no—
467C22×C4—2442no—
468C22×C4—2444no—
469C22×C4—2448no—
470C22×C4—2448no—
471C22×C4—24432no—
472C22×C4—2444no—
473C22×C4C22⋊#692311yescharacteristic
474C22×C4C22⋊#692312yes—
475C22×C4C22×#692311yescharacteristic
476C22×C4C22×#692312yes—
477M16—2448no—
478C2×C8—1224no—
479C2×C8—2444no—
480C4⋊C4—24no—
481C4⋊C4—21no—
482C4⋊C4—612no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1221no—
486C4⋊C4C22×#692312yescomplemented
487C22⋊C4—24no—
488C22⋊C4—1222no—
489C22⋊C4—1222no—
490C22⋊C4—1224no—
491C22⋊C4—1222no—
492C22⋊C4—1222no—
493C22⋊C4—1224no—
494C42—1224no—
495C23—22no—
496C23—22no—
497C23—614no—
498C23—612no—
499C23—612no—
500C23—612no—
501C23—611no—
502C23—611no—
503C23—1224no—
504C23—1222no—
505C23—1224no—
506C23—1222no—
507C23—1224no—
508C23—12216no—
509C23—12216no—
510C23—1222no—
511C23—1222no—
512C23—1224no—
513C23—1222no—
514C23—1224no—
515C23—1222no—
516C23—1222no—
517C23—2442no—
518C23—2442no—
519C23—2442no—
520C23#1451984214yes—
521C23C2×C22⋊#692312yes—
522C23C2×C22⋊#692311yescharacteristic
523Q8—42no—
524Q8—42no—
525D4—2442no—
526D4—2442no—
527D4—2442no—
528D4—2442no—
529D4—2444no—
530D4—2448no—
531D4—2448no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—612no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—1224no—
544C2×C4—1224no—
545C2×C4—1224no—
546C2×C4—1224no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—1228no—
550C2×C4—1222no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2448no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2444no—
561C2×C4—24432no—
562C2×C4—2444no—
563C2×C4—24416no—
564C2×C4—2442no—
565C2×C4C2×C22⋊#692312yes—
566C2×C4C2×C22⋊#692311yescharacteristic
567C2×C4C23×#692311yescharacteristic
568C8—2444no—
569C22—22no—
570C22—22no—
571C22—28no—
572C22—614no—
573C22—611no—
574C22—611no—
575C22—612no—
576C22—1228no—
577C22—1228no—
578C22—12216no—
579C22—1221no—
580C22—1221no—
581C22—1222no—
582C22—1221no—
583C22—1222no—
584C22—1221no—
585C22—1224no—
586C22—1228no—
587C22—1224no—
588C22—4884no—
589C22—2442no—
590C22—2442no—
591C22—2442no—
592C22D61⋊#9912yes—
593C22#1684075312yes—
594C22C2×#1451984214yes—
595C22C2×#1451984212yes—
596C22C22×C22⋊#692311yescharacteristic
597C4—22no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—42no—
602C4—1221no—
603C4—1221no—
604C4—1222no—
605C4—2448no—
606C4—2442no—
607C2—24no—
608C2—1221no—
609C2—1224no—
610C2—1221no—
611C2—1222no—
612C2—4882no—
613C2#2146120614yesdirect product factor
614C2C2×D61⋊#9911yescharacteristic
615C2C2×#1684075311yescharacteristic
616C2C22×#1451984211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840275C2
cosocleC2×C4×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61C2×#1504
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840733C2semidirect
2. C22×(C2×#6923)⋊C4C2semidirect
3. #21461206C2direct (N × H)
4. C2×#16840616C2semidirect
5. C2×#16840614C2semidirect
10. #16840733C22semidirect
16. C2×(C2×#6923)⋊C4C22semidirect
17. #16840616C22semidirect
18. #16840614C22semidirect
19. C22×#11758226C4semidirect
23. #16840275C4semidirect
28. C2×#14519751C4semidirect
32. C2×#14519735C4semidirect
33. C2×C22⋊Q8×C61C4semidirect
51. C2×#11758226C2×C4semidirect
54. C22×D244C2×C4semidirect
71. #14519753C2×C4semidirect
75. #14519752C2×C4semidirect
78. #14519751C2×C4semidirect
86. #14519735C2×C4semidirect
87. C2×C4⋊Dic61C2×C4semidirect
94. C22×Q8×C61C2×C4semidirect
97. C22⋊Q8×C61C2×C4semidirect
99. C2×C4⋊C4×C61C2×C4semidirect
121. C2×Q8×C61C22×C4semidirect
147. C2×D244C22×C4semidirect
173. C4⋊C4×C61C22×C4semidirect
182. C4⋊Dic61C22×C4semidirect
306. C2×C61#1504semidirect
325. C2×C22⋊Q8#6923semidirect
342. C61C2×#1504semidirect
347. C22×Q8C2×#6923semidirect
379. C22⋊Q8C2×#6923semidirect
397. C2×C4⋊C4C2×#6923semidirect
424. C2×Q8C22×#6923semidirect
486. C4⋊C4C22×#6923semidirect
613. C2#21461206direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407332
C22×(C2×#6923)⋊C42
#214612062
C2×#168406162
C2×#168406142
C2×#168402752
C2×#150461