Finite Group Databasebeta

← C2×#21461836 #30615698

Subgroups — C2×#21461836 #30615698

Order 15616.

2514 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×#6923C211yesmaximal, characteristic, complemented
2C22×#14519842C212yesmaximal, complemented
3C2×#16840733C211yesmaximal, characteristic, complemented
4#21461836C218yesmaximal, direct product factor
5C2×#16840632C212yesmaximal, complemented
6C2×#16840275C211yesmaximal, characteristic
7C24×#6923—21no—
8C22×#11758213C2212yes—
9C22×C4×#6923—28no—
10C22×C4×#6923—21no—
11C22×C4×#6923—22no—
12C22×C4×#6923C2212yes—
13C22×C4×#6923C2214yescomplemented
14C2×#14519842—28no—
15C2×#14519842C2218yescomplemented
16#16840733—22no—
17#16840733C2214yescomplemented
18C2×#14519834—21no—
19C2×C22⋊#92420—21no—
20#16840632C2218yescomplemented
21C22×#11758226C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23#16840275—22no—
24#16840275—22no—
25#16840275C414yescomplemented
26#16840275C2214yes—
27C2×#14519762—21no—
28C2×#14519753C411yescharacteristic, complemented
29C2×#14519752C411yescharacteristic, complemented
30C2×#14519751C411yescharacteristic, complemented
31C2×#14519747—21no—
32C2×#14519739—21no—
33C2×#14519737—21no—
34C2×#14519735C2211yescharacteristic
35C2×C22⋊Q8×C61C411yescharacteristic, complemented
36C23×#6923—28no—
37C23×#6923—28no—
38C23×#6923—28no—
39C23×#6923—22no—
40C23×#6923—24no—
41C2×#11758213—24no—
42C2×#11758213—24no—
43C2×#11758213—22no—
44C2×#11758213C2314yes—
45C22×#92420—22no—
46C2×C4×#6923—28no—
47C2×C4×#6923—216no—
48C2×C4×#6923—22no—
49C2×C4×#6923—24no—
50C2×C4×#6923—24no—
51C2×C4×#6923—216no—
52C2×C4×#6923D418yescomplemented
53C2×C4×#6923C2314yes—
54#14519842—216no—
55#14519834—24no—
56C22⋊#92420—24no—
57C24×D61D411yescharacteristic
58C2×#11758226—21no—
59C2×#11758226—21no—
60C2×#11758226—24no—
61C2×#11758226—24no—
62C2×#11758226C2×C412yescomplemented
63C2×#11758226C2312yes—
64C22×D244—21no—
65C22×D244—21no—
66C22×D244C2×C411yescharacteristic, complemented
67C22×C22⋊D61—21no—
68C23×Dic61D411yescharacteristic
69C22×C4×D61—24no—
70C22×C4×D61—24no—
71C22×C4×D61—21no—
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C412yes—
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D412yes—
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D412yes—
78C22×C4×D61C2312yes—
79C22×C4×D61C2311yescharacteristic
80#14519762—24no—
81#14519762—24no—
82#14519753—22no—
83#14519753C2×C414yescomplemented
84#14519752—22no—
85#14519752C2×C414yescomplemented
86#14519751—22no—
87#14519751C2×C414yescomplemented
88#14519747—24no—
89#14519747—24no—
90#14519739—24no—
91#14519739—24no—
92#14519737—24no—
93#14519737—24no—
94#14519735—21no—
95#14519735—21no—
96#14519735C2×C412yescomplemented
97#14519735C2312yes—
98C2×C4⋊Dic61C2×C411yescharacteristic, complemented
99C2×#11758196—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C22×Q8×C61C2×C411yescharacteristic, complemented
106C23×C4×C61C2×C411yescharacteristic
107C22⋊Q8×C61—22no—
108C22⋊Q8×C61C2×C414yescomplemented
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
111C2×C22⋊C4×C61—21no—
112C24×C61C22⋊C411yescharacteristic
113C23×D61—24no—
114C23×D61—24no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—21no—
118C23×D61C22⋊C412yes—
119C23×D61C22⋊C411yescharacteristic
120C23×D61C2×D412yes—
121C23×D61C2×D411yescharacteristic
122C22×#6923—216no—
123C22×#6923—264no—
124C22×#6923—28no—
125C22×#6923—28no—
126C22×#6923—216no—
127C22×#6923—216no—
128C22×#6923—28no—
129C22×#6923—24no—
130C2×Q8×C61—21no—
131C2×Q8×C61—24no—
132C2×Q8×C61C22×C412yescomplemented
133C22×C4×C61—24no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22⋊C412yes—
138C22×C4×C61C22×C412yes—
139C22×C4×C61C22×C411yescharacteristic
140C2×C22⋊D61—24no—
141C2×C22⋊D61—44no—
142C22×Dic61—24no—
143C22×Dic61—21no—
144C22×Dic61C22⋊C411yescharacteristic
145C22×Dic61C22⋊C412yes—
146C22×Dic61C2×D412yes—
147C22×Dic61C2×D411yescharacteristic
148#11758226—28no—
149#11758226—24no—
150#11758226—24no—
151#11758226—42no—
152#11758226—44no—
153#11758226—42no—
154C2×D244—24no—
155C2×D244—22no—
156C2×D244—24no—
157C2×D244—22no—
158C2×D244—21no—
159C2×D244—44no—
160C2×D244—42no—
161C2×D244—42no—
162C2×D244C22×C412yescomplemented
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—24no—
166C2×C4×D61—24no—
167C2×C4×D61—28no—
168C2×C4×D61—24no—
169C2×C4×D61—28no—
170C2×C4×D61—24no—
171C2×C4×D61—24no—
172C2×C4×D61—24no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—44no—
176C2×C4×D61C22⋊C412yes—
177C2×C4×D61C22⋊C412yes—
178C2×C4×D61C22⋊C412yes—
179C2×C4×D61C22×C412yes—
180C2×C4×D61C22×C411yescharacteristic
181C2×C4×D61C2×D412yes—
182C2×C4×D61C2×D412yes—
183C2×C4×D61C2×D414yes—
184C2×C4×D61C2×D411yescharacteristic
185C2×C4×D61C2×D411yescharacteristic
186C2×C4×D61#4114yes—
187C2×C4×D61C2411yescharacteristic
188C2×#92420—24no—
189C2×#92420—44no—
190C4×#6923—216no—
191C4×#6923—28no—
192C4×#6923—24no—
193C4×#6923C2×D418yescomplemented
194#11758213—24no—
195#11758213—24no—
196#11758213—44no—
197C4⋊C4×C61—24no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61C22×C412yescomplemented
200C22⋊C4×C61—24no—
201#11758198—22no—
202#11758198—24no—
203#11758198—22no—
204#11758198—24no—
205#11758198—24no—
206C4⋊Dic61—21no—
207C4⋊Dic61C22×C412yescomplemented
208#11758196—24no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61#10414yescomplemented
214C23×C61C2×C22⋊C412yes—
215C23×C61C2×C22⋊C411yescharacteristic
216C22×D61—216no—
217C22×D61—216no—
218C22×D61—22no—
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—24no—
223C22×D61—24no—
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—24no—
227C22×D61—24no—
228C22×D61—24no—
229C22×D61—22no—
230C22×D61—42no—
231C22×D61—42no—
232C22×D61—42no—
233C22×D61#10414yescomplemented
234C22×D61C2×C22⋊C411yescharacteristic
235C22×D61C2×C22⋊C412yes—
236C22×D61#12012yes—
237C22×D61#12312yes—
238C22×D61C22×D411yescharacteristic
239C2×#6923—264no—
240C2×#6923—28no—
241C2×#6923—28no—
242C2×#6923—232no—
243C2×#6923—28no—
244Q8×C61—24no—
245Q8×C61—42no—
246C2×C4×C61—22no—
247C2×C4×C61—24no—
248C2×C4×C61—24no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61C2×C22⋊C412yes—
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C4×D414yes—
256C2×C4×C61C23×C411yescharacteristic
257C22⋊D61—48no—
258C2×Dic61—22no—
259C2×Dic61—24no—
260C2×Dic61—24no—
261C2×Dic61—22no—
262C2×Dic61—42no—
263C2×Dic61C2×C22⋊C412yes—
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61#12114yes—
266C2×Dic61C22×D411yescharacteristic
267D244—24no—
268D244—42no—
269D244—42no—
270D244—44no—
271D244—48no—
272D244—42no—
273C4×D61—22no—
274C4×D61—22no—
275C4×D61—24no—
276C4×D61—24no—
277C4×D61—24no—
278C4×D61—24no—
279C4×D61—24no—
280C4×D61—44no—
281C4×D61—44no—
282C4×D61C4×D414yes—
283C4×D61#12012yes—
284C4×D61#12114yes—
285C4×D61#12312yes—
286C4×D61C22×D412yes—
287C4×D61C2×#4112yes—
288#92420—44no—
289C2×#1896—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—28no—
292C22×C61—22no—
293C22×C61#38612yes—
294C22×C61C2×#10412yes—
295C22×C61C2×#10412yes—
296C22×C61C2×#10414yescomplemented
297C22×C61C22×C22⋊C411yescharacteristic
298C2×D61—28no—
299C2×D61—28no—
300C2×D61—216no—
301C2×D61—21no—
302C2×D61—21no—
303C2×D61—21no—
304C2×D61—21no—
305C2×D61—22no—
306C2×D61—24no—
307C2×D61—28no—
308C2×D61—24no—
309C2×D61—22no—
310C2×D61—42no—
311C2×D61—42no—
312C2×D61—42no—
313C2×D61—84no—
314C2×D61#38612yes—
315C2×D61C2×#10414yescomplemented
316C2×D61C2×#12011yescharacteristic
317C2×D61C2×#12311yescharacteristic
318#6923—216no—
319C4×C61—22no—
320C4×C61—42no—
321C4×C61—42no—
322C4×C61#38612yes—
323C4×C61C2×C4×D412yes—
324Dic61—22no—
325Dic61—42no—
326Dic61#38612yes—
327Dic61C2×#12112yes—
328C2×#525—611no—
329C23×C42—611no—
330C22×#104—612no—
331C2×#407—611no—
332#1896—618no—
333C2×#339—612no—
334C2×C61—24no—
335C2×C61#189614yescomplemented
336C2×C61C2×#38611yescharacteristic
337C2×C61C22×#10411yescharacteristic
338C2×C61C22×#10411yescharacteristic
339D61—21no—
340D61—21no—
341D61—22no—
342D61—24no—
343D61—82no—
344C22×#41—611no—
345C24×C4—611no—
346C24×C4—1221no—
347C22×M16—612no—
348#525—614no—
349#525—614no—
350#525—1222no—
351#525—1222no—
352C2×#123—1221no—
353C2×C22⋊Q8—611no—
354C2×C22⋊Q8#692311yescharacteristic, complemented
355C2×#121—611no—
356C2×#121—611no—
357C2×#120—1221no—
358C2×C4×D4—1221no—
359C2×C4×D4—1221no—
360C2×#117—611no—
361C22×C42—612no—
362C22×C42—614no—
363C22×C42—1228no—
364C22×C42—1221no—
365C22×C42—1222no—
366C2×#104—618no—
367C2×#104—1228no—
368#407—614no—
369#407—1222no—
370C2×C22⋊C8—1221no—
371C2×C22⋊C8—1221no—
372#339—618no—
373C61C2×#189611yescharacteristic, complemented, Sylow
374C25—611no—
375C2×#41—612no—
376C2×#41—612no—
377C2×#41—1221no—
378C2×#41—1221no—
379C2×#41—1224no—
380C2×#41—1224no—
381C22×Q8C2×#692311yescharacteristic, complemented
382C22×D4—611no—
383C22×D4—1221no—
384C22×D4—1221no—
385C22×D4—1221no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—611no—
390C23×C4—612no—
391C23×C4—612no—
392C23×C4—611no—
393C23×C4—612no—
394C23×C4—612no—
395C23×C4—1224no—
396C23×C4—1224no—
397C23×C4—1221no—
398C23×C4—1222no—
399C23×C4—1224no—
400C23×C4—1228no—
401C23×C4—1228no—
402C23×C4—1228no—
403C23×C4C2×#692311yescharacteristic
404C2×M16—614no—
405C2×M16—1222no—
406C2×M16—1224no—
407C2×M16—1224no—
408C22×C8—1222no—
409#123—1224no—
410#123—1224no—
411C22⋊Q8—22no—
412C22⋊Q8—614no—
413C22⋊Q8—1222no—
414C22⋊Q8C2×#692314yescomplemented
415#121—614no—
416#121—614no—
417#121—1222no—
418#121—1222no—
419#120—1224no—
420#120—1224no—
421C4×D4—1224no—
422C4×D4—1224no—
423C4×D4—1224no—
424C4×D4—1224no—
425#117—612no—
426#117—612no—
427#117—1221no—
428#117—1221no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4C2×#692311yescharacteristic, complemented
433C2×C22⋊C4—21no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C22⋊C4—1221no—
437C2×C22⋊C4—1221no—
438C2×C42—618no—
439C2×C42—614no—
440C2×C42—12216no—
441C2×C42—1221no—
442C2×C42—1222no—
443C2×C42—1224no—
444C2×C42—1224no—
445C2×C42—12216no—
446C2×C42—1228no—
447#104—12216no—
448C22⋊C8—1224no—
449C22⋊C8—1224no—
450C24—611no—
451C24—611no—
452C24—612no—
453C24—612no—
454C24—1222no—
455C24—1222no—
456C24—1224no—
457C24—1224no—
458C24—1221no—
459C24C22⋊#692311yescharacteristic
460#41—1224no—
461#41—1228no—
462#41—1224no—
463#41—2442no—
464#41—2444no—
465#41—2442no—
466C2×Q8—21no—
467C2×Q8—24no—
468C2×Q8C22×#692312yescomplemented
469C2×D4—612no—
470C2×D4—1224no—
471C2×D4—1222no—
472C2×D4—1222no—
473C2×D4—1224no—
474C2×D4—1221no—
475C2×D4—1224no—
476C2×D4—2442no—
477C2×D4—2442no—
478C2×D4—2444no—
479C2×D4—2444no—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—614no—
487C22×C4—614no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—612no—
491C22×C4—612no—
492C22×C4—611no—
493C22×C4—612no—
494C22×C4—612no—
495C22×C4—612no—
496C22×C4—612no—
497C22×C4—612no—
498C22×C4—612no—
499C22×C4—1224no—
500C22×C4—1224no—
501C22×C4—1224no—
502C22×C4—1228no—
503C22×C4—1224no—
504C22×C4—1228no—
505C22×C4—1224no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1224no—
511C22×C4—1228no—
512C22×C4—1224no—
513C22×C4—12216no—
514C22×C4—12216no—
515C22×C4—12264no—
516C22×C4—1228no—
517C22×C4—1228no—
518C22×C4—12216no—
519C22×C4—1224no—
520C22×C4—1221no—
521C22×C4—2444no—
522C22×C4C22⋊#692312yes—
523C22×C4C22⋊#692311yescharacteristic
524C22×C4C22×#692312yes—
525C22×C4C22×#692311yescharacteristic
526M16—1224no—
527M16—1224no—
528M16—2444no—
529C2×C8—1224no—
530C2×C8—2444no—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—612no—
534C4⋊C4—1224no—
535C4⋊C4—1221no—
536C4⋊C4C22×#692312yescomplemented
537C22⋊C4—24no—
538C22⋊C4—1224no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1224no—
542C22⋊C4—1224no—
543C42—618no—
544C42—1222no—
545C42—1222no—
546C42—1228no—
547C42—1224no—
548C42—12216no—
549C23—22no—
550C23—22no—
551C23—612no—
552C23—612no—
553C23—614no—
554C23—612no—
555C23—611no—
556C23—611no—
557C23—1222no—
558C23—1224no—
559C23—1222no—
560C23—1224no—
561C23—1224no—
562C23—12216no—
563C23—12216no—
564C23—1222no—
565C23—1222no—
566C23—1222no—
567C23—1222no—
568C23—1224no—
569C23—1224no—
570C23—1222no—
571C23—2442no—
572C23—2442no—
573C23—2442no—
574C23#1451984214yescomplemented
575C23C2×C22⋊#692312yes—
576C23C2×C22⋊#692311yescharacteristic
577Q8—24no—
578Q8—42no—
579D4—1224no—
580D4—2448no—
581D4—2442no—
582D4—2442no—
583D4—2444no—
584D4—2448no—
585D4—2442no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—614no—
594C2×C4—611no—
595C2×C4—611no—
596C2×C4—612no—
597C2×C4—614no—
598C2×C4—612no—
599C2×C4—614no—
600C2×C4—612no—
601C2×C4—612no—
602C2×C4—612no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1224no—
608C2×C4—1224no—
609C2×C4—1224no—
610C2×C4—1228no—
611C2×C4—12264no—
612C2×C4—12232no—
613C2×C4—1228no—
614C2×C4—1228no—
615C2×C4—1222no—
616C2×C4—1224no—
617C2×C4—1224no—
618C2×C4—1222no—
619C2×C4—2444no—
620C2×C4—2444no—
621C2×C4—2442no—
622C2×C4C2×C22⋊#692312yes—
623C2×C4C2×C22⋊#692311yescharacteristic
624C2×C4D4×#692314yes—
625C2×C4C23×#692311yescharacteristic
626C8—2444no—
627C22—28no—
628C22—22no—
629C22—22no—
630C22—614no—
631C22—611no—
632C22—611no—
633C22—612no—
634C22—1228no—
635C22—1228no—
636C22—12216no—
637C22—1224no—
638C22—1228no—
639C22—1224no—
640C22—1221no—
641C22—1221no—
642C22—1221no—
643C22—1221no—
644C22—1222no—
645C22—1222no—
646C22—4884no—
647C22—2442no—
648C22—2442no—
649C22—2442no—
650C22#1684071012yes—
651C22D61⋊#10412yes—
652C22C2×#1451984212yes—
653C22C2×#1451984214yescomplemented
654C22C22×C22⋊#692311yescharacteristic
655C4—22no—
656C4—42no—
657C4—42no—
658C4—612no—
659C4—612no—
660C4—12216no—
661C4—1222no—
662C4—2442no—
663C4#1684071012yes—
664C4C2×D4×#692312yes—
665C2—24no—
666C2—1221no—
667C2—1224no—
668C2—1221no—
669C2—1222no—
670C2—4882no—
671C2#2146183614yesdirect product factor
672C2C2×#1684071011yescharacteristic
673C2C2×D61⋊#10411yescharacteristic
674C2C22×#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×#1896
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C23×C4×#6923C2semidirect
2. C22×#14519842C2semidirect
3. C2×#16840733C2semidirect
4. #21461836C2direct (N × H)
5. C2×#16840632C2semidirect
13. C22×C4×#6923C22semidirect
15. C2×#14519842C22semidirect
17. #16840733C22semidirect
20. #16840632C22semidirect
25. #16840275C4semidirect
28. C2×#14519753C4semidirect
29. C2×#14519752C4semidirect
30. C2×#14519751C4semidirect
35. C2×C22⋊Q8×C61C4semidirect
52. C2×C4×#6923D4semidirect
62. C2×#11758226C2×C4semidirect
66. C22×D244C2×C4semidirect
83. #14519753C2×C4semidirect
85. #14519752C2×C4semidirect
87. #14519751C2×C4semidirect
96. #14519735C2×C4semidirect
98. C2×C4⋊Dic61C2×C4semidirect
105. C22×Q8×C61C2×C4semidirect
108. C22⋊Q8×C61C2×C4semidirect
110. C2×C4⋊C4×C61C2×C4semidirect
132. C2×Q8×C61C22×C4semidirect
162. C2×D244C22×C4semidirect
193. C4×#6923C2×D4semidirect
199. C4⋊C4×C61C22×C4semidirect
207. C4⋊Dic61C22×C4semidirect
213. C23×C61#104semidirect
233. C22×D61#104semidirect
296. C22×C61C2×#104semidirect
315. C2×D61C2×#104semidirect
335. C2×C61#1896semidirect
354. C2×C22⋊Q8#6923semidirect
373. C61C2×#1896semidirect
381. C22×Q8C2×#6923semidirect
414. C22⋊Q8C2×#6923semidirect
432. C2×C4⋊C4C2×#6923semidirect
468. C2×Q8C22×#6923semidirect
536. C4⋊C4C22×#6923semidirect
574. C23#14519842semidirect
653. C22C2×#14519842semidirect
671. C2#21461836direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×#69232
C22×#145198422
C2×#168407332
#214618362
C2×#168406322
C2×#168402752
C2×#189661