Finite Group Databasebeta

← C2×#21455733 #30547781

Subgroups — C2×#21455733 #30547781

Order 15616.

2378 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2C22×#14519735C211yesmaximal, characteristic, complemented
3#21455733C2116yesmaximal, direct product factor
4C2×#16840095C211yesmaximal, characteristic, complemented
5C2×#16840081C211yesmaximal, characteristic, complemented
6C2×#16840101C212yesmaximal, complemented
7C2×#16840088C212yesmaximal, complemented
8C2×#16840075C211yesmaximal, characteristic, complemented
9C2×#16839797C212yesmaximal, complemented
10C2×#16839757C212yesmaximal, complemented
11C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
12C2×C61×#483C211yesmaximal, characteristic, complemented
13C22×#11758226C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C22×C8×D61C2212yes—
16#16840275—24no—
17#16840275C2218yes—
18C2×#14519762—21no—
19C2×#14519753C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519747—21no—
23C2×#14519739—21no—
24C2×#14519737—21no—
25C2×#14519735—21no—
26C2×#14519735—21no—
27C2×#14519735—24no—
28C2×#14519735C2212yes—
29C2×#14519735C2212yes—
30C2×#14519735C2211yescharacteristic
31C2×#14519735C2218yescomplemented
32C22×C4⋊Dic61C2211yescharacteristic
33C22×#11758198—21no—
34C22×C4×Dic61—21no—
35#16840101C22116yescomplemented
36#16840095C2218yescomplemented
37#16840088C22116yescomplemented
38#16840081C2218yescomplemented
39#16840075C2218yescomplemented
40#16839797C22116yescomplemented
41C2×#14519710C2212yescomplemented
42C2×#14519710C2212yescomplemented
43C2×#14519709C2212yescomplemented
44#16839757C22116yescomplemented
45C2×#14519701C2212yescomplemented
46C2×#14519699C2212yescomplemented
47C2×#14519697C2212yescomplemented
48C2×C22⋊#92418C2211yescharacteristic
49C2×#14519689C2212yes—
50C22⋊C8×D61C2218yescomplemented
51C2×C22⋊Q8×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C61×#483C2218yescomplemented
54C2×#106×C61C2212yescomplemented
55C2×#103×C61C2212yescomplemented
56C2×C22⋊C8×C61C2211yescharacteristic
57C24×D61D411yescharacteristic
58C2×#11758226—22no—
59C2×#11758226—28no—
60C2×#11758226C2314yes—
61C22×D244—21no—
62C22×D244—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C23×Dic61—21no—
66C23×Dic61D411yescharacteristic
67C22×C4×D61—28no—
68C22×C4×D61—21no—
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D414yes—
72C22×C4×D61C2311yescharacteristic
73C22×C4×D61C2314yes—
74C22×C4×D61C2311yescharacteristic
75C22×#92418C2312yes—
76C2×C8×D61—28no—
77C2×C8×D61C2318yes—
78#14519762—28no—
79#14519753—22no—
80#14519753C2314yes—
81#14519752—22no—
82#14519752C2314yes—
83#14519751—22no—
84#14519751C2314yes—
85#14519747—28no—
86#14519739—28no—
87#14519737—28no—
88#14519735—24no—
89#14519735—24no—
90#14519735—28no—
91#14519735—28no—
92#14519735—22no—
93#14519735C2318yes—
94#14519735C2318yes—
95#14519735C2314yes—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61C2312yes—
99C2×C4⋊Dic61C2314yes—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—28no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61—28no—
112C2×C4×Dic61—21no—
113#14519710C2318yescomplemented
114#14519710C2318yescomplemented
115#14519709C2318yescomplemented
116#14519701C2318yescomplemented
117#14519699C2318yescomplemented
118#14519697C2318yescomplemented
119C22⋊#92418C2314yes—
120#14519689C2318yes—
121C22×Q8×C61C2311yescharacteristic
122C23×C4×C61—21no—
123C23×C4×C61C2311yescharacteristic
124C22×C8×C61C2312yes—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61C2314yes—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—22no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61C2312yes—
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2314yes—
133C2×C22⋊C4×C61—21no—
134#106×C61C2318yescomplemented
135#103×C61C2318yescomplemented
136C22⋊C8×C61C2314yes—
137C24×C61C2×D411yescharacteristic
138C23×D61—24no—
139C23×D61—24no—
140C23×D61—21no—
141C23×D61—42no—
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D414yes—
144C23×D61C2×D411yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—24no—
147C2×Q8×C61C2412yes—
148C22×C4×C61—24no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—24no—
152C22×C4×C61—22no—
153C22×C4×C61—44no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2412yes—
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—24no—
159C2×C22⋊D61—44no—
160C22×Dic61—24no—
161C22×Dic61—24no—
162C22×Dic61—22no—
163C22×Dic61—21no—
164C22×Dic61—44no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D414yes—
167C22×Dic61C2×D411yescharacteristic
168#11758226—216no—
169#11758226—48no—
170C2×D244—24no—
171C2×D244—24no—
172C2×D244—24no—
173C2×D244—21no—
174C2×D244—44no—
175C2×D244—44no—
176C2×D244C2412yes—
177C2×C4×D61—24no—
178C2×C4×D61—24no—
179C2×C4×D61—24no—
180C2×C4×D61—216no—
181C2×C4×D61—216no—
182C2×C4×D61—24no—
183C2×C4×D61—44no—
184C2×C4×D61C2×D414yes—
185C2×C4×D61C2×D412yes—
186C2×C4×D61C2×D414yes—
187C2×C4×D61C2×D412yes—
188C2×C4×D61#4118yes—
189C2×C4×D61C2412yes—
190C2×C4×D61C2412yes—
191C2×C8×C61—24no—
192C2×C8×C61C2414yes—
193C4⋊C4×C61—24no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—24no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61C2414yes—
198C4⋊C4×C61C2412yes—
199C22⋊C4×C61—24no—
200#11758198—28no—
201#11758198—28no—
202#11758198—24no—
203#11758198—24no—
204#11758198—24no—
205#11758198—24no—
206C4⋊Dic61—24no—
207C4⋊Dic61—22no—
208C4⋊Dic61—21no—
209C4⋊Dic61C2414yes—
210C4⋊Dic61C2412yes—
211#11758196—24no—
212C4×Dic61—28no—
213C4×Dic61—28no—
214C4×Dic61—24no—
215C2×#92418—24no—
216C2×#92418C2414yes—
217C8×D61—216no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61#13514yes—
221C23×C61C22×D412yes—
222C23×C61C22×D411yescharacteristic
223C22×D61—22no—
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—28no—
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—28no—
230C22×D61—22no—
231C22×D61—44no—
232C22×D61—416no—
233C22×D61—42no—
234C22×D61—42no—
235C22×D61—42no—
236C22×D61#12314yes—
237C22×D61C22×D412yes—
238C22×D61C22×D412yes—
239Q8×C61—24no—
240Q8×C61—42no—
241C2×C4×C61—22no—
242C2×C4×C61—24no—
243C2×C4×C61—24no—
244C2×C4×C61—24no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—42no—
248C2×C4×C61—48no—
249C2×C4×C61—44no—
250C2×C4×C61—42no—
251C2×C4×C61C22×D412yes—
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61C2×#4114yes—
254C2×C4×C61C2511yescharacteristic
255C22⋊D61—48no—
256C2×Dic61—22no—
257C2×Dic61—28no—
258C2×Dic61—24no—
259C2×Dic61—22no—
260C2×Dic61—48no—
261C2×Dic61—42no—
262C2×Dic61—44no—
263C2×Dic61#12314yes—
264C2×Dic61C22×D412yes—
265C2×Dic61C22×D412yes—
266D244—24no—
267D244—48no—
268D244—48no—
269D244—42no—
270C4×D61—28no—
271C4×D61—24no—
272C4×D61—24no—
273C4×D61—28no—
274C4×D61—48no—
275C4×D61#12318yes—
276C4×D61C2×#4118yes—
277C8×C61—24no—
278#92418—24no—
279C2×#3091—611nomaximal, Sylow
280C22×C61—28no—
281C22×C61—22no—
282C22×C61—22no—
283C22×C61C2×#12312yes—
284C22×C61C2×#13514yes—
285C22×C61C2×#13512yes—
286C22×C61#57512yes—
287C22×C61C23×D411yescharacteristic
288C2×D61—28no—
289C2×D61—22no—
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—416no—
295C2×D61—44no—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—84no—
300C2×D61C2×#12314yes—
301C4×C61—22no—
302C4×C61—42no—
303C4×C61—44no—
304C4×C61—42no—
305C4×C61C2×#12312yes—
306C4×C61C22×#4112yes—
307Dic61—22no—
308Dic61—42no—
309Dic61—44no—
310Dic61C2×#12314yes—
311C2×#525—611no—
312C22×#117—611no—
313#3091—6116no—
314C2×#484—611no—
315C2×#481—611no—
316C2×#485—612no—
317C2×#482—612no—
318C2×#483D6111yescharacteristic, complemented
319C2×#480—611no—
320C2×#427—612no—
321C2×#416—612no—
322C22×C22⋊C8—611no—
323C2×C61—24no—
324C2×C61#309114yescomplemented
325C2×C61C22×#12311yescharacteristic
326C2×C61C22×#13511yescharacteristic
327C2×C61C2×#57511yescharacteristic
328D61—24no—
329D61—42no—
330D61—82no—
331C22×#41—611no—
332C24×C4—611no—
333C23×C8—612no—
334#525—618no—
335#525—1224no—
336C2×#123—1221no—
337C2×C22⋊Q8—611no—
338C2×C22⋊Q8C2×D6111yescharacteristic
339C2×#121—611no—
340C2×#121—611no—
341C2×#120—1221no—
342C2×C4×D4—1221no—
343C2×C4×D4—1221no—
344C2×#117—612no—
345C2×#117—618no—
346C2×#117—612no—
347C2×#117—611no—
348C2×#117—1221no—
349C2×#117—1221no—
350C2×#117—1224no—
351C22×C4⋊C4—611no—
352C22×C4⋊C4C2×D6111yescharacteristic
353C22×C22⋊C4—1221no—
354C22×C42—1221no—
355#485—6116no—
356#484—618no—
357#483C2×D6118yescomplemented
358#482—6116no—
359#481—618no—
360#480—618no—
361#427—6116no—
362C2×#107—612no—
363C2×#107—612no—
364C2×#106—612no—
365C2×#106C2×D6112yescomplemented
366#416—6116no—
367C2×#103—612no—
368C2×#103C2×D6112yescomplemented
369C2×#102—612no—
370C2×#102—612no—
371C2×C22⋊C8—611no—
372C2×C22⋊C8—612no—
373C2×C22⋊C8—618no—
374C2×C22⋊C8C2×D6111yescharacteristic
375C61C2×#309111yescharacteristic, complemented, Sylow
376C25—611no—
377C2×#41—614no—
378C2×#41—1222no—
379C2×#41—1228no—
380C22×Q8C22×D6111yescharacteristic
381C22×D4—611no—
382C22×D4—1221no—
383C22×D4—1221no—
384C22×D4—1221no—
385C23×C4—21no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—611no—
390C23×C4—614no—
391C23×C4—611no—
392C23×C4—614no—
393C23×C4—1228no—
394C23×C4—1221no—
395C23×C4—1221no—
396C23×C4C22×D6111yescharacteristic
397C22×C8—612no—
398C22×C8—618no—
399C22×C8—1228no—
400C22×C8C22×D6112yes—
401#123—1228no—
402C22⋊Q8—22no—
403C22⋊Q8—614no—
404C22⋊Q8—1222no—
405C22⋊Q8C22×D6114yes—
406#121—614no—
407#121—614no—
408#121—1222no—
409#121—1222no—
410#120—1228no—
411C4×D4—1228no—
412C4×D4—1228no—
413#117—618no—
414#117—618no—
415#117—614no—
416#117—1224no—
417#117—1228no—
418#117—1224no—
419#117—1228no—
420#117—1222no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—612no—
425C2×C4⋊C4—614no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1222no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4C22×D6112yes—
431C2×C4⋊C4C22×D6114yes—
432C2×C4⋊C4C22×D6111yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1228no—
436C2×C22⋊C4—1222no—
437C2×C22⋊C4—1222no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C42—1228no—
442C2×C42—1222no—
443C2×C42—1222no—
444C2×C42—1221no—
445#107—618no—
446#107—618no—
447#106—618no—
448#106C22×D6118yescomplemented
449#103—618no—
450#103C22×D6118yescomplemented
451#102—618no—
452#102—618no—
453C22⋊C8—614no—
454C22⋊C8—618no—
455C22⋊C8C22×D6114yes—
456C24—611no—
457C24—611no—
458C24—614no—
459C24—1224no—
460C24—1224no—
461C24—1221no—
462C24—2442no—
463C24D4×D6111yescharacteristic
464#41—12216no—
465#41—2448no—
466C2×Q8—21no—
467C2×Q8—24no—
468C2×Q8C23×D6112yes—
469C2×D4—612no—
470C2×D4—1224no—
471C2×D4—1224no—
472C2×D4—1224no—
473C2×D4—1221no—
474C2×D4—1224no—
475C2×D4—2444no—
476C2×D4—2444no—
477C2×D4—2444no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—44no—
484C22×C4—611no—
485C22×C4—612no—
486C22×C4—618no—
487C22×C4—612no—
488C22×C4—614no—
489C22×C4—611no—
490C22×C4—614no—
491C22×C4—612no—
492C22×C4—614no—
493C22×C4—612no—
494C22×C4—1224no—
495C22×C4—12216no—
496C22×C4—12216no—
497C22×C4—1224no—
498C22×C4—1224no—
499C22×C4—1224no—
500C22×C4—1224no—
501C22×C4—1224no—
502C22×C4—1222no—
503C22×C4—1221no—
504C22×C4—2444no—
505C22×C4—2444no—
506C22×C4D4×D6112yes—
507C22×C4D4×D6111yescharacteristic
508C22×C4C23×D6112yes—
509C22×C4C23×D6111yescharacteristic
510C2×C8—24no—
511C2×C8—614no—
512C2×C8—12216no—
513C2×C8—1224no—
514C2×C8C23×D6114yes—
515C4⋊C4—24no—
516C4⋊C4—22no—
517C4⋊C4—24no—
518C4⋊C4—21no—
519C4⋊C4—614no—
520C4⋊C4—612no—
521C4⋊C4—1224no—
522C4⋊C4—1224no—
523C4⋊C4—1222no—
524C4⋊C4—1221no—
525C4⋊C4C23×D6114yes—
526C4⋊C4C23×D6112yes—
527C22⋊C4—24no—
528C22⋊C4—1224no—
529C22⋊C4—1228no—
530C22⋊C4—1228no—
531C22⋊C4—1224no—
532C22⋊C4—1224no—
533C22⋊C4—1224no—
534C42—1228no—
535C42—1228no—
536C42—1224no—
537C23—22no—
538C23—22no—
539C23—614no—
540C23—612no—
541C23—612no—
542C23—1228no—
543C23—1222no—
544C23—1222no—
545C23—1222no—
546C23—1228no—
547C23—1222no—
548C23—1222no—
549C23—1222no—
550C23—2444no—
551C23—24416no—
552C23—2442no—
553C23—2442no—
554C23—2442no—
555C23#1451979814yes—
556C23C2×D4×D6112yes—
557C23C2×D4×D6111yescharacteristic
558Q8—24no—
559Q8—42no—
560D4—1224no—
561D4—2448no—
562D4—2448no—
563D4—2448no—
564D4—2442no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—42no—
572C2×C4—48no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—614no—
576C2×C4—612no—
577C2×C4—618no—
578C2×C4—618no—
579C2×C4—612no—
580C2×C4—1228no—
581C2×C4—1228no—
582C2×C4—1228no—
583C2×C4—1222no—
584C2×C4—1224no—
585C2×C4—1224no—
586C2×C4—1224no—
587C2×C4—1222no—
588C2×C4—2448no—
589C2×C4—2448no—
590C2×C4—2442no—
591C2×C4—2444no—
592C2×C4C2×D4×D6112yes—
593C2×C4C2×D4×D6111yescharacteristic
594C2×C4#41×D6114yes—
595C2×C4C24×D6111yescharacteristic
596C8—24no—
597C8—1224no—
598C22—22no—
599C22—22no—
600C22—28no—
601C22—614no—
602C22—1222no—
603C22—1222no—
604C22—1228no—
605C22—1222no—
606C22—1222no—
607C22—1222no—
608C22—4884no—
609C22—24416no—
610C22—2442no—
611C22—2442no—
612C22—2442no—
613C22—2444no—
614C22#123×D6112yes—
615C22C2×#1451979814yes—
616C22C2×#1451979812yes—
617C22#1684056112yes—
618C22C22×D4×D6111yescharacteristic
619C4—22no—
620C4—44no—
621C4—42no—
622C4—42no—
623C4—614no—
624C4—1222no—
625C4—2442no—
626C4—2444no—
627C4#123×D6112yes—
628C4C2×#41×D6112yes—
629C2—24no—
630C2—1224no—
631C2—4882no—
632C2—2442no—
633C2#2145573314yesdirect product factor
634C2C2×#123×D6111yescharacteristic
635C2C22×#1451979811yescharacteristic
636C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#483C2
socleC23×C61C22×D4
prime radicalC2×#16840275C2
hypercenterC2×#483D61
hypocenterC61C2×#3091
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
2. C22×#14519735C2semidirect
3. #21455733C2direct (N × H)
4. C2×#16840095C2semidirect
5. C2×#16840081C2semidirect
6. C2×#16840101C2semidirect
7. C2×#16840088C2semidirect
8. C2×#16840075C2semidirect
9. C2×#16839797C2semidirect
10. C2×#16839757C2semidirect
11. C2×C22⋊C8×D61C2semidirect
12. C2×C61×#483C2semidirect
31. C2×#14519735C22semidirect
35. #16840101C22semidirect
36. #16840095C22semidirect
37. #16840088C22semidirect
38. #16840081C22semidirect
39. #16840075C22semidirect
40. #16839797C22semidirect
41. C2×#14519710C22semidirect
42. C2×#14519710C22semidirect
43. C2×#14519709C22semidirect
44. #16839757C22semidirect
45. C2×#14519701C22semidirect
46. C2×#14519699C22semidirect
47. C2×#14519697C22semidirect
50. C22⋊C8×D61C22semidirect
53. C61×#483C22semidirect
54. C2×#106×C61C22semidirect
55. C2×#103×C61C22semidirect
113. #14519710C23semidirect
114. #14519710C23semidirect
115. #14519709C23semidirect
116. #14519701C23semidirect
117. #14519699C23semidirect
118. #14519697C23semidirect
134. #106×C61C23semidirect
135. #103×C61C23semidirect
318. C2×#483D61semidirect
324. C2×C61#3091semidirect
357. #483C2×D61semidirect
365. C2×#106C2×D61semidirect
368. C2×#103C2×D61semidirect
375. C61C2×#3091semidirect
448. #106C22×D61semidirect
450. #103C22×D61semidirect
633. C2#21455733direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402752
C22×#145197352
#214557332
C2×#168400952
C2×#168400812
C2×#168401012
C2×#168400882
C2×#168400752
C2×#168397972
C2×#168397572
C2×C22⋊C8×D612
C2×C61×#4832
C2×#309161