Finite Group Databasebeta

← #30620312

Subgroups — #30620312

Order 15616.

1696 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C22⋊#6923C212yesmaximal, complemented
2#21462009C212yesmaximal, complemented
3#21461841C214yesmaximal, complemented
4#21461714C212yesmaximal, complemented
5#21461680C211yesmaximal, characteristic, complemented
6C4×#14519836C211yesmaximal, characteristic, complemented
7C2×#16840640C212yesmaximal, complemented
8C2×#16840407C211yesmaximal, characteristic
9C2×D4×#6923—22no—
10C22×C22⋊#6923C2214yes—
11C2×#14519836C2212yes—
12C2×#14519836C2212yes—
13#16840714—22no—
14#16840710—24no—
15#16840704C2212yes—
16#16840703C2214yes—
17C4×C22⋊#6923C2212yes—
18#16840640C2211yescharacteristic
19#16840640C2214yes—
20#16840640C2212yes—
21#16840640C2211yescharacteristic
22#16840640C2214yes—
23C22×#11758224C411yescharacteristic, complemented
24C22×D4×D61C2211yescharacteristic
25#16840407—22no—
26#16840407—24no—
27#16840407—22no—
28C2×#14519765C411yescharacteristic, complemented
29C2×#14519761C412yescomplemented
30C2×#14519757C2211yescharacteristic
31C2×#14519752C411yescharacteristic, complemented
32C2×#14519751C412yescomplemented
33C2×#14519747C2212yes—
34C2×C4×D244C2211yescharacteristic
35C22×#11758198C2212yes—
36C2×C4×D4×C61C411yescharacteristic, complemented
37C23×#6923—24no—
38D4×#6923—48no—
39C2×C4⋊#6923—22no—
40C2×C22⋊#6923—28no—
41C2×C22⋊#6923—24no—
42C2×C22⋊#6923—24no—
43C2×C22⋊#6923—24no—
44C2×C22⋊#6923—44no—
45C2×C22⋊#6923C2314yes—
46C2×C22⋊#6923C2312yes—
47C2×C22⋊#6923C2312yes—
48C2×C4×#6923—22no—
49#14519836—24no—
50#14519836—42no—
51(C2×#6923)⋊C4—22no—
52(C2×#6923)⋊C4—22no—
53C24×D61C2312yes—
54C2×#11758224—22no—
55C2×#11758224—21no—
56C2×#11758224—21no—
57C2×#11758224—44no—
58C22×Dic122C2×C411yescharacteristic, complemented
59C22×D244C2×C411yescharacteristic
60C22×D244C2×C412yescomplemented
61C22×D244C2311yescharacteristic
62C22×C22⋊D61C2×C412yes—
63C22×C22⋊D61C2×C412yescomplemented
64C2×D4×D61—44no—
65C2×D4×D61D412yes—
66C2×D4×D61D414yes—
67C2×D4×D61D412yes—
68C23×Dic61C2×C412yescomplemented
69C22×C4×D61C2×C411yescharacteristic, complemented
70C22×C4×D61C2311yescharacteristic
71#14519765—22no—
72#14519765—22no—
73#14519761—24no—
74#14519761—24no—
75#14519757—22no—
76#14519757—22no—
77#14519752—22no—
78#14519752—22no—
79#14519751—24no—
80#14519751—24no—
81#14519747—24no—
82#14519747—24no—
83C4×D244—22no—
84C4×D244—22no—
85C2×C4⋊Dic61C2×C411yescharacteristic, complemented
86C2×C4⋊Dic61C2×C412yescomplemented
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198C2×C412yescomplemented
90C2×#11758198C2×C412yescomplemented
91C2×#11758198C2×C411yescharacteristic, complemented
92C2×#11758198C2×C412yescomplemented
93C2×#11758198C2311yescharacteristic
94C2×#11758198C2312yes—
95C22×D4×C61C2×C411yescharacteristic
96C23×C4×C61C2×C412yescomplemented
97C4×D4×C61—22no—
98C4×D4×C61—21no—
99C4×D4×C61—21no—
100C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
101C2×C22⋊C4×C61C2×C412yescomplemented
102C2×C42×C61C2×C411yescharacteristic, complemented
103C24×C61C22×C412yes—
104C23×D61—24no—
105C23×D61—22no—
106C23×D61—22no—
107C23×D61—44no—
108C23×D61—82no—
109C23×D61C22×C411yescharacteristic
110C23×D61C22×C412yes—
111C23×D61C2×D414yes—
112C23×D61C2×D414yes—
113C23×D61C2411yescharacteristic
114C22×#6923—22no—
115C22×#6923—22no—
116C22×#6923—24no—
117C22×#6923—48no—
118C22×#6923—48no—
119C22×#6923—84no—
120C2×D4×C61—24no—
121C2×D4×C61C22⋊C412yes—
122C2×D4×C61C22⋊C411yescharacteristic
123C2×D4×C61C22⋊C411yescharacteristic
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—82no—
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C412yes—
130C22×C4×C61C22×C411yescharacteristic
131C2×C22⋊D61—22no—
132C2×C22⋊D61—22no—
133C2×C22⋊D61—44no—
134C2×C22⋊D61—44no—
135C2×C22⋊D61C22⋊C414yes—
136C2×C22⋊D61C22⋊C414yes—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—44no—
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C412yes—
142C22×Dic61C22×C411yescharacteristic
143#11758224—48no—
144#11758224—44no—
145#11758224—44no—
146D4×D61—28no—
147D4×D61—44no—
148D4×D61—48no—
149C2×D244—22no—
150C2×D244—22no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—24no—
154C2×D244—42no—
155C2×D244—82no—
156C2×D244C22⋊C412yes—
157C2×D244C22⋊C412yes—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C2×C4×D61C2×D412yes—
163C2×C4×D61C2×D412yes—
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—42no—
167C22⋊#6923—22no—
168C22⋊#6923—22no—
169C22⋊#6923—24no—
170C22⋊#6923—24no—
171C22⋊#6923—22no—
172C22⋊#6923—48no—
173C22⋊#6923—48no—
174C22⋊#6923—84no—
175C22⋊#6923#4114yescomplemented
176C4⋊#6923—44no—
177C4×#6923—44no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C42×C61—21no—
183C42×C61—21no—
184#11758198—24no—
185#11758198—24no—
186#11758198—24no—
187#11758198—22no—
188#11758198—24no—
189#11758198—22no—
190C4⋊Dic61—22no—
191C4⋊Dic61—24no—
192C23×C61—22no—
193C23×C61—22no—
194C23×C61—24no—
195C23×C61—42no—
196C23×C61C2×C22⋊C412yes—
197C23×C61C2×C22⋊C412yes—
198C23×C61C23×C411yescharacteristic
199C22×D61—28no—
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—24no—
203C22×D61—24no—
204C22×D61—24no—
205C22×D61—24no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—41no—
210C22×D61—44no—
211C22×D61—41no—
212C22×D61—44no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—44no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—88no—
219C22×D61—84no—
220C22×D61—84no—
221C22×D61C2×C22⋊C414yes—
222C22×D61C22×D412yes—
223C22×D61C2×#4112yes—
224C22×D61H(5,𝔽2)11yescharacteristic
225C22×D612−1+411yescharacteristic
226C2×#6923—24no—
227C2×#6923—42no—
228C2×#6923—42no—
229C2×#6923—42no—
230C2×#6923—44no—
231C2×#6923—42no—
232C2×#6923—44no—
233C2×#6923—44no—
234C2×#6923—42no—
235C2×#6923—816no—
236D4×C61—24no—
237D4×C61—22no—
238D4×C61#9914yescomplemented
239C2×C4×C61—22no—
240C2×C4×C61—21no—
241C2×C4×C61—22no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—42no—
246C2×C4×C61—41no—
247C2×C4×C61—82no—
248C2×C4×C61—82no—
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C22⋊D61—28no—
252C22⋊D61—44no—
253C22⋊D61—44no—
254C22⋊D61—44no—
255C2×Dic61—22no—
256C2×Dic61—21no—
257C2×Dic61—41no—
258C2×Dic61—44no—
259C2×Dic61—44no—
260C2×Dic61—42no—
261C2×Dic61—41no—
262C2×Dic61C2×C22⋊C412yes—
263D244—24no—
264D244—42no—
265D244—42no—
266D244—42no—
267D244—84no—
268C4×D61—24no—
269C4×D61—42no—
270C4×D61—42no—
271C4×D61—42no—
272Dic122—42no—
273Dic122—42no—
274#22476—611nomaximal, Sylow
275C22×C61—22no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—44no—
283C22×C61—44no—
284C22×C61C2×#9914yes—
285C22×C61C22×C22⋊C411yescharacteristic
286C22×C61C4×#4111yescharacteristic
287C22×C61#52011yescharacteristic
288C2×D61—22no—
289C2×D61—22no—
290C2×D61—24no—
291C2×D61—24no—
292C2×D61—24no—
293C2×D61—42no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—48no—
297C2×D61—48no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—84no—
302C2×D61—84no—
303C2×D61—82no—
304C2×D61—82no—
305C2×D61—81no—
306C2×D61—81no—
307C2×D61#54612yes—
308C2×D61#54712yes—
309#6923—44no—
310#6923—82no—
311#6923—84no—
312C4×C61—21no—
313C4×C61—41no—
314C4×C61—42no—
315C4×C61—41no—
316C4×C61C2×#9912yes—
317Dic61—22no—
318Dic61—42no—
319Dic61—41no—
320C2×#546—611no—
321D4×C22⋊C4—612no—
322#1996—612no—
323#1898—614no—
324#1819—612no—
325#1799—611no—
326C4×#99—611no—
327C2×#342—612no—
328C2×C61—24no—
329C2×C61—21no—
330C2×C61—21no—
331C2×C61—42no—
332C2×C61#233911yescharacteristic
333C2×C61C22×#9911yescharacteristic
334C2×C61#288311yescharacteristic
335D61—22no—
336D61—22no—
337D61—44no—
338D61—81no—
339C22×#41—611no—
340C23×D4—611no—
341#546—1222no—
342#546—1224no—
343#546—1222no—
344C2×#124—611no—
345C2×#123—612no—
346C2×C22⋊Q8—611no—
347C2×#121—612no—
348C2×#121—611no—
349C2×#120—612no—
350C2×C4×D4—611no—
351C2×C4×D4—1222no—
352C2×C4×D4#692311yescharacteristic, complemented
353C22×C22⋊C4—612no—
354C22×C22⋊C4—614no—
355C2×#99—612no—
356C2×#99—612no—
357#390—1222no—
358#386—1224no—
359#380—612no—
360#379—614no—
361C4×C22⋊C4—612no—
362#342—612no—
363#342—611no—
364#342—614no—
365#342—614no—
366#342—611no—
367C61#2247611yescharacteristic, complemented, Sylow
368C25—612no—
369C2×#41—1221no—
370C2×#41—1222no—
371C2×#41—1221no—
372C2×#41—2444no—
373C22×Q8—611no—
374C22×D4—612no—
375C22×D4—612no—
376C22×D4—614no—
377C22×D4—612no—
378C22×D4—612no—
379C22×D4—611no—
380C22×D4—611no—
381C22×D4—612no—
382C22×D4—2444no—
383C22×D4C2×#692311yescharacteristic
384C23×C4—611no—
385C23×C4—612no—
386C23×C4—611no—
387C23×C4—1224no—
388C23×C4C2×#692312yescomplemented
389#124—1222no—
390#124—1222no—
391#123—1224no—
392#123—1224no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395#121—1222no—
396#121—1222no—
397#121—1224no—
398#121—1224no—
399#120—1224no—
400#120—1224no—
401C4×D4—22no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—2448no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—612no—
409C2×C4⋊C4—1222no—
410C2×C4⋊C4C2×#692311yescharacteristic, complemented
411C2×C22⋊C4—612no—
412C2×C22⋊C4—611no—
413C2×C22⋊C4—612no—
414C2×C22⋊C4—612no—
415C2×C22⋊C4—612no—
416C2×C22⋊C4—611no—
417C2×C22⋊C4—612no—
418C2×C22⋊C4—614no—
419C2×C22⋊C4—612no—
420C2×C22⋊C4—1228no—
421C2×C22⋊C4—1224no—
422C2×C22⋊C4—1224no—
423C2×C22⋊C4—1224no—
424C2×C22⋊C4—1224no—
425C2×C22⋊C4—1224no—
426C2×C22⋊C4—2444no—
427C2×C22⋊C4C2×#692312yescomplemented
428C2×C42—1222no—
429C2×C42C2×#692311yescharacteristic, complemented
430#99—1224no—
431#99—2442no—
432#95—1222no—
433#95—1222no—
434C24—611no—
435C24—614no—
436C24—614no—
437C24—612no—
438C24—611no—
439C24—1224no—
440C24—1222no—
441C24—1222no—
442C24—4882no—
443C24—2444no—
444C24C22×#692312yes—
445#41—2448no—
446#41—2444no—
447#41—2444no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×Q8—2442no—
451C2×D4—24no—
452C2×D4—614no—
453C2×D4—614no—
454C2×D4—612no—
455C2×D4—612no—
456C2×D4—1224no—
457C2×D4—1222no—
458C2×D4—1221no—
459C2×D4—1222no—
460C2×D4—1221no—
461C2×D4—1228no—
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4—4882no—
465C2×D4—2442no—
466C2×D4—2444no—
467C2×D4—2448no—
468C2×D4—2444no—
469C2×D4—2444no—
470C2×D4C22⋊#692312yes—
471C2×D4C22⋊#692311yescharacteristic
472C2×D4C22⋊#692311yescharacteristic
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—82no—
476C22×C4—611no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—611no—
480C22×C4—612no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1222no—
487C22×C4—1224no—
488C22×C4—4884no—
489C22×C4—2442no—
490C22×C4—2442no—
491C22×C4—2448no—
492C22×C4—2448no—
493C22×C4—2444no—
494C22×C4C22×#692311yescharacteristic
495C22×C4C22×#692311yescharacteristic
496C22×C4C22×#692311yescharacteristic
497C22×C4C22×#692312yes—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—1222no—
501C4⋊C4—1224no—
502C4⋊C4—2444no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—614no—
506C22⋊C4—1222no—
507C22⋊C4—1222no—
508C22⋊C4—1224no—
509C22⋊C4—1224no—
510C22⋊C4—1224no—
511C22⋊C4—1224no—
512C22⋊C4—1222no—
513C22⋊C4—1222no—
514C22⋊C4—1224no—
515C22⋊C4—1224no—
516C22⋊C4—1222no—
517C22⋊C4—4884no—
518C22⋊C4—2448no—
519C22⋊C4—2448no—
520C42—21no—
521C42—21no—
522C42—2444no—
523C23—24no—
524C23—22no—
525C23—22no—
526C23—42no—
527C23—612no—
528C23—612no—
529C23—611no—
530C23—611no—
531C23—614no—
532C23—1224no—
533C23—1224no—
534C23—1224no—
535C23—1224no—
536C23—1222no—
537C23—1222no—
538C23—1228no—
539C23—1221no—
540C23—1221no—
541C23—1221no—
542C23—4884no—
543C23—4888no—
544C23—4884no—
545C23—2444no—
546C23—2442no—
547C23—2442no—
548C23—2444no—
549C23—2444no—
550C23—2441no—
551C23—2441no—
552C23—2441no—
553C23—2441no—
554C23C2×C22⋊#692312yes—
555C23C2×C22⋊#692312yes—
556C23C23×#692311yescharacteristic
557Q8—2442no—
558Q8—2442no—
559D4—24no—
560D4—22no—
561D4—1228no—
562D4—1224no—
563D4—4884no—
564D4—2442no—
565D4—2442no—
566D4—2442no—
567D4—2444no—
568D4—2444no—
569D4—2444no—
570D4#1451983614yescomplemented
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—82no—
580C2×C4—82no—
581C2×C4—612no—
582C2×C4—1224no—
583C2×C4—1224no—
584C2×C4—1221no—
585C2×C4—1222no—
586C2×C4—48816no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2441no—
590C2×C4—2444no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2444no—
595C2×C4—2444no—
596C2×C4—2444no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4—2444no—
600C2×C4—2442no—
601C2×C4—2441no—
602C2×C4—2442no—
603C2×C4C2×C22⋊#692311yescharacteristic
604C2×C4C2×C22⋊#692311yescharacteristic
605C22—22no—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—44no—
613C22—44no—
614C22—612no—
615C22—612no—
616C22—1222no—
617C22—1222no—
618C22—1224no—
619C22—1224no—
620C22—1224no—
621C22—4881no—
622C22—4881no—
623C22—4882no—
624C22—4882no—
625C22—4884no—
626C22—4884no—
627C22—2442no—
628C22—2441no—
629C22—2441no—
630C22—2448no—
631C22—2448no—
632C22—2441no—
633C22—2441no—
634C22—2441no—
635C22C2×#1451983614yes—
636C22C22×C22⋊#692311yescharacteristic
637C22#41×#692311yescharacteristic
638C22#1684083111yescharacteristic
639C4—21no—
640C4—41no—
641C4—41no—
642C4—42no—
643C4—1222no—
644C4—4884no—
645C4—4882no—
646C4—2444no—
647C4—2441no—
648C4—2442no—
649C4C2×#1451983612yes—
650C2—21no—
651C2—21no—
652C2—24no—
653C2—42no—
654C2—1222no—
655C2—1222no—
656C2—4881no—
657C2—2444no—
658C2#2146232211yescharacteristic
659C2C22×#1451983611yescharacteristic
660C2#2146241811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840407C2
cosocleC23×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61#22476
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×D4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×C22⋊#6923C2semidirect
2. #21462009C2semidirect
3. #21461841C2semidirect
4. #21461714C2semidirect
5. #21461680C2semidirect
6. C4×#14519836C2semidirect
7. C2×#16840640C2semidirect
23. C22×#11758224C4semidirect
28. C2×#14519765C4semidirect
29. C2×#14519761C4semidirect
31. C2×#14519752C4semidirect
32. C2×#14519751C4semidirect
36. C2×C4×D4×C61C4semidirect
58. C22×Dic122C2×C4semidirect
60. C22×D244C2×C4semidirect
63. C22×C22⋊D61C2×C4semidirect
68. C23×Dic61C2×C4semidirect
69. C22×C4×D61C2×C4semidirect
85. C2×C4⋊Dic61C2×C4semidirect
86. C2×C4⋊Dic61C2×C4semidirect
89. C2×#11758198C2×C4semidirect
90. C2×#11758198C2×C4semidirect
91. C2×#11758198C2×C4semidirect
92. C2×#11758198C2×C4semidirect
96. C23×C4×C61C2×C4semidirect
100. C2×C4⋊C4×C61C2×C4semidirect
101. C2×C22⋊C4×C61C2×C4semidirect
102. C2×C42×C61C2×C4semidirect
175. C22⋊#6923#41semidirect
238. D4×C61#99semidirect
352. C2×C4×D4#6923semidirect
367. C61#22476semidirect
388. C23×C4C2×#6923semidirect
410. C2×C4⋊C4C2×#6923semidirect
427. C2×C22⋊C4C2×#6923semidirect
429. C2×C42C2×#6923semidirect
570. D4#14519836semidirect

Maximal subgroups

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

subgroupindex
D4×C22⋊#69232
#214620092
#214618412
#214617142
#214616802
C4×#145198362
C2×#168406402
C2×#168404072
#2247661