Finite Group Databasebeta

← C2×#21444144 #29645848

Subgroups — C2×#21444144 #29645848

Order 15616.

2790 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D61C211yesmaximal, characteristic
2C2×#16839724C212yesmaximal, complemented
3#21444144C218yesmaximal, direct product factor
4C2×#16839486C211yesmaximal, characteristic, complemented
5C2×#16839485C212yesmaximal, complemented
6C2×C61×#323C211yesmaximal, characteristic, complemented
7C25×D61C411yescharacteristic
8C23×C4×D61C411yescharacteristic
9C23×C4×D61C2211yescharacteristic
10C22×#11758189—22no—
11C22×C22⋊Dic61C411yescharacteristic
12C22×#11758198C411yescharacteristic
13C22×#11758198C2211yescharacteristic
14C2×C22⋊C4×D61—22no—
15C2×C22⋊C4×D61—22no—
16C2×C22⋊C4×D61—24no—
17C2×C22⋊C4×D61C414yes—
18C2×C22⋊C4×D61C2214yes—
19#16839724—24no—
20#16839724C2218yescomplemented
21C2×C22⋊#92418C2212yescomplemented
22C2×#14519689—22no—
23#16839486C2214yescomplemented
24#16839485C2218yescomplemented
25C22×C22⋊C4×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2212yescomplemented
27C61×#323C2214yescomplemented
28C24×D61—24no—
29C24×D61—22no—
30C24×D61—21no—
31C24×D61—21no—
32C24×D61—24no—
33C24×D61—44no—
34C24×D61—44no—
35C24×D61C2×C411yescharacteristic
36C24×D61C2×C414yes—
37C24×D61C2×C411yescharacteristic
38C23×Dic61C2×C411yescharacteristic
39C23×Dic61C2×C411yescharacteristic
40C22×C4×D61—22no—
41C22×C4×D61—21no—
42C22×C4×D61—21no—
43C22×C4×D61—44no—
44C22×C4×D61—44no—
45C22×C4×D61C2×C414yes—
46C22×C4×D61C2×C412yes—
47C22×C4×D61D412yes—
48C22×C4×D61D412yes—
49C22×C4×D61D414yes—
50C22×C4×D61C2312yes—
51C2×#11758189—28no—
52C2×#11758189—48no—
53C22×#92418—22no—
54C2×C22⋊Dic61—22no—
55C2×C22⋊Dic61—22no—
56C2×C22⋊Dic61C2×C414yes—
57C2×#11758198—22no—
58C2×#11758198—22no—
59C2×#11758198—22no—
60C2×#11758198—22no—
61C2×#11758198C2×C412yes—
62C2×#11758198C2×C414yes—
63C2×#11758198C2312yes—
64C22⋊C4×D61—28no—
65C22⋊C4×D61—28no—
66C22⋊C4×D61—28no—
67C22⋊C4×D61—28no—
68C22⋊#92418—22no—
69C22⋊#92418C2314yescomplemented
70#14519689—28no—
71C25×C61C2×C411yescharacteristic
72C23×C4×C61C2×C411yescharacteristic
73C23×C4×C61C2311yescharacteristic
74C22×C8×C61—22no—
75C2×C22⋊C4×C61—22no—
76C2×C22⋊C4×C61—22no—
77C2×C22⋊C4×C61C2×C412yes—
78C2×C22⋊C4×C61C2312yes—
79C22⋊C8×C61—22no—
80C22⋊C8×C61C2314yescomplemented
81C24×C61—21no—
82C24×C61—21no—
83C24×C61—22no—
84C24×C61—42no—
85C24×C61—42no—
86C24×C61M1614yescomplemented
87C24×C61C22×C411yescharacteristic
88C24×C61C22×C412yes—
89C23×D61—22no—
90C23×D61—22no—
91C23×D61—24no—
92C23×D61—24no—
93C23×D61—216no—
94C23×D61—28no—
95C23×D61—28no—
96C23×D61—21no—
97C23×D61—21no—
98C23×D61—22no—
99C23×D61—28no—
100C23×D61—24no—
101C23×D61—24no—
102C23×D61—28no—
103C23×D61—432no—
104C23×D61—432no—
105C23×D61—44no—
106C23×D61—44no—
107C23×D61—48no—
108C23×D61—48no—
109C23×D61—48no—
110C23×D61—48no—
111C23×D61—44no—
112C23×D61—44no—
113C23×D61—42no—
114C23×D61—42no—
115C23×D61C22⋊C412yes—
116C23×D61C22⋊C411yescharacteristic
117C23×D61C22⋊C411yescharacteristic
118C23×D61M1614yescomplemented
119C23×D61C22×C412yes—
120C23×D61C22×C412yes—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—42no—
124C22×C4×C61—42no—
125C22×C4×C61C22×C412yes—
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C2×D412yes—
128C22×C4×C61C2×D412yes—
129C22×C4×C61C2411yescharacteristic
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—42no—
133C22×Dic61—42no—
134C22×Dic61C22⋊C412yes—
135C22×Dic61C22⋊C412yes—
136C22×Dic61C22×C412yes—
137C22×Dic61C22×C412yes—
138C2×C4×D61—28no—
139C2×C4×D61—24no—
140C2×C4×D61—24no—
141C2×C4×D61—44no—
142C2×C4×D61—48no—
143C2×C4×D61—44no—
144C2×C4×D61—44no—
145C2×C4×D61—44no—
146C2×C4×D61—48no—
147C2×C4×D61—44no—
148C2×C4×D61—48no—
149C2×C4×D61C22⋊C414yes—
150C2×C4×D61C22⋊C414yes—
151C2×C4×D61C2×D414yes—
152C2×C4×D61C2×D414yes—
153C2×C8×C61—24no—
154C2×C8×C61—44no—
155C22⋊C4×C61—24no—
156C22⋊C4×C61—24no—
157C22⋊Dic61—28no—
158#11758198—24no—
159#11758198—24no—
160#11758198—28no—
161C2×#92418—24no—
162C2×#92418—44no—
163#11758189—416no—
164C23×C61—22no—
165C23×C61—22no—
166C23×C61—22no—
167C23×C61—22no—
168C23×C61—24no—
169C23×C61—24no—
170C23×C61—42no—
171C23×C61—42no—
172C23×C61—48no—
173C23×C61—48no—
174C23×C61—42no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61C2×C22⋊C411yescharacteristic
179C23×C61C2×C22⋊C411yescharacteristic
180C23×C61C2×M1612yes—
181C23×C61C2×M1612yes—
182C23×C61C2×M1614yescomplemented
183C23×C61C23×C411yescharacteristic
184C22×D61—216no—
185C22×D61—216no—
186C22×D61—22no—
187C22×D61—22no—
188C22×D61—24no—
189C22×D61—22no—
190C22×D61—22no—
191C22×D61—22no—
192C22×D61—22no—
193C22×D61—24no—
194C22×D61—24no—
195C22×D61—24no—
196C22×D61—24no—
197C22×D61—216no—
198C22×D61—216no—
199C22×D61—22no—
200C22×D61—22no—
201C22×D61—24no—
202C22×D61—24no—
203C22×D61—432no—
204C22×D61—464no—
205C22×D61—432no—
206C22×D61—48no—
207C22×D61—48no—
208C22×D61—432no—
209C22×D61—432no—
210C22×D61—42no—
211C22×D61—42no—
212C22×D61—48no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—48no—
216C22×D61—48no—
217C22×D61—48no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61#9914yes—
221C22×D61#10014yes—
222C22×D61C2×C22⋊C412yes—
223C22×D61C2×C22⋊C412yes—
224C22×D61C2×M1614yescomplemented
225C2×C4×C61—24no—
226C2×C4×C61—22no—
227C2×C4×C61—41no—
228C2×C4×C61—42no—
229C2×C4×C61—41no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61C2×C22⋊C412yes—
234C2×C4×C61C22×D412yes—
235C2×Dic61—24no—
236C2×Dic61—22no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61—42no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61C2×C22⋊C414yes—
243C4×D61—28no—
244C4×D61—28no—
245C4×D61—44no—
246C4×D61—44no—
247C4×D61—48no—
248C4×D61—48no—
249C8×C61—44no—
250#92418—44no—
251C2×#1462—611nomaximal, Sylow
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—24no—
257C22×C61—24no—
258C22×C61—24no—
259C22×C61—44no—
260C22×C61—44no—
261C22×C61—48no—
262C22×C61—42no—
263C22×C61—42no—
264C22×C61—48no—
265C22×C61#40712yes—
266C22×C61#40712yes—
267C22×C61C2×#9912yes—
268C22×C61C2×#10012yes—
269C22×C61C22×C22⋊C411yescharacteristic
270C22×C61C22×M1611yescharacteristic
271C22×C61C22×M1611yescharacteristic
272C2×D61—28no—
273C2×D61—28no—
274C2×D61—216no—
275C2×D61—22no—
276C2×D61—22no—
277C2×D61—22no—
278C2×D61—22no—
279C2×D61—28no—
280C2×D61—28no—
281C2×D61—24no—
282C2×D61—432no—
283C2×D61—432no—
284C2×D61—44no—
285C2×D61—48no—
286C2×D61—42no—
287C2×D61—42no—
288C2×D61—48no—
289C2×D61—44no—
290C2×D61C2×#9914yes—
291C2×D61C2×#10014yes—
292C4×C61—22no—
293C4×C61—22no—
294C4×C61—42no—
295Dic61—24no—
296Dic61—42no—
297C23×C22⋊C4—611no—
298C2×#407—612no—
299#1462—618no—
300C2×#323—612no—
301C2×#323—611no—
302C2×#323D6111yescharacteristic, complemented
303C2×C61—21no—
304C2×C61—21no—
305C2×C61—22no—
306C2×C61—44no—
307C2×C61#146214yescomplemented
308C2×C61C2×#40711yescharacteristic
309C2×C61C22×#9911yescharacteristic
310C2×C61C22×#10011yescharacteristic
311D61—24no—
312D61—24no—
313D61—44no—
314C26—611no—
315C24×C4—611no—
316C24×C4—611no—
317C22×M16—1222no—
318C22×C22⋊C4—611no—
319C22×C22⋊C4—611no—
320C22×C22⋊C4—611no—
321C22×C22⋊C4—614no—
322C22×C22⋊C4—614no—
323C22×C22⋊C4—1222no—
324C22×C22⋊C4—1222no—
325C22×C22⋊C4—1224no—
326C22×C22⋊C4C2×D6111yescharacteristic
327#407—618no—
328#407—1224no—
329C2×C22⋊C8—612no—
330C2×C22⋊C8—1222no—
331C2×C22⋊C8C2×D6112yescomplemented
332#323—614no—
333#323—618no—
334#323C2×D6114yescomplemented
335C61C2×#146211yescharacteristic, complemented, Sylow
336C25—611no—
337C25—611no—
338C25—614no—
339C25—1222no—
340C25—1221no—
341C25—1221no—
342C25—1224no—
343C25—1224no—
344C25—2444no—
345C25—2444no—
346C25C4×D6111yescharacteristic
347C23×C4—611no—
348C23×C4—612no—
349C23×C4—612no—
350C23×C4—612no—
351C23×C4—614no—
352C23×C4—612no—
353C23×C4—611no—
354C23×C4—614no—
355C23×C4—1222no—
356C23×C4—1221no—
357C23×C4—1221no—
358C23×C4—2444no—
359C23×C4—2444no—
360C23×C4C4×D6111yescharacteristic
361C23×C4C22×D6111yescharacteristic
362C2×M16—1228no—
363C2×M16—2448no—
364C22×C8—22no—
365C22×C8—1222no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—614no—
369C2×C22⋊C4—614no—
370C2×C22⋊C4—612no—
371C2×C22⋊C4—612no—
372C2×C22⋊C4—1228no—
373C2×C22⋊C4—1228no—
374C2×C22⋊C4—1228no—
375C2×C22⋊C4—1228no—
376C2×C22⋊C4—1222no—
377C2×C22⋊C4—1222no—
378C2×C22⋊C4—1222no—
379C2×C22⋊C4—1222no—
380C2×C22⋊C4—1222no—
381C2×C22⋊C4—1222no—
382C2×C22⋊C4C4×D6112yes—
383C2×C22⋊C4C22×D6112yes—
384C22⋊C8—22no—
385C22⋊C8—614no—
386C22⋊C8—1228no—
387C22⋊C8—1222no—
388C22⋊C8C22×D6114yescomplemented
389C24—21no—
390C24—21no—
391C24—22no—
392C24—42no—
393C24—42no—
394C24—611no—
395C24—611no—
396C24—612no—
397C24—612no—
398C24—612no—
399C24—614no—
400C24—1224no—
401C24—1224no—
402C24—1224no—
403C24—1224no—
404C24—1228no—
405C24—12216no—
406C24—1228no—
407C24—1228no—
408C24—1222no—
409C24—1222no—
410C24—1221no—
411C24—1221no—
412C24—1222no—
413C24—1228no—
414C24—2442no—
415C24—2442no—
416C24—2444no—
417C24—2444no—
418C24—2448no—
419C24—2448no—
420C24—24432no—
421C24—2448no—
422C24—2448no—
423C24—24432no—
424C24—2444no—
425C24—2444no—
426C24#1175818914yescomplemented
427C24C2×C4×D6111yescharacteristic
428C24C2×C4×D6112yes—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—612no—
434C22×C4—612no—
435C22×C4—612no—
436C22×C4—614no—
437C22×C4—614no—
438C22×C4—614no—
439C22×C4—614no—
440C22×C4—612no—
441C22×C4—1228no—
442C22×C4—1224no—
443C22×C4—1224no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—2444no—
447C22×C4—2444no—
448C22×C4—2448no—
449C22×C4—2444no—
450C22×C4—2444no—
451C22×C4—2448no—
452C22×C4—2444no—
453C22×C4—2448no—
454C22×C4—2442no—
455C22×C4—2442no—
456C22×C4C2×C4×D6112yes—
457C22×C4C2×C4×D6111yescharacteristic
458C22×C4D4×D6112yes—
459C22×C4D4×D6112yes—
460C22×C4C23×D6111yescharacteristic
461M16—24416no—
462C2×C8—24no—
463C2×C8—44no—
464C2×C8—1224no—
465C2×C8—2444no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—1228no—
469C22⋊C4—1228no—
470C22⋊C4—1224no—
471C22⋊C4—1224no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—24no—
476C23—24no—
477C23—22no—
478C23—48no—
479C23—42no—
480C23—42no—
481C23—48no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—612no—
487C23—612no—
488C23—614no—
489C23—614no—
490C23—614no—
491C23—1224no—
492C23—1224no—
493C23—1224no—
494C23—1224no—
495C23—12216no—
496C23—12216no—
497C23—12216no—
498C23—12216no—
499C23—1224no—
500C23—1222no—
501C23—1222no—
502C23—1222no—
503C23—1222no—
504C23—1222no—
505C23—1222no—
506C23—1222no—
507C23—1224no—
508C23—1224no—
509C23—1222no—
510C23—2448no—
511C23—2442no—
512C23—2442no—
513C23—2448no—
514C23—2442no—
515C23—2442no—
516C23—2448no—
517C23—2448no—
518C23—24432no—
519C23—24432no—
520C23—24464no—
521C23—24432no—
522C23—24432no—
523C23—2448no—
524C23—2448no—
525C23—2442no—
526C23—2442no—
527C23C22⋊C4×D6111yescharacteristic
528C23C22⋊C4×D6111yescharacteristic
529C23M16×D6112yes—
530C23C2×#1175818912yes—
531C23C2×#1175818914yescomplemented
532C23C22×C4×D6111yescharacteristic
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—614no—
542C2×C4—1228no—
543C2×C4—1228no—
544C2×C4—1224no—
545C2×C4—1222no—
546C2×C4—2444no—
547C2×C4—2444no—
548C2×C4—2448no—
549C2×C4—2448no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4—2442no—
555C2×C4C22⋊C4×D6112yes—
556C2×C4C2×D4×D6112yes—
557C8—44no—
558C8—2444no—
559C22—24no—
560C22—24no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—24no—
566C22—44no—
567C22—48no—
568C22—44no—
569C22—48no—
570C22—42no—
571C22—42no—
572C22—614no—
573C22—614no—
574C22—12216no—
575C22—1228no—
576C22—1228no—
577C22—1228no—
578C22—1228no—
579C22—1222no—
580C22—1222no—
581C22—1222no—
582C22—1222no—
583C22—1224no—
584C22—2444no—
585C22—2448no—
586C22—2444no—
587C22—24432no—
588C22—24432no—
589C22—2448no—
590C22—2442no—
591C22—2442no—
592C22#1683972412yes—
593C22#1683972412yes—
594C22#99×D6112yes—
595C22#100×D6112yes—
596C22C2×C22⋊C4×D6111yescharacteristic
597C22C2×M16×D6111yescharacteristic
598C22C22×#1175818911yescharacteristic
599C4—22no—
600C4—22no—
601C4—42no—
602C4—1224no—
603C4—2442no—
604C2—22no—
605C2—21no—
606C2—21no—
607C2—44no—
608C2—1224no—
609C2—1224no—
610C2—2444no—
611C2#2144414414yesdirect product factor
612C2C2×#1683972411yescharacteristic
613C2C2×#99×D6111yescharacteristic
614C2C2×#100×D6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#323C2
socleC23×C61C2×C22⋊C4
prime radicalC25×D61C4
cosocleC22×C4×C61C24
hypercenterC2×#323D61
hypocenterC61C2×#1462
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#16839724C2semidirect
3. #21444144C2direct (N × H)
4. C2×#16839486C2semidirect
5. C2×#16839485C2semidirect
6. C2×C61×#323C2semidirect
20. #16839724C22semidirect
21. C2×C22⋊#92418C22semidirect
23. #16839486C22semidirect
24. #16839485C22semidirect
26. C2×C22⋊C8×C61C22semidirect
27. C61×#323C22semidirect
69. C22⋊#92418C23semidirect
80. C22⋊C8×C61C23semidirect
86. C24×C61M16semidirect
118. C23×D61M16semidirect
182. C23×C61C2×M16semidirect
224. C22×D61C2×M16semidirect
302. C2×#323D61semidirect
307. C2×C61#1462semidirect
331. C2×C22⋊C8C2×D61semidirect
334. #323C2×D61semidirect
335. C61C2×#1462semidirect
388. C22⋊C8C22×D61semidirect
426. C24#11758189semidirect
531. C23C2×#11758189semidirect
611. C2#21444144direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D612
C2×#168397242
#214441442
C2×#168394862
C2×#168394852
C2×C61×#3232
C2×#146261