Finite Group Databasebeta

← C2×#21446138 #29681222

Subgroups — C2×#21446138 #29681222

Order 15616.

2310 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519748C211yesmaximal, characteristic
2C22×#14519735C211yesmaximal, characteristic, complemented
3C22×#14519698C211yesmaximal, characteristic, complemented
4C22×#14519689C211yesmaximal, characteristic, complemented
5#21446138C218yesmaximal, direct product factor
6C2×#16839525C211yesmaximal, characteristic, complemented
7C2×#16839524C211yesmaximal, characteristic, complemented
8C22×#102×C61C211yesmaximal, characteristic, complemented
9C23×C22⋊D61—21no—
10C23×C4×D61C2211yescharacteristic
11C23×#92418C2211yescharacteristic
12C2×#14519748—22no—
13C2×#14519748—24no—
14C2×#14519748C418yescomplemented
15C2×#14519748C2214yes—
16C2×#14519735—24no—
17C2×#14519735—24no—
18C2×#14519735—22no—
19C2×#14519735C2214yescomplemented
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61—21no—
23C22×#11758198—21no—
24C22×C4×Dic61—21no—
25C2×#14519698—24no—
26C2×#14519698C2214yescomplemented
27C2×#14519689—24no—
28C2×#14519689C2214yescomplemented
29#16839525C2214yescomplemented
30#16839524C2214yescomplemented
31C23×D4×C61C2211yescharacteristic
32C23×C8×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C2×#102×C61—24no—
35C2×#102×C61C2214yescomplemented
36C24×D61D411yescharacteristic
37C22×C22⋊D61—28no—
38C22×C22⋊D61—24no—
39C22×C22⋊D61—44no—
40C22×C22⋊D61—44no—
41C23×Dic61—21no—
42C23×Dic61—21no—
43C23×Dic61D411yescharacteristic
44C22×C4×D61—22no—
45C22×C4×D61—22no—
46C22×C4×D61—22no—
47C22×C4×D61—22no—
48C22×C4×D61C2×C414yes—
49C22×C4×D61D412yes—
50C22×C4×D61D414yes—
51C22×C4×D61C2312yes—
52C22×#92418—22no—
53C22×#92418—22no—
54C22×#92418—22no—
55C22×#92418C2312yes—
56#14519748—216no—
57#14519748—28no—
58#14519748C2×C4116yescomplemented
59#14519735—216no—
60#14519735—28no—
61#14519735—28no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61C2×C414yes—
67C2×C4⋊Dic61D414yescomplemented
68C2×C4⋊Dic61C2312yes—
69C2×C4⋊Dic61C2312yes—
70C2×C22⋊Dic61—28no—
71C2×C22⋊Dic61—24no—
72C2×#11758198—28no—
73C2×#11758198—24no—
74C2×C4×Dic61—28no—
75C2×C4×Dic61—24no—
76#14519698—28no—
77#14519689—28no—
78C25×C61—21no—
79C22×D4×C61—22no—
80C22×D4×C61—22no—
81C22×D4×C61—21no—
82C22×D4×C61—22no—
83C22×D4×C61—22no—
84C22×D4×C61—22no—
85C22×D4×C61C2×C414yes—
86C22×D4×C61C2312yes—
87C23×C4×C61—21no—
88C23×C4×C61C2311yescharacteristic
89C22×C8×C61—22no—
90C22×C8×C61—22no—
91C22×C8×C61—22no—
92C22×C8×C61C2312yes—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61D414yescomplemented
96C2×C4⋊C4×C61C2312yes—
97#102×C61—28no—
98C24×C61—24no—
99C24×C61—22no—
100C24×C61—42no—
101C24×C61—42no—
102C24×C61—42no—
103C24×C61—42no—
104C24×C61—42no—
105C24×C61—42no—
106C24×C61C2×D411yescharacteristic
107C23×D61—22no—
108C23×D61—22no—
109C23×D61—22no—
110C23×D61—22no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61C22⋊C414yes—
114C23×D61C2×D412yes—
115C2×D4×C61—24no—
116C2×D4×C61—28no—
117C2×D4×C61—28no—
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—22no—
121C2×D4×C61—22no—
122C2×D4×C61—22no—
123C2×D4×C61—42no—
124C2×D4×C61—44no—
125C2×D4×C61—44no—
126C2×D4×C61—42no—
127C2×D4×C61C22×C414yes—
128C22×C4×C61—24no—
129C22×C4×C61—22no—
130C22×C4×C61—42no—
131C22×C4×C61—42no—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×D412yes—
137C22×C4×C61#4112yes—
138C22×C4×C61#4112yes—
139C22×C4×C61C2411yescharacteristic
140C2×C22⋊D61—216no—
141C2×C22⋊D61—48no—
142C2×C22⋊D61—48no—
143C2×C22⋊D61—432no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—24no—
147C22×Dic61—24no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—42no—
151C22×Dic61—42no—
152C22×Dic61—42no—
153C22×Dic61—42no—
154C22×Dic61C22⋊C414yes—
155C22×Dic61C2×D412yes—
156C2×C4×D61—28no—
157C2×C4×D61—28no—
158C2×C4×D61—24no—
159C2×C4×D61—28no—
160C2×C4×D61—28no—
161C2×C4×D61—24no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61C22⋊C418yes—
167C2×C4×D61C22×C414yes—
168C2×C4×D61C2×D414yes—
169C2×C8×C61—22no—
170C2×C8×C61—22no—
171C2×C8×C61—22no—
172C2×C8×C61—44no—
173C4⋊C4×C61—24no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61C2×D414yescomplemented
176C22⋊Dic61—216no—
177#11758198—216no—
178C4⋊Dic61—24no—
179C4⋊Dic61—24no—
180C4⋊Dic61—22no—
181C4⋊Dic61—22no—
182C4⋊Dic61C22×C414yes—
183C4⋊Dic61C2×D414yescomplemented
184C4×Dic61—216no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418—44no—
189C23×C61—24no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61—48no—
197C23×C61—48no—
198C23×C61—48no—
199C23×C61—84no—
200C23×C61—84no—
201C23×C61—84no—
202C23×C61—84no—
203C23×C61C2×C22⋊C412yes—
204C23×C61#12012yes—
205C23×C61#12312yes—
206C23×C61#13512yes—
207C23×C61#13512yes—
208C23×C61AGL(1,ℤ/8)12yes—
209C23×C61AGL(1,ℤ/8)12yes—
210C23×C61C22×D411yescharacteristic
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—28no—
218C22×D61—28no—
219C22×D61—28no—
220C22×D61—44no—
221C22×D61—44no—
222C22×D61—44no—
223C22×D61—44no—
224C22×D61C2×C22⋊C414yes—
225D4×C61—24no—
226D4×C61—24no—
227D4×C61—42no—
228D4×C61—42no—
229D4×C61—48no—
230C2×C4×C61—24no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—48no—
234C2×C4×C61C2×C22⋊C412yes—
235C2×C4×C61C4×D414yes—
236C2×C4×C61C4×D414yes—
237C2×C4×C61#12012yes—
238C2×C4×C61#12114yes—
239C2×C4×C61#12114yes—
240C2×C4×C61#12312yes—
241C2×C4×C61C23×C411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C22⋊D61—432no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—28no—
251C2×Dic61—24no—
252C2×Dic61—24no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—48no—
258C2×Dic61—48no—
259C2×Dic61C2×C22⋊C414yes—
260C4×D61—24no—
261C4×D61—24no—
262C4×D61—24no—
263C4×D61—24no—
264C4×D61—216no—
265C8×C61—42no—
266#92418—42no—
267C2×#1875—611nomaximal, Sylow
268C22×C61—44no—
269C22×C61—44no—
270C22×C61—44no—
271C22×C61—82no—
272C22×C61—82no—
273C22×C61—816no—
274C22×C61—82no—
275C22×C61—82no—
276C22×C61#38614yes—
277C22×C61#41614yes—
278C22×C61#41814yes—
279C22×C61#44914yes—
280C22×C61#44914yes—
281C22×C61#48214yes—
282C22×C61#48214yes—
283C22×C61C22×C22⋊C411yescharacteristic
284C22×C61C2×#12011yescharacteristic
285C22×C61C2×#12311yescharacteristic
286C22×C61C2×#13511yescharacteristic
287C22×C61C2×#13511yescharacteristic
288C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
290C2×D61—24no—
291C2×D61—24no—
292C2×D61—24no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—416no—
296C2×D61—42no—
297C2×D61—42no—
298C4×C61—44no—
299C4×C61#38614yes—
300C4×C61C2×C4×D411yescharacteristic
301C4×C61C2×C4×D411yescharacteristic
302C4×C61C2×#12111yescharacteristic
303C4×C61C2×#12111yescharacteristic
304Dic61—24no—
305Dic61—44no—
306Dic61—44no—
307C22×#121—611no—
308C22×#117—611no—
309C22×#102—611no—
310C22×#102D6111yescharacteristic, complemented
311C22×C22⋊C8—611no—
312#1875—618no—
313C2×#340—611no—
314C2×#340—611no—
315C2×C61—84no—
316C2×C61#187518yescomplemented
317C2×C61C2×#38611yescharacteristic
318C2×C61C2×#41611yescharacteristic
319C2×C61C2×#41811yescharacteristic
320C2×C61C2×#44911yescharacteristic
321C2×C61C2×#44911yescharacteristic
322C2×C61C2×#48211yescharacteristic
323C2×C61C2×#48211yescharacteristic
324D61—44no—
325C23×D4—1221no—
326C23×D4C2×D6111yescharacteristic
327C24×C4—611no—
328C23×C8—611no—
329C23×C8C2×D6111yescharacteristic
330C2×#121—618no—
331C2×#121—614no—
332C2×#121—1222no—
333C2×#121—1224no—
334C2×#117—614no—
335C2×#117—1224no—
336C2×#117—1222no—
337C2×#117—1224no—
338C22×C4⋊C4—611no—
339C22×C4⋊C4—611no—
340C22×C4⋊C4C2×D6111yescharacteristic
341C22×C22⋊C4—1221no—
342C22×C22⋊C4—1221no—
343C22×C42—1221no—
344C2×#102—24no—
345C2×#102—614no—
346C2×#102—1224no—
347C2×#102C2×D6114yescomplemented
348C2×C22⋊C8—614no—
349C2×C22⋊C8—1224no—
350#340—614no—
351#340—614no—
352C61C2×#187511yescharacteristic, complemented, Sylow
353C25—21no—
354C25—611no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—21no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—1224no—
362C22×D4—1228no—
363C22×D4—2444no—
364C22×D4—2444no—
365C22×D4C4×D6114yes—
366C22×D4C22×D6112yes—
367C23×C4—21no—
368C23×C4—611no—
369C23×C4—614no—
370C23×C4—612no—
371C23×C4—614no—
372C23×C4—612no—
373C23×C4—1222no—
374C23×C4—1222no—
375C23×C4—1222no—
376C23×C4—1222no—
377C23×C4—1221no—
378C23×C4—1221no—
379C23×C4C22×D6111yescharacteristic
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—612no—
384C22×C8—1222no—
385C22×C8—1222no—
386C22×C8—1222no—
387C22×C8C22×D6112yes—
388#121—6116no—
389#121—1228no—
390#121—12216no—
391#117—1228no—
392#117—12216no—
393#117—1228no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—614no—
397C2×C4⋊C4—614no—
398C2×C4⋊C4—612no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1222no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4C22⋊D6114yescomplemented
405C2×C4⋊C4C22×D6112yes—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1228no—
408C2×C22⋊C4—1224no—
409C2×C22⋊C4—1228no—
410C2×C42—1224no—
411C2×C42—1228no—
412#102—28no—
413#102—1228no—
414C22⋊C8—1228no—
415C24—22no—
416C24—24no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—612no—
424C24—614no—
425C24—1222no—
426C24—1222no—
427C24—1222no—
428C24—1222no—
429C24—1222no—
430C24—1222no—
431C24D4×D6111yescharacteristic
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—24no—
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—42no—
444C2×D4—12216no—
445C2×D4—24432no—
446C2×D4—2448no—
447C2×D4—2448no—
448C2×D4C2×C4×D6114yes—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—612no—
454C22×C4—614no—
455C22×C4—614no—
456C22×C4—614no—
457C22×C4—618no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1228no—
465C22×C4—1228no—
466C22×C4—1224no—
467C22×C4—1228no—
468C22×C4—1228no—
469C22×C4—1224no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1224no—
473C22×C4—1224no—
474C22×C4—2442no—
475C22×C4—2442no—
476C22×C4—2442no—
477C22×C4—2442no—
478C22×C4C2×C4×D6112yes—
479C22×C4#1175822212yes—
480C22×C4D4×D6112yes—
481C22×C4D4×D6112yes—
482C22×C4D4×D6111yescharacteristic
483C22×C4#1175822412yes—
484C22×C4C2×C22⋊D6112yes—
485C22×C4C23×D6111yescharacteristic
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—44no—
490C2×C8—1222no—
491C2×C8—1222no—
492C2×C8—1222no—
493C2×C8—2444no—
494C4⋊C4—22no—
495C4⋊C4—24no—
496C4⋊C4—614no—
497C4⋊C4—614no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1224no—
501C4⋊C4—1224no—
502C4⋊C4C2×C22⋊D6114yescomplemented
503C22⋊C4—12216no—
504C22⋊C4—12216no—
505C42—12216no—
506C23—24no—
507C23—42no—
508C23—42no—
509C23—48no—
510C23—48no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—48no—
516C23—84no—
517C23—84no—
518C23—84no—
519C23—84no—
520C23—614no—
521C23—1222no—
522C23—1222no—
523C23—1228no—
524C23—1228no—
525C23—1222no—
526C23—1222no—
527C23—1222no—
528C23—1222no—
529C23—1228no—
530C23—2444no—
531C23—2444no—
532C23—2444no—
533C23—2444no—
534C23C22⋊C4×D6112yes—
535C23#1451974512yes—
536C23#1451975912yes—
537C23#1451979612yes—
538C23#1451979812yes—
539C23#1451980112yes—
540C23#1451980412yes—
541C23C2×D4×D6111yescharacteristic
542D4—24no—
543D4—24no—
544D4—42no—
545D4—42no—
546D4—48no—
547D4—24432no—
548C2×C4—24no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—48no—
552C2×C4—614no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1228no—
556C2×C4—1224no—
557C2×C4—1224no—
558C2×C4—1224no—
559C2×C4—1224no—
560C2×C4—12216no—
561C2×C4—1224no—
562C2×C4—1224no—
563C2×C4—2448no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4—2448no—
569C2×C4C22⋊C4×D6112yes—
570C2×C4#1451973714yes—
571C2×C4C4×C22⋊D6114yes—
572C2×C4#1451974512yes—
573C2×C4#1451974814yes—
574C2×C4#1451975014yes—
575C2×C4#1451975912yes—
576C2×C4C22×C4×D6111yescharacteristic
577C2×C4C2×D4×D6111yescharacteristic
578C2×C4C2×D4×D6111yescharacteristic
579C2×C4C22×C22⋊D6111yescharacteristic
580C2×C4C2×#1175822411yescharacteristic
581C2×C4C2×#1175822211yescharacteristic
582C8—42no—
583C8—2442no—
584C22—44no—
585C22—44no—
586C22—44no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22—82no—
591C22—816no—
592C22—1224no—
593C22—1224no—
594C22—1224no—
595C22—2442no—
596C22—2442no—
597C22—2442no—
598C22—2442no—
599C22—24416no—
600C22#1683963814yes—
601C22#1683975514yes—
602C22#1683976514yes—
603C22#1683990414yes—
604C22#1683990614yes—
605C22#1684008414yes—
606C22#1684008514yes—
607C22C2×C22⋊C4×D6111yescharacteristic
608C22C2×#1451974511yescharacteristic
609C22C2×#1451975911yescharacteristic
610C22C2×#1451979611yescharacteristic
611C22C2×#1451979811yescharacteristic
612C22C2×#1451980111yescharacteristic
613C22C2×#1451980411yescharacteristic
614C4—44no—
615C4—1224no—
616C4—2444no—
617C4—2444no—
618C4#1683963814yes—
619C4C2×#1451973711yescharacteristic
620C4C2×C4×C22⋊D6111yescharacteristic
621C4C2×#1451974811yescharacteristic
622C4C2×#1451975011yescharacteristic
623C2—84no—
624C2—2444no—
625C2#2144613818yesdirect product factor
626C2C2×#1683963811yescharacteristic
627C2C2×#1683975511yescharacteristic
628C2C2×#1683976511yescharacteristic
629C2C2×#1683990411yescharacteristic
630C2C2×#1683990611yescharacteristic
631C2C2×#1684008411yescharacteristic
632C2C2×#1684008511yescharacteristic
subgroupG/H
centerC24D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC24×C61C2×D4
prime radicalC22×#14519748C2
cosocleC22×C4×C61C24
hypercenterC22×#102D61
hypocenterC61C2×#1875
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#14519735C2semidirect
3. C22×#14519698C2semidirect
4. C22×#14519689C2semidirect
5. #21446138C2direct (N × H)
6. C2×#16839525C2semidirect
7. C2×#16839524C2semidirect
8. C22×#102×C61C2semidirect
14. C2×#14519748C4semidirect
19. C2×#14519735C22semidirect
26. C2×#14519698C22semidirect
28. C2×#14519689C22semidirect
29. #16839525C22semidirect
30. #16839524C22semidirect
35. C2×#102×C61C22semidirect
58. #14519748C2×C4semidirect
67. C2×C4⋊Dic61D4semidirect
95. C2×C4⋊C4×C61D4semidirect
175. C4⋊C4×C61C2×D4semidirect
183. C4⋊Dic61C2×D4semidirect
310. C22×#102D61semidirect
316. C2×C61#1875semidirect
347. C2×#102C2×D61semidirect
352. C61C2×#1875semidirect
404. C2×C4⋊C4C22⋊D61semidirect
502. C4⋊C4C2×C22⋊D61semidirect
625. C2#21446138direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197482
C22×#145197352
C22×#145196982
C22×#145196892
#214461382
C2×#168395252
C2×#168395242
C22×#102×C612
C2×#187561