Finite Group Databasebeta

← C2×#21446859 #29706965

Subgroups — C2×#21446859 #29706965

Order 15616.

2254 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519803C211yesmaximal, characteristic, complemented
2C2×#16840340C211yesmaximal, characteristic, complemented
3C22×#14519704C211yesmaximal, characteristic, complemented
4C22×#14519703C211yesmaximal, characteristic, complemented
5C2×#16839665C211yesmaximal, characteristic, complemented
6#21446859C218yesmaximal, direct product factor
7C2×#16839530C211yesmaximal, characteristic, complemented
8C22×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C2×#14519803—24no—
11C2×#14519803—24no—
12C2×#14519803—22no—
13C2×#14519803C2214yescomplemented
14C22×#11758200—21no—
15C22×#11758199—21no—
16C22×#11758194C2211yescharacteristic
17#16840340—22no—
18#16840340—22no—
19#16840340—22no—
20#16840340C2214yescomplemented
21C2×#14519756—21no—
22C2×#14519753—21no—
23C2×#14519751—21no—
24C2×#14519749—22no—
25C2×#14519748—21no—
26C22×C4⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61—22no—
28C22×C4×Dic61C2211yescharacteristic
29C2×#14519704—24no—
30C2×#14519704C2214yescomplemented
31C2×#14519703—24no—
32C2×#14519703C2214yescomplemented
33#16839665—22no—
34#16839665C2214yescomplemented
35#16839530C2214yescomplemented
36C22×#41×C61C2211yescharacteristic
37C23×D4×C61C2211yescharacteristic
38C2×AGL(1,ℤ/8)×C61—22no—
39C2×AGL(1,ℤ/8)×C61—24no—
40C2×AGL(1,ℤ/8)×C61—24no—
41C2×AGL(1,ℤ/8)×C61C2214yescomplemented
42C22×SD16×C61—21no—
43C22×D8×C61—21no—
44C22×M16×C61C2211yescharacteristic
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—22no—
48C2×#11758222—22no—
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222D412yes—
52C2×#11758222C2312yes—
53C22×Dic122D411yescharacteristic
54C22×D244D411yescharacteristic
55C22×C22⋊D61—21no—
56C22×C22⋊D61—22no—
57C23×Dic61—21no—
58C23×Dic61D412yes—
59C22×C4×D61—21no—
60#14519803—216no—
61#14519803—28no—
62#14519803—28no—
63C2×#11758200—28no—
64C2×#11758200—24no—
65C2×#11758199—28no—
66C2×#11758199—24no—
67C2×#11758194—22no—
68C2×#11758194—21no—
69C2×#11758194D414yescomplemented
70C2×#11758194C2312yes—
71C22×#92418—21no—
72#14519756—24no—
73#14519756—24no—
74#14519753—24no—
75#14519753—24no—
76#14519751—24no—
77#14519751—24no—
78#14519749—28no—
79#14519749—28no—
80#14519748—24no—
81#14519748—24no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61D412yes—
87C2×C4⋊Dic61C2312yes—
88C2×#11758196—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—28no—
91C2×C22⋊Dic61—48no—
92C2×#11758198—22no—
93C2×C4×Dic61—22no—
94C2×C4×Dic61—22no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61C2312yes—
97#14519704—28no—
98#14519703—28no—
99C25×C61—21no—
100C2×#41×C61—21no—
101C2×#41×C61—21no—
102C2×#41×C61—22no—
103C2×#41×C61—22no—
104C2×#41×C61—22no—
105C2×#41×C61—22no—
106C2×#41×C61D412yes—
107C2×#41×C61C2312yes—
108C22×Q8×C61D411yescharacteristic
109C22×D4×C61—21no—
110C22×D4×C61—21no—
111C22×D4×C61—21no—
112C22×D4×C61—22no—
113C22×D4×C61—21no—
114C22×D4×C61—21no—
115C22×D4×C61—22no—
116C22×D4×C61—21no—
117C22×D4×C61—22no—
118C22×D4×C61D411yescharacteristic
119C22×D4×C61D414yescomplemented
120C22×D4×C61C2312yes—
121C23×C4×C61—21no—
122C23×C4×C61C2311yescharacteristic
123AGL(1,ℤ/8)×C61—216no—
124AGL(1,ℤ/8)×C61—28no—
125AGL(1,ℤ/8)×C61—28no—
126C2×SD16×C61—28no—
127C2×SD16×C61—24no—
128C2×D8×C61—28no—
129C2×D8×C61—24no—
130C2×M16×C61—22no—
131C2×M16×C61—21no—
132C2×M16×C61D414yescomplemented
133C2×M16×C61C2312yes—
134C22×C8×C61—21no—
135C24×C61—21no—
136C24×C61—24no—
137C24×C61—22no—
138C24×C61—44no—
139C24×C61—44no—
140C24×C61—41no—
141C24×C61—41no—
142C24×C61—42no—
143C24×C61C2×D411yescharacteristic
144C23×D61—21no—
145#41×C61—24no—
146#41×C61—24no—
147#41×C61—22no—
148#41×C61—22no—
149#41×C61—22no—
150#41×C61—22no—
151#41×C61—42no—
152#41×C61—42no—
153#41×C61—42no—
154#41×C61—42no—
155C2×Q8×C61—21no—
156C2×Q8×C61—22no—
157C2×Q8×C61—22no—
158C2×Q8×C61C2×D412yes—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—24no—
163C2×D4×C61—24no—
164C2×D4×C61—24no—
165C2×D4×C61—24no—
166C2×D4×C61—21no—
167C2×D4×C61—22no—
168C2×D4×C61—24no—
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61—22no—
173C2×D4×C61—22no—
174C2×D4×C61—42no—
175C2×D4×C61—42no—
176C2×D4×C61—41no—
177C2×D4×C61—41no—
178C2×D4×C61—42no—
179C2×D4×C61—42no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61C2×D412yes—
184C2×D4×C61C2×D414yescomplemented
185C22×C4×C61—21no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—42no—
189C22×C4×C61—42no—
190C22×C4×C61C2×D412yes—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D412yes—
197C22×C4×C61C2×D412yes—
198C22×C4×C61#4112yes—
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—28no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—84no—
206C22×Dic61—24no—
207C22×Dic61—21no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—42no—
212C22×Dic61—42no—
213C22×Dic61—44no—
214C22×Dic61C2×D414yes—
215#11758222—24no—
216#11758222—24no—
217#11758222—22no—
218#11758222—22no—
219#11758222—22no—
220#11758222—22no—
221#11758222—42no—
222#11758222—42no—
223#11758222—42no—
224#11758222—42no—
225C2×D244—22no—
226C2×D244—22no—
227C2×D244—21no—
228C2×D244C2×D412yes—
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×Dic122—22no—
234C2×Dic122—22no—
235C2×Dic122—21no—
236C2×Dic122C2×D412yes—
237SD16×C61—216no—
238D8×C61—216no—
239M16×C61—24no—
240M16×C61—22no—
241M16×C61C2×D414yescomplemented
242C2×C8×C61—24no—
243C2×C8×C61—22no—
244C22⋊Dic61—28no—
245C22⋊Dic61—416no—
246#11758200—216no—
247#11758199—216no—
248#11758198—28no—
249C4⋊Dic61—22no—
250C4⋊Dic61—22no—
251C4⋊Dic61—22no—
252C4⋊Dic61—22no—
253#11758196—28no—
254C4×Dic61—22no—
255C4×Dic61—22no—
256C4×Dic61—42no—
257#11758194—24no—
258#11758194—22no—
259#11758194C2×D414yescomplemented
260C2×#92418—24no—
261C2×#92418—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—24no—
266C23×C61—44no—
267C23×C61—44no—
268C23×C61—416no—
269C23×C61—42no—
270C23×C61—42no—
271C23×C61—42no—
272C23×C61—44no—
273C23×C61—44no—
274C23×C61—42no—
275C23×C61—42no—
276C23×C61—82no—
277C23×C61—82no—
278C23×C61—88no—
279C23×C61—82no—
280C23×C61—82no—
281C23×C61#12011yescharacteristic
282C23×C61#12011yescharacteristic
283C23×C61#12112yes—
284C23×C61#12712yes—
285C23×C61C22×D411yescharacteristic
286C22×D61—22no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—42no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—42no—
293D4×C61—24no—
294D4×C61—22no—
295D4×C61—24no—
296D4×C61—22no—
297D4×C61—42no—
298D4×C61—42no—
299D4×C61—44no—
300D4×C61—42no—
301D4×C61—42no—
302D4×C61—44no—
303D4×C61—44no—
304D4×C61—42no—
305C2×C4×C61—22no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—44no—
310C2×C4×C61#12012yes—
311C2×C4×C61#12012yes—
312C2×C4×C61#12012yes—
313C2×C4×C61#12012yes—
314C2×C4×C61#12011yescharacteristic
315C2×C4×C61#12011yescharacteristic
316C2×C4×C61#12112yes—
317C2×C4×C61#12112yes—
318C2×C4×C61#12112yes—
319C2×C4×C61#12112yes—
320C2×C4×C61#12112yes—
321C2×C4×C61#12712yes—
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C22⋊D61—42no—
329C22⋊D61—42no—
330C22⋊D61—44no—
331C22⋊D61—88no—
332C2×Dic61—24no—
333C2×Dic61—22no—
334C2×Dic61—24no—
335C2×Dic61—42no—
336C2×Dic61—48no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—44no—
340C2×Dic61—44no—
341C2×Dic61—82no—
342D244—22no—
343D244—22no—
344D244—42no—
345C4×D61—42no—
346C4×D61—42no—
347C4×D61—44no—
348Dic122—22no—
349Dic122—22no—
350Dic122—42no—
351C8×C61—24no—
352#92418—24no—
353C2×#2006—611nomaximal, Sylow
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—24no—
359C22×C61—24no—
360C22×C61—48no—
361C22×C61—42no—
362C22×C61—44no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—84no—
366C22×C61—88no—
367C22×C61—82no—
368C22×C61—82no—
369C22×C61—84no—
370C22×C61—88no—
371C22×C61#39212yes—
372C22×C61#39212yes—
373C22×C61#45312yes—
374C22×C61#45412yes—
375C22×C61C2×#12011yescharacteristic
376C22×C61C2×#12111yescharacteristic
377C22×C61C2×#12711yescharacteristic
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—84no—
382C4×C61—42no—
383C4×C61#39212yes—
384C4×C61#39212yes—
385C4×C61C2×#12011yescharacteristic
386C4×C61C2×#12011yescharacteristic
387C4×C61C2×#12111yescharacteristic
388C4×C61C2×#12111yescharacteristic
389Dic61—44no—
390Dic61—42no—
391Dic61—44no—
392C22×AGL(1,ℤ/8)—611no—
393C22×AGL(1,ℤ/8)D6111yescharacteristic, complemented
394C2×#537—611no—
395C22×#104—611no—
396C22×#104—611no—
397C2×#390—611no—
398#2006—618no—
399C2×#343—611no—
400C2×C61—21no—
401C2×C61—21no—
402C2×C61—22no—
403C2×C61—82no—
404C2×C61—84no—
405C2×C61#200614yescomplemented
406C2×C61C2×#39211yescharacteristic
407C2×C61C2×#45311yescharacteristic
408C2×C61C2×#45411yescharacteristic
409D61—82no—
410C22×#41—611no—
411C22×#41C2×D6111yescharacteristic
412C23×D4C2×D6111yescharacteristic
413C2×AGL(1,ℤ/8)—22no—
414C2×AGL(1,ℤ/8)—24no—
415C2×AGL(1,ℤ/8)—24no—
416C2×AGL(1,ℤ/8)—614no—
417C2×AGL(1,ℤ/8)—1224no—
418C2×AGL(1,ℤ/8)—1222no—
419C2×AGL(1,ℤ/8)—1224no—
420C2×AGL(1,ℤ/8)C2×D6114yescomplemented
421C22×SD16—21no—
422C22×SD16—1221no—
423C22×D8—21no—
424C22×D8—1221no—
425C22×M16—611no—
426C22×M16C2×D6111yescharacteristic
427#537—614no—
428#537—1222no—
429#537—1222no—
430#537—1222no—
431C2×C22⋊Q8—1221no—
432C2×C22⋊Q8—1221no—
433C2×#121—1221no—
434C2×#121—1222no—
435C2×#121—1221no—
436C22×C4⋊C4—611no—
437C22×C22⋊C4—1222no—
438C22×C42—611no—
439C2×#104—614no—
440C2×#104—614no—
441C2×#104—1224no—
442C2×#104—1224no—
443#390—614no—
444#390—1222no—
445#343—614no—
446C61C2×#200611yescharacteristic, complemented, Sylow
447C25—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—612no—
455C2×#41—612no—
456C2×#41—1221no—
457C2×#41—1221no—
458C2×#41—1222no—
459C2×#41—1222no—
460C2×#41—1222no—
461C2×#41—1222no—
462C2×#41C22⋊D6112yes—
463C2×#41C22×D6112yes—
464C22×Q8—611no—
465C22×Q8C22⋊D6111yescharacteristic
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—22no—
475C22×D4—611no—
476C22×D4—1222no—
477C22×D4—1221no—
478C22×D4C22⋊D6111yescharacteristic
479C22×D4C22⋊D6114yescomplemented
480C22×D4C22×D6112yes—
481C23×C4—21no—
482C23×C4—612no—
483C23×C4—1221no—
484C23×C4—1221no—
485C23×C4C22×D6111yescharacteristic
486AGL(1,ℤ/8)—216no—
487AGL(1,ℤ/8)—28no—
488AGL(1,ℤ/8)—28no—
489AGL(1,ℤ/8)—1228no—
490AGL(1,ℤ/8)—12216no—
491AGL(1,ℤ/8)—1228no—
492C2×SD16—28no—
493C2×SD16—24no—
494C2×SD16—1224no—
495C2×SD16—1228no—
496C2×D8—28no—
497C2×D8—24no—
498C2×D8—1224no—
499C2×D8—1228no—
500C2×M16—21no—
501C2×M16—22no—
502C2×M16—614no—
503C2×M16—612no—
504C2×M16—1221no—
505C2×M16—1222no—
506C2×M16C22⋊D6114yescomplemented
507C2×M16C22×D6112yes—
508C22×C8—21no—
509C22×C8—1221no—
510C22⋊Q8—1224no—
511C22⋊Q8—1224no—
512C22⋊Q8—1224no—
513C22⋊Q8—1224no—
514#121—1224no—
515#121—1224no—
516#121—1228no—
517#121—1224no—
518#121—1228no—
519#121—1224no—
520C2×C4⋊C4—612no—
521C2×C4⋊C4—612no—
522C2×C4⋊C4—1222no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C22⋊C4—1222no—
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—1228no—
530C2×C22⋊C4—2448no—
531C2×C42—612no—
532C2×C42—1222no—
533C2×C42—1222no—
534C2×C42—1221no—
535#104—1228no—
536#104—1228no—
537C24—22no—
538C24—21no—
539C24—24no—
540C24—44no—
541C24—44no—
542C24—41no—
543C24—41no—
544C24—42no—
545C24—1221no—
546C24D4×D6111yescharacteristic
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—24no—
552#41—24no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—42no—
557#41—1222no—
558#41—1222no—
559#41—1222no—
560#41—1222no—
561#41—1224no—
562#41—1224no—
563#41—2442no—
564#41—2442no—
565#41—2442no—
566#41—2442no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—612no—
571C2×Q8—1221no—
572C2×Q8—1222no—
573C2×Q8—1222no—
574C2×Q8C2×C22⋊D6112yes—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—612no—
600C2×D4—1228no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1221no—
605C2×D4—1222no—
606C2×D4—4884no—
607C2×D4—2442no—
608C2×D4—2442no—
609C2×D4C2×C22⋊D6112yes—
610C2×D4C2×C22⋊D6114yescomplemented
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—614no—
617C22×C4—1222no—
618C22×C4—1224no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1221no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—2444no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4D4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4D4×D6112yes—
632C22×C4D4×D6111yescharacteristic
633C22×C4#1175822412yes—
634C22×C4C2×C22⋊D6112yes—
635C22×C4C2×C22⋊D6111yescharacteristic
636C22×C4C2×C22⋊D6111yescharacteristic
637C22×C4C2×C22⋊D6112yes—
638C22×C4C23×D6111yescharacteristic
639SD16—216no—
640SD16—12216no—
641D8—216no—
642D8—12216no—
643M16—22no—
644M16—24no—
645M16—614no—
646M16—1222no—
647M16—1224no—
648M16C2×C22⋊D6114yescomplemented
649C2×C8—22no—
650C2×C8—24no—
651C2×C8—1222no—
652C2×C8—1224no—
653C4⋊C4—1228no—
654C4⋊C4—1222no—
655C4⋊C4—1222no—
656C4⋊C4—1222no—
657C4⋊C4—1222no—
658C22⋊C4—1228no—
659C22⋊C4—1228no—
660C22⋊C4—24416no—
661C42—1222no—
662C42—1222no—
663C42—2442no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—44no—
669C23—44no—
670C23—416no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—44no—
675C23—44no—
676C23—42no—
677C23—42no—
678C23—82no—
679C23—82no—
680C23—88no—
681C23—82no—
682C23—82no—
683C23—1222no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23#1451974511yescharacteristic
688C23#1451974511yescharacteristic
689C23#1451974912yes—
690C23#1451977312yes—
691C23C2×D4×D6111yescharacteristic
692Q8—22no—
693Q8—22no—
694Q8—42no—
695Q8—1222no—
696Q8—1222no—
697Q8—2442no—
698D4—24no—
699D4—22no—
700D4—24no—
701D4—22no—
702D4—42no—
703D4—42no—
704D4—44no—
705D4—42no—
706D4—42no—
707D4—44no—
708D4—44no—
709D4—42no—
710D4—1222no—
711D4—1222no—
712D4—4888no—
713D4—2442no—
714D4—2442no—
715D4—2444no—
716D4—2442no—
717C2×C4—22no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—1224no—
723C2×C4—1224no—
724C2×C4—1222no—
725C2×C4—4882no—
726C2×C4—2442no—
727C2×C4—2448no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2444no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2444no—
734C2×C4—2444no—
735C2×C4#1451974512yes—
736C2×C4#1451974512yes—
737C2×C4#1451974511yescharacteristic
738C2×C4#1451974511yescharacteristic
739C2×C4#1451974612yes—
740C2×C4#1451974612yes—
741C2×C4#1451974812yes—
742C2×C4#1451974812yes—
743C2×C4#1451974912yes—
744C2×C4#1451974912yes—
745C2×C4#1451974912yes—
746C2×C4#1451977312yes—
747C2×C4C2×D4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4C22×C22⋊D6111yescharacteristic
750C2×C4C22×C22⋊D6111yescharacteristic
751C2×C4C22×C22⋊D6111yescharacteristic
752C2×C4C2×#1175822411yescharacteristic
753C8—24no—
754C8—1224no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—24no—
760C22—24no—
761C22—48no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—84no—
767C22—88no—
768C22—82no—
769C22—82no—
770C22—84no—
771C22—88no—
772C22—4884no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22#1683967012yes—
777C22#1683967012yes—
778C22#1683992812yes—
779C22#1683993312yes—
780C22C2×#1451974511yescharacteristic
781C22C2×#1451974911yescharacteristic
782C22C2×#1451977311yescharacteristic
783C4—42no—
784C4—2444no—
785C4—2444no—
786C4—2442no—
787C4#1683967012yes—
788C4#1683967012yes—
789C4C2×#1451974511yescharacteristic
790C4C2×#1451974611yescharacteristic
791C4C2×#1451974811yescharacteristic
792C4C2×#1451974911yescharacteristic
793C2—21no—
794C2—21no—
795C2—22no—
796C2—84no—
797C2—82no—
798C2—4882no—
799C2#2144685914yesdirect product factor
800C2C2×#1683967011yescharacteristic
801C2C2×#1683992811yescharacteristic
802C2C2×#1683993311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×AGL(1,ℤ/8)×C61C2
socleC23×C61#120
hypercenterC22×AGL(1,ℤ/8)D61
hypocenterC61C2×#2006
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#14519803C2semidirect
2. C2×#16840340C2semidirect
3. C22×#14519704C2semidirect
4. C22×#14519703C2semidirect
5. C2×#16839665C2semidirect
6. #21446859C2direct (N × H)
7. C2×#16839530C2semidirect
8. C22×AGL(1,ℤ/8)×C61C2semidirect
13. C2×#14519803C22semidirect
20. #16840340C22semidirect
30. C2×#14519704C22semidirect
32. C2×#14519703C22semidirect
34. #16839665C22semidirect
35. #16839530C22semidirect
41. C2×AGL(1,ℤ/8)×C61C22semidirect
69. C2×#11758194D4semidirect
119. C22×D4×C61D4semidirect
132. C2×M16×C61D4semidirect
184. C2×D4×C61C2×D4semidirect
241. M16×C61C2×D4semidirect
259. #11758194C2×D4semidirect
393. C22×AGL(1,ℤ/8)D61semidirect
405. C2×C61#2006semidirect
420. C2×AGL(1,ℤ/8)C2×D61semidirect
446. C61C2×#2006semidirect
479. C22×D4C22⋊D61semidirect
506. C2×M16C22⋊D61semidirect
610. C2×D4C2×C22⋊D61semidirect
648. M16C2×C22⋊D61semidirect
799. C2#21446859direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198032
C2×#168403402
C22×#145197042
C22×#145197032
C2×#168396652
#214468592
C2×#168395302
C22×AGL(1,ℤ/8)×C612
C2×#200661