Finite Group Databasebeta

← C2×#21446870 #29707004

Subgroups — C2×#21446870 #29707004

Order 15616.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic, complemented
2C2×#16840329C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic, complemented
4C2×#16839767C211yesmaximal, characteristic, complemented
5C2×#16839736C211yesmaximal, characteristic, complemented
6#21446870C218yesmaximal, direct product factor
7C2×#16839534C211yesmaximal, characteristic, complemented
8C22×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840560—22no—
11#16840560—22no—
12#16840560—22no—
13#16840560C2214yescomplemented
14C2×#14519808—21no—
15C2×#14519807—21no—
16C2×#14519803—21no—
17C2×#14519802—21no—
18C2×#14519797—22no—
19C22×#11758194C2211yescharacteristic
20#16840329—22no—
21#16840329—22no—
22#16840329—22no—
23#16840329C2214yescomplemented
24C2×#14519773—21no—
25C2×#14519764—21no—
26C2×#14519748—22no—
27C2×#14519746—22no—
28C2×#14519736C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30#16839778—22no—
31#16839778C2214yescomplemented
32C2×#14519703—22no—
33#16839767—22no—
34#16839767C2214yescomplemented
35C2×#14519698—22no—
36#16839736—22no—
37#16839736C2214yescomplemented
38C2×#14519692—22no—
39#16839534C2214yescomplemented
40C22×#41×C61C2211yescharacteristic
41C23×D4×C61C2211yescharacteristic
42C2×AGL(1,ℤ/8)×C61—22no—
43C2×AGL(1,ℤ/8)×C61—22no—
44C2×AGL(1,ℤ/8)×C61—22no—
45C2×AGL(1,ℤ/8)×C61—22no—
46C2×AGL(1,ℤ/8)×C61—22no—
47C2×AGL(1,ℤ/8)×C61C2214yescomplemented
48C22×SD16×C61—21no—
49C22×D8×C61—21no—
50C22×M16×C61C2211yescharacteristic
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222D412yes—
62C2×#11758222C2312yes—
63C22×Dic122D411yescharacteristic
64C22×D244D411yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—24no—
67C22×C4×D61—21no—
68#14519808—24no—
69#14519808—24no—
70#14519807—24no—
71#14519807—24no—
72#14519803—24no—
73#14519803—24no—
74#14519802—24no—
75#14519802—24no—
76#14519797—28no—
77#14519797—28no—
78C2×#11758202—22no—
79C2×#11758200—22no—
80C2×#11758201—22no—
81C2×#11758199—22no—
82C2×#11758194—21no—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194D412yescomplemented
87C2×#11758194C2312yes—
88C22×#92418D412yescomplemented
89#14519773—24no—
90#14519773—24no—
91#14519764—24no—
92#14519764—24no—
93#14519748—28no—
94#14519748—28no—
95#14519746—28no—
96#14519746—28no—
97#14519736—21no—
98#14519736—21no—
99#14519736—21no—
100#14519736—21no—
101#14519736—21no—
102#14519736D412yes—
103#14519736C2312yes—
104#14519736C2312yes—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61—21no—
107C2×C22⋊Dic61—24no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61D412yes—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112#14519703—28no—
113#14519698—28no—
114#14519692—28no—
115C25×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×#41×C61—21no—
119C2×#41×C61—21no—
120C2×#41×C61—21no—
121C2×#41×C61—21no—
122C2×#41×C61—21no—
123C2×#41×C61—21no—
124C2×#41×C61—21no—
125C2×#41×C61—21no—
126C2×#41×C61D412yescomplemented
127C2×#41×C61C2312yes—
128C22×Q8×C61D411yescharacteristic, complemented
129C22×D4×C61—21no—
130C22×D4×C61—21no—
131C22×D4×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61—21no—
134C22×D4×C61—21no—
135C22×D4×C61—21no—
136C22×D4×C61—21no—
137C22×D4×C61—21no—
138C22×D4×C61—21no—
139C22×D4×C61—21no—
140C22×D4×C61—21no—
141C22×D4×C61D412yes—
142C22×D4×C61D412yes—
143C22×D4×C61D411yescharacteristic, complemented
144C22×D4×C61C2312yes—
145C23×C4×C61—21no—
146C23×C4×C61C2311yescharacteristic
147AGL(1,ℤ/8)×C61—28no—
148AGL(1,ℤ/8)×C61—28no—
149AGL(1,ℤ/8)×C61—28no—
150AGL(1,ℤ/8)×C61—28no—
151C2×SD16×C61—24no—
152C2×SD16×C61—24no—
153C2×SD16×C61—24no—
154C2×D8×C61—24no—
155C2×D8×C61—24no—
156C2×D8×C61—24no—
157C2×M16×C61—21no—
158C2×M16×C61—21no—
159C2×M16×C61—21no—
160C2×M16×C61D412yescomplemented
161C2×M16×C61D412yescomplemented
162C2×M16×C61C2312yes—
163C22×C8×C61—21no—
164C24×C61—22no—
165C24×C61—22no—
166C24×C61—21no—
167C24×C61—22no—
168C24×C61—41no—
169C24×C61—41no—
170C24×C61—41no—
171C24×C61—41no—
172C24×C61—84no—
173C24×C61C2×D411yescharacteristic
174C23×D61—21no—
175#41×C61—22no—
176#41×C61—22no—
177#41×C61—22no—
178#41×C61—22no—
179#41×C61—22no—
180#41×C61—22no—
181#41×C61—22no—
182#41×C61—22no—
183#41×C61—41no—
184#41×C61—41no—
185#41×C61—41no—
186#41×C61—41no—
187#41×C61—41no—
188#41×C61—41no—
189#41×C61—41no—
190#41×C61—41no—
191C2×Q8×C61—21no—
192C2×Q8×C61—21no—
193C2×Q8×C61—21no—
194C2×Q8×C61—21no—
195C2×Q8×C61—21no—
196C2×Q8×C61C2×D412yescomplemented
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—22no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61—22no—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61—21no—
214C2×D4×C61—22no—
215C2×D4×C61—22no—
216C2×D4×C61—22no—
217C2×D4×C61—22no—
218C2×D4×C61—22no—
219C2×D4×C61—41no—
220C2×D4×C61—41no—
221C2×D4×C61—41no—
222C2×D4×C61—41no—
223C2×D4×C61—41no—
224C2×D4×C61—41no—
225C2×D4×C61—41no—
226C2×D4×C61—41no—
227C2×D4×C61—41no—
228C2×D4×C61—41no—
229C2×D4×C61—41no—
230C2×D4×C61—41no—
231C2×D4×C61—41no—
232C2×D4×C61—41no—
233C2×D4×C61—41no—
234C2×D4×C61—41no—
235C2×D4×C61C2×D414yes—
236C2×D4×C61C2×D412yescomplemented
237C22×C4×C61—21no—
238C22×C4×C61—22no—
239C22×C4×C61—22no—
240C22×C4×C61—41no—
241C22×C4×C61—41no—
242C22×C4×C61—41no—
243C22×C4×C61—41no—
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61#4111yescharacteristic
256C22×C4×C61#4111yescharacteristic
257C22×C4×C61C2411yescharacteristic
258C2×C22⋊D61—22no—
259C2×C22⋊D61—22no—
260C2×C22⋊D61—216no—
261C2×C22⋊D61—41no—
262C2×C22⋊D61—41no—
263C2×C22⋊D61—41no—
264C2×C22⋊D61—41no—
265C2×C22⋊D61—88no—
266C22×Dic61—21no—
267C22×Dic61—22no—
268C22×Dic61—41no—
269#11758222—22no—
270#11758222—22no—
271#11758222—22no—
272#11758222—22no—
273#11758222—22no—
274#11758222—22no—
275#11758222—22no—
276#11758222—22no—
277#11758222—41no—
278#11758222—41no—
279#11758222—41no—
280#11758222—41no—
281#11758222—41no—
282#11758222—41no—
283#11758222—41no—
284#11758222—41no—
285C2×D244—21no—
286C2×D244—21no—
287C2×D244—21no—
288C2×D244—21no—
289C2×D244—21no—
290C2×D244C2×D412yes—
291C2×C4×D61—22no—
292C2×C4×D61—22no—
293C2×C4×D61—41no—
294C2×C4×D61—41no—
295C2×C4×D61—41no—
296C2×C4×D61—41no—
297C2×Dic122—21no—
298C2×Dic122—21no—
299C2×Dic122—21no—
300C2×Dic122—21no—
301C2×Dic122—21no—
302C2×Dic122C2×D412yes—
303SD16×C61—216no—
304D8×C61—216no—
305M16×C61—22no—
306M16×C61—22no—
307M16×C61—22no—
308M16×C61C2×D414yescomplemented
309C2×C8×C61—22no—
310C2×C8×C61—22no—
311C2×C8×C61—22no—
312C22⋊Dic61—216no—
313C22⋊Dic61—22no—
314C22⋊Dic61—22no—
315C22⋊Dic61—41no—
316C22⋊Dic61C2×D414yes—
317#11758202—28no—
318#11758201—28no—
319#11758200—28no—
320#11758199—28no—
321C4⋊Dic61—22no—
322C4⋊Dic61—22no—
323C4⋊Dic61—22no—
324C4⋊Dic61—41no—
325C4×Dic61—22no—
326C4×Dic61—22no—
327C4×Dic61—22no—
328C4×Dic61—41no—
329#11758194—22no—
330#11758194—22no—
331#11758194—22no—
332#11758194—22no—
333C2×#92418—22no—
334C2×#92418—22no—
335C2×#92418C2×D414yescomplemented
336C23×C61—24no—
337C23×C61—22no—
338C23×C61—42no—
339C23×C61—48no—
340C23×C61—42no—
341C23×C61—42no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—42no—
345C23×C61—42no—
346C23×C61—42no—
347C23×C61—42no—
348C23×C61—84no—
349C23×C61—84no—
350C23×C61—82no—
351C23×C61—84no—
352C23×C61—84no—
353C23×C61—84no—
354C23×C61—84no—
355C23×C61#12011yescharacteristic
356C23×C61#12011yescharacteristic
357C23×C61#12111yescharacteristic
358C23×C61#12111yescharacteristic
359C23×C61#12711yescharacteristic
360C23×C61#12711yescharacteristic
361C23×C61C22×D411yescharacteristic
362C22×D61—22no—
363C22×D61—44no—
364C22×D61—41no—
365C22×D61—41no—
366Q8×C61—22no—
367Q8×C61—22no—
368Q8×C61—41no—
369Q8×C61—41no—
370D4×C61—22no—
371D4×C61—22no—
372D4×C61—24no—
373D4×C61—24no—
374D4×C61—42no—
375D4×C61—42no—
376D4×C61—42no—
377D4×C61—42no—
378D4×C61—42no—
379D4×C61—42no—
380D4×C61—42no—
381D4×C61—42no—
382D4×C61—42no—
383D4×C61—42no—
384D4×C61—41no—
385D4×C61—41no—
386C2×C4×C61—22no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—42no—
390C2×C4×C61—42no—
391C2×C4×C61—42no—
392C2×C4×C61—42no—
393C2×C4×C61#12011yescharacteristic
394C2×C4×C61#12011yescharacteristic
395C2×C4×C61#12011yescharacteristic
396C2×C4×C61#12011yescharacteristic
397C2×C4×C61#12011yescharacteristic
398C2×C4×C61#12011yescharacteristic
399C2×C4×C61#12011yescharacteristic
400C2×C4×C61#12011yescharacteristic
401C2×C4×C61#12011yescharacteristic
402C2×C4×C61#12011yescharacteristic
403C2×C4×C61#12111yescharacteristic
404C2×C4×C61#12111yescharacteristic
405C2×C4×C61#12111yescharacteristic
406C2×C4×C61#12111yescharacteristic
407C2×C4×C61#12111yescharacteristic
408C2×C4×C61#12111yescharacteristic
409C2×C4×C61#12111yescharacteristic
410C2×C4×C61#12111yescharacteristic
411C2×C4×C61#12111yescharacteristic
412C2×C4×C61#12111yescharacteristic
413C2×C4×C61#12711yescharacteristic
414C2×C4×C61#12711yescharacteristic
415C2×C4×C61C22×D411yescharacteristic
416C2×C4×C61C22×D411yescharacteristic
417C2×C4×C61C22×D411yescharacteristic
418C2×C4×C61C22×D411yescharacteristic
419C2×C4×C61C22×D411yescharacteristic
420C2×C4×C61C2×#4111yescharacteristic
421C22⋊D61—42no—
422C22⋊D61—42no—
423C22⋊D61—42no—
424C22⋊D61—42no—
425C22⋊D61—816no—
426C2×Dic61—24no—
427C2×Dic61—22no—
428C2×Dic61—44no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—42no—
432C2×Dic61—82no—
433D244—22no—
434D244—22no—
435D244—41no—
436D244—41no—
437C4×D61—42no—
438C4×D61—42no—
439C4×D61—42no—
440C4×D61—42no—
441Dic122—22no—
442Dic122—22no—
443Dic122—41no—
444Dic122—41no—
445C8×C61—24no—
446#92418—24no—
447C2×#2008—611nomaximal, Sylow
448C22×C61—22no—
449C22×C61—22no—
450C22×C61—22no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—48no—
456C22×C61—42no—
457C22×C61—44no—
458C22×C61—82no—
459C22×C61—84no—
460C22×C61—82no—
461C22×C61—84no—
462C22×C61—84no—
463C22×C61—84no—
464C22×C61—84no—
465C22×C61—84no—
466C22×C61—82no—
467C22×C61#39211yescharacteristic
468C22×C61#39211yescharacteristic
469C22×C61#39211yescharacteristic
470C22×C61#39211yescharacteristic
471C22×C61C2×#12011yescharacteristic
472C22×C61C2×#12111yescharacteristic
473C22×C61C2×#12711yescharacteristic
474C2×D61—44no—
475C2×D61—42no—
476C2×D61—82no—
477C2×D61—82no—
478C4×C61—42no—
479C4×C61#39211yescharacteristic
480C4×C61#39211yescharacteristic
481C4×C61#39211yescharacteristic
482C4×C61#39211yescharacteristic
483C4×C61C2×#12011yescharacteristic
484C4×C61C2×#12011yescharacteristic
485C4×C61C2×#12111yescharacteristic
486C4×C61C2×#12111yescharacteristic
487Dic61—44no—
488Dic61—42no—
489Dic61—82no—
490C2×#575—611no—
491C22×AGL(1,ℤ/8)D6111yescharacteristic, complemented
492C2×#535—611no—
493C2×#421—611no—
494C2×#418—611no—
495C2×#410—611no—
496#2008—618no—
497C2×#344—611no—
498C2×C61—21no—
499C2×C61—21no—
500C2×C61—21no—
501C2×C61—21no—
502C2×C61—21no—
503C2×C61—21no—
504C2×C61—84no—
505C2×C61—82no—
506C2×C61#200812yescomplemented
507C2×C61C2×#39211yescharacteristic
508D61—82no—
509C22×#41—611no—
510C22×#41C2×D6111yescharacteristic
511C23×D4C2×D6111yescharacteristic
512#575—614no—
513#575—1222no—
514#575—1222no—
515#575—1222no—
516C2×#137—1221no—
517C2×#137—1221no—
518C2×AGL(1,ℤ/8)—22no—
519C2×AGL(1,ℤ/8)—22no—
520C2×AGL(1,ℤ/8)—22no—
521C2×AGL(1,ℤ/8)—22no—
522C2×AGL(1,ℤ/8)—22no—
523C2×AGL(1,ℤ/8)—1221no—
524C2×AGL(1,ℤ/8)—1221no—
525C2×AGL(1,ℤ/8)C2×D6114yescomplemented
526C2×#135—1222no—
527C22×SD16—21no—
528C22×D8—21no—
529C22×M16—611no—
530C22×M16C2×D6111yescharacteristic
531#535—614no—
532#535—1222no—
533#535—1222no—
534#535—1222no—
535C2×#127—1221no—
536C2×#124—1221no—
537C2×#121—1222no—
538C2×#120—1222no—
539C2×#117—611no—
540C2×#117—611no—
541#421—614no—
542#421—1222no—
543C2×#104—1222no—
544#418—614no—
545#418—1222no—
546C2×#102—1222no—
547#410—614no—
548#410—1222no—
549C2×#99—1222no—
550#344—614no—
551C61C2×#200811yescharacteristic, complemented, Sylow
552C25—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—612no—
564C2×#41—612no—
565C2×#41—1221no—
566C2×#41—1221no—
567C2×#41—1221no—
568C2×#41—1221no—
569C2×#41—1221no—
570C2×#41—1221no—
571C2×#41—1221no—
572C2×#41—1221no—
573C2×#41—1221no—
574C2×#41—1221no—
575C2×#41C22⋊D6112yescomplemented
576C2×#41C22×D6112yes—
577C22×Q8—611no—
578C22×Q8C22⋊D6111yescharacteristic, complemented
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—611no—
592C22×D4—1224no—
593C22×D4—1221no—
594C22×D4C22⋊D6112yes—
595C22×D4C22⋊D6112yes—
596C22×D4C22⋊D6111yescharacteristic, complemented
597C22×D4C22×D6112yes—
598C23×C4—21no—
599C23×C4—1221no—
600C23×C4C22×D6111yescharacteristic
601#137—1224no—
602#137—1224no—
603#137—1224no—
604#137—1224no—
605AGL(1,ℤ/8)—28no—
606AGL(1,ℤ/8)—28no—
607AGL(1,ℤ/8)—28no—
608AGL(1,ℤ/8)—28no—
609AGL(1,ℤ/8)—1224no—
610AGL(1,ℤ/8)—1224no—
611AGL(1,ℤ/8)—1224no—
612AGL(1,ℤ/8)—1224no—
613#135—1228no—
614#135—1228no—
615C2×Q16—1222no—
616C2×SD16—24no—
617C2×SD16—24no—
618C2×SD16—24no—
619C2×SD16—1222no—
620C2×SD16—1222no—
621C2×D8—24no—
622C2×D8—24no—
623C2×D8—24no—
624C2×D8—1222no—
625C2×M16—21no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16—612no—
629C2×M16—612no—
630C2×M16—1221no—
631C2×M16—1221no—
632C2×M16—1221no—
633C2×M16—1221no—
634C2×M16C22⋊D6112yescomplemented
635C2×M16C22⋊D6112yescomplemented
636C2×M16C22×D6112yes—
637C22×C8—21no—
638C22×C8—612no—
639#127—1224no—
640#127—1224no—
641#124—1224no—
642#124—1224no—
643#121—1228no—
644#121—1228no—
645#120—1228no—
646#120—1228no—
647#117—612no—
648#117—612no—
649#117—612no—
650#117—1221no—
651#117—1221no—
652#117—1221no—
653#117—1221no—
654#117—1221no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4—1221no—
657C2×C22⋊C4—612no—
658C2×C22⋊C4—1224no—
659C2×C22⋊C4—1221no—
660C2×C42—1221no—
661C2×C42—1221no—
662#104—1228no—
663#102—1228no—
664#99—1228no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—21no—
669C24—41no—
670C24—41no—
671C24—41no—
672C24—41no—
673C24—84no—
674C24—1221no—
675C24D4×D6111yescharacteristic
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—22no—
684#41—41no—
685#41—41no—
686#41—41no—
687#41—41no—
688#41—41no—
689#41—41no—
690#41—41no—
691#41—41no—
692#41—1222no—
693#41—1222no—
694#41—1222no—
695#41—1222no—
696#41—1222no—
697#41—1222no—
698#41—1222no—
699#41—1222no—
700#41—2441no—
701#41—2441no—
702#41—2441no—
703#41—2441no—
704#41—2441no—
705#41—2441no—
706#41—2441no—
707#41—2441no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—612no—
714C2×Q8—1221no—
715C2×Q8—1221no—
716C2×Q8—1221no—
717C2×Q8—1221no—
718C2×Q8—1221no—
719C2×Q8C2×C22⋊D6112yescomplemented
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—21no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4—41no—
745C2×D4—41no—
746C2×D4—41no—
747C2×D4—41no—
748C2×D4—41no—
749C2×D4—41no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—612no—
759C2×D4—12216no—
760C2×D4—1222no—
761C2×D4—1222no—
762C2×D4—1221no—
763C2×D4—1221no—
764C2×D4—1221no—
765C2×D4—1221no—
766C2×D4—1221no—
767C2×D4—4888no—
768C2×D4—2441no—
769C2×D4—2441no—
770C2×D4—2441no—
771C2×D4—2441no—
772C2×D4C2×C22⋊D6114yes—
773C2×D4C2×C22⋊D6112yescomplemented
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—41no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—41no—
781C22×C4—1222no—
782C22×C4—1221no—
783C22×C4—1222no—
784C22×C4—1222no—
785C22×C4—2441no—
786C22×C4—2441no—
787C22×C4—2441no—
788C22×C4—2441no—
789C22×C4—2441no—
790C22×C4D4×D6111yescharacteristic
791C22×C4D4×D6111yescharacteristic
792C22×C4D4×D6111yescharacteristic
793C22×C4D4×D6111yescharacteristic
794C22×C4D4×D6111yescharacteristic
795C22×C4#1175822411yescharacteristic
796C22×C4#1175822411yescharacteristic
797C22×C4C2×C22⋊D6111yescharacteristic
798C22×C4C2×C22⋊D6111yescharacteristic
799C22×C4C2×C22⋊D6111yescharacteristic
800C22×C4C2×C22⋊D6111yescharacteristic
801C22×C4C2×C22⋊D6111yescharacteristic
802C22×C4C2×C22⋊D6111yescharacteristic
803C22×C4C23×D6111yescharacteristic
804Q16—1228no—
805SD16—216no—
806SD16—1228no—
807SD16—1228no—
808D8—216no—
809D8—1228no—
810M16—22no—
811M16—22no—
812M16—22no—
813M16—1222no—
814M16—1222no—
815M16—1222no—
816M16—1222no—
817M16C2×C22⋊D6114yescomplemented
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—22no—
821C2×C8—614no—
822C2×C8—1222no—
823C2×C8—1222no—
824C4⋊C4—1222no—
825C4⋊C4—1222no—
826C4⋊C4—1222no—
827C4⋊C4—2441no—
828C22⋊C4—614no—
829C22⋊C4—12216no—
830C22⋊C4—1222no—
831C22⋊C4—1222no—
832C22⋊C4—2441no—
833C42—1222no—
834C42—1222no—
835C42—1222no—
836C42—2441no—
837C23—24no—
838C23—22no—
839C23—42no—
840C23—48no—
841C23—42no—
842C23—42no—
843C23—41no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—41no—
848C23—42no—
849C23—82no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23—84no—
856C23—1222no—
857C23—2444no—
858C23—2441no—
859C23—2441no—
860C23#1451974511yescharacteristic
861C23#1451974511yescharacteristic
862C23#1451974911yescharacteristic
863C23#1451974911yescharacteristic
864C23#1451977311yescharacteristic
865C23#1451977311yescharacteristic
866C23C2×D4×D6111yescharacteristic
867Q8—22no—
868Q8—22no—
869Q8—41no—
870Q8—41no—
871Q8—1222no—
872Q8—1222no—
873Q8—2441no—
874Q8—2441no—
875D4—22no—
876D4—22no—
877D4—24no—
878D4—24no—
879D4—42no—
880D4—42no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—41no—
890D4—41no—
891D4—1222no—
892D4—1222no—
893D4—48816no—
894D4—2442no—
895D4—2442no—
896D4—2442no—
897D4—2442no—
898D4—2441no—
899D4—2441no—
900C2×C4—22no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—1224no—
908C2×C4—1222no—
909C2×C4—4882no—
910C2×C4—2442no—
911C2×C4—2444no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2442no—
915C2×C4—2442no—
916C2×C4—2442no—
917C2×C4—2442no—
918C2×C4#1451974511yescharacteristic
919C2×C4#1451974511yescharacteristic
920C2×C4#1451974511yescharacteristic
921C2×C4#1451974511yescharacteristic
922C2×C4#1451974511yescharacteristic
923C2×C4#1451974511yescharacteristic
924C2×C4#1451974611yescharacteristic
925C2×C4#1451974611yescharacteristic
926C2×C4#1451974611yescharacteristic
927C2×C4#1451974611yescharacteristic
928C2×C4#1451974811yescharacteristic
929C2×C4#1451974811yescharacteristic
930C2×C4#1451974811yescharacteristic
931C2×C4#1451974811yescharacteristic
932C2×C4#1451974911yescharacteristic
933C2×C4#1451974911yescharacteristic
934C2×C4#1451974911yescharacteristic
935C2×C4#1451974911yescharacteristic
936C2×C4#1451974911yescharacteristic
937C2×C4#1451974911yescharacteristic
938C2×C4#1451977311yescharacteristic
939C2×C4#1451977311yescharacteristic
940C2×C4C2×D4×D6111yescharacteristic
941C2×C4C2×D4×D6111yescharacteristic
942C2×C4C22×C22⋊D6111yescharacteristic
943C2×C4C22×C22⋊D6111yescharacteristic
944C2×C4C22×C22⋊D6111yescharacteristic
945C2×C4C2×#1175822411yescharacteristic
946C8—24no—
947C8—1224no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—48no—
956C22—42no—
957C22—44no—
958C22—82no—
959C22—84no—
960C22—82no—
961C22—84no—
962C22—84no—
963C22—84no—
964C22—84no—
965C22—84no—
966C22—82no—
967C22—4882no—
968C22—4882no—
969C22—2444no—
970C22—2442no—
971C22#1683967011yescharacteristic
972C22#1683967011yescharacteristic
973C22#1683967011yescharacteristic
974C22#1683967011yescharacteristic
975C22C2×#1451974511yescharacteristic
976C22C2×#1451974911yescharacteristic
977C22C2×#1451977311yescharacteristic
978C4—42no—
979C4—4882no—
980C4—2444no—
981C4—2442no—
982C4#1683967011yescharacteristic
983C4#1683967011yescharacteristic
984C4#1683967011yescharacteristic
985C4#1683967011yescharacteristic
986C4C2×#1451974511yescharacteristic
987C4C2×#1451974611yescharacteristic
988C4C2×#1451974811yescharacteristic
989C4C2×#1451974911yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—84no—
997C2—82no—
998C2—4882no—
999C2#2144687012yesdirect product factor
1000C2C2×#1683967011yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×AGL(1,ℤ/8)×C61C2
socleC22×C61#392
hypercenterC22×AGL(1,ℤ/8)D61
hypocenterC61C2×#2008
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#16840560C2semidirect
2. C2×#16840329C2semidirect
3. C2×#16839778C2semidirect
4. C2×#16839767C2semidirect
5. C2×#16839736C2semidirect
6. #21446870C2direct (N × H)
7. C2×#16839534C2semidirect
8. C22×AGL(1,ℤ/8)×C61C2semidirect
13. #16840560C22semidirect
23. #16840329C22semidirect
31. #16839778C22semidirect
34. #16839767C22semidirect
37. #16839736C22semidirect
39. #16839534C22semidirect
47. C2×AGL(1,ℤ/8)×C61C22semidirect
86. C2×#11758194D4semidirect
88. C22×#92418D4semidirect
126. C2×#41×C61D4semidirect
128. C22×Q8×C61D4semidirect
143. C22×D4×C61D4semidirect
160. C2×M16×C61D4semidirect
161. C2×M16×C61D4semidirect
196. C2×Q8×C61C2×D4semidirect
236. C2×D4×C61C2×D4semidirect
308. M16×C61C2×D4semidirect
335. C2×#92418C2×D4semidirect
491. C22×AGL(1,ℤ/8)D61semidirect
506. C2×C61#2008semidirect
525. C2×AGL(1,ℤ/8)C2×D61semidirect
551. C61C2×#2008semidirect
575. C2×#41C22⋊D61semidirect
578. C22×Q8C22⋊D61semidirect
596. C22×D4C22⋊D61semidirect
634. C2×M16C22⋊D61semidirect
635. C2×M16C22⋊D61semidirect
719. C2×Q8C2×C22⋊D61semidirect
773. C2×D4C2×C22⋊D61semidirect
817. M16C2×C22⋊D61semidirect
999. C2#21446870direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405602
C2×#168403292
C2×#168397782
C2×#168397672
C2×#168397362
#214468702
C2×#168395342
C22×AGL(1,ℤ/8)×C612
C2×#200861