Finite Group Databasebeta

← C2×#21446199 #29681550

Subgroups — C2×#21446199 #29681550

Order 15616.

1794 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic, complemented
2C2×#16840308C211yesmaximal, characteristic
3C2×#16839779C211yesmaximal, characteristic, complemented
4C2×#16839735C211yesmaximal, characteristic, complemented
5#21446199C218yesmaximal, direct product factor
6C2×#16839523C211yesmaximal, characteristic, complemented
7C2×#16839521C211yesmaximal, characteristic, complemented
8C2×C61×#421C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840528—22no—
11#16840528—22no—
12#16840528—22no—
13#16840528C2214yescomplemented
14C2×#14519785—22no—
15C2×#14519783—22no—
16C22×#11758194C2211yescharacteristic
17C2×M16×D61—22no—
18#16840308—22no—
19#16840308—22no—
20#16840308C414yescomplemented
21#16840308C2214yes—
22C2×#14519775C411yescharacteristic, complemented
23C2×#14519773C411yescharacteristic, complemented
24C2×#14519766C411yescharacteristic, complemented
25C2×#14519764C411yescharacteristic, complemented
26C2×#14519749—22no—
27C2×C4×C22⋊D61—22no—
28C2×#14519736C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30#16839779—22no—
31#16839779C2214yescomplemented
32C2×#14519704—22no—
33#16839735—22no—
34#16839735C2214yescomplemented
35C2×#14519691—22no—
36#16839523C2214yescomplemented
37#16839521C2214yescomplemented
38C22×#41×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×#421—22no—
42C61×#421C2214yescomplemented
43C2×#104×C61—22no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222C2×C412yes—
53C2×#11758222D412yes—
54C2×#11758222D412yes—
55C2×#11758222C2312yes—
56C22×Dic122C2×C411yescharacteristic
57C22×D244C2×C411yescharacteristic
58C22×C22⋊D61—22no—
59C22×C22⋊D61D412yes—
60C23×Dic61—21no—
61C22×C4×D61D412yes—
62#14519785—28no—
63#14519785—28no—
64#14519783—28no—
65#14519783—28no—
66C2×#11758194—21no—
67C2×#11758194—21no—
68C2×#11758194—21no—
69C2×#11758194D412yescomplemented
70C2×#11758194D412yescomplemented
71C2×#11758194C2312yes—
72C2×#11758189—24no—
73M16×D61—28no—
74M16×D61—28no—
75C22×#92418—21no—
76C2×C8×D61—24no—
77#14519775—22no—
78#14519775C2×C414yescomplemented
79#14519773—22no—
80#14519773C2×C414yescomplemented
81#14519766—22no—
82#14519766C2×C414yescomplemented
83#14519764—22no—
84#14519764C2×C414yescomplemented
85#14519749—28no—
86#14519749—28no—
87C4×C22⋊D61—28no—
88C4×C22⋊D61—28no—
89#14519736—21no—
90#14519736—21no—
91#14519736—21no—
92#14519736C2312yes—
93C2×C4⋊Dic61—21no—
94C2×#11758196—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—21no—
97C2×#11758198—22no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2×C412yes—
105C2×C4×Dic61C2312yes—
106#14519704—28no—
107#14519691—28no—
108C2×#41×C61—21no—
109C2×#41×C61—21no—
110C2×#41×C61—21no—
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C2×#41×C61—21no—
114C2×#41×C61—21no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×#41×C61C2×C412yes—
119C2×#41×C61C2312yes—
120C22×Q8×C61C2×C411yescharacteristic
121C22×D4×C61—21no—
122C22×D4×C61C2×C411yescharacteristic
123C23×C4×C61—21no—
124C23×C4×C61C2311yescharacteristic
125C2×M16×C61—21no—
126C2×M16×C61—21no—
127C2×M16×C61—21no—
128C2×M16×C61D412yescomplemented
129C2×M16×C61D412yescomplemented
130C2×M16×C61C2312yes—
131C22×C8×C61—21no—
132#117×C61—21no—
133#117×C61—21no—
134#117×C61—21no—
135#117×C61C2312yes—
136C2×C4⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139#104×C61—28no—
140C24×C61—21no—
141C24×C61C2×D411yescharacteristic
142C23×D61C22⋊C412yes—
143#41×C61—22no—
144#41×C61—22no—
145#41×C61—22no—
146#41×C61—22no—
147#41×C61—22no—
148#41×C61—22no—
149#41×C61—22no—
150#41×C61—22no—
151#41×C61—41no—
152#41×C61—41no—
153#41×C61—41no—
154#41×C61—41no—
155#41×C61—41no—
156#41×C61—41no—
157#41×C61—41no—
158#41×C61—41no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61C22×C412yes—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—41no—
173C2×D4×C61—41no—
174C2×D4×C61—41no—
175C2×D4×C61—41no—
176C2×D4×C61C22×C412yes—
177C22×C4×C61—21no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—41no—
181C22×C4×C61—41no—
182C22×C4×C61—41no—
183C22×C4×C61—41no—
184C22×C4×C61—41no—
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C22×C411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61#4111yescharacteristic
195C22×C4×C61#4111yescharacteristic
196C22×C4×C61#4111yescharacteristic
197C22×C4×C61#4111yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—28no—
204C2×C22⋊D61—48no—
205C2×C22⋊D61C22⋊C414yes—
206C2×C22⋊D61C2×D414yes—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—44no—
212C22×Dic61—41no—
213C22×Dic61C22⋊C412yes—
214#11758222—22no—
215#11758222—22no—
216#11758222—22no—
217#11758222—22no—
218#11758222—22no—
219#11758222—22no—
220#11758222—22no—
221#11758222—22no—
222#11758222—22no—
223#11758222—22no—
224#11758222—22no—
225#11758222—22no—
226#11758222—22no—
227#11758222—22no—
228#11758222—22no—
229#11758222—22no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244C22⋊C412yes—
235C2×D244C22×C412yes—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61C22⋊C414yes—
241C2×C4×D61C2×D414yes—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122C22⋊C412yes—
247C2×Dic122C22×C412yes—
248M16×C61—22no—
249M16×C61—22no—
250M16×C61—22no—
251M16×C61C2×D414yescomplemented
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C4⋊C4×C61—22no—
256C4⋊C4×C61—41no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—41no—
259C42×C61—22no—
260C42×C61—41no—
261C22⋊Dic61—28no—
262C22⋊Dic61—22no—
263C22⋊Dic61—41no—
264#11758198—28no—
265C4⋊Dic61—22no—
266C4⋊Dic61—41no—
267#11758196—28no—
268C4×Dic61—22no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271C4×Dic61—22no—
272C4×Dic61—22no—
273C4×Dic61—41no—
274C4×Dic61C22×C412yes—
275C4×Dic61C22×C412yes—
276#11758194—22no—
277#11758194—22no—
278#11758194—22no—
279#11758194C2×D414yescomplemented
280C2×#92418—22no—
281C2×#92418—22no—
282C2×#92418—22no—
283#11758189—216no—
284C8×D61—216no—
285C23×C61—22no—
286C23×C61—42no—
287C23×C61—44no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61C2×C22⋊C411yescharacteristic
291C23×C61C2×C22⋊C411yescharacteristic
292C23×C61#12111yescharacteristic
293C23×C61#12111yescharacteristic
294C23×C61#12111yescharacteristic
295C23×C61#12111yescharacteristic
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—44no—
300C22×D61C2×C22⋊C414yes—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—41no—
304Q8×C61—41no—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—42no—
308D4×C61—42no—
309D4×C61—42no—
310D4×C61—42no—
311D4×C61—41no—
312D4×C61—41no—
313C2×C4×C61—22no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—82no—
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C4×D411yescharacteristic
325C2×C4×C61C4×D411yescharacteristic
326C2×C4×C61C4×D411yescharacteristic
327C2×C4×C61C4×D411yescharacteristic
328C2×C4×C61C4×D411yescharacteristic
329C2×C4×C61C4×D411yescharacteristic
330C2×C4×C61C4×D411yescharacteristic
331C2×C4×C61C4×D411yescharacteristic
332C2×C4×C61#12011yescharacteristic
333C2×C4×C61#12011yescharacteristic
334C2×C4×C61#12011yescharacteristic
335C2×C4×C61#12011yescharacteristic
336C2×C4×C61#12111yescharacteristic
337C2×C4×C61#12111yescharacteristic
338C2×C4×C61#12111yescharacteristic
339C2×C4×C61#12111yescharacteristic
340C2×C4×C61#12311yescharacteristic
341C2×C4×C61#12311yescharacteristic
342C2×C4×C61#12311yescharacteristic
343C2×C4×C61#12311yescharacteristic
344C2×C4×C61C23×C411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C2×#4111yescharacteristic
349C2×C4×C61C2×#4111yescharacteristic
350C22⋊D61—24no—
351C22⋊D61—24no—
352C22⋊D61—24no—
353C22⋊D61—24no—
354C22⋊D61—416no—
355C2×Dic61—24no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—44no—
361C2×Dic61—44no—
362C2×Dic61—42no—
363C2×Dic61—42no—
364C2×Dic61—82no—
365C2×Dic61C2×C22⋊C414yes—
366D244—22no—
367D244—22no—
368D244—22no—
369D244—22no—
370C4×D61—24no—
371C4×D61—24no—
372C4×D61—24no—
373C4×D61—24no—
374Dic122—22no—
375Dic122—22no—
376Dic122—22no—
377Dic122—22no—
378C8×C61—24no—
379#92418—24no—
380C2×#1884—611nomaximal, Sylow
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—44no—
389C22×C61—42no—
390C22×C61—82no—
391C22×C61—82no—
392C22×C61#38611yescharacteristic
393C22×C61#38611yescharacteristic
394C22×C61#38611yescharacteristic
395C22×C61#38611yescharacteristic
396C22×C61C22×C22⋊C411yescharacteristic
397C22×C61C2×#12111yescharacteristic
398C22×C61C2×#12111yescharacteristic
399C2×D61—24no—
400C2×D61—44no—
401C2×D61—44no—
402C2×D61—82no—
403C4×C61—42no—
404C4×C61—82no—
405C4×C61#38611yescharacteristic
406C4×C61#38611yescharacteristic
407C4×C61#38611yescharacteristic
408C4×C61#38611yescharacteristic
409C4×C61C2×C4×D411yescharacteristic
410C4×C61C2×C4×D411yescharacteristic
411C4×C61C2×#12011yescharacteristic
412C4×C61C2×#12311yescharacteristic
413Dic61—24no—
414Dic61—24no—
415Dic61—42no—
416Dic61—82no—
417C2×#568—611no—
418C2×#532—611no—
419C2×#421—611no—
420C2×#421D6111yescharacteristic, complemented
421C2×#410—611no—
422#1884—618no—
423C2×#339—611no—
424C2×#339—611no—
425C2×C61—21no—
426C2×C61—21no—
427C2×C61—21no—
428C2×C61—21no—
429C2×C61—21no—
430C2×C61—21no—
431C2×C61—82no—
432C2×C61#188412yescomplemented
433C2×C61C2×#38611yescharacteristic
434D61—44no—
435C22×#41—611no—
436C22×#41C2×D6111yescharacteristic
437#568—614no—
438#568—1222no—
439#568—1222no—
440#568—1222no—
441C2×#131—1222no—
442C2×#131—1222no—
443C22×M16—611no—
444C22×M16—1222no—
445C22×M16C2×D6111yescharacteristic
446#532—614no—
447#532—614no—
448#532—1222no—
449#532—1222no—
450C2×C4⋊Q8—611no—
451C2×#127—611no—
452C2×#124—611no—
453C2×#124—611no—
454C2×#121—1222no—
455C2×C4×D4—1222no—
456C2×#117—611no—
457C2×#117C2×D6111yescharacteristic
458C22×C42—611no—
459#421—22no—
460#421—614no—
461#421—1222no—
462#421C2×D6114yescomplemented
463C2×#104—22no—
464C2×#104—1222no—
465#410—614no—
466#410—1222no—
467C2×#99—1222no—
468#339—614no—
469#339—614no—
470C61C2×#188411yescharacteristic, complemented, Sylow
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—612no—
482C2×#41—612no—
483C2×#41—612no—
484C2×#41—612no—
485C2×#41—1221no—
486C2×#41—1221no—
487C2×#41—1221no—
488C2×#41—1221no—
489C2×#41—1221no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1221no—
493C2×#41C4×D6112yes—
494C2×#41C22×D6112yes—
495C22×Q8—611no—
496C22×Q8C4×D6111yescharacteristic
497C22×D4—21no—
498C22×D4—612no—
499C22×D4—611no—
500C22×D4—1222no—
501C22×D4C4×D6111yescharacteristic
502C23×C4—21no—
503C23×C4—612no—
504C23×C4—1221no—
505C23×C4C22×D6111yescharacteristic
506#131—1228no—
507#131—1228no—
508#131—1228no—
509#131—1228no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—612no—
514C2×M16—612no—
515C2×M16—612no—
516C2×M16—1224no—
517C2×M16—1228no—
518C2×M16—1228no—
519C2×M16—1221no—
520C2×M16—1221no—
521C2×M16—1221no—
522C2×M16C22⋊D6112yescomplemented
523C2×M16C22⋊D6112yescomplemented
524C2×M16C22×D6112yes—
525C22×C8—21no—
526C22×C8—1224no—
527C22×C8—1221no—
528C4⋊Q8—614no—
529C4⋊Q8—1222no—
530#127—614no—
531#127—1222no—
532#124—614no—
533#124—614no—
534#124—1222no—
535#124—1222no—
536#121—1228no—
537#121—1228no—
538C4×D4—1228no—
539C4×D4—1228no—
540#117—21no—
541#117—21no—
542#117—21no—
543#117—612no—
544#117—1221no—
545#117—1221no—
546#117—1221no—
547#117C22×D6112yes—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—1222no—
550C2×C4⋊C4—1221no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1222no—
553C2×C22⋊C4—1222no—
554C2×C22⋊C4—1221no—
555C2×C42—21no—
556C2×C42—611no—
557C2×C42—611no—
558C2×C42—612no—
559C2×C42—612no—
560C2×C42—1221no—
561C2×C42—1221no—
562C2×C42—1221no—
563C2×C42—1221no—
564#104—28no—
565#104—1228no—
566#99—1228no—
567C24—21no—
568C24—612no—
569C24D4×D6111yescharacteristic
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41—41no—
586#41—1222no—
587#41—1222no—
588#41—1222no—
589#41—1222no—
590#41—1222no—
591#41—1222no—
592#41—1222no—
593#41—1222no—
594#41—1222no—
595#41—1222no—
596#41—1222no—
597#41—1222no—
598#41—1222no—
599#41—1222no—
600#41—1222no—
601#41—1222no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—612no—
608C2×Q8—612no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8C2×C4×D6112yes—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—614no—
626C2×D4—614no—
627C2×D4—612no—
628C2×D4—612no—
629C2×D4—1222no—
630C2×D4—1222no—
631C2×D4—1222no—
632C2×D4—1222no—
633C2×D4—1228no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—2448no—
639C2×D4C2×C4×D6112yes—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—612no—
649C22×C4—614no—
650C22×C4—614no—
651C22×C4—1221no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1221no—
658C22×C4—1222no—
659C22×C4—2444no—
660C22×C4—2441no—
661C22×C4C2×C4×D6111yescharacteristic
662C22×C4C2×C4×D6111yescharacteristic
663C22×C4#1175822211yescharacteristic
664C22×C4#1175822211yescharacteristic
665C22×C4D4×D6111yescharacteristic
666C22×C4D4×D6111yescharacteristic
667C22×C4D4×D6111yescharacteristic
668C22×C4D4×D6111yescharacteristic
669C22×C4D4×D6111yescharacteristic
670C22×C4#1175822411yescharacteristic
671C22×C4#1175822411yescharacteristic
672C22×C4C2×C22⋊D6111yescharacteristic
673C22×C4C2×C22⋊D6111yescharacteristic
674C22×C4C23×D6111yescharacteristic
675M16—22no—
676M16—22no—
677M16—22no—
678M16—614no—
679M16—12216no—
680M16—1222no—
681M16—1222no—
682M16—1222no—
683M16C2×C22⋊D6114yescomplemented
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—12216no—
688C2×C8—1222no—
689C2×C8—1222no—
690C2×C8—1222no—
691C4⋊C4—22no—
692C4⋊C4—41no—
693C4⋊C4—1228no—
694C4⋊C4—1222no—
695C4⋊C4—2441no—
696C22⋊C4—22no—
697C22⋊C4—41no—
698C22⋊C4—1228no—
699C22⋊C4—1228no—
700C22⋊C4—1222no—
701C22⋊C4—2441no—
702C42—22no—
703C42—41no—
704C42—612no—
705C42—612no—
706C42—1222no—
707C42—1222no—
708C42—1221no—
709C42—1221no—
710C42—1222no—
711C42—2441no—
712C23—22no—
713C23—42no—
714C23—44no—
715C23—41no—
716C23—41no—
717C23—614no—
718C23—1222no—
719C23—1222no—
720C23—2444no—
721C23C22⋊C4×D6111yescharacteristic
722C23C22⋊C4×D6111yescharacteristic
723C23#1451974811yescharacteristic
724C23#1451974811yescharacteristic
725C23#1451975011yescharacteristic
726C23#1451975011yescharacteristic
727C23C2×D4×D6111yescharacteristic
728Q8—22no—
729Q8—22no—
730Q8—41no—
731Q8—41no—
732Q8—1222no—
733Q8—1222no—
734Q8—1222no—
735Q8—1222no—
736D4—22no—
737D4—22no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—42no—
742D4—41no—
743D4—41no—
744D4—1224no—
745D4—1224no—
746D4—1224no—
747D4—1224no—
748D4—1222no—
749D4—1222no—
750D4—1222no—
751D4—1222no—
752D4—24416no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—82no—
762C2×C4—614no—
763C2×C4—1224no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1224no—
768C2×C4—1224no—
769C2×C4—1224no—
770C2×C4—1224no—
771C2×C4—1222no—
772C2×C4—4882no—
773C2×C4—2444no—
774C2×C4—2444no—
775C2×C4—2442no—
776C2×C4—2442no—
777C2×C4C22⋊C4×D6111yescharacteristic
778C2×C4C22⋊C4×D6111yescharacteristic
779C2×C4#1451973711yescharacteristic
780C2×C4#1451973711yescharacteristic
781C2×C4#1451973711yescharacteristic
782C2×C4#1451973711yescharacteristic
783C2×C4C4×C22⋊D6111yescharacteristic
784C2×C4C4×C22⋊D6111yescharacteristic
785C2×C4C4×C22⋊D6111yescharacteristic
786C2×C4C4×C22⋊D6111yescharacteristic
787C2×C4#1451974511yescharacteristic
788C2×C4#1451974511yescharacteristic
789C2×C4#1451974511yescharacteristic
790C2×C4#1451974511yescharacteristic
791C2×C4#1451974811yescharacteristic
792C2×C4#1451974811yescharacteristic
793C2×C4#1451975011yescharacteristic
794C2×C4#1451975011yescharacteristic
795C2×C4#1451975911yescharacteristic
796C2×C4#1451975911yescharacteristic
797C2×C4#1451975911yescharacteristic
798C2×C4#1451975911yescharacteristic
799C2×C4C22×C4×D6111yescharacteristic
800C2×C4C2×D4×D6111yescharacteristic
801C2×C4C2×D4×D6111yescharacteristic
802C2×C4C22×C22⋊D6111yescharacteristic
803C2×C4C2×#1175822411yescharacteristic
804C2×C4C2×#1175822211yescharacteristic
805C8—24no—
806C8—1224no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—44no—
815C22—42no—
816C22—82no—
817C22—82no—
818C22—1224no—
819C22—4882no—
820C22—2444no—
821C22—2444no—
822C22#1683963811yescharacteristic
823C22#1683963811yescharacteristic
824C22#1683963811yescharacteristic
825C22#1683963811yescharacteristic
826C22C2×C22⋊C4×D6111yescharacteristic
827C22C2×#1451974811yescharacteristic
828C22C2×#1451975011yescharacteristic
829C4—42no—
830C4—82no—
831C4—1224no—
832C4—1224no—
833C4—4882no—
834C4—2442no—
835C4#1683963811yescharacteristic
836C4#1683963811yescharacteristic
837C4#1683963811yescharacteristic
838C4#1683963811yescharacteristic
839C4C2×#1451973711yescharacteristic
840C4C2×C4×C22⋊D6111yescharacteristic
841C4C2×#1451974511yescharacteristic
842C4C2×#1451975911yescharacteristic
843C2—21no—
844C2—21no—
845C2—21no—
846C2—21no—
847C2—21no—
848C2—21no—
849C2—82no—
850C2—2444no—
851C2#2144619912yesdirect product factor
852C2C2×#1683963811yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC22×C61#386
prime radicalC2×#16840308C2
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61C2×#1884
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839779C2semidirect
4. C2×#16839735C2semidirect
5. #21446199C2direct (N × H)
6. C2×#16839523C2semidirect
7. C2×#16839521C2semidirect
8. C2×C61×#421C2semidirect
13. #16840528C22semidirect
20. #16840308C4semidirect
22. C2×#14519775C4semidirect
23. C2×#14519773C4semidirect
24. C2×#14519766C4semidirect
25. C2×#14519764C4semidirect
31. #16839779C22semidirect
34. #16839735C22semidirect
36. #16839523C22semidirect
37. #16839521C22semidirect
42. C61×#421C22semidirect
69. C2×#11758194D4semidirect
70. C2×#11758194D4semidirect
78. #14519775C2×C4semidirect
80. #14519773C2×C4semidirect
82. #14519766C2×C4semidirect
84. #14519764C2×C4semidirect
128. C2×M16×C61D4semidirect
129. C2×M16×C61D4semidirect
251. M16×C61C2×D4semidirect
279. #11758194C2×D4semidirect
420. C2×#421D61semidirect
432. C2×C61#1884semidirect
462. #421C2×D61semidirect
470. C61C2×#1884semidirect
522. C2×M16C22⋊D61semidirect
523. C2×M16C22⋊D61semidirect
683. M16C2×C22⋊D61semidirect
851. C2#21446199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405282
C2×#168403082
C2×#168397792
C2×#168397352
#214461992
C2×#168395232
C2×#168395212
C2×C61×#4212
C2×#188461