Finite Group Databasebeta

← C2×#21446319 #29681919

Subgroups — C2×#21446319 #29681919

Order 15616.

1798 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840562C211yesmaximal, characteristic
2C2×C4×#11758222C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic, complemented
4C22×#14519705C211yesmaximal, characteristic, complemented
5C2×#16839735C211yesmaximal, characteristic, complemented
6#21446319C218yesmaximal, direct product factor
7C2×#16839534C211yesmaximal, characteristic, complemented
8C2×C61×#339C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C22×#11758222C2211yescharacteristic
11#16840562—22no—
12#16840562—22no—
13#16840562C414yescomplemented
14#16840562C2214yes—
15C2×#14519810—21no—
16C2×#14519810C412yescomplemented
17C2×#14519805—21no—
18C2×#14519805C412yescomplemented
19C2×#14519799—22no—
20C22×#11758194C2211yescharacteristic
21C4×#11758222—22no—
22C4×#11758222—22no—
23C4×#11758222—22no—
24C4×#11758222C2214yescomplemented
25C2×C4×Dic122—21no—
26C2×C4×D244—21no—
27C2×C4×C22⋊D61—22no—
28C2×#14519736C2211yescharacteristic
29C2×#14519734—21no—
30C2×C42×D61—21no—
31#16839780—22no—
32#16839780C2214yescomplemented
33C2×#14519705—21no—
34C2×#14519705—21no—
35C2×#14519705—22no—
36C2×#14519705—22no—
37C2×#14519705C2214yescomplemented
38#16839735—22no—
39#16839735C2214yescomplemented
40C2×#14519691—22no—
41#16839534C2214yescomplemented
42C22×M16×C61C2211yescharacteristic
43C2×#117×C61C2211yescharacteristic
44C22×C42×C61C2211yescharacteristic
45C61×#339C2214yescomplemented
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
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×#11758222—21no—
62C2×#11758222C2×C412yes—
63C2×#11758222C2×C412yes—
64C2×#11758222C2×C412yescomplemented
65C2×#11758222D412yes—
66C2×#11758222D412yes—
67C2×#11758222D412yes—
68C2×#11758222C2312yes—
69C2×#11758222C2312yes—
70C22×Dic122C2×C411yescharacteristic, complemented
71C22×Dic122D411yescharacteristic
72C22×D244C2×C411yescharacteristic, complemented
73C22×D244D411yescharacteristic
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61—22no—
78C22×C4×D61—21no—
79#14519810—24no—
80#14519810—24no—
81#14519810—24no—
82#14519810C2×C418yescomplemented
83#14519805—24no—
84#14519805—24no—
85#14519805—24no—
86#14519805C2×C418yescomplemented
87#14519799—28no—
88#14519799—28no—
89C2×Dic244—22no—
90C2×#11758190—22no—
91C2×#11758190—22no—
92C2×D488—22no—
93C2×#11758194—21no—
94C2×#11758194—21no—
95C2×#11758194—21no—
96C2×#11758194—21no—
97C2×#11758194—21no—
98C2×#11758194C2312yes—
99C22×#92418—21no—
100C4×Dic122—24no—
101C4×Dic122—24no—
102C4×D244—24no—
103C4×D244—24no—
104C4×C22⋊D61—28no—
105C4×C22⋊D61—28no—
106#14519736—21no—
107#14519736—21no—
108#14519736D412yes—
109#14519736C2312yes—
110#14519734—24no—
111#14519734—24no—
112C2×C4⋊Dic61—21no—
113C2×#11758196—22no—
114C2×C22⋊Dic61D412yes—
115C2×#11758198—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—21no—
118C42×D61—24no—
119C42×D61—24no—
120#14519705—28no—
121#14519705—24no—
122#14519705—24no—
123#14519691—28no—
124C23×C4×C61—21no—
125C23×C4×C61C2311yescharacteristic
126C2×M16×C61—21no—
127C2×M16×C61—21no—
128C2×M16×C61—21no—
129C2×M16×C61C2×C412yescomplemented
130C2×M16×C61C2×C412yescomplemented
131C2×M16×C61C2312yes—
132C22×C8×C61—21no—
133#117×C61—21no—
134#117×C61—21no—
135#117×C61—21no—
136#117×C61C2312yes—
137C2×C4⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C42×C61—21no—
140C2×C42×C61—21no—
141C2×C42×C61—21no—
142C2×C42×C61—21no—
143C2×C42×C61D411yescharacteristic
144C2×C42×C61D411yescharacteristic
145C2×C42×C61D412yes—
146C2×C42×C61C2312yes—
147C24×C61C2×D411yescharacteristic
148C23×D61—21no—
149C23×D61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—44no—
155C22×C4×C61—41no—
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61#4111yescharacteristic
166C22×C4×C61#4111yescharacteristic
167C22×C4×C61#4111yescharacteristic
168C22×C4×C61#4111yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—41no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61—41no—
181C2×C22⋊D61—41no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—22no—
185#11758222—22no—
186#11758222—22no—
187#11758222—22no—
188#11758222—22no—
189#11758222—22no—
190#11758222—22no—
191#11758222—22no—
192#11758222—22no—
193#11758222—22no—
194#11758222—22no—
195#11758222—22no—
196#11758222—22no—
197#11758222—22no—
198#11758222—22no—
199#11758222—22no—
200#11758222—22no—
201#11758222—22no—
202#11758222—22no—
203#11758222—22no—
204#11758222—22no—
205#11758222—41no—
206#11758222—41no—
207#11758222—41no—
208#11758222—41no—
209#11758222—41no—
210#11758222—41no—
211#11758222—41no—
212#11758222—41no—
213#11758222C22⋊C414yes—
214#11758222C22⋊C414yes—
215#11758222C22×C414yes—
216#11758222C2×D414yes—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244C22⋊C412yes—
226C2×D244C22⋊C412yes—
227C2×D244C22×C412yescomplemented
228C2×D244C2×D412yes—
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61—22no—
232C2×C4×D61—22no—
233C2×C4×D61—22no—
234C2×C4×D61—22no—
235C2×C4×D61—28no—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—48no—
239C2×C4×D61—41no—
240C2×C4×D61—41no—
241C2×C4×D61—41no—
242C2×C4×D61—41no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122C22⋊C412yes—
252C2×Dic122C22⋊C412yes—
253C2×Dic122C22×C412yescomplemented
254C2×Dic122C2×D412yes—
255M16×C61—22no—
256M16×C61—22no—
257M16×C61—22no—
258M16×C61C22×C414yescomplemented
259C2×C8×C61—22no—
260C2×C8×C61—22no—
261C2×C8×C61—22no—
262C4⋊C4×C61—22no—
263C4⋊C4×C61—41no—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—41no—
266C42×C61—21no—
267C42×C61—21no—
268C42×C61—22no—
269C42×C61—22no—
270C42×C61—22no—
271C42×C61—41no—
272C42×C61C2×D412yes—
273C42×C61C2×D412yes—
274C22⋊Dic61—22no—
275C22⋊Dic61C2×D414yes—
276#11758198—28no—
277C4⋊Dic61—22no—
278C4⋊Dic61—22no—
279#11758196—28no—
280C4×Dic61—28no—
281C4×Dic61—22no—
282C4×Dic61—22no—
283#11758194—22no—
284#11758194—22no—
285#11758194—41no—
286#11758194—41no—
287C2×#92418—22no—
288C2×#92418—41no—
289C2×#92418—41no—
290Dic244—28no—
291D488—28no—
292#11758190—28no—
293#11758190—28no—
294C23×C61—42no—
295C23×C61C4×D411yescharacteristic
296C23×C61C4×D411yescharacteristic
297C23×C61#12011yescharacteristic
298C23×C61#12011yescharacteristic
299C23×C61#12111yescharacteristic
300C23×C61#12111yescharacteristic
301C23×C61C22×D411yescharacteristic
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—44no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—82no—
310C2×C4×C61—24no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—44no—
314C2×C4×C61—44no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—82no—
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C4×D411yescharacteristic
323C2×C4×C61C4×D411yescharacteristic
324C2×C4×C61C4×D411yescharacteristic
325C2×C4×C61C4×D411yescharacteristic
326C2×C4×C61C4×D411yescharacteristic
327C2×C4×C61C4×D411yescharacteristic
328C2×C4×C61#12011yescharacteristic
329C2×C4×C61#12011yescharacteristic
330C2×C4×C61#12111yescharacteristic
331C2×C4×C61#12111yescharacteristic
332C2×C4×C61#12111yescharacteristic
333C2×C4×C61#12111yescharacteristic
334C2×C4×C61#12111yescharacteristic
335C2×C4×C61#12111yescharacteristic
336C2×C4×C61#12311yescharacteristic
337C2×C4×C61#12311yescharacteristic
338C2×C4×C61#12311yescharacteristic
339C2×C4×C61#12311yescharacteristic
340C2×C4×C61C23×C411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61C2×#4111yescharacteristic
346C22⋊D61—24no—
347C22⋊D61—24no—
348C22⋊D61—24no—
349C22⋊D61—24no—
350C22⋊D61—42no—
351C22⋊D61—42no—
352C22⋊D61—42no—
353C22⋊D61—42no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—24no—
359C2×Dic61—44no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362D244—22no—
363D244—22no—
364D244—22no—
365D244—22no—
366D244—22no—
367D244—41no—
368D244—41no—
369D244C2×C22⋊C414yes—
370C4×D61—24no—
371C4×D61—24no—
372C4×D61—24no—
373C4×D61—24no—
374C4×D61—416no—
375C4×D61—42no—
376C4×D61—42no—
377C4×D61—42no—
378C4×D61—42no—
379Dic122—22no—
380Dic122—22no—
381Dic122—22no—
382Dic122—22no—
383Dic122—22no—
384Dic122—41no—
385Dic122—41no—
386Dic122C2×C22⋊C414yes—
387C8×C61—24no—
388#92418—42no—
389C2×#1906—611nomaximal, Sylow
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61#38611yescharacteristic
398C22×C61#38611yescharacteristic
399C22×C61#38611yescharacteristic
400C22×C61#38611yescharacteristic
401C22×C61C2×C4×D411yescharacteristic
402C22×C61C2×#12011yescharacteristic
403C22×C61C2×#12111yescharacteristic
404C2×D61—24no—
405C2×D61—44no—
406C2×D61—44no—
407C2×D61—44no—
408C2×D61—42no—
409C2×D61—82no—
410C2×D61—82no—
411C2×D61—82no—
412C4×C61—24no—
413C4×C61—42no—
414C4×C61—82no—
415C4×C61#38611yescharacteristic
416C4×C61#38611yescharacteristic
417C4×C61#38611yescharacteristic
418C4×C61#38611yescharacteristic
419C4×C61C22×C22⋊C411yescharacteristic
420C4×C61C2×C4×D411yescharacteristic
421C4×C61C2×#12111yescharacteristic
422C4×C61C2×#12311yescharacteristic
423Dic61—24no—
424Dic61—44no—
425Dic61—42no—
426C2×#575—611no—
427C2×C4×#41—611no—
428C2×#421—611no—
429C22×#104—611no—
430C2×#410—611no—
431#1906—618no—
432C2×#344—611no—
433C2×#339D6111yescharacteristic, complemented
434C2×C61—21no—
435C2×C61—21no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—21no—
439C2×C61—21no—
440C2×C61#190612yescomplemented
441C2×C61C2×#38611yescharacteristic
442D61—44no—
443D61—82no—
444C22×#41—611no—
445C22×#41—611no—
446#575—614no—
447#575—614no—
448#575—1222no—
449#575—1222no—
450C2×#137—612no—
451C2×#137—1221no—
452C2×AGL(1,ℤ/8)—612no—
453C2×AGL(1,ℤ/8)—1221no—
454C2×#135—1222no—
455C22×M16—611no—
456C22×M16C2×D6111yescharacteristic
457C4×#41—614no—
458C4×#41—1222no—
459C4×#41—1222no—
460C4×#41—1222no—
461C2×C4×Q8—1221no—
462C2×C4×D4—1221no—
463C2×C4×D4—1222no—
464C2×#117—611no—
465C2×#117—1221no—
466C2×#117C2×D6111yescharacteristic
467C22×C42—1221no—
468C22×C42C2×D6111yescharacteristic
469#421—614no—
470#421—1222no—
471C2×#104—614no—
472C2×#104—1222no—
473C2×#104—1221no—
474C2×#104—1222no—
475C2×#104—1221no—
476#410—614no—
477#410—1222no—
478C2×#99—1222no—
479#344—614no—
480#339C2×D6114yescomplemented
481C61C2×#190611yescharacteristic, complemented, Sylow
482C2×#41—612no—
483C2×#41—612no—
484C2×#41—612no—
485C2×#41—612no—
486C2×#41—612no—
487C2×#41—612no—
488C2×#41—612no—
489C2×#41—612no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1221no—
493C2×#41—1221no—
494C2×#41—1221no—
495C2×#41—1221no—
496C2×#41—1221no—
497C2×#41—1221no—
498C2×#41—1221no—
499C2×#41—1221no—
500C2×#41—1221no—
501C2×#41—1221no—
502C2×#41—1221no—
503C2×#41—1221no—
504C2×#41—1221no—
505C2×#41—1221no—
506C22×Q8—611no—
507C22×Q8—611no—
508C22×D4—611no—
509C22×D4—611no—
510C22×D4—1221no—
511C22×D4—1221no—
512C23×C4—21no—
513C23×C4—1222no—
514C23×C4—1221no—
515C23×C4—1221no—
516C23×C4C22×D6111yescharacteristic
517#137—618no—
518#137—1224no—
519#137—1224no—
520#137—1224no—
521AGL(1,ℤ/8)—618no—
522AGL(1,ℤ/8)—1224no—
523AGL(1,ℤ/8)—1224no—
524AGL(1,ℤ/8)—1224no—
525#135—1228no—
526#135—1228no—
527C2×Q16—1222no—
528C2×SD16—1222no—
529C2×SD16—1222no—
530C2×D8—1222no—
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—21no—
534C2×M16—612no—
535C2×M16—1221no—
536C2×M16—1221no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16C4×D6112yescomplemented
541C2×M16C4×D6112yescomplemented
542C2×M16C22×D6112yes—
543C22×C8—21no—
544C22×C8—1221no—
545C4×Q8—1224no—
546C4×Q8—1224no—
547C4×D4—1224no—
548C4×D4—1224no—
549C4×D4—1228no—
550C4×D4—1228no—
551#117—21no—
552#117—21no—
553#117—21no—
554#117—612no—
555#117—612no—
556#117—1224no—
557#117—1221no—
558#117—1221no—
559#117—1224no—
560#117C22×D6112yes—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—1222no—
563C2×C4⋊C4—1221no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—612no—
566C2×C22⋊C4—1222no—
567C2×C42—21no—
568C2×C42—21no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—1224no—
572C2×C42—1222no—
573C2×C42—1221no—
574C2×C42—1224no—
575C2×C42D24411yescharacteristic
576C2×C42D24412yes—
577C2×C42D24411yescharacteristic
578C2×C42C22×D6112yes—
579#104—1228no—
580#104—1224no—
581#104—1224no—
582#99—1228no—
583C24—1221no—
584C24—1221no—
585C24D4×D6111yescharacteristic
586#41—614no—
587#41—614no—
588#41—614no—
589#41—614no—
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—
602#41—1222no—
603#41—1222no—
604#41—1222no—
605#41—1222no—
606#41—1222no—
607#41—1222no—
608#41—1222no—
609#41—1222no—
610#41—2441no—
611#41—2441no—
612#41—2441no—
613#41—2441no—
614#41—2441no—
615#41—2441no—
616#41—2441no—
617#41—2441no—
618C2×Q8—612no—
619C2×Q8—612no—
620C2×Q8—612no—
621C2×Q8—612no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×Q8—1221no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×D4—612no—
631C2×D4—612no—
632C2×D4—612no—
633C2×D4—612no—
634C2×D4—1222no—
635C2×D4—1222no—
636C2×D4—1222no—
637C2×D4—1222no—
638C2×D4—1222no—
639C2×D4—1222no—
640C2×D4—1222no—
641C2×D4—1222no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—2441no—
651C2×D4—2441no—
652C2×D4—2441no—
653C2×D4—2441no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—44no—
659C22×C4—41no—
660C22×C4—1228no—
661C22×C4—1221no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1222no—
666C22×C4—1222no—
667C22×C4—1222no—
668C22×C4—1221no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—2448no—
673C22×C4—2441no—
674C22×C4—2441no—
675C22×C4—2441no—
676C22×C4—2441no—
677C22×C4C2×C4×D6111yescharacteristic
678C22×C4C2×C4×D6111yescharacteristic
679C22×C4C2×D24411yescharacteristic
680C22×C4C2×D24411yescharacteristic
681C22×C4#1175822211yescharacteristic
682C22×C4#1175822211yescharacteristic
683C22×C4D4×D6111yescharacteristic
684C22×C4D4×D6111yescharacteristic
685C22×C4D4×D6111yescharacteristic
686C22×C4D4×D6111yescharacteristic
687C22×C4D4×D6111yescharacteristic
688C22×C4#1175822611yescharacteristic
689C22×C4#1175822611yescharacteristic
690C22×C4C23×D6111yescharacteristic
691Q16—1228no—
692SD16—1228no—
693SD16—1228no—
694D8—1228no—
695M16—22no—
696M16—22no—
697M16—22no—
698M16—1222no—
699M16—1222no—
700M16—2441no—
701M16—2441no—
702M16C2×C4×D6114yescomplemented
703C2×C8—22no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—1222no—
707C2×C8—2441no—
708C2×C8—2441no—
709C4⋊C4—22no—
710C4⋊C4—41no—
711C4⋊C4—1228no—
712C4⋊C4—1222no—
713C4⋊C4—1222no—
714C22⋊C4—22no—
715C22⋊C4—41no—
716C22⋊C4—614no—
717C22⋊C4—1228no—
718C22⋊C4—1222no—
719C42—22no—
720C42—21no—
721C42—21no—
722C42—22no—
723C42—22no—
724C42—41no—
725C42—1228no—
726C42—1222no—
727C42—1222no—
728C42C2×D24412yes—
729C42C2×D24412yes—
730C23—42no—
731C23—1222no—
732C23—1222no—
733C23—1222no—
734C23—1222no—
735C23—4882no—
736C23—2444no—
737C23—2441no—
738C23—2441no—
739C23#1451973911yescharacteristic
740C23#1451973911yescharacteristic
741C23#1451974711yescharacteristic
742C23#1451974711yescharacteristic
743C23#1451975011yescharacteristic
744C23#1451975011yescharacteristic
745C23C2×D4×D6111yescharacteristic
746Q8—614no—
747Q8—1222no—
748Q8—1222no—
749Q8—1222no—
750Q8—1222no—
751Q8—1222no—
752Q8—2441no—
753Q8—2441no—
754D4—614no—
755D4—1224no—
756D4—1224no—
757D4—1224no—
758D4—1224no—
759D4—1222no—
760D4—1222no—
761D4—1222no—
762D4—1222no—
763D4—1222no—
764D4—2442no—
765D4—2442no—
766D4—2442no—
767D4—2442no—
768D4—2441no—
769D4—2441no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—82no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1224no—
782C2×C4—1224no—
783C2×C4—1224no—
784C2×C4—1224no—
785C2×C4—1222no—
786C2×C4—1224no—
787C2×C4—24416no—
788C2×C4—2444no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4C22⋊C4×D6111yescharacteristic
796C2×C4C22⋊C4×D6111yescharacteristic
797C2×C4C22⋊C4×D6111yescharacteristic
798C2×C4C22⋊C4×D6111yescharacteristic
799C2×C4#1451973911yescharacteristic
800C2×C4#1451973911yescharacteristic
801C2×C4C4×D24411yescharacteristic
802C2×C4C4×D24411yescharacteristic
803C2×C4C4×D24411yescharacteristic
804C2×C4C4×D24411yescharacteristic
805C2×C4#1451974711yescharacteristic
806C2×C4#1451974711yescharacteristic
807C2×C4#1451975011yescharacteristic
808C2×C4#1451975011yescharacteristic
809C2×C4#1451975211yescharacteristic
810C2×C4#1451975211yescharacteristic
811C2×C4#1451975211yescharacteristic
812C2×C4#1451975211yescharacteristic
813C2×C4#1451976211yescharacteristic
814C2×C4#1451976211yescharacteristic
815C2×C4#1451976211yescharacteristic
816C2×C4#1451976211yescharacteristic
817C2×C4C22×C4×D6111yescharacteristic
818C2×C4C2×D4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4C22×D24411yescharacteristic
821C2×C4C2×#1175822211yescharacteristic
822C2×C4C2×#1175822611yescharacteristic
823C8—24no—
824C8—2442no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—1224no—
833C22—4882no—
834C22—4882no—
835C22—4882no—
836C22—2444no—
837C22—2444no—
838C22—2442no—
839C22—2444no—
840C22#1683964011yescharacteristic
841C22#1683964011yescharacteristic
842C22#1683964011yescharacteristic
843C22#1683964011yescharacteristic
844C22C2×#1451973911yescharacteristic
845C22C2×#1451974711yescharacteristic
846C22C2×#1451975011yescharacteristic
847C4—24no—
848C4—42no—
849C4—82no—
850C4—1224no—
851C4—2444no—
852C4—2442no—
853C4#1683964011yescharacteristic
854C4#1683964011yescharacteristic
855C4#1683964011yescharacteristic
856C4#1683964011yescharacteristic
857C4C2×C22⋊C4×D6111yescharacteristic
858C4C2×C4×D24411yescharacteristic
859C4C2×#1451975211yescharacteristic
860C4C2×#1451976211yescharacteristic
861C2—21no—
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—21no—
867C2—4882no—
868C2—2444no—
869C2#2144631912yesdirect product factor
870C2C2×#1683964011yescharacteristic
subgroupG/H
centerC2×C4#14519752
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#339C2
socleC22×C61#386
prime radicalC2×#16840562C2
cosocleC22×C4×C61C24
hypercenterC2×#339D61
hypocenterC61C2×#1906
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758222C2semidirect
3. C2×#16839780C2semidirect
4. C22×#14519705C2semidirect
5. C2×#16839735C2semidirect
6. #21446319C2direct (N × H)
7. C2×#16839534C2semidirect
8. C2×C61×#339C2semidirect
13. #16840562C4semidirect
16. C2×#14519810C4semidirect
18. C2×#14519805C4semidirect
24. C4×#11758222C22semidirect
32. #16839780C22semidirect
37. C2×#14519705C22semidirect
39. #16839735C22semidirect
41. #16839534C22semidirect
45. C61×#339C22semidirect
64. C2×#11758222C2×C4semidirect
70. C22×Dic122C2×C4semidirect
72. C22×D244C2×C4semidirect
82. #14519810C2×C4semidirect
86. #14519805C2×C4semidirect
129. C2×M16×C61C2×C4semidirect
130. C2×M16×C61C2×C4semidirect
227. C2×D244C22×C4semidirect
253. C2×Dic122C22×C4semidirect
258. M16×C61C22×C4semidirect
433. C2×#339D61semidirect
440. C2×C61#1906semidirect
480. #339C2×D61semidirect
481. C61C2×#1906semidirect
540. C2×M16C4×D61semidirect
541. C2×M16C4×D61semidirect
702. M16C2×C4×D61semidirect
869. C2#21446319direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405622
C2×C4×#117582222
C2×#168397802
C22×#145197052
C2×#168397352
#214463192
C2×#168395342
C2×C61×#3392
C2×#190661