Finite Group Databasebeta

← C2×#21446182 #29681488

Subgroups — C2×#21446182 #29681488

Order 15616.

1682 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840562C211yesmaximal, characteristic
2C2×#16840528C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic, complemented
4C2×#16839759C211yesmaximal, characteristic, complemented
5C2×#16839728C211yesmaximal, characteristic, complemented
6#21446182C218yesmaximal, direct product factor
7C2×#16839534C211yesmaximal, characteristic, complemented
8C2×C61×#341C211yesmaximal, 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—
20#16840528—22no—
21#16840528—22no—
22#16840528—22no—
23#16840528C2214yescomplemented
24C2×#14519785—22no—
25C2×#14519783—22no—
26C22×#11758194C2211yescharacteristic
27C2×M16×D61—22no—
28C2×#14519736C2211yescharacteristic
29#16839778—22no—
30#16839778C2214yescomplemented
31C2×#14519703—22no—
32#16839759—22no—
33#16839759C2214yescomplemented
34C2×#14519702—21no—
35C2×#14519699—21no—
36#16839728—22no—
37#16839728C2214yescomplemented
38C2×#14519689—22no—
39#16839534C2214yescomplemented
40C22×M16×C61C2211yescharacteristic
41C22×M16×C61C2211yescharacteristic
42C23×C8×C61C2211yescharacteristic
43C61×#341C2214yescomplemented
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×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222C2×C412yes—
61C2×#11758222C2×C412yes—
62C2×#11758222C2×C412yes—
63C2×#11758222D412yes—
64C2×#11758222D412yes—
65C2×#11758222D412yes—
66C2×#11758222C2312yes—
67C2×#11758222C2312yes—
68C22×Dic122C2×C411yescharacteristic
69C22×Dic122D411yescharacteristic
70C22×D244C2×C411yescharacteristic
71C22×D244D411yescharacteristic
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76#14519810—24no—
77#14519810—24no—
78#14519810—24no—
79#14519810C2×C418yescomplemented
80#14519805—24no—
81#14519805—24no—
82#14519805—24no—
83#14519805C2×C418yescomplemented
84#14519799—28no—
85#14519799—28no—
86C2×Dic244—22no—
87C2×#11758190—22no—
88C2×#11758190—22no—
89C2×D488—22no—
90#14519785—28no—
91#14519785—28no—
92#14519783—28no—
93#14519783—28no—
94C2×#11758194—21no—
95C2×#11758194—21no—
96C2×#11758194—21no—
97C2×#11758194—21no—
98C2×#11758194D412yes—
99C2×#11758194C2312yes—
100C2×#11758189—24no—
101M16×D61—28no—
102M16×D61—28no—
103C22×#92418D412yes—
104C2×C8×D61—24no—
105#14519736—21no—
106#14519736—21no—
107#14519736—21no—
108#14519736C2312yes—
109C2×C4⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C4×Dic61—21no—
112#14519703—28no—
113#14519702—24no—
114#14519699—24no—
115#14519689—28no—
116C23×C4×C61C2311yescharacteristic
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61—21no—
120C2×M16×C61—21no—
121C2×M16×C61—21no—
122C2×M16×C61—21no—
123C2×M16×C61C2×C412yes—
124C2×M16×C61C2×C412yes—
125C2×M16×C61D412yes—
126C2×M16×C61D412yes—
127C2×M16×C61C2312yes—
128C2×M16×C61C2312yes—
129C22×C8×C61—21no—
130C22×C8×C61—21no—
131C22×C8×C61—21no—
132C22×C8×C61—21no—
133C22×C8×C61—21no—
134C22×C8×C61—21no—
135C22×C8×C61—21no—
136C22×C8×C61—21no—
137C22×C8×C61C2312yes—
138C24×C61#4111yescharacteristic
139C23×D61—21no—
140C23×D61—21no—
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C22×C4×C61C2411yescharacteristic
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—41no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—41no—
166C2×C22⋊D61—41no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—41no—
170#11758222—22no—
171#11758222—22no—
172#11758222—22no—
173#11758222—22no—
174#11758222—22no—
175#11758222—22no—
176#11758222—22no—
177#11758222—22no—
178#11758222—22no—
179#11758222—22no—
180#11758222—22no—
181#11758222—22no—
182#11758222—22no—
183#11758222—22no—
184#11758222—22no—
185#11758222—22no—
186#11758222—22no—
187#11758222—22no—
188#11758222—22no—
189#11758222—22no—
190#11758222—41no—
191#11758222—41no—
192#11758222—41no—
193#11758222—41no—
194#11758222—41no—
195#11758222—41no—
196#11758222—41no—
197#11758222—41no—
198#11758222C22⋊C414yes—
199#11758222C22⋊C414yes—
200#11758222C22×C414yes—
201#11758222C2×D414yes—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244C22⋊C412yes—
211C2×D244C22⋊C412yes—
212C2×D244C22×C412yes—
213C2×D244C2×D412yes—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—22no—
222C2×C4×D61—41no—
223C2×C4×D61—41no—
224C2×C4×D61—41no—
225C2×C4×D61—41no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122C22⋊C412yes—
235C2×Dic122C22⋊C412yes—
236C2×Dic122C22×C412yes—
237C2×Dic122C2×D412yes—
238M16×C61—22no—
239M16×C61—22no—
240M16×C61—22no—
241M16×C61—22no—
242M16×C61—22no—
243M16×C61—22no—
244M16×C61C22×C414yes—
245M16×C61C2×D414yes—
246C2×C8×C61—22no—
247C2×C8×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61—22no—
250C2×C8×C61—22no—
251C2×C8×C61—22no—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C2×C8×C61—41no—
256C2×C8×C61—41no—
257C2×C8×C61—41no—
258C2×C8×C61—41no—
259C22⋊Dic61—22no—
260C22⋊Dic61—41no—
261C4⋊Dic61—22no—
262C4⋊Dic61—41no—
263C4×Dic61—22no—
264C4×Dic61—41no—
265#11758194—22no—
266#11758194—22no—
267#11758194—22no—
268#11758194—22no—
269C2×#92418—22no—
270C2×#92418—22no—
271C2×#92418C2×D414yes—
272Dic244—28no—
273D488—28no—
274#11758190—28no—
275#11758190—28no—
276#11758189—216no—
277C8×D61—216no—
278C23×C61—42no—
279C23×C61C4×D411yescharacteristic
280C23×C61C4×D411yescharacteristic
281C23×C61#12111yescharacteristic
282C23×C61#12111yescharacteristic
283C23×C61#12311yescharacteristic
284C23×C61#12311yescharacteristic
285C23×C61C2×#4111yescharacteristic
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—44no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—82no—
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C4×D411yescharacteristic
302C2×C4×C61C4×D411yescharacteristic
303C2×C4×C61C4×D411yescharacteristic
304C2×C4×C61#12011yescharacteristic
305C2×C4×C61#12011yescharacteristic
306C2×C4×C61#12011yescharacteristic
307C2×C4×C61#12011yescharacteristic
308C2×C4×C61#12111yescharacteristic
309C2×C4×C61#12111yescharacteristic
310C2×C4×C61#12111yescharacteristic
311C2×C4×C61#12111yescharacteristic
312C2×C4×C61#12111yescharacteristic
313C2×C4×C61#12111yescharacteristic
314C2×C4×C61#12311yescharacteristic
315C2×C4×C61#12311yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C22⋊D61—24no—
323C22⋊D61—24no—
324C22⋊D61—24no—
325C22⋊D61—24no—
326C22⋊D61—42no—
327C22⋊D61—42no—
328C22⋊D61—42no—
329C22⋊D61—42no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—42no—
337C2×Dic61—82no—
338D244—22no—
339D244—22no—
340D244—22no—
341D244—22no—
342D244—22no—
343D244—41no—
344D244—41no—
345D244C2×C22⋊C414yes—
346C4×D61—24no—
347C4×D61—24no—
348C4×D61—24no—
349C4×D61—24no—
350C4×D61—42no—
351C4×D61—42no—
352C4×D61—42no—
353C4×D61—42no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—22no—
359Dic122—41no—
360Dic122—41no—
361Dic122C2×C22⋊C414yes—
362C8×C61—24no—
363C8×C61—24no—
364C8×C61—42no—
365#92418—24no—
366C2×#1881—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61#38611yescharacteristic
375C22×C61#38611yescharacteristic
376C22×C61#38611yescharacteristic
377C22×C61#38611yescharacteristic
378C22×C61C2×C4×D411yescharacteristic
379C22×C61C2×#12111yescharacteristic
380C22×C61C2×#12311yescharacteristic
381C2×D61—24no—
382C2×D61—44no—
383C2×D61—44no—
384C2×D61—42no—
385C2×D61—82no—
386C2×D61—82no—
387C2×D61—82no—
388C2×D61—82no—
389C4×C61#38611yescharacteristic
390C4×C61#38611yescharacteristic
391C4×C61#38611yescharacteristic
392C4×C61#38611yescharacteristic
393C4×C61C22×C22⋊C411yescharacteristic
394C4×C61C2×C4×D411yescharacteristic
395C4×C61C2×#12011yescharacteristic
396C4×C61C2×#12111yescharacteristic
397Dic61—24no—
398Dic61—42no—
399Dic61—82no—
400C2×#575—611no—
401C2×#568—611no—
402C2×#421—611no—
403C2×#416—611no—
404C2×#408—611no—
405#1881—618no—
406C2×#344—611no—
407C2×#341D6111yescharacteristic, complemented
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61#188112yescomplemented
415C2×C61C2×#38611yescharacteristic
416D61—44no—
417D61—82no—
418C22×#41—611no—
419C22×#41—611no—
420#575—614no—
421#575—614no—
422#575—1222no—
423#575—1222no—
424C2×#137—612no—
425C2×#137—1221no—
426C2×AGL(1,ℤ/8)—612no—
427C2×AGL(1,ℤ/8)—1221no—
428C2×#135—1222no—
429#568—614no—
430#568—1222no—
431#568—1222no—
432#568—1222no—
433C2×#131—1222no—
434C2×#131—1222no—
435C22×M16—611no—
436C22×M16—1222no—
437C22×M16C2×D6111yescharacteristic
438C22×M16C2×D6111yescharacteristic
439C23×C8C2×D6111yescharacteristic
440C2×#117—611no—
441#421—614no—
442#421—1222no—
443C2×#104—1222no—
444#416—614no—
445#416—1222no—
446C2×#103—1221no—
447C2×#102—1221no—
448#408—614no—
449#408—1222no—
450C2×C22⋊C8—1222no—
451#344—614no—
452#341C2×D6114yescomplemented
453C61C2×#188111yescharacteristic, complemented, Sylow
454C2×#41—612no—
455C2×#41—612no—
456C2×#41—612no—
457C2×#41—612no—
458C2×#41—612no—
459C2×#41—612no—
460C2×#41—612no—
461C2×#41—612no—
462C2×#41—1221no—
463C2×#41—1221no—
464C2×#41—1221no—
465C2×#41—1221no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—1221no—
469C2×#41—1221no—
470C2×#41—1221no—
471C2×#41—1221no—
472C2×#41—1221no—
473C2×#41—1221no—
474C2×#41—1221no—
475C2×#41—1221no—
476C2×#41—1221no—
477C2×#41—1221no—
478C22×Q8—611no—
479C22×Q8—611no—
480C22×D4—611no—
481C22×D4—611no—
482C22×D4—1221no—
483C22×D4—1221no—
484C23×C4—1221no—
485C23×C4—1221no—
486C23×C4C22×D6111yescharacteristic
487#137—618no—
488#137—1224no—
489#137—1224no—
490#137—1224no—
491AGL(1,ℤ/8)—618no—
492AGL(1,ℤ/8)—1224no—
493AGL(1,ℤ/8)—1224no—
494AGL(1,ℤ/8)—1224no—
495#135—1228no—
496#135—1228no—
497C2×Q16—1222no—
498C2×SD16—1222no—
499C2×SD16—1222no—
500C2×D8—1222no—
501#131—1228no—
502#131—1228no—
503#131—1228no—
504#131—1228no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—612no—
512C2×M16—612no—
513C2×M16—1224no—
514C2×M16—1228no—
515C2×M16—1221no—
516C2×M16—1221no—
517C2×M16—1221no—
518C2×M16—1221no—
519C2×M16—1228no—
520C2×M16C4×D6112yes—
521C2×M16C4×D6112yes—
522C2×M16D24412yes—
523C2×M16D24412yes—
524C2×M16C22×D6112yes—
525C2×M16C22×D6112yes—
526C22×C8—21no—
527C22×C8—21no—
528C22×C8—21no—
529C22×C8—21no—
530C22×C8—21no—
531C22×C8—21no—
532C22×C8—21no—
533C22×C8—21no—
534C22×C8—612no—
535C22×C8—1224no—
536C22×C8C22×D6112yes—
537#117—612no—
538#117—1221no—
539#117—1221no—
540#117—1221no—
541C2×C4⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C42—1221no—
544#104—1228no—
545#103—1224no—
546#102—1224no—
547C22⋊C8—1228no—
548C24—1221no—
549C24—1221no—
550C24#1175822611yescharacteristic
551#41—614no—
552#41—614no—
553#41—614no—
554#41—614no—
555#41—1222no—
556#41—1222no—
557#41—1222no—
558#41—1222no—
559#41—1222no—
560#41—1222no—
561#41—1222no—
562#41—1222no—
563#41—1222no—
564#41—1222no—
565#41—1222no—
566#41—1222no—
567#41—1222no—
568#41—1222no—
569#41—1222no—
570#41—1222no—
571#41—1222no—
572#41—1222no—
573#41—1222no—
574#41—1222no—
575#41—2441no—
576#41—2441no—
577#41—2441no—
578#41—2441no—
579#41—2441no—
580#41—2441no—
581#41—2441no—
582#41—2441no—
583C2×Q8—612no—
584C2×Q8—612no—
585C2×Q8—612no—
586C2×Q8—612no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×D4—612no—
596C2×D4—612no—
597C2×D4—612no—
598C2×D4—612no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—2441no—
616C2×D4—2441no—
617C2×D4—2441no—
618C2×D4—2441no—
619C22×C4—1221no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1221no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—2441no—
630C22×C4—2441no—
631C22×C4—2441no—
632C22×C4—2441no—
633C22×C4—2441no—
634C22×C4C2×C4×D6111yescharacteristic
635C22×C4C2×C4×D6111yescharacteristic
636C22×C4C2×D24411yescharacteristic
637C22×C4C2×D24411yescharacteristic
638C22×C4#1175822211yescharacteristic
639C22×C4#1175822211yescharacteristic
640C22×C4D4×D6111yescharacteristic
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4D4×D6111yescharacteristic
646C22×C4#1175822611yescharacteristic
647C22×C4C23×D6111yescharacteristic
648Q16—1228no—
649SD16—1228no—
650SD16—1228no—
651D8—1228no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—22no—
657M16—22no—
658M16—12216no—
659M16—1222no—
660M16—1222no—
661M16—1222no—
662M16—1222no—
663M16C2×C4×D6114yes—
664M16C2×D24414yes—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—41no—
675C2×C8—41no—
676C2×C8—41no—
677C2×C8—41no—
678C2×C8—614no—
679C2×C8—12216no—
680C2×C8—1222no—
681C2×C8—1222no—
682C4⋊C4—1222no—
683C4⋊C4—2441no—
684C22⋊C4—1222no—
685C22⋊C4—2441no—
686C42—1222no—
687C42—2441no—
688C23—42no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—4882no—
694C23—2444no—
695C23—2441no—
696C23—2441no—
697C23#1451973911yescharacteristic
698C23#1451973911yescharacteristic
699C23#1451975211yescharacteristic
700C23#1451975211yescharacteristic
701C23#1451976211yescharacteristic
702C23#1451976211yescharacteristic
703C23C2×#1175822611yescharacteristic
704Q8—614no—
705Q8—1222no—
706Q8—1222no—
707Q8—1222no—
708Q8—1222no—
709Q8—1222no—
710Q8—2441no—
711Q8—2441no—
712D4—614no—
713D4—1224no—
714D4—1224no—
715D4—1224no—
716D4—1224no—
717D4—1222no—
718D4—1222no—
719D4—1222no—
720D4—1222no—
721D4—1222no—
722D4—2442no—
723D4—2442no—
724D4—2442no—
725D4—2442no—
726D4—2441no—
727D4—2441no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1224no—
735C2×C4—1222no—
736C2×C4—4882no—
737C2×C4—2442no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4C22⋊C4×D6111yescharacteristic
745C2×C4C22⋊C4×D6111yescharacteristic
746C2×C4C22⋊C4×D6111yescharacteristic
747C2×C4C22⋊C4×D6111yescharacteristic
748C2×C4#1451973911yescharacteristic
749C2×C4#1451973911yescharacteristic
750C2×C4C4×D24411yescharacteristic
751C2×C4C4×D24411yescharacteristic
752C2×C4C4×D24411yescharacteristic
753C2×C4C4×D24411yescharacteristic
754C2×C4#1451974711yescharacteristic
755C2×C4#1451974711yescharacteristic
756C2×C4#1451974711yescharacteristic
757C2×C4#1451974711yescharacteristic
758C2×C4#1451975011yescharacteristic
759C2×C4#1451975011yescharacteristic
760C2×C4#1451975011yescharacteristic
761C2×C4#1451975011yescharacteristic
762C2×C4#1451975211yescharacteristic
763C2×C4#1451975211yescharacteristic
764C2×C4#1451976211yescharacteristic
765C2×C4#1451976211yescharacteristic
766C2×C4C22×C4×D6111yescharacteristic
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4C2×D4×D6111yescharacteristic
770C2×C4C22×D24411yescharacteristic
771C2×C4C2×#1175822211yescharacteristic
772C8—24no—
773C8—24no—
774C8—42no—
775C8—1224no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—1224no—
784C22—4882no—
785C22—4882no—
786C22—4882no—
787C22—4882no—
788C22—2444no—
789C22—2442no—
790C22—2444no—
791C22#1683964011yescharacteristic
792C22#1683964011yescharacteristic
793C22#1683964011yescharacteristic
794C22#1683964011yescharacteristic
795C22C2×#1451973911yescharacteristic
796C22C2×#1451975211yescharacteristic
797C22C2×#1451976211yescharacteristic
798C4—1224no—
799C4—4882no—
800C4—2442no—
801C4#1683964011yescharacteristic
802C4#1683964011yescharacteristic
803C4#1683964011yescharacteristic
804C4#1683964011yescharacteristic
805C4C2×C22⋊C4×D6111yescharacteristic
806C4C2×C4×D24411yescharacteristic
807C4C2×#1451974711yescharacteristic
808C4C2×#1451975011yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—4882no—
816C2—2444no—
817C2#2144618212yesdirect product factor
818C2C2×#1683964011yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#341C2
socleC22×C61#386
prime radicalC2×#16840562C2
cosocleC22×C4×C61C24
hypercenterC2×#341D61
hypocenterC61C2×#1881
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
2. C2×#16840528C2semidirect
3. C2×#16839778C2semidirect
4. C2×#16839759C2semidirect
5. C2×#16839728C2semidirect
6. #21446182C2direct (N × H)
7. C2×#16839534C2semidirect
8. C2×C61×#341C2semidirect
13. #16840562C4semidirect
16. C2×#14519810C4semidirect
18. C2×#14519805C4semidirect
23. #16840528C22semidirect
30. #16839778C22semidirect
33. #16839759C22semidirect
37. #16839728C22semidirect
39. #16839534C22semidirect
43. C61×#341C22semidirect
79. #14519810C2×C4semidirect
83. #14519805C2×C4semidirect
407. C2×#341D61semidirect
414. C2×C61#1881semidirect
452. #341C2×D61semidirect
453. C61C2×#1881semidirect
817. C2#21446182direct (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×#168405282
C2×#168397782
C2×#168397592
C2×#168397282
#214461822
C2×#168395342
C2×C61×#3412
C2×#188161