Finite Group Databasebeta

← C2×#21446307 #29681896

Subgroups — C2×#21446307 #29681896

Order 15616.

1894 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×#14519805C211yesmaximal, characteristic
2C2×#16840236C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic, complemented
4C2×#16839766C211yesmaximal, characteristic, complemented
5C2×#16839735C211yesmaximal, characteristic, complemented
6#21446307C218yesmaximal, direct product factor
7C2×#16839533C211yesmaximal, characteristic, complemented
8C2×C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×D244C2211yescharacteristic
11C2×#14519805—22no—
12C2×#14519805—22no—
13C2×#14519805—22no—
14C2×#14519805—22no—
15C2×#14519805C414yescomplemented
16C2×#14519805C2214yes—
17C22×#11758190C412yescomplemented
18C22×D488C412yescomplemented
19C22×#11758194C2211yescharacteristic
20#16840236—22no—
21#16840236—22no—
22#16840236—22no—
23#16840236C2214yescomplemented
24C2×C4×D244—22no—
25C2×#14519739—22no—
26C2×#14519736C2211yescharacteristic
27C2×C22⋊C4×D61—22no—
28#16839780—22no—
29#16839780C2214yescomplemented
30C2×#14519705—22no—
31#16839766—22no—
32#16839766C2214yescomplemented
33C2×#14519697—22no—
34#16839735—22no—
35#16839735C2214yescomplemented
36C2×#14519691—22no—
37#16839533C2214yescomplemented
38C22×M16×C61C2211yescharacteristic
39C2×#117×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×H(3,ℤ/4)C2214yescomplemented
42C24×D61—21no—
43C2×#11758222—21no—
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×#11758222C2×C412yescomplemented
54C2×#11758222C2312yes—
55C22×Dic122C2×C411yescharacteristic, complemented
56C22×D244—21no—
57C22×D244—21no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—21no—
62C22×D244—21no—
63C22×D244C2×C412yes—
64C22×D244C2×C412yes—
65C22×D244C2×C411yescharacteristic, complemented
66C22×D244D412yes—
67C22×D244D412yes—
68C22×D244D412yes—
69C22×D244D412yes—
70C22×D244C2312yes—
71C22×C22⋊D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—24no—
74#14519805—28no—
75#14519805—28no—
76#14519805—28no—
77#14519805—28no—
78C2×#11758190—24no—
79C2×#11758190—24no—
80C2×#11758190C2×C418yescomplemented
81C2×D488—24no—
82C2×D488—24no—
83C2×D488C2×C418yescomplemented
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194—21no—
87C2×#11758194—21no—
88C2×#11758194—21no—
89C2×#11758194C2312yes—
90C22×#92418—21no—
91C4×D244—28no—
92C4×D244—28no—
93#14519739—28no—
94#14519739—28no—
95#14519736—21no—
96#14519736—21no—
97#14519736D412yes—
98#14519736C2312yes—
99C2×C4⋊Dic61—21no—
100C2×C22⋊Dic61D412yes—
101C2×#11758198—24no—
102C22⋊C4×D61—28no—
103C22⋊C4×D61—28no—
104C2×C4×Dic61—21no—
105#14519705—28no—
106#14519697—28no—
107#14519691—28no—
108C23×C4×C61C2311yescharacteristic
109C2×M16×C61—21no—
110C2×M16×C61—21no—
111C2×M16×C61—21no—
112C2×M16×C61—21no—
113C2×M16×C61C2×C412yescomplemented
114C2×M16×C61C2312yes—
115C22×C8×C61C2×C412yescomplemented
116#117×C61—21no—
117#117×C61—21no—
118#117×C61—21no—
119#117×C61—21no—
120#117×C61—21no—
121#117×C61D412yes—
122#117×C61C2312yes—
123#117×C61C2312yes—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C42×C61—21no—
129C2×C42×C61D412yes—
130C24×C61C2×D411yescharacteristic
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—21no—
139C23×D61—84no—
140C22×C4×C61—22no—
141C22×C4×C61—41no—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
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×C61#4111yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—41no—
162C22×Dic61—21no—
163C22×Dic61—22no—
164#11758222—22no—
165#11758222—22no—
166#11758222—22no—
167#11758222—22no—
168#11758222—22no—
169#11758222—22no—
170#11758222—22no—
171#11758222—22no—
172#11758222—41no—
173#11758222—41no—
174#11758222—41no—
175#11758222—41no—
176#11758222—41no—
177#11758222—41no—
178#11758222—41no—
179#11758222—41no—
180C2×D244—22no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—22no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—22no—
196C2×D244—22no—
197C2×D244—22no—
198C2×D244—22no—
199C2×D244—22no—
200C2×D244—22no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244C22⋊C414yes—
207C2×D244C22⋊C414yes—
208C2×D244C22⋊C414yes—
209C2×D244C22⋊C414yes—
210C2×D244C22×C414yes—
211C2×D244C22×C412yescomplemented
212C2×D244C2×D414yes—
213C2×D244C2×D414yes—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—216no—
217C2×C4×D61—41no—
218C2×C4×D61—41no—
219C2×C4×D61—41no—
220C2×C4×D61—41no—
221C2×C4×D61—88no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122C22×C412yescomplemented
228M16×C61—22no—
229M16×C61—22no—
230M16×C61—22no—
231M16×C61—22no—
232C2×C8×C61—22no—
233C2×C8×C61—22no—
234C2×C8×C61C22×C414yescomplemented
235C4⋊C4×C61—22no—
236C4⋊C4×C61—22no—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—41no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—41no—
243C42×C61—22no—
244C42×C61—22no—
245C42×C61—41no—
246C42×C61C2×D414yes—
247C22⋊Dic61—22no—
248C22⋊Dic61C2×D414yes—
249#11758198—216no—
250C4⋊Dic61—22no—
251C4⋊Dic61—22no—
252C4×Dic61—22no—
253C4×Dic61—22no—
254#11758194—22no—
255#11758194—22no—
256#11758194—41no—
257#11758194—41no—
258C2×#92418—22no—
259C2×#92418—41no—
260C2×#92418—41no—
261D488—216no—
262#11758190—216no—
263C23×C61—42no—
264C23×C61C4×D411yescharacteristic
265C23×C61C4×D411yescharacteristic
266C23×C61#12011yescharacteristic
267C23×C61#12011yescharacteristic
268C23×C61#12111yescharacteristic
269C23×C61#12111yescharacteristic
270C23×C61C22×D411yescharacteristic
271C22×D61—24no—
272C22×D61—24no—
273C22×D61—24no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—22no—
279C22×D61—48no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—84no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—82no—
289C2×C4×C61—24no—
290C2×C4×C61—44no—
291C2×C4×C61—42no—
292C2×C4×C61—82no—
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C4×D411yescharacteristic
302C2×C4×C61C4×D411yescharacteristic
303C2×C4×C61#12011yescharacteristic
304C2×C4×C61#12011yescharacteristic
305C2×C4×C61#12111yescharacteristic
306C2×C4×C61#12111yescharacteristic
307C2×C4×C61#12111yescharacteristic
308C2×C4×C61#12111yescharacteristic
309C2×C4×C61#12111yescharacteristic
310C2×C4×C61#12111yescharacteristic
311C2×C4×C61#12311yescharacteristic
312C2×C4×C61#12311yescharacteristic
313C2×C4×C61#12311yescharacteristic
314C2×C4×C61#12311yescharacteristic
315C2×C4×C61C23×C411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C22⋊D61—42no—
322C22⋊D61—42no—
323C22⋊D61—42no—
324C22⋊D61—42no—
325C2×Dic61—22no—
326C2×Dic61—24no—
327C2×Dic61—44no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330D244—22no—
331D244—24no—
332D244—22no—
333D244—24no—
334D244—24no—
335D244—24no—
336D244—24no—
337D244—24no—
338D244—24no—
339D244—41no—
340D244—41no—
341D244C2×C22⋊C418yes—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61—42no—
346C4×D61—816no—
347Dic122—22no—
348Dic122—22no—
349Dic122—41no—
350Dic122—41no—
351C8×C61—24no—
352#92418—42no—
353C2×#1904—611nomaximal, Sylow
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61#38611yescharacteristic
362C22×C61#38611yescharacteristic
363C22×C61#38611yescharacteristic
364C22×C61#38611yescharacteristic
365C22×C61C2×C4×D411yescharacteristic
366C22×C61C2×#12011yescharacteristic
367C22×C61C2×#12111yescharacteristic
368C2×D61—28no—
369C2×D61—48no—
370C2×D61—48no—
371C2×D61—48no—
372C2×D61—42no—
373C2×D61—84no—
374C2×D61—84no—
375C2×D61—84no—
376C2×D61—84no—
377C2×D61—82no—
378C2×D61—82no—
379C2×D61—82no—
380C4×C61—44no—
381C4×C61—82no—
382C4×C61#38611yescharacteristic
383C4×C61#38611yescharacteristic
384C4×C61#38611yescharacteristic
385C4×C61#38611yescharacteristic
386C4×C61C22×C22⋊C411yescharacteristic
387C4×C61C2×C4×D411yescharacteristic
388C4×C61C2×#12111yescharacteristic
389C4×C61C2×#12311yescharacteristic
390Dic61—44no—
391Dic61—42no—
392C22×AGL(1,ℤ/8)—611no—
393C2×#518—611no—
394C2×#421—611no—
395C2×#418—611no—
396C2×#410—611no—
397#1904—618no—
398C2×#344—611no—
399C2×H(3,ℤ/4)D6111yescharacteristic, complemented
400C2×C61—21no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—21no—
404C2×C61—21no—
405C2×C61—21no—
406C2×C61#190412yescomplemented
407C2×C61C2×#38611yescharacteristic
408D61—48no—
409D61—82no—
410C22×#41—611no—
411C23×D4—611no—
412C2×AGL(1,ℤ/8)—614no—
413C2×AGL(1,ℤ/8)—614no—
414C2×AGL(1,ℤ/8)—1222no—
415C2×AGL(1,ℤ/8)—1222no—
416C2×AGL(1,ℤ/8)—1222no—
417C2×AGL(1,ℤ/8)—1222no—
418C22×SD16—612no—
419C22×D8—612no—
420C22×M16—611no—
421C22×M16C2×D6111yescharacteristic
422#518—614no—
423#518—1222no—
424#518—1222no—
425#518—1222no—
426C2×C4×D4—1222no—
427C2×C4×D4—1222no—
428C2×#117—611no—
429C2×#117C2×D6111yescharacteristic
430C2×#117C2×D6111yescharacteristic
431C22×C22⋊C4—1222no—
432#421—614no—
433#421—1222no—
434C2×#104—1222no—
435#418—614no—
436#418—1222no—
437C2×#102—1222no—
438#410—614no—
439#410—1222no—
440C2×#99—1222no—
441#344—614no—
442H(3,ℤ/4)C2×D6114yescomplemented
443C61C2×#190411yescharacteristic, complemented, Sylow
444C25—1221no—
445C2×#41—612no—
446C2×#41—612no—
447C2×#41—1221no—
448C2×#41—1221no—
449C2×#41—1221no—
450C2×#41—1221no—
451C2×#41—1221no—
452C2×#41—1221no—
453C2×#41—1221no—
454C2×#41—1221no—
455C2×#41—1221no—
456C2×#41—1221no—
457C22×Q8—611no—
458C22×D4—612no—
459C22×D4—612no—
460C22×D4—611no—
461C22×D4—612no—
462C22×D4—612no—
463C22×D4—612no—
464C22×D4—612no—
465C22×D4—612no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1221no—
474C23×C4—1224no—
475C23×C4—1221no—
476C23×C4C22×D6111yescharacteristic
477AGL(1,ℤ/8)—1228no—
478AGL(1,ℤ/8)—1228no—
479AGL(1,ℤ/8)—1228no—
480AGL(1,ℤ/8)—1228no—
481C2×SD16—618no—
482C2×SD16—1224no—
483C2×SD16—1224no—
484C2×D8—618no—
485C2×D8—1224no—
486C2×D8—1224no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—612no—
492C2×M16—1221no—
493C2×M16—1221no—
494C2×M16—1221no—
495C2×M16—1221no—
496C2×M16—1221no—
497C2×M16C4×D6112yescomplemented
498C2×M16C22×D6112yes—
499C22×C8—1221no—
500C22×C8C4×D6112yescomplemented
501C4×D4—1228no—
502C4×D4—1228no—
503C4×D4—1228no—
504C4×D4—1228no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—612no—
511#117—612no—
512#117—1221no—
513#117—1221no—
514#117D24412yes—
515#117C22×D6112yes—
516#117C22×D6112yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—1221no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—612no—
523C2×C22⋊C4—1228no—
524C2×C22⋊C4—1228no—
525C2×C22⋊C4—1224no—
526C2×C42—21no—
527C2×C42—1221no—
528C2×C42D24412yes—
529#104—1228no—
530#102—1228no—
531#99—1228no—
532C24—1222no—
533C24—1222no—
534C24—1222no—
535C24—1222no—
536C24—1222no—
537C24—1222no—
538C24—1222no—
539C24—1221no—
540C24—4884no—
541C24D4×D6111yescharacteristic
542#41—1222no—
543#41—1222no—
544#41—1222no—
545#41—1222no—
546#41—1222no—
547#41—1222no—
548#41—1222no—
549#41—1222no—
550#41—2441no—
551#41—2441no—
552#41—2441no—
553#41—2441no—
554#41—2441no—
555#41—2441no—
556#41—2441no—
557#41—2441no—
558C2×Q8—612no—
559C2×Q8—1221no—
560C2×Q8—1221no—
561C2×Q8—1221no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×D4—614no—
565C2×D4—612no—
566C2×D4—614no—
567C2×D4—614no—
568C2×D4—614no—
569C2×D4—614no—
570C2×D4—614no—
571C2×D4—614no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1221no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—2441no—
601C2×D4—2441no—
602C2×D4—2441no—
603C2×D4—2441no—
604C22×C4—22no—
605C22×C4—41no—
606C22×C4—12216no—
607C22×C4—1221no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—4888no—
612C22×C4—2441no—
613C22×C4—2441no—
614C22×C4—2441no—
615C22×C4—2441no—
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4C2×C4×D6111yescharacteristic
618C22×C4C2×D24411yescharacteristic
619C22×C4C2×D24411yescharacteristic
620C22×C4#1175822211yescharacteristic
621C22×C4#1175822211yescharacteristic
622C22×C4D4×D6111yescharacteristic
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4D4×D6111yescharacteristic
626C22×C4D4×D6111yescharacteristic
627C22×C4#1175822611yescharacteristic
628C22×C4#1175822611yescharacteristic
629C22×C4C23×D6111yescharacteristic
630SD16—12216no—
631D8—12216no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—22no—
636M16—1222no—
637M16—1222no—
638M16—2441no—
639M16—2441no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—1222no—
643C2×C8—2441no—
644C2×C8—2441no—
645C2×C8C2×C4×D6114yescomplemented
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—1222no—
651C4⋊C4—1222no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C22⋊C4—614no—
657C22⋊C4—12216no—
658C22⋊C4—1222no—
659C42—22no—
660C42—22no—
661C42—41no—
662C42—1222no—
663C42—1222no—
664C42C2×D24414yes—
665C23—42no—
666C23—1224no—
667C23—1224no—
668C23—1224no—
669C23—1224no—
670C23—1224no—
671C23—1224no—
672C23—1224no—
673C23—1222no—
674C23—4882no—
675C23—4884no—
676C23—4884no—
677C23—4884no—
678C23—4884no—
679C23—4884no—
680C23—4884no—
681C23—2448no—
682C23—2441no—
683C23—2441no—
684C23#1451973911yescharacteristic
685C23#1451973911yescharacteristic
686C23#1451974711yescharacteristic
687C23#1451974711yescharacteristic
688C23#1451975011yescharacteristic
689C23#1451975011yescharacteristic
690C23C2×D4×D6111yescharacteristic
691Q8—1222no—
692Q8—1222no—
693Q8—2441no—
694Q8—2441no—
695D4—618no—
696D4—1222no—
697D4—1224no—
698D4—1222no—
699D4—1224no—
700D4—1224no—
701D4—1224no—
702D4—1224no—
703D4—1224no—
704D4—1224no—
705D4—2442no—
706D4—2442no—
707D4—2442no—
708D4—2442no—
709D4—2441no—
710D4—2441no—
711C2×C4—24no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—82no—
715C2×C4—1222no—
716C2×C4—1224no—
717C2×C4—48816no—
718C2×C4—2444no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4C22⋊C4×D6111yescharacteristic
726C2×C4C22⋊C4×D6111yescharacteristic
727C2×C4C22⋊C4×D6111yescharacteristic
728C2×C4C22⋊C4×D6111yescharacteristic
729C2×C4#1451973911yescharacteristic
730C2×C4#1451973911yescharacteristic
731C2×C4C4×D24411yescharacteristic
732C2×C4C4×D24411yescharacteristic
733C2×C4C4×D24411yescharacteristic
734C2×C4C4×D24411yescharacteristic
735C2×C4#1451974711yescharacteristic
736C2×C4#1451974711yescharacteristic
737C2×C4#1451975011yescharacteristic
738C2×C4#1451975011yescharacteristic
739C2×C4#1451975211yescharacteristic
740C2×C4#1451975211yescharacteristic
741C2×C4#1451975211yescharacteristic
742C2×C4#1451975211yescharacteristic
743C2×C4#1451976211yescharacteristic
744C2×C4#1451976211yescharacteristic
745C2×C4#1451976211yescharacteristic
746C2×C4#1451976211yescharacteristic
747C2×C4C22×C4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4C2×D4×D6111yescharacteristic
750C2×C4C22×D24411yescharacteristic
751C2×C4C2×#1175822211yescharacteristic
752C2×C4C2×#1175822611yescharacteristic
753C8—24no—
754C8—2442no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—1228no—
763C22—4882no—
764C22—4882no—
765C22—4884no—
766C22—4884no—
767C22—4884no—
768C22—4884no—
769C22—4882no—
770C22—2448no—
771C22—2448no—
772C22—2442no—
773C22—2448no—
774C22#1683964011yescharacteristic
775C22#1683964011yescharacteristic
776C22#1683964011yescharacteristic
777C22#1683964011yescharacteristic
778C22C2×#1451973911yescharacteristic
779C22C2×#1451974711yescharacteristic
780C22C2×#1451975011yescharacteristic
781C4—44no—
782C4—82no—
783C4—2444no—
784C4—2442no—
785C4#1683964011yescharacteristic
786C4#1683964011yescharacteristic
787C4#1683964011yescharacteristic
788C4#1683964011yescharacteristic
789C4C2×C22⋊C4×D6111yescharacteristic
790C4C2×C4×D24411yescharacteristic
791C4C2×#1451975211yescharacteristic
792C4C2×#1451976211yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—4882no—
800C2—2448no—
801C2#2144630712yesdirect product factor
802C2C2×#1683964011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×H(3,ℤ/4)C2
socleC22×C61#386
prime radicalC22×#14519805C2
cosocleC22×C4×C61C24
hypercenterC2×H(3,ℤ/4)D61
hypocenterC61C2×#1904
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. C2×#16840236C2semidirect
3. C2×#16839780C2semidirect
4. C2×#16839766C2semidirect
5. C2×#16839735C2semidirect
6. #21446307C2direct (N × H)
7. C2×#16839533C2semidirect
8. C2×C61×H(3,ℤ/4)C2semidirect
15. C2×#14519805C4semidirect
17. C22×#11758190C4semidirect
18. C22×D488C4semidirect
23. #16840236C22semidirect
29. #16839780C22semidirect
32. #16839766C22semidirect
35. #16839735C22semidirect
37. #16839533C22semidirect
41. C61×H(3,ℤ/4)C22semidirect
53. C2×#11758222C2×C4semidirect
55. C22×Dic122C2×C4semidirect
65. C22×D244C2×C4semidirect
80. C2×#11758190C2×C4semidirect
83. C2×D488C2×C4semidirect
113. C2×M16×C61C2×C4semidirect
115. C22×C8×C61C2×C4semidirect
211. C2×D244C22×C4semidirect
227. C2×Dic122C22×C4semidirect
234. C2×C8×C61C22×C4semidirect
399. C2×H(3,ℤ/4)D61semidirect
406. C2×C61#1904semidirect
442. H(3,ℤ/4)C2×D61semidirect
443. C61C2×#1904semidirect
497. C2×M16C4×D61semidirect
500. C22×C8C4×D61semidirect
645. C2×C8C2×C4×D61semidirect
801. C2#21446307direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198052
C2×#168402362
C2×#168397802
C2×#168397662
C2×#168397352
#214463072
C2×#168395332
C2×C61×H(3,ℤ/4)2
C2×#190461