Finite Group Databasebeta

← C2×#21446312 #29681902

Subgroups — C2×#21446312 #29681902

Order 15616.

1678 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519810C211yesmaximal, characteristic
2C2×#16840239C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic
4C2×#16839772C211yesmaximal, characteristic, complemented
5C2×#16839735C211yesmaximal, characteristic
6#21446312C218yesmaximal, direct product factor
7C2×#16839519C211yesmaximal, characteristic, complemented
8C2×C61×#344C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×Dic122C2211yescharacteristic
11C2×#14519810—22no—
12C2×#14519810—22no—
13C2×#14519810—22no—
14C2×#14519810—22no—
15C2×#14519810C414yescomplemented
16C2×#14519810C2214yes—
17C22×Dic244C412yescomplemented
18C22×#11758190C412yescomplemented
19#16840239—22no—
20#16840239—22no—
21#16840239—22no—
22#16840239C2214yescomplemented
23C2×C4×Dic122—22no—
24C2×#14519742—22no—
25C2×#14519736C2211yescharacteristic
26C2×#14519736C2211yescharacteristic
27C2×#14519733—22no—
28#16839778—22no—
29#16839778C2214yes—
30C2×#14519703—22no—
31#16839772—22no—
32#16839772C2214yescomplemented
33C2×#14519702—22no—
34#16839735—22no—
35#16839735C2214yes—
36C2×#14519691—22no—
37#16839519C2214yescomplemented
38C22×M16×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×#344C2214yescomplemented
42C2×#11758222—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×#11758222C2×C412yes—
53C2×#11758222C2312yes—
54C22×Dic122—21no—
55C22×Dic122—21no—
56C22×Dic122—21no—
57C22×Dic122—21no—
58C22×Dic122—21no—
59C22×Dic122—21no—
60C22×Dic122—21no—
61C22×Dic122C2×C411yescharacteristic
62C22×Dic122C2×C412yes—
63C22×Dic122C2×C412yes—
64C22×Dic122D412yes—
65C22×Dic122D412yes—
66C22×Dic122D412yes—
67C22×Dic122D412yes—
68C22×Dic122C2312yes—
69C22×D244C2×C411yescharacteristic
70C22×C22⋊D61—21no—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73#14519810—28no—
74#14519810—28no—
75#14519810—28no—
76#14519810—28no—
77C2×Dic244—24no—
78C2×Dic244—24no—
79C2×Dic244C2×C418yescomplemented
80C2×#11758190—24no—
81C2×#11758190—24no—
82C2×#11758190C2×C418yescomplemented
83C4×Dic122—28no—
84C4×Dic122—28no—
85#14519742—28no—
86#14519742—28no—
87#14519736—21no—
88#14519736—21no—
89#14519736—21no—
90#14519736—21no—
91#14519736—21no—
92#14519736D412yes—
93#14519736C2312yes—
94#14519736C2312yes—
95#14519733—28no—
96#14519733—28no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61—21no—
99C2×#11758196—24no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C4×Dic61—24no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61D412yes—
105#14519703—28no—
106#14519702—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×C61—21no—
114C2×M16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61C2×C412yes—
119C2×M16×C61C2312yes—
120C2×M16×C61C2312yes—
121C22×C8×C61—21no—
122C22×C8×C61C2×C412yes—
123#117×C61—21no—
124#117×C61—21no—
125#117×C61D412yes—
126#117×C61C2312yes—
127C2×C4⋊C4×C61—21no—
128C2×C22⋊C4×C61D412yes—
129C2×C42×C61—21no—
130C24×C61C2×D411yescharacteristic
131C23×D61—21no—
132C22×C4×C61—22no—
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61#4111yescharacteristic
143C22×C4×C61#4111yescharacteristic
144C22×C4×C61#4111yescharacteristic
145C22×C4×C61#4111yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—41no—
150C2×C22⋊D61—41no—
151C2×C22⋊D61—41no—
152C2×C22⋊D61—41no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—21no—
161C22×Dic61—22no—
162C22×Dic61—41no—
163#11758222—22no—
164#11758222—22no—
165#11758222—22no—
166#11758222—22no—
167#11758222—22no—
168#11758222—22no—
169#11758222—22no—
170#11758222—22no—
171#11758222—41no—
172#11758222—41no—
173#11758222—41no—
174#11758222—41no—
175#11758222—41no—
176#11758222—41no—
177#11758222—41no—
178#11758222—41no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244C22×C412yes—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—41no—
188C2×C4×D61—41no—
189C2×C4×D61—41no—
190C2×C4×D61—41no—
191C2×Dic122—22no—
192C2×Dic122—22no—
193C2×Dic122—22no—
194C2×Dic122—22no—
195C2×Dic122—22no—
196C2×Dic122—22no—
197C2×Dic122—22no—
198C2×Dic122—22no—
199C2×Dic122—22no—
200C2×Dic122—22no—
201C2×Dic122—22no—
202C2×Dic122—22no—
203C2×Dic122—22no—
204C2×Dic122—22no—
205C2×Dic122—22no—
206C2×Dic122—22no—
207C2×Dic122—22no—
208C2×Dic122—22no—
209C2×Dic122—22no—
210C2×Dic122—22no—
211C2×Dic122—22no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122C22⋊C414yes—
218C2×Dic122C22⋊C414yes—
219C2×Dic122C22⋊C414yes—
220C2×Dic122C22⋊C414yes—
221C2×Dic122C22×C412yes—
222C2×Dic122C22×C414yes—
223C2×Dic122C2×D414yes—
224C2×Dic122C2×D414yes—
225M16×C61—22no—
226M16×C61—22no—
227M16×C61—22no—
228M16×C61—22no—
229M16×C61—22no—
230M16×C61—22no—
231M16×C61—41no—
232M16×C61—41no—
233C2×C8×C61—22no—
234C2×C8×C61—22no—
235C2×C8×C61—22no—
236C2×C8×C61—41no—
237C2×C8×C61—41no—
238C2×C8×C61C22×C414yes—
239C4⋊C4×C61—22no—
240C4⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61C2×D414yes—
243C42×C61—22no—
244C42×C61—22no—
245C22⋊Dic61—22no—
246C22⋊Dic61—22no—
247C22⋊Dic61—22no—
248C22⋊Dic61—41no—
249C4⋊Dic61—22no—
250C4⋊Dic61—22no—
251C4⋊Dic61—22no—
252C4⋊Dic61—41no—
253#11758196—216no—
254C4×Dic61—216no—
255C4×Dic61—22no—
256C4×Dic61—22no—
257C4×Dic61—41no—
258C4×Dic61C2×D414yes—
259Dic244—216no—
260#11758190—216no—
261C23×C61—42no—
262C23×C61C4×D411yescharacteristic
263C23×C61C4×D411yescharacteristic
264C23×C61#12011yescharacteristic
265C23×C61#12011yescharacteristic
266C23×C61#12111yescharacteristic
267C23×C61#12111yescharacteristic
268C23×C61C22×D411yescharacteristic
269C22×D61—22no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—82no—
273C2×C4×C61—24no—
274C2×C4×C61—44no—
275C2×C4×C61C2×C22⋊C411yescharacteristic
276C2×C4×C61C2×C22⋊C411yescharacteristic
277C2×C4×C61C2×C22⋊C411yescharacteristic
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61C4×D411yescharacteristic
280C2×C4×C61C4×D411yescharacteristic
281C2×C4×C61C4×D411yescharacteristic
282C2×C4×C61C4×D411yescharacteristic
283C2×C4×C61C4×D411yescharacteristic
284C2×C4×C61C4×D411yescharacteristic
285C2×C4×C61#12011yescharacteristic
286C2×C4×C61#12011yescharacteristic
287C2×C4×C61#12111yescharacteristic
288C2×C4×C61#12111yescharacteristic
289C2×C4×C61#12111yescharacteristic
290C2×C4×C61#12111yescharacteristic
291C2×C4×C61#12111yescharacteristic
292C2×C4×C61#12111yescharacteristic
293C2×C4×C61#12311yescharacteristic
294C2×C4×C61#12311yescharacteristic
295C2×C4×C61#12311yescharacteristic
296C2×C4×C61#12311yescharacteristic
297C2×C4×C61C23×C411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C22⋊D61—42no—
304C22⋊D61—42no—
305C22⋊D61—42no—
306C22⋊D61—42no—
307C2×Dic61—24no—
308C2×Dic61—24no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—24no—
314C2×Dic61—22no—
315C2×Dic61—24no—
316C2×Dic61—44no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—42no—
320C2×Dic61—82no—
321D244—22no—
322D244—22no—
323D244—41no—
324D244—41no—
325C4×D61—42no—
326C4×D61—42no—
327C4×D61—42no—
328C4×D61—42no—
329Dic122—24no—
330Dic122—24no—
331Dic122—24no—
332Dic122—24no—
333Dic122—24no—
334Dic122—24no—
335Dic122—24no—
336Dic122—22no—
337Dic122—22no—
338Dic122—41no—
339Dic122—41no—
340Dic122C2×C22⋊C418yes—
341C8×C61—24no—
342C8×C61—42no—
343C2×#1905—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61#38611yescharacteristic
352C22×C61#38611yescharacteristic
353C22×C61#38611yescharacteristic
354C22×C61#38611yescharacteristic
355C22×C61C2×C4×D411yescharacteristic
356C22×C61C2×#12011yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C2×D61—42no—
359C2×D61—82no—
360C2×D61—82no—
361C2×D61—82no—
362C4×C61—44no—
363C4×C61#38611yescharacteristic
364C4×C61#38611yescharacteristic
365C4×C61#38611yescharacteristic
366C4×C61#38611yescharacteristic
367C4×C61C22×C22⋊C411yescharacteristic
368C4×C61C2×C4×D411yescharacteristic
369C4×C61C2×#12111yescharacteristic
370C4×C61C2×#12311yescharacteristic
371Dic61—28no—
372Dic61—44no—
373Dic61—42no—
374Dic61—82no—
375C22×#137—611no—
376C2×#519—611no—
377C2×#421—611no—
378C2×#419—611no—
379C2×#410—611no—
380#1905—618no—
381C2×#344D6111yescharacteristic, complemented
382C2×H(3,ℤ/4)—611no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—21no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61#190512yescomplemented
390C2×C61C2×#38611yescharacteristic
391D61—82no—
392C22×#41—611no—
393C23×Q8—611no—
394C2×#137—614no—
395C2×#137—614no—
396C2×#137—1222no—
397C2×#137—1222no—
398C2×#137—1222no—
399C2×#137—1222no—
400C22×Q16—612no—
401C22×SD16—612no—
402C22×M16C2×D6111yescharacteristic
403C22×M16C2×D6111yescharacteristic
404#519—614no—
405#519—1222no—
406#519—1222no—
407#519—1222no—
408C2×C4×Q8—1222no—
409C2×C4×Q8—1222no—
410C2×#117—611no—
411C2×#117—611no—
412C2×#117—1222no—
413C2×#117C2×D6111yescharacteristic
414#421—614no—
415#421—1222no—
416C2×#104—1222no—
417#419—614no—
418#419—1222no—
419C2×#103—1222no—
420#410—614no—
421#410—1222no—
422C2×#99—1222no—
423#344C2×D6114yescomplemented
424H(3,ℤ/4)—614no—
425C61C2×#190511yescharacteristic, complemented, Sylow
426C2×#41—612no—
427C2×#41—612no—
428C2×#41—1221no—
429C2×#41—1221no—
430C2×#41—1221no—
431C2×#41—1221no—
432C2×#41—1221no—
433C2×#41—1221no—
434C2×#41—1221no—
435C2×#41—1221no—
436C2×#41—1221no—
437C2×#41—1221no—
438C22×Q8—612no—
439C22×Q8—612no—
440C22×Q8—611no—
441C22×Q8—612no—
442C22×Q8—612no—
443C22×Q8—612no—
444C22×Q8—612no—
445C22×Q8—612no—
446C22×Q8—1221no—
447C22×Q8—1221no—
448C22×Q8—1221no—
449C22×Q8—1221no—
450C22×Q8—1221no—
451C22×Q8—1221no—
452C22×Q8—1221no—
453C22×D4—611no—
454C22×D4—1221no—
455C23×C4—1221no—
456C23×C4—1221no—
457C23×C4C22×D6111yescharacteristic
458#137—1228no—
459#137—1228no—
460#137—1228no—
461#137—1228no—
462C2×Q16—618no—
463C2×Q16—1224no—
464C2×Q16—1224no—
465C2×SD16—618no—
466C2×SD16—1224no—
467C2×SD16—1224no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16C4×D6112yes—
478C2×M16C22×D6112yes—
479C2×M16C22×D6112yes—
480C22×C8—21no—
481C22×C8C4×D6112yes—
482C4×Q8—1228no—
483C4×Q8—1228no—
484C4×Q8—1228no—
485C4×Q8—1228no—
486#117—21no—
487#117—21no—
488#117—612no—
489#117—612no—
490#117—612no—
491#117—1228no—
492#117—1221no—
493#117—1221no—
494#117—1228no—
495#117—1221no—
496#117—1221no—
497#117—1221no—
498#117D24412yes—
499#117C22×D6112yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—1224no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4D24412yes—
507C2×C42—21no—
508C2×C42—612no—
509C2×C42—1224no—
510C2×C42—1221no—
511#104—1228no—
512#103—1228no—
513#99—1228no—
514C24—1221no—
515C24C2×D24411yescharacteristic
516#41—1222no—
517#41—1222no—
518#41—1222no—
519#41—1222no—
520#41—1222no—
521#41—1222no—
522#41—1222no—
523#41—1222no—
524#41—2441no—
525#41—2441no—
526#41—2441no—
527#41—2441no—
528#41—2441no—
529#41—2441no—
530#41—2441no—
531#41—2441no—
532C2×Q8—614no—
533C2×Q8—612no—
534C2×Q8—614no—
535C2×Q8—614no—
536C2×Q8—614no—
537C2×Q8—614no—
538C2×Q8—614no—
539C2×Q8—614no—
540C2×Q8—1222no—
541C2×Q8—1222no—
542C2×Q8—1222no—
543C2×Q8—1222no—
544C2×Q8—1222no—
545C2×Q8—1222no—
546C2×Q8—1222no—
547C2×Q8—1222no—
548C2×Q8—1222no—
549C2×Q8—1221no—
550C2×Q8—1222no—
551C2×Q8—1222no—
552C2×Q8—1222no—
553C2×Q8—1222no—
554C2×Q8—1222no—
555C2×Q8—1222no—
556C2×Q8—1222no—
557C2×Q8—1222no—
558C2×Q8—1222no—
559C2×Q8—1222no—
560C2×Q8—1222no—
561C2×Q8—1222no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×D4—612no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—2441no—
575C2×D4—2441no—
576C2×D4—2441no—
577C2×D4—2441no—
578C22×C4—22no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1221no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—2441no—
591C22×C4—2441no—
592C22×C4—2441no—
593C22×C4—2441no—
594C22×C4—2441no—
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×D24411yescharacteristic
598C22×C4#1175822211yescharacteristic
599C22×C4#1175822211yescharacteristic
600C22×C4D4×D6111yescharacteristic
601C22×C4D4×D6111yescharacteristic
602C22×C4D4×D6111yescharacteristic
603C22×C4D4×D6111yescharacteristic
604C22×C4D4×D6111yescharacteristic
605C22×C4D4×D6111yescharacteristic
606C22×C4#1175822611yescharacteristic
607C22×C4#1175822611yescharacteristic
608C22×C4C23×D6111yescharacteristic
609Q16—12216no—
610SD16—12216no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—22no—
617M16—41no—
618M16—41no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8C2×C4×D6114yes—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—12216no—
628C4⋊C4—1222no—
629C4⋊C4—1222no—
630C4⋊C4—1222no—
631C4⋊C4—2441no—
632C22⋊C4—22no—
633C22⋊C4—1222no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C22⋊C4—2441no—
637C22⋊C4C2×D24414yes—
638C42—22no—
639C42—22no—
640C42—614no—
641C42—12216no—
642C42—1222no—
643C42—1222no—
644C42—2441no—
645C23—42no—
646C23—1222no—
647C23—4882no—
648C23—2441no—
649C23—2441no—
650C23C4×D24411yescharacteristic
651C23C4×D24411yescharacteristic
652C23#1451974711yescharacteristic
653C23#1451974711yescharacteristic
654C23#1451975211yescharacteristic
655C23#1451975211yescharacteristic
656C23C22×D24411yescharacteristic
657Q8—618no—
658Q8—1224no—
659Q8—1224no—
660Q8—1224no—
661Q8—1224no—
662Q8—1224no—
663Q8—1224no—
664Q8—1224no—
665Q8—1222no—
666Q8—1222no—
667Q8—2441no—
668Q8—2441no—
669D4—1222no—
670D4—1222no—
671D4—2442no—
672D4—2442no—
673D4—2442no—
674D4—2442no—
675D4—2441no—
676D4—2441no—
677C2×C4—24no—
678C2×C4—44no—
679C2×C4—1224no—
680C2×C4—1224no—
681C2×C4—1224no—
682C2×C4—1224no—
683C2×C4—1224no—
684C2×C4—1224no—
685C2×C4—1224no—
686C2×C4—1222no—
687C2×C4—1224no—
688C2×C4—4882no—
689C2×C4—2442no—
690C2×C4—2444no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4C22⋊C4×D6111yescharacteristic
698C2×C4C22⋊C4×D6111yescharacteristic
699C2×C4C22⋊C4×D6111yescharacteristic
700C2×C4C22⋊C4×D6111yescharacteristic
701C2×C4#1451973911yescharacteristic
702C2×C4#1451973911yescharacteristic
703C2×C4#1451973911yescharacteristic
704C2×C4#1451973911yescharacteristic
705C2×C4C4×D24411yescharacteristic
706C2×C4C4×D24411yescharacteristic
707C2×C4#1451974711yescharacteristic
708C2×C4#1451974711yescharacteristic
709C2×C4#1451975011yescharacteristic
710C2×C4#1451975011yescharacteristic
711C2×C4#1451975011yescharacteristic
712C2×C4#1451975011yescharacteristic
713C2×C4#1451975211yescharacteristic
714C2×C4#1451975211yescharacteristic
715C2×C4#1451976211yescharacteristic
716C2×C4#1451976211yescharacteristic
717C2×C4#1451976211yescharacteristic
718C2×C4#1451976211yescharacteristic
719C2×C4C22×C4×D6111yescharacteristic
720C2×C4C2×D4×D6111yescharacteristic
721C2×C4C2×D4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×#1175822211yescharacteristic
724C2×C4C2×#1175822611yescharacteristic
725C8—24no—
726C8—42no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—4882no—
735C22—4882no—
736C22—4882no—
737C22—2442no—
738C22#1683964011yescharacteristic
739C22#1683964011yescharacteristic
740C22#1683964011yescharacteristic
741C22#1683964011yescharacteristic
742C22C2×C4×D24411yescharacteristic
743C22C2×#1451974711yescharacteristic
744C22C2×#1451975211yescharacteristic
745C4—44no—
746C4—1228no—
747C4—4882no—
748C4—2444no—
749C4—2442no—
750C4#1683964011yescharacteristic
751C4#1683964011yescharacteristic
752C4#1683964011yescharacteristic
753C4#1683964011yescharacteristic
754C4C2×C22⋊C4×D6111yescharacteristic
755C4C2×#1451973911yescharacteristic
756C4C2×#1451975011yescharacteristic
757C4C2×#1451976211yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—4882no—
765C2#2144631212yesdirect product factor
766C2C2×#1683964011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#344C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×#344D61
hypocenterC61C2×#1905
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
2. C2×#16840239C2semidirect
4. C2×#16839772C2semidirect
6. #21446312C2direct (N × H)
7. C2×#16839519C2semidirect
8. C2×C61×#344C2semidirect
15. C2×#14519810C4semidirect
17. C22×Dic244C4semidirect
18. C22×#11758190C4semidirect
22. #16840239C22semidirect
32. #16839772C22semidirect
37. #16839519C22semidirect
41. C61×#344C22semidirect
79. C2×Dic244C2×C4semidirect
82. C2×#11758190C2×C4semidirect
381. C2×#344D61semidirect
389. C2×C61#1905semidirect
423. #344C2×D61semidirect
425. C61C2×#1905semidirect
765. C2#21446312direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198102
C2×#168402392
C2×#168397782
C2×#168397722
C2×#168397352
#214463122
C2×#168395192
C2×C61×#3442
C2×#190561